The angle relationships which are correct are:
∠4 and ∠6 are same side interior angles.
∠3 and ∠6 are alternate interior angles.
Side interior angles
Two angles that are on the same side of the transversal and written the same side of the transversal when two lines are intersected by a third line are called side angles.
Alternate interior angles
Alternate interior angles are the angles formed on the opposite sides of the transversal.
Hence the correct relationship are ∠4 and ∠6 are same side interior angles and ∠3 and ∠6 are alternate interior angles.
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An English instructor asserted that students' test grades are directly proportional to the amount of time spent studying. Lisa studies 6 hr for a particular test and gets a score of 74. At this rate, how many hours would she have had to study to get a score of 98?
Answer:
Step-by-step explanation:
Set up a proportion. x stands for hours that we need to find out.
[tex]\frac{6hrs}{74score} = \frac{xhrs}{98score}\\ 6(98)=74(x)\\588= 74x\\588/74=x\\8=x[/tex]
**the answer was 7.9 BUT I rounded it to 8.
Lisa would need to study for 8 hours to get a score of 98.
Select the correct answer from each drop-down menu. Consider parallelogram ABCD, where m∠ABC = 135° and the length of diagonal AC is 41 units. A parallelogram ABCD has two diagonals AC and BD, intersects each other at a point E inside it. The length of side AD is 35 units and length of side AB is 7 units. An arc is marked on angle B. Note: figure not drawn to scale Use the figure and given information to complete the statements. m∠BCD = ° The length of segment CD is units. The length of segment AE is units.
The length of segment CD is 7 units. The length of segment AE is 20.5 units. The m∠BCD is 45 degrees.
What is a parallelogram?A parallelogram is always a quadrilateral but a quadrilateral can or cannot be a parallelogram.
Given that parallelogram ABCD, has m∠ABC = 135° and the length of diagonal AC is 41 units.
The measure of length of side AD is 35 units and length of side AB is 7 units.
WE know that the opposite side of a parallelogram are same. Thus,
The length of segment CD = AB = 7 units.
Also, the length of diagonal AC = 41 units. Then;
The length of segment AE = 1/2 AC = 41/2 = 20.5 units.
Therefore, m∠BCD + m∠ABC = 180
m∠BCD + 135 = 180
m∠BCD = 180 - 135
m∠BCD = 45 degrees.
Hence, The length of segment CD is 7 units. The length of segment AE is 20.5 units. The m∠BCD is 45 degrees.
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Answer:
45
7
20.5
Step-by-step explanation:
what is the effect on the graph of the function f(x) = x² when f(x) is changed to f(x) + 9A) shifted up B) shifted left C) shifted rightD) shifted down
When we add a constant on a f(x) graph we have
• f(x) + a ⇒ graph shifted up
,• f(x) - a ⇒ graph shifted down
Therefore, let's see if it's shifting up or down, we have
[tex]f(x)+9[/tex]9 is positive, then it's shifting up 9 units.
please help asap!!! will appreciate it
H=16.4
Step-by-step explanation:
1.2x4=4.8
3.9x4=15.6
so
4.1x4=16.4
the area of the parallelogram below is 59.9m2,What is the height
The height of the parallelogram is 6.97m.
How to calculate the height?It is important to kite that the aea of a parallelogram is calculated as:
= Base × Height
In this case, the base is given as 8.6m. Therefore, the height will be:
Area = Base × Height
59.9 = 8.6 × Height
Now, we will find the height
Height = 59.9 / 8.6
Height = 6.97m
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The area of the parallelogram is 59.9m² and.the vase is 8.6m,What is the height
A local high school runs a game at a fundraising event. In this game, marbles are randomly picked froma bag. The bag contains 5 red marbles, 4 blue marbles, and 1 green marble. If a green marble is drawn, you win $10. If the blue marble is drawn, you win $2, and if you draw a red marble you win nothing. The game costs $3 to play. Find the expected value of playing.
Given:
5 red marbles
4 blue marbles
1 green marble
Upon choosing green marble, we win $10
Upon choosing blue marble, we win $2
Upon choosing red marble, we win $0
It costs $3 to play each game.
