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densk [106]
3 years ago
14

I have the formula A fraction • π r^2

Mathematics
1 answer:
MatroZZZ [7]3 years ago
4 0

Answer:

22.2 ft²

Step-by-step explanation:

The area (A) of a sector is calculated as

A = area of circle × fraction of circle

  = πr² × \frac{50}{360}

  = π × 7.13² × \frac{5}{36}

  = \frac{7.13^2(5)\pi }{36} ≈ 22.2 ft² ( nearest tenth )

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The concentration of particles in a suspension is 50 per mL. A 5 mL volume of the suspension is withdrawn. a. What is the probab
kolezko [41]

Answer:

(a) 0.6579

(b) 0.2961

(c) 0.3108

(d) 240

Step-by-step explanation:

The random variable <em>X</em> can be defined as the number of particles in a suspension.

The concentration of particles in a suspension is 50 per ml.

Then in 5 mL volume of the suspension the number of particles will be,

5 × 50 = 250.

The random variable <em>X</em> thus follows a Poisson distribution with parameter, <em>λ</em> = 250.

The Poisson distribution with parameter λ, can be approximated by the Normal distribution, when λ is large say λ > 10.  

The mean of the approximated distribution of X is:

μ = λ  = 250

The standard deviation of the approximated distribution of X is:

σ = √λ  = √250 = 15.8114

Thus, X\sim N(250, 250)

(a)

Compute the probability that the number of particles withdrawn will be between 235 and 265 as follows:

P(235

                             =P(-0.95

Thus, the value of P (235 < <em>X</em> < 265) = 0.6579.

(b)

Compute the probability that the average number of particles per mL in the withdrawn sample is between 48 and 52 as follows:

P(48

                             =P(-0.28

Thus, the value of P(48.

(c)

A 10 mL sample is withdrawn.

Compute the probability that the average number of particles per mL in the withdrawn sample is between 48 and 52 as follows:

P(48

                             =P(-0.40

Thus, the value of P(48.

(d)

Let the sample size be <em>n</em>.

P(48

                             0.95=P(-z

The value of <em>z</em> for this probability is,

<em>z</em> = 1.96

Compute the value of <em>n</em> as follows:

z=\frac{\bar X-\mu}{\sigma/\sqrt{n}}\\\\1.96=\frac{48-50}{15.8114/\sqrt{n}}\\\\n=[\frac{1.96\times 15.8114}{48-50}]^{2}\\\\n=240.1004\\\\n\approx 241

Thus, the sample selected must be of size 240.

5 0
3 years ago
Will mark BRAINLIEST !
Neko [114]

Step-by-step explanation:

if u like this answer plz mark as brainlist

8 0
3 years ago
Read 2 more answers
Can somebody please answer all of these questions and only if u know how to do this!!! Thanks
aliina [53]

Hi again I helped you on your last question, I love helping people. Anyway here's the answer!

16. 0.188 rounded nearest hundredth = 0.19

17.  0.455 rounded nearest hundredth = 0.46

18. 0.538 rounded nearest hundredth = 0.54

19. 0.417 rounded nearest hundredth = 0.42

20. 2.833 rounded nearest hundredth = 2.83

21. 3.667 rounded nearest hundredth = 3.67

4 0
3 years ago
A pack of 8 batteries cost 4.72!What is cost per battery?
Mrrafil [7]
4.72 x 1 = 4.72
8 x X =8x
We need to let the X alone so
4.72 divided 8 = 0.59
1 battery = 0.59
8 0
2 years ago
Solve for x -16 = 8x/5
11111nata11111 [884]

Answer:

x=-26 2/3

Step-by-step explanation:

Make sure you have a negative in front of the mixed fraction.

6 0
3 years ago
Read 2 more answers
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