3. 140= 3x +x
140= 4x
140/4 = 4x/4
35=x
3x= 35 * 3
3x= 105
The length is 105 ft
4. Number of dimes= d and number of quarters=q
d+q= 27
10d + 25q= 405
d= 27-q
10(27 -q) +25 q= 405
270 -10q + 25q= 405
270 + 15q= 405
15q= 135
q=9
d + q= 27
d +9=27
d=18
She has 18 dimes
5. 6 gal with a 50-50 split means 3 gallons each. The 60-40 has 3 gallons of lime. If 3 gal is 60%, the volume is 5 gal. We need to add 1 gallon
Answer: a) critical value = 0.0853, b) we reject the null hypothesis.
Step-by-step explanation:
Since we have given that
z = -1.37
And the hypothesis are given below:

Since α = 0.01
since critical value = 0.0853
As we can see that 0.853 < 0.25.
so, we reject the null hypothesis.
Hence, a) critical value = 0.0853, b) we reject the null hypothesis.
Answer: 
Step-by-step explanation:
The expression given in the exercise is:

If you descompose the number 8 into its prime factors, you get that:

Therefore, you can rewrite the numerator of the expression as following:

For this exercise you need to remember that for a Difference of cubes:

Then, applying this, you get:

Now, it is necessary to remember the following:

Knowing the above, you can say that:

Therefore applying this, you get that the simplified expression is:

You can do 3 quarter's and 9 nickels. or 12 dimes or half dollar and quarter and 9 nickels