Math Questions

A baby weighs 14 pounds at 5 months and 21 pounds at 10 months. Assume the relationship is linear and that the baby gains the same number of pounds per month. Let x represent the number of months and y represent the weight in pounds. Write an equation in slope-intercept form that models the situation.

An aircraft (at Z) is spotted by two observers (at X and Y) who are L=1000 feet apart. As the airplane passes over the line joining them, each observer takes a sighting of the angle of elevation to the plane, as indicated in the figure. If A=25°, and B=45°, how high is the airplane? The elevation of the plane is approximately feet. (Do not round until the final answer. Then round to two decimal places as needed.)

Which of the following would not be a correct description of slope? a. rise/run b. The height that a line rises. c. How gently or steeply something is slanted. d. The change in vertical distance compared to the change in horizontal distance.

A grocery store sells a bag of 7 oranges for $4.48. If Khloe spent $6.40 on did she buy? oranges, how many did she buy?

A car is purchased for $23,500. After each year, the resale value decreases by 35%. What will the resale value be after 4 years? Use the calculator provided and round your answer to the nearest dollar.

Suppose there is a 22.1% probability that a randomly selected person aged 30 years or older is a jogger. In addition, there is a 25.8% probability that a randomly selected person aged 30 years or older is male, given that he or she jogs. What is the probability that a randomly selected person aged 30 years or older is male and jogs? Would it be unusual to randomly select a person aged 30 years or older who is male and jogs? The probability that a randomly selected person aged 30 years or older is male and jogs is 0.057 (Round to three decimal places as needed.). Would it be unusual? Yes No No

24. A shelf that is 18 cm wide is held up by a triangular bracket. The bracket makes a 37.5° angle with the bottom of the shelf. What is the height of the bracket? Hint: draw a diagram and think about trigonometry a.13.81 cm b.12.94 cm c.10.96 cm d.14.28 cm

How long is a ladder that reaches a height of 4.36 m up a wall and rests on the wall at an angle of elevation of 74°? Hint: Be sure to draw a picture a. 4.54 m b. 15.82 m c. 3.24 m d. 1.25 m

13. Jacob gets paid $21.25 an hour to work on a surveying team, plus $40.00 per day for food. Which of the following equations shows his earnings for a workday that is h hours long? a. earnings = 21.25h + 40 b. earnings = 21.25 × 40 c. earnings (21.25 +40)h d. earnings = 40h + 21.25

Between two telephone poles that are 40 feet apart, there is a wire suspended in the shape of a catenary y = 25 cosh (x/25) - 5, where and y are measured in feet and -20 ≤ x ≤ 20. What is the slope of the curve where the wire meets the right pole? Note: Round to the nearest thousanth.

If you invest $23010.00 at an interest rate of 2.90% per year compounded semi-annually, what will the total value of your investment be after 9 years? Hint: use compound interest formula a. $29801.62 b. $29816.29 C. $23853.03 d. $35779.54

The rectangular coordinates of a point are given. Find polar coordinates (r,0) of this point with 8 expressed in radians. Let r>0 and -2л<0<2л. (-10,10) One possibility for the polar coordinates of this point is. (Simplify your answer. Type an ordered pair. Type your answer in radians. Type exact answers, using as needed. Use integers or fractions for any numbers in the expression.)

The weight of 3-month-old Bullmastiffs follow approximately a normal distribution with a mean of 120 pounds and a variance of 25 pounds. If your 3-month-old Bullmastiff is 130 pounds, how many standard deviations above or below the mean is your pet (i.e., find the Z-score)? 0 1 1.5 2

CREDIT CARDS IN CHINA The total number of credit cards issued in China from 2009 through 2012 grew at the rate of r(t) = 153e0.21t (1 ≤1≤4) million/year, where (t = 1) corresponds to 2009. What was the average growth in the number of credit cards issued in China for the period under consideration?

An amount of $32,000 is borrowed for 11 years at 3.75% interest, compounded annually. If the loan is paid in full at the end of that period, how much must be paid back? Use the calculator provided and round your answer to the nearest dollar.

A certain forest covers an area of 2300 km. Suppose that each year this area decreases by 6.5%. What will the area be after 14 years? Use the calculator provided and round your answer to the nearest square kilometer.

Anthony invested $36,000 in an account paying an interest rate of 5.3% compounded quarterly. Assuming no deposits or withdrawals are made, how long would it take, to the nearest year, for the value of the account to reach $51,800?

