Answer:
It does not appear that, as a group, the students are reasonably good at estimating one minute.
Step-by-step explanation:
We are given the following data in the question:
75, 88, 51, 73, 49, 31, 69, 74, 72, 59, 72, 81, 99, 101, 73
Formula:
[tex]\text{Standard Deviation} = \sqrt{\displaystyle\frac{\sum (x_i -\bar{x})^2}{n-1}}[/tex]
where [tex]x_i[/tex] are data points, [tex]\bar{x}[/tex] is the mean and n is the number of observations.
[tex]Mean = \displaystyle\frac{\text{Sum of all observations}}{\text{Total number of observation}}[/tex]
[tex]Mean =\displaystyle\frac{1067}{15} = 71.13[/tex]
Sum of squares of differences = 4739.733
[tex]S.D = \sqrt{\frac{4739.733}{14}} = 18.39[/tex]
Population mean, μ = 60 minutes
Sample mean, [tex]\bar{x}[/tex] = 71.13 minutes
Sample size, n = 15
Alpha, α = 0.10
Sample standard deviation, s = 18.39 minutes
First, we design the null and the alternate hypothesis
[tex]H_{0}: \mu = 60\text{ minutes}\\H_A: \mu \neq 60\text{ minutes}[/tex]
We use Two-tailed t test to perform this hypothesis.
Formula:
[tex]t_{stat} = \displaystyle\frac{\bar{x} - \mu}{\frac{s}{\sqrt{n}} }[/tex]
Putting all the values, we have
[tex]t_{stat} = \displaystyle\frac{71.13 - 60}{\frac{18.39}{\sqrt{15}} } = 2.34[/tex]
Calculating the p-value from the table, we have,
P-value = 0.034354
Since the p-value is lower than the significance level, we fail to accept the null hypothesis and reject it. We accept the alternate hypothesis.
Thus, we conclude that it does not appear that, as a group, the students are reasonably good at estimating one minute.
Option A is the correct set of hypotheses for testing if students can estimate one minute. The test statistic and p-value are needed to make a decision, typically using a t-test. The conclusion depends on the p-value relative to the significance level.
The null and alternative hypotheses you are working with for testing whether students are good at estimating one minute are:
H0: \\(\mu = 60\\) seconds - This states that the true population mean estimation time is 60 seconds.Ha: \\(\mu \not= 60\\) seconds - This hypothesis asserts that the true population mean estimation time is not 60 seconds.To determine if students are good at estimating one minute, we have option A as correct, which is H0: \\(\mu = 60\\) and Ha: \\(\mu \not= 60\\).
The test statistic and p-value should be calculated using appropriate statistical methods (typically a t-test assuming we do not know the population standard deviation, which would require the mean, standard deviation, and sample size). After calculating the test statistic and p-value, you will compare the p-value to the significance level (alpha). If the p-value is less than alpha, you reject H0; otherwise, you fail to reject H0.
Based on the decision to reject or fail to reject H0, you can make a conclusion regarding the original claim about whether students are reasonably good at estimating one minute.
Which, if any, of A. (4, π/6), B. (−4, 7π/6), C. (4, 13π/6), are polar coordinates for the point given in Cartesian coordinates by P(2, 2 √ 3)?
Final answer:
Explaining the polar coordinates for given Cartesian coordinates.
Explanation:
Polar Coordinates of Points:
Point A(2, 2√3): Polar coordinates are (4, π/6).
Point B(-4, 7π/6): Wrong polar coordinates as it should be (4, 11π/6).
Point C(4, 13π/6): Wrong polar coordinates.
The days maturity for a sample of 5 money market funds areshown here. The dollar amounts invested in the funds areprovided. Use the weighted mean to determine the mean numberof days to maturity for dollars invested in these 5 money marketfunds.COL1 Days tomaturity 20 12 7 5 6COL2 $$ Value (millions) 20 30 10 15 10
Final answer:
The weighted mean number of days to maturity for dollars invested in the 5 money market funds is approximately 11.35 days. This is calculated by taking the product of the days to maturity and the corresponding money value for each fund, summing these products, and then dividing by the total money value invested.
Explanation:
The question asks to calculate the weighted mean of days to maturity for dollars invested in several money market funds with varying maturities and dollar values. To compute this, we multiply each fund's days to maturity by its dollar value (in millions), sum these products, and then divide by the total of the dollar values. Here's the calculation:
(20 days * $20 million) + (12 days * $30 million) + (7 days * $10 million) + (5 days * $15 million) + (6 days * $10 million) = $400 million-days + $360 million-days + $70 million-days + $75 million-days + $60 million-days
Total million-days = $965 million-days
Total value of all funds = $85 million
Weighted mean days to maturity = Total million-days / Total value of all funds = $965 million-days / $85 million = 11.35 days
So, the weighted mean number of days to maturity for the dollars invested in these 5 money market funds is approximately 11.35 days.
The sample space of a random experiment is {a,b,c,d,e} with probabilities 0.1,0.1,0.2,0.4, and 0.2, respectively. Let A denote the event {a,b,c}, and let B denote the even t {c,d,e}. Determine the following:
a. P(A)
b. P(B)
c. P(A’)
d. P(AUB)
e. P(AnB)
Answer with Step-by-step explanation:
We are given that a sample space
S={a,b,c,d,e}
P(a)=0.1
P(b)=0.1
P(c)=0.2
P(d)=0.4
P(e)=0.2
a.A={a,b,c}
P(A)=P(a)+P(b)+P(c)
P(A)=0.1+0.1+0.2=0.4
b.B={c,d,e}
P(B)=P(c)+P(d)+P(e)=0.2+0.4+0.2=0.8
c.A'=Sample space-A={a,b,c,d,e}-{a,b,c}={d,e}
P(A')=P(d)+P(e)=0.4+0.2=0.6
d.[tex]A\cup B[/tex]={a,b,c,d,e}
[tex]P(A\cup B)[/tex]=P(a)+P(b)+P(c)+P(d)+P(e)=0.1+0.1+0.2+0.4+0.2=1
e.[tex]A\cap B[/tex]={c}
[tex]P(A\cap B)=P(c)=0.2[/tex]
The curve given by:
x=sin(????); y=sin(????+sin(????))
has two tangent lines at the point (x,y)=(0,0).
