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melomori [17]
3 years ago
10

For each of the solutions of the equations find two consecutive integers between

Mathematics
1 answer:
ale4655 [162]3 years ago
7 0

Answer:

0 and 1

Step-by-step explanation:

x² = 3

take the square root of both sides

x = {-√3, √3}

x ≈ {-1.73, 1.75}

Two consecutive integers between 1.73 and 1.75

0 and 1

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Name the number property illustrated by this<br>equation:<br>-2(–3 + 7) = -2(-3) + (-2)(7)​
erica [24]

Answer:

The distributive property of multiplication

Step-by-step explanation:

<u>explanation</u>:-

The distributive property of multiplication states that when a number is multiplied by the sum of two numbers, the first can be distributed to both of those numbers and multiplied by each of them separately,then adding the two products together for the same result as multiplying the first number by sum.

a(b+c) = a.b + a.c

so -2 ( -3+7) = -2(-3) + (-2)(7)

   -8  =  6 -14

   -8 = - 8

give data we will use distributive property of multiplication

5 0
3 years ago
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irakobra [83]

Answer:

mok

Step-by-step explanation:

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7 0
3 years ago
How much dollars is in 14 quarters and 5 nickels​
marishachu [46]

Answer:

$4.25

Step-by-step explanation:

4 quarters is 1 dollar

1 nickel is 5 cent

14 divided by 4 = 3.5

3.5 + 5 times 5 =  $4.25

8 0
3 years ago
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Given g(x) = x4 + 2x3 - 7x2 - 8x + 12. When g(x) is divided by x - 1, which conclusion about g(x) is true?
PSYCHO15rus [73]

Answer:

g(1) = 0

There is a remainder of 10 so you can automatically cross out 3 and 4.

7 0
3 years ago
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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
3 years ago
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