Which equation is true

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Complete Question

At one point the average price of regular unleaded gasoline was ​$3.39 per gallon. Assume that the standard deviation price per gallon is ​$0.07 per gallon and use​ Chebyshev's inequality to answer the following.

​(a) What percentage of gasoline stations had prices within 3 standard deviations of the​ mean?

​(b) What percentage of gasoline stations had prices within 2.5 standard deviations of the​ mean? What are the gasoline prices that are within 2.5 standard deviations of the​ mean?

​(c) What is the minimum percentage of gasoline stations that had prices between ​$3.11 and ​$3.67​?

Answer:

a) 88.89% lies with 3 standard deviations of the mean

b) i) 84% lies within 2.5 standard deviations of the mean

ii) the gasoline prices that are within 2.5 standard deviations of the​ mean is $3.215 and $3.565

c) 93.75%

Step-by-step explanation:

Chebyshev's theorem is shown below.

1) Chebyshev's theorem states for any k > 1, at least 1-1/k² of the data lies within k standard deviations of the mean.

As stated, the value of k must be greater than 1.

2) At least 75% or 3/4 of the data for a set of numbers lies within 2 standard deviations of the mean. The number could be greater.μ - 2σ and μ + 2σ.

3) At least 88.89% or 8/9 of a data set lies within 3 standard deviations of the mean.μ - 3σ and μ + 3σ.

4) At least 93.75% of a data set lies within 4 standard deviations of the mean.μ - 4σ and μ + 4σ.

​

(a) What percentage of gasoline stations had prices within 3 standard deviations of the​ mean?

We solve using the first rule of the theorem

1) Chebyshev's theorem states for any k > 1, at least 1-1/k² of the data lies within k standard deviations of the mean.

As stated, the value of k must be greater than 1.

Hence, k = 3

1 - 1/k²

= 1 - 1/3²

= 1 - 1/9

= 9 - 1/ 9

= 8/9

Therefore, the percentage of gasoline stations had prices within 3 standard deviations of the​ mean is 88.89%

​(b) What percentage of gasoline stations had prices within 2.5 standard deviations of the​ mean?

We solve using the first rule of the theorem

1) Chebyshev's theorem states for any k > 1, at least 1-1/k² of the data lies within k standard deviations of the mean.

As stated, the value of k must be greater than 1.

Hence, k = 3

1 - 1/k²

= 1 - 1/2.5²

= 1 - 1/6.25

= 6.25 - 1/ 6.25

= 5.25/6.25

We convert to percentage

= 5.25/6.25 × 100%

= 0.84 × 100%

= 84 %

Therefore, the percentage of gasoline stations had prices within 2.5 standard deviations of the​ mean is 84%

What are the gasoline prices that are within 2.5 standard deviations of the​ mean?

We have from the question, the mean =$3.39

Standard deviation = 0.07

μ - 2.5σ

$3.39 - 2.5 × 0.07

= $3.215

μ + 2.5σ

$3.39 + 2.5 × 0.07

= $3.565

Therefore, the gasoline prices that are within 2.5 standard deviations of the​ mean is $3.215 and $3.565

​(c) What is the minimum percentage of gasoline stations that had prices between ​$3.11 and ​$3.67​?

the mean =$3.39

Standard deviation = 0.07

Applying the 2nd rule

2) At least 75% or 3/4 of the data for a set of numbers lies within 2 standard deviations of the mean. The number could be greater.μ - 2σ and μ + 2σ.

the mean =$3.39

Standard deviation = 0.07

μ - 2σ and μ + 2σ.

$3.39 - 2 × 0.07 = $3.25

$3.39 + 2× 0.07 = $3.53

Applying the third rule

3) At least 88.89% or 8/9 of a data set lies within 3 standard deviations of the mean.μ - 3σ and μ + 3σ.

$3.39 - 3 × 0.07 = $3.18

$3.39 + 3 × 0.07 = $3.6

Applying the 4th rule

4) At least 93.75% of a data set lies within 4 standard deviations of the mean.μ - 4σ and μ + 4σ.

$3.39 - 4 × 0.07 = $3.11

$3.39 + 4 × 0.07 = $3.67

Therefore, from the above calculation we can see that the minimum percentage of gasoline stations that had prices between ​$3.11 and ​$3.67​ corresponds to at least 93.75% of a data set because it lies within 4 standard deviations of the mean.

Answer:

uf

iydit s6jdkyditsk6o

Answer:

9 feet

Step-by-step explanation:

Square root 81 as all the sides of the porch are the same length

Answer:

e7gevey2u2veveve wheheveveg

Step-by-step explanation:

I took the quiz please give me five stars for the memes.pls. I know u will so there is no reason to ask.

Answer:

if x = 12; y = 40

if x = 3; y= 13

Step-by-step explanation:

if x = 12 then,

y = 3(12) + 4

y = 36 + 4

y = 40

if x = 3 then,

y = 3(3) + 4

y = 9 + 4

y = 13

[tex] \sf \: 3x + x \sqrt{3} - 2 = 0 \\ \\ \sf \longrightarrow 3x + \sqrt{3} x = 2 \\ \\ \sf \longrightarrow \sqrt{3}x ( \sqrt{3} +1 ) = 2 \\ \\ \sf \longrightarrow \sqrt{3} x = \frac{2}{ \sqrt{3} + 1 } \\ \\ \sf \longrightarrow x = \frac{2}{ \sqrt{3}( \sqrt{3} + 1) } \\ \\ \sf \longrightarrow x = \frac{2}{3 + \sqrt{3} } \\ \\ \tt{You\:can\:stop\:here\:if\:you\:\bold{don't}\:want\:to }\\ \tt{ \:simplify\:in\:decimal\:form.}\\ \\ \sf \longrightarrow x = \frac{2(3 - \sqrt{3} )}{(3 + \sqrt{3})(3 - \sqrt{3} )} \\ \\ \sf \longrightarrow x = \frac{6 - 2 \sqrt{3} }{ {3}^{2} - {( \sqrt{3}) }^{2} } \\ \\ \sf \longrightarrow x = \frac{6 - 2(1.732)}{9 - 3} \\ \\ \sf \longrightarrow x = \frac{2.536}{6} \\ \\ \leadsto \underline{\boxed{\sf{\pink{x \approx 0.4226}}}}[/tex]

Answer:

Both rates and ratios are a comparison of two numbers. A rate is simply a specific type of ratio. The difference is that a rate is a comparison of two numbers with different units, whereas a ratio compares two numbers with the same unit. For example, in a room full of students, there are 10 boys and 5 girls. This means the ratio of boys to girls is 10:5.

Answer:

It's not 0 I got it wrong.

Step-by-step explanation:

Answer:

-2

Step-by-step explanation:

i just took the test

9514 1404 393

Answer:

  B.  x +6y = 4.45; x +12y = 5.65

Step-by-step explanation:

The problem statement defines the variables for you. Using x and y for the cost of a loaf and the cost of an egg, respectively, each purchase can be represented by an equation of the form ...

  (number of loaves)x + (number of eggs)y = (amount spent)

The first purchase is described as

The second purchase is of a dozen eggs, which is 12 eggs. The description of this purchase can be ...

The situation can be represented by the equations shown in the attachment.

Answer:

[tex]\boxed{2^{\frac{802}{27}} \cdot 3^9}[/tex]

Step-by-step explanation:

I will try to give as many details as possible.

First of all, I just would like to say:

[tex]\text{Use } \LaTeX ![/tex]

Texting in Latex is much more clear and depending on the question, just writing down without it may be confusing or ambiguous. Be together with Latex! （＊＾Ｕ＾）人（≧Ｖ≦＊）/

[tex]$(3^{-2} \cdot 4^{-5} \cdot 5^0)^{-3} \cdot (4^{-\frac{4}{3^3} })\cdot 3^3$[/tex]

Note that

[tex]\boxed{a^{-b} = \dfrac{1}{a^b}, a\neq 0 }[/tex]

The denominator can't be 0 because it would be undefined.