The weight of golden hamsters follows a normal distribution with a mean weight of 4.3 ounces and a standard deviation of 0.25. What is the probability that a randomly chosen hamster weighs less than 4.6 ounces? 0.655 0.788 0.885 0.945

Consult the figure. To find the length of the span of a proposed ski lift from A to B, a surveyor measures the angle DAB to B be 25 and then walks off a distance of L= 1800 feet to C and measures the angle ACB to be 15°. What is the distance from A to B? The distance from A to B is approximately feet. (Do not round until the final answer. Then round to two decimal places as needed.) D

What are the coordinates of the point on the directed line segment from (-8, 1) (2, -7) that partitions the segment into a ratio of 3 to 1?

A perfectly spherical balloon is being inflated such that the radius of the balloon is increasing linearly at a rate of 0.3 inches per t seconds. What would be an expression for calculating the volume of the balloon att seconds? (Remember: Volume of a sphere: V = (4πr3/3)

6. Kelly works two jobs. She usually works at a retail store for 7 hours during the day and is paid $12 per hour by the store. In the evening she works at a restaurant as a manager for 5 hours and is paid $20 per hour. How much does she make on average per hour for the day?

A seventh grade English Language Arts teacher wants to order books for all the seventh grade classes. He wants to determine the favorite type of book among the seventh grade students. Which sample would be the most appropriate for this survey? A 7 girls in each of his classes B every fifth student in the seventh grade C 1 out of 7 students in his middle school D all of the boys in one of his seventh grade classes

8. Sketch a graph on the slope field through (-3,-1) and a point of your choice. Clearly indicate which point you chose.

Select all the correct answers. If the measure of angle is θ 7π/4, which statements are true? sin(θ)= - √2/2 cos(θ)= - √2/2 tan(θ)= -1 The measure of the reference angle is 60°. The measure of the reference angle is 30°. The measure of the reference angle is 45°

The revenue achieved by selling x graphing calculators is figured to be x(45-0.2x) dollars. The cost of each calculator is $33. How many graphing calculators must be sold to make a profit (revenue - cost) of at least $160? A. Between 5 and 25 calculators B. Between 20 and 40 calculators C. Between 22 and 38 calculators D. Between 21 and 19 calculators

Find the weighted average. Round all values to one decimal place. 5. A new cars salesperson sold an average of $28,000 per day for the first 5 days she worked. The next 3 days she worked; she sold an average of $42,000. How much did she sell on average per day over the entire 8 days?

Problem 1: Consumers may be interested in whether the cost of a particular calculator varies from store to store. Based on surveying 43 stores, which yielded a sample mean of $84 and a sample standard deviation of $12, test the claim that the standard deviation is greater than $15.

Taylor and Andrea are 60 miles apart, traveling towards each other. If Andrea travels 13 mph and Taylor travels 7 mph how long until they meet? A) Fill in the following table, where t = travel time in hours until Taylor and Andrea meet. Notice that the time will be t for both people, since they start and stop at the same times. B) Using the basic formula rate x time = distance, write an equation based on the information summarized in the table. C) Solve your equation to determine the amount of time Taylor and Andrea will travel until they meet:

12 people want to buy a new iPad. The store only has 3 left. So the store manager writes the names of the people who want an iPad on smal pieces of paper and mixes them up in a hat. He/she then draws three names out to determine who the lucky 3 people will be who can buy an iPad. No two people have the same name. How many possible outcomes are there?

At Andrew Jackson High School, students are only allowed to enroll in AP U.S. History if they have already taken AP World History or AP European History. Out of 825 incoming seniors, 165 took AP World History, 66 took AP European History, and out of those students 33 took both. Given this information, determine the probability a randomly selected incoming senior is allowed to enroll in AP U.S. History.

Given rectangular prism A is similar to rectangular prism B and the volume of A is 125 ft³ and the volume of B is 27 ft³. What is the ratio of the surface areas for A: B ? 5:3 3:5 125:27 25:9

For a science experiment, students need to find 25% of 60 grams. Jada says, "I can find this by calculating 1/4 of 60." Andre says, "25% of 60 means 25/100 * 60." Lin says both of their methods work. Do you agree with Lin? a Yes, because 25% is equal to 1/4 and 25/100 b No, because 25% is not equal to 1/4 and 25/100

"U2" has a concert that starts in 17 minutes and they must all cross a bridge to get there. All four men begin on the same side of the bridge. You must help them across to the other side. It is night. There is one flashlight. A maximum of two people can cross at one time. Any party who crosses, either 1or 2 people, must have the flashlight with them. The flashlight must be walked back and forth; it cannot be thrown. Each band member walks at a different speed. A pair must walk together at the rate of the slower man's pace: Bono: 1 minute to cross Edge: 2 minutes to cross Adam: 5 minutes to cross Larry: 10 minutes to cross For example: if Bono and Larry walk across first, 10 minutes have elapsed when they get to the other side of the bridge. If Larry then returns with the flashlight, a total of 20 minutes have passed and you have failed the mission.

A sailboat captain has set her course due west at a speed of 6 meters per second. The wind is blowing due north at a rate of 2 meters per second. Draw a vector diagram of this situation on a coordinate grid. Consider the (captain's course) and (the wind) as two forces acting on a point (the sailboat)

The exponential model A=402.6 e0.026t describes the population, A, of a country in millions, t years after 2003. Use the model to determine when the population of the country will be 695 million.

Write inequalities to represent the situations below. To be eligible for financial aid, a student must earn no more than $20,000 per year. Use s to represent the yearly earnings (in dollars) of a student eligible for financial aid. To ride a roller coaster, a visitor must be taller than 60 inches. Use h to represent the height (in inches) of a visitor able to ride.

The perimeter of a rectangular wooden deck is 90 feet. The deck's length, I, is 5 feet less than 4 times its width, w. Which system of linear equations can be used to determine the dimensions, in feet, of the wooden deck?

For a long-distance person-to-person telephone call, a telephone company charges $0.29 for the first minute. $0.19 for each additional minute, and a $1.12 service charge. If the cost of a call is $1.79, how long did the person talk?

Suppose a company has fixed costs of $31,200 and variable costs of 1/3x2+444x dollars, where x is the total number of units produced. Suppose further that the selling price of its product is 1768- 2/3x dollars per unit. (a) Find the break-even points. (Enter your answers as a comma-separated list.) x=24,1300 (b) Find the maximum revenue. (Round your answer to the nearest cent.) (c) Form the profit function P(x) from the cost and revenue functions. P(x) = -x² +1324x-31200 Find maximum profit. $ 407044 (d) What price will maximize the profit? (Round your answer to the nearest cent.)

Round answer to 4 decimal places. Mr. H is playing the batting game at the local fair. He will have six balls pitched to him. The number of balls he can hit determines the prize he wins. He hits the ball 32% of the time (he misses 68% of the time). a. What is the probability he hits exactly two of the pitched balls? b. What is the probability he hits at most 3 of the pitched balls?

For the month of August in a certain city, 57% of the days are cloudy. Also in the month of August in the same city, 19% of the days are cloudy and snowy. What is the probability that a randomly selected day in August will be snowy if it is cloudy? The probability is approximately. (Round to three decimal places as needed.)

Class Survey A student is running a survey for a class project, which asks fellow high school students "What is your favorite sport?" Which of the following would yield the most accurate/most unbiased sample? He hands out a survey to every 3rd classmate to enter his weight training class He hands out the survey to his friends at lunch He passes out surveys as students enter the next soccer game He prints surveys and gives 2 to each teacher to randomly give to a male and female student in their homeroom.

Rewrite In 5 + ln 7 as a In single logarithm.

Suppose you deposit $1000 at 3% interest compounded continuously. Find the average value of your account during the first 4 years.

Savannah and Ariana both leave the college at the same time, but in opposite directions. If Ariana travels 6 mph faster than Savannah and after 7 hours they are 182 miles apart, how fast is each traveling? Savannah is traveling Ariana is traveling

25. A model of a building was made at a scale of 1:16. If the model has dimensions of 2.6 m by 3.8 m by 1.8 m, what are the dimensions of the 'real life' building? a. 41.6 m by 60.8 m by 28.8 m b. 45.8 m by 73 m by 31.7 m c. 49.9 m by 85.1 m by 21.6 m d. 37.4 m by 48.6 m by 25.9 m

From the top of a lighthouse 210 feet high, the angle of depression of a boat is 27°. Find the horizontal distance from the boat to the foot of the lighthouse. The lighthouse was built at sea level.

You buy 12 packages of discounted socks for a total cost of $85.50, which includes a 5% discount. Before the discount, how much did a single package of socks cost? a.) $7.50 b.) $4.75 c.) $10.68 d.) $6.78

Consider the acceleration function of an object on a projectile motion is a (t) = -32. If v (0) = 28 ft/sec and s (0) = 120, what is the maximum height of the object in feet?