Answers
Answer:
Step-by-step explanation:
C = 2 π r
A = π r²
~~~~~~~~~~~
(1). C = 8 π
Let the length of the arc ADB is "x"
x = ( 8π ÷ 360° ) × 340°
x = [tex]\frac{68}{9} \pi[/tex]
(2). A = 16 π
The area of shaded region is
( 16 π ÷ 360° ) × 340° = [tex]\frac{136}{9} \pi[/tex]
[tex]\bold{Answer} \downarrow[/tex]
[tex]Length\ of\ Arc\ ADB = \large\boxed{\frac{68\pi}{9} }[/tex]
[tex]Area\ of\ shaded\ region= \large\boxed{\frac{136\pi}{9} }[/tex]
Formulas needed:
[tex]Arc\ length=\boxed{2\pi r(\frac{\theta}{360} )}[/tex]
[tex]Area \ of\ a\ sector=\boxed{(\frac{n}{360})\times\pi \times r^2}[/tex]
[tex]Area\ of\ Circle=\boxed {\pi\times r^2}[/tex]
Step-by-step explanation:
First, let's find the arc length:
[tex]Arc\ length=2\pi r(\frac{\theta}{360})[/tex]
[tex]=2\pi (4)(\frac{340}{360})[/tex]
[tex]=2\pi (4)(\frac{17}{18})[/tex]
[tex]=2\pi(\frac{68}{18})[/tex]
[tex]=\frac{136\pi }{18}[/tex]
[tex]\longrightarrow \large\boxed{\frac{68\pi}{9} }[/tex]
Next, let's find the area of the sliver of the circle we just found the arc length of.
[tex]Area \ of\ a\ sector=(\frac{n}{360})\times\pi \times r^2[/tex]
[tex]=(\frac{20}{360} )\times \pi \times 4^2[/tex]
[tex]=(\frac{1}{18})\times \pi \times 16[/tex]
[tex]=\frac{16\pi}{18}[/tex]
[tex]\longrightarrow \frac{8 \pi}{9}[/tex]
Finally, find the area of the entire circle and subtract the sliver area by that.
[tex]Area\ of\ Circle= {\pi\times r^2[/tex]
[tex]=\pi \times 4^2[/tex]
[tex]\longrightarrow16\pi[/tex]
Subtracting the area by the sliver.
[tex]Area\ of\ entire\ circle \ -\ Area\ of\ sliver\ of\ circle[/tex]
[tex]=16\pi -\frac{8\pi}{9}[/tex]
[tex]=\frac{144\pi}{9} -\frac{8\pi }{9}[/tex]
[tex]\longrightarrow \large\boxed{\frac{136\pi}{9} }[/tex]
Related Questions
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!!!!!!!!!!!!!!!!
Answers
Answer:
bro it had been decreased
so total had been decreased is (4,000,000-2,900,000)=1,100,000Mike drove 40 miles from his home to his office, and he then drove back home using the same route. The average speed on his return trip was 10 miles/hour more than the average speed on his trip to the office. The total time for the trip is represented by this expression, where x is the average speed on the trip from his home to his office.
The average speed on Mike’s drive home is represented by
x + 10
.
When Mike drives at an average speed of 55 mile/hour on his way home, it takes him approximately
1.6 hours
to drive to work and back.
Answers
Mike's speed driving to his office is 45 miles/hour, which is 10 miles less than his average speed driving back.
How is speed calculated?Speed is an average value of a scalar measurement of the distance covered over the time taken.
Speed is the equation, r = d/Δt, where r = speed or rate, d = distance, and Δt is the change in time.
Thus, when the distance covered by a traveler is divided by the time consumed, one can determine the average speed for the travel.
Data and Calculations:Distance from Mike's home to his office = 40 miles
Distance to and from = 80 miles (40 miles x 2)
Hours covered from office = 1.6 hours
Average speed for the trip = 50 miles/hour (80/1.6)
Average speed to return home = 55 miles/hour
Average speed to office = 45 miles/hour (55 - 10)
Thus, Mike's speed of driving to his office is 45 miles/hour.
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Question Completion:What is Mike's speed driving to his office?
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?
Answers
Answer:
a company powder large group of people to assess the company's reputation in the surrounding
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
Answers
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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When 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.
Answers
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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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
Answers
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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The perimeter is 54 m. The apothem is \root(3)(3) . To the nearest tenth, what is the area of this regular polygon?
Answers
The area of this regular polygon is 46.8 square units
How to determine the area of this regular polygon?The given parameters are:
Perimeter, p = 54 m
Apothem, a = √3
The area of this regular polygon is then calculated as:
Area = 0.5 * Apothem * Perimeter
Substitute the known values in the above equation
Area = 0.5 * √3 * 54
Evaluate the product
Area = 46.8
Hence, the area of this regular polygon is 46.8 square units
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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?
Answers
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
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.
Answers
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
The large rectangle was reduced to create the small rectangle.
A large rectangle has a length of 18 inches and width of 12 inches. A smaller rectangle has a length of 6 inches and width of x inches.
Not drawn to scale
What is the missing measure on the small rectangle?
