Math Questions

The population of Sasquatch in Salt Lake County was modeled by the function P(t)=350t/t +35 t = 0 represents the year 1803. When were there fewer than 125 Sasquatch in Salt Lake County? Present your answer, to the nearest whole year, in interval notation. There were fewer than 125 Sasquatch in Salt Lake City between the years

Show that if is an integer multiple of 7, then sin(2x) = 2 sin(x). Hint: Graph the equations y = sin(2x) and y = 2-sin(x) on graphing paper or use Desmos calculator Where are the two equations equal? Use the Desmos calculator below to graph the equations.

In a hypothesis test with hypotheses Ho:μ< 45 and H₁:μ > 45, a random sample of 60 elements selected from the population produced a mean of 46.8. Assume that o = 7.1, and that the test is to be made at the 2.5% significance level. What is the critical value of z? 1.96 -1.65 -1.96 1.65

You are responsible for an automobile accident. Use the information below to determine: 1. the total amount your liability insurance will pay for the accident 2. the total amount your collision insurance will pay for the accident 3. the amount of additional damages you are responsible for as a result of the accident You and the driver of the other car were the only people involved in the accident. There were no injuries from the accident. ▪ You have a 50/100/50 liability insurance policy with no deductible ▪ You have collision insurance with a deductible of $500 ▪ The other car was valued at $25,000 and requires $10,000 in repairs ▪ Your car was valued at $20,000 and requires $15,000 in repairs

A cannonball was fired during the Battle of Muizenberg. The function h(t) = - 16t² +352t represents the height of the cannonball after t seconds after it was fired. 1) After how many seconds did the cannonball take to reach its maximum height? 1936 sec 0.09 sec 11 sec 13 sec

Edward has x dollars. Jay has 25 dollars less than 4 times the square of Edward's amount. Determine the expression that represents the amount of Jay's money and write it in factored form. (2x+5) (2x-5) (x + 5) (x - 5) (5x+2) (5 x-2)

Suppose you want to build a rectangular picture frame where the width is 2 inches less than the length and the diagonal is 2 inches longer than the length. What are the dimensions of the picture frame?

2. (10 pts) A shipment of 270 cell phones and radar detectors were destroyed in a truck accident. On the insurance claim, the shipper stated that each phone was worth $130, each detector was worth $150, and their total value was $36,700. How many of each were in the shipment?

A company manufactures Handband, a wireless activity tracker. There are initial start-up costs involved. Additionally, the company spends a certain amount of money to manufacture each Handband. The cost of manufacturing h Handbands is given by the function, C(h) = 21h + 15000. Which of the following statements are true? Check all that apply.

Andy estimated that he would need 71 feet of lumber for a tree house project. He later found that the actual amount of lumber needed was 60 feet. What was the percent error of Andy's estimation? A. 15.49% B. 18.33% C. 11% D. 84.51%

Find the product: (x + 1)(x - 5) x² - 6x - 5 x² + 4x - 5 x²-5 x² - 4x - 5

A pizza shop sells pizza by the slice. The size of a pizza is given by the pizza's diameter. The shop makes three different sizes of pizza - a 14-inch pizza which they cut into 60-degree slices, a 16-inch pizza which they cut into 45-degree slices and a 20-inch pizza which they cut into 30-degree slices. They sell a slice of each one for the same price. Complete the statement about the pizza slices using words or values. The [14-inch, 16-inch, 20-inch] pizza is the best deal because the area of the slice is ___. Choose 5b the greatest the smallest equal

Factorize: x³ - y³. (x+y)(x² - xy + y²) x-y (x-y) (x²+ xy + y²)

Simplify the sum 1/x² - 4 + 6/x+2. State any restrictions on the variable. A. 6x-11/x² - 4; x≠±2 B.6X-11/x² - 4;x≠-2 C.6x+13/x² - 4;x≠±2 D.6x+13/x² - 4;x≠-2

Evaluate the following integral using trigonometric substitution. ∫√64-x² dx Be sure your written work includes your trigonometric substitution (for x, dx) and the conversion back to the original variable.

