Answer:
There will be approximately 165,689, 137,264, and 94,207 squirrels in 25, 50, and 100 years respectively.
Step-by-step explanation:
Exponential Decay Function
The exponential function is often used to model natural growing or decaying processes, where the change is proportional to the actual quantity.
An exponential decaying function is expressed as:
[tex]s(t)=s_o\cdot(1-r)^t[/tex]
Where:
s(t) is the actual value of the function at time t
so is the initial value of s at t=0
r is the decaying rate, expressed in decimal
The population of squirrels is decreasing at a rate of r=0.75% = 0.0075. The initial number of squirrels is so=200,00. The exponential model for this situation is:
[tex]s(t)=200,000\cdot(1-0.0075)^t[/tex]
[tex]s(t)=200,000\cdot(0.9925)^t[/tex]
Where s is the number of squirrels at any time t.
We are required to find the number of squirrels in:
t=25 years. Substitute in the formula:
[tex]s(25)=200,000\cdot(0.9925)^25[/tex]
Calculating:
[tex]s(25)\approx 165,689[/tex]
t=50 years. Substitute in the formula:
[tex]s(50)=200,000\cdot(0.9925)^50[/tex]
Calculating:
[tex]s(50)\approx 137,264[/tex]
t=100 years. Substitute in the formula:
[tex]s(100)=200,000\cdot(0.9925)^100[/tex]
Calculating:
[tex]s(100)\approx 94,207[/tex]
There will be approximately 165,689, 137,264, and 94,207 squirrels in 25, 50, and 100 years respectively.
Mark wants to continue using whole liters of paint and thinks he can create a mixture of green paint the is 38 liters. Evaluate Mark's thinking using mathematical reasoning.
The ratio from blue to yellow paint is 2:3
I need helpppppp ASAP
Answer: It's not possible to create 38 liters of green paint with whole liters of blue and yellow paint.
======================================================
Explanation:
The ratio of blue to yellow is 2:3. We have 2 parts blue and 3 parts yellow.
Multiply both parts by x to get 2x:3x
We have 2x parts of blue paint, and 3x parts of yellow paint.
x is some positive whole number.
In total, we have 2x+3x = 5x liters of paint. Set this equal to 38 and solve for x to get
5x = 38
x = 38/5
x = 7.6
We don't get a whole number, which contradicts how we set up x earlier. This must mean that Mark must use a fractional liters, instead of whole liters.
-------------------------
Here's another way to look at it:
Lets say he uses 2 liters of blue and 3 liters of yellow. This mixes to 2+3 = 5 liters of green.
Now let's say he uses 4 liters of blue and 6 of yellow. I multiplied both parts by 2. This mixes to 4+6 = 10 liters of green.
We continue this process to get the following
6 liters of blue + 9 liters of yellow = 15 liters of green8 liters of blue + 12 liters of yellow = 20 liters of green10 liters of blue + 15 liters of yellow = 25 liters of green12 liters of blue + 18 liters of yellow = 30 liters of green14 liters of blue + 21 liters of yellow = 35 liters of green16 liters of blue + 24 liters of yellow = 40 liters of greenAs you can see, we don't land on 38 liters of green. We can get to 35 liters or 40 liters, but not 38. Each of the amounts of green are a multiple of 5.
This is confirmation that Mark will have to use some fractional amount of liters of blue and yellow paint.
Which of the following is equivalent to 7^-2?
Answer:
C
Step-by-step explanation:
Answer:
C. [tex]\frac{1}{49}[/tex]
Step-by-step explanation:
When one puts a number to a negative exponent, such as;
[tex]a^{-b}[/tex]
One is essentially doing;
[tex]\frac{1}{a^{b}}[/tex]
Applying that knowledge;
[tex]7^{-2} \\= \frac{1}{7^{2}}\\= \frac{1}{49}[/tex]
Your middle school is having a carnival. Admission into the carnival is $8, and each game inside the carnival costs $0.50.
Part A: Which inequality represents the possible number of games, g, that can be played with $20?
A. 8g+0.50≤20
B. 8g+0.50≥20
C. 0.50g+8≤20
D. 0.50g+8≥20
8.73x10^-4 in standard form
Answer:
here you go I hope this is right
The sum of the digits of a given two digits the new numbers is 5 .if the digits are reversed, the new number is reduced by 27 . find the given number
Answer:. The numbers are 41 and 14
Step-by-step explanation: X and Y represent the digits. In the Tens place, the digit has 10× its base value. Therefore we can set up equations to model the information given:
10x+y = 10y + x +27
X + Y = 5
y =5-x rewritten to substitute for y
10x + 5-x = 10(5-x)+x +27
Distribute and then combine like terms:
9x +5 = 50 - 9x +27
Add 9x to both sides; subtract 5 from both sides.
9x +9x = 50+27-5
18x = 72 Combine like terms. Then divide both sides to solve for x.
x = 4
4+y=5 Substitute 4 for x; solve for y.
y=1
Substitute values of x and Y into the original equation and check.
40 +1 = 10 +4 + 27
41 = 14+ 27
True! 41=41
The numbers are 41 and 14.
function or not a function? justify your answer
domain:
range:
(please help!!! for both please!!!)
Answer:
function
Step-by-step explanation:
I got that answer correct on ed2020
Find the product.
-0.3(4.1) =
Answer:
-1.23
Step-by-step explanation:
-0.3 x 4.1 = -1.23.
A negative number times a positive number equals a negative number.
Fin in the table to convert the units of measure from milliliters to liters or liters to milliliters.
Milliliters. Liters
1
9
1,000
350
1 millilitre = 0.001 litre
1 litre = 1000 millilitres
9 millilitres = 0.009
9 litres = 9000 millilitres
1,000 millilitres = 1 litre
1,000 litres = 1e+6
350 millilitres = 0.35 litres
350 litres = 350000 millilitres
A line passes through the points (8, 8) and (4, 0). What is its equation in slope-intercept form?
Tim’s age is nine more than his sister, Jill. Twice his age added to twice Jill’s age is 330.
Answer:
jill age is 78 and tim's age is 87
Step-by-step explanation:
let jill age be x then, tim's age is 9+x
by the question,
2(9+x) + 2x = 330
or,18 + 2x + 2x = 330
or,4x = 330-18
or, x = 312÷4
x = 78
9+x= 9+78=87
I PROMISE TO MARK BRAINLIESTTTTT
Answer:
D!
Step-by-step explanation:
Can I get some help with this is the Last question
Answer:
x = 11
Step-by-step explanation:
Here, we want to get the value of x
Let’s start by looking at the point U
Now, we can see angles on a straight line at that point
Mathematically, angles on a straight line are supplementary
What this mean is that they add up to 180
Now, the value of the angle that falls into the triangle on that straight line will be;
180-(11x + 12)
Now, we have all the angles of the triangle
Mathematically, the sum of all is 180 as the a sum of the angles of a triangle is 180
5x + 10 + 58 + 180-(11x+2 )= 180
5x + 10 + 58 -11x-2 = 0
-6x+ 66 = 0
6x = 66
x = 66/6
x = 11
Here are the marks of a student in four exams. 65 80 76 69 The student takes a fifth exam. His mean mark for the five exams is 70 Work out his mark in the fifth exam
Answer:
mark of the fifth exam = 60
Step-by-step explanation:
Mean = sum of all marks / number of exam
Mean = 70
Number of exam = 5
Let x =
Mean = sum of all marks / number of exam
70 = (65 + 80 + 76 + 69 + x) / 5
Cross product
70 × 5 = (290 + x)
350 = 290 + x
350 - 290 = x
x = 60
mark of the fifth exam = 60
A piece of wood is 0.9 metres long.
It is cut into three unequal pieces.
The first piece is 0.2 metres longer than the second piece.
The third piece is 23 hundredths of a metre shorter than the second piece.
How long is each piece of wood?
Answer:
The length of the first piece is 0.51 m
The length of the second piece is 0.31 m
The length of the third piece is 0.28 m
Step-by-step explanation:
The question is a simultaneous equation with word problem
The total length of the wood = 0.9 m
The number of pieces the wood is cut into = 3
The length of the first piece = 0.2 m + The length of the second piece
The length of the third piece = The length of the second piece - 0.23 m
Let "y" represent the length of the second piece, let "x" represent the length of the first piece, and let "z" represent the length of the third piece, we have;
x = 0.2 + y...(1)
z = y - 0.23...(2)
x + y + z = 0.9...(3)
Therefore, by substitution, we have;
0.2 + y + y + y - 0.23 = 0.9
3·y - 0.03 = 0.9
3·y = 0.9 + 0.03 = 0.93
y = 0.93/3 = 0.31
y = 0.31
The length of the second piece = y = 0.31 m
From equation (1), we have;
x = 0.2 + y = 0.2 + 0.31 = 0.51
x = 0.51
The length of the first piece = x = 0.51 m
From equation (2), we have;
z = y - 0.23
z = 0.51 - 0.23 = 0.28
z = 0.28
The length of the third piece = z = 0.28 m.
ILL MARK U BRAINLIEST
At Kroger, milk costs $3.27 per gallon. Which equation best represents y, the total cost of x gallons of milk?
a. x = 3.27 + y
b. y = 3.27 + x
c. y = 3.27x
d. x = 3.27y
Answer:
C y=3.27x
Step-by-step explanation:
total cost = £3.27 times by the gallons
Step-by-step explanation:
B its B I had the same work and its B
can you please help me and explain how to do both of these problems, I don't understand
round to the hundredth 3.5262
Math. Help I really need this giving brainliest to the person with the correct answer, please explain your answer........
Answer:
65-n
Step-by-step explanation:
"less than" means you will subtract the second number by the first, therefore 65 less than a number is 65-n.
Solve using the quadratic formula: 2x^2 + 5x + 1
Answer:
x = -0.22 or x = -2.28
Step-by-step explanation:
2x^2 + 5x + 1 = 0
You use the quadratic formula: -b ±√5² - 4 x 2 x 1 ÷ (2 x 2)
-5 +√17 ÷ 4 = -0.22
-5 - √17 ÷ 4 = -2.28
Help ASAP please help
Answer:
Step-by-step explanation:
b/c this is an isosceles triangle we know that either leg is the same length.. so we can use many trig functions :)
SOH CAH TOA to remember how trig functions fit on the triangle...
we know the hypotenuse and the angle and we want to find the adjacent leg ( which for this triangle is also the opposite leg )
use Cos = Adj / Hyp
Hyp*Cos(45) = adj
16* [tex]\sqrt{2}/2[/tex] = adj
8*[tex]\sqrt{2}[/tex] = adj
each leg is the same [tex]8\sqrt{2}[/tex]
Pedro ordered a 6 footlong sub sandwich and plans to share it with his friends. If each portion is divided evenly in 3/5 of a foot, how many friends will Pedro share his sandwich with?
Answer:
10
Step-by-step explanation:
You would divide 6 feet by 3/5 of a foot would would be .6 so 6/.6 would be 10Aisha purchases a hot chocolate each for $5.87. How much would she paid after 3.5 weeks
PLS PLS HELP ILL GIVE U ALL MY POINTS PLUS BRAINLIEST!! i need this to be right !! asap
Answer:
D
Step-by-step explanation: So, multiplying two rationals is the same as multiplying two such fractions, which will result in another fraction of this same form since integers are closed under multiplication. Thus, multiplying two rational numbers produces another rational number.
Answer:
The product of a rational number and an irrational number is irrational.
Step-by-step explanation:
The product of a rational number and an irrational number is irrational. For example, let p= 1 be a rational number and q= 3.567be an irrational number if multiplied together the result would be 3.567, which is an irrational number.
Hope this helped!
I need some help I rlly appreciate it!!!!
In quadrilateral PQRS, the exterior angle at Q measures 155 and PS = QR. What measure of ∠PSR would confirm that PQRS is a parallelogram?
Answer:
The measure confirming that PQRS would be 25
Step-by-step explanation:
It's easier if you draw it down.
1. We need to make this shape a parallelogram and the way we will do that is by making angle Q and angle S the same, because in parallelograms those opposite angles are required to be the same.
\
155 \
P \ -------------------------\ Q
\ 25 \
\ \ so that's your shape
S \______________\ R
2.We were given that the exterior angle of Q measures 155, and since exterior and interior angles combined make 180, then we can assume that the interior angle of Q is 25.
3. As mentioned before, in a parallelogram, opposite angles are the same and therefore PSR (which is just asking for the middle letter, S) is equal to 25 because Q is also 25.
Tell whether the triangle is right or not
Answer: Solved below...
Answer: Yes, that is a right triangle.
Step-by-step explanation:
To tell whether this is a right triangle or not you use a^2 + b^2= c^2
c is the hypotenuse the hypotenuse is the longest side of a right triangle, opposite the right angle. A and B can be either of the triangles sides.
To get this answer: 80^2+39^2 = 89^2
6400 + 1521 = 7921
7921=7921
Since they are the same this IS a right triangle. Here is a little help for if the a question asks if you have a right acute or obtuse. To tell if you have an acute triangle the sign will be a greater than sign for ex) 180 > 169. If you have a obtuse triangle the sign would be a less than sign for ex) 120 < 200.
Here is a problem like that if you do not understand:
6^2 +12^2 = 13^2 ( remember c is the hypotenuse)
36+144= 169
180 > 169
Have a nice day!
A tree casts a shadow that is 7 feet long. A person nearby casts a shadow that is 3.5 feet long. The person is
5 feet tall. What is the height of the tree?
The three angles of a triangle measure x+37, 90, and x+67. Find the measurement of the smallest angle in degrees.
Please help!!!
Answer:
The first angle is the smallest
Step-by-step explanation:
Step one:
given data
Angle 1= x+37
Angle 2= 90
angle 3= x+67
We know that the sum of angle in a triangle is 180
so
x+3+90+x+67= 180
collect like terms
2x+160= 180
2x=180-160
2x= 20
divide both sides by 2
x= 10
Step two:
so
Angle 1= 10+37= 47 °
Angle 2= 90= 90
angle 3= 10+67= 77 °
solve the system
y=x+5
y=-3x+1
The solution is (__,__)
Can someone plz help!!!! :(
Answer:
60 degress
Step-by-step explanation:
How I got it:
1. Find out the angel of each side. 360 divded by 6 = 60
2. Get the answer of 60
Advice:
-Make an polygon using paper and rotate it. (Use protractor and ruler if your gonna do it)