Math Questions

Solve by completing the square. X^2 + 16x +41 = 0 Write your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.

For the given function: f(x) =x-5/(x^2 -25) A). State the domain of the given function. B). Find the value of limx→5 f(x), if it exists. Justify your answer. C). Find the value of limx,→∞ f(x), if it exists. Justify your answer.

Use DeMoivre's Theorem to find the indicated power of the complex number. Write the result in standard form. (4 + 4i)^6

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.

Vector u has initial point at (4,8) and terminal point at (-12, 14). Which are the magnitude and direction of u? a)lull = 17.088; θ = 159.444° b)|lull = 17.088; θ = 20.556° c)llull = 18.439; θ = 130.601° d)|lull = 18.439; θ = 49.399

Find an equation of the line through (3,7) and parallel to y = 4x - 7. Write the equation using function notation.

Write the equation of the exponential function represented by the table. (round each to the nearest thousandths). X 5 3 1 -1 Y 32 16 8 4

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.)

Given that p₁ (t) = 2t² + 2t - 1 and p₂ (t) = –t² – 2t + 1, which of the following polynomials in P₂ does not belong to span{p₁ , p₂}? Select one: : (A) p(t) = t² - 2t + 1 (B) p(t) = 8t² + 10t -5 (C) None of these. (D) p(t) = -7t² - 10t + 5 (E) 4t² + 2t - 1

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.)

If f(x) = (x²-2)/(x+3) where is f not differentiable? X =

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

A video on Tiktok was posted. on day 4 there was 6 views on day 10 there was 26 views make a point slope or slap-intercept equation with given data. use the equation you have the find how many views on day 0. Do you think this data is accurate.

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

Find the midpoint of the line segment joining the points corresponding to the complex numbers in the complex plane. (8 + i, 2 + 3i) (x, y) =

A hole is cut through the center of a sphere of radius 1.1. The height of the remaining spherical ring is 1.54. Find the volume of the ring. 1). 8.78453 2). 14.1372 3). 4.84905 4). 5.27667 5). 1.91232 6). 2.48271 7). 1.53111 8). 4.44518 9). 6.70882 10).2.85454

A random sample of 40 students ate at a fast-food restaurant an average of 4.3 times a week with a standard deviation of 2.1. Using the table below, find the 90% confidence interval. 3.75 to 4.85 3.65 to 4.95 3.44 to 5.16 3.80 to 4.80

Evaluate the expression ( x⁴+7x³-2)/(y⁴+2) , when x = 4 and y=-2. -39 39 38

Function r(t) gives the amount of rainfall accumulated in inches, when it is t hours after the rain started. Which statement represents the meaning of the equation r(5) = 2.5 in this situation? 2.5 hours after the rain started, it has rained 5 inches 5 days after the rain started, it has rained 2.5 inches 5 hours after the rain started, it has rained 2.5 inches It has rained 5 inches for 2.5 hours

You roll one red die and one green die. Define the random variables X be the number showing on the red die and Y be the number of dice that show the number two. a. Write down a table showing the joint probability mass function for X and Y b. Find the marginal distribution for Y. C. Find E(Y).

You are interested in estimating the the mean age of the citizens living in your community. In order to do this, you plan on constructing a confidence interval; however, you are not sure how many citizens should be included in the sample. If you want your sample estimate to be within 4 years of the actual mean with a confidence level of 96%, how many citizens should be included in your sample? Assume that the standard deviation of the ages of all the citizens in this community is 25 years.

A computer salesperson at Best Buy claims that she has a 18% chance of selling a computer when helping out a customer. If this is true and she talks to four customers before lunch, find the probability that all four will buy computers. Round your answer to at least four decimal places.

Solve by completing the square. k^2 + 18k - 25 = 0 Write your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth,

The function V(t) =33.8 – 7.4t gives the value (in thousands of dollars) of an investment after t years. Interpret the Slope in this situation. The value of this investment is_______ at a rate of_______

Solve by completing the square. p^2 - 24p = -19 Write your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.

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.

Oak Tree circumference and Age Circumference (in) 26 48 46 47 55 Age (years) 22 28 30 26 35 Which issue can be addressed by conducting a statistical analysis of the values given by the table? A relationship exists between the age of an oak tree and its circumference. An older oak tree will have smaller circumference. A younger tree will have a smaller circumference. An oak tree grown in the forest will have a bigger circumference than one grown in a field.

Let f(x) = (1 + 4x^2)(x - x^2). a)Find the derivative by using the Product Rule. f'(x) =_________ b)Find the derivative by multiplying first. f'(x) =_________ c)Do your answers agree? 1)Yes 2)No

Graph the inequality. 5x - 6y >= 0 Use the graphing tool to graph the inequality.

Use a formula to find the sum of the following arithmetic series. 1+2+3+4+ ... +34 The sum of the given arithmetic series is (Simplify your answer)

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.

Suppose a simple random sample of size n = 64 is obtained from a population that is skewed right with μ= 90 and σ = 24. (a) Describe the sampling distribution of x. (b) What is P (x̅>93)? (c) What is P (x̅≤82.5)? (d) What is P (87.9<x̅< 97.05)?

Choose all of the statistical questions. (A) How many texts did you send today? (B) When is your birthday? (C) On average, how old are college graduates? (D) How many texts a day do most high school students send?

Graph the linear equation. f(x) = 3x

The rear wheel of a tractor has a 21-in radius. Find the angle (in radians) through which a wheel rotates in 8 sec if the tractor is traveling at a speed of 24 mph, The wheel rotates through_____radians.

Confirm that the Integral Test can be applied to the series. Then use the Integral Test to determine the convergence or divergence of the series. ∑ 1/2ⁿ ∫ 1/(2^x) dx= _____ converges diverges

A college nursing program has select admissions to their program and only accepts 28% of applicants. Every year, a high school surveys 50 their students who applied and recorded who was accepted. Which of the following distributions is the best approximation of the sampling distribution of sample proportions? not enough information. skewed right. skewed left. approximately normal.

The map of a campground is shown below. Campsite C, first aid station F, and supply station S lie along a straight path. The path from the supply station to the tower, T, is perpendicular to the path from the supply station to the campsite. The length of path FS is 400 feet. The angle formed by path TF and path FS is 72º. The angle formed by path TC and path CS is 55°. Determine and state, to the nearest foot, the distance from the campsite to the tower.

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)? $▢

Use the Direct Comparison Test to determine the convergence or divergence of the series. ∞ Σ 8^n/(9^n) +7 n=0 a)converges b)diverges

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? ▢

A random sample of 318 students from a large college was asked if they plan to visit family during Thanksgiving break. Based on this random sample, a 99% confidence interval for the proportion of all students at this college who plan to visit family during Thanksgiving break is 0.78 to 0.98. Which of the following provides the correct point estimate and margin of error for this interval? a. point estimate = 0.78; margin of error = 0.98 b. point estimate = 0.1; margin of error = 0.68 c. point estimate = 0.88; margin of error = 0.1 d. None of these is correct.