The function that satisfies F Has An Inverse G That Satisfies G'(2) = 1/6 is f(x) = 2x³ (option a).
More precisely, if f(x) is a function, then its inverse function g(x) satisfies the following two conditions:
g(f(x)) = x for all x in the domain of f
f(g(x)) = x for all x in the domain of g
In other words, if we apply f(x) to an input value x, and then apply g(x) to the resulting output, we get back to the original input value.
Now, let's look at the given condition: G'(2) = 1/6. This means that the derivative of the inverse function at x=2 is 1/6. We can use this condition to eliminate some of the options.
f(x) = 2x³
If we take the derivative of f(x), we get: f'(x) = 6x²
To find the inverse function, we can solve for x in the equation y = 2x³:
x = [tex]y/2^{(1/3)}[/tex]
Now we can express the inverse function g(x) in terms of y:
g(y) = [tex]y/2^{(1/3)}[/tex]
To find the derivative of g(x), we use the chain rule:
g'(x) = f'(g(x))⁻¹
g'(2) = f'(g(2))⁻¹
g'(2) = f'([tex]1/2^{(1/3)}[/tex])⁻¹
g'(2) = 6([tex]1/2^{(1/3)}[/tex])²)⁻¹
g'(2) = 6/36 = 1/6
Since g'(2) = 1/6, option a) is the correct answer.
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You have been hired t0 design family-friendly see-saw. Your design will featurc uniform board (mass M , length L) that can be moved so that the pivot is distance d from the center of the board. This will allow riders t0 achieve static equilibrium even if they are of different mass_ as most people are _ You have decided that each rider will be positioned so that hishher center of mass will be distance Xoffset from the end of the board when seated as shown. You have selected child of mass m (shown on the right) , and an adult of mass times the mass of the child (shown On the left) to test out your prototype. (a) Derive an expression for the torque applied by the adult rider (on the left) in terms of given quantities and variables available in the palette. Assume counterclockwise is positive_ Xoffct Xottct (b) Derive an expression for the torque applied by the child rider (on the right) in terms of given quantities and variables available in the palette . Assume counterclockwise is positive. Derive an expression for the torque applied by the board in terms of given quantities and variables available in the palette_ Othcexpertta.COm Determine the distance d in terms of n, g and the masses and lengths in the problem. Determine the magnitude of the force exerted on the pivot point by the see-saw while in use in terms of given quantities and variables available in the palette'
Where F_pivot is the magnitude of the force exerted on the pivot point.
What are perpendicular lines?
Perpendicular lines are lines that intersect at a right angle (90 degrees). In other words, if you draw a line perpendicular to another line, the two lines will form four right angles at the point where they intersect.
(a) The torque applied by the adult rider (on the left) can be calculated as the product of the force applied by the rider and the perpendicular distance from the pivot to the force. Let F_a be the force applied by the adult rider and let r_a be the perpendicular distance from the pivot to the force. Then, the torque applied by the adult rider is:
τ_a = F_a * r_a
The perpendicular distance r_a can be calculated using the Pythagorean theorem:
r_a = sqrt((L/2 - d)^2 + Xoffset^2)
Therefore, the torque applied by the adult rider is:
τ_a = F_a * sqrt((L/2 - d)^2 + Xoffset^2)
(b) Similarly, the torque applied by the child rider (on the right) can be calculated as:
τ_c = F_c * sqrt((L/2 + d)^2 + Xoffset^2)
where F_c is the force applied by the child rider and r_c is the perpendicular distance from the pivot to the force, which can be calculated using the Pythagorean theorem.
(c) The torque applied by the board can be calculated as the sum of the torques applied by the two riders:
τ_b = τ_a + τ_c
Substituting the expressions for τ_a and τ_c, we get:
τ_b = F_a * sqrt((L/2 - d)^2 + Xoffset^2) + F_c * sqrt((L/2 + d)^2 + Xoffset^2)
(d) To determine the distance d in terms of given quantities and variables, we can use the condition for static equilibrium, which requires that the sum of the torques about the pivot point is zero:
τ_a + τ_c = 0
Substituting the expressions for τ_a and τ_c and simplifying, we get:
F_a * (L/2 - d) = F_c * (L/2 + d)
Solving for d, we get:
d = (F_a/F_c - 1) * L/4
Substituting F_a = Mg and F_c = mg, where M is the mass of the adult rider, m is the mass of the child rider, and g is the acceleration due to gravity, we get:
d = (M/m - 1) * L/4
(e) The magnitude of the force exerted on the pivot point by the see-saw while in use can be calculated using the condition for static equilibrium, which requires that the sum of the forces in the vertical direction is zero:
F_a + F_c = Mg + mg
Substituting F_a = Mg and F_c = mg, we get:
F_pivot = Mg + mg
Therefore, where F_pivot is the magnitude of the force exerted on the pivot point.
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FAST
Write two expressions to represent the following situation. Then, find the answer.
When Nathan went to bed, the outside temperature was 28°F. When he woke up the next morning, the temperature had decreased to -13°F. By how many degrees did the temperature change during the overnight hours
The temperature changed by 41°F during the overnight hours, decreasing from 28°F to -13°F.
How is an expression determined?The difference in temperature from 28°F to -13°F can be shown in one of two ways:
Temperature change equals final temperature - The starting temperatureTemperature change: (-13°F) - (28°F)Temperature change: -41°FTemperature change = final temperature minus initial temperature; temperature change = -13°F minus 28°F; temperature change = -41°F; temperature change = 41°F.To calculate the change in temperature, the first exponent equation subtracts the initial temperature from the end temperature. The change in this instance is negative and points to a drop in temperature.
The absolute value function is employed in the second statement to guarantee a positive result regardless of whether the temperature rose or fell. The result is the same as the first expression in this instance, but with a positive sign.
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Mariana and her children went into a movie theater and she bought $51.25 worth of candies and pretzels. Each candy costs $4.75 and each pretzel costs $3.25. She bought a total of 13 candies and pretzels altogether. Write a system of equations that could be used to determine the number of candies and the number of pretzels that Mariana bought. Define the variables that you use to write the system.
pls help i have trouble figuring out what equations im suppose to use to solve.
Answer: 51.25 = 4.75c + 3.25p
Step-by-step explanation:
1. Since she spent $51.25, we can start our equation with this: 51.25=
2. Since she bought candies and pretzels, we can make 2 new variables, c for candies, and p for pretzels.
3. Since she spent $4.75 per candy, we can add this in to our equation:
51.25 = 4.75c +
4. We can do the same for the pretzels, which she spent $3.25 per piece. Adding this into our equation will leave us with: 51.25 = 4.75c + 3.25p.
5. Now we have to find out what c and p are, given the info that she bought 13 altogether.
6. If we c=6 and p=7, (because they add up to 13) we will get: 51.25!
7. Now we know what c and p are.
8. The answers would be 51.25 = 4.75c + 3.25p, or 51.25=28.5+22.75.
Ignacio makes a display shelf from 4 wooden boards. All angles formed by the
boards are right angles. Ignacio plans to stain all faces of the shelf, except the
back face, which will be against the wall. What is the total area Ignacio will
stain? Show your work.
512
7 in.
1
2
32 in.
30 in.
72
17
56
9 in.
4 in.
512
24
A
329-30.7
72
Answer:
shelf area = 19018.33 square inches
Step-by-step explanation:
shelf area calculation:
Ignacio makes a display shelf from 4 wooden boards. All angles formed by the boards are right angles. Ignacio plans to stain all faces of the shelf, except the back face, which will be against the wall. What is the total area Ignacio will stain? Show your work. 512 7 in. 1 2 32 in. 30 in. 72 17 56 9 in. 4 in. 512 24 A 329-30.7 72
To find the total area that Ignacio will stain, we first need to determine the area of each face that will be stained.
Let's label the boards as follows:
Board 1: 512 in x 7 in
Board 2: 12 in x 32 in
Board 3: 30 in x 72 in
Board 4: 17 56/9 in x 4 in
For each board, we need to find the total area of all the faces that will be stained.
Board 1 has two faces that will be stained: the top face and the two side faces. The area of the top face is 512 in x 7 in = 3584 in^2. The area of each side face is 512 in x 12 in = 6144 in^2. So the total area of all three faces is 3584 in^2 + 2 x 6144 in^2 = 15872 in^2.
Board 2 has three faces that will be stained: the top face and the two side faces. The area of the top face is 12 in x 32 in = 384 in^2. The area of each side face is 12 in x 4 in = 48 in^2. So the total area of all three faces is 384 in^2 + 2 x 48 in^2 = 480 in^2.
