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laiz [17]
3 years ago
15

Balance on a 20,000 deposit earning 3.5% compounded quarterly after 10 years

Mathematics
1 answer:
Lemur [1.5K]3 years ago
7 0

~~~~~~ \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 &\$20000\\ r=rate\to 3.5\%\to \frac{3.5}{100}\dotfill &0.035\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{quarterly, thus four} \end{array}\dotfill &4\\ t=years\dotfill &10 \end{cases}

A=20000\left(1+\frac{0.035}{4}\right)^{4\cdot 10}\implies A=20000(1.00875)^{40}\implies A\approx 28338.18

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Using the sine rule, calculate the length y. Give your answer to 2 s.f.​
Tpy6a [65]

Answer:

y = 9.84 mm

Step-by-step explanation:

<h2>Sine rule:</h2>

Law of sine:

   \sf \boxed{\bf \dfrac{a}{Sin \ A}=\dfrac{b}{Sin \ B}= \dfrac{c}{Sin \ C}}

    a = y

    A = 31°

   b  = 17 mm

    B = 117°

\sf \dfrac{y}{Sin \ 31^\circ}=\dfrac{17}{Sin \ 117^\circ}\\\\

          \sf y = \dfrac{17}{Sin \ 117^\circ}*Sin \ 31^\circ\\\\  y = \dfrac{17}{0.89}*0.515\\\\y = 9.84 \ mm

8 0
2 years ago
the school stage is 8 3/4 feet wide and each chair is 1 5/12 feet wide. how many chairs will fit across the stage?
Sedaia [141]

Answer:

6 whole chairs

Step-by-step explanation:

(8 + (3/4)) / (1 + (5/12))

8.75 / 1.42

6.18 chairs

6 0
3 years ago
Willing to give brainliest! Practice question I dont understand the math.
aivan3 [116]

Answer:

Step-by-step explanation:

Part A:

The interquartile range is approximately 10

Part B:

The difference between the median values for each data set  is approximately 6

Part C:

i) More widely distributed and concentrated to the beginning of the month

The better measure of the center for the male dataset is the median

ii) The skewed distribution

The mean is the better measure of center for the dataset

Part D;

A possible reason for the outlier is by chance

4 0
3 years ago
In triangle ABC we have angle C = 3 times angle A, a=27 and c=48 What is b? Note: a is the side length opposite A etc. please he
Dima020 [189]

Answer:

  35

Step-by-step explanation:

The law of sines tells us ...

  sin(C)/c = sin(A)/a

  a·sin(3A) = c·sin(A)

Using the identity sin(3x) = 3cos(x)·sin(x) -sin(x)^3 and sin(x)^2 +cos(x)^2 = 1, we can simplify this to ...

  sin(A)(4cos(A)^2 -1) = (c/a)sin(A)

  4cos(A)^2 = c/a +1 = (48+27)/27 = 75/27 = 25/9

  cos(A)^2 = 25/36

  cos(A) = 5/6

__

Now, the angle B will be the difference between 180° and the sum of the other two angles:

  B = 180° -A -3A = 180° -4A

Using appropriate trig identities, we can write ...

  sin(B) = 4cos(A)^3sin(A) -4sin(A)^3cos(A)

  = 4sin(A)cos(A)(cos(A)^2 -sin(A)^2)

  = 4sin(A)cos(A)(2cos(A)^2 -1)

Filling in our value for cos(A), this becomes ...

  sin(B) = 4sin(A)(5/6)(2(5/6)^2-1) = sin(A)(35/27)

__

The law of sines tells us ...

  b/sin(B) = a/sin(A)

  b = a·sin(B)/sin(A) = 27(35/27)sin(A)/sin(A) = 35

The length of side b is 35 units.

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3 years ago
How many 3/4 cup servings can you serve with 3 1/2 cups of pasta
Salsk061 [2.6K]

Answer:

9 servings

Step-by-step explanation:

4 0
3 years ago
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