Math Questions

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?

At Andrew Jackson High School, students are only allowed to enroll in AP U.S. History if they have already taken AP World History or AP European History. Out of 825 incoming seniors, 165 took AP World History, 66 took AP European History, and out of those students 33 took both. Given this information, determine the probability a randomly selected incoming senior is allowed to enroll in AP U.S. History.

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 a company has fixed costs of $31,200 and variable costs of 1/3x2+444x dollars, where x is the total number of units produced. Suppose further that the selling price of its product is 1768- 2/3x dollars per unit. (a) Find the break-even points. (Enter your answers as a comma-separated list.) x=24,1300 (b) Find the maximum revenue. (Round your answer to the nearest cent.) (c) Form the profit function P(x) from the cost and revenue functions. P(x) = -x² +1324x-31200 Find maximum profit. $ 407044 (d) What price will maximize the profit? (Round your answer to the nearest cent.)

Round answer to 4 decimal places. Mr. H is playing the batting game at the local fair. He will have six balls pitched to him. The number of balls he can hit determines the prize he wins. He hits the ball 32% of the time (he misses 68% of the time). a. What is the probability he hits exactly two of the pitched balls? b. What is the probability he hits at most 3 of the pitched balls?

For the month of August in a certain city, 57% of the days are cloudy. Also in the month of August in the same city, 19% of the days are cloudy and snowy. What is the probability that a randomly selected day in August will be snowy if it is cloudy? The probability is approximately. (Round to three decimal places as needed.)

Class Survey A student is running a survey for a class project, which asks fellow high school students "What is your favorite sport?" Which of the following would yield the most accurate/most unbiased sample? He hands out a survey to every 3rd classmate to enter his weight training class He hands out the survey to his friends at lunch He passes out surveys as students enter the next soccer game He prints surveys and gives 2 to each teacher to randomly give to a male and female student in their homeroom.

Rewrite In 5 + ln 7 as a In single logarithm.

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

From the top of a lighthouse 210 feet high, the angle of depression of a boat is 27°. Find the horizontal distance from the boat to the foot of the lighthouse. The lighthouse was built at sea level.

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

Consider the acceleration function of an object on a projectile motion is a (t) = -32. If v (0) = 28 ft/sec and s (0) = 120, what is the maximum height of the object in feet?

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).

A yogurt shop offers 25 flavors of frozen yogurt. Evie randomly chooses 3 different flavors for her banana split. What is the probability she chooses chocolate, vanilla, and strawberry? (Independent and Dependent Events)

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.

What is the vertex form of the equation? y=-x² + 12x-4

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?

In 2003, David received $10,000 from his grandmother. His parents invested all of the money, and by 2015, the amount will have grown to $16,958.81. Use the exponential function y = 10000 1.045* where y is the amount in the account and x is the number of years since 2003. Assume that the amount of money continues to grow at the same rate. What would be the balance in the account in 2025?

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?

An insurance company crashed four cars of the same model at 5 miles per hour. The costs of repair for each of the four crashes were $429, $437, $476, and $209. Compute the mean, median, and mode cost of repair. Compute the mean cost of repair. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The mean cost of repair is (Round to the nearest cent as needed.) B. The mean does not exist. Compute the median cost of repair. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The median cost of repair is (Round to the nearest cent as needed.) B. The median does not exist. Compute the mode cost of repair. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The mode cost of repair is (Round to the nearest cent as needed.) B. The mode does not exist.

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?

Which of the following is the contrapositive and negation of the following conditional statement? "If I don't have a mask then I cannot go into the store." Contrapositive: If I can go into the store then I have a mask. Negation: I don't have a mask and I can go into the store. Contrapositive: If I can go into the store then I don't have a mask. Negation: I have a mask and I can go into the store. Contrapositive: If I have a mask then I can go into the store. Negation: I have a mask and I cannot go into the store. Contrapositive: If I cannot go into the store, then I don't have a mask Negation: If I don't have a mask, then I can go into the store.

Given tan A = 12/5 and that angle A is in Quadrant I, find the exact value of sin A in simplest radical form using a rational denominator.

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.

A street light is at the top of a 20 ft pole. A 6 ft tall girl walks along a straight path away from the pole with a speed of 6 ft/sec. At what rate is the tip of her shadow moving away from the light (ie. away from the top of the pole) when the girl is 36 ft away from the pole? Answer. How fast is her shadow lengthening?

Select the value needed in the box in order for the expression to be a perfect square trinomial. x² +7x+ 3.5 7 12.25 14.5

Jamie painted a small rectangular drawing at Art Club. He then made a scale drawing of his original painting to create a similar rectangular poster. He used a scale factor of 5/3 to create the rectangular poster. If the perimeter of the smaller rectangle is 45 centimeters, what is the perimeter of the larger rectangle?

Use the triangle shown on the right and the given information to solve the triangle. a=9, A=25°; find b, c, and B b= (Round to two decimal places as needed.) c= (Round to two decimal places as needed.)

Toby owes his Great Aunt $32,000. Toby can pay his aunt $4,000 a year. How long will it take him to pay back his aunt? Function: p(x) = Slope/Meaning in context: m = y-intercept/Meaning in context: b = After five years, how much money does Tobey owe Great Aunt Mildred? How long will it take for Tobey to pay off the loan?

In ΔCDE, the measure of ∠E=90°, EC = 45 feet, and CD = 75 feet. Find the measure of ∠C to the nearest degree.

The half-life of Palladium-100 is 4 days. After 12 days a sample of Palladium-100 has been reduced to a mass of 5 mg. What was the initial mass (in mg) of the sample? What is the mass 6 weeks after the start?