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3 years ago

What are the solutions of the equation?

Mathematics

1 answer:

BARSIC [14]3 years ago

3 0

A solution to a equation is when the variable is substituted fully. That makes the equation true.

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Suppose box A contains 4 red and 5 blue poker chips and box B contains 6 red and 3 blue poker chips. Then a poker chip is chosen

sergejj [24]

Answer:

0.5172 = 51.72% probability a blue poker chip was transferred from box A to box B, given that the coin just chosen from box B is red

Step-by-step explanation:

Conditional Probability

We use the conditional probability formula to solve this question. It is

$P(B|A) = \frac{P(A \cap B)}{P(A)}$

In which

P(B|A) is the probability of event B happening, given that A happened.

$P(A \cap B)$ is the probability of both A and B happening.

P(A) is the probability of A happening.

In this question:

Event A: Coin chosen from box B is red.

Event B: Blue poker chip transferred.

Probability of choosing a red coin:

7/10 of 4/9(red coin from box A)

6/10 of 5/9(blue coin from box A). So

$P(A) = \frac{7}{10}*\frac{4}{9} + \frac{6}{10}*\frac{5}{9} = \frac{28 + 30}{90} = 0.6444$

Blue chip transferred, red coin chosen:

6/10 of 5/9. So

$P(A \cap B) = \frac{6}{10}*\frac{5}{9} = \frac{30}{90} = 0.3333$

What is the probability a blue poker chip was transferred from box A to box B, given that the coin just chosen from box B is red?

$P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.3333}{0.6444} = 0.5172$

0.5172 = 51.72% probability a blue poker chip was transferred from box A to box B, given that the coin just chosen from box B is red

5 0

3 years ago

Rewrite the following equation in standard form.<br> y + 4 = 5(x - 8)

Helen [10]

Answer:

5x-y-36=0

Step-by-step explanation:

y+4=5x-40

5x-y=36

4 0

3 years ago

An angle, θ, is in standard position. The terminal side of the angle passes through the point (4, 5).

lara31 [8.8K]

Answer:

cos Θ = $\frac{4}{\sqrt{41} }$

Step-by-step explanation:

Given the angle passes through (4, 5 ) then the right triangle with sides 4 and 5 has hypotenuse h given by

h² = 4² + 5² = 16 + 25 = 41 ( take the square root of both sides )

h = $\sqrt{41}$

In relation to Θ, 4 is adjacent and 5 is opposite, thus

cos Θ = $\frac{adjacent}{hypotenuse}$ = $\frac{4}{\sqrt{41} }$

5 0

3 years ago

A boat leaves a.M. Marina at 7 AM traveling at 3.4 knots bearing is N38°E the boat docks on an island at 2pm how far north of th

Jlenok [28]

Answer:

The distance between the docks & island is 44.07 km.

Step-by-step explanation:

Speed of the boat S = 3.4 knot = 6.3 $\frac{km}{hr}$

Time taken by bot to reach the island = 7 hr

We know that the distance is given by

Distance = Speed × Time

Put all the values in above equation we get

D = 6.3 × 7

D = 44.07 km

Therefore the distance between the docks & island is 44.07 km.

6 0

3 years ago

The second of two numbers is 8 less than twice the first number, what are the two numbers?

Mashutka [201]

So the two numbers can be represented as x and y

so x is first and y is second

y=2(x)-8

so y=2x-8

IF THEY ARE CONSECUTIVE
If they are consecutive numbers then
x+1=y
subtitute
x+1=2x-8
subtract x from both sides
1=x-8
add 8 to both sides and get
9=x
put it into the equation and get
y=2(9)-8
y=18-8
y=10
so x=9
y=10
IF X AND Y ARE CONSECUTIVE INTEGERS (1,2,3,4 not 2.3 or 1,3,5,8)

3 0

4 years ago

Read 2 more answers