Answers
Answer:
B) x=80°
Step-by-step explanation:
This is a hexagon, so it has interior angles equaling 720°. (N-2)*180
So the equation would be
78+134+136+132+2x+x=720
480+3x=720
3x=720-480
3x=240
x=80°
Related Questions
Salema's score on a test was 80%. If the test was worth a total of 60 points, how many points did Salema earn?
Answers
Answer:
48
Step-by-step explanation:
Do 60*.80
60 represent the total points the test was worth
.80 represents the % number
The percentage is calculated by dividing the required value by the total value and multiplying by 100.
Required percentage value = a
total value = b
Percentage = a/b x 100
100% = 60
80% = 48
The points Salema earned are 48 points.
What is a percentage?The percentage is calculated by dividing the required value by the total value and multiplying by 100.
Example:
Required percentage value = a
total value = b
Percentage = a/b x 100
Example:
50% = 50/100 = 1/2
25% = 25/100 = 1/4
20% = 20/100 = 1/5
10% = 10/100 = 1/10
We have,
Salema's score = 80%
Total score in the test = 60 points
Salema's score.
= 80% of 60 points
= 80/100 x 60
= 48
Thus,
The points Salema earned are 48 points.
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In a random sample of 64 people, 48 are classified as 'successful.' Determine the sample proportion of 'successful' people.
Answers
Answer:
The sample proportion of 'successful' people is [tex]\frac{3}{4}[/tex].
Step-by-step explanation:
The sample consist of 64 people and 48 of them are 'successful'. Hence, the proportion of 'successful' people is:
[tex]p = \frac{n}{N}[/tex]
Where:
[tex]N[/tex] - People that forms the sample, dimensionless.
[tex]n[/tex] - People classified as 'successful', dimensionless.
Given that [tex]n = 48[/tex] and [tex]N = 64[/tex], the sample proportion of 'successful' people is:
[tex]p = \frac{48}{64}[/tex]
[tex]p = \frac{3}{4}[/tex]
The sample proportion of 'successful' people is [tex]\frac{3}{4}[/tex].
Suppose you finance a home in the amount of $425,000 at 4.3% compounded monthly for 30 years. Calculate your payment.
Answers
Answer: $1,540,194.30 .
Step-by-step explanation:
The formula to calculate the accumulated amount earned on principal (P) at rate of interest (r)[ in decimal] compounded monthly after t years :
[tex]A=P(1+\dfrac{r}{12})^{12t}[/tex]
Given: P= $425,000
r= 4.3% = 0.043
t= 30 years
[tex]A=425000(1+\dfrac{0.043}{12})^{12(30)}\\\\=425000(1.003583)^{360}\\\\=425000\times3.62398657958\approx1540194.30[/tex]
Hence, the payment would be $1,540,194.30 .
A box contain 12 balls in which 4 are white 3 are blue and 5 are red.3 balls are drawn at random from the box.find the chance that all three are selected
Answers
Answer:
3/11
Step-by-step explanation:
From the above question, we have the following information
Total number of balls = 12
Number of white balls = 4
Number of blue balls = 3
Number of red balls = 5
We solve this question using combination formula
C(n, r) = nCr = n!/r!(n - r)!
We are told that 3 balls are drawn out at random.
The chance/probability of drawing out 3 balls = 12C3 = 12!/3! × (12 - 3)! = 12!/3! × 9!
= 12 × 11 × 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1/(3 × 2 × 1) × (9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1)
= 220 ways
The chance of selecting 3 balls at random = 220
To find the chance that all the three balls are selected,
= [Chance of selecting (white ball) × Chance of selecting(blue ball) × Chance of selecting(red balls)]/ The chance/probability of drawing out 3 balls
Chance of selecting (white ball)= 4C1
Chance of selecting(blue ball) = 3C1 Chance of selecting(red balls) = 5C1
Hence,
= [4C1 × 3C1 × 5C1]/ 220
= 60/220
= 6/22
= 3/11
The chance that all three are selected is = 3/11
Draw the image of ABC under dilation whose center is P and scale factor is 4.
Answers
Answer:
Step-by-step explanation:
Let the point P is origin (0, 0), segment AB lies on the x-axis and segment PC on the y-axis,
Coordinates of A, B and C will be (1, 0), (2, 0) and (0, 2).
When triangle ABC is dilated by a scale factor 4 about the origin,
Rule for dilation;
(x, y) → (4x, 4y)
New coordinates of the points A, B and C will be,
A(1, 0) → A'(4, 0)
B(-2, 0) → B'(-8, 0)
C(0, 2) → C'(0, 8)
By plotting points A', B' and C' we can get the dilated image A'B'C'.
Dilation involves changing the size of a shape.
Assume point P is the center of origin, then we have the following coordinates of ABC
[tex]A = (1,0)[/tex]
[tex]B = (-2,0)[/tex]
[tex]C = (0,2)[/tex]
The scale factor (k) is given as:
[tex]k= 4[/tex]
So, the dilation rule is represented as:
[tex](x,y) \to (4 \times (x,y)[/tex]
Using the above dilation rule, the following coordinates represent the image of triangle ABC
[tex]A' = (4,0)[/tex]
[tex]B' = (-8,0)[/tex]
[tex]C = (0,8)[/tex]
See attachment for the image of the dilation.
Read more about dilation at:
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Q-The general solution of inequality cos 2 x≤- sin x is
Answers
Answer:
x∈[2nπ−5π/6, 2nπ−π/6]∪{(4n+1)π/2}, n ϵ I
Step-by-step explanation:
1−2sin2 x≤−sin x ⇒ (2sin x+1)(sin x−1)≥0
sin x≤−1/2 or sin x≥1
−5π/6+2nπ≤x≤−π/6+2nπ or , n ϵ I x=(4n+1)π/2, n ϵ I⇒ -5π6+2nπ≤x≤-π6+2nπ or , n ϵ I x=4n+1π2, n ϵ I (as sin x = 1 is valid only)
In general⇒ In general x∈[2nπ−5π/6, 2nπ−π/6]∪{(4n+1)π/2}, n ϵ I
20 applicants are interviewed for a job. The interviewer creates an ordered list (first to last) of the best 6 applicants. How many ways are
Answers
Answer:
38,760 different ways.Step-by-step explanation:
The question is incomplete. Here is the complete question.
20 applicants are interviewed for a job. The interviewer creates an ordered list (first to last) of the best 6 applicants. How many ways are there for the interviewer to create the list?
Since the question deals with selection, we will apply the combination rule. Generally, if r objects are to be selected from n pool of objects, this can be done in nCr number of ways.
nCr = n!/(n-r)!r!
According to the question, if the the interviewer is to select 6 applicants from a pool of 20 applicants that are interviewed for a job, this can be done in 20C6 number of ways.
20C6 = 20!/(20-6)!6!
20C6 = 20!/14!6!
20C6 = 20*19*18*17*16*15*14!/14!*6*5*4*3*2
20C6 = 20*19*18*1716*15/6*5*4*3*2
20C6 = 27,907,200/720
20C6 = 38,760 different ways.
Hence, the interviewer can create the list in 38,760 different ways.
Graph the following set of parametric equations on your calculator and select the matching graph.
Answers
Answer:
Graph 2
Step-by-step explanation:
The equation x = t² - 3 is represented by exponential growth, ( t² ) so it's graph will be similar to the first graph, graph 1, in our options. Then again we have to consider the equation y = √t - 2, which will be similar to graph 4, but with a greater slope. This leaves us with a solution of graph b.
In designing an experiment involving a treatment applied to 4 test subjects, researchers plan to use a simple random sample of 4 subjects selected from a pool of 31 available subjects. (Recall that with a simple random sample, all samples of the same size have the same chance of being selected.) Answer the question below.
What is the probability of each simple random sample in thiscase?
Answers
Answer:
The probability is [tex]p(n ) = 3.18*10^{-5}[/tex]
Step-by-step explanation:
From the question we are told that
The population size is N = 31
The sample size n = 4
Generally the number of way by which the n can be selected from N is mathematically represented as
[tex]\left N} \atop {}} \right. C_n = \frac{N! }{(N-n)!n!}[/tex]
=> [tex]\left 31} \atop {}} \right. C_4 = \frac{31! }{(31-4)!4!}[/tex]
=> [tex]\left 31} \atop {}} \right. C_4 = \frac{31 * 30 * 29 * 28* 27! }{27! * 4*3 * 2 * 1 }[/tex]
=> [tex]\left 31} \atop {}} \right. C_4 = \frac{ 755160 }{ 24}[/tex]
=> [tex]\left 31} \atop {}} \right. C_4 = 31465[/tex]
The number of ways of selecting a particular sample size is is [tex]k = 1[/tex]
Therefore the probability of each simple random sample in this case is mathematically evaluated as
[tex]p(n ) = \frac{1}{31465}[/tex]
[tex]p(n ) = 3.18*10^{-5}[/tex]
Century Roofing is thinking of opening a new warehouse, and the key data are shown below. The company owns the building that would be used, and it could sell it for $100,000 after taxes if it decides not to open the new warehouse. The equipment for the project would be depreciated by the straight-line method over the project's 3-year life, after which it would be worth nothing and thus it would have a zero salvage value. No new working capital would be required, and revenues and other operating costs would be constant over the project's 3-year life. What is the project's NPV? (Hint: Cash flows are constant in Years 1-3.)
Answers
Question Completion:
WACC = 10.0%
Opportunity cost = $100,000
Net equipment cost (depreciable basis) = $65,000
Straight-line deprec. rate for equipment = 33.333%
Sales revenues, each year = $123,000
Operating costs (excl. deprec.), each year = $25,000
Tax rate = 35%
Answer:
Century Roofing
Project's NPV is: ($6,578)
Step-by-step explanation:
a) Data and Calculations:
WACC = 10.0%
Opportunity cost = $100,000
Net equipment cost (depreciable basis) = $65,000
Straight-line deprec. rate for equipment = 33.333%
Sales revenues, each year = $123,000
Operating costs (excl. deprec.), each year = $25,000
Tax rate = 35%
Cash outflow in year 0 = $165,000 (Opportunity and new equipment costs)
Annual Cash inflow = $123,000 - $25,000 - $34,300 = $63,700
PV of annuity for 3 years at 10% = $158,422 ($63,700 x 2.487)
NPV = Cash inflow minus Cash outflow
= $158,422 - $165,000
= ($6,578)
Negative NPV
b) Since Century Roofing could have realized $100,000 from the sale of the building if it decides not to open the new warehouse, this opportunity cost is factored into the calculation of the Net Present Value. It becomes a present cash outflow. Century Roofing's opportunity cost is defined as the loss of $100,000 being the future return from the best alternative project when it chooses to build the new warehouse instead of selling off the building.
The probability of the stock market going up in a single day is 51%. What is the probability that the market will go up 4 consecutive days?
Answers
Answer:
[tex]Probability = 0.068[/tex]
Step-by-step explanation:
Let P(S) represent the probability that stock market will go up in a day
Given
[tex]P(S) = 51\%[/tex]
Required
Determine the probability that stock will go up 4 consecutive days
Start by converting P(S) from percentage to decimal
[tex]P(S) = 51\%[/tex]
[tex]P(S) = \frac{51}{100}[/tex]
[tex]P(S) = 0.51[/tex]
The above expression represents the probability in a day;
For 4 days; we have:
[tex]Probability = P(S) * P(S) * P(S) * P(S)[/tex]
[tex]Probability = (P(S))^4[/tex]
Substitute 0.51 for P(S)
[tex]Probability = (0.51)^4[/tex]
[tex]Probability = 0.06765201[/tex]
[tex]Probability = 0.068[/tex] -- Approximated
Hence, the probability that stock will rise for 4 consecutive days is 0.068
Which of the following is equivalent to –2i(6 – 7i)?
Answers
Answer:
[tex]\boxed{\sf \bf \ \ -2i(6-7i)=-14-12i \ \ }[/tex]
Step-by-step explanation:
Hello, please consider the following.
[tex]-2i(6-7i)=-12i+14i^2=-14-12i[/tex]
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
Answer:
A
Step-by-step explanation:
Answer = A
Need help please! what is the total length of a 20 mm steel coiled like a spring with a 16 turns and an outer diameter of 600 mm. pitch is 300 mm. Show your solution please coz i don't really know how to do it! thanks
Answers
Answer:
L = 29,550 mm (as per BS8110 the length is to the nearest 25)
Step-by-step explanation:
Lets make it so simple and easy.
Let A = 600mm
Let B = 300mm
Let C = 16 as number turns
Let d = 20mm
L = [tex]\sqrt{(3.14 * (600 - 20))^{2} + 300^{2}[/tex] x 16
L = 29,550 mm (as per BS8110 the length is to the nearest 25)
What is the area of the house (including the drawing room, TV room, balcony, hallway, kitchen, and bedroom)?
