The rule for multiplying similar bases with exponents:
(a^b)(a^c)=a^(b+c)
In this case we have:
(5^-2)(5^-1)
5^(-2-1)
5^(-3)
The rule for negative exponents:
a^(-b)=1/(a^b)
So in this case:
5^(-3) is equal to
1/(5^3)
1/125
Answer:
Scale factor of cube to the smaller cube is 5 : 3.
Step-by-step explanation:
Ratio of the volumes of two cubes = 
= 
= 
Scale factor of these cubes = ![\sqrt[3]{\text{ratio of the volumes of the cubes}}](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B%5Ctext%7Bratio%20of%20the%20volumes%20of%20the%20cubes%7D%7D)
= ![\sqrt[3]{\frac{\text{volume of large prism}}{\text{Volume of small prism}}}](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B%5Cfrac%7B%5Ctext%7Bvolume%20of%20large%20prism%7D%7D%7B%5Ctext%7BVolume%20of%20small%20prism%7D%7D%7D)
= ![\sqrt[3]{\frac{125}{27} }](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B%5Cfrac%7B125%7D%7B27%7D%20%7D)
= 
= 5 : 3
Therefore, scale factor of cube to the smaller cube is 5 : 3.
Answer:
29° + (x - 5)° = 180°
29 + x - 5 = 180
29 - 5 + x = 180
24 + x = 180
24 - 24 + x = 180 - 24
x = 156
Step-by-step explanation:
A straight line is 180°.
Set all angles (29° and (x - 5)°) equal to 180°.
Then solve for x.
<span>What is the solution of the system? y=9x-2 y=7x+3
b.(5/2,41/2)
The table below shows the height (in inches) and weight (in pounds)of eight basketball players.
Height=67, 69, 70, 72, 74, 78, 79 Weight=183, 201, 206, 240, 253, 255 what is the correlation of the set of data? Round your answer to the nearest thousandth.
d.0.981
3.The table below shows the average height of a species of tree (in feet) after a certain number of years.
Years=1, 2, 3, 4, 5, 6, 7, 8 Height=2.1, 3.2, 6.8, 7.3, 11.2, 12.6, 13.4, 15.9 about how tall would you expect one of these trees to be after 22 years?
c.44.25ft
4.You use a line of best fit for a set of data to make a prediction about an unknown value. The correlation coefficient for your data set is 0.984. How confident can you be that your predicted value will be reasonably close to the actual value?
c.I can be very confident; it will be close, but it probably won't be exact.
</span>
There’s not enough information to answer your question.
