A cylindrical gas tank has a volume
of 1,808.64 m². Its height is 9 m. What is its radius?

Answer:

1/6

Step-by-step explanation:

To simplify the expression:

      1. Change the divisor into it's reciprocal

     2. Change the sign into a multiplication sign.

     3. Evaluate the product of those fractions.

     4. Simplify the fraction. (If possible)

Given expression:

[tex]\dfrac{1}{6^3 } \div \dfrac{1}{36}[/tex]

According to step 1, we need to convert the divisor of the expression into it's reciprocal.

[tex]\dfrac{1}{6^3 } \div \dfrac{36}{1}[/tex]

According to step 2, we need to change the division sign (÷) into a multiplication sign (×).

[tex]\implies \dfrac{1}{6^3 } \times \dfrac{36}{1}[/tex]

According to step 3, we need to determine the product of these fractions. This can be done by evaluating the exponent.

[tex]\implies \dfrac{1}{(6)(6)(6) } \times \dfrac{36}{1}[/tex]

[tex]\implies \dfrac{1}{216 } \times \dfrac{36}{1}[/tex]

Multiply the fractions as needed. [a/b × c/d = (a × c)/(b × d) = (ac)/(bd):

[tex]\implies \dfrac{36}{216 }[/tex]

According to step 4, (If possible), Simplify the product of 1/216 and 36. In this case, the product of 1/216 and 36 is 36/216. Since both are divisible by 6, we can divide the numerator and the denominator by 6 to simplify the fraction.

[tex]\implies \dfrac{36 \div 6}{216 \div 6 }[/tex]

[tex]\implies \dfrac{1}{6 }[/tex]

Therefore, the quotient of 1/6^3 and 1/36 is 1/6.

Learn more about this topic: https://brainly.com/question/22322495

Answer:

[tex]\large\textsf{$\dfrac{1}{6}$}[/tex]

Step-by-step explanation:

[tex]\large\textsf{$\dfrac{1}{6^3} \div \dfrac{1}{36}$} \implies \normalsize \textsf{Convert 36 into a base with an exponent}[/tex]

[tex]\large\textsf{$\dfrac{1}{6^3} \div \dfrac{1}{6^2}$} \implies \normalsize \textsf{Cross multiply}[/tex]

[tex]\large\textsf{$\dfrac{1 \cdot 6^2}{1 \cdot 6^3}$} \implies \normalsize \textsf{Multiply}[/tex]

[tex]\large\textsf{$\dfrac{6^2}{6^3}$}\implies \normalsize \textsf{Simplify using the Quotient of Powers Property: \normalsize\textsf{$\dfrac{x^m}{x^n} = x^{m-n}$}}[/tex]

[tex]\large\textsf6^{2-3}[/tex]

[tex]\large\textsf6^{-1} \implies \normalsize \textsf{Simplify using the Negative Exponent Property: \normalsize\textsf {${x^{-m}} = \dfrac{1}{x^m}$}}[/tex]

[tex]\large\textsf{$\dfrac{1}{6^1}$} \implies \normalsize \textsf{Simplify}[/tex]

[tex]\large\textsf{$\dfrac{1}{6}$} \implies \normalsize \textsf{Final answer}[/tex]

Hope this helps!

Answer:

y=40/183x

Step-by-step explanation:

y = Rise/Run multiplied plus y intercept by x or Y= mx + b

There is no b

m = 40/183

Y = 40/183x

Answer:

5

Step-by-step explanation:

ty

]

Answer: 64%

Step-by-step explanation:

The score you have entered means that the individual who took the test is at the sixty-fourth percentile – their percentile rank is 64%. This means that the student had a test score greater than or equal to 64% of the reference population. Conversely, 36% of students scored equal to or higher than the individual tested.

System of equations are equations that is more than one and have two or more unknowns. The solution to the given system of equation is expressed as (0, 2)

System of equations are equations that is more than one and have two or more unknowns.

Given the simultaneous equation

m + 4n = 8

m = n - 2

Substitute equation 2 into 1 to have:

n - 2 + 4n = 8

5n - 2  = 8

5n = 10

n = 2

Recall that m = n - 2

m = 2 - 2

m = 0

Hence the solution to the given system of equation is expressed as (0, 2)

Learn more on system of equation here: https://brainly.com/question/25976025

Answer:

He was 11

Step-by-step explanation:

if Camila was 4 years younger than her brother and she was seven. That means he is 4 years older than her. so 7+4=11

Answer:

4 ^3√7m^2

Step-by-step explanation:

^3√64×7m^2

^3√4^3×7m^3

^3√4^3 3^√7m^2

= 4^3√7m^2

Answer:

[tex] \boxed{ \tt = 4 \sqrt[3]{7m {}^{2} } }[/tex]

Step-by-step explanation:

Given,

[tex] \sqrt[3]{448m {}^{2} } [/tex]

Solution:

[tex] = \sqrt{4 {}^{3 } \times 7 \: m {}^{2} } [/tex]

[tex] \tt = 4 \sqrt[3]{7m {}^{2} } [/tex]

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

Answer:

935 yards

Step-by-step explanation:

If she runs 85 yards at each practice you would multiply it by the amount of practices. So 85x11

The unique triangles that can be formed with side lengths of 6.5 centimeters, 6 centimeters, and 2.5 centimeters is[tex]9.[/tex]

A triangle  can be referred to as a polygon with three edges and three vertices.

we can arrange length of one side of a unique triangle in 3 different ways.

Let x,y,z be the length of the three sides.

For triangles to be unique, length of one side can be arranged in 3 different ways.

Then, length of 6.5 cm can be at maximum three positions which is x,y,z.

The 2.5 cm lenght can appear to be at maximum three positions which is  x,y,z.This can as well be done for 6cm.

Therefore, total ways of making unique triangles[tex]= (3 + 3+ 3)= 9[/tex]

Learn more about unique triangle at;

https://brainly.com/question/23180570

Answer:

1

Step-by-step explanation:

Given:

What is the total number of unique triangles that can be formed with side lengths of 6.5 centimeters, 6 centimeters, and 2.5 centimeters?

​Solve:

Define:

What is a unique triangle?

Only one way to create triangle.

Are congruent which means same.

As you may know the word "Unique"

which means : original and unique designs

So without even solving we can see that there is only "One" way .

Kavinsky

========================================================

Explanation:

The order matters because the jobs are different. This means we'll use a permutation.

We have n = 9 workers to pick from and r = 6 jobs to fill.

Plug those values into the nPr permutation formula.

[tex]n P r = \frac{n!}{ (n-r)! }\\\\9 P 6 = \frac{9!}{ (9-6)! }\\\\9 P 6 = \frac{9!}{ 3! }\\\\9 P 6 = \frac{9*8*7*6*5*4*3*2*1}{ 3*2*1 }\\\\9 P 6 = 9*8*7*6*5*4 \ \ \text{.... Note: The 3*2*1 cancels}\\\\9 P 6 = 60480\\\\[/tex]

There are 60480 ways to assign the 9 workers to the 6 different jobs where order matters.

----------------------

Another approach:

Label the 6 jobs as A,B,C,D,E,F

For job A, we have 9 workers to pick from.

For job B, we have 8 workers to pick from. This is because it states that there is "no more than one job to a worker".

For job C, we have 7 workers to pick from. And so on. We have this countdown going on. We stop once we reach job F.

We end up with 9*8*7*6*5*4 = 60480 different permutations

The string "9*8*7*6*5*4" is found in the second to last step of the section above.

There are 20853 ways are there to select the 4 leaders so that either Natasha and Rodrigo are both selected or Natasha and Rodrigo are both not selected.

A combination is a mathematical technique that determines the number of possible arrangements in a collection of items.  

The number of the possible ways will be calculated by:

[tex]=2 ^{28}C_2+^{28}C_4[/tex]

[tex]=\dfrac{28\times 27}{2}+\dfrac{28\times 27\times 26\times 25}{4\times 3\times 2}[/tex]

[tex]=756+28853[/tex]

[tex]=21231[/tex]

Hence there are 20853 ways are there to select the 4 leaders so that either Natasha and Rodrigo are both selected or Natasha and Rodrigo are both not selected.

