Correct answer: 7a+6
Dianna has 'a' strawberries, we know. From the given statement in the question, Jed has 2a+2 strawberries. Lisa has twice as many strawberries as Jed, so she has 4a+4 strawberries. When we add these up, we get 4a+4+2a+2+a = 7a +6.
Correct answer: 2 liters milk
Remember that the final milk-to-water ratio must be 3:2. Now, according to the scenario in the question, we have eight liters of solution with four liters of milk and four liters of water, for a 2:2 ratio. To make it 3:2, we add 2 liters of milk. This results in a total of 6 liters milk and 4 liters water, or a 6:4 ratio that can be simplified to 3:2.
Correct answer: 30
Because the width of the rectangle is 2/3 of its length, which is 9, the width is 6. As a result, the perimeter is 6+6+9+9 = 30. (The perimeter of a rectangle is calculated by adding the lengths of each of its sides.)
Correct answer: m= ∞ , x= (2,0)
Because the given line is parallel to the y-axis and the y-axis slope is infinite, its slope is also infinite. Because the line is defined by x=2, its x intercept will be 2 as well because all of its points are of the form (2,y).
Correct answer: y = x2 + 3
As the parabola is shifted above, the value of y changes, so we increase y, i.e. the entire function, by 3 units. As a result, y=x2+3
Correct answer: 1-π/6
Using the formula length^3, we can calculate the volume of a cube. We then subtract the volume of the sphere from it to get the empty volume. 1*1*1=1 is the volume of a cube. The volume of the sphere is (4/3)* π *(radius)^3. By plugging in the values, we get (4/3)* π *(0.5) ^3. This is equal to pi/6. When the two are subtracted, the result is 1- π /6.
Correct answer: A>|B-C|
The largest side is greater than the sum of the two smaller sides and less than the difference of the two smaller sides. As a result, option A is the correct answer.
Correct answer: 150,000
The volume is equal to the product of the length, width, and height. The original volume of the building is equal to lwh = 9600. The new dimensions are 2.5l x 2.5w x 2.5h, or (lwh) x 2.5 x 2.5 x 2.5 = 15.625(lwh). Given that lwh = 9600, the new volume is 15.625(9600) = 150,000.
Correct answer: 42
Let P represent the number of Psychology majors and C represent the number of Computer Science majors." One-fifth of the legislators are neither, for a total of 1/5 *200 = 40 legislators. As a result, there are 200 – 40 = 160 Psychology and Computer Science majors, or P + C = 160. According to the clause, the number of Psychology majors is 50 less than 4 times that of Computer Science majors." "P = 4C – 50 is the result of plugging these values into an equation.
Correct answer: 20% loss
Profit/Loss % = (Sales Price – Cost Price) / Cost Price x 100 is the key formula here. The stem tells us that 20c = 25s, or 4c = 5s, so the sales price to cost price ratio is 4/5.
Let's simplify our Profit/Loss % formula by dividing each term by its cost:
Profit/Loss % = (S/C – C/C) x 100
P/L% = (S/C – 1) x 100 We know that S/C = 4/5 for this problem. So we can plug in and solve:
P/L% = (4/5 – 1) x 100
P/L% = (-1/5) x 100
P/L% = -20% loss
Correct answer: 14
To calculate the "Average Rate" of the bus, we know we need to know the Total Distance and Total Time, so let's see how we can use the D = R x T formula
For the first leg of the journey, we know that 30 miles = 15mph x T, so T = 2 hours.
For the middle section of the journey, we know that D = 10mph x 3 hours, so D = 30 miles.
For the final leg of the journey, we know that 40 miles = R x 2 hours, so R = 20mph.
We can now calculate the Total Distance and Total Time.
Distance total = 30 miles + 30 miles + 40 miles = 100 miles. Time total = 2 hours + 3 hours + 2 hours = 7 hours. So the average rate is 100 miles per hour divided by 7 hours equals 14.28mph. The closest approximation is A.
