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nevsk [136]
3 years ago
14

1. A teacher had 8 packages of paper she wanted to split equally into 3 piles. How much should be in each pile? Between what two

whole numbers does your answer lie?
Mathematics
1 answer:
castortr0y [4]3 years ago
4 0

Answer:

If division of the packages in fractional numbers was possible, it should be 2.667 packages per pile.

The answer lies between 2 and 3 packages per pile.

Step-by-step explanation:

This can be solved as a simple division.

To split 8 packages in 3, this should correspond to 8/3≈2.667.

If division of the packages in fractional numbers was possible, it should be 2.667 packages per pile.

Other way to think about it is like mentally allocating a package in each pile. We can go up to 2 packages per pile (a total of 6 packages), and we can only add a package to 2 piles, letting the last pile to have only two packages.

Then, we have 2 piles with 3 packages and one pile with 2 packages.

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On a road map with a scale of 1 cm. : 110 mi., the distance between two cities measures 4.5 cm. What is the actual distance betw
Scorpion4ik [409]

Answer:

465 miles

Step-by-step explanation:

So you have the ratio 1 cm: 110 mi, so you can multiply both sides of this ratio by 4.5 to get

4.5 cm: 465 mi

8 0
3 years ago
Evaluate the integral by changing to polar coordinatesye^x dA, where R is in the first quadrant enclosed by the circle x^2+y^2=2
34kurt
\displaystyle\iint_Rye^x\,\mathrm dA=\int_{\theta=0}^{\theta=\pi/2}\int_{r=0}^{r=5}r^2\sin\theta e^{r\cos\theta}\,\mathrm dr\,\mathrm d\theta

which follows from the usual change of coordinates via

\begin{cases}\mathbf x(r,\theta)=r\cos\theta\\\mathbf y(r,\theta)=r\sin\theta\end{cases}

and Jacobian determinant

|\det J|=\left|\begin{vmatrix}\mathbf x_r&\mathbf x_\theta\\\mathbf y_r&\mathbf y_\theta\end{vmatrix}\right|=|r|

Swap the order, so that the integral is

\displaystyle\int_{r=0}^{r=5}\int_{\theta=0}^{\theta=\pi/2}r^2\sin\theta e^{r\cos\theta}\,\mathrm d\theta\,\mathrm dr

and now let \sigma=r\cos\theta, so that \mathrm d\sigma=-r\sin\theta. Now, you have

\displaystyle\int_{r=0}^{r=5}\int_{\sigma=0}^{\sigma=r}re^\sigma\,\mathrm d\sigma\,\mathrm dr=\int_{r=0}^{r=5}r(e^r-1)\,\mathrm dr=4e^5-\dfrac{23}2
7 0
3 years ago
5. Mr. Trimke drove 280 miles in 5 hours. If he drove the same speed, how long would it
serious [3.7K]

Answer:

The answer is B

Explanation:

speed = distance/time

s = 280/5

= 56mi/hr

time = distance/speed

t = 420/56

= 7.5hr

7 0
3 years ago
HELP ASAP with this question.
Soloha48 [4]
The answer is A, 16. Here's some work: 

6x + 2 = 98
6x = 96
x = 16
7 0
3 years ago
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The circumference of a circular field is 285.5 yards. What is the diameter of the field? Use 3.14 for pi and do not round your a
ArbitrLikvidat [17]
Hi hope this helps, thanks

6 0
2 years ago
Read 2 more answers
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