Use substitution to solve the system of equations. 2x+4=32 and -2x-6y= -44

3 3/4 + 2 1/8 = (make sure you simplify the fraction)

dusya [7]

This is 5 7/8 or 47/8

5 0

2 years ago

A survey of 2500 subscribers to a certain news paper revealed that 2250 people subscribe to the daily morning edition and 1250 s

Aleks04 [339]

1500 people subscribed Sunday edition and 250 people subscribed only sunday edition.

<u>Solution:</u>

Given, A survey of 2500 subscribers to a certain news paper revealed that 2250 people subscribe to the daily morning edition

And 1250 subscribe to both the daily and the sunday editions.

We have to find how many subscribe to the Sunday edition? how many subscribe to the Sunday edition only?

Let x denote the number who subscribe to the Sunday edition.

Then the addition rule with overlap tells us that

Those who subscribe daily edition + those who subscribe sunday edition - those who subscribe both daily and sunday edition = total subscribers in survey

2250 + x – 1250 = 2500

1000 + x = 2500

x = 1500

so, 1500 subscribe to the Sunday edition and 1500 – 1250 = 250 subscribe to the Sunday edition only.

Hence, 1500 people subscribed Sunday edition and 250 people subscribed only sunday edition.

6 0

3 years ago

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

Find the value of each variable in the parallelogram. Round your answers to the nearest tenth, if necessary.

lilavasa [31]

Answer:

z = 2

y = 5

Step-by-step explanation:

3 0

2 years ago

If any one answer this question i will give them brainliest

frozen [14]

Answer:

x =9

Step-by-step explanation:

-5x = -45

Divide both sides by -5:

x = 9

5 0

3 years ago

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