Math Questions

Brittany's annual salary is $73,800. She pays 23% in taxes. After taxes, she pays 4% into retirement. How much does Brittany pay into retirement? What is Brittany's annual salary after taxes and retirement?

A YouTube star knows that 56% of her viewers are under the age of 24. She wants to expand to other age groups, so she updates her content to be more universal. Then, she collects a simple random survey of her her followers and finds that 36 of 67 of her viewers are still under the age of 24. Using a 5% significance level, can she conclude that updating her content expanded her viewers' age group? Yes, because .7 < .05 Yes, because .53 > .56 No, because.53 <.56 No, because .7 > .05

Determine the values of a for which the system has no solutions, exactly one solution, or infinitely many solutions. x + 3y - 2z = 4 3x - y + 2z = 3 5x + 5y + (a²-11)z = a +8

Starting with the graph of f(x) = 3^x, write the equation of the graph that results from (a) shifting f(x) 6 units upward. (b) shifting f(x) 7 units to the left. (c) reflecting f(x) about the y-axis.

Find the general solution of the given differential equation. x²y + xy = 4 Give the largest interval over which the general solution is defined. (Think about the implications of any singular points. Enter your answer using interval notation) Determine whether there are any transient terms in the general solution. (Enter the transient terms as a comma-separated list; if there are none, enter NONE.)

Cooper invested $1,100 in an account paying an interest rate of 3.8% compounded daily. Assuming no deposits or withdrawals are made, how much money, to the nearest cent, would be in the account after 10 years?

Find an explicit solution of the given initial-value problem. x2dy/dx = y-xy, y(-1) = -6

Salina, Tamara, and Uma are working on their homework together. Salina tells her friends that she has θ = 52° for the inverse cosine problem she is working on and asks if they have the same answer. Tamara says she has θ = 128°, and Uma volunteers her answer of θ = 308°. Is it possible that these are all solutions to the same problem? Justify your answer.

Ariana invested $7,500 in an account paying an interest rate of 2.9% compounded continuously. Assuming no deposits or withdrawals are made, how much money, to the nearest ten dollars, would be in the account after 14 years?

Triangle 1 has an angle measure 26° and an angle measures 53°. Triangle 2 has an angle that measures a where at # 53°. Based on the information, Frank claims that triangle 1 and triangle 2 cannot be similar. What value of will refute franks claim?

Heights of AHS Girls basketball team players are approximately normally distributed with a mean of 70 inches and a standard deviation of 2.5. If there were 175 players, how many had a height between 71 and 74 inches?

Determine whether the following statement is true or false. Modify each false statement to make it a true statement. 63 is a divisor of 9.

Determine whether the following statement is true or false. Modify each false statement to make it a true statement. 16 is divisible by 8.

Landon is going to invest in an account paying an interest rate of 4.3% compounded continuously. How much would Landon need to invest, to the nearest hundred dollars, for the value of the account to reach $11,300 in 14 years?

Describe the transformations to the parent function. Check all boxes that apply. f(x)=1/3(x - 2)² Reflects across the x-axis (open down) Stretched by a factor of 3 (Narrower) Compressed by a factor of 3 (Wider) shifts right 2 shifts left 2 shifts up 2 shifts down 2

Victoria is going to invest in an account paying an interest rate of 1.5% compounded quarterly. How much would Victoria need to invest, to the nearest hundred dollars, for the value of the account to reach $3,300 in 13 years?

Determine whether the statement is true or false. Modify each false statement to make it a true statement. Every whole number is an integer.

Fill in the blank with an appropriate word, phrase, or symbol. With the quotient rule for exponents, the expression x^8/x^5 can be simplified to ___.

Describe the sampling distribution of p. Assume the size of the population is 20,000. n = 600, p=0.6 Choose the phrase that best describes the shape of the sampling distribution of p below. A. Approximately normal because n≤0.05N and np(1-p)<10. B. Not normal because n≤0.05N and np(1-p)≥10. C. Not normal because n≤0.05N and np(1-p)<10. D. Approximately normal because n≤0.05N and np(1-p)≥10.

A landscaper is designing a display of flowers for an area in a public park. The flower seeds will be planted at points that lie on a circle that has a diameter of 8 feet. The point where any seed is planted must be at least 2 feet away from the seeds on either side of it. Part A What is the maximum number of flower seeds that can be planted using the design? Part B After planting the flower seeds, the landscaper has 20 seeds left over. The landscaper wants to plant all of the remaining seeds in another circle so that the seeds are 2 feet apart. To the nearest tenth of a foot, what is the diameter of the smallest circle that the landscaper can use to plant all of the remaining seeds?

Determine whether the number used is a cardinal number or an ordinal number. Jim B. Brown has directed 8 movies. Choose the correct answer below. A. In this context, the number 8 is used as an ordinal number because it describes the relative position that an element occupies. B. In this context, the number 8 is used as a cardinal number because it describes the relative position that an element occupies. C. In this context, the number 8 is used as a cardinal number because it answers the question "How many movies has Jim B. Brown directed?" D. In this context, the number 8 is used as an ordinal number because it answers the question "How many movies has Jim B: Brown directed?"

