[tex](2x5y6)(4x - 3y - 3) [/tex]
​

Answer:

381 in^3

Step-by-step explanation:

The volume of the green block is V1 = length(width)(height), or

                                                         V1 = (16 in)(7 in)(3 in) = 336 in^3, and

the volume of the red triangular prism is V2 = (1/2)(3 in)(5 in)(6 in) =

                                                           V2 = 45 in^3

So the total volume is the sum of these two results:  381 in^3

Answer:

D

Step-by-step explanation:

please mark brainliest thanks:)

we have proven that (A ∪ C) - B = (A - B) ∪ (C - B) algebraically using the properties of set operations

To prove the equality (A ∪ C) - B = (A - B) ∪ (C - B) for all sets A, B, and C, we'll break down the proof step by step, providing a reason for each step based on set operations and properties.

Step 1: Start with the left-hand side (LHS) of the equation: (A ∪ C) - B.

Step 2: Recall that A - B represents the set of elements that are in A but not in B. Similarly, C - B represents the set of elements that are in C but not in B. Therefore, (A ∪ C) - B can be expanded as (A - B) ∪ (C - B).

Step 3: Distribute the union operator (∪) over the set difference (-).

(A ∪ C) - B = (A - B) ∪ (C - B)

Step 4: Apply the distributive property of set operations.

Step 5: We can justify this step by using the definition of set difference and the associative property of the union. For any set X, (X - B) = X ∩ B', where B' represents the complement of set B. Applying this definition to both (A - B) and (C - B), we can rewrite the equation as:

(A ∩ B') ∪ (C ∩ B').

Step 6: Use the distributive property of intersection (∩) over union (∪).

(A ∩ B') ∪ (C ∩ B') = (A ∪ C) ∩ (B' ∪ B')

Step 7: Apply the complement law, which states that B ∪ B' = Universal set (U). Therefore, B ∪ B' = U.

Step 8: Rewrite the equation as (A ∪ C) ∩ U.

Step 9: Applying the intersection of any set X with the universal set U will give the set X itself.

(A ∪ C) ∩ U = A ∪ C.

Therefore, we have proven that (A ∪ C) - B = (A - B) ∪ (C - B) algebraically using the properties of set operations and justifications for each step.

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Given that the volume of a triangular based pyramid is 316 cm³, we need to find the volume of the prism with the same height and the same triangular base as the pyramid.

Let the height of the pyramid be h cm, and let the base of the pyramid be a cm and the perpendicular height to the base of the pyramid be b cm. '

1. Volume of the pyramid: The volume of a triangular-based pyramid is given by the formula V = 1/3abhGiven V = 316 cm³, a = 7 cm and b = 12 cm, we have; 316 = 1/3 × 7 × 12 × h => h = (316 × 3) / (7 × 12) => h = 9 cm

2. Volume of the prism: Since the prism has the same height and base as the pyramid, the base area of the prism will be equal to that of the pyramid. The base of the pyramid is a triangle and the base of the prism is a rectangle. Let the length of the rectangular base be L cm.

Since the rectangular base has the same area as the triangular base, the product of the length and width of the rectangular base is equal to the area of the triangular base. Therefore, we have L x a = 1/2 ab (the area of the triangular base), where a = 7 cm and b = 12 cm. L = 1/2 b = 1/2 × 12 = 6 cm

The volume of the prism is given by the formula V = La h = 6 × 9 = 54 cm³

Therefore, the volume of the prism is 54 cm³.

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Answer: y = (3^(x-1))*1500

Step-by-step explanation:

We want the relationship

y = f(x)

where y is the number of songs, and x is the number of years.

We know that in the first year, x = 1, the site has 1,500 songs.

The next year, x = 2, the number of songs is tripled, then we will have:

1,500*3 = 4500 songs.

The next year, x = 3, we will have: 3*(3*1500) = (3^2)*1500.

when x = 4, the number is tripled again:

3*(3^2)*1500 = (3^3)*1500

We already can see the pattern, for the year x, the site will have:

y = (3^(x-1))*1500 songs.

This is the equation we are looking for.

Answer:

no

Step-by-step explanation:

4m + 12 ≠ 2m + 12

Answer:

72°

Step-by-step explanation:

From the question,

Area of the circle = πr²

A = πr²................. Equation 1

Where r = radius of the circle.

