Which side lengths can represent the sides of a triangle?

A rectangle has an area of x^2-8x-48. If the width is (x+4) find the length.

inna [77]

Answer:x-12

Step-by-step explanation:

Area=x^2-8x-48

Width=x+4

length=area/width

length=(x^2-8x-48)/(x+4)

length=((x+4)(x-12))/(x+4)

length=x-12

5 0

3 years ago

A teacher needs to cut pieces of yarn, each 3/4 yards in length. How many

otez555 [7]

Answer:

8 pieces

Step-by-step explanation:

Take 6 yds and divide by the length of each piece

6 ÷ 3/4

Copy dot flip

6 * 4/3

24/3

8

We can get 8 peices

6 0

3 years ago

The operations manager of a manufacturer of television remote controls wants to determine which batteries last the longest in hi

Margarita [4]

Answer:

$t=\frac{107.75-116.75}{\sqrt{\frac{2.75^2}{4}+\frac{9.604^2}{4}}}}=-1.802$

The degrees of freedom are given by:

$df=n_{1}+n_{2}-2=4+4-2=6$

The p value for this case would be given by:

$p_v =2*P(t_{(6)}$

Since the p value is higher than the significance level we have enough evidence to FAIl to reject the null hypothesis and we can conclude that the true mean is not significantly different between the two types of battery

Step-by-step explanation:

Information given

Battery 1 106 111 109 105

Battery 2 125 103 121 118

We can calculate the mean and the deviation with the following formulas"

$\bar X =\frac{\sum_{i=1}^n X_i}{n}$

$s =\sqrt{\frac{\sum_{i=1}^n (X_i -\bar X)^2}{n-1}}$

$\bar X_{1}=107.75$ represent the mean for the Battery 1

$\bar X_{2}=116.75$ represent the mean for the Bettery 2

$s_{1}=2.75$ represent the sample standard deviation for the Battery 1

$s_{2}=9.604$ represent the sample standard deviation for the battery 2

$n_{1}=4$ sample size selected for the Battery 1

$n_{2}=4$ sample size selected for the Battery 2

$\alpha=0.1$ represent the significance level

t would represent the statistic

$p_v$ represent the p value

System of hypothesis

We want to check if the difference in longevity between the two batteries, the system of hypothesis would be:

Null hypothesis: $\mu_{1} = \mu_{2}$

Alternative hypothesis: $\mu_{1} \neq \mu_{2}$

The statistic is given by:

$t=\frac{\bar X_{s1}-\bar X_{2}}{\sqrt{\frac{s^2_{1}}{n_{1}}+\frac{s^2_{2}}{n_{2}}}}$ (1)

The statistic is given by:

$t=\frac{107.75-116.75}{\sqrt{\frac{2.75^2}{4}+\frac{9.604^2}{4}}}}=-1.802$

The degrees of freedom are given by:

$df=n_{1}+n_{2}-2=4+4-2=6$

The p value for this case would be given by:

$p_v =2*P(t_{(6)}$

Since the p value is higher than the significance level we have enough evidence to FAIl to reject the null hypothesis and we can conclude that the true mean is not significantly different between the two types of battery

8 0

3 years ago

The diameter of a circle is 4 in. Find its area in terms of π\pi π.

Serggg [28]

The formula for area of a circle is r² x π.

Since we know the diameter, we can firstly divide by 2 to find our radius.

4/2 = 2

Now that we know the radius, we can substitute it in and square the value.

(2)² x π

(4) x π

Since we're finding the area in terms of pi, we won't multiply by pi, giving us the answer of 4π.

Therefore, the area of the circle is equal to 4π.

<em>Hope this helped! :)</em>

4 0

3 years ago

Read 2 more answers

What is -(5) to the power of -1

raketka [301]

The answer would be -0.2 ;)

6 0

3 years ago