Basic Math Questions and Answers

Determine whether the proportion is a true proportion. 7/21 = 8/24 Is the proportion a true proportion? A. No, because 7+248 +21. B. Yes, because 7.24 = 8.21. C. Yes, because 7 + 24 = 8+21. D. No, because 7.24 #8.21.

What is the area of a regular hexagon inscribed in a circle of radius 9 meters? 35.074 square meters 175.370 square meters 192.589 square meters 210.444 square meters

Suppose it was determined that the water footprint for a typical American is 2,483 m³/year. a. A family of three would like to reduce their water footprint so that it is 75% of the typical American's water footprint. Which calculation shows how they can estimate their target water footprint for one day? There may be more than one correct answer. ÷ 365 0 (3) 3 x 2,500 × 3 2,500 × 3 × 4 03 x 2,500 x 0.75 ÷ 365 2,500 (365 × 0.75) × 3 2, 500 x 3 x 0.75 3x (2, 500 x 0.75) ÷ 365 4 3 2, 500 x 3÷ 0.75 ÷ 365

Solve for the roots in simplest form by completing the square: x² + 16x - 61 = 0

An accounting firm has ordered 60 new computers at a cost of $1657 each. The machines will not be delivered for 5 months. What amount could the firm deposit today in an account paying 3.33% simple interest to have enough money to pay for the machines in 5 months? The present value PV of a future amount of FV dollars at a simple interest rate r for t years is given by which formula? A. PV=FV(1 + rt) B. PV= FV c. PV=rt(1 + FV) FV 1 + rt D. PV= The firm should deposit $ (Round to the nearest cent as needed.)

The radius, r, in centimeters, of a melting snowball is given by r = 60 — 2.5t, where t is the time in hours. The snowball is spherical with volume V = πr³ cm³. Find a formula for V = f(t), the volume of the snowball as a function of time. V = f(t) = (Be sure to include units!) help (formulas) with help (units)

Find the real solutions, if any, of the following equation. Use the quadratic formula. 2x(x+2) = 2 Select the correct choice below and, if necessary, fill in the answer box to complete your answer. The solution set is -1+√√2,-1-√√2 (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression. Use a comma to se B. The solution is not a real number.

Let (X) be a sequence of independent exponentialy distributed random variables with means respectively (a) Does (X) converge in distribution? (6) Does (X) converge almost surely?

What effect did population and cultural shifts within New Mexican territory have? A. It allowed New Mexico more representation in the Senate. B. It helped New Mexico finally achieve statehood. C. It forced southern states to continue to refuse statehood. D. It lessened conflict between settlers and indigenous peoples.

For the following list of data, calculate (a) the mean, (b) the median, and (c) the mode or modes (if any). 133, 135, 147, 131, 147, 136 (a) The mean is (Round to the nearest tenth as needed.)

The average forward speed for neotropical butterflies can be modeled by the function, V(m)= 5.2 √m where V(m) represents the average forward body speed in meters per second and m represents the body mass of the butterfly in grams. According to this model, what would be the body mass of a butterfly that has an average forward speed of 10 meters per second? Round to one decimal place. {your final answer only number with one decimal place}

The half-life of the radioactive element unobtanium-59 is 10 seconds. If 176 grams of unobtanium-59 are initially present, how many grams are present after 10 seconds? 20 seconds? 30 seconds? 40 seconds? 50 seconds? The amount left after 10 seconds is grams. The amount left after 20 seconds is grams. The amount left after 30 seconds is grams. The amount left after 40 seconds is grams. The amount left after 50 seconds is grams. (Round to one decimal place.) .....

The factored answer (x-7)(x + 4) is the same as (x + 4)(x − 7). O True O False

A popular brand of pen is available in 7 colors and 2 writing tips. How many different choices of pens do you have with this brand? There are different choices of pens with this brand.

The Best Buy parking lot is a rectangle that measures 385 feet long and 180 feet wide. Each parking space is a rectangle that measures 20 feet long and 9 feet wide. On black Friday, the parking lot is full. How many cars are parked in the parking lot at Best Buy on black Friday? Hint: Calculate the area of the parking lot and the parking space to help find the answer.

Use the formula for simple interest, I=Pxrxt, to find the missing quantity. P=$5,500; r = 7%; t = 6 years A. 1 $2,510 B. 1=$2,310 C. 1 $231,000 D. 1 $23,100

Scores on a dental anxiety scale range from 0 (no anxiety) to 20 (extreme anxiety). The scores are normally distributed with a mean of 11 and a standard deviation of 4. Find the z-score for the given score on this dental anxiety scale. Z4 = (Type an integer or a decimal.) .

Interpret the slope in context for each situation. a. The average height of children ages 8 to 13 can be modeled by the equation y = 35 + 2x, where x is the age in years and y is the average height in inches. b. Researchers found that the weight of an infant less than 12 months old can be predicted using the equation y = 9.9 + 1.1x, where y is the weight in pounds and x is the age in months. www.ncbi.nlm.nih.gov/pubmed/18021105 www.ncbi.nlm.nih.gov/pubmed/18021105 c. The equation of the line that estimates the number of airports, y, a state has given its population in millions, x, is y = 6.1016+ 1.35x.

The population of a city was 132 thousand in 1992. The exponential growth rate was 1.7% per year. a) Find the exponential growth function in terms of t, where t is the number of years since 1992. P(t)= 132000 e 0.017t b) Predict the population in 2010, to the nearest thousand. (Round to the nearest thousand as needed.)

The number of federal income tax returns filed electronically since 1995 is estimated by y = 5.6524x + 8.731, where y is the number of returns (in millions) and x is the number of years since 1995. Which of the following statements interprets the equation for this situation? 1) The number of federal income tax returns filed electronically has decreased at an average rate of about 8.731 million returns per year since 1995. 2) The number of federal income tax returns filed electronically has increased at an average rate of 5.6524 million returns per year since 1995. 3) The number of federal income tax returns filed electronically has decreased at an average rate of 5.6524 million returns per year since 1995. 4) The number of federal income tax returns filed electronically has increased at an average rate of about 8.731 million returns per year since 1995.

Consider the system of equation: x+4y=13 3x+2y=19 (a) Multiply both sides of the second equation by-2. What equation results? (c) Now that you know the value of x, how can you find the value of y? Find it. (b) Add the equation from (a) to the first equation. What happens? What can you now solve for? (d) What could you have multiplied both sides of the first equation by to eliminate the x instead of the y?

Point E with coordinates (5, 7) is translated along a glide reflection to its image of E (4,3). Which best describes the glide reflection? (x,y) → (x-1, y - 4) followed by reflection across the x-axis (x,y) → (x-2, y - 3) followed by reflection across y = x (x,y) → (x-1, y - 4) followed by reflection across y = -x (x,y) → (x-2, y-3) followed by reflection across y = -x

Line A passes through the points (0, 11) and (-5, 1). Line B passes through the points (0, 10) and (1, 12). Which of the following statements is true about the system of equations represented by line A and line B? A. The system of equations has exactly one real solution. B. The system of equations has an infinite number of real solutions. C. The system of equations has exactly two real solutions. D. The system of equations has no real solutions.

Find an equation of the line with the given slope that passes through the given point. Write the equation in the form Ax+By = C. m = -7, (-6, - 3) The equation of the line in the form Ax+By = C is (Simplify your answer. Use integers or fractions for any numbers in the equation.)

A person invests $1625 into a retirement account, with an interest rate of 0.9% compounded quarterly. Find the retirement account balance after two years. 1) The balance will be $1654.48 after two years. 2) The balance will be 1941.60 after two years. 3) The balance will be $1664.41 after two years. 4) The balance will be $3279.34 after two years.

1. Negative ions form when atoms valence electrons. 2. In the formation of an ionic compound, a metal atom is most likely to valence electrons. 3. lonic compounds form because charges attract.

HOW MANY 7 DIGIT TELEPHONE NUMBERS ARE POSSIBLE IF THE FIRST DIGIT CANNOT BE ZERO AND: A) THE TELEPHONE NUMBER MUST BE A MULTIPLE OF 100? B) ONLY ODD DIGITS CAN BE USED? C) THE FIRST 3 DIGITS ARE 277?

Which of the following real-world scenarios can be modeled using sine or cosine? The number of mold spores that grow on a forgotten container of leftovers in the back of your refrigerator. The amount of money you have in your bank account that earns interest quarterly. Assume no deposits or withdrawals. The distance from the earth to the sun over the course of a year. Concert revenue from ticket sales for a sold out show.

Factor the polynomial f(x) = 3x³ + 12x² + 3x - 18 given that x = -3 is a zero of f(x). f(x) = 3(x-2)(x + 1)(x+3) f(x) = (x-2)(x + 1)(x-3) f(x) = (x + 2)(x - 1)(x+3) f(x) = 3(x + 2)(x - 1)(x+3)

Suppose that $2000 is invested at a rate of 5.2%, compounded quarterly. Assuming that no withdrawals are made, find the total amount after 4 years. Do not round any intermediate computations, and round your answer to the nearest cent.

A TV has a listed price of $709.99 before tax. If the sales tax rate is 8.5%, find the total cost of the TV with sales tax included. Round your answer to the nearest cent, as necessary.

If 3 fair coins are tossed, find the probability that no more than 1 is heads. The probability that no more than 1 is heads is (Type an integer or decimal rounded to the nearest thousandth as needed.)

Workers at a certain soda drink factory collected data on the volumes (in ounces) of a simple random sample of 25 cans of the soda drink. Those volumes have a mean of 12.19 oz and a standard deviation of 0.09 oz, and they appear to be from a normally distributed population. If the workers want the filling process to work so that almost all cans have volumes between 12.02 oz and 12.54 oz, the range rule of thumb can be used to estimate that the standard deviation should be less than 0.13 oz. Use the sample data to test the claim that the population of volumes has a standard deviation less than 0.13 oz. Use a 0.05 significance level. Complete parts (a) through (d) below.

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.)

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

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

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:

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 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.

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.

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.)