So, we can solve the expression inside both parentheses.

[tex]\left(\dfrac{1}{3^2} \cdot \dfrac{1}{4^5} \cdot 5^0 \right)^{-3} \cdot \left(\dfrac{1}{4^{\frac{4}{3^3} } }\right)\cdot 3^3[/tex]

Also,

[tex]\boxed{a^{0} = 1, a\neq 0 }[/tex]

[tex]\left(\dfrac{1}{9} \cdot \dfrac{1}{1024} \cdot 1 \right)^{-3} \cdot \left(\dfrac{1}{4^{\frac{4}{27} } }\right)\cdot 27[/tex]

Note

[tex]\boxed{\dfrac{1}{a} \cdot \dfrac{1}{b}= \frac{1}{ab} , a, b \neq 0}[/tex]

[tex]\left(\dfrac{1}{9216} \right)^{-3} \cdot \left(\dfrac{1}{4^{\frac{4}{27} } }\right)\cdot 27[/tex]

[tex]\left(\dfrac{1}{9216} \right)^{-3} \cdot \left(\dfrac{27}{4^{\frac{4}{27} } }\right)[/tex]

[tex]\left( \dfrac{1}{\left(\dfrac{1}{9216}\right)^3} \right)\cdot \left(\dfrac{27}{4^{\frac{4}{9} } }\right)[/tex]

[tex]\left( \dfrac{1}{\left(\dfrac{1}{9216}\right)^3} \right)\cdot \left(\dfrac{27}{4^{\frac{4}{27} } }\right)[/tex]

Note

[tex]\boxed{\dfrac{1}{\dfrac{1}{a} } = a}[/tex]

[tex]9216^3\cdot \left(\dfrac{27}{4^{\frac{4}{9} } }\right)[/tex]

[tex]\left(\dfrac{ 9216^3\cdot 27}{4^{\frac{4}{27} } }\right)[/tex]

Once

[tex]9216=2^{10}\cdot 3^2 \implies 9216^3=2^{30}\cdot 3^6[/tex]

[tex]\boxed{(a \cdot b)^n=a^n \cdot b^n}[/tex]

And

[tex]$4^{\frac{4}{27}} = 2^{\frac{8}{27} $[/tex]

We have

[tex]\left(\dfrac{ 2^{30} \cdot 3^6\cdot 27}{2^{\frac{8}{27} } }\right)[/tex]

Also, once

[tex]\boxed{\dfrac{c^a}{c^b}=c^{a-b}}[/tex]

[tex]2^{30-\frac{8}{27}} \cdot 3^6\cdot 27[/tex]

As

[tex]30-\dfrac{8}{27} = \dfrac{30 \cdot 27}{27}-\dfrac{8}{27} =\dfrac{802}{27}[/tex]

[tex]2^{30-\frac{8}{27}} \cdot 3^6\cdot 27 = 2^{\frac{802}{27}} \cdot 3^6 \cdot 3^3[/tex]

[tex]2^{\frac{802}{27}} \cdot 3^9[/tex]

Answer:

F(d) = 30 + 0.50d

Step-by-step explanation:

Given

Charges = P8.00 ---- first 4 km

Additional = P0.50

Required

Write a function to address the scenario.

Represent the whole distance covered with d.

First,we need to determine the total charges for the first four hours.

Charges = 8.00 * 4

Charges = 32.00

Next, we determine the charges for additional distance.

Charges = 0.50 * (d - 4)

d - 4 is the remaining distance after the first 4.

Charges = 0.50d - 2

The function is then written as;

F(d) = 32 + 0.50d - 2

F(d) = 32 - 2 + 0.50d

F(d) = 30 + 0.50d

Answer:

let Elijah age be a

Then

2*a + 17 =47

2a=47-17

2a=30

a=15

Step-by-step explanation:

Answer:

Something!

Step-by-step explanation:

Do something then do something and thats it!

