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2 years ago

Probability of a standard six side dice landing on a four in the first three rolls?

Mathematics

1 answer:

Illusion [34]2 years ago

6 0

Answer:

91/216

Step-by-step explanation:

The probability of getting a 4 in the first three rolls is 1 minus the probability of not getting a 4 on any of the rolls.

P(at least one 4) = 1 − P(no 4s)

P(at least one 4) = 1 − (5/6)³

P(at least one 4) = 91/216

Alternatively, you can calculate it this way.

The probability of getting a 4 on the first roll is 1/6.

The probability of getting a 4 on the second roll is (5/6) (1/6) = 5/36.

The probability of getting a 4 on the third roll is (5/6) (5/6) (1/6) = 25/216.

The probability of any of the three events is 1/6 + 5/36 + 25/216 = 91/216.

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A team of storm enthusiasts collected data to show the relationship between the time between seeing lightning and then hearing t

never [62]

Answer:

Proportionality constant = $\frac{1}{5}$

Step-by-step explanation:

From the graph attached,

Data set representing the relation between seeing lightning and the hearing thunder is,

{(15, 3), (25, 5), (35, 7), (45, 9)}

Since, Distance from lightening (d) ∝ Time between lightening and thunder (t)

d = kt

Here k = proportionality constant

k = $\frac{d}{t}$

From the data set one point is (15, 3).

k = $\frac{3}{15}$

k = $\frac{1}{5}$ miles per second

Therefore, proportionality constant is $\frac{1}{5}$ miles per second.

3 0

3 years ago

May you please help me I am so confused

Tcecarenko [31]

Answer:

109 students need to attend

Step-by-step explanation:

156 + 280 = 436

436 ÷ 4 = 109

5 0

3 years ago

Read 2 more answers

A small airplane can fly 12 miles in 3 minutes. At this rate, how far can the airplane fly in 1 hour?

Sidana [21]

Answer:

The airplane can fly up to 240 miles in a hour

Step-by-step explanation:

Cross multiply

(12)(60)=3x

720=3x

Divide 3 on both sides

x=240

7 0

3 years ago

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Two boats start their journey from the same point A and travel long directions AC and AD as shown below what is the distance CD

Olegator [25]

I think its B but ima have to check again and get back to you

4 0

3 years ago

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A bridge in the shape of an arch connects two cities separated by a river. The two ends of the bridge are located at (–7, –13) a

sdas [7]

Answer:

$y=-\dfrac{13}{49}x^2$

Step-by-step explanation:

The shape of an arch corresponds to a parabola.

the general equation for a parabola is:

$y=ax^2+bx+c$

we're given three coordinates: (-7,-13),(7,-13) and (0,0)

so we can plug these values in the general equation to make 3 separate equations:

(x,y) = (-7,-13)

$-13=a(-7)^2+b(-7)+c$

$49a-7b+c=-13$

(x,y) = (7,-13)

$-13=a(7)^2+b(7)+c$

$49a+7b+c=-13$

(x,y) = (0,0)

$0=a(0)^2+b(7)+c$

$c=0$

so we have three equations. and we can solve them simultaneously to find the values of a,b, and c.

we've already found c = 0, let's use substitute it to other equations.

$49a-7b+c=-13\quad\Rightarrow\quad49a-7b=-13$

$49a+7b+c=-13\quad\Rightarrow\quad49a+7b=-13$

we can solve these two equation using the elimination method, by simply adding the two equations

$\quad\quad49a-7b=-13\\+\quad49a+7b=-13$

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

$\quad\quad 98a=-26$

$\quad\quad a=-\dfrac{13}{49}$

Now we can plug this value of a in any of the two equations.

$49a-7b=-13$

$49\left(-\dfrac{13}{49}\right)-7b=-13$

$-13-7b=-13$

$-7b=0$

$b=0$

We have the values of a,b, and c. We can plug them in the general equation to find the equation of the arch.

$y=\left(-\dfrac{13}{49}\right)x^2+0x+0$

$y=-\dfrac{13}{49}x^2$

$49y=-13x^2$

This our equation of the arch!

5 0

3 years ago