The table shows the profit from a school book fair based on the number of books sold. What is the rate of change for the function represented in the table?
$0.50
$0.67
$1.07
$1.50
Book sold Profit f(x)
(X)
100 ║ $50.00
250 ║ $275.00
300 ║ $350.00
350 ║ $425.00
answer is A-$0.50
Answers
You are given a table
[tex]\begin{array}{cc}\text{Number of books sold} & \text{Profit}\\100 & \$50\\250 & \$275\\300 & \$350\\350 & \$450\end{array}[/tex]
The rate of change for the function represented in the table can be calculated using the formula
[tex]\dfrac{y_{i+1}-y_i}{x_{i+1}-x_i},[/tex]
where i=1,2,3.
1. When i=1,
[tex]\dfrac{y_2-y_2}{x_2-x_1}=\dfrac{275-50}{250-100}=\dfrac{225}{150}=1.5[/tex]
2. When i=2,
[tex]\dfrac{y_3-y_2}{x_3-x_2}=\dfrac{350-275}{300-250}=\dfrac{75}{50}=1.5[/tex]
3. When i=3,
[tex]\dfrac{y_4-y_3}{x_4-x_3}=\dfrac{425-350}{350-300}=\dfrac{75}{50}=1.5[/tex]
Then the rate of change is $1.5
Answer: correct choice is D.
The rate of change for the function is [tex]\$ 1.5[/tex]
The rate of change for the function is calculate by the formula
[tex]\frac{y_{n+1}-y_n}{x_{n+1}-x_n}[/tex]
Where [tex]n=1,2,3[/tex].
A) when [tex]n=1[/tex]
[tex]\frac{y_{1+1}-y_1}{x_{1+1}-x_1}=\frac{y_{2}-y_2}{x_{2}-x_2}[/tex]
[tex]\dfrac{275-50}{250-100}=\dfrac{225}{100}[/tex]
Hence Rate of change when [tex]n=1[/tex] is [tex]1.5[/tex]
B)when [tex]n=2[/tex]
[tex]\frac{y_{2+1}-y_2}{x_{2+1}-x_2}=\frac{y_{3}-y_2}{x_{3}-x_2}[/tex]
[tex]\dfrac{350-275}{300-250}=\dfrac{75}{50}[/tex]
Hence Rate of change when [tex]n=2[/tex] is [tex]1.5[/tex]
C) when [tex]n=3[/tex]
[tex]\frac{y_{3+1}-y_3}{x_{3+1}-x_3}=\frac{y_{4}-y_3}{x_{4}-x_3}[/tex]
[tex]\dfrac{425-350}{350-300}=\dfrac{75}{50}[/tex]
Hence Rate of change when [tex]n=3[/tex] is [tex]1.5[/tex]
So the rate of change for function represented in the table is same for different value of [tex]n[/tex] i.e, [tex]\$ 1.5[/tex].
Learn more about function here;
https://brainly.com/question/12934295?referrer=searchResults
Related Questions
Write and solve a real-world problem that represents the following one-variable inequality. Then solve the inequality, showing all steps.
200 + 0.75x ≤100 + 2.50x
Answers
so, 300+0.75x ≤ 2.5x
300 ≤ 3.25x
then divide
x ≤ 299 and 1/13
a $58 camera is on sale for 20% off find the sale price
Answers
The sale price is $11.6
The sales price of the camera is $46.4
How to determine the sales price?The given parameters are:
Discount = 20%
Price = $58
The sales price is calculated using:
Sales price = Price * (1 - discount)
This gives
Sales price = $58* (1 - 20%)
Evaluate
Sales price = $46.4
Hence, the sales price of the camera is $46.4
Read more about discount at:
https://brainly.com/question/843074
#SPJ1
You are collecting email addresses from 74 customers per day, which is about 90% of the daily goal of __________ emails per day."
Answers
2. All you have to do for this problem is to divide 74 by 90%. You can put this in the calculator by typing in (74 / .9).
3. The answer you get should be 82.22
4. You can check this by multiplying 82.22 by 90%, and it should bring you back to 74.
A retail store marks up its OTC (over-the-counter) merchandise 50% based on acquisition cost. What's the retail price of an item that costs $2?
Answers
I have 10 minutes, Help! Joani has some stuffed animals. She has 2 times as many as Lily. Lily has 6 stuffed animals. Joanie gave 2 away and bought 4 more. How many stuffed animals does Joani have now?
Students's solution: Lily has 6 stuffed animals, so Joani had 6 × 2 to begin with. So Joani had 12 stuffed animals. She gave away 2, so 12 – 2 = 10. She bought 4, so 10 + 4 = 14. So Joani has 14 stuffed animals.
Here is another problem that can also be solved by working backwards.
Wyatt has 3 times as many baseballs as golf balls. He has 5 fewer tennis balls than baseballs. Wyatt has 4 golf balls.
How many tennis balls does Wyatt have?
Answers
3 times as many baseballs as golf balls; 4x3=12; 12 baseballs
5 fewer tennis balls than baseballs; 12-5=7; 7 tennis balls
7 tennis balls
Solve for d.
13d + 4 = 43
A.3
B.13
C.39
D.None of the above
Answers
Because 43-4=39
39/13=3
5.7x=5.64
what is x?
Answers
you divide 5.7 on both sides ( 5.64/5.7) is 0.989
5.7 cancels out with 5.7
5.64/5.7= 0.989 =0.99
check your answer 0.99 x 5.7= 5.643=5.64
A person sold 100 shares of stock at a loss of 40%. If the selling price for the 100 shares was 3000 which of the following comes closest to what was paid for the stock
Answers
purchase price = $3000/0.60 = $5000
Sarah is blowing up spherical balloons for her brother's birthday party. One of the balloons has a radius of 3 inches. Round to the nearest tenth.
Suppose Sarah can inflate the balloon at a rate of 200 cubic inches per minute. How long will it take her to inflate the balloon?
Answers
[volume of a sphere]=(4/3)*pi*r³
for r= 3 in
calculate the volume of one balloon
balloons=(4/3)*pi*r³-------> (4/3)*pi*3³----------> 113.04 in³
if the rate is 200 in³ --------------------> 1 minute
113.04 in³------------------------> X
X=113.04/200------------> 0.5652
the answer is 0.6 minutes
Final answer:
Sarah will take approximately 0.6 minutes or 34 seconds to inflate a spherical balloon with a radius of 3 inches at a rate of 200 cubic inches per minute, after calculating the volume of the balloon and dividing by the rate.
Explanation:
How long will it take Sarah to inflate a spherical balloon with a radius of 3 inches at a rate of 200 cubic inches per minute?
To solve this problem, we first need to calculate the volume of the spherical balloon using the formula for the volume of a sphere, which is [tex]V = \(\frac{4}{3}\)\pi r^3[/tex], where r is the radius of the sphere. In this case, the radius is 3 inches. Plugging the values into the formula, we get:
[tex]V = \(\frac{4}{3}\)\pi (3)^3 = \(\frac{4}{3}\)\pi (27) = 36\pi cubic inches[/tex]
Now, given that Sarah can inflate the balloon at a rate of 200 cubic inches per minute, we can calculate the time it takes to inflate the balloon by dividing the total volume by the rate:
[tex]Time = \(\frac{Volume}{Rate}\) = \(\frac{36\pi}{200}\) minutes[/tex]
Using the approximation \(\pi = 3.14\), this results in:
[tex]Time = \(\frac{36 \times 3.14}{200}\) = \(\frac{113.04}{200}\) ≈ 0.565 minutes[/tex] or about 33.9 seconds, rounded to the nearest tenth.
Therefore, it will take Sarah approximately 0.6 minutes or 34 seconds to inflate the balloon.
Solve -12>3x then graph on a number line that you create and please please show all of your work step by step.
Answers
.. -4 > x
Because the symbol is "greater than", the circle at x=-4 is an open circle.
Zoe's Fish tank holds 27 L of water she uses a 3L container to fill the tank how many times does she have to fill the three litter container in order to fill the fish tank
Answers
Zoe's Fish tank holds 27 L of water, so this is the capacity of the tank. On the other hand, Zoe uses a 3L container in order to fill the tank, so the question is how many times does she have to fill the three litter container in order to fill the fish tank? Let's solve this as follows:
First time:
She pours 3L
Second time:
She pours another 3L, but she previously poured 3L, so she has poured 6L
Third time:
She pours another 3L, but she previously poured 6L, so she has poured 9L
Fourth time:
She pours another 3L, but she previously poured 9L, so she has poured 12L
Fifth time:
She pours another 3L, but she previously poured 12L, so she has poured 15L
Sixth time:
She pours another 3L, but she previously poured 15L, so she has poured 18L
Seventh time:
She pours another 3L, but she previously poured 18L, so she has poured 21L
Eighth time:
She pours another 3L, but she previously poured 21L, so she has poured 24L
Ninth time:
She pours another 3L, but she previously poured 24L, so she has poured 27L
According to this, she needs to pours the 3L container nine times in order to fill the fish tank. This can also be solved dividing 27L/3L= 9
What is greater 2.159 or 2.259
Answers
Median; 1.5
Median; 3
Mean; 1.5
Mean; 3
Answers
If it was symmetrical, you would do Man/Mean Absolute Deviation
Answer:
the median is the number in the middle the mean is the sum of all numbers and divided
Step-by-step explanation:
mean 1,2,3,4,5,6
1+2+3+4+5+6=21
21/6= 3.5 <- mean
Median 1,2,3,4,5,6
2,3,4,5
3,4
median 3.5
Let f(x)=25x2−2 . The function g(x) is a vertical stretch of f(x) by a factor of 2. What is the equation of g(x)?
Answers
When the function f(x)=25[tex]x^2[/tex]−2 is vertically stretched by a factor of 2 to create the function g(x), the resulting equation is g(x) = 50[tex]x^2[/tex]−4.
Explanation:The equation of g(x) can be found by vertically stretching f(x) by a factor of 2. Since f(x) = 25[tex]x^2[/tex] - 2, we can multiply the function by 2 to get g(x) the equation:
The function g(x) is described as a vertical stretch of the function f(x) by a factor of 2. If f(x)=25[tex]x^2[/tex]−2, a vertical stretch implies that we multiply all y-coordinates by the given factor, which is 2 in this case. Therefore, g(x) will be 2*f(x).
This gives us:
g(x) = 2*(25[tex]x^2[/tex] −2)
Expand this:
g(x) = 50[tex]x^2[/tex]−4
So, the equation of g(x) after the vertical stretch of f(x) by a factor of 2 is g(x) = 50[tex]x^2[/tex] −4.
Learn more about Vertical stretch of a function here:https://brainly.com/question/30105263
#SPJ12
The equation of g(x), which is a vertical stretch of f(x) = 25x² - 2 by a factor of 2, is g(x) = 50x² - 4.
To solve this, we need to apply a vertical stretch to the function f(x).
A vertical stretch by a factor of 2 means multiplying the entire function f(x) by 2.
Given :
f(x) = 25x² - 2
we multiply it by 2:
g(x) = 2 * (25x² - 2)
g(x) = 50x² - 4
So, the equation of g(x) is g(x) = 50x² - 4.
How many triangles exist with the given side lengths?
12 in, 15 in, 18 in
A.
No triangle exists with the given side lengths.
B.
More than one unique triangle exists with the given side lengths.
C.
Exactly one unique triangle exists with the given side lengths.
Answers
Plz help please thanks so much
Answers
1/2(120)
60
He needs to paint 60 sq ft.
what is 64/25 as a mixed number?
Answers
HELPP ME PLZZZZ
Which of the four images was formed by a reflection of the letter T?
A
B
C
D
Answers
The answer is not A because T would be flipped, the answer is not D because T can not be reflected in that area without translations, and the answer is not B because T cannot (once again) be reflected in such locations without translations, Therefore, that leaves us with our best bet being the answer C.
PLEASE HELP ASAP!!!!!!!!!!!
A number cube with six sides numbered 1 through 6 is rolled. The probability of rolling a 5 is 16. What is the probability of not rolling a 5? Enter your answer as a fraction, in simplest form, in the box.
Answers
Which means the probability of not rolling it is the opposite - 5/6
helppppppppppppp meeeeeeeeeeeeeeeee
Answers
X = -10
-10y = -90
Y= 9
For this case what you should do is see the intersections with each of the axes and then join the ordered pairs.
We have then:
For the x axis:
y = 0
Substituting in the equation:
9x-10 (0) = - 90
9x-0 = -90
x = -10
For the y axis:
x = 0
Substituting in the equation:
9 (0) -10y = -90
0-10y = -90
y = 90/10
y = 9
We graph the ordered pairs:
(x1, y1) = (- 10, 0)
(x2, y2) = (0, 9)
Answer:
See attached graph.
Which expression is equivalent to the expression below? Select all that apply. –25(15 – 20d + 5c) A. –30 + 40d – 10c B. –6 + 8d – 2c C. –2c + 8d – 6 D. 6 – 8d + 2c
Answers
The equivalent expressions are [tex]-6+8d-2c[/tex] and [tex]-2c+8d-6[/tex]. So, the correct options are B and C.
Given:
The given expression is:
[tex]-\dfrac{2}{5}(15-20d+5c)[/tex]
To find:
The equivalent expressions.
Explanation:
We have,
[tex]-\dfrac{2}{5}(15-20d+5c)[/tex]
Using the distributive property, we get
[tex]=-\dfrac{2}{5}(15)-\dfrac{2}{5}(-20d)-\dfrac{2}{5}(5c)[/tex]
[tex]=-6+8d-2c[/tex]
It can be rewritten as:
[tex]=-2c+8d-6[/tex]
The equivalent expressions are [tex]-6+8d-2c[/tex] and [tex]-2c+8d-6[/tex]. Therefore, the correct options are B and C.
Learn more:
https://brainly.com/question/7627111
Upon applying the distributive property, the given expression, –25(15 – 20d + 5c), simplifies to –375 + 500d – 125c. None of the options provided match this expression, making the correct answer 'None of the above'.
Explanation:The student is asked to find an expression equivalent to –25(15 – 20d + 5c). To do this, we will apply the distributive property to multiply –25 by each term inside the brackets. This gives us:
–25 × 15 = –375–25 × (–20d) = 500d–25 × 5c = –125cCombining these we get the expression –375 + 500d – 125c. When we look at the options provided, none are equivalent to the expression we derived. Therefore, the correct answer is:
None of the aboveLearn more about Equivalent Expression here:https://brainly.com/question/34140345
#SPJ3
What is the volume of a cube with a side length of 5 cm?
A)
10 cm3
B)
15 cm3
C)
25 cm3
Eliminate
D)
125 cm3
Answers
side x side x side, where each side has the same length.
Since 1 side length is 5cm, we know the other side lengths are also 5cm.
5 cm x 5 cm x 5 cm = D) 125 cm^3
The measures of the angles of triangle ABC are angle a 48 degrees angle B 6x - 28 angle C 2x what is the value of x
Answers
48 + 6x - 28 + 2x = 180
8x + 20 = 180
8x = 160
x = 20
ILL GIVE BRAINLIEST PLEASE ORDER THESE LEAST TO GREATEST
Answers
0.125 being the least and 2.5% being the greatest
Ascending Order: 0.125, 2.5, 1/4 ( Least to Greatest.).
Descending Order: 1/4, 2.5, 0.125 ( Greatest to Least.).
Hope this helps.
what happens in the last part if it is 2/8 + 1
Answers
Hope it helps. :)
Find the area of the regular polygon.
Please explain how you got your answer!
Answers
There are 6 brown, 5 blue, and 2 orange marbles in a hat. What is the probability of picking two orange marbles in a row without returning the marbles back to the hat? (Write your answer as a fraction.)
Answers
Solve the equation and show all work please show steps!!
4f + 11 = 29
Answers
4f=29-11
4f=18
f=9/2
The answer is "x=4.5 or 5".
Reason:
Write the equation:
4f+11=29
Subtract 11 on both sides:
29-11=18
4f=18
Now divide 18 by 4:
18/4=4.5 (rounded to the whole number)
f=5
If you need anymore help feel free to ask me!
Hope this helps!
~Nonportrit
Which of the following values are needed to determine the area of the trapezoid choose all that apply
Answers
answer
8 mm
10 mm
5 mm
Please help asap!
Two angles are supplementary. If one angle measures 43 degrees, what is the measure of the second angle?
A. 47 degrees
B. 57 degrees
C. 137 degrees
D. 147 degrees
Answers
Answer:
147
Step-by-step explanation: