In a state's lottery, you can bet $3 by selecting three digits, each between 0 and 9 inclusive. If the same three numbers are drawn in the same order, you win and collect $500. Complete parts (a) through (e).
Answers
Using the Fundamental Counting Theorem, it is found that:
a) 1000 combinations are possible.
b) The probability of winning is of 0.001.
c) If you win, the net profit is of $497.
d) The expected value of a $3 bet is of -$2.5.
What is the Fundamental Counting Theorem?It is a theorem that states that if there are n trials, each with [tex]n_1, n_2, \cdots, n_n[/tex] possible results, each thing independent of the other, the number of results is given as follows:
[tex]N = n_1 \times n_2 \times \cdots \times n_n[/tex]
In the context of this problem, three digits that can be repeated are chosen, hence the parameters are:
[tex]n_1 = n_2 = n_3 = 10[/tex]
Hence the number of combinations is:
N = 10³ = 10 x 10 x 10 = 1000.
The order also has to be correct, hence the there is only one winning outcome and the probability is:
p = 1/1000 = 0.001.
You bet $3, and if you win you collect $500, hence the net profit is of:
500 - 3 = $497.
Then the distribution of earnings are as follows:
P(X = -3) = 0.999 -> losing.P(X = 497) = 0.001. -> winning.Hence the expected value is:
E(X) = -3 x 0.999 + 497 x 0.001 = -$2.5.
Missing informationThe problem is given by the image at the end of the answer.
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Related Questions
Tom bought 10 cans of Coca cola drink at a cost of USD26.00. How much he will need to pay for 36 cans of Coca Cola?
(20 Points) Working Step
Answers
Tom will need to pay $93.60 for 36 cans of Coca-Cola.
Linear ExpressionA linear expression can be represented by a line. The standard form for this equation is: y=ax+b , for example, y=3x+2.
The question gives:
Tom bought 10 cans of Coca-cola drink at a cost of USD26.00. Here you can convert this text into an algebraic expression, see:
10x = 26, where x represents the unit cost.
You can find x, solving the previous algebraic expression. Thus,
10x=26
x=26/10
x=2.6
So, 1 can of Coca-Cola costs $2.60.
For knowing the cost total for 36 cans of Coca-Cola, you need to multiply 36 units by the unit cost ($2.6). See below:
36*2.6= $93.60
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[tex]3 {}^{2} + ( - 4 {}^{2} ) + 5 {}^{2} [/tex]I'm confused on that can you help me please?
Answers
We have to replace the values in the equation
[tex]x^2+y^2+z^2=(3)^2+(-4)^2+(5)^2=9+16+25=50[/tex]Since the square of a negative number is a positive number, (-4)^2 = +16
4. the probability that an engine overheats is 0.12. the probability that an engine leaks oil is .08. (a) if overheating and leaking oil are independent, what is the probability that an engine overheats and leaks oil?
Answers
The probability that the engine over heats and leaks is 0.0096
The probability is computed by dividing the total number of possible outcomes by the number of possible ways the event could occur. Probability and odds are two distinct ideas. Odds are calculated by dividing the likelihood of an event by the likelihood that it won't.
Probability is a metric used to express the possibility or chance that a particular event will occur. Probabilities can be expressed as fractions from 0 to 1, as well as percentages from 0% to 100%.
Engine leaks oil AND overheats,
hence P(Engine overheats) = P(Engine overheats) X P(Engine leaks oil) = 0.12 X 0.08 = 0.0096
Hence the probability of leaking of engine due to over heating is 0.0096
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Tara's family raises honey bees and sells the honey at the farmers' market. to get ready for market day, tara fills 28 equal sized jars with honey. she brings a total of 14 cups of honey to sell at the farmers' market. use an equation to find the amount of honey each jar holds. to write a fraction, use a slash ( / ) to separate the numerator and denominator.
Answers
The amount of honey each jar holds is 1/2 cup by jar
To solve this exercise we have to perform a mathematical operation of division with fractions:
Information about the problem:
Jars filled = 28 jarsCups brought = 14 cupsTo find the amount of honey each jar holds we state the following equation:
Amount of honey by jar = Cups brought / Jars filled
Amount of honey by jar = 14 cups /28 jar
Simplifying to its minimum expression, we have:
Amount of honey by jar = 7 cups / 14 jar
Amount of honey by jar = 1 cup / 2 jar
Amount of honey by jar = 1/2 cup by jar
What is a fraction?Is a number that expresses the portion of some number over a total. The number that expresses the portion is known as the numerator and the number that expresses the total is known as the denominator.
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The new figure that is produced in a transformation is called the
Answers
Let:
[tex]\begin{gathered} P=(x1,y1)=(-3,4) \\ P^{\prime}=(x2,y2)=(4,0) \end{gathered}[/tex][tex]\begin{gathered} x1+a=x2 \\ -3+a=4 \\ so\colon \\ a=4+3 \\ a=7 \\ ---- \\ y1+b=y2 \\ 4+b=0 \\ b=-4 \end{gathered}[/tex]Therefore:
[tex](x,y)\to(x+7,y-4)[/tex]Karyn proofreads 15 pages in 2 hours for $40. What is her proofreading rate in pages per hour? How much does she earn per hour?
Answers
The proofreading rate of Karyn in pages per hour is $20 per 7.5 pages per hour , and she earn $20 per hour .
In the question ,
it is given that
Karyn proofreads ⇒15 pages in 2 hours for $40
Karyn in 2 hour proofreads 15 pages ,
So, in 1 hour She will proofread = 15/2= 7.5 pages
and will get $40/2 = $20 for 1 hour ,
hence ,her rate in pages per hour is $20 per 7.5 pages per hour .
In 2 hour Karyn earns $40
So , in 1 hour Karyn will earn $40/2 = $20
hence , she earn $20 per hour .
Therefore , the proofreading rate of Karyn in pages per hour is $20 per 7.5 pages per hour , and she earn $20 per hour .
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Hey!
New question 4 today
Nadia is walking a 3.4-mile trail. She stops to take a break after walking 1.6 miles. Which explains whether the distance Nadia already walked is greater than, less than, or equal to the distance she has left to walk?
!PLEASE!
Don't give wrong answers. (its not very nice)
Only use one of the answer options. (other answers are wrong)
Answers
Based on the distance walked by Nadia when she took her break, the statement that explains the distance already walked is C. The distance Nadia already walked is less because 3.4 - 1.6 = 1.8, and 1.6 < 1.8.
How to find the distance?Nadia had already walked 1.6 miles by the time she took her break. This means that the distance she was still left to walk in the mile trail was:
= 3.4 - 1.6
= 1.8 miles
The distance that Nadia had already walked was 1.6 miles and yet she was left to walk 1.8 miles.
We can therefore conclude that the distance that Nadia already walked is less than the distance still to be walked.
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The distance Nadia already walked is less because 3.4 - 1.6 = 1.8, and 1.6 < 1.8 which is the correct answer would be an option (C).
What is the distance?Distance is calculated as the product of a person's movement and time.
Nadia took a rest after covering 1.6 miles of walking.
This indicates that she had the following distance to cover on the mile trail:
⇒ 3.4 - 1.6 = 1.8 miles
Nadia had already walked 1.6 miles, but she still had another 1.8 miles to go.
Therefore, the distance Nadia has already traveled is less than the distance that needs to be covered.
Hence, the correct answer would be an option (C).
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Students in a fitness class each completed a one-mile
Which statements are true about a histogram with one-
walk or run. The list shows the time it took each person
minute increments representing the data? Select three
to complete the mile. Each time is rounded to the
options.
nearest half-minute.
5.5, 6, 7, 10, 7.5, 8, 9.5, 9, 8.5, 8, 7, 7.5, 6, 6.5, 5.5
O A histogram will show that the mean time iS
approximately equal to the median time of 7.5
minutes.
O The histogram will have a shape that is left-skewed.
O The histogram will show that the mean time is greater iS
than the median time of 7.4 minutes.
O The shape of the histogram can be approximated with
a normal curve.
0 The histogram will show that most of the data is
centered between 6 minutes and 9 minutes.
Answers
In linear equation, The histogram will show that most of the data is centered between 6 minutes and 9 minutes.
What in mathematics is a linear equation?
An x-y linear relationship, or two variables in which the value of one of them (often y) relies on the value of the other one, is what is known as a linear equation in two variables (usually x).The dependent variable in this scenario is y since it depends on the independent variable, x.5.5+6+7+10+7.5+8+9.5+9+8.5+8+7+7.5+6+6.5+5.5=111.5
Since there are 15 values,
their mean is 111.5/15=7.43 which is very close to the mean.
A)A histogram will show that the mean time is approximately equal to the median time of 7.5 minutes
D)The shape of the histogram can be approximated with a normal curve.
E)The histogram will show that most of the data is centered between 6 minutes and 9 minutes.
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PLEASE ASAP HELP MEEEEThe longer leg of a right triangle is 3 inches longer than the shorter leg. The hypotenuse is 6 inches longer than the shorter leg. Find the side lengths of thetriangle.Length of the shorter leg:inchesLength of the longer leg:inchesinchesLength of the hypotenuse:
Answers
In order to find the values of the sides of the triangle you take into account the relation between sides and hypotenuse.
h: hypotenuse
c1: shorter leg
c2: longer leg
Longer leg c2 is 3 inches longer than c1:
c2 = c1 + 3
hypotenuse h is 6 inches longer than c1:
h = c1 + 6
The formula for the calculation of the hypotenuse is:
h² = c1² + c2²
you replace for h and c2 in terms of c1:
(c1 + 6)² = c1² + (c1 + 3)²
You solve the previous equation for c1:
c1² + 12c1 + 36 = c1² + c1² + 6c1 + 9
c1² - 6c1 - 27 = 0
the roots of the previous equation are:
(c1 - 9 )(c1 + 3) = 0
c1 = 9
c1 = -3
You take the positive number because there is no length of sides with negative values.
Then, c2 and h are:
c2 = c1 + 3 = 9 + 3 = 12
h = c1 + 6 = 9 + 6 = 15
Hence, shorter leg is 9 inches, longer leg 12 inches and hypotenuse 15 inches
Given the polynomial f(x)=x⁴+3x³-3x²-x, which of the following is true?
a) (x+1) is a factor since f(-1)=0.
b) (x-1) is a factor since f(-1)=0.
c) (x+1) is a factor since f(1)=0.
d) (x-1) is a factor since f(1)=0.
Answers
Julia has a mask collection consisting of 255 masks she keeps on the wall and 45 she keeps in a display case. What percentage of Julias mask collection does she keep on her wall?
Answers
We are told that Julia keeps 255 masks on the wall and 45 on the display case, this means in total the number of masks she has is
[tex]255+45=300\text{masks}[/tex]The number of masks Julia keeps on the wall is 255 masks; therefore, the percentage of fo masks on the wall is
[tex]\frac{255}{300}\times100[/tex][tex]=85.\text{ }[/tex]Hence, Julia keeps 85% of her mask collection on her wall.
a box is constructed out of two different types of metal. the metal for the top and bottom, which are both square, costs 1/ft2 and the metal for teh sides costs 2 ft find the dimensions that minimize cost if the box has a volume of 20 ft 3
Answers
The cost function of the box is C(x) = 2. x² + 160/x and the dimension that lead to the minimum cost is length = ∛40 ft., width = ∛40 ft., height = ∛5 ft.
