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Verdich [7]
2 years ago
9

A number is chosen uniformly at random from among the positive integers less than $10^8$. Given that the sum of the digits of th

e number is 9, what is the probability that the number is prime
Mathematics
1 answer:
Reil [10]2 years ago
3 0

Answer:

 

If the sum of the digits of a number is divisible by 9, then that number is divisible by 9. An..... sorry if this does not help :(

Step-by-step explanation:

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Sin theta+costheta/sintheta -costheta+sintheta-costheta/sintheta+costheta=2sec2/tan2 theta -1
sleet_krkn [62]

\dfrac{sin\theta + cos\theta}{sin\theta-cos\theta}+\dfrac{sin\theta-cos\theta}{sin\theta+cos\theta}=\dfrac{2sec^2\theta}{tan^2\theta-1}

From Left side:

\dfrac{sin\theta + cos\theta}{sin\theta-cos\theta}\bigg(\dfrac{sin\theta+cos\theta}{sin\theta+cos\theta}\bigg)+\dfrac{sin\theta-cos\theta}{sin\theta+cos\theta}\bigg(\dfrac{sin\theta-cos\theta}{sin\theta-cos\theta}\bigg)

\dfrac{sin^2\theta+2cos\thetasin\theta+cos^2\theta}{sin^2\theta-cos^2\theta}+\dfrac{sin^2\theta-2cos\thetasin\theta+cos^2\theta}{sin^2\theta-cos^2\theta}

NOTE: sin²θ + cos²θ = 1

\dfrac{1 + 2cos\theta sin\theta}{sin^2\theta-cos^2\theta}+\dfrac{1-2cos\theta sin\theta}{sin^2\theta-cos^2\theta}

\dfrac{1 + 2cos\theta sin\theta+1-2cos\theta sin\theta}{sin^2\theta-cos^2\theta}

\dfrac{2}{sin^2\theta-cos^2\theta}

\dfrac{2}{\bigg(sin^2\theta-cos^2\theta\bigg)\bigg(\dfrac{cos^2\theta}{cos^2\theta}\bigg)}

\dfrac{2sec^2\theta}{\dfrac{sin^2\theta}{cos^2\theta}-\dfrac{cos^2\theta}{cos^2\theta}}

\dfrac{2sec^2\theta}{tan^2\theta-1}

Left side = Right side <em>so proof is complete</em>

8 0
3 years ago
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Answer: −7g+2

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Answer:

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Step-by-step explanation:

6 0
3 years ago
Miles earns a 6% commission on each vehicle
slamgirl [31]

The total amount of his  commission for these vehicles is $ 1686

<em><u>Solution:</u></em>

Given that,

Miles earns a 6% commission on each vehicle  he sells

Therefore,

Commission rate = 6 %

Today he sold a truck for $18,500 and a  car for $9,600

Therefore,

Commission amount = 6 % of (18500 + 9600)

Commission amount = 6 % of 28100

Calculate the above equation

Commission\ amount = 6 \% \times 28100\\\\Commission\ amount = \frac{6}{100} \times 28100\\\\Commission\ amount = 6 \times 281 = 1686

Thus the total amount of his  commission for these vehicles is $ 1686

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What is 2.1 as a fraction?
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2 1/10 because the 1 in 2.1 is in the tenth place
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