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Andre45 [30]
3 years ago
13

When a trigonometric equation is solvable, it often has infinitely many solutions; and (depending on the context) the first solu

tion we find may not be the one we want. Explain how, given one solution of a trigonometric equation of a trigonometric equation (say, one that reduces down to ), we can find other solutions from the first solution we find, without resorting to a calculator.'
Mathematics
1 answer:
Anit [1.1K]3 years ago
3 0

Answer:

(See explanation for further details)

Step-by-step explanation:

An approach is handling the trigonometric equation so that number of trigonometric functions can be reduce to one, in order to determine the periodicity of complete expression and therefore, to determine the complete set of solutions.

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A popular soft drink is sold in 2-liter (2000 milliliter) bottles. Because of variation in the filling process, bottles have a m
andrezito [222]

Answer:

a) 0.27% probability that the mean is less than 1995 milliliters.

b) 2002.3 milliliters or more will occur only 10% of the time for the sample of 100 bottles.

Step-by-step explanation:

To solve this problem, it is important 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 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 = 2000, \sigma = 18

A) If the manufacturer samples 100 bottles, what is the probability that the mean is less than 1995 milliliters?

So n = 100, s = \frac{18}{\sqrt{100}} = 1.8

This probability is the pvalue of Z when X = 1995. So

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

By the Central Limit Theorem

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

Z = \frac{1995 - 2000}{1.8}

Z = -2.78

Z = -2.78 has a pvalue of 0.0027

So 0.27% probability that the mean is less than 1995 milliliters.

B) What mean overfill or more will occur only 10% of the time for the sample of 100 bottles?

This is the value of X when Z has a pvalue of 1-0.1 = 0.9.

So it is X when Z = 1.28

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

1.28 = \frac{X - 2000}{1.8}

X - 2000 = 1.8*1.28

X = 2002.3

2002.3 milliliters or more will occur only 10% of the time for the sample of 100 bottles.

3 0
3 years ago
An item priced at $10.20 has a sales tax of $0.41.Find the sales tax rate expressed as a percent.
torisob [31]
0.41 / 10.20 = 0.040.....multiply by 100 to get ur percent = 4%
3 0
3 years ago
the amusement park charges a fee of $7.50 and $0.75 for every ride. the carnival charges a fee of $10.00 and$0.50 per ride. when
andrew11 [14]
A equation to represent this situation is:

0.75x+7.50=0.50x+10.00

Now we have to find x.

Step 1: Subtract 0.5x from both sides.

<span><span><span><span>0.75x</span>+7.5</span>−<span>0.5x</span></span>=<span><span><span>0.5x</span>+10</span>−<span>0.5x</span></span></span><span><span><span>0.25x</span>+7.5</span>=10

</span>Step 2: Subtract 7.5 from both sides.

0.25x+7.5−7.5=10−7.50.25x=2.5

Step 3: Divide both sides by 0.25.

<span><span><span>0.25x/</span>0.25</span>=<span>2.5/<span>0.25

</span></span></span>Answer:

<span>x=<span>10</span></span>
They will cost the same after 10 rides.


 
3 0
3 years ago
Tom and Jerry enter a race. Tom runs an average of 10 kilometers per hour, and Jerry runs an average of 9 kilometers per hour. I
Zielflug [23.3K]
I am almost positive that the answer is 45 km
4 0
3 years ago
Read 2 more answers
(2) Using the distance formula, d = √(x2 - x1)2 + (y2 - y1)2, what is the distance between point (-2, 2) and point (4, 4) rounde
monitta

Using the distance formula, d = \sqrt{(x_{2} - x_{1})^2 + (y_{2} - y_{1})^2  } \\, what is the distance between point (-2, 2) and point (4, 4) rounded to the nearest tenth?

Using the points given, plug them into the equation.

d = \sqrt{(x_{2} - x_{1})^2 + (y_{2} - y_{1})^2  } \\d = \sqrt{((4) - (-2))^2 + ((4) - (2)^2  } \\d=\sqrt{(4+2)^2 + (4-2)^2}\\d=\sqrt{(6)^2 + (2)^2}  \\d=\sqrt{36+4} \\d=\sqrt{40} \\

Plug this into a calculator and you get 6.32455532

Since you only need it up to the tenth (0.1), round up 6.32

<em>Five or more, let it soar. Four or less, let it rest.</em>

Since two is lower than four, we drop it.

Therefore, the distance between points (-2, 2) and (4, 4) is 6.3

Hope this helps ^w^

8 0
2 years ago
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