Someone please help me to prove this. ​

Answer:

The volume of the tumor experimented a decrease of 54.34 percent.

Step-by-step explanation:

Let suppose that tumor has an spherical geometry, whose volume ([tex]V[/tex]) is calculated by:

[tex]V = \frac{4\pi}{3}\cdot R^{3}[/tex]

Where [tex]R[/tex] is the radius of the tumor.

The percentage decrease in the volume of the tumor ([tex]\%V[/tex]) is expressed by:

[tex]\%V = \frac{\Delta V}{V_{o}} \times 100\,\%[/tex]

Where:

[tex]\Delta V[/tex] - Absolute decrease in the volume of the tumor.

[tex]V_{o}[/tex] - Initial volume of the tumor.

The absolute decrease in the volume of the tumor is:

[tex]\Delta V = V_{o}-V_{f}[/tex]

[tex]\Delta V = \frac{4\pi}{3}\cdot (R_{f}^{3}-R_{o}^{3})[/tex]

The percentage decrease is finally simplified:

[tex]\%V = \left[1-\left(\frac{R_{f}}{R_{o}}\right)^{3} \right]\times 100\,\%[/tex]

Given that [tex]R_{o} = R[/tex] and [tex]R_{f} = 0.77\cdot R[/tex], the percentage decrease in the volume of tumor is:

[tex]\%V = \left[1-\left(\frac{0.77\cdot R}{R}\right)^{3} \right]\times 100\,\%[/tex]

[tex]\%V = 54.34\,\%[/tex]

The volume of the tumor experimented a decrease of 54.34 percent.

Answer:

x=−9

Step-by-step explanation:

i hope this helps you

Answer:

x=-9

Step-by-step explanation:

Subtracting 53 from both sides, you get -2/3x=6.

-9*2/3x=6

x=-9

Answer:

irrational

Step-by-step explanation:

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

Explanation:

S = sum of the first four values

S/4 = 70 since we divide the sum by 4 to get the mean of the first four values

S = 280 is the result after multiplying both sides by 4

Let x be the fifth unknown value. Adding it onto S leads to S+x = 280+x. This represents the sum of all five values.

Dividing that sum 280+x over 5 leads to the new mean 80, which leads to...

----------

(280+x)/5 = 80

280+x = 5*80

x+280 = 400

x = 400-280

x = 120

The fifth number is 120

The fifth number is 120

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the four numbers be = a , b , c , d

Let the fifth number be = e

Now , the mean of 4 numbers is m = 70

So , the equation will be

( a + b + c + d ) / 4 = 70

Multiply by 4 on both sides , we get

a + b + c + d = 280   be equation (1)

Now , the mean of 5 numbers is m = 80

So , the equation will be

( a + b + c + d + e ) / 5 = 80

Multiply by 5 , we get

a + b + c + d + e = 400   be equation (2)

Substitute the value of equation (1) in equation (2) , we get

a + b + c + d + e = 400

280 + e = 400

Subtracting 280 on both sides , we get

e = 400 - 280

e = 120

Therefore , the value of e is 120

Hence , The fifth number is 120

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Answer:

D

Step-by-step explanation:

Answer:

20=2x

20/2=x

X=10

Step-by-step explanation:

Answer:

x=10

Step-by-step explanation:

20 divided by 2 equals 10.

Answer:

c

Step-by-step explanation:

35/2=17.5 *2= 35+35+35= 105

6.5% of 105 is 6.83, so 105+ 6.83= 111.83

Answer:

3n + 6

Step-by-step explanation:

7.

three times a number: 3n

six more than three times a number: 3n + 6

Answer:

Step-by-step explanation:

-4x - 4 = -4x - 8

=4 ≠ -8

no solution

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Answer:

no solution

Step-by-step explanation:

-4x - 4 = -4(x + 2)

Distribute

-4x -4 = -4x -8

Add 4x to each side

-4x+4x - 4 = -4x+4x -8

-4 = -8

This is never true so there is no solution

Answer:

210 km

Step-by-step explanation:

1cm : 70km

3 x 70 = 210

3cm : 210km

Hopefully this helps you :)

pls mark brainlest ;)

Answer:

[tex]y=-\dfrac{153}{35}[/tex].

Step-by-step explanation:

The given equation is

[tex]0.15(y-0.2)=2-0.5(1-y)[/tex]

Using distributive property, we get

[tex]0.15(y)+0.15(-0.2)=2-0.5(1)-0.5(-y)[/tex]

[tex]0.15y-0.03=2-0.5+0.5y[/tex]

[tex]0.15y-0.03=1.5+0.5y[/tex]

Isolate variable terms.

[tex]0.15y-0.5y=1.5+0.03[/tex]

[tex]-0.35y=1.53[/tex]

Divide both sides by -0.35.

[tex]y=\dfrac{1.53}{-0.35}[/tex]

[tex]y=-\dfrac{1.53}{0.35}\times \dfrac{100}{100}[/tex]

[tex]y=-\dfrac{153}{35}[/tex]

Therefore, [tex]y=-\dfrac{153}{35}[/tex].

Answer:

3n²+3n-60

Step-by-step explanation:

Area of rectangle= L*W

A=3(n-1)(n+2)

A=3(n²+n-2)

A=3n²+3n-6

54=3n²+3n-6

3n²+3n-6-54=0

3n²+3n-60=0

Answer:

3, 3, - 60

Step-by-step explanation:

Area = lw

Therefore 54=(3n-3)(n+2)

Expand and we get:

3n^2+6n-3n - 6=54

Combine terms and move 54 to left side:

3n^2+3n-60

Hope this helped!

Work Shown:

|x-12.2| = 0.3

x-12.2 = -0.3 or x-12.2 = 0.3

x = -0.3+12.2 or x = 0.3+12.2

x = 11.9 or x = 12.5

The min length is 11.9 cm and the max length is 12.5 cm

Subtracting 12.2 from either x value leads to a positive difference of 0.3 which is the margin of error.

Answer:

it’s B. $25.50

Answer:

[tex]xy+3x-23y-3[/tex]

Step-by-step explanation:

[tex]1xy+3x-(23y+3)\\[/tex]

Multiply ; 1× x =x

[tex]=xy+3x-\left(23y+3\right)\\[/tex]

Use - to open the bracket

[tex]-\left(23y+3\right):\quad -23y-3\\\\=xy+3x-23y-3[/tex]

Answer:

Step-by-step explanation:

Answer:

the answer is

36(thirty six)

Answer:

25 years old

Step-by-step explanation:

Let the teacher's age be a.

Then:

a^2 - 23a = 50

In standard form, this quadratic is

x^2 - 23a - 50 = 0

Factoring this, we get (x - 25)(x + 2) = 0

So a is either 25 or a is -2.  Only a = 25 is relevant here.

The teacher is 25 years old (Answer G)

Answer:

scientific notation

Step-by-step explanation:

This number is shown in scientific notation.

Answer:

0.00000146

Step-by-step explanation:

I took the test

Answer:

9 is your answer.

Step-by-step explanation:

Solve for b. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS.

First, add 9 to both sides:

8b - 9 (+9) = b (+9)

8b = b + 9

Next, subtract b from both sides:

8b (-b) = b (-b) + 9

8b - b = 9

7b = 9

Divide 7 from both sides:

(7b)/7 = (9)/7

b = 9/7

Plug in 9/7  for b in the equation given:

7(b) = 7(9/7) = 9

9 is your answer.

~

Are you looking for slope?

if u r the slope is -6/3

A slope of line will be "[tex]-\frac{1}{2}[/tex]".

According to the question,

We know,

Slope of line:

= [tex]\frac{Y2-Y1}{X2-X1}[/tex]

By substituting the values, we get

= [tex]\frac{8-11}{2-(-4)}[/tex]

= [tex]\frac{-3}{6}[/tex]

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

Thus the answer above is correct.

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Answer:

2[tex]\pi[/tex]rh

Step-by-step explanation:

A little easier way to see:

2 * [tex]\pi[/tex] * r * h

Answer:

no solution

Step-by-step explanation:

|x| = -10

Absolute value means that it is positive or 0

It cannot be negative

There is no solution

Step-by-step explanation:

There is no solution

|A|

can be only 0 or positive number

can't be -

from the rule of Mathematics

Answer:8.6

Step-by-step explanation:

Answer:

fourth option

Step-by-step explanation:

Given

[tex]\frac{2x-1}{y}[/tex] = [tex]\frac{w+2}{2z}[/tex] ( cross- multiply )

y(w + 2) = 2z(2x - 1) = 4xz - 2z ( divide both sides by y )

w + 2 = [tex]\frac{4xz-2z}{y}[/tex] ( subtract 2 from both sides )

w = [tex]\frac{4xz-2z}{y}[/tex] - 2

it depends on what your supposed to do i would finish it myself

Answer:

Step-by-step explanation:

0.3(10-5x)=31.5(8x+9)

Expand the terms in the bracket

That's

3 - 1.5x = 252x + 283.5

Subtract 3 from both sides

3-3 - 1.5x = 252x + 283.5 - 3

-1.5x = 252x + 280.5

Subtract 252x from both sides

That's

- 1.5x - 252x = 252x - 252x + 280.5

- 253.5x = 280.5

Divide both sides by -253.5

We have the final answer as

x = - 1.106

Hope this helps you

Answer:

(x,y). y = x + 3 y = -x - 5

Step-by-step explanation:

Answer:

(-4,-1)

Step-by-step explanation:

I graphed the two lines using a graphing tool. When graphed, the lines intercept at (-4,-1). Therefore, (-4, -1) is the solution.

Please see the graph attached.  

Hope this helps.