A player tosses a die 6 times.If gets a number 6 Atleast two times he wins 2 dollars ,otherwise he looses 1 dollar.. Find the expectation of the amount if he wins
Answers
Answer:
\(E(x)=-0.2101\)
Step-by-step explanation:
The expected value for a discrete variable is calculated as:
\(E(x)=x_1*p(x_1)+x_2*p(x_2)\)
Where \(x_1\) and \(x_2\) are the values that the variable can take and \(p(x_1)\) and \(p(x_2)\) are their respective probabilities.
So, a player can win 2 dollars or looses 1 dollar, it means that \(x_1\) is equal to 2 and \(x_2\) is equal to -1.
Then, we need to calculated the probability that the player win 2 dollars and the probability that the player loses 1 dollar.
If there are n identical and independent events with a probability p of success and a probability (1-p) of fail, the probability that a events from the n are success are equal to:
\(P(a)=nCa*p^a*(1-p)^{n-a}\)
Where \(nCa=\frac{n!}{a!(n-a)!}\)
So, in this case, n is number of times that the player tosses a die and p is the probability to get a 6. n is equal to 6 and p is equal to 1/6.
Therefore, the probability \(p(x_1)\) that a player get at least two times number 6, is calculated as:
\(p(x_1)=P(x\geq2)=1-P(0)-P(1) \\\\P(0) =6C0*(1/6)^{0}*(5/6)^{6}=0.3349\\P(1)=6C1*(1/6)^{1}*(5/6)^{5}=0.4018\\\\p(x_1)=1-0.3349-0.4018\\p(x_1)=0.2633\)
On the other hand, the probability \(p(x_2)\) that a player don't get at least two times number 6, is calculated as:
\(p(x_2)=1-p(x_1)=1-0.2633=0.7367\)
Finally, the expected value of the amount that the player wins is:
\(E(x)=x_1*p(x_1)+x_2*p(x_2)\\E(x)=2*(0.2633)+ (-1)*0.7367\\E(x)=-0.2101\)
It means that he can expect to loses 0.2101 dollars.
Answer:
Expected value = -0.2101
Step-by-step explanation :
Givena discrete variable the expected value is given as:
E(x) = xp(x) + yp(y)
Where x and y are the values the variables can assume, and p(x) and p(y) are their respective probabilities.
Probability that a player gets 6 at least twice = p(x ≥ 2) = 1 - p(x≤ 2)
= 1 - p(0) - p(1)
But p(0) = 0.3349
p(1) = 0.4018
p(x ≥ 2) = 1 - 0.3349 - 0.4018
= 0.2633
p(y) = 1 - p(x)
= 1 - 0.2633
= 0.7367
Expected value = 2(0.2633) + (-1)(0.7367)
= -0.2101
A loss of $0.2101 is expected.
Related Questions
there is a 12 question test with 4 multiple choice options for each question. how many ways can a student randomly fill in the answer choices?
Answers
Answer:
16777216 ways
Here, there are 4 choices per question, and 12 questions. Choosing an answer for each question is a sequential task, so there are 4 × 4 × 4 × 4 × 4 × 4 × 4 × 4 × 4 × 4 × 4 × 4 =16777216 ways to answer.
William transforms a figure by reflecting it over y=1 and then dilating it by a scale factor of 1/3 . What must be true of the image and the original figure?
1.They are similar but not congruent.
2.They are both congruent and similiar.
3.They are congruent but not similar.
4.They are neither similar or congruent.
Answers
Answer:
1.
Step-by-step explanation:
Reflection does not change the shape, just the orientation of the shape, also keeping the same size.
Dilation keeps the same shape, but changes the size.
same shape but different size is considered similar.
Answer:
The answer is number 1!!! Hope this helps!!!
Step-by-step explanation:
Find the LCM of 18e2x, e2t and y3.
In a class of 45 students, there are 12 girls. What percentage of the girls are in the class?
Please explain!
