1. Assume that as of today, the annualized interest rate on a three-year security is 8 percent, while the annualized interest rate on a two-year security is 6 percent. Use only this information to estimate the one-year forward rate two years from now.

If x + 1, x - 5, and x - 2 are in a geometric progression, then there is some constant r for which

x - 5 = r (x + 1)

==>   r = (x - 5) / (x + 1)

and

x - 2 = r (x - 5)

==>   r = (x - 2) / (x - 5)

Then

(x - 5) / (x + 1) = (x - 2) / (x - 5)

Solve for x :

(x - 5)² = (x - 2) (x + 1)

x ² - 10x + 25 = x ² - x - 2

-9x = -27

x = 3

It follows that the ratio between terms is

r = (3 - 5) / (3 + 1) = -2/4 = -1/2

Now, assuming x + 1 = 4 is the first term of the G.P., the n-th term a(n) is given by

a(n) = 4 (-1/2)ⁿ⁻¹

The sum of the first 12 terms - denoted here by S - is then

S = 4 (-1/2)⁰ + 4 (-1/2)¹ + 4 (-1/2)² + … + 4 (-1/2)¹¹

Solve for S :

S = 4 [(-1/2)⁰ + (-1/2)¹ + (-1/2)² + … + (-1/2)¹¹]

(-1/2) S = 4 [(-1/2)¹ + (-1/2)² + (-1/2)³ + … + (-1/2)¹²]

==>   S - (-1/2) S = 4 [(-1/2)⁰ - (-1/2)¹²]

==>   3/2 S = 4 (1 - 1/4096)

==>   S = 8/3 (1 - 1/4096)

==>   S = 1365/512

9514 1404 393

Answer:

Step-by-step explanation:

The only factor outside parentheses that contain 2 terms is the factor 3/5. It can be distributed. (The correct response is shown.)

  3/5 can be distributed

__

The only like terms that reside on the same side of the equal sign are ...

  18 and -1

Step-by-step explanation:

Here,

by formula a^2+b^2=(a+b)^2-2ab

so,

or,(a+b)^2-2ab

or,(73)^2-2×65

or,5329-126

=5203 is the answer

Answer:

10 and 16, x+(x+6)=26

Step-by-step explanation:

Michelle has an age we don't know, so we put her age as x.

Yogi is 6 years older than her, so her age is x+6

Michelle=x

Yogi=x+6

we know both their ages equal 26. so we set it up as

x+(x+6)=26

combining like terms we get

2x+6=26

subtract 6 from both sides

2x=20

divide both sides by 2

x=10

now that we have the value for x, we plug it into their original ages

Michelle is 10, because her age is just x.

Yogi is 16, because her age is x+6

Answer:

the second one

Step-by-step explanation:

it is not going in any general direction

Answer:

B

Step-by-step explanation:

9514 1404 393

Answer:

Step-by-step explanation:

In the US, a decimal point is represented by a period. This value is interpreted as an integer with no fractional part, so the fractional part is zero:

 12,963.00

__

Some other places, a comma is used to identify the beginning of the decimal fraction. In that form, this number has a fractional part that has 3 as its thousandths digit. The value of 3 is less than 5, so the number is simply truncated at the hundredths place.

  12,96

If the thousandths digit were 5 or greater, then 1 hundredth would be added to the truncated number.

Answer:

The domain and range remain the same.

Step-by-step explanation:

Hi there!

First, we must determine what increasing a by 2 really does to the exponential function.

In f(x)=ab^x, a represents the initial value (y-intercept) of the function while b represents the common ratio for each consecutive value of f(x).

Increasing a by 2 means moving the y-intercept of the function up by 2. If the original function contained the point (0,x), the new function would contain the point (0,x+2).

The domain remains the same; it is still the set of all real x-values. This is true for any exponential function, regardless of any transformations.

The range remains the same as well; for the original function, it would have been [tex]y\neq 0[/tex]. Because increasing a by 2 does not move the entire function up or down, the range remains the same.

I hope this helps!

9514 1404 393

Answer:

  C.  2cos²(x)

Step-by-step explanation:

The relevant identities are ...

  cos(2x) = cos²(x) -sin²(x)

  cos²(x) = 1 -sin²(x)

__

Then the expression can be simplified to ...

  cos(2x) +1 = (cos²(x) -sin²(x)) +1 = cos²(x) +(1 -sin²(x)) = cos²(x) +cos²(x)

  = 2cos²(x)

Answer:

A. the change in wind speed for every 1 kPa increase in air pressure

Step-by-step explanation:

The equation of a straight line is given by:

y = mx + b;

where y, x are variables, m is the slope (rate of change) of the line and b is the y intercept (value of y when x = 0)

Given the line y=−1.22x+1250 where x is the air pressure in millibars (kPa) and y is the wind speed in knots.

The slope of the line is -1.22. The slope means that there is a decrease in wind speed by 1.22 miles per hour for every increase of 1 kPa in air pressure.

Answer:

1. 15 days

2. 0.17 acre.

Step-by-step explanation:

1. Determination of the number of days.

From the question given above,

The crew clears ⅓ acre of land in 2 days.

Therefore, the crew will clear 2½ acres in = (2½ × 2) / ⅓

= (5/2 × 2) × 3

= 15 days

Thus, the crew will clear 2½ acres in 15 days

2. Determination of the acre of land.

From the question given above,

The crew clears ⅓ acre of land in 2 days.

Therefore, the crew will clear X acre of land in 1 day i.e

X acre of land = ⅓ ÷ 2

X acre of land = ⅓ × ½

X acre of land = 1/6

X acre of land = 0.17 acre

Thus, the crew will clear 0.17 acre of land in 1 day

Answer: x= 2.5, y = 10

Step-by-step explanation:

I'm going to assume that these photocopies are proportional in relations to each other.

If they're proportional, you can set up two proportions:

[tex]1) \frac{x}{5} =\frac{3}{6} \\\\2) \frac{5}{y} =\frac{3}{6}[/tex]

And cross-multiply:

[tex]1) 6x = 5*3 \\\\2) 3y = 5*6[/tex]

Then solved for x and y:

[tex]1) 6x = 15\\x=\frac{15}{6} =\frac{5}{2} =2.5 \\\\2) 3y = 30\\y=\frac{30}{3} =10[/tex]

Answer:

the answer is n, 225 so u can use another app to make sure u find ur answer

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

11/20 = 55/100 = 55%

Answer:

tăng lên 5.000 nghìn đồng

Step-by-step explanation:

mỗi chuyến bay có 0.5% hành khách mất hành lí

mỗi người đòi bồi thường 1.000.000 đồng

do đó vẽ mỗi người tăng lên :0.5%×1.000.000=5.000

Answer:

Option B

Step-by-step explanation:

If the larger triangle (Preimage) is dilated by a scale factor 'k' to form the image triangle (small triangle),

Scale factor = [tex]\frac{\text{Length of one side of the image triangle}}{\text{Length of one side of the preimage}}[/tex]

                 k = [tex]\frac{3}{2.4}[/tex]

Therefore, Option B will be the correct option.

Answer:

C

Step-by-step explanation:

Let me know if you need an explanation

Answer:

x = -2

Step-by-step explanation:

x^2 + 4x + 4 = 0

quadratic formula:

-b +or- sqrt(b^2-4ac)/2a

-4 +/- sqrt ((-4)^2-4*1*4)/2*1

-4+/- sqrt(16-16) / 2

-4 +/- 0 / 2

-4/2

-2

Answer:

I believe it’s 900

Step-by-step explanation:

Find out how much milk per student for one day then time 5 the times 600 if I’m wrong please let me know

The average number of total cartons of milk the [tex]600[/tex] seniors drink each school day will be [tex]400[/tex].

The average is the sum of the numbers divided by total numbers .

We have,

Number of juniors [tex]=450[/tex]

Number of Seniors [tex]=600[/tex]

And,

Cartons of milk Juniors drink in [tex]5[/tex] days [tex]=1500[/tex] cartoons

So,

Cartons of milk Juniors drink in [tex]1[/tex] day [tex]=\frac{1500}{5} =300[/tex]

So,

The average Cartons of milk Juniors drink in [tex]1[/tex] day [tex]=\frac{300}{450} =\frac{2}{3}[/tex]

And,

According to the question,

The average Cartons of milk Juniors drink in [tex]1[/tex] day [tex]=[/tex] The average Cartons of milk Seniors drink in [tex]1[/tex] day

i.e.

The average Cartons of milk Seniors drink in [tex]1[/tex] day [tex]=\frac{2}{3}[/tex]

So,

Number of total cartons of milk the [tex]600[/tex] seniors drink each school day [tex]=\frac{2}{3}*600=400[/tex]

Hence we can say that the average number of total cartons of milk the [tex]600[/tex] seniors drink each school day will be [tex]400[/tex].

To learn more about average click here

https://brainly.com/question/4539347

#SPJ2

Answer:

5/26

Step-by-step explanation:

Answer:

5/26

Step-by-step explanation:

Threre are five vowels in the English alphabet, 26 total

Expand the expression as

(s + 1)³/s ⁵ = (s ³ + 3s ² + 3s + 1)/s ⁵

… = 1/s ² + 3/s ³ + 3/s ⁴ + 1/s ⁵

Then taking the inverse transform, you get

LT⁻¹ [1/s ² + 3/s ³ + 3/s ⁴ + 1/s ⁵]

… = LT⁻¹ [1/s ²] + LT⁻¹ [3/s ³] + LT⁻¹ [3/s ⁴] + LT⁻¹ [1/s ⁵]

… = LT⁻¹ [1!/s ²] + 3/2 LT⁻¹ [2!/s ³] + 1/2 LT⁻¹ [3!/s ⁴] + 1/24 LT⁻¹ [4!/s ⁵]

… = t + 3/2 t ² + 1/2 t ³ + 1/24 t ⁴

Answer:

4300 x 12= 51600

20/100 x 51600

10,320 Rs  (also pay bohat kam hai :D )

Answer:

18

Step-by-step explanation:

Assuming the sides are 12 and 38

Since this is a right triangle, we can use trig functions

We know the opp side and the adj side of the angle in questions

tan ? = opp /adj

tan ? = 12/38

Taking the inverse tan of each side

tan ^-1 (tan ?) = tan ^-1 (12/38)

?=17.52556

To the nearest degree

? = 18

If the side is 36,

tan ? = opp /adj

tan ? = 12/36

Taking the inverse tan of each side

tan ^-1 (tan ?) = tan ^-1 (12/36)

?=18.43494

To the nearest degree

? = 18

Answer: Y=10.76 √(x-9.12)+43.64

Step-by-step explanation:

Answer:

Switch x and y, and solve for y

[tex]f^{-1}(x) =\frac{(x -4)^3}{8}[/tex]

Step-by-step explanation:

Given

[tex]f(x) = 3\sqrt{8x} + 4[/tex]

Required

Complete the steps to determine the inverse function

Solving (a): Complete the blanks

Switch x and y, and solve for y

Solving (b): Determine the inverse function

[tex]f(x) = \sqrt[3]{8x} + 4[/tex]

Replace f(x) with y

[tex]y = \sqrt[3]{8x} + 4[/tex]

Switch x and y

[tex]x = \sqrt[3]{8y} + 4[/tex]

Now, we solve for y

Subtract 4 from both sides

[tex]x -4= \sqrt[3]{8y} + 4-4[/tex]

[tex]x -4= \sqrt[3]{8y}[/tex]

Take cube roots of both sides

[tex](x -4)^3= 8y[/tex]

Divide both sides by 8

[tex]\frac{(x -4)^3}{8} = y[/tex]

So, we have:

[tex]y =\frac{(x -4)^3}{8}[/tex]

Hence, the inverse function is:

[tex]f^{-1}(x) =\frac{(x -4)^3}{8}[/tex]

Answer:

x

y

f^-1(x)= 1/8(x-4)^3 (plug in choices to match)

Step-by-step explanation:

You see, the guy above me already got it right. 1/8(x-4)^3 and (x-4)^3/8 are essentially the same thing. The only difference is either dividing by 8 and multiplying by 1/8, and that's only a visual difference.

Answer:

Angle ADB = 60 degrees

Step-by-step explanation:

This is a 60 60 60 triangle, which means all of its angles equal 60 degrees. Therefore angle ADB is 60 degrees.

Answer:

There were a total of 32 people on the hike.

Step-by-step explanation:

Represent the number of people total by p.  Then:

(5/8)p = c = the number of children

Since there are 20 children on the hike, (5/8)p must equal 20:

(5/8)p = 20

Solve for p by multiplying both sides by (8/5):

(8/5)(5/8)p = 20(8/5), or

              p = 32

There were a total of 32 people on the hike.