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3 years ago

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Supplementary angles are two angles whose measures have a sum of 180∘. What is the value of x? Write and solve an equation for x

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1 answer:

Evgen [1.6K]3 years ago

8 0

I is a good friend and a good uuuuuuyyuyhyyytfikh..

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a bottle of juice holds 3/8 gallon when it is full. if 1/3 of the juice has been poured out, how much juice is left in the bottl

taurus [48]

Let's get the denominators of both fractions to be the same before moving on, aka finding the least common multiple of the denominators.

8 and 3 have a LCM of 24. So, we have to multiply 1/3 by 8 and 3/8 by 3.

1/3 * 8/8 = 8/24

3/8 * 3/3 = 9/24

There is only 1/24 of juice left in the bottle if the remaining amount of juice has 1/3 poured out.

Hope that helped.

4 0

3 years ago

Muriel says she has written a system of two linear equations that has an infinite number of solutions. One of the equations of t

Vanyuwa [196]

An infinite number of solutions means a coincident line...it is the same line
3y = 2x - 9...divide by 3
y = 2/3x - 3...hmm...same line as answer choice b....they are coincident lines and have infinite solutions

3 0

4 years ago

Read 2 more answers

The radius of a cylindrical gift box is (4x + 1) inches. The height of the gift box is three times the radius. What is the sur

user100 [1]

Answer:

S = 128πx² + 64πx + 8π

Step-by-step explanation:

Suraface area of a cylinder is given by:

S = 2πrh + 2πr²

We know that the height is 3 times as big as the radius, hence:

h = 3r

so we can plug in the new h value and rewrite the S equation as:

S = 2πrh + 2πr²

S = 2πr(3r) + 2πr²

S = 6πr² + 2πr²

S = 8πr²

We're given in the question that the radius is (4x + 1) inches, so plug that into r.

Given: r = 4x + 1

Therefore,

S = 8πr²

S = 8π(4x + 1)²

S = 8π(16x²+8x+1)

S = 128πx² + 64πx + 8π

8 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

Please response ASAP!<br><br> 2+3=<br> 9+2=<br> 0+1=<br> 7+4=

Stolb23 [73]

2+3=5

9+2=11

0+1=1

7+4=11

3 0

3 years ago

Read 2 more answers