Each time you roll a die, you have a $\frac{1}{6}$ chance of rolling a 3. It's even rarer to roll two 3s in a row, and to find a consecutive probability, we have to multiply the two probabilities. In this case, both probabilities are $\frac{1}{6}$ .

$\frac{1}{6}\cdot\frac{1}{6}=\frac{1}{36}$

Hope this helped!

4 0

3 years ago

Triangle WXY is isosceles. ∠YWX and ∠YXW are the base angles. YZ bisects ∠WYX. m∠XYZ = (15x)°. m∠YXZ = (2x + 5)°. What is the me

DiKsa [7]

Answer:

Option D is correct.

The measure of $\angleWYX = 150^{\circ}$

Step-by-step explanation:

$\triangle WXY$ is isosceles and $\angle YWX$ and $\angle YXW$ are base angles.

Isosceles Triangle:

A triangle with two equal sides, and two congruent base angles that means the angles are equal

By the definition, the base angles are equal i.e, $m\angle YWX=m\angle YXW$

Since, YZ bisects $m\angle WYX$

Angle Bisector theorem: An angle bisector is a line or ray that divides an angle into two equal angles

then, $\angle WYX =2\angle XYZ$ or

Substitute the value of $\angle XYZ=(15x)^{\circ}$ ;

$\angle WYX =2(15x)^{\circ} = (30x)^{\circ}$

The sum of measures of these three angles of triangle WXY is equal to the 180 degree.

In triangle WXY we have;

$\angle YXW+\angle WYX+\angle YWX=180^{\circ}$

Substitute the value of $m\angle YWX=m\angle YXW=(2x+5)^{\circ}$ and $\angle WYX=(30x)^{\circ}$ in above formula:

$2\angle YXW+30x=180^{\circ}$ or

$2\cdot(2x+5)+30x=180^{\circ}$

Simplify:

$4x+10+30x=180^{\circ}$

Combine like terms ;

$34x+10^{\circ}=180^{\circ}$ or

$34x=170^{\circ}$

Simplify;

$x= \frac{170}{34} =5^{\circ}$

Substitute the value of x in $\angle WYX$ ;

$\angleWYX = (30x)^{\circ} = 30 \cdot 5 = 150^{\circ}$

Therefore, the measure of $\angleWYX = 150^{\circ}$

7 0

3 years ago

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