Answers
Answer:
12/45 = 0.26666666
0.26666666 X 100 = 26.6666666
27%
what is the probability that a single randomly sampled observation have a value above the mean?
Answers
The probability of a single randomly sampled observation having a value above the mean is approximately 0.1587, assuming a normal distribution.
if the mean of the data is μ and the standard deviation is σ, then the probability of a single observation being above the mean is given by:
P(X > μ) = 1 - P(X ≤ μ)
where X is the random variable representing the data. To calculate this probability, we need to standardize the data by subtracting the mean from each observation and dividing by the standard deviation. This gives us a standard normal variable Z, which has a mean of 0 and a standard deviation of 1.
Then, we can look up the probability in a standard normal table or use a calculator or software to find the area under the standard normal curve to the right of Z = 0.
For example, suppose we have a dataset with a mean of 10 and a standard deviation of 2. If we standardize the data, then a value of 12 would correspond to a Z-score of:
Z = (12 - 10) / 2 = 1
The probability of a value being above the mean is then:
P(X > 10) = 1 - P(X ≤ 10) = 1 - P(Z ≤ 1) = 1 - 0.8413 = 0.1587
Therefore, the probability of a single randomly sampled observation having a value above the mean is approximately 0.1587, assuming a normal distribution.
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Lori plans to invest $3,000 today. Assume an annual interest rate of 9%, how much more interest will she receive in the 7 th year with compound interest comparing with simply interest? $213.29 $152.35 $165.20 $274.23 $182.82
Answers
The difference between the compound interest and simple interest for 7 years is $3,944.72 or approximately $3,944.73.
We have to calculate the difference between the compound interest and simple interest for 7 years. The principal amount is $3,000, and the interest rate is 9%. The formula for simple interest can be represented as,
I = Prt
where I is the simple interest, P is the principal amount, r is the rate of interest, and t is the time taken.
The interest for one year using simple interest will be,
I = Prt = $3,000 × 0.09 × 1 = $270
So, the interest for 7 years using simple interest will be $270 × 7 = $1,890.
The formula for compound interest can be represented as,
A = P(1 + r/n)^nt
where A is the amount, P is the principal amount, r is the rate of interest, t is the time taken, and n is the number of compounding periods.
The interest for 7 years using compound interest will be,
A = $3,000(1 + 0.09/1)^(1 × 7) = $5,834.72
The interest Lori will receive in the 7th year with compound interest can be calculated as follows:
Amount for 6 years = $3,000(1 + 0.09/1)^(1 × 6) = $5,178.38
Amount for 7 years = $3,000(1 + 0.09/1)^(1 × 7) = $5,834.72
Interest for 7th year with compound interest = $5,834.72 - $5,178.38 = $656.34
The interest for 7 years using simple interest is $1,890.
The interest for 7 years using compound interest is $656.34 + interest for the first 6 years.
Interest for 6 years using compound interest,
A = $3,000(1 + 0.09/1)^(1 × 6) = $5,178.38
The total interest for 7 years using compound interest is $5,178.38 + $656.34 = $5,834.72.
The difference between the compound interest and simple interest for 7 years is $5,834.72 - $1,890 = $3,944.72, which is the answer.
However, it is not one of the options. So, we need to round it off to the nearest cent.
The difference rounded to the nearest cent is $3,944.73 - $3,944.72 = $0.01
Hence, the difference between the compound interest and simple interest for 7 years is $3,944.72 or approximately $3,944.73.
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A
--6-5- -3 -2-1
D
Mark this and return
4
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4
-3
T
С
6
2
B
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If a translation of (x, y) - (x + 6, y-10) is applied to
figure ABCD, what are the coordinates of D'?
O (-5,-2)
O (1.-12)
O (4, -15)
O (-9,-6)
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Answers
The coordinates of D' after the translation is applied to the figure ABCD are (4, -11). Option (B) (1, -12) seems to be a typographical error as it is not possible to get those coordinates by performing a translation of (-2, -1) using the given translation vector.
