a survey found that the american family generates an average of 17.2 pounds of glass garbage each year. assume the standard deviation of the distribution is 2.5 pounds. find the probability that the mean of a sample of 55 families will be between 17 and 18 pounds. why can the central limit theorem be applied?

part A.

The equation of the ellipse is:

x² / 280900 + y² / 198025 = 1

part B.

The area of the ellipse at the White House is found to be  741,022.16 square feet.

The standard form equation for an ellipse is given as :

(x² / a²) + (y² / b²) = 1

Where "a" =  half the length of the major axis

b =   half the length of the minor axis.

length of the major axis = 1060 feet,

a = 1060 / 2 = 530 feet.

The length of the minor axis is 890 feet,

b = 890 / 2

b= 445 feet.

x² / 530² + y² / 445² = 1

x² / 280900 + y² / 198025 = 1

B.

a = 530 feet and b = 445 feet.

Area = π * 530 * 445

A = 741,022.16 square feet

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The complement set of S is {1, 3, 5, 8, 9, 10}.

To find the complement set of S, we need to identify all the elements in the universal set U that are not present in set S.

Given:

Universal set U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

Set S = {2, 4, 6, 7}

The complement set of S, denoted as S', consists of all the elements in U that are not in S.

Complement set of S (S') = U - S

To find S', we subtract the elements of S from U:

S' = {1, 3, 5, 8, 9, 10}

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Obtuse-angled: This term refers to triangles with one angle greater than 90 degrees. The triangle in question has an angle of 100º, so it is obtuse-angled.

The statement is False" Some seventh graders" isn't a set.

we know, set is a well- defined collection of distinct objects, which are appertained to as rudiments or members of the set.

For illustration, consider the set A = { 1, 2, 3}. This set contains the rudiments 1, 2, and 3.

It's a expression that describes a group of individualities without furnishing a well- defined collection of rudiments.

A set is a well- defined collection of distinct objects.

To represent a set, we generally use curled braces and list the rudiments within the set.

For illustration,{ 1, 2, 3} is a set containing the rudiments 1, 2, and 3.

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Answer:

x = 3 , y = 1

Step-by-step explanation:

[tex]2^{x+y} = 16\\2^{x+y} = 2^4\\x + y = 4 ---- (1)\\\\3^{x-y} = 9\\3^{x-y} = 3^2\\x-y = 2 ----- (2)\\\\Adding 1 and 2 , we get ,\\ 2x = 6\\x = 3\\y = 1[/tex]

Answer:

y = 1, x = 3

Step-by-step explanation:

1.) Based on the given, we have [tex]2^{x+y}[/tex] = 16, and [tex]3^{x-y}[/tex]=9. Since [tex]2^4[/tex] is equal to 16, that means that x + y = 4. Since [tex]3^2[/tex] is equal to 9, that means that x - y = 2

2.) Now, we have a system of equations. By using elimination (adding the two together), you get x + x + y - y = 2 + 4. By simplifying, the y cancels out and you get 2x = 6. Finally, you get x = 3.

3.) To end, you need to find y. Since we have x - y = 2, and x = 3, that means that 3 - y = 2, meaning y = 1.

Answer:

-------------------------

Given data:

Put the data in the ascending order:

The mode, the most repeated term, is 11.

The median is the middle term, also 11.

The mean is the average:

Answer & step-by-step explanation:

Let us find the median of the data set

First, you should arrange the data in ascending to descending to find the median.

4, 7, 10, 11, 11, 12, 16

Now let us use the given formula to find the median.

[tex]\sf \dfrac{n+1}{2} =--^t^h data[/tex]

Here,

n → the number of elements

Let us find it now.

[tex]\sf Median= \dfrac{n+1}{2}\\\\\sf Median=\dfrac{7+1}{2} =4^t^h data\\\\Median=11[/tex]

Let us find the mode of the data set.

Mode is the most frequent number in the data set.

∴ mode → 11

Let us find the mean of the data set

Mean is the average of a data set.

To find that, you have to add all the data together and divide it by number of elements.

Mean = Σx ÷ n

Mean = ( 10 + 11 + 4 + 7 + 12 + 11 + 16 ) ÷ 7

Mean =  71 ÷ 7

Mean =  10.14

The best definition of the test statistic is the number of standard errors above or below the expected outcome that our sample z-score corresponds to. In other words, the test statistic measures how far our sample mean deviates from the expected population mean in terms of standard deviation units.

The test statistic is a crucial element in hypothesis testing as it helps us determine the probability of obtaining our sample mean by chance. We use the test statistic to calculate the p-value, which is the probability of obtaining a result as extreme as our sample mean under the null hypothesis.

The boundary value corresponding to the p-value is determined by the level of significance we choose for our test. If our p-value is less than the level of significance (usually 0.05), we reject the null hypothesis and conclude that there is evidence to support the alternative hypothesis.

In summary, the test statistic is a measure of how far our sample mean deviates from the expected population mean in standard deviation units. It is used to calculate the p-value and determine the level of significance for our hypothesis test.
The best definition of the test statistic among the given terms is: the number of standard errors above or below the expected outcome that our sample represents. A test statistic is a value calculated from sample data that is used to determine whether to reject or fail to reject a null hypothesis in hypothesis testing. It measures how far the sample statistic is from the hypothesized population parameter, considering the sample's variability.

In simpler terms, the test statistic helps us understand how likely our sample results are, given the null hypothesis. It does this by comparing the sample's outcome to what we would expect under the null hypothesis, considering the variability within the sample. By calculating the test statistic, we can then determine the corresponding p-value, which represents the probability of obtaining the observed results or more extreme results, assuming the null hypothesis is true.

In summary, the test statistic quantifies the difference between the sample outcome and the expected outcome under the null hypothesis, expressed in terms of the number of standard errors. It helps us make decisions about the null hypothesis based on the calculated p-value.

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Answer:

gradient = 1 , y- intercept = - 4

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope ( gradient ) and c the y- intercept )

y = x - 4 ← is in slope- intercept form

with gradient m = 1 and y- intercept c = - 4

In a multiple regression model, the variance of the error term e is assumed to be the same for all values of the independent variable. Therefore, the correct option is C) the same for all values of the independent variable.

In multiple regression, we use several independent variables to predict the values of the dependent variable. The model estimates the relationship between the independent variables and the dependent variable by calculating the coefficients of the independent variables.

The error term e represents the difference between the predicted value of the dependent variable and the actual value of the dependent variable.

The assumption of constant variance of the error term e is known as homoscedasticity. It means that the variance of the errors is the same for all levels of the independent variables.

This assumption is important because, if the errors have different variances across the levels of the independent variable, the model may not accurately capture the relationship between the independent variables and the dependent variable, leading to biased and unreliable results. so, the correct answer is C).

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Answer:

  (c)  379.2 in²

Step-by-step explanation:

You want to know the total surface area of 6 cylinders of diameter 3.5 inches and height 4 inches.

The area of a cylinder in terms of diameter and height can be found by ...

  A = πd(d/2 +h)

The area of 6 cylinders with d=3.5 and h=4 is ...

  6A = 6π(3.5 in)(3.5 in/2 +4 in) ≈ 379.2 in²

The minimum wrap needed is 379.2 square inches.

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The equation of the composite function B(d) is B(d) = T(d) - A(d) or B(d) = d² + 8d

From the question, we have the following parameters that can be used in our computation:

T(d) = d² + 20d

A(d) = 12d

The function B(d) is the difference between the functions A(d) and T(d)

Using the above as a guide, we have the following:

B(d) = T(d) - A(d)

In terms of d, we have

B(d) = d² + 20d - 12d

Evaluate the difference

B(d) = d² + 8d

Hence, the composite function B(d) is B(d) = T(d) - A(d) or B(d) = d² + 8d

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[tex]3x + 2y^{2} + xy + x + 7x[/tex]

first, you combine like terms:

[tex]11x + 2x^{2} + xy[/tex]

next, rearrange the terms:

[tex]xy + 2y^{2} + 11x[/tex]

...which brings us to the answer! hope this helps, and please give me brainliest :)

Answer:

missing length= 2.8

Step-by-step explanation:

a^2+b^2=c^2

a^2+1^2=3^2

a^2=3^2-1^2

a^2=8

a=2.8284271247461

a=2.8

The function, f(x) = 10x - 2x² can be evaluated for f(4) by substituting the value of x for 4 to get the answer: f(4) = 8.

A function is an equation that gives an output for every specific input. To evaluate a function for a given input (x), we have to plug in the value of the input into the equation to get the output of the function.

Given the equation of a function as, f(x) = 10x - 2x², to find f(4) means to plug in the value of x = 4 into the equation:

f(4) = 10(4) - 2(4²)

Evaluate:

f(4) = 40 - 32

f(4) = 8

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To determine which ordered pairs satisfy the equation 3x - 4y = 21, we can substitute the given x and y values into the equation and check if the equation holds true.

Let's check each ordered pair:

1. (-1, -6):

  Substituting x = -1 and y = -6 into the equation: 3(-1) - 4(-6) = 3 + 24 = 27, which is not equal to 21. Therefore, (-1, -6) is not a solution.

2. (7, 0):

  Substituting x = 7 and y = 0 into the equation: 3(7) - 4(0) = 21, which is equal to 21. Therefore, (7, 0) is a solution.

3. (-3, 3):

  Substituting x = -3 and y = 3 into the equation: 3(-3) - 4(3) = -9 - 12 = -21, which is not equal to 21. Therefore, (-3, 3) is not a solution.

4. (11, 3):

  Substituting x = 11 and y = 3 into the equation: 3(11) - 4(3) = 33 - 12 = 21, which is equal to 21. Therefore, (11, 3) is a solution.

Based on the calculations, the ordered pairs that are solutions to the equation 3x - 4y = 21 are (7, 0) and (11, 3).

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Answer:

Let's start by assigning variables to the unknown ages:Trisha's age = TAge of Trisha's first brother = T + 3Age of Trisha's second brother = T - 3Age of Trisha's third brother = T/3Age of Trisha's father = 3TWe know that the sum of all their ages is 95:T + (T + 3) + (T - 3) + T/3 + 3T = 95Combining like terms, we can simplify this equation:8T + T/3 = 92Multiplying both sides by 3 to get rid of the fraction:24T + T = 276Simplifying again:25T = 276Dividing both sides by 25:T = 11.04So Trisha is 11.04 years old.We can check our answer by plugging it back into the original equation and verifying that the sum of all their ages is indeed 95:T + (T + 3) + (T - 3) + T/3 + 3T = 95

11.04 + (11.04 + 3) + (11.04 - 3) + 11.04/3 + 3(11.04) = 95

95 = 95The sum of their ages is 95, so our answer is correct. Therefore, Trisha is 11.04 years old.

Step-by-step explanation:

Answer: $34.20

Step-by-step explanation:

$3.80 is for 1 book.

Since she would buy 9 books, you would do the equation of 3.80 x 9.

You'll get the answer of 34.2, but then by making that a dollar amount it would be 34.20. Add the dollar sign, $34.20, and wahlah!

The company will use approximately 7 trucks.

to separate into two or more parts or pieces. : to separate into classes or categories. : cleave entry 2, part.

To calculate the number of trucks needed, divide the total number of bicycles by the number of bicycles that can fit in each truck:

328 bicycles / 50 bicycles per truck = 6.56 trucks.

Since you can't have a fraction of a truck, the company will need to round up to the nearest whole number. Therefore, the company will use 7 trucks to ship the 328 bicycles across the country.

