Because 9 × 10 equals 90
Then 7×90=7×9×10
A company knows that if it sets the price of a product at p dollars, the number of units sold will be x million, where p = 2 - x. If the cost of the product is given by 0.25 + 0.5x million dollars. What price should be set to make a profit of $ 0.25 million?
====================================================
Explanation:
x = number of products, in millions, sold
p = price per product
R = revenue
R = (number of products sold)*(price per product)
R = x*p
R = x(2-x)
R = 2x-x^2
C = costs
C = 0.25 + 0.5x
F = profit
F = revenue - costs
F = R - C
F = (2x - x^2) - (0.25 + 0.5x)
F = -x^2 + 1.5x - 0.25
We want a profit of 0.25 million, so plug in F = 0.25 and solve for x
F = -x^2 + 1.5x - 0.25
0.25 = -x^2 + 1.5x - 0.25
0 = -x^2 + 1.5x - 0.25 - 0.25
-x^2 + 1.5x - 0.5 = 0
Use the quadratic formula to find the two solutions to be x = 0.5 and x = 1
If x = 0.5, then p = 2-x = 2-0.5 = 1.5
If x = 1, then p = 2-1 = 1
There are two price points (p = 1.5 and p = 1) that lead to the same profit F = 0.25
The perimeter of a rectangle is 10 feet. If twice the width is equal to half of the length , find the dimensions of this rectangle.
WRITE AS AN EQUATION
w = 1ft
l = 4ft
Step-by-step explanation:P =2w + 2l
2w = l/2 => l = 4w
10ft = 2w + 2×4w
10ft = 2w + 8w
10ft = 10w
w = 10ft/10
w = 1 ft
l = 4w
l = 4×1ft
l = 4 ft
Answer:
length = 4 ft
Width = 1 ft
Step-by-step explanation:
Let length = l ft
Width = w feet
[tex]\frac{1}{2}l = 2w\\\\l = 2w*2\\\\l = 4w[/tex]
Perimeter = 10 ft
2*(l +w)= 10
2*( 4w + w ) = 10
2*5w = 10
10w = 10
Equation: 10w = 10
Divide both sides by 10
10w/10 = 10/10
w = 1 ft
Plug in the value of w in l = 4w
l = 4 *1
l = 4 ft
What were Malcolm's and Ravi's maximum speeds?
Answer:
Malcom's maximum speed = 200 km/h
Ravi's maximum speed = 320 km/h
Step-by-step explanation:
Represent the maximum speed of Malcolm and Ravi with equation as follows:
Let Malcom's speed be x, and Ravi's speed by y.
The average of speed is said to be 260 km/h. An equation to represent this is: [tex] \frac{x + y}{2} = 260 [/tex]
[tex] x + y = 260*2 [/tex]
[tex] x + y = 520 [/tex] => equation 1.
We are also told that when Malcom's speed (x) is doubled it equal 80 km/hr more than Ravi's speed (y). An equation can be created for this, which is [tex] 2x = y + 80 [/tex]
[tex] 2x - y = 80 [/tex] => equation 2
Now that we have 2 equations as a system, solve for the values of x and y simultaneously.
Add both equations together to eliminate y
[tex] x + y = 520 [/tex]
[tex] 2x - y = 80 [/tex]
[tex] 3x = 600 [/tex]
[tex] x = \frac{600}{3} [/tex]
[tex] x = 200 [/tex]
Plug in the value of x into equation 1 to find y.
[tex] 200 + y = 520 [/tex]
[tex] y = 520 - 200 [/tex]
[tex] y = 320 [/tex]
Malcom's maximum speed = x = 200 km/h
Ravi's maximum speed = y = 320 km/h
The owner of an organic fruit stand also sells nuts. She wants to mix cashews worth $5.50 per pound with peanuts worth $2.30 per pound to get a 1/2 pound mixture that is worth $2.80 per pound. How much of each kind of nut should she include in the mixed bag?
Total weight required is half pound, so let the amount of cashews be [tex] a[/tex] , and amount of peanuts be $b$
$\therefore a+b=0.5$ (1)
And we want this to cost $2.80$
Cost of $a$ pound of cashews will be $5.50\times a$ and cost of $b$ pound peanuts will be $2.30\times b$
$\therefore 5.5a+2.3b=2.8$ (2)
Substitute $a=0.5-b$ from equation (1) in equation (2)
$5.5(0.5-b)+2.3b=2.8$
$\implies -3.2b=2.8+5.5\times0.5 $
$\implies -3.2b=0.05$
$b$ comes out to be negative. That means there's no solution with the given conditions.