The figure ABCD is a set of coordinates representing the corners of a geometric shape. The coordinates represent the x and y values of each corner of the shape. In this case, the shape is a quadrilateral, with the corners labeled as A, B, C, and D.
The problem is asking what are the coordinates of the point D' after a translation of (x, y) -> (x + 6, y - 10) is applied to the original figure ABCD. This translation involves adding 6 to the x-coordinate and subtracting 10 from the y-coordinate of each point.
To find the coordinates of D' after the translation, we need to apply the same translation to the coordinates of point D. The coordinates of D in the original figure are (-2, -1), and applying the translation (x, y) -> (x + 6, y - 10) to these coordinates gives:
D' = (-2 + 6, -1 - 10)
= (4, -11)
Therefore, the coordinates of D' after the translation is applied to the figure ABCD are (4, -11). Option (B) (1, -12) seems to be a typographical error as it is not possible to get those coordinates by performing a translation of (-2, -1) using the given translation vector.
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8. Sam packed 15 boxes in 5 days. Dylan packed 60 boxes 4 weeks and 2 days. Who packed the most
boxes in the least in the least amount of time? Find each unit rate.
Answers
Answer:
sam did the most
Step-by-step explanation:
let's find box packed per day
sam - 15 boxes in 5 days
so 3 boxes in 1 day
Dylan - 60 boxes in 4 weeks and 2 days
that is 60 in 30 days
that will make 2 boxes in 1 day
What relationship do you notice between the total number of fish each has caught after each hour?
Answers
Answer:
Scott always has 2 more fish per hour or S=M+2
Step-by-step explanation:
5-3 = 2, 9-7 = 2,...
For any given hour, Scott has reeled in 2 more fish compared to Megan.
We can see this by subtracting Scott's amount and Megan's amount for any row.
Row One: 5-3 = 2Row Two: 9-7 = 2Row Three: 13-11 = 2Row Four: 17-15 = 2Because any given row has the same difference, this tells us that the slopes of each are the same.
The equation for Megan is y = 4x-1 while Scott's equation is y = 4x+1
x = number of hours, y = number of fish caught
Lines with equal slopes indicate parallel lines. If these trends keep up, then Megan will never catch Scott (she'll always be 2 fish behind him).
Barry made the model to show multiplying a fraction by a fraction. Which multiplication sentence does the model show? A grid with 3 rows of 6 columns showing 18 squares total. The 12 squares in the top two rows are shaded yellow, the 15 squares in the first 5 columns are shaded blue. The shading overaps to make green in 10 squares. 13×23=29 26×56=518 13×26=19 23×56=59
Answers
Given:
Number of rows = 3
Number of columns = 6
Number of square boxes = 18
yellow square boxes in the top two rows = 12
Blue square boxes in the first 5 columns = 15
Number of green boxes (shading overlaps) = 10
To find:
The model to show multiplying a fraction by a fraction.
Solution:
2 rows out of 3 are shaded yellow.
Fraction for yellow = \(\dfrac{2}{3}\)
5 columns out of 6 are shaded blue.
Faction for blue = \(\dfrac{5}{6}\)
10 out of 18 squares are green.
Faction for green = \(\dfrac{10}{18}=\dfrac{5}{9}\)
Now,
\(\dfrac{2}{3}\times \dfrac{5}{6}=\dfrac{10}{18}\)
\(\dfrac{2}{3}\times \dfrac{5}{6}=\dfrac{5}{9}\)
Therefore, the correct option is D.
The correct option is D.
The calculation is as follows:
2 rows out of 3 are shaded yellow.
Fraction should be \(2\div 3\)
Now
5 columns out of 6 are shaded blue.
Fraction should be \(5 \div 6\)
And,
10 out of 18 squares are green.