List both of them in order of increasing slope. Your answers should be in the form of y=????(x) without ????′????.
Answer:
Equations of tangent lines are
y= 2 x
y = 0
Step-by-step explanation:
x = sin t -- (1)
y = sin(t + sin(t)) -- (2)
Differentiating both equations w.r.to t to find slopes.
[tex]\frac{dx}{dt}=\frac{d(sin(t))}{dt}\\\\\frac{dx}{dt}=cos(t)--(3)[/tex]
[tex]\frac{dy}{dt}=\frac{d}{dt}(sin(t+sin(t))\\\\\frac{dy}{dt}=cos(t+sin(t))\frac{d}{dt}(t+sin(t))\\\\\frac{dy}{dt}=cos(t+sin(t)(1+cos(t))\\\\\frac{dy}{dt}=(1+cos(t))cos(t+sin(t))--(4)[/tex]
Dividing (2) by (1) to find slope
[tex]\frac{dy}{dx}=\frac{(1+cos(t))cos(t+sin(t))}{cos(t)}\\[/tex]
at tangent point x=y=0
From (1)
sin (t) = 0
⇒ t = 0, π
At t = 0
[tex]\frac{dy}{dx}\Big|_{t=0}=\frac{(1+cos(t))cos(t+sin(t))}{cos(t)}\\\\\\\frac{dy}{dx}\Big|_{t=0}=\frac{(1+cos(0))cos(0+sin(0))}{cos(0)}\\\\\\\frac{dy}{dx}\Big|_{t=0}=\frac{(1+1)cos(0+0)}{1}\\\\\\\frac{dy}{dx}\Big|_{t=0}=2\\[/tex]
At t= π
[tex]\frac{dy}{dx}\Big|_{t=\pi}=\frac{(1+cos(t))cos(t+sin(t))}{cos(t)}\\\\\\\frac{dy}{dx}\Big|_{t=\pi}=\frac{(1+cos(\pi))cos(\pi+sin(\pi))}{cos(\pi)}\\\\\\\frac{dy}{dx}\Big|_{t=\pi}=\frac{(1-1)cos(\pi+0)}{-1}\\\\\\\frac{dy}{dx}\Big|_{t=\pi}=0\\[/tex]
Equation of tangent
[tex](y-y_o)=m_t(x-x_o)\\[/tex]
[tex]Tangent\,\,point=(x_o,y_o)=(0,0)\\\\For\,\,t=0\\\\(y-0)=(2)(x-0)\\\\y=2x\\\\for\,\,t=\pi\\\\(y-0)=(0)(x-0)\\\\y=0[/tex]
According to CNN business partner Careerbuilder, the average starting salary for accounting graduates in 2018 was at least $57,413. Suppose that the American Society for Certified Public Accountants planned to test this claim by randomly sampling 200 accountants who graduated in 2018. State the appropriate null and alternative hypotheses.
Answer:
Null hypothesis: The American Society for Certified Public Accountants says the average starting salary of accountants who graduated in 2018 is $57,413
Alternate hypothesis: The American Society for Certified Public Accountants says the average starting salary of accountants who graduated in 2018 is less than or equal to $57,413
Step-by-step explanation:
A null hypothesis is a statement from a population parameter that is subject to testing. It is expressed with equality.
An alternate hypothesis is also a statement from the population parameter that negates the null hypothesis. It is expressed with inequality
A forensic psychologist studying the accuracy of a new type of polygraph (lie detector) test instructed a participant ahead of time to lie about some of the questions asked by the polygraph operator. On average, the current polygraph test is 75% accurate, with a standard deviation of 6.5%. With the new machine, the operator correctly identified 83.5% of the false responses for one participant. Using the.05 level of significance, is the accuracy of the new polygraph different from the current one? Fill in the following information: Assuming an ?-0.05, determine the z-score cutoff for the rejection region. Calculate the test statistic for the given data Zobt Based on the data above, finish the statement about your decision: Based on the observed z-score, we would decide to (accept, reject, fail to reject, fail to accept) hypothesis. the (null, alternative)
Answer:
[tex]z=\frac{83.5-75}{6.5}=1.31[/tex]
The rejection zone for this case would be:
[tex] z> 1.96 \cup Z<-1.96[/tex]
[tex]p_v =2*P(z>1.31)=0.1901[/tex]
If we compare the p value and the significance level given [tex]\alpha=0.05[/tex] we see that [tex]p_v>\alpha[/tex] so we can conclude that we have enough evidence to fail reject the null hypothesis, so we can't conclude that the true mean is significantly different from 75 at 5% of significance.
Step-by-step explanation:
Data given and notation
[tex]\bar X=83.5[/tex] represent the sample mean
[tex]\sigma=6.5[/tex] represent the population standard deviation for the sample
[tex]\mu_o =75[/tex] represent the value that we want to test
[tex]\alpha=0.05[/tex] represent the significance level for the hypothesis test.
t would represent the statistic (variable of interest)
[tex]p_v[/tex] represent the p value for the test (variable of interest)
State the null and alternative hypotheses.
We need to conduct a hypothesis in order to check if the mean is different from 75, the system of hypothesis would be:
Null hypothesis:[tex]\mu = 75[/tex]
Alternative hypothesis:[tex]\mu \neq 75[/tex]
For this case we know the population deviation so is better apply a z test to compare the actual mean to the reference value, and the statistic is given by:
[tex]z=\frac{\bar X-\mu_o}{\sigma}[/tex] (1)
z-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".
Calculate the statistic
We can replace in formula (1) the info given like this:
[tex]z=\frac{83.5-75}{6.5}=1.31[/tex]
Cutoff for the rejection regon
Since our significance level is [tex] \alpha=0.05[/tex] and we are conducting a bilateral test we need to find a quantile in the standard normal distribution that accumulates 0.025 of the area on each tail.
And for this case those values are [tex] z_{crit}= \pm 1.96[/tex]
So the rejection zone for this case would be:
[tex] z> 1.96 \cup Z<-1.96[/tex]
Our calculated value is not on the rejection zone. So we fail to reject the null hypothesis.
P-value
Since is a two sided test the p value would be given by:
[tex]p_v =2*P(z>1.31)=0.1901[/tex]
Conclusion
If we compare the p value and the significance level given [tex]\alpha=0.05[/tex] we see that [tex]p_v>\alpha[/tex] so we can conclude that we have enough evidence to fail reject the null hypothesis, so we can't conclude that the true mean is significantly different from 75 at 5% of significance.
