Find the volume of the cone. Round your answer to the nearest tenth.

Answer:

a) 0.719 = 71.90% of children aged 13 to 15 years old have scores on this test above 92

b) A score of 89.8 marks the lowest 25 percent of the distribution

c) A score of 145.48 marks the highest 5 percent of the distribution

Step-by-step explanation:

Problems of normally distributed samples are 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.

In this problem, we have that:

[tex]\mu = 106, \sigma = 24[/tex]

(a) What proportion of children aged 13 to 15 years old have scores on this test above 92 ?

This is 1 subtracted by the pvalue of Z when X = 92. So

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

[tex]Z = \frac{92 - 106}{24}[/tex]

[tex]Z = -0.58[/tex]

[tex]Z = -0.58[/tex] has a pvalue of 0.2810

1 - 0.2810 = 0.719

0.719 = 71.90% of children aged 13 to 15 years old have scores on this test above 92

(b) What score which marks the lowest 25 percent of the distribution?

The 25th percentile, which is X when Z has a pvalue of 0.25. So it is X when Z = -0.675.

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

[tex]-0.675 = \frac{X - 106}{24}[/tex]

[tex]X - 106 = -0.675*24[/tex]

[tex]X = 89.8[/tex]

A score of 89.8 marks the lowest 25 percent of the distribution

(c) Enter the score that marks the highest 5 percent of the distribution

The 100-5 = 95th percentile, which is X when Z has a pvalue of 0.95. So it is X when Z = 1.645

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

[tex]1.645 = \frac{X - 106}{24}[/tex]

[tex]X - 106 = 1.645*24[/tex]

[tex]X = 145.48[/tex]

A score of 145.48 marks the highest 5 percent of the distribution

Final answer:

Using z-scores and the properties of a normal distribution, it was calculated that approximately 71.90% of children score above 92. The score marking the lowest 25 percent is approximately 90.20, and the score that marks the highest 5 percent of the distribution is around 145.88.

Explanation:

To solve the problems about normal distribution and interpreting IQ scores, we use the properties of the normal curve and z-scores. Z-scores help us understand how far away a particular score is from the mean, in terms of standard deviations.

Part (a): Proportion of Children With Scores Above 92

We first calculate the z-score for 92 using the formula: z = (X - μ) / σ, where X is the score, μ is the mean, and σ is the standard deviation. With μ = 106 and σ = 24, the z-score for 92 is (92 - 106) / 24 = -0.5833. Using a standard normal distribution table, we find that the proportion of children scoring above 92 corresponds to the area to the right of the z-score, which is approximately 0.7190. Therefore, the proportion of children aged 13 to 15 with scores above 92 is 0.7190.

Part (b): Lowest 25 Percent of the Distribution

The score marking the lowest 25 percent of the distribution corresponds to the 25th percentile or a z-score of about -0.675. We convert this z-score back to the original scale using the formula: X = μ + zσ, which yields X = 106 + (-0.675)(24) = 90.20. Thus, the score marking the lowest 25 percent is approximately 90.20.

Part (c): Highest 5 Percent of the Distribution

To find the score that marks the highest 5 percent, we locate the z-score that corresponds to the 95th percentile, which is about 1.645. Applying the conversion formula, we get X = 106 + (1.645)(24) = 145.88. Therefore, the score marking the highest 5 percent is approximately 145.88.

Answer:

so the answer is b i did the quiz

Step-by-step explanation:

What is the total surface area of the solid?

A rectangular prism with a length of 14 centimeters, width of 10 centimeters and height of 6 centimeters. A rectangular pyramid with 2 triangular sides with a base of 14 centimeters and height of 11 centimeters, and 2 triangular sides with a base of 10 centimeters and height of 12 centimeters.

558 square centimeters

702 square centimeters

842 square centimeters

982 square centimeters

Answer:

B but i could be wrong

Step-by-step explanation:

Answer:

Check the explanation

Step-by-step explanation:

Kindly check the attached image below to see the step by step explanation to the question above.

Answer:

22650

Step-by-step explanation:

Answer:

i think its c

Step-by-step explanation:

Answer:

C: Columns: likes roller coasters, doesn’t like roller coasters; rows: likes water rides, doesn’t like water rides

Step-by-step explanation:

Like variables need to be together on the columns and rows

Answer:

  B) x = e^x

Step-by-step explanation:

The graphs of y = e^x and y = x never intersect, so the solution set will be the empty (null) set for ...

  x = e^x

_____

There is one intersection of y=x with cos(x) and with sin(x). There are an infinite number of solutions for x = tan(x).

The question is incomplete! Complete question along with answer and step by step explanation is provided below.

Question:

150 students in a tenth grade high school class take a survey about which video game consoles they own. 60  students answer that one of their consoles is a Playstation, 50 answer that one of their consoles is an Xbox. Out  of these, there are 20 who have both systems.

Let A be the event that a randomly selected student in the class has a Playstation and B be the event that the  student has an XBOX. Based on this information, answer the following questions.

a) What is P(A), the probability that a randomly selected student has a Playstation?

b) What is P(B), the probability that a randomly selected student has an XBOX?

c) What is P(A and B), the probability that a randomly selected student has a Playstation and an XBOX?

d) What is P(A | B), the conditional probability that a randomly selected student has a Playstation given that he  or she has an XBOX?

Answer:

a) P(A) = 2/5

b) P(B) = 1/3

c) P(A and B) = 2/15

d) P(A | B) = 2/5

Step-by-step explanation:

Total no. of students = 150

No. of students having playstation = 60

No. of students having xbox = 50

No. of students who have both playstation and xbox = 20

a) What is P(A), the probability that a randomly selected student has a Playstation?

P(A) = No. of students having playstation/Total no. of students

P(A) = 60/150

P(A) = 2/5

b) What is P(B), the probability that a randomly selected student has an XBOX?

P(B) = No. of students having xbox/Total no. of students

P(B) = 50/150

P(B) = 1/3

c) What is P(A and B), the probability that a randomly selected student has a Playstation and an XBOX?

The probability that a students has a Playstation and an Xbox is given by

P(A and B) = P(A)*P(B)

P(A and B) = (2/5)*(1/3)

P(A and B) = 2/15

d) What is P(A | B), the conditional probability that a randomly selected student has a Playstation given that he or she has an XBOX?

The conditional probability is given by

P(A | B) = P(A and B)/P(B)

P(A | B) = (2/15)/(1/3)

P(A | B) = 2/5

Alternatively:

P(A | B) = P(A∩B)/P(B)

Where P(A∩B) is given by

P(A∩B) = No. of students who have both playstation and xbox/Total no. of students

P(A∩B) = 20/150

P(A∩B) = 2/15

P(A | B) = P(A∩B)/P(B)

P(A | B) = (2/15)/(1/3)

P(A | B) = 2/5

Answer: 27.42 ft

Step-by-step explanation:

To find the perimeter first we must find the circumference of the circles.

You can easily find the diameter by subtracting and you get 6.

Using the circle circumference formula c=2piR you get 9.42.

9.42 is our circumference of one circle.

You don't need to divide this by 2 because you already have 2 halves of a circle.

Next add all the sides which is 18.

Add this to the circumference we calculated earlier which gives you 27.42 ft.

Answer:

8

Step-by-step explanation:

Universal Set, U=37

Number who play basketball, n(B)=25

Number who are under six feet, n(U)=15

Number of those who do not play basketball and are six feet or taller, n(B∪U)'=5

From set theory.

U=n(B)+n(U)-n(B∩U)+n(B∪U)'

37=25+15-n(B∩U)+5

37=45-n(B∩U)

Therefore:

n(B∩U)=45-37=8

Therefore, the number of people at the party who play basketball and are under six feet tall is 8.

The number of people at the party who play basketball and are under six feet tall is 1510. These people belong to both the group of basketball players and the group of people under six feet tall.

To answer this question, we first need to understand who are the people at the party who play basketball and are under six feet tall. This group of people belongs to both the basketball players group represented by BB and the group of people under six feet tall, represented by U. We are looking for the intersection of these two groups, represented by |B∩U|.

Out of the 3737 people at the party, 2525 of them play basketball. From these 2525 basketball players, we don't know directly how many are under six feet tall. However, we are told that 1515 people at the party are under six feet tall. We also know that 5 people are over six feet tall and do not play basketball.

