Find x and y. Give reasons to justify your solution.

Given:

Total of raffle tickets = 30

Number of tickets Jason bought = 10

Number of prizes = 3

To find:

The probability that Jason will win all 3 of the prizes if once a raffle ticket wins a prize it is thrown away.

Solution:

Total of raffle tickets = 30

Number of prizes = 3

So, number of total outcomes is

[tex]n(S)=^{30}C_3[/tex]

Number of tickets Jason bought = 10

So, number of favorable outcomes is

[tex]n(A)=^{10}C_3[/tex]

Now,

[tex]\text{Probability}=\dfrac{\text{Favorable outcomes}}{\text{Total outcomes}}[/tex]

[tex]\text{Probability}=\dfrac{n(A)}{n(S)}[/tex]

[tex]\text{Probability}=\dfrac{^{10}C_3}{^{30}C_3}[/tex]

[tex]\text{Probability}=\dfrac{\dfrac{10!}{(10-3)!3!}}{\dfrac{30!}{(30-3)!3!}}[/tex]

[tex]\text{Probability}=\dfrac{10\times 9\times 8\times 7!}{7!3!}\times\dfrac{27!3!}{30\times 29\times 28\times 27!}[/tex]

[tex]\text{Probability}=\dfrac{10\times 9\times 8}{30\times 29\times 28}[/tex]

[tex]\text{Probability}=\dfrac{6}{203}[/tex]

Therefore, the correct option is A.

Answer:

The correct answer is A. 6/203

Answer:

Its D if you think about it

Step-by-step explanation:in your mind move the triangle on the top right down 6 units and then turn your triangle 90 degrees counter clockwise (quick maths)

The only transformation that will move the triangle in quadrant 1 onto the similar triangle in quadrant three is;

Option D; translation 6 units down and rotation 90° counterclockwise

The y-coordinate of the right angle vertex of the triangle in quadrant 1 is y = -2. Meanwhile the y-coordinate of the same right angle point of the triangle in quadrant 3 is y = -4.

Thus, for the triangle in quadrant 1 to be on the same level with that in quadrant 3, we need to translate the triangle in quadrant 1 downwards by 6 units.

Now, since we want to map this newly translated triangle to the one in quadrant 3 and as such we need to rotate it 90° counterclockwise

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Answer:

x-4 = 7 , x-4 = -7

Step-by-step explanation:

IX - 4l+ 1 = 8

Subtract 1 from each side

IX - 4l = 8-1

IX - 4l = 7

Then separate into two equations, one positive and one negative

x-4 = 7      x-4 = -7

Answer:

2/7

Step-by-step explanation:

Given:

Scott and Nikki each have a full 1.5-gallon container of liquid laundry detergent.

Lid on Scott's container can hold 3 fluid ounces of detergent.

Lid on Nikki's container can hold 4 fluid ounces of detergent.

To find:

The number of lids full of detergent Scott have more than Nikki.

Solution:

We know that,

1 gallon = 128 fluid ounces

1.5 gallon = 192 fluid ounces

Lid on Scott's container can hold 3 fluid ounces of detergent. So, number of lids full of detergent Scott have is

[tex]\dfrac{192}{3}=64[/tex]

Lid on Nikki's container can hold 4 fluid ounces of detergent.  So, number of lids full of detergent Nikki have is

[tex]\dfrac{192}{4}=48[/tex]

Difference between number of lids is

[tex]64-48=16[/tex]

Therefore, Scott have 16 lids more than Nikki. Hence, the correct option is B.

Answer: it is 16

Step-by-step explanation:

Answer:

16

Step-by-step explanation:

i got it right on the test

Answer:

16...

hope, it helps! x

Answer:

The input when the output is 17 is x=6.

Step-by-step explanation:

Functions

Assume the input is called x and the output is the function f(x). Two times the input is 2x. 5 more than that is 2x+5.

Knowing the output of the function is 5 more than 2 times the input, we can write the function as:

f(x)=2x+5

Now find the input x when the output is 17:

17=2x+5

Swap sides of the equation:

2x+5=17

Subtract 5:

2x=17-5=12

Divide by 2:

x=12/6=6

The input when the output is 17 is x=6.

Answer:

15%

Step-by-step explanation:

Answer:

15%

Step-by-step explanation:

Answer:

Area = L x B

= 5m x 4m =20m square

Answer:

0.875 or 7/8

Step-by-step explanation:

I put it in a calculator

Answer:

the answer is 7/8

Step-by-step explanation:

7/3 ×3/8 =7/8

Answer:

Minimum: x<-1

Maximum: x> 1

both are also equal to i just don’t have the sign

Answer:

where is the figure

Step-by-step explanation:

Answer:

I think its 3 out of 7

Answer:

Step-by-step explanation:

Since the area is the product of the sides, let's try to factorize the given:

So the dimensions are:

Answer:

1. 1:1500

2. 1500 times

Step-by-step explanation:

1 foot=12 in.

500*12=6000

4:6000=1:1500

Given :

A bucket is filled with 1 3/4 gallons of water.

The bucket has a small hole and 1/4 gallon leaks out every hour.

To Find :

How many hours will it take for the bucket to be completely empty.

Solution :

We know , mixed fraction of form a p/q is given by :

[tex]a\ p/q = \dfrac{(a\times q)+p}{q}[/tex]

So, 1 3/4 = 7/4 .

Let, after t hours bucket is empty.

[tex]\dfrac{7}{4}-\dfrac{1}{4}t = 0\\\\t = 7\ hour[/tex]

Therefore, it takes 7 hours for the bucket to be completely empty.

Hence, this is the required solution.

Answer:

121

Step-by-step explanation:

11 x 11

this is what goes on in my head you don't have to this but this is what i do

10 x 10 = 100

10 x 1 = 10

1 x 10 = 10

1 x 1 = 1

100 + 10 + 10 + 1 = 121

The product of the numbers 11 with 11 is 121.

Given are the numbers 11 and 11.

We have to find the product of these numbers.

This can be found in various ways.

We can study the perfect squares from 1 to 20 to know it fast.

Else you can use normal multiplication.

Or another method is,

Split both 11 as 10 and 1 and then find the product with each.

10 × 10 = 100

Then find 10 with 1.

10 × 1 = 10

Then find 1 with 10.

1 × 10 = 10

Then find 1 with 1.

1 × 1 = 1

Total is 100 + 10 + 10 + 1 = 121

Hence the number is 121.

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Answer:

Like terms are terms that contain the same variables raised to the same power. Only the numerical coefficients are different. In an expression, only like terms can be combined. We combine like terms to shorten and simplify algebraic expressions, so we can work with them more easily.

Answer:

1/12 i hope this is correct i think so i did it in my calculator so i hope it helps

Step-by-step explanation:

Answer:

5x999 urfiwbyginwgf fjkwfg8

Step-by-step explanation:

you take the 5 by x by 999 and kvbbci then you are supposed to uibjouwfbc by owihefojw and oiwhjwnfwfb

Answer:

4995

Step-by-step explanation:

Because

999

x    5

4995

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Answer:

30

hope this helps.

Answer:

35 houses

Step-by-step explanation:

Answer:

I believe c is correct

Answer:2^9

Step-by-step explanation:

The student multiplied the exponents instead of adding the exponents.

Hope this helps.

It's 42.

The equation would be 1/3n - 6 = 8.

Just plug in each number in the place of 'n' then see what actually equals 8.

Answer:

[tex]Total = 38\frac{11}{12}\ miles[/tex]

Step-by-step explanation:

Given

[tex]First\ Route = 12\frac{2}{3}\ miles[/tex]

[tex]Second\ Route = 10\frac{3}{4}\ miles[/tex]

[tex]Third\ Route = 15\frac{1}{2}\ miles[/tex]

Required

Determine the total miles

[tex]Total = First\ Route + Second\ Route + Third\ Route[/tex]

[tex]Total = 12\frac{2}{3} + 10\frac{3}{4} + 15\frac{1}{2}[/tex]

Convert to improper fractions

[tex]Total = \frac{38}{3} + \frac{43}{4} + \frac{31}{2}[/tex]

Take LCM

[tex]Total = \frac{152 + 129 + 186}{12}[/tex]

[tex]Total = \frac{467}{12}[/tex]

[tex]Total = 38\frac{11}{12}\ miles[/tex]

Answer:

B.Economic growth

Step-by-step explanation:

per capita income can't be just improved by making a business successful

stable prices need a good income and that's not a point given in the question

Making business successful doesn't make all the citizens employed. so the most relevant answer is economic growth as grown business in a country provides tax and thus ensures the economic growth