Basic Math Questions and Answers

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?

Given rectangular prism A is similar to rectangular prism B and the volume of A is 125 ft³ and the volume of B is 27 ft³. What is the ratio of the surface areas for A: B ? 5:3 3:5 125:27 25:9

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.

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?

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?

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?

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?

Pizarro's Pizzeria charges $12.50 for a large pizza. Each additional topping is $1.65. Function: P(x) = Slope/Meaning in context: m = y-intercept/Meaning in Context: b = What will the charge be for a pizza with 5 toppings? If Pedro paid $24.05 for his pizza, how many toppings did he get?

The count in a bacteria culture was 700 after 20 minutes and 1600 after 30 minutes. Assuming the count grows exponentially, What was the initial size of the culture? Find the doubling period. Find the population after 65 minutes. When will the population reach 10000. K

4) Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks, A yoga studio offers memberships that cost $30 per month for unlimited classes. The studio also accepts walk-ins, charging $10 per class. If someone attends enough classes in a month, the two options cost the same total amount. What is that total amount? How many classes is that? Each option costs $___if a person takes__classes,

To find the distance from the house at A to the house at B, a surveyor measures the angle ACB, which is found to be 70°, and then walks off the distance to each house, 90 feet and 100 feet, respectively. How far apart are the houses?

One of two complementary angles Is 8 degrees less than the other. Which of the following systems of equations represents the word problem? x+y=90 and 90 - x = 8 x+y=90 and y = 8 x x+y=90 and x - y = 8

Given f(x)= 16/ x+6 and g(x)=3√x, find the following expressions. (a) (fog)(4) (b) (gof)(2) (c) (fof)(1) (d) (gog)(0) (a) (fog)(4) =

25. What is the molarity of sodium chloride in solution that is 13.0% by mass sodium chloride and that has a density of 1.10 g/mL? A) 143 B) 2.45 C) 2.56 D) 2.23 E) 1.43 x 10-2 B) 2.45 C) 2.56 E) 1.43 x 10-2 A) 143 D) 2.23

Linus sells widgets at his store. Today he has sold 21 widgets to three customers. What is the cost per widget? $2.00 $1.50 $3.00 $1.00

The explicit formula for a certain geometric sequence is f(n) =525 (20)^n-1. What is the exponential function for the sequence? Write your answer in the form shown. f(n)= a/r (r) ^n

Find the x-intercepts of the polynomial function. State whether the graph crosses the x-axis, or touches the x-axis and turns around, at each intercept. f(x) = 3x² - x³ A. 0, touches the x-axis and turns around; 3, crosses the x-axis B. 0, touches the x-axis and turns around; 3, touches the x-axis and turns around C. 0, touches the x-axis and turns around; 3, crosses the x-axis; - 3, crosses the x-axis D. 0, crosses the x-axis; 3, crosses the x-axis; - 3, crosses the x-axis

A) The number of students using a certain university's online programs has been increasingly exponentially each year since 2010. The number of students n who use the university's online programs t years after 2010 can be modeled using the function n (t) = 425(1.14)^t . Interpret the meaning of 1.14 in the function n (t) in the context of this situation. The total number of students who attend the university increases by 114% each year since 2010. The number of students who study online at the university increases by 14% each year since 2010. The number of students who study online at the university increases by 114% each year since 2010. The total number of students who attend the university increases by 14% each year since 2010.

An ecologist randomly samples 13 plants of a specific species and measures their heights. He finds that this sample has a mean of 16 cm and a standard deviation of 1 cm. If we assume that the height measurements are normally distributed, find a 95% confidence interval for the mean height of all plants of this species. Then find the lower limit and upper limit of the 95% confidence interval.

A random sample of 200 individuals working in a large city indicated that 70 are dissatisfied with their working conditions. Based upon this, compute a 95% confidence interval for the proportion of all individuals in this city who are dissatisfied with their working conditions. Then find the lower limit and upper limit of the 95% confidence interval.

The length of the first loop of a spring is 20 inches. The length of the second loop is 9/10 the length of the first. The length of the third loop is 9/10 the length of the second, and so on. Suppose the spring had infinitely many loops find the length.