Basic Math Questions and Answers

The following is given in recursive form. a1=8 an=2a-1 +5, for n ≥ 2 What is the value of the third term of this sequence? Type your answer into the box below.

Suppose a plane flies 48 miles in 12 minutes. The relationship between miles flown, x, and minutes flown, y, by the plane can represented by the equation y = 1/4x. How far will the plane fly in 28 minutes? A) 112 miles B) 116 miles C) 120 miles D) 124 miles

Kala needs $4300 for a future project. She can Invest $2000 now at an annual rate of 10%, compounded quarterly. Assuming that no withdrawals are made, how long will it take for her to have enough money for her project? Do not round any Intermediate computations, and round your answer to the nearest hundredth.

25% of the students attended the school dance. If 32 attended the dance, how many students are there in all? A. 128 C. 16 B. 8 D. 140

Express the set using the roster method. {x|X ∈ N and 25<x< 90} Choose the correct answer below. A. Ø B. {26, 27, 28, 29, ..., 89} C. {25, 26, 27, 28, ..., 90} D. {..., 23, 24, 25, 90, 91, 92, ...}

For the real-valued functions f(x)=√(5x+30) and g(x)=x-3, find the composition fog and specify its domain using interval notation.

Casey took a total of 12 quizzes over the course of 3 weeks. After attending 5 weeks of school, how many quizzes (q) will Casey have taken in total? Assume the relationship is directly proportional. A)18 B)20 C)22 D)24

Marla made $42 babysitting for 5 hours. How much money did she make each hour? A. $8.40 C. $1.90 B. $8.10 D. $11.90

What is the volume of a sphere with a diameter of 49.3 cm, rounded to the nearest tenth of a cubic centimeter?

"Payah kun," said the Eldest Magician, meaning, "That is quite right"; and he breathed upon the great rocks and lumps of earth that All-the-Elephant-there-was had thrown up, and they became the great Himalayan Mountains, and you can look them out on the map.... Then the Moon rose big and full over the water, and the Eldest Magician said to the hunchbacked old man who sits in the Moon spinning a fishing-line with which he hopes one day to catch the world, "Ho! Fisher of the Moon, are you playing with the Sea?" -"The Crab That Played with the Sea," Rudyard Kipling How does the use of imagery create meaning? The imagery emphasizes the compassion and authority of the Eldest Magician. The imagery explains how the animals are responsible for creating nature. The imagery reveals the power that the old man has over the moon. The imagery highlights the importance of earth, Moon, and Sea.

Define Euler's Constant and provide its numerical value and what is it also known as (not gamma which is the symbol). Definition: Numerical value (decimal format, 1st 8 numbers):

A designer builds a model of a canoe. The finished model is exactly the same shape as the original, but smaller. The scale factor is 3:11. (a) Find the ratio of the height of the model to the height of the original. (b) Find the ratio of the volume of the model to the volume of the original. (c) Find the ratio of the surface area of the model to the surface area of the original. Write these ratios in the format m:n.

inding the Suppose that the number of bacteria in a certain population increases according to a continuous exponential growth model. A sample of 2400 bacteria selected from this population reached the size of 2556 bacteria in two hours. Find the hourly growth rate parameter. Note: This is a continuous exponential growth model. Write your answer as a percentage. Do not round any intermediate computations, and round your percentage to the nearest hundredth.

When the volume of a gas is changed from 986 mL to mL, the temperature will change from 765 K to 315 K.

A line segment of length is scaled by a factor of 1.5 to produce a segment with length m. The new segment is then scaled by a factor of 1.5 to give a segment of length n. What scale factor takes the segment of length to the segment of length n? Explain your reasoning.

At Marcy's Department Store, all dresses are 40% off. If the regular price of a dress is $85, what is the sale price? A. $51.00 C. $45.00 B. $40.00 D. $58.00

A study shows that, over the course of a lifetime, the average salary of college graduates is greater than the average salary of people with only a high school diploma. The results were published claiming that graduating from college ensures you will make more money over the course of your lifetime. What is the problem with reporting results this way? loaded question voluntary response correlation and causality missing data

Suppose that $2900 is Initially Invested in an account at a fixed Interest rate, compounded continuously. Suppose also that, after two and a half years, the amount of money in the account is $3098. Find the Interest rate per year. Write your answer as a percentage. Do not round any intermediate computations, and round your percentage to the nearest hundredth.

Suppose that $6000 is placed in a savings account at an annual rate of 3%, compounded monthly. Assuming that no withdrawals are made, how long will it take for the account to grow to $7110? Do not round any intermediate computations, and round your answer to the nearest hundredth.

A gas that exerts a pressure of 6.20 atm in a container with a volume mL will exert a pressure of of 9.150 atm when transferred to a "container with a volume of 322 mL.

What is the volume of a sphere with a radius of 8 m, rounded to the nearest tenth of a cubic meter?

How long will it take for a $2000 Investment to grow to $3070 at an annual rate of 6.4%, compounded quarterly? Assume that no withdrawals are made. Do not round any Intermediate computations, and round your answer to the nearest hundredth.

You have been asked to convert a pressure FROM atm TO psi. Which conversion factor would you use? 14.7 psi/1 atm 1 atm/14.7 psi

What is the diameter of a hemisphere with a volume of 74466 cm³, to the nearest tenth of a centimeter? Answer: cm

Artie needs to save $450 to buy the new bicycle that he wants. He currently has $300. What percent of the cost of a new bicycle has he saved? Claire decides to solve this problem by setting up a proportion. What should her proportion look like? A) 300/100 = X/450 B) x/100 = 300/450 C) x/100 = 450/300 D) 450/100 = x/300

The number of frogs (f) in the pond is proportional to the number of salamanders (s) placed in the pond. Suppose there are 10 frogs for each salamander. Which equation represents the total number of frogs in the pond? s=10f f=10s f = 10/s s=f+10

The circumference of a circle with a radius of 5.8 inches is ?in. Use 3.14 for pi. (Round to the nearest hundredth).

The floor area of a furniture storeroom is 500 square yards. One sofa requires 3 square yards and one dining table requires 4 square yards of space. The room can hold a maximum of 150 pieces of furniture. Let s represent the number of sofas and t represent the number of tables. Write a system of inequalities to represent the number of pieces of furniture that can be placed in the storeroom.

# 18. Which of the following is a property of a parallelogram? A The diagonals are congruent. C The diagonals bisect the angles. B The diagonals bisect each other. D The diagonals are perpendicular.

The equation 4 = 1300(1.02) is being used to calculate the amount of money in a savings account. What does 1.02 represent in this equation? 1) 0.02% decay 2) 0.02% growth 3) 2% decay 4) 2% growth

You kick a football at an angle of 55° with an initial speed of 63 feet per second. Estimate to the nearest foot, the horizontal distnace traveled by the football. d = v2/32 sin 2θ.

There is a circular track that surrounds a patch of grass. The radius from the grass to the track is 23 feet. How many feet long is the track? Your answer should be a number only. Use 3.14 for pi. Round your answer to the nearest hundredth.

You want to put edging around your above ground rectangular pool. The dimensions of the pool are 22 ft. by 27 ft. How many feet of edging do you need to purchase to surround the pool? Your answer should be a number only.

Jose' holds a rock 1m above the ground. The rock has 100J of PE and 0 KE while she holds the rock. Which of the following is true if Becky drops the rock? * Electrical Energy It's impossible to tell without knowing the rock's mass. The rock will have OJ of PE and 100J of KE right before it hits the ground. a

Johnny can build 3 1/2 lego planes in 60 minutes. How many can he build in 40 minutes?

A telecommunications company is building a third cell tower in a region with existing towers located at A(-2,-3) and B(5,-3). Each unit in the coordinate plane represents 0.6 mile. They ask you to determine the location of the third tower so that the triangle formed by the three cell towers has an area of about 10.1 square miles and a perimeter of about 15 miles, and the distance from the third tower to tower A is about 6 miles. Estimate the coordinates of the third tower to the nearest integer.

A swimming pool is being filled at the rate of 12 cubic yards per minute. If the pool is 18 yards long, 10 yards wide, and 3 yards deep, how many minutes will it take to fill the pool? 540 minutes 101 minutes 1,233 minutes 45 minutes

Using the formula A = ½bh for the area of a triangle where b is the base and h is the height, find the area of a triangle whose base is 12 units and whose height is 24 units. Enter only the numeric value with no letters or =.

For the polynomial function f(x) = .5x³ + .25x2 + .125x+ .0625, find the zeros. Then determine the multiplicity at each zero and state whether the graph displays the behavior of a touch or a cross at each intercept. x = .5, cross x = .5, touch x = -.5, touch x = -.5, cross

The number of bacteria in a certain sample Increases according to the following function, where y0 is the initial number present, and y is the number present at time t (in hours). y=y0e^0.05671 How many hours does it take for the size of the sample to double? Do not round any Intermediate computations, and round your answer to the nearest tenth.

Anthony owns a small business selling bagels. He knows that in the last week 3 customers paid cash, 33 customers used a debit card, and 34 customers used a credit card. Based on these results, express the probability that the next customer will pay with cash as a fraction in simplest form.

Julie is asked to solve the system below by elimination. Which of the following steps would be the best way to begin? 2x+y=-3 ? 3x-2y = 2 A. Multiply 1 by 2 and multiply by 3 B. Multiply 2 by 2 C. Multiply 1 by 2 D. Multiply 2 by 2 and multiply 1 by -2

Cost to store: $65 Markup: 25% 40% Sale Price Sale Price: $48 Selling Price: $81.25

A group of biologists is surveying the mice population in a forest. The equation n = 75.3¹ gives the total number of mice, n, t years since the survey began. Explain what the numbers 75 and 3 mean in this situation.

You just bought a new car and need to expand your driveway by pouring more concrete. If the dimensions of the addition are 11 ft. by 6.5 ft., how many square feet of concrete do you need to pour? Your answer should be a number only. Do not round.

When Xochitl runs the 400 meter dash, her finishing times are normally distributed with a mean of 84 seconds and a standard deviation of 2.5 seconds. Using the empirical rule, determine the interval of times that represents the middle 68% of her finishing times in the 400 meter race.

In a right triangle the two legs have measurements of 12 inches and 15 inches. Use the Pythagorean theorem to calculate the length of the hypotenuse. 12.96 inches 5.2 inches 19.21 inches 340.00 inches 28.54 inches

Suppose that the functions and g are defined as follows. ƒ(x)= 5/x+1 g(x)=6/x Find f/g. Then, give its domain using an interval or union of intervals. Simplify your answers.

You buy a tarp to cover the driveway when it snows. The dimensions of your driveway are 10 ft. by 15 ft. If the tarp covers your entire driveway, how many square feet are covered? Your answer should be a number only.

Use the Factor Theorem to determine whether x-2 is a factor of P(x) = -2x³ + 3x²-3x+10. Specifically, evaluate P at the proper value, and then determine whether x-2 is a factor.