In an exponential function, what does the 'a' represent?

(NEED HELP FAST , WILL GIVE BRAINLIEST!!!)

Kryger [21]

Answer:

Explained below.

Step-by-step explanation:

The data from the scatter plot is as follows:

Arm Span Height

19.5 25

35.5 35

37.0 39

40.5 40

44.5 45

45.5 50

49.0 49

51.0 55

52.5 47

59.0 60

61.0 58

(1)

Compute the value of slope and intercept as follows:

$\sum{X} = 495 ~,~ \sum{Y} = 503 ~,~ \sum{X \cdot Y} = 23822 ~,~ \sum{X^2} = 23660.5$

$\begin{aligned} b &= \frac{\sum{Y} \cdot \sum{X^2} - \sum{X} \cdot \sum{XY} }{n \cdot \sum{X^2} - \left(\sum{X}\right)^2} = \frac{ 503 \cdot 23660.5 - 495 \cdot 23822}{ 11 \cdot 23660.5 - 495^2} \approx 7.174 \\ \\m &= \frac{ n \cdot \sum{XY} - \sum{X} \cdot \sum{Y}}{n \cdot \sum{X^2} - \left(\sum{X}\right)^2} = \frac{ 11 \cdot 23822 - 495 \cdot 503 }{ 11 \cdot 23660.5 - \left( 495 \right)^2} \approx 0.857\end{aligned}$

The equation of the line of best fit is, y = 0.857·x + 7.174.

(2)

The slope of the line represent the rate of change in y caused by one unit change in x.

In this case the slope of m = 0.857 indicates that as the arm span increases by 1 unit the height increases by 0.857 units.

(3)

To perform the Residual Test, simply take two values from the table and interchange the x and y values.

Consider the values: (37, 39) and (51, 55)

Compute the value of y if x = 39:

$y = 0.857\cdot x + 7.174\\=0.857\times 39+7.174\\=40.597\\\approx 40.6$

The new value of y (40.6) is close to the original value (39.0)

Compute the value of y if x = 55:

$y = 0.857\cdot x + 7.174\\=0.857\times 55+7.174\\=54.309\\\approx 54.0$

The new value of y (54) is close to the original value (55)

Thus, it can be said that the line of best fit models the data provided.

(4)

The line of best fit is:

y = 0.857·x + 7.174

The slope of the line is positive.

This implies that there is a positive relationship between the two variables.

The formula of slope in terms of correlation coefficient is:

$\text{Slope}=r\times\sqrt{\frac{Var(x)}{Var(x)}}$

The correlation coefficient is directly proportional to the slope.

This implies that the correlation coefficient is also positive.

Thus, the variables Arm span and Height are positively correlated.

4 0

3 years ago

Find ratio equal to 4/5

Gnesinka [82]

An equivalent ratio to 4/5 is 8/10

7 0

3 years ago

Peter the optician sees 16 patients one Tuesday. 4 are neither short nor long sighted. The total number of short sighted patient

Juliette [100K]

Answer:

No of patients having longsightedness = 5

No of patient having shortsightedness = 7

Patients requiring varifocal lenses will be =12

Step-by-step explanation:

Total no of patients = 16

As

No of patients having neither long nor shortsightedness = 4

Let

No of patients having longsightedness = x

So

No of patient having shortsightedness = $x+2$

Equation becomes

$x+(x+2)+4= 16\\2x+6 = 16\\2x= 16-6\\2x= 10\\x= \frac{10}{2} \\x= 5$

Now

No of patients having longsightedness = x= 5

No of patient having shortsightedness = $x+2$ = $5+2$

= 7

Patients requiring varifocal lenses will be = 5+7

= 12

3 0

3 years ago

I have no idea how to do this please help

algol [13]

$\begin{gathered} a)slope\colon7 \\ b)y-intercept\colon-6 \end{gathered}$

1) As we can see this is a Linear Equation written in the Slope-intercept form:

$y=mx+b$

Note that "m" stands for the slope of the line, i.e. the measure of how steep a line is.

In the given equation, we can state that the slope is always accompanying the "x" therefore, the slope is m= 7

2) In addition to this, the y-intercept also called the Linear Coefficient is given by the letter"b" and represents the y-coordinate that the graph intercepts. Thus the y-intercept is -6

So we can state the following as the answers:

$\begin{gathered} a)slope\colon7 \\ b)y-intercept\colon-6 \end{gathered}$

And that is the answer

8 0

2 years ago

Luke wants to buy some pre-owned board

olga_2 [115]

Answer:

i think the answer is A

Step-by-step explanation:

3 0

4 years ago

In an exponential function, whatdoes the 'a' represent?​

In an exponential function, whatdoes the 'a' represent?