Math Questions

An existing inventory for a test measuring self-esteem indicates that the scores have a standard deviation of 11. A psychologist gave the self-esteem test to a random sample of 150 individuals, and their mean score was 63. Construct a 95% confidence interval for the true mean of all test scores. Then give its lower limit and upper limit.

Graph the equation y=x+5. Let x = -3, -2, -1, 0, 1, 2, and 3. Find the following y-values. Then choose the correct graph of the equation to the right.

Suppose an open box with a rectangular base is to be constructed from a rectangular piece of cardboard 12 inches wide and 24 inches long by cutting congruent squares from each corner and then bending up the sides. What is the maximum possible volume of the box, in cubic inches?

Olivia's volleyball team is going on a trip to play in a tournament in Oregon. The 12 players all need to fundraise to pay for their trip. Each player needs to pay $20 for the bus plus some amount for food. The total cost of the entire trip for all 12 is $540. How much extra does each player need to fundraise for food? * (3 Points) 1 Point: equation 1 Point: solution to written equation 1 Point: solution is labeled with context

A prescription medication has a half-life of 6 hours and the recommended dosage of the medicine is 2 pills. If each pill is 500 mg, how long will it take for the amount of the medicine to remain in the body to be 200 mg if a person takes the recommended dosage?

Two factory plants are making TV panels. Yesterday, Plant A produced 8000 panels. Ten percent of the panels from Plant A and 3% of the panels from Plant B were defective. How many panels did Plant B produce, if the overall percentage of defective panels from the two plants was 7%? Number of panels produced by Plant B:

Directions: Find each sum or difference. Answers must be in standard form. 11. (x²-4x + 3) + (3x²-3x - 5) 12. (8r^2 -12r + 4)-(3r²+5r-1) 13. (2m-3+ 7m²)-(3-9m² -2m) 14. (7p² + 3p)-(5p² + 4) 15. (3a²-a + 3) + (4a²-5) 16. (5w³-w+ 2u² + 4) + (3w²+1-4w) 17. (2x² +3y^2-2z^2) — (x² − y² − z²) + (4x² − 3y²) 18. (12+ 8k³ + 3k-4k²) + (5k³ + 15-k + 2k²) 19. Find the sum of (2x² - 6x-2) and (x² + 4x). 20. Subtract (-a² - 5ab + 3b²) from (3a²- 2ab + 3b²).

For each of the following, identify the amplitude, period, horizontal (phase) shift, vertical shift, domain, range, y-intercept and any x-intercepts. f(x) = 4 - 2 sin 3 (x - 2π) Amplitude: Period: Hor. Shift: Vert Shift: Domain: Range: y-int: x-int:

A contractor finds that Crew A takes 6 1/2 - hours to construct a retaining wall and Crew B can do the same job in 5 1/2 hours. If Crew A and Crew B work together, how long will it take them to construct the retaining wall? a) Let h= the time to complete the job. Write the equation you would use to solve this problem, b) Now solve your equation. Give your answer first as a reduced fraction, and then a decimal rounded to 3 places. Working together, the two crews will construct the wall in which as a decimal is hours. hours (fraction),

Maria read in the newspaper that 59% of voters in her city were voting "no" on a local initiative measure. The newspaper article stated that 772 people were originally polled. What is the margin of error for this survey? 4.6% 2.6% 3.6% 1.6%

Find the exact value of cos π/3, expressing your answer with a rational denominator.

In testing their recording devices, a team of seismologists positioned two of the devices 2000 feet apart, with the device at point A to the west of the device at point B. At a point between the devices and 200 feet from point B, a small amount of explosive was detonated. A second explosion is to be carried out at a point directly north of point B. How far north should the site of the second explosion be chosen so it is directly north of point B? Imagine what this would look like on the coordinate plane ... what do we know about the graph and/or equation of this hyperbola?

Out of 75 students, 45 are taking Algebra 2 and 32 are taking Chemistry. Sixteen students are taking both Algebra 2 and Chemistry. If a student is chosen at random, what is the probability that the student is taking Algebra 2 but not Chemistry?

Evaluate the integral using the fundamental theorem of calculus when appropriate (your answer should be exact. Make sure you use C if needed.): f(x) = ∫(4x^2 –3x+4+3x-¹-x-^2) da

Sam bought three folders and one notebook from the office store and spent $8.25. He went back the next day and bought two more folders and three more notebooks and spent $16. If the prices did not change between the days, find the cost of one folder.

