Basic Math Questions and Answers

In a triangle, the measure of the first angle is twice the measure of the second angle. The measure of the third angle is 88° more than the measure of the second angle. Use the fact that the sum of the measures of the three angles of a triangle is 180° to find the measure of each angle. The measure of the first angle is

11. Given the equation: y= (3.2)3√z-2, find the value of 'x' that results in y = 10. Hint: Use your graphing calculator to help you. Be sure to explain your reasoning/process of solving. Round your answer to the nearest hundredth, if needed.

Write the following complex number in standard form. z = a + bi. Write the exact answer. Do not round. cos (5π/3) + isim (5π/3)

A sample of bacteria was placed in a petri dish. The number of bacteria changes exponentially over time. The graph describes the number of bacteria over time (in hours). What was the sample's initial size?

In a particular city, taxis charge an initial fee of $3.20 plus $1.70 per mile. How far can a passenger travel for $35.50? The passenger can travel ___ miles. (Type an integer or a decimal.)

Suppose that 8% of the first batch of engines off a new production line have flaws. An inspector randomly selects five engines for testing. What is the expected number of flawed engines in the sample? a. 0.2 b. 4 c. 0.4 d. 5.76

Lin opened a lemonade stand during the summer. She noticed that she sold more lemonade on warmer days. For each day she sold lemonade, she plotted the point (t, c), where t represents high temperature and c represents cups of lemonade sold. On the same axes, draw aline that you think is a good fit for the data.

A pendulum swings such that each swing is 80% the length of the previous swing. Thus, the swings become shorter and shorter. The length of the first swing is 12 inches. What total distance does the pendulum travel? 60 inches 15 inches 67 inches 65 inches

Which of the following represents the unlike terms? 2x and 3x 8m and 12a 3m and 6m

Find the equation of the line that goes through (5,3) and the slope is -1 y=-x-1 y = 5x - 3 y = 8x-1 y=-x+8

The formula A = 128e^0.045 models the population of a particular city, in thousands, t years after 1999. When will the population of the city reach 150 thousand? 2003 2005 1995 1994

A swimming pool has the shape of a box with a base that measures 21 m by 15 m and a uniform depth of 3.1 m. How much work is required to pump the water out of the pool when it is full? Use 1000 kg/m³ for the density of water and 9.8 m/s² for the acceleration due to gravity. You may use the formula: W=∫ p g A(y) D(y) dy Draw a y-axis in the vertical direction (parallel to gravity) and choose one corner of the bottom of the pool as the origin. For 0 ≤ y ≤3.1, find the cross-sectional area A(y). A(y) = (Simplify your answer.) Set up the integral that gives the work required to pump the water out of the pool. Use increasing limits of integration. Select the correct choice below and fill in the answer boxes to complete your choice. (Type exact answers.)

Suppose sin 2x =1/2 Find all solutions 0≤x≤ 2π. Give exact values in radians, and type "pi" for . X = (If there is more than one answer, enter the answers separated by commas)

Find the coefficient of xy³ in 22xy³. 2 -2 22

Find the factored form of x2 - 11x + 24. (x-8)(x-3) (X + 8)(x-3) (x-8)(x+3)

Solve the exponential equation. Express irrational solution 6^(1-7X) = 7^X

Find the factors of m² + 13m + 40. (m+8)(m + 5) (m-8)(m + 5) (m+8)(m-5)

What is the value for x if the perimeter is 42?

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

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?

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

A particle travels in a circular motion counter-clockwise according to the equations x(t) = 4 cos(πt) and y = 4 sin(πt). At what time will the particle have traveled halfway around the circle? a. t = 0 b. t = 1 C. t = 2 d. t = π e. t = 2π

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

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

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) = __

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

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%

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

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

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

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.

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.