The number of the sample that is necessary is 171. The number of employees that would be selected if E is 30 = 476
How to solve for the number of the sampleThe standard deviation = 398
error E = 50
Alpha is = 1-0.90 = 0.10
a. We are to find the value of the size of the sample
Z∝/2 = Z0.05
= 1.645
sample size,n >= [Za/2 *(sigma/E)]^2
n >= [1.645 * (398/50)] ^2
n >= 171.46
n = 171
b.
error,E = 30
n >= [1.645 * (398/30)] ^2
n >= 476.27
n = 476
Complete questionA survey is planned to determine the mean annual family medical expenses of employees of a large company. The management of the company wishes to be 90% confident that the sample mean is correct to within ±$50 of the population mean annual family medical expenses. A previous study indicates that the standard deviation is approximately $398. a. How large a sample is necessary?
b. If management wants to be correct to within ±$30, how many employees need to be selected?
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(0, 9)₂
What is the equation of a line that is parallel to y = 6x + 7 and passes through (0,
Enter your equation in the box.
Answer:
y = 6x+9
Step-by-step explanation:
Equations that are parallel have the same slope
y = 6x+7 is written in slope intercept form where the slope is 6 and the y intercept is 7
The lines will have a slope of 6
The point (0,9) is the y intercept because the x value is 0
We can write the equation in slope intercept form y = mx+b
y = 6x+9
Answer:
Hello! The answer is y = 6x + 9.
Step-by-step explanation:
When lines are parallel, they will have the same slope but a different y-intercept.
The y-intercept, in this case, would be (0, 9) since the x-coordinate equals 0. This leaves us with 9 as the y-intercept.
Our slope-intercept form equation will be written as:
y = 6x + 9
A rectangle has a perimeter of 92cm and its length is 1cm more than twice its width.
Using the definition of perimeter write an equation for P in terms of L and W
Using the relationship given in the problem statement, write an equation for L in terms of W.
Answer: Width = 15cm
L = 31cm
Step-by-step explanation:
P = 92 cm
L = 1 + 2W
P = 2L + 2W
P = 2(1+2W) + 2W
P = 2+4W+2W
P = 2 + 6W
92cm = 2 + 6W
subtract 2 on both sides to cancel the 2 on the right side.
90cm = 6W
W = 90/6
Width = 15cm
L = 1+2W
L = 1 + 30cm
L = 31 cm
Verification:
P = 2L+2W
P = 2(31)+2(15)
P = 62+30
P = 92cm
Hope I Helped!
Answer:
P = 2(L + W) = 2L + 2W (first part)
L = 2W + 1 (second part)
Step-by-step explanation:
L = length of rectangle
W = width of rectangle
P = perimeter of rectangle = 2 * (L + W)
So P = 2(L + W) = 2L + 2W (1)
It is also given that length is 2 * width + 1
So we get the equation
L = 2W + 1 for L in terms of W (2)
This question does not ask you to compute L and W but if you wanted to do that use the following steps
Substitute for L from equation 2 to equation 1 giving
P = 2(2W+1) + 2W = 4W + 2 + 2W = 6W + 2
We know P = 92
So 6W + 2 = 92
Subtracting 2 from both sides we get 6W = 90
Dividing both sides by 6 gives us W = 15
and L = 2 * 15 + 1 = 31
We can check this by finding the perimeter from L and W
perimeter = 2(L+W) = 2(31 + 15) = 2 (46) = 92 which matches the data in the question
find the indefinite integral.
Using substitution, the result of the indefinite integral is:
[tex]3\ln{(1 + x^{\frac{1}{3}})} + C[/tex]
What is the integral?The integral is:
[tex]\int \frac{1}{x^{\frac{2}{3}}(1 + x^{\frac{1}{3}})} dx[/tex]
The substitution is:
[tex]u = 1 + x^{\frac{1}{3}}[/tex]
Then the derivative is:
[tex]du = \frac{1}{3}x^{-\frac{2}{3}} dx[/tex]
ttex]dx = 3dux^{-\frac{2}{3}}[/tex]
Hence the integral is:
[tex]\int \frac{1}{x^{\frac{2}{3}}(1 + x^{\frac{1}{3}})} dx[/tex]
[tex]\int \frac{1}{x^{\frac{2}{3}}u} \times 3dux^{-\frac{2}{3}}[/tex]
[tex]\int \frac{3du}{u}[/tex]
[tex]3\ln{u} + C[/tex]
Returning to x:
[tex]3\ln{(1 + x^{\frac{1}{3}})} + C[/tex]
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Subtract -13f^3+9f2+7f-16-(-8 f^3+5f^2+9f-4)
Answer:
:)\
Step-by-step explanation:
HELP ASAP!!!!!!
Ken and Betty each write a proof of the statement: if m
The statement third "Betty wrote an indirect proof using contradiction' and statement fourth "Ken wrote direct proof using deductive evidence" are correct.
What is an angle?When two lines or rays converge at the same point, the measurement between them is called a "Angle."
We have Ken's statements are shown in the table:
Angle AOC = Angle BOD (given)
Angle AOB + Angle BOC = Angle BOC + Angle COD (angle addition postulate)
Angle AOB = ANgle COD (subtraction property of equality)
Ken wrote direct proof using deductive evidence.
As we can in betty's proof:
Betty wrote an indirect proof using contradiction.
Thus, the statement third "Betty wrote an indirect proof using contradiction' and statement fourth "Ken wrote direct proof using deductive evidence" are correct.
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The height of a projectile launched upward at a speed of 25 meters/second from a height of 70 meters is given by the function h(t)=-5sup(t,2)+25t+70. How long will it take the projectile to hit the ground?
6.5 s take the projectile to hit the ground.
What is projectile?A projectile is any object thrown into space upon which the only acting force is gravity.
Given:
speed = 25 m/s
h(t) = -5t² + 25t + 70
height = 70 m
Time to reach maximum height
( u sin90)/2g
= 25/2*9.8
= 1.275s
Max height = u²Sin²[tex]\theta[/tex]/g
=25*25/9.8
=63.775
So, total height=63.775 + 70 = 133.775 m
Now, time to fall back to the ground
h = ut+(1/2)gt²
t² = (h- ut)2/g
u=0
H= 133.775 m
(133.775*2)/9.8= t²
t² = 27.3010
t= 5.225 s
Total time taken to hit ground
= 5.225 + 1.275
= 6.5 s
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Can it be concluded that AWXY ABCD by SAS? Why or why not?
Ono, because the third corresponding sides must also be given as congruent
Ono, because the corresponding congruent angles listed are not the included angles
Ono, because all corresponding angles must be given as congruent
O yes, because two corresponding sides and a corresponding angle are congruent
It can be concluded that ΔWXY is equivalent to ΔBCD by the SAS rule because the corresponding sides and corresponding angle are congruent. Option D
What is SAS congruency?SAS congruency states that two triangles are said to be congruent if any two sides or angle between the sides of one triangle are equal to the corresponding two sides and also the angle between the sides of the second triangle.
Thus, it can be concluded that ΔWXY is equivalent to ΔBCD by the SAS rule because the corresponding sides and corresponding angle are congruent. Option D
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Answer:
B. No, because the corresponding congruent angles listed are not the included angles.
Step-by-step explanation:
What is x/7 >= -6? Please Answer!
Step-by-step explanation:
x/7 ≥ -6
we rewrite it as :
x/7 = -6
by cross multiplication
x = -42
In order words:
x ≥ -42
Hope this helps
Good luck ✅
9-22 Throughput costing (continuation of 9-21). The variable maufacturing costs per unit of Nascar Motors are as follows:
April May
Direct cost per unit $6,700 $6,700
Direct manufacturing labor cost per unit $1,500 $1,500
Manufacturing overhead cost per unit $1,800 $1,800
1. Prepare income statements for Nascar Motors in April and May 2017 under throughput costing.
2. Contrast the results in requirement 1 with those in requirement 1 of Exercise 9-21.
3. Give one motivation for Nascar Motors to adopt throughput costing.
The Income Statement for Nascar Motors in April and May 2017 under Throughput Costing is given as attached.
What is a throughput costing?This refers a costing technique, also known as super-variable costing, which solely takes direct materials into account when calculating product costs.
The other expenses are all classed as period costs and are all deducted from income in the time period in which they are spent.
What is the Contrast between the results in requirement 1 with those in requirement 1 of Exercise 9-21?It is to be noted that Throughput costing has the lowest operating income in April while having the greatest operating income in May.
More so than either absorption or variable costing, throughput costing emphasizes sales as the source of operational income. See the attached.