Board 3 has three faces that will be stained: the top face and the two side faces. The area of the top face is 30 in x 72 in = 2160 in^2. The area of each side face is 72 in x 4 in = 288 in^2. So the total area of all three faces is 2160 in^2 + 2 x 288 in^2 = 2736 in^2.
Board 4 has two faces that will be stained: the top face and the side face. The area of the top face is 17 56/9 in x 4 in = 71 2/3 in^2. The area of the side face is 17 56/9 in x 9 in = 158 2/3 in^2. So the total area of both faces is 71 2/3 in^2 + 158 2/3 in^2 = 230 1/3 in^2.
To find the total area that Ignacio will stain, we just need to add up the areas of all the faces that will be stained:
15872 in^2 + 480 in^2 + 2736 in^2 + 230 1/3 in^2 = 19018 1/3 in^2
Therefore, the total area that Ignacio will stain is approximately 19018.33 square inches.
original question :
Ignacio makes a display shelf from 4 wooden boards. All angles formed by the boards are right angles. Ignacio plans to stain all faces of the shelf, except the back face, which will be against the wall. What is the total area Ignacio will stain? Show your work. 512 7 in. 1 2 32 in. 30 in. 72 17 56 9 in. 4 in. 512 24 A 329-30.7 72
chatgpt
What is the equation for a cosecant function with vertical asymptotes found at x equals pi over 2 plus pi over 2 times n comma such that n is an integer?
f (x) = 2cscx
g(x) = 4csc2x
h(x) = 4csc3x
j of x is equal to 2 times cosecant of the quantity x over 2 end quantity
The equation for a cosecant function with vertical asymptotes found at x equals pi over 2 plus pi over 2 times n, where n is an integer, is [tex]f(x) = csc(x - \pi/2)[/tex] .
What is the cosecant function ?
The cosecant function is a trigonometric function that is defined as the reciprocal of the sine function. It is denoted as csc(x) and is defined for all values of x except where sin(x) is equal to zero. The graph of the cosecant function shows a series of vertical lines where the function is undefined, called vertical asymptotes. The value of the cosecant function oscillates between positive and negative infinity as it approaches these asymptotes. The cosecant function is used in trigonometry and calculus to model periodic phenomena such as sound and light waves.
Determining the equation for a cosecant function with vertical asymptotes :
The cosecant function has vertical asymptotes at the zeros of the sine function, which are given by
[tex]x = \pi/2 + n\times\pi[/tex], where n is an integer.
To shift the graph of the cosecant function horizontally by [tex]\pi/2[/tex] units to the right, we subtract [tex]\pi/2[/tex] from the input variable x, so the equation becomes [tex]f(x) = csc(x - \pi/2)[/tex].
[tex]f(x) = csc(x - \pi/2)[/tex] is the equation for a cosecant function with vertical asymptotes found at [tex]x = \pi/2 + n\pi[/tex], where n is an integer.
[tex]g(x) = 4csc(2x)[/tex] is the equation for a cosecant function with period pi, amplitude 4, and vertical asymptotes found at [tex]x = \pi/2 + n\pi[/tex], where n is an integer.
[tex]h(x) = 4csc(3x)[/tex] is the equation for a cosecant function with period [tex]2\pi/3[/tex], amplitude 4, and vertical asymptotes found at [tex]x = \pi/6 + n\pi,[/tex] where n is an integer.
[tex]j(x) = 2csc(x/2)[/tex] is the equation for a cosecant function with period 4pi, amplitude 2, and vertical asymptotes found at [tex]x = 2n\pi[/tex], where n is an integer.
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a friend has an 81% average before a final exam. The score includes everything but the final, which counts for 15% of the grade. What is the minimum to earn 75% for the course?
Answer:
57
Step-by-step explanation:
Okay, So we have this person That has 81% average before the quiz. For a course That score includes everything, but the final, which counts for 25% of the course grade, was the best course grade you your friend can earn. Okay, The best course grade given to me makes me. Mhm. 100. So we have .81 times. Actually we'll keep this as 81, times .75 right Plus 100 times. Excuse ME, Time 0.25. This is equivalent to 81 times 0.75. Mhm. This is equivalent to 81 times .75 plus 100 times 0.25, Which equals 85.75%. Now that's for part one. Report to we have what is the minimum score? Turn to 75%. So we have 75 equal to 81 times 0.75 Plus X. Times zero 25. So 81 times 0.75 equals 60.75 75- is value mhm. Is equal to 14.25. So we have 0.25 x. And if we divide 14.25 over 0.25, we isolate X. So the minimum score to get a 75 is a 57
Please answer Full question
(1) 4y-7z is a binomial.
(2) 8-xy² is a binomial.
(3) ab-a-b can be written as ab - (a + b) which is a binomial.
(4) z²-3z+8 is a trinomial.
What are monomials, binomials and trinomials?In algebra, monomials, binomials, and trinomials are expressions that contain one, two, and three terms, respectively.
A monomial is an algebraic expression with only one term. A monomial can be a number, a variable, or a product of numbers and variables.
A binomial is an algebraic expression with two terms that are connected by a plus or minus sign. For example, 2x + 3y and 4a - 5b are both binomials.
A trinomial is an algebraic expression with three terms that are connected by plus or minus signs.
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Classify into monomials, binomials and trinomials.
(1) 4y-7z
(1) 8-xy²
(v) ab-a-b
(ix) z2-3z+8
The simple interest formula 1 =
PRT
100
gives the interest I on a principal P
invested at a rate of R% per annum for
Tyears.
a) Find the interest when GH 2500 is
invested at 5% p.a. for 4 years.
b) Find the principal that gains an interest
of GH 2590 in 5 years at 7% per
annum,
The interest earned on GH 2500 at 5% p.a. for 4 years is GH 500.
The principal that gains an interest of GH 2590 in 5 years at 7% per annum is approximately GH 7400.
What is simple interest ?
Simple interest is a type of interest that is calculated on the principal amount of a loan or investment at a fixed rate for a specified period of time. It is based only on the principal amount, and does not take into account any interest earned on previous periods.
The formula for simple interest is:
I = P * R * T
where:
I is the interestP is the principal amountR is the interest rate per periodT is the number of periodsAccording to the question:
a) Using the simple interest formula, we have:
I = (P * R * T) / 100
Substituting P = GH 2500, R = 5%, and T = 4 years, we get:
I = (2500 * 5 * 4) / 100 = 500
Therefore, the interest earned on GH 2500 at 5% p.a. for 4 years is GH 500.
b) Using the same formula, we can solve for the principal P:
I = (P * R * T) / 100
2590 = (P * 7 * 5) / 100
2590 = (35P) / 100
35P = 2590 * 100
P = (2590 * 100) / 35
P ≈ GH 7400
Therefore, the principal that gains an interest of GH 2590 in 5 years at 7% per annum is approximately GH 7400.
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Question 6 (2 points)
A wire costs $3 per foot. How much will 18 inches of wire cost?
$1.50
$3.00
$4.50
$9
Answer:
$4.50
Step-by-step explanation:
There are 12 inches in a foot. 18 inches is 1.5 feet.
1 foot of wire is $3.00 and a half of foot should be $1.50.
1.5 feet of wire should cost $4.50
1.5 ft × $3/ft
= $4.50
A card is pulled from a deck of cards and noted. The card is then replaced, the deck is shuffled, and a second card is pulled and noted. What is the probability that both cards are face cards?
Answer: There is a 5.32544378% Chance of a face card being pulled twice
Step-by-step explanation: If there is 52 cards in a deck, and 12 of them are face cards, there is roughly a 23% (23.0769%) chance of pulling one in the first draw. Multiply .230769 x .230769 and you get .0532544378 which equals 5.32544378%
please help I know its 9:35 PM I Just need help what this question2.1 × 1.6 =
21
10
×
16
10
= tenths × tenths my parents are gonna kill me help
The value of the expression 2.1 × 1.6 = 3.36.
What are decimals?Decimals are a collection of numbers falling between integers on a number line. They are only an additional mathematical representation of fractions. Decimals allow us to express quantifiable quantities like length, weight, distance, money, etc. with more accuracy. Integers, also known as whole numbers, are represented to the left of the decimal point, while decimal fractions are shown to the right of the decimal point.
Given that the expression is: 2.1 × 1.6.
2.1 × 1.6 can be written as:
2.1 × 1.6 = 21/10 × 16/10
Multiply the numerator and denominator:
21/10 × 16/10 = 336/100
Covert the fraction into decimal:
336/100 = 3.36
Hence, the value of the expression 2.1 × 1.6 = 3.36.
