Math Questions

Solve the following system of equations. 3x² + 3y² = 123 5x² - 4y² = -20 Solution(s): • Enter your answers as points: (x, y) • Because these systems are non-linear, you may have more than one solution. • If you have more than one solution, enter your answers as a list of points: (co, y0), (1.1) • Use 'sqrt(...)' to enter radical answers, do not use decimal approximations.

Which polynomial represents the sum below? 9x² + x + 2 + 3x^4+2x+2 A. 12x^6 + 9x+4 B. 3x^6 + 9x² + 3x+4 C. 3x^4 + 9x² + 3x+4 D. 3x^4 + 9x+4

Each letter of the alphabet is written on separate cards in red ink. The cards are placed in a container. Each letter of the alphabet is also written on separate cards in black ink. The cards are placed in the same container. What is the probability that a card randomly selected from the container has a letter written in black ink or the letter A or Z? 8/13 15/26 1/2 7/13

An education researcher claims that at most 4% of working college students are employed as teachers or teaching assistants. In a random sample of 500 working college students, 6% are employed as teachers or teaching assistants. At a=0.10, is there enough evidence to reject the researcher's claim? Complete parts (a) through (e) below. (a) Identify the claim and state Ho and Ha Identify the claim in this scenario. Select the correct choice below and fill in the answer box to complete your choice. (Type an integer or a decimal. Do not round.) A. % of working college students are employed as teachers or teaching assistants. B. More than % of working college students are employed as teachers or teaching assistants. C. At most % of working college students are employed as teachers or teaching assistants. D. The percentage of working college students who are employed as teachers or teaching assistants is not %.

If a plane intersects a right cylinder, the cross-section is a circle. Which of the following describes a counterexample to this statement? A. If the plane is parallel to the bases, the cross-section is a circle. B. If the plane is perpendicular to the bases, the cross-section is a rectangle. C. If the plane is tangent to the bases, the cross-section is a line. D. None of these, the original statement is always true. (4 pts.)

A scientist concerned about dehydration of soccer players on hot days measured the fluld consumption of twenty-six soccer players. The mean fluid consumption per day was 2,780 milliliters with a standard deviation of 567 milliters. What is the probability that a player consumed between 1,646 and 3,347 milliliters? Use the 68-95-99.7 normal distribution curve. 97.35% 81.5% 83.85% 81.3%

This question does not have an attempt limit. This problem is worth 1 point. Your recorded score for this problem is 0.0%. Your submissions on this problem will be graded. Let f(x) = (3x - 2) (x²-2). Find all the values of x for which f'(x) = 0. Present your answer as a comma-separated list:

A cylinder shaped can needs to be constructed to hold 300 cubic centimeters of soup. The material for the sides of the can costs 0.03 cents per square centimeter. The material for the top and bottom of the can need to be thicker, and costs 0.05 cents per square centimeter. Find the dimensions for the can that will minimize production cost.

Enter the degree of the polynomial below: 6x6 +9x³+3x²-4x10-9x5-5x6

What is the coefficient of the term of degree 1 in the polynomial? 2x8-5x²+3x+4

Which of the following is a polynomial? A. (x6-2)/(x4 + 3) B. + x4 + 16 C. xy + 2 D. x²-1

(A) Find the average rate of change of the area of a circle with respect to its radius r as r changes from (i) 5 to 6 →→ Average rate of change = (ii) 5 to 5.4 → Average rate of change = (iii) 5 to 5.1 → Average rate of change = (B) Find the instantaneous rate of change when r = 5. Instantaneous rate of change =

In the past two years, both product A and product B have had similar sales and the production Investment is also the same for both of them. This year, the manufacturer feels that Product A may have more sales as compared to Product B . Determine the null and alternate hypotheses, as well as what each potential error represents in terms of reality and researcher conclusion. Which potential error do you think is more severe? A Type I error has more severe effects in this scenario. A Type II error has more severe effects in this scenario. A Type I error and a Type Il error have equally severe consequences in this scenario. It is impossible to tell which error type has more severe consequences in this scenario.

If you horizontally compress the quadratic parent function, F(x)=x2, by 7 units, what is the equation of the new function? A. G(x) = (x+7)² B. G(x) = 7x² C. G(x) = (7x)² D. G(x)=x²-7

Sodium chlorate crystals are easy to grow in the shape of a cube by allowing a solution of water and sodium chlorate to evaporate slowly. If V is the volume of such a cube with side length z, calculate dV/dz when x = 5 mm. dV/dz =

The mean age of the people in room 5 is 29 years. The mean age of the people in room 6 is 35 years. If there are 27 people in room 5 and 22 people in room 6, then what is the mean age of all the people in room 5 and room 6 put together? (nearest tenth). 30.7 31.7 29.6 32

A plane is flying at an elevation of 24000 feet. It is within sight of the airport and the pilot finds that the angle of depression to the airport is 14°. Find the diagonal distance between the plane and the base of the airport. Round your answer to the nearest foot. . Note that for this problem, we are using degrees to measure angles. Make sure your calculator is set to degrees instead of radians.

In 2000, the population of St. Louis was 346,904, and it decreased to 319,257 in 2010. If this population decrease were modeled by an exponential decay function, what value would represent the y-intercept? Explain your reasoning.

A given student in the sophomore class has an equal chance of being in room 1, 2, 3, 4, or 5 in any of her six classes. If A is the event that the student is in room 5 for one of her classes, what is the correct calculation to find the probability that she will not be in room 5 for any of her classes? P(A) = 0.28 P(A) = 28 P(A) = 88 P(A')6 = 0.86

A box with a square base and open top must have a volume of 48668 cm³. We wish to find the dimensions of the box that minimize the amount of material used. First, find a formula for the surface area of the box in terms of only a, the length of one side of the square base. [Hint: use the volume formula to express the height of the box in terms of x.] Simplify your formula as much as possible. A(x) = Next, find the derivative, A'(x). A'(x) = Now, calculate when the derivative equals zero, that is, when A'(x) = 0. [Hint: multiply both sides by x².] A'(x) = 0 when x = We next have to make sure that this value of a gives a minimum value for the surface area. Let's use the second derivative test. Find A"(x). A"(x)= Evaluate A"(x) at the x-value you gave above. NOTE: Since your last answer is positive, this means that the graph of A(x) is concave up around that value, so the zero of A'(x) must indicate a local minimum for A(x). (Your boss is happy now.)

Subtract the polynomials: (6x³ - 4x + 5)-(3x3-5x² + 6x-2). Enter your answer as a polynomial in descending order below, and use the caret (^) for exponents. For example, you would write 4x2 as 4x^2.

The angle of elevation to the top of Wayne Tower in Gotham City is found to be 11° from the ground at a distance of 5,280 feet from the base of the building. Using this information, find the height of Wayne Tower. The height of Wayne Tower is feet. Round your answer to the nearest tenth of a foot. . Note that for this problem, we are using degrees to measure angles. Make sure your calculator is set to degrees instead of radians.

For what values of a does the graph of f(x) = 2x³ + 3x² - 12z - 4 have a horizontal tangent line? Answer(separate by commas): x =

Select all of the transformations that always maintain a shape's congruency? * A reflection A dilation A reflection then a dilation A rotation then a translation A translation then a reflection

A jar has two red, three blue, one white, and three yellow jelly beans. How many ways are there to line up the jelly beans? 5,040 20,160 60,480 362,880

The population of a certain city was 3,674 in 1995. It is expected to decrease by about 0.31% per year. Write an exponential decay function, and use it to approximate the population in 2020. The exponential decay function where f(x) is the population of the city x years after 1995 is f(x) =

Dylan bought 3 identical shirts online for a total cost of $71.83 including a flat rate of $7.99 for shipping. Drag numbers to complete an equation to find the cost of each shirt, s. Each number may be used only once.

Which description represents this equation? 7x-2=33 Two times the quantity of seven less than a number equals thirty-three. Seven less than two times a number equals thirty-three. Two less than seven times a number equals thirty-three.

Change 749,921,154 to Roman numeral (Assume the Roman Numerals in blue have double bar over them and Roman Numerals in red have one bar over them) CDCXLVIII MXXI CCXXXIX DCCXLIX CMXXXI CCLIV DCXLVIII MCXXI CLIV DCCXLIX CMXXI CLIV

Nick and Miguel are the partners in a local health food store. They need $85,000 to start the business. They invested in the ratio 3:7, Nick and Miguel respectively. How much money did Nick invest? Just input the numbers in your answer. Do not insert a dollar sign.

Find the rate of increase (with respect to r) in the surface area (S = 47²) of a spherical balloon when: (A) r = 1 inches → Rate of increase = (B) r = 4 inches → Rate of increase = (C) r = 5 inches → Rate of increase =

An energy company wants to choose between two regions in a state to install energy-producing wind turbines. A researcher claims that the wind speed in Region A is less than the wind speed in Region B. To test the regions, the average wind speed is calculated for 60 days in each region. The mean wind speed in Region Ais 13.8 miles per hour. Assume the population standard deviation is 2.8 miles per hour. The mean wind speed in Region B is 15.1 miles per hour. Assume the population standard deviation is 3.2 miles per hour. At a=0.05, can the company support the researcher's claim? Complete parts (a) through (d) below. (a) Identify the claim and state Ho and Ha What is the claim? A. The wind speed in Region A is less than the wind speed in Region B. B. The wind speed in Region A is not less than the wind speed in Region B. C. The wind speed in Region A is not greater than the wind speed in Region B. D. The wind speed in Region A is the same as the wind speed in Region B.

