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DanielleElmas [232]
3 years ago
12

You want to decorate a party hall with a total of least 40 red and yellow baloons. You want a minimum of 25 yellow baloons. Writ

e and graph
Mathematics
2 answers:
aliina [53]3 years ago
7 0
There is 75 balls and thats the answer
vekshin13 years ago
6 0
40-25=15 red balloons. 
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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
natulia [17]

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
What are the restrictions of the domain of the function F(x) = 1/x^2-9
Sonbull [250]
f(x)=\frac{1}{x^2-9}

The denominator can't be equal to 0.
x^2-9 \not= 0 \\&#10;x^2 \not= 9 \\&#10;x \not= -3 \ \land \ x \not= 3

The domain is all numbers except -3 and 3.
x \in \mathbb{R} - \{-3, 3 \}
6 0
3 years ago
What is 4/5 of 20.5?
ira [324]
16.4
20.5/5=4.1
4.1*4=16.4 
............
7 0
3 years ago
What is the value of x in the equation −6 + x = −2? (5 points) a 8 b 4 c −4 d −8
Ymorist [56]
The correct answer is B)4
5 0
3 years ago
Identify as a direct variation, inverse variation or neither. The number of tons of coal burned by an old coal burning locomotiv
pochemuha
Answer: it is a direct variation.

Justification:

In a direct variation the variables are related by a proportionality constant in this way:

y = k x

Tthan means that the value of y is always the product of a constant times the value of x.

The situation discribed for the coal may be written as:
number of tons of coal burned: c

number of hours: h

⇒ c = k × h

Which is that you can calcualte the number of tons of coal burned at any time, once you know the proportionality constant k.




5 0
3 years ago
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