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Veseljchak [2.6K]
3 years ago
6

Can i please get help with these

Mathematics
1 answer:
Kryger [21]3 years ago
8 0

Answer:

7. x=3, 8. x=7, 9. x=15.

Step-by-step explanation:

7. If lines m and n are congruent, then angles DCF and CFE are congruent. 15x+3=18x-6. Solve for x. --> 15x+9=18x-->3x=9-->x=3

8.If line m is parallel to line n, then the corresponding angles are congruent. So, 20x+1=22x-13 Solve for x. 20x+14=22x-->14=2x-->x=7.

9. The supplementary angle of 110 is 70. Note that all of the inner angles of a triangle are equal to 180. Form an equation using the the values: (4x+8)+(2x+12)+70=180. Simplify; 6x+90=180. Solve for x: 6x+90=180-->6x=90-->x=15.

Hope this helps!

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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
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