(a) 14.90 rounded is 15, and 1.25 rounded is 1, so 15-1 is $14.
(b) My estimation will be high because I had to round up on the larger number and round down on the smaller number leaving a larger gap between the answer and the estimation.
(c) 14.90-1.25=13.65, so Pedro has $13.65 left in his wallet. But the difference between the estimation and the answer is 14-13.65=0.35 so its a $0.35 difference between the estimation and the answer for how much would be left in Pedro's wallet.
<u>ANSWER</u>
![\sqrt[3]{- 729{a}^{9} {b}^{6} } = - 9 {a}^{3} {b}^{2}](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B-%20729%7Ba%7D%5E%7B9%7D%20%20%7Bb%7D%5E%7B6%7D%20%7D%20%20%3D%20%20-%209%20%7Ba%7D%5E%7B3%7D%20%7Bb%7D%5E%7B2%7D%20)
<u>EXPLANATION</u>
We want to find the cube root of

We express this symbolically as:
![\sqrt[3]{- 729 {a}^{9} {b}^{6} }](https://tex.z-dn.net/?f=%20%5Csqrt%5B3%5D%7B-%20729%20%7Ba%7D%5E%7B9%7D%20%20%7Bb%7D%5E%7B6%7D%20%7D%20)
The expression under the radical called the radicand.
We need to express this radical in exponential form using the property,
![{x}^{ \frac{m}{n} } = \sqrt[n]{ {x}^{m} }](https://tex.z-dn.net/?f=%20%7Bx%7D%5E%7B%20%5Cfrac%7Bm%7D%7Bn%7D%20%7D%20%20%3D%20%20%5Csqrt%5Bn%5D%7B%20%7Bx%7D%5E%7Bm%7D%20%7D%20)
Applying this rule gives us:
![\sqrt[3]{- 729 {a}^{9} {b}^{6} } = ({- 729 {a}^{9} {b}^{6}})^{ \frac{1}{3} }](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B-%20729%20%7Ba%7D%5E%7B9%7D%20%20%7Bb%7D%5E%7B6%7D%20%7D%20%20%3D%20%20%28%7B-%20729%20%7Ba%7D%5E%7B9%7D%20%20%7Bb%7D%5E%7B6%7D%7D%29%5E%7B%20%5Cfrac%7B1%7D%7B3%7D%20%7D%20)
![\sqrt[3]{- 729{a}^{9} {b}^{6} } = ({- {9}^{3} {a}^{9} {b}^{6}})^{ \frac{1}{3} }](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B-%20729%7Ba%7D%5E%7B9%7D%20%20%7Bb%7D%5E%7B6%7D%20%7D%20%20%3D%20%20%28%7B-%20%7B9%7D%5E%7B3%7D%20%20%7Ba%7D%5E%7B9%7D%20%20%7Bb%7D%5E%7B6%7D%7D%29%5E%7B%20%5Cfrac%7B1%7D%7B3%7D%20%7D%20)
Recall that

We apply this rule on the RHS to get,
![\sqrt[3]{- 729{a}^{9} {b}^{6} } = ({- {9}^{3 \times { \frac{1}{3} } } {a}^{9 \times { \frac{1}{3} } } {b}^{6 \times { \frac{1}{3} } }})](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B-%20729%7Ba%7D%5E%7B9%7D%20%20%7Bb%7D%5E%7B6%7D%20%7D%20%20%3D%20%20%28%7B-%20%7B9%7D%5E%7B3%20%5Ctimes%20%7B%20%5Cfrac%7B1%7D%7B3%7D%20%7D%20%7D%20%20%7Ba%7D%5E%7B9%20%5Ctimes%20%7B%20%5Cfrac%7B1%7D%7B3%7D%20%7D%20%7D%20%20%7Bb%7D%5E%7B6%20%5Ctimes%20%7B%20%5Cfrac%7B1%7D%7B3%7D%20%7D%20%7D%7D%29)
This simplifies to
![\sqrt[3]{- 729{a}^{9} {b}^{6} } = - 9 {a}^{3} {b}^{2}](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B-%20729%7Ba%7D%5E%7B9%7D%20%20%7Bb%7D%5E%7B6%7D%20%7D%20%20%3D%20%20-%209%20%7Ba%7D%5E%7B3%7D%20%7Bb%7D%5E%7B2%7D%20)
Answer:
A) 0.47 km
B) 4.88 km
C) 6.25°
Step-by-step explanation:
Please refer to the attached image for explanations
Answer:
C
Step-by-step explanation:
In this question, we are interested in calculating the z-score of a company employee.
Mathematically;
z-score = (x- mean)/SD
where in this case;
x is the value given which turns out to be the annual salary of the employee = 28,000
Mean = 34,000
standard deviation = 4,000
Plugging these values into the equation above, we have;
z-score = (28000-34000)/4000 = -6000/4000 = -1.5
Answer:
Angle = 45
Supplement = 135
Complement = 45
Step-by-step explanation: