Basic Math Questions and Answers

A sports ball has a diameter of 19 cm. Find the volume of the ball. Round your answer to 2 decimal places. Volume=

If 1 yard = 3 feet and 1 mile 5,280 feet, how many yards are there in 2 miles? 2,640 yards 3,520 yards 10,560 yards 31,680 yards

Solve the system of equations by graphing. - 3x + 3y = 15 2x2y = - 10 Graph the system of equations and write the solution as an ordered pair. Write "DNE" if the solution does not exist, or use the infinity symbol if the system has infinitely many solutions. If the two equations graph as the same line, plot only one line on the graph. The graph will not be scored correctly if you try to plot two lines on top of each other.

The transformation that has translation and a reflection across a line parallel to the direction of translation is called as parallel reflection glide reflection regular reflection diffused reflection

Solve the inequality and write your answer in interval notation. 20x-8 ≥ 16+ 2x

Aria has a points card for a movie theater. • She receives 85 rewards points just for signing up. • She earns 12.5 points for each visit to the movie theater. • She needs 185 points for a free movie ticket. How many visits must Aria make to earn a free movie ticket?

Mandy is making stationery sets from 16 sheets of paper and 12 envelopes. If she wants all the sets to be identical without any paper or envelopes left over, what is the greatest number of sets Mandy can make? Answer: sets.

You have a cylindrical pond that has a diameter of 30 feet and has a depth of 5 feet. If you need to fill the pond one-quarter of the way up with water and water costs $3.25 per cubic foot, how much will you need to spend to fill the pond? $5,643.70 $11,480.63 $382.67 $2,870.16

Select the values that make the inequality 5k < 45 true. Then write an equivalent inequality, in terms of k. (Numbers written in order from least to greatest going across.)

Select the values that make the inequality y/5≤-8 true. Then write an equivalent inequality, in terms of y. (Numbers written in order from least to greatest going across.) Equivalent Inequality: y

Off-Campus Housing. A university's housing and residence office wants to know how much students pay per month for rent in off-campus housing. The university does not have enough on-campus housing for students, and this information will be used in a brochure about student housing. They obtain a list of the 12,304 students who live in off-campus housing and have not yet graduated and mail a questionnaire to 200 students selected at random. Only 78 questionairres are returned. (a) What is the population in this study? Be careful: about what group do they want information? (b) What is the sample? Be careful: from what group do they actually obtain information? The important message in this problem is that the sample can redefine the population about which information is obtained.

The line segment PQ with endpoints P (4, 3) and Q (8, 3) is rotated 180° clockwise. Find the endpoints of the new line segment. P (4, 3) and Q (8,3) P (4, -3) and Q (8, -3) P'(-4, 3) and Q' (-8, 3) P' (-4,-3) and Q' (-8, -3)

Use the rule of order of operations to simplify as much as possible: - ( − 1)² + 4( − 1) =

Kathryn draws three pairs of intersecting lines. In each figure, she measures a pair of vertical angles. What is a reasonable conjecture for Kathryn to make by recognizing a pattern and using inductive reasoning? When a pair of lines intersect, all of the angles formed are right angles. When a pair of lines intersect, the vertical angles are acute. When a pair of lines intersect, the vertical angles are congruent. When a pair of lines intersect, all of the angles formed are congruent.

A solid sphere has a cylindrical portion cut out of the inside. The center of the cylinder is the center of the sphere. If the sphere has a radius of 10 and the cylinder has a radius of 4, what is the volume of the figure if the cylinders height is the diameter of the sphere? Use 3.14 to approximate pi. 2763.2 cubic units 3433.067 cubic units 2386.4 cubic units 3809.867 cubic units

A square is 8 inches on each side. A small square, x inches on each side, is cut out from each corner of the original square. Represent the area of the remaining portion of the square in the form of a polynomial function A(x).

Point U is on line segment TV. Given UV = 13 and TU = 4, determine the length TV.

A coffee distributor needs to mix a(n) Mexican Shade Grown coffee blend that normally sells for $9.90 per pound with a Ethiopian coffee blend that normally sells for $11.30 per pound to create 70 pounds of a coffee that can sell for $10.16 per pound. How many pounds of each kind of coffee should they mix?

Tony buys a new palladium core online. The core costs $139 but the site is offering a 15% discount. Tony purchases the palladium core for the reduced price but must also pay 6.3% tax and $5.75 for shipping. What is the total cost for the palladium core?

A 2005 Gallup Poll found that 7% of teenagers (ages 13 to 17) suffer from arachnophobia and are extremely afraid of spiders. At a summer camp there are 10 teenagers sleeping in a cabin. Assume that these teenagers are independent of each other (i.e., not relatives). This problem is due by Friday 1 October at 11:55PM Submit via Moodle.

Shared Pain and Bonding. Although painful experiences are involved in social rituals in many parts of the world, little is known about the social effects of pain. Will sharing painful experiences in a small group lead to greater bonding of group members than sharing a similar nonpainful experience? Fifty-four university students in South Wales were divided at random into a pain group containing 27 students, with the remaining students in the no-pain group. Pain was induced by two tasks. In the first task, students submerged their hands in freezing water for as long as possible moving metal balls at the bottom of the vessel into a submerged container; in the second task, students performed a standing wall squat with back straight and knees at 90 degrees for as long as possible. The no-pain group completed the first task using room temperature water for 90 seconds and the second task by balancing on one foot for 60 seconds, changing feet if necessary. In both the pain and no-pain settings, the students completed the tasks in small groups, which typically consisted of four students and contained similar levels of group interaction. Afterward, each student completed a questionnaire to create a bonding score based on answers to questions such as "I feel the participants in this study have a lot in common," or "I feel I can trust the other participants."¹1 (a) Outline the design of the experiment, following the model of Figure 9.4. (b) Explain how you will randomly assign the subjects at random to the two groups, and then carry out this randomization using software, the Simple Random Sample applet, or Table B beginning at line 125. (c) Why do you think the experimenter had students in the no-pain group complete similar pain-free tasks in small groups? Do you think this is important for the type of conclusion that can be reached? Explain.

The sample described in the previous exercise produced a list of 5024 licensed drivers. The investigators then chose an SRS of 880 of these drivers to answer questions about their driving habits. (a) How would you assign labels to the 5024 drivers? Choose the first five drivers in the sample. If you use Table B, start at line 119. (b) One question asked was, "Recalling the last ten traffic lights you drove through, how many of them were red when you entered the intersections?" Of the 880 respondents, 171 admitted that at least one light had been red. A practical problem with this survey is that people may not give truthful answers. What is the likely direction of the bias: do you think more or fewer than 171 of the 880 respondents really ran a red light? Why?

The coordinates of the rectangle are (2, 2), (2, -2), (-2, -2), and (-2, 2). If the rectangle is compressed by 1, then which of the following is true? Coordinates of the rectangle gets changed. Coordinates of the rectangle gets inversed. Coordinates of the rectangle remains same. Coordinates of the rectangle changes in sign.

When you manipulate an inconsistent linear equation eventually you will end up with a false statement like 5 =9 or 7=2 or 0=-5. That is your signal that the equation has no solutions. Exercise #4: Manipulate each side of the following equations to determine if it has one solution, infinite solutions (is an identity), or no solutions (is inconsistent). You do not need to solve. (b) 2 (3m+1)+3(m+5)=4m+3(m+1) (a) 3(x+8) −x+6=2(x+¹1) 2xt 22 (c) 5(y-1)-(y-2)=2(2y+3)-9 (d) 4(n+1)+2(n+3)=11n-(5n-2)

Simplify the following expressions completely. Assume the variable represent positive values. A) √(64p^26) B) √(100m^40)

Find the average value of the function over the given interval. Find all values of x in the interval for which the function equals its average value. (Enter your answers as a comma-separated list.)

Problem Number Nine: You roll 2 die and get $400 if you toll a sum = 9. You get $200 if you roll a sum = 7. You get $600 if you roll a sum of 4. You have to pay $50 to roll the dice. Find the expected value in this situation.

Identify the appropriate property that describes the following statement: If m A=37° and m D=m A+ 10°, then m D= 47° Choose the correct answer below. Transitive Property Substitution Property Distributive Property Symmetric Property

Answer the questions about the following function. f(x) = 3x²-x-2 (a) Is the point (-1,2) on the graph of f? (b) If x = 2, what is f(x)? What point is on the graph of f? (c) If f(x) = -2, what is x? What point(s) are on the graph of f? (d) What is the domain of f? (e) List the x-intercept(s), if any, of the graph of f. (f) List the y-intercept, if there is one, of the graph of f. (a) Choose the correct answer below. A. Yes, because substituting x = 2 into the given equation results in -1 B. No, because substituting x=2 into the given equation does not result in C. No, because substituting x= -1 into the given equation does not result D. Yes, because substituting x= -1 into the given equation results in 2.

Slumbertec is a sleep medication designed for patients with severe insomnia. The follow function is a pretty good measure of the dosage a patient needs depending on their weight: d=2w-60 where w represents the patient's weight in pounds, and d represents the dosage required in milligrams (mg). a. Under the function equation above, label the meaning of the variables d and w. b. Evaluate 2w-60 when w=140. c. When w=175, the value of 2w-60 is 290. Explain what this means in the context of this function. In other words, what does this tell you about the patient and this medicine? d. Evaluate 2w-60 when w=25. Explain what this means in the context of this function. Your patient was prescribed 260 mg of Slumbertec by another doctor. What would you guess was the patient's weight at the time when the prescription was written?

