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LiRa [457]
2 years ago
13

suppose you could make a single "lump sum" deposit of $3679, in an investment that provides an annual percentage rate(apr) of 4%

compounded daily. determine the future value(fv) of the investment after 11 years.
Mathematics
1 answer:
yaroslaw [1]2 years ago
3 0

Answer:

\$5,698.30  

Step-by-step explanation:

The compound interest formula is equal to  

A=P(1+\frac{r}{n})^{nt}  

where  

A is the Final Investment Value  (future value)

P is the Principal amount of money to be invested  

r is the rate of interest  in decimal

t is Number of Time Periods  

n is the number of times interest is compounded per year

in this problem we have  

t=11\ years\\ P=\$3,679\\ r=4\%=4/100=0.04\\n=365  

substitute in the formula above

A=3,670(1+\frac{0.04}{365})^{365*11}  

A=\$5,698.30  

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Marty is asked to draw triangles with side lengths of 4 units and 2 units, and a non-included angle of 30°. Select all the trian
777dan777 [17]

Answer:

The drawn in the attached figure

see the explanation

Step-by-step explanation:

<em>First case</em>

In the triangle ABC

Let

a=4\ units\\b=2/ units\\B=30^o

Applying the law of sines

Find the measure of angle A

\frac{a}{sin(A)}=\frac{b}{sin(B)}

substitute the given values

\frac{4}{sin(A)}=\frac{2}{sin(30^o)}

sin(A)=1

so

A=90^o

Find the measure of angle C

In a right triangle

we know that

B+C=90^o ----> by complementary angles

B=30^o

therefore

C=60^o

Find the length side c

Applying the law of sines

\frac{c}{sin(C)}=\frac{b}{sin(B)}

substitute the given values

\frac{c}{sin(60^o)}=\frac{2}{sin(30^o)}

c=2\sqrt{3}\ units

therefore

The dimensions of the triangle are

A=90^o

B=30^o

C=60^o

a=4\ units\\b=2\ units\\c=2\sqrt{3}=3.46\ units

<em>Second case</em>

In the triangle ABC

Let

a=4\ units\\b=2/ units\\A=30^o

Applying the law of sines

Find the measure of angle B

\frac{a}{sin(A)}=\frac{b}{sin(B)}

substitute the given values

\frac{4}{sin(30^o)}=\frac{2}{sin(B)}

sin(B)=0.25

so

using a calculator

B=14.48^o

Find the measure of angle C

we know that

The sum of the interior angles in any triangle must be equal to 180 degrees

so

A+B+C=180^o

A=30^o\\B=14.48^o

therefore

30^o+14.48^o+C=180^o

C=135.52^o

Find the length side c

Applying the law of sines

\frac{c}{sin(C)}=\frac{a}{sin(A)}

substitute the given values

\frac{c}{sin(135.52^o)}=\frac{4}{sin(30^o)}

c=5.61\ units

therefore

The dimensions of the triangle are

A=30^o

B=14.48^o

C=135.52^o

a=4\ units\\b=2\ units\\c=5.61\ units

see the attached figure to better understand the problem

4 0
2 years ago
A while back, either James borrowed $12 from his friend Rita or she borrowed $12 from him, but he can’t quite remember which. Ei
Tamiku [17]

Answer:

First option is correct.

Step-by-step explanation:

Let amounts of money James may have after he sees Rita be x.

It is given that either James borrowed $12 from his friend Rita or she borrowed $12 from him.

So meeting Rita second time either he will $12 or he will receive $12.

The amounts of money James may have after second meeting with Rita is:

Case 1: If he pays $12.

x=42.80-12             .... (1)

Case 1: If he receives $12.

x=42.80+12           .... (2)

On combining equation (1) and (2), we get

x=42.80\pm 12

Subtract 42.80 from both sides.

x-42.80=\pm 12

It can be written as

|x-42.80|=12

Therefore first option is correct.

4 0
2 years ago
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Anvisha [2.4K]

She made a mistake when she subtracted x1 from x2.

Step-by-step explanation:

Step 1 :

a)

The formula used by Lorena to calculate the slope between 2 points is correct

So the statement given in option 1 is not the reason for her mistake

Step 2:

b)

She has taken the fourth and fifth point and correctly used the x and y co ordinates to calculate the slope

Hence the statement in second option is not true

Step 3:

c)

While calculating the slope the denominator is -2 - (-4) . This gives 2 as the answer. But she has made a mistake in this subtraction giving -6 as the answer.

Hence she has made a mistake in subtracting x1 from x2 and this statement is true

Step 4:

d)

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For distance through north and east, we have positive values and negative for west and south. 

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Park:   (3, 5)

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Substituting,
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