Math Questions

A rectangular tank that is 2048 ft³ with a square base and open top is to be constructed of sheet steel of a given thickness. Find the dimensions of the tank with minimum weight. The dimensions of the tank with minimum weight are (Simplify your answer. Use a comma to separate answers.)

Find the third degree polynomial function that has an output of 320 when x = = 4, and has zeros 2 and -8i. Provide your answer below: f(x) = 7

Body Mass Index: In a survey of adults with diabetes, the average body mass index (BMI) in a sample of 0.3. The average BMI in a sample of 1559men was 30.50 with a standard deviation of 0.6, Part: 0/2 Part 1 of 2 99% confidence interval for the difference in the mean BMI between women and men with diabetes is <44-42₂ <0. 31.30 with a standard deviation of 99% Construct confidence interval for the difference in the mean BMI between women and men with diabetes. Let H denote the mean BMI for women with diabetes. Use tables to find the critical value and round the answers to at least two decimal places.

Padlocks with digit dials are often referred to as "combination locks" According to the mathematical definition of combination, is this an accurate description? Explain. A combination is a subset of objects or choices in which the order A permutation is a subset of objects or choices in which the order Therefore, the description of Combination Locks mathematically accurate.

For sin 2x + cos x = 0, use a double-angle or half-angle formula to simplify the equation and then find all solutions of the equation in the interval [0, 2π). The answers are x1 = 12 x3 = x4 =

An art teacher is making packages of paintbrushes and paint for his students. He has 24 brushes and 40 tubes of paint. Each package will have the same number of brushes and the same number of tubes of paint. a. What is the greatest number of packages that the art teacher can make using all the paintbrushes and paint? Show your work. b. How many paintbrushes and tubes of paint are in each package?

Saizon Pen & Office Supply uses a markup of $9 on a calculator that costs $20. What markup rate does this amount represent? _______ %

Dr. Marina Silva, in the Journal of Mammalogy (1998), gives the following formula for the approximate body length of mammals based on the mammal's body mass L(M) = 0.25 M where L(M) represents the body length in meters of a mammal with a body mass of M kilograms. Use this model to estimate the body length of a mammal with a body mass of 2.5 kg. (Round your final answer to two decimal places.)

In a class of 50 students, 21 are Democrats, 9 are business majors, and 7 of the business majors are Democrats. If one student is randomly selected from the class, find the probability of choosing a Democrat or a business major. A) 1/25 B) 23/50 C) 37/50 D) 3/5

A company's revenue from selling x units of an item is given as R = 1000x - x² dollars. If sales are increasing at the rate of 80 per day, find how rapidly revenue is growing (in dollars per day) when 350 units have been sold. $ per day

The magnitude, M, of an earthquake is represented by the equation M = log where E is the amount of energy released by the 104.4 is the earthquake in joules and Eo assigned minimal measure released by an earthquake. In scientific notation rounded to the nearest tenth, what is the amount of energy released by an earthquake with a magnitude of 5.5?

Write the equation in slope-intercept form (if possible) and graph the line. 2x+y=7 Part: 0/2 Part 1 of 2 The equation in slope-intercept form is

Given: tanx = -15/8 and x is in Quadrant IV. Find the exact values of sin (x/2),cos (x/2), and tan (x/2) without solving for x, when 0 ≤ x ≤ 360°. To enter the square root of a number, type "sqrt(a)". For example, type "sqrt(2)" to enter √2. a)sin (x/2)= ___ b)cos (x/2)= ___ c)tan (x/2)= ___

Find the amount of tax and the tax rate. Round to nearest hundredth of a percent. Cost of item: $128 Selling price: $135.55 Tax amount: Tax rate:

Find the distance between the pair of points. (2,3) and (-7, -24) The distance is (Type an integer or a decimal rounded to three decimal places as needed.)

Suppose that x represents one of two positive numbers whose sum is 14. (a) Represent the other of the two numbers in terms of x. (b) What are the restrictions on x? (c) Determine a function P that represents the product of the two numbers. (d) Determine analytically and support graphically the two such numbers whose product is a maximum. What is this maximum product? (a) If x is one of the two numbers, then the other number is

If the probability of winning a race is 1/3 What are the odds in favor of winning the race?

If 29, then x = A. log10 2 B. 2/ C. log, 2 D. log₂ 9 E. 2

Consider the graph of the function f(x) = x²-4x-5/x²+3x-10 What are the vertical asymptotes? List the x-values separated by commas. Provide your answer below: X =

Given: AABC with median AM AB = x + 7 AC = 2x - 1 CM = 2x-5 BM = x +4 Find the length of BC (no image is needed for this picture. Hint: you may sketch the triangle ABC on scratch paper, label AM as a median and then figure out which equations you would use to solve for x) 26 30 13 15

The angle bisectors of AJKL are JQ, KQ, and LQ. They meet at a single point Q. (In other words, Q is the incenter of AJKL.) Suppose NQ=20, LQ=23, mLNLP=34°, and mLMJQ=26°. Find the following measures. Note that the figure is not drawn to scale.

A 19 ft ladder leans against a wall. The bottom of the ladder is 3 ft from the wall at time 0 and slides away from the wall at a rate of 1ft/sec. Find the velocity of the top of the ladder at time t = 2. The velocity of ladder at time t = 2 is ft/sec.

f(x) = 4x²-x-5 What is the value using the theorem for f(5)?

Convert 160° into radian measure: Convert 351° into radian measure: Convert 205° into radian measure: Convert 57° into radian measure: Enter your answer as a fraction of pi You may also use decimal approximation, but your answer must be accurate to at least 3 decimal places.

The rate of change of the number of raccoons N(t) in a population is directly proportional to 380 N(t), where t is the time in years. When t = 0, the population is 120, and when t = 4, the population has increased to 160. Find the population when t = 8. (Round your answer to the nearest integer.) raccoons

Suppose that 9% of voters in California are in favor of Proposition A. In a random sample of 32 voters, A. What is the probability that none of the voters will be in favor of Prop. A? Probability = B. What is the probability that fewer than 5 voters will be in favor of Prop. A? Probability= C. What is the probability that at least 3 voters will be in favor of Prop. A? Probability=

The weight of a body varies inversely as the square of its distance from the center of a planet. If the radius of the planet is 3000 miles, how much would a man weighing 180-pounds on the surface of the planet weigh 3000 miles above the surface of the planet? A 180-pound man will weigh pounds 3000 miles above the surface of the planet. (Simplify your answer. Type an integer or a decimal rounded to one decimal place as needed.)

A company manufactures two models of snowboards, standard and deluxe. Each deluxe model requires 26 hours to produce, and 96 units of material. Each standard model requires 13 hours to produce and 80 units of material. The company has 858 production hours available and 4000 units of material in stock. The deluxe model sells for $272 and the standard model sells for $170. What amount of each model should be produced and sold to obtain the maximum revenue? Adeluxe models standard models What is the maximum revenue? $

Peter withdrew 1000 dollars from his bank account today. He uses 500 to fix his car. Then, he divide the money into 5 equal parts and gave away 4 parts and kept 1 part for himself. Finally, he took to wife to the restaurant and spent 60 dollars on meals. How much money, in dollars, does Peter have now? 40 500 67 100 33

For a data set of the pulse rates for a sample of adult females, the lowest pulse rate is 38 beats per minute, the mean of the listed pulse rates is x = 72.0 beats per minute, and their standard deviation is s = 19.1 beats per minute. a. What is the difference between the pulse rate of 38 beats per minute and the mean pulse rate of the females? b. How many standard deviations is that [the difference found in part (a)]? c. Convert the pulse rate of 38 beats per minutes to a z score. d. If we consider pulse rates that convert to z scores between -2 and 2 to be neither significantly low nor significantly high, is the pulse rate of 38 beats per minute significant?

What numbers must you know to find the surface area and volume of a sphere? The sphere's radius and the area of a great circle The sphere's radius and the circumference of a great circle The sphere's radius and the circumference and area of a great circle The sphere's radius

A jar contains 8 pennies, 3 nickels and 7 dimes. A child selects 2 coins at random without replacement from the jar. Let X represent the amount in cents of the selected coins. Round your answers to 3 decimal places. Find the probability X = 10. Find the probability X = 11.

A total of 380 tickets were sold for the school play. They were either adult tickets or student tickets. The number of student tickets sold was three times the number of adult tickets sold. How many adult tickets were sold?

Starting with the graph of f(x) = 67, write the equation of the graph that results from a. shifting f(x) 7 units left. b. shifting f(x) 5 units downward. c. reflecting f(x) about the x-axis.

Use the formal definition of the derivative to find the derivative of y= 1/x+8 at x= 7 Derivative is Find an equation for the tangent line to the graph of y= 1/x+8 Tangent line is

Rationalize the denominator: -9/4 + √2

Diana had a coupon for c dollars off of each box of crackers. Diana bought 2 boxes of crackers for 4.50 c dollars each. She also bought 8 cans of soup for s dollars each. The total amount, in dollars, she spent on the cans of soup and boxes of crackers is represented by the expression below. 2(4.50 c) +8s Which expression also represents the total amount, in dollars, she spent? a. 6.50 - 2c + 8s b. 6.50 2c + 10s c. 9 - c + 8s d. 9-2c + 8s

If you want to earn $950.00 of simple interest at a rate of 7% in a span of 9 months, how much money must you invest? (Round your answer to two decimal places.) You would need to invest

Find the indefinite integral. 18/1 + 81x² dx

Multiply and simplify completely: (x + 2)(x − 2)

7.40 Testing a random number generator. Statistical software has a "random number generator" that is supposed to produce numbers uniformly distributed between 0 and 1. If this is true, the numbers generated come from a population with = 0.5. A command to generate 100 random numbers gives outcomes with mean = 0.531 and s = 0.294. Because the sample is reasonably large, take the population standard deviation also to be o = 0.294. Do we have evidence that the mean of all numbers produced by this software is not 0.5?

Furnace repair bills are normally distributed with a mean of 269 dollars and a standard deviation of 20 dollars. If 64 of these repair bills are randomly selected, find the probability that they have a mean cost between 269 dollars and 271 dollars. 0.7881 0.2881 0.5517 0.2119

Find the derivative of the function. y = - 8x In (8x + 7) dy/dx

Give the measure of the supplement of the angle. (180-y)° The supplement of the angle (180-y)° is

Consider a population of size N = 9, 800 with a mean of μ = 161 and standard deviation of a = 17. Compute the following z-values for either the population distribution or the sampling distributions of with given sample size. Round solutions to two decimal places, if necessary. Suppose a random single observations is selected from the population. Calculate the z-value that corresponds to x = 165. Suppose a random single observations is selected from the population. Calculate the z-value that corresponds to x = 157.

The power rule for logarithms states that The logarithm of a number with an exponent is the Points: 0 of 1 of the exponent and the logarithm of that number.

Find an equation of the tangent line to f(x) = ex + 7x at the point (0, 1). Write your final answer in the form y = mx + b.

Angle x lies in the first quadrant such that cosx = 3/5the second quadrant such that siny = 7/25. Determine an exact value for cos (x - y).

The two Soup cans are similar. The large can has a height of 4 in in the smaller can has a height of 3 inches. Find the area of the smaller can give in the larger can has an area of 108 in squared. Round your answer to the hundredths of an inch.

Misu Sheet, owner of the Bedspread Shop, knows his customers will pay no more than $135 for a comforter. Misu wants a 20% markup on cost instead of on selling price. What is Misu's cost? (Round your answer to the nearest cent.)