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ra1l [238]
4 years ago
5

2018 copper penny struck at the Philadelphia mint in 1794 was sold for 345000 rate of return

Mathematics
1 answer:
vodomira [7]4 years ago
6 0

Answer:

The rate of return is 8%.

Step-by-step explanation:

The time span from 1794 to 2018 is (2018 - 1794) = 224 years.

Now, a penny i.e. 0.01 pounds of money as a principal gets the final sum of 345000 pounds after 224 years.

Here we have to calculate the rate of return if the interest is compounded yearly.

Using the formula of compound interest of r% APR, we get

345000 = 0.01 (1 + \frac{r}{100})^{224}

⇒ 1 + 0.01r = 1.08

⇒ 0.01r = 0.08

⇒ r = 8% (Answer)

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dem82 [27]

Answer:

"x" cantidad de personas, que será igual a

f(x) = $10x   Si   x < 30

f(x) = $9.5x si x ≥ 30

Si tenemos que son 29 personas entonces el costo es de:

f(x) = $10*29 = $290

Si incluye un miembro adicional

f(x) = $9.5*30 = $285

Ahorra un total de: $290 - $285 = $5

8 0
3 years ago
If I parallel m, find the value of x and y
Veseljchak [2.6K]

Answer:

x=24 y=9.8

Step-by-step explanation:

5y-23=3x

47+3x+2x+13=180

8 0
3 years ago
PLZ HELP ME! I CAN"T FIGURE THIS OUT! HELP! NO LINKS!
wolverine [178]

Answer:

There's only 1 step. It is the second one, "Multiply 4 by 5 and multiply 4 by 3x"

Step-by-step explanation:

4(5 - 3x) =

4(5) - 4(3x) =

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Hope this helps! :)

7 0
3 years ago
Read 2 more answers
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kupik [55]

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7 0
3 years ago
How is this solved using trig identities (sum/difference)?
GenaCL600 [577]
FIRST PART
We need to find sin α, cos α, and cos β, tan β
α and β is located on third quadrant, sin α, cos α, and sin β, cos β are negative

Determine ratio of ∠α
Use the help of right triangle figure to find the ratio
tan α = 5/12
side in front of the angle/ side adjacent to the angle = 5/12
Draw the figure, see image attached

Using pythagorean theorem, we find the length of the hypotenuse is 13
sin α = side in front of the angle / hypotenuse
sin α = -12/13

cos α = side adjacent to the angle / hypotenuse
cos α = -5/13

Determine ratio of ∠β
sin β = -1/2
sin β = sin 210° (third quadrant)
β = 210°

cos \beta = -\frac{1}{2}  \sqrt{3}

tan \beta= \frac{1}{3}  \sqrt{3}

SECOND PART
Solve the questions
Find sin (α + β)
sin (α + β) = sin α cos β + cos α sin β
sin( \alpha + \beta )=(- \frac{12}{13} )( -\frac{1}{2}  \sqrt{3})+( -\frac{5}{13} )( -\frac{1}{2} )
sin( \alpha + \beta )=(\frac{12}{26}\sqrt{3})+( \frac{5}{26} )
sin( \alpha + \beta )=(\frac{5+12\sqrt{3}}{26})

Find cos (α - β)
cos (α - β) = cos α cos β + sin α sin β
cos( \alpha + \beta )=(- \frac{5}{13} )( -\frac{1}{2} \sqrt{3})+( -\frac{12}{13} )( -\frac{1}{2} )
cos( \alpha + \beta )=(\frac{5}{26} \sqrt{3})+( \frac{12}{26} )
cos( \alpha + \beta )=(\frac{5\sqrt{3}+12}{26} )

Find tan (α - β)
tan( \alpha - \beta )= \frac{ tan \alpha-tan \beta }{1+tan \alpha  tan \beta }
tan( \alpha - \beta )= \frac{ \frac{5}{12} - \frac{1}{2} \sqrt{3}   }{1+(\frac{5}{12}) ( \frac{1}{2} \sqrt{3})}

Simplify the denominator
tan( \alpha - \beta )= \frac{ \frac{5}{12} - \frac{1}{2} \sqrt{3}   }{1+(\frac{5\sqrt{3}}{24})}
tan( \alpha - \beta )= \frac{ \frac{5}{12} - \frac{1}{2} \sqrt{3} }{ \frac{24+5\sqrt{3}}{24} }

Simplify the numerator
tan( \alpha - \beta )= \frac{ \frac{5}{12} - \frac{6}{12} \sqrt{3} }{ \frac{24+5\sqrt{3}}{24} }
tan( \alpha - \beta )= \frac{ \frac{5-6\sqrt{3}}{12} }{ \frac{24+5\sqrt{3}}{24} }

Simplify the fraction
tan( \alpha - \beta )= (\frac{5-6\sqrt{3}}{12} })({ \frac{24}{24+5\sqrt{3}})
tan( \alpha - \beta )= \frac{10-12\sqrt{3} }{ 24+5\sqrt{3}}

7 0
3 years ago
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