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elena-s [515]
3 years ago
8

Write an equation for the translation of x^2+y^2=49 by 3 units left and 4 units up

Mathematics
2 answers:
amm18123 years ago
8 0

The answer is:

(x+3)^2+(y-4)^2=49

ludmilkaskok [199]3 years ago
5 0
\bf \textit{equation of a circle}\\\\ 
(x-{{ h}})^2+(y-{{ k}})^2={{ r}}^2
\qquad 
\begin{array}{lllll}
center\ (&{{ h}},&{{ k}})\qquad 
radius=&{{ r}}
\end{array}\\\\
-----------------------------\\\\
x^2+y^2=49\iff (x-0)^2+(y-0)^2=7^2\quad 
\begin{cases}
h=0\\
k=0
\end{cases}
\\\\\\
(x-\underline{(-3)})^2+(y-\underline{(+4)})^2=7^2\quad 
\begin{cases}
h=-3\\
k=4
\end{cases}
\\\\\\
\boxed{(x+3)^2+(y-4)^2=49}
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Which one is correct?
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Answer:

SSS or SAS

Step-by-step explanation:

Remark

Since the two diagonals bisect each other, you have created two sets of equal lines. If that is the case, then you could prove the equality of the triangles 2 different ways.

1) The angles at the center are vertically angles which makes them equal. Since they are equal, the triangles are congruent by SAS. Notice that the angle is between the 2 equal sides.

2) Since CD and AB are marked as being equal, the triangles are congurent by SSS.

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3 years ago
The cost to produce a batch of granola bars is approximately Normally distributed with a mean of $7.19 and a standard deviation
Bumek [7]

Answer:

0.7780

Step-by-step explanation:

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

Normal probability distribution

When the distribution is normal, we use 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 normally distributed random variable X, with mean \mu and standard deviation \sigma, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \mu and standard deviation s = \frac{\sigma}{\sqrt{n}}.

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

Population:

We have that \mu = 7.19, \sigma = 0.86

Sample of 12:

n = 12, s = \frac{0.86}{\sqrt{12}} = 0.2483

What is the probability that the mean cost will be more than $7.00?

This is 1 subtracted by the pvalue of Z when X = 7. So

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

By the Central Limit Theorem

Z = \frac{X - \mu}{s}

Z = \frac{7 - 7.19}{0.2483}

Z = -0.765

Z = -0.765 has a pvalue of 0.222

1 - 0.222 = 0.778

So the answer is 0.7780

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3 years ago
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Genrish500 [490]

Answer:

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2

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