Answer:
<h2>There are 5040 different possible sequences.</h2>
Step-by-step explanation:
Three identical notches and four identical bends are required in the sheet metal operation.
In total 7 things are required in the metal operation.
We can think it as we need to put the 3 notches and 4 bends in 7 places.
First, lets put the 3 notches in 3 places.
In order to do so, we need to choose 3 places from the 7 places.
We can choose 3 places in
ways.
The 3 notches can be arrange in 3! = 6 ways.
The 4 bends can arrange in 4! = 24 ways.
Thus, in total
different possible sequences.
Answer:
We conclude that:
![\:\sqrt[3]{200k^{15}}=2k^5\sqrt[3]{25}](https://tex.z-dn.net/?f=%5C%3A%5Csqrt%5B3%5D%7B200k%5E%7B15%7D%7D%3D2k%5E5%5Csqrt%5B3%5D%7B25%7D)
Hence, option B is correct.
Step-by-step explanation:
Given the expression
![\sqrt[3]{200k^{15}}](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B200k%5E%7B15%7D%7D)
Apply radical rule:
![\sqrt[n]{ab}=\sqrt[n]{a}\sqrt[n]{b},\:\quad \mathrm{\:assuming\:}a\ge 0,\:b\ge 0](https://tex.z-dn.net/?f=%5Csqrt%5Bn%5D%7Bab%7D%3D%5Csqrt%5Bn%5D%7Ba%7D%5Csqrt%5Bn%5D%7Bb%7D%2C%5C%3A%5Cquad%20%5Cmathrm%7B%5C%3Aassuming%5C%3A%7Da%5Cge%200%2C%5C%3Ab%5Cge%200)
so the expression becomes
![\sqrt[3]{200k^{15}}=\sqrt[3]{200}\sqrt[3]{k^{15}}](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B200k%5E%7B15%7D%7D%3D%5Csqrt%5B3%5D%7B200%7D%5Csqrt%5B3%5D%7Bk%5E%7B15%7D%7D)
first solving
![\sqrt[3]{k^{15}}](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7Bk%5E%7B15%7D%7D)
Apply radical rule: ![\sqrt[n]{a^m}=a^{\frac{m}{n}},\:\quad \mathrm{\:assuming\:}a\ge 0](https://tex.z-dn.net/?f=%5Csqrt%5Bn%5D%7Ba%5Em%7D%3Da%5E%7B%5Cfrac%7Bm%7D%7Bn%7D%7D%2C%5C%3A%5Cquad%20%5Cmathrm%7B%5C%3Aassuming%5C%3A%7Da%5Cge%200)
![\sqrt[3]{k^{15}}=k^{\frac{15}{3}}=k^5](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7Bk%5E%7B15%7D%7D%3Dk%5E%7B%5Cfrac%7B15%7D%7B3%7D%7D%3Dk%5E5)
then solving
![\sqrt[3]{200}](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B200%7D)
prime factorization: 200: 2³ · 5²
![=\sqrt[3]{2^3\cdot \:5^2}](https://tex.z-dn.net/?f=%3D%5Csqrt%5B3%5D%7B2%5E3%5Ccdot%20%5C%3A5%5E2%7D)
Apply radical rule:
![\sqrt[n]{ab}=\sqrt[n]{a}\sqrt[n]{b},\:\quad \mathrm{\:assuming\:}a\ge 0,\:b\ge 0](https://tex.z-dn.net/?f=%5Csqrt%5Bn%5D%7Bab%7D%3D%5Csqrt%5Bn%5D%7Ba%7D%5Csqrt%5Bn%5D%7Bb%7D%2C%5C%3A%5Cquad%20%5Cmathrm%7B%5C%3Aassuming%5C%3A%7Da%5Cge%200%2C%5C%3Ab%5Cge%200)
![=\sqrt[3]{2^3}\sqrt[3]{5^2}](https://tex.z-dn.net/?f=%3D%5Csqrt%5B3%5D%7B2%5E3%7D%5Csqrt%5B3%5D%7B5%5E2%7D)
Apply radical rule:
![\sqrt[n]{a^n}=a,\:\quad \:a\ge 0](https://tex.z-dn.net/?f=%5Csqrt%5Bn%5D%7Ba%5En%7D%3Da%2C%5C%3A%5Cquad%20%5C%3Aa%5Cge%200)
so
![=2\sqrt[3]{5^2}](https://tex.z-dn.net/?f=%3D2%5Csqrt%5B3%5D%7B5%5E2%7D)
Thus, the main expression becomes
![\sqrt[3]{200k^{15}}=\sqrt[3]{200}\sqrt[3]{k^{15}}](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B200k%5E%7B15%7D%7D%3D%5Csqrt%5B3%5D%7B200%7D%5Csqrt%5B3%5D%7Bk%5E%7B15%7D%7D)
![=2k^5\sqrt[3]{25}](https://tex.z-dn.net/?f=%3D2k%5E5%5Csqrt%5B3%5D%7B25%7D)
Therefore, we conclude that:
![\:\sqrt[3]{200k^{15}}=2k^5\sqrt[3]{25}](https://tex.z-dn.net/?f=%5C%3A%5Csqrt%5B3%5D%7B200k%5E%7B15%7D%7D%3D2k%5E5%5Csqrt%5B3%5D%7B25%7D)
Hence, option B is correct.
Answer:
The percentage of people who prefer football is approximately the same for the right- and left-handed groups.
Step-by-step explanation:
The bar for the right-handed group representing soccer is between 10% and 20% (below 20%) while the bar for the left-handed group representing soccer is at 20%.
Percentage of left-handed group of people who prefer soccer is higher than the right-handed group who prefer soccer. Therefore, they don't have the same percentage.
Answer:
b = 43
Step-by-step explanation:
So let's plug things in first:
y= 2x - 20 and y= -5x +b which can become →
2x - 20 = -5x + b (now you said that x=9 so let's plug that in)
2(9) -20 = -5(9) + b (now try solving that)
18 -20 = -45 + b → -2 = -45 + b ( so then add 45 to both sides)
43 = b ( and there's your answer )
5.12? Maybe 24? I’m sorry if there wrong which they probably are. Sorry :(