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3 years ago

Solve 3^(2x) = 7^(x_1).

Mathematics

2 answers:

uranmaximum [27]3 years ago

8 0

Applying log to both sides of equation, we get:

2x log 3=(x−1) log 7

x=−0.12915

bulgar [2K]3 years ago

4 0

x=1−log9log7=−0.12915, nearly.

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Answer:

its 7

Step-by-step explanation:

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While shopping at store, Billy

romanna [79]

Answer:

A. 270

Step-by-step explanation:

30% can be rewritten as 3/10

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Bonus: To find the actual price, just subtract this amount (270) from the original price (900).

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Do bonds reduce the overall risk of an investment portfolio? Let x be a random variable representing annual percent return for t

rjkz [21]

Answer:

COV (all stocks) = 0.55

COV (stocks and bonds) = 0.82

Step-by-step explanation:

Coefficient of Variation is used to measure variability.

It is defined as the ration of standard deviation and the mean.

It can be used to compare variability of two population or two samples.

Formula:

$\text{Coefficient of Variation} = \displaystyle\frac{\text{Standard Deviation}}{\text{Mean}}$

$\text{Standard Deviation} = \sqrt{\displaystyle\frac{\sum (x_i -\bar{x})^2}{n-1}}$

where $x_i$ are data points, $\bar{x}$ is the mean and n is the number of observations.

$Mean = \displaystyle\frac{\text{Sum of all observations}}{\text{Total number of observation}}$

x: 14, 0, 39, 25, 32, 27, 28, 14, 14, 15

$Mean = \frac{208}{10} = 20.8$

$Standard~Deviation = \sqrt{\frac{1169.6}{9} } = 11.39$

$Coefficient~of~Variation = \frac{11.39}{20.8} = 0.55$

y = 6, 2, 29, 17, 26, 17, 17, 2, 3, 5

$Mean = \frac{124}{10} = 12.4$

$Standard~Deviation = \sqrt{\frac{924.4}{9} } = 10.13$

$Coefficient~of~Variation = \frac{10.13}{12.4} = 0.82%$

Since coefficient of variation of x is less compared to y, thus it could be said bonds does not reduce overall risk of an investment portfolio.

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3 years ago

The sum of two numbers is 52 . The larger number is 2 less than twice the smaller number .What are the numbers

Nata [24]

Answer:

35.34 and 16.66

Step-by-step explanation:

Given data

let the numbers be x and y

the smaller number = x

the larger number = y

x+y=52--------1

The larger number is 2 less than twice the smaller number

y=2x-2-------2

put y= 2x-2 in eqn 1

x+2x-2=52

3x-2=52

3x=52-2

3x=50

x= 50/3

x= 16.66

put x=16.66 in eqn 1 to find y

x+y=52

16.66+y= 52

y=52-16.66

y= 35.34

Hence the numbers are

35.34 and 16.66

Check

35.34+16.66= 52

4 0

3 years ago

Prove the divisibility: 45^45·15^15 by 75^30

garri49 [273]

Answer:

$3^{75}$ .

Step-by-step explanation:

We have been an division problem: $\frac{45^{45}*15^{15}}{75^{30}}$ .

We will simplify our division problem using rules of exponents.

Using product rule of exponents $(a*b)^n=a^n*b^n$ we can write:

$45^{45}=(9*5)^{45}=9^{45}*5^{45}$

$15^{15}=(3*5)^{15}=3^{15}*5^{15}$

$75^{30}=(15*5)^{30}=15^{30}*5^{30}$

Substituting these values in our division problem we will get,

$\frac{9^{45}*5^{45}*3^{15}*5^{15}}{15^{30}*5^{30}}$

Using power rule of exponents $a^n*a^m=a^{n+m}$ we will get,

$\frac{9^{45}*5^{(45+15)}*3^{15}}{15^{30}*5^{30}}$

$\frac{9^{45}*5^{60}*3^{15}}{15^{30}*5^{30}}$

Using product rule of exponents $(a*b)^n=a^n*b^n$ we will get,

$\frac{(3*3)^{45}*5^{60}*3^{15}}{(3*5)^{30}*5^{30}}$

$\frac{3^{45}*3^{45}*5^{60}*3^{15}}{3^{30}*5^{30}*5^{30}}$

Using power rule of exponents $a^n*a^m=a^{n+m}$ we will get,

$\frac{3^{(45+45+15)}*5^{60}}{3^{30}*5^{(30+30)}}$

$\frac{3^{105}*5^{60}}{3^{30}*5^{60}}$

$\frac{3^{105}}{3^{30}}$

Using quotient rule of exponent $\frac{a^m}{a^n}=a^{m-n}$ we will get,

$\frac{3^{105}}{3^{30}}=3^{105-30}$

$3^{105-30}=3^{75}$

Therefore, our resulting quotient will be $3^{75}$ .

7 0

3 years ago