Math Questions
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Math
TrigonometryWhat are the domain and range of the cosine function?
Domain: All Real Numbers
Range: (-1,1)
Domain: All Real Numbers
Range: [-1,1]
Domain: [-1,1]
Range: All Real Numbers
O Domain: All Real Numbers where ... -, 0, ...
Range: [-1,1]
Math
Basic MathA grocer needs to mix raisins at $2.00 per pound with granola at $3.25 per pound to obtain 10 pounds of a mixture that costs $2.50 per pound. How many pounds of raisins and how many pounds of granola must be used? (5 points)
Math
StatisticsWhat critical value of z or z* should be used in an 85% confidence interval?
1.645
1.282
1.960
1.440
Math
Basic MathScores on an exam are distributed normally with a mean of 72.3 and a standard deviation of 8.9. If 200 students take the exam, how many students would be expected to score higher that 72.3?
100
72.3
200
150
Math
ProbabilityA class has 20 students. What is the probability that at least 5 students were born on a weekend?
82%
1.4%
45%
72%
20 pts
Math
Basic MathA researcher wants a 68 ounce saline solution with a concentration of 6%. She has concentrations of 3% and 15%. How much of each solution must she use to get the desired concentration?
Select the correct answer below:
51 ounces of 3% solution and 17 ounces of 15% solution
49 ounces of 3% solution and 19 ounces of 15% solution
16 ounces of 3% solution and 52 ounces of 15% solution
52 ounces of 3% solution and 16 ounces of 15% solution
19 ounces of 3% solution and 49 ounces of 15% solution
17 ounces of 3% solution and 51 ounces of 15% solution
Math
Basic MathAn airplane travels 1200 miles in 4 hours with the wind. The same trip takes 5 hours against the wind.
What is the speed of the plane in still air and what is the wind speed?
Select the correct answer below:
Speed in still air: 270 mph; Speed of the wind: 30 mph.
Speed in still air: 280 mph; Speed of the wind: 40 mph.
Speed in still air: 290 mph; Speed of the wind: 50 mph.
Speed in still air: 300 mph; Speed of the wind: 60 mph.
Math
Basic MathIn a physiology class, a student mist dissect three different specimens. The student can select one of nine earthworms, one of four frogs, and one of seven fetal pigs. In how many ways can the student select the specimen?
Math
Straight linesDetermine the solution to the system of equations below.
5x+6y=-44
-7x-7y= 49
Select the correct answer below:
(2,-9)
(8,-14)
no solutions
infinitely many solutions
Math
Quadratic equationsSolve by completing the square.
-3f² + 18f = -33
Write your answers as integers, proper or improper fractions in simplest form, or decimal rounded to the nearest hundredth.
f = or f =
Math
Permutations and CombinationsIn 2010, the state of Nevada had two area codes. The first three are the area code and the next seven are the local telephone number. (Note that at this time, a local telephone number cannot begin with 0 or 1) How many telephone numbers could Nevada's phone system have accomodated?
Math
FunctionsThe graph to the right is obtained from the graph of g(x)=√x by applying several transformations. Describe the transformations and give the equation of the graph.
A. Translate g(x) unit(s) down. (Type a whole number.)
B. Translate g(x) 2 unit(s) up. (Type a whole number.)
C. No vertical translation is needed.
Give the equation of the graph.
(Type an equation.)
Math
StatisticsOn Monday, Ms. Liu asked the students how many Harry Potter books they have read in the last month and recorded the information in a dot plot. On Tuesday a new student switched from Launch Ed to F2F and Ms. Liu added his information to the dot plot.
Based on the dot plots above, select whether the value of each statistic for the number of books read, listed below, is greater for Monday's class, equal for both days, or greater for Tuesday's class.
Median
Standard Deviation
Mean
Math
FunctionsIdentify the relevant information given to you in the application problem below. Use that information to answer the questions that follow on Practical Domain and Practical Range.
Round your answers to two decimal places as needed.
A local window washing company charges $9.38 for each window plus a reservation fee of $11. They wash a maximum of 19 windows. Also, they have the policy that once a reservation is made, if you cancel, the reservation fee is non-refundable. Let C represent the total cost from the window washing company and x represent the number of windows washed
Identify the practical domain of this function by filling in the blanks below.
Practical Domain:
Identify the practical range of this function by filling in the blanks below. Do not include the dollar sign in your answers.
Practical Range:
Math
Basic MathA basketball team sold raffle tickets to raise money for the upcoming season. They sold three different types of tickets: premium for $10, deluxe for $3, and regular for $2. The total number of tickets sold was 276, and the total amount of money from raffle tickets was $855. If 90 more regular tickets were sold than deluxe tickets, how many premium tickets were sold? Provide your answer below:
Math
Basic MathDoes the ordered pair (-6, 6, 1) satisfy the following system of equations?
-3x - 5y + 2z = -10
x + 2y - 5z = 1
x-3y - 4z = -28
Select the correct answer below:
Yes
No
Math
Basic MathIn 1955, Life Magazine reported that the 25-year- old mother of three worked, on average, an 80 hour week. Recently, many groups have been studying whether or not the women's movement has, in fact, resulted in an increase in the average work week for women (combining employment and at-home work). Suppose a study was done to determine if the mean work week has increased. 81 women were surveyed with the following results. The sample mean was 83; the sample standard deviation was ten. Does it appear that the mean work week has increased for women at the 5% level?
Math
StatisticsUse the following scenario for questions 1-4. Suppose it is estimated that 14% of American women are currently on a diet. A researcher would like to test this claim, so he sets up a
simple random survey. He asks 200 women if they are on a diet and 39 said yes. Conduct a one-proportion z test to determine if the percent of women on diets is not 14%
Using a significance level of 5%, what conclusion can we make?
Accept the alternative hypothesis
not enough information
Fail to reject the null hypothesis
Reject the null hypothesis
Math
EllipseGraph the given ellipse. Identify the domain, range, center, vertices, endpoints of
the minor axis, and foci in the figure.
(x-1)²/4 + (y + 1)²/9 =1
The center of the ellipse is (1,-1).
(Type an ordered pair.)
The vertices are .
(Type ordered pairs. Use a comma to separate answers as needed.)
Math
Basic MathGiven the following exponential function, identify whether the change represents growth or decay, and determine the percentage rate of increase or decrease per unit of x, to the nearest tenth of a percent.
y = 600(0.71) x/8
Math
Solution of trianglesDetermine whether the Law of Sines or the Law of Cosines is needed to solve the triangle.
A = 41°, B = 36°, c = 3.6
O Law of Sines
O Law of Cosines
Solve (if possible) the triangle. If two solutions exist, find both. Round your answers to two decimal places. (If a triangle is not possible, enter IMPOSSIBLE in each
corresponding answer blank.)
C=
a=
b=
Math
Basic MathInternet Audience At the end of a certain year, the four companies with the largest number of home Internet users in the United States were Microsoft, Time Warner, Yahoo, and Google, with a combined audience of 284 million users. Taking x to be the Microsoft audience in millions, y the Time Warner audience in millions, z the Yahoo audience in millions, and u the Google audience in millions, it was observed that
z - u = 3(x - y) + 28
x + y = 44+ z + u
and x - y + z- u = 52.
How large was the audience of each of the four companies at the end of that year?
Microsoft
Time Warner
Yahoo
Google
Math
TrigonometryStudents were asked to prove the identity (sec x)(csc x) = cot x + tan x. Two students' work is given.
Student A
Step 1:
Step 2:
cos X sin x
Step 5:
1
cos x sin x
Step 4: cos²x
Step 3: cosx+sin²
cos x sin x
cos x sinx
COS X
sinx
11:
= cot x + tan x
cotx + tan x
X
cot x + tan x
sin² x
cos x sin x
sin x
COS X
11
cotx + tan x
Student B
Step 6: cot x + tan x = cot x + tan x
Step 1: secxcsc x =
Step 2: secxcscx =
cotx + tanx Step 4: secxcscx =
Step 3: secxcsc x =
cos x
sin x
Step 5: secxcsc x =
sinx
cos x
cos²x
cosxsin x
cos²x+sin² x
cos x sin x
1
cos x sinx
sin² x
cos xsin x
(x)(sinx)
Step 6: sec x csc X = sec x csc X
Part A: Did either student verify the identity properly? Explain why or why not. (10 points)
Part B: Name two identities that were used in Student A's verification and the steps they appear in. (5 poin
Math
Quadratic equationsSolve by completing the square.
h² + 4h = 29
Write your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.
h
or h=
Math
Permutations and CombinationsIn Pennsylvania, each standard automobile license plate number consists of three letters followed by a four-digit number. How many distinct Pennsylvania license plate numbers can be formed?
Math
Basic MathWhich property is used to simplify 4/5y + 3(2/5x + 7/5y) to 5y + 6/5x?
Distributive property
Associative property of multiplication
Associative property of addition
Math
Functions3. Match the expression to it's completely factored form.
1. x²-1
2. 25x² - 49
3. 9x² + 6x +1
4. 9x² - 1
5. x² - 2x + 1
6. 25x² - 70x+49
a. (x-1)²
b. (x + 1)(x-1)
c. (3x + 1)²
d. (5x+7)(5x-7)
e. (5x - 7)2
f. (3x + 1)(3x - 1)
Math
FunctionsWrite a polynomial f(x) that satisfies the given conditions. Express the polynomial with the lowest possible leading positive
integer coefficient.
Polynomial of lowest degree with lowest possible integer coefficients and zeros of 3i and 5-3i.
