2. A ski resort is building a new ski lift that will transport tourists from the base of the mountain to its highest point. This mountain has a vertical height of 200 yards, and the ski lift will rise at an angle of 40 degrees. When the project is completed, how many yards, d, will a tourist travel from the base of the mountain to its peak?
Part I: Sketch a figure to illustrate the scenario above. Label the vertices and the lengths that are given in the question. (3 points)
Part II: Using your sketch from Part I, write an equation using a trigonometric ratio to find the distance a tourist will travel from the base of the mountain to its peak. Round your answer to the nearest 100th. Show your work. (2 points)
3. Darcy mounted a motion sensor so it would light a path to the door on her deck. If you know AB = 10 feet, and BE and BD trisect ∠ABC, what is the perimeter of the deck area to the right of the beam of light (△BDC)?
Part 1: What other angles or sides of △BDC can you label given that side AB is 10 feet, BE and BD trisect ∠ABC? Label the diagram accordingly, and explain your reasoning. (4 points)
Part 2: Use the trigonometric ratios 30° and 60° to calculate and label the remaining sides of △BDC. Show your work. (3 points)
Part 3: Use the Pythagorean Theorem to calculate the length of side BD. Does this method verify the length you found using trigonometric ratios? (2 points)
Part 4: What is the perimeter of the area to the right of the beam of light on Darcy's deck (△BDC)? Show your work. Use your calculator to round your final answer to the nearest foot. (3 points)
4. Two cars are starting from positions that are 20 miles apart. They are both headed for the same intersection, as depicted in the diagram below. Car A is traveling at 30 mph, and Car B is traveling at 45 mph. Which car will reach the intersection first?
Part I: Use the law of cosines to determine how far Car B has to travel to reach the intersection. (2 points
Part II: Use to determine the time necessary for Car A to reach the intersection. Round your answer to the nearest hundredth of an hour. (1 point)
Part III: Use to determine the time necessary for Car B to reach the intersection. (1 point)
Part IV: Which car reaches the intersection first, and by how many hours? (2 point
5. Solve for the missing length and the other two angles in the triangle below.
Part I: Use the law of cosines to find the missing third side. (2 points)
Part II: Use either the law of cosines or the law of sines to find the measure of angle C. (2 points)
Part III: Use any method you like to find the measure of angle B. (1 point)
6. Solve the triangle below.
Part I: Use the law of cosines to find the measure of angle B. (2 points)
Part II: Use the law of sines to find the measure of angle C. (2 points)
Part III: Use any method you like to find the measure of angle A. (1 point)
7. Assume two people, Swanson and Suzie, are standing 35 feet apart and are watching a boat race. At a given moment, Swanson approximates the angle formed by the lead boat, himself, and Suzie to be . Suzie approximates the angle formed by the lead boat, herself, and Swanson to be . How far is the boat from Swanson?
Part I: What is the missing angle in this triangle? (1 point)
Part II: Use the law of sines to find the distance from Swanson to the boat. (2 points)
8. Solve the following triangle for all missing sides and angles.
Part I: Find the measure of angle B. (1 point)
Part II: Use the law of sines to find the length of side a. (2 points)
Part III: Use any method to find the length of side c. (2 points)
Answer:
156
Step-by-step explanation:
You are given the mountain that has a vertical height of 200 yards, and the ski lift will rise at an angle of 40 degrees. You are asked to find how many yards will a tourist travel from the base of the mountain to its peak. You can solve this using trigonometric function. More importantly, imagine that the mountain has a 90 - degree vertical height so that when you connect the peak of the mountain down to its base and then connected to the ski, you can form a right triangle.
Use the sine function.
sine β = opposite side / hypotenuse side
the opposite side will be the height of the mountain and the hypotenuse side will be the distance of the ski from the bottom going to the peak of the mountain
sine 40° = 100 yards / hypotenuse side
hypotenuse side = 100 yards / sine 40°
hypotenuse side = 156 yards
(01.01) Evaluate −6 − (−3). Answers:18 −9 3 −3
Which of the following are geometric sequences? Check all that apply. A. 10, 5, 2.5, 1.25, 0.625, 0.3125 B. 5, 10, 20, 40, 80, 160 C. 3, 6, 9, 12 ,15, 18 D. 1, 3, 9, 27, 81
The options that are geometric progressions are:
D. 1, 3, 9, 27, 81A. 10, 5, 2.5, 1.25, 0.625, 0.3125B. 5, 10, 20, 40, 80, 160 What is a geometric progression?This is a progression of numbers which usually have a defined ratio that is between them.
The ratio in the options above are:
[tex]\frac{1}{2} , \frac{3}{1} , \frac{2}{1}[/tex]
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Answer:it’s a,c,d
Step-by-step explanation:
An aquarium tank holds 169 gallons of water. How much is this in liters? Use the following conversion: 1 gallon is 3.8 liters.
To convert gallons to liters, you multiply the number of gallons by the conversion factor 3.8. Therefore, an aquarium tank holding 169 gallons contains 641.2 liters of water.
Explanation:The question is asking about converting gallons to liters. The process involves simple multiplication using the conversion rate.
Given that the volume of water in the aquarium tank is 169 gallons and that 1 gallon is equivalent to 3.8 liters, you can find the volume in liters by multiplying the number of gallons by the conversion rate. Therefore, 169 gallons * 3.8 liters/gallon equals 641.2 liters.
This means there are 641.2 liters of water in the aquarium tank.
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Two mechanics worked on a car. the first mechanic worked for 20 hours, and the second mechanic worked for 5 hours. together they charged a total of $1900 . what was the rate charged per hour by each mechanic if the sum of the two rates was $155 per hour?
2x+7=12x-6 looking for x
Which correlation should be used to measure the relationship between gender and grade point average for a group of college students??
a. ?point-biserial correlation
b. ?pearson correlation
c. ?phi-coefficient
d. ?spearman correlation?
Find the value of x to the nearest tenth. See linked picture below. Thanks!
There are 5273 students in school. There are 231 more girls than boys. List the number of boys that attend this school.
A.5042
B.231
C.2752
D.2521
Two horses are ready to return to their barn after a long workout session at the track. the horses are at coordinates H(1,10) and Z(10,1). Their barns are located in the same building, which is at coordinates B(-3,-9). Each unit/grid on the coordinate plane represents 100 meters. Which horse is closer to the barn? Justify your answer?
Jerome earns $200 per month plus $12 for bike he sells at the bike shop.This month, he wants t6o earn at least $400. Whats the least bikes that jerome can sell to reach his goal.
Let f(x) = 27x5 − 33x4 − 21x3 and g(x) = 3x2. Find f of x over g of x
The answer is 9x3 − 11x2 − 7x
Answer: 9x^3 − 11x^2 − 7x
if the reserve rate is 3% and a bank receives a deposit of 16,000 how much of the 16,000 is the bank free to loan out?
that means the bank keeps 3% and can loan out 97% of the total
16000*0.97 = $15,520 can be loaned out
Sean used candle molds, as shown, to make candles that were perfect cylinders and spheres:
What is the approximate difference in the amount of wax needed to make a candle from each of these molds? Use π = 3.14.
18.0 cubic inches
28.26 cubic inches
37.0 cubic inches
56.52 cubic inches
Why are techniques like cluster sampling and multistage sampling just as externally valid as simple random sampling?
Due to the fact that they all contain elements of random selection, techniques like cluster sampling and multistage sampling are just as externally valid as simple random sampling due to the fact that they all contain elements of random selection.
Cluster sampling are more or less alike, each heterogeneous and resembling the overall population. The population is split into representative clusters, then a selection is done one or few from the clusters, then lastly, a census is performed with those selected clusters.