Answer:

Step-by-step explanation:

k - 4 = 3

   9

k/9  = 3(9) + 4

k = 31/9

k = 31/9

8 + b = -5

  -4

8 + b = -5 (-4)

8 +  b = 20

b = 20 - 8

b = 12

Answer:

1/3 cup of juice per cup of berries

Step-by-step explanation:

The table shows that if we go from 0 to 4 cups (a "run" of 4 cups), the juice output is 1 1/3 (or 4/3) (a "rise" of 4/3 cups), and so the desired constant of proportionality is the unit rate

(4/3) cups

------------------------ = 1/3 cup of juice per cup of berries

  4 cups berries

you would divide -> 51/68  and you would get .75. move the 2 first numbers after the dot to the front and you get 75%

Answer:

I the diagram, 17  represents 25% of the total  games. Since 17 times 3 equals 51, you use the first 3 columns to find the answer of 75%.  

Just took test that was the answer they gave.

Step-by-step explanation:

Answer:

1944

Step-by-step explanation:

you times height by width by depth 9×8×27=1944

Answer:

[tex]x^{2}[/tex]  

I hope this helps!

Answer: the answer is -5 subtract 9 and 4 you get 5 then add 8v to -9v you get -1v then you divide it from 5 and v= -5

Step-by-step explanation:

Answer:

0.041

I know this because 1,000 has 3 zeros, so you would move 41 three places to the right.

The decimal equivalent of the fraction 41/1000 is 0.041.

A decimal is represented by a dot that separates the whole part and the fractional part of a number. Decimals can also be converted into fractions and vice versa.

Given, a fraction 41/1000, here the numerator is less than the denominator so it is a proper fraction.

Now, As in the denominator we have three zeroes we'll put a decimal three places before the numerator value which is,

= 0.041/1.

= 0.041.

So, 41/1000 is equal to 0.041.

learn more about decimal numbers here :

https://brainly.com/question/4708407

#SPJ2

Answer:

your answer is b     32/4=8

Step-by-step explanation:

if you take the groups of 4 and count them up it is 32 and then you divide them in to equal groups and it is 8 groups of 4

hope this helped

:)

Step-by-step explanation:

Hey there!

To solve this type of question, you must take square of variable"X" to right side making it ±squareroot. As it is a quadratic equation it will have two values (±).

Given;

[tex] {x}^{2} = 16[/tex]

Taking (square) to right side. It becomes ± square root.

[tex]x = + - \sqrt{16} [/tex]

[tex]x = + - \sqrt{ {4}^{2} } [/tex]

Cancel square and square root.

[tex]x = + - 4[/tex]

Therefore, X = ±4

Hope it helps...

Answer:

There are two I results found which is x=4 and x=-4

Step-by-step explanation:

Step by Step Solution:

More Icon

Rearrange:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

                    x^2-(16)=0  

Step by step solution :

STEP

1 :

Trying to factor as a Difference of Squares:

1.1      Factoring:  x2-16  

Theory : A difference of two perfect squares,  A2 - B2  can be factored into  (A+B) • (A-B)

Proof :  (A+B) • (A-B) =

        A2 - AB + BA - B2 =

        A2 - AB + AB - B2 =

        A2 - B2

Note :  AB = BA is the commutative property of multiplication.

Note :  - AB + AB equals zero and is therefore eliminated from the expression.

Check : 16 is the square of 4

Check :  x2  is the square of  x1  

Factorization is :       (x + 4)  •  (x - 4)  

Equation at the end of step

1 :

 (x + 4) • (x - 4)  = 0  

STEP

2 :

Theory - Roots of a product

2.1    A product of several terms equals zero.  

When a product of two or more terms equals zero, then at least one of the terms must be zero.  

We shall now solve each term = 0 separately  

In other words, we are going to solve as many equations as there are terms in the product  

Any solution of term = 0 solves product = 0 as well.

Solving a Single Variable Equation:

2.2      Solve  :    x+4 = 0  

Subtract  4  from both sides of the equation :  

                     x = -4

Solving a Single Variable Equation:

2.3      Solve  :    x-4 = 0  

Add  4  to both sides of the equation :  

                     x = 4 and/or x=-4

Answer:

if youre trying to find the number then the number is 1

Step-by-step explanation:

the equation would be x/16+1/4=5/16

well we want to make everything have the same denominator and 16 is the LCD ( least common denominator ) so you would multiply 1/4 by 4/4 to get 4/16.

this means x/16+4/16=5/16 and and 4+1=5 so 1 is the answer

Answer:

3/7 is the slope and -5 is the y intercept

Step-by-step explanation:

y=3/7x-5

The equation is written in slope intercept form

y = mx+b where m is the slope and b is the y intercept

3/7 is the slope and -5 is the y intercept

Answer:

B

Step-by-step explanation:

The slope is always the coefficient of the x value in the linear equation. And the y intercept is the constant in the equation.

Answer:

∑ (-1)ⁿ⁺³ 1 / (n^½)

∑ (-1)³ⁿ 1 / (8 + n)

Step-by-step explanation:

If ∑ an is convergent and ∑│an│is divergent, then the series is conditionally convergent.

Option A: (-1)²ⁿ is always +1.  So an =│an│and both series converge (absolutely convergent).

Option B: bn = 1 / (n^⁹/₈) is a p series with p > 1, so both an and │an│converge (absolutely convergent).

Option C: an = 1 / n³ isn't an alternating series.  So an =│an│and both series converge (p series with p > 1).  This is absolutely convergent.

Option D: bn = 1 / (n^½) is a p series with p = ½, so this is a diverging series.  Since lim(n→∞) bn = 0, and bn is decreasing, then an converges.  So this is conditionally convergent.

Option E: (-1)³ⁿ = (-1)²ⁿ (-1)ⁿ = (-1)ⁿ, so this is an alternating series.  bn = 1 / (8 + n), which diverges.  Since lim(n→∞) bn = 0, and bn is decreasing, then an converges.  So this is conditionally convergent.

Answer

1/3

Step-by-step explanation:

Answer:

1/2 is bigger than 1/3 by a little bit

Answer:

The median is [tex]Median = 0.903[/tex]

Step-by-step explanation:

From the question we are told that  

   The sample size is n =  100

   The  [tex]1^{st} \to 45^{th}[/tex] measurements is  [tex]= 0.859 \to 0.900[/tex]

    Generally since that after 0.900 we have  0.901 , then the

     [tex]46^{th} \ measurement \ is \ 0.901[/tex]

in the same manner the  [tex]47^{th} \ measurement \ is \ 0.902[/tex],

Given that 0.902  was observed three times it means that

                                         [tex]47^{th},48^{th},49^{th} \ measurement \ is \ 0.902[/tex],

Given that 0.903  was observed two times it means that

                                          [tex]50^{th},51^{th} \ measurement \ is \ 0.903[/tex],

Given that 0.903  was observed four times it means that

                                         [tex]52^{nd},53^{rd},54^{th},55^{th} \ measurement \ is \ 0.904[/tex],

Given that the highest measurement is  0.958 then then the  [tex]56^{th} \to 100^{th} \ measurement \ is \ between \ 0.905 \to 0.958[/tex]

Generally the median is is mathematically represented as

            [tex]Median = \frac{ [\frac{n^{th}}{2}] + [(\frac{n}{2})^{th} + 1 ]}{2}[/tex]

=>        [tex]Median = \frac{ [\frac{100^{th}}{2}] + [(\frac{100}{2})^{th} + 1 ]}{2}[/tex]

=>        [tex]Median = \frac{ [50^{th}] + [51^{th} ]}{2}[/tex]

=>        [tex]Median = \frac{ 0.903 + 0.903}{2}[/tex]

=>        [tex]Median = 0.903[/tex]

Answer:

x=21

Step-by-step explanation:

x=9+12 x=21

Answer:

Step-by-step explanation:

X-9=12

Reverse the operation into

9+12=x

9+12=21

Now check

21-9=12

Answer:

1.3027

Step-by-step explanation: