In a math class there are 8 male students and 7 female students. A student is

Points C and D divide the semicircle into three equal parts. Match the angles with their measures.

Tresset [83]

∠CAE = 120°
∠CAD = 60°
∠BAE = 180°
∠DEC = 30°

We start out with the fact that points C and D split the semicircle into 3 sections. This means that ∠BAC, ∠CAD and ∠DAE are all 60° (180/3 = 60).

Since it forms a straight line, ∠BAE is 180°.

Since it is formed by ∠CAD and ∠DAE, ∠CAE = 60+60 = 120°.

We know that an inscribed angle is 1/2 of the corresponding arc; since CD is 1/3 of the circle, it is 1/3(180) = 60; and this means that ∠DEC = 30°.

7 0

3 years ago

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Collected 20 cans this week, 25 cans next week what is the percent of increase

BartSMP [9]

Hello!!

25 - 20 = 5

5/20 = 0.25

0.25 * 100 = 25%

Good luck :)

5 0

3 years ago

Which matrix equation represents this linear system?<br> <img src="https://tex.z-dn.net/?f=2x-7y%3D-1%5C%5Cx%2B3y%3D-5" id="TexF

Nikolay [14]

Answer:

The answer is the letter B.

The first column represents the x-values, and the second row represents the y-values.

For that reason, if we have:

2x - 7y = -1

x + 3y = -5

Then, the matrix will be given by:

[ 2 -7

1 3]

Then, the third colum will be the equality:

[ -1

-5]

So the correct option is the letter B.

3 0

3 years ago

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We're testing the hypothesis that the average boy walks at 18 months of age (H0: p = 18). We assume that the ages at which boys

marusya05 [52]

Answer:

II. This finding is significant for a two-tailed test at .01.

III. This finding is significant for a one-tailed test at .01.

d. II and III only

Step-by-step explanation:

1) Data given and notation

$\bar X=19.2$ represent the battery life sample mean

$\sigma=2.5$ represent the population standard deviation

$n=25$ sample size

$\mu_o =18$ represent the value that we want to test

$\alpha$ represent the significance level for the hypothesis test.

t would represent the statistic (variable of interest)

$p_v$ represent the p value for the test (variable of interest)

2) State the null and alternative hypotheses.

We need to conduct a hypothesis in order to check if the mean battery life is equal to 18 or not for parta I and II:

Null hypothesis: $\mu = 18$

Alternative hypothesis: $\mu \neq 18$

And for part III we have a one tailed test with the following hypothesis:

Null hypothesis: $\mu \leq 18$

Alternative hypothesis: $\mu > 18$

Since we know the population deviation, is better apply a z test to compare the actual mean to the reference value, and the statistic is given by:

$z=\frac{\bar X-\mu_o}{\frac{\sigma}{\sqrt{n}}}$ (1)

z-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".

3) Calculate the statistic

We can replace in formula (1) the info given like this:

$z=\frac{19.2-18}{\frac{2.5}{\sqrt{25}}}=2.4$