Answers
Answer:
A
Step-by-step explanation:
In how many years will
The Compounds interest
onRs. 14,000 be Rs. 4, 634 at 10%
p.a?
Answers
Answer:
3 years
Step-by-step explanation:
A = P(1 + r)^t
A = I + P
A = 14,000 + 4,634 = 18,634
18,634 = 14,000(1 + 0.1)^t
18,634/14,000 = 1.1^t
log (18,634/14,000) = log 1.1^t
log (18,634/14,000) = t * log 1.1
t = [log (18,634/14000)]/(log 1.1)
t = 3
The average person lives for about 78 years. Does the average person live for at least 1,000,000 days? (Hint: There are 367 days in each year.)
what i
Answers
Answer:
[tex]\large \boxed{\sf No}[/tex]
Step-by-step explanation:
There are 365 days in 1 year.
The average person lives for about 78 years.
Multiply 78 by 365 to find the value in days.
[tex]78 \times 365= 28470[/tex]
The average person lives for about 28470 days.
Explanation:
78 x 367 = 28,626 days
And 28,626 days < 1,000,000 days
So an average person cannot live 1,000,000 days
Hope this helps!
In how many ways can a subcommittee of 6 students be chosen from a committee which consists of 10 senior members and 12 junior members if the team must consist of 4 senior members and 2 junior members?
Answers
Answer:
The number of ways is 13860 ways
Step-by-step explanation:
Given
Senior Members = 10
Junior Members = 12
Required
Number of ways of selecting 6 students students
The question lay emphasis on the keyword selection; this implies combination
From the question, we understand that
4 students are to be selected from senior members while 2 from junior members;
The number of ways is calculated as thus;
Ways = Ways of Selecting Senior Members * Ways of Selecting Junior Members
[tex]Ways = ^{10}C_4 * ^{12}C2[/tex]
[tex]Ways = \frac{10!}{(10-4)!4!)} * \frac{12!}{(12-2)!2!)}[/tex]
[tex]Ways = \frac{10!}{(6)!4!)} * \frac{12!}{(10)!2!)}[/tex]
[tex]Ways = \frac{10 * 9 * 8 * 7 *6!}{(6! * 4*3*2*1)} * \frac{12*11*10!}{(10!*2*1)}[/tex]
[tex]Ways = \frac{10 * 9 * 8 * 7}{4*3*2*1} * \frac{12*11}{2*1}[/tex]
[tex]Ways = \frac{5040}{24} * \frac{132}{2}[/tex]
[tex]Ways = 210 * 66[/tex]
[tex]Ways = 13860[/tex]
Hence, the number of ways is 13860 ways
What is similar about a line segment and a line? What is different
Answers
Answer:
A line segment has two endpoints. It contains these endpoints and all the points of the line between them. You can measure the length of a segment, but not of a line. Line segments are only a line that goes from one point to another, and lines go on forever. However, a line segment is also part of a line.
Hope this helps!
Answer:
[see below]
Step-by-step explanation:
A line is a straight path of points that has no start and no end. The line has an arrow on each end.
A line segment is part of a line. They have a start and an end. The line segments have a point on each end. You can use a line segment to make polygons and make calculations about them.
Hope this helps.
Find an equation for the line tangent to the curve at the point defined by the given value of d²y/dx².
At this point. x = 2 cos t, y = 2 sin t, t=π/4
Answers
Answer:
Step-by-step explanation:
Given:
x = 2cost,
t = (1/2)arccosx
y = 2sint
dy/dx = dy/dt . dt/dx
dy/dt = 2cost
dt/dx = -1/√(1 - x²)
dy/dx = -2cost/√(1 - x²)
Differentiate again to obtain d²y/dx²
d²y/dx² = 2sint/√(1 - x²) - 2xcost/(1 - x²)^(-3/2)
At t = π/4, we have
(√2)/√(1 - x²) - (√2)x(1 - x²)^(3/2)
The histogram shows that nine students had grades of 80 or higher.
The histogram shows there were 22 students in the class.
The histogram shows there were 25 students in the class.
The histogram is symmetrical.
The histogram has a peak.
The histogram shows the data is evenly distributed.
The histogram shows a gap in the data
Answers
Answer:
bde
Step-by-step explanation:
Answer:
B: The histogram shows there were 22 students in the class.
D: The histogram is symmetrical.
E:The histogram has a peak.
F: The histogram shows the data is evenly distributed.
Step-by-step explanation:
edg 2020
if 2x-7 is 5 more than x+4, what is the value of 3x+5
Answers
Answer:
53
Step-by-step explanation:
Let's start with the given relation:
2x -7 = (x+4) +5
x = 16 . . . . . . . . . add 7-x
3x +5 = 3(16) +5 = 53 . . . . . multiply by 3 and add 5
The value of 3x+5 is 53.
Your investment club has only two stocks in its portfolio. $25,000 is invested in a stock with a beta of 0.8, and $40,000 is invested in a stock with a beta of 1.7. What is the portfolio's beta? Do not round intermediate calculations. Round your answer to two decimal places.
Answers
Answer:
The portfolio beta is [tex]\alpha = 1.354[/tex]
Step-by-step explanation:
From the question we are told that
The first investment is [tex]i_1 = \$ 25,000[/tex]
The first beta is [tex]k = 0.8[/tex]
The second investment is [tex]i_2 = \$ 40,000[/tex]
The second beta is [tex]w = 1.7[/tex]
Generally the portfolio beta is mathematically represented as
[tex]\alpha = \frac{ i_1 * k + i_2 * w }{ i_1 + i_2}[/tex]
substituting values
[tex]\alpha = \frac{ (25000 * 0.8) + ( 40000* 1.7 ) }{40000 + 25000}[/tex]
[tex]\alpha = 1.354[/tex]
What number must be added to the expression below to complete the square? x2-5x
Answers
Answer:
6.25
Step-by-step explanation:
(x-a)^2=x^2-2ax+a^2
2a=5
a=2.5
2.5 ^ 2 = 6.25
The table shows the height, in meters, of an object that is dropped as time passes until the object hits the ground. A 2-row table with 10 columns. The first row is labeled time (seconds), x with entries 0, 0.5, 1.0, 1.5, 2.0, 2.5, 3.0, 3.5, 4.0, 4.6. The second row is labeled height (meters), h with entries 100, 98.8, 95.1, 89.0, 80.4, 69.4, 55.9, 40.0, 21.6, 0. A line of best fit for the data is represented by h = –21.962x + 114.655. Which statement compares the line of best fit with the actual data given by the table? According to the line of best fit, the object would have hit the ground 0.6 seconds later than the actual time the object hit the ground. According to the line of best fit, the object was dropped from a lower height. The line of best fit correctly predicts that the object reaches a height of 40 meters after 3.5 seconds. The line of best fit predicts a height of 4 meters greater than the actual height for any time given in the table.
Answers
Answer: A. According to the line of best fit, the object would have hit the ground 0.6 seconds later than the actual time the object hit the ground.
The statement first "According to the line of best fit, the object would have hit the ground 0.6 seconds later than the actual time the object hit the ground" is correct.
What is the line of best fit?A mathematical notion called the line of the best fit connects points spread throughout a graph. It's a type of linear regression that uses scatter data to figure out the best way to define the dots' relationship.
We have a line of best fit:
h = –21.962x + 114.655
As per the data given and line of best fit, we can say the object would have impacted the ground 0.6 seconds later than it did according to the line of best fit.
Thus, the statement first "According to the line of best fit, the object would have hit the ground 0.6 seconds later than the actual time the object hit the ground" is correct.
Learn more about the line of best fit here:
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suppose a chemical engineer randomly selects 3 catalysts for testing from a group of 10 catalysts, 6 of which have low acidity & 4 have high acidity. What is the probability that exactly2 lower acidic catalysts are selected?
Answers
Step-by-step explanation:
Total catalysts = 10
Probability of 2 lower acidic catalysts = 2/10 = 1/5
please solve quick
Answers
Answer:
x = 5
AC = 6
DC = 8
Step-by-step explanation:
∆ABC ~ ∆CDE
Therefore, [tex] \frac{AB}{ED} = \frac{AC}{DC} [/tex]
AB = 3
ED = 4
AC = x + 1
DC = x + 3
Plug in the values and solve for x:
[tex] \frac{3}{4} = \frac{x + 1}{x + 3} [/tex]
Cross multiply
[tex] 3(x + 3) = 4(x + 1) [/tex]
[tex] 3x + 9 = 4x + 4 [/tex]
[tex] 3x - 4x = -9 + 4 [/tex]
[tex] -x = -5 [/tex]
[tex] x = 5 [/tex]
Plug in the value of x and find AC and DC
AC = x + 1 = 5 + 1 = 6
DC = x + 3 = 5 + 3 = 8
If f is a function that f(f(x)) = 2x² + 1, which is the value of f(f(f(f(3)))? Please help!
Answers
[tex]f(f(3))=2\cdot3^2+1=19\\f(f(f(f(3))))=2\cdot19^2+1=723[/tex]
someone please help it's Multiple Coordinate Transformations
Answers
Answer:
Step-by-step explanation:
Coordinates of the vertices of the given rectangle are,
A(-4, 5), B(-2, 5), C(-2,1) and D(-4, 1).
If the given rectangle ABCD is translated by 1 unit right and 4 units down,
Rule for the translation will be,
(x, y) → [(x + 1), (y - 4)]
Therefore, coordinates of A, B, C and D after translation will be,
A(-4, 5) → A'(-3, 1)
B(-2, 5) → B'(-1, 1)
C(-2, 1) → C'(-1, -3)
D(-4, 1) → D'(-3, -3)
Then A', B', C' and D' are reflected about the y-axis.
Rule for the reflection about y-axis will be,
(x, y) → (-x, y)
New coordinates after the reflection will be,
A'(-3, 1) → A"(3, 1)
B'(-1, 1) → B"(1, 1)
C'(-1, -3) → C"(1, -3)
D'(-3, -3) → D''(3, -3)
Finally these points are rotated 270° clockwise about the origin,
Rule to be followed,
(x, y) → (-y, x)
Therefore, new coordinates will be,
A"(3, 1) → A"'(-1, 3)
B"(1, 1) → B'"(-1, 1)
C"(1, -3) → C"'(3, 1)
D"(3, -3) → D"'(3, 3)
Solve the polynomial x² - 7x + 12 = 0 Show each step used to find the solutions.
Answers
Answer:
x=4 and x=3
Step-by-step explanation:
The first step to find all factors of 12
1,2,3,4,6,12
and their negative form
-1,-2,-3,-4,-6,-12
we must add two of these numbers to get -7
and the two numbers that add up to -7 are -3 and -4
we can simply plot them into the polynomial (x-3)(x-4)
since x-3=0
we add three to both sides to get x=3
and since x-4=0
add four to both sides
we get x=4
and now check out work which
we can use First out in last (foil) method
(x-3)(x-4)
first
x^2
out
-4x
in
-3x
last
12
now we simplify to get x^2-7x+12
so it x=4 x=3 works
Answer:
x² - 7x + 12 = 0
doing middle term factorization
x²-4x-3x+12=0
taking common from each two term
x(x-4)-3(x-4)=0
taking common
(x-4)(x-3)=0
either
x-4=0
:. x=4
or
x-3=0
x=3
:.x=4,3
A spinner has 10 equally sized sections, 5 of which are gray and 5 of which are blue. The spinner is spun twice. What is the probability that the first spin lands on gray and the second spin lands on blue? Write your answer as a fraction in the simplest form.
Answers
Answer:
[tex]P(Gray\ and\ Blue) = \frac{1}{4}[/tex]
Step-by-step explanation:
Given
[tex]Sections = 10[/tex]
[tex]n(Gray) = 5[/tex]
[tex]n(Blue) = 5[/tex]
Required
Determine P(Gray and Blue)
Using probability formula;
[tex]P(Gray\ and\ Blue) = P(Gray) * P(Blue)[/tex]
Calculating P(Gray)
[tex]P(Gray) = \frac{n(Gray)}{Sections}[/tex]
[tex]P(Gray) = \frac{5}{10}[/tex]
[tex]P(Gray) = \frac{1}{2}[/tex]
Calculating P(Gray)
[tex]P(Blue) = \frac{n(Blue)}{Sections}[/tex]
[tex]P(Blue) = \frac{5}{10}[/tex]
[tex]P(Blue) = \frac{1}{2}[/tex]
Substitute these values on the given formula
[tex]P(Gray\ and\ Blue) = P(Gray) * P(Blue)[/tex]
[tex]P(Gray\ and\ Blue) = \frac{1}{2} * \frac{1}{2}[/tex]
[tex]P(Gray\ and\ Blue) = \frac{1}{4}[/tex]