Final answer:
To determine if the new polygraph test's accuracy significantly differs from the current one, we compare the calculated test statistic with the critical z-score of ±1.96 at an alpha level of 0.05. The process involves hypothesis testing, where rejecting or failing to reject the null hypothesis depends on whether the test statistic exceeds the critical value.
Explanation:
The question is about determining if the accuracy of a new type of polygraph test is statistically different from the current one using hypothesis testing. Given an alpha level (α) of 0.05 (5% level of significance), the critical z-score for a two-tailed test is ±1.96. This critical value defines the cutoff points for the rejection regions. To calculate the test statistic (Zobt), we use the formula:
Zobt = (X - μ) / (σ / √n),
where X is the sample mean (83.5%), μ is the population mean (75%), σ is the standard deviation (6.5%), and √n is the square root of the sample size. Given that only one participant's data is used, √n is 1 for this scenario, which simplifies our formula. Unfortunately, without the exact sample size for a more precise calculation or this being a theoretical scenario with one participant, we remark on the process rather than providing a numerical value for Zobt.
Based on the calculated Zobt, if it exceeds the critical z-score (1.96 or -1.96), we reject the null hypothesis indicating that there is a statistically significant difference between the new polygraph's accuracy and the current one. If Zobt does not exceed the critical value, we fail to reject the null hypothesis, indicating no significant difference.
Please help!!!!!!!!
Answer:
a) 62
b) 24
Step-by-step explanation:
For A, add the students who watched only one movie: 18+24+20=62
For B, look at how many students only watched Star Wars: 24
Shaki makes and sells backpack danglies. The total cost in dollars for Shaki to make q danglies is given by c(q)= 75+2q+0.015q^2 . Find the quantity that minimizes Shaki
the quantity that minimizes Shaki's cost is [tex]\( \frac{200}{3} \)[/tex], or approximately [tex]\( 66.67 \)[/tex] danglies.
To find the quantity that minimizes Shaki's cost function [tex]\( c(q) = 75 + 2q + 0.015q^2 \)[/tex], we need to find the value of q where the derivative of [tex]\( c(q) \)[/tex] with respect to [tex]\( q \)[/tex] is zero.
Given the cost function:
[tex]\[ c(q) = 75 + 2q + 0.015q^2 \][/tex]
We'll find the derivative [tex]\( c'(q) \)[/tex] with respect to q and set it equal to zero to find the critical points.
[tex]\[ c'(q) = \frac{d}{dq} (75 + 2q + 0.015q^2) \][/tex]
[tex]\[ c'(q) = 2 + 0.03q \][/tex]
Now, we'll set [tex]\( c'(q) \)[/tex] equal to zero and solve for q:
[tex]\[ 2 + 0.03q = 0 \][/tex]
[tex]\[ 0.03q = -2 \][/tex]
[tex]\[ q = \frac{-2}{0.03} \][/tex]
[tex]\[ q = -\frac{200}{3} \][/tex]
Since the quantity q must be positive in this context, we disregard the negative solution. Therefore, the critical point occurs at [tex]\( q = \frac{200}{3} \)[/tex].
To determine whether this critical point corresponds to a minimum, we'll analyze the second derivative [tex]\( c''(q) \)[/tex]. If [tex]\( c''(q) > 0 \)[/tex] at [tex]\( q = \frac{200}{3} \)[/tex], then it's a local minimum.
[tex]\[ c''(q) = \frac{d^2}{dq^2} (2 + 0.03q) \][/tex]
[tex]\[ c''(q) = 0.03 \][/tex]
Since [tex]\( c''(q) \)[/tex] is positive, the critical point [tex]\( q = \frac{200}{3} \)[/tex] corresponds to a minimum.
Therefore, the quantity that minimizes Shaki's cost is [tex]\( \frac{200}{3} \)[/tex], or approximately [tex]\( 66.67 \)[/tex] danglies.
According to a posting on a website subsequent to the death of a child who bit into a peanut, a certain study found that 7% of children younger than 18 in the United States have at least one food allergy. Among those with food allergies, about 41% had a history of severe reaction.a. If a child younger than 18 is randomly selected, what is the probability that he or she has at least one food allergy and a history of severe reaction? (Enter your answer to four decimal places.) b. It was also reported that 30% of those with an allergy in fact are allergic to multiple foods. If a child younger than 18 is randomly selected, what is the probability that he or she is allergic to multiple foods? (Enter your answer to three decimal places.)
a) The probability that he or she has at least one food allergy and a history of severe reaction is 0.0287.
b) The probability that he or she is allergic to multiple foods is, 0.021
Given that;
A certain study found that 7% of children younger than 18 in the United States have at least one food allergy.
a. Since the probability that a child younger than 18 has at least one food allergy is given as 7%.
Among those with food allergies, the probability of having a history of severe reaction is 41%.
Hence for the probability that a child has both at least one food allergy and a history of severe reaction, multiply these probabilities together:
7% × 41% = 0.07 × 0.41
= 0.0287.
Therefore, the probability is 0.0287.
b) For the probability that a randomly selected child younger than 18 is allergic to multiple foods, consider the information given.
The probability of having at least one food allergy among children younger than 18 is 7%.
And among those with allergies, 30% are allergic to multiple foods.
Hence for the probability, multiply the probability of having at least one food allergy (7%) by the probability of being allergic to multiple foods (30% of those with allergies):
Probability = 7% × 30%
= 0.07 × 0.30
= 0.021.
Therefore, the probability that a randomly selected child younger than 18 is allergic to multiple foods is 0.021.
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The probability that a child younger than 18 has at least one food allergy and a history of severe reaction is approximately 0.029. The probability that a child younger than 18 is allergic to multiple foods is approximately 0.021.
Explanation:To find the probability that a child younger than 18 has at least one food allergy and a history of severe reaction, we can use the information provided. We know that 7% of children younger than 18 have at least one food allergy and among those with food allergies, 41% had a history of severe reaction. To calculate the probability, we multiply these two probabilities together: 0.07 (the probability of having a food allergy) multiplied by 0.41 (the probability of having a severe reaction given a food allergy). So, the probability is 0.07 * 0.41 = 0.0287, which can be rounded to 0.0287 or approximately 0.029.
