Your retirement savings is invested in the stock market, and during the current market downturn, the value of your account has fallen 20%. Your advisor informs you that if you don’t add any money or make any changes, then it will take more than a 20% recovery just to bring your account back to even. Explain how this is possible and create an example to illustrate your explanation.

The solution of the given expression is 9*\(x^{4}\)/100.

GIven an expression equal to 27\(x^{12}\)/300\(x^{8}\).

We have to simplify the expression in which variable comes only once.

Expression is combination of numbers ,symbols, fraction, coefficients, indeterminants,determinants, etc. It is mostly not found in equal to form. It expresses a relationship between variables.

The given fraction is 27\(x^{12}\)/300\(x^{8}\).

When we observe we find that in numerator x has large power and denominator x has small power as compared to power in numerator. So we will deduct the powers so that they will give only one power to us.

=27\(x^{4}\)/300

Now divide numerator an denominator by 3.

=9\(x^{4}\)/300

Hence the expression 27\(x^{12} /300x^{8}\) will look like \(9x^{4} /100\) after simplifying.

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Answer:

\(Simplify:\sqrt\frac{27x^{12} }{300x^{8} }\)

\(O \frac{9}{100}x^{4}\)

✔ \(\frac{3}{10} x^{2}\)

\(O \frac{27}{300} x^{4}\)

\(O\frac{9}{10} x^{2}\)

A. The solution of  linear equation is (x, y) = (-3, 8).

B. The solution is (x, y) = (3/4, -1).

C. The solution is (x, y) = (-31/8, 3/8).

D. The solution is (x, y) = (55/7, -117/14).

A. 3x - y = -11 --- (1)

-x + y = 5 --- (2)

From equation (2), we can write y = x + 5, and substitute it in equation (1):

3x - (x + 5) = -11

2x = -6

x = -3

Substituting x in equation (2):

-y = -8

y = 8

Therefore, the solution of the system is (x, y) = (-3, 8).

To check the solution, we substitute the values of x and y in the original equations:

3(-3) - 8 = -11 (True)

-(-3) + 8 = 5 (True)

So, the solution is correct.

B. -2y + 3 = 4x + 2 --- (1)

6x + 4y = 1 --- (2)

From equation (1), we can write 4x + 2 = -2y + 3, and substitute it in equation (2):

6x + 4y = 1

6x - 4y = 8 (rearranging)

12x = 9

x = 3/4

Substituting x in equation (1):

-2y + 3 = 4(3/4) + 2

-2y + 3 = 5

-2y = 2

y = -1

Therefore, the solution of the system is (x, y) = (3/4, -1).

To check the solution, we substitute the values of x and y in the original equations:

-2(-1) + 3 = 4(3/4) + 2 (True)

6(3/4) + 4(-1) = 1 (True)

So, the solution is correct.

C. 32y - x = -25 --- (1)

5x = 100 + x - 8y --- (2)

From equation (2), we can write 4x = 100 - 8y, and substitute it in equation (1):

32y - x = -25

32y - (100 - 8y) = -25

40y = 75

y = 3/8

Substituting y in equation (1):

32(3/8) - x = -25

x = -31/8.

Therefore, the solution of the system is (x, y) = (-31/8, 3/8).

To check the solution, we substitute the values of x and y in the original equations:

32(3/8) - (-31/8) = -25 (True)

5(-31/8) = 100 + (-31/8) - 8(3/8) (True)

So, the solution is correct.

D. To solve the system of equations:

2y + 3x = 6 --- (1)

4x + 5y + 20 = 0 --- (2)

We can rearrange equation (2) to isolate one of the variables:

4x + 5y = -20 (subtracting 20 from both sides)

5y = -4x - 20 (subtracting 4x from both sides)

y = (-4/5)x - 4 (dividing both sides by 5)

Substituting this value of y in equation (1):

2((-4/5)x - 4) + 3x = 6

(-8/5)x - 8 + 3x = 6

(-8/5)x + 3x = 14

(-8/5 + 3)x = 14

(-8/5 + 15/5)x = 14

(7/5)x = 14

x = 10

Substituting this value of x in the equation for y:

y = (-4/5)(10) - 4

y = -12.

Therefore, the solution of the system is (x, y) = (10, -12).

To check the solution, we substitute the values of x and y in the original equations:

2(-12) + 3(10) = 6 (True)

4(10) + 5(-12) + 20 = 0 (True)

So, the solution is correct.

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Answer:

The GFC would be 8

Step-by-step explanation:

12 - 1,2,3,4,5,6,7,8,12,24

40 - 1,2,4,5,8,10,20,40

Answer: None of the above

Step-by-step explanation:

Let amount of dilute 13% solution be x --> Amount of salt is 0.13x gals.

Answer:

$636.17

Step-by-step explanation:

       First, we need to find the volume of the ball. Then, we will solve for the cost of it.

       Volume of a sphere and solving for the area:

V = \(\frac{4}{3}\)πr³

V = \(\frac{4}{3}\)π(7.5)³

V ≈ 1767.15 in³

       Now that we have the volume, next we need to find the cost. Since the lead costs $0.36 per in³, and our volume is in in³, we can multiply the volume by the cost.

1767.15 in³ * $0.36 = 636.174

       Money rounds to the hundredth place,

636.174 -> $636.17

          It will cost $636.17 to make one ball.

Answer:

Volume of a sphere = 4/3 Pi r³

if r = 7.5

= 4/3 pi 7.5³

= 4/3 pi 421.87

= 1687.5/3 pi

= 562.5 Pi

= 1767.15 in³

then

1767.15 x 0.36 = 636.17

if 1 in³ costs 0.36$

then 1767.15 in³ costs 636.17$

Answer:
V = 180 (vans)

S = 90 (small trucks)

L = 40 (large trucks)

Step-by-step explanation:

Set up the variables: Let V represent the number of vans, S represent the number of small trucks, and L represent the number of large trucks.

Write the equations:

V + S + L = 310 (total number of vehicles)

V = 2S (twice as many vans as small trucks)

35,000V + 70,000S + 60,000L = 15,000,000 (total cost of the vehicles)

Substitute equation 2) into equation 1):

2S + S + L = 310

3S + L = 310

Simplify equation 3) by substituting V = 2S:

70,000S + 70,000S + 60,000L = 15,000,000

140,000S + 60,000L = 15,000,000

Set up a system of equations:

3S + L = 310

140,000S + 60,000L = 15,000,000

Eliminate L by multiplying equation 1) by 60,000:

60,000(3S + L) = 60,000(310)

180,000S + 60,000L = 18,600,000

Subtract equation 2) from the new equation:

(180,000S + 60,000L) - (140,000S + 60,000L) = 18,600,000 - 15,000,000

40,000S = 3,600,000

Solve for S:

S = 90

Substitute the value of S into equation 1) to solve for L:

3(90) + L = 310

270 + L = 310

L = 40

Substitute the values of S and L into equation 2) to solve for V:

V = 2S

V = 2(90)

V = 180

The final answer is:

V = 180 (vans)

S = 90 (small trucks)

L = 40 (large trucks)

Answer:

180 Vans 90 Small trucks and 40 Large trucks

Step-by-step explanation:

Answer:

right π/2

Step-by-step explanation:

The function f(x) = 2sin(x - π/2) is a sine function with a period of 2π, an amplitude of 2, and a phase shift of π/2. The phase shift of π/2 causes the graph of the function to be shifted π/2 units to the right. .

Therefore, the correct answer is right π/2

Answer:

End Balance: $5,160.00

Total Interest: $2,160.00

Step-by-step explanation:

Total Interest =$3000 × 2% × 3 × 12

=$2,160.00

End Balance =$3000 + $2,160.00

=$5,160.00

Answer:

can we get the options

Step-by-step explanation:

Answer:

12.2

Step-by-step explanation:

abc by lc

Answer:

A) 12.2 is the correct answee

Answer: 3/8 * 4 = 12/8 = 1 4/8 = 1 1/2

your answer is 1 1/2

Step-by-step explanation:

Based on these considerations, it is necessary to assess the specific layout plan and the surrounding environment to determine whether the copier is suitably placed in room (3) at Hills Secondary.

To determine whether the copier is suitably placed in room (3) at Hills Secondary, we need to consider factors such as accessibility, noise, and convenience.

Firstly, we need to evaluate the accessibility of the copier in room (3). Is it easily accessible for all students and staff who need to use it? If the copier is located in a central position within the school or close to high-traffic areas, it would be considered suitable.

However, if it is tucked away in a corner or not easily visible, it may cause inconvenience and hinder access for users.

Secondly, we should consider noise levels. Copiers can be noisy machines, and if room (3) is located near classrooms or areas where students require a quiet environment, it may not be an ideal placement. Noise disturbances could disrupt learning activities and cause distractions.

Lastly, convenience plays an important role. Room (3) should be spacious enough to accommodate the copier and allow users to operate it comfortably. If the room is cramped or lacks proper ventilation, it may cause inconvenience for users and impact the overall workflow.

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1. Based on the producer theory, an increase in the demand for labor (L) would be caused by An increase in the productivity of labor, A decrease in the wage rate and A decrease in the rental rate of capital.

2. Missing variables in this simple producer theory would include The technology used to produce output, The preferences of consumers and Quality of labor and capital.

In the standard producer theory, a producer minimizes costs for a given level of output.

This involves choosing the optimal mix of inputs, such as labor (L) and capital (K), to produce the desired output (y).

The cost function is represented by C = wL + rK, where w is the wage rate (cost of labor) and r is the rental rate (cost of capital).

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Answer: 3N+6

Step-by-step explanation:

Step-by-step explanation:

a) Jan = 252.20

Feb = 88

Mar = -198.10

Apr = -836.90

b) 173.70

I got the mean by adding all the totals together and dividing it by 4 bcors there's 4 months.

The value of the probability P(A u B') is 0.8218

The given parameters are

P(A) = 0.67

P(B) = 0.54

P(A u B) = 0.89

From the above parameters, we have

P(B') = 1 - P(B)

P(B') = 1 - 0.54

P(B') = 0.46

So, we have

P(A u B') = P(A) + P(B') - [P(A) * P(B')]

This gives

P(A u B') = 0.67 + 0.46 - (0.67 * 0.46)

Evaluate

P(A u B') = 0.8218

Hence, the value of the probability P(A u B') is 0.8218

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Maya's total savings for 20 years is $90000.

Given that, Maya has savings of $50,000, a rate of interest=4% and time period=20 years.

The interest formula includes two types of interests - simple interest and compound interest. The fee paid to the lender for lending a loan is called the interest. This extra amount or the interest is what needs to be paid along with the actual loan.

The formula to compute the interest=(P×T×R)/100

Where, P=Principal, T=Time period and R=Rate of interest.

Now, the interest=(50000×20×4)/100=$40000

Total savings=50000+40000=$90000

Therefore, Maya's total savings for 20 years is $90000.

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Answer:

5.7 Round it and you will get that

Answer:

cant see pic

Step-by-step explanation:

reply with what it says :) awnser :

5.7

Answer:

\(E(x) = 1.5\\\)

Step-by-step explanation:

Given

\(n = 9\) -- number of rolls

Required

The mean of 2's

The distribution follows binomial distribution where:

\(X \to Binomial(n,p)\)

In this case:

\(p= \frac{1}{6}\) ---- the theoretical probability of rolling 2

So, the mean of 2's is calculated using:

\(E(x) = np\)

\(E(x) = 9 * \frac{1}{6}\)

\(E(x) = \frac{9}{6}\)

Simplify

\(E(x) = \frac{3}{2}\) or

\(E(x) = 1.5\\\)

Yes, a 6-foot-tall person can pass under the chandelier. To calculate this, the following steps need to be taken:

First, calculate the length of the cords. The cords are 91 cm long, so we can take this number away from the 4.0-meter ceiling: 4.0 m - 0.91 m = 3.09 m.

Second, add the length of the chandelier. The chandelier is 52 cm long, so we add this to the result of the first calculation: 3.09 m + 0.52 m = 3.61 m.

Third, calculate the person's height. A 6 feet tall man is 182.88 cm, so we add this to the previous result: 3.61 m + 1.82 m = 5.43 m.

Finally, compare the result to the height of the ceiling. The result of the calculation (5.43 m) is greater than the height of the ceiling (4.0 m), so the brother can easily pass under the chandelier.

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Answer:

Quadrant I: (⅓, 2⅓)

Quadrant II: (-1⅓, 3⅓)

Quadrant III: (-3, -10) (-3⅓, -1⅓)

Quadrant IV: (9, -1)

Step-by-step explanation:

If it is (+, +), it is in quadrant I.

If it is (-, +), it is in quadrant II.

If it is (-, -), it is in quadrant III.

If it is (+, -), it is in quadrant IV.

Answer:

ABC is congruent to EDC because m<3 = m<4 and m<1 = m<5

Step-by-step explanation:

m<3 and m<4 are vertical angles so they are congruent. m<1 and m<5 are alternate interior angles so they are also congruent.

Using the inequality rule we know that 11 is greater than -11, (11 > -11).

Mathematical expressions with inequalities are those in which the two sides are not equal.

Contrary to equations, we compare two values in inequality.

Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.

Two expressions in inequality aren't always equal, which is denoted by the symbols >, <, ≤, or ≥.

So, let's say the inequality equation looks like this: A

Right now, A is valued at

Let p be used to representing the initial number.

P equals 11, so

Let q be used to representing the second number.

Q has a value of -11.

-11 and 11 are both numbers that are greater than zero.

Then, 11 > -11 ... (1)

A has a value of 11 > -11.

Therefore, using the inequality rule we know that 11 is greater than -11, (11 > -11).

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Correct question:
Is 11 greater than, equal to, or less than -11?

Answer:

Step-by-step explanation:

Here you go mate

PEMDAS

Parenthesis

Exponents

Multiplication

DIvision

Addition

Subtraction

Step 1

(r+4-2r-14)>0  equation/Question

Step 2

(r+4-2r-14)>0  Simplify to remove parenthesis

-r-10>0

Step 3

-r-10>0  Add 10 to sides

-r-10+10>0+10

-r>10

Step 4

-r/-1>10/-1  cross multiply (which also means divide)

answer

r<-10

The highest point for the quadratic function for the height of the object, h(t) = -16·t² + 224·t + 816, indicates that the interval over which the height of the object is increasing is; (-∞, 7]

The shape of the graph of a quadratic function is a parabola.

The function for the height of the object in question 3 is; h(t) = -16·t² + 224·t + 816

Where;

t = The time in seconds

The height of the object is increasing in the interval to the left of the highest point, which can be found as follows;

The x-coordinate of the highest point of the quadratic function, f(x) = a·x² + b·x + c is; x = -b/(2·a)

Therefore, the x-coordinates of the highest point of the object is; -224/(2 × (-16)) = 7

Therefore, the height of the object is increasing in the interval; -∞ < t ≤ 7

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Answer:

yes

Step-by-step explanation:

parallel lines and equal

equal angles

Answer:

Yes

Step-by-step explanation:

They both have the same angle, and they are just a translation of each other.

Answer:

12

Step-by-step explanation:

We know that ,

So that ,

PART A: Linda has $4.41 more than Enrique after one year.

PART B: Enrique has $12.10 more than Linda after the second year.

PART A: After one year, we can calculate the amount of money each person has in their respective accounts.

For Linda's account:

Principal amount = $610

Interest rate = 1.2%

\(Interest $ earned = Principal $ amount \times (Interest rate/100) = $610 \times (1.2/100) = $7.32\)

\(Total $ amount after one year = Principal amount + Interest earned = $610 + $7.32 = $617.32\)

For Enrique's account:

Principal amount = $590

Interest rate = 3.9%

\(Interest $ earned = Principal amount \times (Interest rate/100) = $590 \times (3.9/100) = $22.91\)

Total amount after one year = Principal amount + Interest earned = $590 + $22.91 = $612.91

Comparing the two amounts, after one year Linda has more money.

The difference in the amount is:

$617.32 - $612.91 = $4.41

Therefore, Linda has $4.41 more than Enrique after one year.

PART B: After a second year, we need to calculate the amounts again.

For Linda's account:

Principal amount = $617.32

Interest rate = 1.2%

\(Interest earned = Principal amount \times (Interest rate/100) = $617.32 \times (1.2/100) = $7.41\)

Total amount after the second year = Principal amount + Interest earned = $617.32 + $7.41 = $624.73

For Enrique's account:

Principal amount = $612.91

Interest rate = 3.9%

\(Interest earned = Principal amount \times (Interest rate/100) = $612.91 \times (3.9/100) = $23.92\)

Total amount after the second year = Principal amount + Interest earned = $612.91 + $23.92 = $636.83

Comparing the two amounts, after the second year Enrique has more money.

The difference in the amount is:

$636.83 - $624.73 = $12.10

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Answer:

if x is positive the answer is the 4th statement and if it is negative the answer is the 3rd statement

Step-by-step explanation:

We have the statement that tells us: "the graphs of the two lines y = –6 and x =?" x, we do not know it, but from the y coordinate we can do it by discard.

In the case of y-coordinate we have that y = -6 is a horizontal line with a slope of 0, therefore of the 4 statements it is reduced to 2, the third and the fourth.

Depending on the sign that has the value of x, if it is positive or negative it would be the 3rd and 4th answer.

if x is positive it is a vertical line with a slope that is undefined, but if it is negative it is a horizontal line with a slope that is undefined.

The problem says that

Then, if we want to convert yards to feet, we got to multiply it by three. The question is, how many feet is 5 yards? let's use the formula:

Therefore, 5 yards is 15 feet