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4 years ago

Hal Fritz purchased a $5,000 bond at 95. The annual interest is 6%.

1 answer:

4 0

Hi there :-)

Bond Cost = Face Value × Percent
5,000×0.95=4,750

Annual Interest=Face Value×Interest Rate
5,000×0.06=300

Annual Yield=Annual Interest×Bond Cost
(300÷4,750)×100=6.32%

Hope it helps

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Write the standard form of the equation of the circle with endpoints of a diameter at the points (7,2) and (-9,5).

lys-0071 [83]

Answer:

$(x+1)^2 + (y- 3.5)^2 =64$

Step-by-step explanation:

We are given that endpoints of a diameter at the points (7,2) and (-9,5).

Center of the circle is the mid point of diameter

So, first find the mid point of diameter

Formula : $x=\frac{x_1+x_2}{2} , y=\frac{y_1+y_2}{2}$

$(x_1,y_1)=(7,2)\\(y_1,y_2)=(-9,5)$

Substitute the values in formula

$x=\frac{7-9}{2} , y=\frac{2+5}{2}$

$x=-1 , y=3.5$

So, center of circle = (h,k )=(-1,3.5)

To find length of diameter :

$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

$(x_1,y_1)=(7,2)\\(y_1,y_2)=(-9,5)$

$d=\sqrt{(-9-7)^2+(5-2)^2}$

$d=\sqrt{265}$

Length of radius = r = $\frac{Diameter}{2}=\frac{\sqrt{256}}{2}$

Standard form of the equation of the circle : $(x -h)^2 + (y- k)^2 = r^2$

(h,k )=(-1,3.5)

$r=\frac{\sqrt{256}}{2}$

Equation of the circle : $(x+1)^2 + (y- 3.5)^2 =(\frac{\sqrt{256}}{2})^2$

Equation of the circle : $(x+1)^2 + (y- 3.5)^2 =64$

Hence the standard form of the equation of the circle with endpoints of a diameter at the points (7,2) and (-9,5) is $(x+1)^2 + (y- 3.5)^2 =64$

5 0

4 years ago

Investigating the Definition of Absolute Value

boyakko [2]

It's how far a number is from 0.
( ex.) 6 is 6 away from 0 but so is -6; so the absolute value of 6 is 6 and the absolute value of -6 is 6. the symbol "|" is placed on either side to mean absolute value.

(ex.2) |-6| = 6. -|-6|= -6. |6|=6. and -|6|= -6.
if the negative sign is outside of the symbol then the number will always be negative but if there is no negative sign outside of the symbol it will always be positive, even if it looks lile this. |-6| it would still be positive.

4 0

4 years ago

8(x − a) = 2(2a − x); x

TEA [102]

X=5
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6

Yoooooo
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7 0

3 years ago

The chorus club is trying to raise money for new uniforms if the raised $2,486 last year and $3,578 this year,how much money did

yuradex [85]

2486 + 3578 = $6064 raised in total

4 0

4 years ago

Read 2 more answers

pam read 5 pages of a mystery book in 3 minutes. if she continues to read at the same rate how many hours will it take her ro re

Amanda [17]

Pam would read 235 pages in 141 minutes or 2hrs and 21min.
Divide 3 from 5 to get the time it takes her to read 1 page which is 0.6 . Now multiply .6 by the number of total pages (235) to find the time it takes, which would be 141 minutes, 2.35 hours, or 2 hours and 21 minutes (whichever you prefer) ( 3/5 = .6 × 235 = 141 )

6 0

4 years ago

Read 2 more answers