Basic Math Questions and Answers

In the lab, Josh has two solutions that contain alcohol and is mixing them with each other. Solution A is 40% alcohol and Solution B is 10% alcohol. He uses 600 milliliters of Solution A. How many milliliters of Solution B does he use, if the resulting mixture is a 20% alcohol solution? Number of milliliters of Solution B:

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. (1) List the y-intercept, if there is one, of the graph of f.

P is on the interior of ∠QMR. R is on the interior of ∠PMT. T is on the interior ∠RMS. m∠QMP = m∠TMS. Ray MR bisects ∠PMT. If m/QMP = 2x, m∠PMR = 3x + 8, and m∠QMS = x² + 13x - 12, find the m∠QMS.

Nicole bought a desktop computer and a laptop computer. Before finance charges, the laptop cost $450, more than the desktop. She paid for the computers using two different financing plans. For the desktop the interest rate was 9% per year, and for the laptop it was 6% per year. The total finance charges for one year were $300. How much did each computer cost before finance charges?

The medians of a triangle have an intersection point in a triangle called the point of concurrency. This point of concurrency is called the Incenter Circumcenter Inscribed Centroid

Graph the polynomial function f(x) = -2(x - 3)²(x² - 16) using parts (a) through (e). (a) Determine the end behavior of the graph of the function. The graph of f behaves like y = for large values of |x|.

A toy manufacturer needs a piece of plastic in the shape of a right triangle with the longer leg 1 cm more than the shorter leg and the hypotenuse 2 cm more than the shorter leg. How long should the sides of the triangle be?

6. What is the equation of a sphere, with center at the origin, that passes through the point (2,3,4)? (x - 2)² + (y - 3)² + (z-4)² = 9 b. (x - 2)² + (y - 3)² + (z - 4)² = 29 c. x² + y² +2²= 9 d. x² + y² + z²= 29

Nick and Adam workout together. Nick weighs 160 pounds and is gaining about 3 pounds per week. Adam weighs 195 pounds and is losing about 2 pounds each week. Write an equation that can be used to find the number of weeks that it will take them to weigh the same amount. a. Equation: b. Solution: c. How much will Nick and Adam weigh?

Suppose a circle has a radius of 21 cm and central angle is 4.5 radians. What is the length of the arc intercepted by the central angle? 1.65 cm 44.1 cm 94.5 cm 22.1 cm

Line segment AB with endpoints A (2, 2) and B (4, 2) is translated 4 units up and 3 units right. Identify the coordinates of the endpoints of the translated line segment. A' (6,-5) and B' (8,-5) A' (5, 6) and B '(7,6) A' (-6, 5) and B' (-8,5) A' (-6, -5) and B' (-8,-5)

Out of 5000 policies for cell phones, a company received 585 claims. The average amount paid on the claims was $80. If the annual cost of the policy was $48, what was a customers expected value of the cell phone insurance policy?

Central park is a rectangle with an area of 840 acres. It is 1/2 a mile wide. One acre is 43,560 square feet. Two people start at the southwest corner at 1:30 pm and start walking round the park in opposite directions. One walks at 9 mph, the other walks at 2 mph. How long until they meet again? It may help to remember that a mile is 5280 feet.

Which is the possible length of the base of a parallelogram If the area is given by 20x^5 23x^4-41x³ +35x^2 + 40x-70 and the height is given by 4x-7 Select the correct answer below: 5x^4+3x³ +5x² + 10 5x^4-3x³-5x² + 10 5x^4+3x³ - 5x² + 10 5x^4 - 4x³ + 10x³ +8x² + 10x - 15 5x^4-4x³-10x³ + 8x² + 10x - 15

A and B are supplementary angles. If m A = (3x – 17)° and m B = (2x - 23)°, then find the measure of B.

State A and state B are among the states with the most remaining drive-in movie screens. State A has 6 more screens than state B, and there are 58 screens total in the two states. How many drive-in movie screens remain in each state?

A commercial fisherman fishes for haddock, sea bass, and red snapper. He is paid $1.25/lb for haddock, $0.75/lb for sea bass, and $2.00/lb for red snapper. Yesterday he caught 500 lb of fish worth $575. The haddock and the red snapper together are worth $320. How many pounds of each fish did he catch?

The volume of a great pyramid is 91,636,272 ft. If the height of the pyramid is 481 feet and the base is a square what is the length and width of the base? 571,536 feet 756 feet 436 feet 481 feet

A boat travels 15 miles upstream in 3 hours. Going downstream, it can travel 45 miles in the same amount of time. Find the speed of the current and the speed of the boat in still water. mph What is the speed of the current? What is the speed of the boat in still water?mph

A new roller coaster at an amusement park requires individuals to be at least 4' 8" (56 inches) tall to ride. It is estimated that the heights of 10-year-old boys are normally distributed with u=54.0 inches and o=4 inches. a. What proportion of 10-year-old boys is tall enough to ride the coaster? b. A smaller coaster has a height requirement of 50 inches to ride. What proportion of 10-year-old boys is tall enough to ride this coaster? c. What proportion of 10-year-old boys is tall enough to ride the coaster in part b but not tall enough to ride the coaster in part a?

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?