Math Questions

Find the equation of the function that is finally graphed after the following transformations are applied to the graph of y = 3ˣ (write your resulting transformation in every step as well as your final result): a) Shift down 2 units b) Shift the result of a) right 3 units c) Reflect the result of b) about x-axis d) Reflect the result of c) about y-axis

Solve the following compound inequality. x+6≥5 and 3x - 7≥5 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution set in interval notation is ___. B. The solution set is Ø.

In 2012, the population of a city was 6.69 million. The exponential growth rate was 3.15% per year. a) Find the exponential growth function. b) Estimate the population of the city in 2018. c) When will the population of the city be 11 million? d) Find the doubling time. a) The exponential growth function is P(t) = ▢ where t is in terms of the number of years since 2012 and P(t) is the population in millions. (Type exponential notation with positive exponents. Do not simplify. Use integers or decimals for any numbers in the equation.)

Diana has available 3200 yards of fencing and wishes to enclose a rectangular area. (a) Express the area A of the rectangle as a function of the width W of the rectangle. (b) For what value of W is the area largest? (c) What is the maximum area? (a) A(W)= ▢

A random sample of 781 subjects was asked to identify the day of the week that is best for quality family time. Consider the claim that the days of the week are selected with a uniform distribution so that all days have the same chance of being selected. The table below shows goodness-of-fit test results from the claim and data from the study. Test that claim using either the critical value method or the P-value method with an assumed significance level of a = 0.05. Test statistic, Num Categories 7 x^2 3310.036 Degrees of freedom 6 Critical x^2 12.592 Expected Freq 111.5714 P-Value 0.0000 Determine the null and alternative hypotheses. a)Ho: All days of the week have an equal chance of being selected. b)H1: At least one day of the week has a different chance of being selected. identify the test statistic. X^2=___________

You run a regression analysis on a bivariate set of data (n= 33). You obtain the regression equation y = 3.146x + - 12.726 with a correlation coefficient of r = 0.847 (which is significant at α = 0.01). You want to predict what value (on average) for the explanatory variable will give you a value of 130 on the response variable. What is the predicted explanatory value? X=_________

Use function notation to write the equation of the line with the given slope and y-intercept. Slope -5; y-intercept (0.3) The equation is f(x)=_________

Graph the inequality. 4x+y<2 Use the graphing tool to graph the inequality.

Find the magnitude and the positive direction angle for u. u= (12,-5).

Coach Rivera purchases sports equipment. Baseball bats cost $45.00 each, and baseball gloves cost $20.00 each. He has a budget of $250.00. Part B: Given the coach's budget, which of the following is a viable option for the equipment he can purchase? 5 bats and 2 gloves 6 bats and 5 gloves 4 bats and 6 gloves 2 bats and 7 gloves

A Red Cross helicopter takes off from headquarters and flies 115 km in the direction 220° from North. It drops off some relief supplies, then flies 75 km at 325° from North to pick up three medics. .if the helicopter then heads directly back to headquarters, find the distance and direction (rounded to one decimal place it should fly. a)Distance _____km b)Direction _____degrees from North

Nettie's Bargain Clothing is having a huge sale. All shirts are $3 each and all pants are $5 each. You go to the sale and buy twice as many shirts as pants and spend $66. a)Write a system of equations that models this situation where s = number of shirts and p = number of pants Equation 1: Equation 2: b) Solve this system using substitution to determine how many of each item you bought. Write your answer in a complete sentence. You bought ___pairs of pants and ______shirts.

Identify the rate of change and y-intercept in the equation 6x +12y = -9. (A) m=-1/2 and b=-4/3 (B) m = -2 and b = - 4 (C) m=-1/2 and b = -3/4

Find the domain of the function f(x) =(x^2 +2x +1)/x+1 a)Set of negative real numbers b)Set of real numbers except -1 c)Set of real numbers except 1

Solve by graphing: -x+y=-2 -2x+2y=-4 Select the correct answer below: a)Infinite solutions in the form (x,-2-2) b)Infinite solutions in the form (x,-x+2) c)Infinite solutions in the form (x,x - 2) d) Infinite solutions in the form (x, x+2) e)One solution: (1, -1) f)No solution:

Graph the linear equation; f(x) = 3x Use the graphing tool to graph the equation.

In 2005, a CCTV camera producing company made a profit of $38000. In 2015, the same company made a total profit of $54000. Find the average rate of change in the company's profit in dollars per year. (A) $1600 (B) $16000 (C) $160

An online newspaper sent out a poll regarding the highest level of math that adults think they needed. The 90% confidence interval for a random sample of 200 people stated that Geometry was the highest level of math they think they needed was constructed. The confidence interval was (0.12, 0.38). The point estimate (sample proportion) used to construct the confidence interval was: A) 0.38. B) 0.20. C) 0.25. D) 0.13.

Suppose that a Goodness of Fit test is being conducted where n = 15 values which fall into 7 distinct categories. Then, for a value of α = .05 , the critical value for this test will be (A) x² = 42.557 (B) x² = 23.685 (C) x² = 11.071 (D) x² = 12.592

Piper invested $4,700 in an account paying an interest rate of 4.8% compounded continuously. Assuming no deposits or withdrawals are made, how much money, to the nearest cent, would be in the account after 19 years?

To investigate the relation between hair color and eye color, the hair color and eye color of 5383 persons were recorded. The data are given in the following table: Hair Color Eye Color 1 2 3 Light 1168 825 305 Dark 573 1312 1200 (A) Determine the joint and marginal probability distributions of X and Y. (B) P(X + Y = 5) (C) P(1<x<=3, 1 < Y <= 3)

A complicated equation was simplified and factored into (tanx) (sin²x – a ) (sec x - a) = 0. Determine the number of roots of the equation over the domain 0 <= x <= 2π if: a) 0< a < 1 b) a > 1

Solve the compound inequality. 4x + 6≤-6 and 3x≤0 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A). The solution set of the compound inequality is B). The solution set is Ø.

Which of the following are rational numbers? Select all correct answers. Select all that apply: (A) 1.02022022202222... (B) √2 (C) √3 (D) √4 (E) 0.3333 (F) 0.123123123123...

Karlha reads that 38% of American teenagers say chocolate is their favorite flavor of ice cream. Karlha believes that a greater proportion of teenagers in Arizona say chocolate is their favorite flavor of ice cream. She surveys 240 teenagers in Arizona and finds that 106 of them say chocolate is their favorite flavor. Assume the conditions for performing a significance test using a z-statistic are met and use a significance level of α = 0.05. Calculate the p-value and make a conclusion. ○ The p-value is 0.02442. Karlha rejects the null hypothesis because this suggests that more than 38% of teenagers in Arizona say chocolate is their favorite ice cream flavor. ○ The p-value is 0.04884. Karlha rejects the null hypothesis because this suggests that more than 38% of teenagers in Arizona say chocolate is their favorite ice cream flavor. ○ The p-value is 0.03438. Karlha rejects the null hypothesis because this suggests that more than 38% of teenagers in Arizona say chocolate is their favorite ice cream flavor. ○ The p-value is 0.95486. Karlha fails to reject the null hypothesis because this suggests that more than 38% of teenagers in Arizona say chocolate is their favorite ice cream flavor.

Christian is going to invest $310 and leave it in an account for 20 years. Assuming the interest is compounded daily, what interest rate, to the nearest hundredth of a percent, would be required in order for Christian to end up with $1,000?

Solve by graphing: -x + 2y=2 -3x + 6y=6 Select the correct answer below: a)Infinite solutions in the form (x,(-x/2)-1) b) Infinite solutions in the form (x, (-x/2)+1) c)Infinite solutions in the form (x, (x/2)- 1) d) Infinite solutions in the form (x, (x/2)+1) e) One solution: (2,2) f)No solution:

Determine which of the following are true statements. Check all that apply. A. (6, - 6) is a solution to 8x + 2y ≤ 32 B. (7, - 7) is a solution to – 10x - 3y ≥ - 49 C. (9, - 10) is a solution to - 4x + 6y < - 94 D. (5, - 2) is a solution to -5x + 7y > - 37

In the coordinate plane below, plot the three points corresponding to the values x = -1, x = 0, and a = 1 ,in the equation y = - +5

Use a graphing calculator to solve the nonlinear system. y =e^(X+1) X+y =1 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A). The solution set is (Type an ordered pair. Use a comma to separate answers as needed. Type an integer or decimal rounded to the nearest hundred) B). There are infinitely many solutions. C). There is no solution.

Solve the cubic equation. x³ +125=0 The solution set is _______.

Betty has several of the standard six-sided dice that are common in many board games. If Betty rolls one of these dice, what is the probability that: She rolls a three. ▢ She rolls a five. ▢ She rolls a three or a five. ▢ She rolls an even number. ▢

Which of the following represents vector t = PQ in trigonometric form, where P(-10, 13) and Q (-20, 7)? O t = 11.662 cos 30.964°i + 11.662 sin 30.964°j ; O t= 11.662 sin 30.964°i + 11.662 cos 30.964° j O t= 11.662 cos 210.964°i + 11.662 sin 210.964ºj O t= 11.662 sin 210.964°i + 11.662 cos 210.964°j

If three times a number is increased by 24, the result is 16 less than seven times the same number. Find the number. 10 9 11

Lillian is in the business of manufacturing phones. She must pay a daily fixed cost to rent the building and equipment, and also pays a cost per phone produced for materials and labor. Let C represent the total cost, in dollars, of producing p phones in a given day. The table below has select values showing the linear relationship between p and C. Determine the fixed cost for rent and equipment. p C 2 1200 4 1600 6 2000

Suppose that a large farm with a known reservoir of gas beneath the ground sells the gas rights to a company for a guaranteed payment at a rate of 1,500e^0.03t dollars per year. Find the present value of this perpetual stream of income, assuming an interest rate of 7% compounded continuously.

Samuel is going to invest in an account paying an interest rate of 5% compounded continuously. How much would Samuel need to invest, to the nearest dollar, for the value of the account to reach $77,000 in 9 years?

Suppose the binomial expansion of (4x + 5y)^n includes the term 1400000x³y⁴. (A) The x³y⁴ term in the expansion will be? (B) The x⁵y⁴ term in the expansion will be?

The sum of two consecutive numbers is 5. Find the equation representing the same. X+ (x + 2) = 5 X + (x + 1) = 5 2X+ (x + 1) = 5

Solve the compound inequality. - 4x<= -12 or 7x-13 >= 29 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. (A) The solution set is (B) The solution set is Ø.

Fill in the blank. If n(E1 and E2) = 4 and n(E1) = 16, then P(E2 | E1) = _______. If n(E1 and E2) = 4 and n(E1)= 16, then P(E2 | E1) = _______ (Type an integer or a simplified fraction)

A cell culture contains 9 thousand cells, and is growing at a rate of r(t) = 4e^0.24t thousand cells per hour. Find the total cell count after 2 hours. Give your answer accurate to at least 2 decimal places.

Check whether the equation 16 - 4a= 2(8 - 2a) is an identity. O Not an identity O Has solution O Identity Complete Later

The table shows the results of a survey of patrons of a particular restaurant chain. Meals Good Service Poor Service Total Lunch 527 315 842 Dinner 923 612 1535 Total 1450 927 2377 If one of these patrons is selected at random, find the probability that their service was good, given that their meal was dinner. The probability that their service was good, given that their meal was dinner, is ______. (Round to four decimal places as needed.)

An arch is in the shape of a parabola. It has a span of 800 feet and a maximum height of 40 feet. Find the equation of the parabola (assuming the origin is halfway between the arch's feet).Determine the height of the arch 143 feet from the center.

Consider the function f : N→P(N) given by f(x) = {d ∈ N: d|x}. (a) Write out all of the elements of the set f(10) = {d ∈ N: d|x}. (b) Is f one-to-one? Prove your answer.

The total cost to produce x units of perfume is C(x) = (8x + 5)(7x+6). Find the marginal average cost function, C'(x). ○ A. C'(x) = 56x+83+30/x ○ B. C'(x) = 112-83/x ○ C. C'(x)= 112x + 83 ○ D. C'(x)=56-30/x²

In 1997, the cost of tuition at a large Midwestern university was $167 per credit hour. In 2004, tuition had risen to $230 per credit hour. Determine a linear equation to represent the cost, C, of tuition in terms of x, the number of years since 1990. Linear Equation: In the year 2008, tuition will be $____________ per credit hour. In the year _________,tuition will be $338 per credit hour.

How many solutions does the following system have? 2x + y + z=2 2x - 2y - 3z=2 10x - 3y - 4z=-1 Select the correct answer below: a) No solutions b)l solution c)Infinitely many solutions

Graph the linear equation, f(x) = 3x + 2. Use the graphing tool to graph the linear equation.