A change in temperature of 6°C is equivalent to achange in temperature of•F

The average rate of change in population is -35 between 2002 and 2004, and -2.5 between 2002 and 2006 which represents the decrease in the population.

Lagrange mean value theorem states that, if a function f is continuous over the closed interval [a, b] and differentiable over the open interval (a, b), then there must be at least one point c in the interval (a, b) where the slope of the tangent at the point c is equal to the slope of the tangent through the curve's endpoints, resulting in the expression f'(c) = {F(b) -F(a)}/(b-a)

As per the given data in the table, the required solution would be below

The average rate of change in population between 2002 and 2004 as:

⇒ (76-83)/(2004-2002)

⇒ -7/2

⇒ -3.5

The average rate of change in population between 2002 and 2006

⇒ (78-83)/(2006-2002)

⇒ -5/2

⇒ -2.5

This represents the decrease in the population.

Therefore, the average rate of change in population is -35 between 2002 and 2004, and -2.5 between 2002 and 2006.

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The value of b would be 25/4.

An equation is an expression that shows the relationship between two or more numbers and variables.

Since the equation of the line is 2y = 4.5, where c is a constant, the y-coordinate of the intersection point must be c.

The parabola has a equation y = -4x² + bx, where bis a positive constant.

The solution to this quadratic equation will gives the x-coordinate(s) of the point(s) of intersection

Since it’s given that the line and parabola intersect at exactly one point, the equation y = -4x² + bx has exactly one solution.

A quadratic equation in the form ax²+bx+c has exactly one solution when its discriminant b²−4ac is equal to 0.

Therefore, if the line y = 22.5 intersects the parabola defined by exactly one point, then by = 25/4 .

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The amount of money donated by Jacy is $10.

Given that, Jacy made the first donation Gillermo’s donation was twice Jacy’s donation Rosa’s mother tripled what Aurora had raised so far now Aurora has $120.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Let the donation given by Jacy be $x.

Divide that amount by 4. One part is Guillermo's and Jacy's donation and three parts is the amount donated by Rosa's mother = 120 ÷ 4 = $30

Divide that amount by 3. One part is for Jacy's donation ($x) and two part is the amount Guillermo donated x = 30/3 = $10

Jacy was the first to donate. So, Jacy donated is $10

Therefore, the amount of money donated by Jacy is $10.

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There are 13 $20 bills and 17 $10 bills, respectively.

Constants and variables are used in conjunction to create linear equations. A linear equation with one variable is shown in the following standard form: Where a 0 and x is the variable, ax + b = 0.

Due to that,

There are 30 bills in all.

Total = $430

Let,

x = the number of $20 bills.

Amount in $10 banknotes = (30-x)

20x+10(30-x) = 430

20x+300-10x = 430

10x = 430-300

10x = 130

x = 13

$20 bills: x = 20; y = 13.

30 x = 30 13 = 17 = number of $10 banknotes

Therefore, there are 13 $20 bills and 17 $10 banknotes.

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total number of outcomes = 2 + 3 + 5 = 10

The probability of getting a white marble is:

The probability of getting a green marble is:

The events: getting a white marble and getting a green marble are independent since there is a replacement after each drawing. Then, the probability that the first marble was white and the second was Green is:

Answer:

Explanation:

First, the function, g(x):

The function g(x) oscillates, thus, it does not increase.

The value of 'e' is approximately 2.7.

Since 2.7 is greater than 2.5, we can infer that f(x) grows the fastest as x grows without bound.

A(-6, -2)→ A'(-6, 2) B(-3, -6) →B'(-3, 6) C(-2,-2)→ C'(-2, 2)​. The y-coordinates are different with the negative sign in the given transformations.

Given that,

A(-6, -2)→ A'(-6, 2) B(-3, -6) →B'(-3, 6) C(-2,-2)→ C'(-2, 2)​

We have to find the difference of the transformations.

So,

First take A(-6, -2)→ A'(-6, 2)

We can see the difference is the A of y-coordinates have negative sign of the A'.

Now,

Take B(-3, -6) →B'(-3, 6)

We can see the difference is the B of y-coordinates have negative sign of the B'.

Now,

Take C(-2,-2)→ C'(-2, 2)​

We can see the difference is the C of y-coordinates have negative sign of the C'.

Therefore, The y-coordinates are different with the negative sign in the given transformations.

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a. G(x) = 1/4x - 5 Since it's similar to the equation f(x)=mx + b, which is a linear

function, g(x) is a linear function.

b. f(x) = 2*(x - 1)^2 - 5 Since the degree of the polynomial is 2, we deduce it is a cuadratic function.

c. f(x) = 7 Since the degree of x is zero ( there is no x) , we deduce it is a constant function.

Answer: The answer is 570.

Step-by-step explanation:

So, if you know what numbers are, when you round, this question is easy. If you take a number line and put 570 on the left side and 580 on the right side, and 575 in the middle, you almost got it. Since the number we want to round is 573, we put it in the middle of 570 and 575. And since the number is closer to 570 than 580, the answer is 570. Your welcome!

a)The solution of the inequality is 3 < x ≤ 5

c) The solution in interval notation is (3, 5]

Step - by - Step Explanation:

What to find?

• The solution of the inequality.

• The graph of the inequality.

• The solution in interval notation.

Given:

7 < x +4 ≤ 9

Re-write the above inequality.

x + 4 > 7 or x + 4 ≤ 9

Solve for x in each case.

x + 4 > 7

Subtract 4 from both-side of the inequality.

x > 7 - 4

x > 3

x + 4 ≤ 9

Subtract 4 from both-side of the inequality.

x ≤ 9 - 4

x≤ 5

Combine the two solutions.

3Hence, the solution to the inequality is 3 < x ≤ 5

b) We can proceed to graph the inequality.

c) The solution in interval notation is (3, 5]

The coordinates of B after the translation is ( 3 , -2)

What is coordinates in maths?

Transformation involves changing the position of a shape.

The coordinates of B after the translation is (-4,-2)

A = ( 1, 1)

B = ( 3 , 4)

C = ( -1 , 8 )

The translation rule is given as ( x , y-6)

So, the coordinates of B' is calculated using

( x , y ) ⇒   ( x , y-6)

This gives

B = ( 3 , 4) ⇒  ( 3 , 4 - 6 )

( 3 , 4) ⇒ ( 3, -2 )

Rewrite as

B' = ( 3, -2 )

Hence, the coordinates of B after the translation is ( 3 , -2)

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The closest number to 6.3 is the number 40, because when we substract 6.3 from 40, we get the smallest number.

40 - 6.3 = 33.7

748 - 6.3 = 741.7

There is a 0.765 percent chance that the flight will leave on time when it is not raining.

Gonna determine how likely something is to occur, use probability. Many things are hard to predict with 100% certainty. We can only anticipate the possibility of an event occurring using it, or how likely it is. In the probability scale, 0 indicates an impossibility and 1 indicates a certainty.

Given a 0.1 delay probability, the probability of the airplane departing on time is 1-0.1 = 0.9.

The likelihood that it won't rain is 1-0.15 = 0.85.

If it weren't raining, there is a 0.9 (0.85) = 0.765 percent chance that a flight would leave on time.

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Answer:

Step-by-step explanation:

Given: The square STUV

To Determine: The coordinate of the image after reflection over the y-axis

Solution

The reflection over the y-axis rule is

Locate the coordinates of STUV

Let us apply the rule to get the coordinate of the image

Hence, the coordinate of the image after a reflection over the y-axis is

S'(10, - 10)

T'(0, - 10)

U'(0, 0)

V'(10, 0)

cos90° is equal zero

Solution

Population of the town = 3000

Rate = 4%

Amount = 4700

Find log of both side

Therefore the number of years it will take population to reach 4700 = 11.5yrs

Using the area of a triangle, the area of Mr. Knox's garden is: 58 square feet.

