The circumference of a gazebo is 47.1 ft
To calculate the circumference, you can use the formula C=2πr. This formula states that the circumference of a circle is equal to two times the constant π (approximated as 6.28) multiplied by the radius of the circle. The radius of a circle is equal to half of the diameter, so in this case the radius would be 7.5 ft (half of 15 ft).
Therefore, to calculate the circumference of a gazebo with a diameter of 15 ft, you can use the formula C=2πr. Plugging in the radius of 7.5 ft, the equation would become C=2π(7.5) which results in a circumference of 47.12 ft. To round this answer to one decimal place, the final answer is 47.1 ft
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suppose vi pays its phone reps $12 per hour. how many phone reps should it employ if it wants to maximize profit?
Therefore , the solution of the given problem of unitary method comes out to be hourly salary of $144, or 12 times the average hourly wage of $12 for phone reps.
An unitary method is what?This common convenience, already-existing variables, or all important elements from the original Diocesan adaptable study that followed a particular methodology can all be used to achieve the goal. Both of the crucial elements of a term affirmation outcome will surely be missed if it doesn't happen, but if it does, there will be another chance to get in touch with the entity.
Here,
The formula below can be used to determine the ideal amount of phone representatives:
=> MR = MC
Where n is the amount of phone reps and 12 is their hourly wage, the cost is given by C = 12n.
The following results are obtained by taking the derivative of revenue and cost with regard to n:
=> MR=dR/dn = k
=> dC/dn = 12 for MC.
When we set MR equal to MC, we obtain:
=> k = 12
Accordingly, Vi should hire as many phone representatives as are required to produce an hourly salary of $144, or 12 times the average hourly wage of $12 for phone reps.
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8. A rectangular room is shown.
4x - 1
--x
2
3x + 6
A. (4x-1)-2x
B. (3x2+6) + (4x - 1) + x
C. (4-1)-(3x² + 6)
(3x2+6) + 2(4x - 1) + 2x
Door
X
4x - 1
Port A: Which of the following expressions represents the perimeter of the room without th
door?
(3x²+6)+(x-1)x2+²x = (3x²+6) + 2(9x-=
Port B: What is the perimeter of the room without the door in simplest form? Show you
work.
I only need part b
Answer: 14x + 10
Step-by-step explanation: The perimeter of the room without the door can be found by adding up the lengths of all four sides:
Perimeter = 2(4x-1) + 2(3x+6)
Simplifying and combining like terms, we get:
Perimeter = 14x + 10
Therefore, the perimeter of the room without the door in simplest form is 14x + 10.
GM is tangent to circle O at point G, and GS
is a secant line. If mGS = 84°, find
m/SGM.
Since GM is tangent tο circle O at pοint G, the intercepted arc GE has measure zerο. ,then ∠SGM = 84°.
What is secant line?Secant line is alsο knοwn as average rate οf change οf functiοns between twο pοints and alsο called slοpe.
the tangent line is perpendicular tο the radius that passes thrοugh the pοint οf tangency. Therefοre, we have:
m∠MGS = 90°
Alsο, we knοw that the measure οf an angle fοrmed by a tangent line and a secant line that intersect οutside the circle is half the difference οf the intercepted arcs.
m∠SGM = 1/2 (mSE - mGE)
where SE is the intercepted arc by secant GS, and GE is the intercepted arc by tangent GM.
Since GM is tangent tο circle O at pοint G, the intercepted arc GE has measure zerο.
mSE = 2mGS
mSE = 2(84°) = 168°
m∠SGM = 1/2 (mSE - mGE) = 1/2 (168° - 0°) = 84°
Therefοre, m∠SGM = 84°.
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what is the probability that at least 67 out of 100 cars stopped at a roadblock will not be given a ticket? local authorities report that tickets usually are given to 23% of cars stopped
The probability that at least 67 out of 100 cars stopped at a roadblock will not be given a ticket is 2.37.
Given Probability of giving tickets to cars that are stopped = 0.23
Probability of not giving tickets to cars that are stopped = 1 - 0.23 = 0.77
the probability that at least 67 out of 100 cars stopped at a roadblock will not be given a ticket
Here n = 100, p = 0.77, q = 0.23
mean = np = 100*0.77 = 77
standard deviation = [tex](sigma = \sqrt{(100)*(0.77)*(0.23) } = 4.208[/tex]
[tex]P(X\geq 67) = \frac{67 - 77}{4.208}[/tex] = 2.37
P-VALUE is 0.99126 from z-table
Probability is a fundamental concept in mathematics that helps us quantify the likelihood of events occurring and is applicable to a wide range of fields. It is a measure of the uncertainty of an event, expressed as a number between 0 and 1. An event with probability 0 is impossible, while an event with probability 1 is certain.For example, the probability of rolling a six on a fair six-sided die is 1/6, since there is only one favorable outcome out of six possible outcomes.
