Answer:
Volume of cylinder [tex]=2797.7[/tex]
Step-by-step explanation:
Let [tex]a[/tex] be diameter and [tex]b[/tex] the height of the cylinder
[tex]Then\ radius(r)=\frac{diamater\ (a)}{2}\\\\r=\frac{18}{2}\\\\r=9[/tex]
Volume of cylinder [tex]=\pi\times(radius)^2\times(height)[/tex]
[tex]=\pi\times(9)^2\times11\ \ \ \ \ \ (\pi=3.14)\\\\=3.14\times9\times9\times11\\\\=2797.74\\\\\approx2797.7[/tex]
Triangle ABE is similar to triangle ACD. Find y.
3.4
2.7
4.5
2.1
Answer:
Step-by-step explanation:
∆ ABE is similar to angle ACD. This means that the ratio of the length of each side of ∆ABE to the length of the corresponding side of ∆ ACD is constant. Therefore,
AB/AC = BE/CD = AE/AD
Therefore,
5/3 = (y + 3)/y
Cross multiplying, it becomes
5 × y = 3(y + 3)
5y = 3y + 9
5y - 3y = 9
2y = 9
Dividing the left hand side and the right hand side of the equation by 2, it becomes
2y/2 = 9/2
y = 4.5
Answer:
y = 4.5.
Step-by-step explanation:
Triangles ABE and ACD are similar, so their corresponding sides are in the same ratio.
AB/AC = AE / AD
Now AD = y + ED = y + 3, so:
3/5 = y / (y + 3)
5y = 3y + 9
2y = 9
y = 4.5.
which inequality represents all values of x for which the quotient below is defined?
[tex]\sqrt{7x^2 divided by \sqrt{3x}
\\A. x \ \textgreater \ 1 \\B. x \ \textgreater \ -1\\C. x \ \textgreater \ 0\\D. x \geq 0[/tex]
Answer:
C. x>0
Step-by-step explanation:
The given quotient is
[tex] \frac{ \sqrt{7 {x}^{2} } }{ \sqrt{3x} } [/tex]
Recall that the expression in the denominator should not be equal to zero.
Also the expression under the radical should be greater than or equal to zero.
This means that we should have:
[tex] \frac{7 {x}^{2} }{3x} \: > \: 0[/tex]
This implies that:
[tex]x \: > \: 0[/tex]
Option C is correct
Need some help doing this question, thanks!
Answer:
y = -5x + 6
Step-by-step explanation:
y = 1/5 x + 4/5
so that two lines are perpendicular, its slope must be opposite and reciprocal
y = m x + b
m: slope perpendicular -1/m
if our formula is y = 1/5 x + 4/5
m = 1/5
so the slope of our new formula will be
m' = -5/1
m' = -5
now if you tell us that you have to go through a certain point (1/1)
we just have to replace the values in the following formula and solve
y - y1 = m ( x - x1)
y - 1 = -5 ( x - 1)
y = -5x + 5 + 1
y = -5x + 6
What is the side length of the smallest square plate on which a 24-cm chopstick can fit along a diagonal without any overhang?
Answer:
17 cm is the side length of the smallest square plate.
Step-by-step explanation:
Length of the square = l
Length of the diagonal = d
Length of chopstick = s = 24 cm
If chopstick is to be fitted along a diagonal . then length of the diagonal will be:
d = s = 24 cm
Applying Pythagoras Theorem :
[tex]l^2+l^2=(24 cm)^2[/tex]
[tex]2l^2=576 cm[/tex]
[tex]l^2=\frac{576}{2} cm^2[/tex]
[tex]l=\sqrt{\frac{576}{2} cm^2}=16,97 cm \approx 17 cm[/tex]
17 cm is the side length of the smallest square plate.
Final answer:
To determine the size of the smallest square plate that a 24-cm chopstick can fit diagonally on without overhang, the Pythagorean theorem is used, yielding a side length of approximately 16.97 cm.
Explanation:
The question asks for the side length of the smallest square plate on which a 24-cm chopstick can fit along a diagonal without any overhang. To find this, we can use the Pythagorean theorem in the context of a square. The Pythagorean theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. In the case of a square, the hypotenuse is the diagonal, and the other two sides are equal, each being the side length of the square.
Let's denote the side length of the square as s. The diagonal (d) is then given as d = 24 cm. According to the Pythagorean theorem applied to a square, this can be written as √(2*s²) = d, because the diagonal divides the square into two equal right-angled triangles. Solving for s, we get s = √(d² / 2). Substituting 24 cm for d gives:
s = √(24² / 2)
s = √(576 / 2)
s = √(288)
s = 16.97 cm (approximately)
Therefore, the side length of the smallest square plate on which a 24-cm chopstick can fit along a diagonal without any overhang is approximately 16.97 cm.
John has finished compiling a list of the various members of the joint application development (JAD) group and the list is as follows: John is the JAD project leader, Tom is the representative from top management, Jennifer is a manager, Alen and Ian are users, Linda and Alex are systems analysts, and Clark is the recorder. There have been some rumblings within the firm that this development project is not necessary so John and others feel it is important to explain the reason for the project at the outset. Whose name goes next to this point on the agenda?
Answer:
d. His own
Step-by-step explanation:
John is the leader of the particular project team. He is in charge of delegating different tasks to his team members and also endure that everything is in order. He will also develop the necessary agenda and formulate the final report of the project. Therefore, the name that will be attached on the final tasks is his own.
Tom, the representative from top management, should be responsible for explaining the project's necessity, as his role allows him to address strategic concerns and ensure buy-in across the team.
Explanation:In the context of the Joint Application Development (JAD) group, explaining the reason for the project, especially given the internal skepticism about its necessity, is a pivotal responsibility that typically falls onto someone influential and with comprehensive knowledge of the project's goals and business impact. In this scenario, Tom, as the representative from top management, is the most suitable member to address this point on the agenda. Tom's position allows him to articulate the strategic importance of the project to the organization, reassuring the rest of the team and potentially quelling any concerns about its necessity. It is critical that this explanation is conveyed convincingly to ensure buy-in from all members of the team.
It is advantageous for team members to take on tasks that align with their strengths, as suggested in the reference material, but also to challenge themselves and learn by undertaking tasks outside their usual domain, with the support of their colleagues. This approach fosters a collaborative environment and harnesses the diverse skill sets of the team members, leading to a more efficient and innovative project outcome. To help manage this process, tools like the Honeycomb Map encourage the distribution of responsibilities and help with project visualization and tracking.
Use well-ordering property to prove that if n people stand in a line, where n is a positive integer, and if the first person in the line is a woman and the last person in line is a man, then somewhere in the line there is a woman directly in front of a man.
Answer:
The people forming the line form a well ordered set, this means, every non empty subset has a minimum. In other words, in any smaller (but non empty) set of people there will always be one that is last in the line.
Lets take the subset formed of all the Women in the line. This subset in non empty because there is a women in the line (the first person in the line is a women), therefore, there is a women that is behind every other women in the line; this women can only have men behind, if any. If she had no men behind her, then she should be last in the line, bacause the doesnt have any men or women behind her. This is a contradiction because there is a man at the end of the line, not a woman. This shows that this woman that is behind every other woman has men behind, in particularly immediately behind, her.
Using well - ordering property in mathematical induction, we have been able to prove that; if n people stand in a line, where n is a positive integer, then somewhere in the line there is a woman directly in front of a man.
Mathematical inductionMathematical induction is defined as a proof technique that is used to prove that a property Pₙ will hold for every natural number such as n = 0, 1, 2, 3 e.t.c.
Now, we want to prove that If n people stand in a line, where n is a positive integer, and if the first person in the line is a woman and the last person in line is a man, then somewhere in the line, there is a woman directly in front of a man.
Now, let us deduce as follows;
When n = 2; This means that the first person is a woman and last is man.When n = k (k ≥ 2); This means there is a woman in front of a manThus;
When n = k + 1, what we will get is that;
- A new person is before a woman that is directly in front of a man.
- The new person is after the man directly after the woman.
- A new person is added between the woman and the man.
In conclusion;
For every positive integer n(n > 2), there is always a woman directly in front of a man.
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If a hurricane was headed your way, would you evacuate? The headline of a press release issued January 21, 2009 by the survey research company International Communications Research (icrsurvey) states, "Thirty- one Percent of People on High-Risk Coast Will Refuse Evacuation Order, Survey of Hurricane Preparedness Finds." This headline was based on a survey of 5046 adults who live within 20 miles of the coast in high hur- ricane risk counties of eight southern states. In selecting the sample, care was taken to ensure that the sample would be representative of the population of coastal resi- dents in these states.
Use this information to estimate the proportion of coastal residents who would evacuate using a 98% confidence interval.
Write a few sentences interpreting the interval and the confidence level assosiated with the interval.
Answer:
The 98% confidence interval for population proportion of people who refuse evacuation is {0.30, 0.33].
Step-by-step explanation:
The sample drawn is of size, n = 5046.
As the sample size is large, i.e. n > 30, according to the Central limit theorem the sampling distribution of sample proportion will be normally distributed with mean [tex]\hat p[/tex] and standard deviation [tex]\sqrt{\frac{\hat p (1-\hat p)}{n} }[/tex].
The mean is: [tex]\hat p=0.31[/tex]
The confidence level (CL) = 98%
The confidence interval for single proportion is:
[tex]CI_{p}=[\hat p-z_{(\alpha /2)}\times\sqrt{\frac{\hat p (1-\hat p)}{n} },\ \hat p+z_{(\alpha /2)}\times\sqrt{\frac{\hat p (1-\hat p)}{n} }][/tex]
Here [tex]z_{(\alpha /2)}[/tex] = critical value and α = significance level.
Compute the value of α as follows:
[tex]\alpha =1-CL\\=1-0.98\\=0.02[/tex]
For α = 0.02 the critical value can be computed from the z table.
Then the value of [tex]z_{(\alpha /2)}[/tex] is ± 2.33.
The 98% confidence interval for population proportion is:
[tex]CI_{p}=[\hat p-z_{(\alpha /2)}\times\sqrt{\frac{\hat p (1-\hat p)}{n} },\ \hat p+z_{(\alpha /2)}\times\sqrt{\frac{\hat p (1-\hat p)}{n} }]\\=[0.31-2.33\times \sqrt{\frac{0.31\times(1-0.33)}{5046} },\ 0.31+2.33\times \sqrt{\frac{0.31\times(1-0.33)}{5046} } ]\\=[0.31-0.0152,\ 0.31+0.0152]\\=[0.2948,0.3252]\\\approx[0.30,\ 0.33][/tex]
Thus, the 98% confidence interval [0.30, 0.33] implies that there is a 0.98 probability that the population proportion of people who refuse evacuation is between 0.30 and 0.33.
Final answer:
The 98% confidence interval for the proportion of coastal residents who would evacuate is between approximately 67.49% and 70.51%. This reflects our confidence that the true proportion falls within this range, with only a 2% chance of being outside these bounds.
Explanation:
To estimate the proportion of coastal residents who would evacuate using a 98% confidence interval based on the available survey data, we look at the reported figure that 31% of the people will refuse to evacuate, which implies that 69% would evacuate. The sample size is 5046 adults. To calculate the 98% confidence interval for the true proportion, we use the formula for the confidence interval of a proportion:
Confidence interval = p ± Z*sqrt((p(1-p))/n)
where:
p is the sample proportion (0.69 in this case),
Z is the Z-score associated with the confidence level (2.326 for 98% confidence),
sqrt denotes the square root function,
n is the sample size.
Plugging the values into the formula, we get:
Confidence interval = 0.69 ± 2.326 * sqrt((0.69(1-0.69))/5046)
Performing these calculations:
Confidence interval = 0.69 ± 2.326 * sqrt(0.2141/5046)
Confidence interval = 0.69 ± 2.326 * sqrt(0.0000424451086)
Confidence interval = 0.69 ± 2.326 * 0.0065134
Confidence interval = 0.69 ± 0.015143
So the 98% confidence interval for the proportion of coastal residents who would evacuate is approximately 0.6749 to 0.7051, or 67.49% to 70.51%.
Interpreting this confidence interval at the 98% confidence level means that we can be 98% confident that the true proportion of all coastal residents in these high-risk areas who would evacuate falls between 67.49% and 70.51%. This does not mean that the true proportion is within this interval with 100% certainty, but rather that there's a 2% chance that the true proportion lies outside of this interval.
There are 40 math teachers, 45 English teachers, 27 science teachers, and 32 social studies teachers. The superintendent of the region wants to select a board of 20 teachers. How many science teachers should he select?
Answer:
Superintendent of the region will select approximately 4 Science teachers in the board.
Step-by-step explanation:
Given:
Number of math teachers = 40
Number of English teachers = 45
Number of Science teachers = 27
Number Social Studies teachers = 32
Number of teachers to be selected in the board =20
We need to find the number Science teachers should be selected in the board.
Solution:
First we ill find the Total number of teachers.
Now we can say that;
Total number of teachers is equal to sum of Number of math teachers, Number of English teachers,Number of Science teachers and Number Social Studies teachers
framing in equation form we get;
Total number of teachers = [tex]40+45+27+32=144[/tex]
Probability of Science teacher can be calculated by Dividing Number of Science teacher by Total number of teachers.
[tex]P(S)=\frac{27}{144}=0.1875[/tex]
Now the number of Science teachers should be selected in the board we need to multiply P(S) with Number of teachers to be selected in the board.
framing in equation form we get;
number of Science teachers should be selected in the board = [tex]0.1875\times 20=3.75\approx4[/tex]
Hence We can say that;
Superintendent of the region will select approximately 4 Science teachers in the board.
Calculate the proportion of science teachers out of the total and apply it to the board size to determine the number of science teachers to select.
To determine how many science teachers the superintendent should select for a board of 20 teachers:
Calculate the total number of teachers: 40 math + 45 English + 27 science + 32 social studies = 144 teachersFind the proportion of science teachers: 27 science teachers out of 144 total teachers = 0.1875Apply the proportion to the board size: 0.1875 * 20 = 3.75, so the superintendent should select 4 science teachers.The list shows the number of viewers of an online music video each day for 5 consecutive days. 5; 35; 245; 1,715; 12,005; By what factor did the number of viewers change each day to the first day to the fifth day?
Answer: 7
Step-by-step explanation:
Given : The list shows the number of viewers of an online music video each day for 5 consecutive days.
5; 35; 245; 1,715; 12,005;
In exponential growth equation : [tex]y=Ab^x[/tex] , A = initial value , b= growth factor and x = time period.
In the given table A = 5 , at x = 0
Growth factor is the common ratio between the consecutive terms.
So [tex]b=\dfrac{35}{5}=7[/tex]
and we can check that it is common between each consecutive terms is 7.
Hence, the factor by which the number of viewers change each day to the first day to the fifth day = 7
The number of viewers changed by a factor of 2401 from the first day to the fifth day.
Explanation:The number of viewers of an online music video changed each day by multiplying the previous day's viewers by a constant factor. To find this factor, we divide the viewers on the fifth day by the viewers on the first day. By doing this, we get a factor of 12005/5 = 2401.
So, the number of viewers changed by a factor of 2401 from the first day to the fifth day.
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Brainliest ! 40 points , pls answer all or don't answer
Answer:
The answer to your question is below
Step-by-step explanation:
1.- Find the volume of the cylinder
Data
diameter = 9 cm
radius = 4.5 cm
height = 15 cm
Formula
V = πr²h
V = π(4.5)²(15)
V = 303.75π This is te answer for the volume in terms of π
= 952.78 cm³
2.- Find the volume of the cylinder
height = 40 yd
radius = 12 yd
Formula
V = πr²h
V = π(12)²(40)
V = 5760π This is te answer for the volume in terms of π
= 18086.4 cm³
3.- What is the height .......
height = q
side length = r
4.- Volume of a pyramid
Volume = Area of the base x height
Area of the base = 11 x 11 = 121 cm²
Volume = 121 x 18
Volume = 2178 cm³
Answer:
1. 953.775 cm³
2. 18,086.4 yd³
3. height: q ; side: r
4. 726 cm³
Step-by-step explanation:
1. Volume = pi × r² × h
= 3.14 × (9/2)² × 15
= 953.775 cm³
2. Volume = pi × r² × h
= 3.14 × 12² × 40
= 18086.4 yd³
3. height: q ; side: r
4. Volume = ⅓ base area × height
= ⅓ × 11² × 18
= 726 cm³
Maurice's new CD has 12 songs. Each song lasts between 3 and 4 minutes. He estimates that the whole CD is about 30 minutes long. Which statement about Maurice's estimate is true?
Answer:
The estimate is less than the actual length of the CD.
Step-by-step explanation:
Consider the provided information.
Maurice's new CD has 12 songs. Each song lasts between 3 and 4 minutes.
That means the minimum length of the CD should be: 12×3=36 minutes.
The maximum length of the CD should be: 12×4=48 minutes
He estimates that the whole CD is about 30 minutes long.
30 minutes is less than 36 minutes.
That means, the estimate is less than the actual length of the CD.
Hence, the correct statement is: The estimate is less than the actual length of the CD.
Tamira has $55 in her lunch account. Each day she spends $5 on lunch. Which equation represents the amount of money, y, Tamira has left in her lunch account after x days?
Answer:
y=-5x+55
Step-by-step explanation:
i had a quiz and i got the correct answer on the test corrections your welcome
Danny has a coin collection. 20% of his collection are quarters. If Danny has 13 quarters, how many coins does he have in his collection altogether? A) 26 B) 39 C) 42 D) 65
Answer: Danny had 65 coins altogether in his collection.
Step-by-step explanation:
Let x represent the number of coins that Danny has in his collection.
20% of his collection are quarters. This means that the number of quarters that Danny has in his collection is
20/100 × x = 0.2 × x = 0.2x
If Danny has 13 quarters, it means that
0.2x = 13
Dividing the left hand side and the right hand side of the equation by 0.2, it becomes
0.2x/0.2 = 13/0.2
x = 65
A car is driving away from a crosswalk. The formula d = t2 + 2t expresses the car's distance from the crosswalk in feet, d, in terms of the number of seconds, t, since the car started moving. Suppose t varies from t=1to t=5. What is the car's average speed over this interval of time?
Average speed: 8 feet/second. Total distance traveled: 32 feet. Total time: 4 seconds (from[tex]\( t = 1 \)[/tex] to[tex]\( t = 5 \)).[/tex]
To find the average speed of the car over the interval from[tex]\( t = 1 \) to \( t = 5 \),[/tex] we need to find the total distance traveled by the car during this time interval and then divide it by the total time taken.
Given the formula [tex]\( d = t^2 + 2t \)[/tex] for the distance from the crosswalk in terms of time [tex]\( t \),[/tex] we'll find the distance at [tex]\( t = 1 \)[/tex] and[tex]\( t = 5 \),[/tex] and then subtract to find the total distance traveled:
1. At [tex]\( t = 1 \):[/tex]
[tex]\[ d_1 = (1)^2 + 2(1) = 1 + 2 = 3 \text{ feet} \][/tex]
2. At[tex]\( t = 5 \):[/tex]
[tex]\[ d_5 = (5)^2 + 2(5) = 25 + 10 = 35 \text{ feet} \][/tex]
Now, the total distance traveled is [tex]\( d_5 - d_1 = 35 - 3 = 32 \)[/tex] feet.
The total time taken is [tex]\( t = 5 - 1 = 4 \)[/tex] seconds.
To find the average speed, divide the total distance by the total time:
[tex]\[ \text{Average speed} = \frac{\text{Total distance}}{\text{Total time}} = \frac{32 \text{ feet}}{4 \text{ seconds}} = 8 \text{ feet/second} \][/tex]
So, the average speed of the car over the interval from [tex]\( t = 1 \) to \( t = 5 \) seconds is \( 8 \) feet per second.[/tex]
If θ is an angle in standard position that terminates in Quadrant IV such that cosθ = 3/5, then cosθ/2 = _____. -
Answer:
[tex]cos \frac{\theta}{2}= 0.894[/tex].
Step-by-step explanation:
Given:
[tex]cos\ \theta= \frac35[/tex]
We need to find [tex]cos \ \frac{\theta}{2}[/tex]
Solution:
[tex]cos\ \theta= \frac35[/tex]
First we will find the value of [tex]\theta[/tex].
Now taking [tex]cos^{-1}[/tex] on both side we get;
[tex]\theta= cos^{-1} \ \frac{3}{5}\\\\\theta = 53.13[/tex]
Now we will find the [tex]\frac{\theta}{2}[/tex].
[tex]\frac{\theta}{2}[/tex] = [tex]\frac{53.13}{2} = 26.565[/tex]
Now we will find [tex]cos \ \frac{\theta}{2}[/tex] we get;
[tex]cos \frac{\theta}{2}=cos\ 26.565 = 0.894[/tex]
Hence [tex]cos \frac{\theta}{2}= 0.894[/tex].
Answer:
+/- (2\sqrt(5))/(5)
Step-by-step explanation:
Mr. C is such a mean teacher! The next time Mathias gets in trouble, Mr. C has designed a special detention for him. Mathias will have to go out into the hall and stand exactly meters away from the exit door and pause for a minute. Then he is allowed to walk exactly halfway to the door and pause for another minute. Then he can again walk exactly half the remaining distance to the door and pause again, and so on. Mr. C says that when Mathias reaches the door he can leave, unless he breaks the rules and goes more than halfway, even by a tiny amount. When can Mathias leave?
This is based on the mathematical concept of geometric series, where in theoretical terms Mathias would never reach the door because he keeps moving half the remaining distance each time. Although, in practical terms, there comes a point where the remaining distance becomes negligible.
Explanation:The situation you're describing is an example of a geometric series scenario in mathematics. In this case, where Mathias walks half the distance to the door each time, is often referred to as Zeno's paradox.
Zeno's paradox poses the question, how can one ever reach a destination if they are always traveling halfway there? Theoretically, Mathias is never able to fully reach the door, because no matter how small the remaining distance becomes, he is only allowed to cover half. Therefore, there will always technically be some distance remaining.
However, in practical terms, there would come a point where the distance remaining is so minuscule, it could be considered as Mathias having reached the door. For instance, if he started 10 meters away, after the first step he is 5 meters away, then 2.5 meters, then 1.25 meters, and so on. Eventually, this distance becomes negligible.
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What is the best answer
Answer:
The answer to your question is letter A
Step-by-step explanation:
The first inequality is a circle with center (0,0) and radius 4, the inequality indicates that the solution must be greater than the radius (4) so the solutions are letters A and D.
The second inequality is the line, the solutions must be the numbers below the line, areas A and B.
The region where both inequalities cross is the solution letter A.
A Web ad can be designed from four different colors, three font types, five font sizes, three images, and five text phrases. A specific design is randomly generated by the Web server when you visit the site. Let A denote the event that the design color is red, and let B denote the event that the font size is not the smallest one. Use the addition rules to calculate the following probabilities.
A. P(A ∪ B).
B. P(A ∪ B').
C. P(A' ∪ B').
The probability of A = 1/4 = 0.25
The probability of B = 4/5 = 0.80
P(A ∩ B) = P(A) * P (B) = (0.25) * (0.80) = 0.20
P(A ∩ B') = P(A) * P (B') = (0.25) * (1-0.80) = 0.05
P(A' ∩ B') = P(A') * P (B') = (1-0.25) * (1-0.80) = 0.15
Answer:
A. P(A U B) = P(A) + P(B) - P(A ∩ B) = 0.25 + 0.80 - 0.20 = 0.85
B. P(A U B') = P(A) + (1 - P(B)) - P(A ∩ B') = 0.25 + (1-0.80) - 0.05 = 0.40
C. P(A' U B') = (1 - P(A)) + (1 - P(B)) - P(A' ∩ B') = (1-0.25) + (1-0.80) - 0.15 = 0.80
The probabilities using the addition rule of probabilities are P(A ∪ B) = 17/20, P(A ∪ B') = 2/5, and P(A' ∪ B') = 4/5.
In solving this problem, we will use the addition rule for probabilities to find the likelihood of different combinations of randomly generated web ad designs based on given design elements.
A. P(A ∪ B)
We'll start by finding the probability of event A (the design color is red) and B (the font size is not the smallest one) occurring independently. Since there are four different colors, the probability of A is 1/4. When it comes to event B, since there are five different font sizes and the event is that the font size is not the smallest one, there are four font sizes that meet the criteria.
Therefore, the probability of B is 4/5. We can now calculate P(A ∪ B) using the formula P(A) + P(B) - P(A AND B). Assuming that the color choice and font size are independent of each other (the choice of one does not affect the choice of the other), the probability of both A and B occurring (A AND B) is simply the product of their separate probabilities: P(A) x P(B) = (1/4) x (4/5) = 1/5.
So, P(A ∪ B) = P(A) + P(B) - P(A AND B) = (1/4) + (4/5) - (1/5) = 1/4 + 16/20 - 4/20 = 1/4 + 12/20 = 5/20 + 12/20 = 17/20.
B. P(A ∪ B')
To find P(A ∪ B'), we first need to calculate P(B'). Since the probability of B is 4/5, the probability of B' (the font size is the smallest one) is the remaining fraction of 1, which is 1/5. We then apply the addition rule, which becomes P(A \∪\ B') = P(A) + P(B') - P(A AND B'), with P(A AND B') being the probability of choosing the red color and the smallest font size. Because A and B' are independent, P(A AND B') = P(A) x P(B') = (1/4) x (1/5) = 1/20.
Therefore, P(A ∪ B') = P(A) + P(B') - P(A AND B') = 1/4 + 1/5 - 1/20 = 5/20 + 4/20 - 1/20 = 8/20 or 2/5.
C. P(A' ∪ B')
To find P(A' ∪ B'), we need to determine the probabilities of A' and B' occurring separately. P(A') is the probability of not choosing the red color, which is the complement of P(A), meaning P(A') = 1 - P(A) = 3/4. P(B') as we calculated before, is 1/5. As these events are independent, P(A' AND B') = P(A') x P(B') = (3/4) x (1/5) = 3/20.
Thus, P(A' ∪ B') = P(A') + P(B') - P(A' AND B') = 3/4 + 1/5 - 3/20 = 15/20 + 4/20 - 3/20 = 16/20 or 4/5.
Haun and Wendy are 200 feet apart when they begin walking directly toward one another. Ian travels at a constant speed of 2.5 feet per second and Carolyn travels at a constant speed of 4.5 feet per second.
Let t represent the number of seconds that have elapsed since Ian and Carolyn started walking toward one another.
A) write an expression in terms of t that represent the number of feet Ian has traveled since he started walking toward Carolyn.
B) write an expression in terms of t that represents the number of feet Carolyn has traveled since she started walking toward ian.
C) write an expression in terms of t that represents the distance between Ian and Carolyn.
D) how many seconds after the two started walking will they reach each other?
Answer:
A) [tex]d_{I}=2.5t[/tex]
B)[tex]d_{C}=4.5t[/tex]
C) d=200-7t
D) t=28.57s
Step-by-step explanation:
A) in order to solve this part of the problem, we must remember that velocity is the ratio between a displacement and the time it takes for a body to go from one point to the other. So we can write it like this:
[tex]v=\frac{x}{t}[/tex]
when solvin for the distance x, we get the formula to be:
[tex]x=vt[/tex]
We can use this to write the expression they are asking us for, so we get:
[tex]d_{I}=2.5t[/tex]
B) the procedure for part b is the same as the procedure for par A with the difference that Carolyn's speed is different. So by using the same formula with Carolyn's speed we get:
[tex]d_{C}=4.5t[/tex]
C)
In order to find the distance between Ian and Carolyn, we subtract the distances found on the previous two questions from the 200ft, so we get:
[tex]d=200-d_{I}-d_{c}[/tex]
we can further substitute the d's with the equations we found on the previos two parts of the problem, so we get:
[tex]d=200-2.5t-4.5t[/tex]
which simplififfes to the following:
d=200-7t
D) we can figure the seconds out by substituing the distance for 0 and solving for t, so we get:
0=200-7t
which can be solved for t, lke this:
-7t=-200
[tex]t=\frac{-200}{-7}=28.57[/tex]
Plsss help!! Work this travel problem based on the data provided in the table. Choose the correct answer.
What percentage increase occurs in the price of a round-trip economy ship fare from New York to London by electing to go in peak season economy air fare as opposed to a 30-day excursion fare?
41.1
52.1
34.3
Answer:
option 2
52.1
Step-by-step explanation:
Peak season economy air fare: $526.30
30-day excrusion ship fare: $345.95
To know the percentage with respect, we only have to put the most expensive value divided by the smallest value multiplied by one hundred, this will tell us what percentage you have with each other
526.30 / 345.95 * 100 =
1.5213 * 100 =
152.13
Now to know only the percentage that increased, we have to subtract 100 that would be the base value
152.13 - 100 = 52.13
52.1
Determine what type of observational study is described. Explain. Vitamin D is important for the metabolism of calcium and exposure to sunshine is an important source of vitamin D. A researcher wanted to determine whether osteoperosis was associated with a lack of exposure to sunshine. He selected a sample of 250 women with opteoperosis and an equal number of women without osteoperosis. The two groups were matched in other words they were similar in terms of age, diet, occupation, and exercise levels. Histories on exposure to sunshine over the previous twenty years were obtained for all women. The total number of hours that each woman had been exposed to sunshine in the previous twenty years was estimated. The amount of exposure to sunshine was compared for the two groups. a.cohort; Individuals are observed over a long period of time. b.cross-sectional; Information is collected at a specific point in time. c.retrospective; Individuals are asked to look back in time Question 15 4 pts
Answer:
thats too long to read but good luck!
Step-by-step explanation:
A survey was conducted by a website on which online music channels subscribers use on a regular basis. The following
information summarizes the answers.
10 listened to rap, heavy metal, and alternative rock.
13 listened to rap and heavy metal.
16 listened to heavy metal and alternative rock.
26 listened to rap and alternative rock.
37 listened to rap.
30 listened to heavy metal.
49 listened to alternative rock.
18 listened to none of these three channels.
a. How many people were surveyed?
b. How many people listened to either rap or alternative rock?
c. How many listened to heavy metal only?
The total number of people surveyed is 134. The number of people who listened to either rap or alternative rock is 76. The number of people who listened to heavy metal only is 1.
Explanation:To solve this problem, we can use a Venn diagram to organize the given information. Let's start by filling in the total number of people surveyed, which is the sum of those who listened to rap, heavy metal, alternative rock, and none of the three channels. From the given information, we have:
Rap: 37 Heavy Metal: 30 Alternative Rock: 49 None: 18
To find the total number of people surveyed, we add these numbers:
37 + 30 + 49 + 18 = 134.
Therefore, 134 people were surveyed.
b. To find the number of people who listened to either rap or alternative rock, we need to add the number of people who listened to rap and the number of people who listened to alternative rock, while making sure we don't double count those who listened to both:
37 + 49 - 10 = 76.
Therefore, 76 people listened to either rap or alternative rock.
c. To find the number of people who listened to heavy metal only, we need to subtract those who listened to heavy metal and either rap or alternative rock from the total number of people who listened to heavy metal:
30 - 13 - 16 = 1.
Therefore, 1 person listened to heavy metal only.
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Newberg City Cafe recently introduced a new flavor of coffee. They served 23 grande cups and 51 jumbo cups of the new coffee today, which equaled a total of 36,846 grams. The day before, 58 grande cups and 68 jumbo cups were served,which used a total of 59,460 grams. How much coffee is required to make each size?
Answer:
Grand coffee cup = 1469 gm
Jumbo coffee cup = 60 gm
Step-by-step explanation:
Let x be the grande coffee cup and y be the jumbo coffee cup.
Solution:
From the first statement. They served 23 grande cups and 51 jumbo cups of the new coffee today, which equal a total of 36,846 grams.
So, the equation is.
[tex]23x+51y = 36846[/tex] ---------(1)
From the second statement. They served 58 grande cups and 68 jumbo cups of the new coffee tomorrow, which equal a total of 59460 grams.
[tex]58x+68y=59460[/tex] ----------(2)
Solve the equation 1 for x.
[tex]23x = 36846-51y[/tex]
[tex]x=\frac{36846}{23}-\frac{51}{23}y[/tex]
[tex]x=1602-\frac{51}{23}y[/tex] ---------(3)
Substitute [tex]x=1602-\frac{51}{23}y[/tex] in equation 2.
[tex]58(1602-\frac{51}{23}y)+68y=59460[/tex]
[tex]92916-\frac{51\times 58}{23}y+68y=59460[/tex]
[tex]-\frac{2958}{23}y+68y=59460-92916[/tex]
[tex]\frac{-2958+1564}{23}y=-33456[/tex]
[tex]\frac{-1394}{23}y=-33456[/tex]
Using cross multiplication.
[tex]y=\frac{-23\times 33456}{-1394}[/tex]
[tex]y = 55.99[/tex]
y ≅ 60 gram
Substitute y = 60 in equation 3.
[tex]x=1602-\frac{51}{23}\times 60[/tex]
[tex]x=1602-\frac{3060}{23}[/tex]
[tex]x=1602-133.04[/tex]
[tex]x = 1469[/tex] grams
Therefore, grand coffee cup = 1469 gm and jumbo coffee cup = 60 gm
Final answer:
The answer explains how to calculate the amount of coffee required to make each size (grande and jumbo cups) based on the given information. Answer is 722 grams
Explanation:
The coffee required to make each size:
To find the amount of coffee in a grande cup, use the information given:23 grande cups used 36,846 gramsEach grande cup's quantity = 36,846 grams ÷ 23 = 1,603 gramsCalculate the amount of coffee in a jumbo cup:51 jumbo cups used 36,846 gramsEach jumbo cup's quantity = 36,846 grams ÷ 51 = 722 gramsTo ascertain the amount of coffee needed for a jumbo cup, we look at the data indicating 51 jumbo cups utilizing the same 36,846 grams. Dividing this total by the number of jumbo cups, we find that each jumbo cup requires approximately 722 grams of coffee.
Thus, the calculation yields 722 grams of coffee for each jumbo cup, confirming the final answer.
A movie theater sold 4 adult tickets and 7 children's tickets for $83 on friday the next day the theater sold 5 adult tickets and 6 children tickets for $90. What is the price for the adult ticket and the price for a child's ticket
Answer: An adult ticket cost $12
A child ticket cost $5
Step-by-step explanation:
Let x represent the price for one adult ticket.
Let y represent the price for one child ticket.
A movie theater sold 4 adult tickets and 7 children's tickets for $83 on Friday. It means that
4x + 7y = 83 - - - - - - - - - - - -1
The next day the theater sold 5 adult tickets and 6 children tickets for $90. It means that
5x + 6y = 90 - - - - - - - - - - - -2
Multiplying equation 1 by 5 and equation 2 by 4, it becomes
20x + 35y = 415
20x + 24y = 360
Subtracting, it becomes
11y = 55
y = 55/11 = 5
Substituting y = 5 into equation 1, it becomes
4x + 7 × 5 = 83
4x + 35 = 83
4x = 83 - 35 = 48
x = 48/4 = 12
ary Egan needs to drain his 21 comma 000-gallon inground swimming pool to have it resurfaced. He uses two pumps to drain the pool. One drains 15 gallons of water a minute while the other drains 20 gallons of water a minute. If the pumps are turned on at the same time and remain on until the pool is drained, how long will it take for the pool to be drained?
Answer:
600 minutes = 10 hours
Step-by-step explanation:
Egan has to drain 21 000 ga of water out of the pool. Let the number of minutes it takes him to drain the pool be x minutes. The equation for determining x can be set up and solved as follows:
[tex]\frac{15 ga}{min}*xmin+\frac{20ga}{min}*xmin = 21000ga\\\\15x+20x=21000\\\\35x= 21000\\\\x = 600[/tex]
600 minutes = 10 hours
A committee of 9 members is voting on a proposal. Each member casts a yea or nay vote. On a random voting basis, what is the probability that the proposal wins by a vote of 7 to 2?
Answer:
The required probability is [tex]P(x)=\frac{9}{128}[/tex] or [tex]P(x)=0.0703125[/tex].
Step-by-step explanation:
Consider the provided information.
A committee of 9 members is voting on a proposal. Each member casts a yea or nay vote. On a random voting basis,
The probability of yea or nay vote is equal, = [tex]\frac{1}{2}[/tex]
So, we can say that [tex]p=q=\frac{1}{2}[/tex]
Use the formula: [tex]P(x)=\binom{n}{x}p^xq^{n-x}[/tex]
Where n is the total number of trials, x is the number of successes, p is the probability of getting a success and q is the probability of failure.
We want proposal wins by a vote of 7 to 2, that means the value of x is 7.
Substitute the respective values in the above formula.
[tex]P(x)=\binom{9}{7}(\frac{1}{2})^7(\frac{1}{2})^{9-7}[/tex]
[tex]P(x)=\frac{9!}{7!2!}(\frac{1}{2})^7(\frac{1}{2})^{2}[/tex]
[tex]P(x)=\frac{8\times9}{2}\times(\frac{1}{2})^9[/tex]
[tex]P(x)=\frac{4\times9}{2^9}[/tex]
[tex]P(x)=\frac{9}{2^7}[/tex]
[tex]P(x)=\frac{9}{128}[/tex] or [tex]P(x)=0.0703125[/tex]
Hence, the required probability is [tex]P(x)=\frac{9}{128}[/tex] or [tex]P(x)=0.0703125[/tex].
Final answer:
The probability that a proposal wins by a 7 to 2 vote in a committee with 9 members is calculated using the binomial probability formula and is approximately 7.03%.
Explanation:
The question posed involves calculating the probability that a proposal wins by a vote of 7 to 2 in a committee with 9 members. We need to consider each vote as an independent 'yea' or 'nay' and find out the number of ways to get exactly 7 'yea' votes out of 9. This is a problem that can be solved using the binomial probability formula:
Binomial Probability Formula: P(X=k) = (n! / (k! * (n-k)!)) * p^k * (1-p)^(n-k), where 'n' is the total number of trials (or votes), 'k' is the number of successful outcomes need (yea votes), and 'p' is the probability of getting a yea vote. Since the voting is random, p = 0.5 assuming each member has an equal likely chance to vote yea or nay.
Plugging the values in, we get P(X=7) = (9! / (7! * 2!)) * 0.5^7 * 0.5^2. Calculating the factorials and powers of 0.5, the probability is:
P(X=7) = 36 * 0.5^9 = 36/512 = 0.0703125.
So, the probability that the proposal wins by a vote of 7 to 2 is approximately 7.03%.
Please answer all three
Answer:
We conclude that the statement B is true. The solution is also attached below.
Step-by-step Explanation:
As the inequality graphed on the number line showing that solution must be < x (-∞, 3] U [5, ∞)
So, lets check the statements to know which statement has this solution.
Analyzing statement A)
[tex]x^2-3x+5>\:0[/tex]
[tex]\mathrm{Write}\:x^2-3x+5\:\mathrm{in\:the\:form:\:\:}x^2+2ax+a^2[/tex]
[tex]2a=-3\quad :\quad a=-\frac{3}{2}[/tex]
[tex]\mathrm{Add\:and\:subtract}\:\left(-\frac{3}{2}\right)^2\:[/tex]
[tex]x^2-3x+5+\left(-\frac{3}{2}\right)^2-\left(-\frac{3}{2}\right)^2[/tex]
[tex]\mathrm{Complete\:the\:square}[/tex]
[tex]\left(x-\frac{3}{2}\right)^2+5-\left(-\frac{3}{2}\right)^2[/tex]
[tex]\mathrm{Simplify}[/tex]
[tex]\left(x-\frac{3}{2}\right)^2+\frac{11}{4}[/tex]
So,
[tex]\left(x-\frac{3}{2}\right)^2>-\frac{11}{4}[/tex]
Thus,
[tex]x^2-3x+5>0\quad :\quad \begin{bmatrix}\mathrm{Solution:}\:&\:\mathrm{True\:for\:all}\:x\:\\ \:\mathrm{Interval\:Notation:}&\:\left(-\infty \:,\:\infty \:\right)\end{bmatrix}[/tex]
Therefore, option A) is FALSE.
Analyzing statement B)
(x + 3) (x - 5) ≥ 0
[tex]x^2-2x-15\ge 0[/tex]
[tex]\left(x+3\right)\left(x-5\right)=0[/tex] [tex]\left(Factor\:left\:side\:of\:equation\right)[/tex]
[tex]x+3=0\:or\:x-5=0[/tex]
[tex]x=-3\:or\:x=5[/tex]
So
[tex]x\le \:-3\quad \mathrm{or}\quad \:x\ge \:5[/tex]
Thus,
[tex]\left(x+3\right)\left(x-5\right)\ge \:0\quad :\quad \begin{bmatrix}\mathrm{Solution:}\:&\:x\le \:-3\quad \mathrm{or}\quad \:x\ge \:5\:\\ \:\mathrm{Interval\:Notation:}&\:(-\infty \:,\:-3]\cup \:[5,\:\infty \:)\end{bmatrix}[/tex]
Therefore, the statement B is true.
Solution is also attached below.
Analyzing statement C)
[tex]x^2+2x-15\ge 0[/tex]
[tex]\mathrm{Factor}\:x^2+2x-15:\quad \left(x-3\right)\left(x+5\right)[/tex]
So,
[tex]x\le \:-5\quad \mathrm{or}\quad \:x\ge \:3[/tex]
[tex]x^2+2x-15\ge \:0\quad :\quad \begin{bmatrix}\mathrm{Solution:}\:&\:x\le \:-5\quad \mathrm{or}\quad \:x\ge \:3\:\\ \:\mathrm{Interval\:Notation:}&\:(-\infty \:,\:-5]\cup \:[3,\:\infty \:)\end{bmatrix}[/tex]
Therefore, option C) is FALSE.
Analyzing statement D)
- 3 < x < 5
[tex]-3<x<5\quad :\quad \begin{bmatrix}\mathrm{Solution:}\:&\:-3<x<5\:\\ \:\mathrm{Interval\:Notation:}&\:\left(-3,\:5\right)\end{bmatrix}[/tex]
Therefore, option D) is FALSE.
Analyzing statement E)
None of the above
The statement E) is False also as the statement B represents the correct solution.
Therefore, from the discussion above, we conclude that the statement B is true. The solution is also attached below.
Question # 8Find the number that is [tex]\frac{1}{3}[/tex] of the way from [tex]\:2\frac{1}{6}[/tex] to [tex]\:5\frac{1}{4}[/tex].
Answer:
Therefore, [tex]\frac{37}{36}[/tex] is the number that is [tex]\frac{1}{3}[/tex] of the way from [tex]\:2\frac{1}{6}[/tex] to [tex]\:5\frac{1}{4}[/tex].
Step-by-step Explanation:
[tex]\mathrm{Convert\:mixed\:numbers\:to\:improper\:fraction:}\:a\frac{b}{c}=\frac{a\cdot \:c+b}{c}[/tex]
So,
[tex]2\frac{1}{6}=\frac{13}{6}[/tex]
[tex]5\frac{1}{4}=\frac{21}{4}[/tex]
As the length from [tex]\frac{21}{4}[/tex] to [tex]\frac{13}{6}[/tex] is
[tex]\frac{21}{4}-\frac{13}{6}=\frac{37}{12}[/tex]
Now Divide [tex]\frac{37}{12}[/tex] into 3 equal parts. So,
[tex]\frac{37}{12}\div \:3=\frac{37}{36}[/tex]
As we have to find number that is [tex]\frac{1}{3}[/tex] of the way from [tex]\:2\frac{1}{6}[/tex] to [tex]\:5\frac{1}{4}[/tex], it means it must have covered 2/3 of the way. As we have divided [tex]\frac{37}{12}[/tex] into 3 equal parts, which is [tex]\frac{37}{36}[/tex]
Therefore, [tex]\frac{37}{36}[/tex] is the number that is [tex]\frac{1}{3}[/tex] of the way from [tex]\:2\frac{1}{6}[/tex] to [tex]\:5\frac{1}{4}[/tex].
Question # 9Answer:
[tex]\left(2x+3\right)[/tex] is in the form [tex]dx+\:e[/tex].
Step-by-step Explanation:
Considering the expression
[tex]2x^2+11x+12[/tex]
Factor
[tex]2x^2+11x+12[/tex]
[tex]\mathrm{Break\:the\:expression\:into\:groups}[/tex]
[tex]\left(2x^2+3x\right)+\left(8x+12\right)[/tex]
[tex]\mathrm{Factor\:out\:}x\mathrm{\:from\:}2x^2+3x\mathrm{:\quad }x\left(2x+3\right)[/tex]
[tex]\mathrm{Factor\:out\:}4\mathrm{\:from\:}8x+12\mathrm{:\quad }4\left(2x+3\right)[/tex]
[tex]x\left(2x+3\right)+4\left(2x+3\right)[/tex]
[tex]\mathrm{Factor\:out\:common\:term\:}2x+3[/tex]
[tex]\left(2x+3\right)\left(x+4\right)[/tex]
Therefore, [tex]\left(2x+3\right)[/tex] is in the form [tex]dx+\:e[/tex].
Keywords: factor, ratio, solution
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Mrs.Rodriquez is measuring fabric for costumes. She needs 58 feet of fabric. She has 10 1/3 yards of fabric. How many more yards of fabric does she need?
Answer:
9 yards
Step-by-step explanation:
Given data:
Needed fabric = 58feet
Available fabric = 10 1/3 yards
To convert yard to feet, the yards are multiplied by 3
10 1/3 yards = 31/3 * 3 = 31 feet.
More fabric needed = 58 - 31
More fabric needed = 27 feet
More fabric needed in yards = 27/3
More fabric needed in yards = 9
Answer:
9
Step-by-step explanation:
it's nine because 1 yard has three feet and um well like yeah
Find the x-intercepts of the parabola with
vertex (1,-13) and y-intercept (0.-11).
Write your answer in this form: (X1.),(X2,92).
If necessary, round to the nearest hundredth.
Enter the correct answer.
Answer:
[tex]x_1=3.55[/tex]
[tex]x_2=-1.55[/tex]
Step-by-step explanation:
we know that
If the vertex is (1,-13) and the y-intercept is (0.-11) (y-intercept above the vertex), we have a vertical parabola open upward
The equation of a vertical parabola written in vertex form is equal to
[tex]y=a(x-h)^2+k[/tex]
where
a is a coefficient
(h,k) is the vertex
substitute the given value of the vertex
[tex]y=a(x-1)^2-13[/tex]
Find the value of a
Remember that we have the y-intercept
For x=0, y=-11
substitute
[tex]-11=a(0-1)^2-13[/tex]
[tex]a=13-11\\a=2[/tex]
so
[tex]y=2(x-1)^2-13[/tex]
Find the x-intercepts
For y=0
[tex]2(x-1)^2-13=0[/tex]
[tex]2(x-1)^2=13[/tex]
[tex](x-1)^2=6.5[/tex]
[tex]x-1=\pm\sqrt{6.5}[/tex]
[tex]x=1\pm\sqrt{6.5}[/tex]
[tex]x_1=1+\sqrt{6.5}=3.55[/tex]
[tex]x_2=1-\sqrt{6.5}=-1.55[/tex]
Five hundred people attend a charity event, and each buys a raffle ticket. The 500 ticket stubs are put in a drum and thoroughly mixed. Next, 10 tickets are drawn. The 10 people whose tickets are drawn win a prize.This is which type of sample?
Answer:
The sample is a Simple Random sample.
explanation:
A simple random sample is the process where there is equal chance of selecting each member of a population to form a sample. in the example stated in the question there are equal chances of selecting every ticket among the five hundred ticket of the participant so as to form another set of ten tickets that win a prize.