Let h(x) = (gof)(x)=√x+3
Which of the following could be a possible decomposition of h(x)?
A. f(x)=√x; g(x)=x+3
B. f(x)=x; g(x)=x+3
c. f(x)=x+3; g(x)=√x
D. f(x)=3x; g(x)=√x

Answer:

Step-by-step explanation:

The decay rate of 80% per year means that after each year, the value of the quantity decreases by 80/100 * 3600 = 2880.

To find the value of the quantity after 0.2 decades, we need to multiply the number of years by 10, since a decade is equal to 10 years. In this case, 0.2 decades is equal to 0.2 * 10 = 2 years.

The value of the quantity after 2 years can be found using the formula:

3600 * (1 - 0.8)^2

Plugging in the values, we get:

3600 * (1 - 0.8)^2 = 3600 * (0.2)^2 = 3600 * 0.04 = 144

So, the value of the quantity after 0.2 decades, to the nearest hundredth, is 144.

Answer: 726.83

Step-by-step explanation:

Answer:

Below

Step-by-step explanation:

From the image below you can see that

90 F  + 60 L   = 160 miles

and given F + L = 2 hours       re arrange to  F = 2 - L  

                                      and substitute this "F" into the first equation

90 (2-L )  + 60 L = 160           Solve for L

180  - 90 L     + 60 L     = 160

180 - 30 L = 160

- 30 L = -20

L = 2/3 hr       then   F = 1  1/3  hr       ( because they add to '2' )

The equation of the line which is parallel to the line x = -4 will be x = -3.

An equation of the line is defined as a linear equation having a degree of one. The equation of the line contains two variables x and y. And the third parameter is the slope of the line which represents the elevation of the line.

The general form of the equation of the line:-

y = mx + c

m = slope

c = y-intercept

Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given that the equation of the line is x = -4. The y-intercept is zero for the line.

The equation of the line parallel to the equation will be,

x = -3

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The Total Surface Area for given prism will be 166 [tex]cm^2[/tex].

The entire surface area of a rectangular prism may be computed by adding the areas of its six sides. A rectangular prism's surface area may be determined using the following formula:

[tex]Surface Area = 2(l*w) + 2(l*h) + 2(w*h)[/tex]

where:

l = length of the rectangular prism

w = width of the rectangular prism

h = height of the rectangular prism

Using this formula for given problem,

Given,

l=5cm

w=4cm

h=7cm

[tex]\text{Total Surface area}=2.(5.7)+2.(4.5)+2.(4.7)\\\\=70+40+56\\\\=166\;cm^2[/tex]

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The image of the point M(4, -1) after reflection in the line y = 3 would have the x-coordinate of 4.

When you reflect, you are giving something serious thought. [written] I continued my thoughtful stroll to the car while contemplating the unfortunate honeymooners. Synonyms: thoughtful, ponderous, contemplative, and pensive More reflective's opposites.

Cogitate, deliberate, reason, conjecture, and think are a few words that frequently replace the word reflect. All of these terms indicate "to utilise one's faculties of imagination, reasoning, or inference," but reflect denotes thoughtful deliberation over a memory that has just come to mind.

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Answer: Yes, this statement is true. If the number x² y is a negative integer, it means that x² is a positive integer and y is a negative integer. Therefore, -y would be a positive number.

Step-by-step explanation:

Answer:

4 cups of fruit sorbet.

Step-by-step explanation:

There are 128 cups in 1 gallon. So, 1 gallon of fruit sorbet is equal to 128 cups.

Therefore, each person will receive 128 cups / 32 people = 4 cups of fruit sorbet.

The solution is, each person get 4 cups of fruit sorbet.

Division is the process of splitting a number or an amount into equal parts. Division is one of the four basic operations of arithmetic, the ways that numbers are combined to make new numbers. The other operations are addition, subtraction, and multiplication.

here, we have,

given that,

Hugo is serving fruit sorbet at his party.

He has 1 gallon of fruit sorbet to serve to 32 friends .

now. we get,

There are 128 cups in 1 gallon.

So, 1 gallon of fruit sorbet is equal to 128 cups.

so, we have,

Therefore, each person will receive 128 cups / 32 people = 4 cups of fruit sorbet.

If each person receives the same amount,

then, each person will receive 4 cups of fruit sorbet.

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Answer:

Below

Step-by-step explanation:

2^3  /  2^7 =   2^(3-7)   =   2^(-4)   =   1/ (2^4)   =   1/16   =   .0625  

   ~~~~pick your poison

The required expression [tex]2^3/2^7[/tex], after simplification is equivalent to 1/16.

To simplify the expression [tex]2^3/2^7[/tex], we can apply the rule of exponentiation that states when dividing two numbers with the same base, we subtract the exponents.

In this case, the base is 2.

Using the rule, we subtract the exponent of the denominator from the exponent of the numerator:

[tex]2^3/2^7 = 2^{7} = 2^{-4}[/tex]

The expression [tex]2^{-4}[/tex] can be further simplified by using the rule that states any number raised to a negative exponent is equal to the reciprocal of the number raised to the positive exponent:

[tex]2^{-4} = 1/2^4[/tex]
      = 1/16

Therefore, the expression [tex]2^3/2^7[/tex] is equivalent to 1/16.

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Answer:

C = 235

Step-by-step explanation:

given the graph passes through (10, 1 ) then the coordinates of the point make the equation true.

substitute x = 10, y = 1 into the equation and solve for C

10² + 1² + 12(10) + 14(1) - C = 0

100 + 1 + 120 + 14 - C = 0

235 - C = 0 ( subtract 235 from both sides )

- C = - 235 ( multiply both sides by - 1 )

C = 235

The boxplot without the outliers is (c)

Outliers are data points that are significantly different from the other data points in a dataset.

An outlier is an observation that lies an abnormal distance from other values in a random sample from a population.

Using the definition in (a) as a guide, we have the boxplot to be (c)

This is so because it has a minimum of 15 and a maximum of 95 (just as the original boxplot)

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The equation for the function graphed is g(x) = -1/4(x + 2)^2 -  1

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

f(x) = x^2

First the function is reflected across the x-axis

This gives

f'(x) = -x^2

Next,  the function is stretched vertically by 4

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

f'(x) = -1/4(x)^2

Lastly the function is translated 2 units left and 1 units dows

This is represented as

g(x) = -1/4(x + 2)^2 -  1

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Answer:

Below

Step-by-step explanation:

(2x+15) / ( 3x+15)  =  11/14    cross multiply to get

28x + 210 = 33x + 165

45 = 5x

x = 9       so the larger number is   3 X 9 = 27  

                       (smaller number is 2 x 9 = 18)

The IQR is the best measure of variability, and it equals 45.

Data variation can be caused by a variety of sources. Variability is also known as data spread. The standard deviation is a measure of variability since it measures the spread of data.

The range is the best measure of variability for the data shown, and its value is 45.

The range is defined as the difference between the largest and smallest values in a set of data.

In this case, the largest score is 88 and the smallest score is 20, so the range is 88 - 20 = 68.

The IQR (interquartile range) is another measure of variability, but it is not the best measure for this data set because the data set has only a few values and does not form a normal distribution. The IQR is a more appropriate measure for larger data sets that form a normal distribution.

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Answer:

(-4, -1)

Step-by-step explanation:

The system has one solution

if the second number is lower than that's the answer. so in this case kayla

Step-by-step explanation:

Same as the triangles. Find the area of the large rectangle and the small rectangle, then subtract.

A = L x W

For the large rectangle

A = 30 x 25 = 750

For the small rectangle

A = 26 x 21 = 546

Now to subtract these two

750 - 546 = 240

Answer:

Step-by-step explanation:

The long-run behavior of a function can be determined by examining its asymptotes and the behavior of the function near these asymptotes.

For the function f(p)=(p+1)^3(p+4)^3(p-1), there are three points to consider as possible asymptotes: p = -1, p = -4, and p = 1.

At p = -1, the factor (p-1) is equal to zero, so the function has a vertical asymptote there. This means that as p approaches -1 from either side, the function will approach infinity.

At p = -4, the factor (p+4)^3 is equal to zero, so the function also has a vertical asymptote there. Similarly, as p approaches -4 from either side, the function will approach infinity.

At p = 1, the factor (p+1)^3 is equal to zero, so the function has another vertical asymptote there. In this case, as p approaches 1 from either side, the function will approach negative infinity.

So, the long-run behavior of the function can be described as follows:

The function approaches infinity as p approaches -1 or -4 from either side.

The function approaches negative infinity as p approaches 1 from either side.

Therefore, the long-run behavior of f(p)=(p+1)^3(p+4)^3(p-1) is characterized by three vertical asymptotes at p = -1, p = -4, and p = 1.

Answer:

[tex]\text{As } p \to -\infty, f(p) \to -\infty\\\\\text{As } p \to \infty, f(p) \to \infty[/tex]

====================================================

Explanation:

Each factor is a cubic of degree 3.

The degree of the entire polynomial is 3+3+3 = 9.

Since the degree is odd and the leading coefficient is positive, this means the graph falls to the left and rises to the right.

"falls to the left" means [tex]\text{As } p \to -\infty, f(p) \to -\infty[/tex]

"rises to the right" means [tex]\text{As } p \to \infty, f(p) \to \infty[/tex]

This is verified using a graphing tool like Desmos as shown in the screenshot below. I'm using x in place of p.

Answer:

  5/4

Step-by-step explanation:

You want the product abc when 5x^-2y^(3/2)/√(25xy^4) is written as ax^by^c.

The applicable rules of exponents are ...

  [tex]a^ba^c=a^{b+c}\\\\\dfrac{1}{\sqrt{a}}=a^{-\frac{1}{2}}\\\\(a^b)^c=a^{bc}[/tex]

Using these rules, the expression can be simplified to ...

  [tex]\dfrac{5x^{-2}y^{\frac{3}{2}}}{\sqrt{25xy^4}}=(5x^{-2}y^{\frac{3}{2}})(5^2xy^4)^{-\frac{1}{2}}=(5x^{-2}y^{\frac{3}{2}})(5^{2(-\frac{1}{2})}x^{-\frac{1}{2}}y^{4(-\frac{1}{2})})\\\\=5^{1-1}x^{-2-\frac{1}{2}}y^{\frac{3}{2}-2}\\\\=1\cdot x^{-\frac{5}{2}}y^{-\frac{1}{2}}[/tex]

From this last expression, we determine ...

The product of the values of interest is ...

  abc = (1)(-5/2)(-1/2)

  abc = 5/4

For the information provided the x- and y-components of the vector are 1.5 km and 2.6 km, respectively.

To find the x- and y-components of the vector, we can use trigonometry.

The x-component of vector is given by:

d_x = d × cos(θ)

where d is the magnitude of the vector and θ is the angle between the vector and the x-axis.

In this case, d = 3.0 km and θ = 60 degrees (since the vector is 30 degrees to the left of the y-axis).

So, d_x = 3.0 km × cos(60°) = 1.5 km.

The y-component of vector is given by:

d_y = d × sin(θ)

In this case, d_y = 3.0 km × sin(60°) = 2.6 km.

Expressing the answer using two significant figures gives:

d_x = 1.5 km, d_y = 2.6 km.

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The most appropriate viewing range for the quadratic function is given as follows:

The quadratic function for this problem is defined as follows:

f(x) = x² - 11x + 18.

The function can be factored as follows:

f(x) = (x - 2)(x - 9).

Hence the roots are:

Meaning that the viewing range should include x = 2 and x = 9.

The coefficients of the function are:

a = 1, b = -11, c = 18.

Hence the x-coordinate of the vertex is of:

x = -b/2a

x = 11/2

x = 5.5.

Hence the minimum value of the function is the y-coordinate of the vertex, given as follows:

y = 5.5² - 11(5.5) + 18

y = -12.25.

Meaning that Ymin should be less than -12.25.

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Answer:  -1/2

Step-by-step explanation: Down 1 over 2

Answer:

1: 9 polar bears and 38 penguins

2: 47 snowglobes

3: 130 snowballs

4: 97 penguins

Step-by-step explanation:

i did the math

a. A rise in the unemployment rate accompanies a fall in real GDP. - Consistent

b. An exceptionally strong business recovery is associated with a greater percentage of the labor force being employed. - Not consistent

c. Negative real GDP growth is associated with a fall in the unemployment rate. - Not consistent

This is consistent with the observed relationship between real GDP growth and changes in the unemployment rate. An increase in real GDP is associated with a decrease in the unemployment rate, and vice versa.

This is because when GDP increases, businesses are able to hire more workers, leading to a decrease in the unemployment rate. Conversely, when GDP decreases, businesses may have to lay off employees or reduce their hours, leading to an increase in the unemployment rate.

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The complete question is:

Which of the following are consistent with the observed relationship between growth in real GDP and changes in the unemployment rate as shown in Figure 8-5? Which are not?

a. A rise in the unemployment rate accompanies a fall in real GDP.

b. An exceptionally strong business recovery is associated with a greater percentage of the labor force being employed.

c. Negative real GDP growth is associated with a fall in the unemployment rate.

The scaled dimensions of a kitchen with dimensions 6.3m by 4.8m, if the kitchen plan is drawn to a scale of 1:500, are given as follows:

1.26 cm and 0.96 cm.

The scaled dimensions are obtained applying the proportions in the context of the problem.

The scale is of 1:500, meaning that each dimension is divided by 500, as follows:

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The perimeter of the triangle is 3x + 42.This can bean represented mathematically as (xd + 15) + (2x + 15) + (x + 12) = 3x + 42.

The perimeter of a triangle is the sum of the lengths of its three sides. In this problem, the lengths of the three sides of the triangle are given as x + 15, 2x + 15, and x + 12, where x cannot equal zero. To calculate the perimeter of the triangle, we need  to add these three lengths together. This can bean represented mathematically as (xd + 15) + (2x + 15) + (x + 12) = 3x + 42. Therefore, the perimeter of the triangle is 3x + 42.

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Answer:

F = 29

E= 151

D = 90

Step-by-step explanation:

For F:

The angle F is on a 180 degree angle with a degree next to it that is 151. To get the value F subtract 180-151 and you get 29.

For E: If F is 29 then the angle opposite of F is also 29. So again to find the measure of angle E, subtract 180 minus 29 and you get 151.

For D: D is also lying on a 180 degree angle. The angle next to it is 90. To get 180 add 90. 90 is the measure of angle d.

Answer:

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

Angle d is linear pair with a right angle, therefore:

Angle e is vertically opposite with 151° and therefore they are congruent:

Angle f is adjacent with 151° and forming a linear pair, therefore:

The yellow arches of a big M is not an example of a quadratic equation in real life.

What is quadratic equation ?

Quadratic equation can be defined as equation in which it is in the form of ax^2+bx+c = 0

where c is constant.

A quadratic equation is an equation in which the highest power of the variable is 2. In real life, many phenomena can be modeled by quadratic equations, such as the curve of hanging electrical wires, the path of a boat, the path of a tennis ball, and the path of a human cannonball.

However, the yellow arches of a big M is not a mathematical equation or a physical phenomenon that can be described by a quadratic equation. The arches are simply a design element of the McDonald's logo.

Therefore, The yellow arches of a big M is not an example of a quadratic equation in real life.

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Answer:

27,64,216,64,243

Step-by-step explanation:

Any number raise to power 3

Answer:

the coordinate of the R' after the dilation is (-1,-0.5)

Step-by-step explanation: