For a school's annual budget, the total amount of money spent on supplies (s) and textbooks (t) cannot exceed $12,000. Which of the following inequalities represents this scenario?
s + t >= $12,000
s + t > $12,000
s + t < $12,000
s + t <= $12,000
Correct Answer : D
We can interpret ‘cannot exceed” as less than ‘<’. Therefore, in our inequality, the symbol < must be included. Now let’s convert the word problem into a mathematical inequality.
Money spent on supplies=s
Money spent on textbooks=t
Total money spent=money spent on supplies + money spent on textbooks
Total money spent = s+t
But the money spent cannot exceed $12,000. Then,
s+t < $12,000.
However the money spent can still be equal to $12000, as it has not exceeded it.
Therefore, the required inequality is s + t <= $12,000.
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Correct Answer is D
Explanation
Percentages always add up to 100%. If we let x be the percent of graduates working for jobs unrelated to law, then
74%+3%+2%+x=100%
79%+x=100%
Subtract 79% from both sides of the equation
79%-79%+x=100%
x=100%-79%
x=21%
So, the number of graduates working for jobs unrelated to law is 21%.
Correct Answer is B
Explanation
from the provided table, the first option represents the amount of gas in gallons while the second column shows the distance in miles. Thus, (6, 144) will denote that the car can 144 miles by consuming 6 gallons of a gas.
Correct Answer is A
Explanation
In this problem, we take the triangle as a right-angled triangle and label it as follows:
From the Pythagoras theorem A2 + B2= C2, we can look for a combination of A and B that when the squares of A and B are summed give a square of 13. Â Mathematically,
But C=13 inches
If we take A=5 inches and B=12 inches, then
Next, we take A=2.5 inches, B=6 inches
Next, we take A=2.5 inches, B=4 inches
6.25+16=169
22.25≠169
Taking A=5 inches and B=8 inches
From the above computation, the combination of A=5 inches and B=12 inches give a triangle with a hypothenuse of 13 inches.
Correct Answer is D
Explanation
The mean is the total divided by the number of elements in the data set. From the given data set:
Total=30+29+28+30+24+12+26+33+25+23=260
Number of items, N=10
Mean=total/N=260/10=26
The mean is 26.
Correct Answer is D
Explanation
We can interpret ‘cannot exceed” as less than ‘<’. Therefore, in our inequality, the symbol < must be included. Now let’s convert the word problem into a mathematical inequality.
Money spent on supplies=s
Money spent on textbooks=t
Total money spent=money spent on supplies + money spent on textbooks
Total money spent = s+t
But the money spent cannot exceed $12,000. Then,
s+t <$12,000.
However the money spent can still be equal to $12000, as it has not exceeded it.
Therefore, therequired inequality is s + t <= $12,000.
Correct Answer is B
Explanation
The median temperature can be found by organizing the temperature values from the smallest to the largest value as follows:
98.6, 98.7, 99.0, 99.0,99.2, 99.3, 99.7, 100.0
(for an even set of numbers, Median = frac{(frac{n}{2})th observation + (frac{n}{2} + 1) th observation}{2})
From the data set above, there are 8temperature values. The median is the temperature value in the middle position, which falls between the(frac{n}{2} th)and((frac{n}{2} + 1) th) position. Here N=8and median is found as:
(frac{(frac{n}{2})th + (frac{n}{2} + 1) th}{2} = )(frac{(frac{8}{2})th + (frac{8}{2} + 1) th }{2} = 4.5th position)
The element in the 4.5th position is the average of the 4th and 5th element.
(frac{99.0 + 99.2}{2} = 99.1)
Thus 99.1 is the median temperature.
Correct Answer is C
Explanation
When dividing fractions, the division sign is changed into multiply sign and the first fraction is multiplied by the inverse of the second fraction.
Change division to multiply sign and find invers of 5/8. The inverse of a fraction is inverting the given fraction. The denominator becomes the numerator and the numerator becomes the denominator.
Correct Answer is B
Explanation
Here we are required to find the area of the square of sides 3.1 m. The square is a four-sided figure with each side equal and opposite sides making 90 degrees.
Area of the square =side*side
Side=3.1 m
Area of the square =3.1 m *3.1 m=9.61 m2
Note: 3.1 + 3.1 = 6.2 which is a wrong answer.
Correct Answer is A
Explanation
We are given a mix of fractions and decimals and to compare the numbers, we convert the given decimals to fractions.
4.4 becomes 44/10
4.25 becomes 425/100
Now the set of fractions for comparison are: 9/2, 10/3, 44/10, and 425/100. The least common denominator for 2, 3 and 10 is 300. Then,
9/2*300=1350
10/3*300=1000
44/10*300=1320
425/10*300=1275
From the above products, 9/2 gives the greatest value when the fractions are compared with the least common denominator of the given denominators.
Correct Answer is D
Explanation
We solve the problem by first finding the amount of gallons needed for the whole trip then find the cost of the gallon.
The car uses 1 gallon to cover 25 miles, which is same as:
Now, in 3000 miles, the car will use how many gallons of gasoline?
A trip of 3000 miles will need 120 gallons. And to find the cost of 120 gallons, we proceed as follows:
The family will spend $199.20 to drive for 3000 miles.
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