Answers
Zip line B's total length requires 301 feet of cable using the distance between trees and change in height.
How to calculate length?To determine the length of cable needed, we need to calculate the horizontal and vertical distances between the trees, and then apply the constraints.
Let's start by labeling the trees and their distances:
Tree 1: 120 ft from Tree 2, 150 ft from Tree 3
Tree 2: 140 ft from Tree 3
Zip line B is the longest, so calculate the length of cable needed for that option.
Horizontal distance: Tree 2 to Tree 3 is 140 ft.
Vertical distance: The starting platform needs to be 16 ft above the ground, and the harness hangs down 4 ft below the cable, plus an additional 3 ft for the rider's legs. So the total height difference is 16 + 4 + 3 = 23 ft.
Using the slope constraint, we want a vertical change of 6 to 8 feet for every 100 feet of horizontal change. For a horizontal distance of 140 ft, we want a vertical change of:
(6/100) x 140 = 8.4 ft
(8/100) x 140 = 11.2 ft
So the zip line needs to have a vertical drop of between 8.4 and 11.2 ft.
Using the slack constraint, we need to add 5% slack to the length of the cable:
140 ft x 1.05 = 147 ft
Adding 7 ft of extra cable at each end, the total length of cable needed is:
140 ft + 147 ft + 7 ft + 7 ft = 301 ft
Therefore, the total length of cable needed for Zip line B is 301 ft.
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Complete question:
Designing a Zip Line You and your friend Latisha work at the community center. You will be counselors at a summer camp for middle school students. The camp director has asked you and Latisha to design a zip line for students to ride while at camp. A zip line is a cable stretched between two points at different heights with an attached pulley and harness to carry a rider. Gravity moves the rider down the cable. The zip line will be secured to two trees. The camp has a level field with three suitable trees to choose from. All three trees are on level ground. • Tree 1 is 120 feet from Tree 2. • Tree 2 is 140 feet from Tree 3. • Tree 1 is 150 feet from Tree 3. Tree 2 Tree 3 Tree 1 120 ft 140 ft acer Tree 1 is 120 feet from Tree 2. • Tree 2 is 140 feet from Tree 3. Tree 1 is 150 feet from Tree 3. - Tree 2 Tree 3 Tree 1 120 ft 140 ft 150 ft There are three possible zip line locations: Zip line A between Tree 1 and Tree 2, Zip line B between Tree 2 and Tree 3, or Zip line C between Tree 1 and Tree 3. acer Tree 2 Tree 1 Tree 3 Zip line A Zip line 8 Zip linec A professional company will be hired to install the zip line. They will build platforms at the two trees used for starting and ending the zip line. The starting platform will require the cable to start at a height 16 feet above the ground You and Latisha researched how to build a zip line. There are four basic constraints for your design. • Slope Constraint: The slope of the zip line should be 6 to 8 feet of vertical change for every 100 feet of horizontal change. • Slack Constraint: The zip line should have a 5% slack in it. acer • Harness Constraint: The cable must be high enough that the rider, while buckled into the harnese dnes not touch the ground. • The harness hangs down 4 feet below the cable. • An additional 3 feet must be used to allow for a rider's legs to hang down below the harness. • Brake Constraint: A brake must be placed on the cable to ensure the rider does not hit the tree. A bungee cord connects the brake to an anchor in the ground. . The length of the bungee cord is 24 feet. • The bungee cord stretches to a maximum of 175% of its original length. Harness Constraint Brake Constraint Rider 4 ft Rider Brake 3 ft Harness Bungee cord Brake anchor acer Rider 4 ft Rider Brake 3 ft Harness Bungee cord Brake anchor Your task is to choose which zip line to build, Zip line A, Zip line B, or Zip line C, and to design this zip line within the given constraints. acer The camp director is ready to purchase the cable. Use the distance between the trees and the change in height of the cable to determine the length of cable needed. Be sure to include: • the required 5% slack in the line, and • 7 extra feet of cable at each end to wrap around each tree. Enter the total length, in feet, of cable needed.
Related Questions
Mallick Corp. reported the following information for 2013 and 2014.Accounts receivable, December 31, 2013 $ 67,000Accounts receivable, December 31, 2014 63,000Sales (all on credit) -- 2014 745,000How much cash was collected from customers during 2014?A. $741,000B. $745,000C. $749,000D. $753,000
Answers
The cash collection from customers which adds the change in accounts receivable to the sales for the year 2014 is $749,000. Option C is the correct answer.
