Two different businesses model their profits over 15 years, where x is the year, f(x) is the profits of a garden shop, and g(x) is the profits of a construction materials business. Use the data to determine which function is exponential, and use the table to justify your answer.
1. f(x) is exponential; an exponential function increases more slowly than a linear function.
2. f(x) is exponential; f(x) increased more overall than g(x).
3. g(x) is exponential; g(x) has a higher starting value and higher ending value.
4. g(x) is exponential; an exponential function increases faster than a linear function.
Answers
Hi there!
[tex]\large\boxed{\text{Choice 4}}[/tex]
We can look at each function, f(x) and g(x), to determine which is exponential.
Use slope formula: m = y2-y1/x2-x1
f(x) starts off with a slope at about $1800/year, but becomes about $1100/year.
g(x) starts off with a slope of about $1500/year, but becomes about $1874/year.
Thus, g(x) is exponential, because g(x)'s slope is increasing across the interval.
Related Questions
A 4-pound bag of flour costs $10.24. What is the price per ounce if there are 16 ounces in a pound?
Answers
Answer:
The price per ounce is $0.16
Step-by-step explanation:
We have:
Price of a 4-pound bag = $10.24
1 pound = 16 ounces
Price per ounce =?
Hence the price per ounce is:
[tex] \frac{\$ 10.24}{4 pound}*\frac{1 pound}{16 ounces} = \frac{\$ 0.16}{ounce} [/tex]
Therefore, the price per ounce is $0.16
I hope it helps you!
rotation 180 degrees about the origin.
Answers
Answer:
Click the rotate 'button' twice.
Observe.
The rotate button is rotating the image about the orgin.
Answer:
Click the rotate 'button' twice.
Observe.
The rotate button is rotating the image about the orgin.
Step-by-step explanation:
2√m^2 if m is greater than or equal to 0
Answers
Answer:
[tex] \displaystyle \boxed{|2m| }[/tex]
Step-by-step explanation:
we are given that
[tex] \displaystyle 2 \sqrt{ {m}^{2} } [/tex]
since m is greater than or equal to 0 it's a positive number therefore, the square root of m is defined and recall that √x²=|x| thus
[tex] \displaystyle \boxed{2 |m|}[/tex]
remember that,|a|•|x|=|ax| hence,
[tex] \displaystyle \boxed{ |2m|}[/tex]
and we're done!
Answer:
2m
Step-by-step explanation:
Given :-
2√m² , m is greater than or equal to 0 .By question,
→ 2√m²
→ 2 * m
→ 2m
In a mid-size company, the distribution of the number of phone calls answered each day by each of the 12 receptionists is bell-shaped and has a mean of 47 and a standard deviation of 3. Using the empirical rule, what is the approximate percentage of daily phone calls numbering between 41 and 53? Do not enter the percent symbol.
Answers
Prob ( (41-59)/9 = Z = (77-59)/9 ) = --- changes to z scores
Prob ( -18/9 = Z = 18/9 ) =
Prob ( -2 = Z = 2) =
Prob ( z=2) - Prob(Z=-2) = by property of the normal bell curve
= 0.9772 - 0.0228 per the normal distribution table
= 0.9544
Suppose that Bag 1 contains a red (R), a blue (B) and a white (W) ball, while Bag 2 contains a red (R), a pink (P), a yellow (Y) and a green (G) ball. A game consists of you randomly drawing a ball from each of Bag 1 and Bag 2. (a) What are the 12 outcomes in the sample space S for this experiment? (b) You win the prize of baked goods if you draw at least 1 red ball. List the outcomes in the event that you win that prize, and use them to compute the probability of this event. You should assume that all outcomes in the sample spaces obtained in (a) are equally likely.
Answers
Answer:
1 /2
Step-by-step explanation:
Given :
Bag 1 : Red (R) ; Blue (B) ; White (W)
Bag 2 : Red (R) ; Pink (P) ; Yellow (Y) ; Green (G)
Total number of possible outcomes :
3C1 * 4C1 = 3 * 4 = 12 outcomes
Sample space (S) ;
_______ R ______ B _______ W
R_____ RR _____ RB ______ RW
P_____ PR _____ PB ______ PW
Y _____YR_____ YB ______ YW
G _____GR ____ GB ______ GW
To win price of baked goods ; Atleast one red ball must be drawn :
Probability of winning ; P(winning) = required outcome / Total possible outcomes
Required outcome = {RR, RB, RW, PR, YR, GR} = 6
Total possible outcomes = S = 12
P(winning) = 6/12 = 1/2
Place the steps for finding f-1(x)
Answers
9514 1404 393
Answer:
B, C, H, D, F, A
Step-by-step explanation:
Starting with y = f(x), swap x and y to get x = f(y), then solve for y. The solution steps "undo" what is done to y, in reverse order. Y is ...
multiplied by 721 subtracted from the productthe square root of the differenceTo "undo" these steps in reverse order, after swapping x and y, you must square both sides, add 21, then divide by 7.
If the left tiles are labeled A to H from top to bottom, the correct sequence of steps is ...
B, C, H, D, F, A
The fair spinner shown in the diagram above is spun. Work out the probability of getting a 3. Give your answer as a fraction in its simplest form.
Answers
Answer:
The number of fours divided by the total number of possibilities. If there are two fours and 8 spaces, the probability is 2/8 = 1/4.Step-by-step explanation:
A sports company has the following production function for a certain product, where p is the number of units produced with x units of labor and y units of capital.
p(x,y)=2500x1/5y1/5
Find:
1. Number of units produced with 26 units of labor and 1333 units of capital.
2. Marginal productivities.
3. Evaluate the marginal productivities at x=25, and y=1333
Answers
Answer:
(a) 20226 units
(b) Marginal productivities
[tex]P_x =2500x^{-\frac{4}{5}} & y^\frac{1}{5}[/tex]
[tex]P_y =2500 x^\frac{1}{5} y^{-\frac{4}{5}}[/tex]
(c) Evaluation of the marginal productivities
[tex]P_x =803[/tex]
[tex]P_y = 15[/tex]
Step-by-step explanation:
Given
[tex]P(x,y) = 2500x^\frac{1}{5}y^\frac{1}{5}[/tex]
Solving (a): P(x,y) when x = 26 and y = 1333
[tex]P(x,y) = 2500x^\frac{1}{5}y^\frac{1}{5}[/tex] becomes
[tex]P(26,1333) = 2500*26^\frac{1}{5}*1333^\frac{1}{5}[/tex]
[tex]P(26,1333) = 20226[/tex] --- approximated
Solving (b): The marginal productivities
To do this, we simply calculate Px and Py
Differentiate x to give Px, so we have:
[tex]P(x,y) = 2500x^\frac{1}{5}y^\frac{1}{5}[/tex] becomes
[tex]P_x =2500 * x^{\frac{1}{5}-1} & y^\frac{1}{5}[/tex]
[tex]P_x =2500 * x^{-\frac{4}{5}} & y^\frac{1}{5}[/tex]
[tex]P_x =2500x^{-\frac{4}{5}} & y^\frac{1}{5}[/tex]
Differentiate y to give Py, so we have:
[tex]P(x,y) = 2500x^\frac{1}{5}y^\frac{1}{5}[/tex] becomes
[tex]P_y =2500 * x^\frac{1}{5} & y^{\frac{1}{5}-1}[/tex]
[tex]P_y =2500 x^\frac{1}{5} y^{-\frac{4}{5}}[/tex]
Solving (c): Px and Py when x = 25 and y = 1333
[tex]P_x =2500x^{-\frac{4}{5}} & y^\frac{1}{5}[/tex] becomes
[tex]P_x =2500 * 25^{-\frac{4}{5}} * 1333^\frac{1}{5}[/tex]
[tex]P_x =803[/tex] --- approximated
[tex]P_y =2500 x^\frac{1}{5} y^{-\frac{4}{5}}[/tex] becomes
[tex]P_y =2500 * 25^\frac{1}{5} * 1333^\frac{-4}{5}[/tex]
[tex]P_y = 15[/tex]
Tonya wants to estimate what proportion of the students in her dormitory like the dorm food. She interviews a simple random sample of 50 students living in the dormitory. She finds that 14 think the dorm food is good. Find a 90% confidence interval for the true proportion of students that think the dorm food is good.
a. 0.176 to 0.384
b. 28%
c. 0.28 +/- 0.03
d. 0.156 to 0.404
Answers
Answer:
Step-by-step explanation:
The solution of the problem has been solved on paper and attached in the attachment section. Kindly refer to that and feel free to ask any doubt.
Need help on this ASAP
Answers
Answer:
The answer is C
Step-by-step explanation:
The intersection of those figures results to a point
One jar holds 20 green marbles and 4 white marbles. A second jar holds 60 black marbles and 20 white marbles. What is the probability that a white marble will be drawn from both jars?
