1
Is the point (5,-2) a solution for the function: y = 2/5x + 1
(A) Yes
B) No

Finding the average deviation from the mean of all the data points yields the mean absolute deviation, or MAD, which is a measure of variability.

The term "variability" refers to the distance between data points within a distribution and their distance from its center. Measurements of variability give you descriptive statistics that summarize your data in addition to measures of central tendency. Spread, scatter, and dispersion are other terms for variation. The range of extremes, or an interval containing all cases from the smallest to the largest, is one way to characterize variation. The benefit of describing variance through extremes is that every scenario is covered by the range.

Given Data

a) Following are the measures of shape and spread:

On Data set A,

Shape - Non symmetric

Spread - Mean

On Data set B

Shape - Symmetric

Spread - Broad distribution

On Data set C

Shape - Skewed left

Spread - Narrow distribution

b) Measure of variation:

Finding the average deviation from the mean of all the data points yields the mean absolute deviation, or MAD, which is a measure of variability.

c) Importance of variation:

Measures of variation can be used to express important details about data sets. It's crucial to understand the various measures of variance because variability might reveal information about data that is relevant. You can use this data efficiently if you are aware of the measurements of variance.

To learn more about variation, visit:

https://brainly.com/question/13154114

#SPJ13

Answer:

m > -7 OR m < -10

Step-by-step explanation:

5 + m > -2

5 + m + 2 > 0

5 + 2 > - m

7 > -m

-7 > m

2m < -20

m < -20 / 2

m < -10

Given:

A population of rabbits is growing at the rate of 23% per annum.

Required:

To find the number of years that the population would double.

Explanation:

If growth rate remain constant, total number of years it will take to double the population “n" will be:

(where r is annual growth rate)

Hence, for your question it would be

Final Answer:

3 years.

Answer:

x = 24.2

y = 12.1

Explanation:

The side with length x, the side with length 21, and the angle of 60° are related by the trigonometric function sine, so:

Therefore, solving for x, we get:

Then, sin 60 = 0.86, so the value of x is:

In the same way, the value of y is related by the trigonometric function tangent as:

So, solving for y, we get:

Since tan 60 = 1.73, we get:

Therefore, the answers are:

x = 24.2

y = 12.1

EXPLANATION

Given the polynomials in the problem, we can assevere that:

Formula of Perfect Square Trinomial:

(a+b)^2 = a^2 + 2ab + b^2

Difference of Squares formula:

(a^2 - b^2)

Now, we need to find what formula match better.

y^2 + 12y - 36 -----> Neither

Let:

T = number of toppings

P(T) = total price Sean will pay

B = Sean's budget

since the cost of the pizza cannot exceed Sean's budget:

Answer:

On my side I do not see an attached image.

The perpendicular bisector of AB will fall at is (8, 8) and (8, 2)

From the question, the coordinates of the points are given as

A = (4, 10), B = (12, 6), and C = (8, 2).

Remove the coordinates of point C

So, we have the remaining coordinates to be

A = (4, 10) and B = (12, 6)

The perpendicular bisector of AB is the midpoint of endpoints AB

The coordinates of this perpendicular bisector is then calculated using the following midpoint formula

Midpoint = 1/2 * (x₂ + x₁, y₂ + y₁)

Where

(x, y) = (4, 10) and B = (12, 6)

Substitute (x, y) = (4, 10) and B = (12, 6) in Midpoint = 1/2 * (x₂ + x₁, y₂ + y₁)

Midpoint = 1/2 * (4 + 12, 10 + 6)

Evaluate the sum

So, we have

Midpoint = 1/2 * (16, 16)

Evaluate the product

So, we have

Midpoint = (8, 8)

Hence, the point of the perpendicular bisector of AB is (8, 8)

Read more about perpendicular bisector at

https://brainly.com/question/11006922

#SPJ1

Direct variation equations have the following form:

Where "k" is the Constant of variation.

In this case, analyzing the information given in the exercise, you know that the equation for that Direct variation has this form:

You know that:

When:

So you need to make the conversion from feet to miles. Since:

You get:

Then, you can find the value of "k" as following:

The option that is true about the parabola that opens up and has a vertex in the fourth quadrant, and for which the equation is y = a·x² + b·x + c is; a < 0, b > 0, c < 0

The general form of the equation of a parabola is; y = a·(x - h)² + k, where, (h, k) is the vertex of the parabola.

The effect of the coefficients on the graph of a parabola are as follows;

The equation of a parabola is f(x) = a·x² + b·x + c

When the value of a is positive, the parabola opens upwards and when a is negative, the parabola opens downwards.

When a is positive and the coefficient b is negative, or when a is negative and b is negative the axis of symmetry, and therefore, the graph shifts to the right.

The axis of symmetry shifts left when both a and b have the same sign

The constant c determines the y-intercept such as c increases, the y-intercept also increases.

A parabola that opens downward has a negative value of a (a < 0)

A parabola in the fourth quadrant is shifted right, therefore, b is positive (b > 0)

The ty-intercept in the fourth quadrant has a negative y-value, therefore, the constant, c < 0

The correct option is therefore; a < 0, b > 0, c < 0

Learn more about the equation and graph of a parabola in  here:

https://brainly.com/question/28001061

#SPJ1

Answer:6

Step-by-step explanation:

11-5=6 therefore x=6

Ella practices piano for 45 minutes.

She spends m minutes longer working on homework

From the question, The total minutes Ella spend on piano is 45 minutes

If she spend m minutes longer

In mathematics, more in word problem means addition

Total minutes spend on her home work is

m + 45

Let T be the total time she spendon her homework

T = Additional m minutes + 45 minutes spend on her piano

T = m + 45

The answer is T = m + 45

f(x)=2x²-8x+6



Find the AXIS OF SYMMETRY and VERTEX. PLACE THE VERTEX AS THE MIDDLE ROW.

Number up and down, then complete the table.

GRAPH!

f(x)=2x²-8x+6 -------> is a vertical parabola open upward

The vertex represent a minimum

Convert the quadratic equation into vertex form

y=a(x-h)^2+k

where

(h,k) is the vertex

Complete the square

f(x)=2x²-8x+6

Factor 2

f(x)=2(x^2-4x)+6

Complete the square

f(x)=2(x^2-4x+4-4)+6

f(x)=2(x^2-4x+4)+6-8

f(x)=2(x^2-4x+4)-2

REwrite as perfect squares

f(x)=2(x-2)^2-2

therefore

The vertex is the point (2,-2)

In a vertical parabola, the axis of symmetry is equal to the x coordinate of the vertex

so

x=2

using a graphing tool

see the attached figure

please wait a minute

we have

f(x)=2x²-8x+6

where

a=2

b=-8

c=6

the formula to calculate the axis of symmetry is

x=-b/2a

substitute the given values

x=-(-8)/(2*2)

x=8/4

x=2

Answer:

Step-by-step explanation:

We can see that Mr. Conners is descending the miles he drove, let's see if it is a constant descending:

It means he is driving 21/16 miles less on each day, then for Thursday:

Since interior angles of any triangle add up to 180 degrees, we have

Now, by substituting the given values, we get

which gives

Then, by subtracting 141.6 to both sides, we have

Then, by comparing with the given options, the answer is the last option.

Looking at the function f(x), it is in the factored form, so we can easily find the zeros of the function (that is, the x-intercepts) by equating each factor to zero:

The x-coordinate of the vertex is given by the average value of the zeros:

And the y-intercept can be found by using x = 0:

So the graph of this quadratic equation is given by:

Answer:

0.83

Explanation:

Since the probability P(Z > a) = 0.204< 0.5, 'a' must be lying on the right of zero. Draw the graph.

Find P(0 < Z < a).

Find 'a' from the standard normal table.

From the table, P(0 < Z < 0.83) = 0.2967. Thus, 'a' approximately equals 0.83.

The quetion provides two functions, that is f(x) and g(x).

For what value of x is f(x) = g(x)

We can solve this by simply equating both functions, as shown below;

The answer is, when x = 3

**Note**

Thi can also be solved graphically and at the point where the graph of both function intersect, we'll have our answer. The graphs of f(x) and g(x) is shown below;

Note that the blue line represents

The green line represents

Observe carefully that both graphs intersect at the point -3.

Therefore, the value of x that makes f(x) = g(x) is -3

Firstly, the student's graph is not a correct representation of the piecewise function, We would consider each function.

1. f(x) = x + 3 for x ≤ - 2

The graph is correct but the interval was not represented correctly. To correct it, the circle at x = 2 should be solid

2) f(x) = x^2 - 1 for - 2 < x < 1

The graph is correct but the interval was not represented correctly. To correct it, the circles at x = - 2 and x = 1 shouldn't be solid

3) f(x) = log2(- x + 3) for 1 ≤ x < 3

The graph is not correct. To correct it, values of x should be substituted into the function and the correct values of y or f(x) would be calculated for. These values of x and y should be used to plot the graph again. For the intervals, the circle at x = 1 should be solid while the circle at x = 3 shouldn't be solid

Answer:

Shortest = 7, Middle = 24, Longest = 25.

Step-by-step explanation:

7^2 + 24^2 = 25^2

49 + 576 = 625

625 = 625

The population of Australia in 2000 is estimated to be 19.438 million.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

We have,

The population in 1980 = 14.692 million

The population in 1990 = 17.065 million

The change in the population from 1980 to 1990:

= 17.065 - 14.692

= 2.373

This means in 10 years there is an increase of 2.373 million.

The population estimated in 2000:

= 17.065 + 2.373

= 19.438 million

Thus,

The population of Australia in 2000 is estimated to be 19.438 million.

Learn more about equations here:

https://brainly.com/question/17194269

#SPJ1

The density of a substance is its mass per unit volume.

where,

ρ (rho) =density

m=mass

V=volume

in this example

m = 6 grams

V = 2*6*3 = 12*3 = 36 in^3

therefore,

This is the same as:

to solve this we need to multiply and divide by the complex conjugates, so:

and now we solve it

So the answer is:

Option B, Justice is one of four ethical concepts. The definition states that there must be fairness in all medical judgments.

Four ethical principles: autonomy, benevolence, harmlessness, and justice. Each of these principles serves a specific purpose, but all four work together to empower you as healthcare professionals and ensure that your patients receive high-quality, ethical care.

The literal concept of autonomy and the medical concept of autonomy diverge and intersect. Charity is an act of compassion or mercy. The activities of all healthcare workers should always be positive. Of the four principles of medical ethics, harmlessness is the most important.

Learn more about the Healthcare provider's ethical principles at

https://brainly.com/question/24526464?referrer=searchResults

#SPJ4

Given:

sample size = 73

mean = 29.4

standard deviation = 21.3

To find:

98% confidence interval for the sample size and mean

To get the confidence interval, we'll apply the formula:

Answer:

119/100.

Step-by-step explanation:

7.9 means In fraction form 790/ 100

4÷790/100

use LCM method the LCM of 4 and 100 is 100 so,100÷1=100*4=400

100÷100=1*790=790

400+790/100=1190/100( one zero is cancel out with one zero.

the final answer 119/100.

Step 1: There are four consecutive integers that add up to - 362

Step 2: Let's write the equation to find the four consecutive integers, as follows:

• Let x to represent the first consecutive integer

• Let x + 1 to represent the second consecutive integer

• Let x + 2 to represent the third consecutive integer

• Let x + 3 to represent the fourth consecutive integer

Therefore,

x + x + 1 + x + 2 + x + 3 = -362

Step 3: Let's solve for x

4x + 6 = -362

Subtracting 6 at both sides:

4x + 6 - 6 = -362 - 6

4x = -368

Dividing by 4 at both sides:

4x/4 = -368/4

x = -92

Step 4: Let's find the four consecutive integers based on x = -92

• x + 1 = -92 + 1 = -91

• x + 2 = -92 + 2 = -90

• x + 3 = -92 + 3 = -89

Step 5: The four consecutive numbers that add up to -362 are:

-89, -90, -91 and -92

Answer:

you have to turn the fractions into decimals by dividing the numerator by the denominator

When you multiply bothsides of an inequality by a negative sign , the inequality sign changes