The highlighted part of this picture is a good representation of which geometric term?

ou find a deck of cards and know that the deck has too many clubs and spades in it. The deck has 59 cards. If you were to draw t

sashaice [31]

We can find the number of extra clubs in the deck from the given probability, since the probability of drawing a diamond and a club is

$\dfrac{\binom{13}1\binom{13+c}1}{\binom{59}2}=\dfrac{13(13+c)}{1711}$

but this would imply that $c=-4$ , which suggests we're taking 4 clubs out of the original deck and contradicts the problem statement that there are "too many clubs".

Perhaps the question is providing the probability of drawing a diamond, THEN a club, or vice versa. In that case, we have

$\dfrac{\binom{13}1}{\binom{59}1}\cdot\dfrac{\binom{13+c}1}{\binom{58}1}=\dfrac{13(13+c)}{3422}$

and solving gives $c=5$ , which makes more sense. Then the number of extra spades in the deck must be 2.

7 0

3 years ago

Let event Aequalssubject is telling the truth and event Bequalspolygraph test indicates that the subject is lying. Use your own

wariber [46]

Answer:

P( B | A) will actually be the probability of the polygraph test being wrong.

Step-by-step explanation:

The event A represents the event that the subject is telling the truth.

The event B represents the event when he fails the polygraph test, which is indicative of the fact that he is lying.

The notation P( B | A) describes the probability that the subject fails the polygraph test given that he is actually telling the truth.

So in retrospect P( B | A) will actually be the probability of the polygraph test being wrong.

5 0

3 years ago

fine the y intercepts and intersection point for each graph. then write a system of equation for each graph.

vovikov84 [41]

Answer:

In the previous lesson, you learned how to graph points on the coordinate plane. We can connect two points with a straight line.

To graph the equation of a line, we plot at least two points whose coordinates satisfy the equation, and then connect the points with a line. We call these equations "linear" because the graph of these equations is a straight line.

There are two important things that can help you graph an equation, slope and y-intercept.

Slope

We're familiar with the word "slope" as it relates to mountains. Skiers and snowboarders refer to "hitting the slopes." On the coordinate plane, the steepness, or slant, of a line is called the slope. Slope is the ratio of the change in the y-value over the change in the x-value. Carpenters and builders call this ratio the "rise over the run." Using any two points on a line, you can calculate its slope using this formula.

Let's use these two points to calculate the slope m of this line.

A = (1,1) and B = (2,3)

Subtract the y value of point A from the y-value of point B to find the change in the y value, which is 2. Then subtract the x value of point A from the x value of point B to find the change in x, which is 1. The slope is 2 divided by 1, or 2.

When a line has positive slope, like this one, it rises from left to right.

WATCH OUT! Always use the same order in the numerator and denominator!

It doesn't really matter whether you subtract the values of point A from the values of point B, or the values of point B from the values of point A. Try it - you'll get the same answer both ways. But you must use the same order for both the numerator and denominator!

You can't subtract the y value of point A from the y value of point B, and the x value of point B from the x value of point A - your answer will be wrong.

Let's look at another line. This line has a negative slope, it falls from left to right. We can take any two points on this line and find the slope. Let's take C (0, -1) and D (2, -5).

Using these two points, we can calculate the slope of this line. We subtract the y value of point C from the y value of point D, and the x value of point C from the x value of point D, and divide the first value by the second value. The slope is -2.

Y-Intercept

There's another important value associated with graphing a line on the coordinate plane. It's called the "y intercept" and it's the y value of the point where the line intersects the y- axis. For this line, the y-intercept is "negative 1." You can find the y-intercept by looking at the graph and seeing which point crosses the y axis. This point will always have an x coordinate of zero. This is another way to find the y-intercept, if you know the equation, the y-intercept is the solution to the equation when x = 0.

Equations

Knowing how to find the slope and the y-intercept helps us to graph a line when we know its equation, and also helps us to find the equation of a line when we have its graph. The equation of a line can always be written in this form, where m is the slope and b is the y-intercept:

y = mx + b

Let's find the equation for this line. Pick any two points, in this diagram, A = (1, 1) and B = (2, 3).

We found that the slope m for this line is 2. By looking at the graph, we can see that it intersects the y-axis at the point (0, –1), so –1 is the value of b, the y-intercept. Substituting these values into the equation formula, we get:

y = 2x –1

The line shows the solution to the equation: that is, it shows all the values that satisfy the equation. If we substitute the x and y values of a point on the line into the equation, you will get a true statement. We'll try it with the point (2, 3).

Let's substitute x = 2 and y = 3 into the equation. We get "3 = 3", a true statement, so this point satisfies the equation of the line.

back to top

Homework Help | Algebra | Graphing Equations and Inequalities Email this page to a friend Email this page to a friend

6 0

3 years ago

HELP PLEASE PLEASE HELP<br> Solve for t.<br> -10t − -17t − 10t + -13 = 11

Marta_Voda [28]

-10t - (-17t) - 10t + (-13) = 11 (two negative signs makes a positive)

-10t + 17t - 10t - 13 = 11 Combine like terms

-3t - 13 = 11 Add 13 on both sides

-3t = 24 Divide -3 on both sides

t = -8

8 0

3 years ago

The sum of the measures of angle Y and angle Z is 180 degrees. Angle Y measures (3x + 20) degrees and Angle Z measures x degrees

Minchanka [31]

A)
The question tells us that
y + z = 180
And
y=3x+20
z=x

So we put them in the first formula:

y + z = 180
(3x + 20) + x = 180

Add and get x to one side:
4x + 20 = 180
4x + 20 - 20 = 180-20
4x = 160
Divide both sides by 4
x = 40

B)
Put x back in to equation to get size of each angle:

Y =3x +20
Y=3(40)+20
Y=120+20
Y=140

Z=x
Z=40

Verify: y+z=180
140+40=180
180=180

8 0

3 years ago