Answer:
Clearly, the probability of drawing a heart out of the deck is 13/52, or 1/4. The probability of drawing an even number as card #2 (∈{2,4,6,8,10}) for any suit is 20/51, except when the first card drawn is an even heart, then the probability of the second draw is 19/51.
Casey is 18 years old and Ralph is 3 years old.
Step-by-step explanation:
Let,
Age of Casey = x
Age of Ralph = y
According to given statement;
x = 6y Eqn 1
In two years
x+2=4(y+2)
x+2=4y+8
x = 4y+8-2
x = 4y+6 Eqn 2
Putting value of x from Eqn 1 in Eqn 2
Dividing both sides by 2
Putting y=3 in Eqn 1
Casey is 18 years old and Ralph is 3 years old.
Keywords: word problems, substitution method
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Answer:
The measure of the vertex angle is 94 degrees ⇒ A
Step-by-step explanation:
- In any triangle, the sum of the measures of its interior angle is 180°
- In the isosceles triangle, the two base angles are equal in measures
∵ In an isosceles triangle, the measure of the base angle = (2x + 5)
∵ The base angles of the isosceles triangles are equal in measures
∴ The measures of the base angles are (2x + 5), (2x + 5)
∵ The measure of the vertex angle = (5x - 1)
∵ The sum of the measure of the three angles = 180°
∴ (2x + 5) + (2x + 5) + (5x - 1) = 180
→ Add the like terms in the left side
∵ (2x + 2x + 5x) + (5 + 5 + -1) = 180
∴ 9x + 9 = 180
→ Subtract 9 from both sides
∴ 9x + 9 - 9 = 180 - 9
∴ 9x = 171
→ Divide both sides by 9 to find x
∴ x = 19
→ Substitute the value of x in the measure of the vertex angle to find it
∵ The measure of the vertex angle = 5x - 1
∴ The measure of the vertex angle = 5(19) - 1
∴ The measure of the vertex angle = 95 - 1
∴ The measure of the vertex angle = 94°
∴ The measure of the vertex angle is 94 degrees
Answer: 4
Step-by-step explanation:
Hope this helps
<span>Lets find the volume of a cylinder with a diameter D=10 inches and lenght L= 20 inches. First we need to notice that the diameter is twice the size of the radius: D=2r. Then we write the equation for the volume of the cylinder. it is the base times the height: V=pi*r^2 * L. Now we input the nubmers in the equation: V=3.14*(D/2)^2 * L where r=D/2=5 inches and after calculating we get: V=1570 inches^3</span>
