Answers
The slope is 5 and the y-intercept is -2000.
(b) The slope tells us about the rate of change in weekly profit and the y-intercept tells us about the minimum profit.
(c) The situation can be modeled as y = 5x -200. Here, y= profit per week and x= number of customers per week.
(d) If the state world roller rink reached a maximum capacity of 2,500 customers per week then the weekly profit will be $10,500.
What is meant by slope intercept form?In order to make the y-intercept (where the line crosses the vertical y-axis) and slope (steepness) immediately apparent, a line's equation must be written in the slope-intercept form. This version is frequently known as y = mx + b. the equation of a straight line in the form of y = mx + b, where m is the line's slope and b is its y-intercept. The slope intercept formula y = mx + b is used when you know the line's slope and the provided point is also the line's y-intercept (0, b). y = mx + b, where m represents the line's slope, is the slope-intercept form of a line.
(a) Consider two points
(x₁, y₁) = (400, 0)
(x₂, y₂) = (500, 500)
The slope is given as
m = (y₂ - y₁)/ (x₂ - x₁)
= (500-0)/(500-400)
= 500/100
= 5
To find y- intercept put (x, y) = (400,0) in y= mx+b (slope-intercept form of a line)
0 = 5(400)+b
0 = 2000 + b
b= - 2000
(b) The slope tells us about the rate of change in weekly profit and the y-intercept tells us about the minimum profit.
(c) Let the number of customers per week = x
And the profit per week = y
Then, the situation can be modeled using slope-intercept form as
y = 5x -200
(d) Put x= 2500 in y = 5x -200
y = 5(2500)-2000
= 12,500-2000
= 10,500
To know more about slope intercept from, visit:
brainly.com/question/9682526
#SPJ1
Related Questions
PART B
How can the stage manager use the constant of proportionality to find the
dimensions of any new props the director requires?
Answers
a) the constant of proportionality multiplies every actual linear dimension
b) height of a can of fruit juice is 3.85 inches high
What is Proportionality?
The term proportionality describes any relationship that is always in the same ratio.
Explanation for answer:
Since the desire is to have students look twice as tall, we expect the constant of proportionality to be [tex]\frac{1}{2}[/tex].
Instead, we're told that the stage manager is using a height of 44 inches to represent an 80-inch door.
This means their constant of proportionality is [tex]\frac{40}{80} = 0.55[/tex]
a) Any new props can be scaled by this factor (0.55) to find their height on set.
b) A 7-inch can would be scaled to [tex]7\times 0.55 = 3.85\ inches[/tex]
Question: The school's theater club is building sets that will make ordinary students look like giants. The actors need a door, a table, and a stool that will make them look almost twice as tall!
DOOR: actual height is 80 inches and Height on Set is 44 inches
TABLE: actual height is 28 inches
STOOL: actual height is 18 inches
How can the stage manager use the constant of proportionality to find the dimensions of any new props the director requires?
What should the height of a can of fruit juice used as a prop be if its actual height is 7 inches? Show your work.
Find out more about proportionality:
https://brainly.com/question/28413384
#SPJ13
If the sales tax rate is 5% in Texas, then how much sales tax would you pay in Houston for a $52 bag of dog food?
Please answer quickly!
Thank you ^^
Answers
The cost of the sales tax in Houston is $ 2.60 and the total cost of bag of dog food is $ 54.60
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
The sales tax percentage in Texas = 5 %
= 5 / 100
= 0.05
The cost of 1 bag of dog food in Houston = $ 52
Now ,
The sales tax cost is calculated by the equation ,
The sales tax cost =
Sales tax percentage in Texas x cost of 1 bag of dog food in Houston
The sales tax cost = $ 52 x 0.05
= $ 2.60
And , the total cost of 1 bag of dog food = cost of 1 bag of dog food in Houston + sales tax cost
Total cost of 1 bag of dog food = $ 52 + $ 2.60
= $ 54.60
Therefore , the sales tax cost is $ 2.60
Hence , the sales tax cost to pay in Houston is $ 2.60 and the total cost of bag of dog food is $ 54.60
To learn more about equation click :
https://brainly.com/question/10413253
#SPJ1
6x^2+12x+63=0 solve by factor
Answers
Answer:
x=2 and =-4
Step-by-step explanation:
The three angles of a triangle measure x,y and 39. What is the equation to solve ?
Answers
The equation to solve when the three angles of a triangle measure x,y and 39 is x + y + 39 = 180°.
What is an equation?An equation is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe the scenario.
It is vital to note that an equation is a mathematical statement which is made up of two expressions that are connected by an equal sign.
It is important to note that the total angles in a triangle is 180°.
Therefore, in this case, the angles will be illustrated thus:
x + y + 39 = 180. This illustrates the equation.
Learn more about equations on:
brainly.com/question/2972832
#SPJ1
In the fraction three-fifths, which statement best describes the denominator?
A. It tells the number of equal parts out of the total number of parts.
B. It tells how many are shaded.
C. It represents the number of equal parts into which the whole is divided.
D. The denominator means three out of five are shaded.
Answers
Answer:
D. The denominator means three out of five are shaded
I need help with this geometry question
Answers
The value of x will be 9.8 m.
The value of y will be 11.2 m.
What is mean by Triangle?
A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.
Given that;
The two triangles are similar.
Now,
Since, The two triangles are similar.
So, We get the sides are proportional to each other.
Hence, We can formulate;
⇒ 4/5.6 = 7/x
Solve for x as;
⇒ x = 7 × 5.6 / 4
⇒ x = 9.8 m
And, 4/5.6 = 8/y
Solve for y;
⇒ y = 8 × 5.6 / 4
⇒ y = 11.2 m
Thus, The value of x will be 9.8 m.
The value of y will be 11.2 m.
Learn more about the triangle visit:
https://brainly.com/question/17335144
#SPJ1
What is the equation of the line that passes through the point (4, 6) and has a slope
of o?
Answers
Which graph represents an odd function?
There are 6 points on a coordinate plane. The points are (negative 5, 3), (negative 3, 1), (negative 1, 1), (1, 3), (3, negative 5), (5, negative 1).
There are 8 points on a coordinate plane. The points are (negative 4, 2), (negative 3, negative 1), (negative 1, negative 3), (0, 1), (1, 0), (2, negative 4), (4, 5), (5, 4).
There are 8 points on a coordinate plane. The points are (negative 4, 0), (negative 3, 1), (negative 2, negative 3), (negative 1, negative 2), (1, 2), (2, 3), (3, negative 1), (4, 0)
There are 11 points on a coordinate plane. The points are (negative 4, 3), (negative 4, 4), (negative 3, 5), (negative 2, 1), (negative 1, negative 1), (0, negative 3), (1, negative 1), (2, 1), (3, 5), (4, 3), (4, 4).
Answers
Answer: first graph
Step-by-step explanation:
A candidate for mayor is calling 882 registered voters to remind them about the upcoming election if the candidate has 49 volunteers and each person calls the same numbers of voters how many voters will volunteer call
Answers
The number of voters that each volunteer call is 18.
What is voting?It is important to note that voting is done to choose a particular person during elections.
In this case, the candidate for mayor is calling 882 registered voters to remind them about the upcoming election and the candidate has 49 volunteers.
Since they gave same number of voters, this will be:
= Number of voters / Number of volunteers
= 882 / 49
= 18
Learn more about vote on:
brainly.com/question/1330417
#SPJ2
Consider the function graphed at right.
The function has a maximum
of 3
The function is increasing on the interval(s):
The function is decreasing on the interval(s):
at x =
-4
4
-32
-5--
3 4 5
1 2 3 4 5
Answers
Answer:
heyyyyyyyyyyyyyyyyyyyyyyyy
The monthly cost of operation at a company, C, given in dollars as a function of the number of units produced per month, u, is given below.
C = $3,173 + $31u
If the company wants to keep the cost of operation under $14,000 per month, what is the maximum number of units they can produce?
A. 3,490
B. 350
C. 3,491
D. 349
Answers
If the company wants to keep the cost of operation under $14,000 per month, The maximum number of units they can produce is: D. 349.
How to find the number of units?Given function:
C = $3,173 + $31u
Hence,
Let u represent number of units
Let c represent the operation cost
Where c = $14,000 per month
$14,000 = $3,173 + $31u
Combine like terms
$14,000 - $3,173 = $31u
$10,827 = $31u
Divide both side by $31u
u = $10,827 / 31
u = 349 units
Therefore the correct option is D.
Learn more about number of units here: https://brainly.com/question/26770986
#SPJ1
3. Lois Denominator, a mathematics examiner, receives £514.80 after tax has been deducted at 22% for marking papers. Calculate Lois’ pay before the tax had been deducted.
Answers
Lois’ pay before the tax had been deducted is £660.
Given:
Lois Denominator, a mathematics examiner, receives £514.80 after tax has been deducted at 22% for marking papers.
22% = 514.80
divide by 22 on both sides
22%/22 = 514.80/22
1%= 23.4
= 514.8/0.78
= 5148/10/78/100
= 5148*100/10*78
= 66*100/10
= 66*10
= £660.
Therefore Lois’ pay before the tax had been deducted is £660.
Learn more about the mathematics examiner here:
https://brainly.com/question/20297287
#SPJ1
Kaleigh paid $37.45 for a calculator, after-tax, and the tax rate is 7%. What was the original cost of the calculator?
Answers
Step-by-step explanation:
that means that
$37.45 = 107%
as the price was 100% base price + 7% tax.
1% = 107%/107
100% = 1% × 100 = 107% × 100 / 107
so, the basic price (the "original cost") is
37.45 × 100/107 = $35.00
Rewrite −12(4x + 5y) using distribution.
−48x + 60y
−48x + 5y
−48x − 60y
−4x − 17y
Answers
To distribute this, multiply each term in the parentheses by -12
-12(4x) + -12(5y)
-48x - 60y
Hope this helps :)
Comment if you need any more explanation
Answer:
-48x - 60y
Step-by-step explanation:
Distributive Property of multiplication over addition:
[tex]\boxed{a(b + c) = ab + ac}[/tex]
Apply the distributive property to the given expression:
[tex]\begin{aligned}-12(4x + 5y) & = -12 \cdot 4x + (-12) \cdot 5y\\& = -48x +(- 60y)\\&=-48x-60y\end{aligned}[/tex]
Therefore, the given expression rewritten using distribution is:
-48x - 60yIf LM = 2x - 9 and KN = x + 15 in rhombus KLMN, find the value of x.
Answers
The value of x in the rhombus is 24 units.
According to the question,
We have the following information:
LM = 2x - 9 and KN = x + 15 in rhombus KLMN.
Now, we know that in a rhombus opposite sides are equal. In this case, LM and KN are opposite sides.
So, we have the following expression:
2x-9 = x+15
Adding 9 to both sides of the equation:
2x = x+15+9
2x = x+24
Subtracting x from both sides of the equation:
2x-x = 24
x = 24
Hence, the value of x for the given rhombus is 24 units.
To know more about rhombus here
https://brainly.com/question/27870968
#SPJ1
d) Three bus services A, B and C arrive at a station. Service A arrives at the station every 15 minutes, service B arrives every 20 minutes and service C arrives every 30 minutes. All three buses arrive at the station together at 9 a.m. At what time will the three buses next arrive at the station. (Decide which will you use to find the answer: GCF or LCM)
Answers
The time that the three buses will next arrive at the station, given the time between their individual arrivals is 10 am.
How to find the time of arrival?Service A arrives every 15 minutes. Service B arrives every 20 minutes. Service C arrives every 30 minutes.
The goal is to find the time when all services arrive at the same time. This can be found by finding the LCM of all three times. This will show the shortest time till all services arrive.
The LCM of 15 minutes, 20 minutes, and 30 minutes is 60 minutes.
The three bus services will arrive at the same time in 60 minutes which is:
= 9 am + 60 minutes
= 10 am
Find out more on LCM at https://brainly.com/question/16054958
#SPJ1
Which graph represents a system of equations that has no solution?
Answers
Answer:
It is A
Step-by-step explanation:
I have brainly tutor and had that exact question
Select the correct answer.
Which set of absolute values is compared correctly?
A. -71 <181<|9|<1-10|
B.1-41 <1-3/<13<|4|
C. 1211-51> |-7|>1-81
D. 1-41>19> |-31 >|-10|
Answers
Answer: A
Step-by-step explanation:
The absolute value of a number is its relative distance from zero, so it doesn't matter if it is negative. For example, -3 and 3 are both 3 units away from zero on the number line.
A company's identification card consists of 4 letters followed by 2 digits. How many cards can be
made if repetition of digits are allowed, but letters must only be consonants and have NO
repetition. Note: y is not a vowel.
Answers
The possible cards can be made 6719448100.
What is permutation & combination?
Subsets of a set can be created in two separate ways combination and permutation. The subset's components can be listed in any order when combined. The components of the subset are listed in a permutation in a certain order.
We have,
Letters must only be consonants = 26 - 5.
So, the total number of consonants are 21.
There are 21 choices for the first letter, 21 choices for the second letter, 21 choices for the thirds letter, 21 choices for the fourth letter. For each of these letters, therefore 21 × 21 × 21 × 21 = 194481 possible pairs of letters.
There are 10 possibilities for the first digit & 10 possibilities for the second. therefore there are 10 x 10 = 100 different numbers.
Combining these results, it follows that there are 67194481 x 100 = 6719448100 different cards.
Hence, The possible cards can be made 6719448100.
To learn more about the permutation & combination visit,
https://brainly.com/question/4658834
#SPJ9
Find a formula for the nth term in this
arithmetic sequence:
a1 = 9, a2 = 13, a3 = 17, a4 = 21, ...
an =?n+
Answers
Answer: an=4n+5
Step-by-step explanation:
a1 = 9, a2 = 13, a3 = 17, a4 = 21, ...
A formula for the nth term of the arithmetic sequence:
[tex]a_n=a_1+d(n-1)[/tex]
where: a₁ - is the first term of the arithmetic sequence
d - is the difference between the terms of the arithmetic sequence
d=a₂-a₁=a₃-a₂=a₄-a₃= ...
d=13-9=17-13=31-17= ...
d=4
n - is the number of the arithmetic sequence term
[tex]a_n=9+4(n-1)\\\\a_n=9+4n-4\\\\a_n=4n+5[/tex]
The scatter plot shows the relationship between the number of coffee drinks sold and the total expenses of a coffee shop.
The slope of the line is....
The intercept of the line is.....
The regression equation is
Answers
For the linear function built from the scatter plot, it is found that:
The slope of the line is of: 5.The intercept of the line is of: b = 500.The equation is of: y = 5x + 500.What is a linear function?The slope-intercept representation of a linear function is the rule presented as follows:
y = mx + b
The coefficients of the function and their meaning are listed as follows:
m is the slope of the function, representing the change in the numeric value of the output variable y when the input variable x increases by one.b is the y-intercept of the function, which is the numeric value of the output variable y when the input variable x has a value of 0.From the graph, we have that when x = 0, y = 500, hence the intercept of the line is:
b = 500.
When the input increases by 200, the output increases by 1000, hence the slope is:
m = 1000/2 = 5.
Thus the equation is:
y = 5x + 500.
Missing InformationThe graph is given by the image at the end of the answer.
More can be learned about linear functions at https://brainly.com/question/24808124
#SPJ1
If x = -4 and y = 3, what is the value of 1/2x + 3xy^2
Answers
If x = -4 and y = 3, then the value of 1/2x + 3xy² is -110.
What is a value function?
The value function represents the optimal payoff of the system over the interval [t, t1] when started at the time- t state variable x(t)=x.
What is a variable?
A quantity that could take on any of a number of different values. : a sign that denotes a variable. : anything has a range. : a variable that might alter in a scientific experiment.
Here, we have
x = -4 and y = 3
then by putting the value of a function in a given equation, we get
1/2*(-4) + 3*(-4)*(3)²
= -110
Hence, If x = -4 and y = 3, then the value of 1/2x + 3xy² is -110.
To learn more about the value function from the given link
https://brainly.com/question/22788434
#SPJ13
A solution contains 7% salt. How much water should be added to 30 ounces of this solution to make a 5% solution?
Answers
12 ounces of water.
Step-by-step explanation:1. Set the initial values.Total mass of the solution: 30 ounces.
Total mass of salt (solute): (30*0.07)= 2.1 ounces.
Total mass of water (solvent): (30*0.93) 27.9 ounces.
2. Find an equation that relates amount of water and percentage of salt.
Since we know that the amount of salt is 2.1 ounces, and it has to remain constant, we have to create a function such that the variable is the amount of water and it gives us the percentage of solution we are looking for. The function should look like this:
[tex]\frac{2.1}{x} =0.05[/tex]; where x is the mass of the water in the solution.
Side note: The number "0.05" is 5% converted into a decimal.
3. Solve the equation for x.[tex]\frac{2.1}{x} =0.05\\ \\\frac{x}{2.1} =\frac{1}{0.05} \\ \\x=\frac{2.1}{0.05} \\ \\x=42[/tex]
42 would be the total amount of ounces the solution should have in order to be a 5% solution. Therefore, 12 ounces (42-30) have to be added.
4. Conclude.12 ounces of water have to be added to this solution in order to make it a 5% solution, where 2.1 ounces is salt and 39.9 is water.
The second and fifth terms of a geometric sequence are 750 and -6 respectively. Find the
common ratio and first term of the sequence.
Answers
Step-by-step explanation:
T2= -6
T5=750
ar=-6
ar4=750
both a's cancel each other
we have;
r=-6
r4=750
r4-1(The law of indices) =750
r3=750
r=3√750
r=9.1
Select the correct answer. Four figures. Figure 1 shows a right triangle A C B with a line D E parallel to base B C. Figures 2, 3, and 4 shows a triangle A B C with a line D E parallel to base B C. In which figure is ? A. figure 1 B. figure 2 C. figure 3 D. figure 4
Answers
Answer: going to take a wild guess and say figure 2 or figure 4 is correct but I'm going with figure 2
Step-by-step explanation:
Answer: Figure 4
Step-by-step explanation:
I got it right on Edmentum
Eve needed to collect the eye color of 50 random people for a high school statistics project. Being shy, she felt more comfortable collecting the data from 20 arbitrary classmates, 12 arbitrary neighbors, and 18 arbitrary members of her bible study group. Upon hearing of her data collection process, her project partner, Adam, stated that all the data was useless. His rationale was that the data was not truly random since Eve knew the people in her sample. Adam believed random data must come from strangers. Do you believe Adam is correct or is Eve's data actually random? Explain your position.
Answers
Eve's data is a random sampling since she picked the participants randomly.
What is a random sampling?A simple random sample is a subset of a population chosen at random. This sampling strategy gives each person of the population an exact equal chance of being chosen, reducing the likelihood of selection bias.
To be considered a truly random sample, every subject in your target demographic must have an equal chance of being chosen. Conducting a study to estimate the length of time college students workout at your campus each week is an example of breaking this assumption.
In this case, Eve needed to collect the eye color of 50 random people for a high school statistics project and she felt more comfortable collecting the data from 20 arbitrary classmates, 12 arbitrary neighbors, and 18 arbitrary members of her bible study group. In this case, she picked them randomly. In Adam's case, it doesn't necessarily have to be strangers.
Learn more about sampling on:
https://brainly.com/question/24466382
#SPJ1
A certain vehicle can accelerate from a standing start to a speed of v(t) = −0.24t2 + 12t feet per second after t seconds (for 0 ≤ t < 30).
a.
Find a formula for the distance that it will travel from its starting point in the first t seconds. [Hint: Integrate velocity to find distance, and then use the fact that distance is 0 at time
t = 0.]
b.
Use the formula that you found in part (a) to find the distance (in ft) that the car will travel in the first 10 seconds. (Round your answer to the nearest whole number.)
Answers
The distance (in ft) that the car will travel in the first 10 seconds is 16.8 feet.
What is the relation between speed and distance?Speed describes how accelerated something or somebody is moving. If you know the distance traveled and the time it took, you can calculate the average speed of an object.
The speed formula is speed = distance/time.
We have been given certain vehicles that can accelerate from a standing start to a speed of v(t) = −0.24t² + 12t feet per second after t seconds (for 0 ≤ t < 30).
Then the distance that it will travel from its starting point in the first t seconds is;
[tex]\int\limits^{30}_b {v(t) } \, dx \\\\\\\int\limits^{30}_b {-0.24t^2 + 12t } \, dt \\\\\\\int\limits^{30}_b {-0.48t + 12} \, dt \\\\-0.48(30) + 12\\\\14.4 + 12 = 26.4[/tex]
At zero it will be 12 feet.
b. the distance (in ft) that the car will travel in the first 10 seconds.
-0.48(10) + 12 = 16.8 feet.
Learn more about speed here;
https://brainly.com/question/7359669
#SPJ1
A tank contains 60 kg of salt and 2000 L of water. Water containing 0.8kgL of salt enters the tank at the rate 8 L/min. The solution is mixed and drains from the tank at the rate 2 L/min. A(t) is the amount of salt in the tank at time t measured in kilograms.
A(t)= ?kg
Answers
Transcribed image text: (1 point) A tank contains 60 kg of salt and 2000 L of water. Water containing 0.8 min of salt enters the tank at the rate 6 min. The solution is mixed and drains from the tank at the rate 3 IA(t) is the amount of salt in the tank at time t measured in kilograms. min (a) A(0) = (kg) = 0.
#SPJ1
Answer: yes
Step-by-step explanation:
caliper assessment Choose the answer that best completes the visual analogy #64
Answers
The answer that best completes the visual analogy of caliper is the first option (picture attached)
How to get the next movement of the caliperInformation given in the question
A polygon of 5 sides
Visual analogy refers to using the power of sight to detect of feel things
A polygon of 5 sides is called pentagon is used to describe the caliper
The movement is forecasted by:
Firstly, the question mark symbol "?" the line mark will go the spot the symbol ? appearedSecondly, the dot at the center will not be dark but remain a hollow spotconsidering these the first option become the best option
The line mark will align where the ? was positioned and the center will not be a dark spot
Learn more about Visual analogy here:
https://brainly.com/question/28427170
#SPJ1
Type the area of the rectangle into the box.
Answers
Answer:
30
Step-by-step explanation:
Answer:
30
Step-by-step explanation:
A = 15 x 2 = 30