Find the common difference of the arithmetic sequence 13, 16, 19,...13,16,19,...

A 51 foot piece of wire is cut into 3 sections so that the first section is three times as long as the second section and the se

kirill [66]

Answer:

The length of the longest section x = 36 ft

Step-by-step explanation:

Total length of the wire = 51 ft

Let first section of wire = x

Second section of wire = y

Third section of wire = z

According to given data

x = 3 y & y = 4 z

Total length of the wire = x + y + z = 51

$y + 3 y + \frac{y}{4} = 51$

$\frac{17}{4} y = 51$

y = 12

x = 3 × 12 = 36

$z = \frac{y}{4} = \frac{12}{4} = 3$

Therefore the length of the longest section x = 36 ft

8 0

3 years ago

Read 2 more answers

An engineer is going to redesign an ejection seat for an airplane. The seat was designed for pilots weighing between 130 lb and

egoroff_w [7]

Answer:

a) $P(140$

$P(0.036$

b) $P(140< \bar X$

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".

Part a

Let X the random variable that represent the weights of a population, and for this case we know the distribution for X is given by:

$X \sim N(139,28.1)$

Where $\mu=139$ and $\sigma=28.1$

We are interested on this probability

$P(140$

And the best way to solve this problem is using the normal standard distribution and the z score given by:

$z=\frac{x-\mu}{\sigma}$

If we apply this formula to our probability we got this:

$P(140$

And we can find this probability like this:

$P(0.036$

And in order to find these probabilities we can find tables for the normal standard distribution, excel or a calculator.

$P(0.036$

Part b

For this case we select a sample size of n =32. Since the distribution for X is normal then the distribution for the sample mean $\bar X$ is given by:

$\bar X \sim N(\mu=139, \frac{\sigma}{\sqrt{n}}=\frac{28.1}{\sqrt{32}}=4.97)$

And the new z score would be:

$Z=\frac{\bar X -\mu}{\sigma_{\bar x}}$

$P(140< \bar X$

5 0

3 years ago

PLEASE HELP! NEED THIS DONE NOW!!! 2x + 2y = 14 3x - y = 5 Show your work please!!

lorasvet [3.4K]

X is 3 and y is 4 is the answer

7 0

3 years ago

Fifteen less than twice a number is 21. What is the missing number? |

Vikentia [17]

Answer:

2y - 15

Step-by-step explanation:

well 15 LESS than TWICE a number. okay so let’s start off by making a variable for the unknown number.... y. the variable is y. so now we have to think, TWICE that number, but we don’t know the number.

Now that we have the variable and we know it has to be doubled, let’s start off making the first half... we can out that into 2y. which is 2 multiplied by the unknown number.

now that we have the first half done, we have to take the 15 less. Less can mean or subtract in this kind of situation. but for this certain scenario, it will be subtraction. so the equation would be 2y - 15.

4 0

3 years ago

-16 + x = -15 CAN SOMEONE HELP ME PLEASE

Maksim231197 [3]

Answer: x= 1

Step-by-step explanation: Look at pic down below.

7 0

3 years ago