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3 years ago

What is the third angle of a right triangle if one of the angles measures 51.

Mathematics

1 answer:

Elodia [21]3 years ago

3 0

Answer:

Step-by-step explanation:

The short answer is 39.

Every triangle has 180 degrees. There are no exceptions to this rule.

Since a triangle has 3 angles, all three together must add up to 180o

A right angle = 90 degrees always.

You are given 51 degrees as your second angle

The third one is x

x + 51 + 90 = 180 Total of three angles must be 180

x + 141 = 180 The left has been added to give 141

x = 180 - 141 Subtract 141 from both sides

x = 39 The third angle = 39

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consider a sequence of independent tosses of a biased coin at times k=0,1,2,…,n. On each toss, the probability of Heads is p, an

omeli [17]

Answer:

1. p*(1-p)

2. n*p*(1-p)

3. p*(1-p)

4. 0

5. p^2*(1-p)^2

6. 57/64

Step-by-step explanation:

1. Let Ik denote the reward (possibly 0) given at time k, for k∈{1,2,…,n}. Find E[Ik].

E[Ik]= p*(1-p)

2. Using the answer to part 1, find E[R].

E[R]= n*p*(1-p)

The variance calculation is more involved because the random variables I1,I2,…,In are not independent. We begin by computing the following values.

3. If k∈{1,2,…,n}, then

E[I2k]= p*(1-p)

4. If k∈{1,2,…,n−1}, then

E[IkIk+1]= 0

5. If k≥1, ℓ≥2, and k+ℓ≤n, then

E[IkIk+ℓ]= p^2*(1-p)^2

6. Using the results above, calculate the numerical value of var(R) assuming that p=3/4, n=10.

var(R)= 57/64

5 0

3 years ago

How many half metres together measure 4 1-2m

telo118 [61]

Make it an improper fraction with two as the denominator, and you'll get 9/2. There are 9 halves in 4 1/2 meters

5 0

3 years ago

Rewrite each of the following durations using eighth notes. Write in words and as a fraction: 1 quarter note 1 half note 1 full

LenKa [72]

Answer: one third. one half and 1 whole

Step-by-step explanation:

4 0

3 years ago

What is the solution to the following system of equations? x − 4y = 6 2x + 2y = 12 (0, 10) (10, 0) (6, 0) (0, 6)

frozen [14]

Answer:

(6,0)

Step-by-step explanation:

The given system has equations:

$x-4y=6$

$2x+2y=12$

Multiply the top equation by 2 to get:

$2x-8y=12$

$2x+2y=12$

Subtract the top equation form the bottom equation to get:

$2x-2x+2y--8y=12-12$

$\implies 10y=0$

$\implies y=0$

Put y=0 into $x-4y=6$

$x-4*0=6$

$\implies x=6$

Therefore the solution is (6,0)

4 0

3 years ago

R leaks out of a barrel so that the rate of change in the water level is proportional to the square root of the depth of the wat

Irina-Kira [14]

Let y(t) represent the level of water in inches at time t in hours. Then we are given ...
y'(t) = k√(y(t)) . . . . for some proportionality constant k
y(0) = 30
y(1) = 29

We observe that a function of the form
y(t) = a(t - b)²
will have a derivative that is proportional to y:
y'(t) = 2a(t -b)

We can find the constants "a" and "b" from the given boundary conditions.
At t=0
30 = a(0 -b)²
a = 30/b²
At t=1
29 = a(1 - b)² . . . . . . . . . substitute for t
29 = 30(1 - b)²/b² . . . . . substitute for a
29/30 = (1/b -1)² . . . . . . divide by 30
1 -√(29/30) = 1/b . . . . . . square root, then add 1 (positive root yields extraneous solution)
b = 30 +√870 . . . . . . . . simplify

The value of b is the time it takes for the height of water in the tank to become 0. It is 30+√870 hours ≈ 59 hours 29 minutes 45 seconds

5 0

3 years ago