You and your friend enter a drawing with 3 different prizes. A total of 15 people entered the drawing, and prizes are awarded randomly.

There are 2730 ways to award the prizes.

What is the probability that you win first prize and your friend wins second
prize?

A. 1/2730

B. 15/2730

C. 1/15

D. 13/2730

Answers

Answer 1

The probability that you win first prize and your friend wins second

prize is option D: 13/2730.

What is probability?

Probability is a way to gauge how likely something is to happen. Many things are difficult to forecast with absolute confidence. Using it, we can only make predictions about the likelihood of an event happening, or how likely it is. Probability can range from 0 to 1, with 0 denoting an impossibility and 1 denoting a certainty.

Total number of prizes awarded = 3

Number of people entering the drawing competition = 15

Number of ways to award the prize = 2730

Out of the 3 prizes the first and the second is needed.

So, the prize for the first and the second positions are fixed and there is no need to consider the remaining 13 people to win the prize.

Hence the remaining number of people who can win the 3rd prize  = 13

The number of ways one of them wins the 3rd prize = 13

The total number of ways = 2730

Therefore, the probability of the first 2 prizes fixed and the remaining 3rd awarded to the rest of the 13 people is 13/2730.

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Related Questions

y= x^2-4
find the zeros.

Answers

The zeros of the given function y = x²-4 are 2 and -2.

What is zero of a function?

The zeros of a function are defined as the values of the variable of the function such that the function equals 0.

Given is a function, y = x²-4

To find the zeros, equate the function to 0,

x²-4 = 0

x² = 4

x = ±2

Hence, the zeros of the function are 2 and -2.

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What are the examples of logarithmic equation?.

Answers

The examples of logarithmic equation are 625 = [tex]5^{4}[/tex] and 4 = [tex]log_{5}625[/tex], 100000 = [tex]19^{5}[/tex] and 5 = [tex]log_{19}100000[/tex] .

To generate a given number, a base must be raised to a particular exponent, power, or logarithm. The time needed to multiply numbers with numerous digits was drastically decreased thanks to the logarithms, which were developed in the 17th century to speed up calculations.

For more than 300 years, they served as the foundation for numerical labor, but the development of mechanical adding machines in the late 19th century and computers in the 20th century made them obsolete for large-scale calculations.

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Solve the system of equations using any method. Describe the method used.

Answers

The solutions of the system are x = 1, y = 2 and z = -1.

And we solve the system with the help of Jordan-canonical form.

What is matrix?

A collection of numbers lined up in rows and columns to form a rectangular array is called a matrix. The elements, or entries, of the matrix are the numbers.

Given:

A system of equations,

x + y - 2z = 5

-x + 2y + z = 2

2x + 3y - z = 9

In the matrix form;

[tex]\left[\begin{array}{ccc}1&1&-2\\-1&2&1\\2&3&-1\end{array}\right] \left[\begin{array}{c}x\\y\\z\end{array}\right] = \left[\begin{array}{c}5\\2\\9\end{array}\right][/tex]

[tex]\left[\begin{array}{ccc}1&1&-2\\0&0&-10/3\\0&1&3\end{array}\right] \left[\begin{array}{c}x\\y\\z\end{array}\right] = \left[\begin{array}{c}5\\10/3\\-1\end{array}\right][/tex]

That means,

x = 1, y = 2 and z = -1.

Therefore, the solutions of the system are x = 1, y = 2 and z = -1.

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what is the following product? Assume x>0 3root x^2 times 4 root x ^3

Answers

The product is 3x * 4x^(3/2) = 12x^(5/2)

How to do the product of root?

When multiplying two terms with the same base and different exponents, you can add their exponents.

For example, √(a^m) * √(a^n) = √(a^m * a^n) = √(a^(m+n)) = a^((m+n)/2)

The product of 3√(x^2) * 4√(x^3) is equal to:

12x^(5/2)

This is because when you multiply two terms with the same base, you can add their exponents:

3√(x^2) * 4√(x^3) = (3*4)√(x^(2+3/2)) = 12x^(5/2)

This is because

√(x^2) = x^(2/2) = x

√(x^3) = x^(3/2) = x^(3/2)

so we can write 3root x^2 = 3x and 4root x^3 = 4x^(3/2)

Hence, the product is 3x * 4x^(3/2) = 12x^(5/2)

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factorise
12x*2 + 15xy-9x

Answers

Answer:

see picture

Step-by-step explanation:

Factorise for 12[tex]x^{2}[/tex]+15xy-9x is 3x (4x+5y−3)

Solution steps:

The first step is to factor out 3.