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To calculate the incidence of breast cancer in the unexposed group (i0) per 1,000, we need to first calculate the total number of mothers in the unexposed group. The total number of mothers in the study is 1,628 + 4,450 = 6,078.
We know that among the 4,450 mothers who first gave birth before the age of 30, 65 subsequently developed breast cancer.

Therefore, the incidence of breast cancer in this group is 65/4,450 = 0.0146.

To convert this incidence rate to a per 1,000 basis, we multiply by 1,000: 0.0146 x 1,000 = 14.6.

Therefore, the incidence of breast cancer in the unexposed group (i0) per 1,000 is 14.6.

It's important to note that we cannot directly calculate the incidence rate of breast cancer in the exposed group since we do not have information on the total number of mothers in that group who did not develop breast cancer. However, we can still compare the incidence rates between the exposed and unexposed groups to see if there is a significant difference.

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The main difference is interest charged for a payday loan is typically over a short period, whereas  credit card represents the annualized interest rate over a year.

The payday loan interest is a one-time charge, while the credit card APR accumulates over time if the balance is not paid in full.

For a payday loan, the 30% interest is typically charged over a short period, often within a few weeks.

This means that if you borrow $100, you would need to repay $130, including the $30 interest, within that short timeframe.

On the other hand, a 30% APR on a credit card represents the annualized interest rate charged on the outstanding balance. This interest is spread out over a year.

If you have an outstanding balance of $100 on a credit card with a 30% APR, the interest charged over a year would be $30.

In summary, the main difference is that the 30% interest charged for a payday loan is typically applied over a short period, whereas the 30% APR on a credit card represents the annualized interest rate over a year.

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Answer:

a = -3

Step-by-step explanation:

Step 1:  Since we're told that 5 to the power of a = 1/125, we can use the following equation to solve for a:

5^a = 1/125

Step 2:  Take the log of both sides

log(5^a) = log(1/125)

Step 3:  According to the power rule of logs, we can bring a down and multiply it by log(5):

a * log(5) = log (1/125)

Step 4:  Divide both sides by log(5) to solve for a:

(a * log(5) = log(1/125)) / log(5)

a = -3

Optional 5:  We can check our answer by plugging in -3 for a and seeing if we get 1/125 when completing the operation:

5^-3 = 1/125

1/(5^3) = 1/125 (rule of exponents states that a negative exponent creates a fraction with 1 as the numerator and the base (5) and exponent (-3 becoming 3) as the denominator

1/125 = 1/125

Answer:

8 1/15 meters of ribbon left.

Step-by-step explanation:

To find this, we have to find the difference. 16-7 14/15=8 1/15. So, Beth has 8 1/15 meters of ribbon left.

The missing value in the chart will be 1/9.

From the chart, the given function is an exponential function,

Since the function is 3ⁿ.

Thus, the value of the function at n= -2 will be,

=> 3ⁿ=3⁻²

=> 3ⁿ= 1/3²

=> 3ⁿ= 1/9

Therefore, the value of the function at n = -2 will be 1/9.

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Answer: it would be 13 beeps

Step-by-step explanation:

Answer: 9 + 3r

Step-by-step explanation:

To reduce the number of terms we need to combine like terms

15 - (6-3r)

Distributive property (distribute the -1)

15 - 6 + 3r

9 + 3r

The HCF of each of the pair of numbers are 2, 6 and 4

From the question, we have the following parameters that can be used in our computation:

The HCF of each of the pair of numbers is calculated as follows

Pair 1

2 = 2

36 = 2 * 2 * 3 * 3

The highest common factor above is

HCF = 2

Pair 2

42 = 2 * 3 * 7

24 = 2 * 2 * 2 * 3

The highest common factor above is

HCF = 2 * 3

Evaluate

HCF = 6

Pair 3

8 = 2 * 2 * 2

12 = 2 * 2 * 3

The highest common factor above is

HCF = 2 * 2

Evaluate

HCF = 4

Hence, the HCF of each of the pair of numbers are 2, 6 and 4

The venn diagrams are also attached

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Answer:

$38.80

Step-by-step explanation: