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3 years ago

Two dice are numbered 1,2,3,4,5,6 and 1,1,2,2,3,3 respectively. They are rolled and

Mathematics

1 answer:

Alexxx [7]3 years ago

8 0

Answer:

P(2) = 1/18

P(3) = 1/9

P(4) = 1/6

P(5) = 1/6

P(6) = 1/6

P(7) = 1/6

P(8) = 1/9

P(9) = 1/18

Step-by-step explanation:

Each die has six possible outcomes, so both dice together have 6*6 = 36 outcomes:

(1,1), (1,1), (1,2), (1,2), (1,3), (1,3),

(2,1), (2,1), (2,2), (2,2), (2,3), (2,3),

(3,1), (3,1), (3,2), (3,2), (3,3), (3,3),

(4,1), (4,1), (4,2), (4,2), (4,3), (4,3),

(5,1), (5,1), (5,2), (5,2), (5,3), (5,3),

(6,1), (6,1), (6,2), (6,2), (6,3), (6,3).

The sum of the values for each outcome is:

2, 2, 3, 3, 4, 4,

3, 3, 4, 4, 5, 5,

4, 4, 5, 5, 6, 6,

5, 5, 6, 6, 7, 7,

6, 6, 7, 7, 8, 8,

7, 7, 8, 8, 9, 9.

To find the probability of each sum, we just need to divide the number of times this sum appears over the total number of possibilities (36), so we have:

P(2) = 2/36 = 1/18

P(3) = 4/36 = 1/9

P(4) = 6/36 = 1/6

P(5) = 6/36 = 1/6

P(6) = 6/36 = 1/6

P(7) = 6/36 = 1/6

P(8) = 4/36 = 1/9

P(9) = 2/36 = 1/18

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A population of mice is increasing exponentially. On Monday there were 120 mice. One month later there were 132 mice. Write a fu

den301095 [7]

Answer:

$y =120*1.1^x$

$r = 10\%$ --- Percentage increase

Step-by-step explanation:

Given

Let

$x \to months$

$y \to mice$

So, we have:

$(x_1,y_1) = (0,120)$ --- Monday

$(x_2,y_2) = (1,132)$ --- One month later

Required

The function

The function is represented as:

$y = ab^x$

In $(x_1,y_1) = (0,120)$ , we have:

$120 =a * 1$

$120 =a$

Rewrite as:

$a = 120$

In $(x_2,y_2) = (1,132)$ , we have:

$132 = a * b^1$

$132 = a * b$

Substitute $a = 120$

$132 = 120 * b$

Solve for b

$b = \frac{132}{120}$

$b = 1.1$

Recall that:

$y = ab^x$

Hence, the function is:

$y =120*1.1^x$

To get the monthly percentage increase (r), we have:

$y = a(1 + r)^x$

Compare to: $y = ab^x$

So:

$1+r =b$

Make r the subject

$r = b-1$

$r = 1.1-1$

$r = 0.1$

Express as percentage

$r = 0.1*100\%$

$r = 10\%$

8 0

2 years ago

What is -4d 3 + 28d 2 - 4d

Svetlanka [38]

Answer: 20d + 5

Step-by-step explanation:

First we need to combine like terms.

In this equation we can see that they're are 3 numbers containing the letter D we have -4, -4, 28.

We're going to combine -4 and -4 to get -8 and then combine -8 to 28 getting 20d

Afterwards we're going to combine 3, 2 equaling 5.

7 0

3 years ago

Juan is selling tickets for a high school playChild tickets cost $3 and adult tickets cost $10. He selts 205 tickets and collect

SVETLANKA909090 [29]

Answer:

135 Adult tickets and 70 Child tickets sold

Step-by-step explanation:

135*10 (adult ticket price) = 1,350

70*3 (child ticket price) = 210

$1,350 + $210 = $1,560

135 + 70 = 205 tickets sold

6 0

3 years ago

Does anyone know the square root of 10,221? My online teacher wants me to figure it out. :)

faust18 [17]

the square root is 101.

8 0

2 years ago

If you invest x dollars at 3% intrest compounded annually ,then the amount A (x) of the investment after one year is A(x)=1.03x.

GarryVolchara [31]

The "compound amount" formula is A = P(1+r)^t.

Here, the Amount A(x) is (x)(1+0.03)^1= 1.03x.

Please be clearer about what you are asking here. I assume you just wanted to be told that you are right.

5 0

3 years ago