Find the quotient and the remainder of
64−133+32+3−12
-------------------------------
−2

The annual yield to maturity (AYTM) of the Builtrite bonds is at 5.5% for 10 years with a $1,000 par value and the current price of $1,044 is A. 4.9%.

The annual yield to maturity (AYTM) is the total return expected from a bond if the bond is held till maturity.

The AYTM rate is the rate at which all future expected cash flows are discounted to find out the current value or the price of the bond.

We can use the following Yield to Maturity formula to calculate the AYTM.

Yield to Maturity = [Annual Interest + {(FV-Price)/Maturity}] / [(FV+Price)/2]

Annual Interest = Annual Interest Payout by the Bond = $55 ($1,000 x 5.5%)

FV = Face Value of the Bond = $1,000

Price = Current Market Price of the Bond = $1,044

Maturity = Time to Maturity = 10 years

= {$55 + ($1,000 - $1,044)/10} / {($1,000 + $1,044)/2}

= $55 + -4.4 / 1,022

= 50.6/1,022

= 4.95%

We can also use an online finance calculator to check the calculated value above as follows:

N (# of periods) = 10

I/Y (Interest per year) = 4.95%

PMT (Periodic Payment) = $55 ($1,000 x 5.5%)

FV (Future Value) = $1,000

Results:

PV = $1,044

Sum of all periodic payments = $550 ($55 x 10)

Total Interest $503.44

A. 4.9%

B. 5.1%

C. 5.3%

D. 5.5%

Thus, the annual yield to maturity (AYTM) of the Builtrite bonds is at 5.5% for 10 years with a $1,000 par value and the current price of $1,044 is A. 4.9%.

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The time 8:30AM is 3 and half hours before noon.

The fraction that represents 8:30AM is -3 1/2

The time is given as:

Time = 8:30 A.M

Given that Noon is represented by 0.

It means that time before noon would be represented with negative value

8:30AM is 3 and half hours before noon.

So, we have:

8:30AM = -3 1/2

Hence, the fraction that represents 8:30AM is -3 1/2

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Answer:

If the broker Josef employed to purchase these stocks and bonds charges a commission of $72 for each ten shares of stock bought or sold and a commission of 4% of the market value of each bond bought or sold, then the bonds have a yield 1.35 percentage points higher than that of the stocks.

Step-by-step explanation:

Answer:

x+10=-3x+38

Step-by-step explanation:

subtract 10 from both sides Subtract the numbers then add 3x on both sides

Answer:

option d

Step-by-step explanation:

[tex]\sf \boxed{a^m*a^n = a^{m+n}\\\\}[/tex]

[tex]\sf \left(\frac{m^{-1}m^{5}}{m^{-2}} \right)^{-3} =\left(\dfrac{m^{-1+5}}{m^{-2}}\right)^{-3}[/tex]

                 [tex]\sf = \left(\dfrac{m^4}{m^{-2}}\right)^{-3}\\\\[/tex]

[tex]\boxed{\dfrac{a^{m}}{a^{n}}=a^{m+n}}[/tex]

                    [tex]\sf = \left(m^{4-[-2]}\right)^{-3}\\\\ =\left(m^{4+2}\right)^{-3}\\\\ = \left(m^6\right)^{-3}\\\\[/tex]

[tex]\boxed{(a^{m})^n=a^{m*n}}[/tex]

                    [tex]\sf= m^{6*(-3)}\\\\ = m^{-18}[/tex]

[tex]\boxed{a^{-m}=\dfrac{1}{a^m}}[/tex]

                    [tex]\sf=\dfrac{1}{m^{18}}[/tex]

su masa atómica es de 4 creo

Answer:

1111/1250

Step-by-step explanation:

Hey there!

To find what fraction represents the decimal shown, you can take each answer choice, and divide the two numbers

We can do this because a fraction is a simple way of dividing two rational numbers

Our answer is 1111/1250

In order to check if this is correct, we can just divide 1111 and 1250

When you divide this, you get 0.8888...

So the fraction that represents 0.888... is 1111/1250

A fraction that represents the decimal 0.8888 is: 1111/1250

In Mathematics, fractions are represented as a numerical value, can be defined as the parts of a whole. A fraction can be a portion or section of any quantity out of a whole, where, the whole can be any number, a specific value, or a thing.

Given is decimal number 0.8888... we need to convert it into a fraction,

Since the number has 4 decimal places, then the first thing to do is multiply and divide the number by 10000.

We have then:

0.8888* (10000/10000) = 8888/10000

Simplifying we have:

8888/10000 = 4444/5000

4444/5000 = 2222/2500

2222/2500 = 1111/1250

Hence, the fraction that represents the decimal 0.8888 is: 1111/1250

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Answer:

answer below.

Step-by-step explanation:

1.  1/5----0.2

2. 1/3---0.3 repeating

3.  1/2---0.5

4.  7/10---0.7

5. 3/4---0.75

Answer:

  21°

Step-by-step explanation:

Dilation is a similarity transformation. It does not change angles. It changes lengths proportionally.

∠A'B'C' ≅ ∠ABC = 21°

~Denki Kaminari here~

Answer:

5t\sqrt(6su) (THE SECOND ONE)

Step-by-step explanation:

simplify the radical by breaking it up into known factors, assuming positive real numbers.

hope this helps :D

Answer:

Step-by-step explanation:

We are interested in the last two columns.

If we compare them we see that each value of the distance column is the absolute value of corresponding value of difference:

Corect choice is C

Answer:

The distance is the absolute value of the difference.

Step-by-step explanation:

Given table:

[tex]\begin{array}{|c|c|c|c|c|}\cline{1-5} a & b & a+b & a-b & \sf distance\\\cline{1-5} 1 & 2 & 3 & -1 & 1 \sf \: unit\\\cline{1-5} 4 & -1 & 3 & 5 & 5 \sf \: units\\\cline{1-5} -6 & -3 & -9 & -3 & 3 \sf \: units\\\cline{1-5}\end{array}[/tex]

The difference is column 4.

The distance is column 5.

The absolute value of a number is its positive numerical value.  It is denoted by a vertical line either side of the real number.

For example, |5| means 'the absolute value of 5', and |-5| means 'the absolute value of -5'.

Taking the absolute values of the differences:

⇒ |-1| = 1

⇒ |5| = 5

⇒ |-3| = 3

Therefore, the distance is the absolute value of the difference.

Answer:

False

Step-by-step explanation:

Hey there!

If this is a sum of cubes, this means that both numbers have whole numbers as the cube root of that number

The cube root of 125 is 5

But the cube root for 144 is a decimal meaning this is not a sum of cubes

Given :

⠀

To Find :

⠀

Solution :

⠀

Now,

⠀

According to the Question :

⠀

[tex]{\longrightarrow \qquad \sf{ x + {(x - 26.8)}^{ \circ} = {90}^{ \circ} }}[/tex]

⠀

[tex]{\longrightarrow \qquad \sf{ x + {x - 26.8}^{ \circ} = {90}^{ \circ} }}[/tex]

⠀

[tex]{\longrightarrow \qquad \sf{ 2 {x - 26.8}^{ \circ} = {90}^{ \circ} }}[/tex]

⠀

[tex]{\longrightarrow \qquad \sf{ 2 x = {90}^{ \circ} + 26.8^{ \circ}}}[/tex]

⠀

[tex]{\longrightarrow \qquad \sf{ 2 x = 116.8^{ \circ}}}[/tex]

⠀

[tex]{\longrightarrow \qquad \sf{ x = \dfrac{116.8^{ \circ}}{2}}}[/tex]

⠀

[tex]{\longrightarrow \qquad \frak{\pmb{ x =58.4^{ \circ}}}}[/tex]

⠀

Therefore,

⠀

Hence,

Answer:

The measurement of each angle is 58.4° and 31.6°

Step-by-step explanation:

Given :-

To Find :-

Solution:-

let one angle be x and other be x - 26.8°

we know that, Sum of complementary angle is 90°

X + X - 26.8° = 90°

2x = 90° + 26.8°

x = 58.4

So , one angle is 58.4° and other one is 58.4 - 26.8 which is 31.6

B

is the answer. Good luck!!

Answer:

[tex]D)\frac{1}{m^{18} }[/tex]

Step-by-step explanation:

Multiply [tex]m^{-1}[/tex] by [tex]m^{5}[/tex] by adding the exponents.

Use the power rule [tex]a^{m} a^{n} =a^{m+n}[/tex] to combine exponents.

[tex](\frac{m^{-1+5} }{m^{-2} } )^{-3} \\[/tex]

Add -1 and 5.

[tex](\frac{m^{4} }{m^{-2} } )^{-3}[/tex]

Move [tex]m^{-2}[/tex] to the numerator using the negative exponent rule [tex]\frac{1}{b^{-n} } =b^{n}[/tex].

[tex](m^{4} m^{2} )[/tex]

Multiply [tex]m^{4}[/tex] by [tex]m^{2}[/tex] by adding the exponents.

Use the power rule [tex]a^{m} a^{n} =a^{m+n}[/tex] to combine exponents.

[tex](m^{4+2} )^{-3}[/tex]

Add 4 and 2.

[tex](m^{6} )^{-3}[/tex]

Multiply the exponents in [tex](m^6)^{-3}[/tex]

Apply the rule and multiply exponents, [tex](a^m)^n=a^{mn}[/tex].

[tex]m^{6*-3}[/tex]

Multiply 6 by -3.

[tex]m^{-18}[/tex]

Rewrite the expression using the negative exponent rule [tex]b^{-n} =\frac{1}{b^{n} }[/tex].

[tex]\frac{1}{m^{18} }[/tex]

Answer:

111.3 cubic inches

Step-by-step explanation:

The dimensions of the rectangular prism are 5.9 x 3.4 x 5.1

volume = length x width x height

V = 5.9 x 3.4 x 5.3

V = 102.306

The dimesnsions of the triangular prism are 3.4 x 5.9 x ?

to find the missing length, 6 - 5.1 = 0.9

3.4 x 5.9 x 0.9

Volume = (3.4 x 5.9 x 0.9)/2

V = 18.054/2

V = 9.027

Add the volumes together

102.306 + 9.027 = 111.333

Round

111.3

Answer:

the ansewr is eight percent

Answer:

no roots.

Step-by-step explanation:

1)   [tex]\sqrt{8x+16}=2-8; \ - \ correct;[/tex]

2)   [tex]\sqrt{8x+16}=-6; \ - \ correct;[/tex]

note, the value after operation 'square root' cannot be negative ('-6' is on the right side!), then

3) it means, the given equation has no real roots.

Explanation:

How many surface has a pyramid?

5 Faces

It has 5 Faces. The 4 Side Faces are Triangles. The Base is a Square.

Answer:

19.0 cm (3 sf)

Step-by-step explanation:

Formula

[tex]\sf arc \ length=2\pi r \left(\dfrac{\theta}{360}}\right)[/tex]

(where r is the radius)

Arc length of white sector

Radius of white sector = 8 - 4.5 = 3.5 cm

[tex]\sf \implies arc \ length=2\pi \cdot 3.5 \left(\dfrac{50}{360}}\right)=\dfrac{35}{36} \pi \ cm[/tex]

Arc length of grey sector

Radius = 8 cm

[tex]\sf \implies arc \ length=2\pi \cdot 8 \left(\dfrac{50}{360}}\right)=\dfrac{20}{9} \pi \ cm[/tex]

Perimeter of shaded part

Perimeter = arc length (white) + arc length (grey) + 2 x 4.5

                [tex]\sf =\dfrac{35}{36} \pi + \dfrac{20}{9} \pi +9[/tex]

                [tex]\sf =19.0356432...[/tex]

                [tex]\sf =19.0 \ cm \ (3 \ sf)[/tex]

Answer:

196 Miles

Step-by-step explanation:

Jed Rode=20 miles per hour

jog back 8 miles per hour

28×7 = 196

Answer: 196 miles

Step-by-step explanation: 7(20+8) You have to distribute the 7 to each number(20 & 8). Then add the answers you get from the 7x20 and 7x8.

7x20=140

7x8= 56

56+140=196

hmmm so let's see first how much is 10% of the earnings of 1470.

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{a\% of b}\\ \cline{1-1} \\ \left( \cfrac{a}{100} \right)\cdot b \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{10\% of 1470}}{\left( \cfrac{10}{100} \right)1470}\implies 147[/tex]

so then

[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$147\\ r=rate\to 3.5\%\to \frac{3.5}{100}\dotfill &0.035\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{monthly, thus twelve} \end{array}\dotfill &12\\ t=years\dotfill &25 \end{cases}[/tex]

[tex]A=147\left(1+\frac{0.035}{12}\right)^{12\cdot 25}\implies A=147\left( \frac{2407}{2400} \right)^{300}\implies \boxed{A\approx 352.19}[/tex]

We want to evaluate

[tex]\displaystyle \int_{-\frac1{\sqrt2}}^{\frac1{\sqrt2}} \sqrt{\left(\frac{x-1}{x+1}\right)^2 + \left(\frac{x+1}{x-1}\right)^2 - 2} \, dx[/tex]

First we note that the integrand is even (replacing x with -x doesn't fundamentally alter the function being integrated), so this is equal to

[tex]\displaystyle 2 \int_0^{\frac1{\sqrt2}} \sqrt{\left(\frac{x-1}{x+1}\right)^2 + \left(\frac{x+1}{x-1}\right)^2 - 2} \, dx[/tex]

The radicand reduces significantly to

[tex]\displaystyle \left(\frac{x-1}{x+1}\right)^2 + \left(\frac{x+1}{x-1}\right)^2 - 2 = \frac{16x^2}{(1-x^2)^2}[/tex]

so that taking the square root, we simplify the integral to

[tex]\displaystyle 8 \int_0^{\frac1{\sqrt2}} \frac x{1-x^2} \, dx[/tex]

which is trivially computed with a substitution of [tex]y = 1 - x^2[/tex] and [tex]dy=-2x\,dx[/tex]:

[tex]\displaystyle -4 \int_1^{\frac12} \frac{dy}y = 4 \int_{\frac12}^1 \frac{dy}y = -4 \ln\left(\frac12\right) = \ln(2^4) = \boxed{\ln(16)}[/tex]

Answer:

It will take Lainey 9 seconds to travel from top to bottom

Further explanation:

The formula of speed will be used to calculate the time to reach from top to bottom of the slide.

Given

\begin{gathered}Distance=d=423\ feet\\Speed=s=47\ feet\ per\ second\end{gathered}

Distance=d=423 feet

Speed=s=47 feet per second

The formula for speed is:

s=\frac{d}{t}s=

t

d

Putting the values of distance and speed in the formula:

\begin{gathered}47=\frac{423}{t}\\t=\frac{423}{47}\\t=9\ seconds\end{gathered}

47=

t

423

t=

47

423

t=9 seconds

It will take Lainey 9 seconds to travel from top to bottom

Keywords: Speed, distance

Learn more about speed

Answer:

Increase the learning rate after each mini-batch by multiplying it by a small constant.

Answer:

60m

Step-by-step explanation:

The formula for the area of a parallelogram is base x height.

b x h

6m x 10m = 60m