The graph below represents the price of sending video messages using the services of a phone company. What is the constant of proportionality?
Answers
In the question given above, the constant of proportionality is 24. To determine the constant of proportionality, look at the graph and take note of each price and the number of video it can send.
From the graph, it can be seen that, 48 cents will send 2 video messages, 96 cents will send 4 messages, 144 cents will send 6 messages and 192 cents will send 8 messages.
48/2 = 24
96/4 = 24
144/6 = 24
192/8 = 24.
Related Questions
Andreus made $625 mowing yards. He worked for 5 consecutive days and earned the same amount of money each day. How much money did Andreus earn per day
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Enter the degree of the polynomial
5x5 + 8x2 + 2x – 3x9 – 8x4 – 4x5
Answers
The degree of a term is the sum of the exponents of all the variables of the term,. A plain variable has degree 1.
One term is -3x^9.
That has the largest exponent of any term, so the degree is 9.
Answer:
9
Step-by-step explanation:
I got it right on ape-x
Which equation represents a line that passes through (–9, –3) and has a slope of –6?
Answers
i m here to
help u
I hope u know the point -slope form
,here, the equation will be
y+3= -6x -54
write 129.04 in words
Answers
Write these decimal fractions in words 0.17
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One tenth and seven hundredth
Seventeen hundredth
Your hair is 6 inches long and grows at a rate of 144 millimeters per year. a. Convert 144 millimeters per year to inches per year. Round your answer to the nearest tenth. b. Write an equation that represents the length y (in inches) of your hair after x years. c. How long is your hair after 4 years?
Answers
B) 56.7x + 6
C) 232.8 inches
The rate of hair growth in inches is 5.67 inches per year and in 4 years hair will be 28.68 inches long.
As mentioned in the question,
Your hair is 6 inches long and grows at a rate of 144 millimeters per year. a. Convert 144 millimeters per year to inches per year.
The equation model is defined as the model of the given situation in the form of an equation using variables and constants.
Here,
1 inch = 25.4 millimeters,
For, also 1 millimeters = 1 / 25.4 inches,
So,
144 millimeters per year = 144 / 25.4 inches per year
= 5.67 inches per year
Now,
Growth after 4 years,
= 4 × 5.67 + 6
= 28.68
Thus, the rate of hair growth in inches is 5.67 inches per year and in 4 years hair will be 28.68 inches long.
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Find all the real fourth roots of 256.
4
-8 and 8
8
-4 and 4
Answers
The 4th roots are {4, 4, -4 and -4}.
Check for yourself: Does 4^4= 256? does (-4)^4 = 256?
What kind of graph is this?
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Match the pairs of equations that represent concentric circles. Tiles
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1) Two circles are concentric if they have the same center and different radii.
2) The equation of a circle with center xc, yc, and radius r is:
(x - xc)^2 + (y - yc)^2 = r^2.
So, if you have that equation you can inmediately tell the coordinates of the center and the radius of the circle.
3) You can transform the equations given in your picture to the form (x -xc)^2 + (y -yc)^2 = r2 by completing squares.
Example:
Equation: 3x^2 + 3y^2 + 12x - 6y - 21 = 0
rearrange: 3x^2 + 12x + 3y^2 - 6y = 21
extract common factor 3: 3 (x^2 + 4x) + 3(y^2 -2y) = 3*7
=> (x^2 + 4x) + (y^2 - 2y) = 7
complete squares: (x + 2)^2 - 4 + (y - 1)^2 - 1 = 7
=> (x + 2)^2 + (y - 1)^2 = 12 => center = (-2,1), r = √12.
equation: 4x^2 + 4y^2 + 16x - 8y - 308 = 0
rearrange: 4x^2 + 16x + 4y^2 - 8y = 308
common factor 4: 4 (x^2 + 4x) + 4(y^2 -8y) = 4*77
=> (x^2 + 4x) + (y^2 - 2y) = 77
complete squares: (x + 2)^2 - 4 + (y - 1)^2 - 1 = 77
=> (x + 2)^2 + (y - 1)^2 = 82 => center = (-2,1), r = √82
Therefore, you conclude that these two circumferences have the same center and differet r, so they are concentric.
A family pass to amusement park cost $54 using the distributive property write an expression that can be used to find the cost in dollars of 8 family
Answers
I hope this helped! :))
Find the extreme values of the function f(x, y) = 4x + 8y subject to the constraint g(x, y) = x2 + y2 − 5 = 0.
Answers
[tex]L_x=4+2\lambda x=0[/tex]
[tex]L_y=8+2\lambda y=0[/tex]
[tex]L_\lambda=x^2+y^2-5=0[/tex]
[tex]L_y-2L_x=2\lambda y-4\lambda x=2\lambda(y-2x)=0\implies y=2x[/tex]
[tex]xL_x+yL_y=2\lambda(x^2+y^2)+4x+8y=10\lambda+4x+8y=0\iff5\lambda+2x+4y=0[/tex]
[tex]y=2x\implies 5\lambda+5y=0\implies 5(\lambda+y)=0\implies y=-\lambda[/tex]
[tex]4+2\lambda x=0\iff4+\lambda y=0\iff4-y^2=0\implies y=\pm2[/tex]
[tex]y=\pm2\implies x=\dfrac y2=\pm1[/tex]
In other words, there are two critical points, [tex](1,2)[/tex] and [tex](-1,-2)[/tex]. At the first point, there is a maximum of [tex]f(1,2)=20[/tex] and at the second, there is a minimum of [tex]f(-1,-2)=-20[/tex].
Suppose the concentration of a certain pollutant is uniformly distributed in the range of 4 to 20 ppm (parts per million). if a concentration in excess of 15 ppm is considered toxic, what is the probability that a specimen will yield a toxic concentration level
Answers
5(1/16), or 5/16. Thus, the probability that a specimen will yield a toxic concentration level is 5/16.
I have no way of knowing what you already know about probability distributions. If you need a more detailed explanation, please ask questions here.
Which linear inequality is represented by the graph?
a.y >2/3 x – 2
b.y < 2/3x + 2
c.y2/3 > 2/.+ 1
d.y<2/3 x – 1
Answers
Find the intervals of convergence for the function. f(x)=sum_(n=1)^infinity x**n/n**2 32324243232 incorrect: your answer is incorrect. (b) find the intervals of convergence for f '.
Answers
will converge as long as
[tex]\displaystyle\lim_{n\to\infty}\left|\frac{\frac{x^{n+1}}{(n+1)^2}}{\frac{x^n}{n^2}}\right|<1[/tex]
according to the ratio test. We have
[tex]\displaystyle\lim_{n\to\infty}\left|\frac{\frac{x^{n+1}}{(n+1)^2}}{\frac{x^n}{n^2}}\right|=|x|\lim_{n\to\infty}\frac{n^2}{(n+1)^2}=|x|\left(\lim_{n\to\infty}\frac n{n+1}\right)^2=|x|<1[/tex]
so the sum will certainly converge whenever [tex]-1<x<1[/tex], but we also know the series will converge at the endpoints. [tex]\displaystyle\sum\frac1{n^2}[/tex] is a convergent [tex]p[/tex]-series, which means [tex]\displaystyle\sum\frac{(-1)^n}{n^2}[/tex] is also (absolutely) convergent, so in fact the interval of convergence is [tex]-1\le x\le1[/tex] (endpoints included).
The volume of a rectangular prism can be found by multiplying the base area, B, times the height. If the volume of the prism is represented by 15x2 + x + 2 and the height is x2, which expression represents B, the area of the base?
Answers
15x^2 + x + 2
------------------ .
x^2
If you perform this division, you'll obtain 15 + (x+2)/(x^2).
So, again, verify your representation of the height of the prism.
Bx^2 = 15x^2 + x + 2
B = (15x^2 + x + 2) / x^2
or simplified like this
B = 15x^2/x^2 + x/x^2 + 2/x^2
B = 15 + 1/x + 2/x^2
Which linear function has the same y-intercept as the one that is represented by the graph?
Answers
on the graph x = 0 , y = 3
function
y = 2x + 3 when x = 0
y = 3
answer
C. y = 2x + 3
During a catered lunch, an average of 4 cups of tea are poured per minute. The lunch will last 2 hours. How many gallons of tea should the caterer bring if there are 16 cups in one gallon?
Answers
4 X 60 (minutes per hour)
The lunch last 2 hours so if 240 cups is every hour then 480 cups would be for 2 hours.
Now covert 480 cups to gallons. It takes 16 cups to make 1 gallon. We would divide 480/16 = 30 gallons
Answer with sometimes, always, or never true. Give an example/counterexample.
When a point is reflected across the y-axis, the new point has a negative x-coordinate.
Answers
If the original x coordinate is negative, it will become positive. For example, (-5, 5) would become (5,5), which is a positive x. The sign of the x changes when reflected over the y axis.
Final answer:
The statement that a point reflected across the y-axis results in a point with a negative x-coordinate is sometimes true, depending on the original point's location relative to the y-axis.
Explanation:
When a point is reflected across the y-axis, the result depends on the initial position of the point relative to the y-axis. The statement that the new point has a negative x-coordinate is sometimes true. If a point lies to the right of the y-axis (positive x-coordinate), reflecting it across the y-axis will indeed result in a point with a negative x-coordinate. However, if the original point is to the left of the y-axis (already has a negative x-coordinate), reflecting it across the y-axis will give it a positive x-coordinate.
Example
If the original point is (3, 2), reflecting it across the y-axis results in (-3, 2), which supports the statement.
If the original point is (-4, 5), reflecting it across the y-axis yields (4, 5), which contradicts the statement.
Therefore, the correct answer is sometimes true, demonstrating the importance of considering the position of the original point in relation to the y-axis.
What is the sales tax on a jacket priced at $350 if the sales tax rate is 7%
Answers
Your sale tax for a jacket would be $24.50.
dr. lee went to a bank to get a loan for some new furniture for the waiting area at her clinic. she wanted to borrow $5,000 to be paid back over 3 years. last week the interest rate was 4.25%. but this week theinterest rate went up to 4.50%. how much additional interest will Dr. lee pay because she waited the extra week
Answers
additional interest is 12.5 dollars.
Colin drove 45 minutes to the airport. He arrived 90 minutes before his flight departed, and then he spent 70 minutes in the air. Once he landed, Colin spent 20 minutes gathering his luggage, and then he drove 35 minutes to his hotel. What must be true of any expression that represents the total time that Colin spent traveling from his house to the hotel? The numbers can be added in any order. The number 45 must be the first addend, and 35 must be the last addend. The numbers must be added in the order 45, 90, 70, 20, and 35. The numbers must be added in either the order 45, 90, 70, 20, and 35 or the order 35, 20, 70, 90, and 45.
Answers
Answer:
The numbers must be added in the order 45, 90, 70, 20, and 35.
Step-by-step explanation:
Answer:
The numbers must be added in the order 45, 90, 70, 20, and 35
Step-by-step explanation:
:3
The airport garage charges $5 to park for the first hour and then $3.50 an hour for any additional hours. Ben paid $57.50 to park there one day when he flew to another city. How many hours was he parked at the airport?
Answers
Final answer:
Ben was parked at the airport for a total of 16 hours, after calculating the initial cost for the first hour and then dividing the remainder by the hourly rate for additional hours.
Explanation:
The student's question asks how many hours Ben was parked at the airport, given that the parking cost is $5 for the first hour and $3.50 for each additional hour, with a total fee of $57.50.
First, we subtract the initial $5 from the total cost to determine the cost of additional hours:
$57.50 - $5 = $52.50 for additional hours
Next, we divide the remaining cost by the hourly rate for additional hours to find the number of additional hours Ben parked:
$52.50 ÷ $3.50/hour = 15 hours
Finally, we add the first hour to the additional hours to calculate the total hours parked:
15 hours + 1 hour = 16 hours
Thus, Ben was parked at the airport for a total of 16 hours.
Which of the following is the best example of a characteristic of an experiment?
a.Participants should be selected into the treatment group randomly.
b.Participants are rarely aware that they are part of an experiment.
c.Participants are observed without researchers making changes to their behaviors.
d.The results of an experiment are based on a questionnaire given to a random sample of the population.
Answers
One of the basic feature of an experiment is the selection of participants by means of random method. It is very important to select participants randomly in order to avoid experimental bias that may occur as a result of the participants not been an exact representation of the concerned population.
A rectangular field is to be bounded by a fence on 3 sides and a straight stream on the 4th side. Find the dimensions of the field with maximum area that can be enclosed using 1000 ft of rope. This is in the applied maximum and minimum chapter btw.
Answers
[tex]\bf \stackrel{area}{A}=length\cdot width\implies A(w)=(1000-2w)w \\\\\\ \boxed{A(w)=1000w-2w^2} \\\\\\ \cfrac{dA}{dw}=1000-4w\implies 0=1000-4w\implies 4w=1000 \\\\\\ w=\cfrac{1000}{4}\implies \boxed{w=\stackrel{width}{250}} \\\\\\\ [1000-2(250)]\implies 1000-500\implies \boxed{l=\stackrel{length}{500}}[/tex]
and if you run a first-derivative test on say x = 249 and x = 251, you'll notice the slope is positive and negative respectively, meaning, is a maximum.
To maximize the area of the rectangular field, express the area in terms of one variable, derive the area function, and set it to zero for solving. The sides of the field yielding the maximum area are obtained using these calculations.
Explanation:This question involves optimization in calculus, specifically related to finding the maximum area of a rectangle. In such a problem, the first step is to express the area (A) of the rectangle in terms of one variable. Given a fence that is 1000 ft in length, if we name the side perpendicular to the stream as 'x', and the side parallel to it (bounded by the fence) as 'y', the perimeter of the field is 2x + y = 1000.
We can express y in terms of x: y = 1000 - 2x. The area of the rectangle, A = x*y = x*(1000 - 2x).
To find the maximum area, we find the first derivative of A with respect to x, set it to zero and solve for x. The second derivative test will confirm if it's a maximum. Based on the solutions, the maximum area is achieved with the dimensions of the rectangular field being specific values of x and y that you compute.
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Find the equation of the ellipsoid passing through the points (±7,0,0),(0,±1,0)(±7,0,0),(0,±1,0) and (0,0,±4)
Answers
ally and barbara, and katherine will share the cost of a vacation rental for a week. aly agrees to pay 30% of the cost. barbara agrees to pay 0.45 of the coat. katherine will pay the remaining balance. if the total rental coast $960, how much will ally, barbara, and katherine each pay towards the week's rent?
Answers
Ally: $288
Barbara: $432
Katherine: $240
Find the derivative of the function F(x) = (x4 + 9x2 − 5)4
Answers
The required derivative of the function (x⁴ + 9x² − 5)⁴ is f'(x) = 4 (x⁴ + 9x² − 5)³(4x³ + 18x).
As per the question we have to determine the derivative of the f(x) = (x⁴ + 9x² − 5)⁴.
What is derivative?A derivative is defined as the rate of change of the function with respect to the respective variables.
Here,
According to the question,
f(x) = (x⁴ + 9x² − 5)⁴
Differentiate both sides with respect to x.
f'(x) = d[(x⁴ + 9x² − 5)⁴] / dx
f'(x) = 4 (x⁴ + 9x² − 5)³ × (4x³ + 9×2x)
f'(x) = 4 (x⁴ + 9x² − 5)³(4x³ + 18x)
Thus, the required derivative of the function (x⁴ + 9x² − 5)⁴ is f'(x) = 4 (x⁴ + 9x² − 5)³(4x³ + 18x).
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Write the value of 1710 in standard form
Answers
1710 is already in simplest, standard form.
Sometimes you'll see it written as 1,710, which for some people is easier to read.
Is 9/6, 21/14 proportional?
Answers
The fractions 9/6 and 21/14 are proportional because both simplify to the same value, which is 1.5. Cross-multiplication also confirms their proportionality as the cross products are equal.
Explanation:To determine if the fractions 9/6 and 21/14 are proportional, we can simplify each fraction or cross-multiply to see if we end up with an equivalent value. If two ratios are proportional, this means they are equivalent to each other when reduced to simplest form, or the cross products are equal.
Simplifying 9/6, we get 1.5, and simplifying 21/14, we also get 1.5. Since both simplified fractions result in the same value, 9/6 and 21/14 are indeed proportional.
We can also cross multiply to verify: (9×14) should be equal to (6×21). This results in 126 = 126, confirming that both ratios are indeed proportional.
Final answer:
The ratios 9/6 and 21/14 are proportional because both simplify to the same ratio 3/2, and cross-multiplication yields equal products, confirming proportionality.
Explanation:
To determine if the ratios 9/6 and 21/14 are proportional, we simplify each ratio. The ratio 9/6 simplifies to 3/2 and the ratio 21/14 simplifies to 3/2 as well. Since both simplified ratios are equal, we can confirm that 9/6 and 21/14 are indeed proportional ratios.
Another way to check for proportionality is to cross-multiply and see if the products are equal. Multiplying 9 times 14 and 6 times 21 gives us 126 in both cases, which reaffirms our conclusion. Thus, based on these methods, the given ratios are proportional.
Amanda used 3/4 cup of sugar to make 2 dozen cookies. How much sugar is in each cookie? (Dozen=12)