Probability theory has wide applications in fields such as statistics, finance, engineering, and physics, among others. It is used to model and analyze various phenomena, including weather patterns, stock prices, quantum mechanics, and more.
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I've been waiting to order your cupcakes all day!
I'll have 4 Nom-Nom-Nom cupcakes -- that's
80% of my order. The rest of the order are Wow.
Using fraction, the total number of cupcakes is obtained to be 5.
What is fraction?
In mathematics, a fraction is used to denote a portion or component of the whole. It stands for the proportionate pieces of the whole. Numerator and denominator are the two components that make up a fraction. The numerator is the number at the top, and the denominator is the number at the bottom.
If 4 cupcakes represent 80% of the order, then we can use proportional reasoning to find the total number of cupcakes.
Specifically, if x is the total number of cupcakes, then we can write -
4/x = 80/100
where the left-hand side represents the fraction of the order that is Nom-Nom-Nom cupcakes, and the right-hand side represents the percentage of the order that is Nom-Nom-Nom cupcakes.
Solving for x, we get -
x = 4 / (80/100) = 5
So the total number of cupcakes is 5. Since 4 of them are Nom-Nom-Nom cupcakes, the remaining 1 cupcake must be a Wow cupcake.
Therefore, in total there are 5 cupcakes.
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I've been waiting to order your cupcakes all day! I'll have 4 Nom-Nom-Nom cupcakes -- that's 80% of my order. The rest of the order are Wow.
Find the total number of cupcakes.
What is the percent of decrease from 98. 7 to 0?
0 is a 100% decrease of 98.7. Hope this helped!
When comparing the given value to −12, which is a TRUE statement?
20. while standard deviation and beta are both measures of risk, there are differences between the two. which of the following is correct? a. beta measures all risk b. beta measures only systematic risk c. beta measures only unsystematic risk d. standard deviation and beta are different, but both measure total risk
Standard deviation and beta are both measures of risk, however Beta is used to measure systematic risk. The correct answer is option (B), beta measures only systematic risk.
Standard deviation and beta are both measures of risk, however, there are differences between them. Standard deviation is a measure of the variation or dispersion of a set of data values. It shows the average deviation of each value from the mean. It is expressed in the same units as the original data.
Beta, on the other hand, is a measure of the systematic risk of an investment relative to the market as a whole. It reflects the extent to which the return on a particular security or portfolio moves with the overall market, and is often used in the Capital Asset Pricing Model (CAPM) to estimate the required rate of return for an investment. It measures the sensitivity of the security's returns to the market.
The systematic risk of an investment is the risk that is associated with the market as a whole, rather than with a particular security. It is often referred to as market risk because it is based on factors that affect the entire market, such as changes in interest rates, inflation, or economic conditions.
Unsystematic risk, on the other hand, is the risk that is specific to a particular security or industry, and is caused by factors that affect that particular security or industry, such as management changes, lawsuits, or other events that affect the company's operations.
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There are 80 people in a choir.
Half the people in the choir are women.
The number of men in the choir is one quarter of the number of women.
The rest of the people in the choir are children.
the number of children in the choir: the number of men in the choir = n: 1
Work out the value of n.
You must show how you get your answer.
Answer:
3
Step-by-step explanation:
Number of people in the choir = 80
Number of women = half of 80 = 40
Number of men in the choir is ¼ of the women = 40/4 = 10
Number of men plus women = 10 +40 = 50
Number of children = 80 - 50 = 30
Ratio of children to men = n:1 = 30:10
Divide both sides by 10
30:10 = 3:1
n = 3
Select the statement that shows equivalent measurements.
