A graduated cylinder is filled with 36π of liquid. The liquid is poured into a different cylinder that has a radius of 3 cm. What will the height of the liquid be in the new cylinder?

Final answer:

To find the total number of pages they have read so far, add the number of pages Mrs. Ross read to the class and the number of pages Mrs. M read to the class. The total number of pages they have read so far is 5 pages.

Explanation:

To find the total number of pages they have read so far, we need to add the number of pages Mrs. Ross read to the class and the number of pages Mrs. M read to the class.

Mrs. Ross read 1/4 of the chapter, which is 8 x 1/4 = 2 pages.

Mrs. M read 3 pages to the class.

Therefore, the total number of pages they have read so far is 2 + 3 = 5 pages.

Answer:

$29.70

Step-by-step explanation:

The word of in an equation or expression = multiply.

10 percent of $33 =  1/10 x 33/1 or 33/10 ($3.30)

$33 - $3.30 = $29.70

General Idea:

The formula to find the area of parallelogram is given below:

[tex] Area \; of\; the\; parallelogram=BASE \times HEIGHT\\ \\ [/tex]

Applying the concept:

Given, [tex] BASE\; (B)= \; 74\; cm\\ HEIGHT \;(H)=14.8 \;cm\\\\ Area \; of \; the \; Parallelogram = 74 \; cm \times 14.8 \; cm = 1095.2 \; cm^{2} [/tex]

Final answer:

The general solution to the differential equation (8 + x)y' = 3y is y = C(8+x)³, where C is a constant and can be found by integrating and rearranging the separated variables.

Explanation:

To find the general solution of the differential equation (8 + x)y' = 3y, we can separate variables and integrate both sides. First, we divide both sides by (8 + x) and then by y to get [tex]\frac{ y'}{y} = \frac{3}{8 + x}[/tex]

Next, we integrate both sides:

Integrate LHS: [tex]\int \frac{dy}{y} = ln|y| + C_1[/tex]

Integrate RHS: [tex]\int \frac{3dx}{8 + x} = 3ln|8+x| + C_2[/tex]

Now, we can combine the two constants (C₁ and C₂) into a single constant C by writing C = C₂ - C₁. So our solution looks like ln|y| = 3ln|8+x| + C. We can exponentiate both sides to solve for y:

[tex]y = e^{3ln|8+x|+C}[/tex]

Remembering that [tex]e^{ln|a|} = a[/tex], we can simplify this to:

y = C(8+x)³ where C is a constant.

This is the general solution to the differential equation.

Answer:

Cost price of an item = $144.95

Step-by-step explanation:

Cost price is the price at which the article is purchased .

It includes all the expenses incurred on that item till the time it is owned by us .

Selling price is the price at which the item is sold to the customer .

Market price is the price marked on the product . It is basically the current price of the item .

We know that selling price - market price = cost price

Given :

Market price of an item =  $45.00

Selling price of an item = $189.95

To find : cost price of an item

Solution :

Cost price = $189.95 - $45.00 = $144.95

The number 127 is a prime number as it has no divisors other than 1 and itself.

The number 127 is a prime number. A prime number is defined as a number that is greater than 1 and has no positive divisors other than 1 and itself. To determine if 127 is prime, we must check if it can be divided evenly by any number other than 1 and 127. When we perform this check, we find that 127 does not have any divisors other than 1 and itself, confirming that it is indeed a prime number.

The domain of a function is the complete set of possible values of the independent variable.

The range of a function is the complete set of all possible resulting values of the dependent variable (y, usually), after we have substituted the domain.

2x+3y=18

For this equation, domain and range both would be all real numbers.

3x-4y>16

Here domain and range both will be all real numbers.

3 friends equally shared 1/2 pound of trail mix, during the hike.

Total quantity of trail mix = 1/2 pound

Quantity shared by each friend is 1/3 rd of the trial mix

= 1/3 * 1/2 pound

= 1/6 pound

Therefore, during the hike, each friend shared 1/6 pound of the trail mix.

Hope this helps ..!!

Thank you :)

Number of luxury gift tins of biscuits L sold is 18.

Number of mini- packs of 2 biscuits M sold is 80.

Number of normal packets N sold is 2.

Let L, M, N represent the number of Luxury, Mini, and Normal packets sold.

Total earned by selling luxury gift tins of biscuits = 5L

Total earned by selling normal packets =  £1N

Total earned by selling 2 biscuits at 10p = 0.1M

Marianne  tells Amy that she has received exactly 100 donations in total:

Equation becomes:

[tex]L+N+M=100[/tex]     .... (1)

total earning is £100, so another equation becomes:

[tex]5L+N+0.1M=100[/tex]        .......(2)

Given is that stock of £1 packets is very low compared with the other items:  

so, N<L   and N<M

Putting y = 0 in equation 1 and 2

[tex]L+M=100[/tex] or [tex]L=100-M[/tex]    .....(3)

[tex]5L+0.1M=100[/tex]         ......(4)

Replacing L by 100-M in the equation 4

[tex]5(100-M)+0.1M=100[/tex]

[tex]500-5M+0.1M=100[/tex]

4.9M=400

M=81.63

As, L=100-M

[tex]L=100-81.63=18.37[/tex]

L=18.37

We can round L and M to 18 and 81 respectively and solve for N from 1 and 2 equations.

[tex]L+M+N=100[/tex]

=>[tex]18+N+81=100[/tex]

=>[tex]N=1[/tex]

[tex]5(18)+N+0.1(81)=100[/tex]

[tex]90+N+8.1=100[/tex]

=> N=1.9

We will repeat the same process with N = 2 and get the following result.

Number of luxury gift tins of biscuits L sold is 18  

Number of mini- packs of 2 biscuits M sold is 80

Number of normal packets N sold is 2

A direction of 45 degrees clockwise from due east would put you in the South-East quadrant of a compass or geometric plane.

When discussing directions in terms of degrees, it's commonly understood with the idea of a compass rose or a unit circle in mind. Here, 'Due East' is represented as 0 or 360 degrees. A clockwise rotation would mean we are moving in a positive direction.

Therefore, if you start from Due East which is 0 degrees and rotate 45 degrees in the clockwise direction, you would end up in the south-east direction. This is because in the coordinate system, the +x direction is East and moving in the clockwise direction, the next quadrant would be the South-East quadrant. So, 45 degrees clockwise from due east would be considered as South-East direction on a compass rose or geometrically on a plane if you are looking at it in terms of degrees on a circle.

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The ratio is a fraction that tells us how many times longer a thing is compared to another thing. In mathematics, we express a ratio as the relationship between two numbers, namely [tex]a \ and \ b[/tex], so the ratio can be written as:

[tex]r=\frac{a}{b}[/tex]

If we can change this number without changing the ration we need to multiply  both the numerator and the denominator by the same number. For instance, if we have the following ratio:

[tex]r=\frac{2}{3}[/tex]

We can multiply both the numerator and denominator, say, by 7. Then:

[tex]r=\frac{7\times 2}{7 \times 3}=\frac{14}{21}[/tex]

As you can see, the ratio's number has changed but without changing the ratio itself because:

[tex]\frac{2}{3}=\frac{14}{21}[/tex]

OPTION B.

The rectangle with coordinates: (0, 1), (0, 6), (2, 1), and (2, 6) shows the new position of the original rectangle after a translation of 2 units upwards on the y-axis.

In mathematics, a translation moves an object without changing its shape or orientation. You simply move it to another position in the plane. To find the new position of the rectangle after a translation, we need to find which set of coordinates matches those of our original rectangle but is located in a different spot.

Looking at the options given, the only rectangle that represents a translation of the original is the rectangle with coordinates: (0, 1), (0, 6), (2, 1), and (2, 6). This rectangle is similar in shape and orientation to our original rectangle, but it is shifted 2 units upwards on the y-axis.

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A graph that shows the new position of the rectangle after a translation include the following: C. Rectangle with coordinates: (3, 2), (3, 4), (8, 2), and (8, 4).

In Mathematics, a translation is a type of transformation that is typically used for shifting every point of a geometric object in the same direction on the cartesian coordinate, as well as for the same distance.

In this scenario and exercise, we would apply a translation of 2 units to the right and 2 units up to the given rectangle, in order to determine the new position of the rectangle after a translation as follows;

(x, y)                        →           (x + 2, y + 2)

Point (1, 0)               →    (1 + 2, 0 + 2) = (3, 2).

Point (1, 2)                →    (1 + 2, 2 + 2) = (3, 4).

Point (6, 0)               →    (6 + 2, 0 + 2) = (8, 2).

Point (6, 2)               →    (6 + 2, 2 + 2) = (8, 4).

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Complete Question:

Which graph shows the new position of the rectangle after a translation?

Rectangle with coordinates: (1, 0), (1, 2), (6, 0), and (6, 2).

A. Rectangle with coordinates: (0, negative 1), (0, negative 6), (2, negative 1), and (2, negative 6).

B. Rectangle with coordinates: (0, 1), (0, 6), (2, 1), and (2, 6).

C. Rectangle with coordinates: (3, 2), (3, 4), (8, 2), and (8, 4).

D. Rectangle with coordinates: (0, negative 0.5), (1, negative 0.5), (0, negative 3), and (1, negative 3).

When rounding 18.84 to the nearest hundredth, the result is 18.84 that means the number 18.84 remains unchanged when rounded to the nearest hundredth.

Given information:

The number is 18.84 and need to round it to the nearest hundredth.

Steps to round to the nearest hundredth:

Therefore, the number 18.84 remains unchanged when rounded to the nearest hundredth.

Therefore, when rounding 18.84 to the nearest hundredth, the result is 18.84.

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Answer:

150

Step-by-step explanation:

Because, 5 x 3 x 10 = 150.

10 x 3

10 20 30

1    2   3

( add 10 every time )

30 60 90 120 150

1    2   3     4     5

( add 30 every time )

I tried to explain well.

After setting up and correcting a system of equations, the student needs to use 30 kg of the 40% copper alloy and 90 kg of the 80% copper alloy to create 120 kg of a 70% copper alloy.

To solve this problem, we need to set up a system of equations. Let x be the amount of 40% copper alloy needed, and y be the amount of 80% copper alloy needed.

First, we have the total weight equation:

x + y = 120 kg (the final alloy's total weight)

Next, we have the copper content equation:

0.40x + 0.80y = 0.70 × 120 kg (the final alloy's copper content)

Now, let's solve this system of equations:

Address the second equation: 40x + 80y = 8400

Express x in terms of y: 40x = 8400 - 80y

Divide by 40: x = 210 - 2y

Substitute x in the first equation: (210 - 2y) + y = 120

Solve: 210 - y = 120, y = 90 kg

Finally, substitute the value of y back into x = 210 - 2y: x = 210 - 2  imes 90 = 210 - 180 = 30 kg

So, we need 30 kg of the 40% copper alloy and 90 kg of the 80% copper alloy.