To find the probability that a child younger than 18 is allergic to multiple foods, we use the information that 30% of those with an allergy are allergic to multiple foods. So, the probability is 0.07 (the probability of having a food allergy) multiplied by 0.30 (the probability of being allergic to multiple foods given a food allergy). Hence, the probability is 0.07 * 0.30 = 0.021, which can be rounded to 0.021 or approximately 0.021.
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A campus deli serves 300 customers over its busy lunch period from 11:30 a.m. to 1:30 p.m. A quick count of the number of customers waiting in line and being served by the sandwich makers shows that an average of 10 customers are in process at any point in time. What is the average amount of time that a customer spends in process?
Answer:
4 minutes
Step-by-step explanation:
There are two hours from 11:30 a.m. to 1:30 p.m
The hourly rate of service is:
[tex]r=\frac{300}{2}=150\ customers/hour[/tex]
If the average number of customers in the system (n) is 10, the time that a customer spends in process is given by:
[tex]t=\frac{n}{r} =\frac{10}{150}=0.06667\ hours[/tex]
Converting it to minutes:
[tex]t= 0.066667\ hours*\frac{60\ minutes}{1\ hour}\\t=4\ minutes[/tex]
A customer spends, on average, 4 minutes in process.
A box contains 11 two-inch screws, of which 4 have a Phillips head and 7 have a regular head. Suppose that you select 3 screws randomly from the box with replacement. Find the probability there will be more than one Phillips head screw.
Answer:
The probability that there will be more than one Phillips head screw = 0.1803 .
Step-by-step explanation:
We are given that there are 11 two-inch screws in a box of which 4 have a Phillips head and 7 have a regular head.
We are selecting 3 screws randomly from the box with replacement, so the probability that there will be more than one Phillips head screw is given by :
Probability of selecting two Phillips head screw.Probability of selecting three Phillips head screw.Now P(selecting 2 Phillips head screw with replacement) is given by :
Selecting 2 Phillip head screw = [tex]\frac{4}{11}[/tex] * [tex]\frac{4}{11}[/tex] = [tex]\frac{16}{121}[/tex]
P(selecting three Phillips head screw) = [tex]\frac{4}{11}[/tex] * [tex]\frac{4}{11}[/tex] * [tex]\frac{4}{11}[/tex] = [tex]\frac{64}{1331}[/tex]
Therefore, Probability that there will be more than one Phillips head screw
= [tex]\frac{16}{121}[/tex] + [tex]\frac{64}{1331}[/tex] = [tex]\frac{240}{1331}[/tex] = 0.1803 .
A stone is dropped into a lake, creating a circular ripple that travels outward at a speed of 35 cm/s.
Express the radius r of this circle as a function of the time t (in seconds).
Answer:
The radius r of this circle as a function of the time t :
[tex]r(t)=35\times t[/tex]
Step-by-step explanation:
Speed of the circular ripple = S = 35 cm/s
Radius of the ripple at time t = r
[tex]Speed=\frac{Distance}{Time} [/tex]
[tex]35cm/s=\frac{r}{t}[/tex]
[tex]r=35 cm/s \times t[/tex]
The radius r of this circle as a function of the time t :
[tex]r(t)=35\times t[/tex]
The radius r of this circle is a function of the time t (in seconds) is 35t.
Given that
A stone is dropped into a lake, creating a circular ripple that travels outward at a speed of 35 cm/s.
We have to determineThe radius r of this circle is a function of the time t (in seconds).
According to the questionSpeed of the circular ripple = S = 35 cm/s
Radius of the ripple at time t = r
Then
The radius r of this circle is a function of the time t (in seconds) is determined by the following formula;
[tex]\rm Speed = \dfrac{Distance}{Time}[/tex]
Substitute all the values in the formula;
[tex]\rm Speed = \dfrac{Distance}{Time}\\ \\ 35 = \dfrac{r}{t}\\ \\ r = 35 \times t\\ \\ r = 35t[/tex]
Hence, The radius r of this circle is a function of the time t (in seconds) is 35t.
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The list of digits below is from a random number generator using technology. Use the list of numbers to obtain a simple random sample of size 3 from this list. If you start on the left and take the first three numbers between 1 and 9, what three books would be selected from the numbered list?
Question Continuation
5 2 5 5 2 1 0 5 7 5 8 9 3 7 2
Options
A. A Tale of Two Cities, Huckleberry Finn, A Tale of Two Cities
B. A Tale of Two Cities, Huckleberry Finn, The Sun Also Rises
C. A Tale of Two Cities, Huckleberry Finn, Crime and Punishment
D. Huckleberry Finn, Crime and Punishment, The Jungle
E. Crime and Punishment, The Jungle, The Sun Also Rises
Book List
1. Crime and Punishment
2. Huckleberry Finn
3. The Sun Also Rises
4. As I Lay Dying
5. A Tale of Two Cities
6. Death of a Salesman
7. The Jungle
8. Pride and Prejudice
9. The Scarlet Letter
Answer:
C. A Tale of Two Cities, Huckleberry Finn, Crime and Punishment
Step by step explanation
Counting from the left, the selected numbers are 5 , 2 and 1
The books are
5. A Tale of two cities
2. Huckleberry Finn
1. Crime and Punishment
Note that the numbers on the list are 5 2 5 5 2 1
After book 5 and 2 have been selected, the next series of numbers (5 5 2) can not be considered because they've already been selected.
So, the next number after 5 2 5 5 2 is then selected, which is 1
The selected books are:
The books are: A Tale of two cities, Huckleberry Finn, Crime and Punishment
The simple random selection of three books using the random number generated will include the books : The Sun also rises, The Scarlet letter, Crime and Punishment.
The random number generated using technology include :
7, 2, 7, 2, 2, 6, 7, 0, 8, 3, 2, 8, 5, 3, 1
Making a selection of 3 numbers between (1 - 9) starting from the left hand side of the list : 7, 2, 6 ( repeated numbers are only chosen once) as we have to make a unique selection of numbers.From the list of number books attached below :
7. The Sun also rise
2. The Scarlet letter
6. Crime and Punishment
Hence, the randomly selected books will be :
The Sun also rises, The Scarlet letter, Crime and Punishment.
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An adult male African elephant weighs about 9.07*10^3 kg. Compute how many times heavier an adult male blue whale is than an adult male African elephant(I.e., find the value of the ratio). Round your final answer to the nearest tenth.
Answer:
An adult male blue whale is 18.7 times heavier than an adult male African elephant.
Step-by-step explanation:
As the weight of an adult male African elephant weighs about
[tex]9.07\:\times\:10^3[/tex] kgAnd the weight of an adult blue whale is
[tex]1.7\:\times\:10^5[/tex] kgDetermining the ratio of adult male African elephant to the weight of an adult blue whale as:
[tex]\:\:\frac{1.7\:\times\:10^5}{9.07\:\times\:10^3}[/tex]
[tex]\mathrm{Apply\:exponent\:rule}:\quad \frac{x^a}{x^b}=x^{a-b}[/tex]
[tex]=\frac{10^{5-3}\times \:1.7}{9.07}[/tex]
[tex]=\frac{10^2\times \:1.7}{9.07}[/tex]
As [tex]10^2\times \:1.7=170[/tex], So
[tex]=\frac{170}{9.07}[/tex]
[tex]=18.74310\dots[/tex]
Round the answer to the nearest tenth
[tex]=18.7[/tex]
Therefore, an adult male blue whale is 18.7 times heavier than an adult male African elephant.
Keywords: ratio, nearest tenth
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Same-sex unions increasingly become heated political issue. the 2006 GSS asked respondents opinions on homosexual relations. five response categories ranged from always wrong to not wrong at all. see the following frequency distributions. at what level is this variable measured? Homosexual Relations Frequency Percentage Cumulative Percentage Always wrong 467 50.2 50.2Almost always wrong 41 4.4 54.6 Sometimes wrong 76 8.2 62.8Not wrong at all 346 37.2 100.0 Total 930 100.0
Answer:
Ordinal level
Step-by-step explanation:
The variable of interest is opinion on homosexual relations and the frequency distribution for opinion on homosexual relations is given.
The opinion of people is categorized from wrong to not wrong at all. There exists order in the categorizes and measurement of variable indicates the ordinal level of measurement.
Thus, variable is measured at ordinal level.
kevin durant of the oklahoma city thunder & kobe bryant of the los angeles lakers were the leading scorers in the NBA for the 2012-2013 regular season. Together they scored 4413 points, with bryant scoring 147 fewer points than durant. how many pointsdid each of them score?
Answer:
Bryant: 2059.5 (RIP)
Durant:2353.5
Step-by-step explanation:
To find how many points Kevin Durant and Kobe Bryant scored, set up equations based on the given information. Kevin Durant scored 2280 points and Kobe Bryant scored 2133 points during the 2012-2013 NBA regular season.
Explanation:The question asks us to determine how many points Kevin Durant and Kobe Bryant scored individually during the 2012-2013 NBA regular season given that together they scored 4413 points and Kobe Bryant scored 147 fewer points than Kevin Durant.
To solve this, we can set up two equations based on the information provided:
We can substitute the second equation into the first to find Durant's score:
Now that we have Durant's score, we can use it to find Bryant's score:
Therefore, Kevin Durant scored 2280 points and Kobe Bryant scored 2133 points during the 2012-2013 NBA regular season.
In 1990 the Department of Natural Resources released 1000 splake (a crossbreed of fish) into a lake. In 1997 the population of splake in the lake was estimated to be 3000. Using the Malthusian law for population growth, estimate the population of splake in the lake in the year 2020.
Using the Malthusian law for population growth and the given data, the estimated population of splake in a lake in 2020 is approximately 21,485.
Explanation:The question involves estimating the population of splake in a lake in 2020 using the Malthusian law for population growth. The Malthusian law indicates that populations grow exponentially under ideal conditions. Given that the population increased from 1000 to 3000 splake between 1990 and 1997, we can calculate the rate of growth and then apply this rate to predict the population in 2020.
To begin, we identify the years of growth as 1997 - 1990 = 7 years. The formula for exponential growth is P = P0ert, where P is the final population, P0 is the initial population, r is the rate of growth, and t is the time in years. With P = 3000, P0 = 1000, and t = 7, we can solve for r.
3000 = 1000e7r, which simplifies to 3 = e7r. Taking the natural logarithm of both sides gives us ln(3) = 7r, and solving for r gives r ~ 0.1487. Now, to find the population in 2020, which is 30 years from 1990, we use the formula with P0 = 1000, r = 0.1487, and t = 30: P = 1000e0.1487*30.
Upon calculation, the predicted population of splake in the year 2020 is approximately 21,485.
The amount of corn chips dispensed into a 10-ounce bag by the dispensing machine has been identified at possessing a normal distribution with a mean of 10.5 ounces and a standard deviation of 0.2 ounces (these are the population parameters). Suppose a sample of 100 bags of chips were randomly selected from this dispensing machine. Find the probability that the sample mean weight of these 100 bags is less than 10.45 ounces. (Hint: think of this in terms of a sampling distribution with sample size
Answer:
0.62% probability that the sample mean weight of these 100 bags is less than 10.45 ounces.
Step-by-step explanation:
To solve this question, the concepts of the normal probability distribution and the central limit theorem are important.
Normal probability distribution
Problems of normally distributed samples can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], a large sample size can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\frac{\sigma}{\sqrt{n}}[/tex]
In this problem, we have that:
[tex]\mu = 10.5, \sigma = 0.2, n = 100, s = \frac{0.2}{\sqrt{100}} = 0.02[/tex]
Find the probability that the sample mean weight of these 100 bags is less than 10.45 ounces
This is the pvalue of Z when X = 10.45. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{10.45 - 10.5}{0.02}[/tex]
[tex]Z = -2.5[/tex]
[tex]Z = -2.5[/tex] has a pvalue of 0.0062.
So there is a 0.62% probability that the sample mean weight of these 100 bags is less than 10.45 ounces.
The probability of the sample mean weight being less than 10.45 ounces can be found by calculating the Z-score and referencing a standard normal distribution table. The calculated Z-score (-2.5) corresponds to a probability of approximately 0.62%.
Explanation:The problem is about determining the probability that the sample mean weight of corn chip bags is less than 10.45 ounces. This is a problem of finding a probability in a sampling distribution when the population parameters are known. Given the data, we can use the Central Limit Theorem, which states that if the sample size is large enough (usually >30), the sampling distribution approximates a normal distribution.
