Basic Math Questions and Answers
Math
Basic MathThe perimeter of rectangle A is 10 cm and its area is 6 cm². The perimeter of rectangle B is 20 cm.
What is the area of rectangle B assuming these two rectangles are similar?
[?] cm²
Math
Basic MathFind the measure of one interior angle of a regular 12-gon.
A. 128.6
B. 147.3
C. 150
D. 135
Math
Basic MathThe exponential model A=617.2 e 0.008t describes the population, A, of a country in millions, t years after 2003. Use the model to determine the population of the country in 2003.
The population of the country in 2003 was .... million.
Math
Basic MathA twin-engined aircraft can fly 960 miles from city A to city B in 3 hours with the wind and make the return trip in 8 hours against the wind. What is the speed of the wind?
140 mph
100 mph
80 mph
120 mph
Math
Basic MathThe cost, in dollars, to produce x vats of ice cream is C (x ) = 5x + 2. When selling
them to ice cream shops, the price-demand function, in dollars per vat, is p(x) = 125 -3x.
Find the revenue function. R(x) =
Math
Basic MathUse the discriminant to determine whether the equation has two rational solutions,
one rational solution, two irrational solutions or two non-real solutions
x² + 7x - 2 = 0
a) Two rational solutions
b) Two non-real solutions
c) Two irrational solutions
d) One rational solution
Math
Basic MathA radioactive substance decays exponentially. A scientist begins with 170 milligrams of a radioactive substance. After 19 hours, 85 mg of the substance remains.
How many milligrams will remain after 29 hours?
... mg
Give your answer accurate to at least one decimal place.
Math
Basic MathConsider the following exam question and student solution. Determine whether the solution is correct. If it is not correct, write a note to the student explaining why it is wrong and give a correct solution.
Exam Question: A candy store sells chocolate for $6.57 per pound. The piece you want to buy weighs 0.48 pound. How much will it cost, to the nearest cent? (Neglect sales tax.)
Student Solution: 0.48 +6.57 = 0.073. It will cost 7.3c.
Select the correct answer below and, if necessary, fill in the answer box to complete your choice.
A. The student's solution is correct.
B. The student's solution is incorrect. The student's division gives an answer that includes part of a cent. Fractional cents cannot be used. The correct answer in cents is (Simplify your answer. Round to the nearest cent as needed.)
C. The student's solution is incorrect. The student's division gives an answer whose units are square pounds per dollar. The desired units are dollars. The correct answer in dollars is $
(Simplify your answer. Round to the nearest cent as needed.)
Math
Basic MathFind the vertex and the factored form of f(x) = x² + 2x - 8
f(x) = (x-4) (x + 2) and vertex (-1,-9)
f(x) = (x-4) (x + 2) and vertex (1,-5)
f(x) = (x + 4) (x - 2) and vertex (-1,-9)
f(x) = (x+4) (x - 2) and vertex (1,-5)
Math
Basic MathWhich of the following is the variable being manipulated by the researcher in an experimental study?
independent variable
none of these answer choices
dependent variable
random variable
Math
Basic MathYou to the doctor and he gives you 13 milligrams of radioactive dye. After 24 minutes, 5.25 milligrams of dye remain in your system. To leave the doctor's office, you must pass through a radiation detector without sounding the alarm. If the detector will sound the alarm if more than 2 milligrams of the dye are in your arrived?
system, how long will your visit to the doctor take, assuming you were given the dye as soon as you arrived? Give your answer to the nearest minute.
You will spend ..... minutes at the doctor's office.
Math
Basic MathBashir correctly graphed the quadratic function y=-3x2 +5 Which of these is true about Bashir's graph?
a) The graph is much wider than the original parent function y = x²
b) The graph of the function is linear
c) The graph has a vertex at (0, -5)
d) The graph has a maximum value of (0, 5)
Math
Basic MathFind all possible rational zeros of -5x^5 + 3x^4-2x³ + 2x² + 6x - 7.
Use "+-" to represent symbol. Write integers first and rational values second (in simplified form). All values written from the lowest to the highest, and separated by commas.
Integer Zeros:
Rational Zeros:
Math
Basic MathWhat is the measure of each interior angle of a regular nonagon?
9
1260
180
140
None of the other answers
Math
Basic MathGive the names of two other statistics that have the same value as the 50th percentile.
Choose the correct answer below.
A. First quartile; midrange
B. Second quartile; mean
C. Third quartile; mode
D. Second quartile; median
Math
Basic MathSolve: 4x² + 12x + 9 = 0
x = 6 or x = -6
x = -1/3 or x = 1/3
x = -3/2or x = 3/2
x= - 3/2
Math
Basic MathSelect the axis of symmetry and the y-intercept of f (x) = 3x² - 6x-2.
(Choose 2)
(0, 3)
x = 1
(0, -1)
(0,-2)
x = -2
(1,-5)
x=3
(0, 1)
x=6
x=0
x=2
Math
Basic MathAt the beginning of an experiment, a scientist has 372 grams of radioactive goo. After 75 minutes, her sample has decayed to 5.8125 grams.
What is the half-life of the goo in minutes?
Find a formula for G(t), the amount of goo remaining at time t. G(t) =
How many grams of goo will remain after 59 minutes?
Math
Basic MathA bacteria culture initially contains 1500 bacteria and doubles every half hour.
Find the size of the baterial population after 100 minutes.
Find the size of the baterial population after 5 hours.
Math
Basic MathThe small piston in a hydraulic system has an area of 5 in2 and the large piston has an area of 19.2 in2. Input force is 170 lb. What is the mechanical advantage of the system?
1.25
8.01
0.247
3.84
Math
Basic MathThe function below shows the cost of an ice cream sundae with different numbers of toppings (t). f(t) = 2.25 +0.751. What is the y-intercept, and what does it mean in the context of this problem?
The y-intercept is 0.75 and it is the cost per topping added.
The y-intercept is 0.75 and it is the cost of the ice cream without any toppings.
The y-intercept is 2.25 and it is the cost per topping added.
The y-intercept is 2.25 and it is the cost of the ice cream without any toppings.
Math
Basic MathDoes correlation imply causation in the amount of hamburgers/chicken cooked on the grill and the amount of propane gas used on the grill?
yes
no
Math
Basic MathThe half-life of the radioactive element unobtanium-29 is 20 seconds. If 80 grams of unobtanium-29 are initially present, how many grams are present after 20 seconds? 40 seconds? 60 seconds? 80 seconds? 100 seconds?
The amount left after 20 seconds is grams.
Math
Basic MathA driver gear is turning at 310 rpm and has 191 teeth. If the driven gear needs to turn at 750 rpm, how many teeth should the driven gear have?
83 teeth
79 teeth
98 teeth
516 teeth
Math
Basic MathThe function below shows the cost of a hamburger with different numbers of toppings (t).
f(t) = 1.90 +1.401. What is the y-intercept, and what does it mean in the context of this
problem?
Math
Basic MathA 55 gallon barrel of aviation gasoline weighs 383 lbs. You can only supply an effort force of 50 lb. What is the maximum height you can raise the barrel if the ramp length is 17 feet 6 inches?
2 feet
4.17 feet
6.55 feet
2.28 feet
Math
Basic MathThe formula A=21.2e0.0406t models the population of a US state, A, in millions, t years after 2000.
a. What was the population of the state in 2000?
b. When will the population of the state reach 29.8 million?
a. In 2000, the population of the state was 21.2 million.
b. The population of the state will reach 29.8 million in the year
(Round down to the nearest year.)
Math
Basic MathWould you prefer to take a long difficult essay test or a quick easier multiple choice test? Is this question biased or unbiased?
Biased
Unbiased
Math
Basic MathThe following pair of investment plans are identical except for a small difference in interest rates. Compute the balance in the accounts after 10 and 30 years. Discuss the difference.
Chang invests $1100 in a savings account that earns 4.5% compounded annually. Kio invests $1100 in a different savings account that earns 4.75% compounded annually.
After 10 years Chang will have a balance of approximately $. After 30 years Chang will have a balance of approximately $
(Round to the nearest cent as needed.)
Math
Basic MathJohn is twice as old as Mary. The sum of their ages is 21. How old is Mary?
Let J = John's age and M = Mary's age. Select the system equations that represents the problem.
J-2M=0
J-M=2
M-2J=0
J+M=21
Math
Basic MathFactor: 10x2-x-2
(2x - 1) (5x + 2)
(2x + 1) (5x - 2)
(2x - 1) (5x-2)
(2x + 1) (5x + 2)
Math
Basic MathA driver gear is turning at 450 rpm and has 130 teeth. If the driven gear needs to turn at 914 rpm, how many teeth should the driven gear have?
103 teeth
64 teeth
87 teeth
502 teeth
Math
Basic MathClassify this survey: You are interested in the number of students that would be interested in attending a Dance Marathon to benefit Riley Children's Hospital. You survey everyone in their first period class.
Random
Non-random
Math
Basic MathA football is punted into the air. Its height is given by h(t) = -4.9t² +24.5t +1 where h is in meters and t is in seconds Find the maximum height of the ball and the time the ball reaches its maximum height
Math
Basic MathIn an experiment which group receives no special instructions?
the independent group
the control group
the treatment group
the biggest group
Math
Basic MathA manufacturer determines that the number of drills it can sell is given by the
formula D = -4p² + 160p - 305 where p is the price of drills in dollars. At
what price will the manufacturer sell the maximum number of drills?
a) $22
b) $20
c) $40
d) $80
Math
Basic MathA 20% acid solution is mixed with a 70% acid solution to get 50 liters of a 40% solution.
Which of the following expressions is equal to 4(50)?
2x+7y
0.2x-0.7y
x+y
Math
Basic MathWhat are the x-intercepts of the function f (x) = (x − 9) (x - 7)?
x = -9, x = -7
x = 9,x=7
x = -9, x = 7
x = 9, x=-7
Math
Basic MathThe areas of two similar rectangles are 1000 ft² and 360 ft². Compare the larger rectangle to the smaller rectangle. Find the ratio of their perimeters.
A. 3:5
B. 25:9
C. 50:18
D. 5:3
Math
Basic MathWhat is the resulting equation when the expression for y in the second equation is substituted into the first equation?
3x+y=1
y = 6-4x
7x+6=1
x+61
x+6-1
Math
Basic MathWhich method is not used to find the solution of a system of linear equations.
substitution
guess and check
graphing
matrices
Math
Basic Matha square root function that has been vertically stretched by a factor of 4, reflected in the y-axis, horizontally stretched by a factor of 2, and translated 3 units left and 5 units up.
Math
Basic MathWhen transforming any function the rule f(x +3) tells us to move the function left three units.
False
True
Math
Basic MathA rocket is launched at the top of a building. The height of the rocket (in meters) written in terms of time (seconds) can be modeled by h (1) = -4.912 +9.8t + 73.5. What is the maximum height?
73.5 meters
80 meters
78.4 meters
9.8 meters
Math
Basic MathUse the appropriate compound interest formula to compute the balance in the account after the stated period of time
$16,000 is invested for 5 years with an APR of 2% and daily compounding.
The balance in the account after 5 years is $
(Round to the nearest cent as needed.)
Math
Basic MathThe areas of two similar rectangles are 1000 ft² and 360 ft². Compare the larger rectangle to the smaller rectangle. Find the ratio of their perimeters.
A. 3:5
B. 25:9
C. 50:18
D. 5:3
Math
Basic MathIf the zeros of a quadratic equation are -3 and 5, what would be the x-intercepts?
(3, 0) and (5, 0)
(-3,0) and (-5, 0)
(3, 0) and (-5, 0)
(-3,0) and (5, 0)