Answer:
estimate a population proportion
Step-by-step explanation:
The choices are missing in the question, correct question is:
In a January 2017 Washington Post-ABC News poll, respondents were asked “There is a proposal to offer nearly 140 billion dollars in tax cuts for private companies if they pay to build new roads, bridges and transportation projects. The companies then could charge tolls for people to use these roads, bridges and transportation. Do you support or oppose this proposal?” Of the 1005 people polled, 66 percent of those surveyed said they oppose the above proposal. An objective of this study is to ________ .
a. test a claim about a population mean
b. estimate a population mean
c. test a claim about a population proportion
d. estimate a population proportion
Population proportion estimate will give the percentage of people who support or oppose the proposal of 140 billion dollars in tax cuts for private companies so that they build charge tolled new roads, bridges and transportation projects.
People are asked "Do you support or oppose this proposal?", this shows that the purpose of the study is to estimate a population proportion.
The Washington Post-ABC News poll aimed to calculate public opinion on a policy proposal regarding tax cuts and infrastructural developments paid by private companies. The majority of respondents opposed the proposal signifying its unpopularity among the surveyed population. However, results from this single poll may not represent wider public sentiment.
Explanation:The question pertains to a public policy proposal. In a Washington Post-ABC News poll from January 2017, participants were asked to indicate their support or opposition to a proposition concerning tax cuts and infrastructure development funded by private companies. The question revolves around an actual policy proposal that could have impacts on the economy and society. The study's objective in this case is to gauge public opinion on the proposal, which could be used to inform policy decisions or strategies by politicians, businesses, or advocacy groups.
The fact that 66 percent of the 1005 people polled opposed the proposal suggests a majority of the respondents were not in favor of the plan. In recognizing such data and understanding its implications, it is important to remember that this is just one poll and may not necessarily represent the broader public's views.
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Megan’s art class painted two regular murals.The size of the first mural is shown below.
Answer:C) 4 feet and 12 feet
Step-by-step explanation:
The diagram of the first mural is shown. The formula for determining the perimeter of a rectangle is expressed as
Perimeter of rectangle = 2(L + W)
The length of the first mural is given as 8ft while the width of the first mural is given as 6 ft. The perimeter becomes
P = 2(8 + 6) = 2×14 = 28ft
The area of a rectangle is expressed as L×W
The area if the first mural would be
6 × 8 = 48ft^2
The second mural has the same area as the first mural but has a different perimeter. The side lengths of the second mural are
4 ft and 12ft
Area = 4×12 = 48 ft^2
Perimeter = 2(12+4) = 32ft
So area is the same and perimeter is different.
an automobile 16 feet long overtakes a truck that is 28 feet long and is traveling 30 mph. At what rate must the automobile travel to pass the truck in 4 seconds?
Step-by-step explanation:
Length of automobile = 16 feet = 4.88 m
Length of truck = 28 feet = 8.53 m
Speed of truck = 30 mph = 48 km/h = 13.33 m/s
Time in which automobile to pass truck = 4 s
Distance traveled by truck in 4 seconds = 4 x 13.33 = 53.33 m
Distance which need to cover by automobile in 4 seconds to pass truck is the sum of length of automobile, length of truck and distance traveled by truck in 4 seconds.
Distance which need to cover by automobile in 4 seconds = 4.88 + 8.53 + 53.33
Distance which need to cover by automobile in 4 seconds = 66.74 m
Distance = Speed x Time
66.74 = Speed x 4
Speed = 16.69 m/s = 60 km/h = 96 mph
Automobile must travel at 96 mph to pass the truck in 4 seconds.
need help please ty (:
Find x.
===================================
Work Shown:
Through the inscribed angle theorem, we can say that 2 times the inscribed angle gets us the arc that the inscribed angle cuts off.
