2(-x+2)-4=-3(5-x) What is the answer?

A random sample of 56 lithium batteries has a mean life of 645 hours with a population standard deviation of 31 hours. Compute t

bearhunter [10]

Answer: A. (636.9, 653.1)

Step-by-step explanation:

Given : Sample size : n=56

Significance level : $\alpha: 1-0.95=0.05$

Critical value : $z_{0.05}=1.96$

Sample mean : $\overline{x}=645\text{ hours}$

Standard deviation : $\sigma= 31\text{ hours}$

The 95% confidence interval for population mean is given by :-

$\overline{x}\pm z_{\alpha/2}\dfrac{\sigma}{\sqrt{n}}\\\\=645\pm (1.96)\dfrac{31}{\sqrt{56}}\\\\=645\pm8.1\\\\=(636.9, 653.1)$

Hence, 95% confidence interval for population mean is (636.9, 653.1).

8 0

3 years ago

Elena wants to make a scale drawing of her bedroom. Her bedroom is a rectangle with length 5 m and width 3 m. She decides on a s

katovenus [111]

We are given dimensions of rectangular bedroom = length of 5m and width 3 m.

Also scale drawing of factor 1/50 of the original dimension.

In order to find the dimensions of scale drawing, we need to multiply scale factor by each dimension.

Therefore, length of the scale drawing is 5 * 1/50 = 1/10 m and

Let us convert it in centimeter now.

1 m = 100 cm

1/10 m = 100 * 1/10 = 10cm.

Width of the scale drawing = 3 * 1/50 = 3/50 m.

100*3/50 = 6 cm.

Therefore, the dimensions of a scale drawing of Elenas bedroom is length 10cm and width 6cm.

7 0

3 years ago

Read 2 more answers

2 lines intersect to form 4 angles. Clockwise, from top left, the angles are: x degrees, 105 degrees, z degrees, y degrees.

Keith_Richards [23]

X+105°=180, 180°-z°=y°

7 0

3 years ago

Read 2 more answers

(04.02 LC) Rectangle HIJK is dilated to form rectangle TUVW. What corresponding side is proportional to segment JK? Type the ans

8090 [49]

Answer: segment JK is proportional to VW

Step-by-step explanation:

Given: Rectangle HIJK is dilated to form rectangle TUVW.

We know that if a shape is dilated to form a new image, then it will be similar to the original shape.

Therefore, Rectangle HIJK is similar to rectangle TUVW.

Also the criteria of similar shapes says that the corresponding sides of the similar shapes are proportional.

⇒ segment HI is proportional to TU

segment IJ is proportional to UV

segment JK is proportional to VW

segment HK is proportional to TW.

5 0

3 years ago

Factorise this equation

pashok25 [27]

$x^{2} - 2x +35$

To factor we must first find factors of 35

The only factors of 35 are : 5 & 7

-2x is what 5 and 7 make

but only if 7 is negative and 5 is positive

so our final factors are

(x - 7) (x + 5)

______________________________________________

$2x^{2} +7x +6$

For the second equation, were going to multiple the coefficient of $x^{2}$ ( which is 2 ) by 6

We get 12

What factors of 12 add up to 7?

3 and 4

So our final factors are

(2x+3)(x+2)

8 0

3 years ago