In multistage sampling, several methods are combined in sampling schemes and occasionally utilized the same method or different methods or more than once. Though they have different steps in being done, they both have random selection elements.
Jared is in charge of production in a factory that makes lightbulbs. The factory made 2,648 lightbulbs over the weekend. Jared wants to pull a sample of these bulbs for testing. Which sample would give Jared the most-accurate test results? a sample consisting of every 20th lightbulb a sample consisting of every 40th lightbulb a sample consisting of every 50th lightbulb a sample consisting of every 100th lightbulb
BARNEY'S BICYCLE SHOP IS SELLING T-SHIRTS AT THE LOCAL HEALTH FAIR. THEY PLAN ON SELLING SHIRTS FOR $8 EACH. TO HAVE THE SHIRTS MADE, BARNEY'S BICYCLE SHOP PAYS THE SHIRT MAKER $3.50 PER SHIRT PLUS AN INITIAL FEE OF $63. HOW MANY SHIRTS MUST BARNEY'S BICYCLE SHOP SELL BEFORE THEY CAN MAKE A PROFIT?
A. 9 SHIRTS
B. 8 SHIRTS
C. 14 SHIRTS
D. 11 SHIRTS
Barney's Bicycle Shop must sell at least 14 shirts before they can make a profit. Among the given options, the correct answer is C. 14 shirts.
To determine the number of shirts Barney's Bicycle Shop must sell before making a profit, we need to consider the cost of producing the shirts and the revenue generated from selling them.
For each shirt sold, the shop earns $8 in revenue. However, they incur costs to have the shirts made. The shirt maker charges $3.50 per shirt and an initial fee of $63.
Let's calculate the total cost per shirt:
Cost per shirt = $3.50 + ($63 / number of shirts)
To break even or make a profit, the revenue from selling the shirts must exceed the cost per shirt.
Let's calculate the revenue per shirt:
Revenue per shirt = $8
Now we can set up the equation to find the number of shirts needed to break even or make a profit as inequality:
Revenue per shirt ≥ Cost per shirt
$8 ≥ $3.50 + ($63 / number of shirts)
To solve this inequality, we can subtract $3.50 from both sides:
$4.50 ≥ $63 / number of shirts
Multiplying both sides by the number of shirts:
$4.50 x number of shirts ≥ $63
Simplifying the equation:
Number of shirts ≥ $63 / $4.50
Number of shirts ≥ 14
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Today Javier put a cabinet on layaway by making a down payment of $80 and agreeing to pay $24 a month starting next month for 36 months. When will Javier receive the cabinet ?
A. 1 month
B. Today
C in 24 months
D in 36 months
Answer:
Option D is the answer.
Step-by-step explanation:
A layaway is a system of paying a deposit to secure an item that is meant to be purchased later. In this purchasing method, a buyer places a deposit on an item to lay it away. He can pick the item later when he pays the balance. The balance can also be paid in smaller installments until the full amount is paid.
So, here Javier will be paying for 36 months, hence, he will get the cabinet after 36 months.
how do i solve this??
area for the hexagon = 1/2*p*a
p = perimeter = 18*6=108
a = apothem = 15.59
108*15.59 = 1683.72/2 = 841.86 sq units
Area of rectangle = 18 x 21 = 378
841.86-378 = 463.86 rounded to 464 square units
Tables of values for f(x) and g(x) are given below. Write g(x) as a transformation of f(x).
Suppose x=10 and y=10. what is x after evaluating the expression (y>= 10)||(x++ >10)? java
The value of x remains 10 after evaluating the Java expression (y >= 10)||(x++ > 10) due to short-circuit evaluation, as the first condition y >= 10 is true.
Explanation:The student is asking about the value of x after evaluating the Java expression (y >= 10)||(x++ > 10) given that x=10 and y=10. The double pipe || represents a logical OR operator, which evaluates to true if at least one of the operands (conditions) is true. Since y >= 10 is true because y is equal to 10, the OR expression is true, and Java does not evaluate the second operand due to short-circuit evaluation. Short-circuit evaluation means that in an OR expression, if the left-hand side is true, the right-hand side is not evaluated, which in this case means that x++ is not executed. Therefore, x remains 10.
Statistics??? Construct a 95% confidence interval for the population mean. Assume the population has a normal distribution. A sample of 20 college students had mean annual earnings of $3120 with a standard deviation of $677.
A family has 8 girls and 4 boys. A total of 2 children must be chosen to speak on the behalf of the family at a local benefit. What is the probability that 2 girls and no boys are chosen?
A. 7/55
B. 14/33
C. 12/33
D. 1/6
Answer: The correct option is (B) [tex]\dfrac{14}{33}.[/tex]
Step-by-step explanation: Given that a family has 8 girls and 4 boys. A total of 2 children must be chosen to speak on the behalf of the family at a local benefit.
We are to find the probability that 2 girls and no boys are chosen.
Total number of children in the family = 8 + 4 =12.
Let S denote the sample space of choosing 2 children from the family of 12 children and A denote the event of choosing 2 girls and no boys.
Then, according to the given information, we have
[tex]n(S)=^{12}C_2=\dfrac{12!}{2!(12-2)!}=\dfrac{12\times11\times10!}{2\times1\times10!}=66,\\\\\\n(A)=^8C_2\times^4C_0=\dfrac{8!}{2!(8-2)!}\times1=\dfrac{8\times7\times6!}{2\times1\times6!}=28.[/tex]
Therefore, the probability of event A is given by
[tex]P(A)=\dfrac{n(A)}{n(S)}=\dfrac{28}{66}=\dfrac{14}{33}.[/tex]
Thus, the required probability is [tex]\dfrac{14}{33}.[/tex]
Option (B) is CORRECT.
Angle C is an inscribed angle of circle P. Angle C measures (5x-7) degrees and arc AB measures (2x) degrees. Find x.
What is the length of a diagonal of a cube with a side length of 3 cm? (ALL OF THE ANSWERS ARE SQUARE ROOTED) 18,27,33,38
Answer:
27
Step-by-step explanation:
i just took the test
Use Gauss-Jordan elimination to solve the following linear system. –4x + 4y + 5z = 9 –2x + 2y + z = 3 –4x + 5y = 4
A coin is tossed 20 times. A person, who claims to have extrasensory perception, is asked to predict the outcome of each flip in advance. She predicts correctly on 14 tosses. What is the probability of being correct 14 or more times by guessing? Does this probability seem to verify her claim?
To calculate the probability of correctly predicting 14 or more coin tosses out of 20, we can use the binomial probability formula.
Explanation:To calculate the probability of correctly predicting 14 or more coin tosses out of 20, we can use the binomial probability formula. The probability of getting exactly k successes in n independent trials with a probability p of success in each trial is given by:
P(X = k) = C(n, k) * p^k * (1 - p)^(n - k)
Where C(n, k) is the binomial coefficient, n! / (k! * (n - k)!), p is the probability of success (0.5 for a fair coin), and n is the number of trials (20 tosses).
To find the probability of getting 14 or more successes, we need to sum the probabilities of getting 14, 15, 16, ..., 20 successes.
P(X >= 14) = P(X = 14) + P(X = 15) + P(X = 16) + ... + P(X = 20)
We can calculate these probabilities and then add them together to get the overall probability.
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5inches is what fraction of a foot?
A normal distribution has a meaning of 50 and a standard deviation of 6. What is the probability that a value selected at random from this data is in the interval from 50 to 62 ? Express your answer as a percent rounded to the nearest 10th
A-town and b-ville are connected by a straight, 420-mile road. at noon, atu left a-town for b-ville, and brek left b-ville for a-town. if atu travels at 56 miles per hour and brek travels at 49 miles per hour, how many miles apart will atu and brek be 1 hour before they meet?