Math
CircleWrite the equation in standard form for the circle that has a diameter with endpoints (1, 0) and (-1,0). (0)
Math
Permutations and CombinationsHow many three digit numbers can be
formed under each condition?
a) The leading digit cannot be 0.
b) The leading digit cannot be 0 and no
repetition of digits is allowed.
c) The leading digit cannot be 0 and the
number must be a multiple of 5.
Math
Basic MathAileen Uzin runs a retail store. Her net sales for the year were $162,000.
The cost of the merchandise that she sold was $118,500. Her operating
expenses were $28,920. Her net income was what percent of the net
sales for the year?
Math
FunctionsThe function f(t) = 290(0.95)t/24 represents the change in a quantity over t days.
What does the constant 0.95 reveal about the rate of change of the quantity?
The function is_____%
exponentially at a rate of _____% every______
Math
StatisticsA population of values has an unknown distribution with µ= 202.4 and σ = 11.5. You intend to draw a random sample of size n=144.
What is the mean of the distribution of sample means?
(Please enter an exact answer.)
What is the standard deviation of the distribution of sample means?
(Please report your answer accurate to 2 decimal places.)
Math
Basic MathOne hundred rats were exposed to high levels of e-cigarette smoke and were then
put through a simple maze.
They could make a choice between going left and going right.
An SRS of 100 rats was chosen to be part of the experiment..
Eighty of the 100 rats went right when running through the maze.
All conditions for inference have been met,
Construct a 90% confidence interval for the proportion of rats that run right when
going through the maze the first time.
(0.722, 0.878)
(0.734, 0.736)
(0.71, 0.89)
(0.76, 0.84)
Math
Basic MathA hollow glass cone is filled with perfume and placed inside of a hollow cylindrical container with the same height and diameter as the cone. The cylinder will then be
filled with packing material. If the cone occupies 60 cm³ of space, how many cubic centimeters of packing material will be needed?
A, 60
B. 30
C. 120
D 180
Math
TrigonometryWhy type of symmetry does the cosine function have?
Cosine is an odd function, meaning it has rotational symmetry about the origin.
Cosine is an even function, meaning it has symmetry with respect to the y axis.
Cosine is an odd function, meaning it has symmetry with respect to the y axis.
Cosine is an even function, meaning it has rotational symmetry about the origin.
Math
StatisticsA particular brand of tires claims that its deluxe tire averages at least 50,000 miles before it needs to be replaced. From past studies of this tire, the standard deviation is known to be 8,000. A survey of owners of that tire design is conducted. From the 28 tires surveyed, the mean lifespan was 46,500 miles with a standard deviation of 9,800 miles. Using alpha = 0.05, is the data highly inconsistent with the claim?
Math
Basic MathA painting measuring 120 cm wide by 80 cm tall is mounted in a picture frame. There is a margin of 6 cm wide at the top and each side of the painting. If the painting is similar to the frame, what must be the width of the margin at the bottom of the painting?
Math
Basic MathThe average electric bill from Duke Energy is $147 with a standard deviation of $32. What is the probability that the bill will be less than $100?
93%
-7%
17%
10%
Math
Basic MathSuppose it is estimated that 14% of American women are currently on a diet. A researcher would like to test this claim, so he sets up a simple random survey. He asks 200 women if they are on a diet and 39 said yes. Conduct a one-proportion z test to determine if the percent of women on diets is not 14%
Math
Quadratic equationsJohn owns a hot dog stand. He has found that his profit is given by the equation P= -x² + 60x + 71, where x is the number of hot dogs sold. How many hot dogs must he sell to earn the maximum profit?
20 hot dogs
31 hot dogs
41 hot dogs
30 hot dogs
Math
TrigonometryConsider the graph of f(x) = sin(x).
a. Describe the graph.
b. Can this graph be an example of any other function?
Hint (b):
c. Explain why f(x) = sin(x) cannot be a polynomial function.
Hint (c):
Math
Permutations and CombinationsA college student is preparing a course schedule for the next semester. The student must select one of two mathematics courses, one of three science courses, and one of five courses from the social science and humanities. How many schedule are possible?
Math
Basic MathThe following equation:
C 45x + 6900
gives the total cost, in dollars, to produce a units of a product at a factory. If the monthly operating budget of the factor is $40200, how many units can be produced there in that month?
Answer: In that month,units can be produced for $40200.
Math
Basic MathFive players agree to divide a cake fairly using the last diminisher method. The players play in the following order: Anne first, Betty second, Cindy third, Doris fourth, and Ellen last.
In round 1, Ellen is the only diminisher
In round 2, Betty and Cindy are the only diminishers
In round 3, there are no diminishers
Which player gets her fair share at the end of:
Math
Basic MathThe probability that it will snow on the last day of January is 85%. If the probability remains the same for the first eight days of February, what is the probability that it will snow at least five of those days in February?