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The graph of triangle has coordinates E(1,4) F(-1,1) and G(2,-1). Graph triangle of EFG and it’s image after a translation of 3 units left and 1 unit down.
Answer:
Step-by-step explanation:1.4 -1, 1 2, -1
Please help ASAP!!!! The average of two numbers is 13.One number is 10.What is the other number?
Answer:16
Step-by-step explanation:
average is similar to mean
you get the Total value and divide it with the number of values added
Examine the following graphed systems of linear inequalities. Select the points below that are solutions to each system of inequalities. Select TWO that apply.
1. 2.
(2,3) (0,0)
(4,3) (4,3)
(-7,6) (6,1)
(-2,3) (2-5)
I need help D: pls
The solution of the graphs are as follows
first graph
(2, 3)(4, 3)second graph
(4, 3)(6, 1)How to find the ordered pair that are solution of the graphThe graphs consist of two sets of equations plotted, each has shade peculiar to the equation.
The solution of the graph consist of the ordered pair that fall within the parts covered by the two shades
For the first graph by the left, the solutions are
(2, 3)(4, 3)For the second graph by the left, the solutions are
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the value of the given test statistic lies between the given cutoffs -2.58 and 2.58. it falls in acceptance region.
Here the values -0.94 and 2.12 falls between the points -2.58 and 2.58. The area between is the acceptance region. So we cannot reject the null hypothesis.
The given is an example for two tailed test. A two tailed test is used to determine whether the value is greater than or less than the mean value of the population. It represents the area under both tails or sides on a normal distribution curve.
Here the value of the test statistic lies between -2.58 and 2.58. So the values less than -2.58 and greater than 2.58 fall in the rejection region, where the null hypothesis can be rejected.
a) -0.94 falls between -2.58 and 2.58. So it is in the acceptance region. So null hypothesis is accepted.
b) 2.12 lies between -2.58 and 2.58. It is also in acceptance region. So null hypothesis is accepted.
So in both cases null hypothesis cannot be rejected.
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The complete question is :
f the cutoffs for a z test are -2.58 and 2.58, determine whether you would reject or fail to reject the null hypothesis in each of the following cases and explain why:
a. z = −0.94
b. z = 2.12
Each interior angle of a regular polygon is 140 Celcius.How many sides does the polygon have?
Answer:
9 sides
Step-by-step explanation:
180 - 140 = 40
360 ÷ 40 = 9
Represent each number line by an inequality.
Answer:
Step-by-step explanation:
The inequality in the first equation is x > 8.
The inequality for the second graph is x ≤ -4 since it's a dot.
Help please! I have no idea!!!!
The values of the function from the graph are h(7) = 10, h(0) = 9, h(t) = 8, t = 5 and h(t) = 0, t = 4
How to determine the value of the functionGiven that the graph is the graph of height as a function of time
To calculate the values of h(t) from the graph of g(x), we need to follow these steps
Identify the value of t on the x-axis where you want to calculate the value of h(t)Locate that point on the graphWrite the values from the pointUsing the above, we have the following
h(7) = 10
h(0) = 9
h(t) = 8, t = 5
h(t) = 0, t = 4
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Segment AE shown has length of sqrt 20. Which segment is closest in length to sqrt 10?
Segment C has a length of √10, which is the closest to √10 compared to the other segments.
What is Segment?Segment is a customer data platform (CDP) that enables companies to collect, store, and analyze customer data from multiple sources. It helps companies build customer profiles and create personalized experiences for their customers. Segment allows businesses to track website visits, user actions, and other events in real-time, as well as to create custom events and store customer data in a secure and unified data warehouse. With Segment, companies can create powerful customer segmentation, which allows them to target customers with personalized messages and offers. Segment also integrates with various marketing, analytics, and CRM tools to provide a complete picture of customer behavior. It enables companies to build cohesive customer journeys, run campaigns, and optimize their customer experience.
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Complete Question.
Two cars, one going due east at the rate of 90 km/hr and the other going to south at the rate of 60 km/hr are traveling toward the intersection of two roads. At what rate the two cars approaching each other at the instant when the first car is 0.2 km and the second car is 0.15 km from the intersection ?
The two cars are approaching each other at a rate of 36 km/hr at the given instant.
We can solve this problem by using the Pythagorean theorem and differentiating with respect to time. Let's call the distance of the first car from the intersection "x" and the distance of the second car from the intersection "y". We want to find the rate at which the two cars are approaching each other, which we'll call "r".
At any moment, the distance between the two cars is the hypotenuse of a right triangle with legs x and y, so we can use the Pythagorean theorem
r^2 = x^2 + y^2
To find the rates of change of x and y, we differentiate both sides of this equation with respect to time
2r(dr/dt) = 2x(dx/dt) + 2y(dy/dt)
Simplifying and plugging in the given values
dr/dt = (x(dx/dt) + y(dy/dt)) / r
dr/dt = (0.2 x 90 + 0.15 x (-60)) / sqrt((0.2)^2 + (0.15)^2)
dr/dt = (18 - 9) / sqrt(0.04 + 0.0225)
dr/dt = 9 / sqrt(0.0625)
dr/dt ≈ 36 km/hr
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This problem explores some questions regarding the fishery model
dt
dP
=P(1−P)−h
If you have not yet run the Jupyter notebook please do so now. Find analytical expressions for the two fixed points of the model, in terms of
h
. Give an expression for the stable fixed point. You may assume that the larger fixed point is the stable one. For what values of
h
does there exist a fixed point?
a) The expression for the stable fixed point is P* = (1 + sqrt(1 - 4h)) / 2
b) There exists a fixed point for all values of h less than or equal to 1/4.
The fixed points of the model are the values of P at which dP/dt = 0. Therefore, we need to solve the equation
P(1-P) - h = 0
Expanding the left-hand side, we get
P - P^2 - h = 0
Rearranging, we get a quadratic equation
P^2 - P + h = 0
Using the quadratic formula, the two solutions for P are
P = (1 ± sqrt(1 - 4h)) / 2
a) The larger root is the stable fixed point, as it corresponds to a minimum of the fish population growth function. Therefore, the expression for the stable fixed point is
P* = (1 + sqrt(1 - 4h)) / 2
b) For the model to have a fixed point, the quadratic equation must have real roots. This occurs when the discriminant (the expression inside the square root) is non-negative
1 - 4h ≥ 0
Solving for h, we get
h ≤ 1/4
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The given question is incomplete, the complete question is:
This problem explores some questions regarding the fishery model
dP/dt =P(1−P)−h
If you have not yet run the Jupyter notebook please do so now. Find analytical expressions for the two fixed points of the model, in terms of h
a) Give an expression for the stable fixed point. You may assume that the larger fixed point is the stable one. b) For what values of h does there exist a fixed point?
Determine the slope from the table given below.
Answer:
m = 6
Step-by-step explanation:
Slope = rise/run or (y2 - y1) / (x2 - x1)
Pick 2 points on the table (4,6) (5,12)
We see the y increase by 6 and the x increase by 1, so the slope is
m = 6
So, the slope is 6
p(s) = s³ + 10s
f(s) = 6s - 3
Find p(2)-f(2)
Answer:
19
Step-by-step explanation:
We are given the following two functions of s
[tex]p(s) = s^3 + 10s\\f(s) = 6s - 3\\\\\text{To find p(2) substitute 2 for s in p(s)}\\p(2) = (2)^3 + 10(2) = 8 + 20 = 28\\\\[/tex]
[tex]\text{To find f(2) substitute 2 for s in f(s)}\\f(2) = 6(2) - 3= 12 - 3= 9\\[/tex]
[tex]p(2) - f(2) = 28 - 9 = 19[/tex]
If vec r =3 hat i -2 hat j +6 hat k , find the value of ( vec r * hat j ).( vec r * hat k )-12
Answer: We can first find the dot product of vec r with hat j and hat k:
vec r * hat j = (3 hat i - 2 hat j + 6 hat k) * (- hat j) = -2
vec r * hat k = (3 hat i - 2 hat j + 6 hat k) * hat k = 6
Substituting these values into the expression given, we get:
(vec r * hat j).(vec r * hat k) - 12 = (-2) * (6) - 12 = -24
Therefore, the value of (vec r * hat j).(vec r * hat k) - 12 is -24.
Step-by-step explanation:
1) Pendant la période des soldes, tous les manteaux d'un magasin sont soldés à 15%.
a. Marjorie a repéré un manteau qui coûtait initialement 78€.
Quel est son prix après réduction ?
b. Mélanie veut acheter un manteau dont le prix après réduction est de 55,25€.
Quel était son prix initial ?
2) Manu affirme que sur les étiquettes suivantes, le pourcentage de réduction appliqué au prix
de la montre est supérieur à celui appliqué aux lunettes. A-t-il raison ?
45€→ 35,55€
Réduction
de 20%
Answer: Zemāk
Step-by-step explanation:
1)
a. Le prix du manteau après la réduction de 15% est:
78€ - (15/100)*78€ = 66,30€
Le prix du manteau après la réduction est de 66,30€.
b. Soit x le prix initial du manteau.
Le prix du manteau après la réduction de 15% est:
x - (15/100)*x = 55,25€
Simplifions cette équation:
0,85x = 55,25€
x = 65€
Le prix initial du manteau était de 65€.
2)
Pour les lunettes, le prix initial est de 45€ et la réduction appliquée est de 20%:
45€ - (20/100)*45€ = 36€
Pour la montre, le prix initial est de 35,55€ et la réduction appliquée est également de 20%:
35,55€ - (20/100)*35,55€ = 28,44€
On constate que le pourcentage de réduction est le même pour les deux articles, donc Manu a tort.
He has 2 pens. His friend gives him 2 more pens. How many pens he has?
Step-by-step explanation:
4 i guess... sry i m not good at maths
Question content area top
Part 1
Find the future value of an ordinary annuity if payments are made in the amount R and interest is compounded as given. Then determine how much of this value is from contributions and how much is from interest.
R; % interest compounded semiannually for years.
Question content area bottom
Part 1
The future value of the ordinary annuity is $
177,961.83.
(Round to the nearest cent as needed.)
Part 2
The amount from contributions is $
enter your response here and the amount from interest is
$
enter your response here. (Round to the nearest cent as needed.)
The Amount from contributions = R * n
Define the term future value?The future value refers to the value of an asset or investment at a specified time in the future, based on a specific interest rate or rate of return.
Without knowing the specific values of R, interest rate, and number of years, we cannot calculate the amounts from contributions and interest. However, we can provide the general formula for calculating the future value of an ordinary annuity:
FV = R * [(1 + i)ⁿ - 1] / i
where FV is the future value of the annuity, R is the periodic payment, i is the interest rate per period, and n is the number of periods.
To calculate the amount from contributions, we can multiply the periodic payment R by the number of periods n.
Amount from contributions = R * n
To calculate the amount from interest, we can subtract the amount from contributions from the future value of the annuity.
Amount from interest = FV - R * n
Once the specific values for R, interest rate, and number of years are provided, we can use these formulas to calculate the amounts from contributions and interest.
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what does -12x +24= equal
To solve the equation -12x + 24 = 0, we want to get x by itself on one side of the equation.
First, we can subtract 24 from both sides:
- 12x + 24 - 24 = 0 - 24
This simplifies to:
- 12x = -24
Next, we can divide both sides by -12:
- 12x / -12 = -24 / -12
This simplifies to:
x = 2
Therefore, the solution to the equation -12x + 24 = 0 is x = 2.
A survey of 500 music lovers showed that 350 like rock, 300 like country, and 200 like both. How many of the 500 music lovers surveyed dislike both rock and country?
Answer:
50
Step-by-step explanation:
A Venn diagram is very helpful for this picture and I've included one in the attached.
If we look at the numbers we're given, we see that the numbers do not add up to 500 as 350 + 300 + 200 = 850.
However, we can work through the numbers to find the exact values and eventually the number of people that liked neither rock nor country.
Since 200 people like both rock and country, these people are part of the 350 people that like rock.
We can find the number of people who like rock only by subtracting 200 from 350:
350 - 200 = 150 (Rock only)
Using the same logic from above, we know that the 200 people who like both rock and country are a part of the 300 people who like country.
We can find the number of people who like country only by subtracting 200 from 300:
300 - 200 = 100 (Country only)
Currently, we have 450/500 as 150 + 200 + 100 = 450.
Now, we can find the number of people who like neither rock nor country by subtracting 450 from 500:
500 - 450 = 50 (Neither rock nor country)
We can check that the numbers we found equal 500:
Rock only + Both rock and country + Country only + Neither rock nor country = Total amount of music lovers surveyed
150 + 200 + 100 + 50 = 500
500 = 500
(**In the attached Venn diagram, M stands for the total set of music lovers, R stands for rock only, B stands for both, C stands for country only, and N stands for neither)
Por favor, necesito ayuda con esto es de estadística. Muchas gracias
Las calificaciones de 20 alumnos que presentaron exámen de admisión a cierta facultad, utilizando la escala de 0 a 100, fueron:
83 64 51 46 82 91 73 82 65 61 74 64 75 81 94 65 42 81 56 61 72 65 54 39 70 93 42 46 54 72
•Elaborar: diagrama de tallo y hoja
•Calcular: coeficiente de variación
•Realizar un diagrama de caja
•Percentil 85, decil 2
Therefore, the coefficient of variation for the given data is approximately 24.71%.
What is box plot?A box plot, also known as a box-and-whisker plot, is a graphical representation of a data set that shows the distribution of the data using quartiles. It is a standardized way of displaying the distribution of data based on the five-number summary: minimum, first quartile, median, third quartile, and maximum. The box represents the middle 50% of the data, with the median marked by a line inside the box. The whiskers extend from the box to the minimum and maximum values, or to a certain range if there are outliers. Box plots are useful for comparing the distributions of different data sets and identifying potential outliers.
Here,
1. Stem-and-Leaf Plot:
A stem-and-leaf plot is a way to display data that separates the tens digit of each number from the ones digit. Here is the stem-and-leaf plot for the given data:
3 | 9 9
4 | 2 2 6 6
5 | 1 4 4 6
6 | 1 4 5 5 5 5 5 5
7 | 0 2 3 4
8 | 1 2 2 3 5
9 | 3 4
In this plot, the stem represents the tens digit and the leaves represent the ones digit.
2. Coefficient of Variation:
The coefficient of variation is a measure of the relative variability of a data set. It is calculated as the ratio of the standard deviation to the mean, expressed as a percentage. Here is how to calculate the coefficient of variation for the given data:
Calculate the mean of the data:
Mean = (83+64+51+46+82+91+73+82+65+61+74+64+75+81+94+65+42+81+56+61+72+65+54+39+70+93+42+46+54+72)/20 = 68.25
Calculate the standard deviation of the data:
Standard deviation = sqrt((1/20) * ((83-68.25)^2 + (64-68.25)^2 + ... + (72-68.25)^2))
Standard deviation ≈ 16.88
Calculate the coefficient of variation:
Coefficient of variation = (Standard deviation / Mean) * 100
Coefficient of variation ≈ 24.71%
3. Box Plot:
A box plot is a way to visualize the distribution of data. It displays the minimum value, first quartile (Q1), median, third quartile (Q3), and maximum value of the data. Here is the box plot for the given data:
| +----------+
94 | |
| +----------+
93 | |
| +-----+-----+
82 | | |
| | |
81 | | |
| +-----+ |
80 | | |
| | |
79 | | |
| | |
78 | | |
| | |
77 | | |
| | |
76 | | |
| | |
75 | | |
| | |
74 | | |
| | |
73 | | |
| | |
72 | +-----------------+
|
+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
In this plot, the horizontal line inside the box represents the median, the bottom and top edges of the box represent the first and third quartiles (Q1 and Q3), respectively, and the vertical lines extending from the box represent the minimum and maximum values, excluding outliers.
4. To find the 85th percentile, we need to arrange the data in order from smallest to largest:
39, 42, 42, 46, 46, 51, 54, 56, 61, 61, 64, 64, 65, 65, 65, 70, 72, 72, 73, 74, 75, 81, 81, 82, 82, 83, 91, 93, 94
There are a total of 20 scores, so the 85th percentile would be the score at the 0.85(20) = 17th position:
85th percentile = 72
To find the 2nd decile, we first need to calculate the number of scores in each decile. Since there are 20 scores, each decile would have 2 scores. The 2nd decile would be the score at the 0.2(20) = 4th position:
2nd decile = 46
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Complete question:
Please, I need help with this, it's about statistics. Thank you very much. The grades of 20 students who took an admission exam to a certain faculty, using a scale of 0 to 100, were: 83 64 51 46 82 91 73 82 65 61 74 64 75 81 94 65 42 81 56 61 72 65 54 39 70 93 42 46 54 72
• Make: stem-and-leaf plot
• Calculate: coefficient of variation
• Create a box plot
• 85th percentile, 2nd decile.
