Math Questions
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Math
Basic MathA gallon of paint will cover 560 square feet of wall space. If I plan to paint a room whose walls measure 2240 square feet, how many gallons of paint will I need?
To paint the room, __ gallons of paint will be needed.
Math
Basic MathWrite four equivalent expressions for the given expression.
-8v-5/v-2
Choose the expressions that are all equivalent.
A.8v-5/v-2,-(8v-5)/v+2,-8v+5/-v+2,8v-5/v+2
B.-(8v-5)/v-2,-8v+5/v-2,-(8v-5)/-v+2,(8v-5)/-v+2
C.-8v-5/v+2,-(8v-5)/v-2,-8v-5/v+2,8v-5/v+2
Math
Basic Math(1 point) Perform the indicated operation. Note that the
denominators are different. Simplify the result, if possible.
2/y-4
6/y-6
Math
ProbabilityOne bag contains three white marbles and five black marbles, and a second bag contains four white marbles and six black marbles. A person draws one marble from each bag. Find the probability that both marbles are black.
55/91
25/72
3/8
Math
ProbabilityThe amount of time to complete a physical activity
in a PE class is normally distributed with a mean of
39.8 seconds and a standard deviation of 6.3
seconds. Round answers to 4 decimal places.
a) What is the probability that a randomly chosen
student completes the activity in less than 32.3
seconds?
b) What is the probability that a randomly chosen
student completes the activity in more than 45.3
seconds?
c) What proportion of students take between 34.6
and 44.9 seconds to complete the activity?
d) 80% of all students finish the activity in less than
seconds.
Math
Basic MathA company makes three sizes of cardboard boxes: small, medium, and large. It costs $3.50 to make a small box, $5.00 for a medium box, and $5.50 for a large box. Fixed costs are $8000.
(a) Express the cost of making x small boxes, y medium boxes, and a large boxes as a function of three variables: C= f(x, y, z).
f(x, y, z)=
(b) Find (6000, 9000, 8000).
Interpret your answer.
It costs the company $ to make 6000 small boxes, 9000 medium boxes, and 8000 large boxes.
(c) What is the domain of f?
x≥0, -∞≤y≤∞, z≥0
-∞≤x≤∞, -∞≤y≤∞,
x≤0, y ≤0, z≥0
x≥0, y ≥0, z≥0
-∞≤x≤∞, y≥0, z≥0
Math
Basic MathWhich of the following are equivalent forms of the rational
expression.
2x² +5x−3/ x²-x-12
(Select all that apply.)
(2x - 1)(x-3)/(x-4) (x-3)
2x + 1/x-4
(x+3)(2x - 1)/(x-4) (x+3)
2(x2+5x-3)/x²-x-12
2x - 1/x-4
(2x+1)(x-3)/(x-4)(x-3)
Math
Basic MathUse the following function to answer parts a through c
f(x) = 11x³+127x² +67x+11
a. List all rational zeros that are possible according to the Rational Zero Theorem.
+-1, +-1/11+-11
(Type an integer or a simplified fraction. Use a comma to separate answers as needed. Type each answer only once.)
b. Use synthe division to test several possible rational zeros in order to identify one actual zero.
One rational zero of the given function is __
(Simplify your answer)
c. Use the zero from part (b) to find all real zeros of the polynomial function.
The real zeros of the function are
Math
Coordinate systemGraph the funtion.
f(x) = 3√x-2
Plot five points on the graph of the function, as follows.
• Plot the first point using the x-value that satisfies √√x-2 = 0.
• Plot two points to the left and two points to the right of the first point.
Then click on the graph-a-function button.
Math
HyperbolaGiven an hyperbola which passes through point P has vertices V, and V₂, and has foci F, and F₂, which of the following statements is a fact about hyperbolas?
Choose the correct statement below.
