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3 years ago

Which expression is equivalent to 7 (z+2)

Mathematics

1 answer:

lutik1710 [3]3 years ago

6 0

7z+14 because if have to multiply everything on the outside by the inside,so 7 *y=7z and 7*2=14

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An urn contains 5 white and 10 black balls. A fair die is rolled and that number of balls is randomly chosen from the urn. What

galina1969 [7]

Answer:

Part A:

The probability that all of the balls selected are white:

$P(A)=\frac{1}{6}(\frac{1}{3}+\frac{2}{21}+\frac{2}{91}+\frac{1}{273}+\frac{1}{3003}+0)\\ P(A)=\frac{5}{66}=0.075757576$

Part B:

The conditional probability that the die landed on 3 if all the balls selected are white:

$P(D_3|A)=\frac{\frac{2}{91}*\frac{1}{6}}{\frac{5}{66} } \\P(D_3|A)=\frac{22}{455}=0.0483516$

Step-by-step explanation:

A is the event all balls are white.

D_i is the dice outcome.

Sine the die is fair:

$P(D_i)=\frac{1}{6}$ for i∈{1,2,3,4,5,6}

In case of 10 black and 5 white balls:

$P(A|D_1)=\frac{5_{C}_1}{15_{C}_1} =\frac{5}{15}=\frac{1}{3}$

$P(A|D_2)=\frac{5_{C}_2}{15_{C}_2} =\frac{10}{105}=\frac{2}{21}$

$P(A|D_3)=\frac{5_{C}_3}{15_{C}_3} =\frac{10}{455}=\frac{2}{91}$

$P(A|D_4)=\frac{5_{C}_4}{15_{C}_4} =\frac{5}{1365}=\frac{1}{273}$

$P(A|D_5)=\frac{5_{C}_5}{15_{C}_5} =\frac{1}{3003}=\frac{1}{3003}$

$P(A|D_6)=\frac{5_{C}_6}{15_{C}_6} =0$

Part A:

The probability that all of the balls selected are white:

$P(A)=\sum^6_{i=1} P(A|D_i)P(D_i)$

$P(A)=\frac{1}{6}(\frac{1}{3}+\frac{2}{21}+\frac{2}{91}+\frac{1}{273}+\frac{1}{3003}+0)\\ P(A)=\frac{5}{66}=0.075757576$

Part B:

The conditional probability that the die landed on 3 if all the balls selected are white:

We have to find $P(D_3|A)$

The data required is calculated above:

$P(D_3|A)=\frac{P(A|D_3)P(D_3)}{P(A)}\\ P(D_3|A)=\frac{\frac{2}{91}*\frac{1}{6}}{\frac{5}{66} } \\P(D_3|A)=\frac{22}{455}=0.0483516$

7 0

3 years ago

Pls help me i am struggling

deff fn [24]

Answer:

16 square inches

Step-by-step explanation:

4 x 4 = 16

4 0

3 years ago

A person from London, England wants to purchase some paint from you, but they are only familiar with metric measurements. They s

MariettaO [177]

Answer:

1.8492 Gallons

Step-by-step explanation

To convert liters to gallons, multiply the liter value by 0.26417205236 or divide by 3.785411784.

7 0

3 years ago

HEEEEEEELLLPPPPPPPPP!!!!! PLEASEEEEEEEE

Klio2033 [76]

Answer:

a) $a_n=2(a_{n-1})$ , where $a_1=5$ .

b) $a_n=5(2)^{n-1}$

Step-by-step explanation:

The given sequence is

$5,10,20,40...$ .

The first term of the sequence is

$a_1=5$

The second term is $a_2=10$

The common ratio for this sequence can be determined using any two consecutive terms in the sequence.

Using the first two terms, the common ratio is

$r=\frac{a_2}{a_1}$

$\Rightarrow r=\frac{10}{5}=2$

a) The recursive rule is given by,

$a_n=r(a_{n-1})$

$a_n=2(a_{n-1})$ , where $a_1=5$ .

b) The explicit rule is given by $a_n=a_1r^{n-1}$

$\Rightarrow a_n=5(2)^{n-1}$

3 0

3 years ago

HELP!!! I NEED HELP ON MY EXAM. (15PTS)

Olegator [25]

Answer:

its A

Step-by-step explanation:

4 0

3 years ago