Therefore, to find out how many under six feet basketball players there are, we can subtract the 5 people who are over six feet and do not play basketball from the total of the ones who are under six feet: 1515 - 5 = 1510. So, there are 1510 people at the party who play basketball and are under six feet tall.

https://brainly.com/question/33193647

#SPJ12

Answer:

2, 4, 12, 48, 240

Step-by-step explanation:

We have the recursive formula   a_n = 2*(n!)

Find:

a_1 =  2* 1! = 2

a_2 = 2*(2!) = 4

a_3 = 2*(3!) = 2*6 = 12

a_4 = 2*(4!) = 2*24 = 48

a_5 = 2*(5!) = 2*5*24 = 240

Answer: 16.5

Step-by-step explanation:

[tex]\frac{99}{6} = 16.5[/tex]

Answer:

What i got is 16.5 hope this helps!

Answer:

The answer is 42 centimeters.

Step-by-step explanation:

HOPE THIS HELPED!

Answer:

-70

Step-by-step explanation:

40-8-102

= 32 - 102

= -70

To evaluate the expression 40 - 8 - 102, subtract 8 from 40 to get 32, then subtract 102 from 32 to arrive at -70.

40 - 8 - 102

To solve this expression, we need to follow the order of operations. In this case, since there are only subtraction operations involved, we can proceed from left to right.

40 - 8 = 32

32 - 102 = -70

This gives us the final answer: -70.

Answer:

The margin of error for the mean is of 165.18 points.

Step-by-step explanation:

We have the standard deviation of the sample, so we use the t-distribution to solve this question.

The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So

df = 81 - 1 = 80

95% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 80 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.95}{2} = 0.975[/tex]. So we have T = 1.9901

The margin of error is:

M = T*s = 1.9901*83 = 165.18.

In which s is the standard deviation of the sample.

The margin of error for the mean is of 165.18 points.

Final answer:

The answer discusses z-scores for SAT scores, calculating scores above the mean, and comparing performance on different tests.

Explanation:

Z-score for SAT score of 720:

Calculate the z-score: z = (720 - 520) / 115 = 1.74.

Interpretation: A score of 720 is 1.74 standard deviations above the mean.

Math SAT score 1.5 standard deviations above the mean:

Calculate the score: 520 + 1.5(115) ≈ 692.5.

The score of 692.5 is 1.5 standard deviations above the mean of 520.

Better performance on math tests:

For SAT: z = (700 - 514) / 117 ≈ 1.59.

For ACT: z = (30 - 21) / 5.3 ≈ 1.70.

Person with a z-score closer to 2 performed better relative to the test they took.

Final answer:

Mrs. Golden will need 26 squares of silver paper to cover her bulletin board, and there will not be any pieces left over.

Explanation:

To find out how many 1-foot squares Mrs. Golden needs to cover her bulletin board, we first need to calculate the area of the bulletin board. The area of a rectangle can be found by multiplying the length and width. In this case, the length is 6.5 feet and the width is 4 feet, so the area is 6.5 feet x 4 feet = 26 square feet.

Since the silver paper comes in 1-foot squares, we can divide the area of the bulletin board by the area of each square to find out how many squares are needed. In this case, we divide 26 square feet by 1 square foot, giving us a result of 26 squares.

There will not be any pieces left over because 26 squares fully cover the area of the bulletin board. If there were any remaining space, we would need a fraction of a square to cover it.

Journal entry

Explanation:

                                  Books of (----Limited)

                                      Journal Entry

Date         Account Title and Explanation            Debit         Credit

              Cash / Bank                          A/c  Dr.     $750,000

                To Unearned Subscription A/c                               $750,000

                            (Being Unearned Subscription)

Computation:

Amount of Unearned Subscription =  25,000 × $30

Amount of Unearned Subscription =  %750,000

Answer:

The lateral area of the cylinder is 678cm²

Step-by-step explanation:

To calculate the lateral area of ​​the cylinder we have to calculate the circumference and multiply it by the height

To solve this problem we need to use the circumferenc formula of a circle:

c = circumference

r = radius = 9cm

π = 3.14

c = 2π * r

we replace with the known values

c = 2 * 3.14 * 9cm

c = 56.52cm

The length of the circumference is 56.52cm

lateral area = c * h

56.52cm  * 12cm = 678.24 cm²

round to the nearest whole number

678.24 cm² = 678cm²

The lateral area of the cylinder is 678cm²

Answer:

c-678 cm2

Step-by-step explanation:

what i got on edg 2020

Let y represent the y-coordinate of point A.

We have been given that point B has coordinates (5,1) The x-coordinate of point A is 0. So coordinates of point A would be (0,y)

The distance between point A and Point B is 13 units.

We will use distance formula to solve our given problem.

[tex]D=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

Let point A [tex](0,y)=(x_2-y_2)[/tex] and point A [tex](5,1)=(x_1,y_1)[/tex].

Upon substituting coordinates of both points in distance formula, we will get:

[tex]13=\sqrt{(0-5)^2+(y-1)^2}[/tex]

[tex]13=\sqrt{25+y^2-2y+1}[/tex]

[tex]13=\sqrt{y^2-2y+26}[/tex]

Let us square both sides as:

[tex]13^2=(\sqrt{y^2-2y+26})^2[/tex]

[tex]169=y^2-2y+26[/tex]

[tex]169-169=y^2-2y+26-169[/tex]

[tex]0=y^2-2y-143[/tex]

[tex]y^2-2y-143=0[/tex]

Upon splitting the middle term, we will get:

[tex]y^2-13y+11y-143=0[/tex]

[tex]y(y-13)+11(y-13)=0[/tex]

[tex](y-13)(y+11)=0[/tex]

Now we will use zero product property.

[tex](y-13)=0, (y+11)=0[/tex]

[tex]y=13, y=-11[/tex]

Therefore, the possible coordinates of point A would be [tex](0,-11)[/tex] and [tex](0,13)[/tex].

The surface area of the cylinder, when the radius is 3 centimeters and the height is 4 centimeters, is approximately 131.88 square centimeters.

Use the provided formula for the surface area of a cylinder:

[tex]\[ SA = 2\pi r (h + r) \][/tex]

Given:

[tex]r = 3 \text{ centimeters}[/tex]

[tex]h = 4 \text{ centimeters}[/tex]

Now, substitute these values into the formula and calculate the surface area:

[tex]SA = 2\pi \times 3 \times (4 + 3)[/tex]

[tex]SA = 2\pi \times 3 \times 7[/tex]

[tex]SA = 6\pi \times 7[/tex]

[tex]SA = 42\pi[/tex]

Now, let's calculate the numerical value:

[tex]SA \approx 42 \times 3.14[/tex]

[tex]SA \approx 131.88 \text{ square centimeters}[/tex]

Therefore, the surface area of the cylinder, when the radius is 3 centimeters and the height is 4 centimeters, is approximately 131.88 square centimeters.

Answer:

A one-liter bottle of soda has a mass of about 1 kilogram.

Answer:

square root of 96 or 9.79

Step-by-step explanation:

a2+b2=c2

2square+b2=10square

4+b2=100

(4-4)+b2=(100-4)

b2=square root96 or 9.79

Answer:

The value of G is 3/8 .

Step-by-step explanation:

In order to solve G, you have to divide 2/3 to both sides :

[tex] \frac{2}{3} \times G = \frac{1}{4} [/tex]

[tex] \frac{2}{3} \times G \div \frac{2}{3 } = \frac{1}{4} \div \frac{2}{3} [/tex]

[tex]G = \frac{1}{4} \times \frac{3}{2} [/tex]

[tex]G = \frac{3}{8} [/tex]

Answer:

3/8

Step-by-step explanation:

Convert to common denominator which would be 12.

8/12 x G=3/12

Then divide 3/12 by 8/12 and you get 3/8

Answer:

Given:

Sample size, n = 11

P = 0.5

a) The shape of the histogram will be symmetrical. This is because the probability of getting heads and tails is equal.

b) The histogram is centered at

p = 0.5 (because of equal probability of obtaining heads and tails).

c) How much variability would you expect among these​ proportions?

Here, we are to find the standard deviation.

Let's use the formula:

[tex] \sigma = \sqrt{\frac{pq}{n}} [/tex]

Where

p = 0.5(probability of getting heads)

q = 0.5 (probability of getting tails)

Therefore

[tex] \sigma = \sqrt{\frac{0.5 * 0.5}{11}} [/tex]

= 0.0227 ≈ 0.023

The standard deviation is 0.023

d) A normal model should not be use here because the success/failure condition is violated, since each student only flips the coin 11 times, it impossible to obtain both at least 10 heads and at least 10 tails. Here, the sample size is too small.

Answer:

The zeros are x1=4.45 and x2=-0.45.

x1 is between 4 and 5.

x2 is between -1 and 0.

Step-by-step explanation:

We have the function:

[tex]y(x) = x2 - 4x-2[/tex]

As this is a quadratic function, we can calculate the zeros of the function with the quadratic equation:

[tex]x_{1,2}=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\\\x=\dfrac{-(-4)\pm\sqrt{(-4)^2-4\cdot 1\cdot(-2)}}{2\cdot 1}\\\\\\x=\dfrac{4\pm\sqrt{16+8}}{2}\\\\\\x=\dfrac{4\pm\sqrt{24}}{2}\\\\\\x=\dfrac{4\pm4.9}{2}=2\pm2.45\\\\\\x_1=2+2.45=4.45\\\\x_2=2-2.45=-0.45[/tex]

The zeros are x1=4.45 and x2=-0.45.

x1 is between 4 and 5.

x2 is between -1 and 0.

The two real zeros of the quadratic equation are located between -1 and 4.

To determine between which consecutive integers the real zeros of the function y(x) = x² - 4x - 2 are located, we can use the quadratic formula.

The quadratic formula is given as:

x = (-b ± √(b² - 4ac)) / (2a)

In the equation y(x) = x² - 4x - 2, we have a = 1, b = -4, and c = -2.

Let's substitute these values into the quadratic formula to find the values of x:

x = (-(-4) ± √((-4)² - 4(1)(-2))) / (2(1))

x = (4 ± √(16 + 8)) / 2

x = (4 ± √24) / 2

x = (4 ± 2√6) / 2

x = 2 ± √6

From the quadratic formula, we find that the real zeros of the function are x = 2 + √6 and x = 2 - √6.

To determine between which consecutive integers these real zeros are located, we can compare the values to the nearest integers.

x = 2 + √6 is approximately 4.45

x = 2 - √6 is approximately -0.45

Therefore, the real zeros of the function are located between the consecutive integers -1 and 4.

Learn more about quadratic equations at:

https://brainly.com/question/1214333

#SPJ6

Answer:

We are 95% confident that the true weight of the rock is between 25.2 g and 29.1 g.

Step-by-step explanation:

Hello!

A geology student weighted a rock 5 times and estimated the average weight using a 95% CI [25.2; 29.1]gr

The confidence interval is used to estimate the value of the population mean, it gives you a range of values for it.

The 95% level of confidence of the interval indicates that if you were to construct 100 confidence intervals to estimate the population mean, you'd expect 95 of them to include the true value of the parameter.

So with a 95% confidence level, you'd expect the true average weight of the rock to be included in the interval  [25.2; 29.1]gr

I hope this helps!

Answer:

[tex]\binom{ \frac{7 \sqrt{58} }{58} }{ \frac{ - 3 \sqrt{58} }{58} }[/tex]

Step-by-step explanation:

First, find the magnitude of the vector:

[tex] |v| = \sqrt{( {(7)}^{2} + {( - 3)}^{2}) } \\ = \sqrt{(49 + 9)} \\ = \sqrt{58} [/tex]

Then, divide each component of the vector by the magnitude to get the unit vector and rationalise:

[tex]unit \: vector = \binom{ \frac{7}{ \sqrt{58} } }{ \frac{ - 3}{ \sqrt{58} } } \\ = \binom{ \frac{7 \sqrt{58} }{58} }{ \frac{ - 3 \sqrt{58} }{58} } [/tex]

If you add a pic maybe I could help but for now I cant

Answer:

  see below

Step-by-step explanation:

A relation is a function when there is exactly one output for each input. That is the case in this table, so the relation between the original price and sale price is a function.

Answer:

25%

Step-by-step explanation:

Plz mark me brainliest.

Answer:

25%

Step-by-step explanation: