Which statement about the data in the table is true?
O The data represent a proportional relationship, and the constant of proportionality is $10.
The data do not represent a proportional relationship, but the rate of change of the data is $5 per shirt.
There is not a constant rate of change for these data.
The data represent a proportional relationship, and the constant of proportionality is $5.
Answers
B) The data does not represent a proportional relation, but it has constant rate of change of $5 per shirt.
A)
Take number of T-shirts up to 3 and calculate their proportions.
2/1 = 15/10 = 1.5 (3/2) = 20/15 = 1.33
Clearly the rate of T- shirts is not proportional.
B)
From option (A) we found the given data is not proportional but from the table given in question the rate of change of T- shirts is indeed $5.
C)
No, there is a constant rate of change of $5 as shown in the table below.
D)
No, the data does not represent a constant proportionality. The rate varies.
2/1 = 15/10 = 1.5 (3/2) = 20/15 = 1.33
What is rate of change ?Rate of change is the rate that describes how one quantity changes relative to another quantity. If x is the independent variable and y is the dependent variable, then
rate of change change=change in y / change x
Rate of change can be positive or negative. This corresponds to an increase or decrease in the y-value between two data points. If a quantity does not change over time, it is called zero rate of change.
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Related Questions
pleas help quick
What is the value of the expression
Answers
PLUG IN THE VALUES IN THE RIGHT POSITIONS AND SIMPLIFY.
[tex] = 2( \frac{1}{2} + \frac{3}{4} ) + 6 \\ = 2( \frac{5}{4} ) + 6 \\ = \frac{10}{4} + 6 \\ = \frac{5}{2} + 6 \\ = \frac{17}{2} [/tex]
THE ANSWER IS OPTION C.
Factor completely. 4x^2-x-5
Answers
The factors of the given equation 4x^2-x-5 are 5/4 and -1.
What is referred as the factors of the polynomial?Factoring polynomials is the inverse procedure of multiplying polynomial factors. Factors of polynomials are zeros of polynomials that take the form of some other linear polynomial. If we divide a given polynomial by any of its factors after factorisation, the remainder would be zero.Factors are integers which are multiplied together to create the original number. The factors in the particular instance of polynomials are the polynomials that are multiplied to generate the original polynomial.For the given question, the expression is given as;
= 4x^2-x-5
as, 4×5 = 20, break the number such that on subtraction we will get -1.
= 4x^2 - 5x + 4x -5
Taking x common from first two digit.
= x(4x - 5) + (4x - 5)
Taking common again.
= (4x - 5)(x + 1)
Put the equation equal zero to find the factor.
4x - 5 = 0
x = 5/4
and, x + 1 = 0
x = -1
Thus, the factors are found as 5/4 and -1.
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Valeria created a triangular pyramid as part of her science fair project. The triangular base has a height of 8 cm and a length of 6 cm. The height of the pyramid is 12 cm. Determine the volume of Valeria's pyramid.A. 192 cm B. 288 cmC. 96 cmD. 576 cm
Answers
Given:
Height of triangular base = 8 cm
Length of traingular base = 6cm
Height of pyramid = 12 cm
Let's determine the volume of Valeria's pyramid.
To find the volume of the triangular pyramid, apply the formula:
[tex]V=\frac{1}{3}(A\ast h)[/tex]Where A is the area of the triangular base and h is the height of the pyramid
To find the area of the triangular base, apply the area of a triangle formula:
[tex]\begin{gathered} A=\frac{b\ast h}{2} \\ \\ A=\frac{6\ast8^{}}{2}=\frac{48}{2}=24cm^2 \end{gathered}[/tex]To find the volume of the pyramid, substitute 24 for A and 12 for h in the formula above.
Thus, we have:
[tex]\begin{gathered} V=\frac{1}{3}(A\ast h) \\ \\ V=\frac{1}{3}(24\ast12) \end{gathered}[/tex]Solving further:
[tex]\begin{gathered} V=\frac{1}{3}(288) \\ \\ V=\frac{288}{3} \\ \\ \text{ V = 96 cm}^3 \end{gathered}[/tex]Therefore, the volume of Valeria's pyramid is 96 cubic centimeters.
ANSWER:
[tex]\text{ C. 96 cm}^3[/tex]y-1=5/4(x+2) in slope intercept form
Answers
Sal elrove 3000 miles in 75 hours. At this rate how long will it take to drive 4000 miles
Answers
Answer:
Step-by-step explanation:
First, we need to find the rate. miles/hours. 3000/75 = 40mph (miles per hour). to find the answer we need to divide the rate by the distance they want us to find. to see a deeper explanation of why scroll past the answer. 4000/40 = 100 hours.
deeper explanation:
we can set the numbers given to us equal to what we are looking for.
miles/hour
3000/75 = 4000/x x being the time we are looking for
cross multiply 3000x=300000
divide by 3000 x=100 hours
Simplify 6c -2d+9d+10c
Answers
Answer:
16c+7d
Step-by-step explanation:
What is the value of x+ y in the system of equations below?
8x + 9y = 4.92
9x + 14y = 6.93
Answers
The value of x + y in the system of equations is 0.82125.
Given system of equations:-
8x + 9y = 4.92 ...(1)
9x + 14y = 6.93 ...(2)
We have to find the value of x + y in the system of equations.
Multiplying (1) by 9 and (2) by 8, we get,
72x + 81y = 44.28 ...(3)
72x + 112y = 55.44 ...(4)
(4) - (3), we get,
0x + 31y = 11.16
31y = 11.16
y = 11.16/31
y = 0.36
Putting the value of y in (1), we get
8x + 9*(0.36) = 6.93
8x + 3.24 = 6.93
8x = 6.93 - 3.24
8x = 3.69
x = 0.46125
Hence,
x + y = 0.46125 + 0.36 = 0.82125
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Rewrite one fourteenth times x cubed times y plus three fourteenths times x times y squared using a common factor.
Answers
The expression which can be rewritten using a common factor is [tex]\frac{xy}{14} (x^{2} +3y)[/tex].
According to the question,
We have the following information:
One fourteenth times x cubed times y plus three fourteenths times x times y squared.
(We know that 'times' has to be replaced with multiplication.)
Now, we will change this into mathematical expression:
[tex]\frac{x^{3} y}{14} +\frac{3xy^{2} }{14}[/tex]
Now, from these two terms, the common factor can be [tex]\frac{xy}{14}[/tex].
(Common factor means that the number and the variables taken as a common factor should be able to completely divide the terms given any expression.)
Now, taking it as a common factor, we have the following expression:
[tex]\frac{xy}{14} (x^{2} +3y)[/tex]
Hence, the required expression is [tex]\frac{xy}{14} (x^{2} +3y)[/tex].
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Convert to Slope-Intercept Form3x + 4y = 4
Answers
The slope-intercept form generally can be represented as;
[tex]y\text{ = mx + c}[/tex]where m represents the slope and c is the y-intercept
So in this case, we have to make y the subject of the formula;
3x + 4y = 4 will be
4y = 4-3x
4y = -3x + 4
we now need to make y the subject of the formula;
[tex]\begin{gathered} \frac{4y}{4}\text{ = }\frac{-3x}{4}\text{ + }\frac{4}{4} \\ \\ y\text{ = }\frac{-3}{4}x\text{ + 1} \end{gathered}[/tex]Nicole made $91 for 7 hours of work. At the same rate, how much would she make for 11 hours of work?
Answers
Help!!, its a math question... it TIMED! The question is in the pic...
Answers
I think
Answer:
23
Step-by-step explanation:
Isolate the variable. Divide each variable
Three t-shirts for $10. find the unit rate
Answers
Answer:
Step-by-step explanation:I don’t know
Y varies 1/x², when X=2, Y=1. Find the values of X when Y=4/9.
Answers
Answer:
x = ± 3
Step-by-step explanation:
given y varies as [tex]\frac{1}{x^2}[/tex] , then
y = k × [tex]\frac{1}{x^2}[/tex] = [tex]\frac{k}{x^2}[/tex] ← k is the constant of variation
to find k use the condition x = 2 , y = 1
1 = [tex]\frac{k}{2^2}[/tex] = [tex]\frac{k}{4}[/tex] ( multiply both sides by 4 )
4 = k
y = [tex]\frac{4}{x^2}[/tex] ← equation of variation
when y = [tex]\frac{4}{9}[/tex] , then
[tex]\frac{4}{9}[/tex] = [tex]\frac{4}{x^2}[/tex] ( cross- multiply )
4x² = 36 ( divide both sides by 4 )
x² = 9 ( take square root of both sides )
x = ± [tex]\sqrt{9}[/tex] = ± 3
Is 5^x a polynomial?
Answers
yes, 5^x a polynomial. a polynomial is an expression consisting of indeterminates and coefficients, that involves only the operations of addition, subtraction, multiplication, and positive-integer powers of variables
What is Polynomial?a polynomial is an expression consisting of indeterminates and coefficients, that involves only the operations of addition, subtraction, multiplication, and positive-integer powers of variables.
In the given expression 5^x x is a variable and 5 is a real number.
5^x is a finite polynomial or infinite polynomial. It depends upon the value of x. If x is finite then 5^x is a finite polynomial and if x is infinite then 5^x is a infinite polynomial.
Hence If x is finite then 5^x is a finite polynomial and if x is infinite then 5^x is a infinite polynomial.
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100 POINTS!!
Activity
Plane A is descending toward the local airport, and plane B is ascending from the same airport. Plane A is descending at a rate of 2,500 feet per minute. Plane B is ascending at a rate of 4,000 feet per minute. If plane A is currently at an altitude of 14,000 feet and plane B is at an altitude of 1,000 feet, how long will it take them to be at the same altitude? The equation representing plane A’s descent is y = -2,500x + 14,000. The equation representing plane B’s ascent is y = 4,000x + 1,000. In both equations, y represents altitude and x represents time in minutes.
Part A
Go to your math tools and open the Graph tool to graph the two equations and determine the position of the point of intersection for the two equations. To create the graph, select the correct relationship and then enter the values for the variables. Adjust the maximum and minimum y-values until the point of intersection is visible. Paste a screenshot of the graph in your answer.
Part B
From the graph, find the solution to the system of equations. At what point do the lines appear to intersect?
Part C
The x-value for this situation represents time in minutes. So, what does the x-value of the point of intersection represent?
Part D
The y-value for this situation represents altitude. So, what does the y-value of the point of intersection represent?
Answers
Considering the given system of equations, it is found that:
B. They intersect at the point (2,9000).
C. The x-value of the point of intersection represents the time in which they intersect.
D. The y-value of the point of intersection represents the altitude in which they intersect.
How to solve a system of equations graphically?A system is equations is composed by a number of curves, and the solution to the system of equations is the point where all these curves intersect each other on the graph.
In the context of this problem, the curves are given as follows:
Plane A descent: y = -2500x + 14000.Plane B ascent: y = 4000x + 1000.In which the variables are as follows:
Variable x: time in minutes.Variable y: altitude of the plane, in feet.From the graph given in this problem, it is found that they intersect at point (2,9000), that is, they intersect a height of 9000 feet at a time of 2 seconds.
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Answer: Considering the given system of equations, it is found that:
B. They intersect at the point (2,9000).
C. The x-value of the point of intersection represents the time in which they intersect.
D. The y-value of the point of intersection represents the altitude in which they intersect.
How to solve a system of equations graphically?
A system is equations is composed by a number of curves, and the solution to the system of equations is the point where all these curves intersect each other on the graph.
In the context of this problem, the curves are given as follows:
Plane A descent: y = -2500x + 14000.
Plane B ascent: y = 4000x + 1000.
In which the variables are as follows:
Variable x: time in minutes.
Variable y: altitude of the plane, in feet.
From the graph given in this problem, it is found that they intersect at point (2,9000), that is, they intersect a height of 9000 feet at a time of 2 seconds.
Step-by-step explanation:
quick sell outlet sold a total of 40 televisions, each of which was either a model p television or a model q television. each model p television sold for $p and each model q television sold for $q. the average (arithmetic mean) selling price of the 40 televisions was $141. how many of the 40 televisions were model p televisions? (1) the model p televisions sold for $30 less than the model q televisions. (2) either p
Answers
Model P televisions made up 12 of the 40 televisions when Quick Sell outlet sold a total of 40 television, each of which was either a model P television or a model Q television.
Price plus quantity equals revenue.
Let x be the quantity of sold TVs of model p.
40 - x units of the model q TV would have been sold.
Profits from model p TV sales are
px
Sales of the type q TV bring in money.
(40 - x)q
Total income equals px plus (40 - x)q
The average price calculation formula is written as
Total revenue / total number of TVs sold equals average price.
The 40 televisions sold for an average (arithmetic mean) price of $141. It follows that
141 = (px + (40 - x)q)/40
141 × 40 = px + (40 - x)q
5640 = px + (40 - x)q
p = q - 30
5640 = x(q - 30) + (40 - x) (40 - x)
q
30x + 40q - xq = 5640
5640 = - 30x + 40q
Since q = 120,
5640 = - 30x + 40 × 120
5640 = - 30x + 4800
5640 - 4800 = - 30x
840 = - 30x
x = 840/- 30 = - 28
Q cannot equal 120 since x cannot be negative.
Again,
5640 = px + (40 - x)q
If q = 30 + p, then
5640 = px + (40 - x)(30 + p)
5640 = px + 1200 + 40p - 30x - px
5640 = 1200 + 40p - 30x
Therefore,
If p = 120, then
5640 = 1200 + 40 × 120 - 30x
5640 = 6000 - 30x
30x = 6000 - 5640
30x = 360
x = 360/30
x = 12
Therefore, out of 40 televisions 12 tv are of model p
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Fun times Amusement Park Charges a $7 admission fee plus $1.75 per ride. What is the equation, in intercept form for calculating the total cost, C, of going to the park and riding r rides?1. C = 1.75 + 7r2. C = 1.75r3. C = 7r4. C = 7 + 1.75r
Answers
The general form of an equation in intercetp form is:
[tex]y=mx+b[/tex]Where m is the change of y in function of x and b is the value of b when x is 0
In this situation you have:
y=C
x=r
m= 1.75 ( C increase 1.75 each r)
b= 7 (When there is not ride r=0 the admission fee is 7)
Then, you have the equation:[tex]C=1.75r+7[/tex]or C = 7 + 1.75rCan you please help me out with a question
Answers
Formular for total surface area of a cylinder
[tex]TSAofacylinder=2nr^2\text{ + 2nrh}[/tex][tex]\begin{gathered} T\mathrm{}S\mathrm{}A\text{ = 2 }\times\text{ }\pi\text{ }\times7^2\text{ + 2 }\times\pi\times7\times21ft^2^{} \\ \text{ = 307.876 + }923.628 \\ \text{ = 1231.504 ft}^2 \\ =1231.5ft^2\text{ (nearest tenth)} \end{gathered}[/tex]S = 1231.5 sq ft
if the ratio of similarity of the figures above is 2/3, then what is the ratio of the perimeters of the two figures?
Answers
Perimeter = side 1 + side 2 ´+ side 3.
Triangle 1
Perimeter = 6 + 8 + 10
= 24
Triangle 2
Perimeter = 9 + 12 + 15
= 36
Ratio
24/36 = 2/3
The ratio of the perimeters is also 2/3
2x^2-5x-11=1
factor pls
Answers
Answer:
(2x+3)(x-4) = 0
Step-by-step explanation:
In places where there are crickets, the outdoor temperature can be predicted by the rate at which crickets chirp. One equation that models the relationship between f = 1/4 * c + 40 , chirps and outdoor temperature is where c is the number of chirps per minute and ƒ is the temperature in degrees Fahrenheit. a. Suppose 110 chirps are heard in a minute. According to this model, what is the outdoor temperature? b. If it is 75 deg * F outside, about how many chirps can we expect to hear in one minute? c. The equation is only a good model of the relationship when the outdoor temperature is at least 55 deg * F (Below that temperature, crickets aren't around or inclined to chirp.) How many chirps can we expect to hear in a minute at that temperature?
HELPPPP ME PLEASEEEEEEE
Answers
a. Using the equation of the relationship, the temperature outdoor would be 67.5 °F.
b. 140 chirps in a minute.
c. 60 chirps at that temperature is expected.
d. The graph for the relationship is given below.
e. 1/4 is the unit rate or slope = in 1/4°F per chirp.
f. 40 represents the starting or initial temperature.
What is the Graph of a Linear Equation?The graph of a linear equation, y = mx + b, will have a slope value of m, and an initial value or y-intercept of b, which is the point on the y-axis that the line intercepts.
Given the equation, f = ¼c + 40, where:
f = temperature in degrees Fahrenheit
c = number of chirps
1/4 represents the temperature in °F per chirp
40 represents the initial temperature
a. Substitute c = 110 into the equation, f = ¼c + 40:
f = ¼(110) + 40
f = 67.5
The outdoor temperature is predicted to be 67.5 °F.
b. Substitute f = 75 into the equation, f = ¼c + 40:
75 = ¼c + 40
75 - 40 = ¼c
35 = 1/4c
4(35) = c
c = 140
140 chirps would be heard in a minute.
c. Substitute f = 55 into the equation, f = ¼c + 40:
55 = ¼c + 40
55 - 40 = ¼c
15 = c/4
4(15) = c
c = 60
Expect to hear 60 chirps at that temperature.
d. The graph for f = ¼c + 40 is in the attachment.
e. 1/4 is the unit rate or slope, which is the temperature in °F per chirp.
f. 40 tells us about the equation of the relationship that the initial temperature where we can start expecting the crickets to chirp starts from 40 °F.
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On the scale drawing of a small town, 1 inch equals 15 feet. On this scale drawing, a parking lot measures 4 2/5 in. by 8 3/5 in.
What is the area of the actual parking lot?
_________ square feet.
Answers
Answer:
Step-by-step explanation:
4 and 2/5 inches by 8 and 3/5 inches.
60 and 6 feet by 120 and 9 feet.
66 by 129 feet
8514 feet squared
9x+3y=-6 rewrite this equation in slope intercept form (y=Mx+b)
Answers
subtract 9x from 9x
divide each term in 3y=-6-9x by 3 and simplify
after 5 seconds the height of the ballon is 20 feet
Answers
Find A (please help)
Answers
Answer:
a=1
Step-by-step explanation:
Hey need help with this problem! Will give brainliest if right
Answers
Answer: 899.998434785 times more than the loser.
Trapezoid RSTU with vertices R(-13, 7), S(-1, 7), T(-1, -5),
and U(-13,-9); scale factor: k = 1/4,
center of dilation: (-5, 3)
Answers
The coordinates of the trapezoid RSTU with vertices R(-13, 7), S(-1, 7), T(-1, -5), and U(-13,-9) after dilation with scale factor of k= 1/4 are
R' (-7, -2) S' (-4, -2) T' (-4, -2.5)U' (-7, -6) How to determine the coordinates of the image after dilationData gotten from the question
Trapezoid RSTU with vertices R(-13, 7), S(-1, 7), T(-1, -5) U(-13,-9)scale factor: k = 1/4center of dilation: (-5, 3)Dilation refers to an increment or reduction in dimension and location of a preimage to get a new image
The coordinate of the image of dilation is gotten using the formula
x₂ = kx₁ - x₀(k - 1) for x coordinate
y₂ = ky₁ - y₀(k - 1) for y coordinate
definition of terms
terms with subscript 2 is corresponding to the image
terms with subscript 1 is corresponding to the preimage
terms with subscript 0 is corresponding to the center of dilation
\k = scale factor
R(-13, 7) ⇒ R'(-7, -2)
x₂ = 1/4 * -13 - -5(1/4 - 1) = -7
y₂ = 1/4 * 7 - -5(1/4 - 1) = -2
S(-1, 7) ⇒ S' (-4, -2)
x₂ = 1/4 * -1 - -5(1/4 - 1) = -4
y₂ = 1/4 * 7 - -5(1/4 - 1) = -2
T(-1, -5) ⇒ T' (-4, -2.5)
x₂ = 1/4 * -1 - -5(1/4 - 1) = -4
y₂ = 1/4 * -5 - -5(1/4 - 1) = -2.5
U(-13,-9) ⇒ U' (-7, -6)
x₂ = 1/4 * -13 - -5(1/4 - 1) = -7
y₂ = 1/4 * -9 - -5(1/4 - 1) = -6
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PLEASE help thank you!
Answers
Answer:
70
Step-by-step explanation:
So 175% of 40 is the amount in april so we can split it up into 2 problems
100% of 40? 40
75% of 40? 30
Then you add the 2 to get 175% of 40 which will be 70!
At the 6th grade school dance, there are 130 boys, 100 girls, and 20 adults. Write the ratio of the number of girls to the number of adults.
Answers
The ratio of the number of girls to the number of adults is 5 : 1.
What is the ratio?Ratio is used to compare two or more values together. Ratio shows the frequency of one number compared to the frequency of another number. The sign that is used to represent ratio is :.
The ratio of the number of girls to the number of adults = number of girls : number of adults
number of girls = 100
number of adults = 20
The ratio of the number of girls to the number of adults = 100 : 20
Express the ratio in its simplest form. To do this, divide both numbers by the greatest common factor of 100 and 20. The greatest common factor of 100 and 20 is 20.
The ratio of the number of girls to the number of adults = 5 : 1
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I have no clue what to do so pls include an explination
[tex]10=\frac{z}{2} +7[/tex]
Answers
The solution for the given linear equation is z = 6
How to solve the linear equation?
Here we have the following linear equation:
10 = z/2 + 7
To solve it, we need to isolate the variable in one of the sides of the equation.
First, we can subtract 7 in both sides:
10 - 7 = z/2 + 7 - 7
3 = z/2
Now we can multiply both sides by 2 to get:
2*3 = 2*(z/2)
6 = z
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