In 2010, there were approximately 6 million girls living in Orange City. In 2011, the population was down to 4 million girls. How many girls lived in Orange City in 2011 in comparison to 2010? Write your answer in scientific notation.

Question 1-

To determine which two points would a line of fit go through to best fit the data on the scatter plot, we need to visually analyze the pattern of the data points and choose two points that the line would pass through to represent the overall trend.

Without the actual scatter plot provided, I am unable to directly analyze it. However, based on the given answer choices:

A. (1,9) and (9,5)

B. (1,9) and (5,7)

C. (2,7) and (4,3)

D. (2,7) and (6,5)

Since I don't have the scatter plot, I cannot accurately determine which points would best fit the data. I would recommend carefully reviewing the scatter plot and selecting the two points that seem to represent the general trend or pattern of the data. The two points that form a line that closely follows the general direction of the data points would be the best choices.

Question 2-

To determine the slope of the relationship between the number of hours Laila danced, x, and the money she raised, y, we need to examine the graph and calculate the slope using the formula:

Slope = (change in y) / (change in x)

However, since the graph is not provided, it is not possible to directly calculate the slope. However, we can still evaluate the given answer choices based on their explanations:

A. The slope is 1/4, which means that the amount the student raised increases by $0.75 each hour.

B. The slope is 4, which means that the amount the student raised increases by $4 each hour.

C. The slope is 12, which means that the student will finish raising money after 12 hours.

D. The slope is 20, which means that the student started with $20.

From the explanations provided, it seems that option B would be the most reasonable choice. A slope of 4 would indicate that for each additional hour Laila danced, she raised $4. However, without the actual graph, it is challenging to confirm the accuracy of the answer choice or its real-world interpretation.

Let x represent the "smallest number" of a set of three unknown numbers.

• The greatest os 4 times the smallest, symbolically: 4x

• The middle number is three more than the smalles, symbolically x+3

• The sum of the smallest and the greatest is the same as 2 times the middle number, symbolically: x+4x=2(x+3)

Using the last expression you can clear the value of x (the smallest number)

x=2 → The smallest number of the set of three is 2

Now using this value and the given equivalencies we can calculate the midle and greatest number:

Middle number

x+3= 2+3= 5

Greatest number

4x=4*2=8

The set of three numbers is (2, 5, 8)

Answer:

No valid conclusion

Step-by-step explanation:

- All rhombuses are parallelograms

- Not all parallelograms are rhombuses because a rhombus has four equal-length sides and a parallelogram has equal opposite sides.

- all squares are rhombuses but not all rhombuses are squares because a square has 4 right angles (90 degrees) and a rhombus has equal opposite angles

The length and width of the plot that will maximize the area is 60 meters by 120 meters. The largest area that can be enclosed is 7200 square meters.

To maximize the area of the rectangular plot, Farmer Ed must use 9000 meters of fencing to enclose three sides of the plot. The fourth side, which borders the river, does not need to be fenced. To find the length and width of the plot that will maximize the area, the 9000 meters of fencing must be divided into two sides of equal length, with the remaining fencing used for the third side. This results in a length of 120 meters and a width of 60 meters, which maximizes the area of the plot. The largest area that can be enclosed is 7200 square meters.

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Answer:

The function that has a domain of 'x' greater-than-or-equal-to 5 and a range of 'y' less-than-or-equal-to 3 is;

\(y = -\sqrt{x - 5} +3\).

Step-by-step explanation:

The domain of a function are the possible 'x' values of the function

The range of a function are the possible 'y' values of the function

The given possible functions are;

1) \(y = \sqrt{x - 5} +3\)

The range of values for the above function are;

Domain; x ≥ 5

Range; y ≥ 3

2) \(y = \sqrt{x + 5} -3\)

The range of values for the above function are;

Domain; x ≥ -5

Range; y ≥ -3

3) \(y = -\sqrt{x - 5} +3\)

The range of values for the above function are;

Domain; x ≥ 5

Range; y ≤ 3

4) \(y = -\sqrt{x + 5} -3\)

The range of values for the above function are;

Domain; x ≥ -5

Range; y ≤ -3

Therefore, the required function is the third function, \(y = -\sqrt{x - 5} +3\).

Answer:

C on Edge2021

Step-by-step explanation:

Answer:

total number of students =60

Step-by-step explanation:

total number of students 60

used unfair means 1/3= 20

1/4 caught red handed 1/4 of 20= 5

The interval where f is positive is \(0 \le x < 1.5\)

The missing function is added as an attachment

From the attached graph, the function f(x) is positive from x = 0 to x = 1.5

As an interval notation, this can be represented as:

\(0 \le x < 1.5\)

Hence, the interval where f is positive is \(0 \le x < 1.5\)

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(a) 6x + 4y - 7z = 10, (b)L(x, y, z) = (6/7)x + (4/7)y + (2/7)z - 3/7, (c)The approximation to √(3.02)² + (1.97)² + (5.99)² is L(3.02, 1.97, 5.99) ≈ 5.908.

(a) Find the equation of the plane tangent to a level surface of f(x, y, z) at (3,2,6).

We have that, f(x, y, z) = √x² + y² + 2².

Thus,f(x, y, z) = g(x, y, z) = √x² + y² + 4 = k ⇒ x² + y² + (z-4)² = k².

Then, the equation of the plane tangent to a level surface of f(x, y, z) at (3, 2, 6) is obtained as follows.

Since f(3,2,6) = 7, the equation of the level surface isx² + y² + (z-4)² = 7².

Then the plane tangent to this level surface at (3, 2, 6) is

z = f(3,2,6) + fx(3,2,6)(x-3) + fy(3,2,6)(y-2), where fx(a, b, c) = ∂f/∂x(a, b, c) and fy(a, b, c) = ∂f/∂y(a, b, c).Now,

fx(x, y, z) = ∂f/∂x = 2x/2√x²+y²+4fy(x, y, z) = ∂f/∂y = 2y/2√x²+y²+4T

hus, fx(3,2,6) = 6/7fy(3,2,6) = 4/7and

the equation of the plane tangent to a level surface of f(x, y, z) at (3, 2, 6) is z = 7 + 6/7(x-3) + 4/7(y-2) which simplifies to 6x + 4y - 7z = 10.

(b) Find the linear approximation of f at (3,2,6) and then use it to find the approximation to the number √(3.02)2 + (1.97)² + (5.99)².

The linear approximation of f at (3,2,6) is

L(x, y, z) = f(3,2,6) + fx(3,2,6)(x-3) + fy(3,2,6)(y-2) + fz(3,2,6)(z-6),where fz(a, b, c) = ∂f/∂z(a, b, c).

Now, fx(3,2,6) = 6/7 and fy(3,2,6) = 4/7 and fz(3,2,6) = 2/7

Thus,L(x, y, z) = 7 + 6/7(x-3) + 4/7(y-2) + 2/7(z-6)which simplifies to L(x, y, z) = (6/7)x + (4/7)y + (2/7)z - 3/7.

(c)Now, we need to use this linear approximation to find the approximation to the number √(3.02)2 + (1.97)² + (5.99)².

We need to set x = 3.02, y = 1.97, and z = 5.99 in the linear approximation of f to get

L(3.02, 1.97, 5.99) = (6/7)(3.02) + (4/7)(1.97) + (2/7)(5.99) - 3/7 = 5.908.

The approximation to √(3.02)² + (1.97)² + (5.99)² is L(3.02, 1.97, 5.99) ≈ 5.908.

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Answer:

17 1/2

Step-by-step explanation:

make the 1 3/4 into completely quarters which would be 7/4 and then multiply by 10

\( \frac{7}{4} \times \frac{10}{1} \)

then multiply from across and simplify

Use the 3-point curved line drawing tool to draw the average cost curve for quantities q = 1, q = 2, and q = 3. Connect these points smoothly to form the average cost curve.

To calculate the formulas for average fixed cost (AFC), marginal cost (MC), average variable cost (AVC), and average cost (AC) based on the cost function C = 6 + 8q, we can use the following equations: Average Fixed Cost (AFC): AFC = Total Fixed Cost (TFC) / Quantity (q). Since the cost function C = 6 + 8q does not have any fixed cost component, AFC would be zero. Marginal Cost (MC): MC = Change in Total Cost (ΔTC) / Change in Quantity (Δq). The cost function C = 6 + 8q has a constant marginal cost of 8. Average Variable Cost (AVC): AVC = Total Variable Cost (TVC) / Quantity (q). Since the cost function C = 6 + 8q does not have any variable cost component, AVC would be the same as MC, which is 8.

