In a raffle, the winners of the first and second prizes each receive one ticket to an upcoming concert. You and a friend each buy a raffle ticket along with 16 other people. What is the exact probability that you win the first prize and your friend wins the second prize?

Answers

Answer 1

Final answer:

The exact probability that you win the first prize and your friend wins the second prize in a raffle with 18 participants is 1/306.

Explanation:

To calculate the exact probability that you win the first prize and your friend wins the second prize in a raffle, we need to look at the total number of possible outcomes and the number of favorable outcomes. Assuming that there are 18 tickets in total (yours, your friend's, and 16 others), the chance that you win the first prize is 1 in 18. After you win, there are 17 tickets left, so your friend's chance of winning the second prize is 1 in 17. To find the combined probability, we multiply these individual probabilities:

The probability that you win first prize = 1/18
The probability that your friend wins second prize given you've won first = 1/17

Combined probability = (1/18) x (1/17) = 1/306

The exact probability that you win the first prize and your friend wins the second prize is 1/306.

Answer 2

The exact probability that you win the first prize and your friend wins the second prize is[tex]$ \frac{1}{306} $.[/tex]

To determine the probability that you win the first prize and your friend wins the second prize in the raffle, we need to calculate the total number of possible outcomes and the number of favorable outcomes where this specific event occurs.

Total number of participants: You and your friend are among 18 people who bought raffle tickets.

Total number of outcomes: There are 18 people in total, so there are

( 18 ) possible winners for the first prize and ( 17 ) remaining people eligible for the second prize after the first winner is chosen.

Therefore, the total number of outcomes where one person wins the first prize and another wins the second prize is:

[tex]\[ 18 \times 17 = 306 \][/tex]

This represents all possible ways the first and second prize can be awarded to two different individuals.

Favorable outcomes (desired event): There is exactly ( 1 ) way for you to win the first prize and ( 1 ) way for your friend to win the second prize.

So, the number of favorable outcomes where you win the first prize and your friend wins the second prize is:

[tex]\[ 1 \times 1 = 1 \][/tex]

Probability calculation: The probability ( P ) that you win the first prize and your friend wins the second prize is given by the ratio of the number of favorable outcomes to the total number of outcomes:

[tex]\[ P = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} = \frac{1}{306} \][/tex]

Therefore, the exact probability that you win the first prize and your friend wins the second prize is [tex]$ \frac{1}{306} $.[/tex]

Related Questions

What is the value of y?

A. Cannot be determined
B. 120
C. 60
D. 65

Answers

60, since adding all 3 up equals 180

when talking about a trianlge it has to have 3 sides adding up to 180 degress so just take 60 + 60 = 120 then 180 - 120 = 60 degrees. hope this helps! :)

PLEASE HELP ASAAPPPP <3

Answers

the answer is B because 1.02 is 100% (maintaining the population) and 2% (growth) in decimal form.

since it is changing 2 percent every year it is in additionally 2 perecent being added to 100 so it will be 100%+7 (2)%×9,800. First multiply 7 and 2 which gives you 14 then add 100 and 14 and you get 114 percent then multiply 9,800 by 114 percent and you will be ur answer which is 11,172. when multiply with 114 and 9800 take off the zeros to your final answer.

WORTH 30 PTS PLS ANSWER ASAP.
Jordan is a manager of a car dealership. He has two professional car washers, Matthew and Arianna, to clean the entire lot of cars. Matthew can wash all the cars in 14 hours. Arianna can wash all the cars in 11 hours. Jordan wants to know how long it will take them to wash all the cars in the lot if they work together.

Write an equation and solve for the time it will take Matthew and Arianna to wash all the cars together. Explain each step.

Answers

Assuming that X represents the number of hours worked and f(x) the number of cars washed, the equation would be f(x)=11x+14x.

The 11x represents the number of cars washed by Arianna in x number of hours and the 14x represents the number of cars washed by Matthew in x number of hours. You add the two because they are each washing their own car at their own pace but working on one lot.

Answer:

They will take 6.16 hrs or 6 hrs, 9 minutes and 36 seconds.

Step-by-step explanation:

Consider the provided information.

Let x is the number of cars in a lot.

Matthew can wash all the cars in 14 hours. That means in 1 hr he can wash x/14 cars.

Arianna can wash all the cars in 11 hours. That means in 1 hr Aranna can wash x/11 cars.

Together there rate will be:

[tex]\frac{x}{14}+\frac{x}{11}=\frac{x}{y}[/tex]

Here y represent the time taken by them if they work together.

Divide both sides by x, we get

[tex]\frac{1}{14}+\frac{1}{11}=\frac{1}{y}[/tex]

Thus, the required equation is: [tex]\frac{1}{14}+\frac{1}{11}=\frac{1}{y}[/tex]

Now solve for time, Here time is represents by y.

[tex]\frac{1}{14}+\frac{1}{11}=\frac{1}{y}[/tex]

[tex]\frac{11+14}{154}=\frac{1}{y}[/tex]

[tex]\frac{25}{154}=\frac{1}{y}[/tex]

[tex]y=\frac{154}{25}[/tex]

[tex]y=6.16[/tex]

Hence, they will take 6.16 hrs or 6 hrs, 9 minutes and 36 seconds.

A measure of ________ for a numerical data set describes how its values vary with a single number.
center
tendency
variation
shape @NeedHelpQuick546 @paki @texaschic101 @mjoxprm360,

Answers

The measure of variation for a numerical data set describes how the values of a number vary with the single number. This measurement shows the difference in the properties of a certain number to the rest of the numbers in the numerical data set.

Final answer:

The term that describes how values of a numerical data set vary with a single number is 'variation'. It quantifies the spread of data values, helping to add context and meaning to averages in a data set.

Explanation:

A measure of variation for a numerical data set describes how its values vary with a single number. Variation is a statistical concept that is used to quantify the spread or dispersion of a set of data values. A low variation indicates that the data points tend to be close to the mean (or expected value), while a high variation indicates that the data points are spread out over a wider range.

For example, if we have a data set of test scores, the variation can help us understand how close or far the scores are from the average test score. This provides more context and meaning to the overall average.

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HELP PLEASE QUICK!
Triangle MNO is similar to triangle PQR. Which statement is true about the two triangles?
A. Angles M and N are congruent.
B. Angles M and Q are proportional.
C. Angles N and R are proportional
D. Angles O and R are congruent.

Answers

the answer would be D

Answer with explanation:

It is given that, ΔM NO ~ Δ P Q R.

When two triangles are Similar, their Corresponding angles are equal and corresponding Sides are proportional.

So, following holds true by C P C T.

∠M = ∠P

∠N=∠Q

∠O=∠R

Also,

[tex]\frac{MN}{PQ}=\frac{NO}{QR}=\frac{MO}{PR}[/tex]

Option D: Angles O and R are congruent.

4.02 Congruent Triangles, doess anyone have tips on how to do this? im getting confused with the SSS, SSA , SAS

Answers

SSS is side side side so all the sides have to be congruent for the triangles to be congruent.

SSA is side side angle so two sides and an angle needs to be congruent for the triangles to be congruent.

SAS is side angle side so two sides and an included triangle need to be congruent for the triangles to be congruent.

Hope that helps:)

A tree casts a shadow that is about 15ft. long. Javier, who is about 5.5 ft. tall, is standing near the tree. Javier's shadow is about 4.5 ft. long. What is the estimated height, t, of the tree?

A. 9.6 ft.
B. 12 ft.
C. 15 ft.
D. 18 ft.

Answers

the answer would be B

30pts, will give brainliest.

Answers

You could rewrite the second equation as either of the two options:

-3x + 9y = 18 or -4x +12y = 24

Both of these would make one of the variables cancel out when adding together.

Answer:

the answer is 24

Which properties justify the steps taken to solve the system?

4x+3y=25
2x+−5y=19

Drag the answers into the boxes to match each step.

Answers

step 1
Multiplication property of equality
Multiplying the second equation by -2
Step 2
Additional property of equality
We add the two equations generated in step 1
Step 3
The division property of equality
We divide both sides of equation obtained in step 2 by 13
Step 4
Substitution property of equality
We substitute the value obtained in step 3 for y in the first equation.
Step 5
Simplify

Step 6
Additional property of equality
We add +3 on both sides of the equation in order to have an equation with a variable x.
Step 7
Division property of equality
We divide both sides of the equation obtained to get the value of x

Answer:

hope this helps :)

Consider the half reactions below for a chemical reaction.
(pictured below)
What is the overall equation for this chemical reaction?
choices below

Answers

This is redox reaction. Redox is when one species reduces, that means gains electrons therefore known as a reduction reaction and the other species oxidises, gives out electrons and thats the oxidation reaction.
For reaction to be complete there should a oxidising species to give out the electrons and a reducing species to gain those electrons.
In the above reaction, Zn(s) gives out electrons therefore its oxidised to Zn2+ (aq) and Cu2+ (aq) gains electrons therefore its reduced to Cu (s).

2 electrons are being transferred so the 2 equations can be combined as it is, since the number of electrons are equal in both reactions.
When the 2 half equations are added, the 2 electrons are cancelled off leaving only the reactants.
the correct answer is 1st response.

Answer:

The answer is A

Step-by-step explanation:

Suppose you earn 3% on a $1,200 deposit for 5 years. Explain how the simple interest is affected if the rate is increased by 1%. What happened if the time is increased by 1 year?

Answers

[tex]\bf ~~~~~~ \textit{Simple Interest Earned}\\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\\ P=\textit{original amount deposited}\to& \$1200\\ r=rate\to 3\%\to \frac{3}{100}\to &0.03\\ t=years\to &5 \end{cases} \\\\\\ I=1200(0.03)(5)\implies \boxed{I=180}\\\\ -------------------------------[/tex]

[tex]\bf ~~~~~~ \textit{Simple Interest Earned increased by 1\%}\\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\\ P=\textit{original amount deposited}\to& \$1200\\ r=rate\to 4\%\to \frac{4}{100}\to &0.04\\ t=years\to &5 \end{cases} \\\\\\ I=1200(0.04)(5)\implies \boxed{I =240}\\\\ -------------------------------[/tex]

[tex]\bf ~~~~~~ \textit{Simple Interest Earned increased by 1 year}\\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\\ P=\textit{original amount deposited}\to& \$1200\\ r=rate\to 3\%\to \frac{3}{100}\to &0.03\\ t=years\to &6 \end{cases} \\\\\\ I=1200(0.03)(6)\implies \boxed{I =216}[/tex]

I don't know if this is right... please someone help mee

Answers

for the first circle, let's use the pythagorean theorem

[tex]\bf \textit{using the pythagorean theorem}\\\\ c^2=a^2+b^2\implies c=\sqrt{a^2+b^2} \qquad \begin{cases} c=hypotenuse\\ a=adjacent\\ b=opposite\\ \end{cases} \\\\\\ c=\sqrt{8^2+15^2}\implies c=\sqrt{289}\implies c=17[/tex]

now, it just so happen that the hypotenuse on that triangle, is actually 17, but we used the pythagorean theorem to find it, and the pythagorean theorem only works for right-triangles.

so if the hypotenuse is actually 17, that means that triangle there is actually a right-triangle, meaning that the radius there, and the outside line there, are both meeting at a right-angle.

when an outside line touches the radius line, and they form a right-angle, the outside line is indeed a tangent line, since the point of tangency is always a right-angle with the radius.

now, let's check for second circle

[tex]\bf \textit{using the pythagorean theorem}\\\\ c^2=a^2+b^2\implies c=\sqrt{a^2+b^2} \qquad \begin{cases} c=hypotenuse\\ a=adjacent\\ b=opposite\\ \end{cases} \\\\\\ c=\sqrt{11^2+14^2}\implies c=\sqrt{317}\implies c\approx 17.8044938[/tex]

well, low and behold, we didn't get our hypotenuse as 16 after all, meaning, that triangle is NOT a right-triangle, and that outside line is not touching the radius at a right-angle, therefore is NOT a tangent line.

let's check the third circle

[tex]\bf \textit{using the pythagorean theorem}\\\\ c^2=a^2+b^2\implies c=\sqrt{a^2+b^2} \qquad \begin{cases} c=hypotenuse\\ a=adjacent\\ b=opposite\\ \end{cases} \\\\\\ c=\sqrt{33^2+56^2}\implies c=\sqrt{4225}\implies c=\stackrel{33+32}{65}[/tex]

this time, we did get our hypotenuse to 65, the triangle is a right-triangle, so the outside line is indeed a tangent line.

What is the value of t?

Answers

[tex] I = Prt [/tex]

Divide both sides by P and r.

[tex] t = \dfrac{I}{Pr} [/tex]

Answer is: Choice D.

need help ASAP

Noah has 3 3/4 quarts of motor oil. He puts 1/2 that amount into a riding lawn mower.

How much oil does Noah put into the riding lawn mower?
Express your answer in simplest form.

Answers

He used 15/2 or 7 1/2 quarts of oil

If the cos of angle x is 8/17 and the triangle was displayed to be two times big as the original what would be the value of the cos of x for the dilated triangle

Answers

Answer: The value of cos(x) of the dilated triangle would be exactly the same as in the first triangle, cos(8/17).

The cosine ratio is a ratio of two sides.

In the first triangle the ratio is 8/17.

In the second triangle the ratio is 16/34. This could be reduced back to 8/17 which would produce the same cosine value.

The value of cos of angle x of the dilated triangle would be exactly the same as in the first triangle cos (8/17).

How does dilation work?

Dilation of a figure will leave its sides get scaled (multiplied) by same number. That number is called the scale factor of that dilation.

Its also called scaling of a figure, but due the involvement of coordinates, it involves a center of a dilation, which is like a pinned point which stays at same place after dilation.

Its like we enlarge or shorten the size of the figure (or keep it same, when scale factor = 1)

The cosine ratio is a ratio of the two sides.

We have been given If the cos of angle x is 8/17 and the triangle was displayed to be two times big as the original.

In the first triangle, the ratio is 8/17.

In the second triangle, the ratio is 16/34.

The second triangle could be reduced back to 8/17 which produces the same cosine value.

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A stadium that seats 35,000 is slowly filling up with fans. The game starts at four o’clock. At noon the stadium owner estimates there are 4,000 fans who have already arrived early. At one o’clock he estimates just over 11,000 fans have found their seats and they appear to be coming in at a steady rate. He knows his stadium will be more than ninety percent full by game time. Choose the function below that best models this situation and tracks attendance from Noon to game time.

A. f(x)= .90x + 4,000
B. f(x)= 7,000x + 4,000
C. f(x)= 4,000x + 4,000
D. f(x)= 11,000x + 4,000

Answers

Answer:

B. f(x) = 7000x + 4000

Step-by-step explanation:

To find the best function for this situation, we need to list down all the things that we know first.

We currently have:

35000 total seats

4000 fans

11000 fans after an hour

So that means that after an hour, we had:

11000 fans - 4000 fans = 7000 fans

At one o'clock we had 7000 more fans arrive.

So we can assume that:

x = number of hours

f(x) = 7000x + 4000 will be the best function to use to find out if there that 90% of the stadium will be filled by game time.

To test this function let's use it:

f(1) = 7000(1) + 4000

f(1) = 11000

This is after hour 1.

Now let's see after hour 4 since the game starts at 4.

f(4) = 7000(4) + 4000

f(4) = 28000 + 4000

f(4) = 32000

So 90% of 35000 is:

35000 x 0.90 = 31500

By game time we have 32000 fans which is above 90% of the total number of seats.

So the stadium owners estimate is correct.

Which piecewise relation defines a function?

Answers

Answer: h(x)

Explanation:

1) f(x) is not a function because there is an ambiguity for x = 4.

x = 4 belongs to both intervals - 2 ≤ x ≤ 4 and x ≥ 4

Then you find two different possible images for x: 0 and -(2)^2 = - 4.

That makes that f(x) be not a function.

2) similar thing happens with g(x)

as per the given relation the value of g(x) for x = 2 is 4 and 4+1 = 5. Which makes that g(x) be not a function.

3) j(x) is not a function because the image of x = -4 is -3(-4) = 12 and 3.

4) h(x) is a function, because there is not any ambiguity in its definition, for every x in its domain there is only one image h(x).

Answer:

option c is correct

Step-by-step explanation:

The data in the table represents the average number of daylight hours each month in Springfield in 2015, rounded to the nearest quarter.

Jan 9.5
Feb 10.5
March 12
April 13.25
May 14.5
June 15
July 14.75
Aug 13.75
Sept 12.5
Oct 11
Nov 9.75
Dec 9.25

Write the equation that best models the data.

What is the expected number of daylight hours in March 2020? Explain.

Answers

For a better understanding of the solution provided here please go through the graph in the attachment. Please note that the solution provided here will be an approximate solution.

In the graph, the x axis is the number of months. 1 is January, 2 is February, so on and so forth.

The y axis is the expected number of daylight hours in those months. Each point has been depicted in the graph as shown.

Now, when we look at the graph we notice a pattern. The graph is nearly a cosine graph. Thus the equation that will best model the data will be an equation of the cosine form and will look like:

[tex] y=A cos(\omega t)+B [/tex]

where symbols have their usual meanings.

Let us find each term now:

We know that in December, the expected number of daylight hours is 9.25 hours. Thus, let us assume that the expected number of daylight hours in previous December was 9.25 hours too.

With this assumption let us proceed.

Amplitude=[tex] \frac{Highest - Lowest}{2} =\frac{15-9.25}{2} =2.875 [/tex]

The Vertical Shift Up is B=[tex] \frac{9.25+15}{2} = 12.125[/tex]

Also, the frequency can be calculated as: [tex] \omega=\frac{2\pi}{Period}= \frac{2\pi}{12}=\frac{\pi}{6} [/tex]

Thus, plugging in all the values, the final equation will be:

[tex] y=-2.875cos(\frac{\pi}{6}t)+12.125 [/tex]....(Equation 1)

The negative value of A suggests that the function starts below the horizontal y=12.125 line.

The above is the (Equation 1) that best models the given data.

Now, to find the expected number of daylight hours in March 2020, we just have to find the value of the time, t from January 2015 to March 2020.

Now, we know that each year has 12 months. So, 5 years from start of 2015 to end of 2019 will have 12 x 5=60 months. We need to add to this the first three months of the year 2020 to take us till March 2020. Thus, the value of t from January 2015 to March 2020 is 63.

Now, let us use the (Equation 1) to find the value of expected number of daylight in March 2020 by plugging in t=63 in it.

Thus,

Expected number of daylight in March 2020 is:

[tex] y=-2.875cos(\frac{\pi}{6}\times 63)+12.125 [/tex]

[tex] \therefore y=12.125 [/tex] hours.

place the following steps in order to complete the square and solve the quadratic equation,x^2+7=0

Answers

x^2+7=0
this can be written as:
x^2+0x+7=0
To solve using completer square we proceed as follows:
x^2+0x=-7
but
c=(b/2a)^2
c=(0/2*1)^2=0
hence
x^2+0x+0=-7+0
this will be simplified as:
x^2=-7
getting the square root of both sides gives us:
sqrt(x^2)=sqrt(-7)
x=+/-√-7
but √-1=i
hence our answer will be:
x=+/-7i

Identify whether the described situation is an example of experimental probability or theoretical probability.
a.i just flipped a coin several times and the coin landed on heads more than tails. 6 times on heads and 5 times on tails. the probability of landing on heads is 6/11.

Answers

This is experimental probability, since it is based on the outcome of an experiment.

Chord AC intersects chord BD at point P in circle Z.

AP=3.5 in.
DP=4 in.
PC=6 in.

What is BP?

Enter your answer as a decimal in the box.

Answers

1. To solve this exercise, you must use the "Intersecting chords theorem".

2. You have that:

AP=3.5 in
PC=6 in
DP=4 in

3. Then, by applying the "Intersecting chord theorem", you have:

(AP)(PC)=(BP)(DP)

4. When you substitute the values into (AP)(PC)=(BP)(DP), you obtain:

(3.5 in)(6 in)/BP(4 in)

5. Now, you must clear BP. Then:

(3.5 in)(6 in)/4 in=BP
21 in^2/4 in=BP

6. Therefore, the value of BP is:

BP=5.25 in

what ratio is the same as 75 percent

Answers

3/4 for your ratio and .25 for decimal. (just in case)

Why is it advantages to take market trends into consideration when planning a career path?

Answers

It is very important. In the future, things change. Some jobs won't be needed anymore. Jobs like travel agents won't be needed because of technology.

Answer:

Its important because history repeats its self. some jobs won't be available in 5-10 years due to advance in technology, or a job that is fruitful/ profitable in one year may be completely dead and dry in the next.

Step-by-step explanation:

PLEASE HELP ME !!!!!!!!!!!!!!!!!
LET ME KNOW IF ITS RIGHT

Answers

Okay. So the song lasts 221 seconds. 45 seconds have already beem done and 22 seconds is done in an hour. The equation would be set up like this:

45 + 22h = 221

Just by looking at the answer choices, A is already eliminated because it doesn't incorportate the 45 seconds. B does include the 45 seconds, but it subtracts, and in this case, we add time, not subtract. D is eliminated, because the h variable does not go with 45. The only equation that works is C and when you solve it, you get 8 hours. The answer is C.

Note: you solve the equation above by subtract 45 from both sides to get 176 = 22x, and dividing both sides by 22 to get x = 8.

For which polygon is the sum of the interior angles equal to 720 degrees?
A. Quadrilateral
B. Hexagon
C. Octagon

Answers

The answer to this is Hexagon.

The assessed value of property in Enterprise County is $196,000,000. The county supervisors feel the county needs $9,525,000 in revenue.
What is the tax rate (to 0.1 of a percent)?
5.1
4.9
4.7,

Answers

tax rate = ( $9,525,000 / $196,000,000 ) * 100% = 4.9%

Answer:

B. 4.9%.

Step-by-step explanation:

We have been given that the assessed value of property in Enterprise County is $196,000,000. The county supervisors feel the county needs $9,525,000 in revenue.

To find the tax rate we need to find $9,525,000 is what percent of $196,000,000.

[tex]\text{Tax rate}=\frac{\$9,525,000}{\$196,000,000}\times 100[/tex]

[tex]\text{Tax rate}=0.0485969387755102\times 100[/tex]

[tex]\text{Tax rate}=4.85969387755102\%[/tex]

Upon rounding our answer to nearest tenth of percent we will get,

[tex]\text{Tax rate}\approx 4.9\%[/tex]

Therefore, the tax rate is 4.9% and option B is the correct choice.

f(x) = cot x PRE CALC HELP PLS?!

Answers

check the picture below.

is it even? well, even functions use the y-axis as a mirror, so a pre-image on the right-side, will be a mirror of the image on the left-side, but in this case it isn't so, if you put a mirror right on the y-axis, the left-side will look a bit different.

does it have a zero at x = 0? well, just look at the graph, is the line touching the x-axis at 0? nope.

does it have an asymptote at 0? well, surely you can see it right there.

jason built a rectangular tool shed that is 8 meters wide and has an area of 96 square meters what is the length of Jason's tool shed? meters

Answers

Area = length x width
96 = length x 8
Length =96/8
Length = 12 metres

Diego cut 7 smaller boards of equal length from a board that is 9 1/3 feet long. How long is each of the 7 smaller boards? Write your answer as an improper fraction using the / symbol for the fraction.

Answers

It would be 9 1/3 divided by 7/1 or 28/3 * 1/7

It would give you 28/21 which would simplify to 4/3 and still leave you with an improper fraction

A car dealership sold one car in its first month of business. The number of cars it sold doubled each month. What was the total number of cars the dealership sold during the first 12 months?

Answers

Assuming the number of cars it sold doubled each month. The total number of cars the dealership sold during the first 12 months is: 4095.

Total number of cars sold

Using exponential growth formula

Total number of cars sold=2^N - 1

Where:

N = Number of months=12 months

Let plug in the formula

Total number of cars sold=2^12 - 1

Total number of cars sold=4,096 - 1

Total number of cars sold=4,095

Inconclusion the total number of cars the dealership sold during the first 12 months is: 4095.

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