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KATRIN_1 [288]
3 years ago
7

(3x - 2)^5 =(3x - 2)^2

Mathematics
1 answer:
andreyandreev [35.5K]3 years ago
4 0

Answer:

x=3/2,1

Step-by-step explanation:Given

(3x-2)ˆ5-(3x-2)ˆ2=0

(3x-2)ˆ3(3x-2)ˆ2-(3x-2)ˆ2=0

(3x-2)ˆ2{(3x-2)ˆ3-1}=0

(3x-2)ˆ2=0 Or (3x-2)ˆ3-1=0

3x-2=0 Or(3x-2)ˆ3=1

x=3/2 Or 3x-2=1, x=1

You might be interested in
The number of bats in a colony is growing exponentially. After 2 years, there were 180 bats. After 5 years, there were 1440 bats
TEA [102]

Answer:

23040 bats

Step-by-step explanation:

Let N(t) be the number of bats at time t

We know that exponential function

y=ab^t

According to question

N(t)=ab^t

Where t (in years)

Substitute t=2 and N(2)=180

180=ab^2...(1)

Substitute t=5 and N(5)=1440

1440=ab^5...(2)

Equation (1) divided by equation (2)

\frac{180}{1440}=\frac{ab^2}{ab^5}=\frac{1}{b^{5-2}}

By using the property a^x\div a^y=a^{x-y}

\frac{1}{8}=\frac{1}{b^3}

b^3=8=2\times 2\times 2=2^3

b=2

Substitute the values of b in equation (1)

180=a(2)^2=4a

a=\frac{180}{4}=45

Substitute t=9

N(9)=45(2)^9=23040 bats

Hence, after 9 years the expected bats in the colony=23040 bats

8 0
3 years ago
A pension fund manager is considering three mutual funds. The first is a stock fund, the second is a long-term government and co
Firdavs [7]

This problem is about pension fund management. It is to be noted that the best Feasible Capital Allocation Line (CAL) is: 0.3162.

<h3>What is Capital Allocation Line (CAL)?</h3>

A graph's capital allocation line depicts all conceivable combinations of risky and risk-free assets, allowing investors to estimate future returns depending on risk.

<h3>What is the calculation for the above solution?</h3>

It is to be noted that the optimal risky portfolio's stock percentage is determined by:

Weight of Stock = ((Return on Stock - Risk Free Rate) * Variance of bond) - ((Return on Bond - Risk Free Rate) * Co-Variance of bond & Stock)/ ((Return on Stock - Risk Free Rate) * Variance of bond + (Return on Bond - Risk Free Rate) * Variance of Stock - ((Return on Bond - Risk Free Rate + Return on Stock - Risk Free Rate + ) * Co-Variance of bond & Stock)

→ The weight of stock

= ((15% - 5.5%) * 529) - ((9% - 5.5%) * 110.40)/ ((15% - 5.5%) * 529) + (9% - 5.5%) * 1,024 - ((15% - 5.5% + 9% - 5.5%) * 110.40)

= [(50.255) * (3.864) /(50.255) + (46.08) - (14.352)]

Weight of Stock = 0.646628

Weight of  Bonds = 1 - 0.646628

Weight of  Bonds= 0.353372

Expected return of portfolio = 0.646628 * 15% + 0.353372 * 9%

= 12.88%

Standard Deviation of Portfolio (SDP)= (0.6466282² * 1,024 + 0.3533722² * 529 + 2 * 0.646628* 0.353372* 110.40)⁰·⁵

SDP = (544.67)⁰·⁵

SDP = 23.34%

Hence,

Best feasible CAL = (12.88% - 5.5%)/ 23.34%

Best feasible CAL = <u>0.3162</u>

Learn more about Feasible Capital Allocation Line (CAL):

brainly.com/question/24154917

#SPJ1

Full Question

See the attached spread sheet for additional information related to the questions.

Download xlsx
5 0
2 years ago
What is 1’3/4”-2’3/4”
PSYCHO15rus [73]

Answer:

2

7

–

3

8

=

– 5

56

Result in decimals: -0.089285714285714

Calculation steps:

2

7

–

3

8

=

2 × 8

7 × 8

–

3 × 7

8 × 7

=

16

56

–

21

56

=

16 – 21

56

=

– 5

56

5 0
3 years ago
What is 2 6/8 in fraction
sukhopar [10]
1/3ni who’s your not a
5 0
3 years ago
Read 2 more answers
A random sample of 146 recent donations at a certain blood bank reveals that 81 were type A blood. Does this suggest that the ac
Tju [1.3M]

Answer:

We reject H₀  the actual percentage of type A donations differs from 40%

Step-by-step explanation:

Sample information:

sample size   n = 146

Type A   x₁  =  81   and   p₁  = 81 / 146     p₁  =  0,5547

then  q₁   =  1 - p₁    q₁  =  1  -  0,5547    q₁  =  0,4453

We choose as significance level  α  = 5%  α = 0,05   α /2  = 0,025

from z-table we find   z (c) = 1,96

National % of the population  ( μ  = 40 %  μ = 0,4 )

Test hypothesis

Null hypothesis                           H₀           p₁  =  μ

Alternative Hypothesis              Hₐ           p₁   ≠ μ

The Alternative hypothesis indicates that the test is a two-tail test

z(s) =  ( p₁  -   μ )/ √ p₁*q₁ / n

z(s) =  ( 0,5547  -  0,40 )/ √ 0,5547*0,4453 / 146

z(s) =  0,1547 / 0,041

z(s) = 3,77

Comparing  z(s)  and z(c)

z(s) > z(c)  

z(s) is in the rejection region. We reject H₀. Sample does not give evidence to support that the actual percentage of type A donations is equal to the national population

6 0
2 years ago
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