The U.S. Department of Agriculture claims that the mean cost of raising a child from birth to age 2 by husband-wife families in the United States is $13,120. A random sample of 500 children (age 2) has a mean cost of $12,925 with a standard deviation of $1745. At α=.10, is there enough evidence to reject the claim? (Adapted from U.S. Department of Agriculture Center for Nutrition Policy and Promotion).

Answer:

a. [tex]\mu=\bar x =14.6[/tex]

b. The 95% CI for the population mean is (14.22, 14.98).

c. B. "The statement is incorrect. A correct statement would be​"One can be​ 95% confident that the true mean number of people named per person will fall in the interval computed in part b"

d. D. It does not impact the validity of the interpretation because the sampling space of the sample mean is approximately normal according to the Central Limit Theorem.

Step-by-step explanation:

a) The sample mean provides a point estimation of the population mean.

In this case, the estimation of the mean is:

[tex]\mu=\bar x =14.6[/tex]

b) With the information of the sample we can estimate the

As the sample size n=2824 is big enough, we can aproximate the t-statistic with a z-statistic.

For a 95% CI, the z-value is z=1.96.

The sample standard deviation is s=10.3.

The margin of error of the confidence is then calculated as:

[tex]E=z\cdot s/\sqrt{n}=1.96*10.3/\sqrt{2824}=20.188/53.141=0.38[/tex]

The lower and upper limits of the CI are:

[tex]LL=\bar x-z\cdot s/\sqrt{n}=14.6-0.38=14.22\\\\UL=\bar x+z\cdot s/\sqrt{n}=14.6+0.38=14.98[/tex]

The 95% CI for the population mean is (14.22, 14.98).

c. "95% of the​ time, the true mean number of people named per person will fall in the interval computed in part b"

The right answer is:

B. "The statement is incorrect. A correct statement would be​"One can be​ 95% confident that the true mean number of people named per person will fall in the interval computed in part b"

The confidence interval gives bounds within there is certain degree of confidence that the true population mean will fall within.

It does not infer nothing about the sample means or the sampling distribution. It only takes information from a sample to estimate a interval for the population mean with certain degree of confidence.

d. It is unlikely that the personal network sizes of adults are normally distributed. In​ fact, it is likely that the distribution is highly skewed. If​ so, what​ impact, if​ any, does this have on the validity of inferences derived from the confidence​ interval?

The answer is:

D. It does not impact the validity of the interpretation because the sampling space of the sample mean is approximately normal according to the Central Limit Theorem.

The reliability of a confidence interval depends more on the sample size, not on the distribution of the population. As the sample size increases, the absolute value of the skewness and kurtosis of the sampling distribution decreases. This sample size relationship is expressed in the central limit theorem.

The point estimate for μ is 14.6. The confidence interval will provide the range where the true mean falls with 95% confidence. The Central Limit Theorem suggests that the deviation from the normal distribution will not significantly affect the answers.

a- The point estimate for μ is x=14.6. This is calculated as the mean of all measured values.

b- An interval estimate can be calculated with the formula: x ± Z*(s/√n) where Z is the Z-value from a Z-table corresponding to desired confidence level, here, 0.95. The result would give you the range in which the true mean, μ, falls with 95% confidence.

c- The correct answer is B: The statement is incorrect. A correct statement would be "One can be 95% confident that the true mean number of people named per person will fall in the interval computed in part b."

d- If the personal network sizes of adults are not normally distributed and the distribution is highly skewed, it will have an impact on the validity of inferences derived from the confidence interval. The correct answer is D: It does not impact the validity of the interpretation as the sampling space of the sample mean will still be approximately normal due to the Central Limit Theorem.

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Answer:

Approximately 20,579 units.

Answer:

y =20

Step-by-step explanation:

5(y+4)=6y

Distribute

5y +20 = 6y

Subtract 5y from each side

5y-5y+20=6y-5y

20 =y

Answer:

solution

5y+20=6y

5y-6y=20

-y=20

Answer:

0.7

Step-by-step explanation:

0.3+0.7=1.0=100%

Final answer:

The probability of not winning the game that Martin is playing is 0.7 or 70%, which is obtained by subtracting the probability of winning (0.3) from 1.

Explanation:

If Martin is playing a game where the probability of winning is 0.3, then the probability of not winning can be calculated by subtracting the probability of winning from 1. This is because the sum of the probabilities of all possible outcomes must equal 1. Since the probability of winning is 0.3, we calculate the probability of not winning as follows:

Therefore, the probability of not winning is 0.7 or 70%.

Answer:

The sample size is smaller than 30, so we need to assume that the underlying population is normally distributed.

The  sampling distribution of x overbar will be approximately normally distributed with mean 63 and standard deviation 5.69.

Step-by-step explanation:

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

In this problem

The sample size is smaller than 30, so we need to assume that the underlying population is normally distributed.

If it is:

[tex]\mu = 63, \sigma = 18, n = 10, s = \frac{18}{\sqrt{10}} = 5.69[/tex]

The  sampling distribution of x overbar will be approximately normally distributed with mean 63 and standard deviation 5.69.

It's a parallelogram, opposite sides congruent.

6x - 7 = 2x + 9

4x = 16

x = 4

12 = y + 3

9 = y

Answer: x=4, y=9

Answer:

x = 4 and y = 9

Step-by-step explanation:

This is a parallelogram, which we can tell because of the arrows. Basically, opposite sides are parallel. By definition, then, opposite sides of this polygon are equal: LM = ON and LO = MN. That means we can set the various expressions equal to each other:

LM = ON  ⇒  6x - 7 = 2x + 9  ⇒  4x = 16  ⇒  x = 4

LO = MN  ⇒  12 = y + 3  ⇒  y = 9

Thus, x = 4 and y = 9.

Hope this helps!

Answer:

30 square inch

Step-by-step explanation:

[tex]area \: of \: base = 6 \times 5 = 30 \: {inch}^{2} \\ [/tex]

The P-value for this hypothesis test is 0.0228.

To find the P-value for this hypothesis test, we need to calculate the proportion of alumni who favored firing the coach in the sample. Out of 100 alumni, 64 were in favor. So, the sample proportion is 64/100 = 0.64.

Now, we need to calculate the test statistic, which follows a normal distribution. The formula for the test statistic is: z = (p' - p) / sqrt(p * (1-p) / n), where p' is the sample proportion, p is the claimed proportion under the null hypothesis, and n is the sample size.

Plugging in the values, we get: z = (0.64 - 0.50) / sqrt(0.50 * (1-0.50) / 100) = 2.00

The P-value is the probability of observing a test statistic as extreme as 2.00, assuming the null hypothesis is true. We can look up this probability in a standard normal distribution table or use a statistical software. In this case, the P-value is 0.0228.

Answer:

2/5

Step-by-step explanation:

The total number of candies are 2+1+2 = 5 candies

P (peppermint) = number of peppermints/total

                        =2/5

Answer:

2/5

Step-by-step explanation:

The probability is 2/5.There are five in all and two peppermint.Put it as a fraction and you get 2/5.

Answer:

[tex]3,125[/tex]

Step-by-step explanation:

If you want to fill a pool, you will use the formula for finding the volume:

[tex]v=l*w*h[/tex]

In this case, height being depth:

[tex]v=l*w*d[/tex]

Insert values

[tex]v=50*25*2.5[/tex]

Simplify

[tex]v=1,250*2.5\\v=3,125[/tex]

You would need a lot of water.

Answer:

3125000 liter

Step-by-step explanation:

hope i helped

if i can be brainliest that would be great

Answer:

it is 61.3

Step-by-step explanation:

the answer is 89

Step-by-step explanation:

it does not matter if the number is negative the absolute value is the number inside the lines

Answer:

The absolute value of this one is 89. Because for example: |-3|=3 because any number is in that sign || the number will turn to positive. For example, If it is |-3| it will turn to 3

Given:

Given that the table with values of x and y.

We need to determine the relationship between x and y.

Slope:

The slope of the relation can be determined using the formula,

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

Substituting the points (2,11) and (4,9), we get;

[tex]m=\frac{9-11}{4-2}[/tex]

[tex]m=\frac{-2}{2}[/tex]

[tex]m=-1[/tex]

Thus, the slope of the relation is m = -1.

y - intercept:

The y - intercept of the relation is the value of y when x = 0.

Hence, from the table, it is obvious that when x = 0, the value of y is 13.

Thus, the y - intercept of the relation is b = 13.

Relationship between x and y:

The relationship between x and y can be determined using the formula,

[tex]y=mx+b[/tex]

Substituting m = -1 and y =13, we get;

[tex]y=-x+13[/tex]

Thus, the relationship between x and y is [tex]y=-x+13[/tex]

The probability of first selecting a chocolate chip cookie and then selecting a sugar cookie from a box containing 24 cookies in total is 6/46 or approximately 0.1304.

The question refers to calculating the probability of selecting cookies of different flavors one after the other without replacement from a box. To begin with, we must find the probability of selecting a chocolate chip cookie followed by the probability of selecting a sugar cookie after one chocolate chip cookie has been removed.

Firstly, the total count of cookies is 12 chocolate chip + 6 peanut butter + 6 sugar cookies = 24 cookies. The probability (P) of selecting a chocolate chip cookie first is P(chocolate chip) = 12/24 = 1/2. After eating the chocolate chip cookie, there are 23 cookies left and the probability of then selecting a sugar cookie is P(sugar) = 6/23 since there are 6 sugar cookies left out of the remaining 23 cookies.

Since these events are sequential without replacement, we can find the combined probability of both events by multiplying the probabilities of each event. Thus, the combined probability is P(chocolate chip then sugar) = P(chocolate chip) *P(sugar) = (1/2) * (6/23) = 6/46.

The combined probability of first selecting a chocolate chip cookie and then selecting a sugar cookie is therefore 6/46 or about 0.1304.

Answer:

8b+7p=20

p=2b

Step-by-step explanation:

You're welcome. Thou shall complete thou work without any trouble.

Answer:

It is shown in the explanation

Step-by-step explanation:

p(s) = s² + bs + c

a = 1

b = b

c = c

We get Δ as follows

Δ = (b²-4*a*c) = b² - 4*1*c = b² - 4c > 0  ⇒   b² > 4c  ⇔ c > 0

s = (-b + √(b² - 4c))/2(1)

⇒   s₁ = (-b + √(b² - 4c))/2

s₂ = (-b - √(b² - 4c))/2(1)

⇒   s₂ = (-b - √(b² - 4c))/2

We have that -b < 0  ⇔ b > 0

then s₁ < 0 and s₂ < 0 ⇔ c > 0 and b > 0

Answer:

For roots to lie on the left half plane, b ⊃ 0 and c ⊃0

Step-by-step explanation:

From quadratic formula, we have;

x = -b±√(b²-4ac)/2a

From the given expression p(s) = s² + bs + c,

x = s

a = 1

b = b

c = c

The quadratic formula can then be written as;

s =  -b±√(b²-4*1*c)/2*1

   =  -b±√(b²-4c)/2

s₁ =  -b+√(b²-4c)/2

s₂ =  -b±√(b²-4c)/2

From the equation above,

Sum of root = -b

Product of root = c

If both the root lie on left side of the s-plane, then sum of roots will be negative. Hence, -b ∠0. That is, b ⊃0

Also, the product root will be positive, c ⊃ 0

Hence, for roots to lie on the left half plane, b ⊃ 0 and c ⊃0

Use Hooke's law... (just kidding)

Break down each force vector into horizontal and vertical components.

[tex]\vec F_1=(1000\,\mathrm N)(\cos30^\circ\,\vec x+\sin30^\circ\,\vec y)\approx(866.025\,\mathrm N)\,\vec x+(500\,\mathrm N)\,\vec y[/tex]

[tex]\vec F_2=(1500\,\mathrm N)(\cos160^\circ\,\vec x+\sin160^\circ\,\vec y)\approx(-1409.54\,\mathrm N)\,\vec x+(513.03\,\mathrm N)\,\vec y[/tex]

[tex]\vec F_3=(750\,\mathrm N)(\cos195^\circ\,\vec x+\sin195^\circ\,\vec y)\approx(-724.444\,\mathrm N)\,\vec x+(-194.114\,\mathrm N)\,\vec y[/tex]

The resultant force is the sum of these vectors,

[tex]\vec F=\displaystyle\sum_{i=1}^3\vec F_i\approx(-1267.96\,\mathrm N)\,\vec x+(818.916\,\mathrm N)\,\vec y[/tex]

and has magnitude

[tex]|\vec F|\approx\sqrt{(-1267.96\,\mathrm N)^2+(818.916\,\mathrm N)^2}\approx1509.42\,\mathrm N[/tex]

The closest answer is D.

To determine the magnitude of the resultant force acting on a hook when three forces are applied, you can use vector addition. If you have the information of the forces and the angles between them, you can calculate the resultant force using trigonometric functions.

To determine the magnitude of the resultant force when three forces act on a hook, you must realize that forces are vector quantities. This means that they have both a magnitude (how much force is being applied) and a direction (the direction the force is being applied in).

If the forces are concurrent (i.e., they act at the same point), one usually uses the parallelogram law or the triangle rule to find the resultant force. You can add two forces to create a resultant, then add the third force to that resultant to find the total resultant. If the forces and the angles between them are known, you can use trigonometric functions to calculate the resultant force.

For instance, if the three forces are F1, F2, and F3, and the angles between them are θ1, θ2, and θ3, the resultant force R can be found using the following equation:

R = √[ (F1 + F2cosθ2 + F3cosθ3)^2 + (F2sinθ2 + F3sinθ3)^2 ]

This equation will give the magnitude of the resultant force. Please note that to use this equation, you must have enough information about the forces and the angles between them.

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Answer:

x = 4

Step-by-step explanation:

14x - 15 + 139 = 180

(Alternate & Supplementary angles)

14x = 56

x = 4

Answer:

To find why the crimes were committed

Answer:

The player should be required to pay $5 to make this a fair game.

Step-by-step explanation:

U ~ Uniform(0, 10)

E[U] = (0 + 10)/2

         = 5

X | U ~ Poisson(U)

E[X | U] = U

By law of total probability for expectations,

E[X] = E[E[X|U]] = E[U] = $5

Therefore the player should be required to pay $5 to make this a fair game.

Answer:

a) 30.50% probability that  at least 150 stay on the line for more than one minute.

b) 0% probability that more than 200 stay on the line for more than one minute.

Step-by-step explanation:

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

Can be approximated to a normal distribution, using the expected value and the standard deviation.

The expected value of the binomial distribution is:

[tex]E(X) = np[/tex]

The standard deviation of the binomial distribution is:

[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]

Normal probability distribution

Problems of normally distributed samples can be 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.

When we are approximating a binomial distribution to a normal one, we have that [tex]\mu = E(X)[/tex], [tex]\sigma = \sqrt{V(X)}[/tex].

In this problem, we have that:

[tex]n = 800, p = 0.18[/tex]

So

[tex]\mu = E(X) = np = 800*0.18 = 144[/tex]

[tex]\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{800*0.18*0.82} = 10.87[/tex]

a. at least 150 stay on the line for more than one minute.

Using continuity correction, [tex]P(X \geq 150 - 0.5) = P(X \geq 149.5)[/tex], which is 1 subtracted by the pvalue of Z when X = 149.5. So

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

[tex]Z = \frac{149.4 - 144}{10.87}[/tex]

[tex]Z = 0.51[/tex]

[tex]Z = 0.51[/tex] has a pvalue of 0.6950

1 - 0.6950 = 0.3050

30.50% probability that  at least 150 stay on the line for more than one minute.

b. more than 200 stay on the line.

Using continuity correction, [tex]P(X \geq 200 + 0.5) = P(X \geq 200.5)[/tex], which is 1 subtracted by the pvalue of Z when X = 200.5. So

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

[tex]Z = \frac{200.5 - 144}{10.87}[/tex]

[tex]Z = 5.2[/tex]

[tex]Z = 5.2[/tex] has a pvalue of 1

1 - 1 = 0

0% probability that more than 200 stay on the line for more than one minute.

Given:

Given that two similar cylinder have surface areas 24π cm² and 54π cm².

The volume of the smaller cylinder is 16π cm³

We need to determine the volume of the larger cylinder.

Volume of the larger cylinder:

The ratio of the two similar cylinders having surface area of 24π cm² and 54π cm², we have;

[tex]\frac{24 \pi}{54 \ pi}=\frac{4}{9}[/tex]

       [tex]=\frac{2^2}{3^2}[/tex]

Thus, the ratio of the surface area of the two cylinders is [tex]\frac{2^2}{3^2}[/tex]

The volume of the larger cylinder is given by

[tex]\frac{2^2}{3^2}\times \frac{2}{3}=\frac{16 \pi }{x}[/tex]

where x represents the volume of the larger cylinder.

Simplifying, we get;

[tex]\frac{2^3}{3^3}=\frac{16 \pi }{x}[/tex]

[tex]\frac{8}{27}=\frac{16 \pi }{x}[/tex]

Cross multiplying, we get;

[tex]8x=16 \pi \times 27[/tex]

[tex]8x=432 \pi[/tex]

 [tex]x=54 \pi \ cm^3[/tex]

Thus, the volume of the larger cylinder is 54π cm³

Answer:

54π cm³

Step-by-step explanation:

The day when they would meet first time after joining the gym together will be 12.

The analysis of mathematical representations is algebra, and the handling of those symbols is logic.

Kirk goes to the gym every 3 days.

Deshawn goes to the gym every 4 days.

If they join the gym on the same day.

Then the day when they would meet first time after joining the gym together will be

LCM of 4, 3 will be 12.

Then the day will be 12.

More about the Algebra link is given below.

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Final answer:

Kirk and Deshawn will be at the gym together on the 12th day since they joined.

Explanation:

Gym memberships for Kirk and Deshawn occur every 3 days and 4 days respectively. To find the first day they'll be at the gym together, we need to find the lowest common multiple of 3 and 4.

LCM(3, 4) = 12. Therefore, Kirk and Deshawn will be at the gym together on the 12th day since they joined the gym.

Answer:

a. length  = 0.7211 ft

b. width  = 0.7211 ft

c. height = 140.3846 ft

Step-by-step explanation:

This is an optimiztion with restriction problem.

We have to minimize the cost, with the restriction of the volume being equal to 72 ft3.

As the cost for the sides is constant, we know that length and width are equal.

Then, we can express the volume as:

[tex]V=x\cdot y\cdot z=x^2z=73[/tex]

being x: length and z: height

We can express the height in function of the length as:

[tex]x^2z=73\\\\z=73x^{-2}[/tex]

Then, the cost of the box can be expressed as:

[tex]C=0.62(x^2)+4*0.15(xz)+0.18(x^2)=(0.62+0.18)x^2+0.60xz\\\\C=0.8x^2+0.60x*x^{-2}=0.8x^2+0.6x^{-1}[/tex]

To optimize C, we derive and equal to zero

[tex]\dfrac{dC}{dx}=\dfrac{d}{dx}[0.8x^2+0.6x^{-1}]=1.6x-0.6x^{-2}=0\\\\\\1.6x=0.6x^{-2}\\\\x^{1+2}=0.6/1.6=0.375\\\\x=\sqrt[3]{0.375} =0.7211[/tex]

The height z is then

[tex]z=73x^{-2}=\dfrac{73}{0.7211^2}=\dfrac{73}{0.52}=140.3846[/tex]

Answer:

BC = 9

Step-by-step explanation:

Assuming this is a straight line

AB + BC = AC

2x-6 + x+2 = 17

Combine like terms

3x -4 = 17

Add 4 to each side

3x-4+4 = 17+4

3x = 21

Divide each side by 3

3x/3 =21/3

x =7

We want to find BC

BC =x+2

     =7+2

     =9

Answer:

a) 0.214 or 21.4%

b) P=0.011

c) The realtor should sample at least 551 homes.

Step-by-step explanation:

The current thinking is that housing prices follow an approximately normal model with mean $238,000 and standard deviation $5,041.

a) We need to know the proportion of housing prices in Athens that are less than $234,000. We can calculate this from the z-score for the population distribution.

[tex]z=\dfrac{X-\mu}{\sigma}=\dfrac{234,000-238,000}{5,041}=\dfrac{-4,000}{5.041}=-0.793\\\\\\ P(x<234,000)=P(z<-0.793)=0.214[/tex]

The proportion of housing prices in Athens that are less than $234,000 is 0.214.

b) Now, a sample is taken. The size of the sample is n=134.

We have to calculate the probability that the average selling price is greater than $239,000.

In this case, we have to use the standard error of the sampling distribution to calculate the z-score:

[tex]z=\dfrac{\bar x-\mu}{\sigma/\sqrt{n}}=\dfrac{239,000-238,000}{5,041/\sqrt{134}}=\dfrac{1,000}{435.476}= 2.296 \\\\\\P(\bar x>239,000)=P(z>2.296)=0.011[/tex]

The probability that the average selling price is greater than $239,000 is 0.011.

c) We have another sample taken from a distribution with the same parameters.

We have to calculate the sample size so that the margin of error for a 98% confidence interval is $500.

The expression for the margin of error of the confidence interval is:

[tex]E=z\cdot \sigma/\sqrt{n}[/tex]

We can isolate n from the margin of error equation as:

[tex]E=z\cdot \sigma/\sqrt{n}\\\\\sqrt{n}=\dfrac{z\cdot \sigma}{E}\\\\n=(\dfrac{z\cdot \sigma}{E})^2[/tex]

We have to look for the critical value of z for a 98% CI. This value is z=2.327.

Now we can calculate the minimum value for n to achieve the desired precision for the interval:

[tex]n=(\dfrac{z\cdot \sigma}{E})^2\\\\\\n=(\dfrac{2.327*5,041}{500})^2= 23.461 ^2=550.410\approx551[/tex]

The realtor should sample at least 551 homes.

Answer:

a) 0.214 or 21.4%

b) P=0.011

c) The realtor should sample at least 551 homes

Step-by-step explanation:

The Answer is : ABC = 40