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anastassius [24]
3 years ago
15

A triangle with equal sides and a square have the same perimeters. The length of a side of the triangle is 2x + 2. The length of

a side of the square is x + 8. Write and solve an equation to find x.
Mathematics
1 answer:
andreev551 [17]3 years ago
3 0

Answer:

x=13

Step-by-step explanation:

3(2x+2)=4(x+8)\\6x+6=4x+32\\2x+6=32\\2x=26\\x=13

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6.8 Use the Normal approximation. Suppose we toss a fair coin 100 times. Use the Normal approximation to find the probability th
Maru [420]

Answer:

(a) The probability that proportion of heads is between 0.30 and 0.70 is 1.

(b) The probability that proportion of heads is between 0.40 and 0.65 is 0.9759.

Step-by-step explanation:

Let <em>X</em> = number of heads.

The probability that a head occurs in a toss of a coin is, <em>p</em> = 0.50.

The coin was tossed <em>n</em> = 100 times.

A random toss's result is independent of the other tosses.

The random variable <em>X</em> follows a Binomial distribution with parameters n = 100 and <em>p</em> = 0.50.

But the sample selected is too large and the probability of success is 0.50.

So a Normal approximation to binomial can be applied to approximate the distribution of \hat p<em> </em>(sample proportion of <em>X</em>) if the following conditions are satisfied:

  1. np ≥ 10
  2. n(1 - p) ≥ 10

Check the conditions as follows:

 np=100\times 0.50=50>10\\n(1-p)=100\times (1-0.50)=50>10

Thus, a Normal approximation to binomial can be applied.

So,  \hat p\sim N(p,\ \frac{p(1-p)}{n})

\mu_{p}=p=0.50\\\sigma_{p}=\sqrt{\frac{p(1-p)}{n}}=0.05

(a)

Compute the probability that proportion of heads is between 0.30 and 0.70 as follows:

P(0.30

                              =P(-4

Thus, the probability that proportion of heads is between 0.30 and 0.70 is 1.

(b)

Compute the probability that proportion of heads is between 0.40 and 0.65 as follows:

P(0.40

                              =P(-2

Thus, the probability that proportion of heads is between 0.40 and 0.65 is 0.9759.

6 0
3 years ago
Math HW please help.
Margarita [4]

Answer:

A  x = 3

Step-by-step explanation:

A = ½θR²

R = x

x = √(2Α/θ)

θ = (360 - 60)(π/180) = 5π/3 radians

x = √(2(15π/2) / (5π/3))

x = √(15π(3/5π))

x = √9

x = 3

7 0
3 years ago
A store sells a gas can that can hold 35/8 gallons of gasoline. What is of the gas can in gallons, expressed as a mix number?
Novay_Z [31]
I thinks its 4.375 all u do is divide 35 by 8
7 0
3 years ago
Carlo spent $107.60 on 8 books. If each book cost the same amount, how much did one book cost?
dlinn [17]

Answer:

$13.45

Step-by-step explanation:

Divide $107.60 by 8

4 0
3 years ago
Read 2 more answers
How to answer the problem
Snowcat [4.5K]

(3 + 2) - 3² = 5 - 9 = -4

Regards :)

3 0
3 years ago
Read 2 more answers
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