To solve this, you can use the formula Z = (X - μ) / (σ/√n), where X is the sample mean, μ is the population mean, σ is the population standard deviation, and n is the sample size.
Plugging in the given values: Z = (10.45 - 10.5) / (0.2 / √100) = -2.5. The Z-score tells us how many standard deviations away our data point is from the mean. To find the probability that the Z is less than -2.5, you can refer to a standard normal distribution table or use statistical software. According to the Z table, the probability is approximately 0.0062 or 0.62% that the sample mean weight of these 100 bags is less than 10.45 ounces.
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Set up the integral that uses the method of disks/washers to find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified lines.
y=3\sqrt(x), y = 3, x= 0
a.) about the line y = 3
b.) about the line x = 5
The integrals for the volume of the solids
a.) V = ∫[0 to 1] π(3 - 3√x)² dx
b.) V = ∫[0 to 27] π(5 - [tex]x^{2/3}[/tex]))² dx
We have,
To set up the integral using the method of disks/washers to find the volume V of the solid obtained by rotating the region bounded by the curves y = 3√x, y = 3, and x = 0 about the specified lines, follow these steps:
Given curves: y = 3√x, y = 3, x = 0
a.)
Rotating about the line y = 3:
- Draw the region bounded by the curves y = 3√x, y = 3, and x = 0.
- The solid will be formed by revolving this region around the line y = 3.
- For the method of disks/washers, consider a vertical slice (dx) of thickness dx at a distance x from the y-axis.
- The radius of the disk is the distance between the curve y = 3√x and the line y = 3, which is (3 - 3√x).
- The area of the disk is π(radius)^2 = π(3 - 3√x)².
- The volume of the infinitesimally thin disk is dV = π(3 - 3√x)² dx.
- Integrate the volume from x = 0 to x = (3/3)² = 1:
V = ∫[0 to 1] π(3 - 3√x)² dx
b)
Rotating about the line x = 5:
- Draw the region bounded by the curves y = 3√x, y = 3, and x = 0.
- The solid will be formed by revolving this region around the line x = 5.
- For the method of disks/washers, consider a vertical slice (dx) of thickness dx at a distance x from the y-axis.
- The radius of the disk is the distance between the line x = 5 and the curve y = 3√x, which is (5 - [tex]x^{2/3}[/tex]).
- The area of the disk is π(radius)^2 = π(5 - [tex]x^{2/3}[/tex])².
- The volume of the infinitesimally thin disk is dV = π(5 - [tex]x^{2/3}[/tex])² dx.
Integrate the volume from x = 0 to x = 3³ = 27:
V = ∫[0 to 27] π(5 - [tex]x^{2/3}[/tex])² dx
These integrals will give you the volumes of the solid obtained by rotating the region about the specified lines. You can evaluate these integrals to find the exact values of the volumes.
Thus,
The integrals for the volume of the solids
a.) V = ∫[0 to 1] π(3 - 3√x)² dx
b.) V = ∫[0 to 27] π(5 - [tex]x^{2/3}[/tex]))² dx
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A researcher has a hypothesis that a specific drug may have a higher prevalence of side effects among members of the African American population than members of the Caucasian population. Which statistical technique might the researcher want to use when designing a study to test their hypothesis
A. Stratification
B. Crossover matching
C. Matching
D. Randomization
Answer:
A. Stratification
Step-by-step explanation:
Stratified random sampling is used when the researcher wants to highlight a specific subgroup within an entire population.
Stratification technique is mainly used to reduce the population differences and to increase the efficiency of the estimates. In this method the population is divided into a number of subgroups or strata.
Each strata should be so formed such that they are homogeneous as far as possible.
Final answer:
When examining the hypothesis about drug side effects in different populations, Randomization is the most appropriate statistical technique. It helps in reducing bias and ensures equal chances of group assignment, providing more reliable results in comparing the effects across populations.(Option D)
Explanation:
A researcher examining the hypothesis that a specific drug may exhibit a higher prevalence of side effects among the African American population compared to the Caucasian population could employ several statistical techniques to design the study. However, the most appropriate option provided is Randomization. Randomization helps in mitigating bias and ensures that each participant has an equal chance of being assigned to either the experimental or control group. This process decreases the likelihood of systematic differences between groups and allows any effects observed to be more confidently attributed to the drug under study rather than external factors.
Other options like Stratification, Crossover matching, and Matching could also play roles in different aspects of study design, but when testing a hypothesis about a drug's effects across different populations, randomization is crucial. It aligns with principles of experimental design that seek to control, to the extent possible, for variables that could influence the outcome, ensuring that the treatment group and control group are comparable at the beginning of the study.
Suppose that a company’s sales were $5,000,000 three years ago. Since that time sales have grown at annual rates of 10
percent,–10 percent, and 25 percent.
a Find the geometric mean growth rate of sales over this three-year period.
b Find the ending value of sales after this three-year period.
Answer:
≈ 0.07
Step-by-step explanation:
To find the geometric mean over this three-year period, we plug in the values for the yearly return rates into the equation for the geometric mean.
The geometric mean growth rate of sales over this three-year period is 7.36%. Also, the ending value of sales after this three-year period is $6,187,500.
Geometric Mean (GM) is the average value or mean which signifies the central tendency of the set of numbers by finding the product of their values. Basically, we multiply the numbers altogether and take the nth root of the multiplied numbers, where n is the total number of data values.
[tex](1+G)^3 = (1+0.1)(1-0.1)(1+0.25)\\\\(1+G)^3 = 1.2375\\\\(1+G) = \sqrt[3]{1.2375} = 1.0736\\\\G = 0.0736[/tex]
G = 7.36 %
Also,
sales in year 0 = $5,000,000
annual Growth rate of year 1 = 10%
Sales in year 1 : $5,000,000 + 10% of $5,000,000 = [tex]5,000,000 + \frac{10}{100} *$5,000,000 = $5,500,000[/tex]
annual Growth rate of year 2 = -10%
Sales in year 2 : $5,500,000 - 10% of $5,500,000 = [tex]5,500,000 - \frac{10}{100} *$5,500,000 = $4,950,000[/tex]
annual Growth rate of year 3 = 25%
Sales in year 3 : $4,950,000 + 25% of $4,950,000 = [tex]4,950,000 + \frac{25}{100} *4,950,000 = $6,187,500[/tex]
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Investments Suppose that you have $4000 to invest and you invest x dollars at 10% and the remainder at 896, write expressions in x that represent (a) the amount invested at 8%, (b) the interest earned on the x dollars at 10%, (c) the interest earned on the money invested at 8% (d) the total interest earned.
Answer:
Step-by-step explanation:
you have $4000 to invest and you invest x dollars at 10% and the remainder at 8℅.
a) an expression in x that represent the amount invested at 8% is
4000 - x
b) The The formula for simple interest is expressed as
I = PRT/100
Where
P represents the principal
R represents interest rate
T represents time in years
I = interest after t years
From the information given
P = $x
R = 10%
Assuming the investment is for 1 year, then interest,
I = (x × 10 × 1)/100
I = $0.1x
c) P = 4000 - x
R = 8℅
I = [(4000 - x) × 8 × 1)]/100
I = (32000 - 8x)/100
I = 320 - 0.08x
d) the total interest earned is
I = 0.1x + 320 - 0.08x
I = 0.02x + 320
Describe a normal probability distribution. a. bell-shaped.b. mean, median, and mode all equivalent.c. bimodal.d. symmetric around the mean.e. skewed to the right.f. models discrete random variables.g. most of the data fall within 3 standard deviations from the mean. h. uniform-shaped.
Answer:
a) bell-shaped.
b) mean, median, and mode all equivalent.
d) symmetric around the mean.
g) most of the data fall within 3 standard deviations from the mean.
Step-by-step explanation:
We have to describe a normal distribution.
a. bell-shaped.
This is true a normal distribution is a bell shaped distribution.
b. mean, median, and mode all equivalent.
This is true for a normal distribution.
Mean = Mode = Median
c. Bimodal
The is not true about the normal distribution. A normal distribution is unimodal and the mode is equal to the mean of the distribution.
d. symmetric around the mean.
This is true. The normal distribution is centered around the mean
e. skewed to the right.
This is not a property of normal distribution.
f. models discrete random variables.
Normal distribution is a continuous distribution.
g. most of the data fall within 3 standard deviations from the mean.
This is true. According to Empirical rule, almost all the data lies within three standard deviation of mean.
h. uniform-shaped
This is not true. A normal distribution is bell shaped.
The options that properly describe a normal distribution are;
A) Bell Shaped
B) Mean, median and mode are equivalent
D) Symmetric about the mean
G) most of the data fall within 3 standard deviations from the mean
Some of the properties of normal distribution are that;
The mean, mode and median are all equal.The curve is symmetric at the center around the mean. This implies a bell shaped curve. Exactly half of the values are to the left of center and exactly half the values are to the right.The total area under the curve is 1 It's a continuous distributionLet us look at the options;
A) this is correct from the properties listed above. B) This is also correct from the properties listed above. C) This is not true because the mode is equal to the median and the mean and thus can only be unimodal. D) This is true from the properties listed above. E) From property 3, this is wrong as it is not skewed to the right since it has half values to the left and half to the right. F) This is not true because normal distribution is continuous and not discrete. G) This is true based on the empirical rule of normal distribution because Empirical Rule states that 99.7% of data observed following a normal distribution lies within 3 standard deviations of the mean. H) Not true as from property 2 we can see that it is bell shaped.Read more about normal distribution at;https://brainly.com/question/4514629
A line has a slope of -3/5. Which ordered pairs could be points on a parallel line? Select two options.
The question is missing the options. The options are:
(A) (-8, 8) and (2, 2)
(B) (-5, -1) and (0, 2)
(C) (-3, 6) and (6.-9)
(D) (-2, 1) and (3,-2)
(E) (0, 2) and (5,5)
Answer:
Options (A) and (D)
Step-by-step explanation:
Given:
A line with slope (m) = [tex]-\frac{3}{5}[/tex]
Now, a parallel line to the given line will have the same slope.
So, let us check each of the given options.
Option (A)
(-8, 8) and (2, 2)
The slope of line passing through two points [tex](x_1,y_1)\ and\ (x_2,y_2)[/tex] is given as:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
Now, the slope of a line passing through (-8, 8) and (2, 2) is given as:
[tex]m_1=\frac{2-8}{2-(-8)}=\frac{-6}{10}=-\frac{3}{5}[/tex]
So, [tex]m=m_1[/tex]
Therefore, option (A) is correct.
Option (B): (-5, -1) and (0, 2)
The slope of a line passing through (-5, -1) and (0, 2) is given as:
[tex]m_2=\frac{2-(-1)}{0-(-5)}=\frac{3}{5}[/tex]
So, [tex]m\ne m_2[/tex]
Therefore, option (B) is not correct.
Option (C): (-3, 6) and (6, -9)
The slope of a line passing through (-3, 6) and (6, -9) is given as:
[tex]m_3=\frac{-9-6}{6-(-3)}=\frac{-15}{9}=-\frac{5}{3}\ne m[/tex]
Therefore, option (C) is not correct.
Option (D): (-2, 1) and (3, -2)
The slope of a line passing through (-2, 1) and (3, -2) is given as:
[tex]m_4=\frac{-2-1}{3-(-2)}=-\frac{3}{5}=m[/tex]
Therefore, option (D) is correct.
Option (E): (0, 2) and (5, 5)
The slope of a line passing through (0, 2) and (5, 5) is given as:
[tex]m_5=\frac{5-2}{5-0}=\frac{3}{5}\ne m[/tex]
Therefore, option (E) is not correct.
Hence, only options (A) and (D) are correct.
Find the volume of the pyramid. Round your answer to the nearest tenth.
8.6 mm
15.5 mm
12.5 mm
The volume of the pyramid is
mm?.
Answer:
from my opinion second option is right
How many names and binary predicates would a language like the first need in order to say everything you can say in the second?
