Ursula says the distance between -5.47 and 5.47 on a number line is equal to |-5.47|. explain her error

The thicknesses of 81 randomly selected aluminum sheets were found to have a variance of 3.23. Construct the 98% confidence inte

Yuliya22 [10]

Answer:

The confidence interval for the population variance of the thicknesses of all aluminum sheets in this factory is Lower limit = 2.30, Upper limit = 4.83.

Step-by-step explanation:

The confidence interval for population variance is given as below:

$[(n - 1)\times S^{2} / X^{2} \alpha/2, n-1 ] < \alpha < [(n- 1)\times S^{2} / X^{2} 1- \alpha/2, n- 1 ]$

We are given

Confidence level = 98%

Sample size = n = 81

Degrees of freedom = n – 1 = 80

Sample Variance = S^2 = 3.23

$X^{2}_{[\alpha/2, n - 1]} = 112.3288\\\X^{2} _{1 -\alpha/2,n- 1} = 53.5401$

(By using chi-square table)

[(n – 1)*S^2 / X^2 α/2, n– 1 ] < σ^2 < [(n – 1)*S^2 / X^2 1 -α/2, n– 1 ]

[(81 – 1)* 3.23 / 112.3288] < σ^2 < [(81 – 1)* 3.23/ 53.5401]

2.3004 < σ^2 < 4.8263

Lower limit = 2.30

Upper limit = 4.83.

8 0

2 years ago

The formula for the volume of a pyramid is V=(1/3) ⁢B⁢h, where B is the area of the base and h is the height. Rearrange the form

PIT_PIT [208]

To make an equation that solves for the height as according to the volume of a pyramid, you must isolate the variable h on one side.

The first thing you have to do is to multiply both sides by 3 to get 3V=Bh.

Then, divide both sides by B to get your answer as h=3V/B.

6 0

2 years ago

Describe the transformation from the graph of f(x)=x+8 to the graph of g(x)=x-3

andreev551 [17]

Answer:

A.)

Step-by-step explanation:

Translations are as follows: Up is + on Y axis, down is - on Y axis. Right is + on X axis and left is - on X axis.

The function f(x) = x+8 is translated to (0,8) since their is no number in a bracket with x (example: f(x)= (x-2)+5 would be (2,5) since the X axis is taken as the opposite sign).

g(x) = x-3 translates to (0,-3) which is 11 units down from f(x)

7 0

2 years ago

A right rectangular prism is 5 1/4 in. wide, 12 1 2 in. long, and 4 in. tall.

lozanna [386]

Answer: $V = 262\frac{1}{2}$ $cm^{3}$

Step-by-step explanation:

$V = LWH$

$V = 5\frac{1}{4}$ X $12\frac{1}{2}$ X 4

$V = \frac{21}{4}$ X $\frac{25}{2}$ X $\frac{4}{1}$

$V = \frac{525}{2}$

$V = 262\frac{1}{2}$ $cm^{3}$

7 0

2 years ago

Translate the phrase into an algebraic three dollars more than twice the cost of a bowl of soups 2+3

Softa [21]

Answer:

3+2c

Step-by-step explanation:

To translate the phrase into an algebraic expression, you have to analyze the information provided. Three dollars more than twice the cost of a bowl of soups means that given that c is the costs of a bowl of soup, you have to multiply c for 2 as the phrase says twice the cost. Also, it says three dollars more which means that you have to add 3. According to this, the expression is: 3+2c.

7 0

2 years ago