What is one motivation for Nascar Motors to adopt throughput costing?It is to be noted that production that doesn't result in a commensurate sale in the same time period is penalized under throughput costing.
When compared to variable costing, costs that are variable with regard to production but are not direct materials are expensed in the period of incurrence.
In contrast to variable costing or absorption costing, throughput costing offers less of motivation to create inventory.
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Select the correct answer.
Sterling Company is testing the popularity of two products in the first days following their release. The quantity sold for Product 1,
t days after its initial release, is modeled by the following function.
g(t)= 200(1.36)
The quantity sold for Product 2, t days after its initial release, is shown in the following table.
5
859
t
0
1
2 3 4
f(t) 250 320 410 524 671
Based on this information, which product had the greater average rate of increase in sales after three days?
O Product 1
Both had the same average rate of increase in sales.
This cannot be determined from the given information.
O Product 2
Submit
Answer:where are the options ???
Step-by-step explanation:
Answer:
Product 1
Step-by-step explanation:
Got it
Draw the graphs of the lines below on the same grid to find the coordinates of the point of intersection.
y=3x−3 y=7−2x
The coordinates of the point of intersection of y=3x−3 and y=7−2x is (2, 3)
Graphing linear equationsFrom the question, we are to graph the given equations.
The graph of the equations is attached below.
In the graph, we can observe that the coordinates of the point of intersection of the is (2, 3)
Hence, the coordinates of the point of intersection of y=3x−3 and y=7−2x is (2, 3)
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prime factorization of 220
Answer:
The Prime Factorization of 220 is 22 × 51 × 111.
Step-by-step explanation:
Factors of 220 are integers that can be divided evenly into 220. It has total 12 factors of which 220 is the biggest factor and the prime factors of 220 are 2, 5, 11. There for, the Prime Factorization of 220 is 22 × 51 × 111.
From the sample space S= (1, 2, 3, 4..., 15} a single number is to be selected at random. Given the following events, find the indicated probability. A: The selected number is even. B: The selected number is a multiple of 4. C: The selected number is a prime number. P(A and C) P(A and C) = (Simplify your answer. Type an integer or a fraction.)
Probability the selected number is even is 7/15
Probability the selected number is a multiple of 4 is 1/5
Probability the selected number is prime = 2/5
What is probability?Probability is the likelihood of an event happening or an event not happening.
When it is certain an event would happen the probability is 1.
Probability can be independent or mutually exclusive.
Analysis:
Required outcome
A = {2, 4, 6, 8, 10, 12, 14} (even numbers)
Total entry = 7
Total Sample = 15
P(even numbers) = 7/15
B (multiples of 4) = {4, 8, 12}
Total entry = 3
P(B) = 3/15 = 1/5
C(prime numbers) = {2, 3, 5, 7, 11, 13}
Total entry = 6
P(C) = 6/15
P(A and C) = 0.
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A basket of oranges has 10 fruits, of which 4 are bad. Three balls are drawn at random.a)Calculate the probability of getting 3 bad balls.b)Calculate the probability of getting 1 bad fruit.c)Calculate the probability of getting at least one bad fruit.d)Calculate the probability of getting the most 2 bad fruits
Using the hypergeometric distribution, the probabilities are given as follows:
a) 0.0333 = 3.33%.
b) 0.5 = 50%.
c) 0.8333 = 83.33%.
d) 0.9667 = 96.67%.
What is the hypergeometric distribution formula?The formula is:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are:
x is the number of successes.N is the size of the population.n is the size of the sample.k is the total number of desired outcomes.The values of the parameters are:
N = 10, n = 3, k = 4.
Item a:
The probability is P(X = 3), hence:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]P(X = 3) = h(3,10,3,4) = \frac{C_{4,3}C_{6,0}}{C_{10,3}} = 0.0333[/tex]
Item b:
The probability is P(X = 1), hence:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]P(X = 1) = h(1,10,3,4) = \frac{C_{4,1}C_{6,2}}{C_{10,3}} = 0.5[/tex]
Item c:
The probability is:
[tex]P(X \geq 1) = 1 - P(X = 0)[/tex]
In which:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]P(X = 0) = h(0,10,3,4) = \frac{C_{4,0}C_{6,3}}{C_{10,3}} = 0.1667[/tex]
Then:
[tex]P(X \geq 1) = 1 - P(X = 0) = 1 - 0.1667 = 0.8333[/tex]
Item d:
The probability is:
[tex]P(X \leq 2) = 1 - P(X = 3)[/tex].
