(1 point) For the equation given below, evaluate ′ at the point (−1,2). (5−)^4+4^3=2433. ′ at (−1,2) =

Answer:

Kamala had the best GPA compared to other students at his school, since his GPA is 2 standard deviations above his school's mean.

Step-by-step explanation:

The z-score measures how many standard deviation a score X is above or below the mean.

it is given by the following formula:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

In which

[tex]\mu[/tex] is the mean, [tex]\sigma[/tex] is the standard deviation.

In this problem:

The student with the best GPA compared to other students at his school is the one with the higher z-score, that is, the one whose grade is the most standard deviations above the mean for his school

Thuy

Student GPA| School Average GPA| School Standard Deviation

Thuy 2.7| 3.2| 0.8

So [tex]X = 2.7, \mu = 3.2, \sigma = 0.8[/tex]

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{2.7 - 3.2}{0.8}[/tex]

[tex]Z = -0.625[/tex]

Thuy's score is -0.625 standard deviations below his school mean.

Vichet

Student GPA| School Average GPA| School Standard Deviation

Vichet 88| 75| 20

So [tex]X = 88, \mu = 75, \sigma = 20[/tex]

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{88 - 75}{20}[/tex]

[tex]Z = 0.65[/tex]

Vichet's score is 0.65 standard deviation above his school mean

Kamala

Student GPA| School Average GPA| School Standard Deviation

Kamala 8.8| 8| 0.4

So [tex]X = 8.8, \mu = 8, \sigma = 0.4[/tex]

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{8.8 - 8}{0.4}[/tex]

[tex]Z = 2[/tex]

Kamala's score is 2 standard deviations above his school mean.

Kamala has the higher z-score, so he had the best GPA when compared to other students at his school.

The correct answer is:

Kamala had the best GPA compared to other students at his school, since his GPA is 2 standard deviations above his school's mean.

Final answer:

Kamala had the best GPA relative to her school's average, with a z-score of 2.00, indicating her GPA is 2 standard deviations above the average.

Explanation:

To determine which student had the best GPA compared to other students at their school, we need to calculate how many standard deviations each student's GPA is away from their school's average GPA. This can be done using the formula:

z = (x - μ) / σ

Where z is the number of standard deviations, x is the student's GPA, μ (mu) is the school's average GPA, and σ (sigma) is the school's standard deviation.

Kamala has the highest z-score, which means her GPA is the furthest above her school's average when compared to Thuy and Vichet. Therefore, Kamala had the best GPA relative to her peers at her school.

To calculate the initial trust fund deposit for three children of diverse ages, you create an equation reflecting the present value of the future payouts for each child at ages 18 and 21. The equation of value here models the required single investment with respect to the annual interest rate.

The problem presented, concerning setting up a trust fund for three children aged 1, 3, and 6, involves future value of lump sum investments, compound interest, and time value of money. Using an equation of value approach, the equation for the single investment Z made today that will pay each child X at age 18 and Y at age 21 can be modeled as follows:

where r represents the annual interest rate. This equation reflects the present value of the future payouts for each child. The term (1+r)years until payout is used to calculate the present value of each future payment. The equation adds up these present values for each child to calculate the initial trust fund deposit (Z).

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Answer:

(a) P (Both vehicles are available at a given time) = 0.81

(b) P (Neither vehicles are available at a given time) = 0.01

(c) P (At least one vehicle is available at a given time) = 0.99

Step-by-step explanation:

Let A = Vehicle 1 is available when needed and B = Vehicle 2 is available when needed.

Given:

The availability of one vehicle is independent of the availability of the other, i.e. P (A ∩ B) = P (A) × P (B)

P (A) = P (B) = 0.90

(a)

Compute the probability that both vehicles are available at a given time as follows:

P (Both vehicles are available) = P (Vehicle 1 is available) ×

                                                              P (Vehicle 2 is available)

                                  [tex]P(A\cap B)=P(A)\times P(B)[/tex]

                                                  [tex]=0.90\times0.90\\=0.81[/tex]

Thus, the probability that both vehicles are available at a given time is 0.81.

(b)

Compute the probability that neither vehicles are available at a given time as follows:

P (Neither vehicles are available) = [1 - P (Vehicle 1 is available)] ×

                                                                   [1 - P (Vehicle 2 is available)]

                                    [tex]P(A^{c}\cap B^{c})=[1-P(A)]\times [1-P(B)]\\[/tex]

                                                       [tex]=(1-0.90)\times (1-0.90)\\=0.10\times0.10\\=0.01[/tex]

Thus, the probability that neither vehicles are available at a given time is 0.01.

(c)

Compute the probability that at least one vehicle is available at a given time as follows:

P (At least one vehicle is available) = 1 - P (None of the vehicles are available)

                                                          [tex]=1-[P(A^{c})\times P(B^{c})]\\=1-0.01.....(from\ part\ (b))\\ =0.99[/tex]

Thus, the probability that at least one vehicle is available at a given time is 0.99.

Answer:

[tex]R = 59x[/tex]

Step-by-step explanation:

We are given the following in the question:

Cost per unit = $59

Let x units of product be sold.

We have to write an expression the amount of money received (revenue R) from the sale of x units of the product.

Revenue:

Revenue =

[tex]\text{Unit Cost}\times \text{Units sold}\\R = 59x[/tex]

is the required expression of revenue.

Answer:

The sample standard deviation of 5.95.9 inches differs from the population standard deviation of 5.25.2 inches because of their formulas for calculating it.

Step-by-step explanation:

We are given the​ heights, in​ inches, of the starting five players on a college basketball team ;

68, 73, 77, 75 and 84

Now whether we treat this data as sample data or population data, the mean height would remain same in both case because the formula for calculating mean is given by ;

     Mean = Sum of all data values ÷ No. of observations

     Mean = ( 68 + 73 + 77 + 75 + 84 ) ÷ 5 = 75.4 inches

So, numerically, the sample mean of 75.4 inches is the same as the population mean.

Now, coming to standard deviation there will be difference in both sample and population standard deviation and that difference occurs due to their formulas;

Formula for sample standard deviation = [tex]\frac{\sum (X_i - Xbar)^{2} }{n-1}[/tex]

           where, [tex]X_i[/tex] = each data value

                       X bar = Mean of data

                        n = no. of observations

Sample standard deviation = [tex]\frac{ (68 - 75.4)^{2} +(73 - 75.4)^{2}+(77- 75.4)^{2}+(75- 75.4)^{2}+(84 - 75.4)^{2} }{5-1}[/tex]    

                                           = 5.9 inches

Whereas, Population standard deviation = [tex]\frac{\sum (X_i - Xbar)^{2} }{n}[/tex]

   = [tex]\frac{ (68 - 75.4)^{2} +(73 - 75.4)^{2}+(77- 75.4)^{2}+(75- 75.4)^{2}+(84 - 75.4)^{2} }{5}[/tex] = 5.2 inches .

So, that's why sample standard deviation of 5.95.9 inches differs from the population standard deviation of 5.25.2 inches only because of formula.

Answer:

P1: An ant releases a chemical when it dies, and its fellows then carry it away to the compost heap.

P2: A healthy ant painted with the death chemical will be dragged to the funeral heap again and again.

C: Apparently the communication is highly effective

Step-by-step explanation:

Premises are statements that are always assumed to be truth or statements that have been given and made to be true.

Premises will be labelled as P1, P2, P3..........

Conclusions are derived statements from premises. Its truthfulness is derived from the truthfulness of premises. Meaning that, when the premises is true, the conclusion is also true.

Conclusions will be labelled as C1, C2, C3........

In the question above, it's noted that the conclusion starts at "Apparently the" while the premises are statements before "Apparently the"

The argument's premises are as follows:

1. An ant releases a chemical when it dies.

2. Its fellow ants then carry the dead ant to the compost heap.

3. A healthy ant painted with the death chemical will be dragged to the funeral heap again and again.

The conclusion is that the communication among ants when one of them dies is highly effective.

In the given passage, there is an implicit argument about the effectiveness of communication among ants when one of them dies. Let's identify the premises and the conclusion:

Premises:

1. An ant releases a chemical when it dies.

2. Its fellow ants then carry the dead ant to the compost heap.

3. A healthy ant painted with the death chemical will be dragged to the funeral heap again and again.

Conclusion:

4. Apparently, the communication among ants when one of them dies is highly effective.

These premises and conclusion can be organized as follows:

Premise 1: An ant releases a chemical when it dies.

