Answers
Part a
Remember that the linear equation in slope-intercept form is
y=mx+b
where
m is the slope or unit rate
b is the y-intercept or initial value
In this problem
the equation is of the form
C=m(n)+b
where
m=8.50
b=350
therefore
C=8.50n+350Part b
A reasonable domain for n (number of cups)
Remember that the number of cups cannot be a negative number
so
the domain is the interval [0, infinite)
but a reasonable domain could be [0, 500]
Find out the range
For n=0 -----> C=350
For n=500 ----> C=8.50(500)+350=2,100 ZAR
the range is the interval [350,2,100]
Part c
calculate the cost
For n=100 cups ----> C=8.50(100)+350=1,200 ZAR
For n=200 cups ----> C=8.50(200)+350=2,050 ZAR
For n=400 cups ---> C=8.50(400)+350=3,750 ZAR
Part d
Average cost
Divide the total cost by the number of cups
For 100 cups ------> 1,200/100=12 ZAR per cup
For 200 cups ----> 2,050/200=10.25 ZAR per cup
For 400 cups ----> 3,750/400=9.38 ZAR per cup
Part e
it is better to order more cups, to reduce the initial ZAR 350 cost.
Part f
In this problem we have the ordered pairs
(200, 2150) and (400, 3750)
Find out the slope m
m=(3750-2150)/(400-200)
m=8 ZAR per cup
Find out the linear equation
C=mn+b
we have
m=8
point (200,2150)
substitute and solve for b
2150=8(200)+b
b=2150-1600
b=550
therefore
The linear equation is
C=8n+550Part g
A reasonable domain could be [0, 600]
Find out the range
For n=0 ------> C=550
For n=600 ----> C=8(600)+550=5,350
The range is the interval [550,5350]
Part h
The gradient is the same as the slope
so
slope=8
that means ----> the cost of each cup is 8 ZAR
Part i
For n=600
C=8(600)+550=5,350 ZAR
Part j
we have the inequality
8n+550 < 8.50n+350
Solve for x
550-350 < 8.50n-8n
200 < 0.50n
400 < n
Rewrite
n > 400
For orders more than 400 cups is more effective to order from Cupomatic
Verify
For n=401
C=8n+550=8(401)+550=3,758 ZAR
C=8.50n+350=8.5(401)+350=3,758.5 ZAR
the cost is less in CUPOMATIC, is ok
the answer is
For orders more than 400 cups is more effective to order from CupomaticRelated Questions
how many seconds does it take until the ball hits the ground ?
Answers
Given:
The quadratic model of the ball is given as:
[tex]h(t)=-16t^2+104t+56[/tex]Required:
Find the time when it takes to hit the ground.
Explanation:
When the ball hits the ground then h(t)=0.
[tex]\begin{gathered} -16t^2+104t+56=0 \\ -8(2t^2-13t-7)=0 \\ 2t^2-13t-7=0 \end{gathered}[/tex]Solve the quadratic equation by using the middle term splitting method.
[tex]\begin{gathered} 2t^2-14t+t-7=0 \\ 2t(t-7)+1(t-7)=0 \\ (t-7)(2t+1)=0 \\ t=7,-\frac{1}{2} \end{gathered}[/tex]Since time can not be negative.
So t = 7 sec
Final Answer:
The ball will take 7 sec to hits the ground.
I need help with thisIt asks to graph the functionIf you can, use Desmos to graph
Answers
Given the function
[tex]f(x)=\cot (x+\frac{\pi}{6})[/tex]The graph of the function is dhoe below
Isabella and a friend dine out. They have a bill of $52.67. How much will the bill be after a sales tax of 9% and a 30% tip?
Answers
The bill is starting at 52.67
we have to add the percentages for the sales tax and the tip
[tex]52.67+(52.67)\cdot0.09+(52.67)\cdot0.3=\text{Total}[/tex]solve and find the total
[tex]73.2113=\text{Total}[/tex]3. (02.04 MC)
Choose the equation that represents a line that passes through points (-6, 4) and (2, 0).
Answers
The answer to the question is here
If the diameter of a quarter is 24.26 mm and the width of each quarter is 1.75 mm, to the nearest tenth, what is the approximate surface areaof the roll of quarters? Hint there are 40 quarters in a roll of quarters.A)14,366,2 mm
Answers
For this problem, we are given the dimensions of a quarter and we need to determine the surface area of a roll of quarters.
We can approximate the roll as a cylinder, where the height is the sum of the heights of all the quarters and the dimater is equal to the diameter of one quarter. Therefore we have:
[tex]\begin{gathered} A_{base}=\pi r^2=\pi(\frac{24.26}{2})^2=462.24\text{ mm^^b2}\\ \\ h=40\cdot1.75=70\text{ mm}\\ \\ L_{base}=2\pi(\frac{24.26}{2})=76.22\text{ mm}\\ \\ A_{lateral}=70\cdot76.22=5335.4\text{ mm^^b2}\\ \\ A_{surface}=2\cdot462.24+5335.4=6259.88\text{ mm^^b2} \end{gathered}[/tex]The surface area is equal to 6259.88 mm, the correct option is C.
on a map where each unit represents one kilometer two marinas are located at p(4,2) and q(8,12). if a boat travels in a straight line from one marina to the other how far does the boat travel. Answer choices: 14 kilometers 2^296 kilometer 2^5 kilometers
Answers
Solution
Step 1:
Write the two given points:
p(4,2) and q(8,12)
Step 2
Find the distance between the two points:
[tex]\begin{gathered} Distance\text{ = }\sqrt{(8-4)^2+(12-2)^2} \\ \\ =\text{ }\sqrt{4^2+10^2} \\ \\ =\text{ }\sqrt{16+100} \\ \\ =\text{ }\sqrt{116} \\ \\ =\text{ 2}\sqrt{29} \end{gathered}[/tex]Answer
[tex][/tex]I need help with this
Answers
The bike you have been saving for is discounted 25%. You have $400 saved to purchase it. The original, non-discounted price of the bike is $450. There is a 5.44% sales tax added to the price of the bike. After you purchase the bike with the discount and sales tax, how much money will you have left over? Round your answer to the nearest dollar.
Answers
1) Let's begin considering that our budget is $400.
Since the bike is discounted by 25%, we can get to know the price with this formula:
[tex]400\times(1-0.25)=\$300[/tex]2) Note that there is an increase in the price since there are taxes to pay. The original price is taken into consideration to charge the tax. So, let's find how much we have to pay:
[tex]450\times0.0544=\$24.48[/tex]So, let's add that to the discounted price:
[tex]\$300+\$24.48=\$324.48[/tex]3) Since I've got $400 let's find how much is left after that purchase:
[tex]\$400-\$324.48=\$75.52\approx\$76[/tex]Note that as requested we rounded off to the nearest dollar.
Thus, that's what's left after the purchase
Gordin has 4.1 GB of data in one 4-week billing cycle on his cell phone. Any unused data will roll over to the next cycle. The table shows how much data Gordon uses each week before his next billing cycle. WEEK. DATA USAGE (IN GB) 1. 0.8 2. 1.3 3. 0.9 4. 1.1How much data does Gordon have left to roll over to the next billing cycle at the end of the four weeks?A. 0 GB of dataB. 0.8 GB of datac. 3 GB of data
Answers
Gordan have left 0 GB to roll over to the next billing cycle at the end of the four weeks.
What is Addition?
The sum of all the numbers are called the Addition of numbers.
Given that;
Gordin has 4.1 GB of data in one 4-week billing cycle on his cell phone.
And, The table shows how much data Gordon uses each week before his next billing cycle as;
WEEK = 1 2 3 4
DATA USAGE = 0.8 1.3 0.9 1.1
Now,
Since, Gordin has 4.1 GB of data in one 4-week billing cycle on his cell phone.
And, The table shows how much data Gordon uses each week before his next billing cycle.
So, We can add all the given data usage in 1 to 4 week as;
Data usage = 0.8 + 1.3 + 0.9 + 1.1
= 4.1 GB
Thus, Gordan have left 0 GB to roll over to the next billing cycle at the end of the four weeks.
Learn more about the addition visit:
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From 2014-2015 to 2024-2025, the number of students enrolled in an associate degree program is projected to increase by 23.1 %. If the enrollment in associate degree programs in 2014-2015 is 6,400,000 , find the increase and the projected number of students in an associate degree program in 2024-2025.
Answers
The increase in number will be 1,478,400.
The projected number of students in an associate degree program in 2024-2025 is 7878400.
How to calculate the value?The the number of students enrolled in an associate degree program is projected to increase by 23.1 % and the enrollment in associate degree programs in 2014-2015 is 6,400,000.
The increase will be:
= Percentage increase × Enrollment
= 23.1% × 6,400,000
= 1,478,400
The projected number will be:
= Original number + Increase
= 6400000 + 1478400
= 7878400
Learn more about percentages on:
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An airplane travels at 550 mph. How far does the airplane travel in 5 1/2 hours
Answers
Answer:
At a speed of 550mph, the airplane covers 3,025 miles in 5 1/2 hours.
Explanation:
Given:
• The speed of the airplane = 550 miles per hour
,• Time taken = 5 1/2 hours
We want to find out how far the airplane travels.
The distance covered is calculated using the formula:
[tex]Distance=Speed\times Time[/tex]Substitute the given values:
[tex]Distance=550\times5\frac{1}{2}[/tex]Simplify:
[tex]\begin{gathered} Distance=550\times\frac{11}{2} \\ =275\times2\times\frac{11}{2} \\ =275\times11 \\ =3025\text{ miles} \end{gathered}[/tex]The airplane covers 3,025 miles in 5 1/2 hours.
Which of the equations or inequalities below are true?O A. 7-26O B. 7-224O C. 7-23 5O D. 7 - 2 = -5
Answers
Given,
The equation orr inequalities are,
[tex]\begin{gathered} A)7-2\ge6 \\ B)7-2\ne4 \\ C)7-2\leq5 \\ D)7-2=-5 \end{gathered}[/tex]A) In the expression,
7 - 2 = 5
Hence, 7-2 =6 is incorrect.
B) In the expression,
7 - 2 = 5,
Hence,
[tex]7-2\ne4[/tex]Option B is correct.
C) In the expression,
7 - 2 = 5
7 - 2 < 5 is incorrect
Hence, 7 - 2 =< 5 is incorrect.
D)In the expression,
7 - 2 = 5
Hence, 7 - 2 =< -5 is incorrect.
Hence, option B is correct.
which functions are inverses of each other?A. both pair 1 and pair 2B. pair 1 only C. Pair 2 only D. neither pair 1 nor pair 2
Answers
Answer:
The pair one functions are given below as
[tex]\begin{gathered} f(x)=2x-6,g(x)=\frac{x}{2}+3 \\ f(g(x))=2(\frac{x}{2}+3)-6 \\ g(f(x))=\frac{2x-6}{2}+3 \end{gathered}[/tex]Step 1:
From pair 1, substitute the value of x=1 in the
[tex]\begin{gathered} f(x)=2x-6, \\ f(1)=2(1)-6 \\ f(1)=2-6 \\ f(1)=-4 \\ \\ g(x)=\frac{x}{2}+3 \\ g(-4)=-\frac{4}{2}+3 \\ g(-4)=-2+3 \\ g(-4)=1 \end{gathered}[/tex]Step 2:
For pair 2, substitute x=1
[tex]f(x)=7x,g(x)=-7x[/tex][tex]\begin{gathered} f(x)=7x \\ f(1)=7(1) \\ f(1)=7 \\ \\ g(x)=-7x \\ g(7)=-7(7) \\ g(7)=-49 \end{gathered}[/tex]Step 3:
From pair one,
[tex]f(1)=-4,g(-4)=1[/tex]From pair 2,
[tex]f(1)=7,g(7)=-49[/tex][tex]f(x)=y,g(y)=x(\text{inverse)}[/tex]From the above conclusion, we can say that
The final answer is
PAIR 1 ONLY
OPTION B is the right answer
The first 19 terms of the sequence 9, 2, -5, -12,... find the sum of the arithmetic sequence
Answers
To find the sum of the ari
Choose which function is represented by the graph.111032-11-10 9 8 7 6 5 4-3-2-102 3 4 5 6 7 8 9 10 1110O A. 1(x) = (x − 1)(x +2)(x+4)(x+8)B. f(x) - (x-8)(x-4)(x-2)(x+1)C. f(x)=(x-1)(x+2)(x+4)D. f(x)=(x-4)(x-2)(x+1)876544 4 4 & & To-2X
Answers
The factors of a polynomial tell us the points where the graph intersects the x-axis.
From the graph provided in the question, the graph cuts the x-axis at the points:
[tex]x=-4,x=-2,x=1[/tex]Therefore, the factors will be:
[tex]\begin{gathered} x=-4,x+4=0 \\ x=-2,x+2=0 \\ x=1,x-1=0 \\ \therefore \\ factors\Rightarrow(x+4),(x+2),(x-1) \end{gathered}[/tex]Therefore, the polynomial will be:
[tex]f(x)=(x+4)(x+2)(x-1)[/tex]OPTION C is the correct option.
Question 2 write an expression to represent the perimeter of Melissa‘s garden in the terms of X type the correct answer in each box use numerals instead of words
Answers
From the given statement in part A,
There are given that square patch for the tomatoes
Now,
Let x is the length of the tomato patch, w is the width of the garden and L is the length of the garden
So,
[tex]\begin{gathered} L=3x+2 \\ W=x+5 \end{gathered}[/tex]Then,
From the perimeter of the vegetable garden:
[tex]\begin{gathered} P=2(L+W) \\ P=2(3x+2+x+5) \\ P=2(4x+7) \\ P=8x+14 \end{gathered}[/tex]Hence, the perimeter is, 8x + 14.
what is 3 to the negative 8th power divided by 3 to the negative 4th power
Answers
Answer
Answer = 3⁻⁴ = (1/3⁴) = (1/81)
The answer is 3 raised to the power of negative 4 or 3 to the negative 4th power.
Explanation
The law of indices is usually applied when questions that involve same numbers with (different or the same) powers are considered.
When a number carrying a particular power is divided by the same number also carrying another power, the result is that same number raised to the power of the difference between the power of the numerator and the power of the denominator.
It'll be clearer in practice now.
[tex]\frac{3^{-8}}{3^{-4}}=3^{-8\text{ - (-4)}}=3^{-8+4}=3^{-4}[/tex]Hence, the answer is 3 raised to the power of negative 4 or 3 to the negative 4th power.
Hope this Helps!!!
HelpWhich equation can be used to solve for x in the following diagram?
Answers
The sum of the angles is 90° because is a right angle because the square on the angle means it
then if we sum the angles 30° and 2x° we have 90°
[tex]30+2x=90[/tex]or
[tex]2x+30=90[/tex]then right option is A
4. Which of the following represent the distance
formula? Select all that apply.
A d = √(x₁-x₂)² + (y₁ − y₂)²
B d = √(x₂− ×₂)² + (⁄₂ − y,}²
C d = √(x₂+x₂)² + (y₂ + y,)²
D d=√√₂-X₁1² + VY₂ − Y₁1²
Answers
A appears to be the only correct answer
a^2+b^2=c^2
you are solving for c when finding distance, so (a^2 + b^2) must be square rooted, as a whole, not separately
and a = (x1-x2)
and b = (y1-y2)
you can flip the 1 and 2 but you have to flip for both x and y
like x1-x2 means you have to do y1-y2
like x2-x1 means you have to do y2-y1
so both above are correct as long as the order of 1 and 2 stays the same for both x and y
What is the area of the circle to the nearest 10th unit?
Answers
First, lets find the radius of the circle.
For a circle inscribed in a square, the diameter of this circle is equal to the side lenght.
D = 4.4
Since the radius (r) is D/2
r = 4.4/2 = 2.2
Now, we can calcule the area of the circle (A), using the following equation:
[tex]\begin{gathered} A=\pi\cdot r^2 \\ A=\pi\cdot2.2^2 \\ A=4.8\pi units^2 \\ Or,\text{ since }\pi=3.14 \\ A=4.8\cdot3.14 \\ A=15.2\text{ }units^2 \end{gathered}[/tex]What is the measure of EDH?EHFO 10°O 40°50°90
Answers
To find the measure of angle EDH we must solve for x first. Formulating an equation to find x, we have:
5x + 4x= 90 (Given that the sum of the angles EDH and HDG is equal to 90°)
9x = 90 (Adding like terms)
x= 90/9 (Dividing on both sides of the equation by 9)
x= 10
Replacing in the expression for angle EDH, we have:
m∠EDH = 5*(x) = 5*(10) = 50° (Multiplying)
The answer is m∠EDH =50°.
A certain drug dosage calls for 330 mg per kg per day and is divided into four doses (1 every 6 hours). If a person weighs 210 pounds, how many milligrams of the drug should he receive every 6 hours?Round your answer to the nearest milligram. Do not include units with your answer.
Answers
First, we convert the 210 pounds to kilograms as the dose is given in mg per kg.
Recall that:
[tex]1pound=0.453592\text{ kilograms.}[/tex]Therefore:
[tex]210\text{ pounds=95.2544 kilograms.}[/tex]The dose call for 330 mg per kg, therefore, to get the dose for 95.2544 kg, we multiply by 95.2544:
[tex]330*95.2544\text{ mg=31433.952mg.}[/tex]Finally, dividing by 4 we get the dose the person should receive every 6 hours:
[tex]7858.488mg\approx7858mg.[/tex]Answer: [tex]7858.[/tex]
9. ¿Cuál es el equivalente
fraccionario
de 0.2666 ...?
Answers
Answer:
4/15
Step-by-step explanation:
4/15 = 0.26666666...
Sample SpaceFind the number of outcomes in the following experiments. 1. Selecting a letter from the English alphabet
Answers
The English Alphabet consist of 26 letters. The number of outcome of the experiment therefore is 26 which consist of the sample space.
S = {A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z}
Two companies provide service in a community.• The total cost of a service call for x hours of labor at company A is modeled byy = 28x+ 32.5.• The initial charge for a service call at company B is $3 less than at company A, but their hourly rate is 25% greater.What is the expected total cost of a service call for 6 hours of labor at company B?
Answers
Answer:
The expected total cost of a service call for 6 hours of labor at company B is $239.5
Step-by-step explanation:
To solve this, we'll find the expression that models the cost at company B.
First, we'll calculate the hourly rate. We know that is 25% greater than the $28 rate from company A, so we can use a rule of three as following:
This way,
[tex]\begin{gathered} x=28\times\frac{125}{100} \\ \\ \Rightarrow x=35 \end{gathered}[/tex]Therefore, we'll have that the hourly rate for company B is $35.
Now, we know that the charge for service is $3 less than at company A. This way,
[tex]32.5-3=29.5[/tex]We can conclude that the charge for service at company B is $29.5
Using this data, we'll have that the expression that models the cost for company B is:
[tex]y=35x+29.5[/tex]Using x = 6 (six hours of labor),
[tex]\begin{gathered} y=35(6)+29.5 \\ \\ \Rightarrow y=239.5 \end{gathered}[/tex]Therefore, we can conclude that the expected total cost of a service call for 6 hours of labor at company B is $239.5
A. Write an exponential function to model with population Y of bacteria X hours after 2 PM
B. How many bacteria were there at 7 PM that day
Answers
In this problem, we have an exponential growth function of the form
[tex]y=a(b)^x[/tex]where
a=10 bacteria (initial value at 2 pm)
b is the base of the exponential function
[tex]y=10(b)^x[/tex]Find out the value of b
we know that
For x=0 (2 pm), y=10 bacteria
At 5 pm
y=33,750 bacteria
x=(5 pm-2 pm)=3 hours
substitute in the exponential equation
[tex]33,750=10(b)^3[/tex]Solve for b
[tex]b^3=\frac{33,750}{10}[/tex][tex]\begin{gathered} b=\sqrt[3]{\frac{33,750}{10}} \\ b=15 \end{gathered}[/tex]the equation is
[tex]y=10(15)^x[/tex]Part B
At 7 pm
x=(7 pm-2 pm)=5 hours
substitute
[tex]\begin{gathered} y=10(15)^5 \\ y=7,593,750\text{ bacteria} \end{gathered}[/tex]a teacher asks 15 students to estimate an answer to a question the answers or 1, 5, 5, 6, 7, 8, 10, 12 the correct estimate is 7 the teacher wants to calculate how far of the estimate were by finding the absolute value of the difference between each estimate and the answer which estimate was off by the most
Answers
We have the following estimations:
1, 5, 5, 6, 7, 8, 10, 12
The absolute value between each estimate and the answer is calculated as:
Estimate Absolute
Answer value
1 |1-7| = |-6| = 6
5 |5-7| = |-2| = 2
5 |5-7| = |-2| = 2
6 |6-7| = |-1| = 1
7 |7-7| = |0| = 0
8 |8-7| = |1| = 1
10 |10-7| = |3| = 3
12 |12-7| = |5| = 5
So, the estimated answer that was off by the most is 1.
f(x)A6X-868Which of the given functions could this graph represent?OA. f(t) = (x - 1)(x - 2)(x + 1)(x + 2)O B. f(x) = x(x - 1)(1 + 1)Oc. /(x) = x(x - 1)(x - 2)(x + 1)(x + 2)OD. (r) = x(x - 1)(x - 2)
Answers
The Solution:
Given the graph below:
We are required to determine the function that best describes the above graph.
Step1:
Identify the roots of the function from the given graph.
[tex]\begin{gathered} x=-2 \\ x=-1 \\ x=1 \\ x=2 \end{gathered}[/tex]This means that:
[tex]\begin{gathered} x+2=0 \\ x+1=0 \\ x-1=0 \\ x-2=0 \end{gathered}[/tex]So, the required function becomes:
[tex]f(x)=(x-1)(x-2)(x+1)(x+2)[/tex]Therefore, the correct answer is [option A]
hello I just need help with these no need to explain just the answers please
Answers
The two pairs of angles are supplementary
Here, we want to complete the given sentence
We want to find the relationship between two parallel lines which are cut by a transversal
A figure showing the described relationship is given below;
Now, we want to find the relationship between the two marked angles
From what we have, the two marked angles are supplementary
What this mean is that both angles add up to 180 degrees
Solve the system of two linear inequalities graphically.Graph the solution set of the second linear inequality?
Answers
According to the second inequality, y is greater than or equal to -2, which means that the graph will have a solid line, the first step is to pick solid choice.
The boundary line is y=2, we know this by replacing the inequality sign by an equal sign. Two points one this line are (-1,2) and (2,2). We know it because it is an horizontal line that represents a constant function, it means that all the values of y will be 2 (boundary line).
As the equal sign is greater than or equal to, the region that must be shaded is the one above the boundary line.