2*(inscribed angle) = arc measure
2*(2x+2) = 76
4x+4 = 76
4x+4-4 = 76-4 ... subtract 4 from both sides
4x = 72
4x/4 = 72/4 ... divide both sides by 4
x = 18
Answer:
Step-by-step explanation:
2 × inscribed angle = 76
2 × (2x + 2) = 76
Open bracket
4x + 4 = 76
Collect like terms
4x = 76 - 4
4x = 72
Divide both sides by 4
4x/4 = 72/4
X = 18
Therefore X is Equal to 18.
Sara completes 2/5 of her math homework in class. What percent of homework is left for Sara to finish?
Answer:
.006%
Step-by-step explanation:
A firm is hiring labor and capital in the cost-minimizing combination. Which of the following would cause the firm to increase hiring capital and decrease hiring of labor?
The productivity of labor increases by 5% would cause the firm to increase hiring capital and decrease hiring of labor
Step-by-step explanation:
A company can convert input data to output data. So, it gets divided the data into broad categories called production factors. Productivity variations, or more precisely the marginal products of labour, work in the same way as differences in real wages. Remember that marginal prices depend on both - real wages and the productivity.
If in case, productivity increases, perhaps because the company has increased its capital base, thereby marginal costs will decrease. Companies will produce more products and employ more employees. Conversely, if productivity drops, companies will produce less and destroy jobs.
When a firm faces union demands for higher wages, they may increase hiring of capital and decrease hiring of labor. This can result in increased labor productivity. In the United States in the 1970s, firms shifted towards more capital and less labor due to union demands for higher wages.
Explanation:When a firm is confronted with union demands for higher wages, they may choose to increase hiring of capital and decrease hiring of labor. This is because using more physical capital and less labor can result in increased labor productivity.
For example, if the cost of machines increases relative to labor, the firm may shift towards using less capital and more labor to minimize costs. In this situation, the firm would hire more capital and decrease hiring of labor.
In the United States in the 1970s, this situation occurred where firms faced union demands for higher wages, causing a shift towards more capital and less labor in production methods.
Mitch has already spent 26 minutes on the phone, and he expects to spend 2 more minutes with every phone call he routes. Write the relationship between the phone calls routed p and the minutes on the phone t.
Answer:
minutes spent on phone (t) is directly proportional to the phone calls routed (p) with equation [tex]t =26+2p[/tex].
Step-by-step explanation:
Given:
Number of minutes already spent = 26 minutes
Number of minutes expected to spend on each call = 2
Let number of calls routed be 'p'
Also Let number of minutes on the phone be 't'.
We need to find the relationship between phone calls routed and mins spend on the phone.
Solution:
Now we know that;
Total minutes spent on phone is equal to Number of minutes already spent plus Number of minutes expected to spend on each call routes multiplied by number of calls routed.
framing in equation form we get;
[tex]t =26+2p[/tex]
From above we can see that whenever p increases the value of t will increase too .
Hence we can say that minutes spent on phone (t) is directly proportional to the phone calls routed (p) with equation [tex]t =26+2p[/tex].
Mark and his three friends are out of Applebee's. Their total is 52.35 If they left the server a 20% tip how much would each person pay splitting the bill evenly
Answer:
per person$15.71
Given a positive integer N, find all of the positive integers from 1 to N that can be written as a sum of 2 cubic numbers (also have to be positive) in two different ways.
Answer:
There are infinite such positive integers which can be written as a sum of cubes of two positive integers. Some of them are written below:
1³+12³=9³+10³=17292³+24³=18³+20³=1383210³+27³=19³+24³=2068315³+945³=744³+756³=843912000Hence it is not possible to write all such numbers which can be written in this format. Though some of them can be enlisted if the value of maximum integer "N" is given.
Given: ∆AKM, R = 2, m∠A = 33°, O∈ AM . Find: perimeter of ∆AKM
Answer:
∆AKM is a right triangle for it is inscribed in semicircle O.
