Answer:
The model is [tex]P(t) = 2000(1.075)^{t}[/tex].
There will be 4122 fish in 10 years.
Step-by-step explanation:
Exponentially increasing population:
An exponentially increasing population can be represented by the following model:
[tex]P(t) = P(0)(1+r)^t[/tex]
In which P(t) is the population after t years, P(0) is the initial population, and r is the growth rate, as a decimal.
A population of 2000 fish increases at an annual rate of 7.5%.
This means that [tex]P(0) = 2000, r = 0.075[/tex]
So
[tex]P(t) = P(0)(1+r)^t[/tex]
[tex]P(t) = 2000(1+0.075)^t[/tex]
[tex]P(t) = 2000(1.075)^{t}[/tex]
This is the model.
How many fish will there be in 10 years?
This is P(10).
[tex]P(t) = 2000(1.075)^{t}[/tex]
[tex]P(10) = 2000(1.075)^{10} = 4122[/tex]
There will be 4122 fish in 10 years.
Lunches can be made consisting of exactly one entrée, one drink, and one snack. If all lunch options are equally likely, what is the probability of randomly choosing a lunch that
does not contain the veggie wrap
has milk or water, and
has fruit as the snack.
Write your answer as a percentage, to the nearest percent.
Entrée Chicken Cutlet Veggies Wrap Lasagna
Drink Milk Water Iced Tea
Snack Fruit Chips Jello
%
Answer:
4/27=14.8%
Step-by-step explanation:
In order to solve this, we have to see first each option possible, there are 2/3 of possibilities that a random Entrée ends up being Chicken Cutlet or Lasagna, then you have again 2/3 chances to get milk or water, and as you only want fruit the chances are 1/3 that you get that.
In order to calculate if this could happen at random we have to multiply all of the odds:
[tex]Probability: \frac{2}{3} *\frac{2}{3} *\frac{1}{3} \\Probability: \frac{2*2*1}{3*3*3} \\Probability: \frac{4}{27}[/tex]
So we know that for every 27 times you pick a lunch at random, 4 times it will not have the Veggie Wrap, contain milk or water, and will have fruit as the snack.
There are 2/3 of possibilities that a random Entrée ends up being Chicken Cutlet or Lasagna, then you have again 2/3 chances to get milk or water, and as you only want fruit the chances are 1/3 that you get that.
We need to now multiply the odds:
2/3x2/3x1/3
2x2x1/3x3x3
4/27
So we know that for every 27 times you pick a lunch at random, 4 times it will not have the Veggie Wrap, contain milk or water, and will have fruit as the snack.
So now we know it is, %15 rounded but 14.8% not rounded.
The people who live in chicago form a subset of those who rent apartments in chicago
A bag contains tiles number 1-10. What is the probability of first selecting a PRIME number, replacing it, then selecting a number less than or equal to 3?
Answer:
0.12 = 12% probability of first selecting a PRIME number, replacing it, then selecting a number less than or equal to 3
Step-by-step explanation:
A probability is the number of desired outcomes divided by the number of total outcomes.
Probability of independent events:
Suppose we have two events, A and B, that are independent. The probability of both happening is given by:
[tex]P(A \cap B) = P(A) \times P(B)[/tex]
In this question:
Event A: Selecting a prime number.
Event B: Selecting a number less than or equal to 3
Probability of selecting a prime number:
Between 1 and 10, we have 4 prime numbers(2,3, 5 and 7), out of 10. So
[tex]P(A) = \frac{4}{10}[/tex]
Probability of selecting a number less than or equal to 3:
Three numbers(1,2,3) out of 10. So
[tex]P(B) = \frac{3}{10}[/tex]
Probability of both:
[tex]P(A \cap B) = P(A) \times P(B) = \frac{4}{10} \times \frac{3}{10} = \frac{12}{100} = 0.12[/tex]
0.12 = 12% probability of first selecting a PRIME number, replacing it, then selecting a number less than or equal to 3
Please help me with this please!!
Answer:
D
Step-by-step explanation:
Explain 5 different ways you use Math in your everyday life.
Answer:
Buying Groceries, paying for a house, maybe in your job, doing schoolwork of course, and counting money.
Step-by-step explanation:
Answer:
1. you use it to calculate time (managing your day)
2. you use it while driving (use in angles and degrees)
3. you use it while drawing (again, use in angles and degrees)
4. you use it while cooking
5. you use it while banking (financial help)
Step-by-step explanation:
hope this helps:) please mark brainliest
On weekday mornings, it takes Leo 12 minutes to bike 2 miles to his school. This Saturday, Leo will bike to the park to meet his friends. The park is 5 miles away from Leo's house.
Answer:
30 minutes to the park
Step-by-step explanation:
12/2 = 6 min per mile
6 x 5 = 30 mins for 5 miles
Anna has fabric that is 1/4 yard long. She needs to cut the fabric into pieces that are 1/8 yard long. How many 1/8 yard long pieces will she have
Answer:
2
Step-by-step explanation:
1/4= .25
1/8= .125
so 1/4÷ 1/8=2
I need help with 1 through 10
Answer:
1) yes
2) no
3) no
4) no
5) yes
6) yes
7) yes
8) yes
9) circle equation - B
10) circle equation - D
11) 12 people in each team
sorry im not able to answer for 12 , 13 and 14 i have urgent work im so sorry
Express (81^1/4)^3
in simplest radical form.
Which expression is equivalent to-6(-2/3+2x)
A.-4-12x
B.- 4+2x
C. 4-12x
D. 4 + 12x
Answer:
4-12x
Step-by-step explanation:
-6(-2/3 + 2x)
Expand the bracket
12/3 - 12x
4 - 12x
Answer:
The Answer is C
Quentin can read 18 pages of a book in 2 hours. How many pages can he read in 10 hours? PLEASE HELP ASAP FOR 17 POINTS!
Answer:
90 pages in 10 hours :)
Answer:
90 pages
Step-by-step explanation:
First, you need to find the unit rate of how many pages he can read.
So, you divide 18 pages by 2 hours = 9 pages per hour.
Then, you multiply 9*10 hours to find out how many pages he will read in 10 hours.
You get 90.
There are 10 socks in a bag. 5 of those socks are blue.
Answer:
so 1/2 of those socks aren't blue?
please help i have more questions btw
Answer:
B [tex]1/4^2[/tex] and A [tex]4^1/4^3[/tex]
Step-by-step explanation:
Evaluate the following expression
Answer:
1/64 = 0.015625
Step-by-step explanation:
(1/4)^3
Calculate 1/4 to the power of 3 and get 1/64
1/64
the area of a certain desert is nine times the area of another desert. if the sum of their areas is 30,000,000 sq miles. find the area of each.
Here is my house number on Brookview Way. I hope to see you on
Valentine's Day!
CAN SOMEONE HELP ME
Answer:
54318
Step-by-step explanation:
my teacher told me the numbers are 54,3 and 18
Answer:
dont tell people where you live
Step-by-step explanation:
Find the value of
25 - 4g when g = -3
Answer:
37
Step-by-step explanation:
25-4g
25-4(-3)=37
Answer:
the answer is 13
Step-by-step explanation:
Plug g in
24-4×-3
PEMDAS
4×-3=-12
25-12=13
Solve 4 + 1/5r = -1. Single choice.
answer choices:
r=25
r=-25
r=-15
Answer:
-15
Step-by-step explanation:
imma pro
Answer: r = - 25
Step-by-step explanation:
4
Which equation will solve the following word problem? Sue's class has 50 students. 20% of the students are in art class. How many students are NOT in art class?
Will give brainliest for correct answer
a)50/(50 * 0.20) = x
b)50 + (50 * 0.20) = x
c)50 - (50/0.20) = x
d)50 - (50 * 0.20) = x
Answer:
OK thanks
Step-by-step explanation:
The water is shallow but I have a short tour in your head with a bit of
Answer: Letter D
Step-by-step explanation:
is 15.09 less than 12.63
Answer: No
15.09 is greater than 12.63
Question 1 options:
3
8
12
2.5
Answer:
2.5
Step-by-step explanation:
(I'm assuming you're doing this the same way I learned it, if not I'm sorry if it doesn't make sense)
[tex]\frac{2}{x}[/tex]=[tex]\frac{12}{15}[/tex]
Cross multiply
12x=30
Divide
x=2.5
This is just one way to do the problem. An easier way is to simplify the fractions.
[tex]\frac{2}{x}[/tex]=[tex]\frac{4}{5}[/tex]
You can either cross multiply or figure out that 2 is half of four and simply divide 5 by 2 which will also result in 2.5
Answer the question quickly please 3y=24
Answer:
y = 8
Step-by-step explanation:
3y = 24
3y ÷ 3 = 24 ÷ 3
y = 8
Insta: 25k_kemTwo forces with magnitudes 300 pounds and 450 pounds, with an angle of 60° between them, act upon an object. What is the approximate magnitude of the resultant force?
The resultant force in the example presented is approximately 774 pounds.
What is magnitude?The magnitude or size of a mathematical item defines whether it is larger or smaller than other objects of the same kind in mathematics.
Formally speaking, the size of an object is the visible outcome of an ordering—of the class of objects to which it belongs.
Consider the following scenario: the force is 10 N in the east.
The direction is indicated by "towards the east," while the force is indicated by "10."
Magnitude can be thought of as simply the "value" or "amount" of any physical quantity.
So, an object is under the influence of two forces with respective magnitudes of 300 pounds and 450 pounds and an angle of 60 degrees between them.
F₁=300 pounds, F₂=450 pounds and θ=60°
Fr=√300²+450²+2×300×450×cos60°
= √90000+502500+13500×0.5
= √90000+502500+6750
= √599250
= 774 pounds
Therefore, the resultant force in the example presented is approximately 774 pounds.
Know more about magnitude here:
https://brainly.com/question/24468862
#SPJ1
Answer: C. 653.91 pounds.
Step-by-step explanation:
APPLICATION
3. Use the first principle of derivatives to determine the equation of tangent to the
curve y = 1/radical7x at
x = 5
Answer:
[tex]\displaystyle y - \frac{\sqrt{35}}{35} = \frac{-\sqrt{35}}{350}(x - 5)[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
BracketsParenthesisExponentsMultiplicationDivisionAdditionSubtractionLeft to RightAlgebra I
Coordinates (x, y)
Point-Slope Form: y - y₁ = m(x - x₁)
x₁ - x coordinatey₁ - y coordinatem - slopeAlgebra II
Exponential Rule [Rewrite]: [tex]\displaystyle b^{-m} = \frac{1}{b^m}[/tex]Calculus
Derivatives
The definition of a derivative is the slope of the tangent line.Derivative Notation
Basic Power Rule:
f(x) = cxⁿf’(x) = c·nxⁿ⁻¹Chain Rule: [tex]\displaystyle \frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)[/tex]
Step-by-step explanation:
Step 1: Define
[tex]\displaystyle y = \frac{1}{\sqrt{7x}} \\x = 5[/tex]
Step 2: Differentiate
[Function] Rewrite: [tex]\displaystyle y = \frac{1}{(7x)^\frac{1}{2}}[/tex][Function] Rewrite [Exponential Rule - Rewrite]: [tex]\displaystyle y = (7x)^{-\frac{1}{2}}[/tex][Derivative] Chain Rule [Function]: [tex]\displaystyle y' = \frac{-1}{2}(7x)^{-\frac{1}{2} - 1} \cdot \frac{d}{dx}[7x][/tex][Derivative] Simplify: [tex]\displaystyle y' = \frac{-1}{2}(7x)^{-\frac{3}{2}} \cdot \frac{d}{dx}[7x][/tex][Derivative] Basic Power Rule: [tex]\displaystyle y' = \frac{-1}{2}(7x)^{-\frac{3}{2}} \cdot 1 \cdot 7x^{1 - 1}[/tex][Derivative] Simplify: [tex]\displaystyle y' = \frac{-7}{2}(7x)^{-\frac{3}{2}}[/tex][Derivative] Rewrite [Exponential Rule - Rewrite]: [tex]\displaystyle y' = \frac{-7}{2(7x)^{\frac{3}{2}}}[/tex]Step 3: Find Slope of Tangent Line
Substitute in x [Derivative]: [tex]\displaystyle y'(5) = \frac{-7}{2[7(5)]^{\frac{3}{2}}}[/tex][Tangent Slope] [Brackets] Multiply: [tex]\displaystyle y'(5) = \frac{-7}{2[35]^{\frac{3}{2}}}[/tex][Tangent Slope] Evaluate exponents: [tex]\displaystyle y'(5) = \frac{-7}{2(35\sqrt{35})}[/tex][Tangent Slope] Multiply: [tex]\displaystyle y'(5) = \frac{-7}{70\sqrt{35}}[/tex][Tangent Slope] Simplify: [tex]\displaystyle y'(5) = \frac{-1}{10\sqrt{35}}[/tex][Tangent Slope] Rationalize: [tex]\displaystyle y'(5) = \frac{-\sqrt{35}}{350}[/tex]Step 4: Find Tangent Line Equation
Point (x, y)
Substitute in x [Function]: [tex]\displaystyle y(5) = \frac{1}{\sqrt{7(5)}}[/tex][Function] [√Radical] Multiply: [tex]\displaystyle y(5) = \frac{1}{\sqrt{35}}[/tex][Function] Rationalize: [tex]\displaystyle y(5) = \frac{\sqrt{35}}{35}[/tex]Define point: [tex]\displaystyle (5, \frac{\sqrt{35}}{35})[/tex]Equation
Substitute in variables [Point-Slope Form]: [tex]\displaystyle y - \frac{\sqrt{35}}{35} = \frac{-\sqrt{35}}{350}(x - 5)[/tex]Topic: AP Calculus AB/BC
Unit: Derivatives
Book: College Calculus 10e
How many kilometers are in 3 centimeters?
Answer:
0.00003km
....................
kilo means 1000
and centi means 1/100
What is 4^0 in exponential form?
Write a rule for the sequence. 1/9, 1/3, 5/9 Pls hurry Pls S's S's Sissies S's See fast
PLEASE HELP ASAP!!
How many lines of symmetry are there in the object pictured above
A. 3
B. 1
C. 0
D. 2
A certain standardized tests math scores have a bell-shaped distribution with a mean of 530 and a standard deviation of 105. Complete part (a) through (c). (a) what percentage of standardized test scores is between 215 and 845. (b) what percentage of standardized test scores is less than 215 or greater than 845. (c) what percentage of standardized test scores is greater than 740.
1. If AABD - AHGE and AC and HF are angle
bisectors, find x.
B
G
F
24
. م
X
35
E
14
H
Answer:
9.6
Step-by-step explanation:
Find the diagram attached. Using the similarity theorem of triangles
AC/AD = FH/EH
Given
AC = 24
AD = 35
FH = x
EH = 14
Substitute into the formula
24/35 = x/14
Cross multiply
35×x = 24×14
35x = 336
x = 336/35
x = 9.6
Hence the value of x is 9.6