5. The population of deer in a park is growing over the years. The table below gives the population found in a
survey by local wildlife officials.
Year
2000
2003
2006
2009
Deer Population
168
216
264
312
(a) Find the average rate that the deer population is changing over each time interval below:
From 2000 to 2003
From 2003 to 2006
From 2006 to 2009
(b) Why does this calculation indicate a linear (c) Ift stands for the number of years since 2000,
relationship?
write an equation for the deer population, p, as a
function of 1.
(d) What does your model predict the deer (e) How many years will it take for the deer
population to be in the year 2014?
population to reach 500? Round to the nearest
year.

Answers

Answer 1

a) The average rate of change is 16.

b) The Calculation is linear because the average rate of change is same.

c) p= 16t + 168

d) The population in 2014 is 8168.

What is Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

a) The average rate of change

From 2000 to 2003 = (216- 168)/ 3

                                  = 16

From 2003 to 2006 = (264- 216) / 3

                                  = 16

From 2006 to 2009 = (312- 264)/ 3  

                                  = 16

b) The Calculation is linear because the average rate of change is same.

c) From the year 2000, the intercept is 168.

So, p= 16t + 168

e) The population in 2014

p = 16(500)+ 168

  = 8168.

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Related Questions

Suppose the following estimated regression equation was determined to predict salary based on years of experience.

Estimated Salary=22,717.59+2732.16(Years of Experience)
What is the estimated salary for an employee with 7 years of experience?

Answers

The estimated salary for an employee with 7 years of experience will be;

⇒ Estimated Salary = 41,842.71

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The estimated regression equation was determined to predict salary based on years of experience is,

⇒ Estimated Salary = 22,717.59 + 2732.16(Years of Experience)

Now,

Since, The equation is,

⇒ Estimated Salary = 22,717.59 + 2732.16(Years of Experience)

Hence, The estimated salary for an employee with 7 years of experience will be;

⇒ Estimated Salary = 22,717.59 + 2732.16 × 7

⇒ Estimated Salary = 22,717.59 + 19,125.12

⇒ Estimated Salary = 41,842.71

Thus, The estimated salary for an employee with 7 years of experience will be;

⇒ Estimated Salary = 41,842.71

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Greg works two part time jobs. One job is at a gas station that pays $12 an hour and the other is delivering groceries for $15.50 an hour. Between the two jobs Greg wants to earn at least $390 a week. Let x be the number of hours he works at the gas station and let y be the number of hours he works delivering groceries. Write an inequality that models this situation.

Answers

The required inequality model for this situation is 12x + 15.5y ≥ 390.

What are inequalities?

The mathematical expressions with inequalities are those with unequal sides on both sides. Unlike equations, we compare two values when we work with inequality. The equal sign is substituted between by the less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

"A connection is termed an inequality if two real numbers or algebraic expressions are connected by the symbols ">,"< "," <="," or ">=."

For instance, x>3 (x should be greater than 3)

If there is just one variable, the inequality is said to have an open sentence.

Instance: x 6 (x is less than 6)

Double Inequalities: If the statement demonstrates a double relation between the expressions or the numbers, the inequality is said to be a double inequality.

Instance: 3 x 8 ( x is greater than or equal to 3 and less than 8)
Given, the gas station pays $12 an hour and delivers groceries for $15.50 an hour.

And, x be the number of hours he works at the gas station and let y be the number of hours he works delivering groceries.

Then, total earnings in gas station = 12x

total earnings for delivering groceries = 15.5y

So, based on the given inequality condition

12x + 15.5y ≥ 390

Hence, the required inequality model for this situation is 12x + 15.5y ≥ 390.

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write an algebraic expression that marshall can use to determine the total cost of buying a watermelon that weighs w pounds and some tomatoes that weigh t pounds. How much will it cost to buy a watermelon that weighs 18 1/2 pounds and 5 pounds of tomatoes if watermelon cost $0.68 and the tomatoes cost $3.25

Answers

Answer: The cost will be a total of $142.05. That is $125.80 for a Watermelon that weighs 185 lbs and $16.25 for 5 lbs of tomatoes.

Step-by-step explanation:

Given: Watermelons are 0.68 / lb and tomatoes are 3.25 / lb.

Let w = watermelon weight

Let t = tomato weight.

An equation would be:

.68w + 3.25t = Total cost

For 185 lb of Watermelon and 5 lbs of tomatoes:

.68(185) + 3.25(5) =

$125.80 + $16.25 = $142.05

Evaluate the expression when a=10 .
a/4+1/3 =

Answers

Answer:

Step-by-step explanation:

10/8 = n/10 proportions please

Answers

Answer:

[tex]\displaystyle n=\frac{25}{2}[/tex]

Step-by-step explanation:

A proportion is a set of equal ratios.