Answers
Answer:
[tex]\sf \dfrac{1}{24}=0.0417=4.17\%\:\:(3\:s.f.)[/tex]
Step-by-step explanation:
Given information:
Contents of Jar 1:
20 green marbles4 white marblestotal marbles = 20 + 4 = 24Contents of Jar 2:
60 black marbles20 white marblestotal marbles = 60 + 20 = 80Probability Formula
[tex]\sf Probability\:of\:an\:event\:occurring = \dfrac{Number\:of\:ways\:it\:can\:occur}{Total\:number\:of\:possible\:outcomes}[/tex]
Therefore:
[tex]\sf P(white\:marble\:from\:Jar\:1)=\dfrac{4}{24}=\dfrac{1}{6}[/tex]
[tex]\sf P(white\:marble\:from\:Jar\:2)=\dfrac{20}{80}=\dfrac{1}{4}[/tex]
As the events are independent (i.e. drawing a marble from one jar does not influence or affect drawing a marble from the other jar), we can use the independent probability formula:
[tex]\sf P(A\:and\:B)=P(A) \cdot P(B)[/tex]
Therefore, the probability that a white marble will be drawn from both jars is:
[tex]\sf P(white\:marble\:from\:Jar\:1)\:and\:\sf P(white\:marble\:from\:Jar\:2)=\dfrac{1}{6} \cdot \dfrac{1}{4}=\dfrac{1}{24}[/tex]
#Jar 1
Total marbles =20+4=24
P(w)
4/24=1/6#Jar 2
Total marbles=60+20=80
P(w)
20/801/4P(w in total)
1/4(1/6)1/24If the domain of a function that is reflected over the x-axis is (1, 5), (2, 1), (-1, -7), what is the range?
A. (1, -5), (2, -1), (-1, 7)
B. (5, 1), (1, 2), (-7, -1)
C. (-5, -1), (-1, -2), (7, 1)
D. (-1, 5), (-2, 1), (1, -7)
Answers
Answer:
A. (1, -5), (2, -1), (-1, 7)
Step-by-step explanation:
Reflecting a function over the x-axis:
When a function is reflected over the x-axis, the x-value stays the same, while y changes the signal, so the transformation rule is:
[tex](x,y) \rightarrow (x,-y)[/tex]
To find the range:
We apply the transformation to the points in the domain. Thus:
[tex](1,5) \rightarrow (1,-5)[/tex]
[tex](2,1) \rightarrow (2,-1)[/tex]
[tex](-1,-7) \rightarrow (-1,-(-7)) = (-1, 7)[/tex]
Thus the correct answer is given by option a.
Answer:
It is letter A and please give me brainliest
Step-by-step explanation:
Suppose the random variables X, Y, and Z have the following joint probability distribution. x y z f ( x , y , z ) 1 1 1 0.05 1 1 2 0.10 1 2 1 0.15 1 2 2 0.20 2 1 1 0.20 2 1 2 0.15 2 2 1 0.10 2 2 2 0.05 Determine the conditional probability distribution of X given that Y
Answers
Answer:
Determine the conditional probability distribution of X given that Y = 1 and Z = 2. Round your answers to two decimal places (e.g. 98.76).
answer:
Given that Y = 1 : 2/5
Given that Z = 2 : 3/5
Step-by-step explanation:
The conditional probability distribution of X F x | yz^( x )
Given that Y = 1
F x | yz . ( x | yz ) = 2/5
Given that z = 2
= 3/5
attached below is the detailed solution
Please help me to solve it
Answers
What are you trying to solve for?
[tex]824381 + 1654 = - 121[/tex]
is 7/4 bigger than -4 / 7
Answers
Answer:
7/4 is larger than -4/7
Step-by-step explanation:
7/4 is greater than a whole. 4/4 = 1 whole and the fraction is 7/4. -4/7 is smaller than a whole and is a negative number.
Therefore 7/4 is bigger
Hope this helps!
Answer:
yes 7/4 is bigger than -4/7
Step-by-step explanation:
its bigger because its positive!
FREE
Circle O has a circumference of approximately 250 ft.
What is the approximate length of the diameter, d?
O 40 ft
O 80 ft
O 125 ft
O 250 ft
Save and Exit
Next
Submit
Mark this and return
Answers
Answer:
Step-by-step explanation:
circumference = πd ≅ 250 ft
d ≅ 250/π ≅80 ft
is perpendicular to line segment
. If the length of is a units, then the length of is
units.
Answers
Answer:
AB is perpendicular to [GH] and GH is [A]
Step-by-step explanation:
Stuck on this question
Answers
Answer:
the answer of this question is b
Sam works at a shoe store. He earns $300 every week plus $15 for every pair of shoes that he sells. How many pairs of shoes would he need to sell to make $500 in a week?
Answers
Answer:
300 + 15x = 500
15x = 200
x = 200/15
x=13.333
14 pair of shoes
Step-by-step explanation:
Not sure how to do this.
Answers
Answer:
-4 ≤ x ≤ -2, 4 ≤ x ≤ 7
Step-by-step explanation:
A function shows the relationship between two or more variables. A function is said to be constant over an interval if its output value is same for every input value within that interval.
