Answer:
<h3>
- 128 Superscript StartFraction 3 Over x EndFraction
</h3><h3>
- (4RootIndex 3 StartRoot 2 EndRoot)x
</h3><h3>
- (4 (2 Superscript one-third Baseline) ) Superscript x</h3><h3>
Step-by-step explanation:</h3>
Given the indicinal equation ![(\sqrt[3]{128} )^{x}\\](https://tex.z-dn.net/?f=%28%5Csqrt%5B3%5D%7B128%7D%20%29%5E%7Bx%7D%5C%5C)
According to one of the law of indices,
![(\sqrt[a]{m} )^{b}\\= (\sqrt{m})^\frac{b}{a}](https://tex.z-dn.net/?f=%28%5Csqrt%5Ba%5D%7Bm%7D%20%29%5E%7Bb%7D%5C%5C%3D%20%28%5Csqrt%7Bm%7D%29%5E%5Cfrac%7Bb%7D%7Ba%7D)
Applying this law to the question;
![(\sqrt[3]{128} )^{x}\\ = {128} ^\frac{x}{3}\\ \\= (\sqrt[3]{64*2})^{x} \\ = (4\sqrt[3]{2})^{x} \\= (4(2^{1/3} )^{x} )](https://tex.z-dn.net/?f=%28%5Csqrt%5B3%5D%7B128%7D%20%29%5E%7Bx%7D%5C%5C%20%3D%20%7B128%7D%20%5E%5Cfrac%7Bx%7D%7B3%7D%5C%5C%20%5C%5C%3D%20%28%5Csqrt%5B3%5D%7B64%2A2%7D%29%5E%7Bx%7D%20%5C%5C%20%3D%20%284%5Csqrt%5B3%5D%7B2%7D%29%5E%7Bx%7D%20%5C%5C%3D%20%284%282%5E%7B1%2F3%7D%20%29%5E%7Bx%7D%20%29)
The following are therefore true based on the following calculation
128 Superscript StartFraction 3 Over x EndFraction
(4RootIndex 3 StartRoot 2 EndRoot)x
(4 (2 Superscript one-third Baseline) ) Superscript x
Answer:
When multiplying fractions together, you multiply the numerators togethers and the denominators together, unlike adding fractions together. To find this answer, you'd do 3 × 7 (for the numerator) and 8 × 9 (for the denominator), and then write the fraction (the answer) using your answers above.
I hope this helps!
First, split the angle into two angles where the values of the six trigonometric functions are known. In this case, π/12 can be split
into π/3−π/4.
cos(π/3−π/4)
Use the difference formula for cosine to simplify the expression. The formula states that cos(A−B)=cos(A)cos(B)+sin(A)sin(B)
cos(π/3)⋅cos(π/4)+sin(π/3)⋅sin(π/4)
The exact value of cos(π/3) is 12, so:
(12)⋅cos(π/4)+sin(π/3)⋅sin(π/4)
The exact value of cos(π/4) is √22.
(12)⋅(√22)+sin(π/3)⋅sin(π/4)
The exact value of sin(π/3) is √32.
(12)⋅(√22)+(√32)⋅sin(π/4)
The exact value of sin(π/4) is √22.
(12)⋅(√22)+(√32)⋅(√22)
Simplify each term:
√24+√64
Combine the numerators over the common denominator.
<span>(√2+√6)
/ 4</span>
Answer:
Step-by-step explanation:
You would require the table with the number of males and females who prefer either pink or yellow lemonade at the state fair.
Pink Lemonade Yellow Lemonade TOTAL
Male 156 104 260
Female 72 48 120
TOTAL 228 152 380
P(pink lemonade | female) = 72 / (48 + 72) = 72 / 120 = 0.6
P(pink lemonade) = (156 + 72) / (156 + 72 + 104 + 48) = 228 / 380 = 0.6
Therefore, The event "prefers pink lemonade" and "female" are independent because P(pink lemonade | female) = P(pink lemonade) = 0.6
