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Contact [7]
3 years ago
11

Evaluate: 2^-2 x (13x3)-5^3

Mathematics
2 answers:
Lapatulllka [165]3 years ago
6 0

2^-2 x (13x3)-5^3

1/ (2^2) * 39 - 125

1/4 *39 -125

39/4 -125

9 3/4 - 125

factor out -1

- (125-9 3/4)

borrow to subtract the fraction

- (124 4/4 - 9 3/4)

- (115 1/4)

-115 1/4

Rainbow [258]3 years ago
3 0

Answer:

-115.25

2^-2 x (13x3)-5^3

2^-2 x (39)- 5^3

2^-2 x (39)- 125

0.25 x (39) - 125

9.75 - 125

-115.25




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2 years ago
A population of values has a normal distribution with μ = 202.1 and σ = 24 . You intend to draw a random sample of size n = 64 .
n200080 [17]

Answer: p= 0.0532

Step-by-step explanation: from the question

u= population mean = 202.1

σ= population standard deviation = 24

n = sample size = 64.

Since the sample size is greater than 30 and the population standard deviation is known, then the z score is the appropriate to get the probabilistic value.

Z = (x - u) /(σ/√n)

Where x = sample mean.

At x = 204.5, we have the z score as

Z = 204.5 - 202.1/ (24/√64)

Z = 2.4/ (24/8)

Z = 2.4/ 3

Z = 0.8

At x = 205.1, we have the z score as

Z = 205.1 - 202.1/ (24/√64)

Z = 3/ (24/8)

Z = 3/3

Z = 1.

Since the distribution is normal, we compute the probability value attached to the z score using the z table.

Graphical illustration as attachment in the answer.

Note the area under the z score is the probability value of the z score.

As we can see, the area to the left of the shaded area is a, the shaded area is b and the area to the right of the shaded area is c

We have that

a + b + c = 1

Note, the table I'm using only gives area to the left of the distribution.

Area a

To get area a, we use a z score table whose area is to the left of the distribution.

At 0.8, according to the table the area left of 0.8 is 0.78814.

Area c

Area c is right of the distribution and our table is left of the distribution, but 1 - area to the left = area to the right ( since area to left + area to right =1).

Hence area to the left of 1.0 = 0.84134

Area c = 1 - 0.84134 = 0.15866.

Thus, a = 0.78814, c = 0.15866

a + b + c = 1

0.78814 + b + 0.15866 = 1

0.9468 + b = 1

b = 1 - 0.9468

b = 0.0532.

Hence the probability of random variable between 204.5 & 205.1 is 0.0532

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3 years ago
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Answer:

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Step-by-step explanation:

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3 years ago
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