Heights & Distances Questions and Answers

Spencer is going snowboarding. He rode the ski lift to the top of the mountain, which is at an altitude of 1500 feet. The angle of elevation from the bottom to the top of the mountain is 25°. What is the length of Spencer's run (his trip down the hill)? Round your answer to the nearest tenth of a foot.

A golfer is standing at the tee, looking up to the green on a hill. If the tee is 36 yards lower than the green and the angle of elevation from the tee to the hole is 12°, find the distance from the tee to the hole.

What percent of 120 is 72? 60% 86.4 % 0.6% 1.67%

Some farmers use a circular irrigation method. An irrigation arm acts as the radius of an irrigation circle. How much land is covered with an irrigation arm of 310 ft?

Nguyen loaded 12 trucks in 1 hour. Find his loading speed in trucks per hour. 12 trucks per hour 12 hours 12 hours per truck 12 trucks

About how many cells are in the human body? 37.2 trillion cells You can assume that a cell is a sphere with radius 103 cm and that the density of a cell is approximately the density of water which is 1g/cm³.

For a minimisation problem, if the objective coefficient of a decision variable x, that is equal tozero at the optimal, decreases within its allowable range, what can or will happen? Fill in the blanks using the following responses, "can", "will not", "can increase", "can decrease", "can increase or decrease", "will stay the same" Optimal basis (corner that the optimal solution sits) ______change Decision variable x value can________ Objective function value can_______

A barrel of fuel oil is a right circular cylinder where the inside measurements of the barrel are a diameter of 24.5 inches and a height of 34.5 inches. There are 231 cubic inches in a liquid gallon. Determine and state, to the nearest tenth, the gallons of fuel that are in a barrel of fuel oil.

Linear Regression Use linear regression to find the equation for the linear function that best fits this data. Round both numbers to two decimal places. Write your final answer in a form of an equation y = mx + b

Simple interest is given by the formula A = P + Prt. Where A is the balance of the account after t years, and P is the starting principal invested at an annual percentage rate of r, expressed as a decimal. Devante is investing money into a savings account that pays 2% simple interest, and plans to leave it there for 10 years. Determine what Devante needs to deposit now in order to have a balance of $20,000 in his savings account after 10 years. Devante will have to invest $ now in order to have a balance of $20,000 in his savings account after 10 years. Round your answer to the nearest dollar.

This week in the Discussion module, you will be looking into the use of social media for emergency management. While somewhat dated (2013) the FEMA social media document in the reading assignments remains one of the most comprehensive on the topic. After reading the document, and others you may find through research, comment on the pros and cons of social media use in disasters and identify at least one "up to date" or potential future application for social media to address emergency management communications issues.

In the year 1997, the surface elevation of Lake Powell was 3839 feet above sea level. In the year 2005, the surface elevation of Lake Powell was 3221.4 feet above sea level. Interpret the rate of change in this situation. The surface elevation of Lake Powell is Select an answer at a rate of _______Select an answer ✪

10. The first row of a movie theatre has 34 seats. Each successive row has 4 more seats than the row before it. If there are 20 rows in the theatre, what is the seating capacity of the theatre? [P4]

A model is made of a car. The car is10 feet long and the model is 7Inches long. What is the ratio of the length of the car to the length of the model? 07:120 O 120: 7 07:10 O 10:7

Meg rowed her boat upstream a distance of 39 mi and then rowed back to the starting point. The total time of the trip was 16 hours. If the rate of the current was 5 mph, find the average speed of the boat relative to the water.

Convert the measurement. 97 inches per second =_ feet per minute

A bicycle is traveling at 20 miles per hour. How many feet will it cover in 55 seconds? Round your answer to the nearest tenth of a foot. 1466.7 X feet

Give the equation of the line with a slope of - 5 2 and a y-intercept of 4.

The store is selling lemons at $0.39 each. Each lemon yields about 2 tablespoons of juice. How much will it cost to buy enough lemons to make four 9-inch lemon pies, each requiring half a cup of lemon juice?

Convert the measurement to the nearest hundredth . 59 feet per second = _ miles per hour

A bicycle is traveling at 12 miles per hour. How many feet will it cover in 25 seconds? Round your answer to the nearest tenth of a foot.

Apollo Spas services 147 hot tubs. If each hot tub needs 165 mL of muriatic acid, how many liters of acid are needed for all of the hot tubs? ___________ L

Robin randomly selects a number between 1 and 20. What is the probability that the number selected is the square of a natural number? A. 1/2 B. 3/20 C. 3/10 D.1/5 E. 1/3

Brian wants to build a ramp that leads to a storeroom 5 meters above the ground. He wants the ramp to be 10 meters long. What should the angle of elevation of the ramp be? A 15° B. 30° C. 45° D. 60°

Solve x sin x = 1 using the following: (a) MOSS (root = 0.5) (b) Newton Raphson (root = 0.5) (c) Bisection Method (use roots = 0.5 and 2) (d) Secant Method (use roots = 2 and 1.5)

AC has endpoints A(-1, -3.5) and C(5, -1). Point B is on AC and is located at (0.2, -3). What is the ratio of AB /BC ? Please enter your answer as a decimal, rounded to the hundredths place.

There are two shipyards between A and B along the River, the ship trip from A to B , everyday move 600KM, from B to A, everyday move 400KM, if the ship has the roundtrip between A and B for 5 times, it would take the ship totally 5 days. Then what is the distance between A and B?

tell if the statements are proportional. Show your work. 1)3/7 = 81/189 2)22/8 =152/56 3)5/6 =70/82.

Given that P(A) = 0.32 and P(B) = 0.68, what is the P(A∩B) if events A and B are independent? A 1.00 B. 0.36 C. 0.47 D. 0.22

From a group of 10 men and 12 women, how many committees of 5 men and 6 women can be formed?

Type the correct answer in the box. Round off your answer to the nearest tenth. Jill is standing at the base of her apartment building. She measures the angle of elevation to the top of a nearby tower to be 40°. Then Jill goes to the roof of her apartment building, directly above her previous position, and measures the angle of elevation to the top of the same tower to be 30°. If the height of the tower is 100 meters, the height of Jill's apartment building is _____ meters.

Select the correct answer from the drop-down menu. If A and B are independent events, P(A and B) = ________

Alan has 3 quarters and 7 dimes in his pocket. If he takes out a coin, puts it back in his pocket, and then takes out a coin again, what is the probability that both coins are dimes?

A company is promoting two employees to the director and manager roles. If there are currently 35 employees, how many ways can those positions be filled?

The piston moves from the Top dead center as a result of a change crank angle ratio of crank radius to connected length connected length crank radius the distance from TDC to the crank center equal to a=crank radius b= connected length a*b a+b the piston travel changed with connected rod length crank angle R/L crank radius

You bought an eight year bond with annual coupons of $100 each. The bond is redeemed at $1500. As you collect the coupon payments, you deposit them into an account that gains interest at 5% per year. Immediately after you transfer the last coupon along with the redemption value into the 5% interest account, how much is in this account? Round your answer to the nearest dollar. 2682 955 2146 2455 2300 646 1662

Emily is playing a board game that has a spinner divided into equal sections numbered 1 to 18. The probability of the spinner landing on an even number or a multiple of 3 is____ The probability of the spinner landing on an odd number or a number between 4 and 15 (both numbers excluded) is____

Two non-simultaneous events each have an equal likelihood of occurring (50%). If the events are independent of each other, what is the probability that they will both occur? A. 30% B. 35% C. 50% D. 25% E. 40%

Find all non-isomorphic graphs with power sequences (2, 2, 2, 3, 3, 4), (2, 2, 3, 3, 3, 3) and justify that there are no other such graphs.

Find the volume of the three dimensional solid. 3215.36 ft³ 200.97 ft³ 1071.79 ft³ 66.99 ft³

A triangle has vertices of (5,3), (2,-7) and (-1,5). Find the lengths of its sides and determine if the triangle is aute, right, or obture.

An airplane needs to head due north, but there is a wind blowing from the southeast at 30 km/hr. The plane flies at an airspeed of 600km/hr. To end up due north, the pilot will need to fly the plane................degrees east of north.

11. Which of the following expressions is equivalent to -x-x? oldiam nom à bra soldham wolley If soldzam A. -x(x+1) B. -x(x-1) C. -x(1-x) D. x(x+1) E. x(x-1) or od low ti andi tilidadore odd ei Jedwob

Suppose that an air cannon in the Punkin Chunkin contest whose muzzle is 5 feet above the ground fires a pumpkin at an angle of 45° to the horizontal with a muzzle velocity of 303 feet per second. The model s(t) = - 16t² +208t+5 can be used to estimate the heights of an object after t seconds. (a) Determine the time at which the pumpkin is at a maximum height. (b) Determine the maximum height of the pumpkin. (c) After how long will the pumpkin strike the ground?

Suppose that you are headed toward a plateau 29.9 meters high. If the angle of elevation to the top of the plateau is 17.5°, how far are you from the base of the plateau? What is your distance from the base of the plateau? meters (Round to one decimal place as needed.)

The length of the base of an isosceles triangle is 40.47 inches. Each base angle is 37.13°. Find the length of each of the two equal sides of the triangle. (Hint: Divide the triangle into two right triangles.) The other two sides of the triangle have lengths of inches. (Simplify your answer. Type an integer or decimal rounded to the nearest hundredth as needed.)

A building that is 152 feet tall casts a shadow that is 75 feet. A second building next to the other building casts a shadow that is 15 feet. How tall is the second building?

In the video, I drop a ball off a three-story balcony. We know that objects in freefall follow the equation for height h, in meters, h = 4.9t² + c, where t is time in seconds, and c is the initial height. A student timed the drop at 1.29 seconds. Use this to determine the height from which the ball was dropped, to at least 2 decimal places. ______meters

The base of a triangle is 5 meters longer than the height of the triangle. If the area of the triangle is 33 square meters, what are the base and height of the triangle? The height is ____metres The base is _____ metres

A farmer owns a total of 9 1/6 acres of land. The land is separated into 5 equally sized sections. How many acres are in each sect Write your answer as a mixed number in simplest form.