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Arturiano [62]
2 years ago
5

A manufacturing process produces bags of cookies. The distribution of content weights of these bags is Normal with mean 15.0 oz

and standard deviation 1.0 oz. We will randomly select n bags of cookies and weigh the contents of each bag selected. How many bags should be selected so that the standard deviation of the sample mean is 0.1 ounces?
a. 8 bags
b. 10 bags
c. 64 bags
d. 100 bags
Mathematics
1 answer:
NeTakaya2 years ago
4 0

Answer:

100 bags

Step-by-step explanation:

S.E = σ/ √n

0.1 = 1 / √n

Square both sides

0.1² = 1² / n

0.01 = 1 / n

0.01n = 1

n = 1 / 0.01

n = 100

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Determine the number of possible outcomes when tossing one coin ,two coins ,and three coins then determine the number of possibl
m_a_m_a [10]

Number of possible outcome for tossing N coins = 2^N

Solution:

Possible outcomes when tossing one coin = {H, T}

Number of possible outcomes when tossing one coin = 2 =2^1

Possible outcomes when tossing two coins = {HH, HT, TH, TT}

Number of possible outcomes when tossing two coins = 4 =2^2

Possible outcomes when tossing three coins

                                 = {HHH, HHT, HTH, THH, TTH, THT, HTT, TTT}

Number of possible outcomes when tossing three coins = 8 =2^3

Therefore, the sequence obtained is 2^1, 2^2, 2^3.

If continue this sequence, we can obtain number of possible outcome for tossing N coins is 2^N.

7 0
2 years ago
The base of an aquarium with given volume V is made of slate and the sides are made of glass. If the slate costs seven times as
Olin [163]

Answer:

x = ∛(2V/7)

y = ∛(2V/7)

z = 3.5 [∛(2V/7)]

{x,y,z} = { ∛(2V/7), ∛(2V/7), 3.5[∛(2V/7)] }

Step-by-step explanation:

The aquarium is a cuboid open at the top.

Let the dimensions of the base of the aquarium be x and y.

The height of the aquarium is then z.

The volume of the aquarium is then

V = xyz

Area of the base of the aquarium = xy

Area of the other faces = 2xz + 2yz

The problem is to now minimize the value of the cost function.

The cost of the area of the base per area is seven times the cost of any other face per area.

With the right assumption that the cost of the other faces per area is 1 currency units, then, the cost of the base of the aquarium per area would then be 7 currency units.

Cost of the base of the aquarium = 7xy

cost of the other faces = 2xz + 2yz

Total cost function = 7xy + 2xz + 2yz

C(x,y,z) = 7xy + 2xz + 2yz

We're to minimize this function subject to the constraint that

xyz = V

The constraint can be rewritten as

xyz - V = 0

Using Lagrange multiplier, we then write the equation in Lagrange form

Lagrange function = Function - λ(constraint)

where λ = Lagrange factor, which can be a function of x, y and z

L(x,y,z) = 7xy + 2xz + 2yz - λ(xyz - V)

We then take the partial derivatives of the Lagrange function with respect to x, y, z and λ. Because these are turning points and at the turning point, each of the partial derivatives is equal to 0.

(∂L/∂x) = 7y + 2z - λyz = 0

λ = (7y + 2z)/yz = (7/z) + (2/y) (eqn 1)

(∂L/∂y) = 7x + 2z - λxz = 0

λ = (7x + 2z)/xz = (7/z) + (2/x) (eqn 2)

(∂L/∂z) = 2x + 2y - λxy = 0

λ = (2x + 2y)/xy = (2/y) + (2/x) (eqn 3)

(∂L/∂λ) = xyz - V = 0

We can then equate the values of λ from the first 3 partial derivatives and solve for the values of x, y and z

(eqn 1) = (eqn 2)

(7/z) + (2/y) = (7/z) + (2/x)

(2/y) = (2/x)

y = x

Also,

(eqn 1) = (eqn 3)

(7/z) + (2/x) = (2/y) + (2/x)

(7/z) = (2/y)

z = (7y/2)

Hence, at the point where the box has minimal area,

y = x,

z = (7y/2) = (7x/2)

We can then substitute those into the constraint equation for y and z

xyz = V

x(x)(7x/2) = V

(7x³/2) = V

x³ = (2V/7)

x = ∛(2V/7)

y = x = ∛(2V/7)

z = (7x/2) = 3.5 [∛(2V/7)]

The values of x, y and z in terms of the volume that minimizes the cost function are

{x,y,z} = {∛(2V/7), ∛(2V/7), 3.5[∛(2V/7)]}

Hope this Helps!!!

7 0
3 years ago
What is 6.23 million written in scientific notation?
taurus [48]

Answer:

6.23*10^6

Step-by-step explanation:

We first write the answer in full notation 6,230,000.

Then we count how many decimal places it takes before we have one leading digit. Since it is six, we move the decimal place and write 6.23*10^6

7 0
2 years ago
What’s 6.5 inches times 4?
wolverine [178]

Answer:

your answer is 26 inches

8 0
2 years ago
Read 2 more answers
36.24 divided by 9.06 is equal to<br><br> i need step by step
Bezzdna [24]

Answer:

4

Step-by-step explanation:

if 36.24 is divided by 90.6 can be 9.06

36.24÷9.06

4

or by other style

36.24×100=3624

90.6×100= 9060

according to the question

36.24÷90.6 or 3624÷9060

=4 or 0.4

3 0
2 years ago
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