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2 years ago

Expand and simplify (X+5) (x+7)

Mathematics

1 answer:

Hoochie [10]2 years ago

4 0

Answer:

x^2+12x+35

Step-by-step explanation:

x(x+7)+5(x+7)

x^2+7x+5x +35

x^2+12x+35

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If the length of a rectangle is 8 and the width is 10. What is its area?

evablogger [386]

Answer:

Step-by-step explanation:

area is length × width. 8 × 10 = 80

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3 years ago

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The temperature went from -12°F to 18°F. How much did the temperature change?

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Answer: the temperature went up by +30

Step-by-step explanation:

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3 years ago

Let X1, . . . ,Xn ∈ R be independent random variables with a common CDF F0. Let Fn be their ECDF and let F be any CDF. If F = Fn

Georgia [21]

Answer:

See the proof below.

Step-by-step explanation:

For this case we need to proof that: Let $X_1, X_2, ...X_n \in R$ be independent random variables with a common CDF $F_0$ . Let $F_n$ be their ECDF and let F any CDF. If $F \neq F_n$ then $L(F)$

Proof

Let $z_a$ different values in the set { $X_1,X_2,...,X_n}$ } and we can assume that $n_j \geq 1$ represent the number of $X_i$ that are equal to $z_j$ .

We can define $p_j = F(z_j) +F(z_j-)$ and assuming the probability $\hat p_j = \frac{n_j}{n}$ .

For the case when $p_j =0$ for any $j=1,....,m$ then we have that the $L(F) =0< L(F_n)$

And for the case when all $p_j >0$ and for at least one $p_j \neq \hat p_j$ we know that $log(x) \leq x-1$ for all the possible values $x>0$ . So then we can define the following ratio like this:

$log (\frac{L(F)}{L(F_n)}) = \sum_{j=1}^m n_j log (\frac{p_j}{\hat p_j})$

$log (\frac{L(F)}{L(F_n)}) = n \sum_{j=1}^m \hat p_j log(\frac{p_j}{\hat p_j})$

$log (\frac{L(F)}{L(F_n)}) < n\sum_{j=1}^m \hat p_j (\frac{p_j}{\hat p_j} -1)$

So then we have that:

$log (\frac{L(F)}{L(F_n)}) \leq 0$

And the log for a number is 0 or negative when the number is between 0 and 1, so then on this case we can ensure that $L(F) \leq L(F_n)$

And with that we complete the proof.

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3 years ago

What is a Corresponding angle?

leonid [27]

the angles that occupy the same relative position at each intersection where a straight line crosses two others. If the two lines are parallel, the corresponding angles are equal.

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3 years ago

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Bashir works in a weather station and has launched a weather ballon. The height of the baloon is 4 kilometers and it is 1 kilome

andrew-mc [135]

Answer:

Explanation:

We are given that the height of the balloon is 4 km and that it is 1 km away from the station.

Setting up the diagram that describes the given scenario, we would end up with a right-angled triangle as the one shown in the attached image

where:

height of the balloon = 4 km represents one side of the triangle

distance between the base of the balloon and the station = 1 km represents the other side