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 $5 per pound
Related Questions
Look at this square. Find the value of s.
Perimeter = 4 kilometers
S =
kilometers
Answers
Answer:
equivale 15. kilómetros. te lo aseguiro
One way of checking the effect of undercoverage, nonresponse, and other sources of error in a sample survey is to compare the sample with known facts about the population. About 12% of American adults identify themselves as black. Suppose we take an SRS of 1500 American adults and let X be the number of blacks in the sample. Use a Normal distribution to estimate the probability that the sample will contain between 165 and 195 blacks.
Answers
Solution :
Given :
p = 12% = 0.12
n = 15..
Mean is defined as the product of a sample size n and the probability p such that :
[tex]$\mu_X = np = 1500 \times 0.12$[/tex]
= 180
Standard deviation may be defined as the square of a product of the sample size n, the probability p and the probability 1-p :
[tex]$\sigma_X = \sqrt{np(1-p)}$[/tex]
[tex]$\sigma_X = \sqrt{1500 \times 0.12 \times (1-0.12)}$[/tex]
≈ 12.5857
The z-score is given by :
[tex]$z=\frac {x- \mu}{\sigma } $[/tex]
[tex]$z=\frac {165-180} {12.5857 }$[/tex]
≈ -1.19
[tex]$z=\frac {x- \mu}{\sigma } $[/tex]
[tex]$z=\frac{195-180} {12.5857 }$[/tex]
≈ 1.19
Now determining the corresponding probability using table :
P (165 ≤ X ≤ 195 ) = P (-1.19 ≤ Z ≤ 1.19 )
= 1-2 x P(Z < -1.19)
= 1-2 x 0.1170
= 1-0.2340
= 0.7660
= 76.60%
Given values,
p = 12%= 0.12
n = 1500The mean will be
→ [tex]\mu x = np[/tex]
By putting the values,
[tex]= 1500\times 0.12[/tex]
[tex]= 180[/tex]
The standard deviation will be:
→ [tex]\sigma x = \sqrt{np(1-p)}[/tex]
[tex]= \sqrt{1500\times 0.12\times (1-0.12)}[/tex]
[tex]= 12.5857[/tex]
The z-score will be:
→ [tex]z = \frac{x- \mu}{\sigma}[/tex]
[tex]= \frac{165-180}{12.5857}[/tex]
[tex]= -1.19[/tex]
and,
→ [tex]z = \frac{195-180}{12.5857}[/tex]
[tex]= 1.19[/tex]
hence,
The probability will be:
→ [tex]P(165 \leq X \leq 195) = P(-1.19 \leq Z \leq 1.19)[/tex]
[tex]= 1-2\times P(Z < -1.19)[/tex]
[tex]= 1-2\times 0.1170[/tex]
[tex]= 1-0.2340[/tex]
[tex]= 0.7660[/tex]
[tex]= 76.60[/tex] (%)
Thus the answer above is right.
Learn more about probability here:
https://brainly.com/question/13796006
Keisha’s basketball game started at 3:30 and ended at 4:47. How much time elapsed during the game?
Answers
Answer:
1 hour and 17 min
Step-by-step explanation:
it takes 30 min to get to 4 the another 30 min to get to 4:30 then 17 min to get to 4:47
which expression can be used to find the surface area of the following triangular prism. choose 1 answer.
Answers
Answer:
A is in fact correct.
Step-by-step explanation:
Harry wants to ride his bicycle the same of miles every day. His goal is to ride 46 miles. If he rides 4 miles each morning and 3 miles each night,how many days will it take him to reach 46 miles
Answers
If you have $2000 and you made an investment that cost $400 and it gives back 1000 how much
Answers
Answer:
you made 600 profit
Step-by-step explanation:
2000-400=1600
1600+1000=2600
2600-2000=600
Answer: 2600
Step-by-step explanation:
2000 - 400 = 1600 + 1000 = 2600
everyday at 9:15 a.m. Jesse takes his dog for a walk for 30 minutes. he then takes the next 2 hours to work on his computer before he eats lunch. what time does he eat lunch?
Answers
Answer:
Jesse eats lunch at 11:45 a.m.
Without graphing, tell whether the line containing (6. -3) and (0, -8) is horizontal, vertical, or neither.
A neither
O B. vertical
ci horizontal
Answers
4
Brad goes to bed at 21 25.
He is in bed until 0708 the next day.
Work out the length of time that Brad is in bed.
Answers
Answer:
Step-by-step explanation:
help plss i'm lost i need help
Answers
+14 above zero
-100 feet below sea level
-17 u owe ur aunt
-10 candy bars left over
-9 people who didn’t get burgers
-8 years younger
+11 years older
Answer:
2) +20
4) +14
5) -100
6) -17
7) 10
8) -9
9) -8
10) +11
Step-by-step explanation:
look at the words and it will tell you whether it's positive or negative
ex. one hundred feet below sea level- it says below which means you would be going down
Peterson Packaging Inc. does not currently pay dividends. The company will start with a $0.70 dividend at the end of year three and grow it by 10% for each of the next six years. After six years of growth, it will fix its dividend at $1.36 forever. If you want a 15% return on this stock, what should you pay today given this future dividend stream?
Answers
A recent survey showed that among 100 randomly selected college seniors, 20 plan to attend graduate school and 80 do not. Determine a 68 % confidence interval for the population proportion of college seniors who plan to attend graduate school. (Enter each answer rounded to three decimal places.)
Answers
Answer:
The 68% confidence interval for the population proportion of college seniors who plan to attend graduate school is (0.16, 0.24).
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].
A recent survey showed that among 100 randomly selected college seniors, 20 plan to attend graduate school and 80 do not.
This means that [tex]n = 100, \pi = \frac{20}{100} = 0.2[/tex]
68% confidence level
So [tex]\alpha = 0.32[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.32}{2} = 0.84[/tex], so [tex]Z = 0.995[/tex].
The lower limit of this interval is:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.2 - 0.995\sqrt{\frac{0.2*0.8}{100}} = 0.16[/tex]
The upper limit of this interval is:
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.2 + 0.995\sqrt{\frac{0.2*0.8}{100}} = 0.24[/tex]
The 68% confidence interval for the population proportion of college seniors who plan to attend graduate school is (0.16, 0.24).
The 68% confidence interval for the population proportion of college seniors who plan to attend graduate school is (0.16, 0.24).
What is the p-value?The p-value is also known by the probability value. It is the probability of getting a result that is either the same or more than the actual value.
In a given data with a number n of people surveyed with a probability of success [tex]\pi[/tex] and a confidence level [tex]1-\alpha[/tex], we have the confidence interval of proportions.
[tex]\pi[/tex] ± [tex]\rm z\sqrt{\pi (1-\pi )} /n[/tex]
where z has a p-value of 1-[tex]\alpha /2[/tex]
A recent survey showed that among 100 randomly selected college seniors, 20 plan to attend graduate school and 80 do not.
n = 100, [tex]\pi[/tex] = 20/100 = 0.2
So, [tex]\alpha[/tex] = 0.32 where z has a p-value 1-[tex]0.32 /2 = 0.84[/tex]
z = 0.995
The lower limit of this interval
[tex]\pi -\rm z\sqrt{\pi (1-\pi )} /n\\= 0.2 - 0.995 \sqrt{0.2 \times 0.8} /100\\= 0.16[/tex]
The upper limit of this interval
[tex]\pi -\rm z\sqrt{\pi (1-\pi )} /n\\= 0.2 +0.995 \sqrt{0.2 \times 0.8} /100\\= 0.24[/tex]
Hence, The 68% confidence interval for the population proportion of college seniors who plan to attend graduate school is (0.16, 0.24).
Learn more about p-value ;
https://brainly.com/question/15407907
In Ms. Chance's first period class, there are 9 students with hazel eyes, 10 with brown eyes, 7 with blue eyes, and 2 students with green eyes. Ms. Chance picks a student at random. Which color eyes is the student most likely to have?
Answers
Answer:
Brown eyes
Step-by-step explanation:
10/28 Fraction form
0.3571 Decimal form
35.71 % Percentage form
10 is the greatest number out of all the other colors
the arithmetic sequence ai is defined by the formula: a1 = -53 ai = ai-1 + 6 find the sum of the first 880 terms in the sequence
Answers
Answer:
The sum of the first 880 terms in the sequence is 2,273,920.
Step-by-step explanation:
Arithmetic sequence:
The difference between consecutive terms is always the same, called common difference, and the nth term is given by:
[tex]a_{n} = a_0 + (n-1)d[/tex]
In which d is the common difference.
Sum of the first n terms:
The sum of the first n terms of an arithmetic sequence is given by:
[tex]S_{n} = \frac{n(a_1+a_n)}{2}[/tex]
ai = ai-1 + 6
This means that [tex]d = 6[/tex]
In this question:
Sum of the first 800 terms, so [tex]n = 800[/tex]
First term is -53, so [tex]a_1 = -53[/tex]
The 880th term is:
[tex]a_{880} = -53 + (880-1)*6 = 5221[/tex]
Sum
[tex]S_{n} = \frac{880(-53+5221)}{2} = 440(-53+5221) = 2273920[/tex]
The sum of the first 880 terms in the sequence is 2,273,920.
Help me please I’m not smart -
Answers
Helppp meeeee plssss I would me the world
Answers
Answer:
its 3 trust me
Step-by-step explanation:
Answer:I’m thinking it’s the first one but someone else might know for sure sorry
Step-by-step explanation:
HELP PLEASE ! 15 POINTS NO SCAM LINKS OR REPORTED.
Answers
Answer:
I think it is either C or D
Step-by-step explanation:
I'm so sorry id didn't find the answer, i tried
help pls will give brainliest !!!!
Answers
Answer:
can you retake the picture i cant really see this one very well
Step-by-step explanation:
10^(4x−1)=2^5 round the answer to the nearest tenth
HELP!
Answers
Evaluate the following algebraic expression at x = 4 and simplify your answer.
- 5x – 18 – 7x
Answers
first you need to plug in the x into the equation
-5(4)-18-7(4)
now you solve
-20-18-28
which equals
-66
Round the nearest hundredth. 53.789
Answers
Answer: 53.79
Step-by-step explanation:
Please help and explain
Answers
Answer:
(a)
[tex](2,0)[/tex]
(b)
[tex](0,-2)[/tex]
Step-by-step explanation:
Given
[tex](x_1,y_1)= (4,2)[/tex] --- point
[tex]m =1[/tex] -- slope
Solving (a): The zeros of the function
First, we calculate the equation using:
[tex]y = m(x - x_1) + y_1[/tex]
This gives:
[tex]y = 1 * (x - 4) + 2[/tex]
Open bracket
[tex]y = x - 4+ 2[/tex]
[tex]y = x -2[/tex]
The zeros also is: [tex]y=0[/tex]
[tex]0 = x - 2[/tex]
[tex]x =0+2[/tex]
[tex]x =2[/tex]
So, the solution to be is
[tex](2,0)[/tex]
(b) The y intercept is:
Substitute [tex]x=0[/tex]
[tex]y = 0 -2 = -2[/tex]
We have:
[tex](0,-2)[/tex]
WILL GIVE BRAINLIEST IF SOLVED IN 10 MINS : Solve each equation with the quadratic :
Answers
Answer:
5. x = -1 or x = -3
6. b = -2 or b = 6
7. n = 5 or n = 4
Step-by-step explanation:
5. x² + 4x + 3 = 0
Factorize
x² + 3x + x + 3 = 0
x(x + 3) +1(x + 3) = 0
(x + 1)(x + 3) = 0
Set each of the factors equal to zero and solve for x
x + 1 = 0 or x + 3 = 0
x = -1 or x = -3
6. b² - 4b - 14 = -2
Put all terms on one side of the equation leaving zero on one side
b² - 4b - 14 + 2 = 0
b² - 4b - 12 = 0
Factorize
b² - 6b + 2b - 12 = 0
b(b - 6) +2(b - 6) = 0
(b + 2)(b - 6) = 0
Set each of the factors equal to zero and solve for b
b + 2 = 0 or b - 6 = 0
b = -2 or b = 6
7. n² = 9n - 20
Put all terms on one side of the equation leaving zero on one side
n² - 9n + 20 = 0
n² - 5n - 4n + 20 = 0
n(n - 5) -4(n - 5) = 0
(n - 5)(n - 4) = 0
Set each of the factors equal to zero and solve for b
n - 5 = 0 or n - 4 = 0
n = 5 or n = 4
PLEASE HELP ME!!!! PLEASE HELP QUICK ILL GIVE U 73 POINTS PLS HELP
Answers
Answer:
3
Step-by-step explanation:
In this problem we need to kind of write the picture into an equation so the first thing we see are 4 xs on the far left-hand side this is representing "4x" then we see 5 - blocks on the right which represents "-5" because we have 5 minuses then on the other side we see 7 + blocks which represent just "7". After we identify everything in the picture we can write an equation so 4x -5 = 7. Then we solve so we need to separate x on one side and all the other numbers to the other to do that we can move the -5 to the side the 7 is on and because of math when we move a number to another side of the equation we have to switch the sign it has so if it was -5 then on the other side it would be 5 then we add 7 to 5 which would equal 12. Then we are left with 4x = 12 and to keep x on its own side we need to divide 4 from the other side because it is multiplying on the x side and again we need to switch the sign. then we are left with x=3. Hope this helps!
finding missing angles in triangles worksheet answers house
Answers
Step-by-step explanation:
What exactly are you looking for?
What’s the answer and work for this? Someone please tell me
Answers
Answer:
Step-by-step explanation:
# 12
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
12 is a median of a data
Julio spent $52.43 on batteries. If they cost $7.49/pack, how many packs did he buy?
Answers
Answer:
7
Step-by-step explanation:
52.43 ÷7.74=7
Help me with this question please!
Answers
Answer:
84 in²
Step-by-step explanation:
12+9=21
21x0.5=10.5
10.5x8=84
what is the total of 8 and 4 times y
Answers
Answer:
12y?
Step-by-step explanation:
I’m assuming total meansd addition in this case and multiplying that by a variable or “y” would be 12y
i read the question wrong, nvm.
Reuben will rent a car for the weekend. he can choose one of two plans. the first has no initial fee but costs $0.90 per mile driven. The second plan has an initial fee of $65 and costs an additional $0.70 per mile driven. How many miles would Reuben need to drive for the two plans to cost the same?
Answers
Answer:
80 miles for the .9 one.
Step-by-step explanation: