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3 years ago

Does 2^8 equal (3sqrt{16})^6

Mathematics

1 answer:

ale4655 [162]3 years ago

4 0

Answer:

Does 2⁸ = (3√16)⁶? No.

Step-by-step explanation:

2⁸ = (3√16)⁶

Evaluate 2⁸. This can simply be written out as:

2 * 2 * 2 * 2 * 2 * 2 * 2 * 2

4 * 2 * 2 * 2 * 2 * 2 * 2

8 * 2 * 2 * 2 * 2 * 2

16 * 2 * 2 * 2 * 2

32 * 2 * 2 * 2

64 * 2 * 2

128 * 2

256.

256 = (3√16)⁶

Evaluate √16.

256 = (3*4)⁶

Multiply 3 and 4.

256 = 12⁶

Evaluate 12⁶. This can be rewritten as:

12 * 12 * 12 * 12 * 12 * 12

144 * 12 * 12 * 12 * 12

1728 * 12 * 12 * 12

20736 * 12 * 12

248832 * 12

2985984.

Since 256 ≠ 2985984, the answer to this question is no.

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If a fair coin is flipped 15 times, what is the probability that there are more heads than tails?

ludmilkaskok [199]

Answer:

The probability that there are more heads than tails is equal to $\dfrac{1}{2}$ .

Step-by-step explanation:

Since the number of flips is an odd number, there can't be an equal number of heads and tails. In other words, there are either

more tails than heads, or,
more heads than tails.

Let the event that there are more heads than tails be $A$ . $\lnot A$ (i.e., not A) denotes that there are more tails than heads. Either one of these two cases must happen. As a result, $P(A) + P(\lnot A) = 1$ .

Additionally, since this coin is fair, the probability of getting a head is equal to the probability of getting a tail on each toss. That implies that (for example)

the probability of getting 7 heads out of 15 tosses will be the same as
the probability of getting 7 tails out of 15 tosses.

Due to this symmetry,

the probability of getting more heads than tails (A is true) is equal to
the probability of getting more tails than heads (A is not true.)

In other words $P(A) = P(\lnot A)$ .

Combining the two equations:

$\left\{\begin{aligned}&P(A) + P(\lnot A) = 1 \cr &P(A) = P(\lnot A)\end{aligned}\right.$ ,

$P(A) = P(\lnot A) = \dfrac{1}{2}$ .

In other words, the probability that there are more heads than tails is equal to $\dfrac{1}{2}$ .

This conclusion can be verified using the cumulative probability function for binomial distributions with $\dfrac{1}{2}$ as the probability of success.

$\begin{aligned}P(A) =& P(n \ge 8) \cr =& \sum \limits_{i = 8}^{15} {15 \choose i} (0.5)^{i} (0.5)^{15 - i}\cr =& \sum \limits_{i = 8}^{15} {15 \choose i} (0.5)^{15}\cr =& (0.5)^{15} \left({15 \choose 8} + {15 \choose 9} + \cdots + {15 \choose 15}\right) \cr =& (0.5)^{15} \left({15 \choose (15 - 8)} + {15 \choose (15 - 9)} + \cdots + {15 \choose (15 - 15)} \right) \cr =& (0.5)^{15} \left({15 \choose 7} + {15 \choose 6} + \cdots + {15 \choose 0}\right)\end{aligned}$

$\begin{aligned}\phantom{P(A)} =& \sum \limits_{i = 0}^{7} {15 \choose i} (0.5)^{15}\cr =& P(n \le 7) \cr =& P(\lnot A)\end{aligned}$ .

6 0

4 years ago

Points M and N are both on ZB with M between Z and N. ZM = 10

maxonik [38]

Answer:

Your answer is 40%

Step-by-step explanation:

It is 20 units between Z and B.

We add 2 more points, and one of them is at the the halfway point of the entire line.(M)

One of them is only 2 units away from B.(N)

That means our line is halved, so from 20/20 possible places a point could go and land in the right area is now 10/20.

Minus 2 from that; to take into count of the N to B, and you have 8/20

8/20 is just 40%

5 0

3 years ago

3.) The height of the baseball can be modeled by the function Hs= -16s2+96s where s represents the time in seconds the ball is i

Aleks04 [339]

Answer:

what's the topic hahhahahahah

3 0

3 years ago

The sum of 2 consecutive numbers is 69. What are the numbers?

Vaselesa [24]

Answer:

Step-by-step explanation:

z - some integer

then the consecutive integer would be:

z+1, (or z-1)

the sum is 69 so:

z + z+1 = 96

2z = 68

z = 34

z+1 = 34 + 1 = 35

(or:

z + z-1 = 69

2z = 70

z = 35

z-1 = 35 - 1 = 34)

7 0

4 years ago

Can someone please help. ASAP

just olya [345]

Answer:

This is called a <u><em>parallelogram</em></u>

Area = base * Height

Area = 4 * 3

Area = 12 cm²

3 0

3 years ago

Read 2 more answers