Imprudential, Incorporated, has an unfunded pension liability of $850 million that must
be paid in 21 years. To assess the value of the firm's stock, financial analysts want to
discount this liability back to the present. If the relevant discount rate is 9.5 percent,
what is the present value of this liability?

From the given information, Therefore, the function \(= > y = 4(\frac{5}{6} )^x\) is an exponential decay.

The process of decreasing a sum at a constant percentage rate over time is referred to in mathematics as exponential decay. It may be written as the formula y=a(1-b)x, where y represents the final amount and a, b, and x, respectively, represent the initial amount and the decay factor.

The formula for an exponential function is where b is a positive integer that is not equal to 1.

Whether a function is an exponential growth or a decay depends on the value of b. If b > 1 or if b<  1, an exponential function exhibits exponential growth and exponential decline, respectively.

given,

\(= > y = 4(\frac{5}{6} )^x\)

\(= > b = \frac{5}{6} < 1\)

Therefore, the function \(= > y = 4(\frac{5}{6} )^x\) is an exponential decay.

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Answer:

x > -6

Step-by-step explanation:

Move 6 to the other side:

0.5x > -3

x > -6

Answer:

“A systematic arrangement” of data in rows and columns is called Table.

Explanation: A table is used to arrange data in rows and columns

Answer:

$6.39

Step-by-step explanation:

Just add the cost of everything

3.18 + 1.25 + 1.96 = 6.39

Answer:

total bill= 6.40

Step-by-step explanation:

You buy 3.17 pounds of apples, 1.25 pounds of pears, and 2.56 pounds of oranges.

Total bill =  3.18  + 1.25 +1.96 = 6.39

Total bill = 6.39 pounds.

We can see the number after the decimal is greater than 5 so the number would be increased by 1.

Total bill = 6.40 pounds .

Answer:

A∩B={7,9}

Option A is correct option.

Step-by-step explanation:

We are given:

A = {3, 5, 7, 9} and B = {1, 2, 4, 6, 7, 9}

and we need to find A intersects with B i.e. A∩B

We find A intersects with B, we will consider only those terms that are common in both A and B

So,

A∩B= {3, 5, 7, 9} ∩ {1, 2, 4, 6, 7, 9}

As 7 and 9 are only common in both A an B

A∩B={7,9}

So, we get: A∩B={7,9}

Option A is correct option.

Answer:b because the equation is right.

Step-by-step explanation:

Step-by-step explanation:

D.

15 × (1 + 2) is you're answer

The amount that Ethan pays for the video game is 47.988.

From the information illustrated, it should be noted that it was stated that Ethan buys video games for 39.99 sale on 20% tax.

In this case, the amount that he will pay will be:

= Original amount + Tax

= 39.99 + (20% × 39.99)

= 39.99 + 7.998

= 47.988

The amount is 47.988.

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Complete question

Ethan buys vidio games for 39.99 sale on 20% tax how much ethan payed

\(log_{4}(2) + log_{4}(3)+ log_{4}(5+2x)\) is the completely expanded logarithmic expression .

Logarithm, an exponent or power that must be raised to obtain a particular number. Mathematically, if bx = n then x = logb n then x is the logarithm of n to  base b. Example: 23 = 8; so 3 is the base 2 logarithm of 8, or 3 = log2 8.

The most common types of logarithms are  the base 10 common logarithm, the base 2 binary logarithm, and  the base  e ≈ 2.71828 natural logarithm.

the product rule for logarithms is

\(log_{b}(MN) = log_{b}(M) + log_{b}(N)\)  for b > 0

now ,

\(log_{4}(6(5 + 2x)) \\\\log_{4}(6) + log_{4}(5 + 2x)\\ \\ log_{4}(2.3) + log_{4}(5 + 2x) \\\\ log_{4}(2) + log_{4}(3)+ log_{4}(5 +2x)\)

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Answer:

it has to be D for sure trust me

Answer:

C

Step-by-step explanation:

1.6 + 1.4 + 1.1 + 1.8 + 1.3 + 1.8 + 1.2 + 1.4 = 11.6

11.6 / 8 (number of items) = 1.45, which is approximately 1.5

Answer:

3/4 x 9/16 = 27/64

Step-by-step explanation:

Answer:

10

Step-by-step explanation:

x=6, so 6+4=10

Answer:

10

Step-by-step explanation:

so if x is 6 then it would be 6+4=10

Answer:

I think it is the fourth choice :

Arental car costs $25 per day plus $3 per gallon of fuel needed upon return to fill the tank

Step-by-step explanation:

I hope that is useful for you

Step-by-step explanation:

its the fourth option because you pay $3 per gallon, x is the number of gallons and the rental costs $25 so adding them will give the total amount

The amount cheaper is the car washes Malcolm orders than the car washes Martha's order is $13.

The correct answer choice is option B.

Malcolm's gift card = $50.

Cost Malcolm's car wash per visit = $7

Martha's gift card = $180

Cost Martha's car wash per visit = Difference between gift card balance of first and second visit

= $180 - $160

= $20

How cheap is the car washes Malcolm orders than the car washes Martha's order = $20 - $7

= $13

Therefore, Malcolm's car wash is cheaper than Martha's car wash by $13

The complete question is attached in the diagram.

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Lines y = -2x + 8 and y = -x + 5 intersect the y-axis. Option C

To determine the solution to the system of equations, we need to find the point of intersection between the two lines.

The given system of equations is:

y = -2x + 8 ... (Equation 1)

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

To find the point of intersection, we can set the two equations equal to each other:

-2x + 8 = -x + 5

Simplifying the equation, we get:

-x = -3

Dividing both sides by -1, we find:

x = 3

Now, we can substitute this value of x into either Equation 1 or Equation 2 to find the corresponding value of y.

Using Equation 1:

y = -2(3) + 8

y = 2

Therefore, the point of intersection of the two lines is (3, 2).

Now, let's analyze the given options:

a) Line y = -2x + 8 intersects the origin.The origin is (0, 0), and it does not lie on the line y = -2x + 8. Therefore, option a is incorrect.

b) Lines y = -2x + 8 and y = -x + 5 intersect the x-axis.

The x-axis is the line y = 0. Substituting y = 0 into both equations, we find that they do not intersect the x-axis. Therefore, option b is incorrect.

c) Lines y = -2x + 8 and y = -x + 5 intersect the y-axis.

The y-axis is the line x = 0. Substituting x = 0 into both equations, we find that they do intersect the y-axis. Therefore, option c is correct.

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M-5/8 = -1/4

Add 5/8 to both sides:

M = -1/4 + 5/8

Rewrite the fractions to have a common denominator

-1/4 = -2/8

Now you have m = -2/8 + 5/8

M = 3/8

Answer:

The answer is 0.375 (3/8)

Step-by-step explanation:

Since the M is subtracted by 5/8, you add 5/8 to both sides of the equation to get the M by itself and -1/4+5/8 equals 0.375, or 3/8

The graphing form of the function g(x) is: C) none of the answer choices.

The function g(x) = \(x^2 + 4x - 7\)is already in the standard form of a quadratic equation. In graphing form, a quadratic equation can be represented as y =\(ax^2 + bx + c,\) where a, b, and c are constants.

Comparing the given function g(x) =\(x^2 + 4x - 7\)with the standard form, we can identify the coefficients:

a = 1 (coefficient of x^2)

b = 4 (coefficient of x)

c = -7 (constant term)

Therefore, the graphing form of the function g(x) is:

C) none of the answer choices

None of the given answer choices (A, B, D, or E) accurately represents the graphing form of the function g(x) =\(x^2 + 4x - 7\). The function is already in the correct form, and there is no equivalent transformation provided in the answer choices. The given options either represent different equations or incorrect transformations of the original function.

In graphing form, the equation y = \(x^2 + 4x - 7\) represents a parabolic curve. The coefficient a determines the concavity of the curve, where a positive value (in this case, 1) indicates an upward-opening parabola.

The coefficients b and c affect the position of the vertex and the intercepts of the curve. To graph the function, one can plot points or use techniques such as completing the square or the quadratic formula to find the vertex and intercepts. Option C

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Answer:

165 pounds

Step-by-step explanation:

3 times 7 = 21

186 - 21 = 165

Answer:

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

Answer:

.50r + 2p

Step-by-step explanation:

cost of ruler * number of rules  + cost of pens * number of pens

.50 *r + 2 *p

.50r + 2p

Answer:

i think its 700 hope it help

Step-by-step explanation:

the answer would be

70 times

Answer:

y=42 or h=y/42

Step-by-step explanation:

Then the constant would be the number of yards of yarn required for each hat

The correct answer is 3/2. In this case, x = 3/2, and its square, (3/2)^2 = 9/4, is rational. x satisfies the given condition.option (c)

To explain further, we need to understand the properties of rational and irrational numbers.

A rational number can be expressed as a fraction of two integers, while an irrational number cannot be expressed as a fraction and has non-repeating, non-terminating decimal representations.

In the given options, (a) √5102.0 (£) and (b) √2 are both irrational numbers.

Their squares, (√5102.0)^2 and (√2)^2, would also be irrational, violating the given condition. On the other hand, (d) 4/5 is rational, and its square, (4/5)^2 = 16/25, is also rational.

Option (c) 3/2 is rational since it can be expressed as a fraction. Its square, (3/2)^2 = 9/4, is rational as well.

Therefore, (c) 3/2 is the only option where x is rational, but its square is irrational, satisfying the condition mentioned in the question.

In summary, the number x that satisfies the given condition, where x^2 is irrational but x is rational, is (c) 3/2.option (c)

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Answer:

B.150°

Step-by-step explanation:

A regular hexagon has six sides.

The measure of the interior angle is 120°

At the point where vertices B and E share a common edge, angle BED is 90°

The sum of angle measures at point of intersection of edge BE ,ED and FE is equal to 360°

To get measure of angle DEF will be ;

=360° - {90°+120°}

=360°- {210°}

=150°

Anna's total profit was $6000 + $16000 - $4000 = $14000.

How did Anna earn profit

Anna bought $4000 of company stock. The value of the stock doubled when she sold 75% of it, which means she sold 0.75 * $4000 = $3000 worth of stock when its value doubled.

Since the value of the stock doubled, Anna sold the $3000 worth of stock for 2 * $3000 = $6000.

Anna then sold the remainder of the stock (25% of the original amount) for four times the purchase price. Since she originally bought the stock for $4000, the remainder was worth 0.25 * $4000 = $1000.

Selling this remainder for four times the purchase price means that Anna sold it for 4 * $4000 = $16000.

When a variable (or set of letters) in an algebraic statement is substituted, its numerical value is used instead. The expression's total value can then be calculated.

Using the given functions, we have:

\(f(x) = x^2 + 3\)

\(g(x) =\) \(\sqrt{(x-4)}\)

To find f(g(x)), we substitute g(x) for x in the expression for f(x):

\(f(g(x)) = (g(x))^2 + 3\)

= (\(\sqrt{(x-4))^2 + 3}\)

\(= (x-4) + 3\)

\(= x - 1\)

Therefore,\(f(g(x)) = x - 1.\)

To find g(f(x)), we substitute f(x) for x in the expression for g(x):

\(g(f(x)) =\) \(\sqrt{((f(x)) - 4)}\)

= \(\sqrt{((x^2 + 3) - 4)}\)

= \(\sqrt{(x^2 - 1)}\)

= |x|\(\sqrt{(x^2 - 1)}\)

Therefore,  \(g(f(x)) =\) |x|  \(\sqrt{(x^2 - 1)}\)

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Answer:11

Step-by-step explanation:

We should add 25 both side by method of completing the square.

We have to given that;

A student is solving the problem

x² + 10x + _ = 16 + _

Now, We can completing the square as;

⇒ x² + 10x + 5² = 16 + 5²

⇒ x² + 10x + 25 = 16 + 25

⇒ (x + 5)² = 16 + 25

Hence, We should add 25 both side by method of completing the square.

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Answer:

The rate of change is 28.

Step-by-step explanation:

The equation is in slope-intercept form,  y = mx + b, where m is the slope, and b is the y-intercept.