The amount of corn chips dispensed into a bag by the dispensing machine has been identified as possessing a normal distribution with a mean of μ=48.5 ounces and a standard deviation of σ=0.2 ounce. What chip amount represents the 67th percentile, p 67, for the bag weight distribution? Round to the nearest hundredth. Hint: the 67th percentile of the standard normal curve is z=0.44. Round your answer to to decimal places.

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.

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:

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

Answer:

-3

Step-by-step explanation:

i know because i took the test

Answer:

-3 a)

Step-by-step explanation:

bc

Answer:

The net, when folded into a cube, has a total surface area of 2,400 sq.units

Step-by-step explanation:

The length of all sides of a cube are the same.

Now, the surface area of a cube is the sum of the area of all of its faces.

Since the length of all sides are the same and we are told that the length of a side is 20 units, thus, the area of one face is;

A = 20 x 20 = 400 sq.units

So, one the area of a face is 400 sq.units.

Now, since all the faces are the same measurement, thus each face will have an area of 400 sq.units. Cubes have 6 faces, thus the total surface Area is;

Total = 400 x 6 = 2400 sq.units

The net, when folded into a cube, has a total surface area of 2,400 sq.units

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:

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]

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:

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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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

For more such information on: width

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Rewrite the percent as a decimal by moving the decimal point 2 places to the left:

97% = 0.97

Now multiply:

698.04 x 0.97 = 677.0988

Round to 2 decimal places= 677.10

To find 97% of £698.04, you simply multiply £698.04 by 0.97. This gives you an answer of £677.30, rounded to 2 decimal places.

The question is asking for 97% of £698.04. To find this, you would need to multiply £698.04 by 0.97 (which is the decimal equivalent of 97%). Let's do this calculation:

£698.04 * 0.97 = £677.30

Here, the result (rounded to 2 decimal places) is £677.30. So, 97% of £698.04 is £677.30.

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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:

Step-by-step explanation:

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

Answer:

  A.  Three points

Step-by-step explanation:

Tangent circles will intersect at the one point of tangency.

Circles that cross each other will intersect in two points.

Circles that are coincident will intersect in infinitely many points.

It is not possible for two circles to intersect in exactly 3 points.

answer

graph a

speeds up from (0,1) U (2,3) and slows down from (1,2)

if it marks (2,3) incorrectly, it may be from (2,∞) instead

graph b

speeds up from (1,2) U (3,4) and slows down from (0,1) U (2,3)

if it marks (3,4) incorrectly, it may be from (3,∞) instead

step-by-step explanation

looking at the velocity graphs, when the absolute value of velocity is increasing (moving away from the x axis), the particle must be speeding up. we say absolute value because while velocity has direction, speed only has magnitude, so we need to take the absolute value of velocity to get speed.

for graph a, we can see the velocity moving away from the x axis during the interval (0,1), moving towards the x axis during the interval (1,2) and then moving away again during the interval (2,3)

so it speeds up from (0,1) U (2,3) and slows down from (1,2)

if it marks (2,3) incorrectly, it may be from (2,∞) instead since this is at an endpoint

repeat for graph b where it moves toward the x axis from (0,1), moves away from (1,2), moves towards from (2,3), and moves away again from (3,4)

so it speeds up from (1,2) U (3,4) and slows down from (0,1) U (2,3)

if it marks (3,4) incorrectly, it may be from (2,∞) instead since this is at an endpoint

Answer:the answers is B

Step-by-step explanation:

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:

3³ = 27

This is because:

3x3x3 = 27

Answer:

27 stripes

Step-by-step explanation:

162/6=27

Since each zebra has the sam amount of stripes, you will divide the amount of stripes my the amount of zebras.

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:

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:

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:

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:

3.704 Hours

Step-by-step explanation:

This problem can be solved by using concept of relative speed. relative speed is speed of one body in comparison of other.

If two bodies are moving in same direction their relative speed is calculated by taking difference of each other speed.

If two bodies are moving in opposite direction their relative speed is calculated by taking sum of each other speed.

In the problem stated two bodies are moving in north and south direction, hence they are moving in opposite direction, thus their speed can be taken sum of individual speed.

which is

(60+65) Km/Hr =  135 km/hour

Now given in question distance between two bodies is 500 KM

and relative speed = 135 km/hour

using formula of speed distance and time

Time = distance / speed  = 500/135 = 3.704 Hours

Therefore it will take 3.704 Hours for both of the trains to be 500 km apart.

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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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:

0.1111... = 0.1 = 1/9

Step-by-step explanation:

0.1111.. Is a repeating decimal which can be written as 0.1 and 1/9

It is important to know that the decimals which have only 1 digit repeating all come from the fractions which are ninths.

The fraction form of a number 0.11... is,

⇒ 1/9

We have to given that,

A number 0.1 repeating.

Now, We can find the fraction of number 0.111.. as,

Let us take,

x = 0.1111.....   .. (i)

Multiply by 10,

10x = 1.1111....  .. (ii)

Subtract (ii) from (i);

10x - x = 1.111.. - 0.1111....

9x = 1

x = 1/9

Hence, The fraction form of a number 0.11... is,

⇒ 1/9

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