2 inches
3 inches
4 inches
5 inches
Answers
Answer:
4 inches
Step-by-step explanation:
large rectangle - 18:12 ratio = 3:2
small rectangle - 6:4 = 3:2
If the formula r=1/n-1 .....following data, what would be the value of x?
Answers
The solution or the value of x = 14 (Option C). See the explanation below.
Where x (bar) is the mean.
What is the calculation for the above?x = (12 + 13 + 14 + 15 + 16)/5
= 14
Hence option C is correct.
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find the zeros x^4-2x^3-44x^2-88x-32
Answers
The zeros which are the roots of the polynomial expressions are:
x = -4; x = - 2; x = 4 - 2√5; x = 2(2 + √5)
What are the zeros of a polynomial expression?The zeros of a polynomial f(x) are really the values of x that answer the equation f(x) = 0. Thus, f(x) is a function of x, and the polynomial zeros refer to the values of x, which makes the f(x) value equal to zero. The digit of zeros in a polynomial is decided by the degree of equation f(x) = 0.
For a polynomial, there may be specific values of the variable for which the polynomial is zero. These are known as polynomial zeros. They are also known as polynomial roots. In essence, we look for the zeros of quadratic equations to discover the solutions to the given equation.
From the given equation, the zeros of x^4-2x^3-44x^2-88x-32 can be computed as follows:
Using the rational root theorem:
[tex]\mathbf{= (x+2)\dfrac{x^4-2x^3-44x^2-88x-32}{x+2} }[/tex]
[tex]\mathbf{=(x+2) (x^3-4x^2-36x-32) }[/tex]
By factorization, we have:
= (x + 2) (x + 4) (x² - 8x - 4)
The zeros which are the roots of the polynomial expressions are:
x = -4; x = - 2; x = 4 - 2√5; x = 2(2 + √5)
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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?
Answers
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:
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?
Answers
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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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
Answers
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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How does the area below the mean compare to the area above the mean in a normal distribution?
Answers
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
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?
Answers
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
Pls help w this question
Answers
[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]
According to given figure,
Angle 11, Angle 20 and Angle 16 forms angles of a triangle,
so, by angle sum property of a triangle :
[tex]\qquad❖ \: \sf \: \angle11 + \angle20 + \angle16 = 180 \degree[/tex]
[tex]\qquad❖ \: \sf \: \angle11 +66 + 43 = 180 \degree[/tex]
[tex]\qquad❖ \: \sf \: \angle11 +109 = 180 \degree[/tex]
[tex]\qquad❖ \: \sf \: \angle11 = 180 \degree - 109[/tex]
[tex]\qquad❖ \: \sf \: \angle11 =71 \degree [/tex]
[tex] \qquad \large \sf {Conclusion} : [/tex]
Option B is correctA triangle with a base of 16 cm and a height of 9 cm.
Answers
Answer: 288
Step-by-step explanation:
(16x9)x2
Tried doing it myself multiple times , multi choice question, not getting any availabile answer.
Answers
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]
Determine a solution to system of linear inequalities graphed and justify your answer.
Answers
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).
Answers
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]
100% - 20% = 80% or 0.08
358 / 0.8 = $447.50
Check
447.50 * 0.8 = 358
Solve this system. Write your answer as an ordered pair.
-5x + y = -3
3x - 8y = 24
Answers
[tex]\begin{cases} -5x+y=-3\\ 3x-8y=24 \end{cases} \\\\\\ \stackrel{\textit{using the 1st equation}}{-5x+y=-3}\implies \underline{y=-3+5x} \\\\\\ \stackrel{\textit{substituting on the 2nd equation}}{3x-8(\underset{y}{-3+5x})=24}\implies 3x+24-40x=24\implies 3x-40x=0 \\\\\\ -37x=0\implies \boxed{x=0}~\hfill \underline{y=-3+5(\stackrel{x}{0})}\implies \boxed{y=-3} \\\\[-0.35em] ~\dotfill\\\\ ~\hfill (0~~,~~-3)~\hfill[/tex]
Answer:
( 0, -3 )
Step-by-step explanation:
-5x + y = -3 ⇒ ( 1 )
3x - 8y = 24 ⇒ ( 2 )
We can make y the subject of equation 1.
y = 5x - 3 ⇒ ( 3 )
Now let us take equation 2.
Here we can replace y with ( 5x - 3 ) to find the value of x.
Value of x.
3x - 8y = 24
3x - 8 (5x - 3) = 24
3x - 40x + 24 = 24
-37x = 0
x = 0
Now let us take equation 3 to find the value of y.
Here we can replace x with 0.
Let us find it now.
y = 5x - 3
y = 5 × 0 - 3
y = 0 - 3
y = -3
Now, let us write the answer as an ordered pair.
( x, y )
( 0, -3 )
A _____ is a solid consisting of a suite a point not in the same plane as the square and all points between them
Answers
Answer:
Square Pyramid
Step-by-step explanation:
Thats what a Square Pyramid is
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
Answers
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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3(q+ 4/3 )=2 solve for Q
Answers
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
Find the value of b.
Answers
Step-by-step explanation:
The value of b will be 43° as it is vertically opposite angle.. !!
The value of b is 43° since it is vertically opposite
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
Answers
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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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. ( ∩ ) = () (/)
Answers
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
Read more about probabilities at:
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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
Answers
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]
