Math Questions

In a chemistry class, 7 liters of a 4% silver iodide solution must be mixed with a 10% solution to get a 6% solution. How many liters of the 10% solution are needed?

A solution is prepared by dissolving 25.0 g of NaCl in 500.0 g of water. What is the molality (m) of NaCl in the solution? The density of the solution is 1.0 g/mL. A) 0.000856 B) 0.0500 C) 50.0 D) 8.56 E) 0.856

Solve and check the linear equation. 3(x-5)+16=2(x+4) What is the solution? Select the correct choice below and, if necessary, fill in the answer box to complete your choice A. The solution set is {7}. B. The solution set is {x|x is a real number}. C. The solution set is Ø.

The difference of two numbers is 3 and the sum of their squares is 45. Find the numbers. List any unique pairs of numbers that satisfy the given conditions. (Type an ordered pair, with the larger number listed first. Use a comma to separate answers as needed.)

A store sells cashews for $6.00 per pound and peanuts for $3.00 per pound. The manager decides to mix 20 pounds of peanuts with some cashews and sell the mixture for $4.00 per pound. How many pounds of cashews should be mixed with the peanuts so that the mixture will produce the same revenue as would selling the nuts separately? There should be pounds of cashews in the mixture. (Type an integer or a decimal.)

The town of Frostbite Falls records its population at the end of a given year as 70,000. After 1 year, the population increases by 2.4%. After the next year, the population again increases by 2.4%, and the pattern continues each year. What is the y-intercept of the exponential function that models this growth? (1 point) The y-intercept is (0, 0). The y-intercept is (0, 2.4). The y-intercept is (0, 70, 000). The y-intercept is (70, 000, 0)

Find the coordinates of the vertex of the graph of the function. Tell whether the vertex is a maximum or a minimum. y = -2x² -12x - 6 (3,-60); minimum (-3,48); maximum (12,-3); minimum (-3,12); maximum

If you drive 165 miles and have 15 gallons of gas remaining in your tank. Then you continue driving, and calculate that after driving 298 miles you have 8 gallons left. What is your rate?

A wireless store owner takes presale orders for a new smartphone and tablet. He gets 160 preorders for the smartphone and 190 orders for the tablet. The combined sale of the preorders is $181,250. If the price of a smartphone and a tablet together is $1,055, find the cost of one smartphone and the cost of one tablet. What is the cost of one smartphone? What is the cost of one tablet?

A landscaping company charges $40 per cubic yard of mulch plus a delivery charge of $29. Find a linear function which computes the total cost C (in dollars) to deliver x cubic yards of mulch. C(x) =

Gordon has paper strips that are all equal in length. He lines them up end to end. When the line of paper strips is 3 feet long, Gordon says there are 12 paper strips. What is the length, in feet, of one paper strip if Gordon is correct?

Match the trigonometric expression with its simplified form. cos(x)(1+ tan²(x)) sec²(x) + tan²(x) sin(x) tan(x) cos(x) + sin(x) sec(x) sec²(x) csc(x)

In a Northwest Georgia County, the speed limit is 35 miles per hour. The speeding fines are determined by the formula: F(s) = 8(s 35) + 95 where F(s) is the cost, in dollars, of the fine if a person is caught driving at a speed of s miles per hour. If a fine comes to $303, how fast in mph was the person driving?

Between two telephone poles that are 44 feet apart, there is a wire suspended in the shape of a catenary y = 15 cosh (x/15) - 8, where x and y are measured in feet and -22 ≤ x ≤ 22. What is the slope of the curve where the wire meets the left pole?

A group of scientists is studying Streptococcus lactis, which is used in the production of cheese. The initial population for a colony of bacteria is 15,000, and the population can double every 50 minutes under certain conditions. Which graph represents the bacteria's population as a function of time, in minutes? (1 point)

A random variable X can take on three possible values: -5,0, or 10. Each of these values is associated with the following probabilities: P(X=-5) = P(X= 0) = 0.4 and P(X= 10) = 0.2. What is the variance of X?

At noon, ship A is 40 nautical miles due west of ship B. Ship A is sailing west at 21 knots and ship B is sailing north at 24 knots. How fast (in knots) is the distance between the ships changing at 4 PM? (Note: 1 knot is a speed of 1 nautical mile per hour.)

The ideal gas law states that for an ideal gas PV=nRT, where P,V, and T are the pressure, volume, and absolute temperature, n is the number of moles of gas, and R is the ideal gas constant (0.0821). Suppose that currently the P = 8.0 atm (atmospheres) and is increasing at a rate of 0.15 atm/min and V = 9L and is decreasing at a rate of 0.1 L/min. Find the rate of change of T with respect to time at this instant if n = 20 mol. (Hint: You will need implicit differentiation for this problem.)

Find all values of the variable x for which the rational expression is undefined. 3x + 5 / x² + 12x + 20 The expression is undefined when x = If there is more than one answer, write it as a list, using commas to separate your answers.

New York City is a popular field trip destination. This year the senior class at High School A and the senior class at High School B both planned trips there. The senior class at High School A rented and filled 1 van and 6 buses with 324 students. High School B rented and filled 9 vans and 3 buses with 264 students. Every van had the same number of students in it as did the buses. How many students can a van carry? How many students can a bus carry?

The equation of the line L₁ is 2x + y = 10. Write down (i) the gradient of L₁; (ii) the y-intercept of L₁. 1b. [2 marks] The line L, is parallel to L, and passes through the point P(0, 3). Write down the equation of L₂. 1c. [2 marks] The line L, is parallel to L, and passes through the point P(0, 3). Find the x-coordinate of the point where L₂ crosses the x-axis.

CONCENTRATION OF A DRUG IN THE BLOODSTREAM The concen- tration of a certain drug in a patient's bloodstream thr after injection is C (t) = = 0.2t / t² + 1 mg/cm³. Determine the average concentration of the drug in the patient's bloodstream over the first 4 hr after the drug is injected.

If 1400 square centimeters of material is available to make a box with a square base and an open top, find the largest possible volume of the box. Volume= (include units)

The midpoint of AB is at (-1, -1). If A = (9,5), find B. B is:(

A solution is prepared by disserving 15.0 g of NH3 in 250.0 g of water. The density of the resulting solution is 0.974 g/mL. The molarity of NH3 in the solution is M. A) 0.00353 B) 0.882 C) 60.0 D) 3.24 E) 3.53

The number of girls varied directly as the number of boys and inversely as the number of teachers. When there were 50 girls, there were 20 teachers and 10 boys. How many boys were there when there were 10 girls and 100 teachers?

Kendrick's hair was 10 centimeters long after his last haircut, and it grows 4 centimeters every year. Kendrick last got his hair cut 8 years ago. How long is it now?

A magazine had 4000 subscribers at the end of the year 2004. The number of subscribers increased by 10% each year as compared with the previous year. Which of the following is closest to the number of subscribers at the end of the year 2007? 4400 4330 5200 5320

Determine whether each of the following probabilities is either theoretical or empirical. You played blackjack and had one blackjack out of 10 times. Then your probability of getting a blackjack is 1/10 = 10% The probability of blackjack from the first two cards is 32/663 ≈ 4.8% 1. Theoretical probability 2. Relative frequency

Suppose there is a 12.6% probability that a randomly selected person aged 20 years or older is a jogger. In addition, there is a 18.5% probability that a randomly selected person aged 20 years or older is female, given that he or she jogs. What is the probability that a randomly selected person aged 20 years or older is female and jogs? Would it be unusual to randomly select a person aged 20 years or older who is female and jogs?

The current population of a town is 10,000. If the population, P, increases by 20% each year, which equation could be used to find the population after t years? P= 10,000(0.2)t P = 10,000(1.8)t P = 10,000(0.8)t P= 10,000(1.2)t

William and Debra Pierce are celebrating their 20th anniversary by having a reception at a local reception hall. They have budgeted $4,000 for their reception. If the reception hall charges a $80 cleanup fee plus $39 per person, find the greatest number of people that they may invite and still stay within their budget.

Kyle spent more than 37 minutes swimming last night. Which of the following amounts of time could Kyle have been swimming? Select all that apply. Choose all that apply: 2350 seconds 2050 seconds 2250 seconds 2150 seconds

[8 points] Suppose you have invested $2200 at an APR of 3%. Use the Rule of 72 to estimate how long it will be until your investment reaches $4400. It will take approximately Select- years for the investment to reach $4400.

A concrete pillar has the shape of a cylinder. It has a diameter of 8 meters and a height of 6 meters. If concrete costs $106 per cubic meter, how much did the concrete cost for the pillar?

What is the freezing point (°C) of a solution prepared by dissolving 11.3 g of Ca(NO3)2 in 115 g of water? The molal freezing point depression constant for water is (Assume 100% ionization of Ca(NO3)2.) A)-3.34 B) -1.11 C) 3.34 D) 1.11 E) 0.0 B)-1.11 C) 3.34 E) 0.00 A)-3.34 D) 1.11

Which condition makes the statement below false? "If I have an alibi, then I am innocent" Hint: When is a conditional false? I do not have an alibi and I am not innocent I have an alibi and I am not innocent I have an alibi or I am innocent I do not have an alibi or I am innocent

Which segment does not belong with the other three? Explain your reasoning. radius: It is smaller than the other segments. diameter; It is the only segment through the center. tangent, It is the only segment outside the circle. chord; It is the only segment with endpoints on the circle.

The student population in the Greenville school system is increasing about 10% each year. This year there are 3120 students in the Greenville school system. If this trend continues, which of the following is closest to the number of students who will be in this school system 3 years from now? 3400 4000 4200 9400

Let C(x) = 2x + 550 and R(x) = 28x. (a) Write the profit function P(x). P(x) = (b) What is the slope m of the profit function? m= (c) What is the marginal profit MP? MP = (d) Interpret the marginal profit. Each additional unit sold increases the profit by this much. This is the smallest number of units that can be sold in order to make a profit. The profit is maximized when this many units are sold. Each additional unit sold decreases the profit by this much.

Air Transportation: A standard M-6 air cargo container is 19.8 feet long, 7 feet wide and 7.3 feet tall. For the purposes of this project, when it is completely filled each container can hold up to 21,500 cellphones, and the transportation cost is $24,000 per container. How much will it cost per cellphone to use this mode of transportation?

First find f' and then find f. f"(x) = 6x³ + 10x² + 3x +3, f'(1) = -1, f(1) = -9. f'(x) = f(x) =

A recreational softball league is considering some rule changes. In order to know how the players feel, league officials sent out a survey by email to all the players in the league. What type of sampling method did the league use? Self-selected Stratified Systematic Cluster

A pyramid shaped building is 837 ft tall with a square base that is 156 ft on each side. What is the volume of the pyramid?

John invests $2800 into an investment account described by the equation A = 2800 (e-07-t). If interest is compounded continuously, how much is in his investment account at the end of 5 years? (Round to the nearest penny)

William spends $2,500 on a bedroom furniture set on a store credit account. If he is not required to make payments for three years, but the interest is compounded yearly at 8.5%, how much interest will he owe after 3 years? $2,508.50 $693.22 $212.50

A laptop computer is purchased for $1050. After each year, the resale value decreases by 25%. What will the resale value be after 5 years? Use the calculator provided and round your answer to the nearest dollar. $0 X

Suppose that a ball is rolling down a ramp. The distance traveled by the ball is given by the function s(t), where t is the time, in seconds, after the ball is released, and s(t) is measured in feet. For the given function, find the ball's average velocity from t₁ to t₂. s(t) = 12t²; t₁ = 5, t₂ = 5.001 A. 0.12 ft/sec B. 12.012 ft/sec C. 120.012 ft/sec D. -120.012 ft/sec)

A survey of 78 men and women was conducted. Of the 78 surveyed, 41 were women, 28 were married, and 17 were married women. What is the probability of randomly selecting a woman or someone married? (Hint: Draw a Venn diagram) a. 52/78 b. 69/78 c. 41/78 d. 28/78

Use the given circumference to find the surface area of the spherical object. a pincushion with C = 24 cm The surface area of the pincushion is cm².