As seen in the question, the x variable is the input while the y variable is the output. The function is constant from x = -4 to x = -2. Also, the function is constant within the interval from x = 4 to x = 7. Hence, the interval is:
-4 ≤ x ≤ -2, 4 ≤ x ≤ 7
i’ll give brainliest to the right answer plz help
Answers
9514 1404 393
Answer:
water
Step-by-step explanation:
Comparison of numbers can be done a couple of different ways. One way is to subtract one from the other. If the difference is positive, the minuend (first number) is the larger of the two.
Another way is to divide one number by the other. If the ratio is more than 1, then the numerator is the larger number.
For numbers in scientific notation, the division is perhaps the easiest. Here, that gives you ...
[tex]\displaystyle\frac{\text{water mass}}{\text{oxygen mass}}=\frac{2.99\times10^{-26}\text{ kg}}{2.66\times10^{-26}\text{ kg}}=\frac{2.99}{2.66}\approx 1.12[/tex]
This value is greater than 1, so the mass of a water molecule is greater.
__
You will note that the multipliers (10^-26 kg) cancelled because they were equal. If they are unequal, the usual rules of exponents apply.
Amic and Bernie built a maze for their hamsters. Annic's hamster completed the maze 7 seconds less than twice the time it took Bernie's hamster to complete the maze. If Bernie's hamster completed the maze in b seconds, which expression represents the time, in seconds, it took Annie's hamster to complete the maze?
A. 7-2b
B. 2b-7
c. 2b+7
D. 2b/7
Answers
Answer:
2b-7
Step-by-step explanation:
Given that,
Bernie's hamster completed the maze in b seconds.
Annic's hamster completed the maze 7 seconds less than twice the time it took Bernie's hamster to complete the maze.
Twice the time it took Bernie's hamster to complete the maze is 2b.
7 seconds less than twice the time it took Bernie's hamster = 2b-7
So, the correct option is (b) "2b-7".
The cardinal number of {200, 201, 202, 203, ..., 1099}
Answers
Answer:
I have not been able to answer it sorry
Select the correct answer.
What is the domain of y = tan x?
A. (-0,0)
B. (0,7)
c. all stan
D. all x 91
Need Plato help
Answers
Answer: d all
Step-by-step explanation: Because The domain of the function y = tan (x)) is all real numbers except the values where cos (x) is equal to 0, that is, the values π 2 + π n for all integers n. The range of the tangent function is all real numbers.
Find all the roots of the equation
[tex] {x}^{6} - 64 = 0[/tex]
Answers
X^2 -64=0
Factorization:
(x+8)(x-8)=0
Solution:
X+8=0 x^1=-8
X-7=0. X^2=8
Answer:
x = 2
x =-2
x =1 +√3i
x =1 -√3i
x =-1 +√3i
x =-1 -√3i
Step-by-step explanation:
[tex]x^{6} -64 = 0\\(x^{3} -8)(x^{3} + 8) = 0\\ \\( x - 2) (x^{2} + 2x + 4)( x + 2) (x^{2} -2x + 4) = 0\\[/tex]
x = 2
x =-2
x =1 +√3i
x =1 -√3i
x =-1 +√3i
x =-1 -√3i
9. Mariah has 28 centimeters of reed
and 10 meters of reed for weaving
baskets. How many meters of reed
does she have? Write your answer as a
decimal and explain your answer.
Answers
At a sale this week, a sofa is being sold for $117.60. This is a 72% discount from the original price. What is the original price?
Answers
What is the inequality shown?
Answers
Answer:
2<X ,this is because opened and facing towards x
and
–3≤X this is because the circle is closed and also facing towards x
Chang knows one side of a triangle is 13 cm. Which set of two sides is possible for the lengths of the other two sides
of this triangle?
• 5 cm and 8 cm
O 6 cm and 7 cm
O 7 cm and 2 cm
8 cm and 9 cm
Answers
Answer:
8cm and 9cm
Step-by-step explanation:
because for the triangle to work you need the other two other sides when added together needs to be greater then 13
PLEASE HELP ME BE CORRECT PLEASE
TELL ME WHERE to PUT EACH POINT
Answers
Answer:
Point A:
(3, -5)
Point B:
(6, -2)
Point C:
(5, -7)
Step-by-step explanation:
Background:
Moving to the right means adding to the x.
Moving to the left means subtracting from the x.
Moving up means adding to the y.
Moving down means subtracting from the y.
So take each point and add 3 to the x, and subtract 4 from they y.
Point B:
(3, 2) → (6, -2)
Point A:
(0, -1) → (3, -5)
Point C:
(2, -3) → (5, -7)