Premise 2: Its fellow ants then carry the dead ant to the compost heap.

Premise 3: A healthy ant painted with the death chemical will be dragged to the funeral heap again and again.

Conclusion: Apparently, the communication among ants when one of them dies is highly effective.

In this argument, premises 1, 2, and 3 provide evidence or observations related to ant behavior when a member of their colony dies. The conclusion, stated in premise 4, is drawn from these observations and suggests that the communication system among ants regarding the death of a fellow ant is effective.

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Answer:

Step-by-step explanation:

The formula for finding the sum of the measure of the interior angles in a regular polygon is expressed as (n - 2) × 180.

Where

n represents the number of sides of the polygon.

5a) The polygon has 11 sides. Therefore, sum of angles is

(11 - 2) × 180 = 1620

The measure of each angle is

1620/11 = 148.3°

b) n = 24

Therefore, sum of angles is

(24 - 2) × 180 = 3960

The measure of each angle is

3960/24 = 165°

5a) n = 7

Therefore, sum of angles is

(7 - 2) × 180 = 900

The measure of each angle is

900/7 = 128.6°

5b) n = 10

Therefore, sum of angles is

(10 - 2) × 180 = 1440

The measure of each angle is

1440/10 = 144°

Answer: P(AUB) = 0.93 + 0.89 - 0.87 = 0.95

Therefore, the probability that at least one train is on time is 0.95.

Step-by-step explanation:

The probability that at least one train is on time is the probability that either train A, B or both are on time.

P(A) = P(A only) + P(A∩B)

P(B) = P(B only) + P(A∩B)

P(AUB) = P(A only) + P(B only) + P(A∩B)

P(AUB) = P(A) + P(B) - P(A∩B) ......1

P(A) = 0.93

P(B) = 0.89

P(A∩B) = 0.87

Then we can substitute the given values into equation 1;

P(AUB) = 0.93 + 0.89 - 0.87 = 0.95

Therefore, the probability that at least one train is on time is 0.95.

At least 96.00% of the data in any data set lies within three standard deviations of the mean.

The Empirical Rule states that in a bell-shaped and symmetric distribution, approximately 68 percent of the data lies within one standard deviation of the mean, 95 percent lies within two standard deviations of the mean, and more than 99 percent lies within three standard deviations of the mean. Therefore, at least 96.00​% of the data lies within three standard deviations of the mean.

Answer:

the line equation is 2*x - y = 3

Step-by-step explanation:

for the line equation in implicit form

A*x + B*y = C

then if the point (x=4,y=5) belong to the line

4*A + 5*B = C

and  if the point (x=7,y=11) belong to the line

7*A + 11*B = C

then since we can choose C freely , we set C=1 for simplicity , then

4*A + 5*B = 1 → B= (1-4*A)/5

7*A + 11*B = 1

7*A + 11*(1-4*A)/5  = 1

7*A - 44/5*A + 11/5 = 1

-9/5*A = -6/5

A= 2/3

B= (1-4*A)/5 = (1-4*2/3)/5 = -1/3

therefore

2/3*x - 1/3*y = 1

2*x - y = 3

Answer:

1 1/4 cups

Step-by-step explanation:

Their are 8 ounces in one cup and their are 2 ounces in 1/4's of a cup

CUP        FL. OZ

1                8        

3/4            6

2/3            5

1/2             4

1/3             3

1/4            2

1/8            1

1/16         0.5

Answer:

S={1H,2H,3H,4H,5H,6H,1T,2T,3T,4T,5T,6T}

Step-by-step explanation:

The sample space for a six sided die is {1,2,3,4,5,6} as there are 6 possible outcomes and for flipping a coin is {H,T} as there are two possible outcomes.

If a person rolls a six sided die and then flips a coin then the sample space for this event will be written as

S={1H,2H,3H,4H,5H,6H,1T,2T,3T,4T,5T,6T}.

The number of elements in the sample space are

n(S)=12.

Answer:

Step-by-step explanation:If a person draws a playing card and checks its color and then spins a six dash space spinner​, describe the sample space of possible outcomes using Upper B comma Upper R for the card outcomes and 1 comma 2 comma 3 comma 4 comma 5 comma 6 for the spinner outcomes.​ (Make sure your answers reflect the order​ stated.)

