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3 years ago

Given the functions f(x) = 2x + 5 and g(x) = x2 + 8, which of the following functions represents f(g(x)] correctly?

Mathematics

1 answer:

lakkis [162]3 years ago

7 0

Answer:

Choice 4.

Step-by-step explanation:

f(g(x))

Replace g(x) with x^2+8 since g(x)=x^2+8.

f(g(x))

f(x^2+8)

Replace old input,x, in f with new input, (x^2+8).

f(g(x))

f(x^2+8)

2(x^2+8)+5

Distribute:

f(g(x))

f(x^2+8)

2(x^2+8)+5

2x^2+16+5

Combine like terms:

f(g(x))

f(x^2+8)

2(x^2+8)+5

2x^2+16+5

2x^2+21

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A cylindrical package to be sent by a postal service can have a maximum combined length and girth (perimeter of a cross section)

motikmotik

The height of package is 34 inches.

According to the statement

we have given that the perimeter of cylinderical package is 123 inches.

and we have to find the volume of this package.

So,

According to the perimeter

2(Pi)r + h = 123

and then

h = 123 - 2(Pi)r

then the volume become

V = (Pi) r^2h

V= (Pi) r^2 * [ 123 - 2(Pi)r ] = 123 (Pi) r^2 - 2(Pi)r^3

then differentiate it

dV/dr = 246(Pi) r - 6(Pi)r^2

Now take

r(246(Pi) - 6(Pi)r) = 0

then neglect r=0 and then find another value of r.

r = 246(Pi) / 6(pi)

here r=41 then

h = 123 - 2(Pi)r

h = 123 - 2(3.14)41

h = 123 - 2(Pi)r

Then put the value of r then h = 34 inches.

So, The height of package is 34 inches.

Learn more about Volume here brainly.com/question/1972490

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3 0

2 years ago

You have 20 to spend on taxi fare. The ride costs $5 plus $2.50 50 per kilometer.

SashulF [63]

Answer:

5+2.50m <=20

Step-by-step explanation:

<= -- means less than or equal to

8 0

3 years ago

There is 1/5 of a foot of ribbon left on

Andrews [41]

Answer:

1/15th of a foot

Step-by-step explanation:

15 divided by 3 is 5

6 0

3 years ago

In testing the hypothesis H 0 colon mu subscript D less or equal than 5 space v s. space H 1 colon mu subscript D greater than 5

malfutka [58]

Answer:

The null hypothesis failed to be rejected (P-value=0.014).

Step-by-step explanation:

This is a hypothesis test for the population mean.

The null and alternative hypothesis are:

$H_0: \mu=5\\\\H_a:\mu> 5$

The significance level is α=0.01.

The sample has a size n=20.

The sample mean is M=9.

As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=7.5.

The estimated standard error of the mean is computed using the formula:

$s_M=\dfrac{s}{\sqrt{n}}=\dfrac{7.5}{\sqrt{20}}=1.677$

Then, we can calculate the t-statistic as:

$t=\dfrac{M-\mu}{s/\sqrt{n}}=\dfrac{9-5}{1.677}=\dfrac{4}{1.677}=2.385$

The degrees of freedom for this sample size are:

$df=n-1=20-1=19$

This test is a right-tailed test, with 19 degrees of freedom and t=2.385, so the P-value for this test is calculated as (using a t-table):

$P-value=P(t>2.385)=0.014$

As the P-value (0.014) is bigger than the significance level (0.01), the effect is not significant.

The null hypothesis failed to be rejected.

3 0

3 years ago

Which scenario reflects an annual inflation rate of 2%? In year 1, the price of a tire is $100. In year 2, the same tire costs $

katrin [286]

Answer:

The correct answer is 2. 2. In year 1, the price of a candy bar is $0.50. In year 2, the same candy bar is $0.51.

Price of candy bar in Yr 2 should be = 0.50 * 1.02 = 0.51

This scenario reflects an inflation of 2%.

Step-by-step explanation:

Let's check each scenario and select the one that reflects an annual inflation rate of 2%.

1. In year 1, the price of a tire is $100. In year 2, the same tire costs $120.

Price of tire in Yr 2 should be= 100 * 1.02 = 102

This scenario reflects an inflation of 20%. Not the one we're looking for.

2. In year 1, the price of a candy bar is $0.50. In year 2, the same candy bar is $0.51.

Price of candy bar in Yr 2 should be = 0.50 * 1.02 = 0.51

This scenario reflects an inflation of 2%. This is the correct answer.

3. In year 1, the price of a pair of shoes is $30. In year 2, the same pair of shoes is $32

Price of pair of shoes in Yr 2 should be= 30 * 1.02 = 30.60

This scenario reflects an inflation of 6.7%. Not the one we're looking for.

4. In year 1, the price of a pair of headphones is $20. In year 2, the same pair of headphones is $21.

Price of pair headphones in Yr 2 should be= 20 * 1.02 = 20.40

This scenario reflects an inflation of 5%. Not the one we're looking for.

5 0

4 years ago

Read 2 more answers