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3 years ago

PLSSS HELP AND EXPLAIN YOUR ANSWER!! :)

Mathematics

1 answer:

Vilka [71]3 years ago

6 0

t = 14.9 years

Solution:

Given data:

I = $688.38, P = $550, r = 8.4%, t = ____ years

Simple interest formula:

$$I=\frac{Prt}{100}$

$$688.38=\frac{550 \times 8.4 \times t}{100}$

Switch the sides.

$$\frac{550 \times 8.4 \times t}{100}=688.38$

Multiply by 100 on both sides.

$$\frac{100 \times 550 \times 8.4 t}{100}=688.38 \times 100$

$$550 \times 8.4 t=68838$

$4620 t=68838$

Divide by 4620 on both sides.

$$\frac{4620 t}{4620}=\frac{68838}{4620}$

$$t=\frac{149}{10}$

t = 14.9

Hence t = 14.9 years.

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Let

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$\displaystyle y''(x) = \sum_{n=2}^\infty n (n-1) a_nx^{n-2} = \sum_{n=0}^\infty (n+2) (n+1) a_{n+2} x^n$

When x = 0, we observe that y(0) = a₀ and y'(0) = a₁ can act as initial conditions.

Substitute these into the given differential equation:

$\displaystyle \sum_{n=0}^\infty (n+2)(n+1) a_{n+2} x^n - \sum_{n=0}^\infty a_nx^n = 0$

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Then the coefficients in the power series solution are governed by the recurrence relation,

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Since the n-th coefficient depends on the (n - 2)-th coefficient, we split n into two cases.

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$k=2 \implies n=4 \implies a_4 = \dfrac{a_2}{4\cdot3} = \dfrac{a_0}{4\cdot3\cdot2\cdot1}$

$k=3 \implies n=6 \implies a_6 = \dfrac{a_4}{6\cdot5} = \dfrac{a_0}{6\cdot5\cdot4\cdot3\cdot2\cdot1}$

It should be easy enough to see that

$a_{n=2k} = \dfrac{a_0}{(2k)!}$

• If n is odd, then n = 2k + 1 for some k ≥ 0. Then

$k = 0 \implies n=1 \implies a_1 = a_1$

$k = 1 \implies n=3 \implies a_3 = \dfrac{a_1}{3\cdot2}$

$k = 2 \implies n=5 \implies a_5 = \dfrac{a_3}{5\cdot4} = \dfrac{a_1}{5\cdot4\cdot3\cdot2}$

$k=3 \implies n=7 \implies a_7=\dfrac{a_5}{7\cdot6} = \dfrac{a_1}{7\cdot6\cdot5\cdot4\cdot3\cdot2}$

so that

$a_{n=2k+1} = \dfrac{a_1}{(2k+1)!}$

So, the overall series solution is

$\displaystyle y(x) = \sum_{n=0}^\infty a_nx^n = \sum_{k=0}^\infty \left(a_{2k}x^{2k} + a_{2k+1}x^{2k+1}\right)$

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Binomial probability distribution

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$C_{n,x} = \frac{n!}{x!(n-x)!}$

The parameters are:

x is the number of successes.

n is the number of trials.

p is the probability of a success on a single trial.

In this problem:

He makes 90% of the free throws, hence $p = 0.9$ .

He is going to shoot 3 free throws, hence $n = 3$ .

The probability that he makes exactly 1 is P(X = 1), hence:

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To learn more about the binomial distribution, you can take a look at brainly.com/question/24863377

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