Average Cost (AC): AC = Total Cost (TC) / Quantity (q); AC = (Total Fixed Cost + Total Variable Cost) / Quantity; AC = (6 + 8q) / q; AC = 6/q + 8. Now, for the graphical representation: Use the line drawing tool to draw the marginal cost curve, which is a straight line with a slope of 8. Label this line 'MC'. Use the 3-point curved line drawing tool to draw the average cost curve for quantities q = 1, q = 2, and q = 3. Connect these points smoothly to form the average cost curve. Label this curve 'AC'. Please note that the shape and position of the curves will depend on the specific quantities chosen, but the general trend will be a downward-sloping MC curve intersecting the U-shaped AC curve.

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12!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Answer:

No.

General Formulas and Concepts:

Alg I

Step-by-step explanation:

Step 1: Define function

3x - 2 = y

Step 2: Compare

3x - 2 = y

Ax + By = C

It is not in standard form. The y should be with the x and the constant should be isolated.

Step-by-step explanation:

can we just 180° minus with all the angle?

180° - 67° - 75° =

The value of b is degree 104.we can find by using vertically opposite theorem.

Vertical Angles are when two lines intersect each other then the opposite angles formed due to intersection are called vertical angles or vertically opposite angles. A pair of vertically opposite angles are always equal to each other.The point where they meet is called a vertex.

Vertical opposite angles that are opposite each other when two lines cross are also known as vertical angles because the two angles share the same corner. Opposite angles are also congruent angles meaning they are equal or have the same measurement.

Now we have

(b-308)=(-2b+4)

b+2b=4+308

3b=312

b=104

Hence the value of b is 104 degree.

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Answer:

She can make 8 whole dumplings.

Step-by-step explanation:

Divide 5 \(\frac{3}{4}\) by \(\frac{2}{3}\).

Answer:

The $19 car

Step-by-step explanation:

For a one day rental I'd say its pretty average to only be driving for about 160km which is about 100 miles. For those 160km you would only be paying $19. The combined total $38, which is still less than the $42.50 car. The only way this would somewhat equal out is if you drove 200km or 124 miles. That would make the total cost exactly $43. If Meghan plans on driving equal to or more than 200km then she should choose the $42.50 car. In my opinion the $19 should be enough for 1 day.

Explanation:

The blue rectangle has area of 4a^2*6a^2 = 24a^4

The red rectangle has area 4a^2*9a = 36a^3

The green rectangle has area 4a^2*3 = 12a^2

The total area is 24a^4 + 36a^3 + 12a^2

The points with integer coordinates in this rectangular region will be above 50.

You must use graph paper and draw the rectangle. You must draw the picture in order to solve the problem. It is not easy to visualize the rectangle, the coordinates and count the points inside it all at the same time without a picture to help you. You must draw it.


Once you draw it, the vertices are (5,4), (5,-4), (-5,-4) and (-5,4) in the clockwise directions starting from the upper left corner.

Since we are interested in points that are strictly inside the rectangle -4 < y < 4 and -5 < x < 5;
That is y = -3,-2,-1,0,1,2,3 and x = -4,-3,-2,-1,0,1,2,3,4


The points with integer coordinates that are strictly inside the rectangle are then:



(-4,3)   (-3,3),   (-2,3),   (-1,3),   (0,3),   (1,3),   (2,3),   (3,3),  (4,3)
(-4,2)   (-3,2),   (-2,2),   (-1,2),   (0,2),   (1,2),   (2,2),   (3,2),  (4,2)
(-4,1)   (-3,1),   (-2,1),    (-1,1),  (0,1),   (1,1),    (2,1),  (3,1),  (4,1)
(-4,0)   (-3,0),   (-2,0),    (-1,0)   (0,0),   (1,0),    (2,0),   (3,0),  (4,0)
(-4,-1)  (-3,-1),  (-2,-1),  (-1,-1), (0,-1),  (1,-1),  (2,-1),  (3,-1), (4,-1)
(-4,-2) (-3,-2),   (-2,-2), (-1,-2),  (0,-2),  (1,-2),  (2,-2),  (3,-2), (4,-2)
(-4,-3) (-3,-3),   (-2,-3), (-1,-3),  (0,-3),  (1,-3),   (2,-3), (3,-3), (4,-3)

So, The points with integer coordinates in this rectangular region will be above 50.

