PLS HELP (40 POINTS!!)

Mathematics

2 answers:

attashe74 [19]2 years ago

7 0

Okay!

(◍•ᴗ•◍)

⇒first, add all the marks 6+7+8+9+10

⇒the answer will be 40 then there is

⇒5 numbers which were 6+7+8+9+10 the numbers that we were trying to add

⇒so divide 40÷5 is 8

⇒ the mean is 8

ФωФ

sineoko [7]2 years ago

5 0

Answer:

Number of students:

5 + 4 + 7 + 10 + 4 = 30

Total of marks:

5*6 + 4*7 + 7*8 + 10*9 + 4*10 = 244

Mean mark:

244/30 = 8.1333 ≈ 8

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3^x= 3*2^x solve this equation

kompoz [17]

In the equation

$3^x = 3\cdot 2^x$

divide both sides by $2^x$ to get

$\dfrac{3^x}{2^x} = 3 \cdot \dfrac{2^x}{2^x} \\\\ \implies \left(\dfrac32\right)^x = 3$

Take the base-3/2 logarithm of both sides:

$\log_{3/2}\left(\dfrac32\right)^x = \log_{3/2}(3) \\\\ \implies x \log_{3/2}\left(\dfrac 32\right) = \log_{3/2}(3) \\\\ \implies \boxed{x = \log_{3/2}(3)}$

Alternatively, you can divide both sides by $3^x$ :

$\dfrac{3^x}{3^x} = \dfrac{3\cdot 2^x}{3^x} \\\\ \implies 1 = 3 \cdot\left(\dfrac23\right)^x \\\\ \implies \left(\dfrac23\right)^x = \dfrac13$

Then take the base-2/3 logarith of both sides to get

$\log_{2/3}\left(2/3\right)^x = \log_{2/3}\left(\dfrac13\right) \\\\ \implies x \log_{2/3}\left(\dfrac23\right) = \log_{2/3}\left(\dfrac13\right) \\\\ \implies x = \log_{2/3}\left(\dfrac13\right) \\\\ \implies x = \log_{2/3}\left(3^{-1}\right) \\\\ \implies \boxed{x = -\log_{2/3}(3)}$