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aev [14]
2 years ago
11

Does y = 2x + 4 show direct variation?

Mathematics
2 answers:
monitta2 years ago
7 0

Answer:

NO

Step-by-step explanation:

in order for it to be a direct variation, "+4" must be out of the equation. y=kx

Elza [17]2 years ago
5 0

Answer:

no

Step-by-step explanation:

Direct variation is of the form

y = kx

This has a constant added

y = kx+b so it is not a direct variation

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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
3 years ago
When sawyer went to sleep, the temperature outside was -2°
zubka84 [21]
When Sawyer went to sleep it was -2.

Overnight the temperature dropped -15 degrees more.

-2 + -15 = -17

When Sawyer woke up, the temperature was -17 degrees.
6 0
2 years ago
3/4 x 5/6 plssssssssssss help
yan [13]

the answer is 5/8 :)

3 0
3 years ago
Read 2 more answers
Someone help for Brainiest please
Firdavs [7]

Answer:

\sqrt{4}

Is the answer

3 0
2 years ago
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There is 3 4 of an apple pie left from dinner. Tomorrow, Victor plans to eat 1 4 of the pie that was left. Enter how much of the
lora16 [44]

Answer:

3/16

Step-by-step explanation:

Let the size of the whole apple be T

Given that 3/4 of the apple is left, it means the size left

= 3T/4

Since Victor plans to eat 1/4 of the pie that was left, this amounts to

1/4 * 3T/4

= 3T/16

This means that Victor will eat 3/16 of the whole pie tomorrow

5 0
2 years ago
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