In this expression, we can solve it by applying the distributive property
3(2y-7)
6y-21
So, factor 3 multiplies each term inside the parentheses.
2)-(x+4)
The minus outside the bracket works like a -1 multiplying it
-(x+4)
-x-4
3) For this one, remember the rule for multiplying fractions and then simplifying:
[tex]\begin{gathered} \frac{2}{3}(\frac{1}{4}x-6) \\ \frac{2}{12}x\text{ -}\frac{12}{3} \\ \frac{1}{6}x-4 \end{gathered}[/tex]4) 6( x+1) -5(x+2)
6x+6 -5x-10
6x-5x+6-10
x-4
There are three novels on Keisha's reading table: Scoop, Light, and Lanark. On her next trip, she can choose to take some or none, but not all, of these novels. In the braces below, list all the possible sets of novels that Keisha can take.Write each set in your list in roster form..
She could take
1.- {x|x Scoop}
2.- {x|x Light}
3.- {x|x Lanark}
4.- {x|x Scoop, Light}
5.- {x|x Scoop. Lanark}
6.- {x|x Light, Lanark}
I have to send the picCalculate the Area of the figure
The area of the figure is 24 cm²
The figure is divided into two blocks, one is rectangle having the dimensions, length as 5cm and width as 4 cm, another is a square having side of 2 cm.
The area of the figure is the summation of the area of the rectangle and the area of the square.
area of the rectangle = length x width = 4 x 5 = 20cm²
area of the square = side² = 2² = 4cm²
area of the figure = area of rectangle + area of the square
= 20 + 4
area of the figure is 24 cm²
Therefore, the area of the figure is 24 cm²
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Y=x^2 how does Y= (x-4^2) andY = (x+3) differ from theParent function and each other?what causes this to change?
The parent function is:
y = x²
This is a quadratic function
The child functions are:
y = x - 4² whcih can be written as
y = x - 16
The second child function is
y = x + 3
The two child functions are linear functions while the parent function is a quadratic function.
The parent and child functions also differ in their ranges and domains
For y = x²Domain = ( -∞ , ∞ )
Range = [0 , ∞ )
For y = x - 4² and y = x + 3:Domain = ( -∞ , ∞ )
Range = (-∞ , ∞ )
The difference between y = x - 4² and y = x + 3 is their intercepts on the y axis .
For y = x - 4², the y - intercept is -16
For y = x + 3, the y - intercept 3
This change is due to transformation (basically translation) on the x and y axes
1. The endpoints of line PQ on a real number line are -.5 and .72. What is the coordinate of the midpoint of line PQ?
We are given the endpoints of a line PQ
[tex]-0.5\text{ and }0.72[/tex]We are asked to find the midpoint of line PQ.
Let us first find the distance of line PQ
[tex]\begin{gathered} d=|x_2-x_1| \\ d=|0.72_{}-(-0.5)_{}| \\ d=|0.72_{}+0.5| \\ d=|1.22| \\ d=1.22 \end{gathered}[/tex]Recall that the midpoint is at the halfway of the line PQ so divide the distance by 2
[tex]midpoint=\frac{1.22}{2}=0.61[/tex]What is the equation of the horizontal asymptote of the graph of y = 1/x+5 – 4?
We can find the horizontal asymptote of this kind of functions using the limit:
[tex]\begin{gathered} \lim _{x\to\infty}\frac{1}{x+5}-4=\frac{1}{\infty}-4=-4 \\ \lim _{x\to\infty}\frac{1}{x+5}-4=\frac{1}{-\infty}-4=-4 \end{gathered}[/tex]Therefore the equation of the horizontal asymptote is:
[tex]y=-4[/tex]I would love if someone can please help me on this algebra problem??
SOLUTION
From this question, it means that
[tex]\begin{gathered} y=\sin x\text{ was translated to} \\ y=4\sin x \end{gathered}[/tex]To be sure the required translation, let us see a quick look at the graph of the function and it's image
[tex]y=\sin x[/tex]And
[tex]y=4\sin x[/tex]Now, we can see that the image is an enlarged form of the original function
Therefore this is a dilation. And since the increase in size is vertical, that is across the y-axis, It is a Vertical dilation.
Hence the correct answer is Vertical dilation.
In your own words, explain what you know about a number that satisfies theequation x2 = -1.
The number that satisfies the equation is
[tex]x^2=-1[/tex]Doing the square root on both sides
[tex]x=\pm\sqrt{-1}[/tex]On complex number we use the definition:
[tex]i=\sqrt[]{-1}[/tex]Therefore, the number that satisfies the equation is
[tex]x=\pm i[/tex]That means that a solution is a complex number.
Complex numbers have two parts, the complex part and the real part:
[tex]z=a+bi,\quad a,b\in\mathbb{R}[/tex]Look that a and b are real coefficients, but z is a complex number because we have b multiplying i, the complex unit.
But why complex numbers are so important?
• Complex numbers can be used to solve polynomial equations, that we couldn't solve before
,• Complex numbers can connect exponential function with trigonometric functions
[tex]e^{ix}=\cos (x)+i\sin (x)[/tex]Complex numbers are a powerful set that we can use to solve many complex problems in physics and mathematical, it may seem hard but they actually make things easier, sometimes working with complex numbers is way easier than working with real numbers.
Question 21 (1 point)Find the power function that the graph of f given below resembles, but is shifted tothe left by 3 units.f(x)=(x − 3)³Oy=x³Oy=x-27Oy=x⁹Oy=x-³
STEP - BY - STEP EXPLANATION
What to find?
The power function that the given graph resembles.
Given:
f(x)=(x − 3)³
First, we need to note that;
If f(x) is shifted left q - units, then the new formula of the function becomes f(x+q).
Let q=3
[tex]f(x)=(x-3)^3[/tex][tex]f(x)=(x-3+3)^3[/tex][tex]f(x)=x^3[/tex]ANSWER
y=x³
x of Lixin's classmates plan to buy her a birthday gift. The cost of the birthday gift is $36 (i) Given that 5 of Lixin's classmate decided not to contribute to the birthday gift, the rest of her classmates will have to pay an additional $0.24 to make up for the difference. Write down an expression, in terms of x, for the amount which each of the remaining classmates will now have to pay. (ii) Form an equation in x and show that it reduces to x square- 5x - 750 = 0. (i) Find the number of classmates Lixin has.
Lixin has x number of classmates and plan to buy her a birthday gift worth $36.
So basically, they need to contribute 36/x dollars each in order to buy the gift.
But 5 of them will not contribute and it cost them to add $0.24 each
So from 36/x dollars, it become (36/x + 0.24) dollars each
Multiply this individual contribution by the number of her classmates which was reduced by 5. (x - 5)
The equation will be :
[tex]\begin{gathered} \text{contribution}\times\text{ number of classmates}=36 \\ (\frac{36}{x}+0.24)(x-5)=36 \end{gathered}[/tex]Simplify the equation :
[tex]\begin{gathered} (\frac{36}{x}+0.24)(x-5)=36 \\ \frac{36}{x}(x-5)+0.24(x-5)=36 \\ (36-\frac{180}{x})+(0.24x-1.2)=36 \end{gathered}[/tex]Multiply both sides by x to remove the denominator.
[tex]\begin{gathered} x(36-\frac{180}{x})+x(0.24x-1.2)=36x \\ 36x-180+0.24x^2-1.2x=36x \end{gathered}[/tex]Rearrange and combine like terms :
[tex]\begin{gathered} 0.24x^2+36x-1.2x-36x-180=0 \\ 0.24x^2-1.2x-180=0 \end{gathered}[/tex]Divide both sides by 0.24 to make the coefficient of x^2 become 1 :
[tex]\begin{gathered} \frac{0.24x^2}{0.24}-\frac{1.2x}{0.24}-\frac{180}{0.24}=0 \\ x^2-5x-750=0 \end{gathered}[/tex]Solve by factoring completely :
[tex]\begin{gathered} x^2-5x-750=0 \\ (x-30)(x+25)=0 \end{gathered}[/tex]Equate both factors to 0, then solve for x :
x - 30 = 0
x = 30
x + 25 = 0
x = -25
Neglect negative value since there is no negative value for the number of persons.
The answer is x = 30
To summarize :
i Expression in terms of x :
[tex](\frac{36}{x}+0.24)(x-5)=36[/tex]ii Equation in x that reduces to x^2 - 5x - 750 = 0
[tex]\begin{gathered} 0.24x^2-1.2x-180=0 \\ \Rightarrow x^2-5x-750=0 \end{gathered}[/tex]iii Number of classmates Lixin has.
x = 30
Answer:
this is 50. i = 50
Step-by-step explanation:
hope it helps you
Writing an equation of a probably given the vertex and focus
The equation of the vertical parabola in vertex form is written as
[tex]y=\frac{1}{4p}(x-h)^2+k[/tex]Where (h, k) are the coordinates of the vertex and p is the focal distance.
The directrix of a parabola is a line which every point of the parabola is equally distant to this line and the focus of the parabola. The vertex is located between the focus and the directrix, therefore, the distance between the y-coordinate of the vertex and the directrix represents the focal distance.
[tex]p=1-6=-5[/tex]Using this value for p and (3, 1) as the vertex, we have our equation
[tex]y=-\frac{1}{20}(x-3)^2+1[/tex]I have tried 4 tutors who could not answer this question. Someone, please help me.
The expected return of the stock portfolio is 9.3%.
From the properties of stock portfolio we know that,
Expected return of a portfolio = RF + BP ( RM - RF )
E(RP) = RF + BP ( RM - RF )
RF= risk free rate =3%
RM = expected market return = 10%
BP = beta of portfolio
BP = ∑(Wi × Bi)
Wi is weight of stock i and Bi is the beta of stock i .
Wi= investment in stock / total investment
Beta of portfolio(BP)
=(0.5×1) + (0.35×0.2) + (0.33)
= 0.50 +0.07+0.33
=0.9
E(RP)
= RF + BP ( RM - RF )
= 0.03 + 0.9(0.30-0.03)
= 0.03 +0.063
= 0.093
Hence the expected rate = 0.093 × 100% = 9.3%
The stock market portfolio of an investor consists of stocks, funds, and possibly other market-traded securities. In general, cash and bond assets are often present in investment portfolios. Various assets with different sizes, industries, and other characteristics are included in a varied portfolio.
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What is the value of this expression?
5 (912−14 )+ 0.5
Enter your answer, in simplest form, in the box.
Answer:
4490.5
Step-by-step explanation:
5(898)+0.5
=4490.5
In 2018 it was estimated that approximately 41% of the American population watches the Super Bowl yearly. Suppose a sample of 118 Americans is randomly selected. After verifying theconditions for the Central Limit Theorem are met, find the probability that the majority (more than 50%) watched the Super Bow.
We would test if np and n(1 - p) is at least 10
p = sample proportion
p = x/n
where
x = number of success
n = sample size
From the information given,
p = 41% = 41/100 = 0.41
n = 118
np = 48.38
n(1 - p) = 118(1 - 0.41) = 69.62
Both values are greater than or equal to 10. Thus, the distribution is approximately normal.
The mean of the distribution = p = 0.41
Standard deviation = √(p(1 - p)/n
By substituting the values,
standard deviation = √(0.41(1 - 0.41)/118 = √0.00205 = 0.045
We want to find P(p ≥ 0.5)
We would standardize 0.5 into a z score by applying the formula,
z = (x - mean)/standard deviation
z = (0.5 - 0.41)/0.045 = 2
From the normal distribution table, the probability value corresponding to a z score of 2 is 0.9773
P(p ≥ 0.5) = 1 - 0.9773
P(p ≥ 0.5) = 0.023
the probability that the majority (more than 50%) watched the Super Bow is 0.023
which of these situations cannot be represented by the number -10 ?A) A loss of 10 yeards.B) 10 degrees below zero.C) A withdrawal of $10.D) gaining 10 points.
The correct option is D
gaining 10 points cannot be represented by the number -10
Explanation:-10 can represent all the given situations except gaining 10 points.
Because that will be an increase (+10), and not a decrease (-10)
Answer is: A withdrawal of $10.
Find the exact solutions to x2-3x+1-0 by using the Quadratic Formulal
Given
[tex]x^2-3x+1=0[/tex]Find
Exact solution by quadratic formula
Explanation
Quadratic formula is given by
[tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]here a = 1 , b = -3 and c = 1
substitute the values in quadratic formula ,
[tex]\begin{gathered} x=\frac{-(-3)\pm\sqrt{(-3)^2-4\times1\times1}}{2\times1} \\ \\ x=\frac{3\pm\sqrt{9-4}}{2} \\ \\ x=\frac{3\pm\sqrt{5}}{2} \end{gathered}[/tex]Final Answer
Therefore , the correct option is 4.
Forest rangers wanted to better understand the rate of growth for younger trees in the park. They took measurements of a random sample of 50 young trees in 2009 and again measured those same trees in 2019. The data below summarize their measurements, where the heights are in feet.
Year Mean SD n
2009 11.4 3.6 50
2019 24.3 8.8 50
Difference 12.9 5.52 50
Round all calculated values to 4 decimal places as appropriate.
1. Construct a 90 confidence interval for the mean difference between the height of trees in the park in 2009 and in 2019.
2. What conditions must be met if we want to perform a hypothesis test and answer the question of the management? Select all that apply:
A. Large samples and no extreme outliers.
B. There must be at least 3 levels of the categorical variable.
C. np^≥10 and n(1−p^)≥10
D. Independently sampled pairs.
1. The 90% confidence interval for the mean difference between the height of trees in the park in 2009 and in 2019 is given as follows:
(11.59, 14.21)
2. The conditions for the confidence interval are of:
A. Large samples and no extreme outliers.D. Independently sampled pairs.What is a t-distribution confidence interval?The t-distribution is used when the standard deviation for the population is not known, and the bounds of the confidence interval are given according to the following rule:
[tex]\overline{x} \pm t\frac{s}{\sqrt{n}}[/tex]
In which the variables of the equation are presented as follows:
[tex]\overline{x}[/tex] is the sample mean.t is the critical value.n is the sample size.s is the standard deviation for the sample.The critical value, using a t-distribution calculator, for a two-tailed 90% confidence interval, with 50 - 1 = 49 df, is t = 1.6766.
The remaining parameters are given as follows:
[tex]\overline{x} = 12.9, s = 5.52, n = 50[/tex]
Then the lower bound of the interval is of:
12.9 - 1.6766 x 5.52/sqrt(50) = 11.59.
The upper bound of the interval is of:
12.9 + 1.6766 x 5.52/sqrt(50) = 14.21.
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Pam and Rachel buy books at the bookstore where Rachel works. As an employee, Rachel pays only 75% of the advertised price. How many books could each purchase and spend the same amount for the same number of books?
Answer:
0, that is not possible
Step-by-step explanation:
Since she gets a discount she will always pay less
From the Graph, find the constant of proportionality and write the direct variation equation
In this case the answer is very simple. .
We must use the graph to find the answers.
Step 01:
Data
For x = 2 ===> y = 1
Step 02:
Direct variation equation
y = k * x
Constant of proportionality
x = 2 , y = 1
[tex]\text{ y = k }\cdot\text{ x}[/tex][tex]\begin{gathered} 1\text{ = k }\cdot\text{ 2 } \\ \frac{1}{2}\text{ = k } \\ \end{gathered}[/tex]The solution is:
Constant of proportionality = k
k = 1/2
Direct variation equation
y = k * x
y = (1/2) * x
A small yoga studio offers two plans for sessions.•Plan A: Pay a $320 yearly fee and then $5 per session. • Plan B: Pay no yearly fee and $15 per session. Complete each statement. Both plans will cost the same for __?__ sessions. To attend one session each week for a year, plan _?__ will be cheaper.
1) Firstly, let's express each plan by using linear equations.
Plan A:
5x+320
Note that the $320 payment is done once, then 5 per session.
Plan B
15x
2) To get to know when opting for plan A or Plan B is not relevant, we need to equate both equations and solve it for x (x stands for the number of sessions)
[tex]\begin{gathered} 5x+320=15x \\ 5x-15x=-320 \\ -10x=-320 \\ 10x=320 \\ \frac{10x}{10}=\frac{320}{10} \\ x=32 \end{gathered}[/tex]So if you attend 32 sessions then, doesn't really matter which plan is it.
3) Now, let's figure out which plan is more interesting to take:
[tex]\begin{gathered} C_A(x)=5x_{}+320 \\ C(1)=5(1)+320 \\ C(1)=325 \\ --- \\ C_B(x)=15x \\ C_B(1)=15(1) \\ C_B(1)=15 \end{gathered}[/tex]So the plan B is cheaper to attend 1 session
Jeff picks a number with 2 tens 42 ones. victor picks a number with 3 tens 51 ones. what number does each child pick?
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Jeff = 2 tens 42 ones
Victor = 3 tens 51 ones
what number is = ?
Step 02:
Jeff = 2 tens 42 ones
2 * 10 = 20
42 * 1 = 42
----------
Victor = 3 tens 51 ones
Answer:
Jeff: 62
Victor: 81
Step-by-step explanation:
Jeff has a number with 2 tens, and 42 ones. We can write out our 2 tens like this: 10 + 10 = 20
Next, he has 42 ones. This is just another way of saying '42'
So, jeff picked a number that is 20 + 42 = 62
Now, Victor. Victor has a number with 3 tens. This is saying: 10 + 10 + 10 which is 30. He has 51 ones, which is just the number 51.
So, Victor's number is 30 + 51 = 81
??????????????????????The answers got cropped out they are ; 9, 8, 7, 6.
Given that the baker has a total of 18 cups of flour, you know that the baker needs:
- This amount of flour for a batch of banana pancakes:
[tex]1.75\text{ }cups[/tex]- This amount of flour for a batch of apple pancakes:
[tex]0.6\text{ }cups[/tex]You know that the baker makes 8 batches of banana pancakes.
Let be "x" the greatest number of whole batches of apple pancakes that the baker can make.
You can set up this equation using the given data:
[tex]1.75x+(0.6)(8)=18[/tex]Now you need to solve for "x", in order to find its value:
[tex]1.75x+4.8=18[/tex][tex]1.75x=18-4.8[/tex][tex]x=\frac{13.2}{1.75}[/tex][tex]x\approx7.5[/tex]Since the number of cups cannot be greater than 18 cups, you need to round down:
[tex]x\approx7[/tex]Hence, the answer is: Third option.
a local business club has 7 exclusive board members and 31 General members and how many committees of five members can be chosen so that only general managers are included
We need to choose 5 members from the general only
The number of general members = 31
As the arrangement is not required
So, the number of committees will be:
[tex]31C5=\frac{31!}{(31-5)!\cdot5!}=169,911[/tex]so, the answer will be 169,911 committees
The table shows the grading scale for one of your classes. Tell the letter grade that you earn for each score.a. You earn 14 out of a possible 20 points on a quizz.b. You earn 66 out of a possible 80 points on a test.c. You earn 216 out of a possible 250 points for a report.
a.
[tex]\frac{14}{20}=\frac{7}{10}=0.7[/tex]Therefore, your score would be 70% then you will get a C
b.
[tex]\frac{66}{80}=\frac{33}{40}=0.825[/tex]Your score would be 82.5%, then you will get a B
c.
[tex]\frac{216}{250}=\frac{108}{125}=0.864[/tex]Your score would be 86.4%, then you will get a B
Amount of Water (ml) 5 8 8.5 8 8.ŏ 8 8 8 10 I → 0 1 2 3 4 5 6 7 8 9 Days What information does the intercept provide A The amount of water in the beaker decreased by 40 ml. B. The water was gone by the eighth day.
First, we need to identify the y-intercept that is the value of the coordinate y when the coordinate is 0 in this case our y-intercept is in 40
The y-intercept provide the start amount of water therefore the correct choice is D. the water level started at 40 mL
Hii I really need help right now I don’t understand.
The function is given as,
[tex]y=4^x[/tex]For x = -1 , the value of y is calculated as,
[tex]\begin{gathered} y=4^{-1} \\ y\text{ = }\frac{1}{4} \\ y\text{ = 0.25} \end{gathered}[/tex]For x = 0 , the value of y is calculated as,
[tex]\begin{gathered} y=4^0 \\ y\text{ = 1} \end{gathered}[/tex]For x = 1 , the value of y is calculated as,
[tex]\begin{gathered} y=4^1 \\ y\text{ = 4} \end{gathered}[/tex]For x = 2, the value of y is calculated as,
[tex]\begin{gathered} y=4^2 \\ y\text{ = 16} \end{gathered}[/tex]Hello, I need some assistance with this homework question, please? This is for my precalculus homework. Q9
For the given function,
Vertical Asymptote:- x =-3
Horizontal asymptote:- y =20
Oblique asymptote :- No oblique asymptote
Asymptote:
A vertical asymptote is found by letting the denominator equal zero. A horizontal asymptote is found by comparing the leading term in the numerator to the leading term in the denominator. The degree of the numerator is greater than the degree of the denominator, so there is no horizontal asymptote.
Oblique asymptotes occur when the degree of the denominator of a rational function is one less than the degree of the numerator
given,
R(x) = [tex]\frac{20x}{x+3}[/tex]
Vertical Asymptote:-
Equate denominator to zero
x +3 = 0
x = -3
Horizontal asymptote:-
Here degree on x in numerator and denominator is same,
so horizontal asymptote will be,
y= 20/1
y = 20
Oblique asymptote:-
There won't be any slant asymptote, because degree in numerator is equal to the degree in denominator.
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Kevin recorded the distances he ran last week. The total number of miles he ran on Monday through Wednesday is the same as the total number of miles he ran on Thursday and Friday. How many miles did Kevin run on Wednesday?
Kevin recorded the distances he ran last week. The total number of miles he ran on Monday through Wednesday is the same as the total number of miles he ran on Thursday and Friday. How many miles did Kevin run on Wednesday?
_______________________
The total number of miles he ran on Monday through Wednesday is the same as the total number of miles he ran on Thursday and Friday.
x + (x + 9) + (x + 4) = 2x + (4x - 2)
_____________________
Can you see the updates?
__________________
x + (x + 9) + (x + 4) = 2x + (4x - 2)
3x + 13 = 6x -2
6x - 3x = 13 + 2
3 x = 15
x = 15/3 miles
x = 5 miles
___________________________
5 + ( 5 + 9) + ( 5 + 4) = 2x + (4x - 2)
28 = 28
________________________
on Wednesday
x=5
x+ 4 = 9
_________________
Answer
On Wednesday he ran 9 miles
_________________
Can you see the updates?
Do you have any questions regarding the solution?
Write the place of the underlined digit then write its value. what is the value?
EXPLANATION
2) 812: The place of the underlined digits corresponds to UNITS.
VALUE --> 812: eight hundred twelve
5)For positive values of x, which expression isequivalent toSquare root 16x2*x2/3+square root 8x^5/3
The answer is option B
Given:
/16x^2 + x^2/3 + 3/8x^5
You need to simplfiy the expression given which will give you
6 3/x^5 or the second option
[tex]6\sqrt[3]{x^5}[/tex]Sample Data48262191036984391035414135264238472947512227421220143514138142710482529331220229149943521413Computations(Round the mean and sample standard deviation to values to FIVE decimal places)Sample Mean = 25.42Sample Standard Deviation = 14.25724(Round the lower/upper limits and margin of error to THREE decimal places). #1. 80% Confidence Interval: 80% Confidence Interval Margin of Error:What does this confidence interval mean given the data?#2. 95% Confidence Interval:95% Confidence Interval Margin of Error: #3. 99% Confidence Interval:99% Confidence Interval Margin of Error:#4. Make up YOUR OWN Interval.50% Confidence Interval:50% Confidence Interval Margin of Error:
The given information is:
- Sample mean = 25.42
- Standard deviation = 14.25724
Part 1.
We have a confidence interval (C.I.) of 80%.
We need to find the z-score for this C.I., so, let's see a diagram:
We have a two-sided confidence interval. So, we need to find the z-score for a cumulative probability of 80+10=90%=0.9.
By using a standard normal table, we can see that z-score for 0.9 is:
By using an online calculator, we find the exact z-score is 1.282.
The confidence interval is given by the formula:
[tex]C.I=\bar{x}\pm z_c\frac{s}{\sqrt{n}}[/tex]Where x is the mean of the sample, Zc is the z-score for the given confidence level, s is the standard deviation and n is the number of elements in the sample n=50.
By replacing the known values, we obtain:
[tex]\begin{gathered} 80\%C.I.=25.42\pm1.282\frac{14.25724}{\sqrt{50}} \\ \\ C.I.=25.42\pm1.282\times2.016 \\ C.I.=25.42\pm2.585 \end{gathered}[/tex]So, the lower and upper limits are:
[tex]\begin{gathered} lower:25.42-2.585=22.835 \\ upper:25.42+2.585=28.005 \end{gathered}[/tex]The margin of error is equal to half the width of the entire confidence interval, and it is also the value we add and subtract to the mean to find the confidence interval, so the margin of error is 2.585.