To find:
The expected value of playing the game
Step by step solution:
Firstly we need to calculate the probablity of occuring of each event:
P (Choosing a red marble) = 5/10 = 1/2
P (Choosing a blue marble) = 4/10 = 2/5
P (Choosing a green marble) = 1/10 = 1/10
We will now associate the money related to each case:
= 1/2 × $0 + 2/5 × $2 + 1/10 × $10
= 0 + $ 4/5 + $1
= $ 1.8
The cost of 5 gallons of ice cream has a variance of 64 with a mean of 34 dollars during the summer.
What is the probability that the sample mean would differ from the true mean by less than 1.1 dollars if a sample of 38 5-gallon pails is randomly selected? Round your answer to four decimal places.
The probability is [(X - μ) < 1.1] = 0.6046.
What is probability ?A probability is a numerical representation of the likelihood or chance that a specific event will take place. Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to describe probabilities.
Given: σ² = 64
Mean μ = 34
To find: Probability[(X - μ) < 1.1]
Computation: Standard deviation σ = √σ²
Standard deviation σ = √64
Standard deviation σ = 8
Probability[(X - μ) < 1.1] = Probability[-1.1 < (X - μ) < 1.1]
Probability[(X - μ) < 1.1] = Probability[-1.1/(8/√38) < (X - μ) < 1.1/(8/√38)]
Using z table
The probability = [(X - μ) < 1.1] = 0.6046.
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During a family trip, you share the driving with your dad. At most, you are allowed to drive for three hours. While driving, your maximum speed is 55 miles per hour. a) Write a system of inequalities describing the possible numbers of hours, t, and the distance, d, you may have to drive.
Here, we want to writw an inequality to describe the information given.
When we say at most, it means the expected values may be less than or equal to but can never be more than
Mathematically;
[tex]\text{distance d = sp}eed\text{ }\times\text{ time t}[/tex]From the question, we are told that the maximum driving time is 3 hours; the inequality here will be;
[tex]t\text{ }\leq\text{ 3 hours}[/tex]For the distance d, we have;
[tex]\begin{gathered} d\text{ }\leq\text{ 3 }\times\text{ 55} \\ \\ d\text{ }\leq\text{ 165 miles} \end{gathered}[/tex]Solve for r: S= 4 pie r^2
we have
S= 4*(pi)*r^2
solve for r
That means ------> isolate the variable r
step 1
Divide by 4*(pi) both sides
so
S/(4*pi)=r^2
step 2
Square root both sides
so
[tex]\begin{gathered} r=\sqrt[]{\frac{S}{4\pi}} \\ \text{simplify} \\ r=\frac{1}{2}\sqrt[]{\frac{S}{\pi}} \end{gathered}[/tex]M is the midpoint of line AB. Endpoint A is (4, 2). Midpoint M is (6, 0). Endpoint B = ?
The B points are ( 8, -2 ) of Endpoint B when M is the midpoint of line AB.
What is midpoint of a segment?
The midway of a line segment in geometry is where it meets the other end. The centroid of the segment and the endpoints, it is equally spaced from both endpoints. It cuts the section in half.M is the midpoint of line AB.
Endpoint A is (4, 2).
Midpoint M is (6, 0)
Let mid points are ( x,y) and A points are ( x₂ , y₂ ) and B points are ( x₁ , y₁)
x = x₁ + x₂/2 , y = y₁ + y₂/2
6 = x₁ + 4/2 , 0 = y₁ + 2/2
12 = x₁ + 4 , 0 = y₁ + 2
x₁ = 12 - 4 , y₁ = -2
x₁ = 8 , y₁ = -2
So, the B points are ( 8, -2 )
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Really need help solving this Struggling It’s from my trig prep book
Start making the graph of the situation
from this, we can understand that x is Coreys' initial distance, z is Coreys' final distance, and y will be how many feet had Corey to step back in order to gain a better view.
Using the red triangle we find x through the tan of the given angle
[tex]\begin{gathered} \tan \theta=\frac{op}{ad} \\ \tan 68=\frac{80}{x} \\ x=\frac{80}{\tan 68} \\ x\approx32.32 \end{gathered}[/tex]Using the blue triangle we find z through the tan of the given angle the same way as before
[tex]\begin{gathered} \tan \theta=\frac{op}{ad} \\ \tan 41=\frac{80}{z} \\ z=\frac{80}{\tan 41} \\ z\approx92.03 \end{gathered}[/tex]finally, find y as the difference between z and x
[tex]\begin{gathered} z=x+y \\ y=z-x \\ y=92.03-32.32 \\ y=59.71 \end{gathered}[/tex]Corey had to go back 59.71 ft to gain a better view.
You drive 3 hours to reach the waterpark. Driving home along the same route, you increase your
speed by 20 miles per hour, reducing your drive time by 1 hour. Write and solve an equation to find
how fast you were driving to the waterpark.
The initial speed to the waterpark is 40 miles/hr.
The return speed is 60 miles/hr.
How to find the speed?
Given,
t = 3hr
Return speed = s +20m
Return time = 3 -1 = 2hrs
Solution:
s = d/t
s = d/3
d = 3s----1
s + 20 = d/t - 1
s + 20 = d/3-1
s + 20 = d/2
2s + 40 = d------2
Equating equations 1 and 2,
3s = 2s + 40
s = 40 miles/hr
The initial speed to the waterpark is 40 miles/hr.
Return speed = s +20
= 40+20
= 60 miles/hr
The return speed is 60 miles/hr.
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In this diagram, ABAC – AEDF. If thearea of ABAC = 6 in2, what is thearea of AEDF?DE2 inFB3 inСArea = [?] in?Enter a decimal rounded to the tenths.
Answer:
8/3 square inches
Explanation:
First, we need to get the height of the triangle BAC
Area of triangle = 1/2 * base * height
6 = 1/2 * 3 * height
12 = 3 * height
Height = 12/3
The height of triangle BAC is 4inches
Next is to get the height of EDF. Since they are both similar hence;
2/3 = h/4
3h = 2 * 4
3h = 8
h = 8/3
h = 8/3in
Hence the height of triangle EDF is 8/3in
Get the area of triangle EDF
Area of triangle EDF = 1/2 * 2 * 8/3
Area of triangle EDF = 8/3 square inches
Hence the area of triangle EDF is 8/3square inches
M&Ms Data Set 20 in Appendix B lists data from 100 M&Ms, and 8% of them are
brown. Use a 0.05 significance level to test the claim of the Mars candy company that the
percentage of brown M&Ms is equal to 13%.
The rejection region, or area of the rejection zone, is the significance level. The test's tail determines the direction of the rejection region. When the significance threshold is unknown, it is typically considered to be 5%.
What is rejection region ?A collection of values for the test statistic for which the null hypothesis is rejected constitutes a critical zone, sometimes referred to as the rejection region. For example, if the observed test statistic is in the critical range, the null hypothesis is rejected and the alternative hypothesis is accepted.
Consider the crucial value as a cut-off point at a particular importance level. If a test statistic falls on one side of the crucial value and leads to the null hypothesis being accepted, a test statistic falling on the other side will lead to the null hypothesis being rejected.
A set of values for the test statistic for which the null hypothesis is accepted is referred to as a confidence interval and is also referred to as the acceptance area. For example, if the observed test statistic is within the confidence interval, the null hypothesis is accepted and the alternative hypothesis is rejected.
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Technology required. Ramps in a parking garage need to beboth steep and safe. The maximum safe incline for a ramp is8.5 degrees. Is this ramp safe? If not, provide dimensions thatwould make the ramp safe.
Ok, so:
Let me draw the situation here below:
Ok, let's find the angle first:
For this, we shall make use of the trigonometric functions:
In this case, the most useful function which could help us to solve this problem is tan(x). This function relations the opposite side of the angle and its adjacent side, like this:
tan(x) = opposite side / adjacent side
So, if we replace the values:
tan(x) = 15/95
tan(x) = 0,15789474
To find x, we could use the inverse function of tan(x). This one is called arctan(x).
So, arctan(tan(x)) = arctan(0,15789474)
And this is:
x = 8.97 degrees
Now, we can affirm that the angle is 8.97 degrees, which is bigger than 8.5 degrees.
Now, what should be the length of the bottom for the ramp to be safe?
Let me draw the situation:
We know that the ramp is safe if the maximum safe incline is 8.5°. So, what should be the value of x for this occurs?
We use the trigonometric function tan(x) again.
tan(8.5°) = 15/x
Remember that tan(8.5°) is a number
Then, x = 15/tan(8.5°), and this is 100.36
So, we conclude that the lenght of the bottom should be at least, 100.36
One interior angle of a triangle is 98.5°, and the other two interior angles are congruent. What is the degree measure of one of the congruent angles?
81.5°
90°
40.75°
49.25°
Answer:
(c) 40.75°
Step-by-step explanation:
Given an isosceles triangle with one angle 98.5°, you want the measures of each of the other two angles.
Angle sum theoremThe sum of angles in a triangle is 180°, so we have ...
2x + 98.5° = 180° . . . . . . x is the unknown angle measure
x +49.25° = 90° . . . . . . divide by 2
x = 40.75° . . . . . . . . . . subtract 49.25°
The measure of one of the congruent angles is 40.75°.
Sixth grade > FF.24 Surface area of pyramids 5XW
Science
1 yd
What is the surface area of this rectangular pyramid?
Submit
1 yd
1 yd
Surface Area of rectangular pyramid is lw + l√[(w ÷ 2)² + h²] + w√[(l ÷ 2)² + h²].
The area of a rectangular pyramid is equal to the sum of the areas of the sides and faces of the rectangular pyramid. A quadrilateral pyramid is a three-dimensional shape with only a rectangular base and triangles on either side of the base.
The area of the base of the rectangle is calculated by multiplying the length of the rectangle by the width of the rectangle.
The area of a rectangle with a pyramidal formula is determined by observing the width, length, and height of the base,
S.A. = lw + l√[(w ÷ 2)² + h²] + w√[(l ÷ 2)² + h²],
where l is the length of the bottom of the rectangle, w is the width of the bottom of the rectangle, and h is the height.
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Hello, I need some assistance with this homework question, please? This is for my precalculus homework. Q11
Explanation
The vertical asymptote
[tex]\begin{gathered} \mathrm{For\:rational\:functions,\:the\:vertical\:asymptotes\:are\:the\:undefined\:points,\:} \\ \mathrm{also\:known\:as\:the\:zeros\:of\:the\:denominator,\:of\:the\:simplified\:function.} \end{gathered}[/tex]for the given function
[tex]T(x)=\frac{x^3}{x^4-81}[/tex]According to the formula
The denominator will be undefined when
[tex]\begin{gathered} x^4-81=0 \\ x=\sqrt[4]{81} \\ x=3,\text{ x=-3} \\ x= \end{gathered}[/tex]The vertical asymptotes are
[tex]x=-3,3[/tex]For the horizontal function
[tex]\mathrm{If\:denominator's\:degree\:>\:numerator's\:degree,\:the\:horizontal\:asymptote\:is\:the\:x-axis:}\:y=0.[/tex]Since the denominator degree is higher than the numerator
Then
The horizontal asymptote is
[tex]y=0[/tex]For the oblique asymptote
Since the degree of the numerator is not one degree greater than the denominator, then there are no slant asymptotes.
There are no oblique asymptote
please help me identify what was wrong in solving it I know the right answer is 10 but i don't know what was done wrong.
Given:
The coordinates are given as,
[tex]\begin{gathered} (x_1,y_1)=(-1,2) \\ (x_2,y_2)=(-7,-6) \end{gathered}[/tex]The objective is to find the distance between the two points.
Explanation:
The general formula to find the distance between two coordinates is,
[tex]d=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2}\text{ . . . . . (1)}[/tex]Substitute the given coordinates in equation (1),
[tex]d=\sqrt[]{(-7-(-1))^2+(-6-2)^2}[/tex]On further solving the above equation,
[tex]\begin{gathered} d=\sqrt[]{(-6)^2+(-8)^2} \\ =\sqrt[]{36+64} \\ =\sqrt[]{100} \\ =10 \end{gathered}[/tex]Hence, the distance between the two points is 10.
What is the area shaded sector to the nearest 10th of the square centimeter?
The area of a sector of a circumference is given by the following formula:
[tex]A=\frac{\theta r^2}{2}[/tex]Where r is the radius of the circumference, and θ is the angle of the sector in radians.
The radius is already known: 15cm.
We need to estimate the angle of the shaded region. The shaded region and the sector whose angle is 72° form together a 180° angle. (This is according to the figure. That is not said in an explicit way but we will need to assume that since there is not enough information to calculate the area if it is otherwise.)
Then, the angle of the shaded area, plus 72° is 180°:
[tex]\begin{gathered} \theta+72^o=180^o \\ \\ \theta=180^o-72^o \\ \\ \theta=108^o \end{gathered}[/tex]Now, before applying the formula we need to express the angle in radians. Recalling that 180° is equal to π radians:
[tex]\theta=108^o\cdot\frac{\pi\text{ rad}}{180^o}=\frac{108}{180}\pi\text{ rad}[/tex]Now, we have the angle in radians. We can use the equation:
[tex]\begin{gathered} A=\frac{\theta r^2}{2} \\ \\ A=\frac{108}{180}\cdot\frac{\pi\cdot(15\operatorname{cm})^2}{2} \\ \\ A\approx212.1\text{ cm}^2 \end{gathered}[/tex]I need help with this question please. I have options available
Option B is the graph of the given function.
Two buses leave Philadelphia at the same time and travel in opposite directions. The north bound bus travels
at a rate of 55 mph. The southbound bus travels at a rate of 45 mph. When will they be 400 miles apart?
Answer:
4 hours
Step-by-step explanation:
55x + 45x = 400
100x = 400
x = 400/100
x = 4
A function has X-intercept 4 and y-intercept 2. name two other points on the graph of this function. Please explain thoroughly on how to find another point.
Solution
For this case we have the following:
x intercept 4: (4,0)
y intercept 2: (0,2)
Then we can find the slope like this:
[tex]m=\frac{2-0}{0-4}=-\frac{1}{2}[/tex]then the equation is given by:
y= -1/2 x+ 2
and we can use x= 1 and we have y= 3/2
x= 2 , y= 1
Then two other points could be:
(1,3/2) and (2,1)
What is the value of y?
2
4
6
8
Answer: Ima say 6
Explanation: I don't have an explanation
You have 7/8 of a cup of tomato sauce. You must fill small containers with exactly 1/4 of a cup of tomato sauce How many containers can you fill completely?
Using division, If you have 7/8 of a cup of tomato sauce and you must fill small containers with exactly 1/4 of a cup of tomato sauce, then number of containers can fill completely is 3 containers
The total quantity of tomato sauce that you have = 7/8 of a cup
The quantity of tomato sauce with you must fill small containers = 1/4 of a cup
To find the number of containers that you can fill completely, you have to use division
Number of containers can fill completely = The total quantity of tomato sauce that you have / The quantity of tomato sauce with you must fill small containers
= 7/8 ÷ 1/4
= 7/8 × 1/4
= 7/2
= 3.5
≈ 3 containers
Hence, using division, if you have 7/8 of a cup of tomato sauce and you must fill small containers with exactly 1/4 of a cup of tomato sauce, then number of containers can fill completely is 3 containers
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Help with part B please
a) The opposite of the numbers 3, 7.5, and -2(2/3) will be 0.33, 0.133, and -0.375.
b) The sum of the given number and its opposite will be 7.928.
What is an irrational number?It is defined as the numbers in all real numbers which cannot be represented as rational numbers, in other words, the irrational number cannot be expressed in the form of p/q form.
A rational number is a sort of real number that has the form p/q and does not equal zero.
The given number is as,
3, 7.5, and -2(2/3)
a)
The opposite number is obtained as 1 by dividing the given number,
⇒ 1 / 3 = 0.33
⇒ 1 / 7.5 = 0.133
⇒ 1 / -2(2/3) = -0.375
b)
The sum of the given number and its opposite is,
= 3+0.33 + 7.5 + 0.133+ (-2(2/3) ) + (-0.375)
= 7.928
Thus, the opposite of the numbers 3, 7.5, and -2(2/3) will be 0.33, 0.133, and -0.375.and the sum of the given number and its opposite will be 7.928.
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what is the rate if the base is 244 and the portion 50
SOLUTION
Step1:Write out the formula
[tex]\frac{\text{portion}}{base}=\frac{rate\text{ }}{100}[/tex]Step2; write out the parameters
[tex]\begin{gathered} portion=50 \\ \text{Base}=244 \end{gathered}[/tex]Step3: Substitute into the formula and simplify
[tex]\frac{50}{244}=\frac{rate}{100}[/tex]Step4: simplify the expression above
[tex]\begin{gathered} \text{ Multiply both side by 244} \\ \text{rate}\times244=100\times50 \\ \text{then} \\ \text{ Rate=}\frac{100\times50}{244} \end{gathered}[/tex]Then the rate becomes
[tex]20.49\text{ }[/tex]Therefore the rate is 20.49
The company with the common equity accounts shown here has declared a stock dividend of 20 percent at a time when the market value of its stock is $30 per share. Common stock ($1 par value) $ 460,000 Capital surplus 861,000 Retained earnings 3,870,800 Total owners' equity $ 5,191,800 What would be the number of shares outstanding, after the distribution of the stock dividend? (Do not round intermediate calculations.)
1110800. Equity Account will be after stock dividends
What is stock dividend ?Similar to a cash dividend, however instead of cash, stocks are given out. A stock dividend will increase the number of shares outstanding while lowering the stock price.
In this issue, there are 460000 shares outstanding at a price of $30, which equals 13800000
Equity's total market value is $13800000.
Each shareholder will get a 20% increase in stock, and the number of existing shares will increase as a result of the 20% stock dividend.
Shares outstanding after dividend announcement total 460000 + 46000 ×20% =552000.
The number of outstanding common shares will rise to 552000 as a result of the issuance of 92000 more shares.
Common stock only contains the par value; for example, if the market price of a share is $30 and the par value is $1, the excess amount of $29×92000:2668000 is added to the capital surplus account. It will total 861000 + 2668000=3529000.
Due to the absence of any monetary transactions, the total owners' equity is unaltered.
The retained earnings will be decreased by 92000 × 30 = 2760000, resulting in 3870800 – 2760000=1110800.
Equity Account will be after stock dividends.
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14. If the surface area of the cone below is 628.32 m2, find its volume.
You have a cone with surface area of 628.32 m². In order to find the volume of the cone you use the following formula:
V= 1/3 π r² h
r: radius of the base of the cone = 15m/2 = 7.5m
h: heigth of the cone
Then, you have to calculate first the height of the cone. To do that, you use the information about the surface area. You use the following formula:
S = πr² + πrl
l: diagonal of the cone
Then, you have to find l, and then you can calculate hYou solve for l from the surface area formula:
l = (S - πr²)/πr = (628.32 - π(7.5)²)/(π(7.5))
l = 19.16
To calculate the heigth of the cone you use the Pythagoras theorem, just as follow:
h = √(l²-r²) = √((19.16)²-(7.5)²) = 17.63m
Next, you can replace the values of h and r into the formula for the Volume:
V= 1/3 π r² h = (1/3)π (7.5m)²(17.63m) = 1038.5m³
Hence, the volume of the given cone is 1038.49 m3
Complete the work to solve for y7 (22y + 5) - 13 = 2 4 - 1 + 101/4 + 2 - 1/2 = 1 4 - 1 + you
Answer:
11/2
Explanation:
Given:
To find:
The value of y
So we have;
[tex]\frac{11}{5}=\frac{2}{5}y[/tex]Let's go ahead and apply the Division property of equality by dividing both sides of the equation by 2/5;
[tex]\begin{gathered} \frac{\frac{11}{5}}{\frac{2}{5}}=\frac{\frac{2}{5}}{\frac{2}{5}}y \\ \frac{11}{5}\div\frac{2}{5}=y \\ \frac{11}{5}*\frac{5}{2}=y \\ \frac{11}{2}=y \\ \therefore y=\frac{11}{2} \end{gathered}[/tex]So the value of y is 11/2