FREE ACT Math Question and Answers
Mines that have been abandoned often fill with water. The water must be drained out of an abandoned mine before it can be reopened. The size of the pump needed will depend on the mine's depth. If a pump that pumps a minimum of + 4D - 250 gallons per minute is needed to pump out a mine that is D feet deep, how many gallons per minute would be needed to pump out a mine that is 150 feet deep?
In the formula, replacing D with 150 results in (1502/25) + 4(150) - 250 =(22500/25) + 600 - 250 = 1,250.
A box's length in inches is 3 inches shorter than its width in inches. Which of the following calculations converts the box's width, w inches, into its length, l inches?
A number is multiplied by two when written as twice, and a number is deducted by three when written as three less than. When you combine them, you get l = 2w – 3.
When a screw is spun one full turn, the lead is the distance that the screw travels in a straight line. How many full revolutions would it take a screw with a lead of 1/8 inch and a length of 212 inches to insert it all the way into a piece of wood?
The right response is 20, so. 1/8 inch of the screw enters the wood with each full spin. One inch of the screw would thus be in the wood after 8 full revolutions. So, x(⅛) = 2½ . By adding 8, x becomes 8(212) + 8(5/2) = 20.
How often is it that a number drawn at random from the range 2, 3, 7, 12, 15, 22, 72, and 108 will be both divisible by 2 and by 3?
It turns out that the likelihood that the number can be divided by either 2 or 3—but not both—is 7/8.
How much does the value of 3x2 - 2y surpass the value of 2x2 - 3y when x = 3 and y = 5?
The right response is 14, so. When you use the given formulas with x = 3 and y = 5, you get 3x2 - 2y = 3(3)2 - 2(5) = 27 - 10 = 17 and 2x2 - 3y = 2. (3) ² – 3(5) = 18 – 15 = 3. After that, take 3 away from 17 to get 14.
What is the value of x-y if xy = 144, x + y = 30, and x > y?
The first equation, y = 144 over x, must be solved for y. Then, in the second equation, change 144 over x for y: x + 144 over x = 30. Each side is multiplied by x, so x2 + 144 = 30x. 30x from either side is subtracted, giving x2 - 30x + 144 = 0. By factoring (x - 24)(x - 6) = 0, and then assigning each factor to either zero, x = 24 or x = 6, you could find the solution to this equation. As the issue states that x > y, x = 6 will not be valid. If x = 6, then y = 24. So, x= 24. Reintroducing this x value into either of the initial equations results in y = 6. As a result, x - y = 24 - 6 = 18.
The circumference of a circle is 16Ï€ feet. What is the circle's radius in feet?
The right answer is 8, thus. A circle with radius r has a circumference calculated as 2r. Therefore, r = 8 or 2r=16.
What is the measurement in degrees of the sharp angle made by a 12-hour clock's hands when it reads precisely one o'clock?
There are 12 hourly markers on a clock, and the clock hand rotates 360 degrees in one full rotation. The degree measure of the angle created by the clock hands at precisely one o'clock is one-twelfth of a full rotation, or 1/12(360°) = 30°.
What are the midpoint coordinates of a line segment whose endpoints are (-3,0) and (7,4) in the conventional (x,y)coordinate plane?
(2,2) is the right response. Take the average of each coordinate, ((-3+7/2), (0+4/2)) = to determine the midway (2,2).
What do 42, 126, and 210 have in common most?
Since 42 is the greatest number that is a factor of all three numbers given, it is the right response. By writing out the prime factorization of all three integers and then raising each of the shared prime factors to the lowest power that results for that factor, you may get the greatest common factor: 42 = 2 × 3 × 7; 126 = 2 × 3² × 7; and 210 = 2 × 3 × 5 × 7. The largest common factor is therefore 2 3 7 = 42.
Only the three secret substances A, B, and C, which are combined in the proportions of 2:3:5, are used to make industrial cleaners. In a 42-pound (net weight) pail of this cleaner, how many pounds of secret ingredient B are there?
You may set up the equation 2x + 3x + 5x = 42 if you use 3x as the quantity of secret ingredient B. because B = 3x = 12.6 and 10x = 42, x = 4.2.
A company's revenues increased by $3 million from the first to the second year, and they doubled from the third to the second year. What were sales in millions of dollars for the first year if sales for the third year were 38 million?
The right response is this. Sales for the second year are equal to x + 3 if x is the first year's sales. Sales for the third year equal 2(x + 3) since they were twice as high as those for the second year. 38 were the sales for the third year, so 2(x + 3) = 38. You may start by dividing each side of this equation by 2, which would give you x + 3 = 19. x = 16 is then obtained by deducting 3 from both sides.
A automobile gets 27 miles per gallon on average. Which of the following best approximates how much gas would cost for this automobile to travel 2,727 average miles at a price of $4.04 per gallon?
The right response is this. 2,727 miles will equal 101 gallons if you split them by the mileage per gallon, which is 27. The number of gallons is then multiplied by the price per gallon, yielding 101 (4.04), or 488.04. The price of gas for this car to travel 2,727 typical miles is given by this.
Which of the following is an equation for the circle whose center is at (0,0) and which, in the conventional (x,y) coordinate plane, passes through (3,4)?
The distance between (0,0) and (3,4), or (, is the radius of the circle (3–0) ² (4–0) (4–0) ² = 5. (x - h)2+ (y - k)2= r2 is the equation for a circle with (h,k) as the center and r as the radius. Thus, x2 + y2 = 25 or (x - 0)2 + (y - 0)2 = 52.
The length and width of a rectangle with a perimeter of 30 centimeters are divisible by two. What is the square centimeter equivalent of the rectangle's area?
The right response is this. 2w = length if w = width. With w equal to 5, the perimeter is 2(w + 2w) = 30. The breadth is 5, hence the length is 2(5), which equals 10. The area is then 5(10) = 50.
From Port Victoria, Texas, a boat heads out to an oil rig. The distance from the boat's departure location to the oil rig is 9 miles east and 12 miles north. How far away from the starting place is the oil rig?
The right answer is 92 + 122 equals c2 according to the Pythagorean theorem. So c =√9²+12² =√81+144 =√225 = 15.
A DVD player with a $100 list price is discounted by 30%. What does John spend for the DVD player if he receives a 20% employee discount off the retail price?
100(0.70) = 70 is the amount that would be paid if the DVD was marked down 30%; however, there is a second discount of 20%, so the price will only be 80% of the marked-down price. The cost will be 56 ($70(0.80)).
When 2x + 3 Equals 3x - 4 what is the value of x?
The right answer is 7. To solve this issue, first obtain 3 = x - 4 by deducting 2x from each side of the equation. So that x Equals 7, add 4 to each side.
Which of the following claims must be accurate whenever the positive numbers n, a, b, and c are such that n a, c > a, and b > c?
Since b > a, changing the relationship between b and a by deducting n from each side will result in b - n > a - n.
Between 1 and 6, how many irrational numbers are there?
This is the appropriate answer. If you selected this response, you are aware that any two real numbers can be separated by an unlimited amount of irrational integers. For example, 1 and 6 are real numbers.
A high school student typically eats 67.5 pounds of sugar annually. Each track team member intends to reduce their sugar intake by at least 20% over the course of the upcoming year as part of a new nutrition strategy. What is the maximum amount of sugar that each member of the track team may take in the upcoming year, assuming that they will follow this plan and consume sugar at the same rate as the average high school student?
The correct response is 54. To consume 20% less sugar than the average high school student, each member of the track team must consume 100% minus 20%, or 80%, less sugar. 80% of 67.5 = 0.80(67.5) = 54.