Basic Math Questions and Answers

A boat is moving away from shore in such a way that at time t hours its distance from shore, in kilometers, is given by the linear function d(t)=4.5t +6.3. What is the rate of change of the distance from shore? A. 4.5 km/hr B. 6.3 km/hr C. 4.5 m/s D. 6.3 m/s

The arrows below show that the coordinates on the left are mapped to the coordinates on the right. Fill in the blanks to give the coordinates after the translation. original coordinates final coordinates (b) Choose the general rule below that describes the translation mapping AABC to AA'B'C'.

An object thrown directly upward is at a height of s=-161²+1281+256 feet after t seconds (a) What is its initial velocity? (b) When does it reach its maximum height? (c) What is its maximum height? (d) When does it hit the ground? (e) with what speed does it hit the ground?

The length of a rectangle is 3 yd less than twice the width, and the area of the rectangle is 44 yd². Find the dimensions of the rectangle.

A town is using a storage container in the shape of an inverted cone to store salt for treating icy roads. If the town needs to store 10,000 cubic feet of salt, and the cone has a height equal to its diameter, what is the height of the storage container? 42.4 feet 67.4 feet 29.4 feet 33.7 feet

The Howard family and the Watson family each used their sprinklers last summer. The Howard family's sprinkler was used for 30 hours. The Watson family's sprinkler was used for 35 hours. There was a combined total output of 1650 L of water. What was the water output rate for each sprinkler if the sum of the two rates was 50 L per hour? Note that the ALEKS graphing calculator can be used to make computations easier.

Plant Trellis You are building the wood trellis shown in the figure so that you can grow a vine up the side of your home. Write an expression for the total number of feet of wood needed to build the trellis. Hint: Write separate expressions for the number of feet of vertical pieces needed and the number of feet of horizontal pieces needed. Then find the total number of feet of wood needed if the trellis is 8 feet tall and 2 feet wide. xft- y ft

Let f(x) = 1/9 + 6x and g(x) = 7x - 2/9 Find all values of x for which g(x) ≥ f(x).

Find the distance d (P1, P2) between the points P₁ and P2 P₁=(1,-2), P₂=(2,6) (P₁, P₂) = (Simplify your answer. Type an exact answer, using radicals as needed.)

Deshaun is driving to Boston. Let y represent his distance from Boston (in miles). Let x represent the time he has been driving (in hours). Suppose that x and y are related by the equation -55x+275=y. Answer the questions below. Note that a change can be an increase or a decrease. For an increase, use a positive number. For a decrease, use a negative number. What was Deshaun's distance from Boston when he began his drive? miles What is the change in Deshaun's distance from Boston for each hour he drives? miles

Painting Three weeks ago, an art supply store started selling a paint kit for 75% of the original price. Now the kit is 15% off of the sale price. The expression 0.75x -0.15(0.75x) represents the current price of the paint kit where x is the kit's original price (in dollars). Find the current price of the kit if it originally cost $48.

Add as indicated. 5x + 26 / 2x + 7 + 3x + 2 / 2x + 7 Select the correct choice below and fill in the answer box(es) to complete your choice. (Simplify your answer. Use integers or fractions for any numbers in the expression. Use a comma to separate answers as needed.)

Motorcycle A can reach a top speed of 160 miles per hour. Motorcycle B can reach a top speed of 210 feet per second. Which motorcycle has a greater top speed? Motorcycle A Motorcycle B

Use the appropriate reciprocal identity to find the approximate value of sin 8 for the given value of csc 8. Use a calculator. csc 8=2.48003196

True or false: 2 = -5 is a solution to the inequality -2 |z-3|< -20. True False

For what questions is a HISTOGRAM most useful? What about a TABLE? A HISTOGRAM is most useful when I'm being asked . . . A TABLE is most useful when I'm being asked . . .

f(v) is the total revenue from the sale of v sofas. Which of the following does the slope f '(v) represent? Answer 2 Points Total cost of producing v sofas. Increase in total revenue if sales are increased to v + 1 units from v units. Rate of change in additional revenue when v sofas have been sold. Average rate of change in the revenue from the sale of v sofas.

Hong is driving to Miami. Suppose that the distance to his destination (in miles) is a linear function of his total driving time (in minutes). Hong has 56 miles to his destination after 31 minutes of driving, and he has 44.8 miles to his destination after 47 minutes of driving. How many miles will he have to his destination. after 57 minutes of driving?

The area of a rectangle is 77 m², and the length of the rectangle is 10 m less than three times the width. Find the dimensions of the rectangle.

Members of the Wide Waters Club pay $105 per summer season, plus $9.50 each time they rent a boat. Nonmembers must pay $14.75 each time they rent a boat. How many times would a member and a nonmember have to rent a boat in order to pay the same amount?

Which of the following points lie on the line whose equation is y-4=3/5(x + 2)? (1,5) (-7, -1) (8, 11) (3.7) (-1,0)

Drag the linear equation that corresponds to each description. A line parallel to y = x +2. A line perpendicular to x = 3. A line perpendicular to y = 3x - 6.

Directions: Using the digits 1 to 9 at most one time each, fill in the boxes to make a whole number product. How many solutions can you find?

Alan is loading a pallet with boxes that each weighs 65 pounds. The pallet can safely support no more than 2015 pounds. How many boxes can he safely load onto the pallet?

f(x) is the velocity in feet per hour a car is traveling at x hours. Which of the following does the slope f '(x) represent? Distance in feet the car has traveled in x hours. Average rate of change in the velocity of the car in feet per hour atx hours. Direction the car is traveling at x hours. Rate of change of the velocity of the car at x hours.

Julian is taking a multiple choice test with a total of 20 points available. Each question is worth exactly 2 points. What would be Julian's test score (out of 20) if he got 2 questions wrong? What would be his score if he got a questions wrong?

Write a linear expression with all rational coefficients such that simplifying the expression requires using the associative property of addition, the commutative property of addition, the Distributive property, the additive inverse property, and the additive identity property. Show your work and explain how your expression simplifies.

Select the correct definition of an observational study from the choices below. A study where subjects are selected based on convenience to the researcher. A study that rejects or fails to reject a statistical hypothesis about a population parameter. A study where neither the subjects nor the researchers know what treatments are being administered to which subjects. A study where researchers manipulate variables and impose treatments on the subjects in the study, then measure and record the responses of the subjects. A study where researchers measure and record data about the subjects in the study, but do not apply any treatments to the subjects or manipulate any variables.

Barbara's new lunch box is only 5 centimeters in height, so it fits in her backpack along with all her books. The lunch box has 3 sections for different types of food. The length and width of the lunch box are 22 centimeters and 14 centimeters. What is the volume of Barbara's new lunch box? cubic centimeters

Jordyn bought 7 shirts and spent $131. Fancy shirts cost $28 and plain shirts cost $15. Let x represent the number of fancy shirts bought and y represent the number of plain shirts bought. Determine which of the following system of equations model this scenario. x+y=7 28x + 15y = 131 x+y = 131 28x + 15y = 7 x+y=7 15x+28y = 131 7x + 7y= 131 28x + 15y = 131

Laura is now trying to come up with a number where three less than 8 times the number is equal to half of 16 times the number after it was increased by 1. She can't seem to find a number that works. Explain why.

Which of these expresses the rate at which she is earning credits? Select the correct answer below: 14 semesters per credit 15 credits per semester 3 credits per semester 14 credits per semester 7 semesters per credit 56 credits per semester

Make a sine wave with the given amplitude, period or frequency, and phase shift. Use the form y = A sin (B(t – C)). Amplitude 1, frequency 0.5, and phase shift 1 (Express numbers in exact form. Use symbolic notation and fractions where needed.)

Complete the statement. If a transversal intersects two parallel lines, then same-side interior angles are supplementary corresponding angles are complementary none alternate exterior angles are supplementary

Find the x & y intercepts. Write the coordinate for each. 2x - 3y = 12 x-intercept: y-intercept

Milan is going to rent a truck for one day. There are two companies he can choose from, and they have the following prices. Company A charges $114 and allows unlimited mileage. Company B has an initial fee of $75 and charges an additional $0.60 for every mile driven. For what mileages will Company A charge less than Company B? Use m for the number of miles driven, and solve your inequality for m.

It has been determined that the number of fish f(t) that can be caught in t minutes in a certain pond using a certain bait is f(t)=0.22t+1, for t> 10. Find and interpret f(31). Round your answer to the nearest whole number. A. f(31)= 17 which means that approximately 17 fish can be caught in this pond with this bait in 31 minutes. B. f(31)=8 which means that approximately 8 fish can be caught in this pond with this bait in 31 minutes. C. f(31)=17 which means that approximately 31 fish can be caught in this pond with this bait in 17 minutes. D. 1(31)=8 which means that approximately 31 fish can be caught in this pond with this bait in 8 minutes.