Considering item a:
[tex]P(X \leq 2) = 1 - P(X = 3) = 1 - 0.0333 = 0.9667[/tex]
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Let [tex]O[/tex] be the random variable for the number of bad oranges picked out. Then
[tex]P(O=o) = \dfrac{\dbinom6{3-o} \dbinom4o}{\dbinom{10}3}[/tex]
if [tex]o\in\{0,1,2,3\}[/tex] and zero otherwise, where
[tex]\dbinom nk = \dfrac{n!}{k!(n-k)!}[/tex]
is the so-called binomial coefficient.
(a) Of the 6 good oranges, you pick 0. Of the 3 bad oranges, you pick 3. Of the 10 total oranges, you pick 3. So the probability of picking out all bad oranges is
[tex]P(O=3) = \dfrac{\dbinom60 \dbinom43}{\dbinom{10}3} = \boxed{\dfrac1{30}}[/tex]
(b) By similar reasoning, the probability of drawing exactly 1 bad orange is
[tex]P(O=1) = \dfrac{\dbinom62 \dbinom41}{\dbinom{10}3} = \boxed{\dfrac12}[/tex]
(c) "At least 1 bad orange" means you pick out 1, 2, or 3 bad oranges. These events are mutually exclusive, and we already know the probabilities of picking out exactly 1 or all 3 bad oranges. The remaining probability of drawing 2 bad oranges is
[tex]P(O=2) = \dfrac{\dbinom61 \dbinom42}{\dbinom{10}3} = \dfrac3{10}[/tex]
so the overall probability of drawing at least 1 bad orange is
[tex]P(O\ge1) = P(O=1)+P(O=2)+P(O=3) =\dfrac1{30} + \dfrac3{10} + \dfrac12 = \boxed{\dfrac56}[/tex]
(d) I assume you mean "at most 2 bad oranges," meaning you pick out 0, 1, or 2 bad oranges. Again, these events are mutually exclusive, and the probability of picking out no bad oranges is
[tex]P(O=0) = \dfrac{\dbinom63 \dbinom40}{\dbinom{10}3} = \dfrac16[/tex]
hence the probability of drawings at most 2 bad oranges is
[tex]P(O\le2) = P(O=0) + P(O=1) + P(O=2) = \dfrac16 + \dfrac12 + \dfrac3{10} = \boxed{\dfrac{29}{30}}[/tex]
Can somebody walk me through this?
2 y + 14 = 6 ( 4 y + 1 )
-------------------------------------------------------------------------------------------------------------
Answer: [tex]\textsf{y = 4/11}[/tex]
-------------------------------------------------------------------------------------------------------------
Given: [tex]\textsf{2y + 14 = 6(4y + 1)}[/tex]
Find: [tex]\textsf{Solve for y}[/tex]
Solution: In order to solve for y we need to distribute the ride side of the expression, simplify, subtract 14 from both sides, subtract 24y from both sides, and divide both sides by -22.
Distribute and simplify
[tex]\textsf{2y + 14 = (6 * 4y) + (6 * 1)}[/tex][tex]\textsf{2y + 14 = 24y + 6}[/tex]Subtract 14 from both sides
[tex]\textsf{2y + 14 - 14 = 24y + 6 - 14}[/tex][tex]\textsf{2y = 24y + 6 - 14}[/tex][tex]\textsf{2y = 24y - 8}[/tex]Subtract 24y from both sides
[tex]\textsf{2y - 24y = 24y - 24y - 8}[/tex][tex]\textsf{2y - 24y = -8}[/tex][tex]\textsf{-22y = -8}[/tex]Divide both sides by -22
[tex]\textsf{-22y/-22 = -8/-22}[/tex][tex]\textsf{y = -8/-22}[/tex][tex]\textsf{y = 8/22}[/tex][tex]\textsf{y = 4/11}[/tex]Therefore, the expression simplifies down to y = 4/11.
Which statement describes a key feature of function g if g(x) = f(x + 4)?
OA y-intercept at (0,4)
OB. x-intercept at (4,0)
OC. horizontal asymptote of y = 0
OD. horizontal asymptote of y = 4
The statement that describes a key feature of function g if g(x) = f(x + 4) is C. horizontal asymptote of y = 0.
What is a function?It should be noted that a function is an expression that shows the relationship between the variables.
