Basic Math Questions and Answers

Arsenic is a compound that occurs naturally in very low concentrations. Arsenic blood concentrations in healthy individuals are normally distributed, with mean u 3.2 micrograms per deciliter (μg/dl) and standard deviation = 1.5 (μg/dl). Some areas are known to have naturally elevated concentrations of arsenic in the ground and water supplies. We take a random sample of adults residing in a high-arsenic area and ask whether the data provide good evidence that the mean blood arsenic concentration in this population is elevated compared with the 3.2 µg/dl mean of the population of healthy individuals. Define the parameter examined and select the appropriate null and alternative hypotheses. Ho: μ = 3.2 μg/dl; Ha: μ> 3.2 µg/dl None of the options are correct. Ho: μ = 3.2 µg/dl; Ha: μ< 3.2 μg/dl Ho: H=3.2 μg/dl; Ha: ## 3.2 μg/dl

Evaluate the expression when x= 1 and y=4. Hint: the 2x term changes to 2(1), a multiplication problem. 2x+y select one: 4 3 7 6

Let f(x)=2/(x-5) Pick the correct a and y values of the inverse function at x = 1 in the original function. A.y=-1 B.y = 1 C.X=-1/2 D.x = 1

The total cost of 2 bracelets and 3 necklaces is $15.50. The total cost of 4 bracelets and 1 necklace is $13.50. Let b represent the cost of each bracelet and n represent the cost of each necklace. This situation can be represented by the following system of equations. 2b+ 3n = 15.50 4b+ n = 13.50 What is the cost of one bracelet? $7.75 $2.50 $5.00 $3.50

Kayla's school is selling tickets to the annual dance competition. On the first day of ticket sales the school sold 3 senior citizen tickets and 5 child tickets for a total of $70. The school took in $216 on the second day by selling 12 senior citizen tickets and 12 child tickets. Find the price of a senior citizen ticket and the price of a child ticket.

A survey of salaries of employees in a business shows that the mean is greater than the median. Which conclusion is valid? The data distribution is skewed right. The data distribution is symmetric. The data distribution is constant. The data distribution is skewed left.

Suppose that your bank pays 8% interest, compounded semiannually. Use Table 12-2 of your text to find how much should be deposited now to yield an annuity payment of $700 at the END of every six months, for 6 years. $3,669.50 $6,569.55 $6,832.34 $7,394.18

However many tennis rackets the gym teacher, Mr. Marquez, buys for his class, he must buy five more than three times as many tennis balls. Rackets cost $20 each and balls cost $1.50 each. How much does Mr. Marquez spend if he needs 17 tennis rackets 5+ 3x A) $340.00 B) $352.00 C) $421.50 D) $424.00

Ming and Carlos are selling cookie dough for a school fundraiser. Customers can buy packages of chocolate chip cookie dough and packages of gingerbread cookie dough. Ming sold 8 packages of chocolate chip cookie dough and 12 packages of gingerbread cookie dough for a total of $364. Carlos sold 1 package of chocolate chip cookie dough and 4 packages of gingerbread cookie dough for a total of $93. Find the cost each of one package of chocolate chip cookie dough and one package of gingerbread cookie dough.

The commuting times of ten employees (in minutes) are listed below. Find the mode score. 65 66 67 66 67 70 67 70 71 68 67 minutes 65 minutes 66 minutes 68 minutes

According to a New York Times/CBS poll, 54% agreed that Social Security taxes should be raised if necessary to keep the system afloat, and 42% agreed that it would be a good idea to invest part of their Social Security taxes on their own. What is the largest percentage of people who could have agreed with at least one of these statements? What is the smallest percentage of people who could have agreed with at least one of these statements?

Suppose that WHAT is a square where WH=2-20x and AT = 28 + 6x. What is the length of HA? 1 22 -1 18

If two indistinguishable dice are rolled, what is the probability of the event {(4, 4), (6, 4), (1,4)}? What is the corresponding event for a pair of distinguishable dice? {(4,4), (6, 4), (1,4)} {(4, 4), (6, 4), (1, 4), (4, 1), (4, 6)} {(4, 4), (6, 6), (1, 1), (4, 1), (4, 6)} .{(6, 4), (1, 4), (4, 1), (4, 6)} {(6, 4), (1,4)}

Form the converse of each of the following statements. State whether the converse is true or false. (a) If I live in New York, then I live in the United States. (b) If two angles are congruent, then the angles are equal in measure. (c) If two angles are vertical angles, then they are congruent. (d) If two angles are complementary, then the sum of their measures is 90. (e) If two angles are adjacent, then they have the same vertex. (f) If two lines are perpendicular to the same line, then they are parallel.

What is the image of (-1, -8) after a dilation by a scale factor of 4 centered at the origin?

Use an Euler diagram to determine whether the syllogism is valid or invalid. All swimmers float. Duchess does not float. Duchess is not a swimmer. Is this syllogism valid or invalid? Valid Invalid

Claudia invests $2400 in one account and $800 in an account paying 2 % higher interest. At the end of one year she had earned $80 in interest. At what rates did she invest? $2400 invested at $800 invested at

An organization rents a commercial kitchen for an event. The cost to rent the kitchen is $375. The cost will be divided equally among the people who attend. Each person who attends will also pay $20 for expenses. Write a function that represents f(x), the total cost in dollars, for each person who attends the event, based on x, the number of people who attend. Use the on-screen keyboard to enter the function in the box below. f(x) =

An automobile manufacturer is preparing a shipment of cars and trucks on a cargo ship that can carry 21,600 tons. The cars weigh 3.6 tons each and the trucks weigh 7.5 tons each. 1. Write an equation that represents the weight constraint of a shipment. Let c be the number of cars and t be the number of trucks. 2. For one shipment, trucks are loaded first and cars are loaded afterwards. (Even though trucks are bulkier than cars, a shipment can consist of all trucks as long as it is within the weight limit.) Find the number of cars that can be shipped if the cargo already has: a. 480 trucks b. 1,500 trucks c. 2,736 trucks d.t trucks

Eric is planning to build a raised garden. He sketches a plan with a scale of 1.5 inches = 4 feet. If the garden has a width of 4 inches on the drawing, what will be the actual width of the garden?

Classify the variable as qualitative or quantitative. the weights of cases loaded onto an airport conveyor belt qualitative quantitative

Write your answers as integers or simplified fractions. (a) Write the function in vertex form. n(x) = 2x²+6x+9 Factor out the leading coefficient of the x term from the two terms containing x. The leading term within parentheses now has a coefficient of 1. n(x) =

Consider the function below. Which statement about the range of this function is true? f(x) =6/x -5 The range is all real numbers because the output of the function is not restricted The range is all real numbers except for 0 because the output of the function cannot be 0. The range is all real numbers except for 5 because the denominator of the function cannot be 0. The range is all real numbers equal to or greater than 6 because the denominator must be a positive numb

Tessa is making greeting cards, which she will sell by the box at an arts fair. She paid $20 for a booth at the fair, and the materials for each box of cards cost $3. She will sell the cards for $5 per box of cards. At some point, she will sell enough cards so that her sales cover her expenditures. How much will the sales and expenditures be? Write a system of equations, graph them, and type the solution.

14. Simplify the expression. Assume that variables represent positive real numbers. Use the properties of exponents to simplify (don't convert to radical form) and leave your answer in exponent form with no negative exponents. (27a³b-6/c9)(-1/3)

Enter the correct answer in the box. Write an expression to represent the given statement. Use n for the variable. three times the absolute value of the sum of a number and 6

A shelf has 4 books, of which 2 are of science and 2 are of social studies. In how many ways can we select 3 books from the shelf such that we have atleast one science book and atleast one social studies book ? A) 7 B) 8 C) 4 D) 6

Jolene invests her savings in two bank accounts, one paying 3 percent and the other paying 10 percent simple interest per year. She puts twice as much in the lower-yielding account because it is less risky. Her annual interest is 6880 dollars. How much did she invest at each rate? Amount invested at 3 percent interest is $ Amount invested at 10 percent interest is $

(a) Identify the horizontal asymptotes (if any). The degree of the numerator is n = The degree of the denominator is m = Since n< m, then Part: 1/5 Part 2 of 5 (b) If the graph of the function has a horizontal asymptote, determine the point (if any) where the graph crosses the horizontal asymptote. From part(a), the horizontal asymptote is y=0. set x+7/x2-5x-4 equal to

Juan was given a box of assorted chocolates for his birthday. Each night, Juan treated himself to some chocolates. Juan ate 2 chocolates each night and after 13 nights, there were 4 chocolates remaining in the box. Write an equation for C, in terms of t, representing the number of chocolates remaining in the box t days after Juan's birthday.

James invests a total of $16,500 in two accounts paying 10% and 4% annual interest, respectively. How much was invested in each account if, after one year, the total interest was $1,350.00. was invested at 10% and was invested at 4%.

Solve the problem. Franco borrows a total of $5,000 in student loan from two lenders. One charges 4.1% simple interest and the other charges 6.1% simple interest. He is not required to pay off the principal for 3 yr. However, at the end of 3 yr, he will owe a total of $825.00 for interest from both loans. How much did he borrow from each lender? Select one: a. She borrowed $1,100 at 4.1% and $3,900 at 6.1%. b. She borrowed $3,900 at 4.1% and $1,100 at 6.1%. c. She borrowed $1,500 at 4.1% and $3,500 at 6.1%. d. She borrowed $3,500 at 4.1% and $1,500 at 6.1%.

Calculate the (modeled) probability P(E) using the given information, assuming that all outcomes are equally likely. n(S) = 16, n(E) = 8 P(E) =

Diana has 400 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) =

Consider the following relation. x = 2|y| - 3 Step 1 of 2: Find four points contained in the inverse. Express your values as an integer or simplified fraction.

DIAGONALS ARE EQUAL LENGTH GIVEN: THE RECTANGLE DEFG PROVE: DF-FG CONSTRUCTION: LABEL THE QUADRILATERAL AND MARK OPPOSITE SIDES PARALLEL, THEN DRAW THE DIAGONAL EG AND DF. SINCE THIS IS A RECTANGLE INSERT SMALL SQUARE TO INDICATE RIGHT ANGLES

Find the x-intercepts and y-intercept of the following function. f(x) = (x-6) (x − 3) (4x + 4) Write your answer in coordinate pairs of the form (x, y))

A photographer takes an average of 15 pictures per session. The total number of pictures p(s) is a function of the number of sessions s. a. Identify the independent and dependent variables. b. What values of the domain and range make sense for this situation? Explain. c. Write a function to represent the total number of pictures taken. Then determine the number of pictures taken in 22 sessions.

A total of 330 children and adults attended a school play. There were 21 times as many children in attendance as there were adults. This situation is modeled by the given system of equations, where a represents the number of adults and c represents the number of children. c=21a a+c=330

A recreation the summer. On the first day of the offering, a family paid $96 for 4 pool passes and 2 gy memberships. Later that day, an individual bought a pool pass for herself, a pool pass for a friend, and 1 gym membership. She paid $72. 1. Write a system of equations that represents the relationships between pool passes, gym memberships, and the costs. Be sure to state what each variable represents.

Mr. Lings has a plank of wood 118 inches long. He cuts it into two pieces such that the longer piece is 5.5 inches longer than twice the length of the shorter piece. What is the length of the longer piece? 37.5 inches 59 inches 80.5 inches 56.25 inches

A study shows that 77% of the population was vaccinated against the Venusian flu but 2% of the vaccinated population got the flu anyway. Of the total population, 12% got this flu. Let V be the event that a person was vaccinated. Let F be the event that a person gets the flu. Compute the following values. P(V) = P(F) = P(V∩F) P(V∪F) What percentage of the population either got the vaccine or got the disease?

The polygon below was a square with 20-meter sides before a triangle was removed. What is the new perimeter of the polygon, in meters? F. 66 G. 70 H. 76 J. 78 K. 80

A doctor sees between 7 and 12 patients each day. On Mondays and Tuesdays, the appointment times are 15 minutes. On Wednesdays and Thursdays, they are 30 minutes. On Fridays, they are one hour long. The doctor works for no more than 8 hours a day. Here are some inequalities that represent this situation. 0.25 ≤ y ≤ 1 7≤x≤ 12 xy ≤8 a. What does each variable represent? b. What does the expression xy in the last inequality mean in this situation?

Diana has 120 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?

In a certain country, approximately 24 out of 100 people over the age of 12 smoke. How many smokers would you expect in a group of 550 people over the age of 12?

Find the remaining five trigonometic functions of θ. cot θ = 12/5, sin θ >0 Complete the following table. sin θ = cos θ = tan θ = csc θ = sec θ = cot θ = 12/5

In a product liability case, a company can settle out of court for a loss of $350,000, or go to trial, losing $800,000 if found guilty and nothing if found not guilty. Lawyers for the company estimate the probability of a not-guilty verdi be 0.8. Complete parts (a) through (b) below.

Solve the system. If a system has one unique solution, write the solution set. Otherwise, determine the number of solutions to the system, and determine whether the system is inconsistent, or the equation dependent. -9x - 6z = 19 x - 3y = 35 Select one: a. {(0, -18, 16)} b. {(-19/2,2,0)} c. {(-3,2,4)} d. {(-3,-38/3, 4/3,)}

Choose the correct expression equal to sin x. A. sinx= ± √1- cos x B. sinx= 1/1- cos x C. sinx=(1- cos x)(1+ cos x) D. sinx= ± √1- cos^2 x