a. The function that models the population t years after 2000 is
Pf = 15600(1.04)^t
b. The estimate of the fox population in the year 2008 is 21349.67.
Given,
A fox population in a certain region has a continuous growth rate of 4% per year.
It is estimated that the population in the year 2000 was 15600.
we are asked to determine a function that models the popualtion t years after 2000 (t = 0 for 2000)
Pf = Pi(1 + r)^t where Pf is the final population, Pi is the initial population, r is the annual growth rate in decimal (not %), and t is the time in years.
a. Pf = 15600(1.04)^t
b. Pf = 15600(1.04)⁸ = 24497.386
= 21349.67
hence we get the required answers.
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The third term of the sequence is 165. Find the first term
Term to term rule is subtract 2 and then multiply by 3
The value of the first term in the sequence is 21.
How to calculate the first term?Let the second term teen be x.
Since the term to term rule is subtract 2 and then multiply by 3. This will be:
(x - 2) × 3 = 165
3(x - 2) = 165
3x - 6 = 165
Collect like terms
3x = 165 + 6
3x = 171
Divide
x = 171 / 3.
x = 57
Second term = 57
We will do same thing again to get first term. Let first term be a.
(a - 2) × 3 = 57
3a - 6 = 57
Collect like terms
3a = 57 + 6
3a = 63
Divide
a = 63/3
a = 21
The first term is 21.
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A light bulb consumes 8400 watt-hours in 3 days and 12 hours. How many watt-hours does it consume per day?
Answer:
2400Watt Hours isn't it A Right Answer?
Antoinette solves the linear equation 3 (x minus 3) + 2 x + 9 = 2 x + 2 (x minus 1) using the steps shown below.
Step 1: 3 x minus 3 + 2 x + 9 = 2 x + 2 (x minus 1)
Step 2: 5 x + 6 = 4 x minus 1
Step 3: 5 x minus 4 x = negative 1 minus 6
Step 4: x = negative 7
She checks her solution by substituting –7 for x in the original equation. She determines that her answer is incorrect. Which best describes Antoinette’s error?
She distributed incorrectly.
She incorrectly combined like terms.
She incorrectly applied the addition and subtraction properties of equality.
She incorrectly applied the multiplication and division properties of equality.
Answer:
She distributed incorrectly.
Step-by-step explanation:
In the first step, [tex]3(x-3)=3x-9[/tex], not [tex]3x-3[/tex].
Consider a home mortgage of $125,000 at a fixed APR of 4.5% for 15 years. a. Calculate the monthly payment. b. Determine the total amount paid over the term of the loan. c. Of the total amount paid, what percentage is paid toward the principal and what percentage is paid for interest.
Monthly payment would be $956.24
Loan APR is 4.892%
The revenue for a business, as a function of units produced, x, is shown below by R(x). C(x) represents the cost of producing x units. Calculate the profit function and then determine how many units must be produced for the business to break even.
R(x) = 12x
C(x) = x + 264
The profit function for the revenue R(x) = 12x and the cost, C(x) = x + 264 is 11x-264 and units must be produced for the business to break even is 24 units.
What is revenue profit?Profit refers to net income after deducting expenses from earnings, whereas revenue refers to income generated through business operations. Sales, fee-based income, and property-based income are just a few of the different ways that money can come in.
Here,
R(x)=12x
C(x)=x+264
It represents the difference between total revenues and total outlays.
Revenue minus costs equals profit.
Profit = Revenue - Cost
P(x)=R(x)-C(x)
P(x)=12x-x-264
P(x)=11x-264
For the company to break even,
R(x) = C(x)
12x=x+264
11x=264
x=24
The break-even point for the business is 24 units, and the profit function for the revenue R(x) = 12x and the cost C(x) = x + 264 is 11x-264.
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Is it possible for a number to be a product of 2, a product of 5,
and a product of 10? Explain.
Yes, it is possible for a number to be a product of 2, 5, and 10.
All multiples of 10 such as 10, 20, 30, 40, 50, 60, ,,,, are a product of 2, 5, and 10.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
A number that is a product of 2, 5, and 10.
Example:
10 = 2 x 5
10 = 5 x 2
10 = 10 x 1
20
20 = 2 x 10
20 = 5 x 4
20 = 10 x 2
100
100 = 2 x 50
100 = 5 x 20
100 = 10 x 10
We see that all multiples of 10 are a product of 2, 5, and 10.
Thus,
All multiples of 10 are a product of 2,5, and 10.
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Divide:
3⁄5 ÷ 1⁄5 =
. .
Answer: 3/1
Step-by-step explanation:3 ÷ 1 =1÷3 =3
5 5 = 5÷5=1
therefore, 3 by five divided by 1 by five is equal to 3 by 1 ,
A falcon flies 800,000 meters in 4 hours. Use the formula d = rt, where d represents distance, r represents rate, and t represents time, to answer the following questions. Show your work.
Part A: Rearrange the distance formula, d = rt, to solve for rate.
Part B: Find the falcon's rate in meters per hour.
Part C: Find the falcon's rate in kilometers per hour.
Part D: Which unit, meters, or kilometers, makes more sense to use in this scenario, and why?
PLEASE HELP FAST I RLLY NEED THIS
The information about the Falcon fly is represented below
Part A: 800 000 = 4r
part B: 200 000 meters per hour
Part C: 200 kilometer per hour
Part D: Kilometers makes more sense because it makes the number easier to write and remember
How to find the falcon's rate in meters per hourThe rate as used refers to speed which is distance / time
using the representation 800 000 = 4r
rate, r = 800 000 / 4
r = 200 000 meters per hour
converting meter to kilometer is achieved by dividing by 1000
r = 200 000 meters per hour / 1000
r = 200 kilometers per hour
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A rare coin increases in value according to the function f(x)=100(1.07)x
f(x)=100(1.07)x where x represents the amount of years that the coin is owned and value is measured in US dollars. What is the value of the coin after 5 years?
The value of the coin after five years is 535 when the value increases with the function f(x) = 100(1.07)x
The value of a rare coin rises in accordance with the function f(x)
f(x) = 100(1.07)x
where x represents the number of years that the coin is owned and value is measured in US dollars
Now, Simplifying the given function, we have :
f(x) = 100(1.07)x
f(x) = 107x
Now, we need to find the value of the coin after five years, then
Putting x = 5 in the function,
f(x) = 107 * 5 = 535
Hence, the value of the coin after five years is 535 when the value increases with the function f(x) = 100(1.07)x
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A trucking company has 5 trucks and 4 drivers available when requests for 3 trucks are received. How many different ways are there of selecting the trucks and the drivers to meet these requests?
The different ways that are there of selecting the trucks and the drivers to meet these requests is 240 ways.
How to calculate the number of ways?Combinations are also referred to as selections. Combinations imply the selection of things from a given set of things. In this case, we intend to select the objects.
Combination formula
ⁿCr = n! / ((n – r)! r!)
n = the number of items.
r = how many items are taken at a time.
The number of ways to select 3 trucks will be:
= ⁵C₃ = 10
The number of ways to select 3 drivers will be:
= ⁴C₃ = 4
Number of ways to arrange them = 3! = 3 × 2 = 6
Therefore the total number of ways will be:
= 10 × 4 × 6
= 240 ways
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What equation is graphed in this figure?
Responses
y−4=−13(x+2)
y minus 4 equals negative fraction 1 over 3 end fraction open parenthesis x plus 2 close parenthesis
y−3=13(x+1)
y minus 3 equals fraction 1 over 3 end fraction open parenthesis x plus 1 close parenthesis
y+2=−3(x−1)
y plus 2 equals negative 3 left parenthesis x minus 1 right parenthesis
y−5=3(x−1)
y minus 5 equals 3 left parenthesis x minus 1 right parenthesis
Number graph ranging from negative four to four on the x and y axes. A line is drawn on the graph that passes through begin ordered pair negative one comma four end ordered pair and begin ordered pair one comma negative two end ordered pair
The linear equation shown in the graph is the one in the third option.
y + 2 = -3*(x - 1)
What is the equation graphed?Here we have a graph, and there we can see a linear equation, on that graph, we can see that:
The y-intercept is y = 1.
For each horizontal unit, the line goes 3 units down, then the slope is -3.
Then the linear equation is:
y = -3*x + 1
If now we add 2 in both sides, we get:
y + 2 = -3x +1 + 2
y + 2 = -3x + 3
y + 2 = -3*(x - 1)
So the correct option is the third one.
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Can anybody help me with this question?
Answer:
x=3
Step-by-step explanation:
any horizontal line is equal to x
the y is equal to 0
a horizontal line is undefined
HOW TO DETERMINE THE ANSWER?
Answer:
The degree of the polynomial is 4. That is the highest exponent.
Step-by-step explanation:
Answer:
4
Step-by-step explanation:
to find degree you look at what the highest exponent when simplified is and that is your answer and inThis case it’s 4
Hopes this helps please mark brainliest
A light bulb consumes 2100 watt-hours in 3 days and 12 hours. How many watt-hours does it consume per day?
