Answers
Answer:
(a)
[tex]f(x) = \left \{ {{5x;\ 0<x\le 5} \atop {5x-5; x > 5}} \right.[/tex]
(b) Rate = 5
(c) Rate = 5
Step-by-step explanation:
Given
The attached graph
Solving (a): The piece-wise function
For the first line
Calculate the slope of the first line
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
Where
[tex](x_1,y_1) = (0,0)[/tex]
[tex](x_2,y_2) = (5,25)[/tex]
So, the slope is:
[tex]m = \frac{25 - 0}{5 - 0}[/tex]
[tex]m = \frac{25}{5}[/tex]
[tex]m = 5[/tex]
The equation is then calculated as:
[tex]y = m(x - x_1) + y_1[/tex]
Where: [tex]m = 5[/tex] and [tex](x_1,y_1) = (0,0)[/tex]
[tex]y = 5(x - 0) + 0[/tex]
[tex]y = 5(x) + 0[/tex]
[tex]y = 5x[/tex]
So, the function of the first line is:
[tex]f(x) = 5x;\ 0 < x \le 5[/tex]
For the second line
Calculate the slope of the second line
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
Where
[tex](x_1,y_1) = (5,20)[/tex]
[tex](x_2,y_2) = (9,40)[/tex]
So, the slope is:
[tex]m = \frac{40 - 20}{9 - 5}[/tex]
[tex]m = \frac{20}{4}[/tex]
[tex]m = 5[/tex]
The equation is then calculated as:
[tex]y = m(x - x_1) + y_1[/tex]
Where: [tex]m = 5[/tex] and [tex](x_1,y_1) = (5,20)[/tex]
[tex]y = 5(x - 5) + 20[/tex]
[tex]y = 5x - 25 + 20[/tex]
[tex]y = 5x -5[/tex]
So, the function of the second line is:
[tex]f(x) = 5x -5;\ x>5[/tex]
Hence, the piece-wise function is:
[tex]f(x) = \left \{ {{5x;\ 0<x\le 5} \atop {5x-5; x > 5}} \right.[/tex]
Solving (b): The rate at which customers that buy up to 5lb buy.
[tex]x = 5[/tex]
This question implies that, we determine the rate at which this customer buys.
For [tex]x = 5[/tex]
[tex]f(x) = 5x;\ 0 < x \le 5[/tex]
The slope of the above function is 5.
So, this customer buys at the rate of $5 per lb
Solving (b): The rate at which customers that buy more than 5lb buy the extra pounds above 5lb.
For [tex]x > 5[/tex]
[tex]f(x) = 5x -5;\ x>5[/tex]
Assume x = 6
[tex]f(6) = 5 * 6 - 5[/tex]
[tex]f(6) = 30 - 5[/tex]
[tex]f(6) = 25[/tex]
Express as 20 + 5
[tex]f(6) = 20 + 5 * 1[/tex]
Assume x = 7
[tex]f(7) = 5 * 7 - 5[/tex]
[tex]f(7) = 35 - 5[/tex]
[tex]f(7) = 30[/tex]
[tex]f(7) = 20 + 10[/tex]
Express 10 as 5 * 2
[tex]f(7) = 20 + 5 * 2[/tex]
So, we have:
[tex]f(6) = 20 + 5 * 1[/tex]
[tex]f(7) = 20 + 5 * 2[/tex]
This can be generalized as:
[tex]f(x) = 20 + 5(x - 5)[/tex]
For the above functions;
20 represents the amount they buy the first 5
5 represents the rate at which they buy extra pounds above 5
Hence, they buy the extra pounds at the rate of $5 per pound
Related Questions
which is a correct step when using the median fit method for modeling data?
Use the median value of intercepts found
Calculate slope using the right and middle points
Determine three y intercepts by using each summary point along with the slope.
Determine the median of the x values and the median of the y values.
Answers
When using the median fit method to model data, you should Determine three y intercepts by using each summary point along with the slope.
What is the median fit method?This is a model for coming up with trend lines to represent the data given by a data set by dividing the given data into sections where the data points are equal in number.
As there will be three sections, it is important that three y intercepts are determined using summary points and the slope.
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Answer: C
Step-by-step explanation:
which angles are vertical to each other
Answers
Answer:
You need to attach the picture of the angles
Answer:
right
Step-by-step explanation: because ones left and 1 right
What is the conditional relative frequency of a state's popular vote being won by the Democrat in 2012, given that it was won by the Democrat in 1976?
Answers
The frequency data table is missing, so i have attached it.
Answer:
0.5
Step-by-step explanation:
We want to find conditional relative frequency and conditional relative frequency is used to compare the frequency count to the marginal total that represents the particular condition we are dealing with.
In this case, the condition is the popular vote of the state being won by the Democrat in 2012, given that the same popular vote was won by the Democrat in 1976.
In the frequency data table attached, we see that the joint frequency count for Democrat winning in 1976 and 2012 is given as 12.
While the corresponding marginal frequency total is given as 24.
Thus;
Conditional relative frequency = joint frequency count/marginal frequency total = 12/24 = 0.5
The conditional relative frequency of a state's popular vote being won by the Democrat in 2012, given that it was won by the Democrat in 1976:
We need to discover conditional relative recurrence and conditional relative recurrence is utilized to compare the recurrence number to the minimal add up to that speaks to the specific condition we are managing with. In this case, the condition is the prevalent vote of the state being won by the Democrat in 2012, given that the same prevalent vote was won by the Democrat in 1976. In the recurrence information table joined, we see that the joint recurrence check for Democrat winning in 1976 and 2012 is given as 12.
Thus;
Conditional relative frequency = joint frequency count/marginal frequency total = 12/24 = 0.5
The conditional relative frequency of a state's popular vote being won by the Democrat in 2012, given that it was won by the Democrat in 1976 is 0.5.
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What is the difference of 506 and 297
Answers
Answer:
209
Step-by-step explanation:
subtract
Answer:
209
Step-by-step explanation:
subtraction bro
The exchange rate is 156 pesos for 1 US dollar. You have $20.00 US. How many pesos do you have?
A. $128.00
B. $0.13
C. $3,120.00
D. $312.00
Answers
Step-by-step explanation:
C you are gonna have 3,120.00 pesos
A billard ball has a surface area of 84 square centimeters. What is the radius of the ball?
Answers
Answer: √21/√pi
Step-by-step explanation: Surface area of ball is 4(pi)r^2. Divide 84 by 4 and get 21. Dividing 21 by pi and taking the square root therefore is the answer.
If the energy required to harvest and refine an energy resource is 10,000 megawatts (MW) and the energy actually obtained from using the fuel is 12,400 MW, what is the EROEI of this resource?
Answers
Answer:
22,4000 answer i tinking
Directions: Find the surface area of each figure.
1.
20.7 in
4
11 in
11 in
Answers
Answer:
576.4 in²
Step-by-step explanation:
Surface area of square pyramid = Base Area + ½(perimeter of base)(slant height)
Base area = s² = 11² = 121 in.²
Perimeter of base = 4(11) = 44 in.
Slant height = 20.7 in.
Plug in the values
Surface area = 121 + ½(44)(20.7)
= 576.4 in²
32 pages to 28 pages.
Answers
Answer:
12.5%
Step-by-step explanation:
percent change is calculated as
[tex]\frac{change}{original\\}[/tex] x 100
change = 32 − 28 = 4 pages
[tex]\frac{4}{32}[/tex] x 100% = [tex]\frac{100}{8}[/tex] % = 12.5 %
Hope it helps
Last year, Lebron James made $22, 970,000. This year he made $26,440.000. How much did Lebron James make from both years together?
Answers
Answer:
49,410,000
Step-by-step explanation:
because calculator
I NEED HELP PLESE I BEG YOUUUU
Answers
help please ! order the side lengths GH , HI , IG from least to greatest
Answers
Answer:
IH < IG < HG
Step-by-step explanation:
To solve this equation remember that angle measurements correspond with sides. So, the largest angle will be opposite of the longest side and the smallest angle will be opposite of the shortest side.
First, you need to find m<I; do this by subtracting 52 and 45 from 180. This means that m<I=83, making it the largest angle. Therefore, the angles, in order of least to greatest, are <G, <H, <I. So, to find the final answer, find the sides opposite of each of the angles. This means the answer is IH < IG < HG.
BRAINLIEST FOR CORRECT ANSWER, IM FAILING SCHOOL AND NEED HELP ASAP. EVEN OFFICIAL HELP COUNTS
Answers
Answer:
B = 145°
Explanation:
Sorry but m∠C > 90° how could it be 35° ?
However if you still need an answer:
B = 180 - C
B = 180 - 35
B = 145°
A triangular brace has an angle measure of 30 degrees, with a side opposite
this angle measuring 8 inches. The base of the triangular brace, which is
adjacent to the given angle measure, is 6 inches in length. Which of the
following statements is correct?
A. The angle opposite the side measuring 6 inches has one solution
of approximately 28 degrees.
B. The angle opposite the side measuring 6 inches has two solutions
of approximately 28 degrees and 36 degrees.
O C. The angle opposite the side measuring 6 inches has one solution
of approximately 22 degrees.
D. There is not a solution for the angle opposite the side measuring 6
inches.
Answers
The angle opposite the side measuring 6 inches has one solution of approximately 22 degrees.
Sine ruleSine rule is used to show the relationship between the angles of a triangle and the sides opposite to the angles. It is given by:
a / sin(A) = b / sin(B) = c / sin (C)
where A, B, C are the angles and a, b, c are the sides opposite to the angles.
From the question:
let a = 8 in, A = 30°, b = 6 in, hence:
a / sin(A) = b / sin(B)
8 / sin(30) = 6 / sin(B)
B = 22°
The angle opposite the side measuring 6 inches has one solution of approximately 22 degrees.
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Will give brainliest and 50 points
Find the area of this triangle.
Round to the nearest tenth.
7 m
125°
14 m
[?] m2
Answers
Answer
40.1
Area of a triangle using sine rule = 1/2 a b sinC
a and b are the two known sides, sinC is the angle opposite the unknown side
1/2 x 14 x 7 sin(125) = 40.1 to the nearest tenth
Hope this helps
Answer:
40.1
Step-by-step explanation:
the answer to 2x+56=
Answers
Answer:
It can't be simplified or added together because one is multiplied by x and the other is not
Step-by-step explanation:
WILL GIVE BRAINLIEST IF YOU HELP ME
Answers
Answer:
D. Point S
Step-by-step explanation
The opposite of -5.5 is 5.5, therefore since Point S is at 5.5 on the number line, the answer is D.
A high school booster club is selling raffle tickets for three different prizes. The tickets are $1 for the small prize, $2 for the medium prize, and $5 for the large prize. Shiloh spent $35 on 15 tickets. Together, the number of $2 and $5 tickets she bought is 1 more than the number of $1 tickets she bought. If x represents the number of $1 tickets, y represents the number of $2 tickets, and z represents the number of $5 tickets Shiloh bought, which system of equations represents this situation?
Answers
Answer:
x+y+z=15
x+2y+5z=15
-x+y+z=1
Step-by-step explanation:
Answer:
The answer is
x + y + z = 15
x + 2y + 5z = 35
-x + y + z = 1
Step-by-step explanation:
If x -9 is a factor of x^2 -5 -36, what is the other factor?
Answers
Answer:
Factors are (x-9)(x+4)
Step-by-step explanation:
Is 2 a solution of 4.3 + 12 = 4? Complete the statement.
• The equation is ?
when x = 2, so 2 ?
a solution.
Answers
Rana sells 192 cakes in the ratio small: medium: large = 7 : 6 : 11.
The profit for one medium cake is twice the profit for one small cake.
The profit for one large cake is three times the profit for one small cake.
Her total profit is £532.48
Work out the profit for one small cake
Answers
Answer:
S = £1.28
Step-by-step explanation:
Let the small, medium and large cakes be S, M and L respectively.
Given the following data;
Total profits = £532.48
Total number of cake = 192 cakes
Ratio of S:M:L = 7:6:11
Sum of ratio = 7+6+11 = 24
To find number of each cakes, we would divide the total number of cakes by the sum of ratio;
Number of each cakes = 192/24
Number of each cakes = 8
Next, we determine the exact number of each type of cakes.
Small = 7*8 = 56 cakes.
Medium = 6*8 = 48 cakes.
Large = 11*8 = 88 cakes.
For the profits;
Translating the word problem into an algebraic expression, we have;
M = 2S
L = 3S
56S + 48*(2S) + 88*(3S) = £532.48
56S + 96S + 264S = 532.48
416S = 532.48
S = 532.48/416
S = £1.28
Therefore, the profit for one small cake is £1.28
5, 11, 17,...
Find the 35th term.
Answers
Answer:
119 is the 35th term
how does the stimulus check impact society please help me please i really need help please
Answers
People started getting stimulus checks during the time when c0vid-19 was a major issue because most places where people would work were closed, so people were getting money through stimulus checks because they were basically unemployed. This money went back into the economy to buy mostly essentials and health products, so therefore it helped businesses that sold these kinds of things.
Answer this with detail, please!
Answers
Answer:
D
Step-by-step explanation:
Hello There!
In order for a relationship to be proportional it must follow these requirements:
It must have a constant rate of changeIt must go through the origin (0,0)The equation is put in y = kx form (where k = slope)Knowing this let us now look at each relationship
The first one indeed has a constant rate of change
However it has a y intercept of (1,0) so it doesn't go through the origin therefore it is not a proportional relationship
For B:
B is not a proportional relationship because it does not have a constant rate nor can we tell if it goes through he origin
The y value first adds by 7 then by 9 then by 6. (while the x value goes up 1)
in a constant rate of change relationship the slope is constant and goes up by a certain amount each time therefore relation b is not proportional
For C:
Like relation A it has a constant rate of change but its not put in y = kx form and has a y intercept. Because of this it is not considered a proportional relationship
For D:
Relation D happens to have a constant rate of change (as it has a vertical straight line). It also happens to pass through the origin (0,0)
The relation fulfills each requirement therefore D is your answer
Ceasar opens a bank account and makes an initial deposit of $800. The banker tells Ceasar that he is going to receive an annual rate of 10% compounded continuously on his investment. Find the bank balance assuming Ceasar leaves the account untouched for 8 years. asnwer this question using the fomula A(t) = Pe^(rt). please show work plese
Answers
Answer:
Initial Deposit= $800
Annual rate= .1%
Leaves= 8 years
8 x .1= .8
$800 x .8= $640
$800+$640= $1,440
So your answer is $1,440 is the bank balance in 8 years
Step-by-step explanation:
hope i help have a great day
Helppppp pleaseeee xxxxx
Answers
Answer:
a. 28π m²
b. 44π m²
Step-by-step explanation:
a. Lateral surface of the cone = πrl
Where,
r = 4 m
l = 7 m
Lateral surface area = π*4*7 = 28π m²
b. Surface area of cone = πr(l + r)
r = 4 m
l = 7 m
Surface area = π*4(7 + 4)
= 4π(11)
= 44π m²
A recipe for 1 batch of cookies calls for 3/4 cup of flour. How much flour is required to bake 1 1/2 batches of cookies?
Answers
Answer:
1 1/8 cups of flour are required to bake 1 1/2 batches of cookies.
Step-by-step explanation:
Given that a recipe for 1 batch of cookies calls for 3/4 cup of flour, to determine how much flour is required to bake 1 1/2 batches of cookies, the following calculation must be performed:
3/4 = 0.75
1/2 = 0.5
1 = 0.75
1.5 = X
1.5 x 0.75 / 1 = X
1.125 = X
0.125 = 1/8
Thus, 1 1/8 cups of flour are required to bake 1 1/2 batches of cookies.
Simplify the algebraic expression by combining the like (or similar) terms -3+5y+9
Answers
Answer:
5y+6
Step-by-step explanation:
-3 and 9 are like terms which can be simplified to 6.
Answer:
5y+6
Step-by-step explanation:
-3+5y+9
=-3+9+5y
=6+5y
=5y+6
o The day before the exam, Rebecca does a practice run. She attempts 20 glass vases and breaks 3 of them. What is her success rate, shown as a decimal?
Answers
Answer:
If the goal is to break the vases: 3/20 = 15.0% or 0.15
If the goal is to not break the vases: 17/20 = 85.0% or 0.85
Angle 3 is a supplement of angle 4. If the m of angle 3 is 100 degrees, what is the m of angle 4?
Answers
Answer: 80
Step-by-step explanation: Supplements mean they add up to 180. is m of 3 is 100, then m of 4 must be 80 to add up to 180. Hope this helps!