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Daniel [21]
3 years ago
11

Let f(x)=4x+7 and g(x)=3x-5. find (fog)(-4) A. -9 B. -61 C. -32 D. -17

Mathematics
1 answer:
prohojiy [21]3 years ago
3 0

Answer:

B . (fog)(-4)  = - 61

Step-by-step explanation:

Here, given  f(x) = 4 x + 7, g(x) = 3 x- 5

Now, by the COMPOSITE FUNCTION:

(f o g) (x)  = f (g(x))

Now here: )f o g) ( -4)  = f (g(-4))

<u>Simplifying for g(x) =  3 x  - 5</u>

 g(-4)  = 3 (-4) -  5 = -12 - 5  = -17

or, g (-4)  = -17

Now, <u>for f(x) = 4 x + 7 </u>

f ( g(-4))  = f ( -17) = 4 (-17) + 7

= - 68 + 7 =  - 61

or, f ( g(-4))  = - 61

Hence, (fog)(-4)  = - 61

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Answer:

x - 80

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x - 80

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3 years ago
The Resource Conservation and Recovery Act mandates the tracking and disposal of hazardous waste produced at U.S. facilities. Pr
aniked [119]

Answer:

(a) E(X) =  0.383

The expected number in the sample that treats hazardous waste on-site is 0.383.

(b) P(x = 4) = 0.000169

There is a 0.000169 probability that 4 of the 10 selected facilities treat hazardous waste on-site.

Step-by-step explanation:

Professional Geographer (Feb. 2000) reported the hazardous waste generation and disposal characteristics of 209 facilities.

N = 209

Only eight of these facilities treated hazardous waste on-site.

r = 8

a. In a random sample of 10 of the 209 facilities, what is the expected number in the sample that treats hazardous waste on-site?

n = 10

The expected number in the sample that treats hazardous waste on-site is given by

$ E(X) =  \frac{n \times r}{N} $

$ E(X) =  \frac{10 \times 8}{209} $

$ E(X) =  \frac{80}{209} $

E(X) =  0.383

Therefore, the expected number in the sample that treats hazardous waste on-site is 0.383.

b. Find the probability that 4 of the 10 selected facilities treat hazardous waste on-site

The probability is given by

$ P(x = 4) =  \frac{\binom{r}{x} \binom{N - r}{n - x}}{\binom{N}{n}} $

For the given case, we have

N = 209

n = 10

r = 8

x = 4

$ P(x = 4) =  \frac{\binom{8}{4} \binom{209 - 8}{10 - 4}}{\binom{209}{10}} $

$ P(x = 4) =  \frac{\binom{8}{4} \binom{201}{6}}{\binom{209}{10}} $

$ P(x = 4) =  \frac{70 \times 84944276340}{35216131179263320}

P(x = 4) = 0.000169

Therefore, there is a 0.000169 probability that 4 of the 10 selected facilities treat hazardous waste on-site.

8 0
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dybincka [34]

Answer:

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Formula for slope is y1-y2/x1-x2

4--1/-4-0

5/-4

-1.25

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Suppose you are standing in a parking lot near a building, and the winter air temperature is 0 degrees Celsius. At that temperat
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The building is 231.7 m far away.Distance can refer to a physical length or an estimate based on other factors in physics or common use.

<h3>What is distance?</h3>

Distance is a numerical representation of the space between two objects or locations. |AB| is a symbol for the distance between two points A and B.

Given data;

Speed of sound  = 331 meters per second

Time = 0.7 sec

The distance from the building is;

d=v×t

d=331 m/sec × 0.7 sec

d=231.7 m

Hence the building is 231.7 m far away.

To learn more about the distance refer to the link;

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An electrician charges $15 per hour and spends $30 a day on gasoline. At the
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15x - 30 = 105 is the mathematical statement
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