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3 years ago

Jack has two more than half as many cups as

Mathematics

1 answer:

Rufina [12.5K]3 years ago

4 0

Step-by-step explanation:

$(x \div 2 + 2) + \frac{(x \div 2 + 2)}{2} + x$

its hard to determine without the known value of x, but the above would be the equation needed to solve it if you knew what x was

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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

State the domain and the range of each relation. Then determine whether the relation is a function.

IrinaVladis [17]

Answer:

$Domain:$ { $-6,3,4$ }

$Range:$ { $-2,5,6,23$ }

The relation is not a function.

Step-by-step explanation:

By definition, a relation is a function if each input value has only one output value.

Given the relation:

(4,23)

(3,-2)

(-6,5)

(4,6)

The domain is the set of the x-coordinates of each ordered pair (You do not need to write 4 twice):

$Domain:$ { $-6,3,4$ }

The range is the set of the y-coordinates of each ordered pair :

$Range:$ { $-2,5,6,23$ }

Since the input value 4 has two different output values (23 and 6), the relation is not a function.

8 0

3 years ago

Read 2 more answers

(3t^2+1)-t^2. How do you do this equation and what’s the answer. Algebra 1.

Oksana_A [137]

2t^2+1

Subtract t^2 from 3t^2 you get 2t^2

which is 2t^2+1 answer

3 0

3 years ago

1/2b+9/4=7/4 solve the equation

AlladinOne [14]

First subtract 9/4 from each side

1/2b=-2/4

Simplify the 2/4

1/2b=-1/2

Divide each side by 1/2

b = -1

4 0

3 years ago

Help me!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

ahrayia [7]

Answer:

9. x=-6, y=0

10. x=-9, y=-10

11. x=3, y=-1

Step-by-step explanation:

$2x-9y=-12\\3x+18y=-18$

Multiply the first equation by 2.

$4x-18y=-24\\3x+18y=-18$

Add the equations.

$7x=-42$

$x=-6$

We figured out x now we have to figure out y. To figure out y plug in x into any equation.

$2(-6)-9y=-12$

$-12-9y=-12$

$-9y=0$

$y=0$

Your answer is x = -6 and y = 0 for number nine.

$6x+3y=24\\2x+3y=-12$

Change the signs of the second equation becuase 3y and 3y are both positive. We need one of them to be negative.

$6x+3y=24\\-2x-3y=12$

Add them.

$4x = 36$

$x=9$

Now we have to figure out y.

$2(9)+3y=-12$

$18+3y=-12$

$3y=-30$

$y=-10$

x=-9 and y=-10 is your answer to number ten.

$10x+5y=25\\-7x-3y=-18$

$30x+15y=75\\-35x-15y=-90$

$-5x=-15$

$x=3$

$-7(3)-3y=-18$

$-21-3y=-18$

$-3y=3$

$y=-1$

x=3 and y=-1 is the answer to number eleven. I hope this helps! Let me know if I got anything wrong.

4 0

2 years ago

Read 2 more answers