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yKpoI14uk [10]
3 years ago
6

A teacher reviews 4-1/2 papers per hour, how many papers will that teacher review in 6-1/3 hours

Mathematics
1 answer:
MrRa [10]3 years ago
5 0

Answer:

28\frac{1}{2}\ papers

Step-by-step explanation:

step 1

Convert mixed numbers to an improper fractions

4\frac{1}{2}=\frac{4*2+1}{2}=\frac{9}{2}

6\frac{1}{3}=\frac{6*3+1}{3}=\frac{19}{3}

step 2

we know that

A teacher reviews 9/2 papers per hour

using proportion

Find how many papers will the teacher review in 19/3 hours

Let

x-----> the number of papers

(9/2)/1=x/(19/3)

x=(19/3)(9/2)

x=28.5\ papers

Convert to mixed numbers

28.5=28\frac{1}{2}\ papers

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Simplify the algebraic expression: 4(3x + y) – 2(x – 5y)
VladimirAG [237]

Answer:

C

Step-by-step explanation:

First use distribution

4(3x+y)= 12x+4y

and

-2(x-5y)= -2x+10y

combine the 2 answers

10x+14y

3 0
3 years ago
Find the area of the part of the plane 3x 2y z = 6 that lies in the first octant.
gavmur [86]

The area of the part of the plane 3x 2y z = 6 that lies in the first octant  is  mathematically given as

A=3 √(4) units ^2

<h3>What is the area of the part of the plane 3x 2y z = 6 that lies in the first octant.?</h3>

Generally, the equation for is  mathematically given as

The Figure is the x-y plane triangle formed by the shading. The formula for the surface area of a z=f(x, y) surface is as follows:

A=\iint_{R_{x y}} \sqrt{f_{x}^{2}+f_{y}^{2}+1} d x d y(1)

The partial derivatives of a function are f x and f y.

\begin{aligned}&Z=f(x)=6-3 x-2 y \\&=\frac{\partial f(x)}{\partial x}=-3 \\&=\frac{\partial f(y)}{\partial y}=-2\end{aligned}

When these numbers are plugged into equation (1) and the integrals are given bounds, we get:

&=\int_{0}^{2} \int_{0}^{3-\frac{3}{2} x} \sqrt{(-3)^{2}+(-2)^2+1dxdy} \\\\&=\int_{0}^{2} \int_{0}^{3-\frac{3}{2} x} \sqrt{14} d x d y \\\\&=\sqrt{14} \int_{0}^{2}[y]_{0}^{3-\frac{3}{2} x} d x d y \\\\&=\sqrt{14} \int_{0}^{2}\left[3-\frac{3}{2} x\right] d x \\\\

&=\sqrt{14}\left[3 x-\frac{3}{2} \cdot \frac{1}{2} \cdot x^{2}\right]_{0}^{2} \\\\&=\sqrt{14}\left[3-\frac{3}{2} \cdot \frac{1}{2} \cdot x^{2}\right]_{0}^{2} \\\\&=\sqrt{14}\left[3.2-\frac{3}{2} \cdot \frac{1}{2} \cdot 3^{2}\right] \\\\&=3 \sqrt{14} \text { units }{ }^{2}

In conclusion,  the area is

A=3 √4 units ^2

Read more about the plane

brainly.com/question/1962726

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5 0
1 year ago
What should be added to both sides of this equation to solve for the variable?<br> -6 + f = 13
SpyIntel [72]

Answer:

Nesesito ayuda sobre estas dos preguntas la1 y la ocho pero tiene que tener sentido con las demas

Step-by-step explanation:

7 0
3 years ago
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HELP PLZ<br><br> 7k + 4s = 20<br> -8k + 2s = 10<br><br> What is the value of k?
Finger [1]
Divide 20 by 4=5
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k=5/7
8 0
3 years ago
Why is the length of the base of the rectangle the same as the circumference of the circles in the net of a cylinder?
Salsk061 [2.6K]

Answer:

The width of the rectangle is the same as the length of the cylinder (h). The area of each of the two circles is \\ (\\pi r^2\\) and the area of the rectangle is \\ (2 \\pi r times h\\).

Step-by-step explanation:

6 0
3 years ago
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