A gardener brought 5 rabbits, after 2 months rabbits became 10, and after 4 months they became 20. If the growth continues on the same ratio, what would be the amount of rabbits after 1 year?
(a) 300 (b) 435
(c) 535 (d) 635
Answer:
Initial population of Rabbit = 5 rabbit
After 2 months
Population of Rabbit = 10
After 4 months
population of rabbit = 20
Formula for growth is :
G = [tex]G_{0}[1 + R]^n[/tex], where G is final population and [tex]G_{0}[/tex] is initial population, and R is growth rate.
1. 10 = 5 [1 +R]²
Dividing both sides by 5 , we get
2 = (1 + R)²
→ R + 1 = √2 ⇒ taking positive root of 2
→R = √2 -1
Amount of rabbit after 1 year = [tex]20(1 + \sqrt2 -1)^8= 20 \times (\sqrt2)^8= 20 \times 2^4= 20 \times 16= 320[/tex]
The amount of rabbits after 1 year is[tex]\boxed{635}[/tex].
Further explanation:
The terms of the geometric sequence can be written as,
[tex]a,ar,a{r^2},a{r^3}[/tex], ..
Here, is the first term and is the common ratio.
If the first term and the second term is known then, the value of can be obtained.
Now, the value of any term can be easily obtained with the help of a and r.
Explanation:
The initial population of the rabbit is 5.
After two months the population of the rabbit is 10.
After four months the population of the rabbit is 20.
After six months the population of the rabbit is 40.
After eight months the population of the rabbit is 80.
After ten months the population of the rabbit is 160.
After twelve months the population of the rabbit is 320.
The series can be formed as,
[tex]5,{\text{10, 20, 40, 80, 160, 320}}[/tex]
Now find the sum of all the population.
[tex]\begin{aligned}{\text{Sum}} &= 5 + 10 + 20 + 40 + 80 + 160 + 320\\&= 685 \\\end{aligned}[/tex]
The amount of rabbits after 1 year is [tex]\boxed{635}[/tex].
Learn more:
1. Learn more about inverse of the functionhttps://brainly.com/question/1632445.
2. Learn more about equation of circle brainly.com/question/1506955.
3. Learn more about range and domain of the function https://brainly.com/question/3412497
Answer details:
Grade: High School
Subject: Mathematics
Chapter: Geometric progression
Keywords: Rabbit, gardener, same ratio, amount of rabbits, growth, continues, 1 year, Five rabbits, after two months,
rule add 15, subtract 10 first term4
Dritown received 0.135 inches of rain in the spring of 2011. Write this decimal as a fraction in simplest form.
A: 7/50
B: 1/8
C: 13/100
D: 27/200
Answer:
[tex]\frac{27}{200}[/tex]
Step-by-step explanation:
Dritown received 0.135 inches of rain in the spring of 2011.
Convert 0.135 in fraction form
0.135 can be written as 0.135/1
To remove decimal multiply top and bottom by 1000
[tex]\frac{0.135 \cdot 1000}{1000} =\frac{135}{1000}[/tex]
Divide both top and bottom by 5
[tex]\frac{135}{1000}[/tex] becomes [tex]\frac{27}{200}[/tex]
sherry has five times as many computer games as jay . Nairan has three times as many computer games as jay. sherry has 16 computer game's more than Nairan has .hiw many games does jay have?
Answer:
Jay has 8 computer games
Step-by-step explanation:
Let
x -----> the number of computer games Sherry has
y -----> the number of computer games Jay has
z -----> the number of computer games Nairan has
we know that
[tex]x=5y[/tex] ----> equation A
[tex]z=3y[/tex] ----> equation B
[tex]x=z+16[/tex] ----> equation C
Substitute equation A and equation B in equation C and solve for y
[tex]5y=3y+16[/tex]
[tex]5y-3y=16[/tex]
[tex]2y=16[/tex]
[tex]y=8[/tex]
therefore
Jay has 8 computer games
Graph the function y = 2x3 – x2 – 4x + 5. To the nearest tenth, over which interval is the function decreasing?
(1, ∞)
(–∞, –0.7)
(–0.7, 1)
(–1, 0.7)
Answer:
Option 3 - (-0.7,1)
Step-by-step explanation:
Given : Function [tex]y=2x^3-x^2-4x+5[/tex]
To find : Over which interval is the function decreasing?
Solution :
First we plot the graph using graphing calculator.
Refer the attached figure below.
Now, Examining the graph
From [tex]-\infty[/tex] to (-0.667,6.63) the graph is increasing as the curve is increasing.
From (-0.667,6.63) to (1,2) the graph decreasing as the curve is decreasing.
From (1,2) to [tex]\infty[/tex] the graph is increasing as the curve is increasing.
So, The interval in which the function is decreasing is given by (-0.667,1)
Round to nearest tenth, (-0.7,1)
Therefore, Option 3 is correct.
How to solve this?help!
Liam is setting up folding chairs for a meeting. If he arranges the chairs in 6 rows of the same length, he has 7 chairs left over. If he arranges the chairs in 4 rows of that same length, he has 19 left over. How many chairs does Liam have?
Quadrilateral ABCD is the result of a reflection of quadrilateral EFGH over the line. Which line segment in the image corresponds to EH in the pre-image?
A.) AD
B.) AB
C.) BC
D.) CD
Answer: A) AD
Step-by-step explanation:
Given: Quadrilateral ABCD is the result of a reflection of quadrilateral EFGH over the line.
We know that after reflection each point on the pre-image has a corresponding point on its image that is equidistant from a given line of reflection.
Since, EH shows the first and the last character of the name .
Thus, the line segment in the image corresponds to EH in the pre-image is AD because A is the first and D is the last character of the pre-image.
You use a microscope to look at bacteria that is 0.0034 millimeter long. The microscope magnifies the bacteria 430 times. How long does the bacteria appear to be when you look at it through the microscope?
Answer:
1.462 millimeters.
Step-by-step explanation:
You use a microscope to look at bacteria that is 0.0034 millimeter long.
The microscope magnifies the bacteria 430 times.
So the bacteria appears 430 times long through the microscope.
We will multiply the length of bacteria by 430.
The size of bacteria appear = 430 × 0.0034
= 1.462 millimeters
The length of the bacteria would appear 1.462 millimeters through microscope.
Point M is the midpoint of segment QR. If QM = 16 + x and MR = 2(x + 2), find the length of QR. QR = 12 QR = -12 QR = 28 QR = 56
The local newspaper has letters to the editor from 20 people. If this number represents 4% of all of the newspaper's readers, how many readers does the newspaper have?
Answer:
500
Step-by-step explanation:
25 x 20 = 500
It takes 45 minutes or 45 over 60 of an hour to cook a chicken? How many fourths of an hour is that?
A. 1
B. 2
C. 3
D. 4
Answer:
3
Step-by-step explanation:
Divide 60 by 4 and get your answer of 15.
Now, divide 45 by 15 to get 3.
It takes 3 fourths of 60 to cook a chicken.
Therefore, 3 would be your answer.
-kiniwih426
Learn more at, https://brainly.com/question/11642778?referrer=searchResults
Jon invested 6,200 for 6 years at 3%.Calculate the simple interest.
Which number line shows the graph of -0.7
Kelly is saving money to buy a concert ticket. Her savings y for x days can be represented by the equation y=x+10. Graph the solutions of the equations?
Answer:
among us codes!
Step-by-step explanation:
TDGNQQ
When one-fifth of the boys left, there were still b boys and g girls who stayed to see a program. What was the total number of boys and girls at the beginning of the program?
To find the total number of boys and girls at the beginning of the program, use the equations b2 = (1/5)b1, b = (4/5)b1, and g = g1. Then, the total number of boys and girls at the beginning is b1 + g1.
Explanation:To find the total number of boys and girls at the beginning of the program, we need to first determine the number of boys that left. Let's say the total number of boys at the beginning was b1 and the number of boys that left was b2.
Given that one-fifth of the boys left, we can write the equation: b2 = (1/5)b1.
Then, the number of boys remaining is: b = b1 - b2 = b1 - (1/5)b1 = (4/5)b1.
Similarly, the number of girls remaining is: g = g1, where g1 is the initial number of girls. Therefore, the total number of boys and girls at the beginning is: b1 + g1.
Learn more about Total number of boys and girls at the beginning here:https://brainly.com/question/6466256
#SPJ12
The total number of boys and girls at the beginning of the program is represented by 5b + g, where 'b' represents the remaining boys after one-fifth left and 'g' represents all the girls who stayed for the program.
Explanation:To answer this, we must first understand that 'b' represents the number of boys left after one-fifth of them have exited. If we let 'B' denote the total number of boys initially present, then according to the prompt, B - 1/5*B = b. Simplifying this, we get B = 5b.
Now, along with the girls, the total number of children initially present would be B + g (since all girls stayed throughout the program). Plugging in the value of 'B' we found, we get the total as 5b + g.
So, the total number of boys and girls at the beginning of the program is represented by 5b + g.
Learn more about Algebraic Problem here:https://brainly.com/question/30042644
#SPJ12
(03.05) A coal car on a train weighs 30 tons plus 1 ton per cubic yard of coal x that it carries. The total weight of a coal car is: f(x) = x + 30. How will the graph of this function change if the coal car weight is changed to 26 tons? (1 point)
The line will shift vertically up by 4 tons.
The line will shift vertically up 26 tons.
The line will shift vertically down by 4 tons.
The line will shift vertically down by 26 tons.
The line will shift vertically down by 4 tons.
Give the slope of y - 3 = 4 ( x + 8 ) and a point on the line.
Answer:
Slope of the line is 4 and the point on the line is (-8,3)
Step-by-step explanation:
The equation of the line is given by [tex]y-3=4(x+8)[/tex]
The point slope form of a line is
[tex]y-y_1=m(x-x_1)[/tex]
Here, m is the slope of the line
And the point [tex](x_1,y_1)[/tex] lies on the line.
On comparing the given equation with the point slope form of the line
[tex]m=4,x_1=-8,y_1=3[/tex]
Therefore, the slope is 4 and the point on the line is (-8,3)
The slope of the equation is 4, and a point on the line is (0,35)
The equation is given as:
[tex]y - 3 = 4(x + 8)[/tex]
Open the bracket
[tex]y - 3 = 4x + 32[/tex]
Add 3 to both sides
[tex]y = 4x + 35[/tex]
A linear equation is represented as:
y = mx + b
Where m represents the slope
So, by comparison:
The slope of the equation is 4
Set x = 0
y = 4 * 0 + 35
y = 35
Hence, a point on the line is (0,35)
Read more about linear equations at:
https://brainly.com/question/14323743
How do you solve 2 tenths + 11 hundredths
what can you conclude about the product of 7/8 and 8
Final answer:
The product of 7/8 and 8 is the multiplication of a fraction by a whole number, leading to the simplified result of 7. This is because multiplying by 8/8 (which equals 1) does not change the original numerator of the fraction.
Explanation:
When we talk about the product of 7/8 and 8, we are performing a multiplication between a fraction and a whole number. To do this, you can multiply the numerator of the fraction by the whole number and leave the denominator unchanged. Since 7/8 multiplied by 8/1 is the same as 7/8 times 8, you can simplify the equation by multiplying 7 by 8, which gives you 56, and then divide that by the denominator, which is 8. So, the product is 56/8, which simplifies to 7. This is because 8/8 is essentially 1, and multiplying by 1 doesn't change the value of the number, thus the product of 7/8 and 8 is the same as the numerator 7.
Write an expression for the calculation 5 times the number 25 and then subtract the quotient of 14 and 7
Luis purchased 24 purple plants and 8 pink plants. He wants to plant them in equal groups in his garden. What the largest number of groups he can make?