In this case, the statement that describes a key feature of function g if g(x) = f(x + 4) is that the horizontal asymptote of y = 0.
The horizontal asymptote is vital for guiding the variables
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Word Problem
(D) Joshua is going shopping for (E) paintings and (F) spoons. The cost of (E) painting is (B) 10$ and the cost of each (F) spoon is (A) 8$.
If (D) Joshua can spend at most (C) 100$, how many (F) spoons can be purchased?
3. Write an inequality of the form Ax + B ≤ C to represent the word problem using your answers for A, B, and C. Solve the inequality and show your work.
4. Graph the solution to your inequality on a number line or describe, in words, how to graph the inequality on a number line.
The number of spoons that can be purchased is 11, whereas the equation is given as 8x + 10 ≤ 100
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
The cost of each spoon is $8, hence A = 8. The cost of painting is 10, hence B = 10. Joshua can spend at most 100$, C = 100
8x + 10 ≤ 100
x ≤ 11.25
The number of spoons that can be purchased is 11, whereas the equation is given as 8x + 10 ≤ 100
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Answer:
92 spoons can be purchased.
Step-by-step explanation:
10x + 8 ≤ 100
10x + 8 ≤ 100
8 - 8 10x 100 - 8
10x ≤ 92
x = 1/5
10 x 1/5 = 92.
<---------------------------------------------------------------------------------------------------------->
<----------------------------------------------------0---------------------------- 92
Sanjeet paid $32.85 for 1 file and 3 identical pens. Leon paid $83.50 for 2 files and 8 identical pens. Find the cost of one such pen
The cost of the file is $6.15 and the cost of the pen is $8.9
Solving word problems with systems of linear equations.The interpretation of the given word problem leads to a system of linear equations.
From the given information:
Let the file be denoted with f and the pen be denoted with pf + 3p = 32.85 --- (1)
2f + 8p = 83.5 --- (2)
From equation (1)
f = - 3p+32.85
Replace the value of f in the above equation into equation (2)
2(-3p + 32.85) + 8p = 83.5
2p + 65.7 = 83.5
2p = 83.5 -65.7
2p = 17.8
p = 17.8/2
p = 8.9
Replacing the value of p = 8.9 into f = - 3p+32.85
f = -3(8.9)+32.85
f = 6.15
Therefore, we can conclude that the cost of the file is $6.15 and the cost of the pen is $8.9.
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What would be your weight on the Moon if your weight on Earth is 80 lbs?
6 times 80 lbs
one-sixth of 80. Four Times 80 lbs one-fourth of 80 lbs
3y−13≥−9 and 3y−13≤−1
[tex]3y \geqslant 13 - 9[/tex]
[tex]3y \geqslant 4[/tex]
[tex]y \geqslant \frac{4}{3} [/tex]
[tex]3y \leqslant 13 - 1[/tex]
[tex]3y \leqslant 12[/tex]
[tex]y \leqslant 4[/tex]
[tex] \frac{4}{3} \leqslant y \leqslant 4[/tex]
Find the outliers in the given data set below. 69, 16, 79, 80, 82
Answer:
16
Step-by-step explanation:
The outlier in the given dataset is "16".
Given is a data set 69, 16, 79, 80, 82, we need to determine the outliners of the set,
To identify outliers in a dataset, we generally use a statistical method such as the z-score or the IQR (interquartile range).
Since, the provided dataset is small with only five values, we can manually identify the outliers by observing the data.
An outlier is a value that significantly deviates from the rest of the dataset.
Let's examine the given dataset:
69, 16, 79, 80, 82
To identify outliers, we can consider any data points that are notably different from the others.
In this case, it seems that the value "16" is considerably lower than the other values.
Let's label it as a potential outlier.
Therefore, the outlier in the given dataset is "16".
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Kareem wrote the expressions shown below.
[3.2] [2.7] [2.9] [4.8]
Which pair is equivalent?
O [2.7] and [3.2]
O [2.9] and [2.7]
O [3.2] and [2.9]
O [4.8] and [3.21]
The equivalent pair of the given expression is; [4.8] and [3.21]
How to find equivalent pairs?Floor function states that the greatest integer that is less than or equal to x. It is represented by: ⌊ x ⌋.
Ceiling function states that the least integer that is greater than or equal to x. It is represented by ⌈ x ⌉.
Kareem wrote the expressions;
[3.2] [2.7] [2.9] [4.8]
By definition above;
[3.2] = 4
[2.7] = 2
[2.9] = 3
[4.8] = 4
Thus, the equivalent pair is [4.8] and [3.2]
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The graph of the absolute value parent function, f(x) = Ixl, is stretched
horizontally by a factor of 5 to create the graph of g(x). What function is g(x)?
Answer: [tex]g(x)=\left|\frac{x}{5} \right|[/tex]
Step-by-step explanation:
See atached image.
Evaluate: 216 1/2 Question 2 options: A) 9 B) 1 C) 6 D) -3
Which of the following is not an example of like terms?
A. 2 and-6
B.2b and-6b
C.2b and 2
D.2b² and 6b²
Answer:
A. 2 and-6
Step-by-step explanation:
Like terms are terms that contain the same variables raised to the same powers. In other words, they have the same variables with the same exponents.
So in option A, we have the terms 2 and -6. These terms are not like terms because they do not have the same variables.
Will mark brainiest or whatever its called
Answer:
5621 years
Step-by-step explanation:
Plug everything in first.
[tex]N=N_0e^{-kt}\\\\\implies 0.57 = e^{-0.0001t}\\\\\implies\ln \left(0.57\right)=-0.0001t\\\\t=-\frac{\ln \left(0.57\right)}{0.0001}[/tex]
Round to closest amount of years = 5621 years
A cubic yard of topsoil is to be spread evenly in the garden at Prove It! Math Academy. Thegarden measures 10 feet by 8 feet. How many inches deep will the topsoil be?
The topsoil will be 4.05 inches deep
Calculating depthFrom the question, we are to determine how many inches deep the topsoil will be
From the given information,
The volume of the topsoil = 1 cubic yard
Convert to cubic feet
1 cubic yard = 27 cubic feet
∴ The volume of the topsoil = 27 cubic feet
Then,
The depth of the topsoil will be = 27/(8 ×10)
Depth of topsoil = 27/80
Depth of topsoil = 0.3375 foot
Now, convert to inches
1 foot = 12 inches
∴ 0.3375 foot = 0.3375×12 inches
= 4.05 inches
Hence, the topsoil will be 4.05 inches deep
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Let x represent Anna's age. If John's age is Anna's age plus 1 and Tamara is Anna's
decreased by 2, write an expression that represents the sum of Anna's and John's
age, minus Tamara's age?
Answer:
x + 3
Step-by-step explanation:
x = Anna's age
y = John's age
z = Tamara's age
y = x + 1
z = x - 2
the expression for the sum of Anna's and John's age minus Tamara's age is
x + y - z
and when we use the equations above to simplify that :
x + (x + 1) - (x - 2) = x + x + 1 - x + 2 = x + 3
Please help!!! If the first 4 terms of a geometric sequence are...
Answer:
c.) aₙ = 5 × 4ⁿ⁻¹
Explanation:
Geometric sequence: aₙ = a(r)ⁿ⁻¹
where 'a' resembles first term of a sequence, 'r' is the common difference.
Here sequence: 5, 20, 80, 320,...
First term (a) = 5
Common difference (d) = second term ÷ first term = 20 ÷ 5 = 4
Hence putting into equation: aₙ = 5(4)ⁿ⁻¹
Suppose that you and a friend are playing cards and decide to make a bet. If you draw two face cards, where a face card is a Jack, a Queen, or a King, in succession from a standard deck of 52 cards replacing the first card, you win $50. Otherwise, you pay your friend $20. What is the expected value of your bet? Round your answer to the nearest cent, if necessary.
The expected value of your bet will be the negative $16.27 that mean loses.
What is the binomial distribution?Binomial distributions consist of n independent Bernoulli trials.
The expected value will be
E(X) = np
Suppose that you and a friend are playing cards and decide to make a bet.
If you draw two face cards, where a face card is a Jack, a Queen, or a King, in succession from a standard deck of 52 cards replacing the first card, you win $50.
Otherwise, you pay your friend $20.
Then the probability of winning will be
p = (12 / 52)(12 / 52)
p = 9 / 169
Then the probability of loosing will be
q = 1 – p
q = 1 – 9/169
q = 160 / 169
Then the expected value will be
E(x) = (9/169) x 50 + (160/169) x (-20)
E(x) = -$16.27
Learn more about binomial distribution here:
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