a new table needs to be added to the sports physical therapy database to track which sports the patients are playing. this data will be used to analyze the results of the therapies. assuming that many patients play multiple sports, how would you design the table?

The function increased to a maximum value and then decreased.

We know that a graph can be obtained when we plot the points of the data on a graph. In this case we can see that the data have been graphed accurately as we can see here.

If we look at the graph, we can see that the graph went up and then it started coming down. The implication of that is that the function has attained a maximum point and then began to decrease.

This is clear from the graph that has been shown.

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The solution to the equation is a = 3 1/3

From the question, we have the following parameters that can be used in our computation:

a + 5 and two-thirds = 9

Express properly

So, we have

a + 5 2/3 = 9

Subtract 5 2/3 from both sides of the equation

This gives

a = 9 - 5 2/3

Evaluate the difference

a = 3 1/3

Hence, the solution is a = 3 1/3

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Answer:

Step-by-step explanation:

The most precise term for the quadrilateral ABCD with vertices A(4, 7), B(6, 5), C(4, 1), and D(2, 5) is a trapezoid. A trapezoid is a quadrilateral with exactly one pair of parallel sides.

Answer:

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

Step-by-step explanation:

Originally our equation looks like [tex]x^{2}[/tex] + 2y

First, we want to substitute x = [tex]\frac{1}{2}[/tex]  & y= 0 into the equation.

The equation now looks like [tex]([/tex][tex]\frac{1}{2}[/tex][tex])^{2}[/tex] + 2 x 0

The brackets are added to the fraction as we are squaring the WHOLE fraction, and the 2y has a hidden multiplication sign, with it being 2 x y, so it is 2 x 0.

Now that we have our values substituted into the equation, we can solve it!

 [tex]([/tex][tex]\frac{1}{2}[/tex][tex])^{2}[/tex] = [tex]\frac{1}{4}[/tex]  

therefore,

[tex]\frac{1}{4}[/tex]  + 2 x 0

= [tex]\frac{1}{4}[/tex]

The horizontal line of length 7cm is added as an attachment

From the question, we have the following parameters that can be used in our computation:

Line = 7 cm

The following steps would create the perpendicular bisector

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The height of the other tree is 7.25 meters

From the question, we have the following parameters that can be used in our computation:

Using the above as a guide, we have the following:

Ratio = Height : Shadow

So, we have

Height : Shadow = 4 : 16

Simplify

Height : Shadow = 1 : 4

So, we have

Height : 29 = 1 : 4

This means that

Height = 29 * 1/4

Evaluate

Height = 7.25

Hence the height is 7.25 meters

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Answer:

The height of the other tree is 7.25 meters

Step-by-step explanation:

the bus value is depreciating, thus is Decay

[tex]\qquad \textit{Amount for Exponential Decay} \\\\ A=P(1 - r)^t\qquad \begin{cases} A=\textit{current amount}\\ P=\textit{initial amount}\dotfill &250000\\ r=rate\to 20\%\to \frac{20}{100}\dotfill &0.2\\ t=years \end{cases} \\\\\\ A = 250000(1 - 0.2)^{t} \implies \boxed{A = 250000(0.8)^t} \\\\\\ \stackrel{\textit{after 6 years, t=6}}{A=250000(0.8)^6}\implies \boxed{65536}[/tex]

Answer:

10.7 °

Step-by-step explanation:

In this problem, there are two angles with degrees of 2x + 6 and two angles of degrees of 15x - 8. We know the sum of the four angles is 360, as stated in the problem. Thus we can set up the following equation:

2(2x + 6) + 2(15x - 8) = 360

4x + 12 + 30x -16 = 360

34x - 4 = 360

34x = 364

x ≈ 10.7 °

Answer:

-3, 4

Step-by-step explanation:

First, we can simplify this expression by diving both sides by 6. Thus, we get x² - x - 12 = 0. Solving this, we get (x-4)(x+3). Thus, the solutions for x are 4 and -3. So, the answer is x = -3, 4

The equation of line is y = 12x and the number of boxes the shipping company can pack in 18 hour period is 216 boxes

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given data ,

Let the number of hours be x

Let the number of boxes be y

Let the equation of line be represented as A

Now , the value of A is

Let the first point be P ( 5 , 60 )

Now , the slope of the line m = y/x

Substituting the values in the equation , we get

Slope m = 60 / 5 = 12

Now , the equation of line is y - y₁ = m ( x - x₁ )

Substituting the values in the equation , we get

y - 60 = 12 ( x - 5 )

y - 60 = 12x - 60

y = 12x

Now , when x = 18 hours

y = 12 ( 18 ) boxes

y = 216 boxes

Hence , the number of boxes is 216 boxes

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Note that the line of reflection that reflects quadrilateral ABCD onto quadrilateral A'B'C'D' is given as attached. Note that when a shape is reflected, it must be reflected over a line. In this case, the line of reflection is y = -3.

