Answer:
The population in 11 years will be of 53,199.
Step-by-step explanation:
Equation for a population that doubles every n years.
The population of an specie, after t years, considering that is doubles after n years, is given by an equation in the following format:
[tex]P(t) = P(0)(2)^{\frac{t}{n}}[/tex]
In which P(0) is the initial population.
The population doubles every 15 years, and the current population is 32,000
This means that [tex]n = 15, P(0) = 32000[/tex]. So
[tex]P(t) = P(0)(2)^{\frac{t}{n}}[/tex]
[tex]P(t) = 32000(2)^{\frac{t}{15}}[/tex]
What will be the population in 11 years?
This is P(11). So
[tex]P(t) = 32000(2)^{\frac{t}{15}}[/tex]
[tex]P(11) = 32000(2)^{\frac{11}{15}}[/tex]
[tex]P(11) = 53199[/tex]
The population in 11 years will be of 53,199.
Alice and Bob play a game by taking turns removing 1 or 2 stones from a pile that initially has n stones. The person that removes the last stone wins the game. Alice plays always first.
(a) Prove by induction that if n is a multiple of 3 then Bob has a wining strategy.
(b) Prove that if n is not a multiple of 3 then Alice has a wining strategy.
Answer:
Step-by-step explanation:
(a) We will prove by induction that if n is a multiple of 3 then Bob has a winning strategy.
Let n=3
It is given that Alice always plays first.
Then, for the first move, Alice has a choice of removing 1 or 2 stones.
Case 1:
Alice removes 1 stone. Then it is now Bob's turn. There are 2 stones left. Bob has the choice of removing 1 or 2 stones. Then Bob's winning strategy should be to remove 2 stones. Then Bob removes the last stone and wins.
Case 2:
Alice removes 2 stones. Then it is Bob's turn. There is exactly 1 stone left, which Bob removes in his turn. Since he removes the last stone, he wins.
Thus, in either case, for n=3, Bob has a winning strategy. ____ (A)
Now, let us assume that Bob has a winning strategy for n=3p.
We will now check if Bob has a winning strategy for n=3p+3
It is given that Alice plays first.
Case 1:
Alice starts the game by removing 1 stone. Then, Bob has a choice of removing 1 or 2 stones. If he chooses to remove 2 stones, then the number of stones left is 3p+3-3=3p and it is now Alice's turn to play. This is exactly the game when n=3p and we have already assumed that Bob has a winning strategy for n=3p. Thus, in this case Bob has a winning strategy.
Case 2:
Alice starts the game by removing 2 stones. Then, Bob has a choice of removing 1 or 2 stones. If he chooses to remove 1 stone, then the number of stones left is 3p+3-3=3p and it is now Alice's turn to play. This is again exactly the game when n=3p and we have already assumed that Bob has a winning strategy for n=3p. Thus, in this case also, Bob has a winning strategy.
Thus, in either case Bob has a winning strategy for n=3p+3 if he has a winning strategy for n=3p. _______ (B)
Thus, from (A) & (B), using induction, we can say that Bob has a winning strategy if n is a multiple of 3.
(b) We will now prove that if n is not a multiple of 3, then Alice has a winning strategy.
If n is not a multiple of 3, then n can have either of the forms of 3m+1 or 3m+2, m ∈ W.
We will prove the given fact for both the forms simultaneously
Let m=0, i.e., n=1 or n=2
Since Alice starts first, she removes 1 stone, if n=1 or 2 stones if n=2 and thus wins. Thus Alice has a winning strategy if m=0. ______ (A)
Let us assume that Alice has a winning strategy for m=k, i.e., for n=3k+1 & n=3k+2
Now, we will check if Alice has a winning strategy for m=k+1, i.e., for n=3(k+1)+1=3k+4 or n=3(k+1)+2=3k+5
Let n=3k+4
Since Alice plays first, she has a choice to remove 1 or 2 stones.
Note that, if Alice removes 2 stones and in turn Bob removes 2 stones, then the number of stones becomes a multiple of 3 such that it is Alice's turn to play. In that case, Bob will have a winning strategy as shown in the previous part.
Then, Alice should remove 1 stone. Then, it is now Bob's turn and he has a choice of removing 1 or 2 stones.
Case 1:
Bob removes 1 stone. Then there are 3k+4-1-1=3k+2 stones remaining and it is Alice's turn. This is identical to the game where n=3k+2. We have already assumed that Alice has a winning strategy in this case.
Case 2:
Bob removes 2 stones. Then there are 3k+4-1-2=3k+1 stones remaining and it is Alice's turn. This is identical to the game where n=3k+1. We have already assumed that Alice has a winning strategy in this case.
Thus, in either case, Alice has a winning strategy.
Let n=3k+5
Since Alice plays first, she has a choice to remove 1 or 2 stones.
Note that, if Alice removes 1 stone and in turn Bob removes 1 stone, then the number of stones becomes a multiple of 3 such that it is Alice's turn to play. In that case, Bob will have a winning strategy as shown in the previous part.
Then, Alice should remove 2 stones. Then, it is now Bob's turn and he has a choice of removing 1 or 2 stones.
Case 1:
Bob removes 1 stone. Then there are 3k+5-2-1=3k+2 stones remaining and it is Alice's turn. This is identical to the game where n=3k+2. We have already assumed that Alice has a winning strategy in this case.
Case 2:
Bob removes 2 stones. Then there are 3k+5-2-2=3k+1 stones remaining and it is Alice's turn. This is identical to the game where n=3k+1. We have already assumed that Alice has a winning strategy in this case.
Thus, in either case, Alice has a winning strategy.
Then, we can say that Alice has a winning strategy for m=k+1 if she has a winning strategy for m=k. _____ (B)
Then, by induction, from (A) & (B), we can say that if n is not a multiple of 3, then Alice has a winning strategy.
Identify each triangle based on angles. (Acute, Obtuse or Right) PLEASE HELP
Answer:
4.right
5. obtuse
6. acute
7. obtuse
8.acute
9. right
10. right
11. acute
12. obtuse
hope this helps
have a good day :)
Step-by-step explanation:
Using the distributive property, what number would go in the blank in order for the given statement to be correct? 4(x – _) = 4x – 16
Answer:
4(x - 4) = 4x - 16
Step-by-step explanation:
4(x - A) = 4x - 16
4x - 4A = 4x - 16
Equating Constant terms (terms without x): -4A = -16
A = 4
Therefore , 4(x - 4) = 4x - 16
The answer is 4.
In order to find the answer, divide 4 from the each number on the right side. You pull the 4 out from 4x, and 4 from 16 to arrive at 4(x - 4).
Let
tenth of a degree.
tan W = 3.52
Answer:
(d) above [tex]74.1^o[/tex]
Step-by-step explanation:
Given
[tex]\tan w = 3.52[/tex]
Required
Determine w, using a calculator
We have:
[tex]\tan w = 3.52[/tex]
Take arctan of both sides
[tex]w = \tan^{-1}(3.52)[/tex]
Using a calculator, we have:
[tex]w \approx 74.1^o[/tex]
From the given options, (d) is true
PLS HELP!! need the answer asap
I need help asap
Do the following sides form a triangle?
25 cm
17 cm
42 cm
Answer:
no
explanation:
Side lengths do not adhere to the triangle inequality theorem. Which states that the sum of the side lengths of any 2 sides of a triangle must exceed the length of the third side
need help with PART A!!
Answer:
complementary angles
Step-by-step explanation:
Complementary angles add to 90 degrees
Supplementary angles add to 180 degrees
A right angle is 90 degrees so they are complementary angles
Find the area and perimeter of the compound figure
A wall has an area of 40 square feet. Its
height is 8 feet. Which equation could you
use to find its width?
Which shape has the same area as this one?
PLease i need help ;-;
Answer:
purple and red has same area
Step-by-step explanation:
Area of purple = 4 x 4 = 16 square cm
Area of red = 2 x 8 = 16 square cm
Area of yellow = 3 x 5 = 15 square cm
There are 8 blue candies, 5 pink candies, 1 white candy, and 6 green candies in a candy jar. You reach in, without looking, and take one. What is the probability that you will choose a green candy? Report your answer as a percent.
Answer:
30%
Step-by-step explanation:
Find the total number of candies in the jar.
8 + 5 + 1 + 6 = 20
The probability of choosing a green candy is 6/20 = 3/10 = .3 = 30%
Find the vertex of the graph of the quadratic function y=-2xto the 2-8x-16 and determine whether it is absolute maximum or absolute minimum
Answer: It's the absolute maximum, the vertex is (-2, -8).
Step-by-step explanation:
Just go to desmos graphing calculator and input the equation y = -2x^2-8x-16. You'll find the vertex and other things too.
Find the exact value of x.
Answer:
7[tex]\sqrt{2}[/tex] or 9.89
Step-by-step explanation:
sin45= [tex]\frac{7}{x}[/tex]
x=[tex]\frac{7}{sin 45}[/tex]
x= 7[tex]\sqrt{2}[/tex] or 9.89
plz plz plz plz help me plz it is due in 1 hour and no links plz
Answer:
Solution given:
perpendicular [P]=15m
base[B]=8m
hypotenuse [H]=17m
rate :4 plants per square metre
no of plants=?
we have
Area of triangular garden: ½(P*B)=½(15*8)=60m²
Now
Total no of plants =rate ×Area =4×60=240
Michael needs 240 plants in the garden
at what rate percent of interest per annum will #700 gain an interest of #84 in 3 years
Answer:
4% per annum
Step-by-step explanation:
Recall :
Simple interest = principal * rate * time
Given that :
Time = 3 ; simple interest = 84 ; principal = 700
84 = 700 * rate * 3
84 = 2100 * rate
Rate = 84 /2100
= 0.04
= 0.04 * 100% = 4% per annum
Mark of the Expressions below that are equivalent to 320, 000.
Answer:
32x10^4 and 3.2x10^5
Step-by-step explanation:
Mind marking me brainliest? :)
Answer:
first and the 3rd one
Step-by-step explanation:
In a simple random sample of 352 students at a college, 92 reported that they have at least $1000 of credit card debt. Which interval is the 99% confidence interval for the percent of all the students at that college who have at least $1000 in credit card debt
Answer:
The 99% confidence interval for the percent of all the students at that college who have at least $1000 in credit card debt is (20.11%, 32.17%).
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].
In a simple random sample of 352 students at a college, 92 reported that they have at least $1000 of credit card debt.
This means that [tex]n = 352, \pi = \frac{92}{352} = 0.2614[/tex]
99% confidence level
So [tex]\alpha = 0.01[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.01}{2} = 0.995[/tex], so [tex]Z = 2.575[/tex].
The lower limit of this interval is:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.2614 - 2.575\sqrt{\frac{0.2614*0.7386}{352}} = 0.2011[/tex]
The upper limit of this interval is:
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.2614 + 2.575\sqrt{\frac{0.2614*0.7386}{352}} = 0.3217[/tex]
As percent:
0.2011*100% = 20.11%
0.3217*100% = 32.17%.
The 99% confidence interval for the percent of all the students at that college who have at least $1000 in credit card debt is (20.11%, 32.17%).
Jade says that 8÷ 1/2 means the same thing as 1/2 of 8, so the answer is 4 do you agree
Answer:
no
Step-by-step explanation:
8÷ 1/2
Copy dot flip
8 * 2/1 = 16
Divide 8 things in half you get 16
1/2 of 8 = 1/2 * 8 = 4
Half of 8 things is 4
They are not the same
Answer:
8 ÷ 1/2 = 16
I disagree.
Step-by-step explanation:
8 ÷ 1/2
8 × 2/1
8 × 2
16
please help I'll give brilliantist:)
An expression is shown. Which one of the expressions below is equivalent?
Answer:
C
Step-by-step explanation:
PLEASE HELP WITH ALL OF THIS ASAP
Answer:
I cant see the question, sorry bro.
Todd Lyle worked Monday through Friday from 8:00 A.M. to 5:00 P,M. with an hour off for lunch. He is paid $10,50 an hour. Find his earnings for the week.
Answer:
$315
Step-by-step explanation:
He earns $63 everyday, and then you just have to multiply that by 5 since he works 5 days in a week.
What value of m will m+9, 2m-1, and 2m+7 are the consecutive terms of an
arithmetic progression?
9514 1404 393
Answer:
m = 18
Step-by-step explanation:
In an arithmetic progression, the middle term of three is half the sum of the terms on either side.
a1 +a3 = 2(a2)
(m +9) +(2m +7) = 2(2m -1)
3m +16 = 4m -2 . . . . . . collect terms
18 = m . . . . . . . . . . . . . . add 2-3m
Mr. Russo exchanged 200 euros (European money) for 270 dollars. How many dollars would
he get for 300 euros?
Answer: 405 dollars
Step-by-step explanation:
200 * x = 270
x = 270 * 300/200. x =405 dollars
work out the area of the shaded shape
Answer:
theres no photo :))) btw God bless you
Which function is a translation of the parent absolute value function?
A: f(x) = 2/1
B. f(x) = |x+61
C. f(x) = x1
D. f(x) = -4/41
Answer:
B. f(x) = | x + 61 |
Step-by-step explanation:
An absolute value function is known by single vertical parenthesis demarcating the equation on both sides.
The only option with this indication is option B.
B. f(x) = | x + 61 |
This equation can be solved in two ways;
first; f(x) = - (x + 61)
second; f(x) = x + 61
Jessica's teacher asked her to divide 5/8 of the box of crayons
among 10 classmates. How much of a box of crayons did
each one receive?
Answer:
Each classmate received 1/16
Step-by-step explanation:
5/8= 0.625
0.625 ÷ 10 = 0.0625
= 1/16
What is the equation in slope-intercept form of the
line that passes through the points (-4,2) and
(12, 6)?
Naeem bought a dirtbike. The original price
was $1,800, but he got a discount of 30%. What
was the discounted price of the dirtbike?
Answer:
$1,260
Step-by-step explanation:
30% off
pay 70%
70% = 0.7
1,800 * 0.7 = 1,260
$1,260
Aurora wants to make a donation to a charity at the end of the year she starts by saving a small amount of money each week as shown in the graph
Answer:
The relationship between weeks and the total amount is:
[tex]y=10x[/tex]
Step-by-step explanation:
We have here a linear relationship between weeks and the total amount. The equation of a line is:
[tex]y=mx+b[/tex]
Where:
m is the slope b is the y-interceptWe need two points to find the slope.
[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
Let's use any pair points from the plot.
[tex]m=\frac{60-40}{6-4}[/tex]
[tex]m=10[/tex]
And we also see that the y-intercept is 0, therefore the equation will be:
[tex]y=10x[/tex]
I hope it helps you!
Answer:
y=10x and Over 4 weeks, Aurora saves $40
Step-by-step explanation: