Answers
Answer:
1
I've attached a screenshot from my graphing calculator of [tex]f(x)[/tex] in blue and [tex]f^{-1}(x)[/tex] in red. Notice how the red line (inverse function) has (3, 1)
Step-by-step explanation:
[tex]f(x) = 3^x\\f^{-1}(x) =\ ?\\[/tex]
We must first figure out the inverse function of [tex]f(x)[/tex] which is [tex]f^{-1}(x)[/tex]
[tex]y = f(x) = 3^x\\y = 3^x\\log\ y = log\ 3^x\\log\ y = x \times log\ 3\\x = \frac{log\ y}{log\ 3}\\[/tex]
We say y = f(x) to begin with, but after find x = ...
we must 'swap' x and y
[tex]x = \frac{log\ y}{log\ 3}\\y = \frac{log\ x}{log\ 3}\\[/tex]
[tex]f^{-1}(x) = \frac{log\ x}{log\ 3}[/tex]
[tex]f^{-1}(3) = \frac{log\ 3}{log\ 3} = 1[/tex]
Related Questions
The tax rate is 6.8% what is the tax on $9.95 round to the nearest hundredth
Answers
Answer:
$0.68
Step-by-step explanation:
you have to do:
9.95 x .068
or
9.95 x 6.8 ÷ 100
and you would get 0.6766 but rounded to the nearest hundredth would be $0.68
Which answer includes a function, its inverse, and a dashed line that verifies the relationship?
Answers
Answer:
A
Step-by-step explanation:
because that's the answer
The correct graph that includes a function, its inverse, and a dashed line that verifies the relationship is shown in option 1.
Used the concept of function that states,
A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable and another variable.
Ask about the function, its inverse, and a dashed line that verifies the relationship.
Now from the first graph;
The dashed line is y = x.
And the graph shows the functions and their inverse as both graphs are opposite to each other.
Therefore, option 1 is true.
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taking a photo of 3 questions! Please help! with ALL answers if possible! I’m putting it at 30+ points
Answers
Answer:
3 for City A and 6 for City B.
Step-by-step explanation:
All you have to do is look where it stands bye.
Hope this helps!
Solve 4x - 4 = 8.
O A. x= 1
O B. x= 3
O C. x= -1
O D. x = 2
Answers
Answer:
x = 1
Step-by-step explanation:
Question: 4x - 4 = 8
•shifting the -4 to the right side:
⇒4x = 8 - 4
⇒4x = 4
•shifting the 4 to the right side:
⇒x = 4/4
•by cross cancellation we get:
⇒x = 1 Answer...
hope that helps...
Factor the polynomial and use the zeros to identify its graph. x4 − 5x3 − 20x2 + 60x + 144
Answers
The zeros of the polynomial are -3, -2, 4 and 6 and the graph of the polynomial is graph (a)
How to factor the polynomial?The polynomial is given as:
P(x) = x^4 - 5x^3 - 20x^2 + 60x + 144
Expand the polynomial function
P(x) = x^4 - 10x^3 + 5x^3 + 24x^2 - 50x^2 + 6x^2 + 120x - 60x + 144
Rewrite the function as:
P(x) = x^4 - 10x^3 + 24x^2 + 5x^3 - 50x^2 + 120x + 6x^2 - 60x + 144
Factorize the function
P(x) = x^2(x^2 - 10x + 24) + 5x(x^2 - 10x + 24) + 6(x^2 - 10x + 24)
Factor out x^2 - 10x + 24
P(x) = (x^2 + 5x + 6)(x^2 - 10x + 24)
Expand each bracket
P(x) = (x^2 + 3x + 2x + 6)(x^2 - 4x - 6x + 24)
Factorize each bracket
P(x) = [x(x + 3) + 2(x + 3)][x(x - 6) - 4(x - 6)]
Factor out x + 3 and x - 6
P(x) = (x + 3)(x + 2)(x - 4)(x - 6)
Set to 0
(x + 3)(x + 2)(x - 4)(x - 6) = 0
Solve for x
x =-3, -2, 4 and 6
Hence, the zeros of the polynomial are -3, -2, 4 and 6 and the graph of the polynomial is graph (a)
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On a spinner, there are twenty equal-size sections numbered from 1 to 20. Which spinner game is fair? Show your work.
Answers
The spinner game is an illustration of probability, and the spinner game that is fair is (b) If you spin a number greater than 10, you win.
How to determine the fair game?The number of sections in the spinner is given as:
n = 20
There are 10 numbers greater than 10 i.e. 11 to 2.
So, the probability that a number greater than 10 is spun is:
P = 10/20
P = 0.5
The probability that a number that is not greater than 10 is spun is calculated using the following complement rule
q = 1 - p
This gives
q = 1 - 0.5
Evaluate
q = 0.5
Notice that both probabilities are the equal
Hence, the spinner game that is fair is (b) If you spin a number greater than 10, you win.
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Find the circumference.
Answers
69.12ft
11x2 = 22
C= pi x d
= pi x 22
= 22pi
Or
69.11503838
Hope this helps!
4) Cody invests $2,733 in a retirement
account with a fixed annual interest rate of
9% compounded 12 times per year.
How
long will it take for the account balance to
reach $9,589.78?
Answers
Answer:
t = 14 years
Step-by-step explanation:
r = R/100
r = 9/100
r = 0.09 per year,
Then, solve the equation for t
t = ln(A/P) / n[ln(1 + r/n)]
t = ln(9,589.78/2,733.00) / ( 12 × [ln(1 + 0.09/12)] )
t = ln(9,589.78/2,733.00) / ( 12 × [ln(1 + 0.0075)] )
t = 14 years
Summary:
The time required to get a total amount of $9,589.78 with compoundeded interest on a principal of $2,733.00 at an interest rate of 9% per year and compounded 12 times per year is 14 years.
Ignore the other questions I just need help with numbers 18 and 25 how do you work it out please help me out I would of have helped you
Answers
Answer:
25. -7/5 [tex]\leq[/tex] x [tex]\leq[/tex] 1
Step-by-step explanation:
18:
[tex]5-|x|\leq 2\\-|x| \leq -3\\|x|\leq 3\\x\geq -3[/tex]or [tex]x\leq 3[/tex]
25:
[tex]3|5x+1|-6\geq 12\\3|5x+1|\geq 18\\|5x+1|\geq 6\\x\leq -7/5[/tex]or [tex]x\geq 1[/tex]
[tex]-7/5\leq x\leq 1[/tex]
I don't think I explained this well let me know if you need more explanation.
Which of these shows equivalent fractions
1/4=4/8
1/2=2/4
3/5=5/10
2/3=3/6
Answers
Answer:
1/2=2/4
Step-by-step explanation:
1/4=4/8 - no, if you multiply 1/4 x 4 to get numerator match = 4/32
1/2=2/4 - YES , 1/2 x 2 = 2/4
3/5=5/10 = no if you multiply 3/5 x 2 to get denominator match = 6/10
2/3=3/6 = no if you multiply 2/3 x 2 to get denominator match = 4/6
A customer buys a different book for a selling price of 38$.The book is discounted 25%.The customer must pay 6% sales tax on the disocounted price of the book.How much does the customer pay for the book including tax.
Answers
Answer:
$30.21
Step-by-step explanation:
Jesse is making a sundae where she gets to choose one ice cream, one fruit topping, and one sauce. She can choose from chocolate, vanilla, and strawberry ice cream. She can choose from cherries or crushed pineapple as a fruit topping. Fudge and caramel are the sauces. How many outcomes?
Answers
Answer:
EEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEE
What percent of values is between the first and third quartiles?
The data set is 50, 75, 100, 125, 150, 175, 200, 225, 250
Answers
Answer:
[tex]55.555...\ (\%)[/tex]
Step-by-step explanation:
What percent of values is between the first and third quartiles
[tex]\text{Quartile 1} =\frac{75+100}{2} =87.5[/tex]
[tex]\text{Quartile 2} =\frac{200+225}{2} =212.5[/tex]
50 < 75 < 87.5 < 100 < 125 < 150 < 175 < 200 < 212.5 < 225 < 250
Then we have 5 values between the first and third quartiles which are :
100, 125, 150, 175, 200
Therefore,
The percent of values between the first and third quartiles is :
[tex]\frac{5}{9} \times 100=55.555...[/tex]
Thabo bought bread for R9,50, sweets RO,50, biscuits for R2,75 and coldrink for R11,35. a) How much did Thabo spend at the shop? b) If Thabo had R50, how much was his change?
Answers
Answer:
A) R24.10
B) R25.90
((ASSUMING THERES NO TAXES WITH THE PAYMENT))
Step-by-step explanation:
A)
first add up the costs of each item to get the ttal cost with addition as follows...
9.50 + 0.50 + 2.75 + 11.35 ((Adding like terms by adding 0.50 to 9.50 equaling 10.00))
10.00 + 2.75 + 11.35 ((adding the more simple options togeter since .75 is a more common fraction at 3/4))
12.75 + 11.35 ((finnishing off the system by adding the last two numbers together equaling to 24.10))
therefore Thabo spent a total of 24.10
B)
to find out the change, all we need to do is subtract the total cost from the total amount Thabo used to pay as shown below
50.00 - 24.10
in conclusion, Thabo would have R25.90 in change from the transaction ((assuming theres no tax))
500,-100,20,-4 write an equation for the nth term
Answers
Answer:
500(-1/5)^(n-1)
Step-by-step explanation:
Each term after the first is obtained by multiplying by -1/5.
This is a geometric series.
The nth term = a1 r^n-1)
= 500(-1/5)^(n-1)
What is the area of Vivian's backyard
Answers
Identify the center and radius of each equation. (x - 1)² + y² +81
Answers
I don't understand this question at all please help if you do
Answers
Answer:
Answer is [tex]\frac{4}{3}[/tex]
Step-by-step explanation:
To find the interval of x. Use our equations to equal each other.
[tex]-x^2+2x=y,y=0[/tex]
[tex]-x^2+2x=0\\-x(x-2)=0\\-x=0 , (x-2)=0\\x=0 ,2[/tex]
[tex]\int\limits^2_0 {-x^2+2x} \, dx[/tex]
Integrate.
[tex]\frac{-x^3}{3}+x^2\\(\frac{-2^3}{3}+2^2)-[\frac{-0^3}{3}+0^2]\\-\frac{8}{3} +4-0\\-\frac{8}{3}+\frac{12}{3} =4/3[/tex]
Using Desmos I have Graphs of both of the equations you have provided. The problem asks us to find the shaded region between those curves/equations.
Proof Check your interval of x.
I need help too find slope
Answers
Answer:
-2
Step-by-step explanation:
The slope of the function can also be described as its gradient.
To find the gradient of the function you can use:
[tex] \frac{change \: in \: y}{change \: in \: x} [/tex]
This gives us
[tex] \frac{ (- 10) - 10}{8 - ( - 2)} [/tex]
Which equals -2
a playground is 58 M wide and 91 what is the perimeter
Answers
Step-by-step explanation:
To get the perimeter, add up all of the sides.
So, the playground is a rectangle.
It has two sides measuring 58m, and two measuring 91m.
58+58+91+91=298
For the area, length x width
58x90=5278
In a survey of 1,300 women who gave birth in Maine in 2003, a total of 588 reported taking a multivitamin at least 4 times a week during the month before pregnant. Please calculate the prevalence of frequent multivitamin use, i.e., taking a multivitamin at least 4 times a week, among these women
Answers
Using it's concept, it is found that the prevalence of frequent multivitamin use is of 0.4523 = 45.23%.
What is the prevalence of a sample?The prevalence of a sample is given by the number of desired outcomes divided by the number of total outcomes.
In this problem, 588 out of 1300 women reported taking a multivitamin at least 4 times a week during the month before pregnant, hence the prevalence is given by:
p = 588/1300 = 0.4523 = 45.23%.
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A sum of N$2 500 was deposited in a venture account, which pays 12% compounded per year and it accumulated to N$3 950. Calculate the number of years the amount has been in the venture account. Answer must be rounded to the nearest unit?
Answers
The number of years the amount has been in the venture account with 12% interest per year is 4.
What is compound interest?Compound interest is the interest on a loan or deposit calculated based on the initial principal and the accumulated interest from the previous period.
A sum of $2,500 was deposited in a venture account, which pays 12% compounded per year and it accumulated to $3,950.
Then the number of the years will be
We know the compound interest formula
[tex]\rm A = P(1+r)^t[/tex]
where
A = Accumulated amount
P = Deposited value
r = rate of interest
t = time
Then we have
[tex]3950 = 2500 (1.12)^t\\\\1.58\ =1.12^t[/tex]
Taking log both sides, then we have
[tex]\rm \ln 1.58 = t \times \ln 1.12\\\\or \ \ \ \ t = 4.036 \approx 4 \ years[/tex]
Then the number of the years is 4.
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Levi has a fish tank that holds
3
4
8 gallons of water. He wants to fill it
so it is only 3/4
full. How much water,
in gallons, should Levi put in the fish
tank? Explain.
Answers
Using proportions, it is found that Levi should put 2.8125 gallons of water in the tank.
What is a proportion?A proportion is a fraction of a total amount.
Considering the improper fraction, the total amount of water that the tank holds is given by:
T = 3 4/8 = 3 + (4/8) = 3.5 gallons.
He wants the tank to be 75% full, hence, applying the proportion, the amount of water that he should put on the tank is of:
A = 0.75 x 3.5 = 2.8125 gallons.
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2. Solve - 2k + 12 < 30 for k.
Oke-3
Ok<3
Ok>.9
Ok>9
Answers
Answer:
2,012 is greater than 30
Step-by-step explanation:
The correct solution for the inequality is k > -9.
Given is an inequality -2k + 12 < 30, we need to solve for k,
To solve the inequality -2k + 12 < 30 for k, follow these steps:
Subtract 12 from both sides of the inequality to isolate the term with 'k':
-2k + 12 - 12 < 30 - 12
-2k < 18
Divide both sides by -2, but remember that when you divide an inequality by a negative number, the direction of the inequality sign flips:
(-2k)/(-2) > 18/(-2)
k > -9
So, the correct solution for the inequality is k > -9.
Among the options you provided, the correct answer is: k > -9.
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a) Write an equation in terms of x that represents the problem. (b) Solve the problem.
Seven less than the quotient of a number and 2 is equal to − 12. Find the number.
Part 1 of 2
The equation that represents the problem is _____?
The number is______?
Answers
Answer:
Part 1: (n÷2)-7 = -12
Part 2: n = -10
Step-by-step explanation:
Part 1:
Let's first write "the quotient of a number and 2" using numbers and variables. Let "n" represent "a number". The key word that we see here is quotient, meaning we have to divide something by something else. "The quotient of a number and 2 means that "a number" is the dividend (number that is divided) and "2" is the divisor (number that divides the dividend). Therefore we obtain:
n÷2
The first part says "seven less than the quotient of a number and 2". The keyword here is less, meaning we have to use subtraction. Therefore:
(n÷2)-7
The last part says "is equal to -12". Therefore the whole expression we just wrote is equivalent to -12:
(n÷2)-7 = -12
Part 2
Remember the Order of Operations:
Parentheses
Exponents
M/D: Multiplication/Division (whichever comes first in the equation)
A/S: Addition/Subtraction (whichever comes first in the equation)
Start by adding 7 to both sides
(n÷2) = -5
Then, multiply both sides by 2
[tex]\frac{n}{2}=-5\\n=-10[/tex]
Note: I used a fraction to display the division because it is easier to see why we have to multiply both sides by 2; to cancel out the denominator.
Glaucoma is a disease of the eye that is manifested by high intraocular pressure. The
distribution of intraocular pressure in the general population is approximately normal with
mean 16 mm Hg and standard deviation 3.2 mm Hg. If the normal range for intraocular
pressure is between 10 and 22 mm Hg, than what proportion of the general population would
fall within this range?
Answers
A z-table is also known as the standard normal distribution table. The percentage of the population that would fall in the 10 to 22 mm Hg range is 0.9386.
What is a Z-table?A z-table also known as the standard normal distribution table, helps us to know the percentage of values that are below (or to the left of the Distribution) a z-score in the standard normal distribution.
Given the mean and the standard deviation are 16mmHg and 3.2 mmHg, therefore, the percentage of the population whose blood pressure will fall in the range of 10 to 22 mm Hg are,
[tex]P(10 < x < 22) = P(\dfrac{10-16}{3.2} < Z < \dfrac{22-16}{3.2})[/tex]
[tex]= P(-1.875 < Z < 1.875)\\\\=P(Z < 1.875)-P(Z < -1.875)\\\\= 0.9693-0.0307\\\\= 0.9386[/tex]
Hence, the percentage of the population that would fall in the 10 to 22 mm Hg range is 0.9386.
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I WILL GIVE 20 POINTS TO THOSE WHO ANSWER THIS QUESTION RIGHT NOOOO SCAMS AND EXPLAIN WHY THAT IS THE ANSWER
Answers
Answer:
Step-by-step explanation:
This Venn diagram shows the pizza topping preferences for 9 students. LIKES LIKES PEPPERONI OLIVES Joe Kalie Petal Noah Owen Let event A = Student likes pepperoni. Let event B = Student likes olives. What elements are in A and B? OA. (Maria, Zack, Bo} B. (Petal, Owen, Julia) C. (Joe, Kalie, Noah, Maria, Zack, Bo, Julia} OD. (Petal, Owen) Maria... Zack Bo Julia
Answers
The elements that are in A and B in the Venn diagram that represents the pizza topping preferences are (Maria, Zack, Bo).
What elements are in A and B?
A venn diagram represents information in a set using circles. The intersection of both circles represents those that like both pepperoni and olives. This is element A and B.
The names at the intersection of both circles are (Maria, Zack, Bo).
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A store is handing out coupons worth 30%, 35%, or 40% off Each coupon is equally likely to be handed out. Which of the following models could be used to simulate this situation?
Answers
Your correct answer is 3.
Sure hope this helps you and pls mark me brainiest :)
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sketch the region enclosed by y=6x and y=8x^2. find the area of the region.
Answers
Answer:
The area enclosed by the given curves is square units.
Step-by-step explanation:
The given equations are
Draw the graph of the given equations.
From the below graph it is clear that both curves intersect each other at (2,12) and (4,24).
The area of the region enclosed by curves is
Therefore the area enclosed by the given curves is square units.