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3 years ago

Instructions: Problem 1 ! Find the missing angle in the image below. Do not include spaces in your answers

Mathematics

1 answer:

sweet-ann [11.9K]3 years ago

5 0

Answer:

40 degrees

Step-by-step explanation:

The 100 degree angle is supplementary to angle CED. This means CED will end up being 80 degrees. Since the angles in all triangles equate to 180 degrees 80 + 60 + angle D must equal 180 degrees. Therefore, angle D has to be 40 degrees.

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Find the x-intercept and

svetlana [45]

9514 1404 393

Answer:

x-intercept: (16, 0)

y-intercept: (0, 8)

Step-by-step explanation:

Each intercept is found by setting the other variable to zero and solving for the variable of interest.

I like to find the intercepts from this form because it basically involves dividing the constant by the variable coefficient.

x-intercept

y = 0, so we have 4x = 64 ⇒ x = 64/4 = 16

x-intercept is (16, 0)

y-intercept

x = 0, so we have 8y = 64 ⇒ y = 64/8 = 8

y-intercept is (0, 8)

_____

Additional comment

There is a form of the linear equation called the "intercept form" that looks like this:

x/a +y/b = 1

where 'a' is the x-intercept and 'b' is the y-intercept.

You can get this form by dividing the standard form equation by the constant. Here, that gives ...

4x/64 +8y/64 = 1

x/16 +y/8 = 1

This is nice because it gives both intercepts with one operation (divide by the constant). It's easy enough to do, but not always easy to explain. This form of the equation of a line is rarely seen.

5 0

2 years ago

What is the radius of a circle with a circumference of 125.66

Anit [1.1K]

It's about 20 units
Hope this helped :)

7 0

3 years ago

Read 2 more answers

Find the mean, variance &a standard deviation of the binomial distribution with the given values of n and p.

MrMuchimi

A random variable following a binomial distribution over $n$ trials with success probability $p$ has PMF

$f_X(x)=\dbinom nxp^x(1-p)^{n-x}$

Because it's a proper probability distribution, you know that the sum of all the probabilities over the distribution's support must be 1, i.e.

$\displaystyle\sum_xf_X(x)=\sum_{x=0}^n\binom nxp^x(1-p)^{n-x}=1$

The mean is given by the expected value of the distribution,

$\mathbb E(X)=\displaystyle\sum_xf_X(x)=\sum_{x=0}^nx\binom nxp^x(1-p)^{n-x}$
$\mathbb E(X)=\displaystyle\sum_{x=1}^nx\frac{n!}{x!(n-x)!}p^x(1-p)^{n-x}$
$\mathbb E(X)=\displaystyle\sum_{x=1}^n\frac{n!}{(x-1)!(n-x)!}p^x(1-p)^{n-x}$
$\mathbb E(X)=\displaystyle np\sum_{x=1}^n\frac{(n-1)!}{(x-1)!((n-1)-(x-1))!}p^{x-1}(1-p)^{(n-1)-(x-1)}$
$\mathbb E(X)=\displaystyle np\sum_{x=0}^n\frac{(n-1)!}{x!((n-1)-x)!}p^x(1-p)^{(n-1)-x}$
$\mathbb E(X)=\displaystyle np\sum_{x=0}^n\binom{n-1}xp^x(1-p)^{(n-1)-x}$
$\mathbb E(X)=\displaystyle np\sum_{x=0}^{n-1}\binom{n-1}xp^x(1-p)^{(n-1)-x}$

The remaining sum has a summand which is the PMF of yet another binomial distribution with $n-1$ trials and the same success probability, so the sum is 1 and you're left with

$\mathbb E(x)=np=126\times0.27=34.02$

You can similarly derive the variance by computing $\mathbb V(X)=\mathbb E(X^2)-\mathbb E(X)^2$ , but I'll leave that as an exercise for you. You would find that $\mathbb V(X)=np(1-p)$ , so the variance here would be

$\mathbb V(X)=125\times0.27\times0.73=24.8346$

The standard deviation is just the square root of the variance, which is

$\sqrt{\mathbb V(X)}=\sqrt{24.3846}\approx4.9834$

7 0

3 years ago

Reduce to the lowest term: 30/40

natulia [17]

Answer:

3/4

Step-by-step explanation:

Reduce both the numerator and the denominator by 10, their greatest common factor.

6 0

3 years ago

The triangle below is isosceles (two congruent sides). Find the value for x. one side say x + 3.8 and the other says 16 and then

Ugo [173]

The isosceles triangle has two congruent sides

Their lengths are ( x + 3.8 ) and 16

Equate them :

x+3.8=16

Solve for x:
3=16-3.8=12.2

4 0

3 years ago