MATHEMATICS COLLEGE

Consider an investment of $6000 that earns 4.5% interest. How long would it take for the investment to reach 1500 if the interest is compounded monthly?

Answers

Answer 1

Answer:

Answer:

20.4 years

Step-by-step explanation:

The future value formula is ...

FV = P(1 +r/n)^(nt)

where P is the principal invested (6000), n is the number of times per year compounding occurs (12), r is the interest rate (.045), and t is the number of years.

Perhaps you're interested in a future value of $15,000 (not 1500). Then we can find t from ...

15000 = 6000(1 +.045/12)^(12t)

2.5 = 1.00375^(12t) . . . . . divide by 6000

log(2.5) = 12t·log(1.00375) . . . . . take logarithms

log(2.5)/(12log(1.00375)) = t ≈ 20.4

It will take 20.4 years for the investment to reach $15,000.

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Prove
cos A /(1- sin A) = (1 + sin A)/cos A

Answers

Answer:

answer is in exaplation

Step-by-step explanation:

cosA

1+sinA

=2secA

Step-by-step explanation:

\begin{lgathered}LHS = \frac{cosA}{1+sinA}+\frac{1+sinA}{cosA}\\=\frac{cos^{2}A+(1+sinA)^{2}}{(1+sinA)cosA}\\=\frac{cos^{2}A+1^{2}+sin^{2}A+2sinA}{(1+sinA)cosA}\\=\frac{(cos^{2}A+sin^{2}A)+1+2sinA}{(1+sinA)cosA}\\=\frac{1+1+2sinA}{(1+sinA)cosA}\end{lgathered}

LHS=

1+sinA

cosA

1+sinA

(1+sinA)cosA

cos

A+(1+sinA)

(1+sinA)cosA

cos

A+1

+sin

A+2sinA

(1+sinA)cosA

(cos

A+sin

A)+1+2sinA

(1+sinA)cosA

1+1+2sinA

/* By Trigonometric identity:

cos² A+ sin² A = 1 */

\begin{lgathered}=\frac{2+2sinA}{(1+sinA)cosA}\\=\frac{2(1+sinA)}{(1+sinA)cosA}\\\end{lgathered}

(1+sinA)cosA

2+2sinA

(1+sinA)cosA

2(1+sinA)

After cancellation,we get

\begin{lgathered}= \frac{2}{cosA}\\=2secA\\=RHS\end{lgathered}

cosA

=2secA

=RHS

Therefore,

\begin{lgathered}\frac{cosA}{1+sinA}+\frac{1+sinA}{cosA}\\=2secA\end{lgathered}

1+sinA

cosA

1+sinA

=2secA

If the absolute value of the correlation is approximately one, then the points lie close to a line that slopes upward or downward?

Answers

Answer:

if it is positive then it goes upward and if negative it goes downward..so if it is approximately 1 then it will be constant or straight...

Answer the question in the picture

Answers

Recall the angle sum identities:

$\sin(x+y)=\sin x\cos y+\cos x\sin y$

$\cos(x+y)=\cos x\cos y-\sin x\sin y$

Now,

$\tan(x+y)=(\sin(x+y))/(\cos(x+y))=(\sin x\cos y+\cos x\sin y)/(\cos x\cos y-\sin x\sin y)$

Divide through numerator and denominator by $\cos x\cos y$ to get

$\tan(x+y)=(\tan x+\tan y)/(1-\tan x\tan y)$

Next, we use the fact that $x,y$ lie in the first quadrant to determine that

$\sin x=\frac12\implies\cos x=√(1-\sin^2x)=\frac{\sqrt3}2$

$\cos y=\frac{\sqrt2}2\implies\sin x=√(1-\cos^2x)=\frac1{\sqrt2}$

So we then have

$\tan x=(\sin x)/(\cos x)=\frac{\frac12}{\frac{\sqrt3}2}=\frac1{\sqrt3}$

$\tan y=(\sin y)/(\cos y)=\frac{\frac1{\sqrt2}}{\frac{\sqrt2}2}=1$

Finally,

$\tan(x+y)=\frac{\frac1{\sqrt3}+1}{1-\frac1{\sqrt3}}=(1+\sqrt3)/(\sqrt3-1)=2+\sqrt3\approx3.73$

The solution of the equation x2-6x=0 is ?

Answers

The answer is x = 0

X=0 ............................

A physical education class has 21 boys and 9 girls. Each day, the teacher randomly selects a team captain. Assume that no student is absent. What is the probability that the team captain is a girl two days in a row?The probability of choosing a captain that is a girl two days in a row is
9
%.

Answers

The probability of choosing a captain that is a girl two days in a row is 9%

How to determine the probability?

The given parameters are:

Boys = 21

Girls = 9

The total number of students is

Total = 21 + 9

Total = 30

This means that the probability of selecting a girl is:

P(Girl) = 9/30

For two days, the required probability is

P = 9/30 * 9/30

Evaluate

P = 9%

Hence, the probability of choosing a captain that is a girl two days in a row is 9%

Answers

Answer:

in standered form -

3x²+4x−14=0

Step-by-step explanation:

Hope this helps :)

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