In the triangle below, what ratio is cos h?

Using the bijection rule to count binary strings with even parity.

AleksandrR [38]

Answer:

Lets denote c the concatenation of strings. For a binary string a in B9, we define the element f(a) in E10 this way:

f(a) = a c {1} if a has an odd number of 1's
f(a) = a c {0} if a has an even number of 1's

Step-by-step explanation:

To show that the function f defined above is a bijective function, we need to prove that f is well defined, injective and surjective.

f is well defined:

To see this, we need to show that f sends elements fromo b9 to elements of E10. first note that f(a) has 1 more binary integer than a, thus, it has 10. if a has an even number of 1's, then f(a) also has an even number because a 0 was added. On the other hand, if a has an odd number of 1's, then f(a) has one more 1, as a consecuence it will have an even number of 1's. This shows that, independently of the case, f(a) is an element of E10. Thus, f is well defined.

f is injective (or one on one):

If a and b are 2 different binary strings, then f(a) and f(b) will also be different because the first 9 elements of f(a) form a and the first elements of f(b) form b, thus f(a) is different from f(b). This proves that f in injective.

f is surjective:

Let y be an element of E10, Let x be the first 9 elements of y, then f(x) = y:

If x has an even number of 1's, then the last digit of y has to be 0, and f(x) = x c {0} = y
If x has an odd number of 1's, then the last digit of y has to be a 1, otherwise it wont be an element of E10, and f(x) = x c {1} = y

This shows that f is well defined from B9 to E10, injective, and surjective, thus it is a bijection.

3 0

4 years ago

Assume that the wooden triangle shown is a right triangle.

77julia77 [94]

a.

a^2 + b^2 = c^2

The legs are a and b. c is the hypotenuse.

Let a = 6x + 9y; b = 8x + 12y; c = 10x + 15y

The equation is:

(6x + 9y)^2 + (8x + 12y)^2 = (10x + 15y)^2

b.

Now we square each binomial and combine like terms on each side.

36x^2 + 108xy + 81y^2 + 64x^2 + 192 xy + 144y = 100x^2 + 300xy + 225y^2

36x^2 + 64x^2 + 108xy + 192xy + 81y^2 + 144y^2 = 100x^2 + 300xy + 225y^2

100x^2 + 300xy + 225y^2 = 100x^2 + 300xy + 225y^2

The two sides are equal, so it is an identity.

4 0

3 years ago

Read 2 more answers

If the mean of a normally distributed population is -10 with a standard deviation of 2, what is the likelihood of obtaining a va

ira [324]

Answer:

93.32% probability of obtaining a value less than or equal to -7.

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

$\mu = -10, \sigma = 2$

What is the likelihood of obtaining a value less than or equal to -7?

This is the pvalue of Z when X = -7.

So

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{-7 -(-10)}{2}$

$Z = \frac{3}{2}$

$Z = 1.5$

$Z = 1.5$ has a pvalue of 0.9332.

So there is a 93.32% probability of obtaining a value less than or equal to -7.

6 0

3 years ago

PLEASE HELP ASAP!!! I AM REALLY STUCK AND WILL AWARD BRAINLIEST!!!

Setler [38]

Answer:

Does not go

Step-by-step explanation:

$x = \frac{10}{3} \\ y = - 2$

$y = kx \\ - 2 = k( \frac{10}{3} ) \\ \\ k = \frac{ - 2 \times 3}{10} \\ \\ k = \frac{ - 1 \times 3}{5} \\ \\ k = - \frac{3}{5}$

So the equation is

$y = - \frac{ 3}{5} x$

M(-10, 15)

$x = - 10 \\ \\ y = - \frac{3}{5} x \\ \\ y = - \frac{3}{5} ( - 10) \\ \\ y = \frac{3}{5} (10) \\ \\ y = 3 (2) \\ \\ y = 6$

The graph Does not go through point M bcz when the value of x = - 10 then the value of y is 6, not 15

5 0

3 years ago

What is the perimeter of the trapezoid? 10 m 8 m 10 m 18 m meters

matrenka [14]

Answer:

14,400

Step-by-step explanation:

multiply all variables when doing perimeter

4 0

3 years ago