We want the following inequality to be true: IMAGE BELOW!

Answer:

Option B

Step-by-step explanation:

Average rate of change of a function 'f' in the interval x = a and x = b is given by,

Average rate of change of change = [tex]\frac{f(b)-f(a)}{b-a}[/tex]

Given function is,

g(x) = [tex]\frac{5}{x-1}+2[/tex]

We have to calculate the rate of change in the interval [-4, 3],

Average rate of change = [tex]\frac{g(3)-g(-4)}{3-(-4)}[/tex]

g(3) = [tex]\frac{5}{3-1}+1[/tex]

       = 2.5 + 1

       = 3.5

g(-4) = [tex]\frac{5}{-4-1}+1[/tex]

       = -1 + 1

       = 0

Average rate of change = [tex]\frac{3.5-0}{3+4}[/tex]

                                        = [tex]\frac{3.5}{7}[/tex]

                                        = [tex]\frac{1}{2}[/tex]

Therefore, Option B will be the answer.

Answer:

B

Step-by-step explanation:

Edmentum

Answer:

80 square units

Step-by-step explanation:

beep

Answer:

(a) The average rate of change is 0

(b) The values of x are: [tex]x =4\ or\ x = -4[/tex]

Step-by-step explanation:

Given

[tex]f(x) = 16 - x^2; [-4,4][/tex]

Solving (a): The average rate of change (m)

This is calculated using:

[tex]m = \frac{f(b) - f(a)}{b - a}[/tex]

Where

[tex][a,b] = [-4,4][/tex]

So:

[tex]m = \frac{f(4) - f(-4)}{4 - -4}[/tex]

[tex]m = \frac{f(4) - f(-4)}{8}[/tex]

Solve f(4) and f(-4)

[tex]f(4) = 16 - (4^2) = 16 - 16 = 0[/tex]

[tex]f(-4) = 16 - (-4^2) = 16 - 16 = 0[/tex]

So:

[tex]m = \frac{f(4) - f(-4)}{8}[/tex]

[tex]m = \frac{0 - 0}{8}[/tex]

[tex]m = \frac{0}{8}[/tex]

[tex]m = 0[/tex]

Solving (b): All values of x where [tex]f(x) = m[/tex]

In (a), we have:

[tex]m = 0[/tex]

So:

[tex]f(x) = 0[/tex]

So, we have:

[tex]f(x) = 16 - x^2[/tex]

[tex]16 - x^2=0[/tex]

Express 16 as [tex]4^2[/tex]

[tex]4^2 - x^2=0[/tex]

Apply difference of two squares

[tex](4 - x)(4 + x) = 0[/tex]

Split

[tex]4 - x =0; 4 + x = 0[/tex]

Solve for x

[tex]x =4\ or\ x = -4[/tex]

We will find that the average of the function over the given interval is 0, and the two values of x such that the function is equal to the average are x = -4 and x = 4.

To find the average of a function f(x) over an interval [a, b] we need to compute:

[tex]\frac{f(b) - f(a)}{b -a}[/tex]

In this case we have:

f(x) = 16 - x^2

And the interval is:

[-4, 4]

We will get:

[tex]\frac{(16 - (4)^2) - (16 - (-4))^2}{4 - (-4)} = \frac{0}{8} = 0[/tex]

So the function has an average of 0 over that interval.

B) Here we just need to solve:

f(x) = 16 - x^2 = 0

We will get:

16 - x^2 = 0

16 = x^2

±√16 = x

±4 = x

So the solutions are x = 4 and x = -4.

If you want to learn more about averages of functions, you can read:

https://brainly.com/question/16033358

Answer:

Step-by-step explanation:

y= -1/4x

Answer:

Is there any other information?

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

Tust me Plz

Answer:

D

Step-by-step explanation:

5+6 then multiply by 3

(5+6) x 3 or 3 x (5+6)

Answer:

93 becouse you add 75 plus 2x10 is 20 so 75 plus is 105 so 14.75 plus .20 is 15.05

Step-by-step explanation:

Answer:

4 - 20 i

Step-by-step explanation:

you do stuff and you get 4 - 20 i

Answer:

4 Zebras

Step-by-step explanation:

I can only see that she have 5 elephants, possibly more, however it's cut off. If that's true. Then:

If she has 5 elephants (which is currently what she has the most of) and 2 zebras. She needs 4 more zebras. Then she will have 6 zebras. More then any other animal.

Answer:

assuming the elephant has the most dots, as i cant see the full picture, then she needs to collect 4 more because she has 2 already.

Step-by-step explanation:

The elephant has 5 dots

the zebra has 2 dots

4+2=6

Answer:

Step-by-step explanation:

8x+9/x^2-13x+42

Write  8 x  as a fraction with denominator 1

8x+9/x^2-13x+42

then we multipuly 8x/1  by x^2/x^2

Answer:

A = arcTan(8/15) = 0.4900 radians = 28.07°

Step-by-step explanation:

Tan(A) = 8/15

A = arcTan(8/15) = 0.4900 radians = 28.07°

Answer:

.

Step-by-step explanation:

Answer:

If you have 2 decks of 52, it would be 1/52 chance per card, so since there are two, add it up, its 2/104

Step-by-step explanation:

Answer:

1/16

Step-by-step explanation:

:))

Answer:

0.42

Step-by-step explanation:

they are both multiples of 0.06

think of it like 6 x 6= 36 and 6 x 8 = 48

6 x 7 = 42 would be halfway

Answer:

0.42

Step-by-step explanation:

To find the half, add da numbers and divide by 2. So 0.36 and 0.48 added together is 0.84. That divided by 2 is 0.42.

Answer:

the answer is 3/8

Step-by-step explanation:

Answer:

11 c12 cyfiddiddjkssjksajusaahogsyi of

Answer:

x midpoint 5

y midpoint 2

(5,2)

(-b±√(b²-4ac))/(2a)

Answer:

x=120±6434−−−√

x=−4.996

x=244.996

Find the Solution for

−125x2+30000x+153000=0

using the Quadratic Formula where

a = -125, b = 30000, and c = 153000

x=−b±b2−4ac−−−−−−−√2a

x=−30000±300002−4(−125)(153000)−−−−−−−−−−−−−−−−−−−−−√2(−125)

x=−30000±900000000−−76500000−−−−−−−−−−−−−−−−−−−√−250

x=−30000±976500000−−−−−−−−√−250

The discriminant b2−4ac>0

so, there are two real roots.

Simplify the Radical:

x=−30000±1500434−−−√−250

x=−30000−250±1500434−−−√−250

Simplify fractions and/or signs:

x=120±6434−−−√

which becomes

x=−4.996

x=244.996

Answer:

14322 * 10¹²

1.4322 * 10¹⁶

Step-by-step explanation:

14322000000000000

14322 * 10¹²

1.4322 * 10¹⁶

Answer:

After 30 years

Step-by-step explanation:

population×2=20 years

population×2×1.5=20×1.5 years

population×3=30 years

Answer:

B. 4x ≤ 320

Step-by-step explanation:

Not sure how to explain my thinking. However, 4x must be smaller than 320 because she cannot spend more than that.

Answer:

Step-by-step explanation:

b

Answer:

7(-4 - x) = -28 - 7x

-7(4 - x) = -28 + 7x

7(4 + x) = 28 + 7x

-7(-4 + x) = 28 - 7x

Step-by-step explanation:

To apply the distributive property, use the term outside the bracket to multiply each of the term you have inside the bracket.

Thus:

✔️7(-4 - x) = 7(-4) +7(-x)

= -28 - 7x

✔️-7(4 - x) = -7(4) -7(-x)

= -28 + 7x

✔️7(4 + x) = 7(4) + 7(+x)

28 + 7x

✔️-7(-4 + x) = -7(-4) -7(+x)

= 28 - 7x

Answer:

95% of the confidence interval for q is

(0.05809 , 0.1183)

Step-by-step explanation:

Step:1

Given that the random sample of 340 electronic components manufactured by a certain process is tested, and 30 are found to be defective.

sample proportion

                   [tex]q^{-} = \frac{x}{n} = \frac{30}{340} = 0.0882[/tex]

Step:2

95% of the confidence interval is determined by

[tex](q - Z_{0.05} \sqrt{\frac{pq}{n} } , q + Z_{0.05} \sqrt{\frac{pq}{n} } )[/tex]

[tex]((0.0804 -1.96 \sqrt{\frac{0.0804 X0.9118}{340} } ,0.0804 +1.96 \sqrt{\frac{0.0804 X0.9118}{340})[/tex]

[tex]( 0.0882- 1.96 \sqrt{0.000236} , 0.0882 + 1.96 \sqrt{0.000236} )[/tex]

(0.0882 - 0.03011 , 0.0882+0.03011)

(  0.05809 , 0.1183)

Final answer:-

95% of the confidence interval for q is

(0.05809 , 0.1183)

Answer:

A census, because the wholesale prices of all items are listed.

Step-by-step explanation:

9514 1404 393

Answer:

  3 ft

Step-by-step explanation:

The formula for the area of a trapezoid is ...

  A = 1/2(b1 +b2)h

Filling in the given information, we can solve for h.

  15 ft² = 1/2(4 ft +6 ft)h

  15 ft² = (5 ft)h

  h = (15 ft²)/(5 ft) = 3 ft

The height of the trapezoid is 3 feet.

Answer:

A,D,F are less then 1/2

Step-by-step explanation:

Answer:

1/8

1/16

1/6

Step-by-step explanation:

1. 1/2 = 0.5              2. 1/2 = 0.5

  1/6 = 0.167               1/8 = 0.125