Basic Math Questions and Answers

Consider 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.)

Find 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)

Which 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

You 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.

Bashir 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)

Find 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:

What is the measure of each interior angle of a regular nonagon? 9 1260 180 140 None of the other answers

Give 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

Solve: 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

Find the vertex: f (x) = 2x² + 4x - 5. (1,-5) (1, 1) (-1,5) (-1,-7)

Select 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

At 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?

A 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.

The 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

Simplify assume all variables are positive: √72x³ 2x√18x 6x√2x² 36x² √2x 6x√√/2x

The 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.

Does 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

The 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.

A 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

The 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?

A 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

The 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.)

Would you prefer to take a long difficult essay test or a quick easier multiple choice test? Is this question biased or unbiased? Biased Unbiased

The 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.)

John 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

Factor: 10x2-x-2 (2x - 1) (5x + 2) (2x + 1) (5x - 2) (2x - 1) (5x-2) (2x + 1) (5x + 2)

A 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

Classify 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

A 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

In an experiment which group receives no special instructions? the independent group the control group the treatment group the biggest group

A 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

A 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

What 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

The 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

What 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

Which method is not used to find the solution of a system of linear equations. substitution guess and check graphing matrices

a 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.

When transforming any function the rule f(x +3) tells us to move the function left three units. False True

A 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

Use 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.)

The 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

If 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)

Directions - Find the x and y-intercepts from the Standard Form equation. Write your answers as ordered pairs. -5x - 2y = 10 x-intercept = ( y-intercept = (

Sketch the graph of the inequality. 3x - 4y < 12 Step 1 To graph the given inequality, first replace the inequality symbol by an equality sign. 3x - 4y = 12 Graph the equation using a dashed line, as the solution set does not contain the boundary

The length of a rectangle is 4 inches more than its width, and its perimeter is 34 inches. Find the length and width of the rectangle. Find the width of the rectangle. 7.5 in 6.5 in 6 in

Identify the study as observational or experimental. One group of subjects was given an herbal supplement for one year, another group was given a placebo. After one year, the number of illnesses each group had was compared.

In a hydraulic system, an input piston has an area of 22.0 in² and an output piston with an area 70.6 in². A weight or resistance of 150 pounds is on the output piston. What is the pressure? 2.12 psi 5,261 psi 792.3 psi 1,445 psi

Directions - Convert the following equation to Standard Form. Make sure the leading coefficient is positive, and all integers are whole numbers. 2y = -3x+5 Standard Form:

On a second class lever, a 12 lb input force (effort force) is 30 inches from the fulcrum. Where should a 34 lb load (resistance force) be placed so it can be lifted? 5.00 in 27.4 in 10.6 in 83.9 in

Is there a correlation between the salary of a teacher and their shoe size? no correlation correlation correlation that implies causation