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The points with integer coordinates in this rectangular region will be above 50.

You must use graph paper and draw the rectangle. You must draw the picture in order to solve the problem. It is not easy to visualize the rectangle, the coordinates and count the points inside it all at the same time without a picture to help you. You must draw it.

Once you draw it, the vertices are (5,4), (5,-4), (-5,-4) and (-5,4) in the clockwise directions starting from the upper left corner.Since we are interested in points that are strictly inside the rectangle -4 < y < 4 and -5 < x < 5;

That is y = -3,-2,-1,0,1,2,3 and x = -4,-3,-2,-1,0,1,2,3,4

The points with integer coordinates that are strictly inside the rectangle are then:

(-4,3)   (-3,3),   (-2,3),   (-1,3),   (0,3),   (1,3),   (2,3),   (3,3),  (4,3)

(-4,2)   (-3,2),   (-2,2),   (-1,2),   (0,2),   (1,2),   (2,2),   (3,2),  (4,2)

(-4,1)   (-3,1),   (-2,1),    (-1,1),  (0,1),   (1,1),    (2,1),  (3,1),  (4,1)

(-4,0)   (-3,0),   (-2,0),    (-1,0)   (0,0),   (1,0),    (2,0),   (3,0),  (4,0)

(-4,-1)  (-3,-1),  (-2,-1),  (-1,-1), (0,-1),  (1,-1),  (2,-1),  (3,-1), (4,-1)

(-4,-2) (-3,-2),   (-2,-2), (-1,-2),  (0,-2),  (1,-2),  (2,-2),  (3,-2), (4,-2)

(-4,-3) (-3,-3),   (-2,-3), (-1,-3),  (0,-3),  (1,-3),   (2,-3), (3,-3), (4,-3)

So, The points with integer coordinates in this rectangular region will be above 50.

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Answer:

8 Nickels

Step-by-step explanation:

Since a Nickel is worth 5 cents ($0.05)

And a Quarter is worth 25 ($0.25)

and theres 22 coins

8 of those coins would be nickels which would mean we add 8 nickels up

8 x 0.05 = 0.4

then we add the quarters up

14 x 0.25 = 3.5

3.5 + 0.4 = $3.90

The average power output of a bike rider at a speed of 20 miles per hour is 556 W

Given, Riding a bike burns 100 Calories per mile. Speed of riding a bike is 20 miles per hour. Power is a measure of the rate at which work is done over time.

Therefore, the formula for average power is given by,

P = W/t

Where, P is power, W is work and t is time.

Now, We know that riding a bike burns 100 Calories per mile, but we have to find out the work done.

So, work done = 100 Calories × distance traveled= 100 × 1.609 × 1000 = 160900 J

Time taken = distance/speed= 1.609/20 = 0.08045 hours

Putting values in the formula of power, we get,

P = W/t= 160900/0.08045= 1999999.9 J/hour

Converting hour to seconds,1 hour = 3600 seconds1 J/s = 1 watt1 J/hour = 1 / 3600 watt

Therefore, power = 1999999.9 / 3600= 555.5556 watts (approx)

Therefore, the average power output of a bike rider at a speed of 20 miles per hour is 556 W (approx). Answer: 556

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Answer: E

Step-by-step explanation:

The solution means the intersection point, so in this case, it's (3, 2). The intersection point represents a value that is true for both equations, which is why it's considered the solution.

Answer:

Step-by-step explanation:

4x-18>2

4x>2+18

4x>20

x>20/4

x>5      from this it seems that number line 2 is correct

-17x-8≤-25

-17x≤-25+8

-17x≤-17

x≤ 1    from this it is clear that number line 3 is  correct

The probability that the point will also be inside the circle will be 0.7854.

Its fundamental concept is that someone will nearly surely occur. The proportion of positive events in comparison to the total of occurrences.

Then the probability is given as,

P = (Favorable event) / (Total event)

A square has a circle inside it. If a square's the inside point is chosen at random.

The length of the edge of the square and the diameter of the circle will be congruent. Then the probability that the point will also be inside the circle will be given as,

P = [(π/4)a²] / [a²]

P = π/4

P = 0.7854

The probability that the point will also be inside the circle will be 0.7854.

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The equation to model the population is P = \(\frac{1}{40}\) \(e^{0.05t}\) + 30

Here the population P of a small town, measured in hundreds, is modeled by the inverse of the function,P−1(t) = 20ln(40t − 1200)

where t is measured in years.

We need to find an equation to model the population.

let y = \(p^{-1}\)(t)

where t is measured in years.

We need to find an equation to model the population.

20\(ln\)(40y - 1200) = t

\(ln\)(40y - 1200) = t/20

\(e^{ln(40y - 1200)}\) = \(e^{0.05t}\)

(40y - 1200) = \(e^{0.05t}\)

40y = \(e^{0.05t}\) + 1200

y = \(\frac{1}{40}\) \(e^{0.05t}\) + 30

Now, we determine the initial value.

P(0) = \(\frac{1}{40}\) + 30

P(0) = 30

The equation to model the population is P = \(\frac{1}{40}\) \(e^{0.05t}\) + 30

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Answer:

7% decrease

Step-by-step explanation:

12500 - 11625 = 875

875/ 12500 = 0.07

0.07 × 100 = 7

Answer:

7%

Step-by-step explanation:

Step-by-step explanation:

Brian takes = 43 minutes

Colin takes = 1 hour = 60 minutes

In ratio,

43/60

Answer:

\( length = 12 ft \)

\( width = 8 ft \)

Step-by-step explanation:

Earl's garden:

\( length = (x + 6) ft \)

\( width = (x + 2) ft \)

\( perimeter = 2(length) + 2(width) \)

\( perimeter = 2(x + 6) + 2(x + 2) \)

\( perimeter = 2x + 12 + 2x + 4 = (4x + 16) ft \)

Dylan's garden:

\( length = (2x - 2) ft \)

\( width = (x + 4) ft \)

\( perimeter = 2(length) + 2(width) \)

\( perimeter = 2(2x - 2) + 2(x + 4) \)

\( perimeter = 4x - 4 + 2x + 8 = (6x + 4) ft \)

Generate an equation to solve for the value of x.

Since the perimeters of both gardens are the same, therefore:

\( 6x + 4 = 4x + 16 \)

Collect like terms

\( 6x - 4x = - 4 + 16 \)

\( 2x = 12 \)

Divide both sides by 2

\( x = 6 \)

Earl's garden:

\( length = (x + 6) ft \)

Plug in the value of x

\( length = 6 + 6 = 12 ft \)

\( width = (x + 2) ft = 6 + 2 = 8 ft \)

Answer:

l: 12ft

w: 8ft

Step-by-step explanation:

There is no solution to the system. This means that the equation 2 = -2 in the system is inconsistent.

What is a system of equations?

A system of equations is a collection of two or more equations that are solved simultaneously. Each equation in the system represents a constraint or condition that must be satisfied, and a solution to the system is a set of values that satisfies all of the equations in the system simultaneously.

If you attempt to solve a system of equations and you get a statement like 2 = -2, it means that the equations in the system are inconsistent. An inconsistent system of equations has no solution because there is no set of values that can simultaneously satisfy all of the equations.

Hence, as these equations are contradictory, there is no solution to the system. This means that the equations in the system are inconsistent.

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The perimeter of rectangle ABCD is 12 sq. Units

The perimeter of rectangle is defined as the sum of all the sides of a rectangle.

For any polygon, the perimeter formulas are the total distance...

The vertices of the rectangle A (-2,1), B (3,1), C (3,4), and D (-2,4)

From the graph,

The coordinates of point Dare (3,3).

Area of rectangle ABCD=l × b=AB×BC

On further calculation we get

Area of rectangle ABCD=6×2

Area of rectangle ABCD=12 sq. Units

Hence, the perimeter of rectangle ABCD is 12 sq units.

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