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ohaa [14]
2 years ago
9

Multiply me by 4. then substract 13. if you divide me by 3 and add 17, you get 22. what number am i?

Mathematics
1 answer:
Dominik [7]2 years ago
3 0

The answer to the problem is 7 and here's why:

To answer this problem, it’s best to work backwards (start at the end and work towards the beginning). If we know that something plus 17 equals 22, then we can represent this as x + 17 = 22. Solving the equation algebraically, we find that x = 5 (this is done by isolating x on one side of the equation, so by subtracting the 22 by 17, which equals 5).

We then know that something divided by 3 equals 5, so we can represent this as x / 3 = 5. Solving the equation algebraically, we find that x = 15 (this is done by isolating x on one side of the equation, so by multiplying the 5 by 3, which equals 15).

We then know that something subtracted by 13 equals 15, so we can represent this as x - 13 = 15. Solving the equation algebraically, we find that x = 28 (this is done by isolating x on one side of the equation, so by adding the 13 to the 15, which equals 28).

Finally, we know that something multiplied by 4 equals 28, so we can represent this as x times 4 = 28. Solving the equation algebraically, we find that x = 7 (this is done by isolating x on one side of the equation, so by dividing the 28 by 4, which equals 7), so 7 is your answer.

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Listed below are amounts of court income and salaries paid to the town justices. All amounts are in thousands of dollars. Constr
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Answer:

Step-by-step explanation:

Hello!

<em>Full text:</em>

<em>Listed below are amounts of court income and salaries paid to the town justice. All amounts are in thousands of dollars. Construct a scatterplot, find the value of the linear correlation coefficient r, and find the P value using  α  = 0.05. Is there sufficient evidence to conclude that there is a linear correlation between court incomes and justice salaries? Based on the results, does it appear that justices might profit by levying larger fines? </em>

<em> Court Income: 65.0, 402.0, 1567.0, 1132.0, 273.0, 251.0, 112.0, 156.0, 34.0 </em>

<em> Justice Salary: 31, 46, 91, 56, 47, 60, 26, 27, 18 </em>

<em>a. What are the null and alternative hypotheses? </em>

To test if there is a linear correlation between the court income and the justice salary, you have to use the following hypotheses:

H₀: ρ = 0

H₁: ρ ≠ 0

<em>b. Construct a scatterplot.  </em>See attachment.

<em>c. The linear correlation coefficient r is: _____. </em>

r= \frac{sumX_1X_2-\frac{(sumX_1)(sumX_2)}{n} }{\sqrt{[sumX_1^2-\frac{(sumX_1)^2}{n} ][sumX_2^2-\frac{(sumX_2)^2}{n} ]} }

n= 9; ∑X₁= 3992; ∑X₁²= 4078308; ∑X₂= 409; ∑X₂²= 2232; ∑X₁X₂= 262123

r= 0.86

<em>d. The P value is: _____. </em>

This test is two-tailed and so is its p-value. I've calculated it using a statistics software:

p-value: 0.0027

<em>e. Based on the results, does it appear that justices might profit by levying larger fines?</em>

Using the p-value approach, the decision rule is:

If the p-value ≤ α, reject the null hypothesis.

If the p-value > α, do not reject the null hypothesis.

The calculated p-value is less than the significance level, then the decision is to reject the null hypothesis.

At a 5% significance level you can conclude that there is a linear correlation between the "court income" and the "Justice salary"

I hope this helps!

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