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Anvisha [2.4K]
3 years ago
11

a cube is 6.75 cm on each side. Using the formula volume = (length of a side)^3, and 1 inch = 2.54 cm, determine the volume of t

he cube in cubic feet.
Mathematics
1 answer:
andriy [413]3 years ago
7 0
The volume of a cube is then (6.75cm)^3. Here the units are cubic centimeters or cm^3. Since there are 2.54 cm in 1 inch [exact] and 12 inches in 1 foot, the volume of the cube is (6.75 cm)^3 * (1 inch/2.54cm)^3 * (1 ft/12 inch)^3. 0.01086 ft^3 is your answer
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(43 points) In the US, 85% of the population has Rh positive blood. Suppose we take a random sample of 6 persons and let Y denot
VladimirAG [237]

Answer:

a) Binomial distribution with parameters p=0.85 q=0.15 n=6

b) 62.29%

c) 2.38%

d) See explanation below

Step-by-step explanation:

a)

We could model this situation with a binomial distribution

P(6;k)=\binom{6}{k}p^kq^{6-k}

where P(6;k) is the probability of finding exactly k people out of 6 with Rh positive, p is the probability of finding one person with Rh positive and q=(1-p) the probability of finding a person with no Rh.

So

\bf P(Y=k)=\binom{6}{k}(0.85)^k(0.15)^{6-k}

b)  

The probability that Y is less than 6 is

P(Y=0)+P(Y=1)+...+P(Y=5)

Let's compute each of these terms

P(Y=0)=P(6;0)=\binom{6}{0}(0.85)^0(0.15)^{6}=1.139*10^{-5}

P(Y=1)=P(6;1)=\binom{6}{1}(0.85)^1(0.15)^{5}=0.0000387281

P(Y=2)=P(6;2)=\binom{6}{2}(0.85)^2(0.15)^{4}=0.005486484

P(Y=3)=P(6;3)=\binom{6}{3}(0.85)^3(0.15)^{3}=0.041453438

P(Y=4)=P(6;4)=\binom{6}{4}(0.85)^4(0.15)^{2}=0.176177109

P(Y=5)=P(6;5)=\binom{6}{5}(0.85)^5(0.15)^{1}=0.399334781

and adding up these values we have that the probability that Y is less than 6 is

\sum_{i=1}^{5}P(Y=i)=0.622850484\approx 0.6229=62.29\%

c)

In this case is a binomial distribution with n=200 instead of 6.

p and q remain the same.

The mean of this sample would be 85% of 200 = 170.  

In a binomial distribution, the standard deviation is  

s = \sqrt{npq}

In this case  

\sqrt{200(0.85)(0.15)}=5.05

<em>Let's approximate the distribution with a normal distribution with mean 170 and standard deviation 5.05</em>

So, the approximate probability that there are fewer than 160 persons with Rh positive blood in a sample of 200 would be the area under the normal curve to the left of 160

(see picture attached)

We can compute that area with a computer and find it is  

0.0238 or 2.38%

d)<em> In order to approximate a binomial distribution with a normal distribution we need a large sample like the one taken in c).</em>

In general, we can do this if the sample of size n the following inequalities hold:

np\geq 5 \;and\;nq \geq 5

in our case np = 200*0.85 = 170 and nq = 200*0.15 = 30

4 0
3 years ago
The area of a square mural pointed on the side of a building is 110 square feet. What is the best estimate of the side length of
natka813 [3]

Answer:

C

Step-by-step explanation:

Area of a square equals to the square of its side, therefor the side of a given area for a square is the square root of the area.

A = a^{2}\\a = \sqrt{A}\\a = \sqrt{110} = 10.48 ft

8 0
3 years ago
What are the factors in the expression 6(x+5)
madreJ [45]
The answer is 30+6x you would just multiply 6 by 5 then put 6 next to x.
8 0
3 years ago
What is the perimeter of rhombus LMNO? 20 units 24 units 40 units 48 units
NeTakaya
The little lines on each side of the rhombus mean that all the sides are the same length.

We can set line LM and MN equal to solve for X, then we can solve the length of a side.

3x-3 = x+7

Add 3 to each side:
3x = x +10

Subtract x from each side:

2x = 10

Divide both sides by 2:
x = 10/2
x = 5

Now we have the value for x, replace x in one of the side formulas:

x +7 = 5+7 = 12

Each side = 12 units.

 The perimeter would be 12 + 12 + 12 + 12 = 48 units.



3 0
3 years ago
Read 2 more answers
If a 50 ft flagpole casts a 95 ft shadow, then how long is the shadow that a 5 ft tall of man casts ?
lesantik [10]

9.5 feet,to find that you must find out how many times longer the shadow of the pole is than the pole, and to do that you must divide 95 by 50, in which you get 1.9. And then to find the length of the shadow the man casts you must multiply his height by 1.9.

8 0
3 years ago
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