A solid metal cylinder with a length of 24 cm and radius 2cm is melted down to a form of sphere . what is the radius of the sphere.

Step-by-step explanation:

Break it up into two trapezoids as shown

area = trap1 + trap2

      = 2 *   (7+3) / 2   + 3 *  ( 7 + 3) / 2 = 10 + 15 = 25 units^2

Part A: we can set up the following inequality: 230 + 20p > 900,  Part B: p > 33.5 , i.e. Dean must do at least 34 push-ups on each remaining day to reach his goal of more than 900 push-ups this month.

Part A:

To represent the number of push-ups, p, Dean must do on each remaining day to reach his goal, we can set up the following inequality:

230 + 20p > 900

This inequality states that the sum of the push-ups Dean has already done (230) and the total number of push-ups he will do on the remaining days (20p) must be greater than his goal of 900 push-ups.

Part B:

To find the minimum number of push-ups Dean must do on each remaining day to reach his goal, we can solve the inequality:

230 + 20p > 900

Subtracting 230 from both sides:

20p > 670

Dividing both sides by 20:

p > 33.5

Since the number of push-ups cannot be fractional, Dean must do at least 34 push-ups on each remaining day to reach his goal of more than 900 push-ups this month.

To learn more about inequality click here:

brainly.com/question/20383699

#SPJ11

The statement that best proves that <XWY ≅ <ZYW is that two parallel lines are cut by a transversal, then the alternate interior angles are congruent

To determine the correct statement, we need to know the properties of a parallelogram.

These properties includes;

Learn more about parallelogram at: https://brainly.com/question/10744696

#SPJ1

Answer:

C. (-7, -15)

Step-by-step explanation:

Both the x- and the y-coordinates of a point in the third quadrant are negative.  The given point C. (-7, -15) is the only one of the four choices that satisfies this criterion.

Answer:

i got you it 10,000

Step-by-step explanation:

all you have to do is add the zeros

Answer:

y = 1

Step-by-step explanation:

y is inversely proportion to x means that ,

y ∝ 1/x or ,

\(y\ \alpha\ \frac{1}{x}\)

When we remove the proportionality sign we get,

\(y=k(\frac{1}{x})\\y=\frac{k}{x} \\\)

now we know the point is (2 , 3) which means it corresponds to (x , y) which furthermore means y=3 when x=2,

so we insert these values and get the value of k.

\(y=\frac{k}{x} \\\\3=\frac{k}{2}\\\\6=k\\\)

now the equation becomes,

\(y=\frac{6}{x}\)

now we need to find y when x is 6 so just replace x with 6

\(y=\frac{6}{x}\\\\y=\frac{6}{6} \\\\y=1\)

so we get the value of y is 1

The change in volume is -88π

The volume is nothing but the amount of space occupied by a three-dimensional figure as measured in cubic units.

Volume Change is defined as the variation in the existing volume of the service type which is provided by the Supplier under the Agreement

The radius is decreasing at 2 inches per minute

The height is given as decreasing at 4 inches per minute

So let \(\frac{dr}{dt}=-2\) and

\(\frac{dh}{dt}=-4\)

and we have radius r=6,

                     height h=5

The volume of the cone is represented by V as V=\(\frac{1}{3}\pi r^{2}h\)

Then

\(\frac{dv}{dt}=\frac{\pi }{3}[r^{2}\frac{dh}{dt} +h*2r\frac{dr}{dt}]\)

\(=\frac{\pi }{3}[6^{2}(-4)+5*2(6)(-2)]\)

\(=\frac{\pi }{3}[36(-4)+5(12)(-2)]\\ =\frac{\pi }{3}[-144+(-120)]\\ =\frac{-264}{3}\pi \\ =-88\pi\)

So the volume change is \(-88\pi\)

Learn more about volume change here:

https://brainly.com/question/6392516

#SPJ4

When the variables r = 3 and y = -6, the value of the expression is -27.

In Mathematics, an expression is sometimes referred to as an equation and it can be defined as a mathematical equation which is typically used for illustrating the relationship that exist between two (2) or more variables, parameters, and numerical quantities (number).

Based on the information provided, the mathematical expression is given by;

Mathematical expression = √x⁴ - y²

Substituting the given parameters into the mathematical expression, we have;

Mathematical expression = √(3)⁴ - (-6)²

Mathematical expression = √81 - 36

Mathematical expression = 9 - 36

Mathematical expression = -27.

Read more on expression here: https://brainly.com/question/25767785

#SPJ1

Complete Question:

Type the correct answer in the box. use numerals instead of words. Enter the number of the topic sentence.

Consider this expression. √x⁴ - y². When r = 3 and y = -6, the value of the expression is____.

Answer: The exponential function is typically defined as:

f(x) = e^x

where e is a mathematical constant approximately equal to 2.71828.

To understand how this function is derived, we need to start with the concept of compound interest. Suppose we have an investment that earns an annual interest rate of r, and let P be the initial principal investment. After one year, the investment will be worth P(1 + r). If we leave the investment for another year, the value will be P(1 + r)^2, and after n years, the value will be P(1 + r)^n.

Now, suppose we want to know what happens to the value of the investment as the time period becomes infinitely small (i.e., in the limit as n approaches infinity). We can do this by considering the limit of the expression (1 + r/n)^n as n approaches infinity. This limit is known as the exponential constant e.

Using calculus, we can prove that the limit of (1 + 1/n)^n as n approaches infinity is equal to e. We can then use this result to define the exponential function as e^x, where x is any real number.

Using the definition of e^x, we can show that the derivative of the exponential function is itself. That is:

d/dx e^x = e^x

This result is known as the exponential function's own derivative property, and it is one of the reasons why the exponential function is so important in mathematics.

Step-by-step explanation:

The ratio of the error is; 0.3333

The Percent error of the given problem is;  33.33%

We are given;

Amount spent by John on shopping = $75

Amount expected to spend = $100

Since this is what was given then it means we will have the following;

The approximate value to be spent = 100 dollars

Exact Value  spent = 75 dollars

Therefore, the error made is;

Error = Approximate value - Exact value  

Error = 100 - 75

Error =  25 dollars

Thus, the error when it is absolute is;

Absolute Error = ±25 dollars

Now, the ratio will be;

Ratio(e) = Error/exact value spent

e = 25/75 = 0.3333

Percent Error = error * 100%

Percent error = 0.3333 * 100%

Percent error =  33.33%

Read more about Percentage error at; https://brainly.com/question/5493941

#SPJ1

Answer:

7n+5 would get u the perimeter because you can add like terms together so I added all the ns to get that- hope that helps you ❣️

Step-by-step explanation:

Answer:

y = 2

Step-by-step explanation:

Since the y- coordinates of the ordered pairs are all 2

This indicates the line is horizontal with equation y = c

where c is the value of the y- coordinates the line passes through, then

y = 2 ← equation of line

Answer:2

Step-by-step explanation:x/6+29=41

41-29=12

12/6=2

Answer:  Let the 2 numbers be x and  

sum of two numbers is 28....Eq 1:  x + y = 28

sum of 6 times the 1st number and 3 times the 2nd number is 105....Eq 2:  6x + 3y = 105

Rearrange Eq 1 to solve for x.

x + y = 28

x = 28 - y  --> Substitute into Eq 2, you get

6(28 - y) + 3y = 105

168 - 6y + 3y = 105

-3y = -63

y = -63 / -3 = 21

Now solve for x using Eq 1.

x = 28 - y = 28 - 21 = 7

hope  it helped

Step-by-step explanation:

Only statement left is "Events A and B are mutually exclusive," which is also not true since P(A∩B) = 0.1, which is greater than 0.

Thus, none of the statements is true.

None of the statements is true.

If events A and B were independent, then P(A∩B) = P(A)P(B) = 0.4, which is not equal to 0.1.

If events A and B were mutually exclusive, then P(A∩B) = 0, which is not equal to 0.1.

Therefore, neither of the first two statements is true.

Since P(A∪B) = P(A) + P(B) - P(A∩B), we have P(A∩B) = 0.4, which is not equal to 0.1. Therefore, the third statement is not true.

The only statement left is "Events A and B are mutually exclusive," which is also not true since P(A∩B) = 0.1, which is greater than 0.

Thus, none of the statements is true.

To learn more about statements visit:

https://brainly.com/question/30238773

#SPJ11

Answer:

1,318

Step-by-step explanation:

you will multiple 6.59 by 2

Answer:

22.40 pounds

Step-by-step explanation:

2 cashews =13.18 pounds

A quarter of cashew =1/4*6.59

=9.226 pounds

Total amount =22.406 pounds

Nearest cent=22.40 pounds

Answer:

The number is a perfect square because 16 x 16= 256

Step-by-step explanation:

The correct option is; they are both perfect squares and perfect cubes.

Perfect squares are numbers that their square root can be found easily without any remainder. and A perfect cube of a number is a number that is equal to the number, multiplied by itself, three times.

Given the following patterns;

1*1 = 1  and 1*1*1 = 1

It can be seen that 1 is 1 perfect square, since 1*1 = 1² = 1

Also, 1 is perfect cube since 1*1*1 = 1³ = 1 (cube of the value gives 1)

Similarly, for the expression;

8*8 = 64

8² = 64 (since the square of 8 gives 64, then 64 is known to be a perfect square)

Also, 4*4*4 = 64

i.e 4³ = 64 (This shows that the cube root of 64 is 4 making it a perfect cube since we can get a whole number for the cube root of 64)

The same is applicable for other expressions 729 = 27 × 27, and 9 × 9 × 9, 4,096 = 64 × 64, and 16 × 16 × 16

These values are easily expressed as a constant multiple of a number, showing that they are both perfect squares and perfect cubes.

Hence, The correct option is; they are both perfect squares and perfect cubes.

For more references on perfect squares and perfect cubes, click;

https://brainly.com/question/29056294

#SPJ5

Answer:X=-13

Step-by-step explanation:

The minimum amount of green paint he has to throw away so he can use  rest to add blue or yellow paint in order to get exactly 5 liters of correct shade of green is 5/3 liter.

We know that "original-shade" of green color requires "2-liters" of blue paint and "3-liters" of yellow paint.

So, the original-ratio of "yellow-paint" to "total-paint" is = 3 : 5,

He mixes 3-litres of "blue" and 2-litres of "yellow" for 5 liters of paint,

So, he has more blue-paint in mixture than it is required to make green color,

He needs to throw some of green-paint and add yellow-paint to get required shade-of-green.

Let the painter throw away "x-liters" of paint from his mixture and adds "x-liters" of yellow-paint into mixture.

So, New mixture will have same ratio as 3:5,

So, the equation in x is,

⇒ (2/5)×(5 - x) + x = (3/5)×5,

⇒ 2 - (2/5)x + x = 3,

⇒ (3/5)x = 1,

⇒ x = 5/3.

Therefore, the painter needs to throw away 5/3 liters of paint.

Learn more about Ratio here

https://brainly.com/question/14305279

#SPJ4

Answer: 11.78

Step-by-step explanation:

Answer: 27/45 > 20/45

Step-by-step explanation:

You must make the denominator of each fraction equivalent while keeping the value of each individual fraction the same.

3/5 x (9/9) = 27/45

4/9 x (5/5) = 20/45

27/45 > 20/45

Answer: 27/45 > 20/45

Step-by-step explanation:

You must make the denominator of each fraction equivalent while keeping the value of each individual fraction the same.

3/5 x (9/9) = 27/45

4/9 x (5/5) = 20/45

27/45 > 20/45

Answer:

the variable is 9x

Step-by-step explanation:

Answer:

It would take him eight hours, but only if at the end of your sentence you meant miles.

Step-by-step explanation:

8miles_____ 30mn

30miles ____________________ *hrs

8 div by 30, .266667 miles per min

mult by 30

Answer:

$28

Step-by-step explanation:

80% means 80/100

Of means multiplication

So, 80% of $35

= 80/100 X 35

= 0.8 X 35

= 28

The rank-nullity theorem states that for any matrix A, the sum of the rank of A and the dimension of the null space of A is equal to the number of columns of A. The answer is (a) Dim Row A = 5, Dim Col A = 5.

In this case, we know that the null space of the 7 x 6 matrix is 5-dimensional. Therefore, we can use the rank-nullity theorem to solve for the rank of A.
Number of columns of A = 6
Dimension of null space of A = 5
Rank of A = Number of columns of A - Dimension of null space of A
Rank of A = 6 - 5
Rank of A = 1
So the answer is (a) Rank A = 1. To find the dimensions of the row space and column space, we can use the fact that the row space and column space have the same dimension as the rank of the matrix.
Dim Row A = Rank A = 1
Dim Col A = Rank A = 1

Learn more about rank-nullity theorem here:

https://brainly.com/question/31477084

#SPJ11

The price of a season pass at Carowinds is $260.

An equation is a mathematical statement containing two expressions on either sides which are connected with an equal to sign.

Either sides of an equation is called as left hand side and right hand side.

Given that,

At carowinds, a season pass has four times the price of a single day pass.

Let x be the price of a single day pass.

From the information given in the question, Price of a season pass = 4x

Cindy bought two season passes and three single day passes for a total cost of 715$.

So we have an equation as below.

2(4x) + 3x = 715

8x + 3x = 715

11x = 715

x = 65

So, the price of a single day pass = $65

and the price of a season pass = 4x = $260

Hence $260 is the price of a season pass.

Learn more about Equations by clicking here :

https://brainly.com/question/28691809

#SPJ9

Answer:

life is possible on earth due to layers of air that surround it