A total of 1 232 students have taken a course in Spanish, 879 have taken a course in French, and 114 have taken a course in Russian. Further, 103 have taken courses in both Spanish and French, 23 have taken courses in both Spanish and Russian, and 14 have taken courses in both French and Russian. If 2 092 students have taken at least one of Spanish, French, and Russian, how many students have taken a course in all three languages

Final answer:

To find the total cost of the watch and the clock, set up equations based on the given relationships, solve for the individual costs, and then add them together. The total cost amounts to $176.

Explanation:

The student is asking to find the total cost of two items - a watch and a clock. The clock costs 4/7 of what the watch costs, and the watch costs $48 more than the clock. Let's denote the cost of the clock as c and the cost of the watch as w. The problem gives us two equations: w = c + $48 and c = (4/7)w. Now, we can solve these equations to find the individual costs of the clock and the watch, then sum them to find the total cost.

Step-by-step Solution

Substitute the value of c from the second equation into the first equation: w = (4/7)w + $48.

Multiply both sides of the equation by 7 to eliminate the fraction: 7w = 4w + $336.

Subtract 4w from both sides: 3w = $336.

Divide both sides by 3 to find the cost of the watch: w = $112.

Now that we have the cost of the watch, we can substitute it back into the equation c = (4/7)w to find the cost of the clock: c = (4/7) x $112 = $64.

The total cost of both items is the sum of the cost of the clock and the cost of the watch: w + c = $112 + $64 = $176.

Therefore, the total cost of the watch and the clock together is $176.

Answer:

Step-by-step explanation:

FIRST FOR ORANGES SHE BOUGHT 10 SO 10 TIMES 3 IS 30 AND THEN 11 TIMES 2.40 IS 26.40. 30 PLUS 26.40 IS 56.40 THATS YOUR AWNSER

Answer:

The median of the following set of data is 9 since the question is implying, which is the center of the data distribution.

Step-by-step explanation:

Given:

Given that the radius of the merry - go - round is 5 feet.

The arc length of AB is 4.5 feet.

We need to determine the measure of the minor arc AB.

Measure of the minor arc AB:

The measure of the minor arc AB can be determined using the formula,

[tex]Arc \ length=(\frac{\theta}{360})2 \pi r[/tex]

Substituting arc length = 4.5 and r = 5, we get;

[tex]4.5=(\frac{\theta}{360})2 (3.14)(5)[/tex]

Multiplying the terms, we get;

[tex]4.5=(\frac{\theta}{360})31.4[/tex]

Dividing, we get;

[tex]4.5=0.087 \theta[/tex]

Dividing both sides of the equation by 0.087, we get;

[tex]51.7=\theta[/tex]

Rounding off to the nearest degree, we have;

[tex]52=\theta[/tex]

Thus, the measure of the minor arc AB is 52°

Answer:

52°

Step-by-step explanation:

Arc length = (theta/360) × 2pi × r

4.5 = (theta/360) × 2 × 3.14 × 5

theta/360 = 45/314

Theta = 51.59235669

Answer:

434.98

Step-by-step explanation:

Answer:

  The sum of half of a number and three-fourths is at least five and one quarter

Step-by-step explanation:

It's all about making sense of an English sentence.

  "half the sum ..." is different from "the sum of half ..."

And ...

  "at least" and "not less than" mean the same (≥)

  "not more than" and "at most" mean the same (≤)

_____

Since all of the expressions are written out in words, it is a matter of matching the ideas expressed. That's a problem in reading comprehension, not math.

__

"One-half x + three-fourths [is] greater-than-or-equal-to 5 and one-fourth"

  means the same as ...

"The sum of half of a number and three-fourths is at least five and one quarter"

Final answer:

The correct sentence for the inequality one-half x + three-fourths ≥ 5 and one-fourth is 'The sum of half of a number and three-fourths is at least five and one quarter'.

Explanation:

The correct representation of the inequality one-half x + three-fourths ≥ 5 and one-fourth (0.5x + 0.75 ≥ 5.25) in a sentence is The sum of half of a number and three-fourths is at least five and one quarter. This means that when you take half of a certain number (which we call x), add three-fourths to it, the result should be no less than five and one quarter. The other options either incorrectly suggest that the inequality is an equation, or misrepresent the inequality by suggesting the sum is 'at most' or not more or less than the given value, which changes the meaning of the original inequality.

Answer:

3.75

Step-by-step explanation:

Hope this helps

The probability that both students will not wear blue is 0.36, obtained by multiplying the probability of one student not wearing blue, 0.60, by itself.

To find the probability that both students will not be wearing blue, we first need to determine the probability that one student is not wearing blue, and then multiply that probability by itself for two students.

Step 1: Calculate the probability that one student is not wearing blue.

Given that 40% of students wore blue, the probability that one student is not wearing blue is 1 - 0.40 = 0.60.

Step 2: Multiply the probability for one student by itself for two students.

The probability that both students will not be wearing blue is (0.60) ×(0.60) = 0.36.

So, the probability that both students will not be wearing blue is 0.36.

The center of mass of the lamina is located at the point (0, (39/12) (1 / ln(4))).

To find the center of mass of the given lamina, we need to calculate the moment about the x-axis and the y-axis, and then divide them by the total mass of the lamina.

Given information:

- The boundary of the lamina consists of the semicircles y = sqrt(1 - x^2) and y = sqrt(16 - x^2), and the portions of the x-axis that join them.

- The density at any point is inversely proportional to its distance from the origin.

Find the total mass of the lamina.

Let the density function be [tex]\[ \rho(x, y) = \frac{k}{\sqrt{x^2 + y^2}} \][/tex], where k is a constant.

The total mass, M, is given by the double integral of the density function over the region of the lamina.

M = ∫∫ ρ(x, y) dA

To evaluate this integral, we need to express the lamina in polar coordinates.

The semicircles can be represented as:

0 ≤ r ≤ 1, 0 ≤ θ ≤ π

0 ≤ r ≤ 4, π ≤ θ ≤ 2π

The total mass can be calculated as:

[tex]\[ M = \int_{0}^{\pi} \int_{0}^{1} \frac{k}{r} r \, dr \, d\theta + \int_{\pi}^{2\pi} \int_{0}^{4} \frac{k}{r} r \, dr \, d\theta \]\[ M = k \left( \pi \ln(1) + 2\pi \ln(4) \right) \]\[ M = 2\pi k \ln(4) \][/tex]

Calculate the moment about the x-axis.

The moment about the x-axis, Mx, is given by:

[tex]\[ M_x = \int_{0}^{\pi} \int_{0}^{1} \frac{k}{r} r^2 \sin(\theta) \, dr \, d\theta + \int_{\pi}^{2\pi} \int_{0}^{4} \frac{k}{r} r^2 \sin(\theta) \, dr \, d\theta \]\[ M_x = k \left( \frac{\pi}{2} + \frac{32\pi}{3} \right) \]\[ M_x = \frac{39\pi}{6} k \][/tex]

Calculate the moment about the y-axis.

The moment about the y-axis, My, is given by:

My = ∫∫ x ρ(x, y) dA

In polar coordinates:

[tex]\[ M_y = \int_{0}^{\pi} \int_{0}^{1} \frac{k}{r} r^2 \cos(\theta) \, dr \, d\theta + \int_{\pi}^{2\pi} \int_{0}^{4} \frac{k}{r} r^2 \cos(\theta) \, dr \, d\theta \][/tex]

My = 0 (due to symmetry)

Find the coordinates of the center of mass.

The coordinates of the center of mass (x_cm, y_cm) are given by:

x_cm = My / M

y_cm = Mx / M

Substituting the values, we get:

x_cm = 0 / (2πk ln(4)) = 0

y_cm = (39π/6) k / (2πk ln(4)) = (39/12) (1 / ln(4))

Therefore, the center of mass of the lamina is located at the point (0, (39/12) (1 / ln(4))).

Complete question:

The boundary of a lamina consists of the semicircles y=sqrt(1 − x^2) and y= sqrt(16 − x^2) together with the portions of the x-axis that join them. Find the center of mass of the lamina if the density at any point is inversely proportional to its distance from the origin.

The center of mass of the lamina is at the origin (0, 0)

To find the center of mass of the lamina, we first need to find the mass and the moments about the  x- and  y-axes.

The mass  M of the lamina can be calculated by integrating the density function over the lamina. Since the density at any point is inversely proportional to its distance from the origin, we can express the density[tex]\( \delta \) as \( \delta(x, y) = \frac{k}{\sqrt{x^2 + y^2}} \)[/tex], where  k is a constant.

Let's denote [tex]\( \delta(x, y) \) as \( \frac{k}{\sqrt{x^2 + y^2}} \)[/tex]. Then the mass M  is given by the double integral of [tex]\( \delta(x, y) \)[/tex] over the region  R bounded by the semicircles and the portions of the x-axis:

[tex]\[ M = \iint_R \delta(x, y) \, dA \][/tex]

Where  dA  represents the differential area element.

To find the moments about the  x- and  y -axes, we calculate:

[tex]\[ M_x = \iint_R y \delta(x, y) \, dA \]\[ M_y = \iint_R x \delta(x, y) \, dA \][/tex]

Then, the coordinates [tex]\( (\bar{x}, \bar{y}) \)[/tex] of the center of mass are given by:

[tex]\[ \bar{x} = \frac{M_y}{M} \]\[ \bar{y} = \frac{M_x}{M} \][/tex]

Now, let's proceed to find [tex]\( M \), \( M_x \), and \( M_y \)[/tex]

First, let's express the density [tex]\( \delta(x, y) \)[/tex] in terms of k:

[tex]\[ \delta(x, y) = \frac{k}{\sqrt{x^2 + y^2}} \][/tex]

Now, we'll find the mass  M by integrating [tex]\( \delta(x, y) \)[/tex] over the region  R :

[tex]\[ M = \iint_R \frac{k}{\sqrt{x^2 + y^2}} \, dA \][/tex]

Since the region  R  is symmetric about the  x-axis, we can integrate over the upper half and double the result:

[tex]\[ M = 2 \iint_{R_1} \frac{k}{\sqrt{x^2 + y^2}} \, dA \][/tex]

Now, we'll switch to polar coordinates [tex]\( (r, \theta) \)[/tex]. In polar coordinates, the region [tex]\( R_1 \)[/tex]is described by [tex]\( 0 \leq \theta \leq \pi \) and \( 1 \leq r \leq 4 \).[/tex]

So, the integral becomes:

[tex]\[ M = 2 \int_{0}^{\pi} \int_{1}^{4} \frac{k}{r} \cdot r \, dr \, d\theta \]\[ = 2k \int_{0}^{\pi} \int_{1}^{4} 1 \, dr \, d\theta \]\[ = 2k \int_{0}^{\pi} (4 - 1) \, d\theta \]\[ = 2k \int_{0}^{\pi} 3 \, d\theta \]\[ = 6k \pi \][/tex]

For [tex]\( M_x \)[/tex], we integrate [tex]\( x \delta(x, y) \)[/tex] over the region R :

[tex]\[ M_x = \iint_R x \cdot \frac{k}{\sqrt{x^2 + y^2}} \, dA \]\[ = 2 \int_{0}^{\pi} \int_{1}^{4} r \cos(\theta) \cdot \frac{k}{r} \cdot r \, dr \, d\theta \]\[ = 2k \int_{0}^{\pi} \int_{1}^{4} \cos(\theta) \cdot r \, dr \, d\theta \]\[ = 2k \int_{0}^{\pi} \left[ \frac{1}{2} r^2 \cos(\theta) \right]_{1}^{4} \, d\theta \][/tex]

[tex]\[ = 2k \int_{0}^{\pi} \left( 8 \cos(\theta) - \frac{1}{2} \cos(\theta) \right) \, d\theta \]\[ = 2k \int_{0}^{\pi} \left( \frac{15}{2} \cos(\theta) \right) \, d\theta \]\[ = 2k \left[ \frac{15}{2} \sin(\theta) \right]_{0}^{\pi} \]\[ = 2k \cdot 0 \]\[ = 0 \][/tex]

Now, for[tex]\( M_y \)[/tex], we integrate [tex]\( y \delta(x, y) \)[/tex]over the region  R :

