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 equation of line is y = 30x + 75 , where the slope is m = 30 and the y intercept is 75

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 equation of line be represented as A

Now , the value of A is

Let the first point be P ( 1 , 105 )

Let the second point be Q ( 3 , 165 )

Now , the slope of the line is m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Substituting the values in the equation , we get

Slope m = ( 165 - 105 ) / ( 3 - 1 )

Slope m = ( 60 / 2 )

Slope m = 30

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

Substituting the values in the equation , we get

y - 105 = 30 ( x - 1 )

On simplifying the equation , we get

y - 105 = 30x - 30

Adding 105 on both sides of the equation , we get

y = 30x + 75

Hence , the equation of line is y = 30x + 75

To learn more about equation of line click :

https://brainly.com/question/14200719

#SPJ1

Answer:  160 yd^2

Step-by-step explanation:  (120 yards)*(16 inches)*(1 yard/12 inches) = 160 yd^2

Answer:

I=Prt

I/Pr=Prt/Pr

t=I/Pr

The reason why plant roots would take in water after a plant converts 1, 000 Sucrose molecules to 2, 000 glucose molecules.

Sucrose is turned into glucose by plants because glucose is more useful to plant processes than glucose.

The equation for this is:
sucrose + water → glucose + fructose

This means that if a plant should turn 1, 000 Sucrose molecules to 2, 000 glucose molecules, it would have used water to do this. This water needs to be replenished so the plant roots will take in more water.

Find out more on sucrose at https://brainly.com/question/1780920

#SPJ1

Answer:

1. -25

3. 15

5. -5/4

Explanation:

Considering the given functions for a(x)

1. To solve for a(8), we'll have to use the third function since we're given that x > 1 in the 3rd function and we know that 8 is greater than 1.

So we'll have;

3. To solve for a(-7), we'll use the 1st function because -7 is less than -6 and the condition is x <= -6;

5. a(-1/2)

In this case, we'll use the 2nd function is -1/2 lies between -6 and 1.

So, we'll have;

Dividing two polynomials may produce another polynomial only when the divisor has a lower degree than the dividend. Otherwise, it will generally result in a rational function.

No, dividing two polynomials may not result in another polynomial. It can produce a rational function.

A polynomial is an algebraic expression consisting of terms with non-negative integer exponents. When two polynomials are divided, the result is not always a polynomial.

If the degree of the polynomial being divided (dividend) is higher than the degree of the polynomial dividing (divisor), then the result can be a polynomial with a lower degree. However, if the degree of the divisor is equal to or greater than the degree of the dividend, the result will generally be a rational function, which is a ratio of two polynomials.

A rational function has the form P(x)/Q(x), where P(x) and Q(x) are polynomials and Q(x) is not equal to zero. The division can introduce terms with negative or fractional exponents, making the result a rational function rather than a polynomial.

For more such questions on polynomial

https://brainly.com/question/1496352

#SPJ8

Yes, the study group can claim a normal distribution of the sample means.

This is because when a group takes random samples from a population that has a normal distribution, the means of those samples will also follow a normal distribution. The reason for this is due to the Central Limit Theorem, which states that when a large enough number of samples are taken from a population, the distribution of the sample means will become more and more normal.

Since the study group is taking 20 random samples of 15 from a population with a normal distribution, it can be assumed that the means of the sample will have a normal distribution.  Therefore, when the study group draws 20 random samples of 15 from a population that has a normal distribution, they can be certain that the sample means will also follow a normal distribution.

To know more about Central Limit Theorem click here :

https://brainly.com/question/18403552

#SPJ11

Answer:

32.5 units²

Step-by-step explanation:

We can find the area by dividing the figure into two shapes. If we solve for the area of a square and a triangle, we can add them together.

First, we can solve for the area of the 5x5 square. To find the area, we can multiply the two dimensions.

5 · 5 = 25 units²

Next, we can find the area of the triangle. It has an equal height to the square, so the height of the triangle is 5 units. The width isn't specified. Instead, we are shown that the width of both the square and the triangle equals 8 units. If we subtract the width of the square from the total, we can find the width of the triangle, too.

8 - 5 = 3

So, the height and the width of the triangle are 5x3. To find the area we can multiply these together, and then divide the product by two.

5 · 3 = 15

\(\frac{15}{2}\) = 7.5

The area of the triangle is 7.5 units².

Finally, we can add the area of the triangle and the square together.

25 + 7.5 = 32.5

The area of the figure, then, is 32.5 units².

The answer is the last option.

I hope this helps ^^

Answer:

Hold on let me seee!!!!!!!

Answer:

D

Step-by-step explanation:

Each input can not have 2 outputs or else it’s not a function. 2 maps to 21 and 42. It MPs to two outputs. It’s not a function

Answer:

695 km/h

Step-by-step explanation:

3,475 / 5 = 695

Answer:

No

Step-by-step :

n/n + 1 > 1/2, (n + 1)/n < 2, (n+1)/n  - 2 < 0, [(n + 1) - 2n]/n < 0, (1 - n)/n < 0, n > 0, 1 - n < 0, n > 1

n/n + 1 < 99/101, (n + 1)/n > 101/99, [99(n+1)]/n > 101, [(99n + 99)]/n > 101, [(99n + 99)]/n - 101 > 0, (99n + 99 - 101n)/n > 0

(99 - 2n)/n > 0, n > 0, 99 - 2n > 0, 2n < 99, n < 99/2

1 < n < 49.5

Answer:

231.01

Step-by-step explanation:

Answer:

\( {x}^{2} - 3x - 10\)

Step-by-step explanation:

Area= length× width

\((x + 2)(x - 5) \\ {x}^{2} + 2x - 5x - 10 \\ {x}^{2} - 3x - 10\)

Answer:

Inequalities are used to demonstrate relationships between numbers or expressions. An inequality describes a relationship between two different values.

The notation  

a

<

b

means that  

a

is strictly smaller in size than  

b

, while the notation  

a

>

b

means that  

a

is strictly greater than  

b

.

The notion  

a

≤

b

means that  

a

is less than or equal to  

b

, while the notation  

a

≥

b

means that  

a

is greater than or equal to  

b

.

Inequalities are particularly useful for solving problems involving minimum or maximum possible values.

Step-by-step explanation:

\( \fbox{(2,5)}\)

Hello, substitute all the given coordinates & see if RHS match with LHS

given equation,

y = 4x-3

First coordinate,

(x,y) = (2,5)

5= 4×2-3

5=5

Hence, first solution satisfies the given equation,

let's solve for rest other cordinates,

second coordinate,

(x,y) = (5,5)

5= 4×5-3

5 ≠ 17

does not satisfy,

third coordinate,

(x,y) = (4,5)

5= 4×4-3

5 ≠ 13

does not satisfy,

fourth coordinate,

(x,y) = (4,5)

5 = 4×3-3

5 ≠ 9

does not satisfy.

Hence the correct answer is (2,5)

\( \sf \small Thanks \: for \: joining \: brainly \: community! \)

A. The total differential of the utility function U(X,Y) = X^αY^β is dU = αX^(α-1)Y^β dX + βX^αY^(β-1) dY.

B. The total differential of the utility function U(X, Y) = X^2 + Y^3 + XY is dU = (2X + Y) dX + (3Y^2 + X) dY.

A. The total differential of a function represents the small change in the function caused by infinitesimally small changes in its variables. In this case, we are given the utility function U(X, Y) = X^αY^β, where α and β are constants.

To find the total differential, we differentiate the utility function partially with respect to X and Y, and multiply the derivatives by the differentials dX and dY, respectively.

For the partial derivative with respect to X, we treat Y as a constant and differentiate X^α with respect to X, which gives αX^(α-1). We then multiply it by the differential dX.

Similarly, for the partial derivative with respect to Y, we treat X as a constant and differentiate Y^β with respect to Y, resulting in βY^(β-1). We then multiply it by the differential dY.

Adding these two terms together, we obtain the total differential of the utility function:

dU = αX^(α-1)Y^β dX + βX^αY^(β-1) dY.

This expression represents how a small change in X (dX) and a small change in Y (dY) affect the utility U(X, Y).

B. To find the total differential of the utility function U(X, Y) = X^2 + Y^3 + XY, we differentiate each term of the function with respect to X and Y, and multiply the derivatives by the differentials dX and dY, respectively.

For the first term, X^2, we differentiate it with respect to X, resulting in 2X, which is then multiplied by dX. For the second term, Y^3, we differentiate it with respect to Y, resulting in 3Y^2, which is multiplied by dY. Finally, for the third term, XY, we differentiate it with respect to X and Y separately, resulting in X (multiplied by dY) and Y (multiplied by dX).

Adding these three terms together, we obtain the total differential of the utility function:

dU = (2X + Y) dX + (3Y^2 + X) dY.

This expression represents how a small change in X (dX) and a small change in Y (dY) affect the utility U(X, Y).

Learn more about derivatives here: brainly.com/question/29144258

#SPJ11

Answer:

well, the value of x is unknown

Answer:

2c^2

Step-by-step explanation:

Simplify: 8c^3d^2/4cd^2.

The d^2 cancels out leaving 8c^3/4c. 8/4 = 2. c^3/c = c^2.

Therefore, your answer is 2c^2

Answer:

2c^2

Step-by-step explanation:

8c^3d^2 / 4cd^2= 2c^2

Answer:

Let's assume that the original price of petrol is x per liter.

After the increase of R1 per liter, the new price of petrol is (x+1) per liter.

According to the problem, with the new price, you can buy 7 liters less for R504, so we can write:

7(x+1) = 504

Simplifying this equation, we get:

7x + 7 = 504

Subtracting 7 from both sides, we get:

7x = 497

Dividing both sides by 7, we get:

x = 71

Therefore, the original price of petrol was Rx71 per liter.

Answer:

see explanation

Step-by-step explanation:

Given a parabola in standard form

f(x) = ax² + bx + c ( a ≠ 0 )

Then the discriminant Δ = b² - 4ac informs us about the nature of the zeros

• If b² - 4ac > 0 then 2 real and irrational zeros

• If b² - 4ac > 0 and a perfect square then 2 real and rational zeros

• If b² - 4ac = 0 then 2 real and equal zeros

• b² - 4ac < 0 then zeros are not real

Given

f(x) = 3(x - 4)² - 12 ← expand factor using FOIL

     = 3(x² - 8x + 16) - 12 ← distribute parenthesis by 3

     = 3x² - 24x + 48 - 12

     = 3x² - 24x + 36 ← in standard form

with a = 3, b = - 24 , c = 36 , then

b² - 4ac

= (- 24)² - (4 × 3 × 36

= 576 - 432      

= 144 ← a perfect square

Then 2 zeros are real and rational  and produce 2 x- intercepts

True, when plotting an ogive, the plotted points have x-coordinates that are equal to the upper limits of each class. This is because an ogive is a type of graph that shows the cumulative frequency of data in a given set.

The x-coordinates represent the upper limits of each class, while the y-coordinates represent the cumulative frequency up to that point. By plotting the points and connecting them with a line, we can see the overall distribution of the data and identify trends or patterns.To create an ogive, you first need to organize the data into class intervals and calculate the cumulative frequency or relative cumulative frequency for each interval. Then, you plot the points corresponding to the upper limits of each interval on the x-axis, and the cumulative frequency or relative cumulative frequency of each interval on the y-axis

Learn more about statistics and data visualization here:https://brainly.com/question/30665934

#SPJ11

Answer:

bc=  7

Step-by-step explanation:

Answer:

Area = 60

Step-by-step explanation:

you should get the height first

Answer:

67

Step-by-step explanation:

I got it right trust me

The critical t-value is approximately 1.753.

To find the critical value for a 96% confidence interval with a sample size of 15, we need to determine the t-value from the t-distribution table. The t-distribution table is a statistical tool used to determine the probability of a t-value given the degrees of freedom (df) and the desired level of significance (α).

In this case, we have a sample size of 15, which means our degrees of freedom are 14 (n - 1). Looking at a t-distribution table for 14 degrees of freedom and a 96% confidence interval.

This means that if we were to construct a confidence interval from a sample size of 15, the margin of error would be calculated by multiplying the critical t-value of 1.753 by the standard deviation of the sample and dividing by the square root of the sample size. The resulting interval would contain the population mean with 96% confidence.

It's essential to note that the critical value will change as the sample size and confidence level change. Therefore, it's crucial to use the correct table to find the corresponding critical values for a given dataset's sample size and confidence level.

For such more questions on critical

https://brainly.com/question/30459381

#SPJ8

Answer:

either

t - 41

or

41 - t

you choose I don't want to get u a bad mark

Hope this helped!

Step-by-step explanation:

The number of cubes that can be fitted in the crate is 22

To solve this problem, first calculated the volume of the crate and the volume of one cube, both of which are measured in cubic units (cubic centimeters, in this case).

We then divided the volume of the crate by the volume of one cube to find the number of cubes that can fit inside the crate.

Here we have

The dimensions of the crate are 2.4m × 1.8 m ×  1.1 m

The volume of the crate

= 2.4m × 1.8 m ×  1.1 m

=  4.752 m³

Given that side of the cube = 60 cm = 0.6 m

Hence, Volume of the cube = (0.6 m)³ = 0.216 m³  

Using the formula,

Number of boxes = Volume of box/ Volume of the cube

= 4.752 m³/0.216 m³ = 22

Therefore,

The number of cubes that can be fitted in the crate is 22

Learn more about Volume at

https://brainly.com/question/29568631

#SPJ1

Answer:

1/6 probability

Step-by-step explanation:

He only got one even number out of 6 attempts, so its a one in six 1/6.

Answer:

-4 = p

Step-by-step explanation:

3(p-4)=6p

1. Multiply the 3 by everything inside of the parenthesis.

3*p= 3p // 3*4= 12

3p-12=6p

2. divide both sides by 3 to make all the variables go to one side.

-12=3p

3. Divide both sides by 3 to make the variable stand on its own.

-4=p