The range of the following relation R {(3, -5), (1, 2), (-1, -4), (-1, 2)} is (1 point)
{-4, -5, 2, 2)
{-1, 1, 3)
{-1,-1,1,3)
{-5, -4,2)​

Answers

Answer 1

Answer:

{-5,-4,2}

Step-by-step explanation:

The domain is the inputs and the range is the outputs

The outputs are the y values

{ -5,2,-4,2}

We only list them once and in order from smallest to largest

{-5,-4,2}


Related Questions

Simplify [tex]\frac{2\frac{1}{5}-1\frac{1}{2}+1\frac{7}{10} }{\frac{1}{3}of2\frac{2}{5} }[/tex]

Answers

Answer:
3

You need to first subtract everything on the numerator by changing the fractions in the numerator. Each fraction should have a similar denominator. You should end up getting 24/10, simplifying it down to 12/5. After that you multiply the fractions in the denominator part, due to the key word “of” indicating that you need to multiply. Once you do that you have your numerator and denominator simplified down from each equation, you then simplify down further.

The volume of a cube is 27n27 cubic units. What is the lenth of one side of the cube?

Answers

Answer: B . on your test

Step-by-step explanation:

The circle below is centered at (3 1) and has a radius of 2 what is its equation

Answers

Answer:

(x-3)^2 + (y-1)^2 = 4

Step-by-step explanation:

The equation of a circle is usually written in the form

(x-h)^2 + (y-k)^2 = r^2

Where (h,k) is the center and r is the radius

The center is at the origin so (h,k) = (3,1) and  the radius is 2 so r=2

(x-3)^2 + (y-1)^2 = 2^2

(x-3)^2 + (y-1)^2 = 4



Which best describes the transformation from the graph of f(x) = x2 to the graph of 
f(x) = (x – 3)2 – 1? 

left 3 units, down 1 unit

left 3 units, up 1 unit

right 3 units, down 1 unit 

right 3 units, up 1 unit​

Answers

Answer: Third option.

Step-by-step explanation:

These are some transformations for a function f(x):

If [tex]f(x)-k[/tex], then the function is shifted down "k" units.

 If [tex]f(x-k)[/tex], then the function is shifted right "k" units.

Knowing this we can describe the transformation from the graph of the function [tex]f(x) = x^2[/tex] to the graph of the function [tex]f(x) = (x - 3)^2-1[/tex]. This is:

The function  [tex]f(x) = (x - 3)^2-1[/tex] is the function [tex]f(x) = x^2[/tex] but shifted right 3 units and shifted down 1 units.

Therefore, the correct option is the third one.

Answer:

right 3 units, down 1 unit

MARKING BRAINLIEST!

Given that DMKT → FCBN, what is m B?

Answers

Answer:

79°

Step-by-step explanation:

given both figures are congruent, and one is simply a rotation of another

m∠B corresponds to m∠k = 79°

Answer:

Given that DMKT → FCBN, B is 79°

Step-by-step explanation:

m∠D = m∠F, m∠M = m∠C, m∠K = m∠B and m∠T = m∠N

m∠K = 79° therefore m∠B = 79°.

Please mark brainliest and have a great day!

I really dont get this and I really need to get past it help me please ​

Answers

Answer:

26

Step-by-step explanation:

Area of a triangle is:

A = 1/2 b h

Given b = 13 and h = 4:

A = 1/2 (13 cm) (4 cm)

A = 26 cm²

PLEASE HELP ME SUPER FAST IM STICK ON THESE 3!
See attachment below!

Answers

Answer:

25. The area of the trapezoid is 96 cm² ⇒ 2nd answer

26. The area of the kite is 40.8 feet² ⇒ 3rd answer

31. The area of the circle is 6.0025π m² ⇒ 3rd answer

Step-by-step explanation:

* Lets solve the problems

25. The figure is trapezoid

- The trapezoid has two parallel bases base 1 and base 2

- The area of the trapezoid is 1/2(base 1 + base 2) × height

- The length of base 1 is 12 cm

- The length of its height is 6 cm

- The length of the base 2 is (2 + 12 + the adjacent side to ∠45°)

