Answer:
4 inches
Step-by-step explanation:
large rectangle - 18:12 ratio = 3:2
small rectangle - 6:4 = 3:2
consider the function y=-2-cos(x-pi). What effect does pi have on the basic graph?
Using translation concepts, it is found that pi is the phase shift of the graph, and since it is negative, the graph is shifted right pi units.
What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s definition or in it’s domain. Examples are shift left/right or bottom/up, vertical or horizontal stretching or compression, and reflections over the x-axis or the y-axis.
In this problem, the change is given as follows:
x -> x - pi
It means that the change is in the domain, in which pi is the phase shift of the graph, and since it is negative, the graph is shifted right pi units.
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a swimming pool charges £3.60 for entry. you can save 1/3 of entry fee with a membership card. on his first visit, ken spends £5 on a membership card plus the reduced entry fee. how many times does ken visit before he gets back his £5
The number of times Ken visits, given the £3.6 pool charge, and 1/3 savings per visit is 5 times.
Which method can be used to find the number of times Ken visits the pool to get back his £5?The entry fee = £3.60
Amount saved on entry fee by having a membership card = 1/3 of the entry fee
Amount Ken spends on the membership card and the reduced entry fee = £5
Therefore;
Reduced entry fee = £3.60×(1 - 1/3) = £2.4
Amount saved per visit = £3.6 - £2.4 = £1.2
The number of visits, n, before he gets back his £5 is therefore;
n = £5/(£1.2/visit) ≈ 4.17 visitsKen has to visit the swimming pool more than 4 times to get his £5 back.
Rounding to the next larger whole, therefore;
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Determine a solution to system of linear inequalities graphed and justify your answer.
please help!!!
maths functions
Answer:
Point A: (2, 10)
Point B: (-3, 0)
Point C: (-5, -4)
Point D: (-5, -32)
Step-by-step explanation:
Part (a)Points A and B are the points of intersection between the two graphs.
Therefore, to find the x-values of the points of intersection, substitute one equation into the other and solve for x:
[tex]\implies 2x+6=-2x^2+18[/tex]
[tex]\implies 2x^2+2x-12=0[/tex]
[tex]\implies 2(x^2+x-6)=0[/tex]
[tex]\implies x^2+x-6=0[/tex]
[tex]\implies x^2+3x-2x-6=0[/tex]
[tex]\implies x(x+3)-2(x+3)=0[/tex]
[tex]\implies (x-2)(x+3)=0[/tex]
[tex]\implies x=2, -3[/tex]
From inspection of the graph:
The x-value of point A is positive ⇒ x = 2The x-value of point B is negative ⇒ x = -3To find the y-values, substitute the found x-values into either of the equations:
[tex]\begin{aligned} \textsf{Point A}: \quad 2x+6 & =y\\2(2)+6 & =10\\ \implies & (2, 10)\end{aligned}[/tex]
[tex]\begin{aligned} \textsf{Point B}: \quad -2x^2+18 & =y\\-2(-3)^2+18 & =0\\ \implies & (-3,0)\end{aligned}[/tex]
Therefore, point A is (2, 10) and point B is (-3, 0).
Part (b)If the distance between points C and D is 28 units, the y-value of point D will be 28 less than the y-value of point C. The x-values of the two points are the same.
Therefore:
[tex]\textsf{Equation 1}: \quad y=2x+6[/tex]
[tex]\textsf{Equation 2}: \quad y-28=-2x^2+18[/tex]
As the x-values are the same, substitute the first equation into the second equation and solve for x to find the x-value of points C and D:
[tex]\implies 2x+6-28=-2x^2+18[/tex]
[tex]\implies 2x^2+2x-40=0[/tex]
[tex]\implies 2(x^2+x-20)=0[/tex]
[tex]\implies x^2+x-20=0[/tex]
[tex]\implies x^2+5x-4x-20=0[/tex]
[tex]\implies x(x+5)-4(x+5)=0[/tex]
[tex]\implies (x-4)(x+5)=0[/tex]
[tex]\implies x=4,-5[/tex]
From inspection of the given graph, the x-value of points C and D is negative, therefore x = -5.
To find the y-value of points C and D, substitute the found value of x into the two original equations of the lines:
[tex]\begin{aligned} \textsf{Point C}: \quad 2x+6 & =y\\2(-5)+6 & =-4\\ \implies & (-5,-4)\end{aligned}[/tex]
[tex]\begin{aligned} \textsf{Point D}: \quad -2x^2+18 & = y \\ -2(-5)^2+18 & =-32\\ \implies & (-5, -32)\end{aligned}[/tex]
Therefore, point C is (-5, -4) and point D is (-5, -32).
Answer:
a) A = (2, 10) and B = (-3, 0)
b) C = (-5, -4) and D = (-5, -32)
Explanation:
a) To determine the coordinates of A and B, find the intersection points of the line "y = 2x + 6" and curve "y = -2x² + 18".
Solve the equation's simultaneously:
y = y
⇒ 2x + 6 = -2x² + 18
⇒ 2x² + 2x + 6 - 18 = 0
⇒ 2x² + 2x - 12= 0
⇒ 2x² + 6x - 4x - 12 = 0
⇒ 2x(x + 3) - 4(x + 3) = 0
⇒ (2x - 4)(x + 3) = 0
⇒ 2x - 4 = 0, x + 3 = 0
⇒ x = 2, x = -3
Then find value of y at this x points,
at x = 2, y = 2(2) + 6 = 10
at x = -3, y = 2(-3) + 6 = 0
Intersection points: A(2, 10) and B(-3, 0)
b) Given that CD = 28 units. Also stated parallel to y axis so x coordinates for both will be same but differ in y coordinate.
[tex]2x + 6 = -2x^2 + 18 + 28[/tex]
[tex]-2x^2 + 18 + 28-2x - 6 = 0[/tex]
[tex]-2x^2-2x+40=0[/tex]
[tex]-2x^2-10x+8x+40=0[/tex]
[tex]-2(x+5)+8(x+5)=0[/tex]
[tex](-2x+8)(x+5)=0[/tex]
[tex]x = -5, 4[/tex]
[tex]\leftrightarrow \sf C(-5, y_2), \ D(-5, y_2)[/tex]
Find y value for Point C : 2x + 6 = 2(-5) + 6 = -4
Find y value for Point D : -2x² + 18 = -2(-5)² + 18 = -32
[tex]\sf \rightarrow Point \ C = (-5, -4)\\ \\\rightarrow Point \ D = (-5, -32)[/tex]
Find the area of the sector formed by the 60 degree central angle.
503π in2503π in2
103π in2103π in2
100π in2100π in2
None of the Above
The area of the sector of the circle is: A. 50/3π in.².
What is the Area of a Sector of a Circle?The area of a sector that is bounded by two radii of a circle is calculated using the formula, ∅/360 × πr², where we have the following parameters:
r = radius of the circle∅ = central angle formed by the sector.Thus, we are given the following regarding the sector of the circle:
Central angle (∅) = 60 degrees
Radius (r) = 10 inches.
Plug in the values into ∅/360 × πr²:
Area of sector = 60/360 × π(10²)
Area of sector = 1/6 × π(100)
Area of sector = 100/6 × π
Area of sector = 50/3 × π
Area of sector = 50/3π in.²
Thus, the area of the sector of the circle is: A. 50/3π in.².
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Ivan bought two magazines for $4.95 each. If the sales tax was 6.75% what was the total amount that he paid for the magazines?
Step-by-step explanation:
the total sale price for the magazines were
2×4.95 = $9.90
so,
100% = 9.9
1% = 100%/100 = 9.9/100 = 0.099
6.75% = 6.75×1% = 6.75×0.099 = 0.66825 ≈ $0.67
so, he paid in total
$9.90 + $0.67 = $10.57
A home gardener estimates that 18 apple trees will produce an average yield of 80 apples per tree. But because of the size of the garden, for each additional tree planted, the yield will decrease by four apples per tree. How many trees should be planted to maximize the total
19 trees should be planted to maximize the total
How many trees should be planted to maximize the totalFrom the question, we have the following parameters:
Number of apples, x = 18
Yield, f(x) = 80 per tree
When the number of apple trees is increased (say by x).
We have:
Trees = 18 + x
The yield decreases by four apples per tree.
So, we have
Yield = 80 - 4x
So, the profit function is
P(x) = Apples * Yield
This gives
P(x) = (18 + x) *(80 - 4x)
Expand the bracket
P(x) = 1440 - 72x + 80x - 4x^2
Differentiate the function
P'(x) = 0 - 72 + 80 - 8x
Evaluate the like terms
P'(x) = 8 - 8x
Set P'(x) to 0
8 - 8x = 0
Divide through by 8
1 - x = 0
Solve for x
x = 1
Recall that:
Trees = 18 + x
So, we have
Trees = 18 + 1
Evaluate
Trees = 19
Hence, 19 trees should be planted to maximize the total
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6
Select the correct answer.
A company polled a large group of people to assess the company's reputation in the surrounding communities. To save time, the survey was
mailed to the addresses of stockholders and former employees that the company already had on file and that were in the surrounding areas.
Which of the following statements is correct?
Answer:
a company powder large group of people to assess the company's reputation in the surrounding
PLEASE HELP ME WITH THIS QUESTION I NEED HELP
Answer:
True
Step-by-step explanation:
This is true in an equilateral triangle.
HOW MANY DISTINCT ARRANGEMENTS CAN BE MADE WITH THE LETTERS IN THE
WORD CONNECTION?
There are 151200 distinct ways to arrange the letters of the word CONNECTION
How to determine the number of arrangements?The word is given as:
CONNECTION
In the above word, we have the following parameters:
Total number of characters, n = 10
The repeated letters are:
C's = 2
O's = 2
N's = 3
The number of arrangements of the letters is then calculated as:
Arrangements = n!/(C! * O! * N!)
Substitute the known values in the above equation
Arrangements = 10!/(2! * 2! * 3!)
Evaluate the expression
Arrangements = 151200
Hence, there are 151200 distinct ways to arrange the letters of the word CONNECTION
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Jake goes to the grocery store and buys 3 apples, 2 cans of soup, and 1 box of cereal. The apples cost $0.89 each; the soup costs $2.98 per can; and the box of cereal costs $4.99. Write an equation that represents the total cost c of Jake’s purchases.
The equation that represents the total cost, c, of the purchases made by Jake is: c = 3(0.89) + 2(2.98) + 4.99.
How to Write the Equation of Total Cost?To write the equation that represents the total cost of a given scenario like the one given, you can use variables to represent each component that makes up the total cost in the given situation.
Thus, let:
a = apple = 3a
s = can of soup = 2s
b = box of cereal = b
c = total cost
We know that unit price of each items are:
Apple = $0.89
Can of soup = $2.98
Box of cereal = $4.99
Equation would be:
c = 3a + 2s + b
Plug in the values
c = 3(0.89) + 2(2.98) + 4.99
Therefore, the equation that represents the total cost, c, of the purchases made by Jake is: c = 3(0.89) + 2(2.98) + 4.99.
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The Mogul Runners ski club planned a trip to Park City. Of the total number of club members, 11 signed up to go. If this is 25% of the club, how many members does the ski club have?
The ski club has 44 members in all
What is population?
Population refers to the total number of items or individuals that form a group.
In this case, the population means the total number of all members in the Mogul Runners ski club.
What is sample?
Sample means a fraction of the total population, in other words, the 25% of the members, whose number is 11, that signed up to go for the planned trip.
We can convert 25% to 100% by equation 25% to 11 members that signed up to go for the planned trip.
25% of club members=11 members
divide both sides by 25%
25%/25% of club members=11/25% members
club members=44 members
The ski club has 44 members altogether as computed above.
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3(q+ 4/3 )=2 solve for Q
Answer: q = -2/3
Step-by-step explanation:
First, we need to apply the Distributive Law in order to proceed with the problem.
3(q + 4/3) = 2
3q + 3(4/3) = 2
We already know that 3(4/3) = 4, since the 3's cancel out. Or, 3(4/3) = 12/3 = 4.
Our new equation is,
3q + 4 = 2
Through transposition and isolation of variables, we get,
3q = -2
Dividing by 3 on both sides...
q = -2/3
Mr. Gosain?(1 Aana = 31.8 m²) b) A real estate agent bought two triangular Kittas' having a common side as shown in the figure from two people for Rs 20,00,000 altogether. If he immediately sold the land in the shape of a quadrilateral at Rs 15,00,000 per Kattha, find his profit or loss.(1 Kattha= 338.63 sq. m) danta Excel in Mathematics - Book 9 86 36 m Approved by Curriculum Development Cen 20 m 29 m 25 m 21 m aktapur
The information given regarding the computation of the profit or loss shows that there's a loss of RS 500,000.
