a The revenue obtained from selling x pizzas is 25x - x²
b The profit obtained from selling x pizzas, is x² + 21x - 109.25
c The break-even points are approximately x = 9.94 and x = 11.06.
d The vertex of the demand equation is (12.5, 12.5).
e The marginal profit at a production level of 1000 pizzas is $11.
f Increasing x by one at a production level of 1000 pizzas will result in a marginal profit of $10.
How to calculate the valuea) Find R(x), the revenue obtained from selling x pizzas.
R(x) = x * p
R(x) = x * (25 - x)
R(x) = 25x - x²
b) Find P(x), the profit obtained from selling x pizzas, and simplify.
Profit is calculated as revenue minus cost.
P(x) = R(x) - C(x)
P(x) = (25x - x²) - (109.25 + 4x)
P(x) = -x² + 21x - 109.25
c) Find the Break-Even point(s) for P(x).
The break-even point is where the profit is zero.
Setting P(x) = 0:
x² + 21x - 109.25 = 0
x = (-b ± ✓(b² - 4ac)) / (2a)
For our equation:
a = -1, b = 21, c = -109.25
x = (-21 ± ✓(21² - 4(-1)(-109.25))) / (2(-1))
x = (-21 ± ✓(441 - 436.5)) / (-2)
x = (-21 ± ✓(4.5)) / (-2)
x = (-21 ± 2.121) / (-2)
x1 = (-21 + 2.121) / (-2) ≈ 9.94
x2 = (-21 - 2.121) / (-2)
≈ 11.06
The break-even points are approximately x = 9.94 and x = 11.06 (rounded to two decimal places).
d) Using the formula x = -b/2a, we can calculate the x-coordinate of the vertex:
x = -(25)/(2*(-1)) = -25/-2 = 12.5
p = 25 - x = 25 - 12.5
= 12.5
Therefore, the vertex of the demand equation is (12.5, 12.5).
e To find the marginal profit, we need to calculate the derivative of the profit function. The profit function is given by P(x) = xp - C(x).
P'(x) = p - C'(x)
C'(x) = 4
Substituting the values into the formula for marginal profit:
MP = p - C'(x) = 25 - x - 4
= 21 - x
To find the marginal profit at a production level of 1000 pizzas (x = 10), we substitute x = 10 into the marginal profit equation:
MP = 21 - 10 = 11
Therefore, the marginal profit at a production level of 1000 pizzas is $11.
f. Increasing x by one at a production level of 1000 pizzas means x will become 11. To find the new marginal profit, we substitute x = 11 into the marginal profit equation:
MP = 21 - 11
= 10
Therefore, increasing x by one at a production level of 1000 pizzas will result in a marginal profit of $10.
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The coordinates of quadrilateral JKLM are J (1,3), K(3, 1), L (-1, -3) and M(-3,-1). What is the perimeter of quadrilateral JKLM?
the coodrinates of JKLM is,
J(1,3) , K(3,1), L(-1,-3) and M(-3,-1)
the length JK is ,
\(\begin{gathered} JK=\sqrt[]{(1-3)^2+(3-1)^2} \\ =\sqrt[]{4+4} \\ =\sqrt[]{8} \\ =2\sqrt[]{2} \end{gathered}\)length KL is,
\(\begin{gathered} KL=\sqrt[]{(-3-1)^2+(-1-3)^2} \\ =\sqrt[]{16+16} \\ =\sqrt[]{32} \\ =4\sqrt[]{2} \end{gathered}\)Length LM is,
\(LM=\sqrt[]{(-3-(-1))^2+(-1-(-3))^2}\)\(\begin{gathered} LM=\sqrt[]{4+4} \\ LM=2\sqrt[]{2} \end{gathered}\)length MJ
\(\sqrt[]{(-1-3)^2+(-3-1)^2}\)\(\begin{gathered} MJ=\sqrt[]{16+16} \\ MJ=4\sqrt[]{2} \end{gathered}\)so, the perimeter = sum of sides,
= JK + KL + LM + MJ
= 2 root 2 + 4root2 + 2root2 + 4root2
= 12 root 2
thus, the perimeter is 12 root 2
60 points! Need Answer Pl
Drag a statement or reason to each box to complete this proof.
Given: Quadrilateral ABCDwith m∠A=(9x)°, m∠B=(6x)°, m∠C=(9x)°, and m∠D=(6x)°.
Prove: x = 12
Let's prove
Sum of all interior angles of a quadrilateral is 360°
\(\\ \rm\rightarrowtail 6x+9x+9x+6x=360\)
\(\\ \rm\rightarrowtail 12x+18x=360\)
\(\\ \rm\rightarrowtail 30x=360\)
\(\\ \rm\rightarrowtail x=12\)
The value of x is,
⇒ x = 12
What is mean by Rectangle?A rectangle is a two dimension figure with 4 sides, 4 corners and 4 right angles. The opposite sides of the rectangle are equal and parallel to each other.
Given that;
Quadrilateral ABCD is shown in figure, with m ∠A=(9x)°, m ∠B=(6x)°,
m ∠C=(9x)°, and m ∠D=(6x)°
Now, We know that;
The sum of all angles in the Quadrilateral are 360°.
Hence , We get;
⇒ ∠A + ∠B + ∠C + ∠D = 360°
⇒ 9x + 6x + 9x + 6x = 360
⇒ 30x = 360
⇒ x = 360/30
⇒ x = 12
Thus, The value of x is,
⇒ x = 12
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Taisha is making birthday gift bags. she wants to put 1/2 pound of chocolate in each bag. she has 4 3/4 pounds of chocolate. how many gift bags could taisha make?
The number of gift bags that Taisha will make is 10.
How to calculate the value?Fractions represent parts of a whole or group of objects. A fraction is made up of two parts. The number at the top of the line is referred to as the numerator. The denominator is the number below the line. It displays the total number of equal parts into which the whole is divided or the total number of identical objects in a collection.
From the information given, Taisha wants to put 1/2 pound of chocolate in each bag and she has 4 \(\frac{3}{4}\) pounds of chocolate.
The number of bags that she needs will be calculated by dividing the fractions given. This will be:
= Total chocolate / Amount in each bag
= 4 \(\frac{3}{4}\) ÷ 1/2
= 19/4 ÷ 1/2
= 19/4 × 2
= 38/4
= 9 \(\frac{1}{2}\)
Therefore, she will need 10 bags.
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A rectangular container that measures 2cm x 11cm x 20cm is completely filled with water. The water is then poured into a hollow cylindrical container of base radius 5cm.
What is the height of water in the cylindrical container?
Answer:
height of water = 5.60 cm
Step-by-step explanation:
To solve this problem, we must first calculate the volume of water present. Since the rectangular container is completely filled, the volume of water is the same as the volume of the container.
∴ Volume of water = volume of rectangular container
= length × width × height
= 2 cm × 11 cm × 20 cm
= 440 cm³
Therefore the volume of the water is 440 cm³.
The water is poured into a cylindrical container. Therefore, to calculate the height of the water in the cylindrical container, we can use the formula for the volume of a cylinder, and then solve for height:
Volume = \(\pi r^2 h\) = 440
⇒ \(\pi \times (5)^2 \times h = 440\)
⇒ \(25\pi \times h = 440\)
⇒ \(h = \frac{440}{25\pi }\)
⇒ h = 5.60 cm
The height of water in the cylindrical container is 5.60 cm.
the sales data for july and august of a frozen yogurt shop are approximately normal. the mean daily sales for july was $270 with a standard deviation of $30. on the 15th of july, the shop sold $315 of yogurt. the mean daily sales for august was $250 with a standard deviation of $25. on the 15th of august, the shop sold $300 of yogurt. which month had a higher z-score for sales on the 15th, and what is the value of that z-score?
The value of the z-score for August 15th was 2.
Based on the given information, to determine which month had a higher z-score for sales on the 15th, we need to calculate the z-scores for both July 15th and August 15th.
For July 15th:
Mean = $270
Standard Deviation = $30
Value of Sales = $315
To calculate the z-score, we use the formula: z = (x - mean) / standard deviation
z = (315 - 270) / 30
z = 1.5
For August 15th:
Mean = $250
Standard Deviation = $25
Value of Sales = $300
To calculate the z-score, we use the formula: z = (x - mean) / standard deviation
z = (300 - 250) / 25
z = 2
Comparing the z-scores, we can see that August had a higher z-score for sales on the 15th. The value of the z-score for August 15th was 2.
