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Alenkasestr [34]
2 years ago
6

In an experiment, a ball is drawn from an urn containing 12 purple balls and 13 green balls. If the ball is purple, two coins ar

e tossed. Otherwise three coins are tossed. How many elements of the sample space will have a purple ball? How many elements of the sample space are there altogether?
Mathematics
1 answer:
UNO [17]2 years ago
5 0

Answer:

4 elements of the sample space will have a purple ball

There are 10 elements altogether

Step-by-step explanation:

Probability is given by number of possible outcomes ÷ number of total outcomes

Number of purple balls = 12, number of green balls = 13, total number of balls = 12+13 = 25

Probability (a ball drawn is purple) = 12/25

If a purple ball is drawn, two coins are tossed

1 coin has 2 elements

2 coins have 2×2 = 4 elements

Probability (a ball drawn is not purple) = 1 - 12/25 = (25-12)/25 = 13/25

If a ball drawn is not purple, three coins are tossed

1 coin has 2 elements

3 coins have 3×2 = 6 elements

Total elements = 4 + 6= 10 elements

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What is the equation of the following graph in vertex form?
Veronika [31]

Answer:

The equation in vertex form is:

y=(x-2)^2+1

Step-by-step explanation:

Recall that the formula of a parabola with vertex at (x_{vertex},y_{vertex}) is given by the equation in vertex form:

y=a\,(x-x_{vertex})^2+y_{vertex}

where the parameter "a" can be specified by an extra information on any other point apart from the vertex, that parabola goes through.

In our case, since the vertex must be the point (2, 1), the vertex form of the parabola becomes:

y=a\,(x-x_{vertex})^2+y_{vertex}\\y=a\,(x-2)^2+1

we have the information on the extra point (0, 5) where the parabola crosses the y-axis. Then, we use it to find the missing parameter a:

y=a\,(x-2)^2+1\\5=a(0-2)^2+1\\5=a\,*\,4+1\\5-1=4\,a\\4=4\,a\\a=1

The, the final form of the parabola's equation in vertex form is:

y=(x-2)^2+1

5 0
3 years ago
Jake had $4382 each month from his dad for 36 months how much money did Jake receive in those 36 months
Aloiza [94]
$157,752 
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A motorcyclist travels 98 km in 1 hour 10 minutes.calculate his average speed ,giving your answer in kilometres per hour.
joja [24]

10 minutes is 1/6 of an hour.

1 hour and 10 minutes = 7/6 hours

98 km  / 7/6 = 98 x 6/7 = (98 x 6) /7 = 588/7 = 84 km per hour

3 0
3 years ago
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Enter the finite geometric series from its given description, and then enter its sum.
Mama L [17]

Answer:

a_n= 4(-5)^{(n-1)}

-10416

Step-by-step explanation:

a = 4

r = -5

geometric series:  a_n=ar^{(n-1)} = 4(-5)^{(n-1)}

Determine which term = -12500:

a_n=-12500

4(-5)^{(n-1)}=-12500

(-5)^{(n-1)} = -3125

(5)^{(n-1)} = 3125

(n-1)ln(5) = ln(3125)

n-1 = ln(3125)/ln(5) = 5

n = 5 + 1 = 6

a_6=-12500

Using geometric sum series formula: S_n=\frac{a(1-r^n)}{1-r}

Therefore, S_6=\frac{4(1-(-5)^6)}{1-(-5)} =\frac{-62496}{6} =-10416

4 0
2 years ago
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