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NemiM [27]
3 years ago
9

Need answer to A and B!

Mathematics
1 answer:
Roman55 [17]3 years ago
5 0

To find the probability of drawing certain colour of balls, we first need to find the total number of balls:

5 + 7 +5 = 17

<u>For the number of red balls that need to be added</u>

The original probability of drawing a red ball:

red ball/ total number of balls

= 5/17

To find the number of balls required, we can set an equation.

Let the number of red balls that need to be added be x.

5+x / 17+x = 5/6

(5+x) x 6 = (17+ x) x5

30 +  6x = 85 + 5x

6x - 5x = 85 - 30

x = 55

Therefore, <u>55</u> red balls need to be added.

<u>For the number of black balls that need to be added</u>

The original probability of drawing a white ball:

white ball/ total number of balls

=5/17

To find the probability required, we can set an equation.

Let the number of black balls that need to be added be y.

5/ 17 + y = 1/6

5 x 6 = 17 + y

30 = 17 + y

30 - 17 = y

y = 13

Therefore, <u>13</u> black balls need to be added.

Hope it helps!

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Step-by-step explanation:

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Which of the following is equivalent to tan2θcos(2θ) for all values of θ for which tan2θcos(2θ) is defined?
Aloiza [94]

Answer:

2sin²θ - tan²θ

Step-by-step explanation:

Given

tan²θcos(2θ)

Required

Simplify

We start by simplifying cos(2θ)

cos(2θ) = cos(θ+θ)

From Cosine formula

cos(A+A) = cosAcosA - sinAsinA

cos(A+A) = cos²A - sin²A

By comparison

cos(2θ) = cos(θ+θ)

cos(2θ) = cos²θ - sin²θ ----- equation 1

Recall that cos²θ + sin²θ = 1

Make sin²θ the subject of formula

sin²θ = 1 - cos²θ

Substitute sin²θ = 1 - cos²θ in equation 1

cos(2θ) = cos²θ - (1 - cos²θ)

cos(2θ) = cos²θ - 1 +cos²θ

cos(2θ) = cos²θ + cos²θ - 1

cos(2θ) = 2cos²θ - 1

Substitute 2cos²θ - 1 for cos(2θ) in the given question

tan²θcos(2θ) becomes

tan²θ(2cos²θ - 1)

Open brackets

2cos²θtan²θ - tan²θ

------------------------

Simplify tan²θ

tan²θ = (tanθ)²

Recall that tanθ =  sinθ/cosθ

So, we have

tan²θ = (sinθ/cosθ)²

tan²θ = sin²θ/cos²θ

------------------------

Substitute sin²θ/cos²θ for tan²θ

2cos²θtan²θ - tan²θ becomes

2cos²θ(sin²θ/cos²θ) - tan²θ

Open bracket (cos²θ will cancel out cos²θ) to give

2(sin²θ) - tan²θ

2sin²θ - tan²θ

Hence, the simplification of tan²θcos(2θ) is 2sin²θ - tan²θ

Option E is correct

7 0
2 years ago
Help please not much time!!!!
Rzqust [24]

Answer:

I'm here! This Problem is easy :) The answer is 4

Step-by-step explanation:

2x+10=5x−2

<em>Subtract </em>5x from both sides

2x+10−5x=−2

<em>Combine</em> 2x and −5x to get −3x.

−3x+10=−2

Subtract 10 from <em>both sides.</em>

−3x=−12

<em>Divide</em> both sides by −3.

Divide −12 by −3 to get 4.

x=\frac{-12}{-4}

x = 4 (D)

7 0
3 years ago
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