The area of any triangular shape can be calculated using the formula for the area of a triangle.

The area of a triangle = 1/2(base)(height).

The shape of Mr. Knox's garden is triangular. The parameters of his triangular garden are:

Length of the base of the triangular garden = 24½ ft

Height of the triangular garden = 8 ft.

Area of the garden = 1/2(24½)(8)

Area of the garden = 1/2(29/2)(8)

Area of the garden = 1/2(232/2)

Area of the garden = 232/4

Area of the garden = 58 square feet.

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Answer:

y = kx

Step-by-Step explanation:

An equation shows a proportion relationship when it can be written in the following format:

So, in the context of this exercise, we need to pass x to the other side of the equation dividing, by itself.

In this question:

y = k+x

x alone cannot be passed dividing, just k+x

Y = k, there is no x.

The answer is y = kx, because we can also write this as:

The volume of box will be 120 ft.³

What is volume ?

Volume is a three dimensional space occupy by the body of particular shape such as here :

Volume of cuboidal box = lbh

where, length "l" = 4 ft.

width "b" =  5 ft.

height "h" = 6 ft.  

now, the volume of box will be :

V = lbh

V = 4 x 5 x 6

V = 120 ft.³

Therefore, the volume of box will be 120 ft.³

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5.1 is greater than 5.099, because the value of the 1 in 5.1 is more than the value of the 99 in 5.099.

The value of 1 in 5.1 is 0.1, while the value of the 99 in 5.099 is 0.099.

Since 0.1 is bigger than 0.099, then 5.1 is bigger than 5.099.

Also, 5.1 is greater than 5.099 because a bigger number on 5.1 (which is 1) is closer to the decimal point compared to 5.099 (1 is bigger than 0). the closer a decimal is to the decimal point the higher its value.

The diagram of the problem is:

S is the length of the shorter side of the fence. L is the length of the longest side of the field.

We know that the perimeter of the rectangle is 800ft. This means:

And the area:

The smaller rectangles will have dimensions:

The area is:

As we can see, if we maximize the area of the bigger rectangle "A", we are also maximizing the area of the smaller rectangles "a".

Then, we have two equations:

We can solve for L in the first equation:

Then substitute in the second:

Simplify:

This is a function of the area depending on the length of the shorter side of the rectangle:

We can find the maximum of this function if we find the value where the derivative of this function is 0.

Let's differentiate:

And now we find where A'(S) = 0:

We have found that the shorter side must have a length of 200ft to maximize the area. Let's find the length of the larger side:

As expected, the quadrilateral which maximizes the area is the square. Thus, the dimensions of the field are 200ft x 200ft

We have that

The parts the will be rejected when it's above 95 or when it's under 85, if we plot the normal distribution it would be

Then, the percentage of the parts that will be rejected corresponds to the area in blue, then, we must calculate the area under the normal distribution for

The normal distribution is symmetrical, then calculate P(X < 85) is the same as P(X > 95), then we write it as

Calculate that integral is very hard, then, we must transform that in a standard normal X ~ N(0, 1) and use a table to find the result, to do that we must write a value z, it's a transformation to take a value on our normal and leads it to the standard normal, it's

We have X = 95, μ = 90 and σ = 2

Then 2.5 is the value we are going to search in our table, using the complementary cumulative table for 2.5 we get 0.00621, which means

And the total percentage will be

We can write it in percentage

Therefore, only 1.24% will be rejected.

It's a very low value, but it's expected because it's more than 2 standard deviations (95%).

Answer:

c. $16,092

Explanation:

• Fay is paid semimonthly, that is, ,twice a month,.

• There are ,12 months in a year,.

Thus, the number of paychecks she receives annually is: 2 x 12 = 24.

The net amount of each paycheck is $670.50.

In order to get her net annual income, multiply the net amount on each paycheck by the number of payments.

Fay's net annual income is $16,092.

Option C is correct.

For the given values the equation of new line is  y = -3x - 17

The formula for these lines is y = mx + b, where m denotes the slope and b the y-intercept. Our line has a slope of 3 and a y-intercept of -5, which we know from the question. By entering these numbers, we obtain the equation of our line as y = 3x - 5.

Given,

The equation of line is y= -3x+4

as the lines are parallel,

slope of lines will be same,

∴ Slope of new line = -3

The equation of line is:

y - y1 = m(x - x1)

Where x1, y1 are the given coordinates and m is the slope

⇒ y -(-5) = -3 (x - (-4))

⇒ y + 5 = -3 (x + 4)

⇒ y + 5 = -3x - 12

⇒ y = -3x - 17

∴  The equation of the line is y = -3x - 17

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We have the function that relates x and y expressed as:

a) We have to find the x-intercepts.

To do that we can use the quadratic equation:

Then, we have x-intercepts at x = -1 and x = 3.

b) We have to find the vertex.

We can find the x-coordinate of the vertex using the linear coefficient b = -0.4 and the quadratic coefficient a = 0.2:

It can also be calculated as the average of the x-intercepts.

Knowing the x-coordinate of the vertex, we can find the y-coordinate of teh vertex using the formula applied to x = 1:

Then, the vertex is (1, -0.8).

c) The minimum height will be given by the y-coordinate of the vertex.

Relative to the horizontal axis (y = 0), the minimum height will be -0.8 meters below that level.

Answer:

a) The x-intercepts are x = -1 and x = 3.

b) The vertex is (1,-0.8)

c) The minimum height is 0.8 units below the horizontal axis.

Finding the derivative of the function is just a way for us to discuss how the function changes. For example, if we want to get the derivative of function y, with respect to x (dy/dx), then it is a formal way of discussing, how y changes when x changes.

It will take 1 minute to tub to drain to his desired level, by Rate of change.

What is rate of change?

Rate of change is used to mathematically describe the percentage change in value over a defined period of time.

Given, starting water value = 42 and desired water level = 28

Rate of change = 14 gallons.

Let x be the time,

According to question,

42-14x=28

-14x=-14

x=1

Hence, it will take one minute.

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Answer:

28 N/m²

Step-by-step explanation:

Since you are calculating pressure, you want your question in N/m².

Note that the one side of the box has a length of 1.5m, and so to get the area of the bottom face, you need to square 1.5m::

(1.5m)² = 2.25m²

Then you need to use the formula P=F/A

Where P is pressure, F is force, and A is area, plug in your variables::

P = [tex]\frac{63N}{2.25m^{2} }[/tex]

Then you get an answer of:[tex]28 \frac{N}{m^{2} }[/tex]

You always want to make sure that the answer's units align with what you are told to solve for. In this case, they do, so no further steps are needed.

Hope this helps! :)

A. The depletion rate is $0.90 per ton.

B. The amount of depletion expense that Hidden Hollow Mining Co. should recognize for the current year is $15,345,000.

C. The adjusting journal entry to recognize the depletion expense is as follows:

Debit Depletion Expenses $15,345,000

Credit Accumulated Depletion $15,345,000

Adjusting entries are the journal entries made at the end of the accounting period to recognize unrecorded expenses, revenue, and other gains or losses.

An example of an adjusting entry is the entry to recognize depreciation, amortization, or depletion expenses.

The value of the mineral rights = $49,500,000

The estimated mineral deposit = 55,000,000 tons

Depletion rate = $0.90 per ton ($49,500,000/55,000,000)

The current year's tons mined and sold = 17,050,000 tons

Amount of depletion expense for the current year = $15,345,000 (17,050,000 x $0.90)

Depletion Expenses $15,345,000 Accumulated Depletion $15,345,000

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