Find the rates of change in population for both parks between 2009 and 2014, and determine which park showed faster population growthduring those years.

Answer:it takes 1 hor 25 minutes to make a costume

Step-by-step explanation:

20 divided by 16 =1.25

Given:

The number is 60.

Aim is to find the result when 60 is increased by 40%.

First calculate 40% of 60,

Now, add the amount 24 in 60.

Answer: 84 is a 40% increase of 60.

We will find it as follows:

The volume of such a sphere is given by the expression found.

***

When we have a binomial at the power of a number, of the form:

We use Pascal's triangle to determine the expansion. Pascal's triangle is the following:

Each row can be used to calculate a specific power, in our case the binomial is at the power of three, and we will use the 4rth row to expand, that is:

As you can see, the numbers that accompany a & b are the ones found in the 4th row of Pascal's triangle. We also see that the "degree" o the expansion always sums 3, that is a^3 has an overall degree of 3, a^2b has an overall degree of 3, ab^2 has an overall degree of 3 & b^3 has an overall degree of 3.

***

If we, for example, wanted to expand (a + b)^4, we then would have the following:

*We would use the 5th row and get:

[Pascal's triangle expands to infinity. So, you in theory can manually expand any binomial at any power, but for big numbers, it will take a long time]

***

In our case, the binomial was:

And, its respective expansion is:

In order to determine the amount of radium after 800 years, use the following formula:

where,

N: amount of radium after t years = ?

No: initial amount of radium = 50g

λ: decay constant

t = 800

The decay constant is calculated by using the following expression:

where t1/2 = 1960 is the half-life.

Now, by replacing λ, No and t = 800 you obtain:

Hence, after 800 years there are approximately 37.68g of uranium

Answer: 41

so he has 49 books and he sold 15 so its 49-15= 34 so he bought 7 more books so its 34+7=41

Step-by-step explanation:

Have great day

Notice that

Therefore, the range of the function is f(x)>=3, or [3,infinite)

The scatterplot that do not show a clear relationship and would not have a trend line is: graph B.

A trend line is also referred to as a line of best fit and it can be defined as a statistical or analytical tool that is commonly used in conjunction with a scatter plot, in order to determine whether or not there's any association (correlation) between data points.

In Mathematics, there are different types of trend line and these include the following:

By critically observing the scatter plot (see attachment) which models the data in the given table, we can reasonably and logically deduce that the data points in graph B are scattered around and as such, it does not illustrate a clear relationship (pattern).

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Answer:

x = 3

Step-by-step explanation:

When twenty is reduced by one-third of a number, the result is 19. Find the number.

20 - 1/3x = 19

subtract 20 to both sides:

20 - 1/3x - 20 = 19 - 20

-1/3x = -1

multiply both sides by -3:

-3(-1/3x) = -1(-3)

x = 3

The two equivalent expression of the decimal 3.200 is 3200/1000 and 3.2

For the given question, the stated decimal is;

3.200

Removing point will be;

3200/1000 is the equivalent expression.

Divide numerator an denominator by 100 .

32/10 = 3.2 is also the equivalent expression of 3.200.

Thus, the two equivalent expression of the decimal 3.200 is 3200/1000 and 3.2.

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The correct question is-

Write two decimals that are equivalent to the given decimal 3.200

Hey there!

[tex]0.875:1/4\/\\\textmd{To Simplest form}[/tex]

[tex]0.875[/tex] ÷ [tex]\frac{1}{4}[/tex]

[tex]=3.5[/tex]

Your final answer would be 3.5.

Hope this helps!

An equation which could be represented by the number line is: D. -5 + (-1) = -6.

A number line simply means a type of graph with a graduated straight line which comprises both positive and negative numbers that are placed at equal intervals along its length.

This ultimately implies that, a number line can be used to compare or determine the difference between two numbers. Additionally, a number line typically increases in numerical value towards the right and decreases in numerical value towards the left.

From the number line shown above, we have:

Distance = -5 + (-1)

Distance = -5 - 1

Distance = -6.

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Answer:

y= -2x -7

Step-by-step explanation:

The equation of a line in slope-intercept form is given by y= mx +c.

Given that the slope is -2, we can substitute m= -2 into the equation.

y= -2x +c

The value of c can be found by substituting a point in which the line passes through into the equation. In this case, the point is (-4, 1).

y= -2x +c

When x= -4, y= 1,

1= -2(-4) +c

1= 8 +c

Subtract 8 on both sides:

c= 1 -8

c= -7

Substituting c= -7 into the equation:

y= -2x -7

Optional step:

To check our answer, we can substitute one coordinate and see if the other coordinate is the same as the given coordinate. For example, let's substitute the x-coordinate of -4 into the equation.

y= -2(-4) -7

y= 8 -7

y= 1

Since the y-coordinate is indeed 1, the equation above is correct.

Additional reading:

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We are given the following series

-6, -2, 2, 6

Common difference = last term - first term

For the first two terms

The common difference is calculated as

Last term - first term

Last term = -2

First term = -6

Common difference = -2 - (-6)

= -2 + 6

common difference = 4

Common difference = 2 - (-2)

common difference = 2 + 2

Common difference = 4

Last two terms

common difference = 6 - 2

Common difference = 4

The common difference for this sequence is 4

The sequence is arithmetic.

1. Using the order of mathematical operations, the values in brackets are added and multiplied to a product of $4.50 as the total tax.

2. Using the distributive property to expand the expression, 0.05(50 + 40) is  0.05 x 50 +  0.05 x40.

3. The total tax using the expanded expression is $4.50, the same product as when evaluating the original mathematical expression.

4. The original expression involves finding the total cost first before calculating the tax on the total.

The following is the order of mathematical operations:

1) The original expression, 0.05(50 + 40):

= 0.05 x 90

= 4.5

= $4.50

2) The expanded expression, 0.05(50 + 40)

=  0.05 x 50 +  0.05 x40

= 2.5 + 2.0

= 4.5

= $4.50

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Answer:

She ended up with fewer apples by buying the bigger bags.

Explanation:

The total weight of 2 bags of apples weighing 314 pounds each is equal to:

2 x 314 = 628 pounds

At the same way, the total weight of 3 bags weighing 223 pounds each is:

3 x 225 = 675 pounds

Since 628 pounds is less than 675 pounds, Marlene ended up with fewer apples by buying the bigger bags

The solution to the system is the intersection of the graphs.

From the problem, the intersection is at (-3, 2)

The answer is (-3, 2)

let j be justin, e for Eva and m for Emma. We get

so we get that, replacing all the variables

so we get that Eva has $20. therefore Justin has $27.5 and Emma has $15.5

AA (or AAA) or Angle-Angle Similarity

If any two angles of a triangle are equal to any two angles of another triangle, then the two triangles are similar to each other.

We do not have 3 angles.

SAS or Side-Angle-Side Similarity

If the two sides of a triangle are in the same proportion of the two sides of another triangle, and the angle inscribed by the two sides in both the triangle are equal, then two triangles are said to be similar.

We have two sides and 1 angle. But, two sides of a triangle are not in the same proportion of the two sides of another triangle

SSS or Side-Side-Side Similarity

If all the three sides of a triangle are in proportion to the three sides of another triangle, then the two triangles are similar.

Letter D

For k=2 for infinite solutions.

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.

Given:

4(4x + 1) = k(8x + 2)

Now, the equation should have infinite solutions

In consider the situation then we must put value of k such that LHS part become Equal to RHS.

Now, take k=2

4(4x + 1) = k(8x + 2)

LHS: 4(4x+1)= 16x+ 4

RHS: 2(8x+ 2)= 16x+ 4

Hence, k=2 for infinite solutions.

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SOLUTION

Equation of a parabola is given by the equation

Where (h, h) are the coordinates of the vertex.

From the question given, the vertex is (2, 0)

So, h = 2, k = 0.

The y-intercept is given as (0, 12).

So, this means that x = 0 and y = 12

Substituting the values for h, k, x and y into the equation we have

Now, let's substitute the value of a into the equation to get equation for the parabola.

This becomes

Recall that:

Therefore as sin x approaches 0 and cos x approaches 1, the value of cot x approaches infinity.

Answer: True.

The graph of the function f (x) = |x| is shown in attached figure.

Hence, Option A is true.

What is mean by  Modulus function?

The modulus function is the magnitude or absolute value of a positive or negative number. It is defined as y = |x| or f (x) = |x|

Where, f : R → R and x ∈ R.

This is also called the absolute value function.

Given that;

The modulus function is,

⇒ y = |x|

Now, The modulus function is,

⇒ y = |x|

Since, The function y = |x| is not differentiable at x = 0.

So, It break at point x = 0, and have all positive values of y.

Which is shown in image A.

Thus, The graph of function y = |x| is shown in attached figure.

Therefore, In the images;

⇒ Option A is true.

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The secant function is the reciprocal of the cosine function.

We can evaluate trigonometric functions of angles outside the first quadrant using reference angles as we have already done with the sine and cosine functions. The procedure is the same:

Find the reference angle formed by the terminal side of the given angle with the horizontal axis. The trigonometric function values for the original angle will be the same as those for the reference angle, except for the positive or negative sign, which is determined by x– and y-values in the original quadrant. (Figure) shows which functions are positive in which quadrant.

An even function is one in which f(-x) = f(x)

An even function is one in which f(-x) = - f(x)

Cosine and secant are even:

Therefore from the drop down the correct answer : secant function is EVEN

The employee's paycheck after FICA and SDI deductions as well as

withholding tax deductions is $1158.65.

FICA is a federal payroll tax in the US. It is taken out of every paycheck and stands for the Federal Insurance Contributions Act. Your nine-digit number enables Social Security to precisely record your self-employment or insured wages. You accrue credits for Social Security benefits as you work and pay FICA taxes.

The final monthly paycheck of the employee after deducting all taxes is $1158.65.

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Answer:

10.50p+15≤65

p≤ 100/21

Step-by-step explanation:

Let p represent pounds of Pumpkin Spice coffee.

We have been given that Lydia is at a coffee shop and knows she can spend no more than $65 before tax. She sees this price list in the coffee shop.

Item Price per pound

Dark Roast Coffee

$7.50

Pumpkin Spice Coffee

$10.50

Breakfast Tea

$23.50

Lydia wants to buy 2 pounds of Dark Roast coffee, so the cost of 2 pounds of Dark Roast coffee would be $7.50×2=$15 .

We are told that cost of each pound of Pumpkin Spice coffee is 10.50,socostof′ p'

pounds of Pumpkin Spice coffee would be 10.50

Since Lydia can spend no more than $65 before tax, so the cost of 2 pounds of Dark Roast coffee and 'p' pounds of Pumpkin Spice coffee must be less than or equal to 65.

We can represent this information in an inequality as:

10.50p+15≤65

Therefore, our required inequality would be 10.50p+15≤65

10.50+15-15≤65-75

10.50≤50

Divide both sides by 10.50:

10.50p/10.50 ≤ 50/10.50

P ≤ 50*2/10.50*2

P ≤ 100/21

P ≤ 4.76190

Therefore, Lydia can buy less than or equal to 100/21 pounds of Pumpkin Spice coffee.

The value of the functions are;

(f. g)(x) =  9x² + 5  

(g . f)(x) = 3x² + 15

A function can be defined as a law, rule or expression showing the elaborate relationship between two variables in an expression or equation.

The variables are;

Given the functions;

To determine  (f .g)(x), we substitute the value of g(x) as x  in the function, we have;

(g)(x) = (3x)² + 5

expand the bracket

(g)(x)  = 9x² + 5

To determine (g . f )(x), substitute the value of x as fx)

(g . f)(x) = 3(x² + 5)

expand the bracket

(g . f)(x)= 3x² + 15

Hence, the functions are  9x² + 5 and  3x² + 15

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The sum of angle on a straight line is always 180 degree.

Determine the equation for the angle.

Answer:

≈0.694 or rounded to 0.7

Step-by-step explanation:

4.06/5.85≈0.694