Mrs. Browne wants to start a college fund for her newest addition, Wade. She makes a payment of $50 at the end of each month into an ordinary annuity account paying a 3.5% annual interest rate, compounded monthly. How much will be in the account after 18 years and Wade is ready to go to college?

Ith (x) = x² + 16x 10 on the interval [-4, 6]: Apply the mean value theorem to find the value of C in the interval (-4, 6) such that h' (c) equals the average rate of change of h(x) on the interval.

In 2017, the number of students enrolled in a high school was 232. It is estimated that the student population will increase by 3% every year. Estimate the number of students that will be enrolled in 2027.

A new dot.com business began with an initial stock offering of $3,000. At the end of the first year, the management conducted a complete top to bottom audit of the company's profits. The audit revealed that the company profit follows the graph of the function P (t) = t³ - ² +t+ 3, in thousands of dollars where t is months. During what month did the profit change at the same rate as the average rate of change of the profit during the first six months? Note: Convert the month to its corresponding number when answering (e.g., 1 for January, 2 for February, and so on). Round your answer up to the nearest whole number.

Fermium-257 has a half-life of 100 days. A sample has a mass of 60 mg initially. I) What is the formula for finding the amount remaining after t days. II) When will there only be 5 mg remaining? A) y = 60(2) -t 100; 248 days B) y = 60 e -t 100; 248 days C) y = 60(2) -t 100; 358 days D) y = 60e -t 100; 358 days

A 28 ft ladder leans against a wall so that the base of the ladder is 5 ft away from the base of the wall. How far up the wall does the ladder reach? Round to the nearest tenth. Enter your answer, as a decimal, in the box.

Every day, Carmen walks to the bus stop and the amount of time she will have to wait for the bus is between 0 and 12 minutes, with all times being equally likely (i.e., a uniform distribution). This means that the mean wait time is 6 minutes, with a variance of 12 minutes. What is the probability that her total wait time over the course of 60 days is less than 6.5 hours?

Kristina needs to mix a 10% alcohol solution with a 60% alcohol solution to create 100 millileters of a 10% solution. How many millileters of each solution must Kristina use? Answer: Kristina must mix millileters of 10% solution and millileters of 60% solution.

Ms. Kelly is organizing a board game day. She has 7 different board games. She needs to organize the order that the games are played that day. S={Apples To Apples, Balderdash, Carcassonne, Dominion, Terraforming Mars, Wingspan, Galaxy Trucker} a) In how many ways can she play all 7 games? b) In how many ways can she play just 3 of the games? c) In how many ways can she play just 3 games if the last one must be Terraforming Mars because that's everyone's favourite? d) In how many ways can she play just 3 games if Terraforming Mars must be played at some point that day because that's everyone's favourite? e) Apple to Apples and Balderdash are both considered "party" games, in how many ways can all the games be played if Apples to Apples and Balderdash are not played one right after the other?

Choose one of the following questions to answer Level 4- A new supermarket was launched in Kitchener. On opening day customers came to the store and were asked how they heard about the grand opening. They were informed via the following methods: - 119 received flyers in the mail - 131 learned about the launch through the internet - 140 heard about the launch through advertisements on television - 41 were aware of the launch through flyers and the internet - 35 came to know of it through flyers and television - 16 heard about it from all three sources a) Construct a Venn diagram. b) Calculate n(S), what does that mean in the context of this question? c) Calculate n(F ∪ T), what does that mean in the context of this question? Level+4 A survey collects data from people about what pets they like. The choices were cats, dogs, and birds. The results were as follows: - 95 like cats - 165 like dogs -93 like birds - 75 like cats and dogs -20 like dogs and birds - 18 like cats and birds -10 like none of those choices There are 265 people surveyed a) Construct a Venn diagram. b) Calculate n(D ∩ C ∩ B), what does that mean in the context of this question? c) Calculate n(C'), what does that mean in the context of this question?

Hannah can paint a room in 20 hours. Destiny can paint the same room in 12 hours. How long does it take for both Hannah and Destiny to paint the room it they are working together.

A town's population has been growing linearly. In 2003, the population was 57000, and the population has been growing by 700 people each year. Write an equation for the population years after 2003. P(x) =

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)