Look at pic
The function f(x)=223(1.09)^x represents the number of specialty items produced at Iron Man’s old factory x weeks after a change in management. The graph represents the number of specialty items produced at the new factory during the same time period.
During Week 0, how many more specialty items were produced at the old factory than at the new factory? Explain.
Find and compare the growth rates in the weekly number of specialty items produced at each factory. Show your work.
When does the weekly number of specialty items produced at the new factory exceed the weekly number of specialty items produced at the old factory? Explain.
Answers
Answer:
a. 33
b. So we see that at the start of 3rd week, the new factory begins to exceed old production.
Step-by-step explanation:
(a)w = 0
Old factory: p(x)=223(1.09)^x Plug in 0
p(0)= 223(1.09)^(0)
When a number has an exponent of 0, the number becomes 1
p(0) = 223(1)
p(0) = 223
New factory: w = 0, p(0) or y = 190 (0,190)
223 - 190 = 33
During Week 0, 33 more specialty items were produced at the old factory than at the new factory.
(b) i don't know sorry
(c)
The old production tabulated:
w P(w) New
0 223 190
1 243 220
2 265 252
3 289 290
4 315 337
5 343 380
6 374 440
7 408 505
So we see that at the start of 3rd week, the new factory begins to exceed old production.
i hope this helped people in the future.
During week 0 the old factory produced 33 more items than at the new factory.
The weekly number of specialty items produced at the new factory exceed the weekly number of specialty items produced at the old factory at week 4.
What is a function?A function is defined as a relation between a set of inputs having one output each. A function is a relationship between inputs where each input is related to exactly one output. Every function has a domain or range.
According to the given problem,
Specialty items produced at the old factory at week 0,
Given function = [tex]223(1.09)^{x}[/tex]
When x = 0,
f(x) = [tex]223(1.09)^{0}[/tex]
= 223
Specialty items produced at the new factory during 0 = 190
Old factory exceeded the production by:
⇒ ( 223 - 190 )
= 33 specialty items.
Comparing the growth rates of weekly number of specialty items at each factory,
For week 0,
Old factory = 223
New factory = 190
Growth rate = [tex]\frac{223-190}{190}*100[/tex]
≈ 17%
For week 1,
Old factory = 243
New factory = 220
Growth rate = [tex]\frac{243.07-220}{220}*100[/tex]
≈ 10%
For week 2,
Old factory = 265
New factory = 252
Growth rate = [tex]\frac{264.95-252}{252}*100[/tex]
≈ 5%
For week 3,
Old factory = 289
New factory = 290
Growth rate = [tex]\frac{290 -288.79}{288,79}*100[/tex]
≈ 0.41%
For week 4,
Old factory = 325
New factory = 337
Growth rate = [tex]\frac{337-324.78}{324.78}*100[/tex]
≈ 3%
For week 5,
Old factory = 343
New factory = 380
Growth rate = [tex]\frac{380-343.11}{343.11} *100[/tex]
≈ 13%
For week 6,
Old factory = 374
New factory = 440
Growth rate = [tex]\frac{440-374}{374} *100[/tex]
≈ 18%
For week 7,
Old factory = 408
New factory = 505
Growth rate = [tex]\frac{505-408}{408} *100[/tex]
≈ 23%
At week 3, the production at new factory exceeds the production of the old factory.
For old factory,
⇒ f(x) = [tex]223(1.09)^{x}[/tex]
= [tex]223(1.09)^{3}[/tex]
= 289
For new factory at week 3,
Production = 290 items.
Hence, we can conclude, during week 0 the old factory produced 33 more items than at the new factory and the weekly number of specialty items produced at the new factory exceed the weekly number of specialty items produced at the old factory at week 4.
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Related Questions
At a concession stand, seven hot dogs and two hamburgers cost 14.50, two hot dogs and seven hamburgers cost 17.00. Find the cost of one hot dog and the cost of one hamburger
Answers
Given:
Seven hot dogs and two hamburgers cost 14.50
Two hot dogs and seven hamburgers cost 17.00.
To find:
The cost of one hot dog and the cost of one hamburger.
Solution:
Let the cost of one hot dog be x and the cost of one hamburger be y.
According to the question,
[tex]7x+2y=14.50[/tex] ...(i)
[tex]2x+7y=17.00[/tex] ...(ii)
Multiply (i) by 7.
[tex]49x+14y=101.5[/tex] ...(iii)
Multiply (ii) by 2.
[tex]4x+14y=34.00[/tex] ...(iv)
Subtract (iv) from (iii).
[tex]49x-4x=101.5-34[/tex]
[tex]45x=67.5[/tex]
Divide both sides by 45.
[tex]x=1.5[/tex]
Put x=1.5 in (i).
[tex]7(1.5)+2y=14.50[/tex]
[tex]10.50+2y=14.50[/tex]
[tex]2y=14.50-10.50[/tex]
[tex]2y=4[/tex]
Divide both sides by 2.
[tex]y=2[/tex]
Therefore, the cost of one hot dog is 1.5 and the cost of one hamburger is 2.
Answer:
the other person is correct
Step-by-step explanation:
i put in the answers and it’s correct
Solve the following pair of equations simultaneously.
See image for question
Answer question (III)
Answers
Answer:
No solutions.
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDASEquality PropertiesAlgebra I
Solving systems of equations using substitution/eliminationSolving systems of equations by graphingExpandingFinding roots of a quadraticStandard Form: ax² + bx + c = 0Quadratic Formula: [tex]x=\frac{-b\pm\sqrt{b^2-4ac} }{2a}[/tex]Step-by-step explanation:
Step 1: Define systems
2x - y = 9
4x² + 3y² - 2x + y = 16
Step 2: Rewrite systems
2x - y = 9
Subtract 2x on both sides: -y = 9 - 2xDivide -1 on both sides: y = 2x - 9Step 3: Redefine systems
y = 2x - 9
4x² + 3y² - 2x + y = 16
Step 4: Solve for x
Substitution
Substitute in y: 4x² + 3(2x - 9)² - 2x + (2x - 9) = 16Expand: 4x² + 3(4x² - 36x + 81) - 2x + (2x - 9) = 16Distribute 3: 4x² + 12x² - 108x + 243 - 2x + 2x - 9 = 16Combine like terms: 16x² - 108x + 234 = 16Factor GCF: 2(8x² - 54x + 117) = 16Divide 2 on both sides: 8x² - 54x + 117 = 8Subtract 8 on both sides: 8x² - 54x + 109 = 0Define variables: a = 8, b = -54, c = 109Resubstitute: [tex]x=\frac{54\pm\sqrt{(-54)^2-4(8)(109)} }{2(8)}[/tex]Exponents: [tex]x=\frac{54\pm\sqrt{2916-4(8)(109)} }{2(8)}[/tex]Multiply: [tex]x=\frac{54\pm\sqrt{2916-3488} }{16}[/tex]Subtract: [tex]x=\frac{54\pm\sqrt{-572} }{16}[/tex]Here we see that we start to delve into imaginary roots. Since on a real number plane, we do not have imaginary roots, there would be no solution to the systems of equations.
Step 5: Graph systems
We can verify our results.
WILL GIVE BRAINLIEST!!!!!!
If the trapezoid is isosceles, and KL = 2.8 units in length, what is the length of NM? Explain how you determined the length of NM.
Answers
Answer:
MN = 2.8 units
Step-by-step explanation:
By the property of isosceles trapezoid,
1). Bases are parallel.
2). Base angles of an isosceles trapezoid are congruent.
2). Opposite sides of the congruent angles are congruent.
By third property,
Measure of side KL = Measure of side MN
2.8 = Measure of side MN
Another way to find the length of MN is,
Distance between M and N = [tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
MN = [tex]\sqrt{(3-1)^2+(0+2)^2}[/tex] = [tex]\sqrt{8}[/tex]
MN = 2.8 units
Therefore, MN = 2.8 will be the answer.
Please answer correctly !!!!!!!!!!!!!!!!! Will mark brainliest !!!!!!!!!!!!!!!!!!!
Answers
Answer:
chemical mixture is a collection of molecules or atoms of different types. A mixture is distinguished from a pure substance, which has constant composition (is composed of a only one type of molecule or atom), and a unique set of physical properties (no matter how large or small a sample is observed).
Step-by-step explanation:
GET BRANILIEST IF YOUR RIGHT!!!
