Math Questions

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.

13. A cone with a radius of 6 meters has a volume of 542.87 m³. Find the slant height of the cone. height = slant height =

An asteroid is 10^12 miles away from earth, and it is travelling at a speed of 10^5 miles per day. How many days will it take the comet to reach earth? Leave your answer in the form a^b days

f(x)=3600/x+100x+1800 a. what is the domain of f(x)? b. Find the dericative of f(x). c. identify all stationary points of f(x). (if non explain why) d. Identify all singular points of f(x). (if non explain why) e. Identify all endpoints of f(x). (if non explain why)

The slope is 3, and the y-intercept is 9. The slope is 3, and the y-intercept is 12. The slope is 4, and the y-intercept is 9. The slope is 4, and the y-intercept is 12.

Given that x = 15, and y = 60, determine which segments or lines are parallel, and justify your solution. A AB | CD, because alternate interior angles are congruent. B AD | CB, because altemate interior angles are supplementary. C AB CD, because consecutive interior angles are congruent. D AD II CB. because consecutive interior angles are supplementary.

9) Jamal wants to construct a tangent line to circle O that passes through point M. He started by drawing a segment from point O to point M. Next he constructed the midpoint of segment OM. What is the next step in his construction. A) Construct a radius of circle O. B) Set the compass to the width of OP. C) Construct the midpoint of segment OP. D) Draw a diameter passing through point O.

The curve y² = x, the line x = 2, and the x-axis form the sides of the bounded region. Find the volume of the solid generated by revolving about the x-axis. A π/2 B π/4 C 2π D π

17) Jon performs 3 transformations on a pentagon. First, he reflects it over the x-axis. Then, he translates it 3 units to the left and 4 units up. Finally, he reflects the image over the line x = 1. Are the original and transformed images congruent? Justify your answer. A) no; Two reflections will change the size of the original image. B) no; Reflections and translations are fluid motions. Fluid motions change the size of the original image. C) yes; Reflections and translations are rigid motions. Rigid motions preserve the size of the original image. D) yes; Reflections and translations are fluid motions. Fluid motions preserve the size of the original image.

John has a credit card with an APR of 23.95% and a current balance of $12,650.35. He wants to pay it off in 3 years. What will John's monthly payment be? (Remember a credit card is compounded monthly.) Round to the nearest dollar.

A biologist wants to know the width w of a river to properly set instruments for an experiment. From point A, the biologist walks downstream 100 feet and sights to point C (see figure). From this sighting, it is determined that θ = 47°. How wide is the river? (Round your answer to one decimal place.

Write the first five terms of the sequence whose general term, an, is given as an=-5n+ 8.

In Circle O, LAC is a central angle and mzAC = 132°. If Q represents the area of Circle O, write an expression that represents the area of the sector formed by ZAC, in terms of Q. 11/60 Q 6Q 11/30 Q 60/11 Q