The slope of the line tangent to the curve 4x² + 3xy + 2y³ = 44 at the point (2, 2) is:

You want to buy a washing machine, and a salesperson tells you that the mean repair costs for Model A and Model B are equal. You research the repair costs. The mean repair cost of 21 Model A washing machines is $214. Assume the population standard deviation is $17. The mean repair cost of 28 Model B washing machines is $220. Assume the population standard deviation is $22. At a=0.01, can you reject the salesperson's claim? Assume the samples are random and independent, and the populations are normally distributed. Complete parts (a) through (e). (a) Identify the claim and state Ho and H₂- What is the claim? A. The mean repair costs for Model A and Model B are different. B. The mean repair cost for Model A is greater than Model B. C. The mean repair cost for Model A is less than Model B. D. The mean repair costs for Model A and Model B are equal.

The guidance department has reported that of the senior class, 2.3% are members of Key Club, K, 8.6% are enrolled in AP Physics, P, and 1.9% are in both. What is the probability of P given K? a) 22.1% b) 13.4% c) 82.6% d) 26.7%

If you flipped the graph of y=x²+2x-2 vertically, you would get the graph of y = -(x²+2x-2). A. True B. False

The senior class is planning to take two separate trips to Disneyland. On the first trip, the seniors had to rent 12 vans and 10 buses with 690 students. On the second trip, they only needed 7 vans and 10 buses as they only took 615 students. There was no difference in the size of the vans and no difference in the size of the buses. How many students went in each van? How many students went in each bus? Let x = Let y = Equation 1: Equation 2:

If a town with a population of 82000 people increases by 12% annually, what will the population be after 5 years? Round your answer to the nearest whole number.

Emma says that for f(x) = 8,000(0.95)X, the exponential growth is 0.95 and the y-intercept is 8,000. What is her error? Choose the correct answer below and fill in the answer box(es) to complete your choice. A. For f(x) to be an exponential growth model, a>__and b>___Since b = , it should be exponential decay, not growth. B. In an exponential growth model y = a.bx, the exponential growth r is found using the equation r = 1 - b. So, the exponential growth is. C. In an exponential growth model y = a bx, the exponential growth is a and the y-intercept is b. So, the exponential growth is__and the y-intercept is__ D. Emma found the x-intercept instead of the y-intercept. The x-intercept is 8,000 and the y-intercept is__

The distance, d, in kilometres, a spaceship travels in t hours is given by the formula d = 40 000t. How long will it take the spaceship to travel 120 000 km? 3h 30 h 0.3 h 300 h

A consumer group claims that the mean minimum time it takes for a sedan to travel a quarter mile is greater than 14.6 seconds. A random sample of 21 sedans has a mean minimum time to travel a quarter mile of 15.3 seconds and a standard deviation of 2.09 seconds. At a=0.01 is there enough evidence to support the consumer group's claim? Complete parts (a) through (d) below. Assume the population is normally distributed. (a) Identify the claim and state Ho and Ha-

Which values are solutions to the inequality below? Check all that apply. x2≤36 A. 6 B. 7 C. 3 D. 36 E. 39 F. no solutions

The current student population of the Brentwood Student Center is 2,000. The enrollment at the center increases at a rate of 4% each year. To the nearest whole number, what will the student population be closest to in 3 years'? 1) 2,240 2) 2,250 3) 5,488 4) 6,240

Solve the following system of equations. 2x² + 4y² = 132 5x² – 5y² = −45 Solution(s):

What is the coefficient of the term of degree 7 in the polynomial? 4+ 6x^7 +10x-5x^6-2x^5

Which polynomial represents the difference below? (5x^7 +9x^4+3)-(x^4-3x) A. 5x^7 + 8x^4+3x+3 B. 4x^7 + 8x^4 -3x+3 C. 4x^11 +8x³ +3 D. 8x+6

Which of the following is the correct factorization of the polynomial below? 8x3 +64y3 A. (4x+4y)(2x+8y) B.(2x+4y)(4x²-8xy+16y²) C. (4x+2y)(4x²-2xy + 16y²) D. The polynomial is irreducible.

Find the expected frequency, E₁, for the given values of n and pi n = 110, pi = 0.6

In a survey of 2250 adults, 712 say they believe in UFOs. Construct a 95% confidence interval for the population proportion of adults who believe in UFOs. A 95% confidence interval for the population proportion is (Round to three decimal places as needed.) Interpret your results. Choose the correct answer below. A. With 95% confidence, it can be said that the population proportion of adults who believe in UFOs is between the endpoints of the given confidence interval. B. The endpoints of the given confidence interval shows that 95% of adults believe in UFOs. C. With 95% confidence, it can be said that the sample proportion of adults who believe in UFOs is between the endpoints of the given confidence interval. D. With 95% probability, the population proportion of adults who do not believe in UFOs is between the endpoints of the given confidence interval.

A physical fitness association is including the mile run in its secondary-school fitness test. The time for this event for boys in secondary school is known to possess a normal distribution with a mean of 440 seconds and a standard deviation of 60 seconds. Find the probability that a randomly selected boy in secondary school can run the mile in less than 302 seconds. A) .9893 B) .0107 C) .5107 D) .4893