1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Morgarella [4.7K]
3 years ago
8

Each year for 4 years, a farmer increased the number of trees in a certain orchard by of the number of trees in the orchard the

preceding year. If all of the trees thrived and there were 6,250 trees in the orchard at the end of the 4-year period, how many trees were in the orchard at the beginning of the 4-year period?
Mathematics
1 answer:
Neko [114]3 years ago
7 0

Answer:

The number of trees at the begging of the 4-year period was 2560.

Step-by-step explanation:

Let’s say that x is number of trees at the begging of the first year, we know that for four years the number of trees were incised by 1/4 of the number of trees of the preceding year, so at the end of the first year the number of trees wasx+\frac{1}{4} x=\frac{5}{4} x, and for the next three years we have that

                             Start                                          End

Second year     \frac{5}{4}x --------------   \frac{5}{4}x+\frac{1}{4}(\frac{5}{4}x) =\frac{5}{4}x+ \frac{5}{16}x=\frac{25}{16}x=(\frac{5}{4} )^{2}x

Third year    (\frac{5}{4} )^{2}x-------------(\frac{5}{4})^{2}x+\frac{1}{4}((\frac{5}{4})^{2}x) =(\frac{5}{4})^{2}x+\frac{5^{2} }{4^{3} } x=(\frac{5}{4})^{3}x

Fourth year (\frac{5}{4})^{3}x--------------(\frac{5}{4})^{3}x+\frac{1}{4}((\frac{5}{4})^{3}x) =(\frac{5}{4})^{3}x+\frac{5^{3} }{4^{4} } x=(\frac{5}{4})^{4}x.

So  the formula to calculate the number of trees in the fourth year  is  

(\frac{5}{4} )^{4} x, we know that all of the trees thrived and there were 6250 at the end of 4 year period, then  

6250=(\frac{5}{4} )^{4}x⇒x=\frac{6250*4^{4} }{5^{4} }= \frac{10*5^{4}*4^{4} }{5^{4} }=2560.

Therefore the number of trees at the begging of the 4-year period was 2560.  

You might be interested in
Given the points A and BThe coordinates of point A = ( 3 , 1 )The coordinates of point B = (-1 , -1)The midpoint of AB = ([?],[
mr Goodwill [35]

Given the points A and B

The coordinates of point A = ( 3 , 1 )

The coordinates of point B = (-1 , -1)

The midpoint of AB, is the point C

C will be calculated as following :

C=\frac{A+B}{2}=\frac{(3,1)+(-1,-1)}{2}=\frac{(3-1,1-1)}{2}=\frac{(2,0)}{2}=(1,0)

so, the midpoint of AB = (1 , 0 )

3 0
1 year ago
ABC is a tangent to the circle below. O is the centre of the circle. Work out the size of angle 0. Give reasoning to justify you
Delvig [45]

Answer:

Θ = 46°

Step-by-step explanation:

the angle between a tangent and a radius at the point of contact is 90° , so

∠ ABO = 90°

since OB = OD ( radii of circle ) then Δ BOD is isosceles and

∠ OBD = ∠ ODB = 22°

the exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.

∠ AOB is an exterior angle of the triangle , then

∠ AOB = 22° + 22° = 44°

the sum of the 3 angles in Δ AOB = 180° , then

Θ + 44° + 90° = 180°

Θ + 134° = 180° ( subtract 134° from both sides )

Θ = 46°

6 0
1 year ago
What is 9 5/6 - 2 1/3
Mariana [72]
9 5/6 - 2 1/3 is 7 1/2.

You could get this answer by finding the same denominator of the fractions. The LCM of both is 6. Multiply the 1 of the second fraction 2 times because you had to multiply the denominator 2 times to get to 6. 
You should have 2 2/6.

Now get 9 5/6 - 2 2/6.

The answer is 7 3/6, simplifies into 7 1/2.
9 5/6 - 2 1/3 is 7 1/2.


5 0
3 years ago
Read 2 more answers
Write the decimal for the expanded form given below.<br><br> 60+7 + 0.3 + 0.05+0.003
svet-max [94.6K]

Answer: 67.353

Step-by-step explanation:

 60.000

+07.000

+00.300           Writing the numbers like this helps me keep track of them!

+00.050        It lets me see what place each number is in relative to the others

+00.003

67.353

5 0
2 years ago
Anyone who answers correctly gets brainlist!
Alex787 [66]

Answer:

B

Step-by-step explanation:

easy

3 0
2 years ago
Read 2 more answers
Other questions:
  • A box has a volume of 192 cubic inches, a length that is twice as long as its width, and a height that is 2 inches greater than
    14·1 answer
  • A white tailed deer can sprint at speeds up to 30 miles per hour. American bison can run at speeds up to 3,520 feet per minute.
    15·1 answer
  • ⦁ The average distance from the sun to the planet Mercury is about 58,000,000 km. The diameter of a human hair is about 0.0025 c
    8·2 answers
  • DIG DEEPER! The figure shows the angles used to make a double bank shot in an air hockey game. a. Find the value of x. b. How do
    14·1 answer
  • Find the exact value of sin A in simplest radical form. ​
    5·1 answer
  • If it takes 20 minutes to fill a tank completely with the capacity of 1000 l find the rate at which water flows in litres per mi
    6·1 answer
  • PLEASE SCREENSHOT AND MARKUP FOR 40 POINTS
    7·2 answers
  • Triangle rst is dilated by a scale factor of 5 to form triangle r's't'. side r's' measures 40. what is the measure of side rs?
    6·1 answer
  • Linda is training to be an assistant at the local animal shelter. To become an assistant she needs to complete 48 h of training.
    9·1 answer
  • Find the sum and choose the correct answer. <br> 2n 3 + 4n 2 - 7 and -n 3 + 8n - 2
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!