Consider the relationship below.

olga_2 [115]

22. B) $65,000,000 per year.

23. B) Education.

Step-by-step explanation:

Step 1; To find the average rate of change in annual budget between the two given years. We divide the difference in values for the two years by the period in between the two years. In 2008, the budget was $358,708,000 while in 2010 it was $488,106,000. The period in between was 2 years i.e 2009 and 2010.

The average rate of change = $\frac{488,106,000-358,708,000}{2}$ = $\frac{129,398,000}{2}$ = $64,699,000 per year.

So the average rate of change was $64,699,000 which approximately equals option B. $65,000,000.

Step 2; To find the human resources program's 2007 to 2010 ratio we divide the value in 2007 to the value in 2010. To find the other similar ratio, we divide the value in 2007 to the value in 2010 for all the other programs and determine which is closest to the human resources program.

Human resources program ratio = $\frac{4,051,050}{5,921,379}$ = 0.6841,

Agricultural / natural resources ratio = $\frac{373,904}{488,106}$ = 0.766,

Education's ratio = $\frac{2,164,607}{3,008,036}$ = 0.7196,

General government's ratio = $\frac{14,347,325}{14,716,155}$ = 0.9749,

Highways and transportation's ratio = $\frac{1,468,482}{1,773,893}$ = 0.827,

Public safety's ratio = $\frac{263,463}{464,233}$ = 0.5675.

The Human resources' program ratio is 0.6841 and the closest is Education's ratio which is 0.7196. So education is the answer.

4 0

3 years ago

Let f(x)=x−4 and g(x)=−2x+4 Find g(f(2)) 0 −12 8 −8

marin [14]

Answer:

8

Step-by-step explanation:

This one is similar to the other one done with graphs , the only difference is we have equations instead of graphs.

Like the other one, we want to find f(2) and whatever that equals we plug into g(x) to find g(f(2))

So first lets find f(2)

f(x) = x - 4

f(2) = 2 - 4

f(2) = -2

g(f(2)) , f(2) = -2 , g(-2)

now lets find g(-2)

g(x) = -2x + 4

g(-2) = -2(-2) + 4

multiply -2 and -2 to get 4

g(-2) = 4 + 4

add 4 and 4 to get 8

g(-2) = 8

We can conclude that g(f(2)) = 8

8 0

3 years ago

Read 2 more answers

If q (x) = 2(x - 1)^2+ 5, what is the value of q (-3)? A. 13 B. 23 C.37 D. -3

kirill115 [55]

Plug in -3 for x and you will get 37

7 0

3 years ago

Read 2 more answers

Y=6/5x+9 in standard form

Alexxx [7]

Answer: -5Y + 6x = -45

5 0

3 years ago

MAT 171

steposvetlana [31]

Using the Factor Theorem, the polynomials are given as follows:

1. $P(x) = x^5 + 2x^4 - 7x^3 + x^2$

2. $P(x) = 0.8(x^4 - 4x^3 - 16x^2 + 64x)$

3. P(x) = -0.1(x³ - 4x² - 3x + 18)

<h3>What is the Factor Theorem?</h3>

The Factor Theorem states that a polynomial function with roots $x_1, x_2, \codts, x_n$ is given by:

$f(x) = a(x - x_1)(x - x_2) \cdots (x - x_n)$

In which a is the leading coefficient.

Item a:

The parameters are:

$a = 1, x_1 = x_2 = 1, x_3 = x_4 = 0, x_5 = -4$

Hence the equation is:

P(x) = (x - 1)²x²(x + 4)

P(x) = (x² - 2x + 1)(x + 4)x²

P(x) = (x³ + 2x² - 7x + 1)x²

$P(x) = x^5 + 2x^4 - 7x^3 + x^2$

Item b:

The roots are:

$x_1 = x_2 = 4, x_3 = 0, x_4 = -4$

Hence:

P(x) = a(x - 4)²x(x + 4)

P(x) = a(x² - 16)x(x - 4)

P(x) = a(x³ - 16x)(x - 4)

$P(x) = a(x^4 - 4x^3 - 16x^2 + 64x)$

It passes through the point x = 5, P(x) = 36, hence:

45a = 36.

a = 4/5

a = 0.8

Hence:

$P(x) = 0.8(x^4 - 4x^3 - 16x^2 + 64x)$

Item 3:

The roots are:

$x_1 = x_2 = 3, x_3 = -2$

Hence:

P(x) = a(x - 3)²(x + 2)

P(x) = a(x² - 6x + 9)(x + 2)

P(x) = a(x³ - 4x² - 3x + 18)

For the y-intercept, x = 0, y = -1.8, hence:

18a = -1.8 -> a = -0.1

Thus the function is:

P(x) = -0.1(x³ - 4x² - 3x + 18)

More can be learned about the Factor Theorem at brainly.com/question/24380382

#SPJ1

5 0

2 years ago