The fuel tanks on some ships are spheres of which only the top halves are above deck. If one of these tanks is 96 ft in diameter, how many gallons of fuel does it hold? Use
1 ft3 ≈ 7.5 gal

Answer:

a) [tex]654.16-2.01\frac{164.55}{\sqrt{52}}=608.29[/tex]    

[tex]654.16+2.01\frac{164.55}{\sqrt{52}}=700.03[/tex]    

And we can conclude that we are 95% confident that the true mean of Co2 level is between 608.29 and 700.03 ppm

b) [tex]n=(\frac{1.960(175)}{25})^2 =188.23 \approx 189[/tex]

Step-by-step explanation:

Part a

The confidence interval for the mean is given by the following formula:

[tex]\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}[/tex]   (1)

In order to calculate the critical value [tex]t_{\alpha/2}[/tex] we need to find first the degrees of freedom, given by:

[tex]df=n-1=52-1=51[/tex]

Since the Confidence is 0.95 or 95%, the value of [tex]\alpha=0.05[/tex] and [tex]\alpha/2 =0.025[/tex], and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.025,51)".And we see that [tex]t_{\alpha/2}=2.01[/tex]

Replacing we got:

[tex]654.16-2.01\frac{164.55}{\sqrt{52}}=608.29[/tex]    

[tex]654.16+2.01\frac{164.55}{\sqrt{52}}=700.03[/tex]    

And we can conclude that we are 95% confident that the true mean of Co2 level is between 608.29 and 700.03 ppm

Part b

The margin of error is given by :

[tex] ME=z_{\alpha/2}\frac{\sigma}{\sqrt{n}}[/tex]    (a)

The desired margin of error is ME =50/2=25 and we are interested in order to find the value of n, if we solve n from equation (a) we got:

[tex]n=(\frac{z_{\alpha/2} s}{ME})^2[/tex]   (b)

The critical value for 95% of confidence interval now can be founded using the normal distribution. And in excel we can use this formla to find it:"=-NORM.INV(0.025;0;1)", and we got [tex]z_{\alpha/2}=1.960[/tex], and we use an estimator of the population variance the value of 175 replacing into formula (b) we got:

[tex]n=(\frac{1.960(175)}{25})^2 =188.23 \approx 189[/tex]

Answer:

The lower bound for a 90% confidence interval for the percentage of all American adults who believe in ghosts is 0.3549

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which

z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].

For this problem, we have that:

[tex]n = 1012, \pi = 0.38[/tex]

90% confidence level

So [tex]\alpha = 0.1[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.1}{2} = 0.95[/tex], so [tex]Z = 1.645[/tex].

The lower limit of this interval is:

[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.38 - 1.645\sqrt{\frac{0.38*0.62}{1012}} = 0.3549[/tex]

The lower bound for a 90% confidence interval for the percentage of all American adults who believe in ghosts is 0.3549

Answer:

y=10

Step-by-step explanation:

(y-10)^2=0

Take the square root of each side

sqrt((y-10)^2)=sqrt(0)

y-10 =0

Add 10 to each side

y-10+10=0+10

y = 10

Answer:

asdasd

Step-by-step explanation:

miles ÷ miles/hour = hours

Just divide the miles by the mph

4.5/12.5 = 0.36 hours

(0.36 hours)(60 min/hour) = 21.6 minutes

(0.6 minutes)(60 seconds/minute) = 36 seconds

Time:  21 minutes 36 seconds

Answer:

0.36 hours

Step-by-step explanation:

Miles ÷ Miles/hour = hours

4.5 miles ÷ 12.5 mph = 0.36 hours

This is a composite function problem in high school mathematics. To solve the problem, first evaluate g(-4), then substitute that result into the function f(x). Using these steps, the composite function f(g(-4)) equals -114.

First, it is crucial to identify that this is a question involving composite functions, specifically applying the function f(g(x)). In this case, the function g(x) is not provided in the question, so I'll assume we have a typo. If g(x) has been given as 3x + 1, then g(-4) would equal -11. We substitute -11 into the function f(x)=10x-4, we get f(-11)=10*(-11)-4, which results in f(-11)=-114.

The composite function f(g(-4)) is thus -114.

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Answer:

The solutions of a quadratic equation on a graph is the point where the graph cuts across the x and y axes. The maximum number of solutions given by solving a quadratic equation is 2 solutions because the maximum power in a quadratic equation is power 2

The solutions of a quadratic equation represent the points where the graph, or parabola, crosses the x-axis. Those points are known as the roots of the equation. A quadratic equation can have up to two solutions.

In mathematics, the solutions of a quadratic equation graphically represent the points where the parabola (graph of the equation) crosses the x-axis. These points are commonly known as the roots or zeros of the quadratic equation. The maximum number of solutions a quadratic equation can have is two. This is due to the highest power in a quadratic equation (ax² + bx + c = 0) being '2'. However, it's also possible for it to have one or no solutions, depending on the values of a, b, and c, specifically their discriminant value (b² - 4ac).

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Answer:

76 inches

Step-by-step explanation:

It should be understood that 15.2cm is equal to 5 inches.

Since the height = 5 * size of the foot

= 5 * 15.2 = 76

Therefore, a person with 15.2cm as the size of the foot will have the height of 76 inches.

Using the regression model produced by the technology output. The best predicted value for the person's height would be 123.288 cm.

Using the Regression equation produced by the technology used :

For a foot length of 15.2 cm :

The predicted height value can be calculated by substituting the foot length value into the equation thus :

Height = 52.0 + 4.69(15.2)

Height = 52.0 + 71.288

Height = 123.288 cm

The best predicted value for the person's height would be 123.288 cm.

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Answer:

A C(x) =2x³+2x²-18x-11

Step-by-step explanation:

C(x) = W(x) - D(x)

plug W(x) and D(x) into equation

C(x) = 3x³+4x²-18x+4 - (x³+2x²+15)

add like terms now

C(x) =2x³+2x²-18x-11

Answer:

-0.04

Step-by-step explanation:

The initial temperature of the soup is 216° F. After 8 minutes, the temperature of the soup is 180° F.

Set T(x) equal to 180, and set x equal to 8. Then, solve for r.

Therefore, the approximate constant rate of cooling is -0.04.

Answer:

Mark me brainliest please

Step-by-step explanation:

To create a scale drawing of an Olympic standard swimming pool with a scale of 1 inch to 10 meters, the scaled dimensions would be approximately 2.5 inches for the width and 5 inches for the length.

To create a scale drawing of an Olympic standard swimming pool using a scale of 1 inch to 10 meters, we need to find the scaled dimensions. The actual dimensions of the pool are given as 50 meters in length and 25 meters in width.

Width:

Actual width: 25 meters

Scale factor: 10 meters per 1 inch

Scaled width = Actual width / Scale factor

Scaled width = 25 meters / 10 meters per 1 inch

Scaled width = 2.5 inches

Length:

Actual length: 50 meters

Scale factor: 10 meters per 1 inch

Scaled length = Actual length / Scale factor

Scaled length = 50 meters / 10 meters per 1 inch

Scaled length = 5 inches

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Final answer:

The Central Limit Theorem explains the sampling distribution of the sample mean. We calculate probabilities using z-scores in the normal distribution for different scenarios. Understanding the concepts of sampling distributions and z-scores is essential for handling such questions in statistics.

Explanation:

The Central Limit Theorem states that for a large enough sample size, the sampling distribution of the sample mean will be approximately normally distributed, regardless of the population distribution.

(a) The mean of the sampling distribution of x  equals the population mean, which is 74, and the standard deviation of the sampling distribution σ/√n equals 6/√36 = 1.

(b) To find Upper P(x > 75.9), we standardize the value: z = (75.9 - 74) / 1 = 1.9. Consulting a z-table, we find P(z > 1.9) ≈ 0.0287.

(c) For Upper P(x< 71.95), we standardize: z = (71.95 - 74) / 1 = -2.05. From the z-table, P(z < -2.05) ≈ 0.0202.

(d) To find Upper P(73 < x < 75.75), we standardize both values, giving z(73) = (73 - 74) / 1 = -1 and z(75.75) = (75.75 - 74) / 1 = 1.75. Then, P(-1 < z < 1.75) = P(z < 1.75) - P(z < -1) ≈ 0.9599 - 0.1587 = 0.8012.

Complete Question

Suppose that the money demand function takes the form

(M/P)^d = L(i,Y) = Y/(5i)

a. If output grows at rate and the nominal interest rate is constant, at what rate will the demand for real balances grow

b. What is the velocity of money in this economy

Answer:

a. See explanation below

b. Velocity = 5i

Step-by-step explanation:

a. Suppose that the nominal interest rate remains constant, the demand for real balances will grow at the same rate at which the output grows.

b.

Given that (M/P)^d = L(i,Y) = Y/(5i)

Money equation is written as;

Total Spending = MV

Where M = Amount of Money..

V = Velocity of Circulation

Total Spending = PY;

So, PY = MV --- Make V the subject of formula

PY/M = V --- Rearrange

V = PY/M ---- (1)

Also,

M/P = Y/5i --- Cross Multiply

M * 5i = P * Y --- Make 5i the subject of formula

5i = PY/M ---- (2)

Compare 1 and 2

5i = V = PY/M

So, 5i = V

V = 5i

Hence, Velocity = 5i

Answer:

3³ = 27

This is because:

3x3x3 = 27

Answer:the answers is B

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

20+20=40

50-40=10

10/2=5

To check our work we find the perimeter with our new width. 20+20+5+5=50

So we are right!!!

Answer:

[tex]a.\ \mu_p=750\ \ , \sigma_p=0.005\\\\b.\ \mu_p=150\ \ , \sigma_p=0.0113\\\\c.\ \mu_p=75\ \ , \sigma_p=0.0160[/tex]

Step-by-step explanation:

a. Given p=0.15.

-The mean of a sampling proportion  of n=5000 is calculated as:

[tex]\mu_p=np\\\\=0.15\times 5000\\\\=750[/tex]

-The standard deviation is calculated using the formula:

[tex]\sigma_p=\sqrt{\frac{p(1-p)}{n}}\\\\=\sqrt{\frac{0.15(1-0.15)}{5000}}\\\\=0.0050[/tex]

Hence, the sample mean is μ=750 and standard deviation is σ=0.0050

b. Given that p=0.15 and n=1000

#The mean of a sampling proportion  of n=1000 is calculated as:

[tex]\mu_p=np\\\\=1000\times 0.15\\\\\\=150[/tex]

#-The standard deviation is calculated as follows:

[tex]\sigma_p=\sqrt{\frac{p(1-p)}{n}}\\\\\\=\sqrt{\frac{0.15\times 0.85}{1000}}\\\\\\=0.0113[/tex]

Hence, the sample mean is μ=150 and standard deviation is σ=0.0113

c. For p=0.15 and n=500

#The mean is calculated as follows:

[tex]\mu_p=np\\\\\\=0.15\times 500\\\\=75[/tex]

#The standard deviation of the sample proportion is calculated as:

[tex]\sigma_p=\sqrt{\frac{p(1-p)}{n}}\\\\\\=\sqrt{\frac{0.15\times 0.85}{500}}\\\\\\=0.0160[/tex]

Hence, the sample mean is μ=75 and standard deviation is σ=0.0160

Answer:

PLEASE MARK AS BRAINLIEST PLZ

NOPE

Step-by-step explanation:

14:18 if you want to find the divisible number it is 2 now divide them both by 2it will be 7:9 and that's the most simple way

Answer:

No

Step-by-step explanation:

A way you can do it is to simplify the ratio, to make it smaller, but still equal to 14:18.

14:18 can be divided by 2, and turn to 7:9

This cannot be simplified so it is not equivalent.

Final answer

No

Final answer:

To find the population of a town after 12 years with an initial population of 17,000 and an annual growth rate of 4%, use the exponential growth formula. After the calculations, the town's estimated future population would be around 26,533 residents.

Explanation:

To calculate the future population of a town that currently has 17,000 residents and grows at a rate of 4% per year, we can use the formula for exponential growth: future population = current population ×  [tex](1 + growth \ rate)^n,[/tex] where n is the number of years the population is growing. In this case, the formula becomes  [tex]17000 \times (1 + 0.04)^n[/tex], because we're looking to find the population after 12 years.

Calculating this, we have: future population =  [tex]17,000 \times (1.04)^{12}[/tex]. Using a calculator, we get approximately 26,533, meaning after 12 years, the population of the town is expected to be around 26,533 residents.

Answer:

in many random samples, 95% of the confidence intervals will contain a sample average between 24cm and 27cm.

Step-by-step explanation:

We then interpret this interval that  95% would contain a sample average forearm length between 24cm and 27cm.

The average is defined as the mean  equal to the ratio of the sum of the values ​​of a given number to the total number of values ​​in the set.

The formula for finding the average of given numbers or values ​​is very simple. We just need to add all the numbers and  divide the result by the given number of values. So the  formula for mean in mathematics is given as follows:

Mean = sum of values/ number of values ​​

Suppose we have given  n as number of values ​​like x1, x2, x3 ,..., xn. The average or  mean of the given data is equal to:

Mean = (x1 x2 x3 … xn)/n

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Final answer:

The probability of one of the minority candidates being hired is 40%.

Explanation:

To find the probability that one of the minority candidates is hired, we need to determine the number of favorable outcomes (one of the minority candidates being selected) and divide it by the total number of possible outcomes (selecting any candidate from the final list of five).

Since there are two minority candidates and five candidates total, the probability of selecting one of the minority candidates is

P(one of the minority candidates being hired) = 2/5 = 0.4 = 40%

Answer:

95% confidence interval for the percentage of all U.S. public high school students who are obese is [0.110 , 0.190].

Step-by-step explanation:

We are given that 15% of a random sample of 300 U.S. public high school students were obese.

Firstly, the pivotal quantity for 95% confidence interval for the population proportion is given by;

                        P.Q. = [tex]\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex]  ~ N(0,1)

where, [tex]\hat p[/tex] = sample % of U.S. public high school students who were obese = 15%

           n = sample of U.S. public high school students = 300

           p = population percentage of all U.S. public high school students

Here for constructing 95% confidence interval we have used One-sample z proportion statistics.

So, 95% confidence interval for the population proportion, p is ;

P(-1.96 < N(0,1) < 1.96) = 0.95  {As the critical value of z at 2.5% level

                                             of significance are -1.96 & 1.96}  

P(-1.96 < [tex]\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] < 1.96) = 0.95

P( [tex]-1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] < [tex]{\hat p-p}[/tex] < [tex]1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] ) = 0.95

P( [tex]\hat p-1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] < p < [tex]\hat p+1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] ) = 0.95

95% confidence interval for p = [[tex]\hat p-1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] , [tex]\hat p+1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex]]

  = [ [tex]0.15-1.96 \times {\sqrt{\frac{0.15(1-0.15)}{300} } }[/tex] , [tex]0.15+1.96 \times {\sqrt{\frac{0.15(1-0.15)}{300} } }[/tex] ]

  = [0.110 , 0.190]

Therefore, 95% confidence interval for the percentage of all U.S. public high school students who are obese is [0.110 , 0.190].

The correct answer is option (c). The approximate 95% confidence interval is [tex]\[0.1108 \text{ to } 0.1892\][/tex]

To determine the approximate 95% confidence interval for the percentage of all U.S. public high school students who are obese, we'll use the standard error provided and the normal model.

The formula for the confidence interval is:

[tex]\[\hat{p} \pm Z \cdot \text{SE}\][/tex]

Now, we calculate the margin of error:

[tex]\[\text{Margin of Error} = Z \cdot \text{SE} = 1.96 \cdot 0.020 = 0.0392\][/tex]

Then, we determine the confidence interval by adding and subtracting the margin of error from the sample proportion:

[tex]\[\hat{p} - \text{Margin of Error} = 0.15 - 0.0392 = 0.1108\][/tex]

[tex]\[\hat{p} + \text{Margin of Error} = 0.15 + 0.0392 = 0.1892\][/tex]

Therefore, the approximate 95% confidence interval is:

[tex]\[0.1108 \text{ to } 0.1892\][/tex]

Answer:

w = 3(2a + b) - 4

w = 6a + 3b - 4

a = (w - 3b + 4) / 6

Answer:

[tex]a = \frac{w + 4 - 3b}{6} [/tex]

Step-by-step explanation:

[tex]w = 3(2a + b) - 4 \\ w + 4 = 6a + 3b \\ w + 4 - 3b = 6a \\ \frac{w + 4 - 3b }{6} = \frac{6a}{6} \\ \\ a = \frac{w + 4 - 3b}{6} [/tex]

Answer:

There u go

Step-by-step explanation:

(-x+3x+3)×x=2x^2+3x

2x^2+3x=x(2x+3)

The sum of the functions f(x) = -x and g(x) = 3x + 3 is computed as (f+g)(x) = f(x) + g(x), which simplifies to 2x + 3. This denotes a polynomial in simplest form.

The question is asking to compute the sum of two functions, f(x) = -x and g(x) = 3x+3 and to express it as a polynomial or a rational function in simplest form.

The sum of the two functions can be computed by adding together the outputs of the individual functions. In mathematical bricolage, this is known as function addition. The function sum (f+g)(x) can be calculated as f(x) + g(x).

If f(x) = -x and g(x) = 3x + 3, then (f+g)(x) can be calculated as follows:

(-x) + (3x + 3) = (-1x + 3x) + 3 = 2x + 3

So, (f+g)(x), in this case, is 2x + 3 which is a polynomial function in simplest form.

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Answer:

B

Step-by-step explanation:

choose brainliest

Answer:

Q2

a) total sweets: 5 + 3 = 8

i) P(red) = 5/8

ii) P(yellow) = 3/8

b) for the second one:

4 red and 3 yellow left

i) P(red) = 4/7

ii) P(yellow) = 3/7

c) for the second one:

5 red and 2 yellow left

i) P(red) = 5/7

ii) P(yellow) = 2/7

Q3

a) total probability is 1

⅙ + ¼ + ⅓ + x = 1

x = 1 - (⅙ + ¼ + ⅓)

x = ¼

b) most likely is the color with highest probability, which is green

c) P(not red) = 1 - P(red)

= 1 - ⅙ = ⅚

Answer:

A)sample proportion = 0.17,  the sampling distribution of p can be calculated/approximated with normal distribution of sample proportion = 0.17 and standard error/deviation = 0.013281

B) 0.869

C)0.9668

Step-by-step explanation:

A) p ( proportion of population that spends more than $100 per week) = 0.17

sample size (n)= 800

the sample proportion of p = 0.17

standard error of p = [tex]\sqrt{\frac{p(1-p)}{n} }[/tex] = 0.013281

the sampling distribution of p can be calculated/approximated with

normal distribution of sample proportion = 0.17 and standard error/deviation = 0.013281

B) probability that the sample proportion will be +-0.02 of the population proportion

= p (0.17 - 0.02 ≤ P ≤ 0.17 + 0.02 ) = p( 0.15 ≤ P ≤ 0.19)

z value corresponding to P

Z = [tex]\frac{P - p}{standard deviation}[/tex]

at P = 0.15

Z =  (0.15 - 0.17) / 0.013281 = = -1.51

at P = 0.19

z = ( 0.19 - 0.17) / 0.013281 = 1.51

therefore the required probability will be

p( -1.5 ≤ z ≤ 1.5 ) = p(z ≤ 1.51 ) - p(z ≤ -1.51 )

                           = 0.9345 - 0.0655 = 0.869

C) for a sample (n ) = 1600

standard deviation/ error = 0.009391 (applying the equation for calculating standard error as seen in part A above)

therefore the required probability after applying

z = [tex]\frac{P-p}{standard deviation}[/tex] at p = 0.15 and p = 0.19

p ( -2.13 ≤ z ≤ 2.13 ) = p( z ≤ 2.13 ) - p( z ≤ -2.13 )

                               = 0.9834 - 0.0166 = 0.9668

The sampling distribution of the sample proportion can be approximated by a normal distribution. The probability of the sample proportion being within a certain range can be calculated using z-scores.

a. The sampling distribution of p, the sample proportion of households spending more than $100 per week on groceries, can be approximated by a normal distribution with a mean of p and a standard deviation of √[(p(1-p))/n], where p is the population proportion and n is the sample size.

b. To find the probability that the sample proportion will be within ±0.02 of the population proportion, we calculate the z-scores for both values and find the area under the normal curve between those z-scores.

c. The probability of the sample proportion being within ±0.02 of the population proportion will remain the same for a sample of 1600 households, as long as the population proportion remains the same.

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Answer:

Step-by-step explanation:

I can't unless you give me the length and width or its impossible

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