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3 years ago

11

The graph of the function f(x)=x^2-6x shifted 2 units to the left on the graph of g(x). Select the two functions that represent

the shift of f(x) onto g(x)

1 answer:

Nimfa-mama [501]3 years ago

8 0

The correct answer is

g(x) =f(x+2)
And

g(x)=x^2-2x-8

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A facilities manager at a university reads in a research report that the mean amount of time spent in the shower by an adult is

Zolol [24]

Answer:

A) Null Hypothesis;H0: μ = 5

Alternative Hypothesis;Ha: μ ≠ 5

B) test statistic = -2.1226

C) p-value = 0.0598

D) Option A is correct

Step-by-step explanation:

We are given;

x = 4.52 minutes

s = 0.75 minutes

μ = 5 minutes

n = 11

degree of freedom = n - 1 = 11 - 1 = 10

A) The hypotheses are;

Null Hypothesis;H0: μ = 5

Alternative Hypothesis;Ha: μ ≠ 5

B) t-statistic = (x - μ)/(s/√n)

(4.52 - 5)/(0.75/√11) = -2.1226

C) From the t-score calculator results attached, the p-value is approximately 0.0598.

D) The P-value of 0.0598 is is greater than the significance level of 0.01, thus we fail to reject the null hypothesis, and we say that the result is statistically nonsignificant. So option A is correct.

3 0

4 years ago

Find the nonpermissible replacement for 'n' in this expression (-8)/(5n)

seraphim [82]

In any rational function the denominator should never equal to 0, hence in this case since the denominator is 5n the only answer is n should not equal 0

7 0

3 years ago

Read 2 more answers

You are under contract to design a storage building with a square base and a volume of 14,000 cubic feet. the cost of materials

Goryan [66]

The first thing we are going to do for this case is define variables.
We have then:
y = the cost of the box
x = one side of the square base
z = height of the box
The volume of the building is 14,000 cubic feet:
x ^ 2 * z = 14000
We cleared z:
z = (14000 / x ^ 2)
On the other hand, the cost will be:
floor = 4 (x ^ 2)
roof = 3 (x ^ 2)
for the walls:
1 side = 16 (x * (14000 / x ^ 2)) = 16 (14000 / x)
4 sides = 64 (14000 / x) = 896000 / x
The total cost is:
y = floor + roof + walls
y = 4 (x ^ 2) + 3 (x ^ 2) + 896000 / x
y = 7 (x ^ 2) + 896000 / x
We derive the function:
y '= 14x - 896000 / x ^ 2
We match zero:
0 = 14x - 896000 / x ^ 2
We clear x:
14x = 896000 / x ^ 2
x ^ 3 = 896000/14
x = (896000/14) ^ (1/3)
x = 40
min cost (y) occurs when x = 40 ft
Then,
y = 7 * (40 ^ 2) + 896000/40
y = 33600 $
Then the height
z = 14000/40 ^ 2 = 8.75 ft
The price is:
floor = 4 * (40 ^ 2) = 6400
roof = 3 * (40 ^ 2) = 4800
walls = 16 * 4 * (40 * 8.75) = 22400
Total cost = $ 33600 (as calculated previously)
Answer:
The dimensions for minimum cost are:
40 * 40 * 8.75

8 0

4 years ago

Please help! Best answer gets Brainliest!

Elanso [62]

Answer:

pretty sure its B

Step-by-step explanation:

5 0

3 years ago

Read 2 more answers

The population of fish in a lake grew exponentially. In 2000, a researched estimated

cupoosta [38]

Answer:

a) P(t) = P₀ e⁰•⁰⁵⁴ᵗ

b) 2786 fishes

c) The estimated population will be 24000 in the year 2030.

Step-by-step explanation:

The function representing the population of fish in a lake as it grows exponentially

P(t) = P₀eᵏᵗ

If the base year is taken to be 2000

P₀ = 4780 fishes

k = constant

In 2010, P(t=10) = 8200 fishes, we can now solve for the constant

kt = k × 10 = 10k

8200 = 4780 e¹⁰ᵏ

e¹⁰ᵏ = (8200/4780) = 1.7155

In e¹⁰ᵏ = In 1.7155 = 0.5397

10k = 0.5397

k = 0.054 to 3 d.p

P(t) = P₀ e⁰•⁰⁵⁴ᵗ

b) What was the estimated population in 1990?

1990 is 10 years before 2000, hence, t = -10

P(t) = P₀ e⁰•⁰⁵⁴ᵗ

0.054t = 0.054 × -10 = -0.54

P₀ = 4780

P(t) = 4780 e⁻⁰•⁵⁴ = 4780 × 0.5829 = 2,786.4 = 2786 fishes to the nearest thousand

c) When will the population 24,000?

P(t) = 24000

P₀ = 4780

t = ?

24000 = 4780 e⁰•⁰⁵⁴ᵗ

e⁰•⁰⁵⁴ᵗ = (24000/4780) = 5.021

In e⁰•⁰⁵⁴ᵗ = In 5.021 = 1.6136

0.054t = 1.6136

t = (1.6136/0.054) = 29.88 years = 30 years to the nearest whole number.

Since the base year is 2000, 30 years after that is 2000 + 30 = 2030.

Hope this Helps!!!

8 0

3 years ago