The radius of this circle with center (8, 2) is equal to 6.71 units.
How to determine the distance between the coordinates for each points?In Mathematics and Geometry, the distance between two (2) points that are on a coordinate plane can be calculated by using the following mathematical equation:
Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]
Where:
x and y represent the data points (coordinates) on a cartesian coordinate.
By substituting the given points into the distance formula, the radius of this circle can be calculated as follows;
Distance = √[(14 - 8)² + (-1 - 2)²]
Distance = √[(6)² + (-3)²]
Distance = √[36 + 9]
Distance = √45
Distance = 6.71 units.
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Complete Question:
What is the radius of the circle with Center: (8, 2), Point on Circle: (14,-1)? 2 decimal places
Change 14,277 s to h, min, and s.
When 14,277s is converted to hr, min and hr, it gives 3 hours, 57 minutes, 7 seconds.
What is Conversion?Conversion is the process of changing the value of one form to another. It is also the conversion between different units of measurement for the same quantity.
How to determine this
When 60 seconds makes 1 minute
60 minutes makes 1 hour
14,277 seconds to minutes
When 60 seconds = 1 minute
14,277 seconds = x
x = 14,277/60 minutes
x = 237 minutes 7 seconds
By converting 237 minutes to hour
When 60 minutes = 1 hour
237 minutes = x
x = 237/60 hours
x = 3 hours 57 minutes.
Therefore, the conversion is 3 hours 57 minutes 7 seconds
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Use spherical coordinates to evaluate the triple integral ∫∫∫Ex2+y2+z2dV
, where E is the ball: x2+y2+z2≤81
.
[ rate 5stars~ and give thanks for more po! welcome! ]
Step-by-step explanation:
We have the triple integral:
∫∫∫E x^2 + y^2 + z^2 dV
where E is the ball x^2 + y^2 + z^2 ≤ 81.
In spherical coordinates, the volume element is given by:
dV = ρ^2 sin φ dρ dθ dφ
where ρ is the radial distance, φ is the polar angle (measured from the positive z-axis), and θ is the azimuthal angle (measured from the positive x-axis).
Substituting into the integral, we get:
∫φ=0 to φ=π ∫θ=0 to θ=2π ∫ρ=0 to ρ=9 ρ^2 sin φ (ρ^2) dρ dθ dφ
= ∫φ=0 to φ=π ∫θ=0 to θ=2π ∫ρ=0 to ρ=9 ρ^4 sin φ dρ dθ dφ
= ∫φ=0 to φ=π ∫θ=0 to θ=2π (1/5)(9^5) sin φ dθ dφ
= (2π/5)(9^5)(-cos φ)|φ=0 to φ=π
= (2π/5)(9^5)(-(-1 - 1))
= (4π/5)(9^5)
≈ 114413.73
Therefore, the value of the triple integral is approximately 114413.73.
Which of the following is the expanded form of a number? Select all correct answers.
(A) 7·1000+8·100+3· 1/100
(B) 4·100+9·100+3· 1/10 +4· 1/10
(C) 71·10+4·1+6· 1/100 +5· 1/1000
(D) 5·1000+5·100+5·1+5·1/100
(E) 3·1000+8·1000+9·1/1000
(F) 9·1000+3·101+5· 1/10
traveled 1/5 miles in 3/2 hour. how many in 1 hour. show model fraction representation
a)Traveled 0.3 miles in 1 hour.
b) The fraction representation is 3/10 miles per hour.
a) To find out how many miles the person traveled in 1 hour, we need to divide the distance traveled by the time taken.
Distance traveled = 1/5 miles
Time taken = 3/2 hours
To make it easier to divide, we can convert the time taken to a fraction with a common denominator of 10:
3/2 = 15/10
Now we can divide the distance by the time:
1/5 ÷ 15/10 = 1/5 x 10/15 = 2/15
This tells us that the person traveled 2/15 miles in one-tenth of an hour (i.e., 6 minutes).
To find out how many miles per hour they traveled, we can convert the fraction to a rate by multiplying it by the reciprocal of the time fraction (i.e., 10/3):
2/15 x 10/3 = 2/9
Therefore, the person traveled 2/9 miles per hour.
b) To write this as a model fraction representation, we can express it as a single fraction:
2/9 = 3/10 (rounded to the nearest tenth)
So the person traveled at a rate of 3/10 miles per hour.
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point(s) possible
Use the sample data and confidence level given below to complete parts (a) through (d).
A research institute poll asked respondents if they felt vulnerable to identity theft. In the poll, n=1093 and x = 538 who
said "yes." Use a 90% confidence level.
Click the icon to view a table of z scores.
b) Identify the value of the margin of error E.
(Round to three decimal places as needed.)
c) Construct the confidence interval.
what is the product of -6
Answer:
The product of -6 is not a well-formed question. A product refers to the result of multiplying two or more numbers together, but there is no other number specified in the question. If you provide more information or context, I would be happy to assist you.
Step-by-step explanation:
Two forces of 637 newtons and 238 newtons act a point.The resultant force is 714 newtons. find the angle between the forces
When the student gets home, she gives 1/2 of her remaining fudge to her sister.
How many ounces of fudge does she give her sister?
The amount of fudge the student gives to her sister, which is (1/2) of her remaining fudge, calculated using fractions is 16 ounces
What is a fraction?A fraction is a representation of a part of a whole, by setting the quantity representing the part as the numerator and the quantity representing the whole as the denominator with both quantities separated by the fraction bar.
Part of the question obtained from a similar question posted online can be presented as follows;
The amount of fudge the student has = 3 pounds
The amount of fudge the student eats = 1 pound of the fudge
Required; The amount of fudge the student has left
The amount of fudge the student has left = 3 - 1 = 2 pounds
The fraction of the remaining fudge the student gives to her sister = (1/2)
Therefore;
The amount of fudge the student gives her sister = (1/2) × 2 pounds = 1 pound
1 pound = 16 ounces
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y = |x - 5| + |x + 5| if -5 < x < 5
Step-by-step explanation:
This function has two pieces, each of which is the absolute value of a linear expression. We need to consider the function separately for different ranges of x.
When -5 < x < 0, then x + 5 is negative and x - 5 is also negative. Therefore, we have:
y = -(x - 5) - (x + 5) = -2x
When 0 ≤ x < 5, then x + 5 is positive and x - 5 is negative. Therefore, we have:
y = (x - 5) + (x + 5) = 2x
So the function y = |x - 5| + |x + 5| can be written as:
y =
-2x if -5 < x < 0
2x if 0 ≤ x < 5
Notice that the function is not defined for x ≤ -5 or x ≥ 5.
I need help please I can’t figure this out
Answer: Area=3.125 square feet
Step-by-step explanation:
2.5x2.5=6.25
6.25/2= 3.125
Answer:
A = 50 ft²
Step-by-step explanation:
the area (A) of a triangle is calculated as
A = [tex]\frac{1}{2}[/tex] bh ( b is the base and h the perpendicular height )
given that 1 inch equals 4 feet , then
b = 2.5 in = 2.5 × 4 feet = 10 feet
h = 2.5 in = 2.5 × 4 feet = 10 feet
then
A = [tex]\frac{1}{2}[/tex] × 10 × 10 = 5 × 10 = 50 ft²
What is the greatest commen factor of 72 and 96
the greatest common factor of 72 and 96 is 24
based on the value of r^2, which modeling equation is best fit for the data set? a. y=16.5839•1.0185^x
b. y=0.985515x-2.81333
c. y=-0.0000758936x^3+0.0143444x^2+0.207549x+7.70667
d. y=0.00182197x^2+0.785098x+1.195
Okay, let's evaluate each modeling equation candidate based on the r^2 value:
a. y=16.5839•1.0185^x
No r^2 value given, so cannot determine if this is the best fit.
b. y=0.985515x-2.81333
No r^2 value given for this linear model, so cannot determine if it is the best fit.
c. y=-0.0000758936x^3+0.0143444x^2+0.207549x+7.70667
This is a 3rd order polynomial model, but no r^2 is given, so cannot determine if it is the best fit.
d. y=0.00182197x^2+0.785098x+1.195
If this model has the highest r^2 value, it would be the best fit.
Based on the information provided, the only option that could potentially be the best fit is choice d, the quadratic model y=0.00182197x^2+0.785098x+1.195, if it has the highest r^2 value. But without the actual r^2 values for each model, a definitive determination cannot be made.
Does this help explain the approach? Let me know if you have any other questions!
Find the sales tax. Then find the total cost of the item.
$50.00
Sales Tax
Rate of Sales Tax Sales Tax
7%
?
As a result, the item's final price is $53.50 and the sales tax is $3.50.
