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Yakvenalex [24]

3 years ago

6

on a two week job a repairman works a total of 70 hours. He charges $75 plus $40 per hour. An equation shows this relationship w

here x is the number of hours and y is the total fee. Write the equation. What is the slow and y intercept

1 answer:

AlekseyPX3 years ago

6 0

the solution is Y= 40•70+75x

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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

The expression sin 80 cos 70 + cos 80 sin 70 is equivalent to

vekshin1

Sin(70+80) = sin 150.......................

8 0

3 years ago

What is 5 divided by 25

disa [49]

Answer:

0.2

Step-by-step explanation:

5 0

3 years ago

Read 2 more answers

A stadium has 49000 seats. Seats sell for $25 in section A, $20 in section B, and $15 in section C. The number of seats in secti

eimsori [14]

Answer:

A stadium has 49000 seats.

Seats sell for $25 in Section A, z

$20 in Section B,-------------------x seats

$15 in Section C. ------------------y seats

(x+y)=z

25(x+y)+20x+15y=1052000

25x+25y+20x+15y=1052000

45x+40y=1052000

/5

9x+8y=210400------------------1

2x+2y=49000

/2

Step-by-step explanation:

4 0

4 years ago

The graph represents function 1, and the equation represents funtion 2:

horsena [70]

Answer:

8

Step-by-step explanation:

we know that

The rate of change of a linear equation is a constant that is the same that the slope

step 1

we have

The equation of the graph (function 1) is equal to

y=4

Is a horizontal line

The slope is equal to zero

so

The rate of change of function 1 is zero

step 2

The equation of the function 2 is

$y=8x+12$

This is a linear equation in slope intercept form

where

the slope is equal to m=8

so

The rate of change of function 2 is 8

therefore

The rate of change of function 2 is 8 more than the rate of change of function 1

5 0

3 years ago