Why is 50 miles per hour a unit rate, and 150 miles per 3 hours is n
Answers
Answer:
Step-by-step explanation:
In a unit rate, the denominator is always 1. So, to find unit rate, divide the denominator with the numerator in a way that the denominator becomes 1. For example, if 50km is covered in 5.5 hours, the unit rate will be 50km/5.5 hours = 9.09 km/hour.
Answer:
because unit rate means 1 hour not 3 hour.
what is 10.7+ 2 times
30.9
Answers
Answer:
10.7 + 2 + 10.9 10.9 x 30.9 is 336.81
Step-by-step explanation:
BIG BRAIN POWER
1.34 - 1.07 mathematics
Answers
Answer:
0.27
Step-by-step explanation:
If you subtract 1.07 from 1.34 it would equal 0.27.
URGENT PLEASE HELP
What method can be used to prove the triangles below are congruent?
SAS
HL
SSS
Not possible
Answers
The method that can be used to prove the triangles below are congruent is SSS
(side, side, side)
Option C is the correct answer.
What is a triangle?It is a two-dimensional figure which has three sides and the sum of the three angles is equal to 180 degrees.
We have,
Two right triangles.
The hypotenuse of each triangle is equal
The base of each triangle is equal.
The height of the triangle is common to both triangles.
Now,
A
/ | \
/ | \
/ | \
/ | \
B D C
Triangle ABD is congruent with Triangle ADC
AB = AC (side)
BD = CD (side)
AD = AD (side)
Thus,
The method that can be used to prove the triangles below are congruent is SSS
(side, side, side)
Option C is the correct answer.
Learn more about triangles here:
https://brainly.com/question/25950519
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Jared Kushner.......
Answers
Answer:
huh?
Step-by-step explanation:
^,÷&&÷&#^÷^#*#;#^#&
Answer:
what about him-
Step-by-step explanation:
ill answer in comments
3/5x -27 =24 what is x
Answers
Answer:
X = 85
Step-by-step explanation:
what is 90,000 in standard form
Answers
Answer:
9*10^4
Step-by-step explanation:
Answer:
90,000 is written and 9x 10^4 in scientific notation
Let f(n) be the average number of days a house stays on the market before being sold for price p in $1,000s, which statement best describes the meaning
of 1(250)?
Answers
Answer:
b
Step-by-step explanation:
Answer:
B
Step-by-step explanation:
brainlest plz
Using the exchange rate £1 = $1.32, calculate how many £ are in $11.80. Give
your answer rounded to 2 dp.
Answers
Answer:
£8.94
Step-by-step explanation:
Since $1 = £1.32, you can just divide $11.80 by 1.32.
11.80/1.32 = £8.939
£8.939 rounded to 2 dp = £8.94
Answer:
If you do the math 10 euros is 13.20 USD so thats to much so take 1.00 euro away so thats 11.88 USD so its around 8.50 euro for 11.80 USD
Step-by-step explanation:
hey I need help please
Answers
Answer:
1 I think
Step-by-step explanation:
I have test corrections that are due tomorrow at 5pm but I cheated on it but I got some answers wrong on purpose. Now I don't know what to put for the wrong ones since I didn't do the work. She wants us to explain what we did wrong and how we fixed it but I don't know. I need help ASAP
Answers
Answer: Since you know some of the answers you put wrong say what I did wrong was I didn’t put...(and say the correct answer but like in a way )
Step-by-step explanation:
please answer these:)
Answers
Answer:
Step-by-step explanation:
Not a function
In order for an equation to represent a function any single value of x must have at most one corresponding value of y which satisfies the equation.
For
x2+y2=9
(for example)
x=0
there are two values for y (namely +3 and −3) which satisfy the equation
If you plug this graph into a calculator, you will find that it is a graph of a circle.
Circles have the formula x2+y2=r2 if they are centered at the origin.
From that, we can find that the radius is 3, and it is centered at the origin.
To find the domain and range, we just find the largest and smallest x and y values.
Since the radius is 3, and the graph is centered at the origin, the largest x value is 3. Similarly, the smallest x value is -3.
The domain is −3≤x≤3
We can use the same thing for the range. The radius is 3, so the largest and smallest values of the y will be 3 and -3.
The range is -3≤y≤3
Answer:
See below
Step-by-step explanation:
6. Look at the graph of the equation x^2+y^2=8. Give its domain and range.
Both domain and range are: (- √8, √8) or (-2.828, 2.828)7. Use algebraic means to show that x^2+y^2=8 is not a function. Explain your process.
The vertical line test. If more than one point is crossed on the graph by a vertical line, then the relation is not considered to be a function.8. Is there any value(s) of the domain of x^2+y^2=8 that passes the vertical line test? If so, name the value(s) and state whether or not the existence of this value makes this relation a function. You can use Desmos to help you explore this idea, if needed.
There are two points - 2.828 and 2.828 that pass the vertical line test but all the other points don't, therefore this relation is not a functionBryan earns 9$ for each hour of yard work how many hours in all will it take Bryan to earn 27$
Answers
Answer:
3 hours
Step-by-step explanation:
Write a real world story problem that would fit this situation
Answers
Answer:
what's the situation?????????
What is the equation of the line?
y=−1/2x+1
y=−1/2x−1
y=2x−1
y=−2x+1
Answers
Explanation:
Y=Mx+b
M= slope B= y-Int.
Y-intercept=1
Slope= -1/2 (Down 1(-)/(right 2(+))
You buy gallons of gasoline at $2.37 per gallon and pay $21.33. Write an equation to find the number of gallons purchased. Then find the number of gallons of gasoline that you purchased.
Answers
Answer: 2.37x = 21.33
You bought 9 gallons
Step-by-step explanation:
YOULL BE MADE BRAINLIEST IF YOU ANSWER CORRECTLY
Solve the proportion.
15/8=45/c
c=
Answers
Answer:
c=24
Step-by-step explanation:
15/8=45/c
15*c=45*8
15c/15=360/15
c=24
Weekly salary: $650; earnings to date: $30,000.
Answers
Answer:
Step-by-step explanation:
30000/650= 46.15 weeks to accumulate $30000
ss tax rate is 12.4%
Medicare rate is 0.09%
30,000*12.4%= $3720
30,000*9%= $270
Total is $3990
Per pay period is
650*12.4%= $80.60
650*9%=$58.50
Total is $139.10
The vertex of y= 22 - 82 +18 is
Answers
800 children a day ride on the roller coaster, but another 200 are turned away because they're not tall enough. What proportion of the total number of children are turned away?
A) Half are turned away
B) One quarter are turned away
C) One fifth are turned away
Answers
Answer:
Step-by-step explanation:
C
Answer:
B
Step-by-step explanation:
|x+4 | =8
Dont know this
Answers
Answer: 4+4=8
Step by step explanation:
Select the correct answer.
Solve the following inequality for x.
x - 9 ≤ 2(9 - x)
A. x ≤ 9
B. x ≥ 11
C. x < -7
D. x < 10
Answers
Step-by-step explanation:
x-9≤2(9-x)
distribute
x-9≤18-2x
add 2x on both sides
3x-9≤18
add 9 on both sides
3x≤27
divide by 3
x≤9
Answer:
here is the answer verified by edmentum if anyone needs it
Step-by-step explanation:
An inscribed angle in a circle intercepts an arc whose measure is greater than 180
The angle is..
Alway acute
Sometime acute
Never acute
Answers
Answer:
The correct option is;
Never acute
Step-by-step explanation:
When an angle intercepts an ark, we have;
The legs of the angle meets with the endpoints of the arc
Therefore, given that the arc is greater than 180°, and that the angle of the arc is the angle defined at the center of the circle, while the angle defined by the inscribed angle is defined at the circumference of the circle
By circle theorem, the angle at the center is twice that at the circumference, whereby the angle of the arc > 180°, the angle at the subtended by the inscribed angle will > 180°/2, which is > 90° or an obtuse angle
xoxoxoxozooxoxoxoxoo
Answers
PLEASE HELP ASAP!!! IF YOU WANT BRAINLIEST DONT ANSWER GIBBERISH AND BE DESCRIPTIVE!!!
Answers
Total to fish=8/3
Fish to starfish=3/5
Starfish to total=5/8
starfish to fish=5/3
Answer:
i dont know but i need brainliest can you still do it plz
Step-by-step explanation:
A rabbit is running at a speed of 45 miles per hour. How many feet is the rabbit traveling each second?
Answers
Answer:
66
Step-by-step explanation:
The rabbit is traveling 66 ft per second.