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In 32 at-bats,rico got 12 hits. At that rate how many hits would he get in 56 at-bats
The number of hits would Rico get in 56 at-bats is 21 hits if he maintains the same rate of hits per at-bat.
To determine how many hits Rico would get in 56 at-bats, we can use a proportion based on the information given:
Hits / At-bats = Hits / At-bat
We know that Rico got 12 hits in 32 at-bats, so we can plug those values into the proportion:
12 / 32 = Hits / 56
We can then solve for Hits by cross-multiplying:
12 * 56 = 32 * Hits
672 = 32 * Hits
Hits = 672 / 32
Hits = 21
Therefore, if Rico maintains the same rate of hits per at-bat, he would be expected to get approximately 21 hits in 56 at-bats.
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Given that m is parallel to n, what must be true of the two lines? Check all that apply.
Answer:
I don't have the options but I know parallel lines will never touch, they have the same slope, and the distance between the lines never changes
Can someone please help me with this?
Answer:
Yes they are congruent
Option B is correct
Step-by-step explanation:
Opisite sides of parallelogram are congurent so,
BA is congruent to CD (side)
And
BE I congruent to ED (Side)
AE is congruent to EC (Side)
So according to side-side-side congurence theorem triangle ABE is congruent to triangle CDE
Hope you understand :)
The quantities X and Y are proportional
The quantities X and Y are proportional as y = rx then the constant of proportionality r is 1/9.
What is constant of proportionality?Firstly, there is proportional relationship.
Two values x and y are said to be in a proportional relationship if x=ky, where x and y are variables and k is a constant.
The constant k is called constant of proportionality.
WE have been given quantities X and Y are proportional
y = rx
Where r is constant of proportionality.
Then x = 45 and y = 5
Thus,
y = rx
5 = 45r
Now divide by 45 on both side;
r = 5/45
r = 1/9
Therefore, the constant of proportionality r is 1/9.
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What is the Equation of a line that has a slope
of -3 passes to the point (4,-5)
Answer:
y= -3x + 7:)
Step-by-step explanation:
Hope this helps!
Answer:
y = - 3x + 7
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Here m = - 3 , thus
y = - 3x + c ← is the partial equation
To find c substitute (4, - 5) into the partial equation
- 5 = - 12 + c ⇒ c = - 5 + 12 = 7
y = - 3x + 7 ← equation of line
Without multiplying order the following products from least to greatest
Answer:
It would be:
4 5/9 x 1/2
4 5/9 x 10/10
4 5/9 x 6
Step-by-step explanation:
Thi i a pond in the hape of a prim. It i completely full of water. Colin ue a pump to empty the pond. The level goe down by 20cm in the firt 30min. How many minute until completely empty
This is a pond in the shape of a prism. It is completely full of water. Colin has to wait for the pond to completely empty is 2hrs and 30minutes.
We have a pond which is completely filled with the water.
Area of the side face ( trapezium shaped)
= 1/2 x (1.4 + 0.6) x 2
= 2 m²
Volume = area x height (here width)
V = 2x1 = 2 m³
The level goes down by 20cm in the first 30 mins
Volume of water that will be taken down =
=0.2 x 1 x 2
=0.4 m³ ( upper water will form cuboid face)
Now,
⇒0.4 m³ water is taken out in 30 minutes
⇒1 m³ water is taken out in 30/0.4 minutes
⇒2 m³ water is taken out in 30/0.4 x 2 minutes
⇒30x2/0.4
⇒150 minutes.
So the pond will be completely empty in 150 min that is 2hrs30mins.
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A number generator was used to simulate the percentage of people in a town who ride a bike. The process simulates randomly selecting 100 people from the town and was repeated 20 times. The percentage of people who ride a bike is shown in the dot plot.
Which statement is true about the population of the town?
Most likely, 40% to 50% of the town rides a bike.
Most likely, 50% to 60% of the town rides a bike.
Most likely, 60% to 75% of the town rides a bike.
Most likely, 80% to 90% of the town rides a bike.
In the given dot plot, we can see that the percentage of people in a town who ride a bike is shown. We know that the process simulates randomly selecting 100 people from the town and was repeated 20 times. So, the correct option is (A), most likely, 40% to 50% of the town rides a bike.
Now we need to determine which statement is true about the population of the town?Most likely, 40% to 50% of the town rides a bike as we can see that the highest peak in the dot plot is at around 45%.
Also, most of the other data points lie between 40% to 50%. Therefore, most likely, 40% to 50% of the town rides a bike. Thus, option A is the correct answer.
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A table is made using the following two patterns.
Pattern x: Starting number: 6, Rule: add 6
Pattern y: Starting number: 1, Rule: add 1
Complete the table for the given patterns.
2
y
6
1
The terms in pattern y are
times the terms in pattern s.
PLS HELP WILL GIVE BRAINLIEST ALMOST DUE
Which equation could represent the line of best fit for the temperatures based on the altitudes?
Answer:
\(y = - \frac{7}{5} x + 59\)
In a Binomial distribution, where the sample size is 9 and the probability of a success is .45, what is the value of q
The value of q in a Binomial distribution with a sample size of 9 and a probability of success of .45 is 0.55.
The Binomial distribution is a probability distribution that represents the number of successes in a fixed number of independent trials with the same probability of success in each trial. The probability of success in each trial is represented by the letter p and the probability of failure is represented by the letter q, which is equal to 1 minus the probability of success.
In this case, the sample size is 9 and the probability of success is .45, so the probability of failure would be 1 - .45 = .55. Therefore, the value of q in this Binomial distribution is 0.55.
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Find the midpoint of the line segment. (Giving 25 points please hurry)
Answer:
(-4,-3)
Step-by-step explanation:
Answer:
(-4, -3)
Step-by-step explanation:
well, the only points possible are 3 points, a first, 2nd, and 3rd point. And the 2nd point is the mid-point.
the concept of hedonistic calculus is associated with
The concept of hedonistic calculus is associated with utilitarianism and the philosophy of maximizing pleasure and minimizing pain. It is a method for calculating the overall happiness or utility of actions based on the intensity, duration, certainty, propinquity, fecundity, purity, and extent of pleasure or pain they produce.
Hedonistic calculus is a term coined by the philosopher Jeremy Bentham, who was a proponent of utilitarianism. Utilitarianism is an ethical theory that states that the right action is the one that maximizes overall happiness or utility for the greatest number of people. The goal of hedonistic calculus is to measure and compare the happiness or pleasure derived from different actions or situations.
According to Bentham, pleasure and pain are the only relevant factors in determining the moral value of an action. Hedonistic calculus involves quantifying these pleasures and pains in order to assess their overall impact. Bentham proposed seven criteria to evaluate the intensity, duration, certainty, propinquity (nearness in time), fecundity (likelihood of leading to more pleasure or pain), purity (absence of pain mixed with pleasure), and extent of the pleasure or pain produced by an action.
By assigning values to each of these criteria, hedonistic calculus aims to determine the net amount of happiness or utility generated by a particular action or decision. The idea is to maximize pleasure and minimize pain, with the ultimate goal of promoting the greatest happiness for the greatest number of individuals.
Overall, hedonistic calculus provides a systematic approach to assess and compare the consequences of actions based on their impact on pleasure and pain. It serves as a framework for utilitarians to make ethical judgments and decisions by considering the net balance of happiness produced by different choices.
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A student plans to enroll at the university and plans to continue there until earning a PhD degree (a total time of 9 years). If the tuition for the first 4 years will be $7,200 per year and it increases by 5% per year for the next 5 years, what is the present worth of the tuition cost at an interest rate of 8% per year?
The present worth of the tuition cost for a student planning to enroll at the university for 9 years, with the first 4 years costing $7,200 per year and a 5% annual increase for the next 5 years, can be calculated at an interest rate of 8% per year. The present worth is $23,455.297.
To calculate the present worth of the tuition cost, we need to consider the time value of money, which accounts for the fact that money in the future is worth less than money in the present. We can use the concept of present value to determine the worth of future cash flows in today's dollars.
For the first 4 years, the tuition cost is constant at $7,200 per year. To find the present value of these cash flows, we can use the formula for the present value of a fixed cash flow series. Applying this formula, we find that the present value of the first 4 years' tuition cost is
\(7,200 + 7,200/(1+0.08) + 7,200/(1+0.08)^2 + 7,200/(1+0.08)^3.\)
For the next 5 years, the tuition cost increases by 5% per year. We can use the concept of future value to calculate the value of these cash flows in the last year of the 9-year period. Applying the formula for future value, we find that the tuition cost in the last year is \($7,200*(1+0.05)^5.\)
Finally, we can sum up the present value of the first 4 years' tuition cost and the future value of the tuition cost in the last year to obtain the total present worth of the tuition cost for the 9-year period.
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In parallelogram EFGH the measure of angle E is (2x+3) and the measure of angle F is (3x-33) what’s is the measure of angle E
The measure of ∠E = 87° and ∠F = 93°.
What is Parallelogram? What is triangle?In Euclidean geometry, a parallelogram is a simple quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure. A triangle is a polygon with three edges and three vertices. The sum of all the angles of a triangle is 180 degrees. Mathematically -
∠x + ∠y + ∠z = 180°
There are different types of triangles such as -
equilateral triangle , scalene triangle , isosceles triangle etc.
Given is a parallelogram in which EFGH the measure of angle E is (2x+3) and the measure of angle F is (3x - 33).
We can write -
2(2x + 3) + 2(3x - 33) = 360°
4x + 6 + 6x - 66 = 360°
10x - 60 = 360
10x = 420
x = 42
∠E = 2 x 42 + 3 = 84 + 3 = 87°
∠F = 3 x 42 - 33 = 126 - 33 = 93°
Therefore, the measure of ∠E = 87° and ∠F = 93°.
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Can somebody help with me plz
the answer is fifteen (15) weeks
Need help with this
Answer:
y = 130
Step-by-step explanation:
given that y varies directly with x and z then the equation relating them is
y = kxz ← k is the constant of variation
to find k use the condition y = 150 when x = 2.5 and z = 12 , then
150 = k × 2.5 × 12 = 30k ( divide both sides by 30 )
5 = k
y = 5xz ← equation of variation
when x = 4 and z = 6.5 , then
y = 5 × 4 × 6.5 = 20 × 6.5 = 130
The table below represents a linear function for the cost of a gym membership based on the number of months of membership.
Time (month) Cost
1 $105
3 $165
5 $225
7 $285
What is the slope and y-intercept of the linear function?
The slope is ____ and the y-intercept is ___.
Answer:
The slope is 30, and the y-intercept is 75.
Step-by-step explanation:
Use two points from the table, and find the equation of a line given two points.
Point 1: (1, 105)
Point 2: (3, 165)
y = mx + b
slope = m = (y_1 - y_1)/(x_2 - x_1)
m = (165 - 105)/(3 - 1) = 60/2 = 30
y = 30x + b
Use point (1, 105) for x and y.
105 = 30(1) + b
105 = 30 + b
b = 75
y = 30x + 75
The slope is 30, and the y-intercept is 75.
How does the value of the digit 3 in the number 63,297 compare to the value of the digit 3 in the number 60,325? Be sure to include what you know about the place value in your answer. How does the value of the digit 3 in the number 63,297 compare to the value of the digit 3 in the number 60,325? Be sure to include what you know about the place value in your answer.
Answer: See explanation
Step-by-step explanation:
The value of the digit 3 in the number 63,297 is 3,000 while the value of the digit 3 in the number 60,325 is 300.
The difference between value of the digit 3 in the number 63,297 and the value of the digit 3 in the number 60,325 will be:
= 3000 - 300
= 2700
Sherry is buying costume jewelry at an online store. Each pair of earrings costs the same amount
and each bracelet costs the same amount. She can purchase 5 pairs of earrings and 6 bracelets
for $49 or she can purchase 7 pairs of earrings and 1 bracelet for $48.25. Either way, she stays
under her $50 budget. What is the price of a pair of earrings? PLS HELP , IF U EXPLAIN I WILL GIVE BRAINLIEST
Answer:
the 7 pairs of earings because you can buy more for just $1 extra that just geeting 1 thing. that is what i think
Which expression has a value of 35 when p = 7?