I checked once , I don't think there's any mistake. Can someone else verify too?
EDIT
I verified all the given options from calculator, and no option gives 2.80
-36 + x < 8 Solve for x
Answer:
[tex]x < 44[/tex]
Step-by-step explanation:
We can simplify this inequality by isolating x on one side.
[tex]-36 + x < 8[/tex].
Let's add 36 to both sides.
[tex]-36 + 36 + x < 8 +36\\\\x < 44[/tex]
Hope this helped!
Answer:
x<44
Step-by-step explanation:
Add 36 to both sides:
-36 + x < 8
+36 +36
x < 44
in a polynomial function of degree 5, what is the maximum number of extreme that could be possible? (please explain with the answer if possible!)
Answer:
4 maximum extrema
Step-by-step explanation:
5th degree means that it can change direction 5 times, therefore creating a maximum of 4 extrema
Please help me! This is Algerbra 1
Answer:
A. x > -1 or x < -1
Step-by-step explanation:
5x - 29 > -34 or 2x + 31 < 29
Add 29 to both sides. Subtract 31 from both sides.
5x > -5 or 2x < -2
Divide both sides by 5. Divide both sides by 2.
x > -1 or x < -1
Answer: x > -1 or x < -1
Brian is building a wood frame around a window in his house. If the window is 4 feet by 5 feet, how much wood does he need for the frame?
Answer:
18 feet
Step-by-step explanation:
to find the frame around the widow means need to find the perimeter around the window:
P=2l+2w
P= 2(5+4)
P=18 feet
The body paint, an automobile body paint shop, has determined that the painting time of automobiles is uniformly distributed and that the required time ranges between 45 minutes to 11/2hours.
What is the probability that the painting time will be less than or equal to an hour?
What is the probability that the painting time will be more than 50 minutes?
Determine the expected painting time and its standard deviation.
Answer:
a. [tex]\mathbf{P(Y \leq 60) = 0.3333}[/tex]
b. P(Y>50) = 0.8889
c. E(y) = 67.5 and Standard deviation [tex]\sigma[/tex] = 12.99
Step-by-step explanation:
From the information given :
an automobile body paint shop, has determined that the painting time of automobiles is uniformly distributed and that the required time ranges between 45 minutes to [tex]1\frac{1}{2}[/tex]hours.
The objective is to determine the probability that the painting time will be less than or equal to an hour?
since 60 minutes make an hour;
[tex]1\frac{1}{2}[/tex]hours = 60 +30 minutes = 90 minutes
Let Y be the painting time of the automobile; then,
the probability that the painting time will be less than or equal to an hour ca be computed as :
[tex]P(Y \leq 60) = \int ^{60}_{45} f(y) dy \\ \\ \\ P(Y \leq 60) = \int ^{60}_{45} \dfrac{1}{45} dy \\ \\ \\ P(Y \leq 60) = \dfrac{1}{45} \begin {pmatrix} x\end {pmatrix}^{60}_{45} \\ \\ \\ P(Y \leq 60) = \dfrac{60-45}{45 } \\ \\ \\ P(Y \leq 60) = \dfrac{15}{45} \\ \\ \\ P(Y \leq 60) = \dfrac{1}{3} \\ \\ \\ P(Y \leq 60) = 0.3333[/tex]
What is the probability that the painting time will be more than 50 minutes?
The probability that the painting will be more than 50 minutes is P(Y>50)
So;
[tex]P(Y>50) = \int \limits ^{90}_{50} f(y) dy[/tex]
[tex]P(Y>50) = \int \limits ^{90}_{50} \dfrac {1}{45} dy[/tex]
[tex]P(Y>50) = \dfrac{1}{45}[x]^{90}_{50}[/tex]
[tex]P(Y>50) = (\dfrac{90-50}{45})[/tex]
[tex]P(Y>50) = \dfrac{40}{45}[/tex]
P(Y>50) = 0.8889
Determine the expected painting time and its standard deviation.
