If y = 0.5x + 1 and x = 2, what Is y?

Answer:

a) 75%.

b) 84%

c) Within 2 standard deviations from the mean is 95%. The normal distribution has a higher percentage of observations closer to the mean than a non normal distribution, so this percentage is larger.

Step-by-step explanation:

Empirical Rule:

The Empirical Rule states that, for a normally distributed random variable:

Approximately 68% of the measures are within 1 standard deviation of the mean.

Approximately 95% of the measures are within 2 standard deviations of the mean.

Approximately 99.7% of the measures are within 3 standard deviations of the mean.

Chebyshev Theorem:

The Chebyshev Theorem can also be applied to non-normal distribution. It states that:

At least 75% of the measures are within 2 standard deviations of the mean.

At least 89% of the measures are within 3 standard deviations of the mean.

An in general terms, the percentage of measures within k standard deviations of the mean is given by [tex]100(1 - \frac{1}{k^{2}})[/tex].

In this question:

Mean: 6.3 hours

Standard deviation: 1.6 hours

(a) Use Chebyshev's theorem to calculate the minimum percentage of individuals who sleep between 3.1 and 9.5 hours.

3.1 = 6.3 - 2*1.6

9.5 = 6.3 + 2*1.6

Within 2 standard deviations, so the minimum percentage is 75%.

(b) Use Chebyshev's theorem to calculate the minimum percentage of individuals who sleep between 2.3 and 10.3 hours.

How many standard deviations from the mean?

One standard deviation is 1.6

These measures are 10.3 = 6.3 = 6.3 - 2.3 = 4. This is k standard deviations, in which

[tex]k = \frac{4}{1.6} = 2.5[/tex]

The minimum percentage is:

[tex]100(1 - \frac{1}{k^{2}}) - 100(1 - \frac{1}{2.5^{2}}) = 84%[/tex]

So 84%.

(c) Assume that the number of hours of sleep follows a bell-shaped distribution. Use the empirical rule to calculate the percentage of individuals who sleep between 3.1 and 9.5 hours per day.

Within 2 standard deviations from the mean is 95%. The normal distribution has a higher percentage of observations closer to the mean than a non normal distribution, so this percentage is larger.

Answer:

Length of arc AD = 15.7 cm

Step-by-step explanation:

Length of arc = [tex]\frac{\theta}{360}(2\pi r)[/tex]

Here, θ = Central angle subtended by the arc

r = radius of the circle

From the picture attached,

Central angle subtended by arc AD = 360° - (180° + 66.4°)

                                                            = 113.6°

Length of arc AD = [tex]\frac{(113.6)}{360}(2\pi )(7.9)[/tex]

                             = [tex]\frac{113.6}{360}(2)(3.14)(7.9)[/tex]

                             = 15.655 cm

                             ≈ 15.7 cm

Length of arc AD = 15.7 cm

Answer:

12.4

Step-by-step explanation:

Just did it.

Answer:

yes

Step-by-step explanation:

2 + 16(1) = 18

2+16 = 18

2(2) + 11(1) = 15

4+11=15

Answer:

37.5

Step-by-step explanation:

If 50 apples cost 25 then all you need to do is 25 x 1.5 = 37.5

And we know this is correct because 25 divided by 2 is 12.5.

so 12.5 is how much for 25 apples and if you multiply 25 times 3 it is equal to 75 so you need to mutliply 12.5 times 3.

12.5 x 3 = 37.5

Answer:

square pyramid

Step-by-step explanation:

Answer:

star

Step-by-step explanation:

Answer:

The value of 1 is tens =) i hope i help u

Answer:

A

Step-by-step explanation:

2.5 x 3.4 = 8.5

Answer:

96 people

Step-by-step explanation:

i used a calculator

Answer:

[tex]3a(3a - 2)[/tex]

Step-by-step explanation:

[tex]3(3a ^{2} - 2a) \\a(3a - 2) [/tex]

Answer:

the answer is 36

Step-by-step explanation:

beacuse if we use the pythagorean theorem for 9 and 12 we get 15 which means that the perimeter is P=9+15+12=36

Answer:

0.237/3.5

Step-by-step explanation:

In order to rite 237 m as a fraction of 3.5 km, 237m must be in the same unit as 3.5km

it is necessary to convert, 237m to km

1000m = 1 km

so 237m = 237/1000= 0.237

0.237/3.5

Answer:

That is wrong bc it says quotient and quotient means a division sign which i dont see on your answer,

Step-by-step explanation:

The correct answer should be...

3/2x

Im srry if wrong (and the "/" means division)

Answer:

Step-⚫️_by-step explanation:

Answer- y = - x/2 + 5

Step by step - Replace f (x) with y.