What is sales tax?The government levies a consumption tax known as sales tax on the purchase of goods and services. The seller often calculates it as a percentage of the purchase price and collects it. After then, the vendor transfers it to the government .. The funding of government services and programmers comes from sales tax
We can multiply the item's price by the applicable sales tax rate to determine the sales tax:
Price of Item x Sales Tax Rate equals Sales Tax
Sales Tax: $50.00 x 7% = $3.50
We can multiply the item's price by the applicable sales tax to determine the entire cost of the purchase, including tax:
Price of Item + Sales Tax = Total Cost
$50.00 plus $3.50 equals $53.50 as a total
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What is the surface area of this cylinder?
Use 3.14 and round your answer to the
nearest hundredth.
2 ft
5 ft
square feet
The surface area of this cylinder is 942 millimeter square
How to determine the surface areaThe formula for the surface area of a cylinder is expressed as;
SA = 2πr h + 2πr²
Given that the parameters are identified as;
SA is the surface area of the cylinder.r is the radius of the cylinder..h is the height of the cylinderFrom the information given, we have that;
Surface area = 2 × 3.14 × 10 × 5 + 2× 3.14 × 10²
Find the square values
Surface area = 2 × 3.14 × 10 × 5 + 2× 3.14 × 100
Multiply the values
Surface area = 314 + 628
Now, add the values
Surface area = 942 mm²
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If a sound with frequency fs is produced by a source traveling along a line with speed vs. If an observer is traveling with speed vo along the same line from the opposite direction toward the source, then the frequency of the sound heard by the observer is
fo =
c + vo
c − vs
fs
where c is the speed of sound, about 332 m/s. (This is the Doppler effect.) Suppose that, at a particular moment, you are in a train traveling at 32 m/s and accelerating at 1.1 m/s2. A train is approaching you from the opposite direction on the other track at 40 m/s, accelerating at 1.5 m/s2, and sounds its whistle, which has a frequency of 460 Hz. At that instant, what is the perceived frequency that you hear? (Round your answer to one decimal place.)
Doppler Effect happens when there is shift in frequency during a realtive motion between a source and the observer of that source.
It can be calculated as:
[tex]f_o=f_s\huge \text(\dfrac{c+v_o}{c+v_s}\huge \text )[/tex]
where:
c is the speed of light (c = 332m/s)
all the subscripted s is related to the Source (frequency, velocity);
all the subscripted o is related to the Observer (frequency, velocity);
As the source is moving towards the observer and the observer is moving towards the source, the velocities of each are opposite related to direction.
So, the frequency perceived by the observer:
[tex]f_o=460\huge \text(\dfrac{332+32}{332-40}\huge \text)[/tex]
[tex]f_o=460\huge \text(\dfrac{364}{292}\huge \text)[/tex]
[tex]f_o=460(1.247)[/tex]
[tex]f_o= 573.6 \ \text{Hz}[/tex]
At this condition, the observer hears the train's horn in a perceived frequency of 573.6 Hz
Answer:
The perceived frequency of sound is the amount of sound wave that pass a point in a given amount of time
The perceived frequency you hear is
370.9 Hertz
The function is given as:
[tex]f_{o}=\frac{c+V_{o} }{c-V_{o} }[/tex] x [tex]f_{s}[/tex]
From the question
[tex]c=332[/tex] --- speed of the sound
[tex]V_{o} =32[/tex] ---current speed of the train
[tex]V_{s} = 40[/tex] --- speed of the opposite train
[tex]f_{s} =460[/tex] --- frequency of the sound wave
This gives:
[tex]f_{o}= \frac{332-32}{332+40}[/tex] ×[tex]460[/tex]
[tex]f_{o}= \frac{300}{372} x460[/tex]
Rewrite as:
[tex]f_{o}= \frac{300x460}{372}[/tex]
[tex]f_{o}= 370.9[/tex]
Tell whether the given side lengths can represent the sides of a right triangle
10, 12, 20
Determine if the segment lengths form an acute, right, or obtuse triangle,
10, 11, 14
26.