Answer:
below
Step-by-step explanation:
12 hours is .5 day so a total of 3.5 days
2100 w-h / 3.5 d = 600 w-h per day
The students at Britney's school voted for a new school color. 20% of the students voted for green. If there are 585 students in Britney's school, how many students voted for green?
Answer:
117
Step-by-step explanation:
20% = 1/5
585 x 1/5 = 117!
In a garden club, 90% is ladies. The number of ladies is 12 more than 3 times the number of gentlemen.
How many ladies and how many gentlemen are in the club?
(Note: set up a rational equation and solve)
The numbers of ladies and gentlemen in the club are 2 and 18 respectively.
What is the percentage?The percentage is a ratio that can be expressed as a fraction of 100
Given that, there are 90% of ladies in the club, and the number of ladies is 12 more than 3 times the number of gentlemen.
Let the number of gentlemen is x and the number of ladies be y.
Since the number of ladies is 12 more than 3 times the number of gentlemen, it follows:
Calculationy = 12 + 3x (1)
Now, the total number of members in the club is:
x + y
Since there are 90% ladies in the club, it follows:
90%(x + y) = y
90(x + y)/100 = y
90x + 90y = 100y
90x = 100y - 90y
90x = 10y
9x = y (2)
Now, substitute y = 9x into equation (1):
9x = 12 + 3x
9x -3x = 12
6x = 12
x = 2
Substitute x = 2 into equation (2):
9(2) = y
18 = y
Hence, the numbers of ladies and gentlemen in the club are 2 and 18 respectively.
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I need help with this please and thank you
Answer:
length 12width 7Step-by-step explanation:
Adding 5 m to the width of a rectangle makes it a square with area 144 m². You want the length and width of the original rectangle.
AreaThe formula for the area of a square is ...
A = s²
The side length of the square formed from the rectangle is ...
144 = s²
√144 = s = 12 . . . . . meters
RectangleThe length of the rectangle is unchanged when it is made into the square, so the length is 12 m.
The width of the rectangle had 5 m added to make it 12 m, so the width of the rectangle is 7 m.
__
Additional comment
The given relation between length and width is given as L = 2W -2. It is true that 12 = 2(7) -2, but that is not needed in order to solve this problem. It does serve as a check on our answer.
What’s equivalent to 11:1 answer
Answer:
11
Step-by-step explanation:
11:1 = [tex]\frac{11}{1}[/tex] = 11
Answer: 11, 22:2, 33:3, etc.
Step-by-step explanation:
A ratio is dividing.
11/1 = 11.
This means that numerous ratios can be used, to the point where the answers are infinite.
Oliver saves %10 of their weekly earnings for living expenses. oliver usually makes $520 each week. This week oliver made %10 more. incorrectly oliver claims that has $520 left for spending money this week. Calculate the amount of spending money left for this week. What error did olive likely make?
Oliver is left with $514.8
A percentage is a number or ratio expressed as a fraction of one hundred. If we need to calculate a percentage of a number, divide it by the whole and multiply by 100. As a result, the percentage represents one part in a hundred. The term % stands for one hundred percent.
His usual salary = $520 per week
This week he earned = Usual salary + 10% of usual salary
10% of usual salary =520 x (10/100)
Thus, this week's earnings = $520 + $52 = $572
Amount spent = 10% of this week =572 x (10/100)
= 57.2
Thus, the left amount is calculated by:
Left amount = this week's salary - the amount spent
Amount left = $572 - $57.2 = $514.8
Thus, Oliver is left with $514.8
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Which set of side lengths will NOT create a triangle? Responses 3, 4, 5 3,, , 4,, , 5, EndFragment, 10, 13, 14 10, 13, 14, EndFragment, 10, 20, 30 10, 20, 30, 16, 20, 30
The set of side lengths that would not create a triangle is; 10, 20, 30.
Which set of side lengths will not create a triangle?It follows from the task content that the set of side lengths which will not create a triangle are to be determined from the given task content.
Since the triangle inequality theorem states that; the sum of two side lengths of a triangle is always greater than the third side length and also, the difference of two side lengths of a triangle is less than the third side length.
On this note, for a triangle with side-lengths a, b and c; the inequalities which hold are;
a + b > c and a - b < c.
Therefore, the set of side-lengths which will not create a triangle is; 10, 20, 30.
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Please help! What is the equation of the line?
y=-3x
y=3x
y=3x+1
y=4x
Answer: y=3x
Step-by-step explanation:
The equation can be found by finding the slope of the given line. Visually, this can be found by counting the distance between two points. From (1,3) and (2,6), the line "rises" 3 units and "runs" 1 unit to the right. Since slope is calculated as rise over run, this gives us 3/1, or just 3 for slope. In slope-intercept form, this becomes y=3x.
Just to note, we know it is not negative because of the direction of the slope. Visually, if the slope "moves" in the direction of upwards and to the left, it will be positive. This can be calculated more accurately using the slope formula (y2-y1/x2-x1)
A rectangle is drawn so the width is 4 inches longer than the height. If the rectangle's diagonal
measurement is 28 inches, find the height.
The height is 17.69 inches.
From the question, we have
Let height= h
width = h+4
diagonal = 28 inches
Using Pythagoras Theorem
28² = h² + (h+4)²
784 = h² +h² +16+8h
784 = 2h² +16+8h
2h²+8h-768 = 0
Solving this, we get
h=−2+2*√97
h=17.69 inches
Multiplication:
Finding the product of two or more numbers in mathematics is done by multiplying the numbers. It is one of the fundamental operations in mathematics that we perform on a daily basis. Multiplication tables are the main use that is obvious. In mathematics, the repeated addition of one number in relation to another is represented by the multiplication of two numbers. These figures can be fractions, integers, whole numbers, natural numbers, etc. When m is multiplied by n, either m is added to itself 'n' times or the other way around.
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0/1
3. At the carnival, there is a game with 600 ducks. If 25% of the ducks have stars on the
bottom, how many ducks have stars? Make sure to label your answer in ducks
8
The length of a rectangle is 10, the width 3, and the height x. The surface area and the volume are equal. What is the value of x?
Answer:
x = 15
Step-by-step explanation:
Please refer photo
1. Find the equation of the line that has a slope of 7 and passes through the point (-8,3).
The equation of the line has a slope of 7 and passes through the point (-8,3) is y = 7x + 59.
What is a linear function?A straight line on the coordinate plane is represented by a linear function.
A linear function always has the same and constant slope.
The formula for a linear function is f(x) = ax + b, where a and b are real values
The general form of a linear equation is the slope(m) and y-intercept (c) is given as
y = mx + c
Slope m =7
y = 7x + c
Substitute, (-8,3)
3 = 7(-8) + c
c = 59
Thus, y = 7x + 59 will be the equation.
Hence "The equation of the line has a slope of 7 and passes through the point (-8,3) is y = 7x + 59".
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Angelo constructed 8 playing card houses in 4 minutes. How long would it take for him to construct 20
houses?
Answer:
10 minutes.
Step-by-step explanation:
8 houses are done in 4 minutes
The ratio is 2:1
20 houses are done in 10 minutes
20:10 = 2:1
Answer:
It would take Angelo 10 minutes to construct 20 playing card houses.
first way to solve it (recommended):
Step one: See how much it takes to build one house
4 / 8 = 0.5
0.5 minutes to build one house
Step two: multiply by amount of houses (20)
0.5 x 20
Step three: get your answer!
It would take Angelo 10 minutes to make 20 houses.
second way to solve it (ratios):
Step one: see the ratio of minutes to houses
minutes : houses
4 : 8
Step two: simplify the ratio
4 : 8
1 : 2 (divide both sides by four)
Step three: multiply
x minutes : 20 houses
1 minutes : 2 houses
multiply both sides by 10
10 minutes : 20 houses
Step four: get your answer!
It would take Angelo 10 minutes to make 20 houses.
I hope my answer helped you!
Identify the domain and range of each graph
a park has used 4,500 on this month which is 45.50% of its allotted monthly budget how much is the monthly budget
=========================================================
Work Shown:
x = monthly budget
45.50% of x = 0.4550x = 4500
0.4550x = 4500
x = 4500/0.4550
x = 9,890.1098901099 approximately
x = 9,890.11
Quiero el resultado de la ecuación 5 x + 2 y = 90
Answer:
x=18-2/5y
y=-5/2x+45
Step-by-step explanation:
5x+2y=90
Nosotros queremos resolver para x o y
5x=90-2y
x=18-2/5y
o
2y=90-5x
y=-5/2x+45
Answer:
x=18-2y/5
Step-by-step explanation:
Which question can be represented by the equation ? × 1/8 = 3
A) how many 3s are in 1/8?
B) what is 3 groups of 1/8?
C) how many 1/8s are in 3?
D) what is 1/8 of 3?
The question that can be represented by the equation ? × 1/8 = 3 is C. how many 1/8s are in 3?
What is an equation?An equation is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe the scenario.
In this case, the question is how many 1/8s are in 3. This will be:
= 3 ÷ 1/8
= 3 × 8
= 24
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