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The volume of the given solid. Bounded by the cylinder y^2+z^2=4 and the planes x=2y, x=0, z=0 in the first octant is 16/3 unit cute

V = ∫ dV

= ∫0→2 ∫ 0→π/2 ∫ 0→ 2·r·sin(φ) [ r ] dzdφdr

Factorize to have

= ∫0→2 ∫ 0→π/2 [ r·2·r·sin(φ) - r·0 ] dφdr

= ∫0→2 ∫ 0→π/2 [ 2·r²·sin(φ) ] dφdr

= ∫0→2 [ -2·r²·cos(π/2) + 2·r²·cos(0) ] dr

= ∫0→2 [ 2·r² ] dr

= (2/3)·2³ - (2/3)·0³

Conclusively, this implies that the volume is = 16/3

In conclusion, the volume of the given solid is 16/3. cubic units

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The ratios which are equivalent are as follows:

1) 16:4

4) 480:120

6) 4:1

Step-by-step solution:

1) 16:4

[tex]=\frac{16}{4}[/tex]

[tex]=\frac{4}{1}[/tex]

4:1

2) 2:1

[tex]=\frac{2}{1}[/tex]

2:1

3) 32:2

[tex]=\frac{32}{2}[/tex]

[tex]=\frac{16}{1}[/tex]

=16:1

4) 480:120

[tex]=\frac{480}{120}[/tex]

[tex]=\frac{4}{1}[/tex]

=4:1

5) 4:16

[tex]=\frac{4}{16}[/tex]

[tex]=\frac{1}{4}[/tex]

=1:4

6) 4:1

[tex]=\frac{4}{1}[/tex]

=4:1

Therefore, the correct solution to this question is:

1) 16:4

4) 480:120

6) 4:1

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Answer:

16:4 and 480:120 and 4:1 are equivalent.

Step-by-step explanation:

Answer:

[tex]x=6[/tex]

[tex]y=3\sqrt{2}[/tex]

Step-by-step explanation:

[tex]x^2=(3\sqrt{2})^2+(3\sqrt{2)^2}[/tex]

[tex]\sqrt{x^2} =\sqrt{36}[/tex]

[tex]x=6[/tex]

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

hope it helps..

have a great day!!

Answer:

x=6

y=3√2

Step-by-step explanation:

hope it helps you...

Answer:

To solve this system of equations, you can use the method of elimination. To do this, you can add the two equations together:

4x + 5y - 5x - 3y = -7 - 1

-x + 2y = -8

Then, you can divide both sides of the equation by -1 to solve for y:

x - 2y = 8

y = (x - 8) / 2

Now that you have solved for y, you can substitute this expression back into either of the original equations to solve for x. For example, you can substitute y = (x - 8) / 2 into the first equation to get:

4x + 5((x - 8) / 2) = -7

4x + 5x - 40 = -7

9x = 33

x = 3.67

Now that you have solved for both x and y, you can find the solution to the system of equations:

x = 3.67

y = (3.67 - 8) / 2 = -2.17

So, the solution to the system of equations is x = 3.67 and y = -2.17.

The heart pumps around 17280 pints of blood in a day.

To find out how many pints of blood your heart pumps in a day, we need to determine the total volume of blood that your heart pumps in one day.

We know that your heart pumps 1.5 gallons of blood per minute. To find out how much blood your heart pumps in one day, we need to multiply that amount by the number of minutes in a day.

1 day = 24 hours

1 hour = 60 minutes

So, the number of minutes in one day is 24 hours x 60 minutes = 1440 minutes

Now, we can use this information to find out how many gallons of blood your heart pumps in a day.

Gallons of blood pumped per day = 1.5 gallons/minute x 1440 minutes/day

= 2160 gallons

1 gallon = 8 pints

So the number of pints of blood that your heart pumps in a day = 2160 gallons × 8 pints/gallon = 17280 pints.

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your heart pumps 2000 gallons of blood around your body each day.

if your body pumps around 1.5 gallons of blood each minute then a day is 24 hours so yu do that x together which is 20 but as its hours you do it for 2000 and just incase yu need some more info

(1.5 imperial gallons) x 24 hours = 589.173508 m3 s

SORRY IF THIS DONT ALL MAKE SO MUCH SENSE

Answer: [tex]\frac{4^{9} }{4^{3} }[/tex]=4096

Steps:

[tex]\frac{4^{9} }{4^{3} }[/tex]

[tex]\mathrm{Apply\:exponent\:rule}:\quad \frac{x^a}{x^b}=x^{a-b}[/tex]

[tex]\frac{4^9}{4^3}=4^{9-3}[/tex]

[tex]=4^{9-3}[/tex]

[tex]4^{9} -^{3}[/tex]

=4096

The Simplifying the expression 4 ^ 9 / 4 ^ 3 will be 4096.

Simplification is the process of replacing a mathematical expression with an equivalent one, that is simpler (usually shorter), for example.

Simplification of algebraic expressions, in computer algebra.

Simplification usually involves making the expression simple and easy to use later.

We need to Simplifying the expression

4 ^ 9 / 4 ^ 3 .

Now,  4 ^ 9 / 4 ^ 3

Using exponent formula;

= 4 ^ ( 9 - 3 )

= 4 ^ 6

= 4096

Therefore, the Simplifying the expression 4 ^ 9 / 4 ^ 3 will be 4096.

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Step-by-step explanation:

8 1/4 > - 8 1/4

when you plot these two numbers on number line

8 1/4 will lie on the right of the zero and - 8 1/4 will be on the left of the zero. The numbers on right of the zero are +ve and numbers on the left of zero are -ve. +ve numbers are always greater than -ve numbers. So 8 1/4 > - 8 1/4

To solve this problem, we can set up the following equation:

Torrie + John = Sonia - John

This equation represents the fact that John has the same number of dollars more than Torrie as he has less than Sonia. We can then substitute the given values for Torrie, Sonia, and John to solve for John:

430 + John = 760 - John

Combining like terms, we get:

2 * John = 330

Dividing both sides of the equation by 2, we get:

John = 165

Thus, John has $165.

Answer: 5:3

Step-by-step explanation:

note: 16 ounces= one pound          
6 ounces = ?

∴6 ounces = pounds

48 cents = pounds

multiplying both sides by 

108 cents = 1 pound in the new price

= $1.08 in the new price 

ratio of old price to new price = 

therefore ratio of old to the new price = 5:3

Answer:

1/2 and 1/6

Step-by-step explanation:

Answer:

70

Step-by-step explanation:

for every 5 $20 notes is $100 70 notes is $1400 and the other 20 is $2000 which makes 3400

Answer:

10 hrs 35 min

Step-by-step explanation:

ohh yeahh which show tell me in comment lol

btw it would take u total

621 minutes to complete the show

which meaning 10 hrs and 35 min

and if you touch the grass then it would take few hours more

The slope-intercept form of the equations presented on the graph are;

y = 4

y = 3

The slope-intercept form of the equation of a line is; y = m·x + c, where;

m = The slope of the graph

c = The y-intercept of the graph

The equation of the lines in the graphs (blue line, and red line) are found as follows;

The slope of the blue line is found using the points on the graph as follows;

The coordinates of points on the blue line graph are; (0, 4), (2, 4), (4, 4)

The slope is therefore; m = (4 - 4)/(4 - 2) = 0

The y-intercept, obtained from the graph is; c = 4

The value of the slope, m = 0, indicates that the graph is an horizontal line with an equation y = c

c = 4

The equation of the blue line graph in slope-intercept form is therefore;

The coordinates of points on the red line graph are; (0, 3), (2, 3), (4, 3)

The slope of the red line graph is therefore;

m = (3 - 3)/(4 - 2) = 0

The y-intercept of the red line graph is; c = 3

The value of the slope, m = 0, and the y-intercept, c = 3, indicates that the equation of the red line graph is therefore;

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Answer:

5-3=2m

3x2=6m^2

Step-by-step explanation:

I can’t explain

LETTER B I DON’T KNOW THE ANSWER

The essays that she can review in 1 hour would be; 2 2/3.

A fraction represents a part of a number or any number of equal parts.

We are given that English teacher reviewed 2 /3 of an essay in 1/ 4 of an hour.

Thus, Fraction of the essay reviewed = 2/3

Amount of time used = 1/4

Therefore, the fraction of essay for an hour can be calculated as;

= Fraction of the essay reviewed / Amount of time used

= 2/3 ÷ 1/4

= 2/3 × 4

= 8/3

= 2 2/3

Hence, She will review 2 2/3 essay.

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Answer:

a) P₁ = 0,0294

b) P₂ = 0,097

c) P₃  = 0,1264

P₃  is the total probability of the individual having a positive test result

d) P₄ = 0,232

Step-by-step explanation:

a) Probability that an individual has the disease and has a positive result is P₁ :

P₁ = The probability of having the disease * Probability of + in the test result

P₁ = 0,03 * 0,98

P₁ = 0,0294

b) the probability that an individual does not have the disease and has a positive test result P₂ is:

P₂ = 0,97 * 0,1

P₂ = 0,097

c) P₃   the sum of the two previous probabilities is:

P₃  = 0,0294 + 0,097

P₃  = 0,1264

P₃  is the total probability of the individual having a positive test result

d) Applying the Bayes theorem we can get the probability that an individual with a positive test result has the disease.  (P₄ )

Bayes theorem establishes:

P [ A/B ]  =  P[B/A] * P(A) / P(B)

In this case

P[ with disease/ given (+)tr]

= P [(+)Test/ with disease]* P (with disease)/ P of test +

P₄ = 0,98 * 0,03 / 0,1264

P₄ = 0,232

Answer:

6.89

Step-by-step explanation:

Add 6.89 and 14.52 together. Subtract 14.52 from that. You should get 6.89. Hope this helps.

Answer:

y = - 0.32x² - 1.26x + 15.81

Step-by-step explanation:

From the graph, it can be deduced that the graph isn't linear nor exponential. The graph shown is a quadratic graph. Hence the regression equation which best fits the model is represented in the form :

y = Ax² + Bx + C

Using technology, the regression model obtained by fitting the data is :

y = - 0.32x² - 1.26x + 15.8

Fitted model is attached below

Answer:

Step-by-step explanation:

-140

The answer to |-14| is 14

On solving the provided question, we cans ay that the value of x from the polynomial [tex]5x^4 +2y^5)^4[/tex] and [tex](3x^2 +y)^3[/tex]  is = 16 and 1

A polynomial is a mathematical statement made up of coefficients and uncertainty that exclusively uses additions, subtractions, multiplications, and positive integer powers of variables. A single indeterminate x polynomial is represented by the expression x2 4x + 7. A polynomial is an expression in mathematics that consists of variables (sometimes referred to as indeterminates) and coefficients that may be added, subtracted, multiplied, and raised to negative integer powers of non-variables. A polynomial is an algebraic expression made up of coefficients and variables. The only operations that an expression can contain are addition, subtraction, multiplication, and non-negative integer exponents. These expressions are known as polynomials.

here,

[tex]5x^4 +2y^5)^4[/tex] and [tex](3x^2 +y)^3[/tex]  

as x = 0 and y = 1

answer   is = 16 and 1

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Answer:

The Percentage is 50% because 14 is the half of 28.

Answer:

The answer would be A

Step-by-step explanation:

you would need to change the denominator to 14

Answer:

A is the correct answer

Step-by-step explanation:

If you simplify 10/14 and 7/14, you will get 5/7 and 1/2

Answer:

we need more information

Step-by-step explanation:

Answer:

Only the second and third statements are correct:

Doubling r quadruples the volume.

Doubling h doubles the volume.

Step-by-step explanation:

The volume of a cylinder is given by:

[tex]\displaystyle V=\pi r^2h[/tex]

We can go through each statement and examine its validity.

Statement 1)

If the radius is doubled, our new radius is now 2r. Hence, our volume is:

[tex]\displaystyle V=\pi (2r)^2h=4\pi r^2h[/tex]

So, compared to the old volume, the new volume is quadrupled the original volume.

Statement 1 is not correct.

Statement 2)

Using the previous reasonsing, Statement 2 is correct.

Statement 3)

If the height is doubled, our new height is now 2h. Hence, our volume is:

[tex]V=\pi r^2(2h)=2\pi r^2h[/tex]

So, compared to the old volume, the new volume has been doubled.

Statement 3 is correct.

Statement 4)

Statement 4 is not correct using the previous reasonsing.

Statement 5)

Doubling the radius results in 2r and doubling the height results in 2h. Hence, the new volume is:

[tex]V=\pi (2r)^2(2h)=\pi (4r^2)(2h)=8\pi r^2h[/tex]

So, compared to the old volume, the new volume is increased by eight-fold.

Statement 5 is not correct.

Step-by-step explanation:

slope is y2-y1/x2-x1

formula is

y=mx+b where m is the slope

Answer:

17

Step-by-step explanation:

sdfbh

Step-by-step explanation:

a

sa= 6l²

2000=6l²

l²=333.3

l= 18.2565

b.

v=l³

v= 18.2565³

v= 6084cm³

Answer: x = -5, y = 4

Step-by-step explanation:

Align the two equations according to their terms:

[tex]\left \{ {{-3x-3y = 3} \atop {3x+6y = 9}} \right.[/tex]

Add the two equations. Because -3x and 3x equals zero, they can be eliminated from the equation. This results in:

[tex]3y = 12\\y = 4[/tex]

Plug in y = 4 into the first equation:

[tex]-3x - 3(4) = 3\\[/tex]

Solve for x:

[tex]-3x-12 = 3\\-3x = 15\\x = -5[/tex]

Check by plugging in both x and y:

[tex]-3(-5) - 3(4) = 3\\15 - 12 = 3\\3 = 3[/tex]

So, x = -5 and y = 4