Need help with all of these please need this asap. Please show work
23. By the diagram, the triangle is a [tex]45^\circ - 45^\circ-90^\circ[/tex] triangle. Therefore, the triangle is isosceles, so [tex]x=6.[/tex] And by the Pythagorean theorem, [tex]y^2=x^2+6^2=6^2+6^2=72,[/tex] and taking the square root yields [tex]y = 6\sqrt{2}.[/tex]
24. Notice that by the diagram, the triangle is a [tex]30^\circ-60^\circ-90^\circ[/tex] triangle. It is well known that in these special types of triangles, if [tex]a[/tex] is the side length opposite the [tex]30^\circ[/tex] angle, then the side length opposite the [tex]90^\circ[/tex] angle is [tex]2a,[/tex] and finally the side length opposite the [tex]60^\circ[/tex] is [tex]a\sqrt{3}.[/tex] This is shown in the image I've attached below, and can also be easily proven by the fact that two of these triangles combine to form an equilateral triangle.
So using this fact, we know that [tex]x = \frac{8}{2} = 4,[/tex] and [tex]y = x\sqrt{3} = 4\sqrt{3}.[/tex]
25. Tell whether the given side lengths can represent the sides of a right triangle: 10, 12, 20
For this question, we simply use the converse of the Pythagorean theorem. One part of its statement says that if a triangle has sides of length [tex]a, b, c[/tex] such that [tex]a^2 + b^2 = c^2[/tex], and [tex]c[/tex] is the longest side, then the angle opposite the side of length [tex]c[/tex] is a right angle.
Thus, if the triple [tex](a, b, c)[/tex] does not satisfy the equation, the triangle it forms is not a right triangle. In our case, the corresponding values for [tex](a, b, c)[/tex] are [tex](10, 12, 20),[/tex] because [tex]20[/tex] is the largest number in this triple. But [tex]10^2+12^2=244\neq 400 = 20^2,[/tex] so the triangle with side lengths [tex]10, 12, 20[/tex] is not a right triangle.
26. Another statement of the converse of the Pythagorean theorem is that if a triangle has side lengths [tex]a, b, c[/tex] such that [tex]c^2 > a^2+b^2[/tex] , with [tex]c[/tex] being the longest side, then the triangle is an obtuse triangle. So the corresponding values for [tex]a, b, c[/tex] are [tex]10, 11, 14,[/tex] and because [tex]14^2 = 196 < 221 = 10^2+11^2,[/tex] the triangle is an obtuse triangle.
Rajindri, a physician assistant who works in an emergency room, earns $163 for every two hours that she works.
Which equation represents the relationship between d, the number of dollars Rajindri earns, and t, the amount of time Rajindri works, in hours?
A. d= 163 + t
B. d= 163/2 × t/2
C. d = 163t
D. d = 81.50t
Answer:
The correct equation is C. d = 163t.
This equation shows a direct proportionality between the amount of time worked (t) and the amount of money earned (d). For each hour worked, Rajindri earns $163, so the total amount earned (d) is equal to the hourly rate of $163 multiplied by the number of hours worked (t).
Step-by-step explanation:
The circle below has center O, and its radius is 5 m. Given that m LAOB = 30°, find the area of the shaded region and the length of the arc ADB. Give exact answers in terms of it, and be sure to include the correct units in your answer.
Measure of ∠ADB is 240 degrees, the area of the shaded region is 42.67π m² and arc length ADB is 10.67π m
Given that the circle has a center O.
The radius of the circle is 8 m.
The measure of ∠AOB is 120°
We need to determine the area of the shaded region and the length of the arc ADB.
The measure of ∠ADB is given by
∠ADB = 360 - ∠AOB
= 360 - 120
=240 degrees
The area of the shaded region can be determined using the formula,
A = (θ/360) πr²
A = (θ/360) ×3.14× 8²
A = 42.67 m²
Thus, the area of the shaded region is 42.67π m²
The length of arc ADB can be determined using the formula,
Arc length = (θ/360) 2πr
=10.67π m
Hence, measure of ∠ADB is 240 degrees, the area of the shaded region is 42.67π m² and length of arc ADB is 10.67π m
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The volume of blood in a person's body is proportional to body weight. A person who weighs 200 pounds has approximately 6 quarts of blood. Estimate the number of quarts of blood
in a person who weighs 90 pounds.
Complete the proportion, where the ratios have volumes of blood in the numerators and body weights in the denominators.
X
(Doshot simplify.)
X
More
The estimated number of quarts of blood the individual with the given weight will have would be = 2.7 quarts.
How to calculate the number of quarts of blood the individual has?The body weight of the first individual = 200 pounds
The volume of blood = 6 quarts.
Therefore a person of 90 pounds = X quarts.
That is;
200 pounds = 6 quarts
90 pounds = X quarts
make X quarts the subject of formula;
X = 90×6/200
= 540/200
= 2.7 quarts
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Supplementary angles
Answer: ∠EGF and/or ∠CGB
Step-by-step explanation:
Starting Angle: ∠CGE
Possible Supplements: ∠EGF and ∠CGB
Question 9 of 10
A rational expression has been simplified below.
(x+4)(x-2)x+4
9(x-2)
For what values of x are the two expressions equal?
O A. All real numbers except -4 and 2
OB. All real numbers except 2
C. All real numbers
D. All real numbers except -4
The values of x are the two expressions equal to All real numbers except 2.
We are given that rational expression has been simplified below.
(x+4)(x-2)x+4
9(x-2)
WE know that X=4/9 is simplified, but we can simplify the other side by canceling out the (x-2) in the numerator and denominator.
The expression should be;
(x + 4)(x - 2)/9(x - 2)= (x + 4)/9.
After simplification by (x - 2) , the remainder will be;
(x + 4)/9.
When x = -4, both sides equal to zero.
When x = 0 , both sides equal to 4/9
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question in screenshot
Answer:
hope this might help you!!
Football is 360ft.long 160ft.wide use 8lb. Fertilizer per 1000sqft it come in 50lb bag. How many bags will I need
We number of bags is 10 bags of fertilizer to complete the job.
Describe Algebra?Algebra is a branch of mathematics that deals with the study of mathematical symbols and their manipulation. It involves the use of letters, symbols, and equations to represent and solve mathematical problems.
In algebra, we use letters and symbols to represent unknown quantities and then use mathematical operations such as addition, subtraction, multiplication, division, and exponentiation to manipulate those quantities and solve equations. We can use algebra to model and solve real-world problems in various fields such as science, engineering, economics, and finance.
The total area of the football field is:
360 feet × 160 feet = 57,600 square feet
To find out how many bags of fertilizer are needed, we need to calculate how many 1000-square-foot areas there are on the field:
57,600 square feet ÷ 1000 square feet/area = 57.6 areas
So there are 57.6 areas on the football field.
We need 8 pounds of fertilizer per 1000 square feet, so to find out how many pounds we need for the whole field, we can multiply by the number of areas:
8 pounds/1000 square feet × 57.6 areas = 460.8 pounds
Therefore, we need 460.8 pounds of fertilizer to cover the football field.
Since the fertilizer comes in 50-pound bags, we can divide the total amount of fertilizer needed by 50 to find out how many bags we need:
460.8 pounds ÷ 50 pounds/bag ≈ 9.22 bags
We can't buy a fraction of a bag, so we need to round up to the nearest whole bag. Therefore, we need 10 bags of fertilizer to complete the job.
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The complete question is:
You are applying fertilizer to a football field. The field is 360 feet long and 160 feet wide. You use 8 pounds of fertilizer per 1000 square feet. The fertilizer comes in 50- pound bags. How many bags of fertilizer will you need to complete this job?
For each SSA case below, i) solve by the law of cosines, (ii) solve by the law of sines; use degrees for angles, and round each answer to its nearest 100th:
The values of the angles will be 6.67°, 156.78° Be 29.93° and the sides will be 10.01, 34 and 43.
How to explain the angleSSA stands for side side angle postulate. In this postulate of congruence, we say that if two sides and an angle not included between them are respectively equal to two sides and an angle of the other triangle then the two triangles are equal.
By sine rule,
Y = sin156.78 × 44 / 34
= 29
sin Y = 0.499
Y = 29.93°
By the angle sum property. The last angle will be:
180 - 156.78 - 29.93
= 6.67°
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if you rotate cars tires at 10,000 miles, if a car tire has 25,200 rotations per day, how many weeks will it be until you rotate the tires
It will take 4. 09 weeks for the tires to be rotated at the current rate.
How to find the time till rotation ?When rotating a car's tires every 10,000 miles, each tire must complete this distance before being moved.
25, 200 rotations / day x 7 days / week = 176, 400 rotations per week
To solve this predicament, dividing 10,000 miles by the number of rotations/mile (which equates to the tire's circumference) is necessary. The formula for calculating a tire's circumference can aid in obtaining this number along with the weeks required to perform the rotation process:
C = 2πr
Rotation per mile is:
1 mile / 87.96 inches / rotation = 72.26 rotations / mile
Number of weeks:
10, 000 miles x 72. 26 rotations / mile = 722, 600 rotations
722, 600 rotations / 176, 400 rotations/week = 4.09 weeks
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A recipe uses teaspoon of cinnamon for every 4 cups of granola mix.
How many teaspoons are needed for 12 cups of granola mix?
Okay, here are the steps to solve this:
* The recipe calls for 1 teaspoon of cinnamon for every 4 cups of granola mix.
* We are making 12 cups of granola.
* So to make 12 cups, we need 12 / 4 = 3 times as much cinnamon.
* Since each 4 cups uses 1 teaspoon, 12 cups will need 3 teaspoons.
Therefore, for 12 cups of granola mix, the recipe will call for 3 teaspoons of cinnamon.
In the given diagram find the value of x
a) 1
b) 2
c) 3
d) 4
Given
ABCΔ is a triangle.
D is a point on [BC]
|BD|=4
|AD|=|CD|
m(CBAˆ)=α=30∘
m(ACBˆ)=β=20∘
To Find
What is |AC|=x?
Solution
Geometric approaches gave me nothing. Letting |AD|=|CD|=a, |AB|=b
and applying law of cosines to all three triangles yields;
x=2acos20∘16=a2+b2+2abcos70∘(a+4)2=b2+x2+2bxcos50∘respectively, from ACDΔ, ABDΔ and ABCΔ. Directly isolating x from these equations gives an expression involves trigonometric function(s), and i cannot find a way to annihilate trigonometric functions in these equations to reach the answer which is x=4
The complete question is -
In the given diagram find the value of x
a) 1
b) 2
c) 3
d) 4
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Which parent functions have a domain of all real values of x? Select all that apply.
A. Absolute value
B. Linear
C. Reciprocal
D. Quadratic
E. Cube root
F. Cubic
Answer:
D. Quadratic
Step-by-step explanation:
The vertex of the parent function y = x2 lies on the origin. It also has a domain of all real numbers and a range of [0, ∞). Observe that this function increases when x is positive and decreases while x is negative
Running for public office is not a decision to be taken lightly, and requires considerable investments of both time and money. A local businesswoman is considering running for mayor, but will only do so if she has the support of more than 60% of voters in the city. She commissions a polling company, who take a random sample of eligible voters and find 64% would support this businesswoman.
(a) Which hypotheses should the businesswoman test, to determine if she has sufficient community support?
H0:
Ha:
(b) The polling company finds the p-value = 0.076. For = 0.05, what does this suggest the businesswoman should do?
____ for office. There is ___ evidence she ____ enough supporters.
The proportion of eligible voters who would support the businesswoman is less than or equal to 0.6, and the proportion of eligible voters who would support the businesswoman is greater than 0.6.
What is a hypothesis?In statistics, a hypothesis is a statement or assumption about a population parameter that is being tested for its truthfulness based on sample data. It is a tentative explanation for an observation or phenomenon and is used to make predictions about the outcome of an experiment or study. Hypotheses can be either null hypotheses, which state that there is no significant difference or relationship between variables, or alternative hypotheses, which propose that there is a significant difference or relationship.
(a) The hypotheses that the businesswoman should test are:
H0: The proportion of eligible voters who would support the businesswoman is less than or equal to 0.6.
Ha: The proportion of eligible voters who would support the businesswoman is greater than 0.6.
(b) The p-value is greater than the significance level of 0.05, which suggests that the results are not statistically significant. Therefore, the businesswoman should not run for office. There is not enough evidence she has enough supporters.
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Which equation models the relationship between c cups of flour and m muffins baked?
Answer:
constant of proportionality: A 4equation: D m = 4cStep-by-step explanation:
Given a graph of muffins versus cups of flour, you want to know the constant of proportionality and the equation relating muffins (m) and cups (c).
SlopeThe slope of the line on the graph is easily found by looking at the "muffins" (y) value for "cups" (x) equal to 1. That point is (c, m) = (1, 4).
The line goes through the origin (0, 0), so the slope is the ratio of y to x.
m = y/x = 4/1 = 4
This is the constant of proportionality.
The constant of proportionality is 4, choice A.
EquationThe equation of a proportional relationship is ...
y = kx . . . . . . where k is the constant of proportionality
Here, the independent variable (horizontal axis) is "cups", represented by 'c'. The dependent variable is "muffins", represented by 'm'. Using the above constant of proportionality, the equation is ...
m = 4c . . . . . choice D
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