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2 years ago

Given f(x)=2x+1 and g(x)=7-x. Find g(f(x)).

Mathematics

1 answer:

Darina [25.2K]2 years ago

6 0

Answer:

f(g(x)) = 2(7 - x) + 1

Step-by-step explanation:

f(x) = 2x + 1

g(x) = 7 - x

The question in the picture itself says to find f(g(x)) so i'll find that instead

f(g(x)) = 2(7 - x) + 1

f(g(x)) = 14 - 2x + 1

f(g(x)) = -2x + 15

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Water is flowing into a large spherical tank at a constant rate. Let V (t) be the volume of water in the tank at time t, and h(t

aleksley [76]

Answer:

See solutions for detail.

Step-by-step explanation:

a. $\frac{dV}{dt}$ is the instantaneous rate of change of volume given with respect to time, t.

The volume's rate of change is written as a function of time.

- $\frac{dh}{dt}$ is the rate of change in the height of water in the tank with respect to time, t.

b. $\frac{dV}{dt}-$ is the only constant. Water flows into the constant at a constant rate, say $6cm^3$ per minute.

c. $\frac{dV}{dt}$ is positive. Volume water in the take is increasing from time to time.

-The volume at time t=1 is greater than the volume at t=0, hence, it's a positive rate of change.

d. $\frac{dh}{dt}$ is a positive rate. The initial height of water in the tank is zero.

-The final height at time t is 0.25h. The height is increasing with time.

Hence, it is positive.

8 0

3 years ago

Factor 20r+60t to identify the equivalent expression

Nadusha1986 [10]

Answer:

$\boxed{20(r + 3t)}$

Step-by-step explanation:

$20r + 60t$

Factor out 20 from the expression.

$20(r) + 20(3t)$

Take 20 as common.

$20(r + 3t)$

7 0

3 years ago

QUESTION 7 Solve for x. (3x + 32) (5x-8) O a. 3 b. 12 O c. 20 O d. 19.5

Alchen [17]

Answer:

The answer is x = 20

Step-by-step explanation:

If you set both equations equal to each other and solve for x, you will get 20.

3x+32 = 5x-8 add 8 to both sides

3x+40 = 5x subtract 3x from both sides

40 = 2x divide by 2 on both sides

20 = x

7 0

2 years ago

You can buy an 8-pack of paper towels for $7.92 or a 12-pack for $11.64. Which is the better buy?

goldfiish [28.3K]

Answer:

ill say the 8 pack

Step-by-step explanation:

8 0

2 years ago

The director of the library believes that 14% of the library's collection is checked out. If the director is right, what is the

Ksivusya [100]

Answer: 0.2643

Step-by-step explanation:

Let p be the population proportion and $\hat{p}$ be the sample proportion .

As per given question , we have

$p=0.14\\\\ \hat{p}=0.13\\\\ n=478$

z-score : $\dfrac{\hat{p}-p}{\sqrt{\dfrac{p(1-p)}{n}}}$

$z=\dfrac{0.13-0.14}{\sqrt{\dfrac{0.14(1-0.14)}{478}}}\\\\=-0.630087269176\approx-0.63$

The required probability ( using z-table ):-

$P(z$

Hence, the probability that the proportion of books checked out in a sample of 478 books would be less than 13% = 0.2643

5 0

3 years ago