An athlete runs 7 miles in 45 minutes and then changes their pace to run the next 3 miles in 15 minutes. Overall, what is the average time in minutes it takes the athlete to run 1 mile?
9.5 minutes
9 minutes
6 minutes
10minutes
Correct Answer : C
to find the average time the athlete runs in 1 mile; we find total distance and total time the athlete takes in running.
Total distance run by athlete=7+3=10 miles
Total time=45+15 =60 minutes
The athlete runs 10 miles in 60 minutes. For the athlete to cover 1 mile, he will run for a time less than 60 minutes. Thus, in 1 mile, the athlete takes:
So, in 6 minutes, the athlete covers 1 mile.
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Correct Answer is D
Explanation
We use 1 L =1000 mL to convert between the two units. The conversion options of interconversions are:
And
We want millimeters, use the second option to change L to mL as:
Therefore, 2.5 L is equivalent to 2500 mL.
Correct Answer is C
Explanation
In this problem, we need to find the amount of gratuity the couple will leave. The gratuity is 16% of the total bill. Before solving the problem, the following are terms and their meaning in percent problems:
- Is means equals
- Of means multiply
- What means unknown (variable)
If we let x be the amount of gratuity, then translating the given problem into a mathematical equation becomes:
Now we evaluate the above equation noting that of means multiply.
So, the value of x=9.376 and to the nearest cent, x=9.38
There, a couple will leave a gratuity of $9.38.
Correct Answer is C
Explanation
In a bell-shaped curve, the data distribution is symmetric around a single peak. The centering of data around a single peak means the mean, mode and median of the test are all equal to each other.
Correct Answer is D
Explanation
In order for the teacher to better visualize the test performance for his class, he needs to present the mark distribution in chart form. A better chart visualizer is the histogram, which will show the frequency of marks against range of test scores. A bar graph will not be used because the rectangles need to touch one another.
In a bar graph, the rectangles do not touch each other. Therefore, it will not be a good chart visualizer.
Correct Answer is D
Explanation
Based rainfall falling for the first 5 months, a bar graph will give a great display for the farmer to decide when start planting. The horizontal scale will represent months of the year and vertical scale will present the amount of rainfall falling.
Correct Answer is C
Explanation
From the given data, we can draw the following triangle by letting the unknown length to be p.
We apply the Pythagoras theorem, the value of p:
The unknown length of the triangle is about 21.4 feet.
Correct Answer is B
Explanation
The initial step is to convert the decimal numbers into fractions.
5.2 becomes 52/10
5.15 becomes 515/100
Next, find the least common denominator of 3, 10, and 100, which is 300. We use this value and multiply each fraction.
7/3*300=700
52/10*300=1560
13/3*300=1300
515/100*300=1545
From the above, 1560 is the greatest value which corresponds to 52/10. Thus, 5.2 is the greatest value of all the choices given.
Correct Answer is A
Explanation
The selling price of the sweater is marked price less the mark off value.
Mark off value=mark off rate*original price
Mark of value=30% of $95
Mark of value=0.30*$95=$28.50
Now, find the selling price of the sweater
Selling price= marked price-mark off value
Thus, the sweater will be sold for 66.50 after applying a mark off of 30%. The selling price is about $67.
Correct Answer is B
Explanation
To solve this problem, we need to have all options in fraction form.
74Â Â 95 =Â
7/8 = 3/8
0.72 = 72/100
74% = 74/100
Now, find the least common denominator of 95, 8, and 100. The least common denominator is 3800, which we multiply by each fraction as follows:
74/95*3800=2960
7/8*3800=3325
72/100*3800=2736
74/100*3800=2812
We can see that the fraction 7/8 is the greatest among the given options.
Correct Answer is D
Explanation
We are required to find the percent equivalent of the given fraction.
We multiply 7/8 by 100 to convert it to percent. You convert fraction to percent.
Thus 7/8 is equal to 87.5%.
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