Math Questions

A jogger runs around a circular track of radius 65 ft. Let (x, y) be her coordinates, where the origin is the center of the track. When the jogger's coordinates are (39, 52), her x-coordinate is changing at a rate of 16 ft/s. Find dy/dt. dyldt = ft/s

Solve the following triangle. B= 20°, C= 50°, b=3

What happens to the value of a fraction when the numerator (the top) approaches (gets very close to) zero? What happens to the value of a fraction when the denominator (the bottom) approaches (gets very close to) zero? What happens to the value of a fraction when the numerator (the top) gets much much larger than the denominator? What happens to the value of a fraction when the denominator (the bottom) gets much much larger than the numerator? Use at least 4 sentences total in answering thele 4 questions.

Another baseball team had a batting average of 0.290 with a standard deviation of 0.04. What is the probability that a player on that team had a batting average between 0.330 and .410? Use the 68-95-99.7 normal distribution curve.

Each side of a square is increasing at a rate of 4 cm/s. At what rate (in cm2/s) is the area of the square increasing when the area of the square is 64 cm²? cm²/s

Consider the following relation. -5x-3y = 2x + 2y Step 3 of 3: Determine the implied domain of the function found in the first step. Express your answer in interval notation. Answer

The dimensions of a triangular lot are 198 feet by 188 feet by 197 feet. If the price of such land is $3 per square foot, how much does the lot cost? The lot costs $ __ (Do not round until the final answer. Then round to the nearest cent as needed.)

In a mid-size company, the distribution of the number of phone calls answered each day by each of the 12 receptionists is bell-shaped and has a mean of 38 and a standard deviation of 5. Using the empirical rule (as presented in the book), what is the approximate percentage of daily phone calls numbering between 28 and 48? Do not enter the percent symbol. ans = %

)) An angle measures 4° less than the measure of its supplementary angle. What is the measure of each angle? ______° and _______°

Give all solutions of the nonlinear system of equations, including those with nonreal complex components. 4x² + y² =160 36x² - y² = 0 .... 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. Type an exact answer, using radicals as needed. Use integers or fractions for any numbers in the expression. Express complex numbers in terms of i. Use a comma to separate answers as needed.) B. There are infinitely many solutions. C. The solution is the empty set.

Let f(x)=2x²-3x - 2/3x² + 10x - 25 This function has: 1) A y-intercept at the point 2) x-intercepts at the point(s) 3) Vertical asymptotes at x = 4) Horizontal asymptote at y =

In a study of 600 meals served at 75 campus cafeterias, 190 had less than 10 grams of fat but not less than 350 calories; 194 had less than 350 calories b not less than 10 grams of fat; 117 had over 350 calories and over 10 grams of fat. (a) What percentage of meals had less than 10 grams of fat? Round your answer to the nearest tenth of a percent. of the meals studied, __% of them had less than 10 grams of fat. X Ś

Simplify the exponential expression: (2x³y²) ³ (3y³ w)² 72w²x9y12 -1w²x9y 17wx6y10 w²x²y6

Evaluate the function at the given values of the independent variable and simplify. f(x)=6x²-1/x² (a) f(4) (b) f(-4) (c) f(-x)

The measure of an angle is five times the measure of its complementary angle. What is the measure of each angle? ____ and ___

Accounts payable would appear on the balance sheet as a a. current liability. b. long-term liability. c. current asset. d. disclosure in the notes only.

This question: 3 point(s) possible A single die is rolled twice. The set of 36 equally likely outcomes is ((1.1), (1,2), (1,3), (1,4), (1,5), (1,6), (2,1), (2,2), (2,3), (2,4), (2,5), (2,6), (3,1), (3,2), (3,3), (3,4), (3,5), (3,6), (4,1), (4,2), (4,3), (4,4), (4,5), (4,6), (5,1), (5,2), (5,3), (5,4). (5,5), (5,6), (6,1), (6,2), (6,3), (6,4), (6,5), (6,6)). Find the probability of getting two numbers whose sum is less than 13.

Samantha goes on a road trip; she has to drive 1,311 miles and 20 hours to get to her destination but she can only drive 10 hours and 500 per day. Her rental car charges $98 per day and the car goes 22 miles and requires 1 gallon to travel 22 miles. The car can hold 16 gallon of gas and gas costs $4.60 per gallon. Now write an equation for the amount you will spend on the vehicle Rental and Gas. If C is the cost, x is the amount of days, and g is the number of gallons needed for your trip. Now include the cost of the gas in your equation - replace g.

James spent one-half of the money in his account on car repair. Then he spent a third of the remaning amount on his rent. He did not add any money to his account or use the money in his account for any other reason. If we want to know how much is left in his account now, what other information do we need? The name of his bank The starting amount of money in his account What his other expenses are James' age

Solve the following logarithmic equation. log (4x+6)= 1+ log (x - 5) Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution set is {}. (Simplify your answer. Type an exact answer. Use a comma to separate answers as needed. B. There is no solution.

The dimensions of a triangular lot are 165 feet by 49 feet by 154 feet. If the price of such land is $3 per square foot, how much does the lot cost? The lot costs $ (Do not round until the final answer. Then round to the nearest cent as needed.)

Use the echelon method to solve the following system of two equations in two unknowns. Check your answer. 7x+3y= -28 6x-3y=-24 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution is (Type an ordered pair.) B. There are infinitely many solutions. The general solution is (y), where y is any real number. C. There is no solution.

Jennifer just got a new job. The starting salary for the new job is $45,000. The job comes with a choice of two promotion packages. A promotion package is a plan that explains in writing how much Jennifer will make in salary if she continues to do a good job at the company. Jennifer has to decide which of the two promotion packages she wants. The first package increases her salary by 3% each year. The second package increases her salary by $2000 each year. Jennifer plans to stay with the company for 5 years. Which option should she choose? There is not enough information to determine which package is better. Both options would yield the same salary after 5 years. The 3% increase per year yields a higher salary after 5 years. The $2000 increase per year yields a higher salary after 5 years.

A farmer wants to build a new barn between her house and a pasture. She wants the ratio of the distance from the house to the barn and the barn to the pasture to be 7 to 1. She creates a map on a coordinate plane to represent her farm. She draws a point at (-20, 2) to represent her house and a point at (12, −6) to represent the pasture. At what point should she draw the point that represents the barn? Enter the correct answer in the boxes.

A magazine provided results from a poll of 500 adults who were asked to identify their favorite pie. Among the 500 respondents, 11% chose chocolate pie, and the margin of error was given as ±5 percentage points. Describe what is meant by the statement that "the margin of error was given as ±5 percentage points." Choose the correct answer below. A. The statement indicates that the true population percentage of people that prefer chocolate pie is in the interval 11% ± 5%. B. The statement indicates that the study is 100% -5% = 95% confident that the true population percentage of people that prefer chocolate pie is 11%. C. The statement indicates that the study is only 5% confident that the true population percentage of people that prefer chocolate pie is exactly 11%. D. The statement indicates that the interval 11% ± 5% is likely to contain the true population percentage of people that prefer chocolate pie.

Which of the following are statements? Choose each correct answer. Select all that apply: 3+7 I will go for a walk later today. Every prime number has exactly two factors. Papaya is my favorite fruit.

The city of Raleigh has 10200 registered voters. There are two candidates for city council in an upcoming election: Brown and Feliz. The day before the election, a telephone poll of 300 randomly selected registered voters was conducted. 96 said they'd vote for Brown, 187 said they'd vote for Feliz, and 17 were undecided. Give the sample statistic for the proportion of voters surveyed who said they'd vote for Brown. Note: The proportion should be a fraction or decimal, not a percent. This sample statistic suggests that we might expect of the 10200 registered voters to vote for Brown.

Rewrite the following polar equation in rectangular form. r=11/4sinθ-6cosθ

Write the set using roster notation. Do not include repeats. Use the ellipsis button, if necessary. Give at least three terms before the ellipsis and at least two terms after the ellipsis. Z= {x|x ε N and 150 <x< 400) Z=

What is the range of the secant function? A) all real numbers greater than or equal to 1 or less than or equal to -1 B) all real numbers, except odd multiples of π/2(90)⁰ C) all real numbers D) all real numbers from-1 to 1, inclusive

Assume that a procedure yields a binomial distribution with n = 83 trials and the probability of success for one trial is p = 0.86. Find the mean for this binomial distribution. (Round answer to one decimal place.) μ= Find the standard deviation for this distribution. (Round answer to two decimal places.) σ=

Suppose a right triangle contains an angle such that sin(θ) =3/7 Enter the exact values of the trig functions below: cot (θ) = sin (θ) = tan (θ) = cos(θ) = csc (θ) = sec (θ)=

One half of a cantaloupe was shared equally among 3 people. What fraction of the whole cantaloupe did each person get? Explain how you found your answer.

Let p(x) = x³ - x² + 2x - 5. p(-3) can be computed via synthetic division by filling in for the letters α through g in the table 1-1 2-5 b d f a c e g where

Given g(x) (ax3+bx2+cx+d) find the values of a, b, c and d if the function passes through the points (0, 2) and ( 1, 12); and the tangent at either point is horizontal. Indicate the interval(s) on which the function is increasing or decreasing.

Perform the indicated operation. Write the answer in scientific notation, rounding to two decimal places. Then write the rounded answer in decimal notation as well. (4.8x10³) (9.6×102) Write the answer in scientific notation, rounding to two decimal places. (4.8 x 10-3 )(9.6 x 10-2) = x 10

Find the first term, the common difference, and give a recursive formula for the arithmetic sequence. 6th term is -10; 15th term is -46 a₁ = 10, d = 4, an = an-1 + 4 a₁ = 10, d = -4, an = an-1-4 a₁ = -30, d = 4, an = an-1 + 4 a₁ = -10, d=-4, an = an-1-4

If f(x) = x² + 4, g(x) = x − 3 and h(x) = √z, then f(g(h(x))) =

Factor the trinomial completely. If the polynomial cannot be factored, say it is prime. x2+10x +25 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. x²+10x + 25 = __ (Type your answer in factored form.) B. The polynomial is prime.

The data can be modeled by the following system of linear equations. {- 5x+ 20y = 140 Equation 1 {x + 4y = 178 Equation 2 Equation 1 is modeled for the percentage of never-married American adults, y, x years after 1970 and Equation 2 is modeled for the percentage of married American adults, y, x years after 1970. Use these models to complete parts a and b. a. Determine the year, rounded to the nearest year, when the percentage of never-married adults will be the same as the percentage of married adults. For that year, approximately what percentage of Americans, rounded to the nearest percent, will belong to each group? In year the percentage of never-married adults will be the same as the percentage of married adults. For that year, approximately % percentage of Americans will belong to each group.

Karina and Perry are cleaning up litter in the park for community service hours. Karina and to Perry both claim they have covered the greatest area. Who is correct? Justify your answer using mathematical reasoning.

A graphic artist is designing a poster to advertise an upcoming event. The only restrictions regarding the poster size is that it must have a length of 7x inches and a width of 2x + 3 inches. Find a simplified expression for the area of the poster.

Find the z-score corresponding to the given value and use the z-score to determine whether the value is unusual. Consider a score to be unusual if its z-score is less than -2.00 or greater than 2.00. Round the z-score to the nearest tenth if necessary. A body temperature of 96.7° F given that human body temperatures have a mean of 98.20° F and a standard deviation of 0.62⁰.

Use the balanced equation to answer the following question. 6CUNO3 + Al2(SO4)3 -> 3Cu₂SO4 + 2AI(NO3)3 Molar mass of CUNO3 125.56 g/mol Molar mass of Al(NO3)3 213.01 g/mol How many grams of copper (I) nitrate (CUNO3) are required to produce 44.0 grams of aluminum nitrate (Al(NO3)3)? 0.619 g CUNO3 24.88 g CUNO3 77.81 g CUNO3 155.62 g CUNO3

Find the missing coefficient. (2d-6)(2d + 4) = 4d² + __ d-24 a -2 b -4 c 4 d 20

Armando's goal is to find a job that provides an income of $45,000 a year. Natalie's Furniture offers him a job paying a base salary of $28,000 a year, plus a commission of 6% of his sales. Determine what Armando's total sales will need to be for him to have a yearly income of $45,000. If Armando takes the job with Natalie's Furniture, he will need to make $ _________ in total sales in order to have a yearly income of $45,000 per year. Round your answer to the nearest cent.

The function A = Age -0.00866x models the amount in pounds of a particular radioactive material stored in a concrete vault, where x is the number of years since the material was put into the vault. If 200 pounds of the material are placed in the vault, how much time will need to pass for only 65 pounds to remain? Round to nearest whole number. A. 260 years B. 140 years C. 130 years D. 135 years

A researcher wants to learn the effects sleep deprivation has on a person's reflexes. The volunteers were broken into two separate groups. In the first group, forty volunteers were only allowed to sleep for 2 hours a night for five days in a row. In the second group, forty volunteers slept their normal sleep patterns for the same five days. On the sixth day, the researcher tested each participant on his/her reflexes. Control Group: Experimental Group: Treatment: Variable of Study:

Fill in the blank. The graphs of the tangent, cotangent, secant, and cosecant functions all have -Select--- asymptotes. horizontal vertical slant

The function f(x) is continuous over the interval [−2, 5] and has a critical point at x = 1. If f" is negative on this interval, which of the following is true? f has an absolute minimum at x = 1 f has an absolute maximum at x = 1 f has a relative minimum, but not an absolute minimum at x = 1 f has a relative maximum, but not an absolute maximum at x 1