In 2004, a school population was 2122. By 2009 the population had grown to 2647.

1) How much did the population grow between the year 2004 and 2009?

The slope of the line is,

m = - 1

Given that;

Two points on the line are (0, 5) and (5, 0).

Now,

Since, The equation of line passes through the points ((0, 5) and (5, 0).

So, We need to find the slope of the line.

Hence, Slope of the line is,

m = (y₂ - y₁) / (x₂ - x₁)

m = (0 - 5) / (5 - 0)

m = - 5 / 5

m = - 1

Thus, The slope of the line is,

m = - 1

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Answer:

Let x be the measure of the smaller angle.

The larger angle is 4x.

The sum of the angles in a kite is 360 degrees.

So, 100 + 100 + x + 4x = 360

6x = 160

x = 26.67

The larger angle is 4x = 106.67 degrees.

So the answer is 106.67

The solution is:

The average speed of bicyclist is 120 miles per hours

The speed of wind is 30 miles per hours .

Here, we have,

Given as :

The distance that bicyclist cover = d = 30 miles

The time taken by bicyclist to cover 30 miles = t = 5 hours

Let the average speed of bicyclist = x miles per hours

Let The speed of wind = y miles per hours

Now, biking into wind

The time taken in return by bicyclist = 5 hours

∵ Speed = Distance × time

i.e  x + y = d × t

∴  x + y = 30 miles × 5 hours

Or, x + y = 150 mi/h          ...........A

Again

Now, biking against wind

The time taken in return by bicyclist = 3 hours

∵ Speed = Distance × time

i.e  x - y = d × t

∴  x - y = 30 miles × 3 hours

Or, x - y = 90 mi/h                  ......B

Solving equation A and B

(x + y) + (x - y) = 150 mi/h + 90 mi/h

Or, (x + x) + (y - y) = 240 mi/h

Or, 2 x + 0 = 240 mi/h

∴   x = 240/2

i.e. x = 120 mi/h

So, The average speed of bicyclist = x = 120 miles per hours

Now, Put the value of x into eq B

∵ x - y = 90 mi/h

Or,  120 mi/h  - y = 90 mi/h

∴ y = 120 mi/h - 90 mi/h  

I.e.  y = 30 mi/h

So, The  speed of wind = y = 30 miles per hours

Hence, The average speed of bicyclist is 120 miles per hours

And The speed of wind is 30 miles per hours .

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complete question:

Biking into the wind on a flat path, a bicyclist takes 5 hours to travel 30 miles. The return bike takes 3 hours. The wind speed remains constant during the trip. What is the bicyclist's average speed in the air? What is the speed of the wind?

The meaning of "ϕ(x, y, p)" depends on the context in which it is used. Without further information, it is difficult to determine the specific meaning of this expression. However, in mathematics and physics, the symbol "ϕ" often represents a function or a potential.

Symbol "ϕ": The symbol "ϕ" is a Greek letter called "phi" and is commonly used to represent various concepts in mathematics and physics. It is often used to denote a scalar function or a potential.

(x, y, p): The variables x, y, and p represent the independent variables or parameters of the function or potential ϕ. The specific interpretation of these variables depends on the context of the problem.

Function or Potential: In mathematics, a function ϕ(x, y, p) maps elements from the domain (x, y, p) to corresponding values in the range. The function can represent various mathematical relationships or operations.

In physics, the symbol "ϕ" often represents a potential, such as the electric potential or gravitational potential. In this case, ϕ(x, y, p) would represent the potential function that depends on the variables x, y, and p.

Further Context: To fully understand the meaning of "ϕ(x, y, p)", additional information about the specific field of study or problem is necessary. Different disciplines may assign different meanings to this expression.

In conclusion, without additional context, "ϕ(x, y, p)" represents a function or potential with variables x, y, and p. The specific interpretation and meaning of this expression depend on the field of study or problem at hand.

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Answer:

hello

the answer is:

total mass = 3.94 + 14.81 + 11.27 + 7.65 = 37.65 kg

The number which is the result of the exponential expression [tex](-1)^x[/tex], in which x is an even number, is given as follows:

1.

The exponential expression representing the power x of the base -1 is given as follows:

[tex](-1)^x[/tex].

There are two possible results, given as follows, depending if x is even or odd:

For this problem, we have that the exponent x is an even number, hence the result is of 1.

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The margin of error is given as follows:

D) +- 6.7%.

A confidence interval of proportions has the bounds given by the rule presented as follows:

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which the variables used to calculated these bounds are listed as follows:

The confidence level is of 95%, hence the critical value z is the value of Z that has a p-value of [tex]\frac{1+0.95}{2} = 0.975[/tex], so the critical value is z = 1.96.

The margin of error is given as follows:

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

The parameters are given as follows:

[tex]n = 220, \pi = 0.38[/tex]

Hence the margin of error is given as follows:

[tex]M = 1.96\sqrt{\frac{0.38(0.62)}{220}}[/tex]

M = 0.067.

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y = 6x + 2 is the function which Adam charges a rate of $6 per hour and an additional fee of $2 for the bus fare.

The linear function in the form y = mx + b represents the situation where y represents the cost of the babysitting job

x represents the number of hours, "m" represents the hourly rate, and "b" represents the additional fee (bus fare).

y = 3x + 2 represents an hourly rate of 3 and an additional fee of 2.

y = 3x + 1 represents an hourly rate of 3 and an additional fee of 1.

y = 6x + 2 represents an hourly rate of 6 and an additional fee of 2.

y = -6x + 2 represents a negative hourly rate of -6 and an additional fee of 2.

Hence, y = 6x + 2 is the which Adam charges a rate of $6 per hour and an additional fee of $2 for the bus fare.

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Answer:

Step-by-step explanation:

median is 37 mode is 20

The total number of shirts in the dresser is 4y + ×. The correct option is A

We need to add up the number of shirts on each shelf.

The first shelf's shirt count is indicated with the number x.

y indicates how many shirts are present on each of the four remaining shelves.

We may add up the shirts on each rack to determine the overall number of shirts:

Total = x + y + y + y + y

Simplifying the expression, we have:

Total = x + 4y

Therefore, The total number of shirts in the dresser is 4y + ×.

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Answer:

x = 71

Step-by-step explanation:

using the rule of logarithms

[tex]log_{b}[/tex] x = n ⇒ x = [tex]b^{n}[/tex]

then

[tex]log_{4}[/tex] (x - 7) = 3 , then

x - 7 = 4³ = 64 ( add 7 to both sides )

x = 71

Answer:

D

Step-by-step explanation:

To reach this, you would divide both by half.

8.5 ÷ 2= 4.25

11 ÷ 2= 5.5

therefore, D

The value of x, applying the trigonometric ratios, is given by the following option:

B) 8.0.

The three trigonometric ratios are the sine, the cosine and the tangent, and they are obtained according to the rules presented as follows:

For this problem, we have that side x is opposite to the angle of 28º, while the hypotenuse has a length of 17.

Hence the length x is obtained as follows:

sin(28º) = x/17

x = 17 x sine of 28 degrees

x = 8.

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Vector v can be written as the sum of two vector components, [tex]v_x = -5i[/tex]  and [tex]v_y = 6j[/tex]

To write vector v as the sum of two vector components, we need to decompose it into two vectors along different directions.

v = -5i + 6j

w = 3i + 4j

We can decompose vector v into two components, one along the x-axis and the other along the y-axis.

Let's denote the component along the x-axis as [tex]v_x[/tex] and the component along the y-axis as [tex]v_y.[/tex]

The x-component, [tex]v_x,[/tex] represents the projection of vector v onto the x-axis and can be found using the dot product of v and the unit vector i:

[tex]v_x = v . i = (-5i + 6j) . i = -5i . i + 6j . i = -5[/tex]

Similarly, the y-component, [tex]v_y,[/tex] represents the projection of vector v onto the y-axis and can be found using the dot product of v and the unit vector j:

[tex]v_y = v . j = (-5i + 6j) . j = -5i . j + 6j . j = 6[/tex]

Now, we can write vector v as the sum of its components:

[tex]v = v_x + v_y = -5i + 6j[/tex]

So, vector v can be written as the sum of two vector components: -5i along the x-axis and 6j along the y-axis.

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For a call that is under six minutes, the cost is $0.70, the cost of a 14-minute call is $2.62 and the cost of a 9-minute call is $1.90.

For a call that is under six minutes, the cost is $0.70.

This is because the rate schedule specifies that for m ≤ 6 minutes, the cost is a flat rate of $0.70.

For a 14-minute call, we can apply the second part of the rate schedule. Since 14 > 6 and 14 is an integer, the formula to calculate the cost becomes:

c(m) = 0.70 + 0.24(m - 6)

Plugging in m = 14:

c(14) = 0.70 + 0.24(14 - 6)

c(14) = 0.70 + 0.24(8)

c(14) = 0.70 + 1.92

c(14) = 2.62

Therefore, the cost of a 14-minute call is $2.62.

c. For a 9-minute call, we again apply the second part of the rate schedule. Since 9 > 6 and 9 is not an integer, the formula becomes:

c(m) = 0.70 + 0.24([m - 6] + 1)

Plugging in m = 9:

c(9) = 0.70 + 0.24([9 - 6] + 1)

c(9) = 0.70 + 0.24(4 + 1)

c(9) = 0.70 + 0.24(5)

c(9) = 0.70 + 1.20

c(9) = 1.90

Therefore, the cost of a 9-minute call is $1.90.

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The total mass of the packages is 37.04 kg

In math, mass means the amount an object weighs. To find the mass we use a balance or weights. The units used to denote mass are gram (g) and kilogram (kg).

Given that:

Masses (KG) are 3.94, 14.18, 11.27 and 7.65 (KG) for Package 1 to 4 respectively.

The total mass of the packages is:

= 3.94 + 14.18 + 11.27 + 7.65

= 37.04 kg

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Answer:

Domain = (-∞, ∞) Range = (-∞, ∞)

End Behavior: As X -> -∞, Y -> -∞ | As X -> ∞, Y -> ∞

Inflection Point: (2,0)

Step-by-step explanation:

The final transformed graphs are 1) f'(x) = (1/2)|x + 1| + 3, 2) f'(x) = -√x + 1 and 3) f'(x) = -√x - 2.

1. Break down the transformations step by step.

Start with the function f(x) = |x|.

a. Shrink vertically by a factor of 1/2: Multiply the function by 1/2.

g(x) = (1/2)|x|.

b. Shift to the left 1 unit: Replace x with (x + 1).

h(x) = (1/2)|x + 1|.

c. Shift upward 3 units: Add 3 to the function.

f'(x) = (1/2)|x + 1| + 3.

Therefore, the equation for the final transformed graph is f'(x) = (1/2)|x + 1| + 3.

2. Start with the function f(x) = √x.

a. Reflect in the x-axis: Multiply the function by -1.

g(x) = -√x.

b. Shift 1 unit upward: Add 1 to the function.

f'(x) = -√x + 1.

Therefore, the equation for the final transformed graph is f'(x) = -√x + 1.

3. Start with the function f(x) = √x.

a. Reflect in the y-axis: Multiply the function by -1.

g(x) = -√x.

b. Shift 2 units down: Subtract 2 from the function.

f'(x) = -√x - 2.

Therefore, the equation for the final transformed graph is f'(x) = -√x - 2.

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Answer:

------------------

There are 12 months in a year.

Multiply 25 by the number of months to get the number of e-mails per year:

Answer:

300

Step-by-step explanation:

To calculate the number of emails sent in a year based on an average of 25 emails per month, you simply multiply the average monthly emails by the number of months in a year.

Average emails per month: 25

Number of months in a year: 12

Therefore,

Emails per month × Months per year

25 × 12 = 300 emails per year

So, on average, a person would send about 300 emails in a year.

Answer:

There are 47.2242 miles in 76 kilometers.

1.6 km = 1 mile

76 km = 76/1.6 = 47.5 mile

There are 47.5 miles in 76 kilometers.

Answer:

The area of a leaf is obtained by using a graph paper. A graph paper has small squares of area 1 mm 2 each. The area of the leaf will be equal to the number of squares it covers on the graph paper.

Step-by-step explanation:

Using the given percentage, we can see that there are a total of 430 police officers.

If the total number of police officers is N, we know that 60% of that have a ride-along, and 258 police officers have a ride along, then we can write the equation:

258 = 0.6*N

Now we can solve that equation for N (to do so, just divide both sides of the equation by 0.6), we will get:

258/0.6 = N

430 = N

In this way, we can see that the total number of police officers is 430.

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The measure of LA is . B'C'= 1, mLA' = 37"

A dilation is a mathematical operation that involves multiplying the distance between each point in an object and a fixed point, referred to as the center of dilation, by a constant factor known as the scale factor.

In the given scenario, the scale factor is specified as follows:

k = 1/3.

Consequently, the length of B'C' is obtained by multiplying the length of BC by 1/3, which can be understood as dividing the length by 3 after the dilation.

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Answer:

  C.  1000/x + 5000/(2x -10)

Step-by-step explanation:

You want the total time a climber spent when he climbed 1000 feet at x feet per hour, and 5000 more feet at (2x -10) feet per hour.

The relation between time, speed, and distance is ...

  time = distance / speed

The total time is the sum of the times for the two distances.

The time for 1000 ft at x feet per hour is ...

  time 1 = 1000/x

The rate for the second part of the climb was 10 ft per hour less than twice the first rate, so was ...

  2x -10

Then the time for 5000 ft at this rate is ...

  time 2 = 5000/(2x -10)

The total time spent climbing was ...

  total = time 1 + time 2

  total = 1000/x + 5000/(2x -10) . . . . . . matches choice C

__

Additional comment

The relation between speed, time, and distance is usually seen as ...

  speed = miles per hour

As a fraction, this is ...

  speed = distance / time

Above, we rearranged this to ...

  time = distance / speed

It's just another form of the relationship ...

  distance = speed × time

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To reduce his entertainment percentage to 12.5% of his total spending and allocate the savings to his grocery budget, he needs to decrease his entertainment spending and increase his grocery budget accordingly.

To reduce the entertainment percentage to 12.5% of his total spending, the individual needs to make adjustments to his budget.

Calculate the current entertainment percentage:

Let's assume the individual's total spending is $X, and the current entertainment spending is $Y.

The current entertainment percentage can be calculated by dividing Y by X and multiplying by 100.

Current entertainment percentage [tex]= (Y / X) \times 100[/tex]

Determine the desired entertainment spending:

To reduce the entertainment percentage to 12.5%, we need to find the new entertainment spending amount.

Let's call it Z.

Desired entertainment spending [tex]= 0.125 \times X[/tex]

Calculate the amount to be saved:

The amount to be saved is the difference between the current entertainment spending (Y) and the desired entertainment spending (Z).

Amount to be saved = Y - Z

Add the saved amount to the grocery budget:

The individual wants to add the money saved from the entertainment budget to the grocery budget.

Let's call the current grocery budget G.

The new grocery budget (G') will be:

New grocery budget = G + Amount to be saved

By following these steps, the individual can reduce his entertainment percentage to 12.5% of his total spending and allocate the saved money to the grocery budget.

It's important to note that the specific dollar amounts will depend on the individual's current spending and budget.

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Answer:

Hope this helps :)

Step-by-step explanation:

[tex]\frac{1}{2}[/tex] ÷ [tex]\frac{2}{3}[/tex]

When dividing by a fraction, we just have to multiply by the reciprocal, making the equation:

[tex]\frac{1}{2}[/tex] × [tex]\frac{3}{2}[/tex]

Then we multiply and end up with:

[tex]\frac{1}{2}[/tex] × [tex]\frac{3}{2}[/tex] [tex]=\frac{3}{4}[/tex]

The solution for the given expression is  7 + 5/12

First we need to write the expression, using fractions, we will get:

(5 + 6/8) + (4 + 4/15) - (2 + 6/10)

We can group like terms, and we will get:

(5 + 6/8) + (4 + 4/15) - (2 + 6/10) = (5 + 4 -2) + (6/8 + 4/15 - 6/10)

Now just simplify that to get.

(5 + 4 -2) + (6/8 + 4/15 - 6/10) =  7 + 3/4 + 4/15 - 3/5

                                                =  7 + 3/4 + 4/15 - 9/15

                                                = 7 + 3/4 - 5/15

                                                = 7 + 9/12 - 4/12

                                                 = 7 + 5/12

That is the answer.

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Answer:

50 students will pass

Step-by-step explanation:

100÷40=2.5

20×2.5=50

or another way is 20 is half of 40 so half of 100 is 50

Angle EFG is an angle with a measure of 42 degrees is drawn below.

Given that, angle EFG= 42 degrees.

Angle EFG is an angle with a measure of 42 degrees. To draw angle EFG, first draw a line segment and mark two points on the line segment. Label the two points E and F. Then, using a protractor, measure out an angle with a measure of 42 degrees from the line segment EF, starting from point E. Finally, mark the end of the angle as point G.

Therefore, angle EFG is an angle with a measure of 42 degrees is drawn below.

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