⇒ r = √(A/π)............. Equation 2

Given: A = 346.5 cm², π = 3.14

r = √(346.5/3.14)

r = √(110.35)

r = 10.5 cm.

Therefore,

circumference of the circle = 2πr = 2×3.14×10.5

circumference = 65.94 m

If the length of the arc(s) is 1/5 of its circumference.

Therefore, length of arc (s) = 13.188

⇒ length of arc/circumference = 13.188/65.94 =  1/5

s/2πr = θ/360

Where θ = angle substends at the center of the circle

1/5 = θ/360

θ = 360/5

θ = 72°

Answer:

$84

Step-by-step explanation:

Answer:

FV= $3,726.93

Step-by-step explanation:

Giving the following information:

Initial investment (PV)= $2,500

Interest rate (i)= 0.04/12= 0.003333 monthly

Number of periods (n)= x months

To calculate the future value giving any number of months, we need to use the following formula:

FV= PV*(1 + i)^n

For 10 years:

n=10*12= 120 months

FV= 2,500*(1.003333^120)

FV= $3,726.93

a) The value of k for the systematic sample is given as follows: k = 114.

b) The individuals are: 1, 2, 3, 4, 5.

In a systematic sample, every kth element of the sample out of a sample of n elements is taken.

In this problem, we have a total of 5705 employees, and want a systematic sample of 50 employees, hence the value of k is obtained as follows:

k = 5705/50 = 114.

(rounding the value down to the nearest integer, we just divide the number of people by the sample size to obtain the value of k).

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Answer:

Hello! A function is easily identified when an x value does not have more than 1 y value. a y value can have as many x values to infinity, but x can only have one y.

Example...

x                       y

3                       5

4                       5

1                        2

The expression to evaluate is 2xe^y, where x and y are functions of t, and the initial conditions are given by x(t=0) = x_0 and y(t=0) = y_0.

To evaluate 2xe^y, we substitute the values of x and y in terms of t into the expression. Since x and y are functions of t, we need to know their specific forms or have additional information about them to proceed with the evaluation.

Without knowing the explicit expressions for x and y or any additional information, we cannot provide a specific numerical evaluation of 2xe^y. However, if you have the specific forms of x(t) and y(t) or any other relevant information, please provide them so that we can assist you further in evaluating the expression.

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The correct answer to 0.125 x 0.08 is 0.01. Dina's calculator provided the correct result.

The rule Dina mentioned about multiplying 125 x 8 and then moving the decimal point 5 places is not applicable in this case. When multiplying decimal numbers, we need to consider the number of decimal places in each factor.

Here's the correct approach to multiply 0.125 x 0.08:

Step 1: Ignore the decimal point and multiply the numbers as if they were whole numbers:

0.125 x 0.08 = 125 x 8

Step 2: Count the total number of decimal places in the original numbers:

0.125 has three decimal places

0.08 has two decimal places

Step 3: Add the number of decimal places from the original numbers:

Three decimal places + two decimal places = five decimal places

Step 4: Place the decimal point in the result by counting five places from the right:

125 x 8 = 1000

Adding the decimal point five places from the right gives us the final answer: 0.01000

Therefore, the correct answer to 0.125 x 0.08 is 0.01. Dina's calculator provided the correct result.

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It is a fundamental concept in statistical inference and scientific research.

The hypothesis is a statement that the value of a population parameter is equal to some claimed value. A hypothesis serves as a proposed explanation or prediction about the population based on existing knowledge or observations. In statistical hypothesis testing, two types of hypotheses are considered: the null hypothesis (H0) and the alternative hypothesis (Ha). The null hypothesis assumes no significant relationship or difference between variables, while the alternative hypothesis suggests the presence of a significant relationship or difference.

Hypothesis testing involves collecting sample data and performing statistical analysis to evaluate the evidence against the null hypothesis. The goal is to determine whether the data provides enough evidence to reject the null hypothesis in favor of the alternative hypothesis. This process allows researchers to make conclusions about the population based on the available evidence.

Hypothesis testing provides a framework for making objective and informed decisions in various fields of study, such as psychology, biology, economics, and more. It enables researchers to validate or challenge theories, investigate causal relationships, and contribute to the advancement of knowledge in their respective disciplines.

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Answer:

27.6 cm

Step-by-step explanation:

Answer: 44.6

Step-by-step explanation:

It’s not that hard use the formula of the volume of a sphere. And just replace the R with whatever your radius is, if you have a diameter just divide it by 2 to get the radius. Hope this helps

Answer:

A = 1413.72 unit²

Step-by-step explanation:

area of a semicircle formula: A = (πr²)/2

To find the area of a semicircle that has a radius of 30 feet, apply r = 30 to the formula A = (πr²)/2:

A = (π30²)/2

A = 1413.72 unit²

a.  The 68% of the widget weights lie between  33 ounces and  55 ounces.

b. The percentage of widget weights lying between 11 and 55 ounces is approximately 68%.

c. The percentage of widget weights lying above 22 ounces is approximately = 5%.

Based on the given data points: 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, the five-number summary can be identified as follows:

Minimum: 5

First Quartile (Q1): 7

Median (Q2): 11

Third Quartile (Q3): 15

Maximum: 18

Now, let's answer the questions related to the distribution of widget weights using the Empirical Rule:

a) The Empirical Rule states that for a bell-shaped distribution, approximately 68% of the data lies within one standard deviation of the mean. Since the mean is 44 ounces and the standard deviation is 11 ounces, we can say that approximately 68% of the widget weights lie between 44 - 11 = 33 ounces and 44 + 11 = 55 ounces.

b) To determine the percentage of widget weights lying between 11 and 55 ounces, we need to calculate the z-scores for these values. The z-score is calculated using the formula: z = (x - mean) / standard deviation.

For 11 ounces: z1 = (11 - 44) / 11 = -33/11 = -3

For 55 ounces: z2 = (55 - 44) / 11 = 11/11 = 1

Using the Empirical Rule, we know that approximately 68% of the data lies within one standard deviation of the mean. Therefore, the percentage of widget weights lying between 11 and 55 ounces is approximately 68%.

c) To determine the percentage of widget weights lying above 22 ounces, we need to calculate the z-score for 22 ounces: z = (22 - 44) / 11 = -22/11 = -2.

Using the Empirical Rule, we know that approximately 95% of the data lies within two standard deviations of the mean. Therefore, the percentage of widget weights lying above 22 ounces is approximately 100% - 95% = 5%.

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The income elasticity of demand for tennis balls is -1.5. The negative sign indicates an inverse relationship between income and the quantity demanded of tennis balls, suggesting that tennis balls are an inferior good.

To calculate the income elasticity of demand, we need to use the formula:

Income Elasticity of Demand = Percentage change in quantity demanded / Percentage change in income

Given that incomes increase by 58% and the quantity demanded of tennis balls drops by 87%, we can plug these values into the formula:

Income Elasticity of Demand = (-87%)/58%

Simplifying the calculation:

Income Elasticity of Demand = -1.5

The income elasticity of demand for tennis balls is -1.5. The negative sign indicates an inverse relationship between income and the quantity demanded of tennis balls, suggesting that tennis balls are an inferior good.

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The actual values (the specific results from StatCrunch, including the p-value) and interpretation would depend on the sample data and the results of the hypothesis test in StatCrunch.

Hypothesis:

Null hypothesis (H0): The mean student loan debt at StatCrunchU is equal to $4000.

Alternative hypothesis (H1): The mean student loan debt at StatCrunchU is higher than $4000.

Normality Conditions and Test Selection:

To verify normality conditions, we need to check if the distribution of student loan debt at StatCrunchU is approximately normal. Since the prompt does not provide any information on the distribution, we will assume that the sample of student loan debt follows a normal distribution. Additionally, we should consider the sample size. If the sample size is large enough (typically considered n ≥ 30), the Central Limit Theorem ensures that the sampling distribution of the mean will be approximately normal, regardless of the underlying distribution of the individual observations.

Hypothesis Test:

To conduct the hypothesis test, we can use a one-sample t-test. We will compare the sample mean of student loan debt at StatCrunchU to the population mean of $4000.

StatCrunch Output:

Unfortunately, as a text-based AI model, I cannot directly access or interact with external tools like StatCrunch to generate real-time output. However, I can guide you through the steps to conduct the hypothesis test using StatCrunch:

Enter the sample data for student loan debt at StatCrunchU.

Select the appropriate options to conduct a one-sample t-test, with a null hypothesis mean of $4000 and an alternative hypothesis mean greater than $4000.

Run the test to obtain the test statistic, degrees of freedom, p-value, and other relevant information.

Copy and paste the results into your response.

