Suppose that a department contains 11 men and 15 women. How many ways are there to form a committee with six members if it must have more women than men

The slopes of GH, HI, IJ, and JG include the following:

In Mathematics and Geometry, the slope of any straight line can be determined by using the following mathematical equation;

Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope (m) = rise/run

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

By substituting the given data points into the formula for the slope of a line, we have the following;

Slope GH = (-3 + 9)/(-4 + 7)

Slope GH = 6/3

Slope GH = 2.

Slope HI = (5 + 3)/(-6 + 4)

Slope HI = -8/2

Slope HI = -4.

Slope IJ = (-1 - 5)/(-9 + 6)

Slope IJ = -6/-3

Slope IJ = 2.

Slope JG = (-9 + 1)/(-7 + 9)

Slope JG = -8/2

Slope JG = -4.

Read more on slope here: brainly.com/question/3493733

#SPJ1

The coefficient of determination is a statistical measure that indicates the proportion of variability in the dependent variable that can be explained by the independent variable(s) in a regression model. It is also known as R-squared and is expressed as a fraction between 0 and 1. The closer the value is to 1, the better the fit of the model.

The coefficient of determination can be thought of as the fraction of variability that can be accounted for by the slope of the regression model. The slope is the change in the dependent variable per unit change in the independent variable. In other words, it represents the rate of change in the dependent variable due to a change in the independent variable.

Therefore, a higher coefficient of determination means that a larger proportion of the variability in the dependent variable is explained by the slope of the regression model. This is important because it provides information on the accuracy and usefulness of the model. If the coefficient of determination is low, it may indicate that the model is not a good fit for the data and needs to be revised.
In conclusion, the coefficient of determination is a crucial measure in regression analysis that helps to assess the proportion of variability in the dependent variable that can be explained by the slope of the regression model. It is expressed as a fraction between 0 and 1 and provides important information on the accuracy and usefulness of the model.
In other words, it represents the proportion of the total variability in the dataset that the model is able to explain.

The coefficient of determination ranges from 0 to 1, with values closer to 1 indicating that the regression model is better at explaining the variability in the data. When interpreting R-squared, keep in mind that a higher value doesn't always imply a good model, as it can sometimes be due to overfitting.

To calculate R-squared, you would first fit a regression model to your data. The regression model typically consists of a slope, which represents the rate of change between the independent variable (x-value) and dependent variable (response), and an intercept, which is the point where the regression line crosses the y-axis.

Once the model is fit, you can compute the sum of squares due to regression (SSR) and the total sum of squares (SST). The coefficient of determination is then found by dividing SSR by SST.

R-squared = SSR / SST

By understanding the coefficient of determination, you can evaluate the effectiveness of a regression model in accounting for the variability in the data and make informed decisions based on its performance.

Learn more about slope at : brainly.com/question/19131126

#SPJ11

Answer:

\(6^{9} * 6^{-3}\)

The distance between two points on the coordinate geometry is \(d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\).

From the attachment, we have:

\(A = (20,35)\) --- Arthur

\(J = (45,20)\) -- Jamie

\(C = (65,40)\) --- Cameron

The distance between Arthur and Cameron is:

\(AC = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\)

So, we have:

\(AC = \sqrt{(20- 65)^2 + (35 - 40)^2}\)

\(AC = \sqrt{2050}\)

\(AC = 45.3m\)

Hence, the distance between Arthur and Cameron is 45.3 m

To determine the closest to Cameron, we simply calculate the distance between Cameron and Jamie

\(CJ = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\)

So, we have:

\(CJ = \sqrt{(45 - 65)^2 + (20 -40)^2}\)

\(CJ = \sqrt{800}\)

\(CJ = 28.3m\)

By comparison, 28.3 m is less than 45.3 m.

Hence, Jamie is closer to Cameron than Arthur

Also, we have:

\(S=(35,60)\)

To determine the closest to the soccer ball, we simply calculate the distance between each person and the ball using:

\(d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\)

So, we have:

\(AS = \sqrt{(20 - 35)^2 + (35 - 60)^2} = \sqrt{850} =29.2\) --- Arthur

\(JS = \sqrt{(45 - 35)^2 + (20 - 60)^2} = \sqrt{1700} =41.2\)  --- Jamie

\(CS = \sqrt{(65 - 35)^2 + (40 - 60)^2} = \sqrt{1300} =36.1\) --- Cameron

By comparing the calculated values, 29,2 is the smallest.

Hence, Arthur is the closest to the soccer ball

Read more about distance at:

https://brainly.com/question/17207276

Answer:

2

Step-by-step explanation:

If you read for instance January to August, the chart looks like-

January- 2

February- 4

March- 6

April- 8

May-10

June- 12

July-14

August- 16

So reading 2 every month for 8 months is 8x2=16

1) Interest amount = $16.5

2) Interest amount = $4.125

3) Interest amount = $8.36

And, After 5 1/2 years;

Interest amount = $22.99

4) Interest amount = $33.02

5) Interest amount = $45.6

Now, We can simplify as;

1) Principal amount = $550

Rate = 3%

Time = 1 year

Hence, We get;

Interest amount = 550 x 3 x 1 / 100

                         = $16.5

2)  Principal amount = $1500

Rate = 3%

Time = 1/4 year

Hence, We get;

Interest amount = 1500 x 3 x 1 / 100 x 4

                         = $4.125

3) Principal amount = $418

Rate = 2%

Time = 1 year

Hence, We get;

Interest amount = 418 x 2 x 1 / 100

                         = $8.36

And, After 5 1/2 years;

Interest amount = 418 x 11 x 1 / 100 x 2

                         = $22.99

4)  Principal amount = $825.5

Rate = 4%

Time = 1 year

Hence, We get;

Interest amount = 825.5 x 4 x 1 / 100

                         = $33.02

5) Principal amount = $1140

Rate = 6%

Time = 1 year

Hence, We get;

Interest amount = 1140 x 6 x 1 / 100

                         = $68.4

And, After 5 4 years;

Interest amount = 1140 x 4 x 1 / 100

                         = $45.6

Learn more about the multiplication visit:

https://brainly.com/question/10873737

#SPJ1

Shape R and Shape S were put in the same group because they are the shapes with perpendicular line segments. Therefore the correct option is option D.

Shape S, a trapezium with one vertical side, and Shape R, a square, both have perpendicular line segments. All of the sides of a square are perpendicular, while one of the non-parallel sides of a trapezium with a vertical side is perpendicular to the base.

Reasons for ruling out other options

Option A, "Shapes without any right angles," is incorrect because Shape R (a square) has four right angles.

Option B, "Shapes with exactly one pair of parallel sides," is incorrect because Shape S (a trapezoid with one vertical side) has only one pair of parallel sides, while Shape R(a square) has two pairs of parallel sides.

Option C, "Shapes without parallel line segments," is also incorrect because all the other shapes P, Q, and T have parallel line segments.

Know more about shapes and properties,

https://brainly.com/question/23376341

#SPJ1

Answer:

A dot plot is useful for relatively small sets of data. Dot plots clearly display clusters/gaps of data and outliers. They can be used with numerical and categorical data.

Step-by-step explanation:

It will take Emily 12.1 hours to mow 5 acres

Variation is the relation between a set of values of one variable and a set of values of other variables

Let T and A represent the time and area respectively

Since the time it takes Emily to mow a lawn is proportional to its area. We can write:

T α A

T = kA (where k is constant of proportionality)

It takes her about 30 minutes to mow 1,000 square yards. That is:

T = 30 and A = 1,000

T = kA

30 = 1000k

k = 30/1000

k = 0.03

Time for 5 acres:

5 acres = 5 × 4840 = 24200 square yards   (1 acre = 4840 square yards)

T = kA

T = 0.03 × 24200

T = 726 minutes     (divide by 60 to get time in hours)

T = 12.1 hours

Learn more about variation on:

brainly.com/question/2375770

#SPJ1

To divide a circle exactly in half along its diameter, draw three lines: one vertical line passing through the center, and two diagonal lines intersecting at the center.

To divide a circle in half along its diameter, we need to create a line that passes through the center of the circle. This line will split the circle into two equal halves. One way to achieve this is by drawing a vertical line that starts at the top of the circle and ends at the bottom, passing through the center.

Next, we can create two additional lines to further divide the circle into halves. These lines will be diagonal and will intersect at the center of the circle. By positioning the diagonals symmetrically, we ensure that they divide the circle equally, creating two halves that are mirror images of each other.

By drawing these three lines - one vertical and two diagonal - we can accurately divide a circle in half along its diameter. This method ensures that both halves are precisely equal in size and maintains the symmetry of the circle.

Learn more about diagonal lines here:
https://brainly.com/question/33707094

#SPJ11

Answer:

57 1/10

(14× 3/4)+(4× 1/2)+(8× 1/2)+(10× 2/5)+(10× 2/5)+(12× 4/5)= 571/10 or 57× 1/10

Answer:

*See attached image for the 5 points on the graph*

Step-by-step explanation:

Step 1: Find 5 points to calculate inverse

We can use the vertex(-1,-4), 2 y-intercepts(0,-3) and (0,-5) and 2 more points (3,-2) and (3,-6)

Step 2: Find the inverse

You find the inverse when you swap the 'x' and 'y' so it would be

Vertex: (-4,-1)

y-intercept 1:(-3,0)

y-intercept 2:(-5,0)

Point 1: (-2,3)

Point 2: (-6,3)

Step 3: Graph

Graph the points on a graph and connect the points

The inverse of a graph is done by reflecting the graph across the line \(y = x\).

See attachment for the inverse graph.

From the given graph, we have the following 5 points.

\((x_1,y_1) = (8,-1)\)

\((x_2,y_2) = (3,-2)\)

\((x_3,y_3) = (-1,-4)\)

\((x_4,y_4) = (3,-6)\)

\((x_5,y_5) = (8,-7)\)

Reflect the above points across \(y = x\), to get the inverse function

\((x_1,y_1) = (-1,8)\)

\((x_2,y_2) = (-2,3)\)

\((x_3,y_3) = (-4,-1)\)

\((x_4,y_4) = (-6,3)\)

\((x_5,y_5) = (-7,8)\)

The inverse graph must pass through the above points

See attachment for the inverse graph

Read more about inverse graphs at:

https://brainly.com/question/11033643

The angles between the edges of the resulting pieces are approximately \($56.1^\circ$ and $42.5^\circ$.\)

We know that the rectangle has sides of length 4 ft and 5.5 ft, so we can use the Pythagorean Theorem to find the length of the diagonal \($BD$\):

\($$ BD^2 = 4^2 + 5.5^2 $$\)

\($$ BD^2 = 16 + 30.25 $$\)

\($$ BD^2 = 46.25 $$\)

\($$ BD = \sqrt{46.25} $$\)

\($$ BD = 6.8 \text{ ft (rounded to one decimal place)} $$\)

Now, we can use the Law of Cosines to find the angle between sides \($AB$\)and \($AD$\) in triangle \($ABD$\):

\($$ \cos(A) = \frac{BD^2 + AB^2 - AD^2}{2 \cdot BD \cdot AB} $$\)

\($$ \cos(A) = \frac{6.8^2 + 4^2 - 5.5^2}{2 \cdot 6.8 \cdot 4} $$\)

\($$ \cos(A) = 0.5471 $$\)

\($$ A = \cos^{-1}(0.5471) $$\)

\($$ A = 56.1^\circ \text{ (rounded to one decimal place)} $$\)

Similarly, we can use the Law of Cosines to find the angle between sides \($BC$\) and \($CD$\) in triangle:

\($$ \cos(B) = \frac{BD^2 + BC^2 - CD^2}{2 \cdot BD \cdot BC} $$\)

\($$ \cos(B) = \frac{6.8^2 + 5.5^2 - 4^2}{2 \cdot 6.8 \cdot 5.5} $$\)

\($$ \cos(B) = 0.7416 $$\)

\($$ B = \cos^{-1}(0.7416) $$\)

\($$ B = 42.5^\circ \text{ (rounded to one decimal place)} $$\)

Therefore, the angles between the edges of the resulting pieces are approximately \($56.1^\circ$ and $42.5^\circ$.\)

To learn more about Angles refer here:

https://brainly.com/question/7116550

#SPJ11

Answer:

13.4

Step-by-step explanation:

it just is

Answer:

13.4

Step-by-step explanation:

there you go 8.04 divided by 0.6= 13.4

Answer:

16m

8m

50.24m

200.96m^2

Step-by-step explanation:

13. 8*2=16

14. 8m

15. 2pi r = 2* pi* 8= 50.24

16. pi r^2 = pi * 8^2= 200.96m^2

Answer:

c = 314

Step-by-step explanation:

c = d (3.14)

c = 100(3.14)

c = 314

hope this helps!!

Answer:

to get the slope. take the change of y axis value divide by the change of x axis value

B. {(0, 3), (-6, 8), (-3, 5), (0, -3), (7, 11)} are the sets of ordered pairs which are the relation that is a function.

To determine whether a set of ordered pairs is a function, we need to determine whether each x-value corresponds to only one y-value. In other words, the x-values in the set should be unique and not repeated.   For the set A. {(2, 4), (2, 6), (2, 8), (2, 10), (2, 12)}, we can see that the x-value 2 is repeated multiple times, and thus, it is not a function.  For the set B. {(0, 3), (-6, 8), (-3, 5), (0, -3), (7, 11)}, each x-value is unique and thus, it is a function.   For the set C. {(8, 1), (-4, 1), (3, 5), (0, 4), (-1, 2)}, we can see that the y-value 1 is repeated twice, and thus, it is not a function.  For the set D. {(-5, -4), (-4, -3), (-3, -2), (-4, -5), (-2, -1)}, each x-value is unique and thus, it is a function.  Therefore, the answer is B. {(0, 3), (-6, 8), (-3, 5), (0, -3), (7, 11)}.

To know more about relation refer to the link brainly.com/question/6241820

#SPJ4

Answer:

the borison property show the movie tickets

Step-by-step explanation:

Answer:

THE ANSWER IS C

Step-by-step explanation:

The limit of f(x) as it approaches -1 is given as 3/2

In mathematics and computation, the limit can be described to be the value that a sequence is going to approach in such a way that the input would approach or tend towards a given value

The unit is used to assign values to numbers at certain points where there are no defined values.

we have 3/x-1

We have to take the value of x here to be three as the equation tends to 1.

Then we apply it in the formula

3/3-1

= 3/2

Hence the limit of f(x) is given as 3/2

Read more on limit here:

https://brainly.com/question/23935467

#SPJ1

Answer:

3.4

Step-by-step explanation:

the answer would be 3.4

Answer:

Your moving (2, -1)

Step-by-step explanation:

You start at (0, -3) then move to (2, -2)

So your moving (2, -1)

======================================================

Explanation:

Check out the diagram below. Locate -2 on the horizontal x axis. Draw a vertical line through this value. Mark where the vertical line crosses the curve. Call this point P. Then draw a horizontal line through point P to have it cross the y axis. This horizontal line crosses at y = 1

In short, x = -2 leads to y = 1

So that is why f(-2) = 1

This is another way of saying f(x) = 1 when x = -2.

Note: y = f(x) since both are outputs of a function

The speedometer of the car showing error and sent back to be fixed must showing speed less than 1.225 miles per minute.

As given in the question,

Distance covered by car = 10miles

Time taken by car to cover 10 miles = 8 minutes

Formula used:

Speed = ( total distance travelled ) / ( time taken )

           = 10 / 8

           = 1. 25 miles per minute

To pass the speed test ,

Range of the speedometer is 2% of the actual speed

= 2% of 1.25

= ( 2/100) × 1.25

= 0.025

Range of the speed to pass the test

= 0.025 ± 1.25

= (  1.225, 1.275)

Therefore, the speedometer of the car which was sent back to be fixed must showing the speed less than 1.225 miles per minute.

Learn more about speed here

brainly.com/question/7359669

#SPJ4

Answer:

The ratio of number of boxes of brand a sold to the number of boxes sold is 3/20

Step-by-step explanation:

A supermarket sells 4 brands of detergents a, b, c, d.

On this particular day, 15% of the total boxes sold was brand a and 45% was brand c.

ratio of number of boxes of brand a sold to the number of boxes sold = ?

15% of the boxes sold is box a

Total number of boxes sold is 100%,

therefore,

ratio of box a sold to the whole boxes sold will be

15/100 = 3/20   in fraction

Drake should work more than 25.44 hours in a week to save more than $318.

First, the amount Drake earns in a week:

Weekly earnings = Hourly rate × Hours worked

Weekly earnings = $25x

Now we need to subtract the percentages of his expenses from his weekly earnings to find how much he can save:

Amount saved

= Weekly earnings - Food expense - Rent expense - Care expense - Other expenses

= $25x - 0.25($25x) - 0.15($25x) - 0.05($25x) - 0.07($25x)

= $25x - $6.25x - $3.75x - $1.25x - $1.75x

= $12.50x

We want to find the values of x that will make the amount Drake saves in a week greater than $318. So we can set up the inequality:

$12.50x > $318

To solve for x, we need to isolate it on one side of the inequality:

x > $318 ÷ $12.50

x > 25.44

Therefore, Drake should work more than 25.44 hours in a week to save more than $318.

Learn more about Saving problems here:

https://brainly.com/question/26070388

#SPJ1

Answer:

3

Step-by-step explanation:

slope m = (y - y1)/(x - x1)

m = (-3.5 - 1)/(1 - 2.5) = (-4.5)/(-1.5) = 3