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kvv77 [185]
3 years ago
15

The measures of three angles in a triangle are as follows:

Mathematics
2 answers:
muminat3 years ago
6 0
Sorry I’m not sure !
Mrac [35]3 years ago
3 0

Answer:

m∠W = 55°

m∠Y = 45°

m∠Z = 80°

Step-by-step explanation:

In order to solve this problem we need to know that the sum of all angel of the triangle is 180°. Knowing this we can make an equation.

m∠W + m∠Y + m∠Z = 180°

Now we can substitute the angle values and find out what x is equal to. So we do...

(x - 15)° + (3x -165)° + 80° = 180°

x° - 15° + 3x° - 165° + 80° = 180°

4x° - 100° = 180°

4x° = 180° + 100°

4x° = 280°

x° = 70°

x = 70

Now we substitute the x and get the measurements of the angels.

m∠W = x° - 15° = 70° - 15° = 55°

m∠Y = 3x° - 165° = 210° - 165° = 45°

m∠Z = 80°

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An experiment is to be conducted using environmentally safe peppermint oil to study the effectiveness of deterring mice from inf
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Answer:

Option E is correct.

- Treatments: how the peppermint oil is dispersed

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- Response variable: number of mice in the dwellings

Step-by-step explanation:

The treatments in this type of statistical experiment refers to the part of the experiment that is tweaked, controlled or varied in the cases being studied. In this experiment, the method of essential oil dispersal is what is varied in the two experimental cases of this study.

Experimental Unit refers to the subject matters, who are participants in the experiment. They are the ones that the effect of the treatments is tested upon.

For this study, the experimental units are the mice subjected to either of the two methods of peppermint oil dispersal.

The response variable is how the experimental units (participants) respond to the treatments (experimental tweaks). Or how the tweaks manifest observable results in the participants of the study. For this study, the effect of the tweaks in the mice is shown in the number of mice that remain in each dwelling (where the two methods of peppermint oil dispersal have been implemented). Hence, the response variable is the number of mice in each dwelling.

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A research study investigated differences between male and female students. Based on the study results, we can assume the popula
garri49 [273]

Using the <u>normal distribution and the central limit theorem</u>, it is found that the interval that contains 99.44% of the sample means for male students is (3.4, 3.6).

In a normal distribution with mean \mu and standard deviation \sigma, the z-score of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

  • It measures how many standard deviations the measure is from the mean.  
  • After finding the z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X.
  • By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation s = \frac{\sigma}{\sqrt{n}}.

In this problem:

  • The mean is of \mu = 3.5.
  • The standard deviation is of \sigma = 0.5.
  • Sample of 100, hence n = 100, s = \frac{0.5}{\sqrt{100}} = 0.05

The interval that contains 95.44% of the sample means for male students is <u>between Z = -2 and Z = 2</u>, as the subtraction of their p-values is 0.9544, hence:

Z = -2:

Z = \frac{X - \mu}{\sigma}

By the Central Limit Theorem

Z = \frac{X - \mu}{s}

-2 = \frac{X - 3.5}{0.05}

X - 3.5 = -0.1

X = 3.4

Z = 2:

Z = \frac{X - \mu}{s}

2 = \frac{X - 3.5}{0.05}

X - 3.5 = 0.1

X = 3.6

The interval that contains 99.44% of the sample means for male students is (3.4, 3.6).

You can learn more about the <u>normal distribution and the central limit theorem</u> at brainly.com/question/24663213

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