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4 years ago

What object is defined using a directrix and a focus

Mathematics

2 answers:

dedylja [7]4 years ago

6 0

Answer: B

Step-by-step explanation:

A parabola is defined using both a directrix and a focus.

To justify this, let me take a quote from Varsity Tutors (all credit of this quote goes to them) : “A parabola is set of all points in a plane which are an equal distance away from a given point and given line. The point is called the focus of the parabola and the line is called the directrix.”

Hope this helps! :)

SCORPION-xisa [38]4 years ago

6 0

The answer is b!
Because
It’s easy mate c’mon

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How many solutions does the system have?

Mrac [35]

Answer:

A Exactly one solution

Step-by-step explanation:

$\left \{ {{6x-3y=9} \atop {6x+y=9}} \right.\\\\\left \{ {{6x-3y=9} \atop {-6x-y=-9}} \right\\\\Then, \\\\-4y=0\\\\\\ y=0\\\\$

Putting y=0 at second equation, we have

$-6x=-9\\\\x=\frac{9}{6} =\frac{3}{2}$

The unique solution is $(\frac{3}{2} , 0)$

3 0

3 years ago

Suppose a box of Cracker Jacks contains one of 5 toy prizes: a small rubber ball, a whistle, a Captain America decoder ring, a r

lakkis [162]

Answer:

11.42 boxes

Step-by-step explanation:

For the first box bought, there is a 100% chance of getting a unique toy (since you still don't have any). E₁ = 1.

After that, there is a 4 in 5 chance of getting a unique toy from the next box, the expected number of boxes required is:

$E_2 = (\frac{4}{5})^{-1} = 1.25$

For the next unique toy, there is now a 3 in 5 chance of getting it:

$E_3 = (\frac{3}{5})^{-1} = 1.67$

Following that logic, there is a 2 in 5 chance of getting the 4th unique toy:

$E_4 = (\frac{2}{5})^{-1} = 2.5$

Finally, there is a 1 in 5 chance to get the last unique toy:

$E_5 = (\frac{1}{5})^{-1} = 5$

The expected number of boxes to obtain a full set is:

$E=E_1+E_2+E_3+E_4+E_5\\E=1+1.25+1.67+2.5+5\\E=11.42\ boxes$

5 0

3 years ago

Graph the line with slope -2 passing through the point (1,-4)

lorasvet [3.4K]

the equation for the line is:

y = -2( x + 1 )

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3 years ago

The mean points obtained in an aptitude examination is 159 points with a standard deviation of 13 points. What is the probabilit

Korolek [52]

Answer:

0.4514 = 45.14% probability that the mean of the sample would differ from the population mean by less than 1 point if 60 exams are sampled

Step-by-step explanation:

To solve this question, we have to understand the normal probability distribution and the central limit theorem.

Normal probability distribution:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central limit theorem:

The Central Limit Theorem estabilishes that, for a random variable X, with mean $\mu$ and standard deviation $\sigma$ , a large sample size can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$