A farmer has 1200 acres of land on which he grows corn, wheat, and soybeans. It costs $45 per acre to grow corn, $60 per acre to grow wheat, and $50 per acre to grow soybeans. Because of market demand, the farmer will grow twice as many acres of wheat as of com. He has allocated $63,750 for the cost of growing his crops. How many acres of each crop should he plant? Be sure to include units.

How many widgets should Jesaki Inc. produce and sell in order to maximize revenue? widgets. Round to the nearest widget.

A farmhouse shelters 10 animals. Some are pigs and some are ducks. Altogether there are 36 legs. How many of each animal are there? 10 pigs and 0 ducks 2 pigs and 8 ducks 3 pigs and 7 ducks 8 pigs and 2 ducks

A movie theater sells two different sizes of candy. Small boxes cost $4.20 and large boxes cost $9.00. a. Complete the table to the right. b. If the theater sold 45 boxes of candy in one hour, write an equation relating the number of boxes sold. c. If the theater earned a total of $309 in that one hour, write an equation relating the total amount earned. Categories Value Number Amount Small box 4.20 x .... Large box 9.00 y ...

A boat travels between two cities that are 7 miles apart. When going downstream, with the current, the trip takes 1/2 hour(s). Returning upstream, against the current, the boat covers the same 7/6 hour(s).

The perimeter of the rectangle below is 170 units. Find the value of y.

Graham is hiking at an altitude of 14,040 feet and is descending 50 feet each minute. Max is hiking at an altitude of 12,500 feet and is ascending 20 feet each minute. How many minutes will it take Graham and Max to meet at the same altitude? a. Equation: b. Solution: c. At what altitude will Graham and Max meet? text

A rocket is fired upward with a velocity (v) of 580 feet per second. Find how many seconds pass before the rocket reaches the ground (S=0) again. Use the quadratic equation S= - 16t² +580t.

This is page 6 of 6 in section II. Use the "Jump to: Page" links to navigate among the pages. Do not use your browser's " back" button or you will lose any answers entered on the current page. 51. An equation for the line with slope that passes through the point (-6, 3) is A. 2x + 4y = 12 B. 2x - 4y = -12 C. 4x + 2y = -18 D. 2x + 4y = 0 E. 2x - 4y = -24

Find the x-intercepts (horizontal intercepts) of the function: f(x) = 4|x + 4| − 2 The intercepts are at x = Separate values with commas.

The solution of the inequality (x +50)/4 < 2 is A. x < -58 B. x < 42 C. x < -42 D. x < -46 E. x < 58

If x+a/b = 2.5 and a = 28, b = 4 then x = A. 38 B.-18 C.-27.375 D. -28.625 E. -38

In planning her retirement, Liza deposits some money at 4.5% interest, with twice as much deposited at 5%. Find the amount deposited at each rate if the total annual interest income is $2175.

An equation for the line with slope that passes through the point (-6, 3) is A. 2x + 4y = 12 B. 2x - 4y = -12 C. 4x + 2y = -18 D. 2x + 4y = 0 E. 2x - 4y = -24

The volume V, in liters, of air in the lungs during a four-second respiratory cycle is approximated by the model V = 0.1729t + 0.1522t2 0.0374t3, where t is the time in seconds. Approximate the average volume of air in the lungs during one cycle. (Round your answer to four decimal places.)

A woman uses a loan program for small businesses to obtain a loan to help expand her vending machine business. The woman borrows $22,000 for 4 years with a simple interest rate of 1.3%. Determine the amount of money the woman must repay after 4 years.

Lollipops are selling for $5.00 a pound. Tootsie Rolls are selling for $2.50 a pound. Wendy wants to spend exactly $80 to get a total of 30 pounds of candy. How many pounds of each should she get?

Jason is planning to build a gazebo in the shape of a regular octagon. He is laying out his blueprints on a coordinate plane where each grid mark represents 1 foot. Two consecutive vertices are located at (1,4) and (4,8). He wants to enclose the gazebo with fencing. What is the perimeter of the gazebo?

Jenny applied for an $8,000 home improvement loan, which she will start paying back after the interest has accumulated. One bank offered her a simple annual interest rate of 7% for fi years. She decided to consider other options. Which of the following change will decrease the interest she pays the most? (8.1A, 8.1B, 8.1C, 8.1G) A Simple interest, annual rate of 7.2%, term of 5 years B Simple interest, annual rate of 6.75%, term of 5 years C Simple interest, annual rate of 7%, term of 4.75 years D Compound interest, annual rate 7%, term of 5 years

Marissa Chambers wants to open a savings account, but the bank requires a $250.00 initial deposit. She breaks her piggy bank, which contains 4 ten-dollar bills, 7five-dollar bills, 24 one-dollar bills, 11 quarters, 14 dimes, 29 nickels, and 72 pennies. She also has a check from her uncle for $100. If she deposits all her money, how much more will she need to meet the bank's required amount? The required amount is $