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nikdorinn [45]
2 years ago
8

An oil tank is being filled at a constant rate the depth of the oil is a function of the number of minutes has been filling, as

shown in the table find the depth of the oil 1/2 hour after filling begins
Time:0,10,15
Depth:3,5,6
(0,3) (10,5) (15,6)
Mathematics
1 answer:
satela [25.4K]2 years ago
5 0

We are given time in minutes.

According to given table, we are given times 0 minute, 10 minutes and 15 minutes.

And depths are given 3, 5 and 6.

Times represents x coordinates and depths represents y-coordinates.

First we need to find the depth of the tank in per unit time( in a minute).

In order to find the depth of the tank in per unit time, we need to find th slope between two coordinates.

Let us take first two coordinate made using table (0,3) (10,5)

We know, slope formula

m=\frac{y_2-y_1}{x_2-x_1}

Plugging values in slope formula, we get

m= \frac{5-3}{10-0}=\frac{2}{10}=\frac{1}{5}

We got slope m= 1/5=0.2.

We can say that depth of the tank is increasing by rate 0.2 per minute.

From the given table, we can see that for x=0, y value is 3.

Therefore, y-intercept is 3.

Let us write an equation of the line for given table in slope-intercept form y=mx+b.

Plugging values of m and b in slope-intercept form, we get

y= 0.2x+3.

We need to find the depth after 1/2 hours.

1 hour = 60 minutes,

Therefore, 1/2 hours = 60/2 = 30 minutes.

Plugging value of x=30 in above slope-intercept form of the equation, we get

y= 0.2(30)+3.

y= 3+6 = 9.

y=9

Therefore, the depth of the oil 1/2 hour after filling begins is 9 units.

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Josiah works at an electronics store as a salesperson. Josiah earns a 2% commission on the total dollar amount of all phone sale
salantis [7]

Answer: the equations are

0.02x + 0.07y = 156

y = 300 + x

Step-by-step explanation:

Let x represent the total dollar amount of phone sales that she makes.

Let y represent the the total dollar amount of computer sales that she makes.

Josiah earns a 2% commission on the total dollar amount of all phone sales he makes, and earns a 7% commission on all computer sales. She earned a total of $156 in commission. This means that

0.02x + 0.07y = 156 - - - - - - - - - - -1

Josiah had $300 more in computer sales than in phone sales. This means that

y = 300 + x

4 0
1 year ago
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Suppose that 20% of the adult women in the United States dye or highlight their hair. We would like to know the probability that
Rasek [7]

Answer:

71.08% probability that pˆ takes a value between 0.17 and 0.23.

Step-by-step explanation:

We use the binomial approxiation 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 = 0.2, n = 200. So

\mu = E(X) = np = 200*0.2 = 40

\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{200*0.2*0.8} = 5.66

In other words, find probability that pˆ takes a value between 0.17 and 0.23.

This probability is the pvalue of Z when X = 200*0.23 = 46 subtracted by the pvalue of Z when X = 200*0.17 = 34. So

X = 46

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

Z = \frac{46 - 40}{5.66}

Z = 1.06

Z = 1.06 has a pvalue of 0.8554

X = 34

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

Z = \frac{34 - 40}{5.66}

Z = -1.06

Z = -1.06 has a pvalue of 0.1446

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71.08% probability that pˆ takes a value between 0.17 and 0.23.

6 0
2 years ago
a rectangle pyramid fits exactly on top of a rectangular prism. the prism has a length of 18 cm, a width of 6 cm, and a height o
irina1246 [14]
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Now that you have that you need to find the volume of the pyramid using the formula V= L x W x H /3 and when you plug that in it looks like
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Upon simplifying that you get 540.

Now you have the volume of your rectangular prism and your rectangular pyramid add them together and you should get 1512



I recommend drawing it out... it helps a lot:)
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Answer:

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Answer:

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Step-by-step explanation:

The testing phase tells us that \frac{1}{500} is the probability that a person will finish with a perfect score.

This means 1 out of 500 people will be able to finish with perfect score.

Now,

the game is given to 1,000,000 (1 million) people and how much do we expect to finish with perfect score?? Simple! It would be  \frac{1}{500}the of 1 million!

We do the calculation shown below:

\frac{1}{500}*1,000,000=2000

So, 2000 players will complete the game with a perfect score.

3 0
2 years ago
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