A projectile is launched from ground level with an initial velocity of vo feet per second. Neglecting air resistance, its height in feet t seconds after launch is given by s = -16t²+vot. Find the time(s) that the projectile will (a) reach a height of 192 ft and (b) return to the ground when vo= 128 feet per second. (a) Find the time(s) that the projectile will reach a height of 192 ft when vo = 128 feet per second. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. seconds (Use a comma to separate answers as needed.) B. The projectile does not reach 192 feet. (b) The projectile returns to the ground after second(s).

Determine a viewing window that will provide a complete graph of the function. y = 2x4 + 2x³ − 4x² − 3x − 6 A. [-2.2] by [-10,-5] B. [-10,10] by [- 8,8] C. [-3,3] by [-10,5] D. [-5,5] by [-5.5]

Twiigs is an online polling website that allows users to easily create polls and to vote on polls created by other users. A March 2010 poll asked, "Has concern about autism influenced your decision about whether to vaccinate your child?" Of the 182 votes cast, 80% selected "No, I'm not worried about it." Which type of sample was used in this poll? simple random sample stratified random sample multistage random sample voluntary response sample

Complete the sentence below. The polynomial 2x5 -3x4 + 12x3 - 2 is of degree The leading coefficient is

Researchers enrolled a group of 10,892 middle-aged adults and studied them over a period of nine years. They found that smokers who quit had a higher risk for diabetes within three years of quitting than either nonsmokers or continuing smokers. (a) What type of observational study is this? This is a sample survey study. This is a cohort observational study. Actually this is not an observational study, this is a controlled experiment. This is a case-control study. (b) Does this show that stopping smoking causes the short-term risk for diabetes to increase? Should a doctor cite this study to tell a middle-aged adult patient who smokes that stopping smoking can cause diabetes and advise him or her to continue smoking?

We have found f(a+h) = 9a2 + 18ah + 9h² - 11a - 11h + 2 and f(a) = 9a2 - 11a + 2. We utilize these to f(a+h)-f(a), giving the following result. write h f(a+h)-f(a) h = (9a2 + 18ah + 9h² - 11a - 11h + 2) - h

Experiment 1: A study is done to determine which of two fuel mixtures allows a rocket to travel farther over a period of time. Rocket A, which requires additional equipment to keep it stable, is used to test one fuel mixture, and rocket B is used to test the other. Both rockets are identical aside from their mass. The results indicate that rocket B traveled farther than rocket A over the same period of time. Experiment 2: A double-blind experiment is performed to test whether a new drug is effective in lowering blood pressure. A random sample of subjects with high blood pressure is assigned to two groups. One group receives the new drug and the other group does not. Neither group is permitted to take any other medications during the experiment or to change their lifestyles in any way. The results of the experiment show that the drug is effective in lowering blood pressure. Identify the experiment in which confounding occurs and the reason for its occurrence. Experiment 1 has a confounding variable related to the fuel mixtures. Varying the fuel mixture could skew the results of the study and should be kept constant. Neither experiment has a confounding variable. Experiment 2 has a confounding variable related to the type of experiment. A double-blind experiment may increase the risk of the placebo effect and possibly skew the results.

The length, in inches, of a box is 3 inches less than twice its width, in inches. Which of the following gives the length, / inches, in terms of the width, w inches, of the box? F. I = 1/2w + 3 G. I = W+3 H. I= w-3 I. I = 2w + 3 J. I=2w-3

Select the correct answer from each drop-down menu. In a circle with a radius of 7 feet, the radian measure of the central angle subtended by an arc with a length of 4 feet is area of the sector formed by the arc is Assume π = 3.14, and round your answers to the nearest hundredth. square feet.

The mathematical model C(x) = 300x+20,000 represents the cost in dollars for a company to manufacture x items a month. Based on this, how much does it cost to produce 800 items? A. $20,300 B. $16,000,000 C. $260,000 D. $240,000

Aria is ordering a taxi from an online taxi service. The taxi charges $4 just for the pickup and then an additional $1.25 per mile driven. How much would a taxi ride cost if Aria is riding for 2 miles? How much would a taxi ride cost that is m miles long?

State the number of possible real zeros and turning points of f(x) = x² - 6x + 8x5. Then determine all of the real zeros by factoring. 7 real zeros and 6 turning points; 0, 2, and 4 7 real zeros and 6 turning points; 0, –2, and –4 6 real zeros and 5 turning points; 0, 2, and 4 6 real zeros and 5 turning points; 0, -2, and —4

A bike company sells 30,000 bikes in their first year of business. Their business model predicts that sales will increase at 1% each year. How many years after they began business will it take for the company to have sold a total of 200, 000 bikes, (rounding-up to a whole number)?