A 20-year U.S. Treasury bond has a 3.50 percent interest rate, while a same maturity corporate bond has a 5.25 percent interest rate. Real interest rates and inflation rate expectations would be the same for the two bonds. If a default risk premium of 1.50 percentage points is estimated for the corporate bond, determine the liquidity premium for the corporate bond.

SOLUTION

Given the question in the image, the following are the solution steps to answer the question.

STEP 1: Place the numbers from the least to greatest

STEP 2: Find the median

The median is the number in the middle position. The middle position will be the 8th and the number there is 50.

Median is 50

STEP 3: Find the lower quartile

The lower quartile is the median of the data set to the left of the median

16 is the lower quartile

STEP 4: Find the upper quartile

The upper quartile is the median of the data set to the right of the median

84 is the upper quartile

STEP 5: Find the maximum and minimum of the data

STEP 6: Find the Interquartile range

Hence, the 5-number summary is given as:

Minimum = 3

Lower quartile = 16

Median = 50

Upper quartile = 84

Maximum = 90

Answer:

0

Step-by-step explanation:

14=14 so plus 0 is 14 i gues

Using the ratio of the sides, we have:$x\sqrt{3} = 12\sqrt{3}$ (opposite the $60^{\circ}$ angle is 12$\sqrt{3}$)$x = 2\sqrt{3}\cdot6$ (the hypotenuse is $2x = 12\sqrt{3}$)Simplifying, we have:$x = 12\sqrt{3}$. Therefore $x=y=12\sqrt{3}$, which is our answer

In a 30-60-90 triangle, the sides have the ratio of $1: \sqrt{3}: 2$. Let's apply this to solve for the variables in the given problem.

Instructions: Use the ratio of a 30-60-90 triangle to solve for the variables. Leave your answers as radicals in simplest form. x=y=Let's first find the ratio of the sides in a 30-60-90 triangle.

Since the hypotenuse is always twice as long as the shorter leg, we can let $x$ be the shorter leg and $2x$ be the hypotenuse.

Thus, we have: Shorter leg: $x$Opposite the $60^{\circ}$ angle: $x\sqrt{3}$ Hypotenuse: $2x$

Now, let's apply this ratio to solve for the variables in the given problem. We know that $x = y$ since they are equal in the problem.

Using the ratio of the sides, we have:$x\sqrt{3} = 12\sqrt{3}$ (opposite the $60^{\circ}$ angle is 12$\sqrt{3}$)$x = 2\sqrt{3}\cdot6$ (the hypotenuse is $2x = 12\sqrt{3}$)Simplifying, we have:$x = 12\sqrt{3}$

Therefore, $x=y=12\sqrt{3}$, which is our answer.

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The least number that needs to multiply to 504 to make perfect cube is 49.

A perfect cube of a number is a number that is equal to the number, multiplied by itself, three times. If x is a perfect cube of y, then x = y³.

The given number is 504.

Now,

504=2×2×2×3×3×3×7

= 2³×3³×7

To make perfect cube we need to multiply 49=7×7

That is, 2³×3³×7³

= 8×27×343

= 74088

Therefore, the least number that needs to multiply to 504 to make perfect cube is 49.

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Answer:

253 units

Step-by-step explanation:

-253 is 253 units behind 0.

Answer:

x=15°

Step-by-step explanation:

5x-12°+95°+x+7°=180°

6x+90°=180°

6x=90°

x=15°

Answer:

neither

Step-by-step explanation:

Answer:

neither

Step-by-step explanation:

to be parallel you much have the same slope, so be perpendicular you must have the opposite reciprocal slope, and this has neither.

In this triangle, the product of sin B and tan C is\(b^2/(ac)\)  , and the product of sin C and tan B is \(c^2/(ab)\).

In a right-angled triangle ABC, where angle A is 90 degrees, we have the following side lengths:

AB = c (base)

BC = a (hypotenuse)

AC = b (perpendicular)

We need to calculate the products of sin B and tan C, and sin C and tan B.

First, let's calculate sin B and tan C:

sin(B) = opposite/hypotenuse = AC/BC = b/a

tan(C) = opposite/adjacent = AC/AB = b/c

The product of sin B and tan C is sin(B) * tan(C) = (b/a) * (b/c) = \(b^2\)/(ac).

Next, let's calculate sin C and tan B:

sin(C) = opposite/hypotenuse = AB/BC = c/a

tan(B) = opposite/adjacent = AB/AC = c/b

The product of sin C and tan B is sin(C) * tan(B) = (c/a) * (c/b) = \(c^2\)/(ab).

Therefore, in the given right-angled triangle ABC, the product of sin B and tan C is\(b^2\)/(ac), and the product of sin C and tan B is \(c^2\)/(ab).

These formulas hold true for any right-angled triangle, where the base is AB, the hypotenuse is BC, and the perpendicular is AC.

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The question probable may be:

In this triangle, the product of sin B and tan C is _____ , and the product of sin C and tan B is _______.

The value of a in the equation is 4

The quadratic equation is given as

g(x) = ax² - 12x + 9

Start by differentiating the equation

So, we have the following representation

g'(x) = 2ax - 12

Next, we set the differentiated equation to 0

So, we have

2ax - 12 = 0

Divide through by 2

ax = 6

Make a, the subject

a = 6/x

The graph intersect the x-axis at the vertex

So, we solve graphically

From the graph, we have x = 1.5

This gives

a = 6/1.5

Evaluate

a = 4

Hence, the value is 4

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Answer: 110

Step-by-step explanation:

I did it it’s correct :)

Answer:

The maximum distance between supports for the beam to support a weight of 1600 lb is also 4.5 feet.

Step-by-step explanation:

We are given that weight P is inversely proportional to the distance D between the supports of the beam, and for this certain type of wooden beam, we have:

P = 7200/D

To find the distance between supports needed to carry 1600 lb, we can substitute P = 1600 in the above equation and solve for D:

1600 = 7200/D

D = 7200/1600

D = 4.5 feet

So the distance between supports needed to carry 1600 lb is 4.5 feet.

To find the maximum distance between supports for the beam to support a weight of 1600 lb, we can use the same equation and solve for P = 1600:

1600 = 7200/D

D = 7200/1600

D = 4.5 feet

Therefore, the maximum distance between supports for the beam to support a weight of 1600 lb is also 4.5 feet.

Answer:

TU = 46

Step-by-step explanation:

Here, we are concerned with finding TU

Mathematically;

Since U is between T and B, by convention;

TB = TU + UB

Substituting the values so we can find x;

55 = 6x + 16 + 2x -1

55 = 6x + 2x + 16-1

55 = 8x + 15

8x = 55-15

8x = 40

x = 40/8

x = 5

But TU = 6x + 16; substitute the value of 5 for x

TU = 6(5) + 16

TU = 30 + 16

TU = 46

Answer:

24;6

Step-by-step explanation:

Answer: B, Desiree is correct because there are 24 students to 6 tables in the room. A ratio must account for the total number of each value.

answer:

9/4

step-by-step explanation:

2 as a fraction is 8/4

seeing as how 9/4>8/4

or you could convert 9/4 to a decimal which is 2.25 and 2.25>2

the larger number is 9/4

good luck :)

hopefully, this helps

have a good day !!

Answer: 9/4

Step-by-step explanation:

Answer:

4.667

Step-by-step explanation:

f(x) = 2/3 × x^(3/2) + 4

the arc length of a function f(x) between 2 points A and B is

A integral B (sqrt(1 + f'(x)²)dx)

in our case

f'(x) = 3/2 × 2/3 × x^(1/2) = x^(1/2)

f'(x)² = (x^(1/2))² = x^(2/2) = x¹ = x

A = 0

B = 3

0 integral 3 (sqrt(1 + x))dx) = 0 integral 3 ((1 + x)^(1/2) dx)

0 interval 3 (2/3 × (1 + x)^(3/2)) =

= 2/3 × (1 + 3)^(3/2) - 2/3 × (1 + 0)^(3/2) =

= 2/3 × sqrt(4³) - 2/3 × 1 = 2/3 × 8 - 2/3 = 16/3 - 2/3 =

= 14/3 = 4.66666666... ≈ 4.667

Solving a system of equations we will see that two large trucks and one small truck can hold 2.625 tons

Let's define the variables:

x = volume that a small truck holds.

y = volume that a large truck holds.

Then we can write the system of equations:

4x + 4y = 10.5 tons

y = 2x

Replacing the second equation into the first one we get.

4x + 4*(2x) = 10.5 tons

12x = 10.5 tons

x = 10.5 tons/12 = 0.875 tons

and:

y = 2x = 2*0.875 tons = 1.75 tons

Then the cargo that two large trucks and one small truck can hold is:

2* 1.75 tons + 0.875 tons = 2.625 tons

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The reasoning presented lacks explicit explanations and logical connections between the steps, making it difficult to fully understand the intended proof strategy.

The given proof aims to show that the Separation Axioms can be derived from the Replacement Schema using a particular construction involving a formula p(x, y). Let's analyze the proof step by step:

Define the formula p(x, y) as x = yo(x).

This formula states that for each x, y pair, x is equal to the unique object y such that y is obtained by applying the operation o to x.

Define the set F as {(x, x) (x)}.

This set F contains pairs (x, x) where x is the unique object obtained by applying the operation (x) to x.

Claim: F(X) = {y (x = X)p(x, y)} = {y: (x = X)x = y^o(x)} = {x: (3x € X)o(x)} = {x X: (x)}.

This claim asserts that F(X) is equivalent to {y (x = X)p(x, y)}, which is further equivalent to {y: (x = X)x = y^o(x)}, and so on.

The proof states that since (x, y) satisfies the functional formula VaVyVz(p(x, y)^(x, z) y = z), it follows that (x, y) is a functional formula.This step emphasizes that the formula p(x, y) satisfies certain properties that make it a functional formula, which is relevant for the subsequent deductions.

Finally, the proof concludes that the Separation Axioms follow from the Replacement Schema, based on the previous steps.

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Answer: 7

Step-by-step explanation:

We can use the Pythagorean theorem (a^2+b^2=c^2) so 25^2=625, and 24^2=576

576+b^2=625 b^2=49 b - (a)=7

9514 1404 393

Answer:

  A.  2k -13

Step-by-step explanation:

-3(2 +4k) +7(2k -1)

= -6 -12k +14k -7 . . . . . . eliminate parentheses

= (-12 +14)k -6 -7 . . . . . . group like terms

= 2k -13 . . . . matches choice A

Answer:

3(x-4)(x-2)

Step-by-step explanation:

Hope this helps! Please mark brainliest. :)

Step-by-step explanation:

Vertex form is: \(a(x-h)^2+k\)

a) \(a(x+2)^2+3=y\)

To find a, plug (-4,1) in for x and y.

\(a(-4+2)^2+3=1\)

\(4a=-2\)

\(a=-1/2\)

so a) is \(\frac{-1}{2} (x+2)^2+3\)

b) .... I'm not sure what the second coordinate is.

c) \(a(x+2)^2-3\)

Plug in (-5,6) for x and y.

\(6=a(-5+2)^2-3\)

\(9=9a\)

\(a=1\)

so c) is \((x+2)^2-3\)

d) \(a(x+2)^2+5\)

Plug (1,-4) in for x and y.

\(-4=a(1+2)^2+5\)

\(-9=9a\)

\(a=-1\)

so d) is \(-(x+2)^2+5\)

Answer:

\(\textsf{(a)}\quad y=-\dfrac{1}{2}(x+2)^2+3\)

\(\textsf{(b)}\quad y=a(x+1)^2-1\)

\(\textsf{(c)}\quad y=(x+2)^2-3\)

\(\textsf{(d)}\quad y=-(x+2)^2+5\)

Step-by-step explanation:

Vertex form

\(y=a(x-h)^2+k\)

where (h, k) is the vertex

-------------------------------------------------------------------------------------------

Part (a)

Given:  vertex at (-2, 3) passes through (-4 ,1)

Substituting the given vertex into the equation:

\(\implies y=a(x-(-2))^2+3\)

\(\implies y=a(x+2)^2+3\)

Substitute the given point into the equation to find a:

\(\implies 1=a(-4+2)^2+3\)

\(\implies 1=4a+3\)

\(\implies a=-\dfrac{1}{2}\)

Substitute the found value of a to form the final equation:

\(y=-\dfrac{1}{2}(x+2)^2+3\)

-------------------------------------------------------------------------------------------

Part (b)

Given:  vertex at (-1, -1) passes through ?)

Substituting the given vertex into the equation:

\(\implies y=a(x-(-1))^2+(-1)\)

\(\implies y=a(x+1)^2-1\)

Substitute the given point into the equation to find a:

**no point given**

-------------------------------------------------------------------------------------------

Part (c)

Given:  vertex at (-2, -3) passes through (-5, 6)

Substituting the given vertex into the equation:

\(\implies y=a(x-(-2))^2+(-3)\)

\(\implies y=a(x+2)^2-3\)

Substitute the given point into the equation to find a:

\(\implies 6=a(-5+2)^2-3\)

\(\implies 6=9a-3\)

\(\implies a=1\)

Substitute the given point into the equation to find a:

\(y=(x+2)^2-3\)

-------------------------------------------------------------------------------------------

Part (d)

Given:  vertex at (-2, 5) passes through (1, -4)

Substituting the given vertex into the equation:

\(\implies y=a(x-(-2))^2+5\)

\(\implies y=a(x+2)^2+5\)

Substitute the given point into the equation to find a:

\(\implies -4=a(1+2)^2+5\)

\(\implies -4=9a+5\)

\(\implies a=-1\)

Substitute the given point into the equation to find a:

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

Answer:

\( log_{2}(x) \times \frac{1}{3} log_{2}(x) \\ \\ = log_{2}x + log_{2}(x) {}^{ \frac{1}{3} } \\ \\ { \boxed{ \boxed{= log_{2} \{x + ({x})^{ \frac{1}{3} } \}}}}\)

(a) To meet the desired 20g protein and 80g carbohydrate intake, prepare 4 servings of Pork & Beans and combine with 15 slices of "lite" rye bread.

(b) Bread: A/4 slices, Beans: B/21 - (A/4) * (12/21) servings.

(a) To prepare a meal of "beans-on-toast" that supplies 20 grams of protein and 80 grams of carbohydrates, you can use the following combination:

- Servings of Campbell's Pork & Beans: 4 servings.

- Slices of "lite" rye bread: 15 slices.

By using 4 servings of Campbell's Pork & Beans, you will obtain a total of 20 grams of protein (5 grams per serving) and 84 grams of carbohydrates (21 grams per serving).

Combining this with 15 slices of "lite" rye bread will contribute an additional 60 grams of carbohydrates (12 grams per slice) and 4 grams of protein (4 grams per slice). Thus, your meal will meet the desired nutritional requirements of 20 grams of protein and 80 grams of carbohydrates.

(b) The formula to determine the number of slices of bread and servings of Pork & Beans needed to meet specific protein and carbohydrate requirements is as follows:

- Number of slices of bread (Bread): A divided by 4.

- Number of servings of Pork & Beans (Beans): (B divided by 21) minus ((A divided by 4) multiplied by (12 divided by 21)).

Using this formula, you can calculate the appropriate quantities of bread and beans based on the desired protein (A) and carbohydrate (B) values.

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Answer:

It’s probably infinitely many solutions

Step-by-step explanation:

See attached picture

*sorry if that doesn’t help