Simplify. 25√+35√−5√
Answer:
4√5
Step-by-step explanation:
i did the quiz
Answer:
4√5
Step-by-step explanation:
Which is greater 7 1/8 or 7.025
Kendall recently received a job offer which required him to move his house full of furniture across the country from Columbia, South Carolina, to Riverside, California. To manage his moving expenses, Kendall kept track of the amount of gasoline used by the moving truck he rented. The truck used 109 gallons of gas to drive 1,092 miles from Columbia to Des Moines, Iowa. On the next leg of the drive, the truck used 67 gallons of gas to drive 671 miles from Des Moines to Denver, Colorado. Finally, he used 99 gallons of gas to drive 985 miles from Denver to Riverside, California. Using x to represent the number of miles and y to represent the number of gallons, create a table of values to represent this relation.
Answer:
Step-by-step explanation:
A table of values is generally used when there are few values of the independent variable "x" and their corresponding values of the dependent variable "y".
x = Number of miles (Independent variable)
y = Number of gallons (dependent variable)
The table of values can be represented as follows:
x ------------------- y ------- Relationship (x / y)
1,092 ------------ 109 --------- 10.02
671 -------------- 67 ---------- 10.02
985 ------------- 99 ----------- 9.95
--------------------------------------------------
Total 2,748 ----------- 275 ---------- 9.99
Hope this helps!
find the error sienna used base-ten blocks to find 45÷3 .explain her error
Final answer:
To spot Sienna's error in using base-ten blocks for dividing 45 by 3, we need to verify the even distribution of tens and ones among three groups. The correct result should be 15, with each group receiving 1 ten block and 5 ones blocks.
Explanation:
To find the error made by Sienna in dividing 45 by 3 using base-ten blocks, we need to visualize the process. The number 45 consists of 4 tens (which are blocks representing the number 10) and 5 ones (single blocks representing the number 1). Since she is dividing by 3, Sienna should group the blocks into 3 equal groups to find the quotient, which should be the same number in each group when the blocks are divided evenly.
If Sienna were to correctly divide the blocks to find 45 ÷ 3, she would need to distribute the 4 tens blocks evenly among 3 groups, which would give each group one ten blocks, with one ten blocks remaining. These remaining ten blocks should then be exchanged for ten one's blocks, which, added to the existing five one's blocks, makes a total of fifteen one's blocks. These fifteen blocks can then be evenly distributed, giving each group five blocks. In the end, each group will have one ten-block and five blocks, meaning the quotient is 15.
Therefore, the error that Sienna could have made could include not exchanging a remaining tens block for ones blocks, or not distributing the ones blocks correctly after exchanging. It’s important to keep track of remainders and ensure even distribution among the groups to find the correct quotient in division with base-ten blocks.
Aubrey and Charlie are driving to a city that is 120 mi from their house. They have already traveled 20 mi, and they are driving at a constant rate of 50 mi/h. Complete the function that models the distance they drive as a function of time. Then complete a reasonable domain for this situation.
The distance function for Aubrey and Charlie's trip is d(t) = 20 + 50t, accounting for an initial 20 miles already traveled. The reasonable domain for time t in this situation is from 0 to 2 hours since they are traveling at 50 miles per hour and have 100 miles remaining.
Aubrey and Charlie have already traveled 20 miles and are continuing to travel towards a city that is 120 miles away from their start at a constant rate of 50 miles per hour. To complete the function that models the distance they drive as a function of time, we use the formula distance traveled is velocity imes time. With a start of 20 miles, the function can be written as:
d(t) = 20 + 50t
Where d(t) represents the distance traveled at time t in hours. For the domain, since they have already traveled 20 miles, the remaining distance is 100 miles. At a rate of 50 miles/hour, the maximum time needed to cover the remaining distance is 2 hours. Hence, the reasonable domain for time t is 0 ≤ t ≤ 2.
How can the properties of operation be used to solve problems involving integers and rational numbers?
To solve problems with integers and rational numbers, one should apply operations' properties such as commutativity, associativity, and distributivity, which streamline calculations and assist in combining numbers in an order that simplifies the process.
Integers and rational numbers are essential elements of algebra that allow for diverse mathematical operations. Integers are the set of whole numbers including zero, and their negative counterparts (e.g., -1, 0, 1), while rational numbers are ratios of integers (e.g., 2/1, 3/4) that can represent fractions and decimals that terminate or repeat. When solving problems, it is crucial to remember the properties of operations, which include commutativity associativity , distributivity, the additive inverse and the multiplicative inverse.
For example, when adding fractions with different denominators, you find a common denominator and use commutativity and associativity to combine these fractions. A problem involving multiplication of a negative integer and a fraction may require both the distributive property and understanding of the multiplicative inverse. Mastering these properties provides a foundation for solving algebraic expressions and equations, ensuring accuracy whether the numbers are complex, real, rational, or integers.
0.770000 in scientific notations
Mrs. Gibbs goes to the store to buy AA and 9V batteries. She needs at least 6 AA batteries. In all, she wants to buy at least 20 batteries. The store has 12 AA batteries and 15 9V batteries in stock.
The graph shows the feasible region, where x represents the number of AA batteries and y represents the number of 9V batteries.
Which ordered pairs meet all the constraints and make sense in the context of the situation?
Select each correct answer.
(7, 13)
(8,11)
(10,16)
(12,12)
Let
x------> represents the number of AA batteries
y------> represents the number of 9V batteries
we know that
The constraints are
[tex]x\geq 6[/tex]
[tex]x\leq 12[/tex]
so
[tex]6\leq x\leq 12[/tex] --------> inequality A
[tex]y\leq 15[/tex] --------> inequality B
[tex](x+y)\geq 20[/tex]
[tex](x+y)\leq 27[/tex]
so
[tex]20\leq (x+y) \leq 27[/tex]-----> inequality C
The solution of the system of inequalities is the shaded area in the attached figure
If a ordered pair meet all the constraints and make sense in the context of the situation, then the ordered pair is a solution of the system of inequalities
let's check each of the ordered pairs
case A) point [tex](7,13)[/tex]
[tex]x=7\ y=13[/tex]
Verify inequality A
[tex]6\leq 7\leq 12[/tex]--------> is true
Verify inequality B
[tex]13\leq 15[/tex] -------> is true
Verify inequality C
[tex]20\leq (7+13) \leq 27[/tex]
[tex]20\leq (20) \leq 27[/tex]------> is true
The ordered pair [tex](7,13)[/tex] meets all restrictions, therefore the ordered pair is a solution of the system of inequalities
case B) point [tex](8,11)[/tex]
[tex]x=8\ y=11[/tex]
Verify inequality A
[tex]6\leq 8\leq 12[/tex]--------> is true
Verify inequality B
[tex]11\leq 15[/tex] -------> is true
Verify inequality C
[tex]20\leq (8+11) \leq 27[/tex]
[tex]20\leq (19) \leq 27[/tex]------> is not true
The ordered pair [tex](8,11)[/tex] does not meet all the restrictions, therefore the ordered pair is not a solution of the system of inequalities.
case C) point [tex](10,16)[/tex]
[tex]x=10\ y=16[/tex]
Verify inequality A
[tex]6\leq 10\leq 12[/tex]--------> is true
Verify inequality B
[tex]16\leq 15[/tex] -------> is not true
Verify inequality C
[tex]20\leq (10+16) \leq 27[/tex]
[tex]20\leq (26) \leq 27[/tex]------> is not true
The ordered pair [tex](10,16)[/tex] does not meet all the restrictions, therefore the ordered pair is not a solution of the system of inequalities.
case D) point [tex](12,12)[/tex]
[tex]x=12\ y=12[/tex]
Verify inequality A
[tex]6\leq 12\leq 12[/tex]--------> is true
Verify inequality B
[tex]12\leq 15[/tex] -------> is true
Verify inequality C
[tex]20\leq (12+12) \leq 27[/tex]
[tex]20\leq (24) \leq 27[/tex]------> is true
The ordered pair [tex](12,12)[/tex] meets all restrictions, therefore the ordered pair is a solution of the system of inequalities
the answer is
[tex](7,13)[/tex]
[tex](12,12)[/tex]