Find the standard form of the equation of the hyperbola satisfying the given conditions. x-intercepts ±6, foci at (-10,0) and (10,0)

Simplify. Enter the result as a single logarithm with a coefficient of 1. log9(7x^5)+log9(6x^4)

Suppose the binomial expansion of (2x−3y)^n includes the term -15120x^4y^3 The x^4y^3 term in the expansion will be The x^5y^3 term in the expansion will be

Use the method of cylindrical shells to find the volume V generated by rotating the region bounded by the given curves about y = 8. 64y=x^3, y=0, x=8

Suppose a simple random sample of size n = 81 is obtained from a population that is skewed right with µ=73 and σ=9. (a) Describe the sampling distribution of x. (b) What is P (x>74.1)? (c) What is P (x≤70.55) ? (d) What is P (72.15<x<74.85)?

The acceleration function (in m/s2) and the initial velocity are given for a particle moving along a line. a(t)=t+6, v(0)=6, 0≤t≤10 (a) Find the velocity at time t. (b) Find the distance traveled during the given time interval.

A standard deck of cards contains 52 cards. One card is selected from the deck. (a) Compute the probability of randomly selecting a two or ten. (b) Compute the probability of randomly selecting a two or ten or ace. (c) Compute the probability of randomly selecting a two or diamond.

A concrete mix is designed to withstand 3000 pounds per square inch (psi) of pressure. The following data represent the strength of nine randomly selected casts 3960, 4090, 3200, 3200, 2950, 3830, 4100, 4040, 3570 Compute the mean, median and strength of the concrete (in psi).

Suppose that a set of test scores is normally distributed with mean 55 and standard deviation 22. What is the probability that score pulled at random is less than 48.4? Express your answer rounded correctly to the thousandths place.

Aldo is staining the wooden floor of a court. The court is in the shape of a rectangle. Its length is 46 feet and its width is 35 feet. Suppose each can of wood stain covers 115 square feet. How many cans will he need to cover the court?

Construct a 95% confidence interval of the population proportion using the given information. x=40, n=200

The effectiveness of a blood-pressure drug is being investigated. An experimenter finds that, on average, the reduction in systolic blood pressure is 48.7 for a sample of size 981 and standard deviation 17.6. Estimate how much the drug will lower a typical patient's systolic blood pressure (using a 80% confidence level).

Describe the transformations to the parent function. Check all boxes that apply. y = - 2x² - 1 Reflects across the x-axis (open down) Stretched by a factor of 2 (Narrower) Compressed by a factor of 2 (Wider) shifts up 1 shifts down 1 shifts right 2 shifts left 2 shifts up 2 shifts down 2

Suppose the binomial expansion of (x - y)^n includes the term - 84x^6y^3. The x^5y^4 term in the expansion will be The x^6y^8 term in the expansion will be

The expected value when you purchase a lottery ticket is - $2.00 and the cost of the ticket is $8.00. Determine the fair price of the lottery ticket.

Recall that the properties of logarithms also apply to the natural logarithms. a. Rewrite 3In(x)+4ln(2)-2ln(y) using a single natural logarithm. b. Rewrite In[(x - 3)(3x + 2)]³ in expanded form.

Consider the binomial expansion of (4x + 3y)^n. Suppose the expansion includes a x^4y^8 term. Then n = ___ Check ALL of the following which will NOT in the simplified expansion of (4x + 3y)^n. x^8y^4 x^8y^6 x^9y^3 x^6y^8

Describe the transformations to the parent function. Check all boxes that apply. y = x² + 3 Reflects across the x-axis (open down) shifts right 2 shifts left 2 shifts up 2 shifts down 2 shifts right 3 shifts left 3 shifts up 3 shifts down 3

A bank features a savings account that has an annual percentage rate of r quarterly. Manuel deposits $5,000 into the account. (A) What values should be used for a, r, and k? (B) How much money will Manuel have in the account in 8 years? (C) What is the annual percentage yield (APY) for the savings account?

A binomial probability experiment is conducted with the given parameters. Compute the probability of x successes in the n independent trials of the experiment. n=9, p=0.4, x≤ 3

Use vertices and asymptotes to graph the hyperbola. State the coordinates of the vertices. Find the equations of the asymptotes. 1) (x^2/4)-(y^2/16)=1

Describe the transformations to the parent function. Check all boxes that apply. y = -(x - 5)² +3 Reflects across the x-axis (opens down) shifts right 5 shifts left 5 shifts up 5 shifts down 5 shifts right 3 shifts left 3 shifts up 3 shifts down 3

Mrs. Y spent about 30 minutes every day to get to work by driving her car. The one-way commute cost her $5.00 in total including parking -while her wages per hour were $19.00. Alternatively, she took the city's subway that cost her $2.00 for a 40-minute commute to work. She noted that the opportunity costs of driving were______ and taking the public transportation were ______ respectively. $14.50; $14.87 $14.50; $14.67

Determine the point estimate of the population proportion, the margin of error for the following confidence interval, and the number of individuals in the sample with the specified characteristic, x, for the sample size provided. Lower bound=0.309, upper bound = 0.681, n = 1000

Write the equation of the straight line passing through the point (5, 2) and having a slope of 1/2. y =1/2(x-1) y=2(x-2) y=1/2(x + 1)

An object with initial temperature 200° F is submerged in large tank of water whose temperature is 40° F. Find a formula for F(t), the temperature of the object after t minutes, if the cooling constant is k = 0.6

Find the equation of the line with the slope m = 3/2 and passes through the point (-4,-2). y=-3/2x+4 y=3/2x-4 y=3/2x+4

Determine the area under the standard normal curve that lies between (a) Z=-1.02 and Z=1.02, (b) Z= -0.36 and Z=0, and (c) Z=-2.19 and Z=0.64.

Is it more convenient to complete the square for x^2 + bx when bis odd or when b is even? Explain.