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Tasya [4]
3 years ago
5

I need help solving for X

Mathematics
2 answers:
8_murik_8 [283]3 years ago
6 0

Answer:

x = 63

Step-by-step explanation:

This is a right angle, and we know that there are 90 total degrees in a right angle. Because of this information, we know that the degrees of both angles, added together, should come out to 90. This reasoning looks like this:

25+(x+2)=90

Now, it's much easier to solve for x. I'll start by removing the parentheses and combining like terms.

25+x+2=90\\25+2+x=90\\27+x=90

Now, let's remove 27 both sides to isolate x and figure out what it's equal to.

27+x=90\\x = 63

So, the measure of x is 63 degrees. We can make sure this is correct by using our equation:

Is 25+(63+2)=90? Yes, because 63 + 2 is equal to 65, and 65 plus 25 is equal to 90. So our answer is correct.

If you need any more help, let me know! :)

finlep [7]3 years ago
4 0

Answer:

x = 63°

Step-by-step explanation:

(x + 2) + 25 = 90

x + 2 = 90 - 25

x + 2 = 65

x = 65 - 2

x = 63°

(x + 2) + 25 = 90

(63 + 2) + 25 = 90

65 + 25 = 90

90 = 90

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4 years ago
Factor the following expression using the GCF. Type your factored expression below.
never [62]

Answer:

4(xy + 3w + 3z)

Step-by-step explanation:

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5 0
4 years ago
Sylvia buys a case of water that contains 24 bottles and sells x number of bottles to her co-workers. Sam buys a case of water t
zzz [600]

Answer:

6

Step-by-step explanation:

Number of water bottles bought by Sylvia = 24

Number of water bottles sold by Sylvia = x

Number of water bottles left with Sylvia = 24-x

Number of water bottles bought by Sam = 36

Number of water bottles sold by Sam = Three times as many as bottles as Sylvia sold = 3x

Number of water bottles left with Sam = 36-3x

It is given that the number of water bottles left with Sylvia and Sam are equal.

i.e.

24-x=36-3x\\\Rightarrow 2x=12\\\Rightarrow x =\bold{6}

So, number of water bottles sold by Sylvia = <em>6</em>

7 0
3 years ago
Time spent using​ e-mail per session is normally​ distributed, with mu equals 11 minutes and sigma equals 3 minutes. Assume that
liq [111]

Answer:

a) 0.259

b) 0.297

c) 0.497

Step-by-step explanation:

To solve this problem, it is important to know the normal probability distribution and the central limit theorem.

Normal probability distribution

Problems of normally distributed samples are 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.

Central limit theorem

The Central Limit Theorem estabilishes that, for a random variable X, with mean \mu and standard deviation \sigma, a large sample size can be approximated to a normal distribution with mean \mu and standard deviation s = \frac{\sigma}{\sqrt{n}}

In this problem, we have that:

\mu = 11, \sigma = 3

a. If you select a random sample of 25 ​sessions, what is the probability that the sample mean is between 10.8 and 11.2 ​minutes?

Here we have that n = 25, s = \frac{3}{\sqrt{25}} = 0.6

This probability is the pvalue of Z when X = 11.2 subtracted by the pvalue of Z when X = 10.8.

X = 11.2

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

By the Central Limit Theorem

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

Z = \frac{11.2 - 11}{0.6}

Z = 0.33

Z = 0.33 has a pvalue of 0.6293.

X = 10.8

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

Z = \frac{10.8 - 11}{0.6}

Z = -0.33

Z = -0.33 has a pvalue of 0.3707.

0.6293 - 0.3707 = 0.2586

0.259 probability, rounded to three decimal places.

b. If you select a random sample of 25 ​sessions, what is the probability that the sample mean is between 10.5 and 11 ​minutes?

Subtraction of the pvalue of Z when X = 11 subtracted by the pvalue of Z when X = 10.5. So

X = 11

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

Z = \frac{11 - 11}{0.6}

Z = 0

Z = 0 has a pvalue of 0.5.

X = 10.5

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

Z = \frac{10.5 - 11}{0.6}

Z = -0.83

Z = -0.83 has a pvalue of 0.2033.

0.5 - 0.2033 = 0.2967

0.297, rounded to three decimal places.

c. If you select a random sample of 100 ​sessions, what is the probability that the sample mean is between 10.8 and 11.2 ​minutes?

Here we have that n = 100, s = \frac{3}{\sqrt{100}} = 0.3

This probability is the pvalue of Z when X = 11.2 subtracted by the pvalue of Z when X = 10.8.

X = 11.2

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

By the Central Limit Theorem

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

Z = \frac{11.2 - 11}{0.3}

Z = 0.67

Z = 0.67 has a pvalue of 0.7486.

X = 10.8

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

Z = \frac{10.8 - 11}{0.3}

Z = -0.67

Z = -0.67 has a pvalue of 0.2514.

0.7486 - 0.2514 = 0.4972

0.497, rounded to three decimal places.

5 0
3 years ago
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