A. If 2a is the length of the conjugate axis, then |d (P,V₁)-d(P,V₂)|= 2a.
B. If 2a is the length of the transverse axis, then d (P,F₁)-d(P,F₂)|=2a.
C. If 2a is the length of the transverse axis, then |d (P,V₁)-d(P,V₂)|=2a.
D. If 2a is the length of the conjugate axis, then |d (P,F₁) -d (P,F₂)|=20.
Math
Basic MathCookies are packaged in boxes that measure 18 cm by 20 cm by 6 cm. A larger box is being designed by increasing the length, width and height of the smaller box by the same amount so that the volume is at least 5280 cm³. What are the minimum dimensions of the larger box?
Math
Basic MathClassify the following events as either independent or dependent.
Independent Dependent
Add an answer item! Add an answer item!
Math
Mathematical ReasoningIf n + 1 integers are chosen from the set
{1, 2, 3,..., 2n},
where n is a positive integer, must at least one of them be even?
To answer this question, let S = {1, 2, 3,..., 2n}, where n is a positive integer, and note that in S there are exactly _____
number of odd integers in T, it is ______ odd integers. Since n + 1 is _____ v for at least one of the elements of T to be even. Thus, the answer to this question is _____
Math
Basic MathA corporation issues for cash $1,000,000 of 8%, 20-year bonds, interest payable annually, at a time when the market rate of interest is 10%. The straight-line method is adopted for the amortization of a bond discount or premium. Which of the following is true?
a. The amount of unamortized premium decreases from its balance at issuance date to a zero balance at maturity.
b. The amount of unamortized discount decreases from its balance at issuance date to a zero balance at maturity.
c. The amount of the annual interest expense gradually decreases over the life of the bonds.
d. The amount of the annual interest expense is computed at 8% of the bond carrying amount at the beginning of the year.
Math
Basic MathA construction crew has just finished building a road. The crew worked for 43/8 days. If they built 21/7 kilometers of road each day, what is the total length of road they built?
Math
Basic MathWhich great Mosque might have inspired Guarino Guarini for the design of the vaults of S. Lorenzo church in Turin?
a. The Friday Mosque, Isfahan
b. The Sehzade Mosque in Istanbul
c. Taj Mahal, Agra
d. Great Mosque of Córdoba
Math
ProbabilityWhich of the following statements is true?
"Unusual" values of z are those such that |z| < 1
If the confidence level increases then the critical values will move away from 0.
If the number of items in a sample is increased, then the margin of error computed within a confidence interval will also increase.
A 95% confidence interval for the population mean can be interpreted to say that the population mean has a 95% chance of falling within the limits of the
confidence interval
Math
Basic MathAt the fair you buy an unlimited ride pass for $28 and plan to play some games costing $1.50 per game. Write a function in x that represents the total amount you spend on rides and games at the fair. Be sure to indicate any domain restrictions.
Answer
f(x) =______ for x ___
Math
Basic MathA grocery store buys cereal using the cost function
c(n) = {
2n when n < 100
1.9n when 100 ≤ n ≤ 500
1.8n when n > 500
where n is the number of boxes of cereal the
grocery store buys and c(n) is the cost of the
cereal. The grocery store then sells the cereal
using the sales function s(c) = 1.3c. What is the
cost of the cereal if the grocery store buys 250
boxes?
Math
Basic MathThere are thirty-six students in your chemistry class, including yourself. You will be in a randomly selected lab group of four people, counting yourself. What is the probability that your three friends Ann, Bob, and Carlos are in your lab group?
Math
Indefinite IntegrationFind the indefinite integral using the substitution x = 10 sin(θ). (Use C for the constant of integration.)
∫1/(100 - x²)3/2dx
Math
Basic MathAmy and Chuck each buy a house in the same
neighborhood for $250,000. Amy's monthly
mortgage payment is $400 more per month than
Chuck's. Which one of the following statements
could explain this difference?
Amy chose a shorter term for her
mortgage, so her monthly payments are
higher.
Chuck has a lower credit score, so his
interest payments are also lower.
Amy made a larger down payment, so her
monthly payments are also larger.
Chuck made a larger down payment, so
his monthly payments are larger.
Math
Application of derivativesFind the intervals where the graph is concave up or concave down. Also find all inflection points and critical points. Do not graph. (V.A. -vertical asymptote, I.P.= inflection point, C.U. = concave up, C.D. = concave down)
f(x) = (x - 5)4/3
C.D. x < 5, C.D. x > 5, I.P. x = 5
C.D. x < 5, C.U. x > 5, I.P. x = 5
C.U. x < 5, C.D. x > 5, stationary point x = 5
C.U. x < 5, C.U. > 5, LP. x=5
C.U. x < 5, C.U. x > 5, V.A. x = 5
Math
Indefinite IntegrationFind the indefinite integral. (Note: Solve by the simplest method-not all require integration by parts. Use C for the constant of integration.)
∫ xe4x dx
Math
Permutations and CombinationsExplain how you know when a scenario describes a permutation situation versus a combination situation.
Give an example of a permutation scenario not mentioned in this lesson.
Math
Basic MathFind the compound interest and future value. Round your answers to the nearest cent. Do not round intermediate steps.
Principal Rate Compounded Time
$530 4.35% Quarterly 5 years
The future value is $ and the compound interest is $
Math
Basic MathWrite the exponential function y= 500e-0.07t in the form y =abt
(a) Once you have rewritten the formula, give b accurate to at least four decimal places.
b= _______ help (numbers)
If t is measured in years, indicate whether the exponential function is growing or decaying and find the annual growth/decay rate. The rate you determine should be
positive in either the case of growth or the case of decay (by choosing decay, the negative rate is implied).
(b) The annual ? rate is
% per year (round to the nearest 0.01%).
Math
Basic MathFor the polynomial below, 1 is a zero.
f(x) = x³ - 7x² + 8x - 2
Express f(x) as a product of linear factors.
Math
Basic MathIf a building contractor hires 6 day laborers and 1 concrete finisher, his payroll for the day is $1110. If he hires 1 day laborer and 4 concrete finishers, his daily cost is $875. Find the daily wage for each type of worker. Solve the problem using matrices.
The daily wage for the laborer is $. The daily wage for the concrete finisher is
Math
Basic MathIn the Ohio lottery Classic Lotto game 6 numbers are drawn at random from 49 possible numbers. What is the probability of your lottery ticket matching all six numbers?
Hint: Order is not important.
Math
Basic MathIn 2012, there were about 313 million people in the United States, and just under 9 million of them had assets of $1
million or more. At the same time, there were 8,336,697 people in New York City, and 727,100 of them had assets of $1 million or more. Compute the density of millionaires in the general population for New York City and the whole United States. Based on those numbers, select any of the choices below which are true.
New York has a density of millionaires more than twice that of the country as a whole.
The density of millionaires is about the same for New York City as for the United States.
Millionaires seem to prefer New York City to much of the rest of the United States.
There is something in the water of New York City that encourages millionaires.
Math
Mathematical ReasoningWhich of the following is true for Walter Gropius? (Select all that apply)
□ a. Gropius envisioned that workshop projects would attract commissions or production licenses
□ b. Gropius arranged painters such as Paul Klee and Wassily Kandinsky to teach principles of form
□ c. In Staatliches Bauhaus he created a new type of institution dedicated to training students in all aspects of de
□ d. He firmly believed that fine art came through mastery of craft
□ e. Gropius believed that students do not need to be given manual instructions in craft workshops
□ f. He saw the curriculum of the Bauhaus as a continuation of the Beaux-Arts training
Math
Basic MathDavid has available 400 yards of fencing and wishes to enclose a rectangular area. Express the area A of the rectangle a a function of the width w of the rectangle. For what value
of w is the area largest? What is the maximum area? Sketch the graph of A(w).
Math
ProbabilityA restaurant packed lunches for an event. Each lunch had a sandwich, a side, and a cookie.
•Sandwich choices: ham, turkey, cheese
• Sides: chips, apple, carrot sticks, celery, orange
• Cookie choices: chocolate chip, oatmeal, sugar, snickerdoodle
Assuming the probabilities of each selection are the same for all options in a category, what is the probability of randomly choosing a lunch containing a cheese sandwich, chips, and a chocolate chip cookie?
1/60
60
1/1.320
1,320
Math
Basic MathEstacia wants to learn more about excluded
values.
a. Explain to Estacia why x cannot be 4
in the expression x+2/x-4
b. Find the excluded values of x in each
of the expressions of problem 3-99.
c. Create an expression that has the
excluded values of x = -6 and
x≠1/3 . Be prepared to share your
expression to the class.
Math
Basic MathThe cost of reserving a particular domain name is $22 up front plus $4.89 per month. Find the cost of reserving that domain name for the following:
(a). 2 months
The cost of reserving a particular domain name for 2 months is
Math
Differential equationsA jogger runs around a circular track of radius 65 ft. Let (x, y) be her coordinates, where the origin is the center of the track. When the jogger's coordinates are (39, 52), her x-coordinate is changing at a rate of 16 ft/s. Find dy/dt.
dyldt = ft/s
Math
Basic MathWhat happens to the value of a fraction
when the numerator (the top) approaches
(gets very close to) zero?
What happens to the value of a fraction
when the denominator (the bottom)
approaches (gets very close to) zero?
What happens to the value of a fraction
when the numerator (the top) gets much
much larger than the denominator?
What happens to the value of a fraction
when the denominator (the bottom) gets
much much larger than the numerator?
Use at least 4 sentences total in answering
thele 4 questions.
Math
StatisticsAnother baseball team had a batting average of 0.290 with a standard deviation of 0.04. What is the probability that a
player on that team had a batting average between 0.330 and .410? Use the 68-95-99.7 normal distribution curve.
Math
Basic MathEach side of a square is increasing at a rate of 4 cm/s. At what rate (in cm2/s) is the area of the square increasing when the area of the square is 64 cm²?
cm²/s
Math
FunctionsConsider the following relation.
-5x-3y = 2x + 2y
Step 3 of 3: Determine the implied domain of the function found in the first step. Express your answer in interval notation.
Answer
Math
AreaThe dimensions of a triangular lot are 198 feet by 188 feet by 197 feet. If the price of such land is $3 per square foot, how much does the lot cost?
The lot costs $ __
(Do not round until the final answer. Then round to the nearest cent as needed.)
Math
StatisticsIn a mid-size company, the distribution of the
number of phone calls answered each day by each of
the 12 receptionists is bell-shaped and has a mean of
38 and a standard deviation of 5. Using the empirical
rule (as presented in the book), what is the approximate percentage of daily phone calls numbering between 28 and 48?
Do not enter the percent symbol.
ans = %
Math
Basic Math)) An angle measures 4° less than the measure of its supplementary angle. What is the
measure of each angle?
______° and _______°
Math
Basic MathGive all solutions of the nonlinear system of equations, including those with nonreal complex components.
4x² + y² =160
36x² - y² = 0
....
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. The solution set is {}
(Type an ordered pair. Type an exact answer, using radicals as needed. Use integers or fractions for any numbers in the expression. Express complex
numbers in terms of i. Use a comma to separate answers as needed.)
B. There are infinitely many solutions.
C. The solution is the empty set.
Math
Basic MathLet f(x)=2x²-3x - 2/3x² + 10x - 25
This function has:
1) A y-intercept at the point
2) x-intercepts at the point(s)
3) Vertical asymptotes at x =
4) Horizontal asymptote at y =
Math
Basic MathIn a study of 600 meals served at 75 campus cafeterias, 190 had less than 10 grams of fat but not less than 350 calories; 194 had less than 350 calories b not less than 10 grams of fat; 117 had over 350 calories and over 10 grams of fat.
(a) What percentage of meals had less than 10 grams of fat? Round your answer to the nearest tenth of a percent.
of the meals studied, __% of them had less than 10 grams of fat.
X
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