QUESTION 14

Solve each equation 3x^2=80

Lapatulllka [165]

Answer:

$x = \frac{4\sqrt{15}}{3}, x = \frac{-4\sqrt{15}}{3}$

or

$x = \frac{\pm4\sqrt{15}}{3}$

Step-by-step explanation:

Hello!

Use the quadratic formula: $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

First, let's convert our equation to standard form of a Quadratic: ax² + bx + c = 0

3x² = 80

3x² - 80 = 0

Note, thats the value of b will be 0, as there is no "bx"

Now, solve:

$x = \frac{-(0) \pm \sqrt{(0)^2 - 4(3)(-80)}}{2(3)}$ Plug in values
$x = \frac{\pm\sqrt{960}}{6}$ Simplify the radical (Discriminant)
$x = \frac{\pm8\sqrt{15}}{6}$ Pull out perfect squares
$x = \frac{4\sqrt{15}}{3}, x = \frac{-4\sqrt{15}}{3}$ Reduce factors

The solutions are $x = \frac{4\sqrt{15}}{3}, x = \frac{-4\sqrt{15}}{3}$

5 0

2 years ago

The number of years a radio functions is exponentially distributed with parameter λ = 1 8 . If Jones buys a used radio, what is

blsea [12.9K]

Answer:

$P(X>8)=e^{-1}$

Step-by-step explanation:

The exponential distribution is "the probability distribution of the time between events in a Poisson process (a process in which events occur continuously and independently at a constant average rate). It is a particular case of the gamma distribution". The probability density function is given by:

$P(X=x)=\lambda e^{-\lambda x}, x>0$

And 0 for other case. Let X the random variable that represent "The number of years a radio functions" and we know that the distribution is given by:

$X \sim Exp(\lambda=\frac{1}{8})$

We can assume that the random variable t represent the number of years that the radio is already here. So the interest is find this probability:

$P(X>8|X>t)$

We have an important property on the exponential distribution called "Memoryless" property and says this:

$P(X>a+t| X>t)=P(X>a)$

Where a represent a shift and t the time of interest.

On this case then $P(X>8|X>t)=P(X>8+t|X>t)=P(X>8)$

We can use the definition of the density function and find this probability:

$P(X>8)=\int_{8}^{\infty} \frac{1}{8}e^{-\frac{1}{8}x}dx$

$=\frac{1}{8} \int_{8}^{\infty} e^{-\frac{1}{8}x}dx$

$=[lim_{x\to\infty} (-e^{-\frac{1}{8}x})+e^{-1}]=0+e^{-1}=e^{-1}$

8 0

3 years ago

12

Slav-nsk [51]

Triangles ABC and DEF may or may not be congruent, because the angle-angle-angle (AAA) postulate is not a criterion for congruency of any two triangles. This is because the angle-angle-angle postulate only incorporates the angles of the triangles, and the side lengths are not specified, so congruency may or may not be true for these triangles.

3 0

2 years ago

There were 160 people who voted at the town council meeting. Of these people, 30% voted for building a new basketball court in t

tatuchka [14]

Answer:

there are a 112 against

Step-by-step explanation:30% of 160=48 ( 160*0.30=48)

160-48=112

6 0

2 years ago

Thetime(inhours)requiredtorepairamachineis an exponentially distributed random variable with parameter λ = 1 . What is 2 (a) the

mihalych1998 [28]