Ray and Jon play a game of chance with two dice. If the sum of the dice is seven, Ray pays Jon $15. But if the sum is anything else, Jon pays Ray $10. What is the expected value of the game for Jon?Answer:
Answers
Step 1
[tex]\text{Probability of any event = }\frac{\text{number of required outcomes}}{n\text{umber of possible outcomes}}[/tex]Step 2:
Draw the table of the possible outcomes.
Step 3:
Draw the table for the expected value
Number of the sum of seven = 6
Number of anything else = 30
Total possible outcomes = 36
[tex]\begin{gathered} \text{Expected value formula = Value }\times\text{ Probability of event} \\ \text{Expected value formula = xp(x)} \end{gathered}[/tex]Final answer
The expected value of the game for Jon
[tex]\begin{gathered} =\text{ }\frac{15}{6}\text{ + }\frac{50}{6} \\ =\text{ }\frac{65}{6}\text{ } \\ =\text{ 10.83} \end{gathered}[/tex]
Related Questions
ylinders, cone Justin uses the mold picture cement column posts to use a height of the Cylinder = 18 in To make a post, Justin completel wet cement How much wet cement, in cubic inche make 4 posts? dus 3 in Formula Sheet
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A plan for a park has a rectangular plot of wild flowers that needs to be enclosed by 54 feet of fencing. Only three sides need to be enclosed because one side is bordered by the parking lot. use Desmos to get your answers. 1. What is the largest area possible for the garden? DO NOT ROUND YOUR ANSWER. ____ squared feet2. What width will produce the maximum area? ____ feet3. What is the length of the garden that will produce the maximum area?
Answers
SOLUTION:
Step 1:
In this question, we are given the following:
Step 2:
a) What is the largest area possible for the garden?
Now, let the length of the rectangular plot be 54 -2x,
and the width of the rectangular plot be x,
so that:
[tex]\begin{gathered} \text{Area = (54 -2x) x = 54 x -2x}^2 \\ \frac{dA}{dx}=\text{ 54 - 4x = 0} \\ We\text{ have that:} \\ 54\text{ = 4x } \\ \text{Divide both sides by 4, we have that:} \\ \text{x = }\frac{54}{4} \\ \text{x = 13. 5} \end{gathered}[/tex]Then, the largest area possible for the garden will be:
[tex]\text{Area = 54x -2x}^2=54(13.5)-2(13.5)^2=729-364.5=364.5ft^2[/tex]b) What width will produce the maximum area?
[tex]Width,\text{ x = 13. 5 fe}et[/tex]c) The length of the garden that will produce the maximum area:
[tex]\text{Length = 54 - 2x = 54 - 2( 13. 5) = 54 -27 = 27 fe}et[/tex]е A Chinese restaurant has a large goldfish pond. Suppose that an inlet pipe and a hose together can fill the pond in 3 hours. The inlet pipe alone can complete the job in one hour less time than the hose alone. Find the time that the hose can complete the job alone and the time that the inlet pipe can complete the job alone. ntents Library The time that the hose can complete the job alone is (?) hours. (Round to the nearest tenth.) The time that the inlet pipe can complete the job alone is (? )hours. (Round to the nearest tenth.) nizer
Answers
SOLUTION
Let the time for the pipe to complete the Job be represented as
[tex]p[/tex]Let the time for the hose to complete the Job be represented as
[tex]h[/tex]The pipe and the hose completed the job in 3hours
Hence we have the equation
[tex]p+h=3[/tex]The inlet pipe alone can complete the job in one hour less time than the hose alone implies that
[tex]h-p=1[/tex]This leads to a system of equation which we now solve simultaneously
[tex]\begin{gathered} h+p=3\ldots\text{.eq}1 \\ h-p=1\ldots\text{.}\mathrm{}eq2 \end{gathered}[/tex]Adding eq1 and eq2, we o btain
[tex]\begin{gathered} 2h=4 \\ h=\frac{4}{2}=2 \end{gathered}[/tex]Substituting the value of h into eq1 we have
[tex]\begin{gathered} h+p=3 \\ 2+p=3 \\ p=3-2 \\ p=1 \end{gathered}[/tex]Therefore
[tex]h=2,\text{ p=1}[/tex]The time that the inlet pipe can complete the job alone is 1 hours
The time that the hose can complete the job alone is 2 hours
the total amount of flour in a bakery after receiving new stock equal to 3/10 of its current stock (x)Find the expression that represents the scenario
Answers
Answer:
(3/10)x
Explanation:
The expression that represents the scenario is an expression that we can use to calculate the total amount of flour, so the correct expression is:
[tex]\frac{3}{10}x[/tex]Because the amount of flour is 3/10 of x ( the current stock)
solve for the value of s
110°
(8s-2)°
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The value of s for equation 110=8s-2 will be 14 by solving the linear equation.