- To find the missing part in the base 2 use the trigonometry

  function tan 45° = opposite/adjacent

∵ tan 45° = opposite/adjacent

∵ The opposite = 6

∵ tan 45° = 1

∴ 1 = 6/adjacent ⇒ by using cross multiplication

∴ The adjacent = 6 cm

∴ The length of base 2 = 2 + 12 + 6 = 20 cm

∵ The area of the trapezoid is 1/2(base 1 + base 2) × height

∵ The length of base 1 = 12 cm

∵ The length of base 2 = 20 cm

∵ The length of its height = 6 cm

∴ The area = 1/2(12 + 20) × 6 = 1/2(32) × 6 = 16 × 6 = 96 cm²

* The area of the trapezoid is 96 cm²

26. The figure is kite

- The kite has two diagonals

- Its diagonals perpendicular to each other

- The longest diagonal bisects the shortest diagonal

- The area of the kite is 1/2(diagonal 1 × diagonal 2)

∵ The length of diagonal 1 = 10.2 feet

∵ The length of diagonal 2 = 8 feet

∵ The area of the kite = 1/2(diagonal 1 × diagonal 2)

∴ The area = 1/2(10.2 × 8) = 1/2(81.6) = 40.8 feet²

* The area of the kite is 40.8 feet²

31. The figure is a circle

- The circle has diameter

- The radius is half the diameter

- The area of the circle is π r²

∵ The length of the diameter = 4.9 m

∵ The length of the radius 1/2 the length of the diameter

∴ The length of the radius = 1/2 (4.9) = 2.45 m

∵ The area of the circle = π r²

∴ The area = π (2.45)² = 6.0025π m²

* The area of the circle is 6.0025π m²

Answer:

25) 96 cm²

26)  40.8 ft ²

31).  6.0025π m²

Step-by-step explanation:

25) To find the area of trapezoid

Area of trapezoid = h(a + b)/2

Here a = 6 + 12 + 2 = 20 cm

b = 12 cm and h = 6

Area =  h(a + b)/2

 = 6(20 + 12)/2

 = 96 cm²

26) To find the area of kite

Area of kite = pq/2

Where p and q are the two diagonals

Here p = 10.2 ft and q = 8 ft

Area = pq/2

 = (10.2 * 8)/2 = 40.8 ft²

31) To find the area of circle

Area of circle = πr²

Here r = 4.9/2 = 2.45 m

Area = πr²    

 = π *(2.45)²

 = 6.0025π m²

Rewrite the quadratic function in vertex form. Then, determine the maximum or minimum and the axis of symmetry.

y = -3x 2 + 18x - 2

Answers

Answer:

See below in BOLD.

Step-by-step explanation:

y = -3x 2 + 18x - 2

y = -3(x^2 - 6x) - 2

y = -3 [ (x - 3)^2 - 9] - 2

y = -3(x - 3)^2  + 25  is vertex form.

The  coefficient of x^2 is negative so we have a maximum  value of the function.

The maximum value is 25 and the axis of symmetry is x = 3.

Answer: The maximum value is 25 and the axis of symmetry is x = 3.




plz answer How many solutions can be found for the system of linear equations represented on the graph?
A) no solution
B) one solution
C) two solutions
D) infinitely many solutions

Answers

Answer:

Two solutions

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

The solution to a system of equations given graphically is at the point of intersection of the 2 lines.

Both lines have a slope m = - [tex]\frac{1}{2}[/tex]

Hence the lines are parallel and have no points of intersection

Thus the system has no solution → A

you are recreating a scale drawing at a different scale. The orginal scale is 1 cm : 4m The new scale is 1cm : 2cm. In the original drawing, the length of a segment is 7 cm. How long should the segment represnting the same distanc be in the new drawing?

Answers

Answer:

14 cm

Step-by-step explanation:

step 1

Find the actual length of the segment

we know that

The original scale is 1 cm : 4m

In the original drawing, the length of a segment is 7 cm

therefore

Let

x ----> the actual length of the segment

by proportion

1/4=7/x

x=4*7

x=28 m

step 2

Find the length of the segment in the new drawing

The new scale is 1cm : 2m

Let

x ---> the length of the segment in the new drawing

by proportion

Remember that

The actual length is 28 m

1/2=x/28

x=28/2

x=14 cm

Solve the system of equations. 4x + 2y = –14 6x + 3y = –22 (0, –7), (–1, –6), no solutions, infinitely many solutions. Plz and Thank You

Answers

Answer:

no solutions

Step-by-step explanation:

4x + 2y = –14

6x + 3y = –22

Divide the first equation by 2 and the second equation by 3

4x/2 + 2y/2 = –14/2     2x +y = -7

6x/3 + 3y/3 = –22/3    2x + y = -22/3

The left hand sides are the same but the right hand sides are different.

