Math Questions

ΔABC is dilated by a scale factor of 2 to create ΔDEF, where ΔABC ΔDEF. Which of the following statements are true? 1 m∠A= m∠D II DE = AC III. The area of ΔDEF is 4 times as large as the area of ΔABC A I only B. I and II only C.II and III only D.I. II, and III

Suppose that a company's daily sales volume attributed to an advertising campaign is given by the following equation. S(t)=4/t+9 - 28/(t + 9)² (a) Find how long it will be before sales volume is maximized. t= (b) Find how long it will be before the rate of change of sales volume is minimized. That is, find the point of diminishing. returns. t=

A woman expects to have $10,000 in 4 years to buy a pair of earrings. She plans to create a sinking fund by depositing an amount every 6 months. If the fund earns 16% interest compounded semi-annually, find the semi-annual deposit and construct a sinking fund schedule.

Simplify the given expression: 9/x+9 - 9/ x-9 2x²/x²+81 -162/x^2-81 2x²+(-162)/x²+81

A small city had a population of 110000 in 2010. Concerned about rapid growth, the residents passed a growth control ordinance limiting population growth to 1.7% each year. If the population grows at this 1.7% annual rate, what will the population be in 2020? What is the maximum growth rate cap that will prevent the population from reaching 150000 in 2025?

Consider the following equation of an ellipse. (x - 2)²/4+(y + 2)² /16 =1 Step 3 of 3: Find the coordinates of the two foci of this ellipse. Round your answer to two decimal places Enter the coordinates to plot points on the graph.

An arrow is shot vertically upward from a platform 16 ft high at a rate of 191 ft/sec. When will the arrow hit the ground? Use the formula: h= -16r² + vot + ho (Round your answer to the nearest tenth.)

Find the magnitude and direction angle of the following vector. Write your angle in degrees rounded to four decimal places. u = 3i + 7j

Solve ΔABC, given A=43°, a = 2.5 cm, and b= 3.6 cm. Begin by sketching and labeling a diagram. Account for all possible solutions. Express each angle to the nearest degree and each length to the nearest tenth of a unit.

Isaiah reads articles about the insufficient savings of those in retirement and decides he needs to start saving now, even though he's in his 50s. He saves $500 per month for 15 years and earns 7% by investing in the stock market through an index fund. The value of his retirement account after 15 years will be $ How much of the toal did Isaiah contribute himself? $ How much mondy did Isaiah make through compounded returns in this investment account? $

The New York Knicks play in Madison Square Garden, the Los Angeles Lakers play in the Staples Center, and the Miami Heat play in American Airlines Arena. Madison Square Garden is about 2.8 x 10³ miles from the Staples Center and Madison Square Garden is about 1.4 x 10³ miles from American Airlines Arena. A. How many times of the distance the Knicks travel to play the Heat is the distance the Knicks travel to play the Lakers? B. How much further is the Staples Center than American Airlines Arena from Madison Square Garden?

3. Find the first three terms of the geometric sequence where the first term is 4 and the common ratio is 1/2 a₁ = 4, a₂ = 1, a3 =1/4 a₁ = 4 , a₂ = 9/2, a3 = 5 a₁ = 4 , a₂ = 8, a3 = 16 a₁ = 4 , a₂ = 2, a3 = 1

Let g(x) = ∫f(t) dt, where f is the function whose graph is shown. (a) Evaluate g(0), g(1), g(2), g(3), and g(6). g(0) = 0 g(1)=2 g(2) = 5 g(3) = 7 g(6) = 3 (b) On what interval is g increasing? (Enter your answer using interval notation.)

Here are three problems. (x-1)³-4 = 24 5^(x-1)-4 = 24 5^(x-1) — 4 = 24 Only one of these problems requires logarithms to solve. Which one? Explain why the other two problems do not require logarithms to solve. Please explain your justification with as much mathematical detail as possible.

I arrive home to find that my 40 foot by 30 foot basement has 3 inches of water in it. a) If 1 cubic foot of water is about 7.48 gallons, how much water will I be pumping out of my basement? Express your answer rounded to the nearest tenth of a gallon. b) If I have a pump that can pump 450 gallons of water per hour, how long will it take to empty the basement? Express your answer rounded to the nearest tenth of an hour.

Examine this expression and answer the following questions: 4log8x + 3log8(2x-5)-7log8(x-3) (a) After you condense this into one logarithm, what would the exponent in the denominator be (in the bottom part of the fraction)? (b) After you condense this into one logarithm, what would the base of the logarithm be?

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

Graph the function. h(x) = 6. (4/3)^x

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

A game costs $1 to play where you win $5 when a coin lands on heads but lose $6 when a coin lands on tails. Calculate the expected payoff to the nearest cent, being sure to show all work.

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?

A particle moves along a line so that its acceleration function a(t) (in m/s²). The initial velocity v(0) = -1 (in m/s). Find the total distance (not displacement) traveled during the time period 0 ≤ t ≤ 1.

The mean consumption of water per household in a city was 1215 cubic feet per month. Due to a water shortage because of a drought, the city council campaigned for water use conservation by households. A few months after the campaign was started, the mean consumption of water for a sample of 95 households was found to be 1149 cubic feet per month. The population standard deviation is given to be 233 cubic feet. a. Find the p-value for the hypothesis test that the mean consumption of water per household has decreased due to the campaign by the city council. Would you reject the null hypothesis at a = 0.01? Round your answer to four decimal places. p-value =

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