Answer:The same number of names and 4 predicates
Step-by-step explanation:
Answer:
The same number of names and 4 predicates
Step-by-step explanation:
f left parenthesis x right parenthesis equals StartFraction 16 x squared Over x Superscript 4 Baseline plus 64 EndFractionf(x)=16x2 x4+64(a) Is the pointleft parenthesis negative 2 StartRoot 2 EndRoot comma 1 right parenthesis−22,1on the graph of f?(b) Ifx equals 2 commax=2,what is f(x)? What point is on the graph of f?(c) If f left parenthesis x right parenthesis equals 1 commaf(x)=1, what is x? What point(s) is (are) on the graph of f?(d) What is the domain of f?(e) List the x-intercepts, if any, of the graph of f.(f) List the y-intercept, if there is one, of the graph of f.
Answer:
a) Yes
b) (2,0.8)
c)[tex](2\sqrt2,1), (-2\sqrt2,1)[/tex]
d) [tex]x \in (-\infty,\infty)[/tex]
e) (0,0)
f) (0,0)
Step-by-step explanation:
We are given the following function in the question:
[tex]f(x) = \displaystyle\frac{16x^2}{x^4 + 64}[/tex]
a) We have to check whether given point lies on the function or not.
[tex](-2\sqrt2,1)\\\\f(-2\sqrt2) = \displaystyle\frac{16(-2\sqrt2)^2}{(-2\sqrt2)^4 + 64} = \frac{128}{128} = 1[/tex]
b) Find value of f(x) at x = 2
[tex]f(2) = \displaystyle\frac{16(2)^2}{(2)^4 + 64} =\frac{64}{80}= 0.8[/tex]
Thus, (2,0.8) lies on the graph of given function.
c) We have to find the value of x, when f(x) = 1
[tex]1 = \displaystyle\frac{16x^2}{x^4 + 64}\\\\x^4 -16x^2 + 64 = 0\\(x^2-8)^2 = 0\\x^2 - 8 = 0\\x = \pm 2\sqrt2[/tex]
[tex](2\sqrt2,1), (-2\sqrt2,1)[/tex] lies on he graph of function.
d) Domain is the collection of all values of x for which the function is defined.
[tex]x \in (-\infty,\infty)[/tex]
e) x-intercepts
This is the value of x such that the function is zero.
[tex]0 = \displaystyle\frac{16x^2}{x^4 + 64}\\\\16x^2 = 0\\x = 0[/tex]
f) y-intercept
It is the value of function when x is zero.
[tex]f(0) = \displaystyle\frac{16(0)^2}{(0)^4 + 64} = 0[/tex]
The function passes trough origin.
The solution involves determining if a specific coordinates exist on the graph, calculating the function value for specific x-values, determining x-values for a specific function value, finding the domain of the function, and identifying the x and y intercepts of the function.
Explanation:The function is f(x) = 16x²/(x⁴ + 64).
To check if the point (-2√2, 1) is on the graph, substitute x = -2√2 into f(x). If f(-2√2) equals 1, the point is on the graph.For x = 2, substitute x = 2 into f(x) to get f(2). The point on the graph for this x-value will be (2, f(2)).To find x when f(x) = 1, set f(x) equal to 1 and solve for x. The points on the graph will be (x, 1), where x are the solutions to the equation.The domain of the function f is all real numbers except for x-values that make the denominator zero. Solve x⁴ + 64 = 0 to find x-values to exclude from the domain.To find the x-intercepts of the graph, set f(x) equal to zero and solve for x.The y-intercept of the graph is the value of f(x) at x = 0, which is f(0).Learn more about Function Analysis here:https://brainly.com/question/34156091
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The time to fly between New York City and Chicago is uniformly distributed with a minimum of 120 minutes and a maximum of 150 minutes.
What is the probability that a flight is between 125 and 140 minutes?
A. 1.00.
B. 0.50.
C. 0.33.
D. 0.12.
E. 0.15
Answer:
B. 0.50.
Step-by-step explanation:
An uniform probability is a case of probability in which each outcome is equally as likely.
For this situation, we have a lower limit of the distribution that we call a and an upper limit that we call b.
The probability of a measure X being between two values c and d, in which d is larger than c, is given by the following formula:
[tex]P(c \leq X \leq d) = \frac{d - c}{b - a}[/tex]
Uniformly distributed with a minimum of 120 minutes and a maximum of 150 minutes.
This means that [tex]a = 120, b = 150[/tex]
What is the probability that a flight is between 125 and 140 minutes?
This is
[tex]P(125 \leq X \leq 140) = \frac{140 - 125}{150 - 120} = 0.5[/tex]
So the correct answer is:
B. 0.50.
The heights of apricot trees in an orchard are approximated by a normal distribution model with a mean of 18 feet and a standard deviation of 1 feet. What is the probability that the height of a tree is between 16 and 20 feet
Answer:
0.9544
Step-by-step explanation:
We are given that mean=18 and standard deviation=1 and we have to find P(16<X<20).
P(16<X<20)=P(z1<Z<z2)
z1=(x1-mean)/standard deviation
z1=(16-18)/1=-2
z2=(x2-mean)/standard deviation
z2=(20-18)/1=2
P(16<X<20)=P(z1<Z<z2)=P(-2<Z<2)
P(16<X<20)=P(-2<Z<0)+P(0<Z<2)
P(16<X<20)=0.4772+0.4772=0.9544
The probability that the height of a tree is between 16 and 20 feet is 95.44%
The sum of the diameters of the largest and smallest pizzas sold at a pizza shop is 25 inches. The difference in their diameters is 15 inches. Find the diameters of the largest and smallest pizzas.
Answer:
20 inches and 5 inches
Step-by-step explanation:
Let the diameter of the largest and the smallest pizza be Y and X respectively.
Then,
Y+X = 25 ........................... Equation 1
Y-X = 15 ............................ Equation 2
Solve equation 1 and equation 2 simultaneously.
Add equation 1 and equation 2
Y+Y = +X+(-X)+25+15
2Y = 40
Y = 40/2
Y = 20 inches.
Also,
Substitute the value of Y into equation 1
20+X=25
X = 25-20
X = 5 inches.
Hence the diameter of the largest and the smallest pizzas = 20 inches and 5 inches
Final answer:
The smallest pizza has a diameter of 5 inches, and the largest pizza has a diameter of 20 inches.
Explanation:
The diameters of the largest and smallest pizzas are 20 inches and 5 inches, respectively.
To find the diameters of the pizzas:
Let x be the diameter of the smallest pizza and y be the diameter of the largest pizza.
We have the system of equations x + y = 25 and y - x = 15.
Solving these equations simultaneously, we get y = 20 and x = 5.