What is equation?A mathematical statement known as an equation is made up of two expressions joined together by the equal sign. A formula would be 3x - 5 = 16, for instance. When this equation is solved, we discover that the value of the variable x is 7. a formula that expresses the connection between two expressions on each side of a sign. The point-slope form, standard form, and slope-intercept form are the three main types of linear equations.
Here,
110=8s-2
8s=112
s=14
By resolving the linear equation, we obtain the value of s for equation 110=8s-2 as 14.
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If a = 6, which of the following is equal to a 2?1o-36O O-122
Answers
Solution:
The question given is a negative exponent.
To solve this, we apply the law of indices for negative exponents.
Negative exponent law is indicated below;
[tex]a^{-x}=\frac{1}{a^x}[/tex]Thus, applying this law to the question;
[tex]a^{-2}=\frac{1}{a^2}[/tex]Given:
a = 6
Substituting a = 6 into the expression, we have;
[tex]\frac{1}{a^2}=\frac{1}{6^2}[/tex]Therefore, the correct answer is;
[tex]\frac{1}{6^2}[/tex]Select the values that make the inequality u≥8u≥8 true.(Numbers written in order from least to greatest going across.)
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To make u >= 8 true, we need to select all of the values that are either equal to OR greater than 8. This means that we must check the following:
8
8.001
8.01
8.1
9
11
13
16
Given the Exponential Equation, determine the Initial Value and Rate of Change as a Percent for each of the following.
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The formula for calculating exponential growth is expressed as
y = a(1 + r)^n
where
a is the initial value
y is the final value
n is the time
r is the growth rate
The formula for calculating exponential decay is expressed as
y = a(1 - r)^n
For y = 1010(1.05)^x,
initial value = 1010
1 + r = 1.05
r = 1.05 - 1 = 0.05
Since it is positive, it is exponential growth
Growth percent = 0.05 x 100 = 5%
For y = 4932(1.26)^x,
initial value = 4932
1 + r = 1.26
r = 1.26 - 1 = 0.26
Growth percent = 0.26 x 100 = 26%
For y = 2835(1.065)^x,
initial value = 2835
1 + r = 1.065
r = 1.065 - 1 = 0.065
Since it is positive, it is exponential growth
Growth percent = 0.065 x 100 = 6.5%
For y = (0.96)^t,
initial value = 1
1 - r = 0.96
r = 1 - 0.96 = 0.04
decay percent = 0.04 x 100 = 4%
For y = 4660(0.89)^x,
initial value = 4660
1 - r = 0.89
r = 1 - 0.89 = 0.11
decay percent = 0.11 x 100 = 11%
For y = 3078(1.09)^t,
initial value =3078
1 + r = 1.09
r = 1.09 - 1 = 0.09
Growth percent = 0.09 x 100 = 9%
solve the system. given your answer as (x, y, z)-4x -y - 3z = -5-6x + y - 3z = -172x + 2y - z = - 10
Answers
Answer:
(1, -5 ,2)
Explanation:
Given the system of equations:
[tex]\begin{gathered} -4x-y-3z=-5\ldots(1) \\ -6x+y-3z=-17\ldots(2) \\ 2x+2y-z=-10\ldots(3) \end{gathered}[/tex]Make z the subject in the third equation:
[tex]z=2x+2y+10[/tex]Substitute z=2x+2y+10 into the first and second equations:
First Equation
[tex]\begin{gathered} -4x-y-3z=-5 \\ -4x-y-3(2x+2y+10)=-5 \\ -4x-y-6x-6y-30=-5 \\ -4x-6x-y-6y=-5+30 \\ -10x-7y=25\ldots(4) \end{gathered}[/tex]Second Equation
[tex]\begin{gathered} -6x+y-3z=-17 \\ -6x+y-3(2x+2y+10)=-17 \\ -6x+y-6x-6y-30=-17 \\ -6x-6x+y-6y=-17+30 \\ -12x-5y=13\ldots(5) \end{gathered}[/tex]Next, solve equations 4 and 5 simultaneously:
[tex]\begin{gathered} -10x-7y=25\ldots(4) \\ -12x-5y=13\ldots(5) \end{gathered}[/tex]Multiply equation (4) by 5 and equation (5) by 7.