The sample space is Sequals​{

012

12​}.

​(Use a comma to separate answers as​ needed.)

Answer:

Subjective probability

Step-by-step explanation:

At first we should know the following:

Classical probability ⇒ when there are n equally likely outcomes.

Subjective probability ⇒ is based on whatever information is available.

Empirical probability ⇒ when the number of times the event happens is divided by the number of observations.

So, according to the previous definitions:

This person has a 75% chance of a full recovery

There is no equally likely outcomes, and the percentage of full recovery is based on the information available about the person and also it is based on educated guess.

So, this is Subjective probability

Answer: Breed for black-haired pigs

Step-by-step explanation:

Now according to the statement, the farmer catches  wild pigs and mostly are brown.

Since black hair is dominant over brown and also black and brown are dominant over red,  this implies that red is the least dominant color meaning if breeding occurs, there would be less chance of getting red colored pigs.

She wants to breed either black or red haired pigs and since black is more dominant so she should breed the black ones with the brown ones or with themselves so she would eventually get pure-breeding herd i.e. of black color.

Answer:

The question is incomplete. Below is the complete question

"A fair die is tossed. A is the event that the outcome is odd. B is the event that the outcome is even. C is the event that the outcome is less than 4. Determine P(A), P(B), P(C), P(A∩B), P(B∩C), P(A|B), P(A|C), P(B|C).

answers:

a.1/2

b. 1/2

c. 1/2

d.0

e. 1/6

f. 0

g. 2/3

h. 1/3

Step-by-step explanation:

lets write out the probability of each event

a.A=outcome is odd

A={1,3,5}

P(A)=1/2

b.B=outcome is even

B={2,4,6}

P(B)=1/2

c. C=outcome is less than 4

C={1,2,3}

P(C)=1/2

d.P(AnB)={its odd and even i.e what is common between set A and B}

Therefore, P(AnB) is a null set i.e P(AnB)={ }=0

e. BnC= {2} i.e elements common between set B and C

Hence P(BnC)=1/6

f. P{A|B}= P(AnB)/P(B) since P(AnB)=0, P(B)=1/2. then, P(A|B)=0

g. P(A|C)= P(AnC)/P(C) since P(AnC)=1/3, P(C)=1/2. therefore, P(A|C)=2/3

h. P(B|C)= P(BnC)/P(C), since P(BnC)=1/6, P(C)=1/2. therefore, P(B|C)=1/3

There are

[tex]5! = 5\cdot 4 \cdot 3 \cdot 2 = 120[/tex]

possible arrangements of 5 students. So, if you pick a particular one, you'll have a probability of 1/120 to guess the correct one.

The probability of getting the order used in the spelling bee is 1/120 or approximately 0.0083.

The probability of randomly selecting an order and getting the order used in the spelling bee is 1 divided by the number of possible orders. To find the number of possible orders, we use the concept of permutations. If there are 5 students participating in the spelling bee, there are 5 factorial (5!) possible orders. So the probability is 1/5! which is equal to 1/120 or approximately 0.0083.

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Answer:

The probability that a person is willing to commute more than 25 miles is 0.2865.

Step-by-step explanation:

Exponential probability distribution is used to define the probability distribution of the amount of time until some specific event takes place.

A random variable X follows an exponential distribution with parameter m.

The decay parameter is, m.

The probability distribution function of an Exponential distribution is:

[tex]f(x)=me^{-mx}\ ;\ m>0, x>0[/tex]

Given: The decay parameter is, [tex]\frac{1}{20}[/tex]

X is defined as the distance people are willing to commute in miles.

Compute the probability that a person is willing to commute more than 25 miles as follows:

[tex]P(X>25)=\int\limits^{\infty}_{25} {\frac{1}{20} e^{-\frac{1}{20}x}} \, dx \\=\frac{1}{20}|20e^{-\frac{1}{20}x}|^{\infty}_{25}\\=|e^{-\frac{1}{20}x}|^{\infty}_{25}\\=e^{-\frac{1}{20}\times25}\\=0.2865[/tex]

Thus, the probability that a person is willing to commute more than 25 miles is 0.2865.