Let consider E to be the expected painting time
Then :
[tex]E(y) = \int \limits ^{90}_{45} y f(y) dy \\ \\ \\ E(y) = \int \limits ^{90}_{45} y \dfrac{1}{45} dy \\ \\ \\ E(y) = \dfrac{1}{45} [\dfrac{y^2}{2}]^{90}_{45} \\ \\ \\ E(y) = \dfrac{1}{45}[\dfrac{(90^2-45^2)}{2}] \\ \\ \\ E(y) = \dfrac{1}{45} (\dfrac{6075}{2}) \\ \\ \\ E(y) = \dfrac{1}{45} \times 3037.8 \\ \\ \\ \mathbf{E(y) = 67.5}[/tex]
[tex]E(y^2) = \int \limits ^{90}_{45} y^2 f(y) dy \\ \\ \\ E(y^2) = \int \limits ^{90}_{45} y^2 \dfrac{1}{45} dy \\ \\ \\ E(y^2) = \dfrac{1}{45} [\dfrac{y^3}{3}]^{90}_{45} \\ \\ \\ E(y^2) = \dfrac{1}{45}[\dfrac{(90^3-45^3)}{3}] \\ \\ \\ E(y^2) = \dfrac{1}{45} (\dfrac{637875}{3}) \\ \\ \\ E(y^2) = \dfrac{1}{45} \times 2126.25 \\ \\ \\ \mathbf{E(y^2) = 4725}[/tex]
To determine the standard deviation, we need to first know what is the value of our variance,
So:
Variance [tex]\sigma^2[/tex] = E(x²) - [E(x)]²
Variance [tex]\sigma^2[/tex] = 4725 - (67.5)²
Variance [tex]\sigma^2[/tex] = 4725 - 4556.25
Variance [tex]\sigma^2[/tex] = 168.75
Standard deviation [tex]\sigma[/tex] = [tex]\sqrt{variance}[/tex]
Standard deviation [tex]\sigma[/tex] = [tex]\sqrt{168.75}[/tex]
Standard deviation [tex]\sigma[/tex] = 12.99
there are 63 students marching in a band, and they're marching in 7 rows how many students are in each row
Answer:
9 people per row
Step-by-step explanation:
63/7=9
let me now if right
Write your answer in scientific notation.
(6.4 x 10^3 ) + (5.2 x 10^4 )
Answer:
5.84 x10.^4
Step-by-step explanation:
Move the decimal so there is one non-zero digit to the left of the decimal point. The number of decimal places you move will be the exponent on the
10
If the decimal is being moved to the right, the exponent will be negative. If the decimal is being moved to the left, the exponent will be positive.
Observe how the land division was planned for the preparation of a vegetable garden.
In it, lettuce, tomatoes, carrots, beets and corn will be planted.
Determine the monomial that represents the measure:
1-lettuce
2-beets
3-tomato
4-corn
5-carrot
Answer:
1-lettuce 4ab x 12ab = 48a²b²
2-beets 3ab x 3ab = 9a²b²
3-tomato 4ab x 5ab = 20a²b²
4-corn 2ab x 3ab = 6a²b²
5-carrot 12ab x 3ab = 36a²b²
Step-by-step explanation:
one-third of a number is subtracted from 11.The result is one and half times the original number. what is the number.
If 11 is subtracted from 3 times the number, the result is the square of 5 less than the number. What are the set of numbers that satisfy
A laptop has a listed price of $703.98 before tax. If the sales tax rate is 9.25% , find the total cost of the laptop with sales tax included. Round your answer to the nearest cent, as necessary.
Answer:
The cost of the laptop is $769.10Step-by-step explanation:
In this problem we are required to find the cost of the laptop when 9.25% of the cost is added as tax
we are given that the tax rate is 9.25% of the initial cost
and the initial cost is $703.98
let us calculate 9.25% of $703.98
(9.25/100)* 703.98= 0.0925*703.98= $65.12
Hence the charges for tax is $65.12
The total cost of the laptop when tax is included is
the initial cost Plus the tax charges= $703.98+$65.12= $769.098
$769.10
What two times could this be on the 24-hour clock?
Which of the following statements about fractions is not true? a. Proper fractions have a greater numerator than denominator b. Improper fractions are percentages greater than 100% c. Mixed fractions can be written as improper fractions d. The product of a fraction and its reciprocal is 1
Answer:
c
Step-by-step explanation:
Answer:
A. Proper fractions have a greater numerator than denominator.
Find the coordinates of point X that lies along the directed line segment from Y(-8, 8) to T(-15, -13) and partitions the segment in the ratio of 5:2. A. (-5, -15) B. (-23, -5) C. (-13, -7) D. (-11.5, -2.5)
Answer:
C. (-13, -7)
Step-by-step explanation:
The location of a point O(x, y) that divides a line AB with location A[tex](x_1,y_1)[/tex] and B[tex](x_2,y_2)[/tex] in the ratio m:n is given by:
[tex]x=\frac{m}{m+n} (x_2-x_1)+x_1\\\\y=\frac{m}{m+n} (y_2-y_1)+y_1[/tex]
Therefore the coordinates of point X That divides line segment from Y(-8, 8) to T(-15, -13) in the ratio 5:2 is:
[tex]x=\frac{5}{5+2} (-15-(-8))+(-8)\\\\x=\frac{5}{7} (-15+8)-8=\frac{5}{7}(-7)-8=-5-8=-13 \\\\\\y=\frac{5}{5+2} (-13-8)+8\\\\y=\frac{5}{7} (-21)+8=5(-3)+8=-15+8=-7[/tex]
Therefore the coordinates of point X is at (-13, -7)
3(x-4)=-5 solve for x
Answer:
x = 7/3
Step-by-step explanation:
3(x-4)=-5
Distribute
3x - 12 = -5
Add 12 to each side
3x -12+12 = -5+12
3x = 7
Divide by 3
3x/3 = 7/3
x = 7/3
Answer:
x = 7/3
Step-by-step explanation:
3(x-4)=-5
3x -12= -5
3x = 7
x =7/3
I have no chair, no church, no philosophy, I lead no man to a dinner-table, library, exchange, But each man and each woman of you I lead upon a knoll, My left hand hooking you round the waist, My right hand pointing to landscapes of continents and the public road. Which statement best describes how these lines reflect the theme of the poem?
This question is missing the options, here is the complete question:
Read the quotation from "Song of Myself."
I have no chair, no church, no philosophy,
I lead no man to a dinner-table, library, exchange,
But each man and each woman of you I lead upon a knoll,
My left hand hooking you round the waist,
My right hand pointing to landscapes of continents and the public road.
Which statement best describes how these lines reflect the theme of the poem?
A. They indicate that Whitman is more interested in communicating with individuals than society.
B. They show Whitman’s sociability and his interest in human nature.
C. They reflect Whitman’s desire to share his love of the wilderness.
D. They suggest that Whitman views all individuals as equals who should communicate with each other as such.
The answer to this question is A. They indicate that Whitman is more interested in communicating with individuals than society.
Explanation:
In the poem "Song of Myself", Walt Whitman focuses on recognizing his value as an individual and the value of other individuals in society. In the section presented, the author shows the importance of communicating and interacting with individuals as he explains "My left hand hooking you round the waist", which shows through figurative language the interaction between individuals. This is emphasized by the use of "each man and each woman" as Whitman does not refer to others as a group but recognizes individuality. Thus, the theme or message about the importance of individuals is reflected in these lines because "they indicate that Whitman is more interested in communicating with individuals than society."
Answer:
A: They indicate that Whitman is more interested in communicating with individuals than society.
Step-by-step explanation:
Edge 2021
We can calculate E, the amount of euros that has the same value as D U.S. dollars, using the equation e=17/20d. How many U.S. dollars have the same value as 1 euro?
Answer:
1.18 dollar.
Step-by-step explanation:
E = 17/20D
E => The amount in euros.
D => The amount in dollars.
From the question given,
E = 1
D =?
E = 17/20D
1 = 17/20D
Cross multiply
20 x 1 = 17D
20 = 17D
Divide both side by 17
D = 20/17
D = 1.18
Therefore, 1.18 dollar is equivalent to 1 euro.
Answer:
How many Euros have the same value as 1 U.S. dollar?
17/20 euros
How many U.S. dollars have the same value as 1 euro?
59/50 dollars
(or 0.85 either one is correct)
Step-by-step explanation:
Khan Academy
Hope this helps! ;)
420 miles in 6.5 hours unit rate
Step-by-step explanation:
Given,
distance =420 miles
time 6.5 hrs
now,
420miles took 6.5 hrs.
1mile took 6.5/420hrs
=0.015476hrs
Therefore, 0.015476hrs to cover 1 mile distance.
Hope it helps...
Answer:
64.6153846 miles/hour
0.0154761905 hours/mile
Step-by-step explanation:
If we want to find the miles driven in one hour, we must divide the total miles by the total hours.
miles / hours
We know that 420 miles were driven in 6.5 hours
420 miles/ 6.5 hours
Divide 420 by 6.5
420/6.5=64.6153846
64.6153846 miles/hour
In one hour, 64.6153846 miles are driven.
If we want to find the time to drive one mile, divide the time (hours) by the miles.
hours / miles
We know that 420 miles were driven in 6.5 hours.
6.5 hours/420 miles
Divide 6.5 by 420
6.5/420=0.0154761905
0.0154761905 hours/ mile
It will take 0.0154761905 of an hour to drive one mile.
find the interest rate r when p = 800, a = 2700, and t = 3.
Answer:
r = 0.5 or 1/2
Step-by-step explanation:
Simple Interest Rate Formula: A = P(1 + r)^t
Simply plug in our known variables:
2700 = 800(1 + r)³
Now we solve for r:
Divide both sides by 800
27/8 = (1 + r)³
Take the cube root on both sides
∛27/8 = ∛(1 + r)³
Simplify
3/2 = 1 + r
Subtract 1 on both sides
r = 1/2
r = 0.5
Answer:
For compound interest, 50%.
Step-by-step explanation:
(I'm assuming this question is asking for the compound interest):
The formula for compound interest is given by:
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]
Plug in the values we know. We can use 1 for n:
[tex]2700=800(1+r)^3\\27/8=(1+r)^3\\1+r=\sqrt[3]{27/8}\\r=3/2-1\\r=1/2=.5[/tex]
So, the interest rate is 50%.
What is the length of the shortest altitude in a triangle, if the lengths of the sides are 24 cm, 25 cm, 7 cm?
Answer:
The shortest altitude is 6.72 cm
Step-by-step explanation:
Given that the side lengths are
24 cm, 25 cm, 7 cm
The area of a triangle =
[tex]A = \sqrt{s \cdot (s-a)\cdot (s-b)\cdot (s-c)}[/tex]
Where;
s = Half the perimeter = (24 + 25 + 7)/2 = 28
A = √((28×(28 - 24)×(28 - 25)×(28 - 7)) = 84 cm²
We note that 84/7 = 12
Therefore, the triangle is a right triangle with hypotenuse = 25, and legs, 24 and 7, the height of the triangle = 7
To find the shortest altitude, we utilize the formula for the area of the triangle A = 1/2 base × Altitude
Altitude = A/(1/2 ×base)
Therefore, the altitude is inversely proportional to the base, and to reduce the altitude, we increase the base as follows;
We set the base to 25 cm to get;
Area of the triangle A = 1/2 × base × Altitude
84 = 1/2 × 25 × Altitude
Altitude = 84/(1/2 × 25) = 6.72 cm
The shortest altitude = 6.72 cm.
Please help! I’m this figure, which angles are congruent? Find the measure of all the angles if m< 2= 76 degrees
Problem 1.
Yes it is true that vertical angles are congruent, but that's not what your teacher is asking. Instead, your teacher is asking basically how the term "congruent" is defined.
Two segments are congruent if they are the same length. Two angles are congruent if they are the same measure. Two triangles are congruent if they have the same angles and sides.
So in short, "congruent" just means "same". You can think of having mirror copies.
==========================================
Problem 2.
Angles 2 and 4 are one pair of vertical angles. They are opposite one another in this X shape formed by the two lines. The other pair of vertical angles are angle 1 and angle 3.
Angle 2 is given to be 76 degrees, so this means angle 4 is this measure as well.
Angle 1 = 180 - (angle 2) = 180 - 76 = 104, which is also the measure of angle 3 as well. I'm using the idea that the adjacent angles form a straight angle. This is known as a linear pair (ie the angles form a straight line).
==========================================
Problem 3.
If all three angles are the same (all 60 degrees), then we have an equilateral triangle. We could say it's equiangular, but it's also equilateral as well meaning all 3 sides are the same length. "equi" means "equal", "angular" means what you'd expect, and "lateral" means "side".
If only two angles are equal with the third one different, then we have an isosceles triangle. An isosceles triangle is one where only two sides are the same length.
If none of the angles are the same, then we have a scalene triangle. As you probably expect, none of the sides are the same length with a scalene triangle.
----
If all three angles are less than 90 degrees, then the triangle is acute
If one angle is 90 degrees, then we have a right triangle
If one angle is over 90 degrees (but less than 180), then the triangle is obtuse
---
Often you'll see the terms of the previous two sections combined. For instance, we could have an isosceles right triangle. Or we might have an obtuse scalene triangle. Any equilateral triangle is acute (as all three angles are less than 90).
To solve this problem we have to understand what congruent angles are and then find the angles that are congruent to one other in this given question.
What are Congruent Angles?Congruent angles are angles that are equal to one another and in the given question, we were given m<2 = 76 degrees.
Data;
m<2 = 76 degreesIf we look critically at the angles, we can use opposite angle theorem here to predict angles that are congruent to another here.
angles 2 and angle 4 are congruent to one another while angle 1 and angle 3 are congruent to one another.
This implies that
m<2 = 76°m<4 = 76°Let's solve for other angles.
But the some of angles at a point is equal to 360°
Applying that theorem here,
[tex]m > 1=x\\m > 2 = 72^0\\m > 3 = x\\m > 4 = 72^0[/tex]
Let's substitute the values and solve.
[tex]x+ x + 72+72 = 360\\2x + 144 = 360\\2x = 360 - 144\\2x = 216\\x = \frac{216}{2} \\x = 108^0[/tex]
This can be further summarized as
m<1 = 108°m<2 = 72°m<3 = 108°m<4 = 72°Learn more on corresponding angles here;
https://brainly.com/question/2009183
#SPJ2
how many are 1 raised to 2 ???
Answer:
1
Step-by-step explanation:
1^2
Means 1 multiplied by itself 2 times
1*1
1
Where r is the radius of the cylinder and h is the height of the cylinder. Find the surface area when r is 3 inches and h is 5 inches. A. 50π in² B. 112π in² C. 48π in² D. 80π in²
Answer:
C
Step-by-step explanation:
The surface area of a cylinder is given by this formula:
● Sa = 2×r^2× PI + 2r×Pi×h
r is 3 inches and h is 5 inches.
● Sa = 2×3^2 × Pi + 2×3×Pi×5
● Sa = 48 × Pi in^2
Given that f(x)=2x+1 and g(x)=-5x+2 slice for f(g(x)) when x=3?
Answer:
x = -25.
Step-by-step explanation:
If f(x) = 2x + 1, and g(x) = -5x + 2, then f(g(x)) = 2(-5x + 2) + 1 = -10x + 4 + 1 = -10x + 5.
f(g(x)) = -10x + 5, and x = 3.
-10 * 3 + 5
= -30 + 5
= -25.
Hope this helps!
Make the biggest possible number using the digits below only once 4 , 5 , 5 answer
Answer:
554
Step-by-step explanation:
The largest number (5) should go in the hundreds place, the second-largest number (also 5) should go in the tens place and the smallest number (4) should go in the units place so the answer is 554.
y-3x=13 solve for y ♀️
Answer:
y = 3x+13
Step-by-step explanation:
y-3x=13
Add 3x to each side
y-3x+3x=3x+13
y = 3x+13
The value of y for the given equation y - 3x = 13 is calculated to be y = 3x + 13.
Given that:
y - 3x = 13
It is required to find the value of y.
In order to find the value of y, the equation has to be solved in such a way that y has to be kept on one side.
Consider:
y - 3x = 13
Add 3x on both sides.
y - 3x + 3x = 13 + 3x
y = 13 + 3x
Hence, the value of y is 13 + 3x.
Learn more about Equations here :
https://brainly.com/question/29657992
#SPJ6
Please answer quickly i will give you brainliest if its correct- it has to be a simplified fraction please
Answer:
[tex]\large \boxed{{r=\frac{1}{9}}}[/tex]
Step-by-step explanation:
x and y are proportional.
[tex]y=rx[/tex]
Let x = 45 and y = 5.
[tex]5=r(45)[/tex]
Solve for r (constant of proportionality).
Divide both sides by 45.
[tex]\displaystyle \frac{5}{45} =r[/tex]
Simplify and switch sides.
[tex]\displaystyle r=\frac{1}{9}[/tex]
