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Marina CMI [18]
3 years ago
11

A high-interest savings account pays 5.5% interest compounded annually. If $300 is deposited initially and again at the first of

Mathematics
2 answers:
Juli2301 [7.4K]3 years ago
7 0
The owner's account would have a balance of $4075.05 in 10 years.
Xelga [282]3 years ago
4 0

Answer:

\sum_{n=1}^{10} 316.5 (1.055)^{n-1}

Step-by-step explanation:

The amount (A) in a deposit after 1 year is calculated as follows:

A = P*(1 + r)

where:

P is the present value

r is the annual rate (decimal)

After the first year:

A = 300*(1 + 0.055) = $316.5

After the second year, the account will have a new amount of $316.5 due to the new $300 and the interest gained with the previous $316.5:

A = 316.5 + 316.5*(1 + 0.055)

After the third year:

A = 316.5 + [316.5 + 316.5*(1 + 0.055)]*(1 + 0.55)

A = 316.5 + 316.5*(1 + 0.055) + 316.5*(1 + 0.055)^2

After 10 years:

\sum_{n=1}^{10} 316.5 (1.055)^{n-1}

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Find the measure indicated. Assume that the lines which appear to be tangent are tangent. PART 3
ludmilkaskok [199]

I'll do problems 13 and 14 to get you started.

=====================================================

Problem 13

<h3>Answer:  32 degrees</h3>

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

Explanation:

Refer to the diagram below for problem 13. Since BD is a tangent of the circle, this means angle ABD is 90 degrees, and furthermore x+y = 90. This solves to y = 90-x.

If we focus on triangle ABC, then we can add the interior angles and set the sum equal to 180

A+B+C = 180

z+y+y = 180

z+2y = 180

z+2(90-x) = 180 .... plug in y = 90-x

z+180-2x = 180

z-2x = 180-180

z-2x = 0

z = 2x

We'll use this later.

Now move onto triangle ABD. This is a right triangle due to angle ABD being 90 degrees. The acute angles z and 26 are complementary, meaning they add to 90. So,

z+26 = 90

z = 90-26

z = 64

Now plug this into z = 2x and solve for x

z = 2x

64 = 2x

2x = 64

x = 64/2

x = 32

=====================================================

Problem 14

<h3>Answer: 31 degrees</h3>

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

Explanation:

Refer to the image shown below for problem 14. Like before, I've added various labels to it to help find the angle we're after (the red angle x).

Note how I've drawn a dashed line from point A to point D. This splits up quadrilateral ABCD into two triangles ABD and ACD. These triangles can be shown to be congruent using the HL (hypotenuse leg) theorem.

The congruent triangles also implies that angle DBC and angle BCD are the same measure (both are shown in green as the variable y).

Focus on triangle BCD. It has interior angles of: y, y and 62. Add them up, set the sum equal to 180.

y+y+62 = 180

2y+62 = 180

2y = 180-62

2y = 118

y = 118/2

y = 59

As the image attachment mentions, the angles x and y add to 90 degrees. This is because angle ABD is 90 degrees, due to segment BD being tangent to the circle. So x+y = 90 leads to x = 90-y, and therefore,

x = 90-y

x = 90-59

x = 31

Side note: it is not a coincidence that we ended up with half of the value of 62.

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3 years ago
2+2=4 or your IQ which one?
Alenkasestr [34]

Answer:

Your iq

Step-by-step explanation:you pick this because you can get a very highscore

6 0
2 years ago
Read 2 more answers
A photo is 4 inches by 6 inches. What is the area of the photo?
kolezko [41]
4 * 6 = 24
The answer is, the area of the whole photo is 24. 
Hope this helped :)
4 0
3 years ago
What is the slope of line M.<br> What is a?<br> What is B?
lesantik [10]

Answer: A 2,2

Step-by-step explanation: 1 - 1 something

7 0
2 years ago
5. Class 7887 has 2:7 math classes daily. How many math classes do they have
ANTONII [103]

Answer:

56.7

Step-by-step explanation:

2.7 x 21 = 56.7

5 0
3 years ago
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