Let:
x = the bottom's side length
h = the height of the box
Then, the surface area of top and bottom:
A1 = 2. x²
The surface area of vertical sides:
A2 = 4 x. h
The cost function is:
C(x) = 2. x² . 1 + 4 x. h . 2
C(x) = 2. x² + 8 x. h
The volume of the box is:
V = x² . h
20 = x² . h
h = 20 / x²
Substitute h = 20 / x² into the cost function:
C(x) = 2. x² + 8 x. h
C(x) = 2. x² + 8 x. 20 / x²
C(x) = 2. x² + 160/x
At the minimum point, the derivative of a function is equal to zero. Hence,
C'(x) = 4x -160 / x² = 0
x³ = 40
x = ∛40
Substitute x = ∛40 to find the height:
h = 20 / x²
= 2 . 10 / (∛4² . ∛10²)
= ∛10 / ∛2 = ∛5
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Determine the intervals on which the function is increasing, decreasing, and constant.
A) Increasing on (- 5, - 3) and (2, 5) Decreasing on (- 3, 0) Constant on (0, 2) B) Increasing on (- 3, - 1) Decreasing on (- 5, - 2) and (2, 4) Constant on (- 1, 2) C) Increasing on (- 3, 1) ; Decreasing on (- 5, - 3) and (0, 5) ; Constant on (1, 2) D ) Increasing on (- 3, 0) Decreasing on (- 5, - 3) and (2, 5); Constant on (0, 2)
Answers
The intervals on which the function is increasing, decreasing and constant are (-5,-3) and (2,5) on increasing (-3,0) on decreasing and (0,2) on constant.
What is intervals?
An interval in math is the measured in terms of the numbers. An interval to includes all the numbers that come between two of particular numbers. This is the range includes all of the realistic numbers between those two of numbers. Real numbers are the any kind of number you can definitely think of.
Sol-by showing in the figure the function is increasing on the (-3,0)
Decreasing on (-5,-3) and (2,5)
Constant on (0,2)
Thus, the correct option is A
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I need help 9th grade math
Answers
Answer:
D
Step-by-step explanation:
The slope of line ℓ
is greater than 0 and less than 1. Write an inequality for the slope of a line perpendicular to ℓ
.
Answers
By properties of perpendicular lines and algebra properties, the slope of the line perpendicular to line ℓ is represented by m' > 1.
How to represent an inequality associated with a line perpendicular to another line
Let m be the slope of a line, in accordance with analytic geometry, the slope of line perpendicular to the first one is equal to m' = - 1 / m. The statement can be summarized by the following inequality:
0 < m < 1
Then, by algebra properties for inequalities we find that that slope for the perpendicular line is:
0 < m · m⁻¹ < m⁻¹
0 < 1 < m⁻¹
1 < m⁻¹
- m⁻¹ > 1
- 1 / m > 1
m' > 1
The slope of the line perpendicular to line ℓ is represented by m' > 1.
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Marilyn wants to use a non-price competitive marketing strategy to gain more customers. Which of the following might she use?
Answers
As Marilyn wants to use a non-price competitive marketing strategy to gain more customers, the strategy that she might use is offering a promotion.
What is a Non-price competition in marketing?In marketing, the non-price competition refers to a marketing strategy in which a firm tries to distinguish its product or service from competing products on the basis of attributes like design and workmanship.
This competition most often occurs in an imperfectly competitive markets because it exists between producers that sell goods and services at same prices but competes to increase their respective market shares through different non-price measures such as marketing schemes and greater quality.
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Multiply and write in standard form: 10x + 3)(2x - 1) Show all work
Answers
Explanation
[tex](10x+3)(2x+1)[/tex]Step 1
apply distributive property
[tex]\begin{gathered} (10x+3)(2x+1)=(10x\cdot2x)+(10x\cdot1)+(3\cdot2x)+(3\cdot1) \\ (10x+3)(2x+1)=20x^2+10x+6x+3 \end{gathered}[/tex]Step 2
add similar terms and order
[tex]\begin{gathered} (10x+3)(2x+1)=20x^2+10x+6x+3 \\ (10x+3)(2x+1)=20x^2+16x+3 \\ \text{the standard form is} \\ ax^2+bx+c,so \\ ax^2+bx+c\Rightarrow20x^2+16x+3 \end{gathered}[/tex]so, the answer is
[tex]20x^2+16x+3[/tex]I hope this helps you
Two companies are competing for a contract to make the programs for middle school gymnastics meets. Nadia’s Printing charges a $19.99 fee for printing and $0.25 for each program printed. Simone’s Stylish Print charges a $29.99 fee for printing and $0.10 for each program printed. For the most recent meet, Nadia’s Printing charged more than Simone’s Stylish Print.
Which inequality models this situation?
Answers
Answer:
the second answer
Step-by-step explanation:
A hiker descended 450 feet down to an elevation of 2300 feet. Which equation models this scenario?
Answers
The equation models this scenario regarding the hiker is x - 450 = 2300.
Whet is elevation?Elevation is simply used to illustrate the height above the sea level.
In this case, the hiker descended 450 feet down to an elevation of 2300 feet.
The equation that can model the scenario will be x - 450 = 2300
where x = Initial elevation
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2. What is the slope-intercept form of 9x + 3y = 15?
y = 3x - 5
y = 3x + 5
y=-3x - 5
y=-3x+5
Answers
Answer:
y=3x+5
Step-by-step explanation:
a school nurse can give 25 eye tests in a two-hour period. how long will it take the nurse to give eye tests to all 600 stuents in her school.
Answers
24•2 = 48
48 hours for all 600 students
Select all ratios equivalent to 13:14
52:56. 39:42. 3:4
Answers
Answer:
52:56 and 39:42
Step-by-step explanation:
The ratios equivalent to 13:14 are:
52:56
39:42
3:4 is not equivalent to 13:14 because 3 is not a multiple of 13.
according to the chart, approximately how many times more likely is a 16-year-old driver to crash with two passengers as opposed to with no passengers?
Answers
About twice as likely is a 16-year-old driver to crash with two passengers as opposed to with no passengers.A 16 or 17-year-old driver has a higher risk of dying every mile they drive compared to operating a vehicle alone. increases by 44% when one of the passengers is under the age of 21. while transporting two passengers who are under 21 in doubles.
Are 16 year olds more likely to crash?Teenagers between the ages of 16 and 19 had the highest crash risk of any age group. Teen drivers in this age range have a roughly three times higher risk of being in a fatal collision per mile traveled than drivers who are at least 20 years old.According to CDC research, there are a few main factors that increase the likelihood of young drivers being in auto accidents: insufficient experience Due in part to their inability to identify and avoid road dangers, teen drivers have a fatal crash risk that is three times higher than that of older drivers.To learn more about crash with two passengers refer to:
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16-year-old driver to crash with two passengers as opposed to with no passengers is about twice as likely.
Are 16 year old's more likely to crash?Teenagers between the ages of 16 and 19 had the highest crash risk of any age group. Teen drivers in this age range have a roughly three times higher risk of being in a fatal collision per mile traveled than drivers who are at least 20 years old.According to CDC research, there are a few main factors that increase the likelihood of young drivers being in auto accidents: insufficient experience Due in part to their inability to identify and avoid road dangers, teen drivers have a fatal crash risk that is three times higher than that of older drivers.The complete question is,
According to the chart, approximately how many times more likely is a 16-year-old driver to crash with two passengers as opposed to with no passengers?
just as likely
about twice as likely
about three times more likely
about four times more likely
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PLSSSSS
WILL MARK BRAINLIEST!!!
SIMPLEEE
(Yr7)
Answers
Answer:
Step-by-step explanation:
the answer I have given below
kind regards
WRITE AN EQUATION TO DESCRIBE THE RELATIONSHIP BETWEEN J AND Mj | 4 | 12 | 20m | 3 | 9 | 15
Answers
First, we can use the points (4,3) and (20,15) to find the slope of the line:
[tex]\begin{gathered} s=\frac{m_2─m_1}{j_2─j_1}=\frac{15─3}{20─4}=\frac{12}{16}=\frac{3}{4} \\ s=\frac{3}{4} \end{gathered}[/tex]Now we can find the relation function using the point (4,3) and the slope s=3/4
[tex]\begin{gathered} m─m_1=s(j─j_1) \\ \Rightarrow m─3=\frac{3}{4}(j─4)=\frac{3}{4}j─(\frac{12}{4})=\frac{3}{4}j─3 \\ m=\frac{3}{4}j \end{gathered}[/tex]therefore, the equation to describe the relationship between J and M is m=3/4j
1. Is 26 divisible by 2? (1 point)
ONO
O Yes, because 2 +6=8 and 8 is divisible by 2.
O Yes, because the last digit is 6, which is divisible by 2.
Answers
Answer:
Yes, because the last digit is 6, which is divisible by 2.
Step-by-step explanation:
The solution is, Yes, because the last digit is 6, which is divisible by 2.
What is division?Division is the process of splitting a number or an amount into equal parts.
Division is one of the four basic operations of arithmetic, the ways that numbers are combined to make new numbers. The other operations are addition, subtraction, and multiplication.
here, we have,
26 divisible by 2
i.e. 26/2 = 13
so, it is divisible.
now, we know that,
because the last digit is 6, which is divisible by 2.
Hence, The solution is, Yes, because the last digit is 6, which is divisible by 2.
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suppose an opaque jar contains 4 red marbles and 11 green marbles. this exercise refers to the experiment of picking two marbles from the jar without replacing the first one. what is the probability of getting a green marble first and a red marble second?
Answers
The probability of getting a green marble first and a red marble second exists 5/26.
What is meant by probability?A probability is a numerical representation of the likelihood or chance that a specific event will take place. Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to describe probabilities.
Given: Red marbles = 3
Green marbles = 10
So, the total marbles = 3 + 10 = 13
Probability = Favorable outcomes / Total outcomes
Since, here replacement is not allowed,
Therefore, the probability of getting a green marble and a red marble
= first red and second green + first green second red
= 3/13 × 10/12+ 10/13 × 3/12
= 2 × 3/13 × 10/12
= 30/78
= 5/13
The probability of getting a green marble first and a red marble second
= 10/13 × 3/12
= 30/156
= 5/26
Therefore, the probability of getting a green marble first and a red marble second exists 5/26.
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Tell whether the given situation is an example of Direct Variation or Inverse Variation. Write DV if it is a Direct Variation and IV for Inverse Variation. (NEED THE ANSWER ASAP)7. The height of a person and his weight
Answers
Given,
The statement is "The height of a person and his weight".
Required/
Identify the statement is inverse or direct variation.
As the height of the person increase then its their weight is also increased.
Similarly,
The height of the person decrease then its their weight is also decreased.
Hence, it is direct variation.
How can I work out the size of angle y?
Answers
Answer:
180 degrees converted is 3.14159 i think
Step-by-step explanation:
Answer:
< y = 17 degrees.
Step-by-step explanation:
x + y = 180 - 112 = 68 (as there are 180 degrees in a triangle)
Also, x = 3y, so substituting for x in the first equation:
3y + y = 68
4y = 68
y = 17.
So,
x = 3*17 = 51,
Alvin paddled for 2 hours with a 5-km/h current to reach a campsite. The returntrip against the same current took 7 hours. Find the speed of the boat in stillwater.
Answers
Given:
Alvin paddled for 2 hours with a 5-km/h current to reach a campsite.
Let n be the speed of boat.
Distance is calculated as,
[tex]\begin{gathered} d=rt \\ d=2\mleft(n+5\mright) \end{gathered}[/tex]The return trip against the same current took 7 hours.
[tex]\begin{gathered} d=rt \\ d=7(n-5) \end{gathered}[/tex]Equate both the equations,
[tex]\begin{gathered} 2(n+5)=7(n-5) \\ 2n+10=7n-35 \\ 7n-2n=10+35 \\ 5n=45 \\ n=\frac{45}{5} \\ n=9 \end{gathered}[/tex]Answer: the speed of the boat is 9 mph.