P-value and Interpretation:

Once you have conducted the hypothesis test in StatCrunch, you will obtain a p-value. The p-value represents the probability of obtaining a test statistic as extreme as, or more extreme than, the observed value, assuming the null hypothesis is true.

Using a significance level of 5% (α = 0.05), if the p-value is less than 0.05, we would reject the null hypothesis in favor of the alternative hypothesis. Conversely, if the p-value is greater than or equal to 0.05, we would fail to reject the null hypothesis.

Conclusion:

Please provide the specific results from StatCrunch, including the p-value, and I can assist you in interpreting the results and formulating a conclusion based on the research question.

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Answer:

1/10

Step-by-step explanation:

1) find a common factor between the two denominators.

2 and 5 have a common factor of 10. you can find this by multiplying the denominators.

2) now that you have a common denominator of 10, you'll need to change the numerators too. you do this by finding out how many times the denominator goes into your common factor. 5 goes into 10 two times so you would multiply 2 x 2. two goes into 10 five times so multiply 5 x 1.

3) you now have both fractions that share a common factor. now you have to subtract them.

5/10 - 4/10 = 1/10

The number of conversions Mrs. Yellow's company can achieve is 10, and the revenue they can earn is $10,000.

Mrs. Yellow is an email marketing manager and her company has the following characteristics:

20% open rate, 5% click-through rate, 5% conversion rate, and $1000 average order value. She is sending the promotion email to a list of 20000 members.

To calculate the number of conversions and revenue, we need to use the following formula:

Revenue = Number of conversions × Average order value

Number of conversions = Total number of emails × Conversion rate

Total number of emails = Total number of opened emails × Click-through rate

Total number of opened emails = Total number of sent emails × Open rate

Total number of sent emails = 20,000

Revenue = Number of conversions × Average order value

Total number of sent emails = 20,000

Total number of opened emails = 20,000 × 20/100 = 4,000

Total number of emails = 4,000 × 5/100 = 200

Number of conversions = 200 × 5/100 = 10

Revenue = 10 × 1,000 = $10,000

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The given set of vectors which are represented as {(1, -4), (4, 1)} is orthogonal.

To determine whether the set of vectors in ℝⁿ is orthogonal, we need to check if all the pairs of vectors in the set are orthogonal to each other.

In this case, the set of vectors is {(1, -4), (4, 1)}. To determine if these vectors are orthogonal, we calculate their dot product.

The dot product of two vectors (a, b) and (c, d) is given by a * c + b * d.

For the first pair of vectors (1, -4) and (4, 1), the dot product is 1 * 4 + (-4) * 1 = 4 + (-4) = 0.

Since the dot product is zero, we can conclude that the vectors (1, -4) and (4, 1) are orthogonal to each other.

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Answer:

Part I:  The degree of a polynomial is the greatest of the degrees of its terms.

Part II:  In order to write a polynomial in descending order, you must write the terms with the exponents decreasing from left to right.

Part III: A. -4x² + 11x - 12, degree = 2,

B. 5x³ + 4x + 14, degree = 3.

Step-by-step explanation:

Part I : Since the degree of a polynomial is the highest power of its monomials ( single term ),

e: degree of is 5.

Thus, in part I, the correct option is 'greatest'

Part II: When we write a polynomial then we write the terms of the polynomial in descending order of their degrees.

Thus, in part II the correct option is 'least'

Part III: A.  

∵ -4x² has the highest power in the polynomial.

⇒ Degree = 2,

Also, in the polynomial descending order of degrees,

2 > 1 > 0

⇒ polynomial in descending order,

B.  

Combining like terms,

∵ 5x³ has the highest degree,

⇒ Degree = 3,

Also, the order of the degrees in the polynomial is,

3 < 2 < 1 < 0

Thus, the polynomial in descending order,

Answer: I had trouble with this one too.

Step-by-step explanation:

Covariance is the measure of the joint variability of two random variables. It measures how much two random variables are linearly related to each other. It is denoted by Cov(X, Y).

f(x, y) = 2(xo-* yot) _40536 orgs 7.6, otherwise, covariance X1j = ?The value of covariance X1j can not be determined from the given equation f(x, y) = 2(xo-* yot) _40536 orgs 7.6. There is no relation mentioned between the variables of x and y in the equation. The equation f(x, y) = 2(xo-* yot) _40536 orgs 7.6 means that the function f(x, y) is the multiplication of the value of x to the value of y and then multiplying it by a constant value. The value of the constant is 2(xo-* yot) _40536 orgs 7.6 but the actual value of x and y is unknown. Therefore, we can not calculate the covariance X1j using the given equation. The covariance X1j needs at least two random variables to determine their interdependence, whereas the given equation is a single-variable function that has no relation between two variables .

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Statistic 1 would you recommend for estimating average of smallest and largest values in the sample

To compute Statistics 1, 2, and 3 for the given samples, and determine which statistic would be recommended for estimating the average of the smallest and largest values, let's go through each sample one by one:

1. 2,3,3*

 Statistics 1: Sum of the values = 2 + 3 + 3 = 8

 Statistics 2: Average of the values = (2 + 3 + 3) / 3 = 2.67

 Statistics 3: Median of the values = 3

2. 2,3,4

   Statistics 1: Sum of the values = 2 + 3 + 4 = 9

   Statistics 2: Average of the values = (2 + 3 + 4) / 3 = 3

   Statistics 3: Median of the values = 3

3.  2,3,4*

    Statistics 1: Sum of the values = 2 + 3 + 4 = 9

    Statistics 2: Average of the values = (2 + 3 + 4) / 3 = 3

    Statistics 3: Median of the values = 3

4. 2,3*,4*

Statistics 1: Sum of the values = 2 + 3 + 4 = 9

Statistics 2: Average of the values = (2 + 3 + 4) / 3 = 3

Statistics 3: Median of the values = 3

5. 2,4,4*

Statistics 1: Sum of the values = 2 + 4 + 4 = 10

Statistics 2: Average of the values = (2 + 4 + 4) / 3 = 3.33

Statistics 3: Median of the values = 4

6. 3,3*,4

Statistics 1: Sum of the values = 3 + 3 + 4 = 10

Statistics 2: Average of the values = (3 + 3 + 4) / 3 = 3.33

Statistics 3: Median of the values = 3

7.  3,3*,4*

Statistics 1: Sum of the values = 3 + 3 + 4 = 10

Statistics 2: Average of the values = (3 + 3 + 4) / 3 = 3.33

Statistics 3: Median of the values = 3

8.  3,4,4*

Statistics 1: Sum of the values = 3 + 4 + 4 = 11

Statistics 2: Average of the values = (3 + 4 + 4) / 3 = 3.67

Statistics 3: Median of the values = 4

9.  3*,4,4*

Statistics 1: Sum of the values = 3 + 4 + 4 = 11

Statistics 2: Average of the values = (3 + 4 + 4) / 3 = 3.67

Statistics 3: Median of the values = 4

For estimating the average of the smallest and largest values in the sample, the recommended statistic would be Statistics 1, which is the sum of the values. Taking the average of the smallest and largest values can be obtained by dividing the sum by the number of values, which in this case is 3.

Therefore, the recommended statistic for estimating the average of the smallest and largest values is Statistics 1 (sum of the values).

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Answer:

230.98 meters

Step-by-step explanation:

Answer:

126m

Step-by-step explanation:

Use sine because we want to find the opposite length but only know the hypotenuse.

Answer:

no

Step-by-step explanation:

To determine if (1, 6) is a solution, substitute x = 1, y = 6 into the left side of both equations and if the value obtained equals the right side then it is a solution.

10(1) - 6 = 10 - 6 = 4 ≠ - 6

- 10(1) + 5(6) = - 10 + 30 = 20 ≠ 30

Then (1, 6 ) is not a solution to the system

Answer:

The sales tax rate is 8%.

C. The sale price is 20% less than the regular price

Step-by-step explanation:

Here are the options to this question :

A) The sales tax rate is 6%

B) The sales tax rate is 8%.

C. The sale price is 20% less than the regular price

Sales tax rate = (tax paid / discounted selling price) x 100

tax paid = amount customer paid - discounted selling price

$73.44 - $68 = $5.44

($5.44 / $68) x 100 = 8%

The sales tax is 8%

Sales price = (discount / initial price) x 100

discount = $85 - $68 = $17

($17 / 85) x 100 = 20%

Answer:

B.) The Sales Tax Rate is 8%

C.) 85-68/85 = discount rate

E.) The Sale Price is 20% less than the regular price.

Step-by-step explanation:

i did the usatestprep :)