Plz help and explain

The function y = f (x) is graphed below. What is the average rate of change of the function f(x) on the interval - 1 ≤ x ≤ 3?

jonny [76]

Answer:

$\displaystyle -2$

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

Algebra I

Average Rate of Change: $\displaystyle \frac{f(b) - f(a)}{b - a}$

Step-by-step explanation:

Step 1: Define

Interval -1 ≤ x ≤ 3

a = -1, b = 3

f(a) = f(-1) = 4

f(b) = f(3) = -4

Step 2: Find Average

Substitute in variables [ARC]: $\displaystyle \frac{f(3) - f(-1)}{3 + 1}$
Substitute: $\displaystyle \frac{-4 - 4}{3 + 1}$
[Fraction] Subtract/Add: $\displaystyle \frac{-8}{4}$
[Fraction] Divide: $\displaystyle -2$

4 0

2 years ago

If the composition of two functions is:

NARA [144]

9514 1404 393

Answer:

x ≠ 3

Step-by-step explanation:

In any case, the domain is restricted to values of the variable for which the function is defined. The value 1/0 is not defined, so the variable cannot allow the denominator to be zero. The denominator x-3 will be zero for x=3, so that value of the variable cannot be in the domain.

The domain is all real numbers except x=3.

_____

Additional comments

It is useful to become familiar with the domains of different functions. As we saw above, the reciprocal of 0 is undefined. The square root of a negative number is undefined. The log of a non-positive number is undefined. Trig functions are defined everywhere, but their inverse functions are not. Polynomial functions are defined everywhere, but ratios of polynomials have the same restriction on denominators that we see above.

8 0

3 years ago

kayla is drawing a picture of her favorite building in her city, the height of the building on her drawing is 3 inches tall, the

Stolb23 [73]

Answer:

1/12

Step-by-step explanation:

3/36 can easily be simplified into 1/12 you're welcome :)

4 0

3 years ago

The mayor of a town has proposed a plan for the annexation of an adjoining community. A political study took a sample of 900 vot

Stells [14]

Answer:

$z=\frac{0.75 -0.72}{\sqrt{\frac{0.72(1-0.72)}{900}}}=2.00$

Now we can calculate the p value. Since is a bilateral test the p value would be:

$p_v= P(Z>2) =0.0228$

Since the p value is lower than the significance level of 0.05 we have enough evidence to conclude that the true proportion of residents favored annexation is higher than 0.72 or 72%

Step-by-step explanation:

Information given

n=900 represent the random sample selected

$\hat p=0.75$ estimated proportion of residents favored annexation

$p_o=0.72$ is the value that we want to test

represent the significance level

z would represent the statistic

$p_v$ represent the p value

Hypothesis to test

The political strategist wants to test the claim that the percentage of residents who favor annexation is above 72%.:

Null hypothesis: $p\leq 0.72$

Alternative hypothesis: $p > 0.72$

The statistic for this case is given by:

$z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}$ (1)

Replacing the data given we got:

$z=\frac{0.75 -0.72}{\sqrt{\frac{0.72(1-0.72)}{900}}}=2.00$

Now we can calculate the p value. Since is a bilateral test the p value would be:

$p_v= P(Z>2) =0.0228$

Since the p value is lower than the significance level of 0.05 we have enough evidence to conclude that the true proportion of residents favored annexation is higher than 0.72 or 72%

3 0

2 years ago

You will get 10 points! thanks

Marianna [84]

Answer: y=-1/6x+2

Step-by-step explanation: The point goes through (0,2), aka, the b point in y=mx+b (The slope intercept form). Then because it’s proceeding downwards, we know that the slope is negative. So down one, over 6. This make its -1/6.

7 0

2 years ago