A rectangular athletic field is twice long as it is wide the perimeter is 90 yard dismention?

A. Describe the connection of the pattern of outcomes to Pascal’s triangle.

pychu [463]

Answer:

The answer to the question is;

A. The pattern of outcomes of 0 heads, 1 head, 2 heads ... n heads when arranged in the Pascal's triangle is given by the row of the triangles with the lowest at the edges and highest outcome in the middle potion of the rows in the Pascal's triangle.

B. The number of total possible outcomes in a row n is 2ⁿ.

Step-by-step explanation:

To solve the question, we note that.

Pascal's triangle is an important sequence of numbers formed by starting with 1 at the top of the triangle followed by 1s on the outer edges of the triangle and the numbers directly below two adjacent numbers is the sum of the two adjacent numbers.

In probability theory, such as in throwing a coin, Pascal's triangle indicates the number of possible heads obtained when n number of coins is thrown, that is, 0 heads, 1 head 2 heads etc. as follows

Number of coins Possible head outcome Total outcome

0 coin 1 1

1 coin 1 1 2

2 coins 1 2 1 4

3 coins 1 3 3 1 8

4 coins 1 4 6 4 1 16

The above triangle means that when

0 coin is flipped, the number of 0 heads is 1

1 coin is flipped, the number of 0 heads is 1 (T) and 1 head is 1 (H)

2 coins are flipped, the number of 0 heads is 1, (TT), 1 head is 2 (TH), (HT) and 2 heads is 1 (HH)

3 coins are flipped 0 heads = 1 (TTT), 1 head = 3, (TTH), (THT), (HTT), the number of 2 heads = 3, (HHT), (HTH), (TTH) and the number of 3 heads = 1, (HHH).

B. The pattern in the number of total possible outcomes is

1, 2, 4, 8, 16 which is =2 raised to the power of the number of coin tossed for a particular row as follows

Number of coin tossed = 0 = 2⁰ = 1 = Total possible outcome

Number of coin tossed = 1 = 2¹ = 2 = Total possible outcomes

Number of coin tossed = 2 = 2² = 4 = Total possible outcomes

Number of coin tossed = 3 = 2³ = 8 = Total possible outcomes

Number of coin tossed = 4 = 2⁴ = 16 = Total possible outcomes

Therefore total number of possible outcome = 2ⁿ where n = number of coins tossed.

6 0

3 years ago

Two numbers N and 16 have LCM = 48 and GCF = 8. Find N.

RSB [31]

LCM=product of highest occurring primes in the numbers prime factorization.

GCF=product of shared primes in the numbers prime factorization.

16=2*2*2*2

Since the GCF is 8 N and 16 share only 2*2*2

Since the LCM is 48 and 16 has 2*2*2*2 the other number has a factor of 3

So the other number is 2*2*2*3=24

N=24

7 0

3 years ago

A new shop is being built in town and the design shows that it will be a rectangular prism with 8 meters along the front 12 mete

Kisachek [45]

Volume of space inside shop is 288 m³

<u>Given that;</u>

Dimensions of rectangle = 8 meter , 12 meter , 3 meter

Volume of space inside shop

<u>Computation:</u>

Volume of rectangle = [l][b][h]

Volume of rectangle = Volume of space inside shop

So,

Volume of space inside shop = [8][12][3]

Volume of space inside shop = [96][3]

Volume of space inside shop = 288 m³

Learn more;

brainly.com/question/15019502?referrer=searchResults

8 0

2 years ago

2. Find the general relation of the equation cos3A+cos5A=0

mars1129 [50]

<h2>Answer:</h2>

$A=\frac{\pi}{8}+\frac{n\pi}{4}or\ A=\frac{\pi}{2}+n\pi$

<h2>Step-by-step explanation:</h2>

<h3>Find angles</h3>

$cos3A+cos5A=0$

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<h3>Transform the expression using the sum-to-product formula</h3>

$2cos(\frac{3A+5A}{2})cos(\frac{3A-5A}{2})=0$

________________________________________________________

<h3>Combine like terms</h3>

$2cos(\frac{8A}{2})cos(\frac{3A-5A}{2})=0\\\\ 2cos(\frac{8A}{2})cos(\frac{-2A}{2})=0$

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<h3>Divide both sides of the equation by the coefficient of variable</h3>

$cos(\frac{8A}{2})cos(\frac{-2A}{2})=0$

________________________________________________________

<h3>Apply zero product property that at least one factor is zero</h3>

$cos(\frac{8A}{2})=0\ or\ cos(\frac{-2A}{2})=0$

________________________________________________________

<h3>Cross out the common factor</h3>

$cos\ 4A=0$

________________________________________________________

<h3>Solve the trigonometric equation to find a particular solution</h3>

$4A=\frac{\pi}{2}or\ 4A=\frac{3\pi}{2}$

________________________________________________________

<h3>Solve the trigonometric equation to find a general solution</h3>

$4A=\frac{\pi}{2}+2n\pi \ or\\ \\ 4A=\frac{3 \pi}{2}+2n \pi\\ \\A=\frac{\pi}{8}+\frac{n \pi}{4\\}$

________________________________________________________

<h3>Reduce the fraction</h3>

$cos(-A)=0$

________________________________________________________

<h3>Simplify the expression using the symmetry of trigonometric function</h3>

$cosA=0$

________________________________________________________

<h3>Solve the trigonometric equation to find a particular solution</h3>

$A=\frac{\pi }{2}\ or\ A=\frac{3 \pi}{2}$

________________________________________________________

<h3>Solve the trigonometric equation to find a general solution</h3>

$A=\frac{\pi}{2}+2n\pi\ or\ A=\frac{3\pi}{2}+2n\pi,n\in\ Z$

________________________________________________________

<h3>Find the union of solution sets</h3>

$A=\frac{\pi}{2}+n\pi$

________________________________________________________

<h3>Find the union of solution sets</h3>

$A=\frac{\pi}{8}+\frac{n\pi}{4}\ or\ A=\frac{\pi}{2}+n\pi ,n\in Z$

<em>I hope this helps you</em>

5 0

2 years ago

What is the y- coordinate of point W

Alexeev081 [22]

Answer: -1.5

Step-by-step explanation:

because the y-axis is the one that goes up and down and w is on -1.5 of it

5 0

3 years ago