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FinnZ [79.3K]
3 years ago
14

1000 was invested at 5.5% interest, compounded annually. After sometime the amount had grown to 1550. How long was the money inv

ested?
Mathematics
1 answer:
scZoUnD [109]3 years ago
4 0

compound interest equation for annually compounded

A=P(1+r)^t

A=final amount

P=principal

r=rate in decimal

t=time in years


given that

A=1550

P=1000

r=5.5%=0.055

find t


1550=1000(1+0.055)^t

divide both sides by 1000

1.55=1.055^t

take ln of both sides

ln(1.55)=ln(1.055^t)

use ln rule ln(a^b)=b(ln(a))

ln(1.55)=t(ln(1.055))

divide both sides by ln(1.055)

\frac{ln(1.55)}{ln(1.055)}=t

using a calculator, we get that t=8.18544 yrs

so about 8.2yrs

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X+2y=0<br> 3x+4y=4<br><br> find the solution
Nady [450]

Answer:

  (x, y) = (4, -2)

Step-by-step explanation:

The coefficient of y in the second equation is double the coefficient of y in the first. We can subtract twice the first equation from the second to eliminate y.

  (3x +4) -2(x +2y) = (4) -2(0)

  x = 4 . . . . . . . . . simplify

Substituting into the first equation, we have ...

  4 +2y = 0

  2 +y = 0 . . . . . . divide by 2

  y = -2 . . . . . . . . subtract 2

The solution is (x, y) = (4, -2).

4 0
2 years ago
A high school mathematics teacher can grade a set of exams in 7 hours working alone. If their student teacher helps​ them, it wi
Stels [109]

It takes 9 hrs 19.8 minutes  for the student teacher to grade the exams if they worked​ alone

<u>Solution:</u>

Let the efficiency of the school teacher be “x” and the efficiency of the student teacher be “y”

Here the word efficiency means the rate of doing work

Let the total work to be completed be W

According to the question,

The time taken by the school teacher to complete the work is 7 hrs.

So we can write it in equation form

W = x \times 7  ---- eqn 1

where W is the total work and x is the efficiency

Similarly for student teacher and school teacher doing the work simultaneously, we can write the equation as

W =(x +y ) \times 4

Equating eqn 1 and 2

x \times 7=(x+y) \times 4

7x = 4x + 4y

3x = 4y

So in ratio x : y = 4 : 3

Now putting value of x = 4 in equation (1) we get total work to be 28

Now, <em>total time taken by the student teacher = total work ÷ efficiency of student teacher</em>

Hence, total time taken by the student teacher = 28 ÷ 3 = 9.33 hrs

= 9 hrs 19.8 minutes

Hence it takes 9 hrs 19.8 minutes  for the student teacher to grade the exams if they worked​ alone

4 0
3 years ago
55) A dilation of scale factor of 4 will produce a congruent figure<br>True or False​
vivado [14]

Answer:

False

Step-by-step explanation:

When a figure is dilated by a scale factor of 4, the new figure produced will be 4 times the size of the original figure. This means that, the size would change while the shape remains the same as the original figure.

Congruent figures must have the same shape and size.

Therefore, the figure produced when a dilation of scale factor of 4 is done is not a congruent figure. Rather, it is a similar figure.

So, get statement is FALSE.

6 0
3 years ago
14 The straight line, L, has the equation y = 5 - 2x
lozanna [386]

Answer:

Step-by-step explanation:

(a) the co-ordinates of the point where the line crosses the y-axis,

y intercept occurs when x = 0

y = 5 - 2(0)

y = 5

(0, 5)

(b) the gradient of the line,

the general line formula is y = mx + b, where m is the slope and b is the y intercept.

y = 5 - 2x

y = -2x + 5

m = -2

(c) the equation of a line parallel to L.

Parallel lines have the same slope, but different y intercepts.

The simplest parallel line formula is

y = -2x + 0

y = -2x

7 0
3 years ago
In 15–20, write the number positioned at each point.
Mumz [18]

Answer:

See below.

Step-by-step explanation:

15.) -3.25

16.) -4.5

17.) 1.25

18.) -5.75

19.) 0.5

20.) -2.5

5 0
3 years ago
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