[tex]\[ M_y = \iint_R y \cdot \frac{k}{\sqrt{x^2 + y^2}} \, dA \\\[ = 2 \int_{0}^{\pi} \int_{1}^{4} r \sin(\theta) \cdot \frac{k}{r} \cdot r \, dr \, d\theta \\\[ = 2k \int_{0}^{\pi} \int_{1}^{4} \sin(\theta) \cdot r \, dr \, d\theta \\\[ = 2k \int_{0}^{\pi} \left[ \frac{1}{2} r^2 \sin(\theta) \right]_{1}^{4} \, d\theta \\[/tex]

[tex]\[ = 2k \int_{0}^{\pi} \left( 8 \sin(\theta) - \frac{1}{2} \sin(\theta) \right) \, d\theta \\\[ = 2k \int_{0}^{\pi} \left( \frac{15}{2} \sin(\theta) \right) \, d\theta \\\[ = 2k \left[ -\frac{15}{2} \cos(\theta) \right]_{0}^{\pi} \\\[ = 2k \cdot 0 \\\[ = 0 \][/tex]

Now, we have [tex]\( M = 6k \pi \), \( M_x = 0 \), and \( M_y = 0 \).[/tex]

Finally, we can find the coordinates of the center of mass [tex]\( (\bar{x}, \bar{y}) \):[/tex]

[tex]\[ \bar{x} = \frac{M_y}{M} = \frac{0}{6k \pi} = 0 \]\[ \bar{y} = \frac{M_x}{M} = \frac{0}{6k \pi} = 0 \][/tex]

So, the center of mass of the lamina is at the origin (0, 0) .

Answer: b. A 90% confidence level and a sample of 24 observations. 1.714 1.714 Correct

Step-by-step explanation:

Answer:

Step-by-step explanation:

Hello!

The researcher's objective is to test if the variance of the annual repair costs increases with the age of the automobile, i.e. the older the car, the more the repairs costs. The parameters of the study are the population variances of the annual repair costs of 4 years old cars and 2 years old cars.

X₁: Costs of annual repair of a 4 years old car.

Assuming X₁~N(μ₁;δ₁²)

A sample of 26 automobiles 4 years old showed a sample standard deviation for annual repair costs of $170

n₁= 26 and S₁= $170

X₂: Costs of annual repair of a 2 years old car.

Assuming X₂~N(μ₂;σ₂²)

A sample of 25 automobiles 2 years old showed a sample standard deviation for the annual repair cost of $100.

n₂= 25 and S₂= $100

a. State the null and alternative versions of the research hypothesis that the variance in annual repair costs is larger for older automobiles.

H₀: δ₁² ≤ σ₂²

H₁: δ₁² > σ₂²

b. At a .01 level of significance, what is your conclusion? What is the p-value? Discuss the reasonableness of your findings.

This is a variance ratio test and you have to use a Snedecor's F-statistic:

[tex]F= \frac{S^2_1}{S_2^2} * \frac{Sigma_1^2}{Sigma_2^2}~~F_{n_1-1;n_2-1}[/tex]

[tex]F_{H_0}= \frac{28900}{10000}*1= 2.89[/tex]

This test is one-tailed to the right and so is the p-value, you have to calculate it under a F₂₅;₂₄

P(F₂₅;₂₄≥2.89)= 1 - P(F₂₅;₂₄<2.89)= 1 - 0.994= 0.006

Using the p-value approach the decision rule is:

If p-value ≤ α, reject the null hypothesis.

If p-value > α, do not reject the null hypothesis.

α: 0.01

The p-value is less than the level of significance, the decision is to reject the null hypothesis.

Then using a 1% level, you can conclude that the population variance of the cost of annual repairs for 4 years old cars is greater than the population variance of the cost of annual repairs for 2 years old cars.

I hope this helps!

