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3 years ago

Solve 1/3x-6=2/3. answer plz

Mathematics

2 answers:

MaRussiya [10]3 years ago

8 0

Answer: -16

Step-by-step explanation:

Reika [66]3 years ago

4 0

1/3x-6=2/3
1/3x=2/3+6
1/3x=20/3
=20

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Luba_88 [7]

476+23.8+11.9= 499 510 the answer is 511.70

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3 years ago

During a cold winter, the temperature stayed below zero for 10 days (ranging from −20 to −5). The variance of the temperatures o

Serjik [45]

Answer:

The variance of the temperatures of the 10 day period must be at least zero.

Step-by-step explanation:

The variance is the expectation of the squared deviation of a random variable from its mean. It measures how far a set of numbers are spread out from their average value.

Its unit of measure corresponding to the square of the unit of measure of the variable. In this case, the variance of the temperatures is expressed in (°C)². The variance has a minimum value of 0.

Since the variance is squared, it will always have values greater than zero.

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3 years ago

Which relation is also a function?

ratelena [41]

Answer:

{ (0, 0), (4, 0), (6, 0) }

Step-by-step explanation:

In order to be a function, ordered pairs must have values of x, or the domain, that are different and do not repeat.

4 0

3 years ago

10. Simplify the rational expression by rationalizing the denominator. 3 sqrt 160/sqrt 1350x A) 2 sqrt 15x/15x B) 3 sqrt 160/135

Viefleur [7K]

The simplified expression by rationalizing the denominator is (C) $\frac{4 \sqrt{15x} }{15x}$ .

First we must simplify the expression:
$\frac{3 \sqrt{160} }{\sqrt{1350x} } = \frac{12 \sqrt{10} }{15 \sqrt{6x} } = \frac{4 \sqrt{10} }{5 \sqrt{6x} }$

Then we factor the rational parts and cancel it out:
$\frac{4 \sqrt{2} \sqrt{5} }{5 \sqrt{2} \sqrt{3x} } = \frac{4\sqrt{5} }{5\sqrt{3x} }$

Then we rationalize the expression:
$\frac{4\sqrt{5} }{5\sqrt{3x} } * \frac{\sqrt{3x} }{\sqrt{3x} } = \frac{4 \sqrt{15x} }{5*3x} = \frac{4 \sqrt{15x} }{15x}$

<span>Finally, the simplified expression by rationalizing the denominator is (C) $\frac{4 \sqrt{15x} }{15x}$ .</span>

7 0

3 years ago

A bus travels on an east-west highway connecting two cities A and B that are 100 miles apart. There are 2 services stations alon

melamori03 [73]

Answer:

51/4

Step-by-step explanation:

To begin with you have to understand what is the distribution of the random variable. If X represents the point where the bus breaks down. That is correct.

X~ Uniform(0,100)

Then the probability mass function is given as follows.

$f(x) = P(X=x) = 1/100 \,\,\,\, \text{if} \,\,\,\, 0 \leq x \leq 100\\f(x) = P(X=x) = 0 \,\,\,\, \text{otherwise}$

Now, imagine that the D represents the distance from the break down point to the nearest station. Think about this, the first service station is 20 meters away from city A, and the second station is located 70 meters away from city A then the mid point between 20 and 70 is (70+20)/2 = 45 then we can represent D as follows

$D(x) =\left\{ \begin{array}{ll} x & \mbox{if } 0\leq x \leq 20 \\ x-20 & \mbox{if } 20\leq x < 45\\ 70-x & \mbox{if } 45 \leq x \leq 70\\ x-70 & \mbox{if } 70 \leq x \leq 100\\ \end{array}\right.$

Now, as we said before X represents the random variable where the bus breaks down, then we form a new random variable $Y = D(X)$ , $Y$ is a random variable as well, remember that there is a theorem that says that

$E[Y] = E[D(X)] = \int\limits_{-\infty}^{\infty} D(x) f(x) \,\, dx$

Where $f(x)$ is the probability mass function of X. Using the information of our problem

$E[Y] = \int\limits_{-\infty}^{\infty} D(x)f(x) dx \\= \frac{1}{100} \bigg[ \int\limits_{0}^{20} x dx +\int\limits_{20}^{45} (x-20) dx +\int\limits_{45}^{70} (70-x) dx +\int\limits_{70}^{100} (x-70) dx \bigg]\\= \frac{51}{4} = 12.75$

3 0

3 years ago