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8_murik_8 [283]
3 years ago
6

A card is drawn from a standard deck of 52 cards. What is the probability of drawing a face card (jack, king, or queen) or a bla

ck card? (Hint: Half of a standard deck of 52 cards has black cards.)
Mathematics
1 answer:
Shkiper50 [21]3 years ago
3 0
Probability of drawing a face card =
4 suits x 3 = 12
\frac{12}{52}  =  \frac{3}{13}
Probability of drawing a black card =
\frac{26}{52}  =  \frac{1}{2}
Hope this helps. - M
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Which line is parallel to the line<br> shown below?
Travka [436]
<h3>Answer:  Choice D</h3>

4x - 3y = 15

====================================================

Explanation:

The two points (-1,-1) and (2,3) are marked on the line

Let's find the slope of the line through those two points.

(x_1,y_1) = (-1,-1) \text{ and } (x_2,y_2)  = (2,3)\\\\m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}\\\\m = \frac{3 - (-1)}{2 - (-1)}\\\\m = \frac{3 + 1}{2 + 1}\\\\m = \frac{4}{3}\\\\

The slope is 4/3 meaning we go up 4 and to the right 3.

-------------

Parallel lines have equal slopes, but different y intercepts. We'll need to see which of the four answer choices have a slope of 4/3.

Solve the equation in choice A for y. The goal is to get it into y = mx+b form so we can determine the slope m.

3x + 4y = -4\\\\4y = -3x-4\\\\y = -\frac{3}{4}x-\frac{4}{4}\\\\y = -\frac{3}{4}x-1

Equation A has a slope of -3/4 and not 4/3 like we want.

Therefore, this answer choice is crossed off the list.

Follow similar steps for choices B through D. I'll show the slopes of each so you can check your work.

  • slope of equation B is 3/4
  • slope of equation C is -4/3
  • slope of equation D is 4/3

We have a match with equation D. Therefore, the equation 4x-3y = 15 is parallel to the given line shown in the graph.

You can use graphing tools like Desmos or GeoGebra to confirm the answer.

4 0
1 year ago
How can 1/5x − 2 = 1/3x + 8 be set up as a system of equations? a . 5y − 5x = −10. 3y − 3x = 24 b. 5y − 5x = −10. 3y + 3x = 24 c
VMariaS [17]
The answer is d. 5y − x = −10. 3y − x = 24

\frac{1}{5}x-2=  \frac{1}{3}x+8=y
⇒   y= \frac{1}{5}x-2
      y= \frac{1}{3}x+8
________________________
y= \frac{x}{5} -2= \frac{x}{5} - \frac{10}{5} = \frac{x-10}{5}
y= \frac{x}{3} +8= \frac{x}{3} + \frac{24}{3} = \frac{x+24}{3}
________________________
y= \frac{x-10}{5}            ⇒     5y=x-10
y= \frac{x+24}{3}           ⇒     3y=x+24
________________________
5y-x=-10
3y-x=24
5 0
3 years ago
The sum of the digits of a two-digit number is 10. When the digits are reversed, the new number is 18 less than the original num
eimsori [14]
<h3>Answer:</h3>

64

<h3>Explanation:</h3>

6+4= 10

Then reverse the digits of 64, and you have 46

64-46= 18

3 0
3 years ago
Using long division, what is the quotient of this expression?<br> X^4+4x^3-5x^2+x-3/x^2+x-3
Paladinen [302]

Answer:

Using long division method the answer is B

Step-by-step explanation:

x²+3x-5+(15x-18)/x²+x-3

7 0
3 years ago
Drag the tiles to the boxes to form correct pairs.
SOVA2 [1]

Answer:

Step-by-step explanation:

Hello

Match the points on the number line with the rational numbers.

a __ -6/8 = -(2 x 3)/(2 x 4) = -3/4

b __ -2/8 = -2/(2 x 4) = -1/4

c __ -4/8 = -4/(4 x 2) = -1/2

d __ 8/8 = 1

e __ 13/8

3 0
3 years ago
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