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3 years ago

What is the probability of getting tails 4 times in a row while flipping a coin?

Mathematics

1 answer:

skelet666 [1.2K]3 years ago

7 0

Answer:

$P=0.0625$

Step-by-step explanation:

The probability of getting one tails is a half.

The probability of getting another tails given you had a tails is:

$\frac{1}{2}*\frac{1}{2}=(\frac{1}{2})^2=\frac{1}{4}$

The probability of getting n tails in general is given by:

$(\frac{1}{2})^n = \frac{1}{2^n}$

So, when we have four tails - our value for n is four.

$(\frac{1}{2})^4=\frac{1}{2^4}=\frac{1}{16}=0.0625$

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Minnesota Public Radio wants to duplicate a survey conducted in 2016 that found that 65% of adults living in Minnesota felt that

vesna_86 [32]

Answer:

The number of people needed is $n =684$

Step-by-step explanation:

From the question we are told that

The population proportion is $p = 0.65$

The margin of error is $E = 0.03$

From the question we are told the confidence level is 90% , hence the level of significance is

$\alpha = (100 - 90 ) \%$

=> $\alpha = 0.10$

Generally from the normal distribution table the critical value of $\frac{\alpha }{2}$ is

$Z_{\frac{\alpha }{2} } = 1.645$

Generally the sample size is mathematically represented as

$n =[ \frac{Z_{\frac{\alpha }{2} }}{E} ]^2 * p(1-p)$

=> $n =[ \frac{1.645 }{0.03} ]^2 * 0.65(1-0.65)$

=> $n =684$

6 0

3 years ago

The radius of a circle is 3 m. Find its circumference in terms of pi.

kozerog [31]

The circumference of a circle is $2\pi r$

r is the radius --> 3m

Circumference = $2\pi (3) = 6\pi$

It says to leave in terms of pi which means that we won't solve $6\pi$

Thus the answer is $6\pi$ .

Hope that helped!

7 0

2 years ago

Simplify the expression: <br> a.<br> b^2+49–(b–7)^2<br> b.<br> 2a+6b)^2–24ab

klemol [59]

Part a b2+49−(b−7)2

Distribute:

=b2+49+−b2+14b+−49

Combine Like Terms:

=b2+49+−b2+14b+−49

=(b2+−b2)+(14b)+(49+−49)

=14b

Answer:

=14b
part b

(2a+6b)2−24ab

Distribute:

=4a2+24ab+36b2+−24ab

Combine Like Terms:

=4a2+24ab+36b2+−24ab

=(4a2)+(24ab+−24ab)+(36b2)

=4a2+36b2

Answer:

=4a2+36b2

5 0

3 years ago

Use the properties of addition to simplify 2d + 2 - 7f+ 4d - f.

Rudik [331]

6d - 8f + 2

hope this helps

8 0

3 years ago

Read 2 more answers

Rania solves the equation below by first squaring both sides of the equation.

Anuta_ua [19.1K]

Answer:

The extraneous solution is 4.

Step-by-step explanation:

First, let us calculate the value of 'x' without squaring both side of the expression. This is illustrated below:

-5 = 3x - 7

Collect like terms

-5 + 7 = 3x

2 = 3x

Divide both side by 3

x = 2/3.

Now, let us calculate the value of 'x' by squaring both side of the expression. This is illustrated below:

(-5)^2 = (3x - 7)^2

25 = (3x - 7)(3x - 7)

25 = 9x^2 - 21x - 21x + 49

9x^2 - 42x + 49 - 25 = 0

9x^2 - 42x + 24 = 0

Solving by factorisation:

Multiply the first term i.e 9x^2 and 3rd term i.e 24 together. The result is 216x^2.

Next, we shall obtain two factors of 216x^2 such that when we add them together, it will give the 2nd term i.e -42x in the equation. These factors are: -6x and -36x

Now we can write the above equation as:

9x^2 - 42x + 24 = 0

9x^2 - 6x - 36x + 24 = 0

3x(3x - 2) - 12(3x - 2) = 0

(3x - 12)(3x - 2) = 0

3x - 12 = 0 or 3x - 2 = 0

3x = 12 or 3x = 2

x = 12/3 or x = 2/3

x = 4 or 2/3.

We can see that when we solve the question without squaring both side, the value of x is 2/3. But when we solve by squaring both side, the value of x are 4 and 2/3.

Therefore, the extraneous solution to the question is 4.

6 0

3 years ago