Math Questions

Find the first four nonzero terms in a power series expansion about x=0 for the solution to the given initial value problem. w" +5xw'-w=0; w(0)=4, w'(0) = 0

Convert the point from polar to Cartesian coordinates. Write your answer in the simplest form or rounded to the nearest hundredth.

Solve the equation 10z² - 9z+ 2 = 0. Answer: z = 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 as your answers, then enter 4,-2/3 in the box.

Consider the following matrix: Step 3 of 3: Determine the value of C11, if possible. If the element indicated is not in the matrix, state "None".

Emily and Beth each improved their yards by planting hostas and ornamental grass. They bought their supplies from the same store. Emily spent $81 on 4 hostas and 3 bunches of ornamental grass. Beth spent $233 on 13 hostas and 7 bunches of ornamental grass. Find the cost of one hosta and the cost of one bunch of ornamental grass.

Points that quit (H). In the diagram to the left, find a point whose iterations hit the diagonal in three different points and then remain fixed.

Lorena has a bag containing 5 marbles of different colors to use for a statistics experiment. She asks a person to pull out 2 marbles, one at a time, without replacing them. Then she tallies the colors chosen. How many pairs of colored marbles are there?

Find the complex zeros of the following polynomial function. Write f in factored form. f(x)=x³ +27 The complex zeros of f are Use the complex zeros to factor f f(x) =

The number of new members joining Facebook each year in the period from 2005 to the middle of 2008 can be modeled by m(t) 12t² - 20t + 10 million members per year (0 ≤ t ≤ 3.5), where t is time in years since the start of 2005.+ What was the average number of new members joining Facebook each year from the start of 2005 to the start of 2007?

Solve the absolute value equation. |2a + 10 = |3a-6 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 phone carrier claims that 90% of customers are very satisfied with the service they receive. The local paper thinks the true proportion is lower and decides to test the claim, they surveyed 100 customers using a simple random sampling. Among the sampled customers, 79% percent say they are very satisfied. What is an appropriate null and alternative hypothesis? Hx: p = 79 H.: p <.79 OH, p = 9 H.: p<.9 Hx p = .79 H₂:p>.9 Ho: p= .9 H.:p>.9

FIND THE ANGLE Measure INDICATED. assume THAT LINES WHICH appear TO BE TANGENT are TANGENT.

A company claims that 9% of the items produced on a new machine are defective. The factory will get rid of the machine if the data indicates that the proportion of defective items is more than 9%. They take a random sample of 300 items and 50 are defective. What null hypothesis is appropriate? Ho: p>0.09 Ho: p=0.17 Ho: p<0.09 Ho: p=0.09

A sample of 500 items produced on a new machine showed that 28 of them are defective. The factory will get rid of the machine if the data indicates that the proportion of defective items is significantly more than 5%. At a significance level of 10% does the factory get rid of the machine or not? No. there is not enough evidence to suggest getting rid of the machine Yes, there is enough evidence to suggest getting ride of the machine

Solve the compound inequality. -4xs-12 or 2x-262-12 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.

Solve the compound inequality. -14≤4x-6≤ 10 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.

How long will it take for $4,200 to grow to $52,500 at an interest rate of 6.1% if the interest is compounded continuously? Round the number of years to two decimal places.

Find the following information for f(x) = x²-x-12 ( (Hint: Do not forget to factor before you do anything else)

The length of human pregnancies varies normally with a mean of 266 days and a standard deviation of 16 days. What percentage of pregnancies last longer than 282 days? 32% 68% 5% 16%

Kelsey has p pennies and n nickels that add up to more than 40 cents. She has no more than 50 coins altogether. Write a system of inequalities that represents how many pennies and nickels that Kelsey could have.

A research group polls 120,000 Americans to find the mean income of people under 30 is $36,450. That $36,450 represents a proportion statstic standard deviation parameter

Every hour the number of bacteria in an experiment increase at a rate of 25%. If there were 100 bacteria present at the beginning of the experiment, how many bacteria will be present after 2 days? A. 4, 484, 155 B. 44,842 C.250 D. 156

Christine went shopping and bought each of her nine nephews a gift, either a video costing $14.95 or a CD costing $16.88. She spent $136.48 on the gifts. How many videos and how many CDs did she buy? She bought videos and CDs

A grocery store would like to determine whether or not they should continue to sell shortbread cookies. They take a random sample of 550 customers. 30% of the customers purchase shortbread cookies. Construct a 95% confidence interval to estimate the proportion of customers that purchase shortbread cookies. All conditions for confidence intervals have been met. (0.28, 0.320) (0.261, 0.338) (0.20, 0.40) (0.25, 0.35)

Solve the following quadratic expressions by factoring. First write the expressions in completely factored form. Then write the real number solutions. [Hint: Remember to use proper notation when writing the real number solutions. For example: if the solutions are a = 1 and x = 4, write x 1,4

Suppose Carolina Hurricane hockey player Martin Necas has an 18% chance of scoring every time he takes a shot at the goal. During one particular game, he gets 6 shots at the goal. Use the binomial distribution to calculate the following probabilities. a) Find the probability he makes exactly 1 goal. b) Find the probability he makes at most 2 goals c) Find the probability that he makes at least 4 goals.

Find the area of the region enclosed by f(x) and the x-axis for the given function over the specified interval. x²+3x+4 x<1

When constructing a 99% confidence interval which of the following is true? If you construct 100 intervals, 99 of the intervals will NOT contain the population proportion. When you construct the confidence interval you are sure you have created an interval that will capture the population proportion. If you construct 100 intervals, 99 of the intervals will contain the population proportion. Because the confidence level is so high, we used the population proportion to construct the confidence interval instead of the sample proportion.

Graph f(x)=x2-4 Identify any positive intervals A. The interval (-2,2) is positive OB. The intervals (-2,0) and (2,0) are positive OC. The intyerval (-4,0) is positive D. The intervals (-∞, -2) and (2, ∞ ) are positive

Use implicit differentiation to find the tangent line of the function In(y) = x ln(x) at the point (2,4).

Every year, Danielle Santos sells 120,366 cases of her Delicious Cookie Mix. It costs her $1 per year in electricity to store a case, plus she must pay annual warehouse fees of $4 per case for the maximum number of cases she will store. If it costs her $743 to set up a production run, plus $10 per case to manufacture a single case, how many production runs should she have each year to minimize her total costs?

Graph the solution of the system of linear inequalities. y |< 4x-4 y >| x+3 Use the graphing tool to graph the inequality. Click to enlarge graph

The wingspans of a common bird are normally distributed with a mean of 6 inches. Suppose that a local zoo regularly collects random samples of size 15 for this bird and then calculates the sample mean wingspan from each sample. What will be the shape of the sampling distribution of the sample mean of wingspans? skewed right skewed left not enough information appropriately normal

Find Z₁ Z₂, and if z₁ = 2( cos 45° + i sin 45°) and Z₂ = 4( cos 25° + i sin 25°). Write your answers in standard polar form with the argument in degrees.

Let VC R5 be the subspace V span {(1, 0, -3, 5, 0), (0, 2, 0, 0,3)} and let w = (-5, 0,5, -3, -4). (a) Find the orthogonal projection of w onto V, using exact values in your answer. (b) Find the component of w orthogonal to V using exact values.

The number of books in a small library increases according to the function B = 7,500 e 0.05t, where t is measured in years. How many books will the library have after 4 years? Round to the nearest book. A. 7,885 books B. 11,887 books C. 9,161 books D. 6,140 books

Given the function g(x) = 6x³ + 45x² + 72x, find the first derivative, g'(x) = 0 when a = 4, that is, g'(-4) = 0. Now, we want to know whether there is a local minimum or local maximum at z = 4, so we will use the second derivative test. Find the second derivative, g''(x). g''(x) = Evaluate g''(-4). g''(-4)= Based on the sign of this number, does this mean the graph of g(x) is concave up or concave down at a = - 4? At = - 4 the graph of g(x) is concave Based on the concavity of g(x) at x = At z = - 4 there is a local

Let B = be any 2 x 2 matrix. and a such that (i) Show that there are real numbers as a scalar multiple of a unit vector, and hence find an expression for u in terms of a and c.

Graph the solution of the system of linear inequalities. 5x-2y ≤ 10 y ≤ -3 Use the graphing tool to graph the solution. Click to enlarge graph the solution.

Consider the integral which of the following is the resulting integral. You do not need to evaluate this integral.

Graph the solution of the system of linear inequalities. x ≥ 5y x+4y ≤ 4

An arrow is shot from a bow at a rate of 160 mph at an angle of 25 from the horizontal. The bow sits on a platform 5 feet above the ground. Step 3 of 6: How high is the arrow 5 seconds after leaving the bow? Round your answer to the nearest integer.

Benji has $3,100 in a savings account which earns 7% interest compounded quarterly. He made no additional withdrawals or deposits. What was the amount in the account after two quarters? $3,209.45 $3,219.55 $3,199.44 $3,290.54

Solve the compound inequality. 2(x-4) <4 orx+6>11 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.

Solve the compound inequality. 5<x-15<8 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 fractions for any numbers in the expression.) B. The solution set is Ø.

A manufacturer has a steady annual demand for 16,000 cases of sugar. It costs $10 to store 1 case for 1 year, $32 in set up cost to produce each batch, and $18 to produce each case. Find the number of batches of sugar that should be manufactured annually if 320 cases of sugar are produced in each batch.

Solve the compound inequality. -3x≤-12 or 3x-302 - 12 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.

Graph the solutions of the given system of linear inequalities. y<5x -5 y≤x+4

Graph the following inequality. y≥1 Use the graphing tool to graph the inequality.

Using a significance level of 5%, what conclusion can we make? Fail to reject the null hypothesis Accept the alternative hypothesis Reject the null hypothesis not enough information