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daser333 [38]
3 years ago
7

Two cars leave towns 360 kilometers apart at the same time and travel toward each other. One car's rate is 12 kilometers per hou

r less than the other's. If they meet in 2 hours, what is the rate of the slower car?
Mathematics
1 answer:
mixer [17]3 years ago
5 0
Let x = speed of the first car

the second car is 12 km slower so the seconds car speed is x-12

 they each drove 2 hours so 1st car = 2x
2nd car = 2(x-12)
 
they drove 360 km
 so you have 2x + 2(x-12) = 360
 solve for x

2x+2(x-12) = 360

2x + 2x-24 = 360

4x-24 = 360

4x = 384
x = 384/4
x = 96

1st car drove at 96 km per hour

slower car drove at 96-12 = 84 km per hour



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In a recent year, 31% of all college students were enrolled part-time. If 8.6 million college students were enrolled part-time t
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28 million college students.

Step-by-step explanation:

We can represent all college students as x. This means that all part-time college students are \frac{31}{100}x. Because all part-time college students are also equal to 8.6 million, we have 8,600,000=\frac{31}{100}x. To find the number of total college students, or x, we have to multiply by 100/31 to get rid of the fraction on the other side:

8,600,00\cdot\frac{100}{31}=x

The left side of the equation evaluates as 27,741,935.5. Because we are asked to round to the nearest million, we have to round to 28 million, which is the closest.

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2 years ago
The permiter of a square must be less than 160 feet. What is the maximum length of a side in feet?
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39 ft

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3 0
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A local company is concerned about the number of days missed by its employees due to ill ness. A Random Sample of 10 employees i
sukhopar [10]

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The incentive program does not cuts down on the number of days missed by employees.

Step-by-step explanation:

The dependent t-test (also known as the paired t-test or paired samples t-test) compares the two means associated groups to conclude if there is a statistically significant difference amid these two means.

A paired <em>t</em>-test would be used to determine whether the incentive program cuts down on the number of days missed by employees.

The hypothesis for the test can be defined as follows:

<em>H₀</em>: The incentive program does not cuts down on the number of days missed by employees, i.e. <em>d</em> ≥ 0.

<em>Hₐ</em>: The incentive program cuts down on the number of days missed by employees, i.e. <em>d</em> < 0.

From the information provided the data computed is as follows:

 n=10\\\bar d=-1.1\\SD_{d}=2.99

Compute the test statistic value as follows:

 t=\frac{\bar d}{SD_{d}/\sqrt{n}}

   =\frac{-1.1}{2.99/\sqrt{10}}\\\\=-1.16

The test statistic value is -1.16.

Decision rule:

If the p-value of the test is less than the significance level then the null hypothesis will be rejected and vice-versa.

Compute the p-value of the test as follows:

p-value=P(t_{n-1}

*Use a t-table.

The p-value of the test is 0.1379.

The p-value of the test is very large for all the commonly used significance level. The null hypothesis will not be rejected.

Thus, there is not enough evidence to support the claim.

Conclusion:

The incentive program does not cuts down on the number of days missed by employees

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Answer:

Step-by-step explanation:

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=7/9 ((10+10^2+10^3...n)-(1+1+1+1.....n))

=7/9 ((10 (10^n-1)/(10-1))-n)

4 0
3 years ago
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