Answer:

$6.31

Step-by-step explanation:

We are going to use the compound simple interest formula for this problem:

[tex]A=P(1+\frac{r}{n} )^{nt}[/tex]

P = initial balance

r = interest rate (decimal)

n = number of times compounded annually

t = time

Our first step is to change 5% into its decimal form:

5% -> [tex]\frac{5}{100}[/tex] -> 0.05

Next, plug in the values:

[tex]A=40(1+\frac{0.05}{1})^{1(3)}[/tex]

[tex]A=46.31[/tex]

Lastly, subtract 40 (our original value) from 46.31:

[tex]46.31-40=6.31[/tex]

Victor earned $6.31 in interest after 3 years.

Answer: 27?

Step-by-step explanation:

Answer

The best estimate for 48 and 21 is 50 and 20.  50-20= 30 so 30 is ur answer

Step-by-step explanation:

Answer:

The truck will skid for 151 ft before stopping when the brakes are applied

Step-by-step explanation:

From the equations of motion, we will use

[tex]v^{2} = u^{2}-2aS[/tex]

We have to make sure that the parameters we are working with are in the same unit of length. Here, we will be converting from ft to miles

When the truck is travelling at 10 mph.

S = distance the truck skids = [tex]\frac{5ft}{5286ft/mile}= 0.00094697miles[/tex]

Final velocity of truck, v = 0 m/s (this is because the truck decelerates to a halt)

Initial velocity of truck u = 10 mph

Hence, we have

[tex]0^{2}=10^{2}-2a\times 0.00094697[/tex]

[tex]a= 52799.9miles/hr^{2}[/tex]

This is the deceleration of the truck

We will work based on the assumption that the car decelerates at the same rate each time the brakes are fully applied.

When the truck is travelling at u= 55 mph.

We will need to use the deceleration of the car to find the distance traveled when it skids.

[tex]0^{2}=55^{2}-2\times52799.98\times S[/tex]

[tex]S= 0.0286 miles\approx 151 ft[/tex]

∴The car skids for about 151 ft when it is travelling at 55 mph and the brakes are applied.

Answer:

a) Type 1 Error: 1.5%

b) Type 2 Error: 5.5%

Step-by-step explanation:

Probability of positive reaction when infact the person has disease = 94.5%

This means, the probability of negative reaction when infact the person has disease = 100- 94.5% = 5.5%

Probability of positive reaction when the person does not have the disease = 1.5%

This means,

Probability of negative reaction when the person does not have disease = 100% - 1.5% = 98.5%

Our Null Hypothesis is:

"The individuals does not have the disease"

Part a) Probability of Type 1 Error:

Type 1 error is defined as: Rejecting the null hypothesis when infact it is true. Therefore, in this case the Type 1 error will be:

Saying that the individual have the disease(positive reaction) when infact the individual does not have the disease. This means giving a positive reaction when the person does not have the disease.

From the above data, we can see that the probability of this event is 1.5%. Therefore, the probability of Type 1 error is 1.5%

Part b) Probability of Type 2 Error:

Type 2 error is defined as: Accepting the null hypothesis when infact it is false. Therefore, in this case the Type 2 error will be:

Saying that the individual does not have the disease(negative reaction) when infact the individual have the disease.

From the above data we can see that the probability of this event is 5.5%. Therefore, the probability of Type 2 error is 5.5%

Answer:

The final integration in the given limits will be 89.876

Answer:

We conclude that % of DC area adults who have traveled outside of the United States is different from 40%.

Step-by-step explanation:

We are given that 40% of DC area adults have traveled outside of the United States. Nardole wants to know if his customers are typical in this respect. He surveys 40 customers and finds 60% have traveled outside of the U.S.

We have to test is this result a statistically significant difference.

Let p = % of DC area adults who have traveled outside of the United States

SO, Null Hypothesis, [tex]H_0[/tex] : p = 40%  {means that 40% of DC area adults have traveled outside of the United States}

Alternate Hypothesis, [tex]H_a[/tex] : p [tex]\neq[/tex] 40%  {means that % of DC area adults who have traveled outside of the United States is different from 40%}

The test statistics that will be used here is One-sample z proportion statistics;

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

where, [tex]\hat p[/tex] = % of customers who have traveled outside of the United States

                  in a survey of 40 customers = 60%

          n  = sample of customers = 40

So, test statistics = [tex]\frac{0.60-0.40}{\sqrt{\frac{0.60(1-0.60)}{40} } }[/tex]

                             = 2.582

Since in the question we are not given with the significance level so we assume it to be 5%. So, at 0.05 level of significance, the z table gives critical value of 1.96 for two-tailed test. Since our test statistics is more than the critical value of z so we have sufficient evidence to reject null hypothesis as it will fall in the rejection region.

Therefore, we conclude that % of DC area adults who have traveled outside of the United States is different from 40%.

Answer:

Step-by-step explanation:

Table(2) shows the relative frequency opted from the table(1).

It is defined as the number of waves that crosses a fixed point in one second known as frequency. The unit of frequency is per second.

We have a table in which data has shown:

To find the relative frequency:

For the first cell:

[tex]=\frac{67}{92} \times100 \approx 73\%[/tex]

For the second cell:

= 100 - 73 ⇒ 27%

For the third cell:  

[tex]\rm = \frac{46}{66} \times 100 \approx 70\%[/tex]

For the fourth cell:

= 100 - 70 = 30%

Thus, table(2) shows the relative frequency opted from table(1).

Learn more about the frequency here:

brainly.com/question/27063800

Answer:

0.0668

Step-by-step explanation:

Assuming the distribution is normally distributed with a mean of $75,

with a standard deviation of $12.

We can find the z-score of 78 using;

[tex]z=\frac{x-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex]

[tex]\implies z=\frac{78-75}{\frac{12}{36} } =1.5[/tex]

Using our normal distribution table, we obtain the area that corresponds to 0.25 to be 0.9332

This is the area corresponding to the probability that, the average is less or equal to 78.

Subtract from 1 to get the complement.

P(x>78)=1-0.9332=0.0668

The probability that the average sales per customer from a sample of 36 customers, taken at random from this population, exceeds $78 is 0.0668.

Since The average sales per customer at a home improvement store during the past year is $75 with a standard deviation of $12.

Here  we need to find out the z score

= [tex]78-75\div 12\div 36[/tex]

= 1.5

Here we considered normal distribution table, we obtain the area that corresponds to 0.25 to be 0.9332

So,  the average is less or equal to 78.

Now

Subtract from 1 to get the complement.

So,

P(x>78)=1-0.9332

=0.0668

Learn more about probability here: https://brainly.com/question/24613748

Answer: It would make the meal $40.00 and with tax it would be $42.80

Step-by-step explanation: 50 - 10 = 40

                                              40 / 0.07 = 2.8

                                              40 + 2.8 = 42.8

Answer:

Step-by-step explanation:

Answer:

Answer : D

Step-by-step explanation:

A school has two kindergarten classes. There are 21 children in Ms. Toodle's kindergarten class. Of these, 17 are "pre-readers" children on the verge of reading. There are 19 children in Mr. Grimace's kindergarten class. Of these, 13 are pre-readers. Using the plus four confidence interval method, a 90% confidence interval for the difference in proportions of children in these classes that are pre-readers is â0.104 to 0.336.  

Which of the following statements is correct?

A) This confidence interval is not reliable because the samples are so small.  

B)This confidence interval is of no use because it contains 0, the value of no difference between classes.  

C)This confidence interval is reasonable because the sample sizes are both at least 5.  

D) This confidence interval is not reliable because these samples cannot be viewed as simple random samples taken from a larger population.

The Answer is D - This confidence interval is not reliable because these samples cannot be viewed as simple random samples taken from a larger population.

In this setup, all the students are already involved in the data. This is not a sample from a larger population, but probably, the population itself.

Answer:

10.0

Step-by-step explanation:

4.0+8.0=12.0-2.0=10.0

Answer: G=21

Step-by-step explanation:

Solve for G by simplifying both sides of the equation, then isolating the variable.

Answer:

Hire 2 more employees.

Step-by-step explanation:

Multiply 45 by 8 to find out how many shirts 1 employee can fold for one day, one employee can fold 360 shirts in one day, then multiply that by 3 to see how many shirts they can fold a day with only the three employees. They can fold 1080 shirts in one day.

1600-1080= 520. Subtracting the demand by how many his store already can fold shows how many more he needs.

1 employee isn't enough because they can only fold 360 shirts a day so he would need to hire 2 employees because they can fold 720 shirts which meets the demand of shirts that need to be folded.

To calculate the probability that the sample mean would differ from the true mean by greater than $38, if a sample of 208 persons is randomly selected, we need to use the Central Limit Theorem. First, we determine the standard error of the mean (SEM) using the formula SEM = standard deviation / square root of sample size. Then, we calculate the Z-score using the formula Z = (sample mean - true mean) / SEM. Finally, we find the probability associated with the Z-score using a Z-table or calculator.

To calculate the probability that the sample mean would differ from the true mean by greater than $38, if a sample of 208 persons is randomly selected, we need to use the Central Limit Theorem.

According to the Central Limit Theorem, the distribution of sample means will be approximately normal regardless of the shape of the population distribution, as long as the sample size is large enough.

Since the sample size is greater than 30, we can assume that the distribution of sample means will be approximately normal.

To calculate the probability, we first need to determine the standard error of the mean (SEM), which is the standard deviation divided by the square root of the sample size. In this case, the SEM = $397 / √208.

Next, we calculate the Z-score using the formula Z = (sample mean - true mean) / SEM = ($38 - 0) / ($397 / √208). Finally, we can use a Z-table or calculator to find the probability associated with the Z-score.

In this case, it is the probability that Z is greater than the calculated Z-score. Hence, the probability that the sample mean would differ from the true mean by greater than $38 is the probability that Z is greater than the calculated Z-score.

Answer:

$420

Step-by-step explanation:

To work this out you would need to find the 25% decrease of 560. To do this you would first divide 25 by 100, which gives you 0.25. Then you would minus 0.25 from 1, which gives you 0.75. This is because when finding percentage decreases you would first have to convert it into a decimal. Then you would have to minus it from 1 , to make sure that it will be a 25% decrease not a 75% decrease. Then you would multiply 560 by 0.75, which gives you 420.

1) Divide 25 by 100.

[tex]25/100=0.25[/tex]

2) Minus 0.25 from 1.

[tex]1-0.25=0.75[/tex]

3) Multiply 560 by 0.75.

[tex]560*0.75=$420[/tex]

Answer:

28.57% probability that the oldest is a girl and the youngest is a boy​, given that there is at least one boy and at least one girl.

Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

These are all the possible outcomes: from youngest to oldest, b is boy and g is girl

b - b - b - g

b - b - g - b

b - b - g - g

b - g - b - b

b - g - b - g

b - g - g - b

b - g - g - g

g - b - b - b

g - b - b - g

g - b - g - b

g - b - g - g

g - g - b - b

g - g - b - g

g - g - g - b

The nuber of total outcomes is 14.

Desired outcomes:

Oldest(last) girl, youngest(first) boy

b - b - b - g

b - b - g - g

b - g - b - g

b - g - g - g

So 4 desired outcomes

Probability:

4/14 = 0.2857

28.57% probability that the oldest is a girl and the youngest is a boy​, given that there is at least one boy and at least one girl.

Final answer:

The probability that a family with four children will have the oldest being a girl and the youngest being a boy, given that there is at least one boy and one girl, is 1/4.

Explanation:

To solve this probability question, we need to consider all possible combinations of children while adhering to the given conditions: the oldest child must be a girl (G), the youngest must be a boy (B), and there must be at least one boy and at least one girl in the family.

The possible genders for the four children can be represented as a sequence of G (girl) and B (boy) like this: G---B. There are two positions in the middle that can be either a boy or a girl. Since each position can be filled independently with either a boy or a girl, there are 2 options for each of the middle children, giving us 2 x 2 = 4 combinations: GBGB, GBBB, GGBB, GGBG.

To calculate the probability of any single one of these combinations occurring, we need to remember that the probability of giving birth to a boy or a girl is equal, which means each event (birth of a child) has a probability of 1/2. Thus, the probability of each combination is (1/2)^4 since there are four independent events (births). However, since we have 4 combinations that meet the criteria, we multiply this probability by 4. So, the probability is 4 * (1/2)^4 = 1/4.

Therefore, the probability that a family with four children will have the oldest being a girl and the youngest being a boy, given that there is at least one boy and at least one girl, is 1/4.