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3 years ago

A. 35 B. 85 C. 50 D. 25

Mathematics

1 answer:

vivado [14]3 years ago

4 0

Answer: B

Step-by-step explanation:

Use the exterior angle theorem, which states that the exterior angle of a triangle is equal to the sum of the two remote interior angles.

In this case: 120-x= 10+x+60

Simplifying it by combining like terms: 120-x=70+x

Solving by isolating the variable: 50= 2x, x=25

Now use what we know, which is that angle A is 35 degrees, and angle B is 60, to find out that the correct answer is B, 85 degrees.

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First you have to find the angle B (check attachment)

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Then you can find the last angle inside the triangle, which I'll call C

$C = 180^{\circ} - 102^{\circ} - 43^{\circ} = 35^{\circ}$

Now you can find angle A

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valentina_108 [34]

Answer:

$t=\frac{58.875-60}{\frac{5.083}{\sqrt{8}}}=-0.626$

The degrees of freedom are given by:

$df=n-1=8-1=7$

The p value would be given by:

$p_v =P(t_{(7)}$

Since the p value is higher than 0.1 we have enough evidence to FAIl to reject the null hypothesis and we can't conclude that the true mean is less than 60

Step-by-step explanation:

Information given

60, 56, 60, 55, 70, 55, 60, and 55.

We can calculate the mean and deviation with these formulas:

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

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

Replacing we got:

$\bar X=58.875$ represent the mean

$s=5.083$ represent the sample standard deviation for the sample

$n=8$ sample size

$\mu_o =60$ represent the value that we want to test

$\alpha=0.1$ represent the significance level

t would represent the statistic

$p_v$ represent the p value

Hypothesis to test

We want to test if the true mean is less than 60, the system of hypothesis would be:

Null hypothesis: $\mu \geq 60$

Alternative hypothesis: $\mu < 60$

The statistic would be given by:

$t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}$ (1)

Replacing the info we got:

$t=\frac{58.875-60}{\frac{5.083}{\sqrt{8}}}=-0.626$

The degrees of freedom are given by:

$df=n-1=8-1=7$

The p value would be given by:

$p_v =P(t_{(7)}$

Since the p value is higher than 0.1 we have enough evidence to FAIl to reject the null hypothesis and we can't conclude that the true mean is less than 60

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