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3 years ago

Suppose a game of 3-D tic tac toe is played on a 6x6x6 cube. How many winning lines of 6-in-a-row are there through the cube?

1 answer:

3 0

There would be 84 winning rows of 6 in a row.

On each face of a cube, there would be 6 vertical rows, 6 horizontal rows and 2 diagonal rows. That is a total of 14 rows per face.

A cube has 6 faces.
6 x 14 = 84

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Given that the points (-1, 10), (2, 10), (2, -2), and (-1, -2) are vertices of a rectangle, what is the ratio of the rectangle's

Helga [31]

Check the picture below.

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3 years ago

A university found that 20% of its students withdraw without completing the introductory statistics course. Assume that 20 stude

Mkey [24]

Answer:

(a) Probability that 2 or fewer will withdraw is 0.2061.

(b) Probability that exactly 4 will withdraw is 0.2182.

(c) Probability that more than 3 will withdraw is 0.5886.

(d) The expected number of withdrawals is 4.

Step-by-step explanation:

We are given that a university found that 20% of its students withdraw without completing the introductory statistics course.

Assume that 20 students registered for the course.

The above situation can be represented through binomial distribution;

$P(X =r) = \binom{n}{r} \times p^{r} \times (1-p)^{n-r};x=0,1,2,3,......$

where, n = number of trials (samples) taken = 20 students

r = number of success

p = probability of success which in our question is probability

that students withdraw without completing the introductory

statistics course, i.e; p = 20%

Let X = Number of students withdraw without completing the introductory statistics course

So, X ~ Binom(n = 20 , p = 0.20)

(a) Probability that 2 or fewer will withdraw is given by = P(X $\leq$ 2)

P(X $\leq$ 2) = P(X = 0) + P(X = 1) + P(X = 2)

= $\binom{20}{0} \times 0.20^{0} \times (1-0.20)^{20-0}+ \binom{20}{1} \times 0.20^{1} \times (1-0.20)^{20-1}+ \binom{20}{2} \times 0.20^{2} \times (1-0.20)^{20-2}$

= $1 \times1 \times 0.80^{20}+ 20 \times 0.20^{1} \times 0.80^{19}+ 190\times 0.20^{2} \times 0.80^{18}$

= 0.2061

(b) Probability that exactly 4 will withdraw is given by = P(X = 4)

P(X = 4) = $\binom{20}{4} \times 0.20^{4} \times (1-0.20)^{20-4}$

= $4845\times 0.20^{4} \times 0.80^{16}$

= 0.2182

(c) Probability that more than 3 will withdraw is given by = P(X > 3)

P(X > 3) = 1 - P(X $\leq$ 3) = 1 - P(X = 0) - P(X = 1) - P(X = 2) - P(X = 3)

= $1-(\binom{20}{0} \times 0.20^{0} \times (1-0.20)^{20-0}+ \binom{20}{1} \times 0.20^{1} \times (1-0.20)^{20-1}+ \binom{20}{2} \times 0.20^{2} \times (1-0.20)^{20-2}+\binom{20}{3} \times 0.20^{3} \times (1-0.20)^{20-3})$

= $1-(1 \times1 \times 0.80^{20}+ 20 \times 0.20^{1} \times 0.80^{19}+ 190\times 0.20^{2} \times 0.80^{18}+1140\times 0.20^{3} \times 0.80^{17})$

= 1 - 0.4114 = 0.5886

(d) The expected number of withdrawals is given by;

E(X) = $n\times p$

= $20 \times 0.20$ = 4 withdrawals

3 0

4 years ago

Write an equation in point-slope form of the line that passes through the point (−3,6) and has a slope of 5.

strojnjashka [21]

Answer:

Below in bold.

Step-by-step explanation:

Point slope form is y - y1 = m(x - x1)

where m = the slope of the line and (x1, y1) is a point on the line.

Here m = 5, x1 = -3 and y1 = 6.

So we have:

y - 6 = 5( x - (-3))

y - 6 = 5(x + 3) (Answer)

3 0

2 years ago

2. The student council at Camp Creek Middle School determines that 3 out of 4

Gemiola [76]

Answer:

Hi there!

Your answer is:

996 students were apart of this survey!

Step-by-step explanation:

3 out of 4 students means that 75% of students prefer the assemblies be held on Friday.

If 75% = 747 students then:

/75

1% = 9.96 students

×100

100% = 996 students

I hope this makes sense!

8 0

3 years ago

A baker uses 4 berries for every muffin which equation can be used to find the number of berries b needed to make m muffins

KATRIN_1 [288]

Answer:

b = 1/4m

Step-by-step explanation:

A baker uses 4 berries for every muffin which equation can be used to find the number of berries b needed to make m muffins

Given :

Berries = b

Muffins = m

4 berries for every muffin

4b = m - - - (1)

Th number of berries to make m muffins:

Make b the subject :

Divide both sides by 4

b = m/4

5 0

3 years ago