The range of scores for 95% of the class is 63.8 to 86.6 using the empirical rule.
What is the empirical rule?A statistical principle known as the empirical rule, also known as the three-sigma rule or 68-95-99.7 rule, holds that with a normal distribution, almost all observed data will lie within three standard deviations.
The empirical rule specifically states that 68 percent of data will fall inside the first standard deviation, 95 percent will fall within the first two standard deviations, and 99.7 percent will fall within the first three standard deviations.
According to the question,
μ=75.2 and σ=5.7
So, according to the empirical rule, the range of scores for 95% of the class:
μ – 2σ =75.2-2*5.7=63.8
and μ + 2σ=75.2+2*5.7=86.6
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Easy! 40 PTS!!! Log Functions
Answer:
C
Step-by-step explanation:
When x is negative 1/2 ^x becomes 1 / ( 1/2 ^x) meaning it is quite large as x becomes more negative
when x = 0 the value is 1
as x increases from 0 to + inf the value becomes smaller...but never negative
the only graph that fits is C
Given the following graph of a point on the polar plane, name another set of coordinates that could also represent this point using a
positive "value and a negative "O" value, where -360 ≤ 0 ≤ 0. State your answer in the form: (r,0) with "O" in degrees without the
degree symbol.
Answer:
(r,0)
Step-by-step explanation:
What second degree polynomial function has a leading coefficient of -2 and root 4 with a multiplicity of 2
The second degree polynomial with leading coefficient of -2 and root 4 with multiplicity of 2 is:
[tex]p(x) = -2*(x - 4)*(x - 4) = -2*(x - 4)^2[/tex]
How to write the polynomial?
A polynomial of degree N, with the N roots {x₁, ..., xₙ} and a leading coefficient a is written as:
[tex]p(x) = a*(x - x_1)*(x - x_2)*...*(x - x_n)[/tex]
Here we know that the degree is 2, the only root is 4 (with a multiplicity of 2, this is equivalent to say that we have two roots at x = 4) and a leading coefficient equal to -2.
Then this polynomial is equal to:
[tex]p(x) = -2*(x - 4)*(x - 4) = -2*(x - 4)^2[/tex]
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A book seller gains 30% on the cost price by selling a book for $130.Calculate the cost price of the book.
Answer:
Let the cost price be x
Selling price, S.P. = 130Gain % = 30%[tex]\rm{C.P. = \dfrac{S.P. \times 100}{100+ gain \% }}[/tex]
[tex]\rm{C.P. = \dfrac{130 \times 100}{100+30}}[/tex]
[tex]\rm{ C.P. = \dfrac{130}{30} }[/tex]
[tex]\large{\boxed{\rm{ C.P. = \dfrac{13}{3}}}}[/tex]
What is the diameter of this circle if the circumference is 30 inches?
Answer:
d≈9.55
Step-by-step explanation:
the answer is 9.55 inches
Answer:
diameter = 9.55 in
Step-by-step explanation:
Circumference = pi x diameter so re-arrange
circumference / pi = diameter
30 / pi = diameter
9.55 in = diameter
A bucket is in the shape of a frustum with top diameter 20cm and bottom diameter 12cm. If the height of the bucket is 8cm, calculate the volume of the bucket
Answer: V≈1642 cm³.
Step-by-step explanation:
D=20 cm d=12 cm h=8 cm V=?
[tex]R=\frac{D}{2}=\frac{20}{2} =10 \ (cm).\\ r=\frac{d}{2}=\frac{12}{2}=6 \ (cm).\\ \boxed {V=\frac{1}{3} *\pi *h*(R^2+R*r+r^2)} \ \ \ \ \ \Rightarrow\\V=\frac{1}{3}*\pi *8*(10^2+10*6+6^2)\\V=\frac{1}{3}*\pi *8*(100+60+36)\\ V=\frac{8}{3} *\pi *196\\V=\frac{8*196*\pi }{3} \\V\approx1642\ cm^3.[/tex]
Which of the following is a valid probability distribution? Probability distribution A is shown. The probabilities of 1, 2, 3, 4, 5 and 6 are all 0.2. Probability distribution B is shown. The probability of 1 is 0.1; 2 is 0.2; 3 is 0.3; 4 is 0.3; 5 is 0.2; 6 is 0.1. Probability distribution C is shown. The probability of 1 is 0.1; 2 is 0.2; 3 is 0.4; 5 is 0.1; 6 is 0.1. Probability distribution D is shown. The probability of 1 is 0.2; 2 is 0.1; 3 is 0.1; 4 is 0.5; 5 is 0.1.
Considering the given probability distributions, distribution D is valid.
When a probability distribution is valid?A probability distribution is valid if:
There are no negative probabilities.The sum of all probabilities is of 1.In this problem, only distribution D has a sum of 1, hence it is the only valid distribution.
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Answer:
Probability distribution D is shown. The probability of 1 is 0.2; 2 is 0.1; 3 is 0.1; 4 is 0.5; 5 is 0.1.
Step-by-step explanation:
The answer above is correct.
Triangle not drawn to scale
Given: m&A=40°,m&B=88°,a=15cm. Then b
= _?__cm to the nearest hundredth
Answer:
b = 23.3
Step-by-step explanation:
First, we need to determine whether this is a right or non-right triangle.
We know that the sum of all the angles in a triangle must add up to 180, so we can add angles A and B and subtract the sum from 180:
[tex]180-(40+88)=180-128=52[/tex]
The 52 indicates that it is a non-right triangle, so we must rely on either the law of sines or law of cosines to find the measure of b.
Given that we have angle A and its resulting side, a, along with angle B, we can use the law of sines:
[tex]\frac{sin A}{a}=\frac{sin B}{b}[/tex]
[tex]\frac{sin 40}{15}=\frac{sin 88}{b}\\ \\ 15*sin 88=b * sin 40\\\\b=\frac{b*sin 40}{sin 88}\\ \\b=23.3216=23.3[/tex]
Maira has a total of Rs.1040 as currency notes in the denomination of Rs.10, Rs.20 and Rs.50. The ratio of the number of Rs.10 notes and Rs.20 notes is 2:5. If she has a total of 30 notes, how many notes of each denomination she has.
Answer:
Given that,
Maira has a total of Rs.1040 as currency notes in the denomination of Rs.10, Rs.20 and Rs.50.
The ratio of the number of Rs.10 notes and Rs.20 notes is 2:5.
She has a total of 30 notes with her.
Let assume that
Number of Rs 10 notes be 2x
Number of Rs 20 notes be 5x
Number of Rs 50 notes be 30 - (2x + 5x) = 30 - 7x
So,
[tex]\begin{gathered}\qquad \:\boxed{\begin{aligned}& \qquad\sf \:Denomination \: of \: Rs \: 10=2x\qquad \: \\ \\& \qquad \:\sf \: Denomination \: of \: Rs \: 20=5x\\ \\& \qquad \:\sf \: Denomination \: of \: Rs \: 50=30 - 7x\end{aligned}} \qquad \\ \\ \end{gathered}[/tex]
Now,
Amount in form of Rs 10 = 10 × 2x = Rs 20x
Amount in form of Rs 20 = 20 × 5x = Rs 100x
Amounts in form of Rs 50 = 50 × (30 - 7x) = Rs 1500 - 350x
Now, According to statement
[tex]\begin{gathered}\sf \: 20x + 100x + 1500 - 350x = 1040 \\ \\ \end{gathered}[/tex]
[tex]\begin{gathered}\sf \: 120x + 1500 - 350x = 1040 \\ \\ \end{gathered}[/tex]
[tex]\begin{gathered}\sf \: 1500 - 230x = 1040 \\ \\ \end{gathered}[/tex]
[tex]\begin{gathered}\sf \:- 230x = - 460 \\ \\ \end{gathered}[/tex]
[tex]\sf \: \implies x = 2 [/tex]
Hence,
[tex]\begin{gathered}\qquad \:\boxed{\begin{aligned}& \qquad \:\sf \:Denomination \: of \: Rs \: 10=4\qquad \: \\ \\& \qquad \:\sf \: Denomination \: of \: Rs \: 20=10\\ \\& \qquad \:\sf \: Denomination \: of \: Rs \: 50=16\end{aligned}} \qquad \\ \\ \end{gathered}[/tex]
━━━━━━━━━━━━━━━━━━━━━Please help I’ve tried to answer this 3 times and I keep getting it wrong
Answer:
[tex] \boxed{\bf A. \: x - 2}[/tex]
Step-by-step explanation:
[tex] \sf ( x + 1)^2-9/ x + 4 [/tex]
First, we need to factor the expressions that are not already factored.
[tex] \sf ( x - 2) ( x + 4) / x + 4 [/tex]Now, let's Cancel out x+4 in both numerator and denominator.
[tex] \sf x - 2 [/tex]----------------------------
what’s the sun of -6 4/5 and 6 4/5
Answer:
the answer is 0.
Step-by-step explanation:
When you are adding two of the same numbers together, and one of them is positive while the other is negative, they cancel each other out.
[tex]\huge\textbf{Hey there!}[/tex]
[tex]\mathsf{-6 \dfrac{4}{5} + 6 \dfrac{4}{5}}[/tex]
[tex]\mathsf{= \dfrac{-6 \times 5 + 4}{5}+ \dfrac{6 \times 5 + 4}{5}}[/tex]
[tex]\mathsf{= \dfrac{-30 + 4}{5}+ \dfrac{30 + 4}{5}}[/tex]
[tex]\mathsf{= \dfrac{-34}{5} + \dfrac{34}{5}}[/tex]
[tex]\mathsf{= 0}[/tex]
[tex]\huge\textsf{Therefore, your answer should be: \boxed{\mathsf{0}}}\huge\checkmark[/tex]
[tex]\huge\textbf{Good luck on your assignment \& enjoy}\\\huge\textbf{your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
A grandfather is 51, while his grandson is 11. in how many years will the grandfather's age be twice the age of his grandson?
Answer:
29 years
Step-by-step explanation:
In 29 years the grandson will be 40 and the grandfather will be 80. 80 is twice as much as 40.
Answer: 29 years
Step-by-step explanation: if the grandfather is 51 when the grandson is 11 then the grandfather was 40 when his grandson was born. This mean the grandfather will be 80 when the grandson is 40. 40-11=29
i am not able to solve this problem
Answer:
C
Step-by-step explanation:
you know the drill
I really need help on this question
Answer:
24Step-by-step explanation:
Since 20 is 4/3 * 15, the answer must be 4/3 * 18
4/3 * 18 = 24, so the answer is 24
which of the following statements must be true abut this diagram. check all that apply
The options w > x, w > y, and x + y = w are correct because the sum of the two interior angles is equal to the exterior angle.
What is an angle?When two lines or rays converge at the same point, the measurement between them is called a "Angle."
The question is incomplete.
The complete question is in the picture, please refer to the attached picture.
From the figure,
The interior angle of a triangle is w
w > x (true)
w > y (true)
x + y = w (sum of the two interior angles is equal to the exterior angle)
Thus, the options w > x, w > y, and x + y = w are correct because the sum of the two interior angles is equal to the exterior angle.
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Cai invests £2500 in an account that pays 3.55% simple interest interest per year. He takes out his money after 2.75years. what is the value of the investment when he takes out the investment
Answer:
So now,
you know the formula for simple interest is P×R×T divided by a hundred?
So 2500 times 3.55 times 2.75 divided by 100
If AABD
ACBD,
LA = 32° and ZC = 5x - 13
A
C
x =
B
D
[?]
Answer: 9
Step-by-step explanation:
By CPCTC,
[tex]32=5x-13\\\\45=5x\\ \\ x=9[/tex]
If the set u = {all positive integers} and set a = {x|x ∈ u and x is an odd positive integer}, which describes the complement of set a, ac?
A = {x|x ∈ U and is an even positive integer}
The universal set(U) consists of only positive integers.
Given, A = {x|x ∈ U and x is an odd positive integer}.
That means the set A contains all those elements which belongs to the universal set and should be a positive odd number.
refers to the complement of A. It means that it will contain all those elements that belong to U but does not belong to A.
All the positive odd integer is made up of two types of number ,i.e, positive and negative number.
So,this set will contain all the element belonging to U and should be an even positive integer.
Therefore,Ac = {x|x ∈ U and is an even positive integer}.
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Answer:D:Ac = {x|x ∈ U and is an even positive integer}
Step-by-step explanation:
edge 2022
(y^3-2)(y^2+11) what is the answer
Answer:
[tex]y^{5}[/tex] + 11y³ - 2y² - 22
Step-by-step explanation:
(y³ - 2)(y² + 11)
each term in the second factor is multiplied by each term in the first factor.
y³(y² + 11) - 2(y² + 11) ← distribute both parenthesis
= [tex]y^{5}[/tex] + 11y³ - 2y² - 22
Ryan Massey wants to deposit the following into his savings account: 28 ten-dollar bills, 9 five-dollar bills,
20 quarters, 85 dimes, 32 pennies, and three checks for $654.24, $100.00, and $458.92. He wants to
receive $50.00 in cash.
After he withdraws $50.00 in cash the bank reconciliation shows that Ryan would have: $1 501.98 in bank balance.
What is the solution to the above?Add all the deposits
Total = $338.82
Add the checks
654.24 + 100.00 + 458.92
= $1,213.16
Total amount deposited is: Cash + Check
1,213.16 + 338.82
Total Deposit = $1,551.98
Less withdrawal of $50
$1,551.98 - $50
Balance left = 1 501.98
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Full Question:
Ryan Massey wants to deposit the following into his savings account: 28 ten-dollar bills, 9 five-dollar bills, 20 quarters, 85 dimes, 32 pennies, and three checks for $654.24, $100.00, and $458.92. He wants to receive $50.00 in cash.
How much cash would he lave left after he withdraws $50.00 in cash?
A random sample of 16 ATM transactions at the Last National Bank of Flat Rock revealed a mean transaction time of 2.8 minutes with a standard deviation of 1.2 minutes. The width (in minutes) of the 95 percent confidence interval for the true mean transaction time is
The width (in minutes) of the 95 percent confidence interval for the true mean transaction time is 1.2786 minutes.
Sample size (n) = 16.
Sample mean = 2.8 minutes.
Sample standard deviation (σ) = 1.2 minutes.
Confidence interval given = 95%.
The degree of freedom (df) can be calculated as n - 1.
df = n - 1 = 16 - 1 = 15.
Since, the level of confidence is 95%, the level of significance α = 1 - 0.95 = 0.05.
From the T-Distribution table, we take the value at critical value α/2 with the degree of freedom 15.
[tex]t_{\frac{\alpha }{2} ,15}[/tex] = 2.131.
Now, the margin of error can be shown as follows:
[tex]E = t_{\frac{\alpha }{2} ,15} * \frac{\sigma}{\sqrt{n} } \\\Rightarrow E = 2.131 * \frac{1.2}{\sqrt{16} }\\ \Rightarrow E = 0.6393[/tex]
The width at the confidence interval of 95%, is twice the margin of error, that is:
Width = 2*E = 2*0.6393 = 1.2786.
Thus, the width (in minutes) of the 95 percent confidence interval for the true mean transaction time is 1.2786 minutes.
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A coordinate grid showing Number of Classes on the horizontal x-axis and Total Cost in dollars on the vertical y-axis with 2 lines. The first line passes through (0, 10) and a point at (4, 32). The second line passes through (0, 0) and a point at (2, 15).
Anna wants to take fitness classes. She compares two gyms to determine which would be the best deal for her. Fit Fast charges a set fee per class. Stepping Up charges a monthly fee, plus an additional fee per class. What is the system of equations representing these costs?
y = 5.5x and y = 7.5x + 10
y = 7.5x and y = 5.5x
y = 7.5x and y = 5.5x + 10
y = 7.5x + 10 and y = 5.5x + 10
The system of equations representing these costs are; y = 7.5x and y = 5.5x + 10
How to find the equation of a line?The slope of the first line is;
m = (y2 - y1)/(x2 - x1)
m = (32 - 10)/(4 - 0)
m = 5.5
Now, the first coordinate has a y-intercept of 10. Thus, the equation here for the cost is; y = mx + c = 5.5x + 10
The slope of the second line is;
m = (y2 - y1)/(x2 - x1)
m = (15 - 0)/(2 - 0)
m = 7.5
Now, the first coordinate has a y-intercept of 0. Thus, the equation here for the cost is; y = mx + c = 7.5x + 0 = 7.5x
Thus, the system of equations representing these costs are;
y = 7.5x and y = 5.5x + 10
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Answer:
y = 7.5x and y = 5.5x + 10
Step-by-step explanation:
Metallic spheres of radii 6 cm, 8 cm and 10 cm, respectively, are melted to form a single solid sphere. Find the radius of the resulting sphere.
Kindly help!
[tex]{\large{\textsf{\textbf{\underline{\underline{Given :}}}}}}[/tex]
★ Radius of first sphere [tex]\sf r_{1}[/tex] = 6cm.
★ Radius of second sphere [tex]\sf r_{2}[/tex] = 8cm.
★ Radius of third sphere [tex]\sf r_{3}[/tex] = 10cm.
[tex] {\large{\textsf{\textbf{\underline{\underline{To \: Find :}}}}}}[/tex]
★ The radius of the resulting sphere formed.
[tex] {\large{\textsf{\textbf{\underline{\underline{Formula \: used :}}}}}}[/tex]
[tex]\star \: \tt Volume \: of \: sphere = {\underline{\boxed{\sf{\red{ \dfrac{ 4}{3}\pi {r}^{3} }}}}}[/tex]
[tex] {\large{\textsf{\textbf{\underline{\underline{Concept :}}}}}}[/tex]
★ As, three spheres are melted to from one new sphere. Therefore, volume of three old sphere is equal to volume of new sphere.
i.e, Volume of first sphere + volume of second sphere + volume of third sphere = Volume of new sphere.
[tex] {\large{\textsf{\textbf{\underline{\underline{Solution :}}}}}}[/tex]
Let,
The radius of resulting sphere be [tex]R[/tex]
According to the question,
• Volume of first sphere + volume of second sphere + volume of third sphere = Volume of new sphere.
[tex] \longrightarrow \sf \dfrac{4}{3} \pi {(r_{1})}^{3} + \dfrac{4}{3} \pi {(r_{2})}^{3} + \dfrac{4}{3} \pi {(r_{3})}^{3} = \dfrac{4}{3} \pi {(R)}^{3} [/tex]
• here
☆[tex]\: \sf r_{1}[/tex] = 6cm
☆[tex]\: \sf r_{2}[/tex] = 8cm
☆[tex]\: \sf r_{3}[/tex] = 10cm
Putting the values,
[tex] \longrightarrow \sf \dfrac{4}{3} \pi {(6)}^{3} + \dfrac{4}{3} \pi {(8)}^{3} + \dfrac{4}{3} \pi {(10)}^{3} = \dfrac{4}{3} \pi {(R)}^{3} [/tex]
Taking " [tex]\dfrac{4}{3} \pi [/tex]" common,
[tex] \longrightarrow \sf \dfrac{4}{3} \pi \bigg[ {(6)}^{3} + {(8)}^{3} + {(10)}^{3} \bigg] = \dfrac{4}{3} \pi {(R)}^{3} [/tex]
[tex]\longrightarrow \sf \cancel{ \dfrac{4}{3} \pi} \bigg[ {(6)}^{3} + {(8)}^{3} + {(10)}^{3} \bigg] = \cancel{ \dfrac{4}{3} \pi } {(R)}^{3} [/tex]
[tex]\longrightarrow \sf \bigg[ {(6)}^{3} + {(8)}^{3} + {(10)}^{3} \bigg] = {(R)}^{3} [/tex]
[tex]\longrightarrow \sf \bigg[ 216 +512 + 1000 \bigg] = {(R)}^{3} [/tex]
[tex]\longrightarrow \sf 1728 = {(R)}^{3} [/tex]
[tex]\longrightarrow \sf \sqrt[3]{1728} = R[/tex]
[tex]\longrightarrow \sf \sqrt[3]{ 12 \times 12 \times 12 } = R[/tex]
[tex]\longrightarrow \sf \sqrt[3]{ {(12)}^{3} } = R[/tex]
[tex]\longrightarrow \sf R = \red{12 \: cm} [/tex]
Therefore,
Radius of the resulting sphere is 12cm.
[tex]{\large{\textsf{\textbf{\underline{\underline{Note :}}}}}}[/tex]
★ Figure in attachment.
[tex]{\underline{\rule{290pt}{2pt}}}[/tex]
[tex] \bf \huge x {}^{2} + 5 = 6[/tex]
solve for x :
[tex] \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ [/tex]
[tex] \tiny \textsf{Song recommendations \:? }~ [/tex]
Given :
x² + 5 = 6Subtract 5 from each side :
x² + 5 - 5 = 6 - 5x² = 1Take the root on each side :
√x² = √1x = ±1Hence, the values of x are :
[tex]\fbox {x = 1}[/tex][tex]\fbox {x = -1}[/tex][tex]x^2+5=6\\x^2=1\\x=1 \vee x=-1[/tex]
Identify the axis of symmetry the function graphed below.
Answer: A. X = -1
Step-by-step explanation:
An axis of symmetry is the line that divides the object into two equal halves, creating a mirror-like reflection. Only at x = -1 will that occur.
The Ramos family drove to their family reunion. Before lunch, they drove at a constant rate of 55 miles per hour for 3 hours. After lunch, they drove at a constant rate of 45 miles per hour for 2 hours. How many total miles did the Ramos family drive?
ASAP
Anyone is here
Before lunch, they drove at a constant rate of 55 miles per hour for 3 hours -> They drove a total of 55 x 3 = 165 miles.
After lunch, they drove at a constant rate of 45 miles per hour for 2 hours -> They drove a total of 45 x 2 = 90 miles.
So, the total amount of miles the Ramos family drove is 165 + 90 = 255 miles.
Before lunch, they drove at a constant rate of 55 miles per hour for 3 hours.
[tex]\longrightarrow \tt{55*3=165}[/tex]
After lunch, they drove at a constant rate of 45 miles per hour for 2 hours.
[tex] \longrightarrow \tt{45*2=90}[/tex]
Total miles the Ramos family drive
[tex] \longrightarrow \tt{165+90=255}[/tex]
[tex]answer : \pink{255} \: \tt{miles}[/tex]
What is the slope of each of these three graphs?
[5] No slope (or a slope of 0)
There is no incline or decline to the line, so there is no slope.
[6] 1
We can use "rise over run" since we have clear points on the graph. See attached.
[7] Undefined slope
This slope of this line is undefined. The formula for slope is [tex]\frac{\text{change in y}}{\text{change in x}}[/tex] which becomes [tex]\frac{0}{0}[/tex] in a case like this. You cannot divide by 0, giving a slope of undefined.
What is the radius of the circle with equation (x + 1/5) ^ 2 + (y - 2/5) ^ 2 = 1/25
Answer:
1/5
Step-by-step explanation:
In the circle equation shown, the 1/25 all by itself on the right side of the equation is r^2.
r^2 = 1/25
Squareroot both sides.
r = 1/5
5x-4y=19
x+2=8
Solve simultaneous equation
Answer:
x = 6, y = 5
Step-by-step explanation:
5x - 4y = 19 -------> equation 1
x + 2 = 8 --------> equation 2
Step 1 : Subtract 2 on both sides in equation 2.
x + 2 - 2 = 8 - 2
x = 6
Step 2 : Substitute the value of x is equation 1.
5 ( 6 ) - 4y = 19
( 5 * 6 ) - 4y = 19
30 - 4y = 10
Step 3 : Subtract 30 on both sides.
30 - 30 - 4y = 10 - 30
- 4y = - 20
Step 4 : Multiply - 1 on both sides.
- 1 * - 4y = - 1 * - 20
4y = 20
Step 5 : Divide 4 on both sides.
4y / 4 = 20 / 4
y = 5
Hence,
x = 6
y = 5
Answer:
x = 5, y = 3/2.
Step-by-step explanation:
5x-4y=19
x+2y =8 Multiply this by 2:
2x + 4y = 16 Adding this to first equation 1:
7x = 35
x = 5
So
5 + 2y = 8
2y = 3
y = 3/2.
Help fast. i really need help fast
Answer: 80 miles
Step-by-step explanation:
- 400/5 = 80
- so 80 is 1/5 of 400
hope this helps :)
Answer:
80 miles
Step-by-step explanation:
The whole journey is 400 miles, so we say that he traveled x miles, where x equals 400.
if we multiple 1/5 by x miles, then we will get how much he travels
1/5*x = 1/5*(400), since x = 400, so you can replace x with 400
1/5*x=1/5*400=400/5=80 miles