Answer:
![E = 30 \times H](https://tex.z-dn.net/?f=E%20%3D%2030%20%5Ctimes%20H)
$570
Step-by-step explanation:
Given that:
For each hour of tutoring, Lena earns 30 dollars.
E is her earning and
H is the number of hours for which she tutors.
To find:
Equation relating E to H.
Solution:
Let Lena tutors for 1 hour, then the earning = 30 dollars
Let Lena tutors for 2 hours, then the earning = 30+30 OR 2
30 = 60 dollars
Let Lena tutors for 3 hours, then the earning = 30+30 +30 OR 3
30 = 90 dollars
If Lena tutors for H number of hours, then the earning, E = 30 + 30 + .... + 30 (H times) i.e.
![E = 30 \times H](https://tex.z-dn.net/?f=E%20%3D%2030%20%5Ctimes%20H)
So, the equation that relates E to H is given as:
![E = 30 \times H](https://tex.z-dn.net/?f=E%20%3D%2030%20%5Ctimes%20H)
Now, it is given that she tutors for 19 hours.
Let us put H = 19 hours in the above equation:
![E = 30 \times 19 \\\Rightarrow E = \$570](https://tex.z-dn.net/?f=E%20%3D%2030%20%5Ctimes%2019%20%5C%5C%5CRightarrow%20E%20%3D%20%5C%24570)
Therefore, the earning for 19 hours of tutoring is <em>570 Dollars.</em>
Answer:
The volume of a box is:
V = 560 cubic inches or
cubic inches.
Step-by-step explanation:
Given
The width of a box = w = 2 2/3 inches
i.e. ![\:w=2\frac{2}{3}=\frac{8}{3}](https://tex.z-dn.net/?f=%5C%3Aw%3D2%5Cfrac%7B2%7D%7B3%7D%3D%5Cfrac%7B8%7D%7B3%7D)
The length of a box = l = 3 1/3 inches
i.e. ![l=\:3\frac{1}{3}=\frac{10}{3}](https://tex.z-dn.net/?f=l%3D%5C%3A3%5Cfrac%7B1%7D%7B3%7D%3D%5Cfrac%7B10%7D%7B3%7D)
The height of a box = h = 2 1/3 inches
i.e. ![\:h=2\frac{1}{3}=\frac{7}{3}](https://tex.z-dn.net/?f=%5C%3Ah%3D2%5Cfrac%7B1%7D%7B3%7D%3D%5Cfrac%7B7%7D%7B3%7D)
Using the formula to determine the volume of a box
![V=w\times l\times h](https://tex.z-dn.net/?f=V%3Dw%5Ctimes%20l%5Ctimes%20h)
substitute
,
and
,
![V=\frac{8}{3}\times \frac{10}{3}\times \frac{7}{3}](https://tex.z-dn.net/?f=V%3D%5Cfrac%7B8%7D%7B3%7D%5Ctimes%20%5Cfrac%7B10%7D%7B3%7D%5Ctimes%20%5Cfrac%7B7%7D%7B3%7D)
Apply the fraction rule: ![\frac{a}{b}\times \frac{c}{d}=\frac{a\:\times \:c}{b\:\times \:d}](https://tex.z-dn.net/?f=%5Cfrac%7Ba%7D%7Bb%7D%5Ctimes%20%5Cfrac%7Bc%7D%7Bd%7D%3D%5Cfrac%7Ba%5C%3A%5Ctimes%20%5C%3Ac%7D%7Bb%5C%3A%5Ctimes%20%5C%3Ad%7D)
![=\frac{8\times \:10\times \:7}{3\times \:3\times \:3}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B8%5Ctimes%20%5C%3A10%5Ctimes%20%5C%3A7%7D%7B3%5Ctimes%20%5C%3A3%5Ctimes%20%5C%3A3%7D)
or
cubic inches
Therefore, the volume of a box is:
V = 560 cubic inches or
cubic inches.
They are trying to spen on a long trip