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Anna007 [38]
2 years ago
14

What is the surface area of this right rectangular prism glass slab with dimensions of 20 inches by 3 inches by 12 inches?

Mathematics
1 answer:
Art [367]2 years ago
7 0

Answer:

C. 672

Step-by-step explanation:

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g A psychic was tested for extrasensory perception (ESP). The psychic was presented with cards face down and asked to determine
diamong [38]

Answer:

Step-by-step explanation:

Hello!

The objective is to test ESP, for this, a psychic was presented with cards face down and asked to determine if each of the cards was one of four symbols: a star, cross, circle, square.

Be X: number of times the psychic identifies the symbols on the cards correctly is a size n sample.

p the probability that the psychic identified the symbol on the cards correctly

You have to calculate the sample size n to estimate the proportion with a confidence level of 95% and a margin of error of d=0.01

The CI for the population proportion is constructed "sample proportion" ± "margin of error" Symbolically:

p' ± Z_{1-\alpha /2} * (\sqrt{\frac{p'(1-p')}{n} } )

Where  d= Z_{1-\alpha /2} * (\sqrt{\frac{p'(1-p')}{n} } ) is the margin of error. As you can see, the formula contains the sample proportion (it is normally symbolized p-hat, in this explanation I'll continue to symbolize it p'), you have to do the following consideration:

Every time the psychic has to identify a card he can make two choices:

"Success" he identifies the card correctly

"Failure" he does not identify the card correctly

If we assume that each symbol has the same probability of being chosen at random P(star)=P(cross)=P(circle)=P(square)= 1/4= 0.25

Let's say, for example, that the card has the star symbol.

The probability of identifying it correctly will be P(success)= P(star)= 1/4= 0.25

And the probability of not identifying it correctly will be P(failure)= P(cross) + P(circle) + P(square)= 1/4 + 1/4 + 1/4= 3/4= 0.75

So for this experiment, we'll assume the "worst case scenario" and use p'= 1/4 as the estimated probability of the psychic identifying the symbol on the card correctly.

The value of Z will be Z_{1-\alpha /2}= Z_{0.975}= 1.96

Now using the formula you have to clear the sample size:

d= Z_{1-\alpha /2} * (\sqrt{\frac{p'(1-p')}{n} } )

\frac{d}{Z_{1-\alpha /2}} = \sqrt{\frac{p'(1-p')}{n} }

(\frac{d}{Z_{1-\alpha /2}})^2 =\frac{p'(1-p')}{n}

n*(\frac{d}{Z_{1-\alpha /2}})^2 = p'(1-p')

n = p'(1-p')*(\frac{Z_{1-\alpha /2}}{d})^2

n = (0.25*0.75)*(\frac{1.96}{0.01})^2= 7203

To estimate p with a margin of error of 0.01 and a 95% confidence level you have to take a sample of 7203 cards.

I hope this helps!

5 0
3 years ago
Read 2 more answers
In which number does the 5 represent 5x 10,000?
lyudmila [28]
It would be 50,000, because 5*10,000=50,000.
6 0
3 years ago
Sally has twice as many dimes as nickels. The total value is $3.50 how many nickels and dimes does she have?
Murljashka [212]
D=2n
.05n+.1d=3.5
I multiplied the nickels and dimes by these values because that is their actual monetary value 
.05n=3.5-.1d
multiply everything by 20
n=70-2d
d/2=70-2d
.5d+2d=70 
2.5d=70
d=28 
n=14 
so there are <u>28 dimes and 14 nickels 
</u>
checking this answer 
28 dimes = $2.8
14 nickels = .70
2.8+.7=3.5

3 0
3 years ago
Read 2 more answers
What is 3 3/8 +3 1/2 using common denominator
horrorfan [7]
1/2=4/8. 3 and 4/8+ 3 and 3/8 is 6 and 7/8.
8 0
3 years ago
Read 2 more answers
Factorise fully 6ac + 10ac​
ikadub [295]

Step-by-step explanation:

6ac+10ac

2ac(6ac+10ac)

2ac(3+5)

4 0
3 years ago
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