To determine the cash collected from customers during 2014, we need to find out the change in accounts receivable from the beginning to the end of the year.
The change in accounts receivable is calculated as follows:
Change in accounts receivable = Accounts receivable, December 31, 2014 - Accounts receivable, December 31, 2013
= $63,000 - $67,000
= -$4,000
The negative sign indicates a decrease in accounts receivable, meaning that cash was collected from customers.
Now, to find the cash collected from customers, we need to add the change in accounts receivable to the sales for the year:
Cash collected from customers = Sales - Change in accounts receivable
= $745,000 - (-$4,000)
= $749,000
Therefore, the answer is C. $749,000.
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The question is -
Mallick Corp. reported the following information for 2013 and 2014.
Accounts receivable, December 31, 2013, $ 67,000
Accounts receivable, December 31, 2014, 63,000
Sales (all on credit) -- 2014 745,000
How much cash was collected from customers in 2014?
A. $741,000
B. $745,000
C. $749,000
D. $753,000
consider the raoll of the two dice. let x ve a random vasriable representing the sumof the dots appearing on each of the dice. the probability of each possible value of x are as follow
Answers
The expected value of X is 7, and the standard deviation of X is 2.42 respectively.
The average of X's potential values is the expected value of X. We must first determine the sum of all potential x values multiplied by each value's associated probability before we can determine the expected value.
Calculate the expected value of X
Expected value = (2×(1/36)) + (3×(2/36)) + (4×(3/36)) + (5×(4/36)) + (6×(5/36)) + (7×(6/36)) + (8×(5/36)) + (9×(4/36)) + (10×(3/36)) + (11×(2/36)) + (12×(1/36))
Expected value = 7
Calculate the variance of X
Variance = (2-7)2×(1/36) + (3-7)2×(2/36) + (4-7)2×(3/36) + (5-7)2×(4/36) + (6-7)2×(5/36) + (7-7)2×(6/36) + (8-7)2×(5/36) + (9-7)2×(4/36) + (10-7)2×(3/36) + (11-7)2×(2/36) + (12-7)2×(1/36)
Variance = 5.83
Calculate the standard deviation of X
Standard deviation = √(variance)
Standard deviation = 2.42
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Complete Question:
Consider the roll of two dice. Let X be a random variable representing the sum of the number of dots appearing on each of the dice. The probabilities of each possible value of X are as follows:
x P(x)
2 1/36
3 2/36
4 3/36
5 4/36
6 5/36
7 6/36
8 5/36
9 4/36
10 3/36
11 2/36
12 1/36
Determine the expected value and standard deviation of X.
You have 8 donuts to share evenly between you and your four brothers.
Which fraction describes how many donuts each of you will receive?
Answers
I need some help pretty please
Answers
Answer:
y - 2 = 2(x + 3)
Step-by-step explanation:
the equation of a line in point- slope form is
y = b = m(x - a)
where m is the slope and (a, b ) a point on the line
calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (- 3, 2 ) and (x₂, y₂ ) = (2, 12 )
m = [tex]\frac{12-2}{2-(-3)}[/tex] = [tex]\frac{10}{2+3}[/tex] = [tex]\frac{10}{5}[/tex] = 2
using (a, b ) = (- 3, 2 ) , then
y - 2 = 2(x - (- 3) ) , that is
y - 2 = 2(x + 3)
What is the missing number in [_] -3/4=2/3
Answers
Answer:
17/12
Step-by-step explanation:
What is the missing number in [_] -3/4=2/3?
Let the missing number be x
We have
x - 3/4 = 2/3
x = 2/3 + 3/4
x = 8/12 + 9/12
x = 17/12
So, the missing number is 17/12
In 2010, the population of a city was 89,000. From 2010 to 2015, the population grew by 6.8%. From 2015 to 2020, it fell by 4.9%. To the nearest whole number, by what percent did the city grow from 2010 to 2020?
Answers
1.35% is the percentage change in the population of the city that grew from the years 2010 to 2020.