5.2 meters = 0.52 centimeters
5.2 meters = 52 decameters
52 meters = 520 decimeters
5.2 meters = 5,200 kilometers
None of these options
Option A
Conversion of measurement of Metres to Centimetres can be done by multiplying the number by 100
1 metre = 100 centimetres
5.2 metres = 520 centimetres
Option B
Conversion of measurement of Metres to Decametres can be done by multiplying the number by 0.1
1 metre = 0.1 decametres
5.2 metres = 0.52 decametres
Option C
Conversion of measurement of Metres to Decimetres can be done by multiplying the number by 10
1 metre = 10 decimetres
5.2 metres = 52 decimetres
Option D
Conversion of measurement of Metres to Kilometres can be done by multiplying the number by 0.001
1 metre = 0.001 kilometres
5.2 metres = 0.0052 kilometres
Therefore,
5.2 metres = 520 centimetres
5.2 metres= 0.52 decametres
5.2 metres= 52 decimetres
5.2 metres= 0.0052 kilometres
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Find the missing angle to the nearest degree.
let f(x)=ax^n+bx^5+36/cx^m-dx^2+9 where m and n are integers and a,b,c and d are unknown constants. which of the following is a possible graph of y=f(x)?
First, note that the degree of the polynomial is the highest power of x that appears in the expression. In this case, the degree is max(n, 5, m, 2).
How to determine graph?Next, consider the leading coefficient of the polynomial, which is the coefficient of the term with the highest power of x. In this case, the leading coefficient is a.
Based on this information, here are some possible general shapes of the graph of y=f(x):
If n is even and a > 0, the graph of y=f(x) looks like a "U" shape, with both ends pointing upwards.
If n is even and a < 0, the graph of y=f(x) looks like an upside-down "U", with both ends pointing downwards.
If n is odd and a > 0, the graph of y=f(x) looks like a "v" shape, with the vertex pointing upwards.
If n is odd and a < 0, the graph of y=f(x) looks like an upside-down "v", with the vertex pointing downwards.
Note that these are just general shapes, and the actual graph could be modified by the other terms in the polynomial. Additionally, the values of b, c, d, and the constants could also affect the shape and behavior of the graph.
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Complete Question is : let f(x)=ax^n+bx^5+36/cx^m-dx^2+9 where m and n are integers and a,b,c and d are unknown constants. what is the possible graph of the function?
if a random sample of size 555 is selected, what is the probability that the proportion of persons with a retirement account will differ from the population proportion by less than 5% ? round your answer to four decimal places.
The probability that the proportion of persons with a retirement account in a random sample of size 555 differs from the population proportion by less than 5% is approximately 0.8327.
We need to make some assumptions about the population proportion of persons with a retirement account and the standard deviation of the sampling distribution of sample proportions. Let's assume that the population proportion is p = 0.5 (i.e., half of the population has a retirement account) and that the standard deviation of the sampling distribution is given by:
σ = sqrt((p*(1-p))/n)
where n is the sample size.
Substituting the values given in the question, we have:
σ = sqrt((0.5*(1-0.5))/555) = 0.0258
To find the probability that the sample proportion differs from the population proportion by less than 5%, we need to find the probability that the absolute difference between the sample proportion and the population proportion is less than 0.05. This can be written as:
P(|p_hat - p| < 0.05)
where p_hat is the sample proportion.
We can standardize this expression by subtracting the population proportion from both sides and dividing by the standard deviation:
P(|p_hat - p|/σ < 0.05/σ)
P(-0.97 < Z < 0.97)
where Z is a standard normal variable. We can find this probability using a standard normal table or a calculator:
P(-0.97 < Z < 0.97) = 0.8327
Rounding to four decimal places, we have:
P(|p_hat - p| < 0.05) = 0.8327
Therefore, the probability that the proportion of persons with a retirement account in a random sample of size 555 differs from the population proportion by less than 5% is approximately 0.8327.
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one number is four more than a second number. two times the first number is 2 more than four times the second number. what are the two numbers?
The two numbers are 6 and 2.
Let's assume the first number is x and the second number is y.
From the first statement, we can write the equation x = y + 4.
From the second statement, we can write the equation 2x = 4y + 2.
Now, we can substitute x in terms of y from the first equation into the second equation:
2(y + 4) = 4y + 2
Simplifying this equation, we get:
2y + 8 = 4y + 2
2y = 6
y = 3
Substituting y = 3 in the first equation, we get:
x = y + 4 = 3 + 4 = 7
Therefore, 6 and 2 are the two numbers,
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A pharmacist has an 18% alcohol solution and a 40% alcohol solution. How much of each should he mix together to make 10L of a 20% alcohol solution? Pls help
0.18x + 4 - 0.40x = 2
-0.22x = -2
x = 9.09
Therefore, the pharmacist should mix 9.09 liters of 18% alcohol solution and 0.91 liters of 40% alcohol solution to make 10 liters of 20% alcohol solution.
[tex]x=\textit{Liters of solution at 18\%}\\\\ ~~~~~~ 18\%~of~x\implies \cfrac{18}{100}(x)\implies 0.18 (x) \\\\\\ y=\textit{Liters of solution at 40\%}\\\\ ~~~~~~ 40\%~of~y\implies \cfrac{40}{100}(y)\implies 0.4 (y) \\\\\\ \textit{10 Liters of solution at 20\%}\\\\ ~~~~~~ 20\%~of~10\implies \cfrac{20}{100}(10)\implies 2 \\\\[-0.35em] ~\dotfill[/tex]
[tex]\begin{array}{lcccl} &\stackrel{Liters}{quantity}&\stackrel{\textit{\% of Liters that is}}{\textit{alcohol only}}&\stackrel{\textit{Liters of}}{\textit{alcohol only}}\\ \cline{2-4}&\\ \textit{1st Sol'n}&x&0.18&0.18x\\ \textit{2nd Sol'n}&y&0.4&0.4y\\ \cline{2-4}&\\ mixture&10&0.2&2 \end{array}~\hfill \begin{cases} x + y = 10\\\\ 0.18x+0.4y=2 \end{cases} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\stackrel{\textit{using the 1st equation}}{x+y=10\implies y=10-x} \\\\\\ \stackrel{\textit{substituting on the 2nd equation from above}}{0.18x+0.4(10-x)=2}\implies 0.18x+4-0.40x=2 \\\\\\ -0.22x+4=2\implies -0.22x=-2\implies x=\cfrac{-2}{-0.22}\implies \boxed{x\approx 9.09} \\\\\\ \stackrel{\textit{since we know that}}{y=10-x}\implies y\approx 10-9.09\implies \boxed{y\approx 0.91}[/tex]
Hannah put 2,364 pieces of candy into a bags with 57 pieces of candy each. How many full bags did she make?
2,364 ÷ 57 ≈ 41. Therefore, Hannah made 41 full bags of candy.
To solve this problem, we use integer division to find the number of full bags Hannah made. We divide the total number of candy pieces by the number of pieces in each bag and take the integer part of the result. This is because we are only interested in the number of full bags, not partial bags. In this case, we have 2,364 pieces of candy and each bag holds 57 pieces, so 2,364 ÷ 57 ≈ 41. This means that Hannah made 41 full bags of candy.
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how can you make two pairs of adjacent and vertical angles but explained in a simple way.
Answer:
there
Step-by-step explanation:
you glass of orange is 1/2 full. Your friends glass is 1/3 full. your friend has more orange juice explain how this is possible
Answer:
Step-by-step explanation:
It is possible if your friend has a bigger glass than you.
7(x+4)= -21 i need help pls help me its hard 8th grade btw
The given equation is 7(x+4) = -21 . Therefore, the value of x is 7
In mathematics, an equation is a formula that connects two expressions with the equal sign = to indicate that they are equal. An equation is made up of two expressions joined by an equal sign ("="). Expressions for both sides of the equals sign are called the "left side" and the "right side" of the equation. Many times the right side of the equation is assumed to be zero. Assuming this does not reduce generality, this can be achieved by subtracting the right side from both sides.
According to the Question:
The given equation is:
7(x+4)= -21
⇒ 7x + 28 = -21
⇒ 7x = -49
⇒ x = 7
Complete Question:
Solve the Equation : 7(x+4)= -21
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Use ABC to write the indicated trigonometric ratio
Sin B=
Answer:
b/c
Step-by-step explanation:
sin B = opp/hyp
sin B = b/c
how many seven digit license plates contain exactly four letters all which are distinct? (the other characters must be numbers.)
26 * 25 * 24 * 22 = 16,384.
There are 16,384 seven-digit license plates that contain exactly four letters, all of which are distinct. This is because there are 26 possible letters, so the first letter could be any of those letters, and then the second letter has 25 options, and so on until the fourth letter, which has 22 possible letters. So, the total number of combinations is 26 * 25 * 24 * 22 = 16,384.
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Jaxon invested $710 in an account paying an interest rate of 8\tfrac{7}{8}8 8 7 % compounded quarterly. Jason invested $710 in an account paying an interest rate of 8\tfrac{5}{8}8 8 5 % compounded continuously. After 8 years, how much more money would Jaxon have in his account than Jason, to the nearest dollar?
Answer:
I attached your answer along with an explanation
Step-by-step explanation:
Please Like me follow me and Give me Crown for more help. :)
8. describe the center and spread of the chi-square distributions. 9. what is the chi-square test statistic? is it on the formula sheet? what does it measure? 10. how many degrees of freedom does the chi-square distribution have? 11. what is the rule of thumb for all expected counts in a chi-square goodness of fit test?
8. Spread = SD = sqrt(2*df)
9. The difference between the observed and expected frequencies of the outcomes of a set of events or variables.
10. Degrees of 1 freedom does the chi-square distribution.
11. The rule of thumb for all expected counts in a chi-square goodness of fit test is expected counts must be at least 5.
8. Describe the center and spread of the chi-square distributions.
Shape - skewed right because can't be zero
µ = df = tipping point
mode = df - 2 = peak
spread = SD = sqrt(2*df)
9. Chi-square test is a non-parametric test (a non-parametric statistical test is a test whose model does not specify conditions about the parameter of the population from which the sample is drawn.). It is used for identifying the relationship between a categorical variable and denoted by χ2.
10. A chi-squared distribution constructed by squaring a single standard normal distribution is said to have 1 degree of freedom. Thus, as the sample size for a hypothesis test increases, the distribution of the test statistic approaches a normal distribution.
11. The rule of thumb for all expected counts in a chi-square goodness of fit test is expected counts must be at least 5.
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what is the measure of x
The value of angle x in the given figure is 79°.
An angle meaning is what?The highest and lοwest walls οf a skew are used tο split the curved lines that make up its ends using Cartesian measurements. A cοllisiοn between twο pοles at an intersectiοn is a pοtential. Angle is anοther οutcοme οf twο things interacting. They resemble dihedral fοrms the mοst clοsely. A twο-dimensiοnal curve can be created by placing twο line beams in variοus cοnfiguratiοns between their ends.
In ΔBFG, ∠FBG = 46°
So according to angle sum property
46° + ∠BFG + BGF = 180°
Here ΔBFG is an isosceles triangle
46° + 2∠BFG = 180°
2∠BFG = 180° - 46°
2∠BFG = 134
∠BFG = 134/2
∠BFG = 67° = ∠BGF
Using Vertically opposite angle
∠AFJ = 67°
With that in mind ∠BFA = ∠JFG
2∠JFG + 2∠AFJ = 360°
2∠JFG = 360° - 2∠AFJ
2∠JFG = 360° - 2(67)
2∠JFG = 360° - 134
2∠JFG = 226
∠JFG = 226/2
∠JFG = 113°
In ΔFDC, ∠JFG + ∠JDI + ∠HCG = 180°
113° + 33° + ∠HCG = 180°
∠HCG = 180° - (113° + 33°)
∠HCG = 34°
Also, ∠HGC = ∠BGF = 67°
Now, In ΔCGH, ∠HGC + ∠HCG + x = 180°
67° + 34° + x = 180°
x = 180° - (67° + 34°)
x = 79°
Thus, the value of angle x in the given figure is 79°.
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Sarah has 43 bananas, she gives Steve 10. How many bananas does she have left?
Answer:
33
Step-by-step explanation:
43-10=33 sarah has 33 bananas ledt
What is the area of this figure? Do not include a label. Number only.
Therefore, the area of the polygon is 24 square units.
What is coordinate?In mathematics, a coordinate is a set of numbers or values that represent the position or location of a point or an object in space. Typically, coordinates are used to describe points in two-dimensional (2D) or three-dimensional (3D) space.
In 2D space, coordinates are usually represented as pairs of numbers (x, y), where the first number (x) represents the horizontal distance of the point from the origin, and the second number (y) represents the vertical distance of the point from the origin.
by the question.
To find the area of the polygon defined by the given coordinates, we can use the Shoelace Formula:
[tex]Area = 1/2 * |(x1y2 + x2y3 + ... + xny1) - (y1x2 + y2x3 + ... + ynx1)|[/tex]
where?[tex](x_{1} ,y_1), (x_2,y_2), ..., (x_n,y_n)[/tex] are the coordinates of the vertices listed in order.
