Basic Math Questions and Answers

Divide and simplify: x + 4/3x + 12/ x + 5/8x + 40 Enter the numerator and denominator separately in the boxes below. If the denominator is 1, enter the number 1. Do not leave either box blank. Answer:

(d) A wind turbine has a capacity of 3 MW. Assuming the turbine operates at 50 percent of its capacity all day and every day for a week, calculate how many kWh of electricity the wind turbine will produce by the end of the week. Show your work (e) if a typical house uses 10,900 kWh per year, calculate how many bouses could have their full energy needs provided for one year by the turbine above if it continued to operate as described for one year. Show your work

You have 268 feet of fencing to enclose a rectangular region. What is the maximum area of the region? A. 17,956 square feet B. 4,485 square feet C. 4,489 square feet D. 71,824 square feet

Coast Guard Station Able is located L = 120 miles due south of Station Baker. A ship at sea sends an SOS call that is received by each station. The call to Station Able indicates that the ship is located N55°E; the call to Station Baker indicates that the ship is located S60°E. Use this information to answer the questions below. (a) How far is each station from the ship?

A contractor finds that Crew A takes 9 1/2 hours to construct a retaining wall and Crew B can do the same job in 7 1/2 hours. If Crew A and Crew B work together, how long will it take them to construct the retaining 2 wall? a) Let h = the time to complete the job. Write the equation you would use to solve this problem. b) Now solve your equation. Give your answer first as a reduced fraction, and then a decimal rounded to 3 places. Working together, the two crews will construct the wall in which as a decimal is hours. hours (fraction),

Middle Creek High is selling tickets to a choral performance. On the first day of ticket sales the school sold 12 adult tickets and 3 child tickets for a total of $198. The school took in $172 on the second day by selling 3 adult tickets and 13 child tickets. Find the price of an adult ticket and the price of a child ticket. Make sure to set up the system first, and answer the question using proper units and a sentence. Enter your answer as a=# and c=#. Submit your work. *

A pendulum is swinging next to a wall. The distance from the bob of the swinging pendulum to the wall varies in a periodic way that can be modeled by a trigonometric function. The function has period 0.8 seconds, amplitude 6 cm, and midline H = 15 cm. At time t = 0.5 seconds, the bob is at its midline, moving towards the wall. Find the formula of the trigonometric function that models the distance H from the pendulum's bob to the wall after t seconds. Define the function using radians.

A baby weighs 14 pounds at 5 months and 21 pounds at 10 months. Assume the relationship is linear and that the baby gains the same number of pounds per month. Let x represent the number of months and y represent the weight in pounds. Write an equation in slope-intercept form that models the situation.

A grocery store sells a bag of 7 oranges for $4.48. If Khloe spent $6.40 on did she buy? oranges, how many did she buy?

24. A shelf that is 18 cm wide is held up by a triangular bracket. The bracket makes a 37.5° angle with the bottom of the shelf. What is the height of the bracket? Hint: draw a diagram and think about trigonometry a.13.81 cm b.12.94 cm c.10.96 cm d.14.28 cm

If you invest $23010.00 at an interest rate of 2.90% per year compounded semi-annually, what will the total value of your investment be after 9 years? Hint: use compound interest formula a. $29801.62 b. $29816.29 C. $23853.03 d. $35779.54

The weight of 3-month-old Bullmastiffs follow approximately a normal distribution with a mean of 120 pounds and a variance of 25 pounds. If your 3-month-old Bullmastiff is 130 pounds, how many standard deviations above or below the mean is your pet (i.e., find the Z-score)? 0 1 1.5 2

An amount of $32,000 is borrowed for 11 years at 3.75% interest, compounded annually. If the loan is paid in full at the end of that period, how much must be paid back? Use the calculator provided and round your answer to the nearest dollar.

A certain forest covers an area of 2300 km. Suppose that each year this area decreases by 6.5%. What will the area be after 14 years? Use the calculator provided and round your answer to the nearest square kilometer.

Anthony invested $36,000 in an account paying an interest rate of 5.3% compounded quarterly. Assuming no deposits or withdrawals are made, how long would it take, to the nearest year, for the value of the account to reach $51,800?

The weight of golden hamsters follows a normal distribution with a mean weight of 4.3 ounces and a standard deviation of 0.25. What is the probability that a randomly chosen hamster weighs less than 4.6 ounces? 0.655 0.788 0.885 0.945

What are the coordinates of the point on the directed line segment from (-8, 1) (2, -7) that partitions the segment into a ratio of 3 to 1?

6. Kelly works two jobs. She usually works at a retail store for 7 hours during the day and is paid $12 per hour by the store. In the evening she works at a restaurant as a manager for 5 hours and is paid $20 per hour. How much does she make on average per hour for the day?

A seventh grade English Language Arts teacher wants to order books for all the seventh grade classes. He wants to determine the favorite type of book among the seventh grade students. Which sample would be the most appropriate for this survey? A 7 girls in each of his classes B every fifth student in the seventh grade C 1 out of 7 students in his middle school D all of the boys in one of his seventh grade classes

8. Sketch a graph on the slope field through (-3,-1) and a point of your choice. Clearly indicate which point you chose.

Select all the correct answers. If the measure of angle is θ 7π/4, which statements are true? sin(θ)= - √2/2 cos(θ)= - √2/2 tan(θ)= -1 The measure of the reference angle is 60°. The measure of the reference angle is 30°. The measure of the reference angle is 45°

Find the weighted average. Round all values to one decimal place. 5. A new cars salesperson sold an average of $28,000 per day for the first 5 days she worked. The next 3 days she worked; she sold an average of $42,000. How much did she sell on average per day over the entire 8 days?

Problem 1: Consumers may be interested in whether the cost of a particular calculator varies from store to store. Based on surveying 43 stores, which yielded a sample mean of $84 and a sample standard deviation of $12, test the claim that the standard deviation is greater than $15.

Taylor and Andrea are 60 miles apart, traveling towards each other. If Andrea travels 13 mph and Taylor travels 7 mph how long until they meet? A) Fill in the following table, where t = travel time in hours until Taylor and Andrea meet. Notice that the time will be t for both people, since they start and stop at the same times. B) Using the basic formula rate x time = distance, write an equation based on the information summarized in the table. C) Solve your equation to determine the amount of time Taylor and Andrea will travel until they meet:

12 people want to buy a new iPad. The store only has 3 left. So the store manager writes the names of the people who want an iPad on smal pieces of paper and mixes them up in a hat. He/she then draws three names out to determine who the lucky 3 people will be who can buy an iPad. No two people have the same name. How many possible outcomes are there?

For a science experiment, students need to find 25% of 60 grams. Jada says, "I can find this by calculating 1/4 of 60." Andre says, "25% of 60 means 25/100 * 60." Lin says both of their methods work. Do you agree with Lin? a Yes, because 25% is equal to 1/4 and 25/100 b No, because 25% is not equal to 1/4 and 25/100

"U2" has a concert that starts in 17 minutes and they must all cross a bridge to get there. All four men begin on the same side of the bridge. You must help them across to the other side. It is night. There is one flashlight. A maximum of two people can cross at one time. Any party who crosses, either 1or 2 people, must have the flashlight with them. The flashlight must be walked back and forth; it cannot be thrown. Each band member walks at a different speed. A pair must walk together at the rate of the slower man's pace: Bono: 1 minute to cross Edge: 2 minutes to cross Adam: 5 minutes to cross Larry: 10 minutes to cross For example: if Bono and Larry walk across first, 10 minutes have elapsed when they get to the other side of the bridge. If Larry then returns with the flashlight, a total of 20 minutes have passed and you have failed the mission.

A sailboat captain has set her course due west at a speed of 6 meters per second. The wind is blowing due north at a rate of 2 meters per second. Draw a vector diagram of this situation on a coordinate grid. Consider the (captain's course) and (the wind) as two forces acting on a point (the sailboat)

The exponential model A=402.6 e0.026t describes the population, A, of a country in millions, t years after 2003. Use the model to determine when the population of the country will be 695 million.

Write inequalities to represent the situations below. To be eligible for financial aid, a student must earn no more than $20,000 per year. Use s to represent the yearly earnings (in dollars) of a student eligible for financial aid. To ride a roller coaster, a visitor must be taller than 60 inches. Use h to represent the height (in inches) of a visitor able to ride.

The perimeter of a rectangular wooden deck is 90 feet. The deck's length, I, is 5 feet less than 4 times its width, w. Which system of linear equations can be used to determine the dimensions, in feet, of the wooden deck?

For a long-distance person-to-person telephone call, a telephone company charges $0.29 for the first minute. $0.19 for each additional minute, and a $1.12 service charge. If the cost of a call is $1.79, how long did the person talk?

Suppose you deposit $1000 at 3% interest compounded continuously. Find the average value of your account during the first 4 years.

Savannah and Ariana both leave the college at the same time, but in opposite directions. If Ariana travels 6 mph faster than Savannah and after 7 hours they are 182 miles apart, how fast is each traveling? Savannah is traveling Ariana is traveling

25. A model of a building was made at a scale of 1:16. If the model has dimensions of 2.6 m by 3.8 m by 1.8 m, what are the dimensions of the 'real life' building? a. 41.6 m by 60.8 m by 28.8 m b. 45.8 m by 73 m by 31.7 m c. 49.9 m by 85.1 m by 21.6 m d. 37.4 m by 48.6 m by 25.9 m

You buy 12 packages of discounted socks for a total cost of $85.50, which includes a 5% discount. Before the discount, how much did a single package of socks cost? a.) $7.50 b.) $4.75 c.) $10.68 d.) $6.78

The perimeter of an octagon is 24 inches. A larger octagon is similar to the first with a scale factor of 2/3. What would the perimeter be of this larger octagon? 72 inches 16 inches 48 inches 36 inches

A bouncy ball is dropped such that the height of its first bounce is 6.5 feet and each successive bounce is 61% of the previous bounce's height. What would be the height of the 6th bounce of the ball? Round to the nearest tenth (if necessary).

Find the exact value of each of the following under the given conditions below. tan α = -4/3, π/2 < α < π, cos ß= √3/2, 0< ß < π,/2 (a) sin (α +ß) (b) cos (α +ß) (c) sin (α -β ) (d) tan (α - β )

A video game company used a line graph to track the sales of a new video game from its release in March to July. The company then used the graph to predict the number of sales that would occur in September. This is an example of: a. interpolation b. extrapolation c. statistics d. graphical prospecting

An element has a volume of 20.2 cubic centimeters and a mass of 121.2 grams. Find the density (in grams per cubic centimeter). Round to the whole number and include units. Show all work.

As expected, a startup company began by losing money during the first months of operation. The company's profit-loss function, during the first year, follows the graph of the function P (m)=m²-12m/12 where m is months. During which month, 1-12, during the first year does the company lose the most money?

If a cup of coffee has temperature 97°C in a room where the ambient air temperature is 21°C, then, according to Newton's Law of Cooling, the temperature of the coffee after t minutes is T(t) = 21 + 76e^-t/47. What is the average temperature of the coffee during the first 26 minutes? average temp =

Sanchez Corado rented a minivan for 4 days at $38.00 a day plus $0.30 a mile. He purchased collision waiver insurance for $8.50 per day. He drove 420 miles and paid $49.64 for gasoline. What was the total cost of renting the minivan? What was the cost per mile?

Savannah is going to buy a new home in the amount of $175,500.00. She is going to use Wells Fargo and approve her for a loan with 7% APR for 30 years. How much will her monthly payment be? What will she pay over the course of the 30 years? How much will she pay in interest?

Change CMLIV CDLXXXVI CCIX to base ten (Assume that the Roman Numerals in blue has two bars over them and the Roman Numerals in red have one bar over them) 954,486,209 954,496,109 964,486,219 904,476,209

A bag contains yellow marbles and blue marbles, 20 in total. The number of yellow marbles is 1 less than 2 times the number of blue marbles. How many yellow marbles are there? Answer: 12 yellow marbles

Assume that you wish to save $1800 in a sinking fund in 2 years. The account pays 6% compounded quarterly and you will also make payments quarterly. What should be your quarterly payment? How many payments are you making in the 2 years?

An investment account pays 4.2% annual interest compounded continuously. If $2,500 is invested in this account, how long will it take for the money to double? Round your answer to the nearest tenth of a year.

Choose the correct unit for each measurement. Then write your answer. linear units square units cubic units 1a. the area of the surface of a table 1b. the perimeter of a fenced-in field 1c. Explain your answer choices. Include a sketch in your explanation.