Twelve less than thrice a number
Which of the following translates the phrase above into a mathematical expression?
3x - 12
12 - 3x
12x - 2
3x + 12
Correct Answer : A
We need to form a mathematical expression from the given word problem.
Let the unknown number be x.
Thrice a number is three times = 3x
Twelve less than thrice a number = 3x-12
Thus, the mathematical expression from the word problem is 3x-12
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Correct Answer is A
Explanation
The truck carries a whole cargo which equals 1. If we let the weight of the cargo to be p, then we set up a proportion equation with weight as numerator and fraction of cargo as denominator.
Solve for value of p by cross products
Multiply both sides by 3/2 a reciprocal of 2/3
The truck carries a cargo weighing 795 lb.
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 A
Explanation
We need to form a mathematical expression from the given word problem.
Let the unknown number be x.
Thrice a number is three times = 3x
Twelve less than thrice a number = 3x-12
Thus, the mathematical expression from the word problem is 3x-12
Correct Answer is A
Explanation
An independent variable is a change that when modified brings a change in other variables. In this case, the person increases his climbing rate, calories burned, distance traveled and energy used increases. Therefore, the walking speed is the independent variable while other variables are dependent.
Correct Answer is A
Explanation
The first five months of the year are January, February, March, April, and May. We use to graph to find the amount of rainfall in each month as follows:
In the month of January, rainfall was between o and 1, which is halfway. Therefore, rainfall in January is 0.5 inches
On February, rainfall was 1 inch and on March the rainfall was 2 inches.
On April, the rainfall amount was 4 inches while on month of May, the rainfall was about 3.5 inches. Therefore, total rainfall in the first 5 months was:
Total rainfall=0.5 inches+1 inches+ 2 inches+4 inches + 3.5 inches =11 inches
Correct Answer is B
Explanation
We need to find the radius of the circle from the given value of area. Then, the radius of the circle will be used to find the circumference of the circle.
The first step is to find the radius, r of the circle as
Thus, the circumference of a circle whose area is \(9\pi\ in\ ^2\)is 6 in.
Correct Answer is D
Explanation
Before finding the area of the pizza, we need to find the radius of the pizza.
Find radius of the pizza in terms of diameter
Next, find area of the pizza using the radius of 6 inches
Substituting r=6 in the equation of the area of a circle
Thus, the pizza has an area of 36 π in2.
Correct Answer is D
Explanation
To solve the equation this equation, we compute the multiplication of the two numbers using the calculator
3.60 * 0.75 = 2.7
Correct Answer is C
Explanation
Let x be the original price of the recliner.
Step 1: Apply the 30% discount
The recliner is on sale for 30% less than the original price:
SalePrice=x−0.3x=0.7x
Step 2: Apply the 25% coupon discount
The consumer gets an additional 25% off the sale price:
FinalPrice=0.7x−0.25(0.7x) = 0.525x
Step 3: Solve for x
The consumer paid $237, so:
0.525x=237
​ x≈451.43x
Rounding to the nearest dollar, the original price is $451.
Correct Answer is D
Explanation
We use the order of operation to solve for the unknown value of x.
3(3x+3)=8x+5
Multiply 3 with each number in the brackets
(3*3x)+(3*3)=8x+5
9x+9=8x+5
Subtract 9 from both sides
9x+9-9=8x+5-9
9x=8x-4
Subtract 8x on both sides
9x-8x=8x-8x-4
x=-4
Thus, the unknown value of x is -4.
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