The population of the city = 89,000
Percentage in the growth of people from 2010 to 2015 = 6.8%
Percentage in the decline of people from 2015 to 2020 = 4.9%
The formula to calculate the percentage change is:
percentage change = (new value - old value) / old value x 100%
To calculate the population of the city after the growth of 6.8%
Population in 2015 = 89,000 x (1 + 6.8/100)
Population in 2015 = 95,012
To calculate the population of the city after the decline of 4.9%
Population in 2020 = 95,012 x (1 - 4.9/100)
Population in 2020 = 90,199.88
Population in 2020 = 90,200
The total change in the percentage of growth of population in the city is:
percentage change = (new population - old population) / old value * 100%
percentage change = (90,200 - 89,000) / 89,000 x 100%
percentage change = 1,200 / 89,000 x 100%
percentage change = 1.35%
Therefore, we can conclude that the population in the city grew by 1.35% from 2010 to 2020.
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4) Which statement about having a salaried job is true?
Question 4 options:
The employee must work over forty hours to receive a salary each week.
The employee is paid the same amount each week regardless of the number of hours worked.
The employee must have more experience than anyone else.
The employee is paid salary only if they work exactly forty hours each week.
Answers
The statement that is true about having a salaried job is "The employee is paid the same amount each week regardless of the number of hours worked." So, correct option is B.
Salaried jobs typically offer a set salary for a specified period, such as weekly, bi-weekly, or monthly, regardless of the number of hours worked. This is in contrast to hourly jobs where an employee is paid based on the number of hours worked.
Salaried employees often have a contract that specifies their salary and may include additional benefits, such as health insurance, paid vacation days, or retirement plans.
The amount of the salary is often negotiated during the hiring process and may be based on factors such as the employee's experience, education, and qualifications.
While salaried employees are expected to work a certain number of hours per week, the salary remains the same regardless of whether the employee works more or less than the expected hours.
So, correct option is B.
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t C(t)
−2 7
−1 4
0 3
1 4
2 7
What is the equation of C(t)?
C(t) = −(x − 3)2
C(t) = (x − 3)2
C(t) = −x2 + 3
C(t) = x2 + 3
Answers
Answer:
the answer is c(t)=x2 +3
Step-by-step explanation:
because if u insert every x value in x place u will get the 2nd coordinate or y value so it is the correct equation
If the height is tripled, then which of the following statements about its volume will be true
Answers
Answer: 3:1
Step-by-step explanation:
what is the image of
(0,3) after a dilation by a scale factor of
2 centered at the origin? PLEASE HURRY ITS DUE TODAY :((
Answers
The image of the point (0, 3) after dilation by a scale factor of 2 centered at the origin is (0, 6).
What is the image of (0,3) after a dilation by a scale factor of 2 centered at the origin?Dilation is a transformation in which a figure is enlarged or reduced by a scale factor.
We are to find the image of (0,3) after a dilation by a scale factor of 2 centered at the origin.
The scale factor is 2, which means the figure will be enlarged.
To find the image of (0, 3) after dilation, we multiply its x-coordinate and y-coordinate by 2.
Hence;
(0, 3)
Multiply the coordinates by 2.
(0 × 2, 3 × 2)
= (0, 6)
Therefore, the image after dilation is (0, 6).
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Todd throws a ball from his tree house. The height in feet of the ball, h(t), above the ground after t seconds is modeled by the function h(t) = −3t2 + 9t + 12. Select the appropriate domain for the function.
A. 0 ≤ t ≤ 4
B. 0 ≤ t ≤ 12
C. t ≥ 0
D. 0 ≤ t ≤ 18.75
Answers
The solution of the given problem of function comes out to be Option C, t ≥ 0, which is the proper domain for the specified function
Explain function.Each subject will include a range of problems on the final exam covering both real and fictitious locations as well as the formation of numerical factors. a diagram illustrating the connections between various components that work together to produce the same outcome. A service is made up of several individual components that work together to produce unique outcomes for each input.
Here,
In order to represent the height of the ball above the ground after t seconds, the function
=> h(t) = -3t² + 9t + 12
has the correct domain of C. t ≥ 0.
Reason: Since time (t) here refers to the duration in seconds since the ball was thrown, it cannot be negative.
Therefore, t values greater than or equal to 0 should be the only values allowed in the function's domain.
Option C, t ≥ 0, is the proper domain for the specified function and accurately represents this limitation.
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In an illustration of an ant, the length of the ant is 6.5 centimeters. The actual size of the ant is 1.3 centimeters. What is the scale of the illustration?
Answers
Answer:
5
Step-by-step explanation:
6.5 / x = 1.3
multiply by x on each side to cancel it out
6.5 = 1.3x
/1.3 /1.3
x = 5
1.3 x 5 = 6.5
Solve for the value of X 130 degrees X+134
Answers
Answer:
-4. my answers need to be 20 characters+ soooo
what is the total amount of water that Kiesha drinks during the 12 days
Answers
The total amount of water Keisha drinks in 12 days is 12 + 18 = 30 quarts.
Describe Algebra?Algebra is a branch of mathematics that involves using letters and symbols to represent numbers and quantities in mathematical equations and formulas. It includes a variety of topics, such as solving equations, manipulating expressions, working with functions and graphs, and studying abstract structures such as groups and rings.
At its core, algebra is about understanding the relationships between numbers and how they can be manipulated using various operations such as addition, subtraction, multiplication, and division. Algebraic expressions can be used to model real-world situations and solve problems in fields such as physics, engineering, and finance.
To find the total amount of water Keisha drinks in 12 days, we need to add up the amounts of water she drinks each day:
1 1/2 + 2 1/4 + 2 + 1 1/2 + 1 3/4 + 1 1/2 + 1 1/4 + 2 + 2 1/4 + 1 1/2 + 2 + 1 1/2
We can simplify the mixed numbers by converting them to improper fractions:
3/2 + 9/4 + 2 + 3/2 + 7/4 + 3/2 + 5/4 + 2 + 9/4 + 3/2 + 2 + 3/2
Then we can add the fractions together:
(3/2 + 3/2 + 3/2 + 2 + 2 + 2) + (9/4 + 7/4 + 5/4 + 9/4 + 3/2 + 3/2)
Simplifying the sum of the whole numbers, we get:
12
Simplifying the sum of the fractions, we get:
(18/4 + 14/4 + 10/4 + 18/4 + 6/4 + 6/4) = 72/4 = 18
So the total amount of water Keisha drinks in 12 days is:
12 + 18 = 30 quarts.
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The complete question is:
For 12 days, Keisha keeps track of how much water she drinks per day. 1 1/2 quarts, 2 1/4 quarts, 2 quarts, 1 1/2 quarts, 1 3/4 quarts, 1 1/2 quarts, 1 1/4 quarts, 2 quarts, 2 1/4 quarts, 1 1/2 quarts, 2 quarts, 1 1/2 quarts. What is the total amount of water that Keisha drinks the 12 days?
what does -8-12 equal to and how
Answers
According to operations in maths, -8 - 12 is solved by adding the two numbers together and maintaining the negative sign, which will give us: -20.
How to Carry Out Operations in Mathematics?Operations in mathematics are often guided by these rule listed below:
minus + plus = minus
minus + minus = minus
minus × minus = plus
minus × plus = minus
Thus, if we are given the expression, -8 - 12, applying the second rule stated above, we will have:
-8 - 12 = -20
This means we are adding two negative numbers together, which will give us the negative value of their sums.
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You want to make a rectangular banner that is 16 feet long. You have no more than 50 feet of trim for the banner. What are the possible widths of the banner?
Answers
Answer:
So, the possible width of the banner would be 9 feet or less, since we have assumed a maximum total trim of 50 feet. If the width exceeds 9 feet, the total trim required would exceed the available trim of 50 feet. Therefore, the possible widths of the banner are 9 feet or less.
Step-by-step explanation:
Given:
Length of the banner (L) = 16 feet
Total trim available (T) = 50 feet
The perimeter of a rectangle is given by the formula:
Perimeter = 2 * (Length + Width)
In this case, the perimeter of the banner would be equal to the total trim available, since the trim goes all the way around the banner.
So, we can set up the equation as follows:
2 * (L + w) = T
Plugging in the given values:
2 * (16 + w) = 50
Simplifying the equation:
32 + 2w = 50
2w = 50 - 32
2w = 18
w = 18 / 2
w = 9
17swtchPLEASE HELP ME THIS IS URGENT I WILL GIVE BRAINLIEST ALL FAKE ANSWERS WILL BE REPORTED AND PLS PLS PLS EXPLAIN THE ANSWER OR HOW U GOT IT PLEASE AND TY
Answers
For given triangle, Length of XY and YZ is equal to 7√2.
What is a triangle's definition?
A triangle has three straight sides and three angles. It is one of the basic shapes in geometry and has many properties and applications in mathematics and everyday life. The sum of the interior angles of a triangle is always 180 degrees, and there are different types of triangles depending on their side lengths and angle measures and it includes 6 types of triangles.
Now,
If one of the angles of a right triangle is 90 degrees and another angle is 45 degrees, then the third angle must also be 45 degrees. This means that the triangle is a 45-45-90 triangle, which has a special property that the two legs are congruent and the hypotenuse is the square root of 2 times the square length of each leg.
In this case, the hypotenuse is given as 14, so we can set up the following equation:
14 = √2x²
where x is the length of each leg of the triangle. To solve for x, we can square both sides of the equation:
14² = 2x²
196 = 2x²
x² = 98
x = 7√2
So, each leg of the triangle has a length of 7√2, and the hypotenuse has a length of 14.
Hence,
Length of XY and YZ is equal to 7√2.
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Sheryl makes $7 per pair of earrings, e and $13 per necklace, n, she sells what expression represents her total income
Answers
Answer:
You just need to create an expression with the variables then add them together to get the total income: 7e + 13n
8s + 8 < s + 9 solve the following inequality for a( simplest form)
Answers
Answer:
s < [tex]\frac{1}{7}[/tex]
Step-by-step explanation:
8s + 8 < s + 9
7s + 8 < 9
7s < 1
s < [tex]\frac{1}{7}[/tex]
What type of skew is observed in this histogram?
Answers
The type of skewness that can be observed in an histogram are positive and negative skewness.
What type of skew can be observed in an histogram?An histogram can display both positive and negative skewness.
A positive skew means that the tail of the histogram is longer on the positive side of the distribution, indicating that there are more data points with smaller values, and fewer data points with larger values.
A negative skew, on the other hand, means that the tail of the histogram is longer on the negative side of the distribution, indicating that there are more data points with larger values, and fewer data points with smaller values.Read more about histogram at
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In a probability experiment, Karen flipped a coin 51 times. The coin landed on heads 31 times. What percentage of the coin flips resulted in tails? Round to the nearest percent.
PLSSSSSSSSSSSSS HELP 50 PTSSSSSSSSSS I WILL GIVE YOU BRAINLYIEST
Answers
Approximately 39% of coin tosses resulted in tails
What is probability in math and example?Probability is the likelihood or possibility of an event. For example, the probability of tossing a coin is ½ because there is 1 way to get heads and the total number of possible outcomes is 2 (heads or tails).
Since the coin landed heads 31 times in 51 tosses, it must be 51 - 31 = 20 times.
We can use the following formula to figure out the percentage of conversions that result in leads.
percentage of tails = (number of tails / total number of spins) x 100
Let's paste the values we have:
percentage of heads = (20/51) x 100
percentage of heads = 0.39215686274 x 100
percentage of tails = 39.215686274
Rounding to the nearest percentage, we get: tail rate ≈ 39%
Thus, approximately 39% of coin tosses resulted in tails
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Select the correct answer.
What is the range of the function graphed below?
A. -∞
B.-2
C. -∞
D.-∞
Answers
The range of the function graphed above include the following: D. -∞ ≤ y ≤ 2.
What is a range?In Mathematics and Geometry, a range can be defined as the set of all real numbers that connects with the elements of a domain.
Additionally, the vertical extent of any graph of a function represents all range values and they are always read and written from smaller to larger numerical values, and from the bottom of the graph to the top.
By critically observing the graph shown in the image attached above, we can reasonably and logically deduce the following range and domain:
Range = {-∞, 2} or -∞ ≤ y ≤ 2.
Domain = {-1, ∞} or -1 < x < ∞.
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1. According to the podcast, why and how is chicken the reason American trucks dominate the truck market in the United States? Briefly explain. 2. Name two reasons a party (e.g., a politician or an industry association) may want to impose a tariff? 3. Who are they usually trying to protect? Who would be hurt by a tariff on automobiles? Explain. 4. Describe how competition encourages innovation? In your answer to this question, include a discussion on why American trucks "basically stayed the same over the years. 5. Describe ways foreign companies tried to get around American-imposed tariffs on automobiles. 6. Do you think the methods you described in your previous answer are efficient for an economy? Why or why not? 7. Lastly, how can a tariff be used as a bargaining chip? In your opinion, is that a good reason to impose tariffs - why or why not?
Answers
1. Chicken became the key product that drove the creation of the Interstate Highway System, which led to the dominance of American trucks in the US truck market.
2. A party may want to impose a tariff to protect domestic industries from foreign competition or to generate revenue for the government.
3. A party is usually trying to protect domestic industries, but a tariff on automobiles would hurt both domestic consumers who would pay higher prices and foreign producers who would face reduced demand.
4. Competition encourages innovation by providing incentives for companies to improve their products and services to stay ahead of their rivals; American trucks stayed the same because they faced little competition due to protectionist policies.
5. Foreign companies tried to get around American-imposed tariffs on automobiles by establishing factories in the US, forming joint ventures with American companies, or exporting through third countries.
6. The methods used to get around tariffs can be efficient in the short term, but they may not be sustainable or desirable in the long term as they can lead to trade imbalances and undermine the competitiveness of domestic industries.
7. Tariffs can be used as a bargaining chip to negotiate better trade deals, but they should be imposed judiciously and only as a last resort to avoid damaging the economy and harming consumers.
1. In the podcast, chicken is cited as the reason why American trucks dominate the truck market in the United States.
This is because in the 1960s, the government imposed regulations on the trucking industry that limited the amount of weight a truck could carry.
To get around these regulations, the industry started using smaller trucks to transport goods, which were often not strong enough to handle the weight.
However, they found that if they put chicken on the back of the trucks, the weight of the cargo would distribute more evenly and the smaller trucks could handle the load.
This led to the development of the modern pickup truck, which is now a staple of the American automobile market.
2. Parties may want to impose tariffs for various reasons, such as to protect domestic industries and jobs from foreign competition, to raise revenue for the government, or to level the playing field in international trade.
Two specific reasons for imposing tariffs could be to protect national security interests or to address unfair trade practices by other countries.
3. Tariffs are usually imposed to protect domestic industries and jobs, and the parties that are being protected are typically the producers of the goods or services in question.
However, tariffs can also harm consumers who may have to pay higher prices for imported goods or may have fewer choices in the marketplace. For example, if a tariff is imposed on automobiles, domestic car manufacturers may benefit, but consumers may have to pay more for cars, and foreign automakers may lose market share.
4. Competition encourages innovation by creating incentives for companies to improve their products or services to gain a competitive advantage.
In the case of American trucks, the lack of competition may have contributed to their lack of innovation over the years. Since they dominated the market, there was little pressure to improve or innovate, and as a result, they have largely stayed the same.
However, the rise of foreign competition in recent years has led American truck manufacturers to invest more in innovation to stay competitive.
5. Foreign companies have tried to get around American-imposed tariffs on automobiles in various ways, such as by moving production to countries not subject to the tariffs, by exporting parts and assembling them in the United States, or by lobbying the government for exemptions or tariff reductions.
6. The methods used by foreign companies to get around tariffs may not be efficient for the economy as a whole because they can lead to higher costs and inefficiencies in the supply chain.
However, they may be necessary for individual companies to remain competitive in the short term.
Ultimately, a more efficient solution would be to address the root causes of the trade imbalances that lead to tariffs in the first place.
7. A tariff can be used as a bargaining chip by threatening to impose tariffs on imports from a country unless they make concessions in trade negotiations.
While this can be an effective strategy in certain situations, it can also lead to a trade war and harm both economies.
In general, tariffs should be used sparingly and as a last resort, and efforts should be made to address underlying trade issues through diplomacy and negotiation.
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Sravya earns $42,820 per year in take home pay. What is the most money a housing expert would advise her to spend on a monthly mortgage payment?
Answers
Answer:
3568 or 3567
Step-by-step explanation:
42820 divided by 12
How to calculate 1over4 to a equivalent factions with denominator?
Answers
To express 1/4 as an equivalent fraction with a different denominator, we need to find a common multiple of 4 and the desired denominator.
Let's say we want to express 1/4 as an equivalent fraction with a denominator of 12. To do this, we can multiply both the numerator and denominator of 1/4 by 3, which gives us:
1/4 x 3/3 = 3/12
So 1/4 is equivalent to 3/12 when the denominator is 12.
In general, to express a fraction a/b as an equivalent fraction with a different denominator c, we can multiply both the numerator and denominator by the same value that makes b equal to c.
This is because when we multiply both the numerator and denominator by the same value, we are essentially multiplying the fraction by 1, which does not change its value.
For example, to express 2/5 as an equivalent fraction with a denominator of 15, we can multiply both the numerator and denominator by 3, which gives us:
2/5 x 3/3 = 6/15
Therefore, 2/5 is equivalent to 6/15 when the denominator is 15.
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Help PLEASEEEE!!!!!!!!!
Answers
A parabola opening up or down has vertex (0,-6) and passes through (-6,3). Write its equation in vertex form.
Answers
The equation of the parabola in vertex form is y = (1/4)x² - 6.
What is the equation of the parabola?To write the equation of the parabola in vertex form, we use the formula:
y = a(x-h)² + k
Where (h,k) is the vertex and "a" is a constant that determines the shape of the parabola.
Given that;
The vertex is (0,-6)
Hence:
h = 0 and k = -6.
We can substitute these values into the formula to get:
y = a(x-h)² + k
y = a(x - 0)² - 6
y = ax² - 6
Now we need to find the value of "a". We are also given that the parabola passes through the point (-6,3).
x = -6 and y = 3
We can substitute this point into the equation to get:
y = a(x - h)² + k
3 = a( - 6)² - 6
3 = 36a - 6
9 = 36a
a = 1/4
Now we know the value of "a", we can substitute it back into the equation we derived earlier:
y = ax² - 6
y = (1/4)x² - 6
Therefore, the equation in vertex form is y = y = (1/4)x² - 6.
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Use limits to determine if
x+3
f(x) = is continuous at x = 3.
Answers
The correct answer is (d) No, it is not continuous because lim x→3 f(x) ≠ lim x→3 f(x).
To determine if the function f(x) = (x+3)/(x²-9) is continuous at x=3, we need to check if the limit of the function exists as x approaches 3 from both the left and the right, and whether this limit is equal to the value of the function at x=3.
First, we can check the limit as x approaches 3 from the left:
lim x→3- f(x) = lim x→3- (x+3)/(x²-9) = (-3)/(0-) = ∞
Next, we can check the limit as x approaches 3 from the right:
lim x→3+ f(x) = lim x→3+ (x+3)/(x²-9) = (6)/(0+) = ∞
Since both one-sided limits are infinite, the limit as x approaches 3 does not exist.
Therefore, the function f(x) = (x+3)/(x²-9) is not continuous at x=3.
The correct answer is (d) No, it is not continuous because lim x→3 f(x) ≠ lim x→3 f(x).
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12. Look for Relationships In the graph of a
vertical motion model shown, how is the initial
velocity related to the vertex of the parabola?
Answers
The vertical component of the initial velocity will basically decide where the vertices will be. that is how the initial velocity is related to the vertex of the parabola.
Describe Parabola?A parabola is a symmetrical curve that is formed by the intersection of a plane and a cone, where the plane is parallel to one of the cone's generating lines. The shape of a parabola is similar to that of a U-shaped curve, but with a sharper curve near the bottom of the U.
The parabola has several important properties, including a focus and a directrix. The focus is a point on the axis of symmetry of the parabola that is equidistant from every point on the curve. The directrix is a line that is perpendicular to the axis of symmetry and is equidistant from every point on the curve.
The equation of a parabola in standard form is y = ax² + bx + c, where "a" determines the direction and shape of the parabola, "b" determines the horizontal shift of the parabola, and "c" determines the vertical shift of the parabola.
The initial velocity will have two component basically, a horizontal component and a vertical component. The vertical component will decide how high the object will go, or in other words the vertical component of the velocity will decide the position of the vertex of the parabolis path which the object is going to follow.
When the vertical component of the velocity becomes 0, the object will be at it's maximum height (i.e the object will be at the vertex of the parabola)
The vertical component of the initial velocity will basically decide where the verties will be. that is how the initial velocity is related to the vertex of the parabola.
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Rewrite 11,000,000 as a power of 10.
Answers
Rewriting 11,000,000 as a power of 10 using scientific notation is: 1.1 * 10⁷
How to write the number in Scientific form?A number is written in scientific notation whenever a number between 1 and 10 is multiplied by a power of 10. For example, 650,000,000 can be written in scientific notation as 6.5 * 10^8.
Now, we want to write the number 11000000 as a power of 10. Using the concept of scientific notation, we have:
11000000 = 1.1 * 10⁷
That is the final expression of the given number as a power of 10
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