A line of reflection is a line that acts as a mirror, reflecting a figure across the line so that the image is a mirror image of the original.

When a shape is reflected, it must be reflected over a line. The line of reflection of quadrilateral ABCD onto quadrilateral A'B'C'D is

From the given graph, we have the following observations

ABCD was flipped over to form A'B'C'D'

The line of reflection is between both shapes.

Using points C and C' as references;

We have:

C = (-3, -1)

C" = (-3, -5)

Notice that both points have the same x-coordinate

This means that the line of reflection is parallel to the x-axis and passes through the y-axis.

The point at which it passes through the y-axis is calculated using the mid-point formula.

Therefore, we have:

y = (y1+y2)/2

y = (-1-5)/2

y = -6/2

y = -3

Hence, the line of reflection is y = -3
See the attachment for the line of reflection.

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Answer:

Step-by-step explanation:

Answer:

8 hours

Step-by-step explanation:

We know that since Lila earns $12/hr and works 6 hr/week, she earned 72 since 12 * 6 = 72.

We can let the amount Patrick earns each week represent 9h, where h is the amount of hours he works.

We can solve for h by setting Patrick's equation equal to 72, which is Lila's earnings:

[tex]9h=72\\h=8\\\\9(8)=72\\12(6)=72[/tex]

The factor of quadratic equation is x√17

A quadratic equation is one that contains a second-degree polynomial. They are extensively utilized in a wide range of disciplines, including engineering, architecture, finance, biology, and, of course, mathematics.

Factoring is frequently the simplest way to solve a quadratic equation. Finding expressions that can be multiplied together to get the expression on one side of the problem is the process of factoring. A quadratic equation is represented as a product of linear terms if it can be factored.

First you need to find perfect square factors of 17

17 = 1*17

√17  = √1*√17 = 1√17 = √17

we had also √x² = x

So the answer is x√17

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The length of the cable is, 252.57 m.

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

Given that;

A cable is used to support a 245-m television tower.

And, the angle the cable makes with the ground is 78°.

Let the length of the cable = x

Hence, We can formulate;

⇒ sin 78° = 245 / x

⇒ 0.97 = 245 / x

⇒ x = 245/0.97

⇒ x = 252.57 m

Thus, The length of the cable is, 252.57 m.

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Bethany says, Using these exchange rates, £1 is worth 1.17 euros.

Step-by-step explanation

1 euro = 1.07 dollars

£1 = 1.25 dollars

Now ,

⇒ £1 = 1.25 dollars

⇒ £1 =

⇒ £1 =

⇒ £1 =

⇒ £1 =

⇒ £1 =1.17 euros

Therefore , Bethany says, Using these exchange rates, £1 is worth 1.17 euros.

The amount in the account after t years is given as follows:

A(t) = A(0)(1 + r)^t.

In which:

The standard definition of an exponential function is given as follows:

y = a(b)^x.

In which:

For an increasing exponential function, the rate of change is given as follows:

b = 1 + r.

In which r is the growth rate, as a decimal.

Considering that the balance increases according to the yearly dividend, the equation is given as follows:

A(t) = A(0)(1 + r)^t.

The problem is incomplete, hence the general procedure in obtaining the equation was presented, which can be used to analyze the statements.

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Answer:

4min:1min

Step-by-step explanation:

60:15

divide by 5

12:3

divide by 3

4:1

The center of gravity of the combination of the two circles is at (x, y) = (0, 4/5).

The center of gravity, or the center of mass, of a two-dimensional object can be found by taking the weighted average of the x-coordinates and y-coordinates of the individual masses making up the object.

In this case, the two circles can be treated as point masses, with the mass of each circle being proportional to its area. The area of a circle with radius r is given by pi * r^2.

So, for circle c1 with radius 2, its mass is given by:

m1 = pi * 2^2 = 4 * pi

And for circle c2 with radius 1, its mass is given by:

m2 = pi * 1^2 = pi

The x-coordinate of the center of gravity is given by the weighted average of the x-coordinates of the two masses:

x = (m1 * 0 + m2 * 0) / (m1 + m2) = 0

Similarly, the y-coordinate of the center of gravity is given by the weighted average of the y-coordinates of the two masses:

y = (m1 * 0 + m2 * 4) / (m1 + m2) = 4 * (m2 / (m1 + m2)) = 4 * (pi / (4 * pi + pi)) = 4 * (pi / 5 * pi) = 4/5

So, the center of gravity of the combination of the two circles is at (x, y) = (0, 4/5).

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Answer: true

Step-by-step explanation:

Step-by-step explanation:

What graph are we talking about?

Answer:

c (c - 8)

Step-by-step explanation:

c² - 8c

First, you have to find the GCF

The Greatest Common Factor is the factor that all have in common. Here the GCF is c

So, we factor c out and has left (c - 8)

So, our equation is

c (c - 8)

The area of the given given shape which consists of a triangle and a quarter circle to 1 decimal place would be =161.04m².

The formula used to calculate the are of triangle= ½base×height.

where; Base= 12m

height= 20-12 = 8 m

area = 1/2×12×8 = 48m²

The formula for the area of a quarter circle = πr²/4

where r = 12m

Area = 3.14 × 12²/4

= 3.14×144/4

= 452.16/4

= 113.04m²

Therefore, the area of the figure = 48+ 113.04 = 161.04m²

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Two gardeners can cut a similar field in three hours. A soccer field might be cut in two hours by six grounds-keepers, every one of whom works at a pace of one-6th of the field every hour.

To get the number of grounds-keepers expected to cut the very field in that timeframe, we should initially decide the speed at which the field can be cut in 3 hours, which is 1/3 of the field consistently.

To get the required number of groundskeepers, we partition this rate by the pace of every nursery worker, which is 1/6 of the field every hour, yielding the condition 1/3 / 1/6 = 2.

Subsequently, two nursery workers might cut similar regions in three hours.

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The expected value of M does not change in a predictable manner when sample size increases; it can increase, decrease, or stay the same.

The expected value of M, or the mean of a sample, is determined by the values of the individual elements that comprise it. As such, when the sample size increases, the expected value of M could increase, decrease, or remain constant, depending on the particular values of the individual elements in the sample. This is because the expected value of M is the average of the individual elements and the contribution of each element to the average depends on its value and the number of elements in the sample. Therefore, the expected value of M does not change in a predictable manner when sample size increases. Depending on the individual elements in the sample, the expected value of M could be higher, lower, or constant.

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One way we can check this is to simply multiply 15 by 12 to get 180.

Or you could even switch the numbers around.

But if we wanted to check it further, we can take the total and divide that by one of the multiplican or multipliers (15 or 12) to get the correct product.

Therefore, these are some ways to use the numbers 180, 15 and 12 in expressions.

The equations with no solutions are   −60x+32=−60x+60 and −60x+32=−60x−32. Options B and D

Algebraic expressions are described as expressions that are made up of terms, variables, coefficients, constants and factors.

They are also composed of arithmetic operations, such as;

From the information given, we have that the expression or equation without solutions are those with the value of x as 0.

−60x+32=−60x+60

collect like terms

-60x + 60x = 28

Hence, the equations are  −60x+32=−60x+60 and −60x+32=−60x−32

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When a region is rotated about the x-axis, a cylinder is formed. The volume of a cylinder is given by the formula V = πr²h, where r is the radius and h is the height of the cylinder.

The volume of a cylinder is the amount of space the cylinder takes up. It is found by multiplying the area of the cylinder's base by its height. The formula for finding the volume of a cylinder is V = πr²h, where r is the radius of the cylinder's base, and h is its height.

The radius of the cylinder is equal to the distance from the x-axis to the highest point on the graph of y = 9/(x² + 3x + 2).

To find the highest point on the graph, we differentiate the function and find the critical points.

Differentiating y = 9/(x² + 3x + 2):

dy/dx = -18x / (x² + 3x + 2)²

Setting dy/dx = 0 and solving for x:

-18x / (x² + 3x + 2)² = 0

x = -3, 2

For x = -3, y = 9/(-3² + 3(-3) + 2) = 9/1 = 9

For x = 2, y = 9/(2² + 3(2) + 2) = 9/8 = 1.125

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The First graph represents the equation y = 3x

The y intercept = 1.5

The horizontal asymptote = infinity

The y -intercept is a point at which the graph of the function touches the y -axis. It is only possible for a function to have zero or one y -intercept.

A horizontal asymptote of a graph is a horizontal line y = b where the graph approaches the line as the inputs approach ∞ or –∞.

Therefore the y intercept is 1.5 from the graph. and the horizontal asymptote is infinity

The power of the numerator is great than that of denominator.

3x²/1x^0

= 2/0

= infinity.

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The price paid for the chair will be $90.18

The price for the pen will be $4.23.

A percentage simply has to do with the a value or ratio which can be stated as a fraction of 100. It should be noted that when we want to we calculate a percentage of a number, we simply divide it and then multiply the value that is gotten by 100.

The price paid for the chair will be:

= $83.50 + (8% × $83.50)

= $90.18

The price for the pen will be:

= $4.50 - (60% × 4.50)

= $4.23

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Answer:

1 1/3  or just 1/3

Step-by-step explanation:

What percent of the shape is shaded in?

Alright to start, let's look at the shape, it is divided into 4 equal parts, one part is shaded, which gives us 1/4, or 25% or 0.25. Then there's another part, which is half shaded, that'll be half of 1/4 or 25% or 0.25, which is 1/8 or 12.5% or 0.125. Now all you have to do is add them together.

1/4 + 1/8 = 3/8

25% + 12.5% = 37.5%

0.25 + 0.125 = 0.3725

These are your three answers you can choose from, I guess the second one won't work because the problem states not to include a % sign.

Hope this helped!