Math Questions

1. Mr. Tyler is 6 feet tall. His youngest son Sean is 4 feet tall. Which equation correctly represents the relationship between Mr. Tyler's height (H) and Sean's height (h)? A. H = 4/6 × h B. H = 6/1 × h C. h = 4/6 × H D. h = 1/4 × H

Whenever Nicole rents a movie from iTunes, the probability that it will be a comedy is 52%. Of the next seven movies she rents, what is the probability that she rents no more than two comedies?

A CBS News/New York Times poll found that 350 out of 796 randomly selected adults said they would travel to outer space in their lifetime, given the chance. Estimate the upper bound limit of the true proportion of adults who would like to travel to outer space with 99% confidence. Round your answer to 3 decimal places.

An advertisement for a video game claims that 75% of people who own the game have completed the game's final quest. Avery believes that is not an accurate proportion of the game's owners. She surveys 120 people who own the game and finds that 78 of them have completed the final quest. Calculate the p-value that would be used in a significance test for this situation. ○ The p-value is 0.2144. ○ The p-value is 0.00570. ○ The p-value is 0.0114. ○ The p-value is 0.01072.

A paper manufacturer produces packs of colored paper. The machines are set to dye 20% of the paper pink. The manager suspects the machines are producing too many pink pieces of paper. He randomly samples 100 pieces of paper and finds that 25 of them are pink. Assume that all three conditions to perform a significance test for a z-statistic are met. Calculate the Z-statistic that would be used in the significance test for this situation. ○ z = 1.15 ○ z = 1.25 ○ z = -1.25 ○ z = -1.15

Sketch the graph of the quadratic function and the axis of symmetry. State the vertex, and give the equation for the axis of symmetry. h(x) = (x + 3)^2 Use the graphing tool to graph the function as a solid curve and the axis of symmetry as a dashed line. Click to enlarge graph. The vertex is ____. (Type an ordered pair.) The axis of symmetry is _______. (Type an equation.)

Which step is necessary in verifying that InB + 3 = -3t is a solution to dB/dt=-3B? a)e^InB + e^3 = e^-3t b)1/B (dB/dt)=-3 c) edB = -3dt d)∫(InB+3)dB = ∫-3t dt

Graph the linear equation; f(x) =8x

Alyssa was given a gift card for a coffee a shop. Each morning, Alyssa uses the card to buy one cup of coffee. Let A represent the amount money remaining on the card after buying x cups of coffee. The table below has select values showing the linear relationship between x and A. Determine the original amount of money on the gift card. X A 2 15.00 4 10.00 6 5.00

A bean bag is randomly thrown onto the square table top shown and does not touch a line. Determine the probability that the bean bag lands on a green area. P(green)=__________

In the following game, decide on the payoff when the strategy (3,1) is used. Assume that the payoff amounts given are in dollars. 1 2 3 1 [12 -11 0] 2 [7 -10 8] 3[- 6 3 11] When the strategy (3,1) is used, the payoff is $

A 4-kg object's position, p, is changing with respect to time, t. The object experiences a force, F, that is proportional to the object's acceleration times its mass. What differential equation represents this dynamic? A. F = 4p' B. F = 4p" C. F = 4v D. F = 4t

If a cup of coffee has temperature 92°C in a room where the ambient air temperature is 21°C, then, according to Newton's Law of Cooling, the temperature of the coffee after t minutes is T(t) = 21 + 71e^-t /45. What is the average temperature of the coffee during the first 32 minutes?

A father and his son can clean the house together in 2 hours. When the son works alone, it takes him an hour longer to clean than it takes his dad alone. Find how long it takes the son to clean alone. It takes the son ____ hours to clean alone. (Round to the nearest tenth.)

Fill in the blank __________Theorem states that if z = r(cosθ + isinθ) is a complex number and n is a positive integer, then z^n = r^n (cos nθ + i sin nθ).

A pyramid-shaped grain storage funnel is 8 m wide, 11 m long and has a height of 12 m. (a) Draw a diagram of the funnel and label the dimensions. (b) What is the volume of the funnel? (c) If the funnel is 50% full, how many litres of grain is it holding?

The expression lim (3 + h)² - 9/h h->0 represents which of the following? (A) The derivative of f(x) = x² – 3x at x = 3. (B) The derivative of f(x) = x² at x = 3. (C) The derivative of f(x) = x² - 9 at x = 0. (D) The derivative of f(x) = x² at x = 0.

Graph the linear equation. f(x) = -3x + 4 Use the graphing tool to graph the linear equation.

The differential equation y' = 3x will produce which of the following? A. A slope field with parallel tangents along the diagonal B. A slope field that does not have rows or columns of parallel tangents C. A slope field with columns of parallel tangents D. A slope field with rows of parallel tangents

The average daily volume of a computer stock in 2011 was u = 35.1 million shares, according to a reliable source. A stock analyst believes that the stock volume in 2018 is different from the 2011 level. Based on a random sample of 30 trading days in 2018, he finds the sample mean to be 32.1 million shares with a standard deviation of s = 12.3 million shares. Test the hypotheses by constructing a 95% confidence interval. Complete parts (a) through (c) below. (a) State the hypotheses for the test. Ho ____ ______35.1 million shares H1_____ _______35,1 million shares (b) Construct a 95% confidence interval about the sample mean of stocks traded in 2018 With 95% confidence, the mean stock volume in 2018 is between_____ million shares and____ million shares. (Round to three decimal places as needed).

Given the vector u defined by the points: (3,4), (8, -7). Find the component form of the vector. Assume the first point is the initial point and the second point is the terminal point.

Consider the following first order initial value problem: dy/dt= = 2y +t, y(0) = 0 (a) Compute the laplace transform to the both sides of the equation. (b) Substitute the initial conditions and solve for the Laplace transform of the equation. (c) Find the solution by taking inverse Laplace transform.

The function f(t) = 8000(0.15)^24t represents the change in a quantity over t days. What does the constant 0.15 reveal about the rate of change of the quantity? The function is____exponentially at a rate of____ % every

Use the English and metric equivalents to the right, along with dimensional analysis, to convert the given measurement to the unit indicated. 169 km to mi Approximate English and Metric Equivalents 1 in. = 2.54 cm 1 ft = 30.48 cm 1 yd ≈ 0.9 m 1 mi ≈ 1.6 km

Fill in the blank with an appropriate word, phrase, or symbol(s). A controlled operation that yields a set of results is called a(n)_________.

Decide if regression should be done at the alpha 0.05 level, then use that information to find the number of ice creams sold when the temp = 51°F. temp (F) 33 49 52 60 63 71 80 Ice creams 5 11 19 35 34 46 59 a). = 25.8 ice creams b.) = 21.0 ice creams C.) = 31.6 ice creams d.) = 19.7 ice creams .

A concession stand sold hamburgers, salted pretzels, and hot dogs at a baseball game. Hamburgers were sold for $3.50, salted pretzels were sold for $2.50, and hot dogs were sold for $1.25. The total number of hamburgers, salted pretzels, and hot dogs sold was 135, and the total amount of money from these items was $297.25. If $140.00 was made just from selling salted pretzels, how many hot dogs were sold?

Each individual letter of the word Oklahoma is placed on a piece of paper, and all 8 pieces of paper are placed in a hat. If one letter is selected at random from the hat, find the probability that a vowel is selected. P (vowel) = ___________

Solve the equation 10z^2 + 11z – 6 = 0. Write your answers as a list of integers or reduced fractions, with your answers separated by (a) comma(s). For example, if you get 4 and -2/3 as your answers, then enter 4,-2/3 in the box.

The Malones' electric bills for January through June, 2006, were $95.37, $106.51, $87.73, $83.07, $76.57, and $68.28. For these bills, determine the (a) mean and (b) median. a) The mean is $ 86.26. (Round to the nearest cent as needed.) b) The median is $ 85.2. (Round to the nearest cent as needed.)

Check off the vocabulary words that you understand. □ complex fraction □ least common denominator (LCD) Rate how well you can add and subtract rational expressions.

Consider the differential equation dy/dx=x^2(y + 1). Sketch a slope field for the given differential equation on your paper for the domain (-3, 3) and the range (-3, 3). A): List five coordinates and the corresponding slope of their segments. B): Using the slope field that you drew, describe all points in the xy-plane for which the slopes are negative.

Bob is thinking deeply about the following equation: y= ax^2 + c He comes to the conclusion that if 'a and 'c' have the same sign that there will be no x-intercepts. His is conclusion correct? If yes, justify his reasoning. If no, provide a counterexample.

Information about △ABC is given. Determine all remaining information about the triangle. Answers must be accurate to three decimal places. If there are multiple triangles with the given information, determine all of them. If a triangle cannot be solved, explain why not. a) A = 60°2 a = 52 b= 6 b) a = 3, b = 8, c = 50°

For the game, if a saddle point exists, find the strategies producing it and the value of the game. Identify whether the game is strictly determined [-2 1] [9 4] Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. A). The saddle point(s) is/are produced by the strategies described by the ordered pair(s)____ The value of the game is_____ B). There is no saddle point

Shara collected two different data sets and labeled them data set Sand data set T. Data set S has a correlation coefficient of -0.91, and data set T has a correlation coefficient of 0.89. A) Which data set has a stronger linear relationship? B): How do you know this?

Consider a Poisson process with rate λ = 2 and let T be the time of the first arrival. a) Find the conditional PDF of T given that the second arrival came before time t = 1. Enter an expression in terms of λ and t. b) Find the conditional PDF of T given that the third arrival comes exactly at time t =1.

Determine whether the improper integral diverges or converges. ∞ ∫ x^2(e^-x)dx 0 a) converges b) diverges Evaluate the integral if it converges. (If the quantity diverges, enter DIVERGES.)

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.