Math Questions

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?

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) =

Let f(x) = 9x^4 - 6x³ +23x + 25. Use Descartes' Rule of Signs to answer the following questions. (a) List the possible number of positive real zeros (counting multiplicities) of f(x): (b) List the possible number of negative real zeros (counting multiplicities) of f(x): (c) May anything definitive be said about the exact number of positive real zeros? Select an answer (d) May anything definitive be said about the exact number of negative real zeros? Select an answer There are no negative real zeros. There are exactly two real negative zeros. There is exactly one negative real zero. No conclusion may be made about the exact number of negative real zeros.

Captain Ahab needs $6000.00 worth of harpoons. He started with $1500.00 and has been saving $350 a week to buy the harpoons. Write a function that illustrates this situation. Function: h(x)= Slope/Meaning in context: m = y-intercep/Meaning in context: b = How much will Captain Ahab have saved after seven weeks? How many weeks will it take the captain to buy the harpoons he needs? Write an equation to model this situation and solve.

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

The senior classes at High School A and High School B planned separate trips to the indoor climbing gym. The senior class at High School A rented and filled 12 vans and 9 buses with 435 students. High School B rented and filled 5 vans and 3 buses with 155 students. Every van had the same number of students in it as did the buses. How many students can a van carry? How many students can a bus carry?

Consider the function f(x) = -1/2 x² + 3x + 9. What is the overestimate of the area under the curve of f using rectangular approximations on the interval [-2, 3] with five equal subintervals?

y=x² + 4x-5 Before we calculate important features of this quadratic function, identify a, b, &c. Remember, the standard form quadratic functions: y = ax^2 + bx + c. a = | b= C=

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

Select the correct answer. Bacteria begins to grow on the water's surface in a non-operational swimming pool on September 20. The bacteria grows and covers the water's surface in such a way that the area covered with bacteria doubles every day. If It continues to grow in this way, the water's surface will be entirely covered with bacteria on September 28. When will a quarter of the water's surface be covered? A The water's surface will be covered a quarter of the way on September 24. B. The water's surface will be covered a quarter of the way on September 27. C. The water's surface will be covered a quarter the way on September 26. D. The water's surface will be covered a quarter of the way on September 25.

Mia baked a very large apple pie that she cuts into slices to share with her friends. The smallest slice is cut first. The volume of each successive slice of pie forms a geometric sequence. The second smallest slice has a volume of 30cm³. The fifth smallest slice has a volume of 240cm³. Find the common ratio of the sequence. Find the volume of the smallest slice of pie. The apple pie has a volume of 61425cm³. Find the total number of slices Mia can cut from this pie.

Find zw and z/w. Write each answer in polar form and in exponential form. z=4( cos 2π/9 + i sin 2π/9) w= 16 (cos π/9 + i sin π/9)

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 owner of a video store has determined that the cost C, in dollars, of operating the store is approximately given by C(x)=2x² - 22x+780, where x is the number of videos rented daily. Find the lowest cost to the nearest dollar. A. $841 B. $659 C. $538 D. $720

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.