Math Questions

Find an equation of the line that passes through the given point and has the indicated slope m. Point (-2,-5) Slope m= 4/5

Lighthouse Master Olivia is atop her 300 ft lighthouse and spots a boat in the distance at an angle of depression of 18º. Along the same line of sight, she spots another boat at an angle of depression of 62º. How far are the boats from other? Round your answer to the nearest tenth. distance = ft.

Ni Hua is an adventurous traveler. He skydives twice in every island he visits and skydives thrice in every peninsula he visits. In the last decade, Ni Hua went skydiving a total of 45 times in the 19 islands and peninsulas that he visited. How many islands and peninsulas did Ni Hua visit? Choose 1 answer: Ni Hua visited 12 islands and 7 peninsulas. Ni Hua visited 7 islands and 12 peninsulas. There is not enough information to determine the exact number of islands and peninsula Ni Hua visited. The given information describes an impossible situation.

How are chords and secants alike? How are they different? They are alike because they both intersect the circle___They are different because chords are____and__ secants are

A sandwich shop is ordering apples and grapes to make chicken salad. Apples cost $2.19 per pound and grapes cost $2.60 per pound. If they ordered a total of 20 pounds of apples and grapes and paid $35.80, how many pounds of grapes did they order?

In Exercises 1-4, find the indicated measure. 1. radius of a circle with a circumference of 42π meters 2. circumference of a circle with a radius of 27 feet 3. circumference of a circle with a diameter of 15 inches 4. diameter of a circle with circumference 39 centimeters

Given that a parabola has its vertex at (-2, 1). Which of the following can not be the function expression of the parabola? f(x) = -(x + 2)²+1 f(x)=(x-2)²+1 f(x)=(x + 2)²+1 f(x)=3(x+2)²+1

Two vessels are pulling a broken-down ship toward a boathouse with forces of 750 lb and 630 lb. The angle between the forces is 34.5°. Determine the magnitude of the equilibrant force. Show your work.

In 2016, 5,200 parking permits were issued in a city. The number of parking permits increases by 5% every year. Let y represent the number of parking permits issued xyears since 2016. Which type of sequence does the situation represent? A The situation represents an arithmetic sequence because the successive y-values have a common difference of 1.5. B. The situation represents a geometric sequence because the successive y-values have a common ratio of 1.5. C. The situation represents an arithmetic sequence because the successive y-values have a common difference of 1.05. D. The situation represents a geometric sequence because the successive y-values have a common ratio of 1.05.

In a Northwest Washington County, the speeding fines are determined by the formula: F(s) = 13(s 40) + 35 where F(s) is the cost, in dollars, of the fine if a person is caught driving at a speed of s miles per hour. If a fine comes to $308, how fast in mph was the person speeding? -

Let S be the universal set, where: S = {1,2,3,4,5,6,7,8,9,10} Let sets A and B be subsets of S, where: Set A={1,2,7,9,10} Set B= {1,2,4,5,6,7,8,10} Find the following: LIST the elements in the set (A'): (A) = { } Enter the elements as a list, separated by commas. If the result is the empty set, enter DNE LIST the elements in the set (B'): (B')={ } Enter the elements as a list, separated by commas. If the result is the empty set, enter DNE You may want to draw a Venn Diagram to help answer this question.

After a 40% reduction, you purchase a new stereo for $273. What was the price of the stereo before the reduction? A) First write an equation you can use to answer this question. Use x as your variable and express any percents in decimal form in the equation. The equation is B) Solve your equation in part [A] to find the original price of the stereo. Answer: The original price of the stereo was dollars.

Claire has received scores of 85, 88, 87, and 95 on her algebra tests. What score must she receive on the fifth test to have an overall test score average of at least 90? A. 95 or greater B. 96 or greater C. 94 or greater D. 93 or greater

The following equation: P = 139t + 9900 gives the total population, P, of a small city t years after 1971. Use the equation to determine when (what year) the population reached a population of 11707 people. Answer: The population reached a total of 11707 people in the year

The perimeter of a rectangle is 48 feet. Describe the possible lengths of a side if the area of the rectangle is to be greater than 95 square feet. A. The length of the rectangle must be greater than 19 ft or less than 5 ft B. The length of the rectangle must lie between 1 and 95 ft C. The length of the rectangle must lie between 5 and 19 ft D. The length of the rectangle must be greater than 19 ft

A ball is thrown upward from the top of a building 340 feet tall. The height of the ball is described by the function h(t) = -16t² +320t + 340, where t is in seconds and t = 0 corresponds to the moment the ball is thrown. Determine for what value of t the ball reaches the maximum height and determine this maximum height t=__ and maximum height=___

8) A cylindrical can without a top is to be made to contain 150 cubic centime- ters of liquid. Find the dimensions that will minimize the cost of the metal to make the can. (Recall that the volume formula for a cylinder is: V = r²h.)

Use the given sets below to find the new set. Enter each number separated by a comma. If there are no numbers in the resulting set, leave the answer blank. A = {-9, 2, 6} and B = {-3, 0, 4} AUB={

1. Mallory bought a computer system to start her business from home for $5,995. It is expected to depreciate at a rate of 8% per year. After how many years will the value of her home computer system depreciate to approximately $2,250. Hint: depreciate means decay

Determine whether the following are permutations or combinations The ways to form a three person committee of a chair, a treasurer, and a secretary from a group of eighteen people The ways to form a three 1. Permutations person committee from a group of eighteen people The ways to arrange the 2. Combinations letters Q, U, E, S, T, I, O, N The ways to get exactly three heads in ten tosses of a coin

A wire of length 15 is cut into two pieces which are then bent into the shape of a circle of radius r and a square of side a. Then the total area enclosed by the circle and square is the following function of sand r If we solve for s in terms of r. we can reexpress this area as the following function of r alone Thus we find that to obtain maximal area we should let r To obtain minimal area we should let r

A function f(z) and interval [a, b] are given. Check if the Mean Value Theorem can be applied to fon [a, b]. If so, find all values c in [a, b] guaranteed by the Mean Value Theorem Note, if the Mean Value Theorem does not apply, enter DNE for the c value. C= (Separate multiple answers by commas.) f(x) =z2-1/z²-16 on [0,8]

Geraldo earns $505 from his summer job and deposits it in a savings account that earns 4% simple interest. After 3 years, he moves all his money to another savings account at another ank that earns 6.5% simple interest. What formula below can be used to calculate Geraldo's total account balance after 7 years? (505 x 0.04 x 3) + (565 x 0.065 x 4) [(505 x 0.4 x 3) x 0.65 x 7] [(505 x 0.04 x 3 + 505) x 0.065 x 4]+ (505 x 0.04 x 3 +505) (505 x 0.065 x 7) + (505 x 0.04 x 3)

Alex is taking two courses; algebra and history. Student records indicate that the probability of passing algebra is 0.55, that of passing history is 0.4, and that of passing at least one of the two courses is 0.7. Find the probability that Alex will pass both courses. • Write the probability as a decimal For example, 0.22

The Franklins inherited $3,500, which they want to invest for the child's future college expenses. If they invest it at 8.25% with interest compounded monthly, determine the value of the account, in dollars, after 5 years. $5,270.61 $6,200.53 $3,200.47 $5,279.61

Points (4, 5) and (10, 5) are vertices of a rectangle. The length of the rectangle is twice the width. The other vertices are located at (4,) and (10,). What could these ordered pairs be?

A lumber yard has fixed costs of $7259.40 per day and variable costs of $0.07 per board-foot produced. Lumber sells for $1.87 per board-foot. How many board-feet must be produced and sold daily to break even?

Which data set is the farthest from a normal distribution? . 2, 3, 3, 4, 4, 4, 5, 5, 6 3, 4, 5, 6, 6, 7, 7, 7, 8, 8, 9, 10 0.9, 1.0, 1.0, 1.1, 1.1, 1.1, 1.2, 1.2, 1.3 4, 4, 4, 5, 5, 6, 7, 7, 8, 8, 8 2, 4, 5, 5, 6, 6, 7, 7, 7, 8, 8, 9, 9, 10

A box with an open top has vertical sides, a square bottom, and a volume of 32 cubic meters. If the box has the least possible surface area, find its dimensions. Height = (include units) Length of base= (include units)

Use finite approximations to estimate the area under the graph of the function f(x) = 24-x² - 2x between x = -6 and x = 4 for each of the following cases. a. Using a lower sum with two rectangles of equal width b. Using a lower sum with four rectangles of equal width c. Using an upper sum with two rectangles of equal width d. Using an upper sum with four rectangles of equal width

The quadratic function R(p)= 70p - 5.2p² models the amount of revenue in dollars R(p), generated from a product priced at p dollars. Question: What price(s) generate a revenue of $250? Enter the two solutions rounded to the nearest penny (hundredth of a dollar) in order from least to greatest. IF there is no valid answer enter N/A in all blanks. *Remember: When calculating, do not do any rounding until the end of Answer: The prices that generate a revenue of $250 are $ your calculations. and $

A computer purchased for $1,100 loses 16% of its value every year. The computer's value can be modeled by the function v(t) = ab^t, where v is the dollar value and t the number of years since purchase. (A) In the exponential model a =__and b =___ (B) In how many years will the computer be worth half its original value? Round answer to 1 decimal place. The answer is ___years

What is the solution to the following system? 3x+10y-12z=40 x-5y=0 X-4z=0 (8, 40, 32) (10, 2, 3) (20, 4, 5) (40, 8, 10)

Gordon invested $100,000 into a CD compounded quarterly with an annual interest rate of 6.00%. Determine how much money Gordon would have after 8 years. Round your answer to the nearest cent. Provide only a numerical answer (For example, if the final amount came to $5,023.97, then you would input 5023.97). Your Answer:

Translate the following verbal statement into an algebraic equation and then solve: Rachael bought a bookcase on sale for $220, which was two-fifths of the original price. What was the original price of the bookcase? Use p for your variable. Equation= p=

Kalesha has a statue that is in the shape of a square pyramid. One of the side of the square base is 17 in. long and the volume of the pyramid is 2023 in³. What is the height of the pyramid? Enter your answer in the box. in.

