Answer:
The profit on 5 L moisturizer bottle is $797.25.
Step-by-step explanation:
The cost of 5 L of moisturizer bottle = $146.50
The cost of each milliliter jar = $0.40
Total number of small jars = 125
⇒ The total Cost price of 125 jars = 125 x Cost of each jar
= 125 x $0.40 = $50
So, the Total Cost Price = Cost of Big Bottle + Cost of small 125 bottles
= $146.50 + $50 = $196.50
Now, Selling price of each jar = $7.95
⇒ The total Selling price of 125 jars = 125 x Selling price of each jar
= 125 x $7.95 = $993.75
Now Profit on 5 L bottle = TOTAL S.P - TOTAL C.P
= $993.75 - $196.50
= $797.25
Hence, the profit on 5 L moisturizer bottle is $797.25.
Answer:
x=-1 or x=4
Step-by-step explanation:
38 is the correct answer because 80-4=76 then divide that by 76/2 give you 38
Answer
we have,
a=[2,-1,4], b=[0,1,1/2]
we need to find projection of b onto a.
scalar projection
= ![\dfrac{a.b}{|a|}](https://tex.z-dn.net/?f=%5Cdfrac%7Ba.b%7D%7B%7Ca%7C%7D)
= ![\dfrac{(2,-1,4).(0,1,1/2)}{\sqrt{2^2+(-1)^2+4^2}}](https://tex.z-dn.net/?f=%5Cdfrac%7B%282%2C-1%2C4%29.%280%2C1%2C1%2F2%29%7D%7B%5Csqrt%7B2%5E2%2B%28-1%29%5E2%2B4%5E2%7D%7D)
= ![\dfrac{2\times (0)+(-1)\times 1 + 4\times 0.5}{\sqrt{2^2+(-1)^2+4^2}}](https://tex.z-dn.net/?f=%5Cdfrac%7B2%5Ctimes%20%280%29%2B%28-1%29%5Ctimes%201%20%2B%204%5Ctimes%200.5%7D%7B%5Csqrt%7B2%5E2%2B%28-1%29%5E2%2B4%5E2%7D%7D)
=![\dfrac{1}{\sqrt{21}}](https://tex.z-dn.net/?f=%5Cdfrac%7B1%7D%7B%5Csqrt%7B21%7D%7D)
now, vector projection
= ![\dfrac{a.b}{|a|^2}.a](https://tex.z-dn.net/?f=%5Cdfrac%7Ba.b%7D%7B%7Ca%7C%5E2%7D.a)
= ![\dfrac{(2,-1,4).(0,1,1/2)}{(\sqrt{2^2+(-1)^2+4^2})^2}.(2,-1,4)](https://tex.z-dn.net/?f=%5Cdfrac%7B%282%2C-1%2C4%29.%280%2C1%2C1%2F2%29%7D%7B%28%5Csqrt%7B2%5E2%2B%28-1%29%5E2%2B4%5E2%7D%29%5E2%7D.%282%2C-1%2C4%29)
= ![\dfrac{2\times (0)+(-1)\times 1 + 4\times 0.5}{21}.(2,-1,4)](https://tex.z-dn.net/?f=%5Cdfrac%7B2%5Ctimes%20%280%29%2B%28-1%29%5Ctimes%201%20%2B%204%5Ctimes%200.5%7D%7B21%7D.%282%2C-1%2C4%29)
=![\dfrac{1}{21}.(2,-1,4)](https://tex.z-dn.net/?f=%5Cdfrac%7B1%7D%7B21%7D.%282%2C-1%2C4%29)
=![(\dfrac{2}{21},\dfrac{-1}{21},\dfrac{4}{21})](https://tex.z-dn.net/?f=%28%5Cdfrac%7B2%7D%7B21%7D%2C%5Cdfrac%7B-1%7D%7B21%7D%2C%5Cdfrac%7B4%7D%7B21%7D%29)
Answer:
Answer: -4 > x > 3 or x < -4 and x > 3
Step-by-step explanation:
» On the negative side,
![{ \tt{ \hookrightarrow \: x < - 4}}](https://tex.z-dn.net/?f=%7B%20%5Ctt%7B%20%5Chookrightarrow%20%5C%3A%20x%20%3C%20%20-%204%7D%7D)
» On the positive side,
![{ \tt{ \hookrightarrow \: x > 3}}](https://tex.z-dn.net/?f=%7B%20%5Ctt%7B%20%5Chookrightarrow%20%5C%3A%20x%20%3E%203%7D%7D)
» Overall inequality,
![{ \tt{x < - 4 \: \: or \: \: x > 3}} \\ \\ { \boxed{ \tt{ \: 3 < x < - 4}}} \\ { \rm{or : }} \\ { \boxed{ \tt{ \: - 4 > x > 3}}}](https://tex.z-dn.net/?f=%7B%20%5Ctt%7Bx%20%3C%20%20-%204%20%5C%3A%20%20%5C%3A%20or%20%5C%3A%20%20%5C%3A%20x%20%3E%203%7D%7D%20%5C%5C%20%20%5C%5C%20%7B%20%5Cboxed%7B%20%5Ctt%7B%20%5C%3A%20%203%20%3C%20x%20%3C%20%20-%204%7D%7D%7D%20%5C%5C%20%7B%20%5Crm%7Bor%20%3A%20%7D%7D%20%5C%5C%20%7B%20%5Cboxed%7B%20%5Ctt%7B%20%5C%3A%20%20-%204%20%3E%20x%20%3E%203%7D%7D%7D)