Raul sets aside $100 per month during his career of 40 years to prepare for a comfortable retirement. He does not like the idea of investing so he puts his money in a savings account which earns 1.5% interest per year. The balance of his retirement account after 40 years will be $ How much of the total did Raul contribute himself? $ How much money did Raul make through compound interest in this savings account? (Hint: balance - contributions) $

A pizza shop offers a "free pizza" coupon under 8% of its pizza boxes. You have purchased 15 pizzas and are surprised to find that you have still not won a pizza. Should you be? Mathematically justify your answers for full marks.

A farmer has 3 cylindrical grain silos on his farm. Each silo has a radius of 25 ft and a height of 60 ft. What is the approximate total volume of the 3 silos? A. 88,357 ft³ B. 14,137 ft3 C. 353,429 ft³ D. 212,058 ft³

Suppose that 15% of surveyed kids say that chocolate is their favourite food to eat. If 40 kids are asked what their favourite food is, what is the probability that between 80-85% (inclusive) of them, will say something other than chocolate? [4]

What are the magnitude and direction of w = <-10, -12>? Round your answer to the thousandths place. ||w|| = 6.325; θ = 39.806° ||w|| = 14.422; θ= 219.806° ||w|| = 14.560; θ = 205.346° ||w|| = 15.620; θ= 230.194°

Sheila is a wildlife biologist. At the beginning of each year, she tracks the wild turkey and white-tail deer population in the game reserve where she works. At the first year Sheila counted 12 wild turkeys, and their number increases by approximately 40% each year. At the first year Sheila counted 18 white-tail deer, and their number increases by 10 additional deer per year. What is the first year in which Sheila counts more turkeys than deer?

A circle has a diameter of 7 units. Find the area 14π 12.25π 49π 7π

Use DeMoivre's Theorem to calculate the following expression. Express your answer in the form found using Euler's Formula. |z|n ein0 [3 (cos(240°) + isin (240°))]8

Three ballet dancers are positioned on stage. Erica is straight behind Vivian and directly left of Kevin. If Vivian and Erica are 3 meters apart, and Kevin and Vivian are 7 meters apart, what is the distance between Erica and Kevin? If necessary, round to the nearest tenth.

The exponential function f, represented in the table, can be written as f(x) =a.bx. x f(x) 0 15 1 9 Complete the equation for f(x). f(x) = __

A circle has a diameter of 20 units. Find the area 100π 10π 20π 400π

Write the following complex number in standard form, z = a + bi. Use the exact form if possible; otherwise, use a decimal approximation rounded to the hundredths place. 5 (cos(315°) + isin (315°))

The minute hand on the clock shown below has a length of 7.5 cm. Which of the following is closest to the distance that the tip of the hand travels as it moves from 12 to 4? A16 cm B 44 cm C 59 cm D70 cm

Given the side lengths 5,12, and 13; what kind of triangle can you make? you can not make a triangle right acute obtuse

Perform the following division and write the quotient in trigonometric form. Write the magnitude in exact form. Write the argument in radians and round it to two decimal places if necessary. -6i/ 2+i

Each year, a diesel engine manufacturing plant tests a sample of twenty-five of their engines to make sure the horsepower is to specification. This year, the average was 2,538 horsepower, with a 99% confidence interval of [2,494,2,582]. If they do not change any processes for next year's manufacturing run, what is the probability that the average horsepower next year will be outside this range? 1% 0.1% 5% 10%

Perform the following multiplication and write the product in standard form. Express your result in the exact form, if possible; otherwise, use a decimal approximation rounded to the nearest hundredth. (-1-3i)(-2+3i)

One serving of a certain brand of yogurt contains 11 g of fat. The low-fat version contains 40.25% less fat per serving. How many grams of fat does one serving the low-fat yogurt contain? The low-fat yogurt contains __ g gf fat. (Type an integer or decimal rounded to the nearest tenth as needed.)

Which of the following describes p(x) after the following transformations: • Horizontal shrink of a factor of 1/2 • Translated horizontally 5 units right . Translated 3 units down 0.5p(x - 5)-3 2p(x-5)-3 p(0.5(x - 5)) -3 p(2(x - 5)) -3

In a manufacturing process of Headache medicine (pills), the company is aware of a defect rate of 0.02%. Given that this defect is in the shape only of the pill (not the medicinal ingredients) they are okay with this defect rate and decide to continue production. If a small pharmaceutical company decides to purchase 1000 pills... a. Find the probability that at least 1 is defective. [2] b. Find the probability that no more than 2 are defective [3] c. What is the expected number of defective pills in this purchase? [1]

Brady has a Sports Academy credit card. The card has a balance of $5451.29 with an APR of 26.79%. The Academy expects the minimum payment to be 3.5% of the balance. What is Brady's minimum payment? How long will it take Brady to pay off his Sports Academy credit card? How much interest will Brady pay if he only pays the minimum payment? Minimum payment Months to payoff Interest

Write the following complex number in trigonometric form. Write the argument in radians, and if possible, use the exact form. Otherwise, use a decimal approximation rounded to the hundredths place. -4-2i

Evaluate the following integral. ∫x2 +40x-16/x3-16x dx

Jerome will be buying a used car for $6,000 in 2 years. How much money should he ask his parents for now so that, if he invests it at 3% compounded continuously, he will have enough to buy the car? Jerome should ask for $ __.

Mr. Tyler has to mow a large field on his farm. He will mow 1/4 of the field in the morning and 2/3 of the field right after lunch. At that point, how much of the field will he have mowed? F 5/12 G 11/12 H 3/4 J 5/6

To show similarity between Circle A and Circle B, Simeon translates Circle A so that the center of Circle A coincides with the center of Circle B. He then dilates Circle A by a scale factor of Carly chooses to translate Circle B so that the center of Circle B coincides with the center of circle A. Part A: What scale factor should Carly use to dilate Circle B so that it maps onto Circle A? k = Part B: Complete the conclusion that can be made from Simeon's and Carly's transformations. Circles A and B are congruent similar because both Simeon's and Carly's transformations resulted in congruent circles similar

Write the terms for the series. Evaluate the sum, given that x₁ = -4, X₂ = -3,x3 = -2, x4 = -1, and X5 = 0. 5 Σ ×i +3/ xi+4 i=2 X; +4

Which of the following is NOT a property of the t distribution? A) It is symmetric. B Its exact shape (i.e., spread) is characterized by the degrees of freedom. C) All of the above are properties of the t distribution. D As the sample size grows, it gradually approaches the normal distribution.

The Varners live on a corner lot. Often, children cut across their lot to save walking distance. The diagram to the right represents the corner lot The children's path is represented by a dashed line. Approximate the walking distance that is saved by cutting across their property instead of walking around the lot.

Rewrite the following rectangular equation in polar form. y=3x

8. Which of these discrete variables has a binomial distribution? a. The number of diamonds dealt from a deck of cards b.The number of men selected in a 5-member committee from Q6. c. The number of Os produced by a random-number generator d. None of the above

Which of the following is an example of a uniform distribution? a. Length of time you play in a baseball game b.A coin toss 8 times, probability you get heads c.A random number generator d. The number of votes in an election for a particular party

1. Follow the steps below to help you prove or disprove that the point (1, V15) lies on the circle that is centered at the origin and contains the point (0, 4). To earn full credit, you must show your work. Step 1: Plot a point at the origin and at (0, 4). Use these to help you draw the circle centered at the origin that contains (0, 4). Step 2: Determine the radius. Step 3: Use the radius and the coordinates of the center to write the equation of the circle. Step 4: Substitute the x- and y-coordinates of the point (1, V15) in the equation of the circle to check whether they satisfy the equation.

Kylie explained that (-4x+9)2 will result in a difference of squares because (-4x+9)²-(-4x)²+(9)²-16x²+81. Which statement best describes Kylie's explanation? Kylie is correct. Kylie correctly understood that it is a difference of squares, but she did not determine the product correctly. Kylie did not understand that this is a perfect square trinomial, and she did not determine the product correctly. Kylie determined the product correctly, but she did not understand that this is a perfect square trinomial.

The recommended daily allowance of niacin for adults is 20 mg. One serving of a certain breakfast cereal provides 5 mg of niacin. What percent of the recommended daily allowance of niacin does one serving of this cereal provide? One serving of this cereal provides % of the recommended daily allowance of niacin.