Which of the following is true for a circle that has an area of approximately 113 square feet?

a
The diameter is 6 feet and the circumference is 38 square feet.
b
The radius is 6 feet and the circumference is 38 square feet.
c
The diameter is 6 feet and the circumference is 38 feet.
d
The radius is 6 feet and the circumference is 38 feet.

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:

≈3.99938

Step-by-step explanation:

The scatterplot demonstrates the strongest relationship is, a graph has x on the x-axis, and y on the y-axis. Points increase loosely together.

The correlation coefficient of scatterplot is used to demonstrate the relationship between variables.

When two variables increases together, they are said to have positive correlation.

When one is increasing and another is decreasing, they are said to have negative correlation.

When most of  data points form a straight line or lies close to the straight line, it indicates strong linear correlation.

From the given options;

Option A, zero correlation

Option B, less than 1

Option C, 1 or greater than 1

Option D, -1 or less than 1

Thus, the scatterplot demonstrates the strongest relationship between two quantitative variables is option C, "a graph has x on the x-axis, and y on the y-axis. Points increase loosely together".

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#SPJ2

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:

3/8

Step-by-step explanation:

Answer:

x=−2, 2.6666

Step-by-step explanation:

Let's solve your equation step-by-step.

4=(1/2(2x+4+x))(x−2)

Step 1: Simplify both sides of the equation.

4=3/2 x2−x−4

Step 2: Subtract 3/2x^2-x-4 from both sides.

4−(3/2 x2−x−4)=

3/2 x2−x−4−(3/2 x2−x−4)

−3/2 x2 +x+8=0

For this equation: a=-1.5, b=1, c=8

−1.5x2+1x+8=0

Step 3: Use quadratic formula with a=-1.5, b=1, c=8.

x=−b±√b2−4ac

2a

x=−(1)±√(1)2−4(−1.5)(8)

2(−1.5)

x=−1±√49

−3

x=−2,2.66666666666666666666666666666

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]

Answer:

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

Step-by-step explanation:

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

Answer:

yes

Step-by-step explanation:

2 + 16(1) = 18

2+16 = 18

2(2) + 11(1) = 15

4+11=15

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:

square pyramid

Step-by-step explanation:

Answer:

star

Step-by-step explanation:

Answer:

Stratified sampling

Step-by-step explanation:

key word "groups"

The sampling scheme did she used is stratified sampling.

It is a method of sampling where the division of the population should be split into the smaller subgroup called a strata. The strata should be created depending upon on the members shared like the income etc. Here the sample should be needed for applicants for across the US also it randomly selects the applicants for each state.

So, The sampling scheme did she used is stratified sampling.

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Answer:

2

Step-by-step explanation:

It's the smallest one.

Answer:

96 people

Step-by-step explanation:

i used a calculator

Answer:

Step-⚫️_by-step explanation:

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:

1: 7/10

2: 3/10

3: 4/8 (2/4 or 1/2 if you need to simplify it)

Step-by-step explanation:

1: Convert 2/5 to tenths by multiplying the denominator and numerator by two. 3/10 plus 4/10 is 7/10

2: Convert 4/5 and 1/2 to tenths.

4/5 is going to be 8/10, 1/2 is going to be 5/10.

Subtract 5/10 from 8/10 to get 3/10

3: Convert 1/4 to eighths to get 2/8. Then add 2/8 and 2/8 to get 4/8.

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:

B

Step-by-step explanation:

√c^2-b^2

√15^2-9^2

√225-81

√144

= 12

B

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:

yes, yes, no, no

Step-by-step explanation:

Answer:

There are 479,001,600 arrangments of 12 distinct items.

Step-by-step explanation:

Arrangements of n items:

The number of possible arrangements of n itens is given by the factorial of n, that is:

[tex]A_{n} = n![/tex]

12 items:

[tex]A_{12} = 12! = 479001600[/tex]

There are 479,001,600 arrangments of 12 distinct items.

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:

88.2 is your answer.

Answer:500

Step-by-step explanation:on delta math

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.

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