[tex]\begin{gathered} -50x-35y=125 \\ -84x-35y=91 \\ \text{Subtract same sign} \\ 34x=34 \\ x=\frac{34}{34} \\ x=1 \end{gathered}[/tex]Substitute x=1 into equation (4):
[tex]\begin{gathered} -10x-7y=25\ldots(4) \\ -10(1)-7y=25 \\ -7y=25+10 \\ -7y=35 \\ y=\frac{35}{-7} \\ y=-5 \end{gathered}[/tex]Recall: z=2x+2y+10
[tex]\begin{gathered} z=2x+2y+10 \\ =2(1)+2(-5)+10 \\ =2-10+10 \\ z=2 \end{gathered}[/tex]The solution of the system is:
[tex](1,-5,2)[/tex]I NEED SOME HELP PLEASE ;n; .Zan took her dog, Simba, to the dog park on Saturday afternoon. There were less than 15 dogs running around the park when they arrived.
Determine which inequality describes the dogs at the park.
d < 15
d > 15
d ≤ 15
d ≥ 15
Answers
Answer:
I am pretty sure that it is d < 15
Explanation:
> means greater than
< means less than
≤ means less than or equal too
≥ means greater than or equal to
So the only only one that makes sense is <
A scale for a skyscraper blueprint is 1 inch = 40 feet. The height of theskyscraper is 640 feet and the width is 540 feet. What are the height andwidth in inches of the scale drawing of the skyscraper
Answers
Answer:
The height of the scale drawing of the skyscraper is 16 inches.
The width of the scale drawing of the skyscraper is 13.5 inches.
Explanation:
Given the scale of the model as 1 inch = 40 feet.
Let h represent the height of the scale drawing of the skyscraper. Given the actual height of the skyscraper as 640 feet, we can go ahead and determine h by setting up proportions as shown below;
[tex]\begin{gathered} \frac{1\text{inch}}{40\text{ ft}}=\frac{h\text{ in}}{640ft} \\ h=\frac{640\times1}{40} \\ h=16\text{inches} \end{gathered}[/tex]Let w represent the width of the scale drawing. Given the actual width of the skyscraper as 540 feet, we can go ahead and solve for w by setting up proportions as shown below;
[tex]\begin{gathered} \frac{1in}{40ft}=\frac{w\text{ in}}{540ft} \\ w=\frac{540\times1}{40} \\ w=13.5\text{inches} \end{gathered}[/tex]Over the weekend, Devon baked 12 muffins. She divided them evenly among 3 plates to giveto neighbors.The letter m stands for the number of muffins on each plate. Which equation can you use tofind m?12 x 3 = m12 : 3 = m
Answers
The information given is listed below:
number of muffins (m) = 12, number of plates = 3
number of muffin on each plate = number of muffins /
The directions says state if the two triangles are congruent. If they are state how you know
Answers
From the diagram, we see that the triangles have:
• equal hypotenuse,
,• equal base.
HL Theorem states that if the hypotenuse and leg of a right triangle are congruent to the hypotenuse and leg of another right triangle, then the two triangles are congruent.
We conclude that the triangles are congruent because of HL Theorem.
AnswerB) HL
this is a practice problem with more than one answer. it won't allow to me to send the whole picture so the question got cut off and another potential answer. I'll put it here. In the diagram, which of these objects is a radius? Select all that apply. the other option for an answer was EG
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We are asked to determine which of the objects are a radius. To do that, let's remember that a radius is a line segment that has one end at the center of a circle and the other end at any circumference point of the circle. Therefore, the segments that are radii are:
[tex]\begin{gathered} \bar{CD} \\ \bar{CB} \\ \bar{CH} \\ \bar{GE} \\ \bar{GF} \end{gathered}[/tex]A metal plate has the form of a quarter circle with a radius of R = 106cm . Two 3 cm holes are to be drilled in the plater r = 95cm from the corner at 30 degrees and 60as shown above. To use a computer controlled milling machine you must know the Cartesian coordinates of the holes. Assuming the origin is at the corner what are the coordinates of the holes (x_{1}, y_{1}) and (x_{2}, y_{2}) ? Round your answer to 3 decimal places
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1) Considering that this quarter circle is one sector of the unit circle and that
[tex]30^{\circ}=\frac{\pi}{6}[/tex]2) Let's sketch this out to better grasp the idea:
Note that the first coordinate will be given by its cos(theta), and the second one by its sine(theta)
3) Based on that principle, we can tell the following:
[tex]\begin{gathered} (x_1,y_1)--->(cos(30^{\circ}),\sin(30^{\circ}))=(\frac{\sqrt{3}}{2},\frac{1}{2}) \\ \\ (x_{2,}y_2)-->(\cos(60),\sin(60))=(\frac{1}{2},\frac{\sqrt{3}}{2}) \\ \end{gathered}[/tex]As the holes need to be drilled by the machine, so we need to find approximations to those coordinates:
[tex]\begin{gathered} (x_1,\:y_1)-->(0.866,0.500) \\ (x_2,y_2)-->(0.500,0.866) \end{gathered}[/tex]Thus, these are the coordinates to be put into the computer.
I’m in AP Calc AB and can’t figure this out. Any idea?
Answers
Answer::
[tex]f^{\prime}(x)=7x\sec x\tan x+7\sec x+\frac{1}{x}[/tex]Explanation:
Given f(x) defined below:
[tex]f(x)=\ln x+7x\sec x[/tex]The derivative is calculated below.
[tex]\begin{gathered} \frac{d}{dx}\lbrack f(x)\rbrack=\frac{d}{dx}\lbrack\ln x+7x\sec x\rbrack \\ =\frac{d}{dx}\lbrack\ln x\rbrack+\frac{d}{dx}\lbrack7x\sec x\rbrack \\ Take\text{ the constant 7 outside the derivative sign.} \\ =$$\textcolor{red}{\frac{d}{dx}\lbrack\ln x\rbrack}$$+7\frac{d}{dx}\lbrack x\sec x\rbrack \\ \text{The derivative of }\ln (x)=\frac{1}{x},\text{ therefore:} \\ $$\textcolor{red}{\frac{d}{dx}\lbrack\ln x\rbrack}$$+7\frac{d}{dx}\lbrack x\sec x\rbrack=$$\textcolor{red}{\frac{1}{x}}$$+7\frac{d}{dx}\lbrack x\sec x\rbrack\cdots(1) \end{gathered}[/tex]Next, we find the derivative of x sec x using the product rule.
[tex]\begin{gathered} \frac{d}{dx}\lbrack x\sec x\rbrack=x$$\textcolor{blue}{\frac{d}{dx}\lbrack\sec x\rbrack}$$+\sec x\frac{d}{dx}\lbrack x\rbrack\text{ } \\ The\text{ derivative of sec(x), }\text{\textcolor{red}{ }}\textcolor{red}{\frac{d}{dx}\lbrack\sec x\rbrack=\sec x\tan x} \\ =x$$\textcolor{blue}{\lbrack\sec x\tan x\rbrack}$$+\sec x \end{gathered}[/tex]Substitute the result into equation (1) above.
[tex]\begin{gathered} \frac{1}{x}+7\frac{d}{dx}\lbrack x\sec x\rbrack=\frac{1}{x}+7(x\sec x\tan x+\sec x) \\ =7x\sec x\tan x+7\sec x+\frac{1}{x} \end{gathered}[/tex]Therefore:
[tex]f^{\prime}(x)=7x\sec x\tan x+7\sec x+\frac{1}{x}[/tex]A variable needs to be eliminated to solve the system of equations. Choose the correct first step: -3x+8y=-294x-8y=28A. Add to eliminate xB.Subtract to eliminate yC.Add to eliminate yD. Subtract to eliminate x
Answers
From the given equations, we can note that coeffcients of variable y are opposite. This means that, in order to eliminate y, we can add both equations. Then, the answer is C
Find the y-intercept of the line.y = 3.1x+2.6y-intercept:
Answers
To find the y-intercept in any equation equate x by 0
The given equation is
[tex]y=3.1x+2.6[/tex]Substitute x by 0 to find the y-intercept
[tex]\begin{gathered} y=3.1(0)+2.6 \\ \\ y=0+2.6 \\ \\ y=2.6 \end{gathered}[/tex]The y-intercept is 2.6
a total of 200 video game players take a survey on their favorite game unknown Kingdom gets 55% of the votes the video game designer wants to know how many players voted for unknown Kingdom write 55% as a rate per hundred
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to find out how many players are on the 55% of 200, we can multiply the total players by 55% in decimal form:
[tex]undefined[/tex]-Convert the following into given base units of measurement. (Refer to slide 21 &27 on uploaded ppt).
1. 3.65 mg =______ dg
2. 9.987 g =______ hg
3. 12.203 km =______ mm
Answers
The conversion of the given base units of measurements are
Part 1
3.65 mg = 0.0365 dg
Part 2
9.987 g = 0.09987 hg
Part 3
12.203 km = 12203072.2 mm
Part 1
The given quantity is 3.65 mg
mg is the milligram and dg is the decigram
We know
1 mg = 0.01 dg
Then,
3.65 mg = 3.65×0.01
Multiply the terms
3.65 mg = 0.0365 dg
Part 2
The given quantity is 9.987 g
g is the gram and hg is the hectogram
1 g = 0.01 hg
Then,
9.987 g = 0.09987 hg
Part 3
The given quantity is 12.203 km
km is the kilometer and mm is the millimeter
1 km = 1000000 mm
12.203 km = 12203072.2 mm
Hence, the conversion of the given base units of measurements are
Part 1
3.65 mg = 0.0365 dg
Part 2
9.987 g = 0.09987 hg
Part 3
12.203 km = 12203072.2 mm
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question is in image
Answers
The function f(x) is given by,
[tex]f(x)=x^2[/tex]The function g(x) is given by,
[tex]g(x)=\frac{-2}{3}x^2[/tex]If f(x) becomes -kf(x), where 0Comparing the above functions, we get
[tex]g(x)=-\frac{2}{3}f(x)[/tex]So, k=2/3. Hence, 0 < 2/3 < 1.
Therefore, the graph of g(x) is the graph of f(x) compressed vertically and reflected across the x axis.
Hence, option D is correct.
metro atlanta home prices are rising rapidly, and much of its a soaring demand from deep-pocketed investors,as reported in the AJC March 21st of this year. In March2022, the median sale price of a home in the Metro area was $401,500. Before the the pandemic hit, in january2020, the median sale price was $279,000 Find the rate increase of the average cost of a home in Atlanta from january2020 before the pandemic hit Atlanta to the present
Answers
We are asked to determine the rate of increase in the value of a home,
We need to have into account that at the beginning of the considered period the cost was 279000 and after two years the cost is 401500, therefore, we can use the following formula:
[tex]r=\frac{\Delta C}{\Delta t}[/tex]Where:
[tex]\begin{gathered} \Delta C=\text{ difference in cost} \\ \Delta t=\text{ difference in time} \end{gathered}[/tex]Now, we substitute the values:
[tex]r=\frac{401500-279000}{2}[/tex]Solving the operations:
[tex]r=61250[/tex]Therefore, the rate is an increase of $61250 per year.
The table below shows the average amount of time spent per person on entertainment per year from 2000 to 2005.Year Hours2000 34922001 35402002 36062003 36632004 37572005 3809(a) Use a graphing calculator or spreadsheet program to find a quadratic model that best fits this data. Let t represent the year, with t=0 in 2000. Round each coefficient to two decimal places.Pt =(b) Based on this model, how many hours would you expect the average person to spend on entertainment in 2012? Round your answer to the nearest whole number.hours(c) When would you expect the average amount of entertainment time to reach 4000? Give your answer as a calendar year (ex: 1997).During the year
Answers
EXPLANATION
Given the table,
Year Hours
2000 3492
2001 3540
2002 3606
2003 3663
2004 3757
2005 3809
Plugging in the data into a graphing calculator with a quadratic regression model AX^2+BX+C:
The function is:
P(t) = 2.35714 X^2 -9376.16 X +9325921.701
B)
When the time is 2012 substituting on the function:
P(t) = 2.357*(2012)^2 - 9,374.84*(2012) + 9.3246X10^6 = 3897.32
Hence, the number of hours spent in 2012 would be 3897 hours.