Fraction should be \(10 \div 18 = 5\div 9\)
Now
\(\frac{2}{3} \times \frac{5}{6} = \frac{10}{18}\\\\ \frac{2}{3} \times \frac{5}{6} = \frac{5}{9}\)
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3+(_8
\(3 + ( - 8 \\ \)
Answers
Answer:
-5Step-by-step explanation:
\(3 + ( - 8)\)
Follow rule :
+ × - = -
\(3 - 8 \\ = - 5\)
What are the coordinates of the point on the directed line segment from (-6, 8)(−6,8) to (-2, -8)(−2,−8) that partitions the segment into a ratio of 5 to 3?
Please help im having issue with this
Answers
The coordinates of the point on the directed line segment that partitions the segment into a ratio of 5 to 3 are [-3.5, -2].
How to determine the coordinates of P?In this exercise, line ratio would be used to determine the coordinates of the point on the directed line segment that partitions the segment into a ratio of 5 to 3.
Mathematically, line ratio can be used to determine the coordinates of P and this is modeled by this mathematical expression:
P(x, y) = [(mx₂ + nx₁)/(m + n)], [(my₂ + ny₁)/(m + n)]
Given the following parameters:
Point (x, y)= (-6, 8)Point (x, y) = (-2, -8)m:n = 5:3Substituting the given parameters into the line ratio formula, we have;
P(x, y) = [(mx₂ + nx₁)/(m + n)], [(my₂ + ny₁)/(m + n)]
P(x, y) = [(5(-2) + 3(-6))/(5 + 3)], [(5(-8) + 3(8))/(5 + 3)]
P(x, y) = [(-10 + (-18))/(5 + 3)], [(-40 + 3(8))/(5 + 3)]
P(x, y) = [(-10 - 18)/(8)], [(-40 + 24)/(8)]
P(x, y) = [(-28)/(8)], [(-16)/(8)]
P(x, y) = [-3.5, -2]
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I need help with this question
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The length of the legs of the right triangle are 2.83 units.
How to find the side of a right triangle?A right tangle triangle is a triangle that has one of its angles as 90 degrees. The sum of angles in a triangle is 180 degrees.
Therefore, the legs of the triangle can be found using trigonometric ratios.
Hence,
sin 45 = opposite / hypotenuse
sin 45 = a / 4
cross multiply
a = 4 × 0.70710678118
a = 2.83 units
Therefore,
cos 45 = b / 4
cross multiply
b = 0.70710678118 × 4
b = 2.82842712475
b = 2.83 units
Therefore, the legs are 2,83 units
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suppose quadrilaterals a and b are both squares. determine whether the statement below is true or false. select the correct choice.a and b are scale copies of one another.
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The statement "Quadrilaterals A and B are both squares" does not provide enough information to determine whether A and B are scale copies of one another.
To determine if two quadrilaterals are scale copies of each other, we need to compare their corresponding sides and angles. If the corresponding sides of two quadrilaterals are proportional and their corresponding angles are congruent, then they are scale copies of each other.
In this case, since both A and B are squares, we know that all of their angles are right angles (90 degrees). However, we do not have any information about the lengths of their sides. Without knowing the lengths of the sides of A and B, we cannot determine if they are scale copies of each other.
Therefore, the statement cannot be determined as true or false based on the given information.
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hi pls help urgent <3
Answers
Answer:
-548
Step-by-step explanation:
Let x be the number
Plug x in: x - -150 = -398Simplify: x + 150 = -398Subtract 150 from each side, so it now looks like this: x = -548I hope this helps!
Which of the following types of statements can explain the steps of a proof?
Answers
Answer:
Guess and Conjecture is the answers that apply.
Also known as B. and C.
Find the mean of these numbers: 5, 11, 2, 12, 4, 2Need solution :Dhave a good night ^^ from Philippines
Answers
Given:
5, 11, 2, 12, 4, 2
Required:
To find the mean of the given numbers.
Explanation:
Consider the given numbers
5, 11, 2, 12, 4, 2
Now the mean is
\(\begin{gathered} =\frac{2+2+4+5+11+12}{6} \\ \\ =\frac{36}{6} \\ \\ =6 \end{gathered}\)Final Answer:
The mean is 6.
For the following argument, construct a proof of the conclusion from the given premises, -(3x) (PX Mx), (3x) (Mx Sx) 1:. -(x) (SxPx)
Answers
To construct a proof of the conclusion "-(∀x) (S(x) ∧ P(x))" from the given premises "-(3x) (P(x) ∧ M(x))" and "(3x) (M(x) ∧ S(x))," we can use a proof by contradiction.
We will assume the negation of the conclusion and derive a contradiction. Here's the proof:
-(∀x) (S(x) ∧ P(x)) (Assumption)(3x) (P(x) ∧ M(x)) (Given premise)
(3x) (M(x) ∧ S(x)) (Given premise)
P(a) ∧ M(a) (Existential instantiation from 2)
M(a) ∧ S(a) (Existential instantiation from 3)
M(a) (Simplification from 5)
P(a) ∧ M(a) (Repetition from 4)
-(P(a) ∧ M(a)) (Negation introduction from 7)
-(P(a) ∧ M(a)) ∧ M(a) (Conjunction introduction with 6 and 8)
-M(a) (Simplification from 9)
P(a) ∧ M(a) (Repetition from 4)
P(a) ∧ M(a) ∧ -M(a) (Conjunction introduction with 10 and 11)
⊥ (Contradiction introduction from 12)
-(∀x) (S(x) ∧ P(x)) (Negation introduction from 1-13)
Therefore, we have derived a contradiction, which allows us to conclude that the negation of the assumption is false. Thus, we can conclude:
-(∀x) (S(x) ∧ P(x))
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Given y=f(x), when f(x) = -3 on the graph of y=√f(x)
a. is undefined
b. intersects y=f(x) on the x-axis
c. is above the graph of y=f(x)
d. intersects the graph of y=f(x)
e. is below the graph of y=f(x)
Answers
I WILL MARK AS BRAINLIEST PLS PLS PLS HELP
Answers
Answer:
1) is height(age)
2) should be shipping(distance)
3) g(8) = 28
4) f(3) = 18
Step-by-step explanation:
plug in 8 as x. 5(8)- 12 --> 40 -12 = 28.
plug in 3 as x. 2x² --> 2(3)^2--> 2(9) = 18.
What is System Effectiveness, if Operational Readiness is 0.89, Design Adequacy is 95%, Availability is 98%, Maintainability is 0.93, and Mission Reliability is 0.99? a. 0.763 b. 0.881 c. 0.837 d. 0.820
Answers
The System Effectiveness is approximately 0.763.
To calculate the System Effectiveness, we need to multiply the values of Operational Readiness, Design Adequacy, Availability, Maintainability, and Mission Reliability.
System Effectiveness = Operational Readiness * Design Adequacy * Availability * Maintainability * Mission Reliability
Plugging in the given values:
System Effectiveness = 0.89 * 0.95 * 0.98 * 0.93 * 0.99
System Effectiveness ≈ 0.763
Therefore, the System Effectiveness is approximately 0.763.
The correct answer is a. 0.763.
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WHAT IS THE AREA OF THE CURVED SURFACE OF A CYLINDER OF BASE RADIUS 4 CM AND HEIGHT 10 CM
Answers
Answer:
The curved surface area of cylinder is 251.42 cm².
Step-by-step explanation:
Here's the required formula to find the curved surface area of cylinder :
\(\star\underline{\boxed{\sf{CSA_{(Cylinder)}} = 2\pi rh}}\)
Csa = Curved surface areaπ = 22/7r = radius h = heightSubstituting all the given values in the formula to find the curved surface area of cylinder :
\(\implies{\tt{CSA_{(Cylinder)}= 2\pi rh}}\)
\({\implies{\tt{CSA_{(Cylinder)} = 2 \times \dfrac{22}{7} \times 4 \times 10}}}\)
\({\implies{\tt{CSA_{(Cylinder)} = 2 \times \dfrac{22}{7} \times 40}}}\)
\({\implies{\tt{CSA_{(Cylinder)} = \dfrac{2 \times 22 \times 40}{7}}}}\)
\({\implies{\tt{CSA_{(Cylinder)} = \dfrac{44 \times 40}{7}}}}\)
\({\implies{\tt{CSA_{(Cylinder)}= \dfrac{1760}{7}}}}\)
\({\implies{\tt{CSA_{(Cylinder)} \approx 251.42 }}}\)
\({\star{\underline{\boxed{\tt{\red{CSA_{(Cylinder)} \approx 251.42 \: {cm}^{2}}}}}}}\)
Hence, the curved surface area of cylinder is 251.42 cm².
\(\rule{300}{2.5}\)
What would be the degree of financial leverage for Foggy Futures Weather Forecasters if the company has earnings before interest and taxes of $750,000, has a 4. 5% loan on $1,000,000, and is in the 38% tax bracket? The firm does not have any preferred stock outstanding. A. 1. 22 b. 0. 97 c. 1. 06 d. 1. 78
Answers
The degree of financial leverage for Foggy Futures Weather Forecasters
is 1.06
Degree of Financial leverage (DFL) = (EBIT) / (EBT)
Earnings Before Interest and Taxes (EBIT) = $750,000
Amount to be given as loan on $1000000
$1,000,000 x 4.5% = $1,000,000 x 4.5/100
= $45000
To find EBT ( Earnings Before Tax),
EBT = EBIT - 45000
= 750000 - 45000
EBT = 705000
∴ DFL = (EBIT) / (EBT)
= 750000/705000
DFL = 1.06
The DFL is a percentage that accountants and financial professionals use to show changes in a company's net income due to changes in its profits before interest and taxes (EBIT).
Earnings before interest and taxes (EBIT) is a measurement of a company's profit in accounting and finance that takes into account all revenues and costs (both operating and non-operating), with the exception of interest costs and income tax costs.ve
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9. Jenna graphed a circle centered at the (-3, 4). If the circle that Jenna graphed, also
contains (2, -8), then what is the value of the radius of the circle?
Answers
The radius of the circle is the distance between the center and the point on the circle
The radius of the circle is 13 units
How to determine the radiusThe given parameters are:
Center = (-3,4)
Point = (2,-8)
The radius is the distance between the points.
So, we have:
\(r = \sqrt{(-3-2)^2 + (4 --8)^2}\)
Evaluate
\(r = \sqrt{169}\)
Solve
\(r = 13\)
Hence, the radius of the circle is 13 units
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Is (x-7) a factor of (x2-5x+14)?
Yes or no
Answers
Answer:
Step-by-step explanation:
Is the given equation factorable?
(x - 7)(x - 2) = x^ - 9x + 14 That doesn't work.
-7 * - 2 = 14 but the middle term is - 9 not - 5
x - 7 is not a factor of x^ - 5x + 14
What is?
Something very ugly (x - 2.5 +/- 2.783 i )
If there are 48 lollipops and 60 candy bars for a gift bag, fill out all of the possible ratios of lollipops to candy bars that could be made
Answers
Answer:
Step-by-step explanation:
The ratio formula is given as a:b = a/b for any two quantities, let's say a and b. Given that a and b are separate amounts for two quantities, the combined total quantity is denoted by (a + b).
There are 48 lollipops and 6 candy bars for a gift bag.
Then the possible ratios of lollipops to candy bars are:
( 48 / 6 ) ÷ ( 2 / 2) = ( 24 / 3 )
( 48 / 6 ) ÷ ( 3 / 3) = ( 16 / 2 )
( 48 / 6 ) ÷ ( 6 / 6) = ( 8 / 1 )
There are 48 lollipops for every 6 candy bars.
There are 24 lollipops for every 3 candy bars.
There are 16 lollipops for every 2 candy bars.