Correct answer: 17.6
For every 5 necklaces purchased by these ladies, 3 are Joy's and 2 are Princess'. We can use the following equation to calculate the total amount spent:
Total Amount Spent for every 5 Necklaces = 3(16) + 2(20).
88 = Total Amount Spent for each of the 5 necklaces
To calculate the average price of the necklaces, divide 88 by 5. 88/5 = 17.6.
Correct answer: 9, 10, 13
On this type of question, the process of elimination is more convenient. Let's look at the second requirement now that all of the answer choices contain at least one single-digit number. If only one of the numbers was divisible by 3, we can eliminate the following answer choices: (A), (C), and (D) (D).
Correct answer: 200x/(y + 3)
This is an excellent question for determining x and y values. Assume x = 2. “Twice the value of x” equals 4. Assume that y = 5. “Three more than y” equals 8. The question now is: what percentage of 8 is 4? We know that 4 equals half of 8.
When we enter our values into the answer choices, the correct answer will also yield 50%: (200x/(y + 3) = 200(2)/(5) + 3 = 400/8 = 50.
Correct answer: 4/7
Converting all fractions to decimals is one way to deal with them. In this case, all that is required is to determine which is greater than 0.5. Otherwise, to determine which is greater than 1/2, multiply the numerator by the denominator and see if the result is greater than the denominator. In answer B, doubling the numerator yields 8, which is greater than 7.
Correct answer: 100
You could add all multiples of 10 (10 + 20 + 30....+190) and divide by the number of terms (19). Or you could realize that the average of an evenly spaced series of numbers equals the value of the middle term (or the average of the two middle terms if the number of terms is an odd number). The tenth term in the series is the middle term out of 19 = 100.
Correct answer: 48
If you double the sides of a cube, the surface area ratio of the old and new cubes is 1:4. The volume ratio of the old and new cubes will be 1:8. Volume is proportional to weight. As a result, if the first weighs 6 pounds, the second weighs 6x8 pounds = 48.
Correct answer: 35
There will be one more post than there are chains on the fence. (For example, P-c-P-c-P). As a result, the total length must be a multiple of the chain length plus one post (5.5) plus one post extra. Length = (5.5n + 0.5), where n is any positive whole number. If n=3, length=17; if n=5, length=28, and so on, but there is no whole number that equals 35.
Correct answer: 1/4
First, we can compute the two individual probabilities.
Prob (as determined by the die) = 3/6 = 1/2 (2,4 and 6 out of 1,2,3,4,5 and 6)
Second, Prob(even AND tail) is P(even) x P(tail) = 1/2 x 1/2.
Correct answer: $5000
We must understand that Gross Profit = Revenue — Total Cost.
There are 600 trucks manufactured. The first 500 trucks, according to the question, cost $7.00 each. As a result, the total cost of the first 500 trucks is $7.00 x 500 = $3500. The remaining 100 trucks cost $5.00 each for a cost of $5.00. 100 = $500.
Add these up to get the price of the 600 trucks:
$3500 + $500 = $4000
Because the selling price remains constant, calculating the total profit is simplified:
$15.00 x 600 = $9000
Because we now have both revenue and total cost, the answer to the question of gross profit is
$9000 — $4000 = $5000.
Correct answer: 9%
27 is slightly less than 29, which is 10% of $290. As a result, 9 percent is the best approximation.
Correct answer: 52
To determine how many problems are in the series, take the difference and add one.
125 - 74 = 51; 51 + 1 =52
Correct answer: 8
Because two members do not participate in either sport, there are 28 members who participate in one or both. Let the number who play both be n. Total (28) will consist of only badminton players (17 - n), tennis players (19 - n), and those who play both (n).
28 = (17 - n) + (19 - n) + n
28 = 36 - n ; n = 8
Correct answer: 0.2025
Four tenths = 0.4
Five thousandths = 0.005
(0.4 + 0.005)/2 = 0.2025 is the average.
Correct answer: 1/500
0.127 expressed as a fraction = 127/1000
1/8 is also expressed as (1 x 125) / (8 x 125) = 125/1000.
The difference is 2/1000, or 1/500.
