Solve the system of equations by graphing on your own paper. What is the x-coordinate of the solution?

Backgammon is a board game for two players in which the playing pieces are moved according to the roll of two dice. players win

Ivahew [28]

The rolls of the dice are independent, i.e. the outcome of the second die doesn't depend in any way on the outcome of the first die.

In cases like this, the probability of two events happening one after the other is the multiplication of the probabilities of the two events.

So, the probability of rolling two 6s is the multiplication of the probabilities of rolling a six with the first die, and another six with the second:

$P(\text{rolling two 6s}) = P(\text{rolling a 6}) \cdot P(\text{rolling a 6}) = \dfrac{1}{6} \cdot \dfrac{1}{6} = \dfrac{1}{36}$

Similarly,

$P(\text{rolling two 3s}) = P(\text{rolling a 3}) \cdot P(\text{rolling a 3}) = \dfrac{1}{6} \cdot \dfrac{1}{6} = \dfrac{1}{36}$

Actually, you can see that the probability of rolling any ordered couple is always 1/36, since the probability of rolling any number on both dice is 1/6:

$P(\text{rolling any ordered couple}) = P(\text{rolling the first number}) \cdot P(\text{rolling the second number}) = \dfrac{1}{6} \cdot \dfrac{1}{6} = \dfrac{1}{36}$

7 0

3 years ago

PLEASE PLEASE HELP! Find the measure of APB^.

Whitepunk [10]

Answer:

65°

Step-by-step explanation:

Radii CA and CB are perpendicular to tangent lines AT and BT, so

$\angle CAT=\angle CBT=90^{\circ}$

Since angle BAT is equal to 65°, angle CAB has measure

$\angle CAB=90^{\circ}-65^{\circ}=25^{\circ}.$

Consider triangle ACB. This triangle is isosceles, because CA=CB as radii of the circle. Two angles adjacent to the base are congruent, thus

$\angle CBA=\angle CAB=25^{\circ}$

The sum of the measures of all interior angles in triangle is always 180°, so

$\angle CAB+\angle CBA+\angle ACB=180^{\circ}\\ \\25^{\circ}+25^{\circ}+\angle ACB=180^{\circ}\\ \\\angle ACB=130^{\circ}$

Angle ACB is central angle subtended on the minor arc AB, angle APB is inscribed angle subtended on the same minor arc AB. The measure of inscribed angle is half the measure of central angle subtended on the same arc, so

$x=\angle APB=\dfrac{1}{2}\cdot 130^{\circ}=65^{\circ}$

8 0

3 years ago

Alan is connecting three garden hoses to make one longer hose.The green hose is 6.25 feel long the orange hose is 5.755 feet lon

nevsk [136]

We will use addition to find the length of the new, longer hose.

6.25 feet + 5.755 feet + 6.5 feet = 18.505 feet is the length of the new longer hose.

8 0

4 years ago

What is the length of if ? 8 in. 8.75 in. 10.25 in. 14 in.

Ket [755]

Answer:

A=8.75 in.

Step-by-step explanation:

Since ∆ HBA & ∆HKJ are similar,

HB/HA = HK/HJ

3/5.25 = 8/HJ

3HJ/5.25 = 8

3HJ = 42

HJ = 14 in.

AJ = 14 - 5.25

AJ = 8.75 in.

Therefore

A=8.75 in.

I hope this helped you.

5 0

4 years ago

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Newton Street and Oakland Avenue intersect. If the diagonal distance across the intersection is 17 meters and Newton Street is 1

Margarita [4]

The Oakland Avenue is approximately what the time you think is it now though you have 120 days to

8 0

2 years ago