To know more about Combination follow

https://brainly.com/question/11732255

#SPJ1

Answer:

This would be a statistical question.

Step-by-step explanation:

Answer:

1.2 m

Step-by-step explanation:

1 meter = 100 cm

120-100(1m)=20

.2 meters would be 20 cm if we're going by 1 m = 100cm.

We already have 1 meter from 100 cm and then we add the .2 meters to the 1 meter. 1+.2= 1.2 m

Answer:

1.2

Hope this helped!

Answer:

d.  5490

Step-by-step explanation:

[tex]\begin{aligned}\displaystyle \sf \sum_{n=1}^{60} 3n & =3(1)+3(2)+3(3)+...+3(49)+3(50)\\ & = 3+6+9+...+147+150\end{aligned}[/tex]

Therefore, this is an arithmetic series with:

Sum of the first n terms of an arithmetic series:

[tex]S_n=\dfrac12n[2a+(n-1)d][/tex]

Therefore, the sum of the first 60 terms:

[tex]\begin{aligned}S_{60} &=\dfrac12(60)[2(3)+(60-1)3]\\ & =30[6+(59)3]\\ & = 30[6+177]\\ & = 30[183]\\ & = 5490 \end{aligned}[/tex]

Answer:

The answer is D) 5,490.

Step-by-step explanation:

please view the calculations section of this ans

The easiest way to determine the sine, cosine, and tangent of a number is to utilize the calculator, which we are asked to do.

cos (89) = 0.017

sin (17) = 0.29

tan (35) = 0.700

hope helpful ~

Answer:

A

Step-by-step explanation:

Every 360 degrees (full circle) that you add or subtract from 140 is coterminal

140 + 360 = 500

Answer:

1 time they will only cross 1 time

Answer:

one, in a linear equation a line will only cross the x-axis and y-axis once.

#1

Slope:-

Equation in point slope form

Shading done to right means towards origin

So

shading is towards origin

The inequality is

Dashed line given so we remain it <

#2

Slope:-

Equation in point slope form

Put (0,0)

The inequality is(solid line given)

Graph attached

Answer:

c and b was right for me

Step-by-step explanation:

Answer:

25.796... km

Step-by-step explanation:

We are given that:

Formula of circumference:

Thus, we can rewrite the circumference as:

Since we are asked to determine the diameter, it is recommended to use the formula (πd). Therefore,

Divide π both sides to isolate the diameter:

Substitute π as 3.14 and simplify:

Therefore, the diameter of the circle is 25.796... km.

Answer: is 832cm

Step-by-step explanation:

Answer:

The boat is 26 mi far from dock .

Step-by-step explanation:

By using PGT

P²+B² = H²

=> 10² + 24² = c²

=> 100 + 576 = c²

=> 676 = c²

=> √676 = c

=> 26 = c

Answer:

26 miles

Step-by-step explanation:

We can use Pythagorean's Theorem for right triangles which states that:

[tex]a^2+b^2=c^2[/tex]

The values 'a' and 'b' are the shorter sides of the triangle, while the value 'c' is the longest side of the triangle. We are given the two shorter sides 'a' and 'b', so let's now find 'c':

[tex](24mi)^2+(10mi)^2=c^2[/tex]

[tex]576mi^2+100mi^2=c^2[/tex]

[tex]c^2=676mi^2[/tex]

[tex]c=\sqrt{676mi^2}[/tex]

[tex]c=26mi[/tex]

Answer:

Assuming that the circle bissects the triangles equal sides at their midpoints, the ratio of the larger to smaller triangle should be close to 1/3

The interval of times which represents the middle 68% of Ryan's finishing times in the 400 meter race, using the empirical rule, is 74.5 seconds to 75.5 seconds.

According to the empirical rule, also known as 68-95-99.7 rule, the percentage of values that lie within an interval with 68%, 95% and 99.7% of the values lies within one, two or three standard deviations of the mean of the distribution.

[tex]P(\mu - \sigma < X < \mu + \sigma) = 68\%\\P(\mu - 2\sigma < X < \mu + 2\sigma) = 95\%\\P(\mu - 3\sigma < X < \mu + 3\sigma) = 99.7\%[/tex]

Here we had  where mean of distribution of X is [tex]\mu[/tex]  and standard deviation from mean of distribution of X is [tex]\sigma[/tex].

When Ryan runs the 400 meter dash, his finishing times are normally distributed with a mean of 75 seconds and a standard deviation of 0.5 seconds.

The interval of times that represents the middle 68% of his finishing times in the 400 meter race is,

[tex]P(75 - 0.5 < X < 75 + 0.5) = 68\%\\P(74.5 < X < 75.5) = 68\%[/tex]

Thus. the interval of times which represents the middle 68% of Ryan's finishing times in the 400 meter race, using the empirical rule, is 74.5 seconds to 75.5 seconds.

Learn more about empirical rule here:

https://brainly.com/question/13676793

#SPJ1

Based on the calculations, the chemical element (X) in this nuclear equation is equal to ²³⁵U₉₂.

An alpha decay refers to a type of nuclear reaction in which the atomic nucleus of a radioactive element emits an alpha particle (atom of helium), thereby, producing chemical elements with a different atomic nucleus.

In this exercise, we are given the following nuclear equation with an alpha decay:

²³⁹Pu₉₄  -----> X + ⁴He₂

For the superscript, we have:

239 - 4 = 235.

For the subscript, we have:

94 - 2 = 92.

Therefore, the chemical element (X) is equal to ²³⁵U₉₂.

Read more on alpha decay here: https://brainly.com/question/23303931

Answer:

its c

Step-by-step explanation:

trust

Answer:

266

Step-by-step explanation:

Let the attendence of 5days be a,b,c,d,e

given,

(a+b+c+d+e)/5=264

a+b+c+d+256=264*5 [since 5th day=256]

(a+b+c+d+)/4=1(320-256)/4 [dividing both side by 4]

average attendence of 4 days =266

Answer:

y = negative 5 x + 4

Step-by-step explanation:

Hope it helps you in your learning process

The inverse of the function is f ( x )⁻¹ = x + 4

The function rule is the relationship between the input or domain and the output or range. A relation is a function if and only if there exists one value in the range for every domain value.

A function is a relation from a set of inputs to a set of possible outputs where each input is related to exactly one output.

Given data ,

Let the function be represented as f ( x )

Now , the value of f ( x ) is

f ( x ) = x - 4   be equation (1)

On simplifying , we get

The inverse of the function is given by replacing x with y

So , the value of the function is

y = x - 4

x = y + 4

On interchanging , we get

f ( x )⁻¹ = x + 4

Hence , the inverse is f ( x )⁻¹ = x + 4

To learn more about function rule click :

https://brainly.com/question/3760195

#SPJ7

[tex]5 \frac{1}{4} + 1 \frac{3}{8} [/tex]

Lets solve it

[tex]5 \frac{1}{4} + 1 \frac{3}{8} [/tex]

[tex] \frac{21}{4} + \frac{11}{8} [/tex]

Taking the LCM of both denominator which is 8

[tex] \frac{42 + 11}{8} [/tex]

[tex] \frac{53}{8} [/tex]

Hey ! there

Answer:

Step-by-step explanation:

In this question we are given with two whole fraction . And we are asked to simplify them by adding .

Solution : -

Step 1 : Converting the fractions into improper fraction :

[tex]\dashrightarrow \: \qquad \: \dfrac{21}{4} + \dfrac{11}{8} [/tex]

Step 2 : We know that L.C.M of 4 and 8 is 8. So,

[tex]\dashrightarrow \: \qquad \: \dfrac{42 + 11}{8} [/tex]

Step 3 : Adding 42and 11 :

[tex]\dashrightarrow \: \qquad \: \dfrac{53}{8} [/tex]

Step 4 : Converting it in form of whole fraction :

[tex]\dashrightarrow \: \qquad \blue{\underline{\boxed{\frak{ \:6 \dfrac{5}{8} }}}} \quad\bigstar[/tex]