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3 years ago

In transformations, "Y + means to move

Mathematics

1 answer:

Mademuasel [1]3 years ago

7 0

Answer:

Step-by-step explanation:

Reflection in the x-axis: When you reflect a point across the x-axis, the x-coordinate remains the same, but the y-coordinate is transformed into its opposite.

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When the effective interest rate is 9% per annum, what is the present value of a series of 50 annual payments that start at $100

ser-zykov [4K]

Answer:

$1,109.62

Step-by-step explanation:

Let's first compute the future value FV.

In order to see the rule of formation, let's see the value (in $) for the first few years

End of year 0

1,000

End of year 1(capital + interest + new deposit)

1,000*(1.09)+10

End of year 2 (capital + interest + new deposit)

(1,000*(1.09)+10)*1.09 +10 =

$\bf 1,000*(1.09)^2+10(1+1.09)$

End of year 3 (capital + interest + new deposit)

$\bf (1,000*(1.09)^2+10(1+1.09))(1.09)+10=\\1,000*(1.09)^3+10(1+1.09+1.09^2)$

and we can see that at the end of year 50, the future value is

$\bf FV=1,000*(1.09)^{50}+10(1+1.09+(1.09)^2+...+(1.09)^{49}$

The sum

$\bf 1+1.09+(1.09)^2+...+(1.09)^{49}$

is the sum of a geometric sequence with common ratio 1.09 and is equal to

$\bf \frac{(1.09)^{50}-1}{1.09-1}=815.08356$

and the future value is then

$\bf FV=1,000*(1.09)^{50}+10*815.08356=82,508.35564$

The present value PV is

$\bf PV=\frac{FV}{(1.09)^{50}}=\frac{82508.35564}{74.35572}=1,109.616829\approx \$1,109.62$

rounded to the nearest hundredth.

5 0

3 years ago

Heidi takes 45 minutes to cover a distance of 5.4 miles on a treadmill. Find the average distance covered by Heidi in one minute

Natali5045456 [20]

Heidi goes 0.12 miles a minute

5 0

3 years ago

There are 600 students at a middle school. If 60% of the students are girls, how many students at the middle school are girls?

mash [69]

Answer:

360!

Step-by-step explanation:

4 0

3 years ago

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Wheels on some in-line skates can be removed using a 5/32 in. Allen wrench. What is 5/32

kupik [55]

Answer:

0.15625

Step-by-step explanation:

No specific method, but only using calculator

5÷32

=0.15625

3 0

3 years ago

{x + 8y = -16 {x-3y = -5

Anna007 [38]

Answer: y= -1 and x=-8

x+8y=-16

x=-8y-16

so x-3y=-5

-8-16-3y=-5

-11y-16=-5

-11y=-5+16

-11y=11

y=-1

x-3y=-5

x+3=-5

x=-8

8 0

2 years ago

Read 2 more answers