Solve the proportion x+1/x-1 = 14/20

Marvin invested 65% of his retirement account in stocks and 35% in gold. Marvin believes that the return to stocks over the next

ser-zykov [4K]

Answer:

1)

the mean rate of return is 17 %

the standard deviation of return is 17.06055

2)

the probability that Marvin's portfolio will make at least 20% over the next 12 months is 0.4325

Step-by-step explanation:

Given the data in the question;

1)

For the portfolio, the mean return and standard deviation are computed as follows;

Mean = Return = 0.65 × 10 + 0.35 × 30

= 6.5 + 10.5

= 17 %

Therefore, the mean rate of return is 17 %

Standard deviation will be;

σp = √( 0.65² × 15² + 0.35² × 40² )

= √( 0.4225 × 225 + 0.1225 × 1600 )

= √( 95.0625 + 196 )

= √291.0625

= 17.06055

Therefore, the standard deviation of return is 17.06055

2)

probability that Marvin's portfolio will make at least 20% over the next 12 months.

P( X > 20 )

we convert to a standard normal variable;

Z = $\frac{20-17}{17.06055}$ )

Z = 0.17

from z table, p-value is;

p( X < 20 ) = 0.5675

P( X > 20 ) 1 - 0.5675 = 0.4325

Therefore, the probability that Marvin's portfolio will make at least 20% over the next 12 months is 0.4325

5 0

3 years ago

PLEAse i need help brainlist if u get it right

Naya [18.7K]

Answer:

C) The resulting figure will be congruent to the original rectangle, because dilations with a scale factor of 1 have the same coordinates.

Step-by-step explanation: Multiplying any number by 1 will result in the same number, this applies to coordinates as well.

7 0

3 years ago

Children who have lost some baby teeth have better arithmetic skills than children who have not lost any baby teeth. In fact, th

Tems11 [23]

Answer:

B. There is correlation but no direct casual relation, but losing teeth and arithmetic skills.

Step-by-step explanation:

Given:

Correlation between lost of baby teeth and arithmetic skills.

Solution:

Correlation and causality concepts are so used here.

Correlation is the relationship between two variables to get or to predict information.

Correlation is not always causation.

So here the correlation is used to predict the arithmetic skills based on lost teeth.

i.e. More teeth lost more arithmetic skills.

Causality means change in one variable changes value of other variable.

So it gives direct causal relation between the variables.

Here they given relationship between the children lost teeth and arithmetic skills to predict information.

But ,there no actual imply on correlation.

Arithmetic skills can also depends upon third variable.

Hence there is no direct causal relationship between them.

8 0

2 years ago

_ 5x^20-7x^10+15 in quadratic form

Tpy6a [65]

Answer:

x = -(sqrt(349) - 7)^(1/10)/10^(1/10) or x = (sqrt(349) - 7)^(1/10)/10^(1/10) or x = -((-1)^(1/5) (sqrt(349) - 7)^(1/10))/10^(1/10) or x = ((-1)^(1/5) (sqrt(349) - 7)^(1/10))/10^(1/10) or x = -((-1)^(2/5) (sqrt(349) - 7)^(1/10))/10^(1/10) or x = ((-1)^(2/5) (sqrt(349) - 7)^(1/10))/10^(1/10) or x = -((-1)^(3/5) (sqrt(349) - 7)^(1/10))/10^(1/10) or x = ((-1)^(3/5) (sqrt(349) - 7)^(1/10))/10^(1/10) or x = -((-1)^(4/5) (sqrt(349) - 7)^(1/10))/10^(1/10) or x = ((-1)^(4/5) (sqrt(349) - 7)^(1/10))/10^(1/10) or x = -(1/10 (-7 - sqrt(349)))^(1/10) or x = (1/10 (-7 - sqrt(349)))^(1/10) or x = -(-1)^(1/5) (1/10 (-7 - sqrt(349)))^(1/10) or x = (-1)^(1/5) (1/10 (-7 - sqrt(349)))^(1/10) or x = -(-1)^(2/5) (1/10 (-7 - sqrt(349)))^(1/10) or x = (-1)^(2/5) (1/10 (-7 - sqrt(349)))^(1/10) or x = -(-1)^(3/5) (1/10 (-7 - sqrt(349)))^(1/10) or x = (-1)^(3/5) (1/10 (-7 - sqrt(349)))^(1/10) or x = -(-1)^(4/5) (1/10 (-7 - sqrt(349)))^(1/10) or x = (-1)^(4/5) (1/10 (-7 - sqrt(349)))^(1/10)

Step-by-step explanation:

Solve for x:

-5 x^20 - 7 x^10 + 15 = 0

Substitute y = x^10:

-5 y^2 - 7 y + 15 = 0

Divide both sides by -5:

y^2 + (7 y)/5 - 3 = 0

Add 3 to both sides:

y^2 + (7 y)/5 = 3

Add 49/100 to both sides:

y^2 + (7 y)/5 + 49/100 = 349/100

Write the left hand side as a square:

(y + 7/10)^2 = 349/100

Take the square root of both sides:

y + 7/10 = sqrt(349)/10 or y + 7/10 = -sqrt(349)/10

Subtract 7/10 from both sides:

y = sqrt(349)/10 - 7/10 or y + 7/10 = -sqrt(349)/10

Substitute back for y = x^10:

x^10 = sqrt(349)/10 - 7/10 or y + 7/10 = -sqrt(349)/10

Taking 10^th roots gives (sqrt(349)/10 - 7/10)^(1/10) times the 10^th roots of unity:

x = -(1/10 (sqrt(349) - 7))^(1/10) or x = (1/10 (sqrt(349) - 7))^(1/10) or x = -(-1)^(1/5) (1/10 (sqrt(349) - 7))^(1/10) or x = (-1)^(1/5) (1/10 (sqrt(349) - 7))^(1/10) or x = -(-1)^(2/5) (1/10 (sqrt(349) - 7))^(1/10) or x = (-1)^(2/5) (1/10 (sqrt(349) - 7))^(1/10) or x = -(-1)^(3/5) (1/10 (sqrt(349) - 7))^(1/10) or x = (-1)^(3/5) (1/10 (sqrt(349) - 7))^(1/10) or x = -(-1)^(4/5) (1/10 (sqrt(349) - 7))^(1/10) or x = (-1)^(4/5) (1/10 (sqrt(349) - 7))^(1/10) or y + 7/10 = -sqrt(349)/10

Subtract 7/10 from both sides:

x = -(sqrt(349) - 7)^(1/10)/10^(1/10) or x = (sqrt(349) - 7)^(1/10)/10^(1/10) or x = -((-1)^(1/5) (sqrt(349) - 7)^(1/10))/10^(1/10) or x = ((-1)^(1/5) (sqrt(349) - 7)^(1/10))/10^(1/10) or x = -((-1)^(2/5) (sqrt(349) - 7)^(1/10))/10^(1/10) or x = ((-1)^(2/5) (sqrt(349) - 7)^(1/10))/10^(1/10) or x = -((-1)^(3/5) (sqrt(349) - 7)^(1/10))/10^(1/10) or x = ((-1)^(3/5) (sqrt(349) - 7)^(1/10))/10^(1/10) or x = -((-1)^(4/5) (sqrt(349) - 7)^(1/10))/10^(1/10) or x = ((-1)^(4/5) (sqrt(349) - 7)^(1/10))/10^(1/10) or y = -7/10 - sqrt(349)/10

Substitute back for y = x^10:

x = -(sqrt(349) - 7)^(1/10)/10^(1/10) or x = (sqrt(349) - 7)^(1/10)/10^(1/10) or x = -((-1)^(1/5) (sqrt(349) - 7)^(1/10))/10^(1/10) or x = ((-1)^(1/5) (sqrt(349) - 7)^(1/10))/10^(1/10) or x = -((-1)^(2/5) (sqrt(349) - 7)^(1/10))/10^(1/10) or x = ((-1)^(2/5) (sqrt(349) - 7)^(1/10))/10^(1/10) or x = -((-1)^(3/5) (sqrt(349) - 7)^(1/10))/10^(1/10) or x = ((-1)^(3/5) (sqrt(349) - 7)^(1/10))/10^(1/10) or x = -((-1)^(4/5) (sqrt(349) - 7)^(1/10))/10^(1/10) or x = ((-1)^(4/5) (sqrt(349) - 7)^(1/10))/10^(1/10) or x^10 = -7/10 - sqrt(349)/10

Taking 10^th roots gives (-7/10 - sqrt(349)/10)^(1/10) times the 10^th roots of unity:

Answer: x = -(sqrt(349) - 7)^(1/10)/10^(1/10) or x = (sqrt(349) - 7)^(1/10)/10^(1/10) or x = -((-1)^(1/5) (sqrt(349) - 7)^(1/10))/10^(1/10) or x = ((-1)^(1/5) (sqrt(349) - 7)^(1/10))/10^(1/10) or x = -((-1)^(2/5) (sqrt(349) - 7)^(1/10))/10^(1/10) or x = ((-1)^(2/5) (sqrt(349) - 7)^(1/10))/10^(1/10) or x = -((-1)^(3/5) (sqrt(349) - 7)^(1/10))/10^(1/10) or x = ((-1)^(3/5) (sqrt(349) - 7)^(1/10))/10^(1/10) or x = -((-1)^(4/5) (sqrt(349) - 7)^(1/10))/10^(1/10) or x = ((-1)^(4/5) (sqrt(349) - 7)^(1/10))/10^(1/10) or x = -(1/10 (-7 - sqrt(349)))^(1/10) or x = (1/10 (-7 - sqrt(349)))^(1/10) or x = -(-1)^(1/5) (1/10 (-7 - sqrt(349)))^(1/10) or x = (-1)^(1/5) (1/10 (-7 - sqrt(349)))^(1/10) or x = -(-1)^(2/5) (1/10 (-7 - sqrt(349)))^(1/10) or x = (-1)^(2/5) (1/10 (-7 - sqrt(349)))^(1/10) or x = -(-1)^(3/5) (1/10 (-7 - sqrt(349)))^(1/10) or x = (-1)^(3/5) (1/10 (-7 - sqrt(349)))^(1/10) or x = -(-1)^(4/5) (1/10 (-7 - sqrt(349)))^(1/10) or x = (-1)^(4/5) (1/10 (-7 - sqrt(349)))^(1/10)

8 0

3 years ago

8x+16=14x<br><br><br>checking my awnser

Firdavs [7]

8x + 16 = 14x

To solve this equation, move everything containing the variable you want to solve for on one side of the equation and everything else to the other side of the equation.

Let's start by subtracting 8x from both sides to have the variable x all on the right side of the equation. Once you subtract 8x from both sides, your equation will now look like this:

16 = 6x

To solve for the variable x, you want to divide both sides of the equation by 6 to isolate x and therefore find your answer. Divide both sides by 6 and your equation should look like this:

16/6 = x

Simplifying 16/6 into a mixed number ⇒ 2 2/3

Your answer is x = 16/6 or 2 2/3.

8 0

3 years ago