The length of a rectangular room is 5 feet greater than its width. Which of the following equations represents the area (A) of the room?
A = 5x
A = 2x+2(x+5)
A = x(x+5)
A = x+(x+5)
Correct Answer : C
We need to find the are of the rectangle from the given case. Letting x represent the width of the rectangle. Then, we can find the area of the rectangle as follows.
Length of rectangle=(x+5)
Width of the rectangle= x
Area of the rectangle, A= Length*width=(x+5)*x
A=x(x+5)
Thus, the area of the rectangle is x(x+5).
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Correct Answer is B
Explanation
We are asked to find the number of cups of flour that will be used to make 90 cookies.
Letting x be the number of cups of flour and setting the proportion equation with number of cookies on numerator and number of cups of flour on the denominator. We have
Solve the value of x by cross-multiplying
We convert the mixed fraction into improper fraction in order to carry out multiplication
\(x =\ \frac{9}{4}\ cups\ *\ 90\ cookies\ *\ \frac{1}{36}\ cookies\)
The number of cups of flour needed to make 90 cookies is 5.625 cups, which is equal to 5 5/8 cups(Choice B).
Correct Answer is A
Explanation
We follow the order of operations to solve the given expression.
First, we start with the numerator and solve it as follows
[2(3+5*3)]
We start with multiplication in inner brackets, 5*3=15. The expression becomes
[2(3+15)]
Then, we conduct the addition of 3+15=18. Then, the expression yields
[2(18)]=2*18=36
Now, we solve for denominator, which is 12/2=6.
Thus, the expression is reduced into
The expression reduces into 6.
Correct Answer is A
Explanation
The mean of a data set is the total scores divided by the number of tests.
Total test scores =100+78+47+84+93+78=480
Number of tests =6
Mean test score =480/6=80
The mean test score is 80.
Correct Answer is C
Explanation
We use the relation 1 L=1000 mL to convert 0.5 L to mL as follows.
Thus, 0.5 L is 500 mL.
Correct Answer is D
Explanation
The slope represent the ratio between the vertical height to the horizontal length. Let x be the minimum length of the ramp, we can set a proportion with height on the numerator and length on denominator. Then,
Cross-multiply to find the value of x
Thus, the minimum length of the ramp needed is 30 feet to access to a door that is 2.5 feet above the sidewalk.
Correct Answer is C
Explanation
We are asked to convert kg to pounds using the given relation. Letting x to represent the lb we are looking for.
Nest, we set the proportion with kg in the numerator and lb on the denominator as follows.
We find the value of x by cross-multiplication
The value of x is 110 lb.
Correct Answer is D
Explanation
We let x represent the amount of vanilla in mL, since this is what the question is asking us to find.
Next, we will set up a proportion with number of teaspoons on the numerator and amount in mL in the denominator.
Cross-multiply to find the value of x
A recipe of 2.5 teaspoons equals 12.325 mL.
Correct Answer is B
Explanation
We need to find the circumference of the circle from the given area.
To find the circumference, we need to find the radius of the circle from the given area.
Let r be the radius of the circle, and the area of the circle is given by
Substituting the value of area in the above equation becomes
Dividing both sides by pi and taking square root on both sides yields
The radius of the circle is 7 in. and the circumference of the circle is given by the relation:
Â
Correct Answer is A
Explanation
What fraction of the pizza the other three friends get is what is asked to find.
First, the pizza is whole, representing a value of 1. Then, one friend ate half of the pizza. Thun, the fraction of the pizza the friend gets is:
First friend eats =1/2 of 1=1/2
Remaining fraction of the pizza=1-1/2=1/2
Now, the three friends share ½ amongst themselves equally. Then, each friend gets
The three friends each gets 1/6 of the pizza.
Correct Answer is D
Explanation
Percentages are fractions with denominator equal to 100. The given percent is divided by 100. To convert it to a decimal form, we move the decimal point two points to the left from the current position. Thus
The decimal form of 87.5% is 0.875.
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