So,

3 (4[tex]x^{2}[/tex]+5xy-3x)

The second step is to consider 4[tex]x^{2}[/tex]+5xy−3x. Factor out x.

So,

x (4x+5y−3)

The third step is to rewrite the complete factored expression.

3x (4x+5y−3)

Evaluate:

3x (4x+5y−3)

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The power, P (watts), of a car engine is proportional to the square of its speed,
s (m/s).
When s= 25, P = 1400.
Work out the speed (to 1 DP) when the power is 1820 watts
m/s

Answers

Answer:

  28.5 m/s

Step-by-step explanation:

Given that power is 1400 W when speed is 25 m/s, and power is proportional to the square of speed, you want the speed when the power is 1820 W.

Proportion

Since power is proportional to the square of speed, the ratio of speed squared to power is a constant:

  s²/P = 25²/1400 = x²/1820

where x is the unknown speed.

Solution

We can find the value of x by multiplying by 1820 and taking the square root:

  x² = 25²(1820/1400)

  x = 25√(1820/1400) = 25√1.3 ≈ 28.5 . . . . m/s

The speed is 28.5 m/s when the power is 1820 watts.

What is the slope of 3x 4y =- 12?.

Answers

The slope of the equation 3x + 4y = -12 is -3/4

Slope in math is defined as the ratio of the amount that y increases as x increases some amount

Here we have given the equation 3x + 4y = -12.

As we all know that the general form of the equation of the line is written as,

y = mx + c

here m refers the slope of the line and c refers the y intercept of the line.

Now, we have to convert the given equation into the general form then it can be look like the following,

=> 4y = -12 - 3x

=> y = -12/4 - 3x/4

It can be rewritten as,

=> y = -3x/4 - 12/4

Then the resulting slope is -3/4.

Complete Question:

What is the slope of the equation 3x + 4y = -12?

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4 A popular board game includes a five-section
spinner to determine the number of spaces a
player moves during a turn. The results of
10 spins are shown.
Spin
Spaces
Moved
1 2 3
F 0.1
G 0.6
5 4
4 5 6 7 8 9 10
2 5 1 3 5 4 5 2
What is the experimental probability a player
will move 2 spaces and 5 spaces during a
game?
H 0.08
J Not here

Answers

In an experiment, there is a H 0.08 probability that a player will move both two and five spaces during a game.

What is the simple definition of probability?

Player movement during a turn is determined by a spinner. It displays the outcomes of 10 spins.The likelihood or chance that a specific event will occur is represented by a probability. Both proportions between 0 and 1 and percentages between 0% and 100% can be used to describe probabilities. chances in multiples.

A (1): the probability that a particular occurrence will take place. (2): the proportion of the number of outcomes in a comprehensive set of equally likely options that result in a specific event to the total number of conceivable outcomes. How likely something is to occur is known as its probability. when we are unsure of how an event will turn out.

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What is the inverse equation of the function, y = 3x - 6? y -1 = y -1 = x + 6 x -1 = 3 y - 6 y -1 = 3 x + 6.

Answers

The best answer (and only correct answer) among the options given is: option [C]:    y⁻¹ = (x+6) / 3  .

What is the inverse function?

The inverse function returns the original value for which a function gave the output. If you consider functions, f and g are inverse, f(g(x)) = g(f(x)) = x.

Given the original function:  y = 3x - 6 ;

To find the "inverse equation" of said function; we change the "x" to a y"; and the "y" to an "x"; and rewrite:

x = 3y − 6 ;

Now, rewrite in "slope-intercept form" ; or y = mx + b ;

    that is, with y as "single, isolated" variable on the left-hand side of the equation (with an "implied coefficient of positive one", only);  then an "equal sign, then "mx + b" ; in which: "m" is the coefficient of the variable, "x"; and in which "m" refers to the "slope";  and "b" refers to the 'y-intercept".

So, we have the inverse function:

x = 3y − 6  ;  we want to write in slope-intercept form;

Add "6" to each side of the equation:

x + 6 = 3y − 6 + 6 ;

x + 6 = 3y ;  

Rewrite as:   3y = x + 6 ;

Divide EACH side of the equation by "3" ; to isolate "y" one side of the equation; specifically, the left-hand side of equation; and to write in "slope-intercept form:

3y / 3 = (x + 6) / 3  ;

to get:

y = (x + 6) / 3 ;

y = (x/3)  + (6/3) ;

y = (x/3 ) + 2 ;

or;  write as: y = (1/3)x + 2 ;

Now, let us examine the answer choices given:

Note that all the answer choices begin with "y-1" ;

(except "answer choice: [B]" , which begins with "x-1").  This seems confusing; however, in reality, this does not mean, "y minus 1"; or "x minus 1".  Rather, it mean y⁻¹  or x⁻¹  as notation for the "inverse" (not to be confused with the exponent notation.  The confusion stems from the fact that it can be difficult to make such notations on the "Brainly" system.

That being said, we can write the aforementioned "rewritten equations" (see above in THIS VERY ANSWER) as:

y⁻¹ = (x + 6) / 3 ;

y⁻¹ = (x/3)  + (6/3) ;

y⁻¹ = (x/3 ) + 2 ;

or;  write as: y⁻¹ = (1/3)x + 2

That being said:

Therefore, the best answer (and only correct answer) among the options given is:  option  [C]:  y⁻¹ = (x+6) / 3  .

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What distance on the map (in centimeters) represents an actual distance of 4 kilometers

Answers

The distance on the map, in centimeters, that represents an actual distance of 4 kilometers, is 3. 2 cm

How to find the distance ?

The map is such that the scale is 4 cm on the map, equals 5 km on the ground.

If we have a distance of 4 km therefore, the distance on the map would be:

= ( Distance on ground x scale on map ) / Kilometers on scale

= ( 4 x 4 ) / 5

= 16 / 5

= 3. 2 cm

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Full question is:

Scale of a map says that 4 cm represents 5 km. What distance on the map (in centimeters) represents an actual distance of 4 kilometers?

I need help with this question, please

Answers

The credit utilization ratio would be 11.7%.

What is credit utilization?

The credit utilization ratio is a measure of how much of a person's credit limit is being used. It is calculated by dividing the total credit card balances by the total credit limit.

In Mary's case, the total credit card balances are $150 + $200 = $350

The total credit limit is $2000 + $1000 = $3000

To find the credit utilization ratio, we divide the total credit card balances by the total credit limit:

$350 / $3000 = 0.117 or 11.7%.

Hence, the credit utilization ratio would be 11.7%.

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what is the highest fraction that is reduced to 1/2
I WILL MARK U BRAINLIST

Answers

Answer:

I think its two

Step-by-step explanation:

If I am wrong sorry

What is a 1 in 3 angle?.

Answers

1 in 3 angle of slope in degree is 18.435°.

In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction.

An angle is a shape created by two rays that share a terminus and are referred to as the angle's sides and vertices, respectively. Angles created by two rays are in the plane where the rays are located.

The inverse tangent function is called arctangent, often known as arctan or tan-1. Tangent only has a limited domain for its inverse function.

So to find the 1 in 3 angle we have to put the value 1/3 in arctan function

∴ arctan (1/3) = 18.43494882° ≈ 18.435.

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ASAP!! Please help me answer all of these questions! No links or files please! I will report!



Thank you have a good day!

Answers

The questions 18, 19, and 20 have the values of x for the bisected angle to be 6, 15, and 8 respectively.

How to derive values of x for the bisected angles

If line UW bisects m∠TUV then;

m∠TUW = m∠WUV

13x - 5 = 7x + 31

13x - 7x = 31 + 5 {collect like terms}

6x = 36

x = 36/6 {divide through by 6}

x = 6

If line MO bisects m∠PMN then;

2(m∠OMN) = m∠PMN

2(2x + 7) = 74 {divide through by 2}

2x + 7 = 37

x = (37 - 7)/2 {make x the subject}

x = 15

If line EF bisects m∠CEB then;

m∠FEB = m∠CEF

10x - 3 = 7x + 21

10x - 7x = 21 + 3 {collect like terms}

3x = 24

x = 24/3 {divide through by 3}

x = 8

Therefore 6, 15, and 8 are the values of x for questions 18, 19, and 20 respectively for the bisected angles.

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n + 3 = -6
pls solve for n :)

Answers

N + 3 = -6
-3 -3
N= -9
n + 3 = -6
Step 1: get n alone by itself on one side, so subtract 3 to both sides to remove the 3 next to n.
n = -9
That’s your answer

If
CE
and
FH
are parallel lines and mCDB= 65°, what is mEDB?

Answers

Answer:

65° or 115°

Step-by-step explanation:

there is no picture but if

mEDB looks like mCDB then its 65°

but if they dont look alike then

180-65=115

straight line is 180°

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you invested 52,400 at 7% compounded annually for 10 years what is your total return on this investment

Answers

Answer:

$50678.73

Step-by-step explanation:

Answer:

103,078.73.

Step-by-step explanation:

Amount after n years = P(1 + r/100)^n       where P is amount invested, r is the percentage rate and n = number of years.

So, here we have:

Total after 10 years = 52400(1 + 7/100)^10

= 52400 * 1.967151357

= 103,078.73.

Two hiker walk on a trail in the direction of increaing mile marker number. Mandy tart at mile marker 1 and hike at a rate of 2. 5 mile per hour. At the ame time, Rita tart at mile marker2 and hike at a rate of 3 mile per hour. The equation 2. 5h1= 3h 2 repreent the number of hour h it will take Mandy to catch up with Rita

Answers

Mandy will catch up Rita at 0.5 hour after they start walking.

When will Mandy catch up Rita?

As per data given are Mandy start = 1, Rita start = 2, Mandy speed = 5 and Rita speed = 2. Based on this explanation we can determine the formula for Mandy time to catch up Rita as follow

s1 = s2

Rita start + Rita speed x t = Mandy start + Mandy speed x t

2 +3 x t = 1 + 5 x t

2 + 3t = 1 + 5t

2 - 1 = 5t - 3t

1 =  2t

t = 0.5 h

Hence, Mandi will catch up with Rita at 0.5h after start.

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Erika i purchaing a new cooler from outdoor World. The cooler cot $125. If Erika ha a coupon for 15% off, and ha another coupon for $15 off, which coupon hould he ue?

Answers

Erika should use the coupon which gives her a discount of 15% as it will bring down the cost of the cooler to $106.25.

Given,

          The initial cost of the cooler = $125

Erika has two options: (i) 15% off coupon

                                     (ii) $15 off coupon

Cost of the cooler that Erika gets from option (i):

                                [tex]= 125 - \frac{15}{100} * 125\\= 125 - 18.75\\= 106.25\\[/tex]

Cooler costs $106.25 to Erika from option (i).

Cost of the cooler that Erika gets from option (ii):

                                [tex]= 125 -15\\=110[/tex]

Cooler costs $110 to Erika from option (ii).

We can clearly see, $106.25 < $110

Therefore, Erika should use the coupon which gives her a discount of 15%.

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How do you change improper fractions to mixed numbers for kids?.

Answers

The way to change improper fractions to mixed numbers for kids is solved by using the division operation.

In math the term called fraction is defined as a part of a whole number, and a way to split up a number into equal parts

Here we need to identify the way to change improper fractions to mixed numbers for kids.

As from the definition of fraction we have identified that the way to solve the improper fraction into mixed fraction is written as follows:

Here we have to convert an improper fraction to a mixed number,

Then we have to work out how many whole numbers there are by dividing the numerator by the denominator.

And then we have to make the remainder the new numerator and leave the denominator as it was.

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Where would the intensity of an earthquake be higher?.

Answers

The intensity of an earthquake generally higher near the epicenter.

Intensity is based on observed effects of ground motion on people, buildings and natural features. This varies from site to site within the fault region, depending on the observer's position relative to the earthquake epicenter. The seismic intensity of an earthquake decreases as the distance from the epicenter increases, and decreases as the distance from the epicenter increases. An epicenter is a point on the surface of the Earth directly above where an earthquake begins. Earthquakes with a moment magnitude of approximately 6.5 or less occur in a concentrated area directly below the epicenter. Therefore, apart from the effects of different rock types and different soil types, the greatest shaking occurs at the epicenter. Earthquakes with a moment magnitude greater than 6.5 cause faults at some distance from the epicenter. At these large sizes, it is common for fractures to reach the surface. In such cases, the maximum shaking may or may not occur at the epicenter..

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make x the subject of the formula 13x=6y

Answers

The formula which represents the solution of the given equations; 13x = 6y for variable, x is; x = 6y / 13.

What is the solution of the given equation for x?

It follows from the task content that the solution of the given equation for variable, x is to be determined.

Since the given equation is; 13x = 6y.

It follows that the equation can be solved as follows;

13x = 6y

Divide both sides of the equation by 13 so that we have;

x = 6y / 13.

Ultimately, the formula for x is; x = 6y / 13.

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How to determine if a differential equation is linear?

Answers

It is linear if and only if the coefficients of y (the dependent variable) and all order derivatives of y are functions of t or constant terms.

What is equation?

An equation is a formula in mathematics that expresses the equality of two expressions by connecting them with the equals sign =. In its most basic form, an equation is a mathematical statement that shows that two mathematical expressions are equal. 3x + 5 = 14, for example, is an equation in which 3x + 5 and 14 are two expressions separated by a 'equal' sign. A mathematical equation that depicts the relationship between two expressions on opposite sides of the sign. It mostly consists of one variable and one equal to symbol. 2x - 4 = 2 is an example.

Here,

It is linear if and only if all order derivatives of y (the dependent variable) are functions of t or constant terms.

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What are the two types of indirect proof in geometry?.

Answers

There are two methods of indirect proof:

Proof of the contrapositive and proof by contradiction.

Now, According to the question:

Let's know:

An indirect proof, also called a proof by contradiction, is a roundabout way of proving that a theory is true. When we use the indirect proof method, we assume the opposite of our theory to be true. In other words, we assume our theory is false.

Hence, There are two methods of indirect proof:

Proof of the contrapositive and proof by contradiction.

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A family ha two car. During one particular week, the firt car conumed 30 gallon of ga and the econd conumed 40 gallon of ga. The two car drove a combined total of 1850 mile, and the um of their fuel efficiencie wa 55 mile per gallon. What were the fuel efficiencie of each of the car that week?

Answers

The fuel efficiency of the first car was 40.72 miles per gallon and the fuel efficiency of the second car was 14.28 miles per gallon.

The problem can be solved by using a system of equations.

We can call the fuel efficiency of the first car x and the fuel efficiency of the second car y.

From the problem, we know:

x + y = 55 (the combined fuel efficiency of the two cars is 55 miles per gallon)

We can also use the information about the amount of gas consumed and the distance has driven to set up another equation:

(30 gallons) * (x miles per gallon) + (40 gallons) * (y miles per gallon) = 1850 miles

Now we have a system of two equations with two variables (x and y):

x + y = 55

(30)x + (40)y = 1850

We can solve this system of equations using any method of solving such as substitution or elimination.

x = 55 - y

and substitute it in the second equation

(30)(55-y) + (40)y = 1850

1650 - 30y + 40y = 1850

-14y = -200

y = 14.28

x = 55 - 14.28 = 40.72

So the fuel efficiency of the first car was 40.72 miles per gallon and the fuel efficiency of the second car was 14.28 miles per gallon.

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How do you find the nth sum?.

Answers

The nth partial sum of a geometric sequence can be calculated using the first term a1 and common ratio r as follows: Sn=a1(1−rn)1−r. The infinite sum of a geometric sequence can be calculated if the common ratio is a fraction between −1 and 1 (that is |r|<1) as follows: S∞=a11−r.

In arithmetic, a chain is an enumerated series of gadgets in which repetitions are allowed and order matters. Like a hard and fast, it consists of contributors (additionally referred to as elements, or terms). The quantity of elements (possibly endless) is called the duration of the series.

Unlike a fixed, the same factors can appear a couple of times at distinct positions in a chain, and unlike a fixed, the order does be counted. formally, a chain can be described as a function from herbal numbers (the positions of elements inside the collection) to the factors at each position. The belief of a sequence may be generalized to a listed family, defined as a character from an arbitrary index set.

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Uie buy 3 piece of pizza and 2 cookie for a total of 6. 50. The next day he buy 1 piece of pizza and 1 cookie for 2. 50. How much doe a cookie cot

Answers

The cost of one cookie is 1. This value can be determine from the eliminate methods or substitution methods.

How to determine the cookie cost?

As per data given is a two different formula of pizza and cookie, we can determine it by elimination methods or substitution methods. Let do it by elimination methods. As per formula given are first buy 3 pizza + 2 cookie =  6.50 and the second buy 1 pizza + 1 cookie = 2.50. The calculation will be:

3 pizza + 2 cookie =  6.50

1 pizza + 1 cookie = 2.50     multiply with 3 because we want eliminate pizza

3 pizza + 2 cookie =  6.50

3 pizza + 3 cookie = 7.50       -

0 pizza - 1 cookie = - 1

1 cookie = 1

Hence the price of one cookie will cost you 1.

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Is 999 a cube number?.

Answers

=> 999 is not a perfect cube.

Because cube root of 999 is 3 [tex]\sqrt[3]{37}[/tex] .

Now, According to the question:

A cube number is the result when a number has been multiplied by itself twice. The symbol for cubed is 3. For example, 8 is a cube number because it's 2 x 2 x 2 (2 multiplied by itself twice); this is also written as [tex]2^3[/tex] (“two cubed”).

It is the real solution of the equation [tex]x^3[/tex] = 999.

The cube root of 999 is expressed as [tex]\sqrt[3]{999}[/tex] or 3 [tex]\sqrt[3]{37}[/tex] in the radical form and as[tex](999)^\frac{1}{3}[/tex] or [tex](999)^0^.^3^3[/tex] in the exponent form.

The prime factorization of 999 is 3 × 3 × 3 × 37, hence, the cube root of 999 in its lowest radical form is expressed as 3 [tex]\sqrt[3]{37}[/tex].

Cube root of 999: 9.996665555Cube root of 999 in Exponential Form: [tex](999)^\frac{1}{3}[/tex]Cube root of 999 in Radical Form:  [tex]\sqrt[3]{999}[/tex] or 3 [tex]\sqrt[3]{37}[/tex] .

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What is the perfect square trinomial of 36?.

Answers

A perfect square trinomial is a polynomial of the form (x + b)^2 = x^2 + 2bx + b^2. It is called a "perfect square" because when it is multiplied out, the resulting polynomial is a square of a binomial.

To find the perfect square trinomial of 36, we need to find two numbers that when added, give us b and when multiplied give us b^2=36.

Those two numbers are 6 and -6, since 6*-6 = -36 = 36.

So, the perfect square trinomial of 36 is (x + 6)(x - 6) = x^2 - 36

Another way to find the perfect square trinomial is to take the square root of the constant term (36) and then add and subtract that value to the variable.

√36 = 6

then x^2 + 6x - 6x + 36 = x^2 - 36

So, the perfect square trinomial of 36 is x^2 - 36.

[tex]36[/tex] is the square of [tex]6[/tex]. The square of a binomial is called a perfect square trinomial. [tex]X^2+12x+36[/tex] is a perfect square trinomial.

maya reads 6 3/4 chapters in 1 7/8 hours


what is the unit rate in chapters per hour?
write your answer as a fraction or a mixed number in simplest form

Answers

Answer:To find the unit rate in chapters per hour, we need to divide the number of chapters read by the amount of time it took to read them.

6 3/4 chapters / 1 7/8 hours = (64+3)/(18+7) chapters/hours

= (25/8) chapters/hours

To simplify this fraction, you can divide both the numerator and denominator by their greatest common factor which is 1.

25/8 chapters/hours = (25/8) chapters/hours

So the unit rate in chapters per hour is 25/8 chapters per hour.

Step-by-step explanation:

3 3/5 chapters per hour
6 3/4 = 27/4
1 7/8 = 15/8
1. You turn those two numbers into a complex fraction which is 27/4/15/8
2. You then multiply by the reciprocal which is 8/15/8/15
3. The bottom cancels out leaving you with the top to solve
4. By cross canceling you have to do 27x4 and 2x15 which is 108/30
5. By diving 108/30 by 6/6 you get 18/5 which equals 3 3/5 as a mixed fraction

I hoped this helped :)
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