StartFraction 49 Over p EndFraction
5p
45 minus p
25 + p
Answer:
5p
Step-by-step explanation:
if p=7, 5p=35
Answer:
5p
Step-by-step explanation:
Monica swims the 200, 400, and 1,000 meter freestyle swimming events. At the last swimming meet she swam the 200m in 1 minute 4 seconds, 400m in 2 minutes 31 seconds, and the 1,000 meter in 7 minutes 11 seconds. What were her average speeds in all these events (meters/second)?
Answer:
a) 200 meters = 3.125 meters/seconds
b) 400 meters = 2.649 meters per second
c ) 1000 meters = 2.320 meters per second
Step-by-step explanation:
The formula for Average speed = Distance/ Time
Monica swims the 200, 400, and 1,000 meter freestyle swimming events.
We are to calculate: average speeds in all these events (meters/second).
At the last swimming meet she swam
For the 200m
Time 1 minute 4 seconds
60 seconds = 1 minutes
Hence, Time = 60 + 4 = 64 seconds.
Average speed = 200m/64 seconds
= 3.125 meters/seconds
For 400m
Time = 2 minutes 31 seconds
1 minute = 60 seconds
2 minutes = 60 × 2 = 120 seconds
Total time = 120 + 31 seconds = 151 seconds
Hence, Speed = 400m/151 seconds
= 2.649 meters per second
For 1,000 meter
Total time = 7 minutes 11 seconds.
1 minute = 60 seconds
7 minutes = 60 × 7 = 420 seconds
Total time = 420 + 11 seconds = 431 seconds
Hence, Speed = 1000m/431 seconds
= 2.3201856148 meters per second
Approximately = 2.320 meters per second
Therefore her speed were
a) 200 meters = 3.125 meters/seconds
b) 400 meters = 2.649 meters per second
c ) 1000 meters = 2.320 meters per second
Answer:
3.125m/s
2.469 m/s
2.320 m/s
Step-by-step explanation:
Average speed = total distance / total time
60 seconds = 1 minute
Converting minute into second = (1 x 60) + 4 = 64 seconds
(2 x 60) + 31 = 151 seconds
(7 x 60) + 11 = 431 seconds
Average speed = 200 meters / 64 seconds = 3.125m/s
Average speed = 400 meters / 151 seconds = 2.469 m/s
Average speed = 1000 meters / 431 seconds = 2.320 m/s
2/5(a+2b)^2 (if a=3 and b=-4)
The answer is 10. Hope this helps.
Multiply the numbers
2/5 •(3-8)^2
Subtract (3-8)
2/5• (-5)^2
A negative base raised to an even power equals a positive
2/5• (5)^2
Reduce the expression with 5.
2•5
10
The following table shows the daily receipts in millions of dollars of the movie "Avatar" for successive Fridays after its opening on Friday 18 December 2009.Weeks$Receipts2 68.494 42.7856 31.288 23.61110 13.65512 6.52614 2.04716 0.84418 0.9220 0.42522 0.18824 0.07626 0.04528 0.028Estimate the instantaneous rate of change of daily receipts 20 weeks after the opening day.
Solution
As given from the question, we want to estimate the instanteneous rate of change of daily receipts 20 weeks after the opening day
To do this, You approximate it by using the slope of the secant line through the two closest values to your target value.
To get the instanteneous rate of change of week 20, we will be using
\(\begin{gathered} week22=0.188 \\ week18=0.92 \end{gathered}\)Thus,
\(\begin{gathered} Ins\tan teneousRateOfChangeForWeek20=\frac{week22-week18}{22-18} \\ Ins\tan teneousRateOfChangeForWeek20=\frac{0.188-0.92}{22-18} \\ Ins\tan teneousRateOfChangeForWeek20=\frac{-0.732}{4} \\ Ins\tan teneousRateOfChangeForWeek20=-0.183 \end{gathered}\)The answer is
\(Ins\tan teneousRateOfChangeForWeek20=-0.183\)help pls its due today
Answer:
Slope- 2
Y-intecerpt- 7
Equation- y=2x+7
Step-by-step explanation:
Answer:
4
Step-by-step explanation:
4x + 0