Basic Math Questions and Answers
Math
Basic MathFind the monthly payment R needed to have a sinking fund accumulate the future value A. The yearly interest rate r and the time t in years are given below. Interest is compounded monthly.
A=$7,000; r=7%; t = 1
R=$
(Round up to the nearest cent.)
Math
Basic MathMichelle is a sales representative for a publishing company. For the past 16 years, she has exceeded her annual sales goal, primarily by selling mathematics textbooks. Therefore, she will also exceed her annual sales goal this year.
Math
Basic MathLauren's science class is taking a field trip to the nearest natural history museum. The museum is 62.5 miles from Lauren's school. The class plans to stop after 30 minutes, or 0.5 hours, to visit a local wildlife refuge. The bus driver plans to drive at an average speed of 50 miles per hour. How many hours will the second part of the trip take?
Write your answer as a whole number or a decimal.
hours
Math
Basic Mathf(x) = 2x and g(x) = x + 3
Step 1 of 2: Find the formula for (f + g)(x) and simplify your answer. Then find the domain for (f + g)(x). Round your answer to two decimal places, if necessary.
Answer
(f + g)(x) =
Domain=
Math
Basic MathGiven that f(x) = x² + 2x and g(x) = x + 2, calculate
(a) (fog)(-2)=
(b) (gof)(-2)=
Enter an integer or decimal number [more..]
Math
Basic MathTeresa wants to save $600 to buy a TV. She saves $17 each week. The amount, A (in dollars), that she still needs after w weeks is given by the following function.
A (w)=600-17w
Answer the following questions.
(a) If Teresa still needs $277, how many weeks has she been saving?
weeks
(b) How much money does Teresa still need after 7 weeks?
Math
Basic MathThe following exercise presents problems similar to exercises from the previous sections of this chapter. Use Newton's Method to approximate the solution.
the point on the graph of f(x) = 8 - x² that is closest to the point (1, 0). (Round your answer to three decimal places.)
Math
Basic MathA certain species of fish is to be introduced into a lake, and wildlife experts estimate the population will grow to P(t) = (684)2^1/3, where t represents the number of years from the time of introduction.
Step 1 of 2: What is the doubling-time for this population of fish?
Math
Basic MathSolve the following equation for B, where -π ≤ β < π.
sec^2β-1/tan(-β) = -√3/3
Select the correct answer below:
β = π/6
β = -π/6
β = -5π/6 and π/6
β = -π/6 and 5π/6
Math
Basic MathA ball is thrown from a height of 160 feet with an initial downward velocity of 12 ft/s. The ball's height h (in feet) after t seconds is given by the following.
h=160-12t-167²
How long after the ball is thrown does it hit the ground?
Round your answer(s) to the nearest hundredth.
(If there is more than one answer, use the "or" button.)
Math
Basic MathThe average score of all golfers for a particular course has a mean of 70 and a standard deviation of 3.5. Suppose 49 golfers played the course today. Find the probability
that the average score of the 49 golfers exceeded 71.
0.1293
0.0228
0.4772
0.3707
Math
Basic MathIn the Bible, Joash was 7 years old when he became king; Uzziah was 16; Ahaz was 20; Manasseh was 12; Josiah was 8; and Jehoiachin was 18. What was the average age of these young men when they became kings of Judah? Write the remainder as a fraction. On the blank, write the answer in simplest form.
Math
Basic MathFor f(x) = x² +4 and g(x)=√x-2, find the following composite functions and state the domain of each.
(a) fog
(b) gof
(c) fof
(d) gog
(a) (fog)(x) = (Simplify your answer.)
Select the correct choice below and fill in any answer boxes within your choice.
A. The domain of fog is {x}.
(Type an inequality. Simplify your answer. Use integers or fractions for any numbers in the expression.)
B. The domain of f o g is all real numbers.
(b) (gof)(x) = (Simplify your answer.)
Select the correct choice below and fill in any answer boxes within your choice.
Math
Basic MathSolve the following equation for a. Be sure to take into account whether a letter is capitalized or not.
D = Ga +3h³a
Math
Basic MathA pet store has 7 puppies, including 4 poodles, 2 terriers, and 1 retriever. Rebecka and Aaron, in that order, each select one puppy at random without replacement. Find the probability that Aaron selects a retriever, given Rebecka selects a retriever.
The probability is
(Type an integer or a simplified fraction.)
Math
Basic MathThree friends split the cost of a pizza and a salad. The pizza costs $15
and the salad costs $6.
Which expression can you use to find how much each person owes?
(15+6)÷3
15+(6x3)
(15+3)+6
Math
Basic Math4. As you've heard, the smallest pair of amicable numbers, 220 and 284, were known to the ancient Greeks, the next pair of amicable numbers, 17296 and 18416, were discovered by the Islamic mathematician Ibn al-Banna in the 14th century (and rediscovered by Fermat). Thousands more have been found since. In Italy in 1866, however, 16-year-old Nicolo Paganini discovered a small pair of amicable numbers, 1184 and 1210, that had been overlooked for centuries. Verify that 1184 and 1210 are an amicable pair.
