Math pweasee 15 points

The height odf a regtangular pyramid is 4 inches. The base of the pyramid measures 9 inches by 9 inches. What is the volume of t

mrs_skeptik [129]

Answer:

$V=108\ \text{inches}^3$

Step-by-step explanation:

Given that,

The height of a rectangular pyramid is 4 inches

The base of the pyramid measures 9 inches by 9 inches.

We need to find the volume of the rectangular pyramid. The formula for the volume of the rectangular pyramid is given by :

$V=\dfrac{lbh}{3}$

Substitute all the values,

$V=\dfrac{4\times 9\times 9}{3}\\\\V=108\ \text{inches}^3$

So, the volume of the rectangular pyramid is $108\ \text{inches}^3$ .

8 0

3 years ago

Adriana went to school for 6 2/5 hours on Tuesday. What is 6 2/5 expressed as a decimal?

lozanna [386]

Answer:

6.4 .

Step-by-step explanation:

this was on my test

3 0

3 years ago

Which statement is true for the equation 3x − 3x − 2 = −2?

coldgirl [10]

It would come out to 3x = 3x so it would be infinitely many solutions

4 0

4 years ago

Read 2 more answers

A company president randomly selects 5 employees to complete a survey. There are 50 employees in the company. In how many differ

Gre4nikov [31]

Answer:

254,251,200

Step-by-step explanation:

This is a combination question, since the order doesn't matter, the formula for combinations is n!/(n-r)! n is the amount of things we can choose from but r is the amount of things (employees in this case) we actually select. n = 50 and r = 5. This we get 50!/(50-5)! or 50!/45!, using a calculator, we can find that 50!/45! is equal to 254,251,200. That is our final answer for the amount of combinations available.

8 0

3 years ago

Use the Alternating Series Approximation Theorem to find the sum of the series sigma^infinity_n = 1 (-1)^n - 1/n! with less than

DanielleElmas [232]

Answer:

$\sum_{n=1}^{\infty} \frac{(-1)^{n-1}}{n!} = 1-0.5+0.16667-0.04167 +0.00833-0.001389 +0.000198 -0.0000248$

For the 7th term we have 3 decimals of approximation but our value is 0.000198 higher than the error required, so we can use the 8th term and we have that $|-0.0000248|= 0.0000248$ and with this we have 4 decimals of approximation so if we add the first 8 terms we have a good approximation for the series with an error bound lower than 0.0001.

$\sum_{n=1}^{\infty} \frac{(-1)^{n-1}}{n!} = 1-0.5+0.16667-0.04167 +0.00833-0.001389 +0.000198-0.0000248 =0.632118$

Step-by-step explanation:

Assuming the following series:

$\sum_{n=1}^{\infty} \frac{(-1)^{n-1}}{n!}$

We want to approximate the value for the series with less than 0.0001 of error.

First we need to ensure that the series converges. If we have a series $\sum a_n$ where $a_n = (-1)^n b_n$ [/tex] or $a_n =(-1)^{n-1} b_n$ where $b_n \geq 0$ for all n if we satisfy the two conditions given:

1) $lim_{n \to \infty} b_n =0$

2) { $b_n$ } is a decreasing sequence

Then $\sum a_n$ is convergent. For this case we have that:

$lim_{n \to \infty} \frac{1}{n!} =0$

And $\frac{1}{n!}$ because $\frac{1}{n!} =\frac{1}{n (n-1)!}$ and $\frac{1}{n(n-1)!} < \frac{1}{(n-1)!}$

So then we satisfy both conditions and then the series converges. Now in order to find the approximation with the error required we can write the first terms for the series like this:

$\sum_{n=1}^{\infty} \frac{(-1)^{n-1}}{n!} = 1-0.5+0.16667-0.04167 +0.00833-0.001389 +0.000198 -0.0000248$

For the 7th term we have 3 decimals of approximation but our value is 0.000198 higher than the error required, so we can use the 8th term and we have that $|-0.0000248|= 0.0000248$ and with this we have 4 decimals of approximation so if we add the first 8 terms we have a good approximation for the series with an error bound lower than 0.0001.

$\sum_{n=1}^{\infty} \frac{(-1)^{n-1}}{n!} = 1-0.5+0.16667-0.04167 +0.00833-0.001389 +0.000198-0.0000248 =0.632118$

6 0

4 years ago