What is the equation of a circle with center (-2, 3) and radius 4?

Two ballpoint pens are selected at random from a box that contains 3 blue pens, 2 red pens, and 3 green pens. If X is the number

Flauer [41]

Answer:

a) f(x,y) = $\frac{\binom{3}{x}\binom{2}{y}\binom{3}{2-x-y}}{\binom{8}{2}}$ ; x = 0, 1 , 2; y = 0, 1 , 2; 0 ≤ x+y ≥ 2

b) = $\frac{9}{14}$

Step-by-step explanation:

joint probability is a function that characterizes the distribution of a random variable. If X and Y be two random variables then the joint probability will be P(X = x, Y=y)

Given Data,

X = The number of blue Pens

Y = The number of red Pens

a)

possible outcomes(X, Y) are (0, 0), (0, 1), (1, 0), (1, 1), (0, 2), (2,0)

Please refer fig. also

total number ways of selecting any 2 pens = $\binom{8}{2}$ = $\frac{8!}{2! 6!}$ =28

f(x,y) = $\frac{\binom{3}{x}\binom{2}{y}\binom{3}{2-x-y}}{\binom{8}{2}}$ ; x = 0, 1 , 2; y = 0, 1 , 2; 0 ≤ x+y ≥ 2

b)

P(X,Y)∈A = P(X + Y ≤ 1)

= P(0,0) + P(1,0) + P(0,1)

= $\frac{3}{28}$ + $\frac{3}{14}$ + $\frac{9}{28}$

= $\frac{9}{14}$

4 0

3 years ago

4. Is the point (3,-4) a solution to the given system? Justify your answer.

Zigmanuir [339]

Answer: No, it is not a solution

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Explanation:

The point (3,-4) means that x = 3 and y = -4 pair up together

Let's plug these x,y values into each equation

Starting with the first equation, we get,

y = 4x-16

-4 = 4(3)-16 ... x replaced with 3; y replaced with -4

-4 = 12-16

-4 = -4 .... this is a true statement

Repeat for the second equation

y = 2x-6

-4 = 2(3)-6

-4 = 6-6

-4 = 0 ... this is false

Since we get a false statement, this means (3,-4) is not on the line y = 2x-6, which means that overall (3,-4) is not a solution to the system of equations. The point (3,-4) must make both equations true for it to be a solution.

5 0

3 years ago

10(y+2)-y=2(9y-8) i need to know how to solve it

vlabodo [156]

10(y+2)-y=2(9y-8)

Mutiply the first bracket by 10

Mutiply the second bracket by 2

(10)(y)(10)(2)= 10y+20

(2)(9y)(2)(-8)= 18y-16

10y+20-y= 18y-16

10y-y+20= 18y-16

9y+20= 18y-16

move 18y to the other side

sign changes from +18y to -18y

9y-18y+20= 18y-18y-16

-9y+20= -16

move +20 to the other side

sign changes from +20 to -20

-9y+20-20=-16-20

-9y= -36

divide by -9

-9y/-9= -36/-9

y= 4

Answer: y= 4

6 0

3 years ago

Match the vocabulary to the correct definition. (only choose 4 to match)

Ivanshal [37]

Answer:

discount:deduct an amount from (the usual price of something).

tip:give (someone) a sum of money as a reward for a service

markup:the amount added to the cost price of goods to cover overheads and profit.

Sales tax:a tax on sales or on the receipts from sales

4 0

2 years ago

Which theorem or postulate proves the two triangles are similar?

Andre45 [30]

Answer:

The corresponding pair of sides are in the same ratio.

Step-by-step explanation:

For two triangles to be similar, the theorem that is required is the corresponding sides of the two triangles are in the same ratio.

Now, see the diagram of two triangles given with the question.

The ratios of the corresponding sides are $\frac{20}{16} = \frac{19}{\frac{76}{5} } = \frac{5}{4}$

If two pairs corresponding sides are in 5 : 4 ratio, then the third pair of corresponding sides will also be in 5 : 4 ratio.

Therefore, the two triangles are similar. (Answer)

5 0

3 years ago