Answer:

The standard deviation of given probability distribution is 0.8292

Step-by-step explanation:

We are given the following in the question:

              q:        0          1          2

Probability:    0.25     0.25    0.50

Formula:

[tex]E(q) = \displaystyle\sum q_ip(q_i)\\=0(0.25) + 1(0.25) + 2(0.50) = 1.25[/tex]

[tex]E(q^2)= \displaystyle\sum q_i^2p(q_i)\\=0^2(0.25) + 1^2(0.25) + 2^2(0.50) = 2.25[/tex]

Variance =

[tex]\sigma^2 = E(q^2) = (E(q))^2\\= 2.25- (1.25)^2\\=0.6875\\\sigma = \sqrt{0.6875} = 0.8292[/tex]

Thus, the standard deviation of given probability distribution is 0.8292

The standard deviation of a random variable can be calculated using the formula: √∑(xi-μ)2 ⋅ P(xi) . We find the mean (μ) by multiplying each value of q by its corresponding probability and summing them up. Next, we calculate the squared difference between each value of q and the mean, multiplied by their respective probabilities. Finally, we take the square root of this value to obtain the standard deviation.

The standard deviation of a random variable can be calculated using the formula:

\sqrt{\sum (x_i - \mu)^2 \cdot P(x_i)}

First, we need to find the mean (μ) of the probability distribution. The mean can be calculated by multiplying each value of q by its corresponding probability and summing them up:

μ = (0 × 0.25) + (1 × 0.25) + (2 × 0.5) = 0.5

Next, we calculate the squared difference between each value of q and the mean, multiplied by their respective probabilities:

(0 - 0.5)^2 × 0.25 + (1 - 0.5)^2 × 0.25 + (2 - 0.5)^2 × 0.5 = 0.5

Finally, we take the square root of this value to obtain the standard deviation:

√0.5 ≈ 0.7071

Therefore, the standard deviation of the random variable q is approximately 0.7071.

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The water level in the bowl is rising at a rate of approximately 0.00269 meters per second when the water is 4 meters deep.

Let's address each part of the problem:

a. To find the volume of water in a hemispherical bowl of radius "a" to a depth "h," we can use the formula for the volume of a spherical cap. The volume of a spherical cap is given by:

V = (1/3)πh^2(3a - h)

In this case, "a" is the radius of the hemisphere, and "h" is the depth of the water.

So, the volume of water in the bowl is:

V = (1/3)πh^2(3a - h)

b. To find how fast the water level in the bowl is rising, we can use related rates. Let's denote the radius of the water-filled hemisphere as "R" (which is equal to "a" since it's the same hemisphere), and the depth of the water as "h."

Given that water is running into the bowl at a rate of 0.2 cubic meters per second, we can express the change in volume with respect to time:

dV/dt = 0.2 m^3/sec

We want to find dh/dt, the rate at which the water level is rising when the water is 4 meters deep.

We have the formula for the volume of water in the hemisphere from part (a):

V = (1/3)πh^2(3a - h)

Differentiate both sides of this equation with respect to time (t):

dV/dt = (1/3)π(2h)(dh/dt)(3a - h) - (1/3)πh^2(d(3a - h)/dt)

Now, plug in the values we know:

dV/dt = 0.2 m^3/sec

h = 4 m

a = 5 m

Now, solve for dh/dt:

0.2 = (1/3)π(24)(dh/dt)(35 - 4) - (1/3)π(4^2)(d(3*5 - 4)/dt)

0.2 = (8/3)π(dh/dt)(15 - 4) - (16/3)π(d(15 - 4)/dt)

0.2 = (8/3)π(11)(dh/dt) - (16/3)π(d(11)/dt)

0.2 = (88/3)π(dh/dt) - (16/3)π(0)

Now, solve for dh/dt:

(88/3)π(dh/dt) = 0.2

dh/dt = 0.2 / [(88/3)π]

Now, calculate dh/dt:

dh/dt ≈ 0.00269 meters per second

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Final answer:

To find the volume of water in a hemispherical bowl, subtract the volume of the upper portion of the hemisphere from the volume of the entire hemisphere. Therefore, the volume of the water in the hemispherical bowl is (2/3)πa³ - (1/3)π(h²)(3a - h).

Explanation:

To find the volume of water in a hemispherical bowl, we need to consider the shape of the bowl. The volume of a hemisphere is given by the formula V = (2/3)πr³, where r is the radius of the hemisphere. However, we only need to find the volume of the water in the bowl, not the entire bowl. To do this, we can subtract the volume of the upper portion of the hemisphere that is not filled with water.

Let's break down the steps:

Therefore, the volume of the water in the hemispherical bowl is (2/3)πa³ - (1/3)π(h²)(3a - h).

To lift a 1400-kg satellite to an altitude of 2×10⁶ meters above the Earth's surface, the work required is approximately 2.079×10¹¹ Joules. This is calculated based on changes in gravitational potential energy using given values for mass, radius, and the gravitational constant.

To calculate the work required to lift a 1400-kg satellite to an altitude of 2×10⁶ meters (2000 km) above the Earth's surface, we need to consider the gravitational potential energy change.

Given:

The total distance from the center of the Earth to the satellite is:

The work required is equal to the change in gravitational potential energy:

The gravitational potential energy at a distance r from the Earth’s center is given by:

The work done (W) to move the satellite from the Earth's surface to this altitude is the difference in potential energy:

Substitute the given values:

Calculate the values inside the brackets first:

Now, multiply:

The work required to lift the satellite to the desired altitude is approximately 2.079×10¹¹ Joules.

Answer:

a) quantitative discrete data

b)  categorical variable

c)  categorical variable

d) quantitative continuous variable

e) quantitative discrete variable

f)  categorical variable

Step-by-step explanation:

a) The number of days (to the nearest day) the dog has been at Huron Valley Humane Society

Since days will always have whole number numerical values it is a quantitative discrete data.

b) Whether or not the dog has a microchip

This will be answered with a yes or a no. Thus, it is a categorical variable. It does not have any numerical value.

c) The breed of the dog

This is a categorical variable. It does not have any numerical value. It will have non-parametric values.

d) How much the dog weighs (in pounds)

Since weight is always measured and not counted. Also weight can take decimal values, thus it is quantitative continuous variable.

e) The amount of food (in cups) the dog eats

Since this will have whole number values. Also, number of cups will be counted. Thus, it is a quantitative discrete variable.

f) The number of people who have taken the dog out for a walk

Since this will have whole number values. Also, number of people will be counted. Thus, it is a quantitative discrete variable.

g) Whether you decide to adopt the dog

This will be answered with a yes or a no. Thus, it is a categorical variable. It does not have any numerical value.

a,f are quantitave discrete b,c,g are categorical d,e,are quantitative continous.

a.he number of days (to the nearest day) the dog has been at Huron Valley Humane Society: This is quantitative discrete data because the number of days is counted in whole numbers.
b.Whether or not the dog has a microchip: This is categorical data because it categorizes the dog as either having or not having a microchip.
c.The breed of the dog: This is categorical data because breeds represent different categories.
d.How much the dog weighs (in pounds): This is quantitative continuous data because weight can be measured to a very fine degree.
e.The amount of food (in cups) the dog eats: This is quantitative continuous data because the amount can be measured to any level of precision.
f.The number of people who have taken the dog out for a walk: This is quantitative discrete data because it involves counting distinct individuals.
g.Whether you decide to adopt the dog: This is categorical data because it categorizes your decision into adopt or not adopt.

Answer:

The answer to your question is below

Step-by-step explanation:

Inequality 1

                       -4x + 1 > 13

                       -4x > 13 - 1

                      -4x > 12

                         x < 12/-4

                         x < -3

Inequality 2

                      4(x + 2) ≤ 4

                      4x + 8 ≤ 4

                      4x ≤ 4 - 8

                       4x ≤ - 4

                         x ≤ -4/4

                         x ≤ -1

Interval notation (-∞, -3)

See the graph below

The solution to these inequalities in where both intervals crosses

Answer:

2.5 weeks

Step-by-step explanation:

Data provided in the question:

Number of container ships operated by the company = 10

Number of containers carried by each container = 5000

Number of container to be unloaded = 20,000

A shipping company operates 10 container ships

Now,

Capacity of 10 container ships = 10 × 5000 containers = 50,000 containers

Time required to load and upload 50,000 containers

= 50,000 containers  ÷ 20,000 containers per week

= 2.5 weeks

Answer:

[tex] P(T>1) = e^{-\frac{1}{10}}= e^{-0.1}= 0.9048[/tex]

Step-by-step explanation:

Previous concepts

The exponential distribution is "the probability distribution of the time between events in a Poisson process (a process in which events occur continuously and independently at a constant average rate). It is a particular case of the gamma distribution". The probability density function is given by:

[tex]P(X=x)=\lambda e^{-\lambda x}[/tex]

Solution to the problem

For this case the time between breakdowns representing our random variable T is exponentially distirbuted [tex] T \sim Exp (\mu = 10)[/tex]

So on this case we can find the value of [tex]\lambda[/tex] like this:

[tex] \lambda = \frac{1}{\mu} = \frac{1}{10}[/tex]

So then our density function would be given by:

[tex]P(T)=\lambda e^{-\frac{t}{10}}[/tex]

The exponential distribution is useful when we want to describe the waiting time between Poisson occurrences. If we assume that the random variable T represent the waiting time between two consecutive event, we can define the probability that 0 events occurs between the start and a time t, like this:

[tex]P(T>t)= e^{-\lambda t}[/tex]

And on this case we are looking for this probability:

[tex] P(T>1) = e^{-\frac{1}{10}}= e^{-0.1}= 0.9048[/tex]

The probability that a randomly chosen household has at least two televisions can be calculated by dividing the number of households with at least two televisions by the total number of households.

To find the probability that a randomly chosen household has at least two televisions, we need to use the data from the marketing survey. Let's assume there are 'n' households in total. The probability of a household having at least two televisions can be calculated by dividing the number of households with at least two televisions by the total number of households, which is 'n'.

Let's say there are 'x' households with at least two televisions. The probability can be expressed as:

P(at least 2 TVs) = x/n

For example, if there are 100 households in total and 30 of them have at least two televisions, then the probability would be P(at least 2 TVs) = 30/100 = 0.3, which is 30%.

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Step-by-step explanation:

Infinitely many equations can be written that will be equal to 100.

x + y = 100

2x - y = 100

and many more..

Answer:

(-2.95,0)

x = -2.95 is the zero of the function.                                                      

Step-by-step explanation:

We are given the function:

[tex]f(x) = 1.5x + 3(x-3) + 5.5(x+7)[/tex]

We have to find the zero of the function.

Zero of function:

We can find zero of the function in the following manner:

[tex]f(x) = 1.5x + 3(x-3) + 5.5(x+7) = 0\\1.5x + 3x -9 + 5.5x + 38.5 = 0\\(1.5x + 3x + 5.5x) + (38.5-9) = 0\\10x + 29.5 = 0\\10x = -29.5\\x = -2.95[/tex]            

Thus, x = -2.95 is the zero of the function.        

Answer:

Step-by-step explanation:

First let's identify decision variables:

X1 - acres of corn

X2 - acres of tobacco

Bradley needs to maximize the profit, MAX = 300X1 + 520X2

The Bradley family owns 410 acres, X1+X2≤410

Each acre of corn costs $105,  each acre of tobacco costs $210

The Bradleys have a budget of $52,500

So 105X1 +210X2≤52,500

There is a restriction on planting the tobacco - 100acres

X2≤100

Also, since outcomes can be only positive, X1X2 ≥0

So, what we have:

MAX = 300X1 + 520X2

X1+X2≤410

105X1 +210X2≤52,500

X2≤100

X1X2 ≥0

To maximize profit, the Bradleys can formulate a linear programming model based on the costs and profits of each crop, subject to budget and government constraints.

Linear programming model formulation:

Answer:

P ( P U T ) = 0.6481

Dependent events

P ( P / T ) = (359/756) = 0.4749

Step-by-step explanation:

Given:

- Pink : P

- Teenagers: T

Find:

- P( T u P )

- Are the events T and R dependent, independent, mutually exclusive, or complementary

- If the events are independent, then we can compare P ( P / T ).

Solution:

a)

For first part we will determine the total outcome for T and P:

                   Total outcomes P or T =  359 + 252 - 121 = 490

                                             (P U T) = (P) + (T) - (P n T)

The total number of possible outcomes are = 756

Hence, P ( P U T ) = 490 / 756 = 0.6481

b)

We are to investigate how the two events are related to one another:

- Check for dependent events:

              P ( T n P ) = P( T ) * P ( P / T )

              (121 / 756 ) = (252/756) * ( 121 / 252 )

              (121 / 756) = (121/756)  ....... Hence, events are dependent

- Check for independent events:

              P ( T n P ) = P( T ) * P ( P )

              (121 / 756 ) = (252/756) * ( 359 / 756 )

              (121 / 756) =/ (359/756)  ....... Hence, events are not independent

- Check for mutually exclusive events:

              P ( T U P ) = P( T )  + P ( P )

              (490 / 756 ) = (252/756) + ( 359 / 756 )

              (121 / 756) =/ (611/756)  ... Hence, events are not mutually exclusive

Hence, the two events are dependent on each other.

c)

If the events are said to be independent then the event:

               P ( P / T ) = P (P)

               P ( P / T ) = (359/756) = 0.4749

The probability that a randomly selected survey respondent is a Teenager OR selects Pink (Strawberry) as their favorite Starburst color (flavor) can be calculated by adding the individual probabilities of these two events occurring.

The probability of a respondent being a Teenager is 85/756, and the probability of selecting Pink (Strawberry) as their favorite flavor is 359/756. So, the probability of either event happening is (85/756) + (359/756) = 0.4749.

Based on these calculations, the events "a randomly selected person is a Teenager" and "a randomly selected person selects Pink (Strawberry) as their favorite Starburst color (flavor)" are NOT mutually exclusive events because they can both happen.

They are also NOT complementary events because they don't cover all possible outcomes.

Whether they are independent or dependent events can be determined by comparing P(Pink | Teenager) with the probability of Pink (Strawberry) regardless of age group, P(Pink).

If P(Pink | Teenager) is equal to P(Pink), they are independent events; otherwise, they are dependent.

In this case, P(Pink | Teenager) is 114/85, and P(Pink) is 359/756. Comparing these probabilities, we find that P(Pink | Teenager) is not equal to P(Pink), so the events are dependent.

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Answer and Step-by-step explanation:

From the question statement we get know that it is Binomial distribution because there are only two possible outcomes so we need to use Binomial Probability Distribution for this question.

Formula for the Binomial Probability Distribution:

P(X)=   p^x q^(n-x)

Where,

Answer and explanation for each part of the question are as follow:

a.What is the probability that among 10 randomly observed individuals exactly 4 do not cover their mouth when sneezing?

Solution:

Given that

n=10  

p=0.267 (because p is the probability of success which is “number of individuals not covering their mouths when sneezing” in the question)

q=1-0.267=0.733  

x=4 (number of successes i.e. individuals not covering their mouths)

C_x^n=n!/(n-x)!x!=10!/(10-4)!4!=210

P(X)=C_x^n   p^x q^(n-x)=210×〖(0.267)〗^4×〖0.733〗^(10-4)

P(X)=210×0.00508×0.155  

P(X)=0.165465  

b. What is the probability that among 10 randomly observed individuals fewer than 3 do not cover their mouth when sneezing?

Solution:

Given that

n=10  

p=0.267 (because p is the probability of success which is “number of individuals not covering their mouths when sneezing” in the question)

q=1-0.267=0.733  

x=3 (number of successes i.e. individuals not covering their mouths)

C_x^n=n!/(n-x)!x!=10!/(10-3)!3!=120

P(X)=C_x^n   p^x q^(n-x)=120×(0.267)^3×〖0.733〗^(10-3)

P(X)=120×0.01903×0.1136  

P(X)=0.25962  

c. Would you be surprised if, after observing 18 individuals, fewer than half covered their mouth when sneezing? why?

Solution:

Given that

n=18  

p=0.267 (because p is the probability of success which is “number of individuals not covering their mouths when sneezing” in the question)

q=1-0.267=0.733  

x=9 (x is the number of successes “number of individuals not covering their mouths when sneezing”, if less than half cover their mouth then more than half will not cover), so let x=9

C_x^n=n!/(n-x)!x!=18!/(18-9)!9!=48620

P(X)=48620×(0.267)^9×〖0.733〗^(18-9)  

P(X)=48620×0.00000689×0.0610  

P(X)=0.020  

Yes, I am surprised that probability of less than 9 individuals covering their mouth when sneezing is 0.020. Which is extremely is small.