The fox population in a certain region has a continuous growth rate of 4 percent per year. It is estimated that the population in the year 2000 was 15600.

(a) Find a function that models the population t years after 2000 ( t=0 for 2000).
Hint: Use an exponential function with base e.
Your answer is P(t)=

(b) Use the function from part (a) to estimate the fox population in the year 2008.
Your answer is (the answer must be an integer)

Answer:

Step-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.

The 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

The 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.

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 ,

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 different ways that are there of selecting the trucks and the drivers to meet these requests is 240 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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The equation of the line has a slope of 7 and passes through the point (-8,3) is y = 7x + 59.

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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Monthly payment would be $956.24
Loan APR is 4.892%

Answer:

2400Watt Hours isn't it A Right Answer?

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:

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.

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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The set of side lengths that would not create a triangle is; 10, 20, 30.

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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Answer:

x = 15

Step-by-step explanation:

Please refer photo

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.

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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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.

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)

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

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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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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The value of the first term in the sequence is 21.

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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The numbers of ladies and gentlemen in the club are 2 and 18 respectively.

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:

y  = 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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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

The 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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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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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

The question that can be represented by the equation ? × 1/8 = 3 is C. how many 1/8s are in 3?

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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Answer:

She distributed incorrectly.

Step-by-step explanation:

In the first step, [tex]3(x-3)=3x-9[/tex], not [tex]3x-3[/tex].

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!

=========================================================

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

The linear equation shown in the graph is the one in the third option.

y + 2 = -3*(x - 1)

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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Answer:

117

Step-by-step explanation:

20% = 1/5

585 x 1/5 = 117!