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Bezzdna [24]
3 years ago
15

Fellow person with an easy question here :))

Mathematics
1 answer:
Leviafan [203]3 years ago
3 0

The actual wingspan of fly is 5.5cm

Step-by-step explanation:

Given,

Scale of drawing;

4mm = 1cm

Ratio of mm to cm = 4:1

Wingspan of fly in drawing = 22mm

Let,

x be the actual wingspan.

Ratio of mm to cm = 22:x

Using proportion;

Ratio of mm to cm :: Ratio of mm to cm

4:1::22:x\\

Product of extreme = Product of mean

4*x=22*1\\4x=22

Dividing both sides by 4

\frac{4x}{4}=\frac{22}{4}\\x=5.5

The actual wingspan of fly is 5.5cm

Keywords: proportion, division

Learn more about division at:

  • brainly.com/question/11150876
  • brainly.com/question/11175936

#LearnwithBrainly

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Pls somebody solve this I still don’t understand it yet :/ please
Fofino [41]

Answer:

first blank 39, second 9/39 i think, and third 351

Step-by-step explanation:

i haven't done something like this in a long time so i dont know if its completely correct or correct at all

8 0
2 years ago
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The lifetime X (in hundreds of hours) of a certain type of vacuum tube has a Weibull distribution with parameters α = 2 and β =
stich3 [128]

I'm assuming \alpha is the shape parameter and \beta is the scale parameter. Then the PDF is

f_X(x)=\begin{cases}\dfrac29xe^{-x^2/9}&\text{for }x\ge0\\\\0&\text{otherwise}\end{cases}

a. The expectation is

E[X]=\displaystyle\int_{-\infty}^\infty xf_X(x)\,\mathrm dx=\frac29\int_0^\infty x^2e^{-x^2/9}\,\mathrm dx

To compute this integral, recall the definition of the Gamma function,

\Gamma(x)=\displaystyle\int_0^\infty t^{x-1}e^{-t}\,\mathrm dt

For this particular integral, first integrate by parts, taking

u=x\implies\mathrm du=\mathrm dx

\mathrm dv=xe^{-x^2/9}\,\mathrm dx\implies v=-\dfrac92e^{-x^2/9}

E[X]=\displaystyle-xe^{-x^2/9}\bigg|_0^\infty+\int_0^\infty e^{-x^2/9}\,\mathrm x

E[X]=\displaystyle\int_0^\infty e^{-x^2/9}\,\mathrm dx

Substitute x=3y^{1/2}, so that \mathrm dx=\dfrac32y^{-1/2}\,\mathrm dy:

E[X]=\displaystyle\frac32\int_0^\infty y^{-1/2}e^{-y}\,\mathrm dy

\boxed{E[X]=\dfrac32\Gamma\left(\dfrac12\right)=\dfrac{3\sqrt\pi}2\approx2.659}

The variance is

\mathrm{Var}[X]=E[(X-E[X])^2]=E[X^2-2XE[X]+E[X]^2]=E[X^2]-E[X]^2

The second moment is

E[X^2]=\displaystyle\int_{-\infty}^\infty x^2f_X(x)\,\mathrm dx=\frac29\int_0^\infty x^3e^{-x^2/9}\,\mathrm dx

Integrate by parts, taking

u=x^2\implies\mathrm du=2x\,\mathrm dx

\mathrm dv=xe^{-x^2/9}\,\mathrm dx\implies v=-\dfrac92e^{-x^2/9}

E[X^2]=\displaystyle-x^2e^{-x^2/9}\bigg|_0^\infty+2\int_0^\infty xe^{-x^2/9}\,\mathrm dx

E[X^2]=\displaystyle2\int_0^\infty xe^{-x^2/9}\,\mathrm dx

Substitute x=3y^{1/2} again to get

E[X^2]=\displaystyle9\int_0^\infty e^{-y}\,\mathrm dy=9

Then the variance is

\mathrm{Var}[X]=9-E[X]^2

\boxed{\mathrm{Var}[X]=9-\dfrac94\pi\approx1.931}

b. The probability that X\le3 is

P(X\le 3)=\displaystyle\int_{-\infty}^3f_X(x)\,\mathrm dx=\frac29\int_0^3xe^{-x^2/9}\,\mathrm dx

which can be handled with the same substitution used in part (a). We get

\boxed{P(X\le 3)=\dfrac{e-1}e\approx0.632}

c. Same procedure as in (b). We have

P(1\le X\le3)=P(X\le3)-P(X\le1)

and

P(X\le1)=\displaystyle\int_{-\infty}^1f_X(x)\,\mathrm dx=\frac29\int_0^1xe^{-x^2/9}\,\mathrm dx=\frac{e^{1/9}-1}{e^{1/9}}

Then

\boxed{P(1\le X\le3)=\dfrac{e^{8/9}-1}e\approx0.527}

7 0
3 years ago
Suppose that lithium calculator battery with a charge of 3 volts, actually has a voltage with uniform distribution between 2.93
Dmitrij [34]

Answer:

b. E(X) = 3.015, STDEV(X)= 0.049, P (X ≤ 2.98) = 0.2941

Step-by-step explanation:

An uniform probability is a case of probability in which each outcome is equally as likely.

For this situation, we have a lower limit of the distribution that we call a and an upper limit that we call b.

The mean of the uniform probability distribution is:

M = \frac{a + b}{2}

The standard deviation of the uniform distribution is:

S = \sqrt{\frac{(b-a)^{2}}{12}}

The probability that we find a value X lower than x is given by the following formula.

P(X \leq x) = \frac{x - a}{b-a}

Uniform distribution between 2.93 and 3.1 volts

This means that a = 2.93, b = 3.1. So

Mean:

M = \frac{2.93 + 3.1}{2} = 3.015

Standard deviation:

S = \sqrt{\frac{(3.1 - 2.93)^{2}}{12}} = 0.049

What is the probability that a battery has a voltage less than 2.98?

P(X \leq 2.98) = \frac{2.98 - 2.93}{3.1 - 2.93} = 0.2941

So the correct answer is:

b. E(X) = 3.015, STDEV(X)= 0.049, P (X ≤ 2.98) = 0.2941

6 0
3 years ago
Does anyone know this??
HACTEHA [7]
Answer: 0.34

Explanation: First, you add all of the probabilities together to find the total probability when Dr. Green is missing. (You will get 0.66.) Next, you will need to subtract this from 1.00. 1 - 0.66 = 0.34. 0.34 is your final answer.
8 0
2 years ago
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If a cone shaped vase can hold 45 cubic centimeter of water and has a radius of 2 centimeters what is the height of the vase use
xz_007 [3.2K]

Answer:

The height of the vase is h=10.75\ cm

Step-by-step explanation:

we know that

The volume of a cone is equal to

V=\frac{1}{3}\pi r^{2} h

we have

V=45\ cm^{3}

r=2\ cm

\pi =3.14

substitute and solve for h

45=\frac{1}{3}(3.14)(2)^{2} h

135=(3.14)(4)h

135=12.56h

h=135/12.56

h=10.75\ cm

3 0
3 years ago
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