Explanation:
Recall that 18% is equivalent to both 0.18 and 18100.
Consequently, 18% of 222 is the same as 0.18⋅222 or 18100⋅222.
Find the product and round to the nearest whole number to solve:
18100⋅222=18⋅2.22=39.96 rounded to the nearest whole number is 40.
Explanation:
To find the area Joey needs to cover, 7 x 10 = 70 square feet.
Convert inches to feet: 6 inches = .5 feet.
Each board measures .5 x 2 feet, which equals coverage of 1 square foot.
He will need 70 of these to cover 70 square feet.
Explanation:
Joan’s discount was $6.00 since $30.00 - $24.00 = $6.00.
This amount (6) / the original price (30) = .2
.2 equals .20, which is equal to 20%.
Explanation:
Isolate the variable to solve.
Begin by subtracting 3.98 from both sides of the equation:
−0.8y = −2.86−3.98
−0.8y = −6.84
Divide both sides by -0.8 to solve for y:
y = −6.84−0.8
y = 8.55
Explanation:
Use the information given to generate two equations.
The sum of the child tickets, C, and the adult tickets, A, is 28.
Stated algebraically:
C+A = 28
The cost per child’s ticket is $2.50 and the cost per adult’s ticket is $3.75, and the total cost was $82.50.
Stated algebraically:
2.5C+3.75A = 82.5
Multiply the first equation by −3.75 and use the method of elimination to directly solve for C:
−3.75C−3.75A=−105, which can be added to the second equation in order to eliminate the C variable:
2.5C+(−3.75C)+3.75A+(−3.75A)=82.5+(−105), which becomes:
−1.25C=−22.5, so C = 18
Explanation:
5x+2y = 18
2y = −5x+18
y = −2.5x+9
This is now in the form y = mx+b, so m must be −2.5
Explanation:
A percentage is a number represented as a fraction of 100.
In this case, the basketball player has made 17 of the 25 total shots taken.
This can be first represented as a fraction then converted to a percentage.
Expressed as a fraction:
(made)/ (total) = 17/25
To represent this as a percentage, we would usually divide 17 into 25 and then multiply the resulting decimal by
100 to convert it. But if we recognize that 25 is a factor of 100, we can express this fraction as a percentage in
one step by multiplying the numerator and denominator by 4:
17/25⋅4/4 = 68/100 = 68
Explanation:
Remember y = mx+b.
The equation 2y = 4x+5 can be rewritten as y = 2x+2.5, showing that its graph would have a slope of 2.
The equation 12x+y = 6 can be rewritten as y = −12x+6, showing that its graph would have a slope of −12.
The slopes are negative reciprocals of each other, indicating that the lines are perpendicular.
Explanation:
All four numbers are factors of 300, but 4 is not a prime number.
Explanation:
0.9% expressed as a decimal is 0.009.
0.009×500 g = 4.5 g
Explanation:
If we let the width be w, the length will be w+8.
We can write an equation for the perimeter.
P=2l+2w
P=2(w+8)+2w
2w+16+2w=60
4w+16=60
4w=44
w=11
l=11+8=19
A=lw=11×19=209
Explanation:
The percent of people believing this is 57/380
Multiply this percentage by 40,000 to find the number of people believing this in the city.
40,000×57/380
6,000
Explanation:
Take any size cube you want, say a 1 by 1 by 1 cube, which would have a volume of 1×1×1=1. If you double the
edge length, it will now have a volume of 2×2×2=8. The new volume is 8 times the original volume. This works
the same for any size cube you start with.
Explanation:
Reduce 60/96
5⋅12/8⋅12
5/8
Reduce 45/72
5⋅9/8⋅9
5/8
Explanation:
Substitute the given values for a and b into the equation and then evaluate to find y:
y = 3ab + 2b3
y = 3(1)(2) + 2(23)
y = 6 + 16
y = 22
Explanation:
Recall that the % symbol means ‘per hundred.’ So, 181.5% is equivalent to 181.5100 or 1.815.
Converting a percentage to a decimal always entails moving the decimal point two places to the left.
Multiply this decimal value with 18 to answer the question:
1.815 × 18 = 32.67
Explanation:
Begin by assessing the form in which the answer choices are written. As no answer choice contains a parenthetical
expression, start by distributing the 3x through the parentheses. Multiply 3x by each of the terms inside of the parentheses
and combine any like terms to simplify:
3x(2 + 5y)
= 3x(2) + 3x(5y)
= 6x + 15xy
Explanation:
We can use PEMDAS to evaluate the expression. (PEMDAS is a technique for remembering the order of operations.
It stands for Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction) According to the
rules, we must evaluate the expression in the parentheses first:
26 − 7(3 + 5) ÷ 4 + 2
= 26 − 7(8) ÷ 4 + 2
Then we perform multiplication and division in order from left to right as follows:
26 − 7(8) ÷ 4 + 2
= 26 − 56 ÷ 4 + 2
= 26 − 14 + 2
Finally, we perform addition and subtraction in order from left to right as follows:
26 − 14 + 2
= 12 + 2
= 14
Explanation:
A prime number is a number with no factors other than 1 and itself. Therefore, we can solve this problem by listing the
numbers from 10 to 25 and eliminating those which are clearly divisible by some other number.
It is only necessary to list the odd numbers in this range, since the even numbers are all divisible by 2:
11, 13, 15, 17, 19, 21, 23, 25
Eliminate numbers divisible by 3: 15, 21
Eliminate numbers divisible by 5: 25
A quick check will tell us that none of the remaining numbers are divisible by anything other than themselves and 1.
That leaves: 11, 13, 17, 19, and 23, for a total of 5 numbers.
Explanation:
If you want to know what percent A is of B, you divide A by B, then take that number and move the decimal place
two spaces to the right:
10.16 ÷ 86.89 = 0.1169
Move the decimal two spaces to the right to find the percentage:
= 11.69%
This is approximately equal to 12%.
Explanation:
One way to solve this problem is to draw the figure and then count how many units each point is from the y-axis,
and to then count the same number of units in the opposite direction to find each point’s reflection. A more efficient
method is to recognize that reflecting over the y-axis causes the x-value to switch sign and does not influence the
y-value of the point.
Reflecting (−2,7), (−3,6), (4,5) across the y-axis produces the points (2,7), (3,6), (−4,5).
Explanation:
The general slope-intercept form of the equation of a line is y = mx + b, where m is the slope and
b is the y-intercept.
By substitution of the given point and given slope, we have:
–1 = (–5)(4) + b
So, b = –1 + 20 = 19, and the required equation is y = –5x + 19.
Explanation:
The percentage discount is the reduction in price divided by the original price. The difference between
original price and sale price is:
$9.20 − $5.06 = $4.14
The percentage discount is this difference divided by the original price:
$4.14 ÷ $9.20 = 0.45
Convert the decimal to a percentage by multiplying by 100%:
0.45 × 100% = 45%
Explanation:
The rule of translation is the rule, which when applied to the first set of points, yields the second set of points.
The difference between the x values of the non-translated and translated points is:
(x2 − x1) = (−3 − 3) = (0 − 6) = (−5 − 1) = −6
This corresponds to a shift of 6 units to the left.
Likewise, for the y values:
(y2 − y1) = (3 − 1) = (3 − 1) = (5 − 3) = 2
This corresponds to a vertical shift of 2 units.
Explanation:
The percentage of squares that are shaded can be expressed as the ratio of the number of shaded squares to the
total number of squares all multiplied by 100%, stated algebraically:
%=shaded squarestotal squares∗100%
And, substituting the values:
%=83100∗100%=83%
