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2 years ago

What does 3ˣ + 4·3ˣ⁺¹ = a. 13·3ˣ⁺¹ b. 5·3ˣ⁺¹ c. 5·3²ˣ⁺¹ d. 13·3ˣ

Mathematics

1 answer:

Crazy boy [7]2 years ago

3 0

Answer:

D. 13*3^x

Step-by-step explanation:

$3^x +4*3^x^+^1= \\3^x+4*3(3^x)=\\3^x(1+[4*3])=\\3^x(1+12)=\\3^x(13)=\\13*3^x$

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Answer: <u>Last option</u>

$Z_ {13} = 0.5,\ Z_ {17} = 2.5$

Step-by-step explanation:

The z-scores give us information about how many standard deviations from the mean the data are. This difference can be negative, if the data are n deviations to the left of the mean, or it can be positive if the data are n deviations to the right of the mean.

To calculate the Z scores, we calculate the difference between the value of the data and the mean and then divide this difference by the standard deviation.

$Z = \frac{x- \mu}{\sigma}$ .

Where x is the value of the data, μ is the mean and σ is the standard deviation

In this case :

μ = 12 $/h

$\sigma$ = 2 $/h

We need to calculate the Z-scores for $x = 17$ and $x = 13$

Then for $x = 17$ :

$Z_{17} = \frac{17-12}{2}$ .

$Z_{17} = 2.5$

Then for $x = 13$ :

$Z_{13} = \frac{13-12}{2}$ .

$Z_{13} = 0.5$

Therefore the answer is:

$Z_ {13} = 0.5,\ Z_ {17} = 2.5$

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A chef makes 3 containers of soup that fill a total of 120 soup bowls. Each container of soup costs $30 to make. What is the cos

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A triangle is rotated 90° about the orgin. Which rule describes the transformation

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Step-by-step explanation:

If a triangle is rotated 90° about the origin.

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At one gas station, gas costs $2.75 per gallon. Write an equation that relates the total cost, C, to the number of gallons of ga

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Answer:

The equation will be:

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Step-by-step explanation:

Given that at one station, gas costs $2.75 per gallon.

Let 'g' be the number of gallons of gas purchases

Let 'C' be the total cost

Thus, the expression for total cost can be generated by multiplying the price per gallon by the number of gallons.

Thus,

C = 2.75g

Therefore, the equation will be:

C = 2.75g

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2 years ago

Which statement describes function composition with respect to the commutative property? Given f(x) = x² – 4 and g(x) = x – 3, (

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Answer:

The correct option are;

f(x) = x² - 4 and g(x) = x - 3, (f ο g)(2) = -3 and (g ο f)(2) = -3, so the function is commutative

Given f(x) = 4·x and g(x) = x², (f ο g)(x) = 4·x² and (g ο f)(x) = 16·x²

So the function is not commutative

Step-by-step explanation:

For the equations f(x) = x² - 4 and g(x) = x - 3, we have;

(f ο g)(x) = f(g(x)) = (x - 3)² - 4 = x² - 6·x + 9 - 4 = x² - 6·x + 5

At x = 2, we have;

(f ο g)(2) = f(g(2)) = 2² - 6×2 + 5 = - 3

Similarly, we have;

(g ο f)(x) = g(f(x)) = x² - 4 -3 = x² - 7

At x = 2, we have;

(g ο f)(2) = g(f(2)) = 2² - 7 = 4 - 7 = -3

Therefore, by commutative property, we have that the result of an operation does not change by changing the order of the operands such that we have;

a + b = b + a or a·b = b·a from which we have resolved also the following operation is commutative

(f ο g)(2) = (g ο f)(2)

Similarly given f(x) = 4·x and g(x) = x², (f ο g)(x) = 4·x² and (g ο f)(x) = 16·x²

So the function is not commutative

(f ο g)(x) = f(g(x)) = 4·x²

(f ο g)(x) = 4·x²

(g ο f)(x) = g(f(x)) = (4·x)² = 16·x²

(g ο f)(x) = 16·x²

∴ (f ο g)(x) = 4·x² ≠ (g ο f)(x) = 16·x²

(f ο g)(x) ≠ (g ο f)(x) the function is not commutative.

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