How to calculate the profit?From the information given, it was stated that the real estate agent bought two triangular Kittas' having a common side as shown in the figure from two people for Rs 2000,000 altogether.
It was further depicted that he sold the land in the shape of a quadrilateral at Rs 1,500,000. In their case, the sale is less than the cost and therefore, there's a loss.
The loss will be:
= 2,000,000 - 1,500,000
= 500,000
Therefore, the information given regarding the computation of the profit or loss shows that there's a loss of RS 500,000.
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Tried doing it myself multiple times , multi choice question, not getting any availabile answer.
Answer: The given integral is impossible to solve.
Step-by-step explanation: I tried solving it right now with integration by parts and trigonometric substitution, and I was unable to solve it.
So I looked at two math solvers and tried inputting the question, and it either says "There is nothing more you can do with this problem," or "We are unable to solve this problem."
First, let's substitute [tex]x=\frac w4[/tex] and [tex]dx=\frac{dw}4[/tex] to get rid of the fraction.
[tex]\displaystyle \int \csc^6\left(\dfrac w4\right) \cot^4\left(\dfrac w4\right) \, dw = 4 \int \csc^6(x) \cot^4(x) \, dx[/tex]
Recall that
[tex]\cot^2(x) + 1 = \csc^2(x)[/tex]
[tex]\dfrac{d}{dx} \cot(x) = -\csc^2(x)[/tex]
We can the rewrite the integrand as
[tex]\displaystyle 4 \int \csc^6(x) \cot^4(x) \, dx = 4 \int \left(\cot^2(x) + 1\right)^2 \cot^4(x) \csc^2(x) \, dx[/tex]
then substitute [tex]y=\cot(x)[/tex] and [tex]dy=-\csc^2(x)\,dx[/tex] to get
[tex]\displaystyle -4 \int (y^2 + 1)^2 y^4 \, dy[/tex]
Expand the integrand.
[tex]\displaystyle -4 \int (y^4 + 2y^2 + 1) y^4 \, dy = -4 \int (y^8 + 2y^6 + y^4) \, dy[/tex]
Now integrate with the power rule.
[tex]\displaystyle -4 \left(\frac{y^9}9 + \frac{2y^7}7 + \frac{y^5}5\right) + C[/tex]
[tex]\displaystyle -\frac{4y^9}9 - \frac{8y^7}7 - \frac{4y^5}5 + C[/tex]
Put everything back in terms of [tex]x[/tex], then [tex]w[/tex].
[tex]\displaystyle -\frac{4\cot^9(x)}9 - \frac{8\cot^7(x)}7 - \frac{4\cot^5(x)}5 + C[/tex]
[tex]\displaystyle \boxed{-\frac49 \cot^9\left(\dfrac w4\right) - \frac87 \cot^7\left(\dfrac w4\right) - \frac45 \cot^5\left(\dfrac w4\right) + C}[/tex]
you are considering an investment into Company XYZ and need to determine the company's value and the appropriate investment amount. You have been provided with historical financial statements for the past three years in order to build a forecast model. Key assumptions to use include:
Future sales revenue is assumed to increase at 2.5% annually.
Gross margin for 2021E is assumed to be equal to the average gross margin % for 2019 and 2020, but will decrease by 2.5% (i.e. 250 bps) each year thereafter
SG&A expense is assumed to be a percentage of revenue for the forecast period. That percentage is equal to the 2018-2020 average
Depreciation expense is assumed to be a percentage of revenue for the forecast period. That percentage is equal to the 2018-2020 average
The tax rate for the forecast period is assumed to be equal to the effective tax rate for 2018
Capital expenditures for any given year in the forecast period is assumed to be 3x the prior year's depreciation expense. For example, 2021 capital expenditures is equal to 3x 2020 depreciation expense.
No new debt or equity is assumed to be issued
Download CFI_-_FMVA_Practice_Exam_Case_Study_A.xlsx and answer the following 12 questions.
1
What is Gross Profit in 2028E using the assumptions listed above and on the Control Panel?
$17,545
$30,704
$27,780
$40,938
Option A is correct. The gross profit that has been calculated for this year is given as 17545
How to solve for the gross profit22050 × 97.5%(100-2.5%) = 21498.75
= 21498.75 × 0.975 = 20961.28
= 20961.28 x 0.975 = 20437.24
= 20437.24 x 0.975 = 19926.31
= 19926.31 × 0.975 = 19428.15
= 19428.15 x 0.975 = 18942.45
= 18942.45 x 0.975 = 18468.80
= 18468.89 × 0.975 = 18017
= 18007 × 0.975 = $17545
Hence we can see at the end of the solution that the value of the gross profit in 2028 = $17545
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HOW MANY DIFFERENT COMMITTEES CAN BE FORMED FROM 4 TEACHERS AND 20
STUDENTS IF THE COMMITTEE IS TO CONSIST OF TWO TEACHERS AND THREE
STUDENTS?
Answer:
6840
Step-by-step explanation:
multiply combinations
n!/(r!(n − r)!)
n choose r
n (objects) = |n
r (sample) = r
(4 teachers, CHOOSE 2)*(20 students, CHOOSE 3)
C(4,2) times C(20,3) =
C(n,r)=?
C(n,r) = C(4,2)
4! / (2!(4-2)!)
4! /2! x 2!
= 6
C(n,r)=?
C(n,r) = C(20,3)
20! / (3!(20-3)!)
20! / 3! x 17!
= 1140
6 * 1140 = 6840
alegbracom Edwin McCravy
A _____ is a solid consisting of a suite a point not in the same plane as the square and all points between them
Answer:
Square Pyramid
Step-by-step explanation:
Thats what a Square Pyramid is
Which expression correctly represents "six more than the quotient of three and a number, decreased by eight"?
6+3/n-8
6+n/3-8
6+3/n+8
6+n/3+8
The option A is correct because the value of the statement is 6+3/n-8.
According to the statement
we have given that the statement and we have to write the statement in the numerical form.
So, For this purpose
we know that the given statement is
"Six more than the quotient of three and a number, decreased by eight".
In this statement "Six more than" indicates the sum between the quotient and 6.
And "The quotient of three and a number" indicates a fraction where the numerator is 3 and the denominator is , a number.
"Decreased by eight" indicates a subtraction between the quotient an 8 units".
If we unit all parts of the statements, we would have
6+3/n-8
So, From the given statement, The option A is correct because the value of the statement is 6+3/n-8.
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Exercise 18: 3 1. The populations of a city increased from 4 million to 1.1 million. Write in digits the number by which the population increased.
pls as fast as u can!!!!!!!!!!!!!!!!
Answer:
bro it had been decreased
so total had been decreased is (4,000,000-2,900,000)=1,100,000When we use statistical software to compare the means with a significance test, we obtain the following printout: Variance T DF Prob>|T| Unequal 2.9146 41.9 0.006 1.3.1 Interpret the P-value, in context, based on its definition. (Note: You are not being asked to make a decision at some α-level.
The interpretation of the p-value is that there is a 0.006 = 0.6% probability of the sample means differing by the amount that they differed on the sample.
What are the hypothesis tested?At the null hypothesis, it is tested if the means are equal, that is:
[tex]H_0: \mu_1 = \mu_2[/tex]
At the alternative hypothesis, it is tested if the means are different, that is:
[tex]H_1: \mu_1 \neq \mu_2[/tex]
Since we are testing if the means are different, we have a two-tailed test, which means that the p-value is the probability of the means differing by the amount they different on the sample, or a greater amount.
Hence, the interpretation is that there is a 0.006 = 0.6% probability of the sample means differing by the amount that they differed on the sample.
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6n−8(n+4)= what? Please help me
Answer:
-2n -32
Step-by-step explanation:
Acc. to BODMAS
we multiply first
⇒-6n - -8 x [(+4) (n)]
⇒ 6n - 8n x -32
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\textbf{Equation:}[/tex]
[tex]\mathsf{6n - 8(n + 4)}[/tex]
[tex]\huge\textbf{Solve: }[/tex]
[tex]\mathsf{6n - 8(n + 4)}[/tex]
[tex]\huge\textbf{Distribute \boxed{\bf -8} within the parenthesis:}[/tex]
[tex]\mathsf{= 6n - 8(n) - 8(4)}[/tex]
[tex]\mathsf{= 6n - 8n - 32}[/tex]
[tex]\huge\textbf{Combine the like terms: }[/tex]
[tex]\mathsf{= (6n - 8n) - (32)}[/tex]
[tex]\mathsf{= 6n - 8n - 32}[/tex]
[tex]\mathsf{= -2n - 32}[/tex]
[tex]\huge\textbf{Therefore, your answer should be:}[/tex]
[tex]\huge\boxed{\frak{{ -2n - 32}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}}[/tex]
Adult tickets to the fall play cost $8 and student tickets cost $4. The drama class sold 20 more adult tickets han student tickets to the fall play. to If the
class collected $880 from ticket sales, how many adult tickets were sold?
The drama class sold
adult tickets.
The solution
Answer:
80
Step-by-step explanation:
Let the number of adult tickets sold be a and the number of student tickets sold be s.
"The drama class sold 20 more adult tickets han student tickets to the fall play." means that a-20=s."the class collected $880 from ticket sales" means that 8a+4s=880, which is the same as 2a+s=220.Substituting the first equation into the second,
[tex]2a+a-20=220 \\ \\ 3a-20=220 \\ \\ 3a=240 \\ \\ a=80[/tex]
Which of the following is not true about two integers p and q, where p is even and g is odd? A p+q is odd. B. pq is even C q +1 even. D. q + 5 is odd.
Answer:
The statement "q + 5 is odd" is FALSE.
Step-by-step explanation:
Let p = 2 and q = 3.
A. p + q is odd ... 2 + 3 = 5 TRUE
B. pq is even ... 2*3 = 6 TRUE
C. q + 1 is even ... 3 + 1 = 4 TRUE
D. q + 5 is odd ... 3 + 5 = 8 FALSE
PLEASE HELP URGENT
Which equation could be solved using this application of the quadratic formula?
Answer:
Step-by-step explanation:
D because the quadratic formula is basically [tex]\frac{-b+\sqrt{b^{2}-4ac } }{2a}[/tex]±
so if we place the equation D into the formula
a = 1
b = +3
c = +24
we can clearly say that D eq is correctly used and can be.
When pricing out a menu, we know it is important to use the Edible a portion Price. What would the effect on your profit margin be, if we only used the as purchased price to determine our cost and selling price?
The effect of Edible a portion Price on your profit margin , if we only use the as purchased price to determine our cost and selling price is that it will maximize the profit because it will account for every part of the production.
What is edible portion cost?
The portion cost can be calculated by multiplying the cost of a usable kg with the portion size.
This can be represented as : portion cost = (portion size x cost of usable kg)
It should be noted that Edible portion (EP) serves as the portion of food which will be given top the customer after the preparation.
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Answer:
Step-by-step explanation:
Find the value of b.
Step-by-step explanation:
The value of b will be 43° as it is vertically opposite angle.. !!
Question 25: [1 + 2 + 2 + 2 + 2 + 1= 10 points]
Given student of classified as belonging to three colleges and gender males and Females in the following table.
Eng (E) Life (L) Sci (S) sum F 60 40 30 130
M 40 20 10 70 sum 100 60 40 200
a) [1 points] Find the probabilities whole events. () , (), (), () , and ()
b) [2 points] Find the probabilities of Intersection (AND) Events:
( ∩ ) = ( ∩ ) ( ∩ ) = ( ∩ ) ( ∩ ) = ( ∩ )
( ∩ ) = ( ∩ ) ( ∩ ) = ( ∩ ) ( ∩ ) = ( ∩ )
c) [2 points] Find the probabilities of Union (OR) disjoint Events:
( ∪ ) = ( ∪ ) ( ∪ ) = ( ∪ )
( ∪ ∪ ) = ( ∪ ∪ ) ( ∪ ) = ( ∪ )
d) [2 points] Find the probabilities of Union (OR) joint events: ( ∪ )
( ∪ )
e) [2 points] Find the probabilities of Conditional Probabilities
(/) (/)
(/) (/)
(/) (/)
(/) (/)
f) [1 points] Use The multiplication low for dependent events to find the Conditional probability. ( ∩ ) = () (/)
See below for the values of the probabilities
How to determine the probabilities?The probabilities of the whole events
For event A, the probability of the whole event is calculated using
P(A) = n(A)/Total
Using the table of values, we have:
P(F) = 130/200 = 0.65
P(M) = 70/200 = 0.35
P(L) = 60/200 = 0.30
P(S) = 40/200 = 0.20
The probabilities of the intersection events
For events A and B, the probability of the intersection events is calculated using
P(A n B) = n(A n B)/Total
Using the table of values, we have:
P(F n E) = P(E n F) = 60/200 = 0.30
P(F n L) = P(L n F) = 40/200 = 0.20
P(F n S) = P(S n F) = 30/200 = 0.15
P(M n E) = P(E n M) = 40/200 = 0.20
P(M n L) = P(L n M) = 20/200 = 0.10
P(M n S) = P(S n M) = 10/200 = 0.05
The probabilities of the Union (OR) disjoint events
For events A and B, the probability of the union (OR) disjoint events is calculated using
P(A u B) = P(A) + P(B)
Using the table of values, we have:
P(E u S) = P(E) + P(S) = 100/200 + 40/200 = 0.70
P(E u L) = P(E) + P(L) = 100/200 + 60/200 = 0.80
P(E u L u S) = P(E) + P(L) + P(S) = 100/200 + 60/200 + 40/100 = 1
P(F u M) = P(F) + P(M) = 130/200 + 70/200 = 1
The probabilities of the Union (OR) joint events
For events A and B, the probability of the union (OR) joint events is calculated using
P(A u B) = P(A) + P(B) - P(A n B)
Using the table of values, we have:
P(E u F) = P(E) + P(F) - P(E n F) = 100/200 + 130/200 - 60/100 = 0.85
P(L u M) = P(L) + P(M) - P(L n M) = 60/200 + 70/200 - 20/100 = 0.55
The probabilities of the conditional probabilities
For events A and B, the conditional probability is calculated using
P(A/B) = P(A n B)/P(B)
Using the table of values, we have:
P(F/S) = P(F n S)/P(S) = 0.15/0.20 = 0.75
P(F/E) = P(F n E)/P(E) = 0.30/0.50 = 0.60
P(M/S) = P(M n S)/P(S) = 0.05/0.20 = 0.25
P(M/L) = P(M n L)/P(L) = 0.10/0.30 = 0.33
P(S/F) = P(F n S)/P(F) = 0.15/0.65 = 0.23
P(E/F) = P(F n E)/P(F) = 0.30/0.65 = 0.46
P(S/M) = P(M n S)/P(M) = 0.05/0.35 = 0.14
P(L/M) = P(M n L)/P(M) = 0.10/0.35 = 0.29
The multiplication of dependent events
For events A and B, the conditional probability is calculated using
P(A n B) = P(A) * P(B/A)
Using the table of values, we have:
P(F n L) = P(F) * P(L/F)
This gives
P(F n L) = 0.65 * (0.20/0.30)
Evaluate
P(F n L) = 0.43
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How does the area below the mean compare to the area above the mean in a normal distribution?
The area below the mean compares to the area above the mean in a normal distribution as the areas are always equal regardless of the mean. Option A This is further explained below.
What is a normal distribution?Generally, The normal distribution, also known as the Gaussian distribution, is a kind of probability distribution that is symmetric around the mean. This means that it demonstrates that data that are closer to the mean are more likely to occur than data that are farther away from the mean. When represented graphically, the normal distribution takes the shape of a "bell curve."
In conclusion, In a normal distribution, the area below the mean is compared to the area above the mean since the areas are always equal regardless of the mean. This is true even if the mean is different.
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Complete Question
How does the area below the mean compare to the area above the mean in a normal distribution?
A. the areas are always equal regardless of the mean
B. the areas are sometimes equal depending upon the standard deviation of the distribution
C. the area above the mean is larger since the values are larger as you move above the mean
D. the areas are sometimes equal depending upon the value of the mean
Fatima purchased a new mattress when it was on sale. The sale price was 20% less than the regular price. If the sale price was $358, what was the original price? (Round your answer to the nearest dollar).
well, the regular price is really "x", which oddly enough is 100%, but we also know that $358 is really the discounted price by 20%, namely 100% - 20% = 80%, so we know that 358 is really just 80% of "x", so
[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} x & 100\\ 358& 80 \end{array} \implies \cfrac{x}{358}~~=~~\cfrac{100}{80} \\\\\\ \cfrac{x}{358}=\cfrac{5}{4}\implies 4x=1790\implies x=\cfrac{1790}{4}\implies x\approx 448[/tex]