AM = diameter of semi-circle O = 2R = 2(2) = 4
%22AK%22%2F%22AM%22=cos%2833%5Eo%29
AK+=+AM%2Acos%2833%5Eo%29
AK+=+4cos%2833%5Eo%29
%22KM%22%2F%22AM%22=sin%2833%5Eo%29
KM+=+AM%2Asin%2833%5Eo%29
KM+=+4sin%2833%5Eo%29
The perimeter of a triangle is the sum of the three sides.
perimeter=AK%2BKM%2BAM
perimeter=4cos%2833%5Eo%29%2B4sin%2833%5Eo%29%2B4
Approximately 9.533238412
Step-by-step explanation:
Answer:
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Step-by-step explanation:
a basketball coach is ordering new basketballs for the upcoming season. Let X be the number ball she can buy. Balls cost $65 and she will buy at least one shopping is a flat fee of $25 she has a budget of $545 that she can spend. Which inequality and solution set best model this situation?
A. 545>25x+65
B. 545>65x+25
C. 545(65+25)x
D. The solution set is all positive integers less than or equal to 6
E. Solution set is all positive integers less than or equal to 8
F. The solution set is all positive integers less than or equal to 19
Select each correct answer
Answer:
B & E.
Step-by-step explanation:
$25 is the y value, because she has to pay the fee no matter what.
Integers can be less than or equal to 8 because 65(8) + 25 is equal to 545, which does not exceed the budget.
Hope this helps!
question : The diagram shows a plan for creating a zoo’s elephant exhibit. The elephant pen will be surrounded on two sides by a walkway with a viewing area in one corner. The sides, shown as dotted lines, will be fenced. How much fencing separates the elephant area from the walkways
answer choices :
(A) 180 feet
(B) 250 feet
(C) 540 feet
(D) 750 feet
Answer:
C
Step-by-step explanation:
We need to find the length of the red dotted line.
It is divided into 3 parts: the top, the middle slant, and the bottom
The top
Goes from y = 50 to y = 120, the length is:
120 - 50 = 70 units
The bottom
Goes from x = 60 to x = 120, the length is:
120 - 60 = 60 units
The middle slant
This is hypotenuse of the right triangle shown.
We will use Pythagorean Theorem to solve for this length, let it be x.
The theorem is:
Leg^2 + Another Leg^2 = x^2
One leg goes from x = 20 to x = 60, the length is 60 - 20 = 40
Another leg goes from y = 20 to y = 50, the lenth is 50 - 20 = 30
So, we have:
[tex]30^2+40^2=x^2\\2500=x^2\\x=\sqrt{2500}\\x=50[/tex]
THe slant length is 50 units
TOtal fencing is: 70 + 60 + 50 = 180 units
1 unit is 3 feet, so
180 units * 3 = 540 feet
C is the correct answer
math please help! thanks
Answer:
B
Step-by-step explanation:
For a function to be true, there cannot be any same x value for two different y value. Therefore, B, there is the same x value for 4 but with 2 different ys, 4 and 1.
Answer:
B.
Step-by-step explanation:
It is B because it contains a one-to-many relation.
4 maps to 4 and also 4 maps to 1.
Sheila predicts that 480 people will attendthe fall concert. There was an actual total of 350 people who attended the fall concert. What is the percent error?
Final answer:
To calculate the percent error, subtract the actual attendance from the predicted attendance, take the absolute value, divide by the actual attendance, and multiply by 100%. Sheila's prediction has a percent error of 37.14%.
Explanation:
The question is asking for the calculation of the percent error between Sheila's prediction for concert attendance and the actual attendance. To find the percent error, you subtract the actual value from the predicted value, take the absolute value of the difference, divide by the actual value, and then multiply by 100 to convert it to a percentage.
Steps to Calculate Percent Error
Subtract the actual number of attendees (350) from the predicted number (480) to get the difference: 480 - 350 = 130.Take the absolute value of the difference: |130| = 130.Divide the absolute difference by the actual number of attendees: 130 / 350 = 0.3714.Multiply by 100 to get the percent: 0.3714 * 100 = 37.14%.The percent error in Sheila's prediction is 37.14%.
