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3 years ago

Algebraic expression represents the statement “4 more than the product of 6 and a number?

Mathematics

1 answer:

Varvara68 [4.7K]3 years ago

7 0

The answer is “6x+4”

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a sail that is in the form of a right triangle is four times as high as it is wide.The sail is made from 8 square meters of mate

patriot [66]

I think it is 2 by 4 so the height of the triangle would be 4

5 0

3 years ago

(I’ll brainlist)

Sonja [21]

Kind of depends. What was the loan you took out? From there I believe you find 5% of the loan total. That will be what they charge you. Not sure about 2) because the loan is what you took from them, so you would kind of already start with the answer.
So just find 5% of the loan. Again, I am not 100% sure but I think that’s how you would find the answer.

7 0

3 years ago

Read 2 more answers

Use the Integral Test to determine whether the series is convergent or divergent

Inga [223]

Answer:

A. $\sum_{n=1}^{\infty}\frac{n}{e^{15n}}$ converges by integral test

Step-by-step explanation:

A. At first we need to verify that the function which the series is related ( $\frac{n}{e^{15n}}$ ) fills the necessary conditions to ensure that the test is effective.

*f(x) must be continuous or differentiable

*f(x) must be positive and decreasing

Let´s verify that $f(x)=\frac{n}{e^{15n}}$ fills these conditions:

*Considering that eˣ≠0 for all x, the function $f(x)=\frac{n}{e^{15n}}$ does not have any discontinuities, so it´s continuous

*Because eˣ is increasing:

if a<b ,then eᵃ<eᵇ

if 0<eᵃ<eᵇ ,then 1/eᵃ > 1/eᵇ

if 1/eᵃ > 1/eᵇ and a<b, then a/eᵃ<b/eᵇ

We conclude that $f(x)=\frac{n}{e^{15n}}$ is decreasing

*Because eˣ is always positive and the sum is going from 1 to ∞, this show that $f(x)=\frac{n}{e^{15n}}$ is positive in [1,∞).

Now we are able to use the integral test in $f(x)=\frac{n}{e^{15n}}$ as follows:

$\sum_{n=1}^{\infty}\frac{n}{e^{15n}}\ converges\ \leftrightarrow\ \int_{1}^{\infty}\frac{x}{e^{15x}}\ dx\ converges$

Let´s proceed to integrate f(x) using integration by parts

$\int_{1}^{\infty}\frac{x}{e^{15x}}\ dx=\int_{1}^{\infty}xe^{-15x}\ dx$

Choose your U and dV like this:

$U=x\ \rightarrow dU=1\\ dV=e^{-15x}\ \rightarrow V=\frac{-e^{-15x}}{15}$

And continue using the formula for integration by parts:

$\int_{1}^{\infty}Udv = UV|_{1}^{\infty} - \int_{1}^{\infty}Vdu$

$\int_{1}^{\infty}xe^{-15x}\ dx= \frac{-x}{15e^{15x}}|_{1}^{\infty} -\frac{-1}{15} \int_{1}^{\infty}e^{-15x}\ dx$

$\int_{1}^{\infty}xe^{-15x}\ dx= \frac{-x}{15e^{15x}}|_{1}^{\infty} -\frac{-1}{15}(\frac{-1}{15e^{15x}})|_{1}^{\infty}$

$\int_{1}^{\infty}xe^{-15x}\ dx= \frac{-x}{15e^{15x}}|_{1}^{\infty} -\frac{1}{225e^{15x}}|_{1}^{\infty}$

Because we are dealing with ∞, we´d rewrite it as a limit that will help us at the end of the integral:

$\int_{1}^{\infty}xe^{-15x}\ dx= \lim_{b \to{\infty}}(\frac{-x}{15e^{15x}}|_{1}^{b}-\frac{1}{225e^{15x}}|_{1}^{b})$

$\int_{1}^{\infty}xe^{-15x}\ dx= \lim_{b \to{\infty}} \frac{-b}{15e^{15b}}-\frac{1}{225e^{15b}}-(\frac{-1}{15e^{15}}-\frac{1}{225e^{15}})$

$\int_{1}^{\infty}xe^{-15x}\ dx= ( \lim_{b \to{\infty}} \frac{-b}{15e^{15b}}-\frac{1}{225e^{15b}})+\frac{1}{15e^{15}}(1-\frac{1}{15})$

We only have left to solve the limits, but because b goes to ∞ and it is in an exponential function on the denominator everything goes to 0

$\lim_{b \to{\infty}} \frac{-b}{15e^{15b}}-\frac{1}{225e^{15b}} = 0$

$\int_{1}^{\infty}xe^{-15x}\ dx= \frac{1}{15e^{15}}(1-\frac{1}{15})$

Showing that the integral converges, it´s the same as showing that the series converges.

By the integral test $\sum_{n=1}^{\infty}\frac{n}{e^{15n}}$ converges

7 0

3 years ago

What is the slope of the line that passes through the points (10,5)and (15,20)

kupik [55]

Answer:

<h2>The answer is 3</h2>

Step-by-step explanation:

The slope of a line given two points can be found by using the formula

$m = \frac{ y_2 - y _ 1}{x_ 2 - x_ 1} \\$

where

(x1 , y1) and (x2 , y2) are the points

From the question the points are

(10,5)and (15,20)

The slope is

$m = \frac{20 - 5}{15 - 10} = \frac{15}{5} = 3 \\$

We have the final answer as

Hope this helps you

8 0

3 years ago

Twelve different video games showing violence were observed. The duration times of violence were recorded, with the times (sec

Softa [21]

Answer:

The requirements that must be satisfied are:

- The sample should be reasonably random.

- The sample size should not be higher than 10% of the population.

- The data should not have outliers or excessive skewness.

- The data should be normal or with a sample large enough (usually n>30).

There is no enough information to know if the requirements are satisfied.

Step-by-step explanation:

Ths test hypothesis would be a t-test.

The requirements that must be satisfied are:

- The sample should be reasonably random.

- The sample size should not be higher than 10% of the population.

- The data should not have outliers or excessive skewness.

- The data should be normal or with a sample large enough (usually n>30).

Some conditions are not met, as the sample size (n=12) which is not big enough.

We don't know also if the sample was taken randomly. The size of the sample respect to the population is also unknown.

In conclusion, we can not tell if the requirements are satisfied.

5 0

4 years ago