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Masja [62]
3 years ago
12

Angle Sum Theorem, thank you so much for the help, in advance! ​

Mathematics
1 answer:
daser333 [38]3 years ago
7 0

Answer:

x=20°, and y is 90° btw

Step-by-step explanation:

This is an iscoceles triangle, since the base angles are equal and the altitude bisects one of the angles. 180 - 110 = 70, meaning the angles are 70 , 70 and 2x. We know that 70 + 70 + 2x = 180 from the angle sum theorem, so 140 + 2x = 180, and 40 = 2x. x = 20°

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An article written for a magazine claims that 78% of the magazine's subscribers report eating healthily the previous day. Suppos
Schach [20]

Answer:

89.44% probability that less than 80% of the sample would report eating healthily the previous day

Step-by-step explanation:

We use the binomial approximation to the normal to solve this question.

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

Can be approximated to a normal distribution, using the expected value and the standard deviation.

The expected value of the binomial distribution is:

E(X) = np

The standard deviation of the binomial distribution is:

\sqrt{V(X)} = \sqrt{np(1-p)}

Normal probability distribution

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the zscore of a measure X is given by:

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

The Z-score 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. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

When we are approximating a binomial distribution to a normal one, we have that \mu = E(X), \sigma = \sqrt{V(X)}.

In this problem, we have that:

p = 0.78, n = 675

So

\mu = E(X) = np = 675*0.78 = 526.5

\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{675*0.78*0.22} = 10.76

What is the approximate probability that less than 80% of the sample would report eating healthily the previous day?

This is the pvalue of Z when X = 0.8*675 = 540. So

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

Z = \frac{540 - 526.5}{10.76}

Z = 1.25

Z = 1.25 has a pvalue of 0.8944

89.44% probability that less than 80% of the sample would report eating healthily the previous day

8 0
3 years ago
A bakery sells 3 muffins for every 5 pizza pies.The bakery sold a total of 24 muffins and pizzas pies together.how many of each
Rudiy27

Number of muffins sold=9

and number of pizza pies sold=15

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3 years ago
The sum of thrice a number and 5 is 17.
Gnoma [55]

Answer:

The number is 4

Step-by-step explanation:

17 - 5 = 12

12 ÷ 3 = 4

5 0
3 years ago
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Answer:

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2 years ago
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Answer:

Mostly for simplifying, the restrictions are the same no matter is being simplified or not. The restriction of a rational expression is always in the denominate

Step-by-step explanation:

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