Y = - 2x + 10

Interchange the variables.

x= -2y + 10

Solve for y.

Y= x/2 +5

Answer: The answer is C

Step-by-step explanation:

C is the answer because the base is +2 and the coefficent  is  1/2 which is rise over run so you go up one space and to the right two spaces.          

Answer:

≈3.99938

Step-by-step explanation:

Answer:

yes, yes, no, no

Step-by-step explanation:

Answer:

3/8

Step-by-step explanation:

Answer:

2.5 half-lives

Step-by-step explanation:

Find [tex]t_{h}[/tex] in [tex]N(t)=N_{0}e^{-kt}[/tex] given [tex]N(t) = 2, N_{0} =64,t=\frac{25}{2}[/tex]

[tex]N(t)[/tex] is the amount after the time [tex]t[/tex], [tex]N_0[/tex] `is the initial amount, [tex]t_{h}[/tex] is the half-life

We know that after half-life there will be twice less the initial quantity:

[tex]N(t_{h})=\frac{N_{0} }{2}=N_{0}e^{kt_{h} }[/tex].

Simplifying gives [tex]\frac{1}{2} =e^{-kt_h} or k = -\frac{In(\frac{1}{2}) }{t_{h} } .[/tex]

Plugging this into the initial equation, we obtain that [tex]N(t)=N_{0}e^\frac{In(\frac{1}{2}) }{t_{h} }[/tex]or [tex]N(t)= N_{0} (\frac{1}{2})^\frac{t}{t_h}.[/tex]

Finally, just plug in the given values and find the unknown one.

From [tex]2=64(\frac{1}{2})^\frac{\frac{25}{2} }{t_h}[/tex], we have that [tex]t_h[/tex] = [tex]\frac{25 In (2)}{2 In (32)\\}[/tex]

So you should get: [tex]t_{h} =\frac{25 In (2)}{2 In (32)\\}=2.5.[/tex]

The number of half-lives that transpired during this time period is equal to 2.5 hours.

Given the following data:

Time = 12.5 hours.

Initial mass = 64 grams.

Remaining mass = 2.0 grams.

Mathematically, the amount of a radiocative element that is remaining after time (t-hours) is given by this formula:

[tex]ln(\frac{A}{A_0} )=ln(\frac{1}{2} )\frac{t}{H}[/tex]

Where:

Substituting the given parameters into the formula, we have;

ln(2/64) = ln(1/2) × 12.5/H

-3.466 = -0.693 × 12.5/H

H = 12.5 × -0.693/-3.466

H = 12.5 × 0.1999

H = 2.5 hours.

Read more on half-life here: https://brainly.com/question/25750315

Answer:

Her friend got the better deal.

Step-by-step explanation:

For Jillians equation look at

$22.56/4 = $6.39 per CD

For her friends equation look at

$18.45/3 = $6.15 per CD

Jillian's friend got the better deal because she paid less per CD as shown in the equations above.

Answer:

88.2 is your answer.

Answer:500

Step-by-step explanation:on delta math

Answer: c is the answer

Step-by-step explanation: the formuals for volume is length x width x height, 6x7x5, which is 210

Answer: C

Step-by-step explanation: Easy, just do length x width x height(l x w h). So, 6x7x5 = 210

Answer:

Answer as a fraction: 4/15

Answer as a decimal: 0.267

The decimal version is approximate rounded to three decimal places.

Step-by-step explanation:

6 apples, 4 peaches

6+4 = 10 pieces of fruit total

The probability of picking an apple is 6/10 = 3/5

After you pick and eat the apple, there are 10-1 = 9 pieces of fruit left. Also, the probability of picking a peach is 4/9, as there are 4 peaches out of 9 fruit left over.

Multiply out 3/5 and 4/9 to get (3/5)*(4/9) = (3*4)/(5*9) = 12/45 = 4/15

Using a calculator, 4/15 = 0.267 approximately.

Answer:

15

Step-by-step explanation:

a:b::c:d

a/b=c/d .......(eq 1)

let a=0.2, b=0.5, c=6, d=x

Not put values in eq 1

0.2/0.5 = 6/a

By cross multiplication we get:

0.2xa = 6x0.5

0.2a = 3

Dividing by 0.2 on both sides we get

0.2a/0.2 = 3/0.2

a = 15

Therefore The fourth proportional is 15

Answer:

two solutions work: x = 5 + [tex]\sqrt{19}[/tex] and x = 5 - [tex]\sqrt{19}[/tex]

Step-by-step explanation:

x + 6 ( 1/x ) = 10

x^2 + 6 = 10x

x^2 - 10x + 6 = 0

x = 5 + [tex]\sqrt{19}[/tex], 5 - [tex]\sqrt{19}[/tex]