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MrRa [10]
2 years ago
15

If f(x)=-x-2 and g(x)=x^2, what is (g°f)(-6)

Mathematics
1 answer:
Leto [7]2 years ago
6 0
(g \circ f)(x)=(-x-2)^2=x^2+4x+4\\\\
(g\circ f)(-6)=(-6)^2+4\cdot(-6)+4=36-24+4=16
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Read the sentence below and answer the following question: Roy was very careful to cleave the apple into even portions. What doe
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To separate into parts
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A small diner has one employee and a counter with seating for 8 customers. The diner does not package food for takeout. Customer
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Answer:

12 customers are waiting each hour to enter the diner

Step-by-step explanation:

20 customers arrive each hour to the diner. 8 customers ocuppy the seats each hour, and 12 are left waiting outside.

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3 years ago
Complete the solution of the equation. Find the value of y when x equals -15. -x ‒ 8y = -1
valkas [14]
To complete the solution of - x - 8y = -1, we first need to substitute x for -15.
As so:

-(-15) - 8y = -1
15 - 8y = -1

Next, we can subtract 15 from each side to get:

15 - 15 - 8y = -1 - 15
- 8y = -16

Now, we can divide by -8 on each side to get the y by itself:

-8y / -8 = -16 / -8 
y = -16 / -8
y = 2

There we go! <em>y</em> = 2 when x = -15! Hope I could help you out! Have a good one.
5 0
3 years ago
Coach Posey has $10,000 to invest. He can go to Bryant Bank that pays 5% simple interest or Hornets Bank that pays 4% interest c
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5 0
3 years ago
An automobile manufacturer finds that 1 in every 2500 automobiles produced has a particular manufacturing defect. ​(a) Use a bin
Advocard [28]

Answer:

a) 0.1558 = 15.58% probability of finding 4 cars with the defect in a random sample of 7000 cars.

b) 0.1557 = 15.57% probability of finding 4 cars with the defect in a random sample of 7000 cars. These probabilities are very close, which means that the approximation works.

Step-by-step explanation:

Binomial distribution:

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

In which C_{n,x} is the number of different combinations of x objects from a set of n elements, given by the following formula.

C_{n,x} = \frac{n!}{x!(n-x)!}

And p is the probability of X happening.

Poisson distribution:

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:

P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}

In which

x is the number of sucesses

e = 2.71828 is the Euler number

\mu is the mean in the given interval.

To use the Poisson approximation for the binomial, we have that:

\mu = np

1 in every 2500 automobiles produced has a particular manufacturing defect.

This means that p = \frac{1}{2500} = 0.0004

a) Use a binomial distribution to find the probability of finding 4 cars with the defect in a random sample of 7000 cars.

This is P(X = 4) when n = 7000. So

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

P(X = 4) = C_{7000,4}.(0.0004)^{4}.(0.9996)^{6996} = 0.1558

0.1558 = 15.58% probability of finding 4 cars with the defect in a random sample of 7000 cars.

(b) The Poisson distribution can be used to approximate the binomial distribution for large values of n and small values of p.

Using the approximation:

\mu = np = 7000*0.0004 = 2.8. So

P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}

P(X = 4) = \frac{e^{-2.8}*(2.8)^{4}}{(4)!} = 0.1557

0.1557 = 15.57% probability of finding 4 cars with the defect in a random sample of 7000 cars. These probabilities are very close, which means that the approximation works.

6 0
3 years ago
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