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3 years ago

Solve x2-14x+21=0 by completing the square

1 answer:

4 0

$x^2-14x+21=0\\\\x^2-2x\cdot7+7^2-7^2+21=0\\\\(x-7)^2-49+21=0\\\\(x-7)^2-28=0\\\\(x-7)^2=28\iff x-7=-\sqrt{28}\ \vee\ x-7=\sqrt{28}\\\\x=7-\sqrt{4\cdot7}\ \vee\ x=7+\sqrt{4\cdot7}\\\\x=7-2\sqrt7\ \vee\ x=7+2\sqrt7$

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When planning road development, the road commission estimates the future population using the function represented in the table,

Sindrei [870]

The significance of 160,000 in the function is the initial population at the time of the estimation.

The correct option is (C)

A collection of facts, such as numbers, words, measurements, observations or even just descriptions of things.

Given:

As per the table attached below:

F(x) signify the total population when the time was x hour.

So, 160,000 in the function signifies that the population at starting i.e., initial point.

Learn more about this concept here:

brainly.com/question/17112729

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7 0

2 years ago

What is 9.33 as a fraction in simplest form

netineya [11]

9 33/100 is the answer

3 0

2 years ago

Read 2 more answers

"the life length x (in years) of a dvd player" is exponentially distributed with mean 5 years. what is the probability that a mo

loris [4]

The exponential distribution is:
$\lambda e^{- \lambda x}$
where $\lambda = \frac{1}{mean}=\frac{1}{5}$

The probability we want is how likely will a dvd player last more than 8 years, given it has already lasted 5 years
To find this, you use conditional probability.
$P(A|B) = \frac{P(A and B)}{P(B)}$
where A is P(x>8) and B is P(x>5)
To find these probabilities, integrate over the distribution:
$P(x \ \textgreater \ N) = \int_N^{\infty} \frac{1}{5} e^{-x/5} dx = e^{-N/5}$

Sub into conditional probability formula:

$P(x \ \textgreater \ 8 | x\ \textgreater \ 5) = \frac{P(x\ \textgreater \ 8)}{P(x\ \textgreater \ 5)} = \frac{e^{-8/5}}{e^{-5/5}} = e^{-3/5} = 0.549$

Final Answer: Given a dvd player is more than 5 years old, the probability that it will last another 3 more years is about 54.9%

3 0

3 years ago

What fraction of the dunk tanks require at least 500 gallons of water? Write the fraction in simplest form.

Cerrena [4.2K]

Answer:

1/2

Step-by-step explanation:

Based on the information observed from the attached box and whisker plot, the Fraction of dunk tanks which requires atleast 500 gallons of water. This fractional value will be the property of plot in the position marked as 500 on the plot. The point which refers to 500 gallons on the plot is the ticked point in between the box. This point represents the median value in a box and whisker plot.

The median value represents the 50th percentile value which relates to half of the distribution. This means that fraction of dunk which requires atleast 500 gallons is : (50/100) = 1/2

7 0

3 years ago

Could you help me find X,

lisov135 [29]

when running a line, in a right-triangle, from the 90° angle perpendicular to its opposite side, we will end up with three similar triangles, one Small, one Medium and a containing Large one. Check the picture below.

$\cfrac{4}{x}~~ = ~~\cfrac{x}{9}\implies 36=x^2\implies \sqrt{36}=x\implies 6=x$

3 0

1 year ago