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Art [367]
3 years ago
13

Question 1 (2 points)

Mathematics
1 answer:
Liula [17]3 years ago
6 0

Answer:

The vertex is (-1, 4), the domain is all real numbers, and the range is y less than 4

Step-by-step explanation:

Given

f(x) = -(x+1)^2 + 4

Solving (a): The vertex;

Assume the general form of a function is

f(x) = a(x-h)^2+k

The vertex is determined by (h,k)

By comparison, we have:

-h = 1

Solve for h, we have:

h = -1

k = 4

So, the vertex is:

(h,k) = (-1,4)

The domain; x is all real numbers

From the function;

f(x) = -(x+1)^2 + 4

This can be rewritten as:

f(x) = 4 - (x+1)^2

This implies that:

Whatever the value of (x + 1)^2 is, it will be subtracted from 4 to give y or f(x);

Hence:

y is less than 4

<em>Option B answers the question</em>

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Step-by-step explanation:

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Answer:

1) f(g(2)) = 24

2) f(g(-1)) = -4

Step-by-step explanation:

1) GIven f(x) = x²+2x and g(x) = 2x

f(g(x)) = f(2x)

f(2x) = (2x)² + 2(2x)

f(2x) = 4x² + 4x

f(g(x)) = 4x² + 4x

f(g(2)) = 4(2)² + 4(2)

f(g(2)) = 16+8

f(g(2)) = 24

2) f(x) = x+1 and g(x) = 5x

f(g(x)) = f(5x)

f(5x)= 5x + 1

f(g(x)) = 5x + 1

f(g(-1)) = 5(-1) + 1

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8 0
3 years ago
A researcher wishes to​ estimate, with 99​% ​confidence, the population proportion of adults who think the president of their co
scoray [572]

Answer:

a. n=4148

b. n=3909

c. The sample size is smaller if a known proportion from prior study is used. The difference in sample sizes is 239

Step-by-step explanation:

a. For sample where no preliminary estimate is given, the minimum sample size is calculated using the formula:

n=p(1-p)(\frac{z}{ME})^2

Where:

  • ME=Margin of error
  • p= is the assumed proportion

#Let p=0.5, substitute in the formula to solve for n:

n=0.5(1-0.5)\times (2.576/0.02)^2\\\\=4147.36\approx 4148

Hence, the minimum sample size is 4148

b. If given a preliminary estimate p=0.38, we use the same formula but substitute p with the given value:

n=p(1-p)(z/ME)^2\\\\=0.38(1-0.38)(2.576/0.02)^2\\\\=3908.47\approx3909

Hence, the minimum sample size is 3909

c. Comparing the sample sizes from a and b:

n_{0.5}>n_{0.38}\\\\n_{0.5}-n_{0.38}=4148-3909=239

Hence, the actual sample size is smaller for a known proportion from prior a prior study.

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3 years ago
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