What is the product?

The values of the composite functions are

(1) (f + g)(x) = 4x² + 2x - 2

(2) (fg)(x) = 8x³ - 4x² - 2x + 1

(3) (fⁿ)(x) = (4x² - 1)ⁿ

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

f(x) = 4x² - 1

g(x) = 2x - 1

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

(f + g)(x) = f(x) + g(x)

(f + g)(x) = 4x² - 1 + 2x - 1

Evaluate the like terms

(f + g)(x) = 4x² + 2x - 2

(fg)(x) = f(x) * g(x)

(fg)(x) = (4x² - 1) * (2x - 1)

Evaluate the products

(fg)(x) = 8x³ - 4x² - 2x + 1

(fⁿ)(x) = (f(x))ⁿ

So, we have

(fⁿ)(x) = (4x² - 1)ⁿ

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Answer:91.26ft squared

Answer: the height of the equilateral triangle is 6√3 inches.

Step-by-step explanation:

To find the height of an equilateral triangle, we can use the formula:

height = (√3/2) * side

In this case, we are given the perimeter of the triangle, which is 36 inches.

Since an equilateral triangle has three equal sides, each side would be 36 inches divided by 3, which is 12 inches.

Now we can substitute the side length into the formula:

height = (√3/2) * 12

Simplifying:

height = (√3/2) * 12

height = (√3 * 12)/2

height = (12√3)/2

height = 6√3

Therefore, the height of the equilateral triangle is 6√3 inches.

Answer:

RG

Step-by-step explanation:

The slope of each line is given as follows:

58) -2.

59) 1.

60) -2/3.

61) 2.

The slope-intercept equation for a linear function is presented as follows:

y = mx + b

The parameters of the definition of the linear function are given as follows:

When two lines are parallel, they have the same slope, which are the cases for itens 58 and 59, as the slope is given by the multiplier of x.

When two lines are perpendicular, we have that the multiplication of the slopes of the line is of -1, hence the slope for item 60 is given as follows:

3m/2 = -1

3m = -2

m = -2/3.

For item 61, the slope is given as follows:

-m/2 = -1

m = 2.

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The description of the location of the point, (−7, 6, −4) in three-dimensional coordinate space is this: A.  From the origin, move 7 units back, 6 units right, and 4 units down.

The meaning of a three-dimensional coordinate space is a requirement for three units to come together to form a point. In the location of the point above, we are given three units namely, -7, 6, and -4.

The indication of signs in front of them are as follows; -7, means moving 7 units back, 6 means moving 6 units right, ad -4 means moving 4 units down.

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Answer: Is it x=y(4)? Can someone tell me if that's right?

Step-by-step explanation:

Answer:

$0.20 per orange

Step-by-step explanation:

We Know

A fruit stand sells 5-pound bags of oranges for $3.00 each.

There are 15 oranges in each bag.

What is the price per orange?

We Take

3 / 15 = $0.20 per orange

So, the price per orange is $0.20

Step-by-step explanation:

40 :100        yellow to purple,  divide both sides by 20

2:5

Answer:

the ratio of yellow to purple is 40:100 that is 2:5 in the simplest form.

Step-by-step explanation:

Hope it helps.

The proportion is solved and the variables are a/b = c/d

Given data ,

Let the proportion be represented as A

Now , the value of A is

a / b = c / d

On simplifying the equation , we get

( a + b ) / b = ( c + d ) / d

On dividing the numerator of the fraction by the denominator , we get

( a / b ) + ( b / b ) = ( c / d ) + ( d / d )

On further simplification , we get

( a / b ) + 1 = ( c / d ) + 1

Subtracting 1 on both sides , we get

( a / b ) = ( c / d )

Hence , the proportion is ( a / b ) = ( c / d )

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The function which has a range of real numbers is f(x) = -x + 2

Range is the set of the values that the function obtains this set is the values that the function obtains when we put an x value in the function.

In f(x) = -x + 2 when we put any value of x we get real number so the function range is ( -∞ , ∞ )

In g(x) = -x² when we put any value of x we get all negative number function range is (-∞ , 0]

In h(x) = [tex]2^{x}[/tex] + 1 when we put any value of x we get all positive number so the function range is (1 , ∞)

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One-way ANOVA utilizes the five steps of hypothesis testing to determine if there are significant differences among the means of three or more groups.

One-way ANOVA, or analysis of variance, is a statistical test used to compare the means of three or more groups to determine if there are significant differences among them. It helps in determining whether the variations between the group means are due to random chance or if they are statistically significant.

The five steps of hypothesis testing are commonly used in one-way ANOVA to analyze and draw conclusions from the data. These steps are as follows:

1. Formulating the null and alternative hypotheses: In one-way ANOVA, the null hypothesis (H0) states that there are no significant differences between the group means, while the alternative hypothesis (Ha) states that at least one group mean differs significantly from the others.

2. Choosing a significance level: The significance level, denoted as α, represents the threshold below which the null hypothesis is rejected. Commonly used values for α are 0.05 or 0.01, indicating a 5% or 1% chance, respectively, of rejecting the null hypothesis incorrectly.

3. Computing the test statistic: In one-way ANOVA, the test statistic is the F-statistic, which compares the between-group variation to the within-group variation. It measures the ratio of the mean square between (MSB) to the mean square within (MSW).

4. Determining the critical value: The critical value is derived from the F-distribution table and depends on the significance level and the degrees of freedom associated with the numerator and denominator of the F-statistic.

5. Making a decision: If the calculated F-value is greater than the critical value, the null hypothesis is rejected, and it can be concluded that there are significant differences between at least two group means. Conversely, if the calculated F-value is smaller than the critical value, the null hypothesis is not rejected, indicating that there is no significant difference between the group means.

If the null hypothesis is rejected, post-hoc tests can be conducted to determine which specific group means differ significantly from each other.

one-way ANOVA utilizes the five steps of hypothesis testing to determine if there are significant differences among the means of three or more groups.

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Another representation of (1, 1/4 π)  in which r> 0, 2π < θ < 4π is (1, 3/4 π)

In Bi-polar Coordinates, the point (1, 1/4 π) can be represented in polar coordinates as (r, θ).

Where r is the distance from the origin to the point and θ is the angle between the positive x-axis and the line segment connecting the origin to the point.

a. For r> 0, 2π < θ < 4π

Add 2π to the original angle of 1/4 π:

(r, θ+2π) = (1, 1/4 π + 2π)

              = (1, 9/4 π)

b. For r < 0, 0 < θ < 2π,

Add  π and reflect the original point across the origin:

(r, θ+π) = (-1, 1/4 π + π)

           = (-1, 5/4 π)

c. For r> 0, -2π < θ < 0,

Subtract 2π from the original angle of 1/4 π:

(r, θ-2π) = (1, 1/4 π - 2π)

             = (1, -7/4 π)

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Median of the set is 34, as it is the middle value of the ordered set (32, 33, 33, 33, 34, 35, 35, 36, 38).

To find the middle of a bunch of numbers, the initial step is to organize the numbers all together from least to most prominent. For this situation, the arranged set is: 32, 33, 33, 33, 34, 35, 35, 36, 38.

The middle is the center number in the arranged set. On the off chance that there is an odd number of values, the middle is the center worth. On the off chance that there is a considerably number of values, the middle is the normal of the two center qualities.

For this situation, there are nine qualities in the set, which is an odd number. The center worth is the fifth worth, which is 34. Thusly, the middle of the set is B. 34.

To confirm, we can count four qualities before 34 and four qualities after 34 in the arranged set. Since there are an equivalent number of values when the middle, we can infer that 34 is for sure the middle.

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Answer:no idea

Step-by-step explanation:

The domain and the range of the graph are Domain = [-10, -8] and Range = [-10, -1]

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

The graph

The above graph can be represented as a list of ordered pairs

The rule of a graph is that

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

Domain = [-10, -8]

Range = [-10, -1]

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Sneha actually got 2475 g of sugar instead of 2500 g.

We have,

If the shopkeeper uses a weight of 990 g for measuring 1 kg, it means that he is using a weight that is 10 g less than the actual weight of 1 kg.

So, the actual weight of 1 kg is 1000 g.

Now,
If Sneha bought 5/2 kg of sugar, she should have received:

= (5/2) x 1000 g

= 2500 g

But since the shopkeeper uses a weight of 990 g for measuring 1 kg, the weight of 5/2 kg would be:

= (5/2) x 990 g

= 2475 g

Thus,

Sneha actually got 2475 g of sugar instead of 2500 g.

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Answer: Blue

Step-by-step explanation:

Half of the entire freaking bag is blue,it states it in the question.If there is so many,unless by pure blind luck you will get that.

I hope it helps!

The measure of arc angle QTP is 204 degrees.

When a tangent and a secant intersect outside a circle then the measure of the angle formed is one-half the positive difference of the measures of the intercepted arcs.

Therefore, let's find the measure of arc angle QTP as follows:

90 = 0.5(x - 68)

90 = 0.5x - 34

0.5x = 124

x = 124 / 0.5

x = 248 degrees

Where

x = arc angle TSQ

Therefore,

arc QP = 44 degrees

Therefore,

arc QTP = 248 - 44

arc QTP = 204 degrees

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The relative frequency of selecting the number 2 is 0.16 or 16%.

Relative Frequency is a proportion or percentage which is calculated with the help of given frequency.

To calculate the relative frequency of selecting the number 2, you need to divide the number of times 2 was selected by the total number of selections. In this case, 2 was selected 8 times out of a total of 50 selections.

Relative frequency of selecting 2 = (Number of times 2 was selected) / (Total number of selections)

= 8 / 50

= 0.16

Therefore, the relative frequency of selecting the number 2 is 0.16 or 16%.

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Answer:

Because equations is not counting, and multiply is not addition.  

Step-by-step explanation:

Addition is: a process of combining two or more numbers. Addends are the numbers being added, and the result or the final answer we get after the process is called the sum. It is one of the essential mathematical functions we use in our everyday activities. There are many situations in which we add numbers.

Like lets say you have 1 apple, and your friend gives 2 more, then you have 3. If you have 4 apples, and your friend gives 5 more, then you have 9 apples.

Its always better to start with the bigger number, it makes it easier, like 2 + 1 = 3, or 5 + 4 = 9.

Now multiplication is harder. Multiplication is: the basic explanation of multiplication is adding a number, with respect to another number, repeatedly. For example, if we are multiplying 2 by 3, that means 3 is added to itself two times, i.e. 3 + 3 = 6. This is a simple technique for kids to multiply numbers.  

(Answer) 2 x 2 would equal 4. (Explanation) Add a 2, with respect to 2, repeatedly, would equal 4.

(Answer) 4 x 4 would equal 16. (Explanation) Add a 4, with respect to 4, repeatedly, would equal 16.

Answer: Step-by-step explanation:

because 1 + 2  does equal 3 but 4 + 5 does not equal to 6 because it equals to 9.

and 2 x 2  does equal to 4 but 4 x 4 does not equal to 8 because it equals to 16.

The equation of the line that passes through (4, 3) and (-4, -1) is y = -x/2 + 5. So, correct option is A.

To find the equation of the line that passes through two given points, we use the slope-intercept form of a linear equation, which is:

y = mx + b

where m is the slope of the line and b is the y-intercept.

First, we need to find the slope of the line using the two given points. The formula for finding slope between two points is:

m = (y₂ - y₁) / (x₂ - x₁)

where (x₁, y₁) and (x₂, y₂) are the coordinates of the two points.

Substituting the given points into the formula, we get:

m = (-1 - 3) / (-4 - 4) = -4/8 = -1/2

Now we know the slope, we can use one of the given points (4, 3) and substitute the slope into the slope-intercept form of the equation and solve for b.

y = mx + b

3 = (-1/2)(4) + b

3 = -2 + b

b = 5

Therefore, the equation of the line that passes through (4, 3) and (-4, -1) is:

y = -x/2 + 5

So, correct option is A.

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Complete question is:

What is the equation of the line that passes through (4, 3) and (-4, -1)?

Choices:

y = -x/2 + 5

y=2x+7

y=x/2 +1

y= -x/2 +7

Answer:

To convert square millimeters to square centimeters, we need to divide the area in square millimeters by 100 (since there are 100 square millimeters in a square centimeter).

So, the area of the top of Katrina's laptop in square centimeters would be:

57,000 mm² ÷ 100 = 570 cm²

Therefore, the area of the top of Katrina's laptop in square centimeters is 570 cm².

The statement Y = {u: (z X)uez) = U{z: zEX}=UX, means that the set Y is the union of all the sets z that are elements of X. In other words, Y is the set of all elements that are in at least one of the sets in X.

The statement can be broken down into two parts:

The first part, Y = {u: (z X)uez), says that Y is the set of all elements u such that u is an element of at least one set z that is an element of X.

The second part, U{z: zEX}=UX, says that the union of all the sets z that are elements of X is equal to the set UX.

The two parts of the statement can be combined to say that Y is the union of all the sets z that are elements of X.

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Step-by-step explanation:

(540×45) + ( 540×55)

(24300) +(29700)

54000

Answer:

540*45+540*55=540*45=24300 540*55=29700=24300+29700=54000

Step-by-step explanation:

by solving the the first bracket to get the answer then the other one, after getting the both answer, then add it together

Answer:

B} 7/20

Step-by-step explanation:

total: 80

section 1: 28

p(section 1) = 28/80 = 7/20

Answer:  $130 money did Brenda and Hazel have all together before buying decorations and snacks.

Here, we have,

You want to know Brenda and Hazel's combined money when the ratio of their remaining balances is 1 : 4 after Brenda spent $58 and Hazel spent $37. They had the same amount to start with.

Setup

Let x represent the total amount the two women started with. Then x/2 is the amount each began with, and their fnal balance ratio is ...

 (x/2 -58) : (x/2 -37) = 1 : 4

Solution

Cross-multiplying gives ...

 4(x/2 -58) = (x/2 -37)

 2x -232 = x/2 -37 . . . . . . eliminate parentheses

 3/2x = 195 . . . . . . . . . . . . add 232-x/2

 x = (2/3)(195) = 130 . . . . . multiply by 2/3

Brenda and Hazel had $130 altogether before their purchases.

Alternate solution

The difference in their spending is $58 -37 = $21.

This is the same as the difference in their final balances.

That difference is 4-1 = 3 "ratio units", so each of those ratio units is $21/3 = $7.

Their ending total is 1+4 = 5 ratio units, or $35.

The total they started with is $58 +37 +35 = $130.

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complete question:

Brenda and Hazel decide to throw a surprise party for their friend, Aerica. Brenda and Hazel each go to the store with the same amount of money. Brenda spends $58 on decorations, and Hazel spends $37 on snacks. When they leave the store, the ratio of Brenda’s money to Hazel’s money is 1 : 4. How much money did Brenda and Hazel have all together before buying decorations and snacks?

If an auto body shop repaired 22 cars and trucks and there were 8 fewer cars than trucks, 15 trucks were repaired.

Let's assume the number of trucks repaired is "x". We know that the total number of cars and trucks repaired is 22. Since there were 8 fewer cars than trucks, the number of cars repaired must be x-8. Therefore, we can set up the following equation:

x + (x-8) = 22

Simplifying, we get:

2x - 8 = 22

Adding 8 to both sides:

2x = 30

Dividing by 2:

x = 15

We can check this by plugging x back into the equation and verifying that the number of cars repaired is 7, which is 8 fewer than 15.

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Answer:

The correct answer:

(B) reduction