By using words per sentence and characters per words, we can create formulas for the Flesch-Kincaid grade level readability. The readability statistics for random pages from a Harry Potter novel are given below.

Words/Sentence 15.7 9 16.3 14.5 9.7 7.4 14 16.1 13.9 12.5 17.2 11.5
Characters/Word 41 4.2 4.2 4.3 4.3 4.2 4.5 4.5 4.3 4 4.4 4.3
F-K Grade Level 5.2 3.7 6.1 4.9 4.4 3.2 5.6 6.9 5.7 4.1 6.7 4.4

What is the correct analysis statement for the coefficient of determination between words per sentence (x-variable) and characters per word (y-variable)?

a. 1.5% of the variance in characters per word is accounted for by words per sentence.
b. 8% of the variance in characters per word is accounted for by words per sentence.
c. 10% of the variance in characters per word is accounted for by words per sentence.
d. 31% of the variance in characters per word is accounted for by words per sentence.
e. None of these

Answers

Answer 1

Answer:

d. 31% of the variance in characters per word is accounted for by words per sentence.

Step-by-step explanation:

The coefficient of determination is the statistical measurement that determines the impact in difference of one variable which is explained by the difference in another variable. It is denoted by [tex]R^{2}[/tex] or R-squared. It helps in predicting the outcome of the event.


Related Questions

The distance between Ali's house and 1 point
college is exactly 135 miles. If she
drove 2/3 of the distance in 135
minutes. What was her average speed
in miles per hour?

Answers

First we have to figure out how long it would take for the full voyage and that would be 135 + (135 x 1/3) and the answer to that would be 135 + 45 = 180 and that means that 180 is the total minutes it would take to travel the whole trip, now we have to calculate average speed which would be 135(distance)/180(time) which would end up being 135 miles/ 3 hours, now we divide the entire equation by 3 which would be 45/1
CONCLUSION ——————————
Ali would be driving 45 miles per hour

Ali's average speed was 40 miles per hour.

What is an average speed?

The total distance traveled is to be divided by the total time consumed brings us the average speed.

How to calculate the average speed of Ali?

The total distance between the college from Ali's house is 135 miles.

She drove 2/3rd of the total distance in 135 minutes.

She drove =135*2/3miles

=90miles.

Ali can drive 90miles in 135 mins.

Therefore, her average speed is: 90*60/135 miles per hour.

=40 miles per hour.

Learn about average speed here :

https://brainly.in/question/14787217

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If the half-life of cesium-137 is 30 years, find the decay constant, r. (Round your answer to nine decimal places.)

Answers

Answer:

r = 0.023104906

Step-by-step explanation:

Given half life = T = 30 yrs.

Decay constant = r.

Using the decay constant formula:

[tex]r=\frac{\ln2}{T}\\r=\frac{\ln2}{30}\\r=0.023104906[/tex]

Learn more: https://brainly.com/question/1594198

Prove that if n is an integer, these four statements are equivalent: (i) n is even, (ii) n 1 is odd, (iii) 3n 1 is odd, (iv) 3n is even.

Answers

Answer:

Step-by-step explanation:

Hello,

If n is even, it means that we can find k integer such that n = 2 * k.

Then n+1=2*k+1 is odd.

3n+1=6k+1=2*(3k)+1 where 3k is an integer so 3n+1 is odd.

3n = 2*(3k) is even.

Besides, if n+1 is odd we can find an integer p so that n+1=2p+1 so n = 2p is even.

3n+1 is odd means that we can find an integer q such that 3n+1=2q+1 so 3n=2q as 3 is not dividable by 2, it means that n is a multiple of 2, then n is even.

3n is even means that we can write 3n = 2z where z is an integer and again it means that n is a multiple of 2 and then n is even.

Thank you.

Find the reciprocal of the equation in standard form. The selected answer is incorrect.

Answers

Answer:

C

Step-by-step explanation:

reciprocal of z=1/z

[tex]z=2(cos \frac{\pi }{4} +i sin\frac{\pi }{4} )=2e ^{i \frac{\pi } {4}\\\frac{1}{z}=\frac{1}{2e^{i \frac{\pi}{4} } }\\\frac{1}{z} =\frac{1}{2} e^{-i\frac{\pi}{4} } \\\frac{1}{z} (cos\frac{\pi}{4} -isin\frac{\pi}{4} ) \\\frac{1}{z}=\frac{1}{2} (\frac{\sqrt{2} }{2} -\frac{\sqrt{2} }{2} )\\\frac{1}{z} =\frac{\sqrt{2} }{4} -i \frac{\sqrt{2 } }{4}[/tex]

It’s question 14 I need help with please it’s due soon

Answers

if you are trying to work out -3/4 - (-1/4 - 1/2) then the answer is 0

A bag contains two six-sided dice: one red, one green. The red die has faces numbered 1, 2, 3, 4, 5, and 6. The green die has faces numbered 1, 2, 3, 4, 4, and 4. A die is selected at random and rolled four times. You are told that two rolls were 1's and two were 4's. Find the probability the die chosen was green.

Answers

Answer:

the probability the die chosen was green is 0.9

Step-by-step explanation:

Given that:

A bag contains two six-sided dice: one red, one green.

The red die has faces numbered 1, 2, 3, 4, 5, and 6.

The green die has faces numbered 1, 2, 3, 4, 4, and 4.

From above, the probability of obtaining 4 in a single throw of a fair die is:

P (4  | red dice) = [tex]\dfrac{1}{6}[/tex]

P (4 | green dice) = [tex]\dfrac{3}{6}[/tex] =[tex]\dfrac{1}{2}[/tex]

A die is selected at random and rolled four times.

As the die is selected randomly; the probability of the first die must be equal to the probability of the second die = [tex]\dfrac{1}{2}[/tex]

The probability of two 1's and two 4's in the first dice can be calculated as:

= [tex]\begin {pmatrix} \left \begin{array}{c}4\\2\\ \end{array} \right \end {pmatrix} \times \begin {pmatrix} \dfrac{1}{6} \end {pmatrix} ^4[/tex]

= [tex]\dfrac{4!}{2!(4-2)!} ( \dfrac{1}{6})^4[/tex]

= [tex]\dfrac{4!}{2!(2)!} \times ( \dfrac{1}{6})^4[/tex]

= [tex]6 \times ( \dfrac{1}{6})^4[/tex]

= [tex](\dfrac{1}{6})^3[/tex]

= [tex]\dfrac{1}{216}[/tex]

The probability of two 1's and two 4's in the second  dice can be calculated as:

= [tex]\begin {pmatrix} \left \begin{array}{c}4\\2\\ \end{array} \right \end {pmatrix} \times \begin {pmatrix} \dfrac{1}{6} \end {pmatrix} ^2 \times \begin {pmatrix} \dfrac{3}{6} \end {pmatrix} ^2[/tex]

= [tex]\dfrac{4!}{2!(2)!} \times ( \dfrac{1}{6})^2 \times ( \dfrac{3}{6})^2[/tex]

= [tex]6 \times ( \dfrac{1}{6})^2 \times ( \dfrac{3}{6})^2[/tex]

= [tex]( \dfrac{1}{6}) \times ( \dfrac{3}{6})^2[/tex]

= [tex]\dfrac{9}{216}[/tex]

The probability of two 1's and two 4's in both dies = P( two 1s and two 4s | first dice ) P( first dice ) + P( two 1s and two 4s | second dice ) P( second dice )

The probability of two 1's and two 4's in both die = [tex]\dfrac{1}{216} \times \dfrac{1}{2} + \dfrac{9}{216} \times \dfrac{1}{2}[/tex]

The probability of two 1's and two 4's in both die = [tex]\dfrac{1}{432} + \dfrac{1}{48}[/tex]

The probability of two 1's and two 4's in both die = [tex]\dfrac{5}{216}[/tex]

By applying  Bayes Theorem; the probability that the die was green can be calculated as:

P(second die (green) | two 1's and two 4's )  = The probability of two 1's and two 4's | second dice)P (second die) ÷ P(two 1's and two 4's in both die)

P(second die (green) | two 1's and two 4's )  = [tex]\dfrac{\dfrac{1}{2} \times \dfrac{9}{216}}{\dfrac{5}{216}}[/tex]

P(second die (green) | two 1's and two 4's )  = [tex]\dfrac{0.5 \times 0.04166666667}{0.02314814815}[/tex]

P(second die (green) | two 1's and two 4's )  = 0.9

Thus; the probability the die chosen was green is 0.9

What is 17,210,000,000 written in scientific notation?

Answers

Answer and Step-by-step explanation:

The answer is 1722.1 x [tex]10^8[/tex]

#teamtrees #PAW (Plant And Water)

Answer:

1.72x10^10

Step-by-step explanation:

POSITIVE EXPONENT: means a number is huge

NEGATIVE EXPONENT: indicates a number is teeny-tiny

Practice Exercise 3.1 Fill in the blanks: (i) The factors of 12 are (ii) The least non-zero multiples of any number is (iii) ......... is a factor of every number. ing with Numbers​

Answers

Answer:

i.)1,2,3,4,6,12

ii).the number itself

iii.)1

2**2-5 what is answer of this equation

Answers

Answer:

[tex]\huge\boxed{-1}[/tex]

Step-by-step explanation:

=> 2 * 2 -5

Multiplying first according to DMAS rule

=> 4 - 5

=> -1

P.s. This is not an equation. This is an expression!

Answer:

[tex]\Huge \boxed{-1}[/tex]

Step-by-step explanation:

[tex]\Rightarrow 2 \times 2 -5[/tex]

Division and multiplication to be performed first.

[tex]\Rightarrow 4-5[/tex]

Addition and subtraction next.

[tex]\Rightarrow -1[/tex]

Amanda has 1 3/4yds of red ribbon and 7/8yds of green
ribbon. What is the total amount of ribbon that
Amanda has? (write answer as a fraction)

Answers

Answer:

21/8 yds or 2 5/8 yds

Step-by-step explanation:

First turn 1 3/4 yards into an improper fraction so you can add it to 7/8 yards.

1 3/4 as an improper fraction is 7/4 yds

7/4 yds = 14/8 yds

14/8 yds + 7/8 yds = 21/8 yds

So the total amount of ribbon Amanda has is 21/8  yds or 2 5/8 yds

Mr. Howe ate 1/3 of a pizza and then Mr. Kurt ate 1/8 of the same pizza. How
much of the pizza has been eaten? *

Answers

12/24

Step One: We need to convert 1/3 and 1/8 so both have the same denominator, so we need to find the a number that is able to be multiply by 3 and 8 for the process.

Step Two: 1/3 x 8= 8/24 and 1/8x3= 3/24

Step Three: Add our new fractions: 3/24+8/24= 12/24

Step Four: Subtract 12 by 24: 24-12= 12; our answer is 12/24 or half the pizza was eaten

I hope I've help!

which of the following greatest
6+(-2)
6-(-2)
6×(-2)
6+(-2)​

Answers

Out of
4
8
-12
4

8, or 6-(-2) is greatest

Four items are purchased at prices of $5.30, $1.29, $.53, and $.68. Sales tax applies at 5% of the total purchase price. What is the total charge?

Answers

Answer:

$8.19

Step-by-step explanation:

1. Add the cost of the items together

5.3 + 1.29 + 0.53 + 0.68 = 7.8

2. Solve for 5% of the cost of the items

5% = 0.05

7.8 · 0.05 = 0.39

3. Add the sales tax to the price of the items

7.8 + 0.39 = 8.19

Answer:  $8.19

Explanation:

Add up the prices

5.30 + 1.29 + 0.53 + 0.68 = 7.80

This is the total amount before tax is added. To find the amount after tax, we multiply by 1.05 to get

1.05*7.80 = 8.19

Or a longer way is to find 5% of 7.80 getting 0.05*7.80 = 0.39 in the amount of tax owed, which is added on top of the previous total we got earlier. So we have 7.80 + 0.39 = 8.19

The use of the multiplier 1.05 is handy when you need to apply multiple percentage increases (it also works if you have multiple discounts as well).

Can someone help me?

Answers

Answer:

7w

Step-by-step explanation:

What is the value of the product (3 – 2i)(3 + 2i)?

Answers

Answer:

13

Step-by-step explanation:

(3 - 2i)(3 + 2i)

Expand

(9 + 6i - 6i - 4i^2)

Add

(9 - 4i^2)

Convert i^2

i^2 = ([tex]\sqrt{-1}[/tex])^2 = -1

(9 - 4(-1))

Add

(9 + 4)

= 13

Answer:

13.

Step-by-step explanation:

(3 - 2i)(3 + 2i)

= (3 * 3) + (-2i * 3) + (2i * 3) + (-2i * 2i)

= 9 - 6i + 6i - 4[tex]\sqrt{-1} ^{2}[/tex]

= 9 - 4(-1)

= 9 + 4

= 13

Hope this helps!

∫∫D(x2 + y2 + 2020)dxdy D: x2 +y2 +2ax ≤ 0 (a > 0)

Answers

Answer:

good morning

Step-by-step explanation:

hope u have a nice day

Use spherical coordinates. Evaluate e x2 + y2 + z2 dV, E where E is enclosed by the sphere x2 + y2 + z2 = 25 in the first octant.

Answers

Answer:

[tex]\displaystyle \iiint_E {e^{\sqrt{x^2 + y^2 + z^2}}} \, dV = \frac{\pi (17e^5 - 2)}{2}[/tex]

General Formulas and Concepts:
Calculus

Integration

Integrals

Integration Rule [Reverse Power Rule]:
[tex]\displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C[/tex]

Integration Rule [Fundamental Theorem of Calculus 1]:
[tex]\displaystyle \int\limits^b_a {f(x)} \, dx = F(b) - F(a)[/tex]

Integration Property [Multiplied Constant]:
[tex]\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx[/tex]

Integration Property [Addition/Subtraction]:
[tex]\displaystyle \int {[f(x) \pm g(x)]} \, dx = \int {f(x)} \, dx \pm \int {g(x)} \, dx[/tex]

Integration Method [Integration by Parts]:
[tex]\displaystyle \int {u} \, dv = uv - \int {v} \, du[/tex]

[IBP] LIPET: Logs, Inverses, Polynomials, Exponentials, Trig

Multivariable Calculus

Triple Integrals

Cylindrical Coordinate Conversions:

[tex]\displaystyle x = r \cos \theta[/tex][tex]\displaystyle y = r \sin \theta[/tex][tex]\displaystyle z = z[/tex][tex]\displaystyle r^2 = x^2 + y^2[/tex][tex]\displaystyle \tan \theta = \frac{y}{x}[/tex]

Spherical Coordinate Conversions:

[tex]\displaystyle r = \rho \sin \phi[/tex][tex]\displaystyle x = \rho \sin \phi \cos \theta[/tex][tex]\displaystyle z = \rho \cos \phi[/tex][tex]\displaystyle y = \rho \sin \phi \sin \theta[/tex][tex]\displaystyle \rho = \sqrt{x^2 + y^2 + z^2}[/tex]

Integral Conversion [Spherical Coordinates]:
[tex]\displaystyle \iiint_T {f( \rho, \phi, \theta )} \, dV = \iiint_T {\rho^2 \sin \phi} \, d\rho \, d\phi \, d\theta[/tex]

Step-by-step explanation:

*Note:

Recall that φ is bounded by 0 ≤ φ ≤ 0.5π from the z-axis to the x-axis.

I will not show/explain any intermediate calculus steps as there isn't enough space.

Step 1: Define

Identify given.

[tex]\displaystyle \iiint_E {e^{\sqrt{x^2 + y^2 + z^2}}} \, dV[/tex]

[tex]\displaystyle \text{Region E:} \ x^2 + y^2 + z^2 = 25 \ \text{bounded by first octant}[/tex]

Step 2: Integrate Pt. 1

Find ρ bounds.

[Sphere] Substitute in Spherical Coordinate Conversions:
[tex]\displaystyle \rho^2 = 25[/tex]Solve:
[tex]\displaystyle \rho = 5[/tex]Define limits:
[tex]\displaystyle 0 \leq \rho \leq 5[/tex]

Find θ bounds.

[Sphere] Substitute in z = 0:
[tex]\displaystyle x^2 + y^2 = 25[/tex][Circle] Graph [See 2nd Attachment][Graph] Identify limits [Unit Circle]:
[tex]\displaystyle 0 \leq \theta \leq \frac{\pi}{2}[/tex]

Find φ bounds.

[Circle] Substitute in Cylindrical Coordinate Conversions:
[tex]\displaystyle r^2 = 25[/tex]Solve:
[tex]\displaystyle r = 5[/tex]Substitute in Spherical Coordinate Conversions:
[tex]\displaystyle \rho \sin \phi = 5[/tex]Solve:
[tex]\displaystyle \phi = \frac{\pi}{2}[/tex]Define limits:
[tex]\displaystyle 0 \leq \phi \leq \frac{\pi}{2}[/tex]

Step 3: Integrate Pt. 2

[Integrals] Convert [Integral Conversion - Spherical Coordinates]:
[tex]\displaystyle \iiint_E {e^{\sqrt{x^2 + y^2 + z^2}}} \, dV = \iiint_E {e^{\sqrt{x^2 + y^2 + z^2}} \rho^2 \sin \phi} \, d\rho \, d\phi \, d\theta[/tex][dρ Integrand] Rewrite [Spherical Coordinate Conversions]:
[tex]\displaystyle \iiint_E {e^{\sqrt{x^2 + y^2 + z^2}}} \, dV = \iiint_E {e^{\rho} \rho^2 \sin \phi} \, d\rho \, d\phi \, d\theta[/tex][Integrals] Substitute in region E:
[tex]\displaystyle \iiint_E {e^{\sqrt{x^2 + y^2 + z^2}}} \, dV = \int\limits^{\frac{\pi}{2}}_0 \int\limits^{\frac{\pi}{2}}_0 \int\limits^5_0 {e^{\rho} \rho^2 \sin \phi} \, d\rho \, d\phi \, d\theta[/tex]

We evaluate this spherical integral by using the integration rules, properties, and methods listed above:

[tex]\displaystyle \begin{aligned} \iiint_E {e^{\sqrt{x^2 + y^2 + z^2}}} \, dV & = \int\limits^{\frac{\pi}{2}}_0 \int\limits^{\frac{\pi}{2}}_0 \int\limits^5_0 {e^{\rho} \rho^2 \sin \phi} \, d\rho \, d\phi \, d\theta \\ & = \int\limits^{\frac{\pi}{2}}_0 \int\limits^{\frac{\pi}{2}}_0 {\bigg[ (\rho^2 - 2 \rho + 2) e^{\rho} \sin \phi \bigg] \bigg| \limits^{\rho = 5}_{\rho = 0}} \, d\phi \, d\theta\end{aligned}[/tex]

[tex]\displaystyle \begin{aligned}\iiint_E {e^{\sqrt{x^2 + y^2 + z^2}}} \, dV & = \int\limits^{\frac{\pi}{2}}_0 \int\limits^{\frac{\pi}{2}}_0 {(17e^5 - 2) \sin \phi} \, d\phi \, d\theta \\& = \int\limits^{\frac{\pi}{2}}_0 {\bigg[ -(17e^5 - 2) \cos \phi \bigg] \bigg| \limits^{\phi = \frac{\pi}{2}}_{\phi = 0}} \, d\theta \\& = \int\limits^{\frac{\pi}{2}}_0 {17e^5 - 2} \, d\theta \\& = (17e^5 - 2) \theta \bigg| \limits^{\theta = \frac{\pi}{2}}_{\theta = 0} \\& = \frac{\pi (17e^5 - 2)}{2}\end{aligned}[/tex]

∴ the given integral equals [tex]\displaystyle \bold{\frac{\pi (17e^5 - 2)}{2}}[/tex].

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Learn more about spherical coordinates: https://brainly.com/question/16415822

Learn more about multivariable calculus: https://brainly.com/question/4746216

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Topic: Multivariable Calculus

Unit: Triple Integrals Applications

joe went to to the store and spent a total of $37 .84. if paid with a $50 then how much change did he get back?

Answers

Answer:

$ 12.16

Step-by-step explanation:

Spent = $ 37.84

Paid = $ 50

Change = $50 - $37.84

Change = $ 12.16

[tex]\rule[225]{225}{2}[/tex]

Hope this helped!

~AH1807Peace!

Answer:

$12.16

Step-by-step explanation:

You must subtract his total from his payment. $50-$37.84=$12.16

A random number generator is used to create a list of 300 single digit numbers

Answers

What are we trying to find?

5) Suppose a slice of a 12-inch pizza has an area of 20 square inches. What is the angle of
this slice?

Answers

Answer:

The angle of the slice is 63.64 degrees

Step-by-step explanation:

Here in this question, we are concerned with calculating the angle of the slice.

What we should know are as follows;

1. A pizza is a perfect circular shape

2. A 12-inch pizza means the diameter of the pizza is 12 inches and consequently its radius will be 12/2 = 6 inches

3. A slice of a pizza represents a sector of the circle( a sector is part of a circle bounded by 2 radii and an arc)

Mathematically, to calculate the angle of the slice, we simply use the formula for the area of a sector.

Area of sector = theta/360 * pi * r^2

where Area of sector = 20 square inches

theta is the center angle we are looking for

r is the radius of the pizza which is 6 inches

Plugging these values into the area of sector equation, we have

20 = theta/360 * 22/7 * 6^2

20 = theta/10 * 22/7

22 theta = 10 * 20 * 7

theta = 1400/22

theta = 63.64 degrees which is approximately 64 degrees to the nearest degree

What is the rise over run for the slope -11/9

Answers

Answer:  11 down and 9 right

Step-by-step explanation:

Slope IS rise over run where the top number of the fraction (numerator) determines the vertical distance --> positive is up, negative is down

and the bottom number of the fraction (denominator) determines the horizontal distance --> positive is right, negative is left.

Given slope = -11/9

the numerator is -11 so the "rise" is  DOWN 11 units

the denominator is 9 so the "run" is RIGHT 9 units

At the "cloth for you" shop, you can buy a top for £10.00 and a Bermuda trouser for £12.00. Due to a sensational sell, there is a 20% discount on all tops. If you buy one top and two Bermuda trousers, how much money do you spend in total?

Answers

Answer:

£32 in total for the top and two trousers

Step-by-step explanation:

The price for a top In the "cloth for you" shop= £10

The price for a bermuda trouser In the "cloth for you" shop= £12

There is a 20% discount on tops

The price If I bought one top and would trouser will be

(10-(0.2*10)) for the top

2(12) for the trouser

Total= (10-(0.2*10))+ 2(12)

Total = 10-2+24

Total = £32

So I spent £32 in total for the top and two trousers

The double number line shows that Toni can type 180 words in
2 minutes.



Based on the ratio shown in the double number line, how many words can Toni type in 3 minutes?

Answers

Answer:

120 words

Step-by-step explanation:

as a ratio it's

2:180

In real life the longer you do something the more words you type

so since you can't get to 3 from 2 easily you go to 1 instead.

2:180

1:360

3:120

The Downtown Parking Authority of Tampa, Florida, reported the following information for a sample of 229 customers on the number of hours cars are parked and the amount they are charged.

Number of Hours Frequency Amount Charged 1 16 $ 3 2 34 6 3 51 12 4 39 16 5 34 21 6 16 24 7 9 27 8 30 29 229

a. Convert the information on the number of hours parked to a probability distribution. (Round your answers to 3 decimal places.) Hours Probability 1 2 3 4 5 6 7 8

a-2. Is this a discrete or a continuous probability distribution?

b-1. Find the mean and the standard deviation of the number of hours parked. (Do not round intermediate calculations. Round your final answers to 3 decimal places.)

b-2. How long is a typical customer parked? (Do not round intermediate calculations. Round your final answers to 3 decimal places.)

c. Find the mean and the standard deviation of the amount charged. (Do not round intermediate calculations. Round your final answers to 3 decimal places.)

Answers

Answer:

a

See in the explanation

a-2.

Discrete

b-1.

Mean = 4.201

Standard Deviation = 2.069

b-2.

4.201

c.

Mean = 16.153

Standard Deviation = 8.079

Step-by-step explanation:

Given Data:

Number of Hours         Frequency               Amount Charged  

          1                                 16                                $3        

          2                                34                                 6  

          3                                51                                  12  

          4                                39                                 16  

          5                                34                                 21

          6                                 16                                 24

          7                                  9                                  27

          8                                 30                                 29

                                       ∑f = 229

a. Convert the information on the number of hours parked to a probability distribution:

The probability is calculated by dividing each frequency by 229. For example probability of Hour 1 is calculated as:

16 / 229 = 0.06987

This way all the hours probabilities are computed. The probability distribution is given below

Hours          Probability

   1                0.06987

   2               0.14847

   3               0.2227

   4               0.1703

   5               0.1485

   6               0.0699

   7               0.0393

   8               0.1310

   ∑                    1

a-2. Is this a discrete or a continuous probability distribution?

This is a discrete probability distribution as the probability of each hour of between 0 and​ 1 and the sum of all the probabilities of hours is 1.

b-1. Find the mean and the standard deviation of the number of hours parked.

First multiply each value of Number of hours by the corresponding frequency. Let x represents the number of hours and f represents frequency. Then:

Number of Hours Parked

fx

16

68

153

156

170

96

63

240

Now add the above computed products.

∑fx = 16+68+153+156+170+96+63+240  = 962

Compute Mean:

Now the formula to calculate mean:

Mean = Sum of the value / Number of value

         = ∑fx / ∑f

         = 962 / 229

Mean = 4.201

Compute Standard Deviation:

Let x be the Number of hours.        

Let f be the frequency

First calculate (x-x_bar) where x is each number of hours and x_bar is mean. The value of x_bar i.e. [tex]\frac{}{x}[/tex] = 4.201

For example for the Hour = 1 , and mean = 4.201

Then (x-[tex]\frac{}{x}[/tex]) = 1 - 4.201 = -3.201

So calculating this for every number of hour we get:

(x-[tex]\frac{}{x}[/tex])

-3.201

-2.201

-1.201

-0.201

0.799

1.799

2.799

3.799

Next calculate (x-[tex]\frac{}{x}[/tex])². Just take the squares of the above column (x-[tex]\frac{}{x}[/tex])

For example the first entry of below calculation is computed by:

 (x-[tex]\frac{}{x}[/tex])² = (-3.201 )² = 10.246401

  (x-[tex]\frac{}{x}[/tex])²

10.246401

4.844401

1.442401

0.040401

0.638401

3.236401

7.834401

14.432401

Next multiply each entry of  (x-[tex]\frac{}{x}[/tex])² with frequency f. For example the first entry below is computed by:

(x-[tex]\frac{}{x}[/tex])² * f = 10.246401  * 16 = 163.942416

(x-[tex]\frac{}{x}[/tex])² * f

163.942416

164.709634

73.562451

1.575639

21.705634

51.782416

70.509609

432.97203

Now the formula to calculate standard deviation is:

S = √∑(x-[tex]\frac{}{x}[/tex])² * f/n

Here

n = ∑f = 229

∑(x-[tex]\frac{}{x}[/tex])² * f  is the sum of all entries of (x-[tex]\frac{}{x}[/tex])² * f

∑(x-[tex]\frac{}{x}[/tex])² * f = 980.759829

S = √∑(x-[tex]\frac{}{x}[/tex])² * f/n

  = √980.759829  /  229

  = √4.2827940131004

  = 2.0694912449924

S = 2.069

b-2) How long is a typical customer parked?

That is the value of mean calculated in part b-1. Hence

Typical Customer Parked for 4.201 hours

c) Find the mean and the standard deviation of the amount charged.

First multiply each value of Amount Charged by the corresponding frequency. Let x represents the number of hours and f represents frequency. Then:

fx

48

204

612

624

714

384

243

870

Now add the above computed products.

∑fx = 48+204+612+624+714+384+243+870  = 3699

Compute Mean:

Now the formula to calculate mean:

Mean = Sum of the value / Number of value

         = ∑fx / ∑f

         = 3699 / 229

Mean = 16.153

Compute Standard Deviation:

Let x be the Amount Charged.        

Let f be the frequency.

First calculate (x-x_bar) where x is each value of Amount charged and x_bar is mean. The value of x_bar i.e. [tex]\frac{}{x}[/tex] = 16.153

For example for the Amount Charged = 3 , and mean = 16.153

Then (x-[tex]\frac{}{x}[/tex]) = 3 - 16.153 = -13.153

So calculating this for every number of hour we get:

(x-[tex]\frac{}{x}[/tex])

-13.153

-10.153

-4.153

-0.153

4.847

7.847

10.847

12.847

Next calculate (x-[tex]\frac{}{x}[/tex])². Just take the squares of the above column (x-[tex]\frac{}{x}[/tex])

For example the first entry of below calculation is computed by:

 (x-[tex]\frac{}{x}[/tex])² = (-13.153  )² = 173.001409

  (x-[tex]\frac{}{x}[/tex])²

173.001409

103.083409

17.247409

0.023409

23.493409

61.575409

117.657409

165.045409

Next multiply each entry of  (x-[tex]\frac{}{x}[/tex])² with frequency f. For example the first entry below is computed by:

(x-[tex]\frac{}{x}[/tex])² * f = 173.001409  * 16 =  

   (x-[tex]\frac{}{x}[/tex])² * f

2768.022544

3504.835906

879.617859

0.912951

798.775906

985.206544

1058.916681

4951.36227

∑(x-[tex]\frac{}{x}[/tex])² = 14947.65066

Now the formula to calculate standard deviation is:

S = √∑(x-[tex]\frac{}{x}[/tex])² * f/n

Here

n = ∑f = 229

∑(x-[tex]\frac{}{x}[/tex])² * f  is the sum of all entries of (x-[tex]\frac{}{x}[/tex])² * f

∑(x-[tex]\frac{}{x}[/tex])² * f = 14947.65066

S = √∑(x-[tex]\frac{}{x}[/tex])² * f/ ∑f

  = √65.273583668122

  = 8.0792068712295

S = 8.079

SHALL GIVE BRAINLIEST ANSWER!! A ​40% solution of fertilizer is to be mixed with an ​80% solution of fertilizer in order to get 80 gallons of a ​70% solution. How many gallons of the ​40% solution and ​80% solution should be​ mixed? 40% solution =? gallons, 80% solution =? gallons

Answers

Answer:

20 gallons of the 40% solution, 60 gallons of the 80% solution

Step-by-step explanation:

Let x = the gallons of the 40% solution, and y = the gallons of a 80% solution. The first thing we want to do here is to convert each percentage into decimal form - including the ​70% solution mixture.

40% = 0.40,

80% = 0.80, respectively 70% = 0.70

As you can tell, 0.40 is associated with x gallons, 0.80 is associated with y gallons, and the mixture contains 0.70 [tex]*[/tex] 80 solution, as 0.70 is associated with 80. Therefore we can formulate the following expression,

0.40x + 0.80y = 0.70 [tex]*[/tex] 80

At the same time x + y = 80, as the solution ( mixture ) is present with 80 gallons. Isolating x, x = 80 - y. Let us plug that into our expression, solving for y, following by x gallons.

[tex]0.40\left(\:80\:-\:y\:\right)\:+\:0.80y\:=\:0.70\:\cdot \:80[/tex]

[tex]0.4\left(80-y\right)+0.8y=56[/tex] ( Multiply either side by 10 )

[tex]4\left(80-y\right)+8y=560[/tex] ( Expand )

[tex]320-4y+8y=560[/tex]

[tex]320+4y=560[/tex]

[tex]4y=240[/tex]

[tex]y = \frac{240}{4} = 60[/tex] ( Substitute to solve for x )

[tex]x = 80 - y = 80 - 60 = 20[/tex]

As you can see there are 20 gallons of the 40% solution, and 60 gallons of the 80% solution.

A function does not have any x-intercepts. What
might be true about its domain and range?

Answers

The domain exists on all real numbers i.e {x∈R}∈

The range exists all on real numbers except at y = 0

Domains are all input values of a function for which the function exists while ranges are all the output values for which the function exists.

Since the x-intercept of a function exists at where y = 0, this means that the point where a function does not have any x-intercepts are all other points on the graph except at y = 0.

The following statements are therefore true;

The domain exists on all real numbers i.e {x∈R}The range exists all on real numbers except at y = 0

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Write an expression to represent the given statement. Use n for the variable. Three times the absolute value of the sum of a number and 6

Answers

Answer:

3 · |x+6|

Step-by-step explanation:

Write out what you see. "Three times" is 3 · something; "the absolute value of the sum of a number and 6" is |number + 6|. We'll use x for our number. Put it all together and you get 3 · |x+6|

The expression of the statement, Three times the absolute value of the sum of a number and 6 is  [tex]\[3\left| n+6 \right|\][/tex] .

Representation of statement:Let n be the number.The sum of the numbers n and 6 is n+6.The absolute value of the sum of the numbers n and 6 is  [tex]\[\left| n+6 \right|\][/tex].Hence, three times the absolute value of the sum of a number and 6 is [tex]\[3\left| n+6 \right|\][/tex].

 

Learn more about the representation of an expression:

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3/4=x/20,find the value of 'x'​

Answers

Answer:

[tex]\boxed{x=15}[/tex]

Step-by-step explanation:

[tex]\frac{3}{4} =\frac{x}{20}[/tex]

[tex]\sf Cross \ multiply.[/tex]

[tex]4 \cdot x = 20 \cdot 3[/tex]

[tex]4x=60[/tex]

[tex]\sf Divide \ both \ sides \ by \ 4.[/tex]

[tex]\frac{4x}{4} =\frac{60}{4}[/tex]

[tex]x=15[/tex]

Find the first six terms of the sequence.
a1=- 6, an= 4 • an-1

Answers

Answer:

I think it's 3

Step-by-step explanation:

because an=4 and the question is

an-1

=4-1

=3

find the surface area of the prism HURRY HURRY

Answers

Answer:

should be 192

Step-by-step explanation:

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