Answer:
There will be 13 such bags and Jesse will earn $ 78 by selling the energy bars.
Step-by-step explanation:
Jesse made 312 mini energy bars. She put 24 bars in each bag. So, there will be, 
= 13 such bags.
She plans to sell each bag for $6, so she will earn
$ 
= $ 78 by selling the energy bars.
9514 1404 393
Answer:
Step-by-step explanation:
The ratio of smallest sides in the two triangles is ...
smaller / larger = 4/10
To find A and B, we write proportions involving corresponding side lengths.
__
Side A in the smaller triangle is ...
A/15 = 4/10
A = (4/10)(15) = 6
__
The ratio of larger to smaller is the inverse of the above ratio, so ...
B/9 = 10/4
B = (10/4)(9) = 22.5
Work the information to set inequalities that represent each condition or restriction.
2) Name the
variables.
c: number of color copies
b: number of black-and-white copies
3)
Model each restriction:
i) <span>It
takes 3 minutes to print a color copy and 1 minute to print a
black-and-white copy.
</span><span>
</span><span>
3c + b</span><span>
</span><span>
</span><span>ii) He needs to print
at least 6 copies ⇒
c + b ≥ 6</span><span>
</span><span>
</span><span>iv) And must have
the copies completed in
no more than 12 minutes ⇒</span>
3c + b ≤ 12<span />
4) Additional restrictions are
c ≥ 0, and
b ≥ 0 (i.e.
only positive values for the number of each kind of copies are acceptable)
5) This is how you
graph that:
i) 3c + b ≤ 12: draw the line 3c + b = 12 and shade the region up and to the right of the line.
ii) c + b ≥ 6: draw the line c + b = 6 and shade the region down and to the left of the line.
iii) since c ≥ 0 and b ≥ 0, the region is in the
first quadrant.
iv) The final region is the
intersection of the above mentioned shaded regions.v) You can see such graph in the attached figure.
Answer:
![(\sqrt[7]{3} )^{4}](https://tex.z-dn.net/?f=%28%5Csqrt%5B7%5D%7B3%7D%20%29%5E%7B4%7D)
Step-by-step explanation:
The only radical that matches the equivalent answer is the fifth one down. We can easily eliminate the radicals without exponents on the outside, since we know they won't create leftover fractions. So that leaves us with the second, fourth and fifth answers to contemplate.
Let's look at ![(\sqrt[4]{3} )^{7}](https://tex.z-dn.net/?f=%28%5Csqrt%5B4%5D%7B3%7D%20%29%5E%7B7%7D)
and ![\sqrt[4]{3^{7} }](https://tex.z-dn.net/?f=%5Csqrt%5B4%5D%7B3%5E%7B7%7D%20%7D)
first. It's good to know that these are equivalent radicals. The numbers are the same, and they will produce the same answers.
When you do the math, the exponent rule gives us fractions of 
for exponents, and eventually, a 
for both answers. So these are eliminated.
Now, for ![(\sqrt[4]{3}^{7}](https://tex.z-dn.net/?f=%28%5Csqrt%5B4%5D%7B3%7D%5E%7B7%7D)
, we can easiy simplify by changing the 7th root to a fraction in our exponent. Use the rule: ![\sqrt[n]{x} = x^{\frac{1}{n} }](https://tex.z-dn.net/?f=%5Csqrt%5Bn%5D%7Bx%7D%20%3D%20x%5E%7B%5Cfrac%7B1%7D%7Bn%7D%20%7D)
- <em>Multiply the exponents:</em>
- <em>Insert the product into the exponent: </em> <u>
</u>
And we can see the answer we're looking for! If you use this method to look at the other problems, you'll see that this is the only radical that simplifies to the required answer.
Answer:
![\dfrac{\sqrt[5]{810x^3}}{3x}](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Csqrt%5B5%5D%7B810x%5E3%7D%7D%7B3x%7D)
Step-by-step explanation:
As a rule, the "simplified form" means there are no fractions under a radical.
![\sqrt[5]{\dfrac{10x}{3x^3}}=\sqrt[5]{\dfrac{10x(3^4x^2)}{3x^3(3^4x^2)}}=\sqrt[5]{\dfrac{810x^3}{(3x)^5}}=\boxed{\dfrac{\sqrt[5]{810x^3}}{3x}}](https://tex.z-dn.net/?f=%5Csqrt%5B5%5D%7B%5Cdfrac%7B10x%7D%7B3x%5E3%7D%7D%3D%5Csqrt%5B5%5D%7B%5Cdfrac%7B10x%283%5E4x%5E2%29%7D%7B3x%5E3%283%5E4x%5E2%29%7D%7D%3D%5Csqrt%5B5%5D%7B%5Cdfrac%7B810x%5E3%7D%7B%283x%29%5E5%7D%7D%3D%5Cboxed%7B%5Cdfrac%7B%5Csqrt%5B5%5D%7B810x%5E3%7D%7D%7B3x%7D%7D)
