Basic Math Questions and Answers

If 3 times a certain number is increased by 4 the result is 28. What is the number? If x is "the number," which of the following equations could be used to solve for the number? 3(x+4)=28 3x=4+28 3x+4-28

A man divided $9,000 among his wife, son, and daughter. The wife received twice as much as the daughter, and the son received $1,000 more than the daughter. How much did each receive? If x is the amount the wife received, then which of the following expressions represents the amount received by the son?

A cellular service provider is expanding the number of cell towers it has in Butler County. At one place, there are 9 kilometers between two towers. On a map with a scale of 1 centimeter : 1 kilometer, how far apart are the two cell towers?

The width of a rectangle is y feet long. The rectangle is 4 feet longer than it is wide. What is the area of the rectangle? Which expression represents the area? y+4 sqft y(x+4) sq ft 4ysqft

The sum of three numbers is 69. If the second number is equal to the first diminished by 8, and the third number is 5 times the first. What are the numbers? If x represents the first number, then which of the following equations could be used to solve the problem? 69-6x-8 x=6x-8 69=7x-8

Solve the following system of equations graphically. x = -5 y=-6 What is the solution set? 69 ((-5,5)) -6,-5)

Create a 5-question survey on a topic of your choice. Use at least 3 different types of questions. Describe the type of data you are collecting and what sampling method you would use. Explain how you would prevent bias in your survey. You should use at least 5 keywords from Unit 2.

Two fewer than a doubled number is the same as the number decreased by 38. Find the number. If n is "the number, which equation could be used to solve for the number? 2(n-2)=n+38 2(n-2)-n-38 2n-2=n-38

Thomas has $6.35 in dimes and quarters. The number of dimes is three more than three times the number of quarters. How many quarters does he have? If q represents the number of quarters, then which of the following expressions represents the value of the number of dimes in cents? 3q+3 635-q 10(3c+3)

The quotient of a number and 2 is the same as the difference of the number doubled and 3. What is the number?

Consider functions fand g. f(x) = 4(x − 3)² + 6 g(x) = -2(x + 1)² + 4 Which statements are true about the relationship between the functions? The vertex of function g is 4 units to the left of the vertex of function f. Function g opens in the same direction as function f. The vertex of function gis 2 units below the vertex of function f. Function g opens in the opposite direction of function f. The vertex of function gis 2 units above the vertex of function f. The vertex of function g is 4 units to the right of the vertex of function f.

Twice a certain number is tripled. The resulting number is 1/3(2x) (2x)3 2x+3 2x-3

Determine the end behavior for function f(x) = −x(x − 8)(2 − x). as x→∞, ƒ(x) → ∞ and as x →-∞, ƒ(x) ⇒ −00 as x→∞o, f(x) →∞ and as x→-00, f(x) →∞ as x→∞, f(x) →-∞ and as x→-00, f(x) →∞ as x→∞, f(x) →∞ and as x→∞, f(x) ➜ -∞

Choose what the expressions below best represent within the context of the word problem. If Sarah is 24 years younger than her mother and if the sum of their ages is 68, how old is Sarah? x best represents x-24 best represents

A boat makes a 120-mile trip downstream in 3 hours but makes the return trip in 4 hours. If b = the rate of the boat in still water and c = the rate of the current, which of the following equations represents the trip downstream? 4(b + c) = 120 3(b-c) = 120 O3(b + c) = 120

For the function f(x)=x²+2x-24 solve the following. f(x) ≥ 0 Select the correct choice below and fill in the answer box within your choice. A. The solution is (Type your answer in interval notation.) B. The solution is. (Use a comma to separate answers as needed.)

Solve by the quadratic formula. 5x +x-4=0 X= (Simplify your answer. Type an exact answer, using radicals and i as needed. Use integers or fractions for any numbers in the expression. Use a comma to separate answers as needed.)

A standardized exam's scores are normally distributed. In a recent year, the mean test score was 1463 and the standard deviation was 311. The test scores of four students selected at random are 1890, 1230, 2170, and 1340. Find the z-scores that correspond to each value and determine whether any of the values are unusual. The Z-score for 1890 is 1.37. (Round to two decimal places as needed.). The Z-score for 1230 is -0.75. (Round to two decimal places as needed.). The Z-score for 2170 is 2.27. (Round to two decimal places as needed.). The Z-score for 1340 is 0.40. (Round to two decimal places as needed.). Which values, if any, are unusual? Select the correct choice below and, if necessary, fill in the answer box within your choice. A. The unusual value(s) is/are (Use a comma to separate answers as needed.) B. None of the values are unusual.

Harvey plans to use 5 ft of shelving for four shelves whose lengths are to be a series of consecutive even numbers. How many inches long should each shelf be? If x represents the length of the shortest shelf, which expression would represent the length of the longest shelf? X+6 x+3 x+4

The following situation involves a rate of change that is constant. Write a statement that describes how one variable changes with respect to the other, give the rate of change numerically (with units),and use the rate of change rule to answer any questions. You run along a path at a constant speed of 4.9 miles per hour. How far do you travel in 1.4 hours? in 3.7 hours? Which statement describes this situation? A. Time varies with respect to distance traveled with a rate of change of 4.9 h/mi. B. Time varies with respect to distance traveled with a rate of change of 4.9 mi/h. C. The distance traveled varies with respect to time with a rate of change of 4.9 h/mi. D. The distance traveled varies with respect to time with a rate of change of 4.9 mi/h. What is the distance traveled after 1.4 hours? 6.86 miles (Type an integer or a decimal.) What is the distance traveled after 3.7 hours? miles (Type an integer or a decimal.)

If the balance at the end of eight years on an investment that has been invested at a rate of 9% compounded semi-annually was $5096.37, how much was the principal? a) $2557.70 b) $3583.69 c) $2520 d) $1283.62

An editorial points out that the crime rate has decreased from 2.3% to 1.5% from 2012 to 2013, concluding that the police budget should be cut. Is this a valid conclusion? Give a reason for your answer.

Seven times a number minus the number is -48. Find the number. the number is 8 the number is 8 the number is 6

Factor completely. 5x2 - 45 A 5(x+3)(x-3) B. 5(2-45) C 5(x-9Xx+9) D. (5x+9XX-5)

Traffic flow at 1st Ave and High St is twice the traffic flow at 2nd Ave and Central. Compare the graph of the traffic flow at 1st Ave and High St to the graph of the traffic flow at 2nd Ave and Central over time. The period of the graph of the traffic flow at 1st Ave and High St is four times as long as the period of the graph of the traffic flow at 2nd Ave and Central. The period of the graph of the traffic flow at 1st Ave and High St is twice as long as the period of the graph of the traffic flow at 2nd Ave and Central. The period of the graph of the traffic flow at 1st Ave and High St is equally as long as the period of the graph of the traffic flow at 2nd Ave and Central. The period of the graph of the traffic flow at 1st Ave and High St is half as long as the period of the graph of the traffic flow at 2nd Ave and Central.

Person A is breathing five times as fast as person B. Compare the graphs of the breathing of the two people over time. The period of the graph for person A is 2 times longer than the period of the graph for person B. The period of the graph for person A is 5 times shorter than the period of the graph for person B. The period of the graph for person A is 5 times longer than the period of the graph for person B. The period of the graph for person A is 2 times shorter than the period of the graph for person B.

A parade departs from City Hall and finishes at a park, 8 kilometers away. On a map with a scale of 1 centimeter : 1 kilometer, what is the distance between City Hall and the park? centimeters

Suppose your parents decide to give you $10,000 to be put in a college trust fund that will be paid in equally quarterly installments over a 5 year period. If you deposit the money into an account paying 1.5% per quarter, how much are the quarterly payments (Assume the account will have a zero balance at the end of period.)

Answer the questions for the problem given below. The average price of a home in a town was $178,000 in 2007 but home prices are rising by 4% per year. a. Find an exponential function of the form Q = Q0x (1 + r)t (where r> 0) for growth to model the situation described.

A bank loans a family $90,000 at 4.5% annual interest rate to purchase a house. The family agrees to pay the loan off by making monthly payments over a 15 year period. How much should the monthly payment be in order to pay off the debt in 15 years? Show all your calculations

The red blood cell counts (in millions of cells per microliter) for a population of adult males can be approximated by a normal distribution, with a mean of 5.8 million cells per microliter and a standard deviation of 0.4 million cells per microliter. (a) What is the minimum red blood cell count that can be in the top 23% of counts? (b) What is the maximum red blood cell count that can be in the bottom 15% of counts?

Consider the following case of exponential decay. Complete parts (a) through (c) below. A privately owned forest that had 2,000,000 acres of old growth is being clear cut at a rate of 7% per year. a. Create an exponential function of the form Q = Qox (1 + r), (where r> 0 for growth and r<0 for decay) to model the situation described.

A truck with 46-in.-diameter wheels is traveling at 45 mi/h. Find the angular speed of the wheels in rad/min: How many revolutions per minute do the wheels make?

Pistons in car A are extending twice as long as pistons in car B. Compare the graphs of the piston extension of car A to the graph of the piston extension of car B over time. The amplitude of the graph for the pistons in car A is half the amplitude of the graph for the pistons in car B. The amplitude of the graph for the pistons in car A is twice the amplitude of the graph for the pistons in car B. The period of the graph for the pistons in car A is half the period of the graph for the pistons in car B. The period of the graph for the pistons in car A is twice the period of the graph for the pistons in car B.

For the function h(x)= 8x/(x-9)(x+4), solve the following inequality. h(x) < 0 Select the correct choice below and fill in the answer box within your choice. A. The solution is. (Use a comma to separate answers as needed.) B. The solution is (Type your answer in interval notation.)

The drug Valium is eliminated from the bloodstream exponentially with a half-life of 36 hours.. Suppose that a patient receives an initial dose of 70 milligrams of Valium at midnight. a. How much Valium is in the patient's blood at noon on the first day? b. Estimate when the Valium concentration will reach 15% of its initial level. a. How much Valium is in the patient's blood at noon on the first day? There is approximately 55.6 mg of Valium in the patient's blood at noon on the first day. (Round to the nearest tenth as needed.) b. Estimate when the Valium concentration will reach 15% of its initial level. After approximately hours the Valium concentration will reach 15% of its initial level. (Round to the nearest hour.)

In Beverly Hills, two Hollywood actors own houses that are just 8 kilometers apart. On a map of stars' houses, these two houses are 4 centimeters away from each other. What is the map's scale? Write your answer as a decimal or whole number. 1 centimeter = kilometers

Determine the amplitude (A), period (P) and phase shift (PS) of the function f(x) = 8sin (2(x - 4)) + 10.

Maddie is a high school student who is also taking a class at her local community college. Maddie rides the bus from the high school to the college, which are shown 4 inches apart on a map. What is the actual distance between the college and the high school if the scale of the map is 2 inches : 2.3 miles?

Solve this problem on paper using all four steps. A girl scout troop sold cookies. If the girls sold 5 more boxes the second week than they did the first, and if they deúbled the sales of the second week for the third week to sell a total of 431 boxes of cookies, how many did they sell each week? They sold b boxes the first week, boxes the second week, and boxes the third week.

Solve the equation by using the square root property. 2x²-90=0

Solve the equation by using the square root property. (x-7)² = 28

Select the equation that most accurately depicts the word problem. Jim weighs 30 pounds less than Tom, and together they weigh 210 pounds. Let n = Tom's weight in pounds. (n+30) n 210 (n-30) n-180 (n-30)+n+ 180 (n-30) n = 210

Select the correct answer for each statement. will yield consecutive odd integers will yield consecutive integers

Decide whether the graph represents a discrete random variable or a continuous random variable. The length of time students use a computer each week Does the graph represent a discrete or continuous random variable? Choose the correct answer below. The length of time is a random variable that is countable, so it is a discrete. Continuous, because the length of time is a random variable that is uncountable.

You can construct triangles by connecting three vertices of a convex polygon with n sides. The number of all possible such triangles can be represented with the function below. Find the value of n such that you can construct 84 such triangles from the polygon. f(n)= n³ - 3n² + 2n/6

The width of a plastic storage box is 1 ft longer than the height. The length is 4 ft longer than the height. The volume is 36ft³. What is the shortest dimension of the box? The shortest dimension is ft.

An exponential function f(z) = a . bx passes through the points (0, 10000) and (3, 2160). What are the values of a and b?

Solve this problem in your notebook using all four steps. Harvey is 3 times as old as Jane. The sum of their ages is 48 years. Find the age of each years old Jane is Harvey is years old,

Solve for c. 3abc + b = 5 c=(5-b)/(3ab) c=2-ab c= -5/3ab