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3 years ago

A survey was given to 339 people asking whether people like dogs and/or cats.

Mathematics

1 answer:

lina2011 [118]3 years ago

5 0

Answer:

Step-by-step explanation:

Think of it as a Venn diagram. One circle is the people who like dogs, and one circle is the people who like cats. The overlap is people who like both dogs and cats.

190 people in the survey said they like dogs. That includes the people who like both dogs and cats.

141 people in the survey said they like cats. That includes the people who like both dogs and cats.

If we simply add the two numbers together, we'll be counting the overlap twice. So to find the total number of people who like dogs or cats, we have to subtract one overlap.

dogs or cats = 190 + 141 − x

Therefore:

190 + 141 − x + 88 = 339

419 − x = 339

x = 80

80 people said they liked both cats and dogs.

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How to solve this?

nevsk [136]

Answer:

Answer of 17 is ㏒( $x^{2}$ +15x), Answer of 33 is x = 8 , Answer of 35 is x = ㏒10/㏒2 , Answer of 37 is x = -㏒12/㏒8 and Answer of 39 is x = 5

Step-by-step explanation:

17. ㏒x + ㏒(x+15)

Using property ㏒a + ㏒b = ㏒a×b

∴ ㏒x + ㏒(x+15)

㏒x×(x+15)

㏒( $x^{2}$ +15x)

The answer is ㏒( $x^{2}$ +15x)

33. 2^(x-5) = 8

2^(x-5) = 2^3

Using property 2^a = 2^b

Then a = b

∴x-5 = 3

x = 8

The answer is x = 8

35. 2^x = 10

Taking log on both sides gives

㏒2^x = ㏒10

x×㏒2 = ㏒10

x = ㏒10/㏒2

The answer is x = ㏒10/㏒2

37. 8^-x = 12

Taking log on both sides gives

㏒8^-x = ㏒12

-x×㏒8 = ㏒12

x = -㏒12/㏒8

The answer is x = -㏒12/㏒8

39. 5(2^3 × x) = 8

5(8×x) = 8

x = 5

The answer is x=5

5 0

3 years ago

The diameter of a particle of contamination (in micrometers) is modeled with the probability density function f(x)= 2/x^3 for x

RoseWind [281]

Answer:

a) 0.96

b) 0.016

c) 0.018

d) 0.982

e) x = 2

Step-by-step explanation:

We are given with the Probability density function f(x)= 2/x^3 where x > 1.

<em>Firstly we will calculate the general probability that of P(a < X < b) </em>

P(a < X < b) = $\int_{a}^{b} \frac{2}{x^{3}} dx$ = $2\int_{a}^{b} x^{-3} dx$

= $2[ \frac{x^{-3+1} }{-3+1}]^{b}_a dx$ { Because $\int_{a}^{b} x^{n} dx = [ \frac{x^{n+1} }{n+1}]^{b}_a$ }

= $2[ \frac{x^{-2} }{-2}]^{b}_a$ = $\frac{2}{-2} [ x^{-2} ]^{b}_a$

= $-1 [ b^{-2} - a^{-2} ]$ = $\frac{1}{a^{2} } - \frac{1}{b^{2} }$

a) Now P(X < 5) = P(1 < X < 5) {because x > 1 }

Comparing with general probability we get,

P(1 < X < 5) = $\frac{1}{1^{2} } - \frac{1}{5^{2} }$ = $1 - \frac{1}{25}$ = 0.96 .

b) P(X > 8) = P(8 < X < ∞) = 1/ $8^{2}$ - 1/∞ = 1/64 - 0 = 0.016

c) P(6 < X < 10) = $\frac{1}{6^{2} } - \frac{1}{10^{2} }$ = $\frac{1}{36} - \frac{1}{100 }$ = 0.018 .

d) P(x < 6 or X > 10) = P(1 < X < 6) + P(10 < X < ∞)

= $(\frac{1}{1^{2} } - \frac{1}{6^{2} })$ + (1/ $10^{2}$ - 1/∞) = 1 - 1/36 + 1/100 + 0 = 0.982

e) We have to find x such that P(X < x) = 0.75 ;

⇒ P(1 < X < x) = 0.75

⇒ $\frac{1}{1^{2} } - \frac{1}{x^{2} }$ = 0.75

⇒ $\frac{1} {x^{2} }$ = 1 - 0.75 = 0.25

⇒ $x^{2}$ = $\frac{1}{0.25}$ ⇒ $x^{2}$ = 4 ⇒ x = $2$

Therefore, value of x such that P(X < x) = 0.75 is 2.

8 0

2 years ago

I NEED HELP PLEASE, THANKS! :)

Elena L [17]

Answer:

First option is the right choice.

Step-by-step explanation:

$\frac{1}{\cos \left(x\right)+1}+\frac{1}{\cos \left(x\right)-1}\\\\\frac{\cos \left(x\right)-1}{\left(\cos \left(x\right)+1\right)\left(\cos \left(x\right)-1\right)}+\frac{\cos \left(x\right)+1}{\left(\cos \left(x\right)+1\right)\left(\cos \left(x\right)-1\right)}\\\\=\frac{\cos \left(x\right)-1+\cos \left(x\right)+1}{\left(\cos \left(x\right)+1\right)\left(\cos \left(x\right)-1\right)}\\\\=\frac{2cos\left(x\right)}{cos^2\left(x\right)-1}\\\\=\frac{2cos\left(x\right)}{sin^2\left(x\right)}$