Cross Multiplication

The most common (and easiest) way to solve a proportion is cross multiplication. To cross-multiply, multiply the numerators by the opposite denominators. So, you are multiplying across the proportion.

After cross multiplying you get 10*10 = 8n.

Solving For n

Now, we can use algebra to find n.

100 = 8n

Just, divide both sides by 8.

[tex]n=\frac{100}{8}[/tex]

Then, simplify.

[tex]n=\frac{25}{2}[/tex]

Checking The Answer

To check your answer all you have to do is plug n back into the equation.

[tex]\frac{10}{8}=\frac{25/2}{10}[/tex]

This can be rewritten as

[tex]\frac{10}{8}= \frac{25}{2} *\frac{1}{10}[/tex]

Then, the right side can be solved.

[tex]\frac{10}{8}= \frac{10}{8}[/tex]

What is the range of the function?

f(x)=3x−1−2

Enter your answer, in interval notation, in the box.
range:

Answers

The range of a function f(x)=3ˣ⁻¹-2 is (-2, ∞)

What is meant by a function?

A function from a set X to a set Y in mathematics assigns to each element of X exactly one element of Y. The domain of the function is the set X, and the codomain of the function is the set Y.

The first known attempt to define function can be found in the writings of Persian mathematicians Al-Biruni and Sharaf al-Din al-Tusi. The concept of a function was codified in terms of set theory at the end of the nineteenth century, which substantially expanded its realms of applicability. The range of possibilities for variation or the distances between them: pricing for various grades of steel; a variety of designs. a thing's operation or action's reach or extent: accessible to the eye. a projectile's range is how far a weapon can or will shoot it.

Given,

f(x)=3ˣ⁻¹-2

Range=(-2, ∞)

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which property in math is (n+2.9)+0.3=n+(2.9+0.3)

Answers

Notice that the order the numbers are written on both sides is the same:

   n, then 2.9, then 0.3

Because the order is the same and all that changed were the parentheses (the way the numbers were grouped), this is the associative property of addition.

The associative property is about the groupings.  You can remember this by thinking about that fact that associations are groups.

Find the area of a Shaded portion

Answers

Find the area of a Shaded portion.

D. 68

What is the average rate of change of this function on the interval from x = 1 to x = 3? f(x)=10(2)x Enter your answer in the box.

Answers

Answer:

30

Step-by-step explanation:

The way to figure out the average rate of change is to divide the change in f(x) and divide that by the change in x. A formula for this is [tex]\frac{f(x_{1})-f(x_{2})}{x_{1}-x_{2}}[/tex]
1.) By this definition, we need to figure out our x1 and x2. We can say the x1 = 3 and x2 = 1
2.) Next, we plug it into the formula. We will get [tex]\frac{f(3)-f(1)}{3-1}[/tex].

3.) If we simplify, we will get 10(2)^3 - 10*2 divided by 2, which is equal to 10*4 - 10 = 30.

Jenny had 947 marbles.

She gave 515 of these marbles away.

How many marbles does she have left?

Answers

She has 432 marbles left

Answer: 432

Step-by-step explanation:  947- 515 = 432.

My subtracting 515 from 947, the answer becomes 432. You can double check this statement by adding 515 and 432 together.

Cari is searching online for airline tickets. Two weeks​ ago, the cost to fly from boston to denver was ​$220. Now the cost is ​$295. What is the percent​ increase? What would be the percent increase if the airline charges an additional​ $50 baggage fee with the new ticket​ price?

Answers

The percent increase with the additional baggage fee for airline would be $125 / $220 x 100% = 56.82%.

What is meant by the term percentage?

A number can be expressed as a fraction of 100 using a percentage. It may be computed by dividing the number by the total and multiplying by 100. It is commonly represented by the sign "%". The percentage of men, for instance, would be 25/100 x 100, or 25%, if there were 100 persons in all.

In a variety of areas, including statistics, finance, and education, percentages are often employed. For instance, in finance, percentage increase in stock prices are used to gauge a market's or company's success. In education, grades are frequently given as percentages to represent class marks.

How to solve?

The increase in the cost of the ticket is $295 - $220 = $75

The percent increase is $75 / $220 x 100% = 34.09%.

If the airline charges an additional $50 baggage fee, the new ticket price would be $295 + $50 = $345.

The increase in the cost of the ticket with the additional baggage fee would be $345 - $220 = $125.

The percent increase with the additional baggage fee would be $125 / $220 x 100% = 56.82%.

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-7(1+9a) have no idea how to do this

Answers

Answer:

-7-63a

Step-by-step explanation:

-7(1 + 9a)

(use the distributive property of multiplication to simplify)


-7-63a

Given the definitions of f(x) and g(x) below, find the value of (ƒ o g)(2).
f(x) = -x + 2
g(x) = x² – 5x – 2

Answers

Wdym by definition Answer:

Step-by-step explanation:

Please help me on this question and thank you!

Answers

Answer:

{YH, YT, BH, BT, TH, TT}

where Y = yellow, B = blue, T = turquoise

H = heads, T= tails

6 possible outcomes

Step-by-step explanation:

There are 2 independent events

Spinner which can land on one of three colors - Yellow(Y), Blue(B) and Turquoise(T)

Flipping a coin which has two outcomes Heads(H) and Tails(T)

Both events are independent of each other

So the sample space is:
{YH, YT, BH, BT, TH, TT}

Total of 6 outcomes

2. How much is 50 percent of 1025

Answers

512.5 is the answer

6. Alex says he can find the product for
(3 X 5) X 2 by solving 3 X (5 × 2).
Is Alex correct?

Answers

Answer: Yeah

Step-by-step explanation: Multiplication can be done in any order, so using parenthesis to denote which numbers to multiply first should not matter.

if you have a square with a length of 5x, write an expression for the perimeter of the square.​

Answers

The perimeter of a square with a length of 5x can be represented by the expression 45x. This is because the perimeter of a square is equal to the length of any side of the square multiplied by the total number of sides, which is 4 for a square. So, for a square with a length of 5x, the perimeter would be 45x, or 20x.

A triangle has sides with lengths of 25 centimeters, 60 centimeters, and 68 centimeters. Is it a right triangle?
PLSSS HURRY !!!!!!!!!!

Answers

For the triangle has sides with lengths of 25 centimeters, 60 centimeters, and 68 centimeters is the right triangle.

What is a right-angle triangle?

It is a triangle in which one of the angles is 90 degrees and the other two are sharp angles. The sides of a right-angled triangle are known as the hypotenuse, perpendicular, and base.

It is given that, A triangle has sides with lengths of 25 centimeters, 60 centimeters, and 68 centimeters.

We have to verify whether it is a right-angle triangle or not.

A right-angle triangle must follow the Pythagoras theorem.

The square of the hypotenuse in a right-angled triangle is equal to the sum of the squares of the other two sides.

If the longest side is the hypotenuse.

h²=p²+b²

LHS

68² = 1424

RHS

60²+25²

3600+625

4225

L.H.S=R.H.S

Thus, the triangle has sides with lengths of 25 centimeters, 60 centimeters, and 68 centimeters in the right triangle.

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The perimeter of a rectangle is 34 centimeters. The length is two more than twice the width. Find the length and the width of the rectangle.

Answers

The length of a rectangle is 12 units and width is 5 units.

What is Algebra?

A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.

To determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.

Given that the Perimeter of a rectangle = 34 cm.

and, length is two more than twice the width.

Thus the width be x.

So, the length = 2x + 2

So,

Perimeter of rectangle = 2 ( l +w )

34 = 2( x+ 2x+ 2)

17 = 3x +2

3x = 15

x= 5

2(5)+2 = 12

So, The length is 12 units and width is 5 units.

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As a project manager, you need to plan production runs over the next 3 1/2 weeks. If your team is able to produce 1,250 widgets in one week, how many widgets can they produce in 3 1/2 weeks?

Answers

Answer: 4,375.

Step-by-step explanation: If your team is able to produce 1,250 widgets in one week, then in 3 1/2 weeks, they will be able to produce 3 1/2 * 1,250 = <<3.5*1250=4375>>4,375 widgets.

Use two different methods to find and explain a formula for the area of a trapezoid
that has parallel sides of length a and b and height h. Consider these ideas or others: (a)
Combine two copies of the trapezoid to make a parallelogram. (b) Subdivide the trapezoid
into two triangles, one with base b and one with base a.

Answers

The two possible ways to find the area are -

A = (1/2) × {a + b} × {h}A = {b x h} - (1/2) x {(b - a} x h}

What is trapezoid?

A trapezoid, also known as a trapezium, is a flat closed shape having 4 straight sides, with one pair of parallel sides.

Area : ½ x (sum of the lengths of the parallel sides) x perpendicular distance between parallel sidesPerimeter : sum of lengths of sides of trapezoidNumber of vertices : 4Number of edges : 4Properties : Convex polygonType : QuadrilateralSum of interior angles : 360°

We have a trapezoid.

Now, we can find the area in two ways -

[1] -

A = (1/2) × {a + b} × {h}

[2] -

A = {b x h} - (1/2) x {(b - a} x h}

Therefore, the two possible ways to find the area are -

A = (1/2) × {a + b} × {h}A = {b x h} - (1/2) x {(b - a} x h}

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Zeg has $9.20 left on a gift card to the candy store. He has the following items in his shopping basket: 2 giant lollipops, 3 popcorn balls, 1 candy bar and 5 candy sticks . Zeg wants to buy two more items name two more possible items he can buy using his gift card

Answers

Answer:

Zeg can buy a candy stick and a Popcorn ball.

Step-by-step explanation:

After calculating the total based on the following:

Candy bars are $0.99, Candy sticks are $0.45, Giant lollipops are $1.75, and Popcorn balls are $0.50.

the total was $8.24. [tex]9.20[/tex] [tex]-8.24 = 0.96[/tex] The only two items that can fit into this are a popcorn ball, and a candy stick.

The graph shows the amount of gas that Dario's car uses to travel different distances.

Complete the statement about the graph.

Gas Mileage

100

The number of miles is always

20

times

90

the number of gallons of gas.

80

70

Dario's car can travel

?

miles using

60

12 gallons of gas

Distance Traveled (miles)

50

40

30

20

.

10

0

0 1 2 3

4 5 6 7 8 9 10

Gas (gallons)

Answers

Answer: 46 miles

Step-by-step explanation: according to my calculations i minus te total mileage gas times the current philosphy of the number of gallons with 50 - 30

ILL GIVE BRAINLIESTTTT PLEASE HELP ILL GIVE BRAINLIESTTTT

Answers

Answer:

c) Propability of rolling doubles=6

Propability of rolling a sum grrater then or equal to 8 = 15

(Together add up to 21)

d)6 ->(1,1)(1,2)(1,3)(2,1)(2,2)(3,1)

e)9 ->(1,6)(3,4)(5,2)(3,5)(5,3)(3,6)(5,4)(5,5)(5,6)

Translate the following phrase into an algebraic expression. Do not simplify. Use the variable names "x" or "y" to describe the unknowns.

the product of two numbers divided by 5

Answers

Step-by-step explanation:

xy/5

.........

....................

Which of the following points lie on a line that passes through the origin with a slope of −25? Select all that apply. Multiple select question. cross out A) (0, 0) cross out B) (1, −25) cross out C) (−2, 5) cross out D) (−1, 25) cross out E) (4, 10) cross out F) (−5, 2)

Answers

The points that will lie on the line will be (0, 0) , (1, - 25) , (- 1, 25).

What is the general equation of a straight line?

The general equation of a straight line is : y = mx + c.

[m] is called slope and it tells the unit rate of change in [y] with respect to [x].

[c] is called the [y] - intercept.

We have some points that lie on a line that passes through the origin with a slope of −25.

The equation of a straight line that passes through the origin and has slope of -25 will be -

y = - 25x

The points that will lie on the line will be -

(0, 0) , (1, - 25) , (- 1, 25)

Therefore, the points that will lie on the line will be (0, 0) , (1, - 25) , (- 1, 25).

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PLEASE ASAP I NEED HELP
Given the inequality 4x ≤ 28, which of the following is a solution that makes the inequality true?

Answers

The value of the inequality equation is x ≤ 7

What is an Inequality Equation?

Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

In an inequality, the two expressions are not necessarily equal which is indicated by the symbols: >, <, ≤ or ≥.

Given data ,

Let the inequality equation be represented as A

Now , the value of A is

4x ≤ 28   be equation (1)

Now , on simplifying the equation , we get

Divide by 4 on both sides of the inequality equation , we get

x ≤ 7

Therefore , the value of x is less than or equal to 7

All the numbers less than or equal to 7 satisfies the condition for x

The value of the equation x ≤ 7 is shown in the graph below

Hence , The value of the inequality equation is x ≤ 7

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need help with this one keep getting wrong answer

Answers

Answer:

try socratic

Step-by-step explanation:

During WW! mortars were fired from trenches 3 feet down The mortars had a velocity of 150 ft/s. Determine how long it will take for the mortar shell to strike its target?

Answers

In 0.02 seconds, the mortar shell will make contact with the target.

How to determine the time it will take the mortar shell to strike the target

The formula for velocity, which is equal to distance / time, is used to calculate how long it will take to hit the target.

In the problem, the distance is 3 feet, and the velocity is given to be 150ft/s

therefore

150 = 3 / time

time = 3 / 150

time = 0.02 seconds

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If $8000 is invested at an annual interest rate of 5% and compounded annually, what is the balance after 4 years?

Answers

Answer: 7 years

Step-by-step explanation:  

We make the assumption that 8000 is 100% since it is our output value.

Step 2: We next represent the value we seek with $x$.

Step 3: From step 1, it follows that $10\%=8000$.

Step 4: In the same vein, 100%=8000$.

So divide that by 5% 0.05%

Then multiply it by 5   0.0025%

Then convert it into money  26$

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