C) By using the graph, we can expect that the average amount of entertainment time to reach 4000 would be 9,540,465 hours.
Michael earns a weekly salary of $365 plus a 6% commission of sales for the week. Last week, Michael's sales totaled $3200. How much did he make in commission? What was Michael's total pay?
Answers
Michael's sales are $3200, then the comission is
[tex]3200\times0.06=192,[/tex]$192 in comission.
Then the total pay is
[tex]365+192=557.[/tex]$567
Express the given Hindu-Arabic numeral in expanded form 26
Answers
Given:
The numeral is 26.
To find: The expanded form
Explanation:
As we know,
Expanded form or expanded notation is a way of writing numbers to see the math value of individual digits.
Separating the numbers into the individual place values, we get
[tex]26=(2\times10)+(6\times1)[/tex]Final answer: The expanded form of 26 is,
[tex](2\times10)+(6\times1)[/tex]what will the inflation-adjusted cost of a $154,600 house be in 5 years? round to two decimal places.
Answers
The inflation-adjusted cost of the house is $166,548.11
Explanation:[tex]\begin{gathered} The\text{ funcion the inflation adjusted cost:} \\ C(t)\text{ = C}_0(1\text{ + r\rparen}^t \\ r\text{ = rate} \\ \text{t = time} \\ C_0\text{ = cost of product} \end{gathered}[/tex][tex]\begin{gathered} From\text{ the information in the question:} \\ C_0\text{ = cost of house =\$154600} \\ r\text{ = 1.5\% = 0.015} \\ t\text{ = 5 years} \\ C(t)\text{ = ?} \\ We\text{ need to find the inflation adjusted cost using the function we were given in the question} \end{gathered}[/tex]substitute the values into the formula:
[tex]\begin{gathered} C(t)\text{ = 154600\lparen1 + 0.015\rparen}^5 \\ C(t)\text{ = 154600\lparen1.015\rparen}^5 \\ C(t)\text{ = 166548.107} \\ \\ To\text{ 2 decimal place, C\lparen t\rparen = 166548.11} \end{gathered}[/tex]The inflation-adjusted cost of the house is $166,548.11
In a class of 10 students, the ratings are given based on their performance on a test. The following data was taken from ratings given by the class teacher:5, 1, 2, 4, 2, 3, 5, 3, 3, 4Do the ratings earned by the students follow a normal distribution? aNo, because the mean and mode are same bYes, because the data is symmetrical about the mean 3 cNo, because the data is not symmetrical dYes, because the mean is greater than the mode of the data set
Answers
Given:
In a class of 10 students, the ratings are given based on their performance on a test. The following data was taken from ratings given by the class teacher:
5, 1, 2, 4, 2, 3, 5, 3, 3, 4
Required:
To choose the correct option
The table shows x- and y-values for the equation y = 3x -1 Which number is missing in the table? 23 15 20 37
Answers
y = 3x-1
When x = 8
y = 3(8) -1
y = 24-1
y = 23
My teacher gave the answer on the right but I want know how he did it
Answers
the given number is 6^4
here is the calculation.
[tex]6^4=6\times6\times6\times6[/tex]multiply the number 6 by the times of 4
now by multiplication, the answer is
[tex]6^4=1296[/tex]so, the answer is 1296.
Saul reads every week. In his first week of reading, he read 50 pages. Each week after that, he read 65 pages. Which expression represents the total number of pages Saul has read, where w represents the number of weeks since he first started reading.
Answers
Given
In first week , he read 50 pages.
After first week , he read 65 pages.
Find
Expression represents the total number of pages Saul has read
Explanation
Let w represents the number of weeks since he first started reading.
Assume y represent number of pages.
when w = 1 then y = 50 ; w = 2 then y = 65+50=115
we know the equation of line
y = mw + c
so ,
50 = m + c .........(1)
and
115 = 2m + c ............(2)
on solving equation (1) and (2) , we get m = 65 and c = -15
so ,
y = 65w - 15
Final Answer
Therefore , the correct option is 3rd