A) Find the exact value for each, given the information. B) In which quadrant is the angle (a + B)? sin a = -4/5 and cos b = 12/13 ; a & ß are in the same quadrant. Find sin(a +b) and cos(a + b). sin a = 8/17 and cos b = 7/25 ; a & ß are in the same quadrant. Find sin(a +b) and cos(a + b).

Sarah borrows a $300 to purchase a new computer and is charged 12% simple interest. She is not required to make payments on the loan for two years, and she makes one payment to pay off the loan after two years. How much was the payment she made? 172 $372 $720 $327

Last week Marcus travelled 150 miles in 3 hours. This week he wants to go on a 300 mile trip in 5 hours. Will it be possible to make this trip if she travels at the same speed as last week's trip? Show your work and explain why or why not this would be possible.

If a stone is thrown vertically upward from the surface of the moon with a velocity of 10 m/s, its height (in meters) after t seconds is h(t) = 10t - 0.83² (a) What is the velocity of the stone after 4 seconds? (b) What is the velocity of the stone after it has risen 25 m?

Grace collected data from twenty of her friends about the number of pets they have. The median number of pets is two. What does the median say about Grace's data set? A. Everyone Grace surveyed has two pets. B. More of Grace's friends have two pets than any other number. C Two is the middle number when the number of pets in the data set is ordered from least to greatest. D. Two is the difference between the greatest and least number of pets Grace's friends have.

In order for applicants to work for the foreign- service department, they must take a test in the language of the country where they plan to work. The data below shows the relationship between the number of years that applicants have studied a particular language and the grades they received on the proficiency exam. # of years,x 2 3 3 4 5 5 6 6 8 Grade on test,y 59 62 70 72 78 85 80 88 92 Find the test value for testing linear correlation. 4.26 7.08 1.97 .937

The manufacturer of a refrigerator system for beer kegs produces refrigerators that are supposed to maintain a true mean temperature, μ, of 41F, ideal for a certain type of German pilsner. The owner of the brewery does not agree with the refrigerator manufacturer, and claims he can prove that the true mean temperature is incorrect. Assuming that a hypothesis test of the claim has been conducted and that the conclusion is to reject the null hypothesis, state the conclusion in nontechnical terms. There is not sufficient evidence to support the claim that the mean temperature is different from 41°F. There is sufficient evidence to support the claim that the mean temperature is different from 41°F. There is sufficient evidence to support the claim that the mean temperature is equal to 41°F. There is not sufficient evidence to support the claim that the mean temperature is equal to 41°F.

Select all the correct answers. Which statements are true about function g? g(x) =(1/2)^x-2 x<2 x^3 -9 x^2 +27x -25 , x≥2 Function g is continuous. Function g is increasing over the entire domain. As x approaches negative infinity, g(x) approaches positive infinity. As x approaches positive infinity, g(x) approaches positive infinity. Function g includes an exponential piece and a quadratic piece.

The population of a small town in North Carolina is 4,000, and it has a decay rate of 3% per year. Which expression can be used to calculate the town's population x years from now? 4,000x1.03 4,000x³ 4,000(1.03)* 4,000(.97)*

A poll of 1567 adults in a certain country found that 23% identified themselves as the followers of some religion. The margin of error was 4 percentage points with 90% confidence. Which of the following represents a reasonable interpretation of the survey results? A. In 90% of samples of adults in a certain country, the proportion who identify themselves as the followers of some religion is between 19% and 27%. B. There is 90% confidence that 23% of adults in a certain country identify themselves as the followers of some religion. C. There is 90% confidence that the proportion of adults in a certain country who identify themselves as the followers of some religion is between 19% and 27%. D. There is between 86% and 94% confidence that 23% of adults in a certain country identify themselves as the followers of some religion.

The equation for line t can be written as y = -4x + 8. Perpendicular to line t is line u, which passes through the point (-8, -8). What is the equation of line u? Write the equation in slope-intercept form. Write the numbers in the equation as proper fractions, improper fractions, or integers.

A 10-foot ladder is to be placed against the side of a building. The base of the ladder must be placed at an angle of 72° with the level ground for a secure footing. Find, to the nearest inch, how far the base of the ladder should be from the side of the building and how far up the side of the building the ladder will reach.

Find the equation of the tangent line to y = 4^(x^2-6z+1) at x=2 y=

Sand is poured onto a surface at 20 cm³/s, forming a conical pile whose base diameter is always equal to its altitude. How fast (in cm/s) is the altitude of the pile increasing when the pile is 3 cm high? Remember, the volume of a cone is V =πr ². Note: Round to the nearest hundredth.