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2 years ago

Given that x is an even number, express, in terms of x, the product of the next two odd numbers.

Mathematics

1 answer:

wariber [46]2 years ago

6 0

Answer:

Odd is the answer.

Step-by-step explanation:

An even number can be written in the form 2x, where x is an integer.

An odd number can be written in the form 2x + 1, where x is an integer.

So two odd numbers can be represented by 2a +1 and 2b +1, the product would be:

(2a + 1)(2b +1) = 4ab + 2a + 2b + 1 = which can be written as 2(2ab + a +b) + 1, but 2ab +a + b represents some integer, so 2ab + a + b = x.

So (2a + 1)(2b + 1) = 2(2ab + a + b ) + 1 = 2x +1 which is odd.

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Which system of measurement uses the minim as the basic unit of liquid measure?

Alex777 [14]

<u>The apothecary system</u><u> uses the minim as the basic unit of liquid measure and the grain as the basic unit of solid measure.</u>

What is apothecary measurement?

The apothecary system was once a system of weights and measurements used for drug prescription and dispensing.
A pound was divided into 12 ounces in the English version, which also divided an ounce into eight drams or drachms and a dram into three scruples, or 60 grains.

What are the units of the apothecary system?

The grain, scruple (20 grains), dram (3 scruples), ounce (8 drams), and pound—a ancient scale of weight used in the British Isles for measuring and distributing pharmacological goods (12 ounces).

Learn more about apothecary system

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6 0

1 year 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.

8 0

3 years ago

The gross weight of a package and its contents is 11 pounds 5 ounces. If the packaging weighs 1 pound 15 ounces, what's the net

umka21 [38]

11 lbs 5 oz - 1 lb 15 oz...we are gonna have to borrow...there is 16 oz in a lb.
11 lbs 5 oz....we r going to borrow 1 lb from the right side and add it to the left side making it 10 lbs and 21 oz...u see what I did...I borrowed 1 lb from the right side and added 16 oz to the left.Now we can subtract.

10 lbs 21 oz - 1 lb 15 oz = 9 lbs 6 oz <== ur answer

3 0

2 years ago

Read 2 more answers

Is my answer correct? // tell me if i'm wrong with details!!

Anna11 [10]

Answer:

Step-by-step explanation:

This is vertical reflection, because reflections are made across vertical lines.

5 0

3 years ago

The point is plotted on the number line.What whole number best approximates the value of x?

sattari [20]