JUST ONE MORE I NEED HELP ON HW IM STRUGGLING 15pts
A pilot was scheduled to depart at 4:00 pm, but due to air traffic, her departure has been delayed by 16 minutes. Air traffic control approved a new flight plan that will allow her to arrive four times faster than she calculated in her original flight plan. Let x represent the time, in minutes, of her original flight. Create an equation that can be used to predict the number of minutes after 4:00 pm she will arrive at her destination.
y equals one fourth times x minus 16
y = 4x − 16
y equals one fourth times x plus 16
y = 4x + 16
Answer:
y equals one fourth times x minus 16
y = 4x − 16
Step-by-step explanation:
this is because you're taking the time it took to get there minus 16 because of the delay
Answer:
Answer is three because it is one fourth of the time don't listen to the other person's.
Step-by-step explanation:
Write an equation for the line that is parallel to y = −2x and passes through the point (0,7).
A. y=2x–7
B. y=-2x + 7
C. y=-2x-7
D. y=2x+7
Answer:
B. [tex]\displaystyle y = -2x + 7[/tex]
Step-by-step explanation:
The y-intercept is given to us, which is [tex]\displaystyle [0, 7],[/tex]and Parallel Lines have SIMILAR RATE OF CHANGES [SLOPES], so −2 remains the way it is.
I am joyous to assist you anytime.
The shadow of the moon during a solar eclipse travels 2300 miles in one hour in the first 20 minutes the Shoadow traveled seven 66 2/3 miles how long does it take for the Shadow to reach 1150 miles
Final answer:
It takes 30 minutes for the moon's shadow to travel 1150 miles during a solar eclipse based on the speed of 2300 miles per hour.
Explanation:
The question asks us to calculate the amount of time it takes the moon's shadow to travel a certain distance during a solar eclipse, based on given speeds and distances. We know that the shadow travels 2300 miles in one hour, so the speed of the shadow is 2300 miles per hour. In the first 20 minutes, the shadow traveled 766 ⅓ miles. To find the time it takes the shadow to reach 1150 miles, we set up a proportion since the motion of the shadow is at a constant speed.
First, let's convert the 20-minute travel time to hours by dividing by 60, which is ⅓ of an hour (20 / 60 = ⅓). Then we can set up the proportion as follows:
766 ⅓ miles is to ⅓ hour, as 1150 miles is to T hours. Which gives us:
(766 ⅓ / 2300) = (⅓ / 1)
(1150 / 2300) = (T / 1)
Now, we solve for T:
⅓ = 1150 / 2300
T = ⅓
So, T is ⅓ of an hour, which means that it takes ⅓ of an hour for the shadow to reach 1150 miles. We can convert ⅓ of an hour to minutes by multiplying by 60, thus:
T = ⅓ × 60
T = 30 minutes
Therefore, it takes 30 minutes for the shadow to reach 1150 miles.
Joe wants to build a doll house for his daughter. He wants the doll house to look just like his house. His house is 28 feet wide and 36 feet tall at the highest point of the roof. If the dollhouse will be 2.5 feet wide, how many feet will its highest point be?
The highest point for the dollhouse will be 3.12 feet
What is Proportional?Any relationship that is always in the same ratio and quantity which vary directly with each other is called the proportional.
Given that;
His house is 28 feet wide and 36 feet tall at the highest point of the roof.
And, The dollhouse will be 2.5 feet wide.
Now,
Let the highest point for the dollhouse = x
So, By definition of proportion, we get;
⇒ 28 / 36 = 2.5 / x
Solve for x as;
⇒ x = 2.5 × 36/28
⇒ x = 3.12 feet
Thus, The highest point for the dollhouse = 3.12 feet
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help me on this question please
Answer:
Step-by-step explanation:
The diameter equals the side length of the outer square. The radius of the circle is √2. The diameter of the circle would be
2 × radius = 2 × √2 = 2√2
The area of a square is expressed as length^2. This means that the area of the outer square would be
( 2√2)^2 = 4×2 = 8
The area of the circle is expressed as πr^2. Therefore, the area of the circle would be
π×√2^2 = 2π = 2×3.14 = 6.28
Looking at the inner square, to find the length of the base, we would apply Pythagoras theorem.
√2^2 = base^2 + 1^2
2 = base^2 + 1
base^2 = 2 -1 = 1
base = √1
Area of the inner square would be
√1^2 = 1
Total shaded area would be
6.28 - 1 = 5.28
The probability that the dart will land on the shaded area is
5.28/8 = 0.66
Jess wants to make tarts. To make tarts, she needs 8/9 of a cup of flour per batch of tarts. If Jess has 8 cups of flour, then how many batches of tarts can Jess make?
Answer:
9 batches of tarts.
Step-by-step explanation:
This is 8 / (8/9)
= 8 * 9/8
= 9 batches of tarts.
Madhu is hanging a string of flowers on the perimeter of a rectangular pool deck. The deck is 30 feet long and 24 feet wide. How long does the string of flowers need to be?
Answer:
108 feet long
Step-by-step explanation:
You know that to find the perimeter you have to add up all the sides. A rectangle has 4 sides, so 30+30 is 60 and 24+24 is 48. Add 60 and 48 up and you get 108 as the perimeter. Since Madhu is hanging a string of flowers on the PERIMETER, the flower string will need to be 108 feet long.
Hope this Helped!
Twenty years ago, you began investing $3,000 a year. Because your investments earned an average of 8 percent a year, your investment portfolio has a current dollar value of $92,000. How much did you earn on your investments over the 20-year period of time? a.) $40,000
b.) $132,000
c.) $92,000
d.) $52,000
e.) $2,000
Answer:
$32,000
Step-by-step explanation:
Yearly investment = $3,000
Number of years = 20
Investments earned an average of 8 percent a year.
Total invested amount = $3,000 × 20 = $60,000
Current value of investment = $92,000.
We need to find the total earnings on the investment.
Earnings = Current value of investment - Total invested amount
Earnings = $92,000 - $60,000
Earnings = $32,000
Therefore, the total earnings is $32,000.
To find out how much was earned on the investments over a 20-year period, we subtract the total amount invested ($60,000) from the final value of the portfolio ($92,000), yielding $32,000 as the total earnings. However, this option is not offered in the question.
Explanation:This type of question is typically encountered in personal finance or mathematics related to investment portfolios. The total amount invested over twenty years is calculated by multiplying the yearly investment by the number of years, so $3,000 * 20 years = $60,000. This is the amount you've put in from your own pocket. The value of the investment portfolio now is given as $92,000, which is the sum of your investment and the earnings. So to calculate your earnings alone, you subtract the total amount you invested from the current value of your portfolio: $92,000 (total value) - $60,000 (your total investment) = $32,000. So the amount you earned on your investments over this 20-year period is not given in the question as none of the options match our calculation of $32,000.
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Using the diagram, find the value of x.
←—→–————↗———→
10x
7x-7
←—→–—↙——————→
A. -9
B. 2
C. 8
D. 11
If you could elaborate on what this is, I would be gladly to assist you, but there is uncertainty going on here. I apologise.
I don’t get this please help ASAP
Answer:
AE = 70
Step-by-step explanation:
Given that ACE is a triangle and B , D , F are mid-points of AC, CE, AE respectively.
⇒ BF, FD, BD are mid-segments.
Mid-segment is a line segment joining mid points of two sides of a triangle,
And it as two properties :
1) mid-segment is always parallel to the third side
2) mid-segment is half in length of the third side
⇒ Here, BD is the mid-segment and is parallel to third side AE
And also BD is half of AE
⇒ AE = 2×BD = 2×35
⇒ AE = 70.
The height of water in a rectangular tank is given by h(w), where w is the volume of water (in liters) that has been removed from the tank. The height of the water decreases 10mm per liter removed.
a. From the time when 7 L have been removed to the time when 15 L have been removed, the accumulated change in the height of the water is
b. If the initial height of the water is 600mm, then the height of the water after w liters have been removed is
Answer:
a) ΔL = 80mm
b) h = 600 - 10w mm
Step-by-step explanation:
a. From the time when 7 L have been removed to the time when 15 L have been removed, the change in the volume has been 8L and how the height of the water decreases 10mm per liter removed, then the acumulate change in the height of water has been (8lt)(10mm/lt) = 80 mm
b) If w liters have been removed, then the change in the height of water is (10mm/lt)(wlt) = 10w mm and thus the water's height at this precise point in time is 600 - 10w mm
A pile of newspaper was 17 3/4 inches high. Each consecutive week for the next 5 weeks the height of pile increase by 8 7/12 inches. What is the height in inches, of the pile after 3 weeks?
Answer: the height in inches, of the pile after 3 weeks is 34 11/12 inches
Step-by-step explanation:
Each consecutive week for the next 5 weeks the height of pile increase by 8 7/12 inches. Converting 8 7/12 inches to improper fraction, it becomes 103/12 inches. The height is increasing in an arithmetic progression. The formula for determining the nth term of an arithmetic sequence is expressed as
Tn = a + (n - 1)d
Where
a represents the first term of the sequence.
d represents the common difference.
n represents the number of terms in the sequence.
From the information given,
a = 17 3/4= 71/4 inches
d = 103/12 inches
n = 3 weeks
the height in inches, of the pile after 3 weeks, T3. Therefore,
T3 = 71/4 + (3 - 1)103/12
T3 = 71/4 + 2 × 103/12 = 71/4 + 103/6
T3 = 419/12 inches = 34 11/12 inches
As you move the pointer over font names in the font list, the text on the slide displays a ____ of the different font choices.
Answer:
Live preview
Step-by-step explanation:
Live preview
When looking for a font name live preview is the real time view of how a font looks. Software which provides a live preview allows the person to see their font as it would appear if published, updated live as they make changes
Moving the pointer over font names in the font list displays a preview of the different font choices.
Explanation:As you move the pointer over font names in the font list, the text on the slide displays a preview of the different font choices. This allows you to see how the text will look with different fonts before making a selection. It helps in making a decision based on the visual appearance of the text.
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It takes 2 minutes to print out 3 photos. Write an equation relating the number of photos N to the number of minutes M. At this rate, how long will it take to print 10 photos? 14 photos?
Answer:
Part a) [tex]M=6\frac{2}{3}\ min[/tex]
Part b) [tex]M=9\frac{1}{3}\ min[/tex]
Step-by-step explanation:
we know that
A relationship between two variables, M, and N, represent a proportional variation if it can be expressed in the form [tex]k=\frac{N}{M}[/tex] or [tex]N=kM[/tex]
In this problem, the relationship between the number of photos N to the number of minutes M represent a proportional variation
we have that
For M=2, N=3
Find the the constant of proportionality k
[tex]k=\frac{N}{M}[/tex]
substitute the value of N and M
[tex]k=\frac{3}{2}[/tex]
so
[tex]N=\frac{3}{2}M[/tex]
Part a) How long will it take to print 10 photos?
For N=10
substitute in the linear equation
[tex]10=\frac{3}{2}M[/tex]
solve for M
[tex]M=\frac{10*2}{3}[/tex]
[tex]M=\frac{20}{3}\ min[/tex]
Convert to mixed number
[tex]M=\frac{20}{3}\ min=\frac{18}{3}+\frac{2}{3}=6\frac{2}{3}\ min[/tex]
Part b) How long will it take to print 14 photos?
For N=14
substitute in the linear equation
[tex]14=\frac{3}{2}M[/tex]
solve for M
[tex]M=\frac{14*2}{3}[/tex]
[tex]M=\frac{28}{3}\ min[/tex]
Convert to mixed number
[tex]M=\frac{28}{3}\ min=\frac{27}{3}+\frac{1}{3}=9\frac{1}{3}\ min[/tex]
Please I need help
Solve the system by substitution.
{
2
.
5
x
−
3
y
=
−
13
3
.
25
x
−
y
=
−
14
Answer:
(x, y) = (-3 5/8, 1 5/16)
Step-by-step explanation:
Add y+14 to the second equation to get ...
3.5x +14 = y
Substitute this for y in the first equation:
2.5x -3(3.5x +14) = -13
2.5x -10.5x -42 = -13
-8x = 29
x = -29/8 = -3 5/8
Using this in the formula for y, we get ...
3.5(-29/8) +14 = y
-203/16 +14 = y = 21/16 = 1 5/16
Answer : The value of x and y is, 4 and 27 respectively.
Step-by-step explanation :
The given equations are:
[tex]2.5x-3y=-13[/tex] ...........(1)
[tex]3.25x-y=-14[/tex] .........(2)
or,
[tex]y=3.25x+14[/tex] ..........(3)
Now put equation 3 in 1, we get the value of 'x'.
[tex]2.5x-3y=-13[/tex]
[tex]2.5x-3(3.25x+14)=-13[/tex]
[tex]2.5x-9.75x-42=-13[/tex]
[tex]-7.25x=-13+42[/tex]
[tex]-7.25x=29[/tex]
[tex]x=-\frac{29}{7.25}[/tex]
[tex]x=-4[/tex]
Now put the value of 'x' in equation 3, we get the value of 'y'.
[tex]y=3.25x+14[/tex]
[tex]y=3.25(4)+14[/tex]
[tex]y=13+14[/tex]
[tex]y=27[/tex]
Therefore, the value of x and y is, 4 and 27 respectively.
Two roads that cross at right angles are used as coordinate axes for a map. A library is located at point L . Use the drop-down menus to complete the statements about the location of the library.
The question is incomplete. Here is the complete question:
Two roads that cross at right angles are used as coordinate axes for a map. A library is located at point L.
Use the drop-down menus to complete the statements about the location of the library.
(a) The library is located at point (_,_).
(b) The library is __ miles from Road X and __ miles from Road Y.
Answer:
(a) The library is located at point (3.25, -1.5).
(b) The library is 1.5 miles from Road X and 3.25 miles from Road Y
Step-by-step explanation:
Given:
The roads are at right angles to each other. Point 'L' is the location of the library.
(a)
From the graph, we can conclude that,
The length of each square in the graph is 0.5 miles. So,
The coordinates of point L are (3.25, -1.5).
The 'x' value is 3.25 and the 'y' value is -1.5.
Since the point 'L' is the location of library, therefore, the library is located at point (3.25,-1.5).
(b)
The distance of point L from road X is obtained by moving vertically up from point L till we reach the road X. In other words, the perpendicular distance between point L and horizontal x axis is the required distance.
The perpendicular distance is the absolute value of the y-coordinate of point L. The absolute value of 'y' of point L is |-1.5| = 1.5 miles.
Hence, the library is 1.5 miles from road X.
Similarly, the distance of point L from road Y is the perpendicular distance of point L to the road Y.
The perpendicular distance is the absolute value of the x-coordinate of point L. The absolute value of 'x' of point L is |3.25| = 3.25 miles.
Therefore, the library is 3.25 miles from road Y.
So, the library is 1.5 miles from Road X and 3.25 miles from Road Y
What is the vertex of the graph of y = -2|x-4|+ 11?
Please show work on how to get the answer. Thanks!
Answer:
The vertex is the point [tex](4,11)[/tex]
Step-by-step explanation:
we know that
The equation of the absolute value in vertex form is equal to
[tex]y=a\left|x-h\right|+k[/tex]
where
a is a coefficient
(h,k) is the vertex
In this problem we have
[tex]y=-2\left|x-4\right|+11[/tex]
so
[tex]a=-2[/tex] ---> the vertex represent a maximum
[tex]h=4[/tex]
[tex]k=11[/tex]
therefore
The vertex is the point [tex](4,11)[/tex]