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PIT_PIT [208]
2 years ago
12

Trigonometric equations 5sinx = 3sinx + square root of 2

Mathematics
1 answer:
Lera25 [3.4K]2 years ago
4 0

\qquad\qquad\huge\underline{{\sf Answer}}♪

Let's solve for x ~

\qquad \sf  \dashrightarrow \:5 \sin(x)  = 3 \sin(x)   +  \sqrt{2}

\qquad \sf  \dashrightarrow \:5 \sin(x)  - 3 \sin(x)  =  \sqrt{2}

\qquad \sf  \dashrightarrow \:2 \sin(x)  =  \sqrt{2}

\qquad \sf  \dashrightarrow \: \sin(x)  =  \sqrt{2}  \div 2

\qquad \sf  \dashrightarrow \: \sin(x) =  \frac{1}{ \sqrt{2} }

\qquad \sf  \dashrightarrow \:x = 45 \degree \:  \: or \:  \:  \frac{\pi}{4}  \: rad

・ .━━━━━━━†━━━━━━━━━.・

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The mean number of words per minute (WPM) read by sixth graders is 97 with a standard deviation of 19 WPM. If 75 sixth graders a
andrey2020 [161]

Answer:

0.0174 = 1.74% probability that the sample mean would be greater than 101.63 WPM

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 problem, we have that:

\mu = 97, \sigma = 19, n = 75, s = \frac{19}{\sqrt{75}} = 2.1939

What is the probability that the sample mean would be greater than 101.63 WPM?

This is 1 subtracted by the pvalue of Z when X = 101.63. So

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

By the Central Limit Theorem

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

Z = \frac{101.63 - 97}{2.1939}

Z = 2.11

Z = 2.11 has a pvalue of 0.9826.

1 - 0.9826 = 0.0174

0.0174 = 1.74% probability that the sample mean would be greater than 101.63 WPM

5 0
3 years ago
Cat este 5 la puterea 5?
8090 [49]
5^5=5*5*5*5*5=25*25*5=625*5=3125
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3 years ago
Question 1
KatRina [158]

Answer:

x2+x-4=0

Step-by-step explanation:

7 0
2 years ago
-3x-(3x-1)=-4x-9 what is the answer​
Karolina [17]

Answer: x = 5

Step-by-step explanation:

Want me to show this, or did you just want the answer?

3 0
3 years ago
Rex mixed x liters of fruit syrup with y liters of water to make a fruit punch. Three times the number of liters of water he mix
irga5000 [103]
3y = 2x + 6
x + y = 7

y = 7 - x
3(7 - x) = 2x + 6
21 - 3x = 2x + 6
21 - 6 = 2x + 3x
15 = 5x
15/5 = x
3 = x

x + y = 7
3 + y = 7
y = 7 - 3
y = 4

Solution is (3,4)

6 0
3 years ago
Read 2 more answers
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