Tosh. Inc.'s bonds currently sell for $980 and have a par value of $1,000. They pay a $95 annual coupon and have a 12-year maturity, but they can be called in 3 years at $1,150. What is their yield to call (YTC)?

Answer:

27

Step-by-step explanation:

First, we need to find x. We are given the perimeter, which is 2l + 2w, so from there, we have an equation of 2(4x-1) + 2(3x+2) = 100. By working through it, we get that x = 7. We're asked to find WX, so plug 7 into 4x - 1 and get 27.

Answer:

Step-by-step explanation:

Perimeter of rectangle is 2(l) + 2(w).

The perimeter is given 100 units.

2(4x-1) + 2(3x+2) = 100

Solve for x.

8x-2+6x+4=100

14x+2=100

14x=98

x=7

Plug x as 7 for the side WX.

4(7) - 1

28-1

= 27

Answer:

The plane is 388 miles far from the airport.

Step-by-step explanation:

We know that, the angle between southeast and south directions is [tex]135^\circ[/tex].

The plane travels as per the triangle as shown in the attached image.

A is the location of airport.

First it travels for 210 miles southeast from A to B and then 210 miles south from B to C.

[tex]\angle ABC = 135^\circ[/tex]

To find:

Side AC = ?

Solution:

As we can see, the [tex]\triangle ABC[/tex] is an isosceles triangle with sides AB = BC = 210 miles.

So, we can say that the angles opposite to the equal angles in a triangle are also equal. [tex]\angle A = \angle C[/tex]

And sum of all three angles of a triangle is equal to [tex]180^\circ[/tex].

[tex]\angle A+\angle B+\angle C = 180^\circ\\\Rightarrow \angle A+135^\circ+\angle A = 180^\circ\\\Rightarrow \angle A = \dfrac{1}{2} \times 45^\circ\\\Rightarrow \angle A =22.5^\circ[/tex]

Now, we can use Sine Rule:

[tex]\dfrac{a}{sinA} = \dfrac{b}{sinB}[/tex]

a, b are the sides opposite to the angles [tex]\angle A and \angle B[/tex] respectively.

[tex]\dfrac{210}{sin22.5^\circ} = \dfrac{b}{sin135^\circ}\\\Rightarrow \dfrac{210}{sin22.5^\circ} = \dfrac{b}{cos45^\circ}\\\Rightarrow b = 210\times \dfrac{1}{\sqrt2 \times 0.3826}\\\Rightarrow b = 210\times \dfrac{1}{0.54}\\\Rightarrow b \approx 388\ miles[/tex]

So, the answer is:

The plane is 388 miles far from the airport.

inital height is 2 meters

Step-by-step explanation:

Answer:

Miss Pepper Mills

Credit Card Statement for the month of April:

a. Average Daily Balance:

Average balance = $618.66/5 = $123.73

b. Calculation of Miss Pepper Mill's Finance Charge for the month of April:

Finance charge

= 18.5% of $20.55 x 1/12

= $0.32

Step-by-step explanation:

a) Data and Calculations:

Activity on the credit card statement for April

Beginning balance = $342.57

Date    Activity    Location       Amount     Daily Balance

04/01  Balance                                           $342.57

04/05 Payment  Payment     $200.00       $142.57

04/15  Charge    Gas               $26.37        $116.20

04/22 Charge    Macy's        $105.42          $10.78

04/25 Charge    Starbuck's     $4.24          $6.54

30 days   Total =                                       $618.66

Average balance = Total of the daily balances divided by 30 days

= $618.66/30 = $20.55

The value of the average daily balance and the finance charge for Miss pepper mills are $123.732 and $0.32 respectively.

The average daily balance :

Sum of balances = (342.57+ (342.57-200) +(342.57 - 200 - 26.37) +(342.57-200-26.37-105.42) + (342.57-200-26.37-105.42-4.24)) = $618.66

Average daily balance :

Finance charge for April :

Average balance × daily rate

Therefore, the average daily balance and finance charge are $123.732 and $0.32 respectively

Learn more : 149.9448066146972668163077278862934016

Answer:

Initial amount (a)= 620

Growth factor (b)= 7.8

Step-by-step explanation:

620 is the initial amount and is multiplied by 7.8 x which is the growth factor.

Answer:

P [ Z > 21 ] = 0,5   or   P [ Z > 21 ] = 50 %

Step-by-step explanation:

Normal Distribution N(21;4)

The question here is what is the area of the bell shape curve. As 21 is a mean for this distribution is in the middle of the bell, so values bigger than 21 will have a probability of 0,5, and values smaller than 21 will have the same probability 0,5. We must remember that the whole area under the curve has an area of 1 ( or 100% )

Answer:

x = 1.5

Step-by-step explanation:

5(4x-10)+10x=4(2x-3)+2(x-4)

Distribute(5)

20x-50+10x=4(2x-3)+2(x-4)

Distribute(4)

20x-50+10x=8x-12+2(x-4)

Distribute(2)

20x-50+10x=8x-12+2x-8

Combine like terms

30x-50=10x-20

Subtract(10x)

20x-50=-20

Add(50)

20x=30

Divide(20)

x = 1.5

Hope it helps <3

Answer:

Step-by-step explanation:

5 ( 4x - 10) + 10x = 4(2x - 3) + 2(x - 4)

Expand the terms

That's

20x - 50 + 10x = 8x - 12 + 2x - 8

Simplify

30x - 50 = 10x - 20

Group the constants at the right side of the equation

That's

30x - 10x = - 20 + 50

20x = 30

Divide both sides by 20

x = 3/2

Hope this helps you

Step-by-step explanation:

Each number cube has 6 possible values, so there are 6⁴ = 1296 possible permutations.  Only 1 of those permutations is all ones.  Therefore, the probability is 1/1296.

Answer:

2 inches

Step-by-step explanation:

x= smallest

3x=largest

2x=medium

x+3x+2x=12

6x=12

x=2

so smallest is 2

largest is 6 (3x)

medium is 4 (2x)

2+6+4=12

Answer:

x=8/3 OR 2.7

Step-by-step explanation:

-1.3+4.6x=0.3+4x

4.6x-4x=0.3+1.3

0.6x=1.6

x=1.6/0.6=8/3

x=8/3 OR 2.7

Hope this helps!

Answer:

[tex]\boxed{x = 2\frac{2}{3} }[/tex]

Step-by-step explanation:

[tex]-1.3+4.6x = 0.3 +4x[/tex]

Collecting like terms

[tex]4.6 x -4x = 0.3+1.3[/tex]

[tex]0.6x = 1.6[/tex]

Dividing both sides by 0.6

x = 1.6 / 0.6

x = 2 2/3

Answer:

51.339

Step-by-step explanation:

Hello,

At the beginning Holly has $500

After one year

   he will get 500*(1+6.75%)=500*1.0675

After n year (n being real)

   he will get

   [tex]500\cdot1.0675^n[/tex]

and we are looking for n so that

   [tex]500\cdot1.0675^n=14,300\\<=> ln (500\cdot1.0675^n)=ln(14,300)\\<=>ln(500)+n\cdot ln(1.0675)=ln(14,300)\\<=> n= \dfrac{ln(14,300)-ln(500)}{ln(1.0675)}=51.338550...\\[/tex]

so we need 51.339 years

Hope this helps

Answer: Yes

Step-by-step explanation:

See explanations in the attached document

Answer:

100yd²

Step-by-step explanation:

length=4x

width=x

perimeter=2(l+w)

50=2(4x+x)

50=2(5x)=10x

50=10x

x=5yd

width=5yd

length=20yd

area=length×width

=20×5

=100yd²

Answer:

[tex]\boxed{\red{100 \: \: {yd} ^{2}}} [/tex]

Step-by-step explanation:

width = x

length = 4x

so,

perimeter of a rectangle

[tex] p= 2(l + w) \\ 50yd = 2(4x + x) \\ 50yd= 2(5x) \\ 50yd= 10x \\ \frac{50yd}{10} = \frac{10x}{10} \\ x = 5 \: \: yd[/tex]

So, in this rectangle,

width = 5 yd

length = 4x

= 4*5

= 20yd

Now, let's find the area of this rectangle

[tex]area = l \times w \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 20 \times 5 \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 100 {yd}^{2} [/tex]

Answer: all of them have one solutions

Step-by-step explanation:

Answer:

1024

Step-by-step explanation:

4 * 4 * 4 * 4 * 4

Answer:

A. 1 milliliter

Step-by-step explanation:

1000 milliliters = 1 liter

0.001 liters = 1 milliliter

Looks like the series is

[tex]\displaystyle\sum_{k=1}^\infty\left(\frac4{\sqrt{k+5}}-\frac4{\sqrt{k+6}}\right)[/tex]

This series has n-th partial sum

[tex]S_n=\displaystyle\sum_{k=1}^n\bullet[/tex]

(where [tex]\bullet[/tex] is used as a placeholder for the summand)

[tex]S_n=\displaystyle\left(\frac4{\sqrt6}-\frac4{\sqrt7}\right)+\left(\frac4{\sqrt7}-\frac4{\sqrt8}\right)+\cdots+\left(\frac4{\sqrt{n+4}}-\frac4{\sqrt{n+5}}\right)+\left(\frac4{\sqrt{n+5}}-\frac4{\sqrt{n+6}}\right)[/tex]

In each grouped term, the last term is annihilated by the first term of the next group; that is, for instance,

[tex]\displaystyle\left(\frac4{\sqrt6}-\frac4{\sqrt7}\right)+\left(\frac4{\sqrt7}-\frac4{\sqrt8}\right)=\frac4{\sqrt6}-\frac4{\sqrt8}[/tex]

Ultimately, all the middle terms will vanish and we're left with

[tex]S_n=\dfrac4{\sqrt6}-\dfrac4{\sqrt{n+6}}[/tex]

As [tex]n\to\infty[/tex], the last term converges to 0 and we're left with

[tex]\displaystyle\sum_{k=1}^\infty\bullet=\lim_{n\to\infty}S_n=\frac4{\sqrt6}=\boxed{2\sqrt{\dfrac23}}[/tex]

Answer:

The transformations needed to obtain the new function are horizontal scaling, vertical scaling and vertical translation. The resultant function is [tex]z'(x) = \frac{1}{2} + \frac{9}{2} \cdot \cos \left(\frac{\pi\cdot x}{90^{\circ}} \right)[/tex].

The domain of the function is all real numbers and its range is between -4 and 5.

The graph is enclosed below as attachment.

Step-by-step explanation:

Let be [tex]z (x) = \cos x[/tex] the base formula, where [tex]x[/tex] is measured in sexagesimal degrees. This expression must be transformed by using the following data:

[tex]T = 180^{\circ}[/tex] (Period)

[tex]z_{min} = -4[/tex] (Minimum)

[tex]z_{max} = 5[/tex] (Maximum)

The cosine function is a periodic bounded function that lies between -1 and 1, that is, twice the unit amplitude, and periodicity of [tex]2\pi[/tex] radians. In addition, the following considerations must be taken into account for transformations:

1) [tex]x[/tex] must be replaced by [tex]\frac{2\pi\cdot x}{180^{\circ}}[/tex]. (Horizontal scaling)

2) The cosine function must be multiplied by a new amplitude (Vertical scaling), which is:

[tex]\Delta z = \frac{z_{max}-z_{min}}{2}[/tex]

[tex]\Delta z = \frac{5+4}{2}[/tex]

[tex]\Delta z = \frac{9}{2}[/tex]

3) Midpoint value must be changed from zero to the midpoint between new minimum and maximum. (Vertical translation)

[tex]z_{m} = \frac{z_{min}+z_{max}}{2}[/tex]

[tex]z_{m} = \frac{1}{2}[/tex]

The new function is:

[tex]z'(x) = z_{m} + \Delta z\cdot \cos \left(\frac{2\pi\cdot x}{T} \right)[/tex]

Given that [tex]z_{m} = \frac{1}{2}[/tex], [tex]\Delta z = \frac{9}{2}[/tex] and [tex]T = 180^{\circ}[/tex], the outcome is:

[tex]z'(x) = \frac{1}{2} + \frac{9}{2} \cdot \cos \left(\frac{\pi\cdot x}{90^{\circ}} \right)[/tex]

The domain of the function is all real numbers and its range is between -4 and 5. The graph is enclosed below as attachment.

Answer:

[tex]79591.8872 in^3/s[/tex]

Step-by-step explanation:

we know that the volume of a right circular cone is give as

[tex]V(r,h)= \frac{1}{3} \pi r^2h\\\\[/tex]

Therefore differentiating partially  with respect to  r and h we have

[tex]\frac{dV}{dt} = \frac{1}{3}\pi [2rh\frac{dr}{dt} +r^2\frac{dh}{dt}][/tex]

[tex]\frac{dV}{dt} = \frac{\pi}{3} [218*198*1.1+109^2*2.4][/tex]

[tex]\frac{dV}{dt} = \frac{\pi}{3} [47480.4+28514.4]\\\\\frac{dV}{dt} = \frac{\pi}{3} [75994.8]\\\\ \frac{dV}{dt} = 3.142 [25331.6]\\\\ \frac{dV}{dt} =79591.8872 in^3/s[/tex]

Answer:

x = ±sqrt(7)

Step-by-step explanation:

x^2 - 8 = -1

Add 8 to each side

x^2 - 8+8 = -1+8

x^2 = 7

Take the square root of each side

sqrt(x^2) = ±sqrt(7)

x = ±sqrt(7)

Answer:

Step-by-step explanation:

Let b represent the number of cups of butter needed.

Let s represent the number of cups of sugar needed.

Let o represent the number of cups of oat needed.

Let f represent the number of cups of flour needed.

The recipe calls for two times as many cups of sugar as butter. It means that

s = 2b

Two times as many cups of oats as sugar. It means that

o = 2s

Two times as many cups of flour as oats. It means that

f = 2o

If Duane puts in one cup of butter, it means that b = 1

Therefore,

s = 2 × 1 = 2 cups

o = 2s = 2 × 2 = 4 cups

f = 2o = 2 × 4 = 8 cups

Therefore, he needs to add 8 cups of flour

Answer: Let b represent the number of cups of butter needed. Let s represent the number of cups of sugar needed. Let o represent the number of cups of oat needed. Let f represent the number of cups of flour needed. The recipe calls for two times as many cups of sugar as butter. It means that s = 2bTwo times as many cups of oats as sugar. It means that o = 2sTwo times as many cups of flour as oats. It means that f = 2oIf Duane puts in one cup of butter, it means that b = 1Therefore, s = 2 × 1 = 2 cupso = 2s = 2 × 2 = 4 cupsf = 2o = 2 × 4 = 8 cups Therefore, he needs to add 8 cups of flour

Step-by-step explanation:

Answer:

x is 2

Step-by-step explanation:

To solve this you have to use the Pythagoram theorem A^2+B^2=C^2. So 9+16=C^2.

25=C^2

c=5

Than since u know the radius of the circle is 3, its 5-3 so x is 2.

Answer:

94.25 kg I think

Step-by-step explanation:

58/4 =14.5 kg per bushel

6.5 x 14.5=94.25 kg

Answer:

94.25

Step-by-step explanation:

First you need to find the unit rate which is 58/4 which equals to 14.5 then you multiply by 6.5 to find 94.25

Answer:

115 miles

Step-by-step explanation:

First find the distance at 50 mph

d = 50 mph * .5 hours

   = 25 miles

Then find the distance at 60 mph

d = 60 mph * 1.5 hours

   = 90 miles

Add the distances together

25+90

115 miles

Answer:

he drives a 115 miles

Step-by-step explanation:

if he drives 50 mph for half an hour he drove 25 miles then if he drives 60 mph for 1 hour and 30 minutes he would of drove 90 miles. 60 + 30=90

90+25=115 so he drove 115 miles.

Answer: Because 4 is the base of what is being exponentially multiplied, you can multiply 256 by 4 to get 4^5

Hi there! Hopefully this helps!

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

So, we know that 4 to the 4th power equals 256.

4 to the 4th power = 4 x 4 x 4 x 4.

So we can add another 4 to the equation to quickly get out answer for 4 to the 5th power.

4 to the 5th power = 4 x 4 x 4 x 4 x 4 = 1024.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Or you could break the equation into parts.

For example, there are FOUR 4s in the equation.

4 x 4 = 16.

4 x 4 = 16.

16 x 16 = 256.

Now since we've added ANOTHER 4, it should look like this:

16 x 16 = 256.

256 x 4 = 1024.

Option B

Because the average points scored in the night is more than that of the day

Answer:

Step-by-step explanation:

Hope you can see it.

Answer:

The answer is option 2.

Step-by-step explanation:

Quadratic function is always written in the form of ax² + bx + c where the highest power of x is 2.

In the options above :

Option 1 is Cubic function.

Option 2 is Quadratic function.

Option 3 and 4 are Linear function.

Answer:

I guess....

Step-by-step explanation:

option 2............

Answer:

H0 :

a. mu is greater than or equal to $108.50

Ha:

c. mu is less than or equal to $108.50

Step-by-step explanation:

The correct order of the steps of a hypothesis test is given following  

1. Determine the null and alternative hypothesis.

2. Select a sample and compute the z - score for the sample mean.

3. Determine the probability at which you will conclude that the sample outcome is very unlikely.

4. Make a decision about the unknown population.

These steps are performed in the given sequence

In the given scenario the test is to identify whether the average room price significantly different from $108.50. We take null hypothesis as mu is greater or equal to $108.50.

According to the given situation, the computation of two number in a given ratio is shown below:-

We assume the numbers is x and y

Given that

[tex]\frac{x}{y} = \frac{3}{1}[/tex]

x = 3y

and

[tex]\frac{x^2-y^2}{x + y} = \frac{6}{1} \\\\\frac{(x + y) (x - y)}{(x + y)} = 6[/tex]

With the help of above formula we will put the value and be able to find the values of x and y

x - y = 6

3y - y = 6

2y = 6

y = 3

x = 3y = 9

x = 9, y = 3

Therefore the correct answer is x = 9 where as y = 3