There are 8 lollipops for every 1 candy bar.
There are 4 lollipops for every 5 candy bars (4 :5 ratio)
There are 8 lollipops for every 10 candy bars (8 :10 ratio)
There are 24 lollipops for every 30 candy bars (24:30 ratio)
There are 12 lollipops for every 15 candy bars (12:15 ratio)
An isosceles triangle had two base angles equal to 13 degrees. What is the measure of the third angle?
Answers
The measure of the third angle of the isosceles triangle is θ = 154°
Given data ,
In an isosceles triangle, two sides are of equal length, and thus two base angles are also of equal measure.
Given that the two base angles of the isosceles triangle are both 13 degrees, we can denote one of the base angles as 13 degrees, and the other base angle as 13 degrees as well.
Let's denote the measure of the third angle as "x" degrees
The sum of angles in any triangle is always 180 degrees.
So , 13 + 13 + x = 180
Simplifying the equation:
26 + x = 180
Subtracting 26 from both sides of the equation:
x = 180 - 26
x = 154°
Hence , the measure of the third angle in the isosceles triangle is 154°
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help please this is math work
Answers
A rectangle with an area of x2 - 4x – 12 square units is
represented by the model.
What side lengths should be used to model the
rectangle?
(x + 2) and (x - 6)
(x + 6) and (x - 2)
(x + 2) and (x – 10)
(x + 10) and (x - 2)
+42
X X X X
-
HEL
is
TIREISE
Mark this and retum
Save and Exit
Answers
Hello there! :)
Answer:
First choice, (x + 2) and (x - 6).
Step-by-step explanation:
To solve for the dimensions, recall that the formula for the volume of a rectangle is:
A = l × w
Simply factor x² -4 - 12. Find two numbers that add up to -4 and multiply into -12.
2, -6 satisfy these conditions. Use these numbers to write this equation in factored form:
(x + 2) (x - 6). Thus, the first option is the correct answer.
Answer:
(x-6) (x+2)
Step-by-step explanation:
x^2 - 4x – 12
Factor
What two numbers multiply to -12 and add to -4
-6*2 = -12
-6+2 = -4
(x-6) (x+2)
Suppose bob's exam score was at the 80th percentile on an exam whose mean was 90. what was bob's exam score?
Answers
The mean score of 90, and percentile of Bob's score of 80, gives Bob's exam score as approximately 92.5%
What is the formula that gives the exam score from the percentile?The Z-Score of the 80th percentile is 0.8416
The formula for Z-Score is presented as follows;
\(z = \frac{x - \mu}{ \sigma} \)
Where;
\( \sigma = The \: standard \: deviation\)
\( \mu = The \: mean = 90\%\)
x = The given score
Taking the mean as a proportion, we have;
\( \sigma = \sqrt{\frac{\mu \cdot (1-\mu)}{n}}\)
Which gives;
\( \sigma = \sqrt{\frac{0.9 \times (1-0.9)}{100}}= 0.03\)
Therefore, when z = 0.8416, gives;
\(0.8416 = \frac{x - 0.9}{ 0.03} \)
x = 0.8416 × 0.03 + 0.9 ≈ 0.925
Therefore;
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what's the area of a circle with diameter 18 units? question 5 options: a) 18π units2 b) 81π units2 c) π units2 d) 9π units2
Answers
The area of a circle can be found using the formula A = πr^2, where r is the radius of the circle. Since the diameter is given as 18 units, the radius would be half of that, which is 9 units. Now, substitute the value of the radius into the formula: A = π(9^2) = 81π units^2. Therefore, the correct answer is option b) 81π units^2.
1. Use the formula A = πr^2, where A is the area and r is the radius of the circle.
2. The diameter is given as 18 units, so the radius would be half of that, which is 9 units.
3. Substitute the value of the radius into the formula: A = π(9^2) = 81π units^2.
Therefore, the area of the circle with a diameter of 18 units is 81π units^2.
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