The probability is a ratio of the possible events to the total events. The total is 52 cards, so the denominator is 52. The individual properties of the specific cards are the following:
Any face or number cards is 4/52, because there are 4 cards for each symbol. On the other hand, each symbol like heart, diamond, club or spade would each have a probability of 13/52 (counting numbers 2 to 10, Ace card, and the 3 face cards). Also, there are 26 each of red and black cards. Furthermore, the words 'or' and 'and' are hint words. When you see 'or', you have to add their individual probabilities. If you see the word 'and', you'll have to multiply them. With that said, the solution is as follows:
a.) P = 4/52 + 4/52 + 4/52 = 3/13
b.) P = (13/52 + 13/52 + 4/52)(26/52) = 15/52
c.) P = 13/52
d.) P = 13/52 + 13/52 + 13/52 = 3/4
The answer is in the image. We need 3.625 gallons to fill the tank.
Answer:
Step-by-step explanation:
x+y=a
a=x+y
x−y=b
b=x−y
Good luck honey!
The slope of the line passes through the points (-5,6) and (-3,2) is 2.
<h3>What is a slope?</h3>
Slope or the gradient is the number or the ratio which determines the direction or the steepness of the line. The slope is also defined as the ratio of the rise to the run.
Given that the line that passes through the points (-5,6) and (-3,2).
The slope of the line is calculated by the formula,
Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )
Slope = ( 6 - 2) / ( -3 + 5)
Slope = 4 / 2
Slope = 2
Therefore, the slope of the line passes through the points (-5,6) and (-3,2) is 2.
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Answer: D
Step-by-step explanation:
Consider the first equation. Subtract 3x from both sides.
y−3x=−2
Consider the second equation. Subtract x from both sides.
y−2−x=0
Add 2 to both sides. Anything plus zero gives itself.
y−x=2
To solve a pair of equations using substitution, first solve one of the equations for one of the variables. Then substitute the result for that variable in the other equation.
y−3x=−2,y−x=2
Choose one of the equations and solve it for y by isolating y on the left hand side of the equal sign.
y−3x=−2
Add 3x to both sides of the equation.
y=3x−2
Substitute 3x−2 for y in the other equation, y−x=2.
3x−2−x=2
Add 3x to −x.
2x−2=2
Add 2 to both sides of the equation.
2x=4
Divide both sides by 2.
x=2
Substitute 2 for x in y=3x−2. Because the resulting equation contains only one variable, you can solve for y directly.
y=3×2−2
Multiply 3 times 2.
y=6−2
Add −2 to 6.
y=4
The system is now solved.
y=4,x=2
