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Vesna [10]
3 years ago
13

Find the height of this triangle.

Mathematics
1 answer:
Bogdan [553]3 years ago
7 0

Answer:

\sqrt{3}

Step-by-step explanation:

x^2 + 1 = 4

x^2 = 3

\sqrt{3}

You might be interested in
An HP laser printer is advertised to print text documents at a speed of 18 ppm (pages per minute). The manufacturer tells you th
anastassius [24]

Answer:

0.288

Step-by-step explanation:

To solve this question, we need to understand 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 normally distributed random variable X, with mean \mu and standard deviation \sigma, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \mu and standard deviation s = \frac{\sigma}{\sqrt{n}}.

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

In this question, we have that:

\mu = 17.48, \sigma = 3.25, n = 10, s = \frac{3.25}{\sqrt{10}} = 1.027740

Find the probability that the mean printing speed of the sample is greater than 18.06 ppm.

This is 1 subtracted by the pvalue of Z when X = 18.06. So

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

By the Central Limit Theorem

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

Z = \frac{18.06 - 17.48}{1.027740}

Z = 0.56

Z = 0.56 has a pvalue of 0.712

1 - 0.712 = 0.288

The answer is 0.288

7 0
3 years ago
A study shows that 78​% of the population of all calculus students consider calculus an exciting subject. Suppose 20 students ar
alexdok [17]

Answer:

0.046145 = 4.6145%

Step-by-step explanation:

We need to find the probability of 19 or 20 (all) students considering calculus to be an exciting subject, so first we find the probability for 19 students, then for 20 students, and we sum these probabilities.

The probability of the student NOT considering calculus to be an exciting subject is 1 - 0.78 = 0.22

For 19 students, we also have to calculate a combination of 20 choose 19, as these 19 students can be in different "position" among the 20 students, so:

C(20,19) = 20!/19! = 20

Probability of 19 students considering calculus to be an exciting subject:

C(20,19) * 0.78^19 * 0.22^1 = 0.039196756

Probability of 20 students considering calculus to be an exciting subject:

C(20,20) * 0.78^20 = 1 * 0.78^20 = 0.006948516

The final probability is:

0.039196756 + 0.006948516 = 0.046145272 = 4.6145272%

Rounding to six decimal places: 0.046145 = 4.6145%

5 0
3 years ago
As a salesperson, you are paid $50 per week plus $3 per sale. This week you want your pay to be at least $110. What is the minim
alexgriva [62]
110 (goal) - 50 (base pay) = 60 (pay from sales only)

60 (total pay from sales) / 3 (cost per individual sale) = 20 (qty of sales)
7 0
3 years ago
Read 2 more answers
F(x) = 4x^2 + 3x - 11<br> f(-3)
Mnenie [13.5K]
Just plus in x for -3
f(x) = 4(-3)^2 + 3(-3) - 11
f (x) = 4(9) -9 - 11
f(x) = 36 - 20
f(x) = 16
3 0
3 years ago
If y=6 when x=10 find x when y=18 equation
egoroff_w [7]
I believe x would equal to 30.

Since 6 * 3 =18, 10 * 3 = 30.
What you do to one side, you must do to the other.

Hope I helped!

6 0
3 years ago
Read 2 more answers
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