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elena-14-01-66 [18.8K]
2 years ago
13

In a board game, students draw a number do not replace it, and then draw a second number. Determine the probability of each even

t occurring. Drawing an odd number then drawing a 6? dependent events. PLEASE HELP ME
Mathematics
1 answer:
murzikaleks [220]2 years ago
7 0

The figure depicting the board game is attached below.

Answer:

Step-by-step explanation:

Kindly note that selections done without replacement.

Count of numbers on the board game = 8

Count of odd numbers = (1, 9, 1) = 3

Count of digit 6 = 3

Probability = required outcome / Total possible outcomes

P(picking an odd number) = 3 / 8

Without replacement

Numbers left on board game = 8 - 1 = 7

P(picking a 6) = 3 / 7

Hence,

P(picking an odd number then, a 6) = 3/8 * 3/7 = 9 / 56

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B.consecutive interior angles

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Ruth buys 19 identical tickets for £280.25.<br> Estimate the cost of one ticket.
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Answer:

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Step-by-step explanation:

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3 years ago
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Evaluate -2 with an exponent of 3
zheka24 [161]
When raised to the third power, it is the number times itself three times.

-2(-2) = 4

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6 0
2 years ago
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Dave and Sandy Hartranft are frequent flyers with a particular airline. They often fly from City A to City B, a distance of 756
horsena [70]

Answer:

Plane = 441 mi/h; wind =  63 mi/h

Step-by-step explanation:

distance = rate × time

 Let p = the plane's speed in still air

and w = the wind speed . Then,

p + w = speed with wind

 p - w = speed against wind

We have two conditions:

(1)  756 = (p - w) × 2

(2) 756 = (p + w) × 1.5

Distribute the constants                  (3)    756 = 2p - 2w

                                                          (4)   756 = 1.5p + 1.5 w  

Multiply Equation (3) by 3                (5) 2268 = 6p  -  6w

Multiply Equation (4) by 4                (6) 3024 = 6p + 6w

Add Equations (5) and (6)                     5292 = 12p

Divide each side by 12                     (7)        p = 441 mi/h

Substitute (7) into Equation(3)                 756 = 882 - 2w

Add 2w to each side                      2w + 756 = 882

Subtract 756 from each side                    2w = 126

Divide each side by 2                                 w = 63 mph

The plane's speed in still air is 441 mi/h.

The wind speed is 63 mph.

Check:

(1) 756 = (441 - 63) × 2     (2) 756 = (441 + 63) × 1.5

   756 = 378 × 2                   756 = 504 × 1.5

   756 = 756                         756 = 756

8 0
3 years ago
Steve likes to entertain friends at parties with "wire tricks." Suppose he takes a piece of wire 60 inches long and cuts it into
Alex_Xolod [135]

Answer:

a) the length of the wire for the circle = (\frac{60\pi }{\pi+4}) in

b)the length of the wire for the square = (\frac{240}{\pi+4}) in

c) the smallest possible area = 126.02 in² into two decimal places

Step-by-step explanation:

If one piece of wire for the square is y; and another piece of wire for circle is (60-y).

Then; we can say; let the side of the square be b

so 4(b)=y

         b=\frac{y}{4}

Area of the square which is L² can now be said to be;

A_S=(\frac{y}{4})^2 = \frac{y^2}{16}

On the otherhand; let the radius (r) of the  circle be;

2πr = 60-y

r = \frac{60-y}{2\pi }

Area of the circle which is πr² can now be;

A_C= \pi (\frac{60-y}{2\pi } )^2

     =( \frac{60-y}{4\pi } )^2

Total Area (A);

A = A_S+A_C

   = \frac{y^2}{16} +(\frac{60-y}{4\pi } )^2

For the smallest possible area; \frac{dA}{dy}=0

∴ \frac{2y}{16}+\frac{2(60-y)(-1)}{4\pi}=0

If we divide through with (2) and each entity move to the opposite side; we have:

\frac{y}{18}=\frac{(60-y)}{2\pi}

By cross multiplying; we have:

2πy = 480 - 8y

collect like terms

(2π + 8) y = 480

which can be reduced to (π + 4)y = 240 by dividing through with 2

y= \frac{240}{\pi+4}

∴ since y= \frac{240}{\pi+4}, we can determine for the length of the circle ;

60-y can now be;

= 60-\frac{240}{\pi+4}

= \frac{(\pi+4)*60-240}{\pi+40}

= \frac{60\pi+240-240}{\pi+4}

= (\frac{60\pi}{\pi+4})in

also, the length of wire for the square  (y) ; y= (\frac{240}{\pi+4})in

The smallest possible area (A) = \frac{1}{16} (\frac{240}{\pi+4})^2+(\frac{60\pi}{\pi+y})^2(\frac{1}{4\pi})

= 126.0223095 in²

≅ 126.02 in² ( to two decimal places)

4 0
3 years ago
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