Basic Math Questions and Answers

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.

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.

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=___________

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

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

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

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

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)

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...

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:

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

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?

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.

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 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.

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

The Aquarium charges $22 for adult admission and $9 for each child. The Aquarium bill for a school field trip was $452. a)Write a linear equation in general form to represent this situation. Let C represent the number of children and A represent the number of adults attending the field trip. Equation:______________ b)If 38 children attended the field trip, how many adults were there? There were__________adults.

The equation y = 123.1(1.065)^x models the number of college students (in thousands) who studied abroad each year from 1998 through 2013. In this equation, y is the number of students from a certain country studying abroad (in thousands) and x represents the number of years after 1998. a. Estimate the number of students studying abroad in 2005. b. Assuming this equation continues to be valid in the future, use this equation to predict the number of students studying abroad in 2018. a. The number of students studying abroad in 2005 is _______ thousand. (Round to the nearest tenth as needed.) b. The number of students studying abroad in 2018 is _______ thousand (Round to the nearest tenth as needed.)

Solve the equation: p² + 16p + 60 = 0 p = Write your answers as a list of integers or simplified 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. -

Determine the unit mark for Parker is he earned 19/30 on an assignment that has a 15% weight for the course, 6.5/10 on a project that has a 10% weight for the course, 34/50 on a midterm test that has a 20% weight for the course, 25/28 on an assignment that has a 15% weight for the course, 18/20 on a project that has a 10% weight for the course, and 85/105 on the final exam that has a 30% weight for the course.

The following table gives the approximate energy values of some foods and the approximate energy consumption of some activities in kilojoules (kJ). Determine how long it would take for you to use up the energy from the following. Energy Value, Food (kJ) Energy Consumption, Activity (kJ/min) chocolate milkshake 2000 walking 25 fried egg 470 cycling 35 hamburger 1570 swimming 50 strawberry shortcake 1420 running 80 glass of skim milk 340 It would take _______ minutes to use up the energy from a fried egg by cycling. (Round to three decimal places as needed.) It would take _____ minutes to use up the energy from a chocolate milkshake by walking. (Round to three decimal places as needed.) It would take ▢ minutes to use up the energy from a strawberry Shortcake by running. (Round to three decimal places as needed.)

Reena collects postage stamps to create an album. The album has 14 pages. The first five pages of her stamp album holds 4 stamps per page. The remaining pages of the album have 14 stamps per page. Which equation can be used to find the total number of stamps (n)? O n= (5 x 14) + (14 x 14) O n=(14 x 4) + (14 x 9) O n= (5 x 4) + (9 x 14)

How much money would Karl have in his account after five years if he started with $200, deposits $200 per year, and earns 3 percent interest, compounded annually? a) $1,325.54 b)$1,200 c)$400 d)$13,255.40

Carolina is making punch for a party. • She made 6 bowls of punch. • Each bowl holds 2½ gallons of punch. • 1 gallon is equal to 4 quarts. She thinks each person will drink about 1 quart of punch. How many people will the 6 bowls of punch serve? [1 gallon (gal) = 4 quarts (qt)] A. 10 B. 30 C. 45 D. 60

300 juniors at Central High School took the ACT last year. The scores were distributed normally with a mean of 24 and a standard deviation of 4. How many students scored between 16 and 32? 204 299 285 150

Two different courier companies charge 3x + 5 and 2x + 7, respectively where x represents the weight of the parcel in pounds. Find the weight for which the charges are same in both couriers. a)X= 2 lb b)X=3 lb c)X= 0.075 lb

If the alternator-to-engine drive ratio is 2.55 to 1, what rpm will the alternator have when the engine is idling at 400 rpm? Hint: Use a direct proportion. The alternator will have rpm when the engine is idling at 400 rpm. (Type a whole number or a decimal.)

A concession stand sold pizza slices, ice cream cones, and tacos at a basketball game. Pizza slices were sold for $2.75, ice cream cones were sold for $2.25, and tacos were sold for $1.75. The total number of pizza slices, ice cream cones, and tacos sold was 121, and the total amount of money from these items was $260.75. If $87.50 was made just from selling tacos, how many ice cream cones were sold?

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

Solve the compound inequality. -x+5 > 6 and 5+2x≤-1 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution set is ___. (Type your answer in interval notation. Simplify your answer. Use integers or tractions for any numbers in the expression.) B. The solution set is Ø.

If two people are selected at random, find the probability that they were born in the same month. Write your answer as a fraction in simplest terms.

Use the compound interest formula, A(t) = P(1+r/n)ⁿᵗ An account is opened with an initialy deposit of $10,500 and earns 3.8% interest compounded semi-annually. Round all answers to the nearest dollar. a. What will the account be worth in 30 years? $▢ b. What if the interest were compounding monthly? $▢ c. What if the interest were compounded daily (assume 365 days in a year)? $▢

Two hundred college students were recently asked if they participated in music or sports. 127 students said they were involved in music. 78 students said they participated in both activities, while 20 students did not participate in either. How many students participated in only music? ▢ How many students participated in only sports? ▢ How many students were involved in music or sports? ▢

Which property is used to compare two linear functions? 1. All of the choices 2. Rate of change 3. Slope

Identify the dependent and independent variable in y = 12x - 30. a)Dependent variable: x and Independent variable: x b)Dependent variable: x and Independent variable: y c)Dependent variable y and Independent variable: x

In order to estimate the population proportion of students at Sandy Beach High that are going to attend prom a random sample of 200 students was taken. The resulting confidence interval was (73%, 80%). Someone in your class believes that 90% of the students will attend prom. Based on the confidence interval constructed, what would you say to your classmate? They are most likely correct because 90% is not in the confidence interval. They are most likely correct because 90% is in the confidence interval. They are most likely incorrect because 90% is not in the confidence interval. They are most likely incorrect because 90% is in the confidence interval.

– 7x – 2y = 37 – 8x + 8y = 40 Is ( – 5, – 1) a solution to the first equation? True False Is (– 5, – 1) a solution to the second equation? True False Is ( – 5, – 1) a solution to the system of equations above? True False

Solve the equation by factoring: 2w(3w + 1) = 3w + 1. 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 and as your answers, then enter 4,-2/3 in the box.

Suppose f(c) has zeros at x = -2, c = 4, x = 6 and a y-intercept of 11. In addition, f(x) has the following long-run behavior: as x --> ∓∞, y + ∞. Find the formula for the polynomial f(x) which has the minimum possible degree. f(x) =