Multiply the second equation by -1

2x+y = -7

-2x -y = 22/3

-------------------

0 = -7+22/3

0 = 1/3

This is never true, so there are no solutions

Answer:

B, No Solutions

Step-by-step explanation:

Let FGHB a right triangle with right angle G and an altitude as shown find XYZ

Answers

Answer:

Part 1) [tex]z=4\sqrt{2}\ units[/tex]

Part 2) [tex]x=18\ units[/tex]

Part 3) [tex]y=12\sqrt{2}\ units[/tex]

Step-by-step explanation:

step 1

Find the value of z

In the smaller right triangle IFG of the figure

Applying the Pythagoras Theorem

[tex]6^{2}=2^{2}+z^{2}[/tex]

[tex]z^{2}=6^{2}-2^{2}[/tex]

[tex]z^{2}=32[/tex]  

[tex]z=4\sqrt{2}\ units[/tex]

step 2

In the right triangle HFG

Applying the Pythagoras Theorem

[tex]x^{2}=y^{2}+6^{2}[/tex]

[tex]y^{2}=x^{2}-36[/tex] -----> equation A

step 3

In the right triangle HIG

Applying the Pythagoras Theorem

[tex]y^{2}=z^{2}+(x-2)^{2}[/tex]

[tex]y^{2}=32+(x-2)^{2}[/tex] -----> equation B

step 4

equate equation A and equation B

[tex]x^{2}-36=32+(x-2)^{2}\\x^{2}-36=32+x^{2}-4x+4\\4x=36+36\\4x=72\\x=18\ units[/tex]

step 5

Find the value of y

Substitute the value of x in the equation B

we have

[tex]x=18\ units[/tex]

[tex]y^{2}=32+(18-2)^{2}[/tex]

[tex]y^{2}=32+(16)^{2}[/tex]

[tex]y^{2}=288[/tex]

[tex]y=12\sqrt{2}\ units[/tex]

Teresa is on her way home in her car. Her drive is 6miles long. She has finished two-thirds of the drive so far. How far has she driven?

Answers

Answer:

4 miles

Step-by-step explanation:

6 divided by 3 = 2 = one-third of 6

--> multiply by two to get two thirds of six = 4 miles

Answer:

4 miles

Step-by-step explanation:

Write the linear Inequality shown in the graph. The gray area represents the shaded region.

Answers

ANSWER

[tex]y \leqslant - x + 4[/tex]

EXPLANATION

The equation of the boundary line is

[tex]y = - x + 4[/tex]

Hence the inequality is either

[tex]y \leqslant - x + 4[/tex]

or

[tex]y \geqslant - x + 4[/tex]

We test the origin to get determine which one represents the shaded

We substitute (0,0) into the first inequality to get;

[tex]0\leqslant - (0) + 4[/tex]

This implies that,

[tex]0 \leqslant 4[/tex]

Hence the correct answer is

[tex]y \leqslant - x + 4[/tex]

Answer: Second Option

[tex]y \leq -x +4[/tex]

Step-by-step explanation:

The region is bounded by a line of negative slope that cuts the y-axis at the point y = 4 and cuts the x-axis at the point x = 4.

So the equation of this line is

[tex]y = -x + 4[/tex]

If the region is composed of all the points that lie below the line y = -x + 4 then it means that the region is formed by all the values of y less than or equal to the line [tex]-x + 4[/tex].

Therefore the inequation is:

[tex]y \leq -x +4[/tex]

Second Option

Using the given points, determine the delta symbol y. (-3,-5) and (0,10)

Answers

Answer:

Δy = 15

Step-by-step explanation:

Δy represents the change in the y-coordinates

We are given points (-3,-5) and (0,10)

here y₁ = -5 and y₂ = 10

so, delta y will be

Δy = y₂ - y₁

Δy = 10 -(-5)

Δy = 10 + 5

Δy = 15

So, delta y Δy =15

PLEASE HELP ME!!! I don’t understand

Answers

Answer:

   √6 + √2

= --------------

        4

Step-by-step explanation:

15° = 45° - 30°

So

cos(15)  = cos(45 - 30)

=cos(45)  × cos(30) + sin(45) × sin(30)

= 1/√2  × (√3)/2  + 1/√2 × 1/2

    (√3) + 1

= --------------

     2√2

    (√3) + 1              √2

= -------------- x       ---------

     2√2                  √2

   √6 + √2

= --------------

        4

Answer:

see explanation

Step-by-step explanation:

Using the addition formula for cosine

cos(x ± y) = cosxcosy ∓ sinxsiny

and exact values

sin45° = cos45° = [tex]\frac{\sqrt{2} }{2}[/tex]

c0s30° = [tex]\frac{\sqrt{3} }{2}[/tex] , sin30° = [tex]\frac{1}{2}[/tex]

Express cos15° = cos(45 - 30 )°, then

cos(45 - 30)°

= cos45°cos30° + sin45°sin30°

= [tex]\frac{\sqrt{2} }{2}[/tex] × [tex]\frac{\sqrt{3} }{2}[/tex] + ( [tex]\frac{\sqrt{2} }{2}[/tex] × [tex]\frac{1}{2}[/tex] )

= [tex]\frac{\sqrt{6} }{4}[/tex] + [tex]\frac{\sqrt{2} }{4}[/tex]

= [tex]\frac{\sqrt{6}+\sqrt{2}  }{4}[/tex] ← exact value

For which values of P and Q does the following equation have infinitely many solutions?
Px+35=−6x+Q

Answers

[tex]\bf Px+35=-6x+Q\implies \stackrel{P}{~~\begin{matrix} -6 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}}x+35=~~\begin{matrix} -6x \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~+\stackrel{Q}{35}\implies 35=35[/tex]

whenever you get an equality like so, that's a flat that both equations are exactly one and the same and thus the system has "infinitely many solutions".

Find y if the line through (1,y) and (5,7) has a slope of 6.

Answers

I don’t know what the answer is I wish I could help
7-y/ 5-1 = 6

7-y/4 = 6

7-y = 24

-y = 17

Y= -17


7-(-17)/ 5-1 = 24/4 = 6


Hope this helps!

(07.09) Jonah is purchasing a car that is on sale for 15% off. He knows the function that represents the sale price of his car is c(p) = 0.85p, where p is the original price of the car. He also knows he has to pay 9% sale's tax on the car. The price of the car with tax is f(c) = 1.09c, where c is the sale price of the car. Determine the composite function that can be used to calculate the final price of Jonah's car by solving for f[c(p)]. (1 point) f[c(p)] = 0.9265cp f[c(p)] = 0.9265p f[c(p)] = 1.94cp f[c(p)] = 1.94p

Answers

Answer:

Answer: f[c(p)] = 0.9265p

Step-by-step explanation:

Given: Jonah is purchasing a car that is on sale for 15% off. He knows the function that represents the sale price of his car is , where p is the original price of the car.

He also knows he has to pay 9% sale's tax on the car. The price of the car with tax is , where c is the sale price of the car.

Now, the composite function that can be used to calculate the final price of Jonah's car is given by :-

Answer:

f[c(p)] = 0.9265p

Step-by-step explanation:

c(p) = 0.85p

f(c) = 1.09c

f[c(p)] = f[0.85p] = 1.09(0.85p) = 0.9265p

Answer: f[c(p)] = 0.9265p

One box of clips weighs 4 2/3 ounces. Another box weighs 5 3/8 ounces. What is the total weight of the two boxes?

Answers

For this case, we convert the mixed numbers to fractions:

Box 1: [tex]4 \frac {2} {3} = \frac {3 * 4 + 2} {3} = \frac {14} {3}[/tex]

Box 2: [tex]5 \frac {3} {8} = \frac {8 * 5 + 3} {8} = \frac {43} {8}[/tex]

We add the fractions to find the total weight of the boxes:

[tex]\frac {14} {3} + \frac {43} {8} = \frac {8 * 14 + 43 * 4} {3 * 8} = \frac {112 + 172} {24} = \frac {284 } {24} = \frac {142} {12} = \frac {71} {6}[/tex]

Thus, between the two boxes weigh[tex]\frac {71} {6}[/tex] ounces.

In mixed number: [tex]11 \frac {5} {6}[/tex]

Answer:

[tex]11 \frac {5} {6}[/tex]ounces

Final answer:

The total weight of the two boxes is 10 1/24 ounces, found by converting the mixed numbers into improper fractions, finding a common denominator, and adding the fractions together.

Explanation:

To find the total weight of two boxes when one weighs 4 2/3 ounces and the other weighs 5 3/8 ounces, we first convert the mixed numbers into improper fractions. For 4 2/3 ounces, this would be (4 × 3) + 2 = 14/3 ounces. For 5 3/8 ounces, it is (5 × 8) + 3 = 43/8 ounces. Once in improper fraction form, we find a common denominator, which is 24, and then we add the two fractions together.

The first box in twenty-fourths is (14/3) × (8/8) = 112/24. The second box is (43/8) × (3/3) = 129/24. Adding them gives us 112/24 + 129/24 = 241/24. We divide 241 by 24, which results in 10 with a remainder of 1, giving us 10 1/24 ounces.

Therefore, the total weight of the two boxes is 10 1/24 ounces.

Find the sum of the roots the following equation. The subject is quadratic equations with a maximum power of two (things like a(x^3)^2 + b(x^3) + c = 0 also count as a power of two) so we have to find a way to turn this into a quadratic equation. Please help.

[tex]\left(2x\:^2-3x\right)^2+4\left(2x^2-3x\right)+3=0[/tex]

Answers

[tex]\bf (2x^2-3x)^2+4(2x^2-3x)+3=0\qquad \boxed{a=2x^2-3x}\implies a^2+4a+3=0 \\\\\\ (a+3)(a+1)=0\implies a= \begin{cases} -3\\ -1 \end{cases}\qquad \stackrel{\textit{their sum}}{-3-1\implies -4}[/tex]

Answer:

3/2

Step-by-step explanation:

(2x² − 3x)² + 4 (2x² − 3x) + 3 = 0

We can simplify this using substitution.  Let's say that u = 2x² − 3x.

u² + 4u + 3 = 0

Factoring:

(u + 3)(u + 1) = 0

u = -3, u = -1

Therefore:

2x² − 3x = -3, 2x² − 3x = -1

2x² − 3x + 3 = 0, 2x² − 3x + 1 = 0

For a quadratic ax² + bx + c = 0, the sum of the roots is -b/a.  So in both cases, the sum is 3/2.

A runner can run at 7.5 miles per hour. Write an equation that compares the time (t) with the distance (d).

Answers

Answer:

d = 7.5t

Step-by-step explanation:

t = time

d= distance

you want to write an equation that compares time with distance.

in the question it says per hour whoch means 7.5 miles have been ran each hour. however we dont know how mmany hour lets say tom has ran. therefore, we use t instead. we got d to go behind the = sign because we are comparing. When we multiply 7.5t we are going to get the distance he ran, d.

hope this helps!

Answer:

d=7.5t

Step-by-step explanation:

Sparkles the unicorn is in the forest. She is helping herself to a nice big juicy apple. The monkey grabs the apple out of her mouth and starts to eat it. Sparkles notices that there are 18 pairs of eyes staring at the monkey. Based on the information you have been given, how many animals are in the forest in this moment?

Answers

Answer:

11 animals

Explanation:

-Sparkles is the first animal that is introduced, then the monkey is the second. Since there are 18 eyes, that can be divided by 2 to tell you how many of the remaining animals there are. Which would lead up to 9 and 9+2=11

Eleven (11) Animals

Based on the above given information, it can be construed that that Eleven (11) animals are in the forest.

Further Explanation

The first mentioned animal is Sparkles the Unicorn (Animal 1) who probably might be hungry and, might have searched through the forest to get the nice big juicy apple.

She might have dodged several wild predating animals just for luck to smile on her through the discovery of a big juice apple. She plucks it, and starts eating. A nearby lurking, cunning monkey (Animal 2), snatches the fruit from Sparkles the Unicorn, due to her carelessness, and as she proceed to retrieve the fruit, she discovered that that wasn’t the only monkey around. She sees eighteen (18) pairs of eyes which means, there are nine (9) other animals i.e. 18 pairs of eyes divided by 2 (18/2 = 9) are also in the forest.

Therefore:

Animal 1 + Animal 2 + 9 other Animals = 11 Animals

This kind of question can be said to be a Mathematical Puzzle.

Mathematical puzzle is a form of recreational mathematics, which helps to enhance students’ knowledge.

Mathematical puzzle helps students to understand different concepts of mathematical problems.

This form of mathematical improve students’ learning ability

KEYWORDS:

forestpuzzleanimalwildstudents

There are 85 apples on the big tree, John picked out 15%. How many did John pick out?

Answers

Answer:

12.75

Step-by-step explanation:

John picked out 12.75 apples on the big tree.

15% of 85 is 12.75.

Hope this helps! Please mark brainliest!

Answer:

approx 13 apples

Step-by-step explanation:

total apples : 85

given john picked 15% = 0.15 of the total apples

number of apples john picked = 0.15 x 85 = 12.75

rounding off to nearest whole number (because you can't really pick 0.75 of an apple) = 13 apples

Solve the system of equations. 2x+2y+3z=5, 6x+3y+6z=6 and 3x+4y+4z=9

Answers

Hope this is what you are looking for: x=-1 y=2 and z=1

Answer:

it's d or the fourth option

Step-by-step explanation:

Evaluate the following expression for d=-5 and w=6

[tex] \frac{d {}^{0} }{w {}^{ - 3} } [/tex]


A. -23

B. 1/216

C. 216

D. -18​

Answers

Answer:

216

Step-by-step explanation:

Anything to the zero power is equal to 0.

The denominator can be moved to the numerator because the exponent is negative. So it is now 1*6^3. This is equal to 216.

The value of expression [tex]\frac{d^{0} }{w^{-3} }[/tex] is 216

The correct option is (B).

What is exponents and power?

Power can be defined as an expression that represents repeated multiplication of the same number whereas exponent is the quantity that represents the power to which the number is raised.

Given:

[tex]\frac{d^{0} }{w^{-3} }[/tex]

put d=-5 and w=6

So, [tex]\frac{-5^{0} }{6^{-3} }[/tex]

=1/[tex]6^{-3}[/tex]   [a°=1]

=6³      [[tex]1/a^{-b} = a^{b}[/tex]]

=216.

hence,  [tex]\frac{d^{0} }{w^{-3} }[/tex] = 216.

Learn more about exponents and power here:

https://brainly.com/question/15722035

#SPJ2

write a function rule for the output is 5 less than the input

Answers

Answer:

y=x-5

Step-by-step explanation:

"output" means  y

and "input" means  x

So all you need to find is the =

Please mark brainliest and have a great day!

help simplify please choose the correct answer~!!!!!

Answers

Answer:

A

Step-by-step explanation:

Given

-4x²(5[tex]x^{4}[/tex] - 3x² + x - 2)

Multiply each term in the parenthesis by - 4x²

= - 20[tex]x^{6}[/tex] + 12[tex]x^{4}[/tex] - 4x³ + 8x²

Answer:

A

Step-by-step explanation:

A man earns a base salary of 2000$ and every year he got araise of 7% on his total income.huv much total income would he get by end of 4 years

Answers

Answer:

his total income by the end of 4 years will be: $2622.

Step-by-step explanation:

A man earns a base salary of $2000, and every year he got a raise of 7% on his total income.

The first year, he will earn: 1.07($2000) = $2140

The second year he will earn: 1.07($2140) = $2289.8

The third year he will earn: 1.07($2289.8) = $2450.086

The fourth year he will earn: 1.07($2450.086) = $2621.59202

Therefore, his total income by the end of 4 years will be: $2622.

An organization surveyed a random sample of their employees about their new vacation policy. Out of the employees surveyed, 83% rated the vacation policy as "delightful" with a margin of error of ±2% and a confidence interval of 95%.

What does the margin of error imply?

Answers

Answer:C.It can be concluded, with 95% confidence, that between 81% and 85% of all employees will rate the vacation policy as "delightful."

Step-by-step explanation:

The margin of error implies that 81% to 85% of all employees will judge the vacation policy as "delightful" with 95% confidence.

What is the margin of error?

The margin of error is a statistic that expresses how much random sampling error there is in a survey's results. The wider the margin of error, the less confident one should be that a poll result reflects the outcome of a population-wide survey.

Given that the organization polled a random sample of its employees regarding their new vacation policy.

Now, 83% of the workers polled assessed the vacation policy as "delightful," with a margin of error of ±2% and a confidence interval of 95%, implying that 81% to 85% of all employees will judge the vacation policy as "delightful" with 95% confidence.

Hence, the margin of error implies that 81% to 85% of all employees will judge the vacation policy as "delightful" with 95% confidence.

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