Math
Basic MathConsidering only the values of β for which csc² βcos (2β) is defined, which of the following expressions is equivalent to csc² βcos (2β)?
Select the correct answer below:
2
2 - sec² β
2sin²β - tan² β
2sin β
cot²β - 1
Math
Basic MathSelect the correct answer from each drop-down menu.
ΔABC has vertices at A(11, 6), B(5, 6), and (5, 17).
ΔXYZ has vertices at X-10, 5), -12, -2), and Z-4, 15).
ΔMNO has vertices at M-9, -4), M-3, -4), and O(-3, -15).
ΔJKL has vertices at 17, -2), K12, -2), and L(12, 7).
ΔPQR has vertices at P(12, 3), Q(12, -2), and A(3,-2).
Triangle ABC and triangle XYZ
Triangle ABC and triangle MNO
Triangle JKL and triangle ABC
Triangle PQR and triangle XYZ
can be shown to be congruent by a sequence of reflections and translations.
can be shown to be congruent by a single rotation.
Math
Basic MathUse synthetic division to rewrite the following fraction in the form g(x) +r(x) d(x) ,where d(x) is the denominator of the original fraction, q(x) is the quotient, and r(x) is
6x^6 + 12x³ − 2x³ − 4x² + 4x + 8
x + 2
Math
Basic MathState Gasoline Taxes A random sample of state gasoline taxes (in cents) is shown here for 11 states. Round sample statistics and final answers to at least two decimal places.
58.6 46.7 58.1 43.8 43.7 46.7
48.9 42.1 55.5 48.5 47.2
Use the data to estimate the true population mean gasoline tax with 98% confidence. Assume the variable is normally distributed.
< µ <
Math
Basic MathA woman 5 ft tall is standing near a street lamp that is 12 ft tall, as shown in the figure. Find a function that models the length L of her shadow in terms of her distance d from the base of the lamp.
L(d) =
Math
Basic MathLet f(x) = -x³ + 9x on [-3,5].
a. Locate the critical points of f.
b. Use the First Derivative Test to locate the local maximum and minimum values.
c. Identify the absolute maximum and minimum values of the function on the given
a. Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. The critical point(s) of f is/are x =
(Type an exact answer, using radicals as needed. Use a comma to separate answers as needed.)
B. The function f has no critical points.
Math
Basic MathConsider the following equation.
3x - y = 1
Step 2 of 2: Determine the missing coordinate in the ordered pair (?, 3) so that it will satisfy the given equation.
Math
Basic MathFor every 40 pounds of body weight, the dosage for a medication is 1/2 ounce. If a person weighs 180 pounds, how many ounces of medication should be given?
a. 1 oz.
c. 2.5 oz
d. 2.25 oz
b. 2 oz
Math
Basic MathGraph the polar equation below by first selecting the correct symmetry, then selecting the correct radius.
r = -5 cos (θ)+5
Provide your answer below:
Math
Basic MathA consumer agency wants to estimate the proportion of all drivers who wear seat belts while driving. What is the most conservative estimate of the sample size that would limit the margin of error to within 0.47 of the population proportion for a 99% confidence interval?
Round your answer up to the nearest whole number.
Math
Basic MathOver what interval is the cosine graph negative and the sine graph positive?
[0, π]
[3π/2, 2π]
[π/2, π]
[π/2,3π/2]
Compare the graphs of sine and cosine and make sure you find the intervals where sine is positive and cosine is negative.
Math
Basic MathWhich of the following cannot be the lengths of the three sides of a triangle?
A 6 inches, 8 inches, 10 inches
B 7 centimeters, 8 centimeters, 15 centimeters
C 3 yards, 5 yards, 7 yards
D 4 millimeters, 6 millimeters, 9 millimeters
Math
Basic MathSolve the equation
5 (2x - 1)^2/3 = 125
Assume x is positive. Give your answer as a simplified integer or improper fraction, if necessary.
Note: Divide both sides with 5. first.
Provide your answer below:
x=
Math
Basic MathOssie owns some property which has an assessed value of $179,800. Find the tax due if the tax rate is $8.28 per $100 of the assessed value. (Round your answer to the nearest
cent.)
$1,488.74
$14,204.20
$14,887.44
$17,980.00
Math
Basic MathYour local pizza store sells medium pizzas for $6.89 each, and breadsticks for $2.49 per order.
For a party, you decide to order 5 pizzas and 2 orders of breadsticks. There is a $2 delivery fee, and a 9.4% sales tax will be added to the total. What will be the total bill after tax?
Math
Basic MathA game has 49 green balls and 1 red ball in a bag, and you will randomly select one ball from the bag. If the selected ball is green, you lose $1. And, if the ball is red, you win $100. What is the expected value of the game?
Math
Basic MathThere are 15 black balls, 14 red balls, and 11 white balls in a jar, and you get to randomly pick one ball without looking. If you draw a black ball, you win $500. If you pick a red one, you lose $10. If you pick a white one, you lose $100. What is the expected value of picking a ball?
Math
Basic MathCollege Courses At a large university, the probability that a student takes calculus and is on the dean's list is 0.049. The probability that a student is on the dean's list is 0.29. Find the probability that the student is taking calculus, given that he or she is on the dean's list. Please round the final answer to 2 or 3 decimal places.
P (the student is taking calculus given that he or she is on the dean's list)=
Math
Basic MathName the property used to go from step to step each time the (why?) occurs.
Choose the correct property for each step below.
5+2(x+6)
= 5+ (2x+12) (why?)
=5+(12+2x) (why?)
= (5+12)+2x (why?)
= 17+ 2x
= 2x+17 (why?)
commutative property of addition
associative property of multiplication
distributive property
commutative property of multiplication
associative property of addition
.....
5+2(x+6)
= 5+ (2x+12)
= 5+ (12+2x)
= (5+12) + 2x
= 17 + 2x
= 2x + 17
Math
Basic MathFind the all solutions of this equation in the interval [0, 2π):
2 cos(x) sin(x) + sin(x) = 0
X=
Give your answers in radians.
Do not use decimal approximations. Use 'pi' to represent .
Use commas to separate your answers.
Math
Basic MathA poster is to have a total area of 500 square centimeters. There is a margin around the edges of 10 cm at the top and 9 cm on the bottom and sides where nothing is printed. Express the printed area A in terms of the width w (in centimeters) of the bottom.
A(w) = cm²
Math
Basic MathA commuter railway has 800 passengers a day and charges each one 2 dollars. For each 6 cents the fare is increased, 5 fewer people will ride the train. Express the income I from the train in terms of the ticket price p (in dollars).
I (p) = $
Math
Basic Math2 sandwiches and a bag of chips costs $4.25. A sandwich costs $0.50 more than a bag of chips. Find the cost of a sandwich and a bag of chips
Math
Basic MathUse the long division method to find the result when 3x³-4x^2+10x - 11 is
divided by x – 1. If there is a remainder, express the result in the form q(x) + r(x)/b(x)
Math
Basic MathIf f(x)= a*, show that f(A + B) = f(A). f(B).
Rewrite f(A + B) by substituting A + B for x in the given function.
f(A + B)=
Which law of exponents can be used to rewrite the expression above as a product?
A. a^-s= 1/a^s= (1/a)^s
C. a^0 = 1
E. (ab)^s = a^s.b^s
B. a^s.a^t = a^(s+t)
D. 1^5=1
F. (a^s)^t = a^st
Math
Basic MathThe area of a right triangle is 210 square inches. The height of the right triangle is 35 inches. What is the length of the hypotenuse of the right triangle?
Enter your answer in the box.
Math
Basic Math1. A block of clay contains twenty 4-ounce portions of clay. A ceramics teacher wants to use the block to make as many spheres of clay as possible, each weighing 2/5 pound. How many spheres can she make?
Math
Basic MathConsider these functions: f(x) = 5x² +2 g(x)=x²-1 What is the value of g(f(-1))? A. 2 B. 8 C.22 D.48
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Basic MathAnswer the following. (a) The total surface area of Africa is approximately 11,700,000 square miles. Write this number in scientific notation. (b) The signal from a certain satellite takes approximately 1.3 × 10-3 seconds to reach Earth. Write this number in standard notation.
Math
Basic MathA waterfall has a height of 700 feet. A pebble is thrown upward from the top of the falls with an initial velocity of 16 feet per second. The height of the pebble h in feet after t seconds is given by the equation h= - 16t² + 16t+ 700. How long after the pebble is thrown will it hit the ground? The time it takes for the pebble to hit the ground is about
Math
Basic MathGiven that the polynomial f(x) has 7 x-intercepts, which of the following most accurately describes the degree of f(x)? Select the correct answer below: The degree of f(x) is at least 6. The degree of f(x) is at least 8. The degree of f(x) is at most 7. The degree of f(x) is at most 8. The degree of f(x) is at least 7. The degree of f(x) is at most 6.
Math
Basic MathUse the properties of exponents to simplify the following as much as positive. (X^5/6) / (x^3/5)=
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Basic MathA pharmacy produces a certain medication in a daytime variety and a nighttime variety. A bottle of the daytime variety contains 2 ounces of the active ingredient and 6 ounces of flavored syrup. A bottle of the nighttime variety contains 3 ounces of the active ingredient and 5 ounces of flavored syrup. The pharmacy currently has no more than 385 ounces of the active ingredient and no more than 850 ounces of flavored syrup available. If at least 65 bottles of the daytime variety must be filled, what is the maximum number of bottles of the nighttime variety that can be filled? A) 78 B) 85 C) 92 D) 106