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3 years ago

Solve for x.

1 answer:

8 0

The answer is 4.

you just do (2)4x-1 = 30
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since the midseg. is half the parall side

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Calculate the sum of the first 36 terms of the arithmetic sequence defined in which a36=14 and the common difference is d=1/8

user100 [1]

Answer:

425.25

Step-by-step explanation:

Since we are given 36th term as 14 and we know common difference is $\frac{1}{8}$ , it means that from the first term, we add $\frac{1}{8}$ to each and get 14 on the 36th term. To figure out the first term, thus, we have to subtract $\frac{1}{8}$ 35 times from 14. Let's do it to get first term:

$14-35(\frac{1}{8})=\frac{77}{8}=9.625$

The sum of arithmetic sequence formula is:

$S_{n}=\frac{n}{2}[2a+(n-1)d]$

Where,

$S_{n}$ is the sum of nth term (we want to figure this out for first 36 terms)
$a$ is the first term (we figured this out to be 9.625)
$n$ is the term number (36 for our case)
$d$ is the common difference (given as $\frac{1}{8}$ )

Substituting all the values, we get:

$S_{36}=\frac{36}{2}[2(9.625)+(36-1)(\frac{1}{8})]\\S_{36}=18[19.25+4.375]\\S_{36}=18[23.625]\\S_{36}=425.25$

First answer choice is right.

7 0

3 years ago

Read 2 more answers

The LB Company has long manufactured a light bulb with an average life of 5400 hours. Company researchers have recently develope

elena55 [62]

<h2><u>Answer with explanation</u>:</h2>

Let $\mu$ be the average life of light bulbs.

As per given , we have

Null hypothesis : $H_0 : \mu =5400$

Alternative hypothesis : $H_a : \mu >5400$

Since $H_a$ is right-tailed and population standard deviation is also known, so we perform right-tailed z-test.

Formula for Test statistic : $z=\dfrac{\overlien{x}-\mu}{\dfrac{\sigma}{\sqrt{n}}}$

where, n= sample size

$\overline{x}$ = sample mean

$\mu$ = Population mean

$\sigma$ =population standard deviation

For $n=95,\ \overline{x}=5483\ \&\ \sigma=500$ , we have

$z=\dfrac{5483-5400}{\dfrac{500}{\sqrt{95}}}=1.61796786124\approx1.6180$

Using z-value table , Critical one-tailed test value for 0.06 significance level :

$z_{0.06}=1.5548$

Decision : Since critical z value (1.5548) < test statistic (1.6180), so we reject the null hypothesis .

[We reject the null hypothesis when critical value is less than the test statistic value .]

Conclusion : We have enough evidence at 0.06 significance level to support the claim that the new filament yields a longer bulb life

8 0

3 years ago

What is the greatest common factor of 11,44?

mylen [45]

11, because 11 times 1 is 11 and 11 times 4 is 44.

4 0

3 years ago

Area of a triangle with verticals of (-4,1),(-7,5),(0,1)

Lynna [10]

Answer:

$8 ft^2$

Step-by-step explanation:

I assume that the three points given are the vertices of the triangle. So the three points are:

A (-4,1)

B (-7,5)

C (0,1)

The area of a triangle is given by:

$A=\frac{1}{2}bh$

where b is the base and h is the height.

Here we can take as follows:

- We can take the base to be the side AC, so that its length is equal to the distance between the two points:

$AC=\sqrt{(0-(-4))^2+(1-1)^2}=4$

- The height of the triangle is therefore the perpendicular distance between AC and point B. This is equivalent the difference in the x-coordinate between any point on AC and B, so:

$h=(5-1)=4 ft$