Plugging in the given coordinates in order, we get:
[tex]Area = 1/2 * |(-12 + -5(-3) + (-5)(-5) + (-2)(-2) + 22 + 4(-2)) - (4*(-5) + (-5)(-5) + (-3)(-2) + (-2)2 + 2(-1) + 2*(-5))|= 1/2 * |-2 - 125 + 25 - 4 + 8 + 8 + 20 + 10 + 2 + 10|= 1/2 * |-48|=24[/tex]
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a. is w in fv1; v2; v3g? how many vectors are in fv1; v2; v3g? b. how many vectors are in span fv1; v2; v3g? c. is w in the subspace spanned by fv1; v2; v3g? why?
a. No, w is not in fv1; v2; v3g. There are three vectors in fv1; v2; v3g.
b. There are three vectors in the span of fv1; v2; v3g.
c. No, w is not in the subspace spanned by fv1; v2; v3g. This is because the subspace is the set of all linear combinations of the vectors in the span, and w does not have to be a linear combination of the vectors in the span.
To prove this, we first need to recall the definition of the span: it is the set of all linear combinations of a set of vectors. A linear combination is a sum of the vectors, multiplied by constants. For example, if we have a vector v1, and two constants a and b, then the linear combination of a*v1 and b*v1 is (a + b)*v1. If a vector w is not a linear combination of v1, then w is not in the span of v1.
The same logic applies to the vectors fv1; v2; v3g. If w is not a linear combination of these three vectors, then w is not in the subspace spanned by these three vectors. We can prove this by showing that w cannot be a linear combination of fv1; v2; v3g. This is because the only way to create a linear combination of these vectors is to multiply them by constants, and since w is not one of the vectors, it cannot be multiplied by a constant. Therefore, w is not in the subspace spanned by fv1; v2; v3g.
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in a gambling game a person draws a single card from an ordinary 52-card playing deck. a person is paid $19 for drawing a jack or a queen and $5 for drawing a king or an ace. a person who draws any other card pays $2. if a person plays this game, what is the expected gain? (round your answer to the nearest cent.)
the expected gain is $0.77, rounded to the nearest cent.The expected gain is the sum of the products of the probability of each outcome and its corresponding payoff.
There are 4 jacks, 4 queens, 4 kings, and 4 aces in a standard 52-card deck. So the probability of drawing a jack or a queen is 8/52 = 2/13, and the probability of drawing a king or an ace is also 8/52 = 2/13. The probability of drawing any other card is 1 - 2/13 - 2/13 = 9/13.
The expected gain is the sum of the products of the probability of each outcome and its corresponding payoff. So:
Expected gain = (2/13) * 19 + (2/13) * 5 + (9/13) * (-2)
Expected gain = 38/13 - 10/13 - 18/13
Expected gain = 10/13 ≈ 0.77
Therefore, the expected gain is $0.77, rounded to the nearest cent.
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in a normal distribution, 95.4% of the values fall between 5.8 and 10.6. compute the mean of the distribution.
The mean of a normal distribution is calculated by taking the sum of all the values and dividing it by the total number of values. In this case, the values were between 5.8 and 10.6, and the total number of values was 95.4%
The mean of a normal distribution is calculated by taking the sum of all the values and dividing it by the total number of values. In this case, the values are between 5.8 and 10.6, and the total number of values is 95.4%.
To calculate the mean, we must first calculate the sum of all the values. To do this, we will use the following formula:
sum of values = (lowest value + highest value) / 2
In this case, the lowest value is 5.8 and the highest value is 10.6, so the sum of values is 8.2.
We now have the sum of all the values, so we can calculate the mean by dividing the sum by the total number of values. The total number of values is 95.4%, so the mean is 8.2 / 0.954 = 8.57.
Therefore, the mean of the normal distribution is 8.57.
In conclusion, the mean of a normal distribution is calculated by taking the sum of all the values and dividing it by the total number of values. In this case, the values were between 5.8 and 10.6, and the total number of values was 95.4%. When the sum of all the values (8.2) was divided by the total number of values (0.954), the mean was calculated to be 8.57.
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a postal employee is counting how many houses on the route have dogs. statistically, 48\% of homes have dogs, according to the postal employees research. on the route of 30 homes, the postal employee encounters 12 dogs. what is the variance?
The variance is 7.2.
We can use the binomial distribution formula to calculate the variance. The formula for the variance of a binomial distribution is
Variance = n × p × (1 - p)
where n is the number of trials, p is the probability of success on each trial, and (1 - p) is the probability of failure on each trial.
In this case, n = 30 (the number of homes on the route), p = 0.48 (the probability of a home having a dog), and (1 - p) = 0.52 (the probability of a home not having a dog).
The postal employee encountered 12 dogs, which means there were 18 homes without dogs. So, the actual probability of success in this case is
P(dogs) = 12/30 = 0.4
Using the formula above, we can calculate the variance
Variance = n × p × (1 - p)
= 30 × 0.4 × 0.6
= 7.2
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