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3 years ago

The left and right page numbers of an open book are two consecutive integers whose sum is 87.

1 answer:

3 0

Left page numbers are always even and right page will have a number 1 greater that the left. so its not possible to have a sum of 87.
If even page is 2n then right page = 2n + 1:-

2n + 2n + 1 = 87

4n = 86

n = 86 / 4 = 21.5 and 2n = 43 but left page is even so its not possible to have a sum of left + right = 87.

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25 points! <br> 2400000 in scientific notation

gavmur [86]

2.4 x 10^6 the answer to the question

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3 years ago

which complex number has a distance of √17 from the origin on the complex plane?a. 2 15ib. 17 ic. 20 - 3id. 4 - i

Rus_ich [418]

Let $z=a+bi$ . $|z| = \sqrt{a^2+b^2}$ , so:
$|z_a| = \sqrt{0+15^2} = 15 \neq \sqrt{17} \\ |z_b| = \sqrt{0+17^2} = 17\neq \sqrt{17} \\ |z_c| = \sqrt{20^2+3^2} \ \textgreater \ \sqrt{20^2} = 20\ \textgreater \ \sqrt{17} \\\\ \boxed{|z_d| = \sqrt{4^2+1^2} = \sqrt{16+1} = \sqrt{17}}$

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3 years ago

Which number sentence states that x is at most 50?

san4es73 [151]

Answer:

its A & B, x<50

Step-by-step explanation:

atmost means till 50.

atleast means more than 50.

4 0

3 years ago

A boiler has five identical relief valves. The probability that any particular valve will open on demand is 0.95. Assuming indep

Gre4nikov [31]

Answer:

a) There is a 99.99997% probability that at least one valve opens.

b) There is a 22.62% probability that at least one valve fails to open.

Step-by-step explanation:

For each valve, there are only two possible outcomes. Either it open, or it does not. So we use the binomial probability distribution to solve this problem.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

In this problem we have that:

$p = 0.95, n = 5$

(a) What is the probability that at least one valve opens?

Either no valves open, or at least one opens. The sum of the probabilities of these events is decimal 1. So

$P(X = 0) + P(X \geq 1) = 1$

We want $P(X \geq 1)$

$P(X \geq 1) = 1 - P(X = 0)$

$P(X = 0) = C_{5,0}.(0.95)^{0}.(0.05)^{5} = 0.0000003$

$P(X \geq 1) = 1 - P(X = 0) = 1 - 0.0000003 = 0.9999997$

There is a 99.99997% probability that at least one valve opens.

(b) What is the probability that at least one valve fails to open?

Either all valves open, or at least one does not open. The sum of the probabilities of these events is decimal 1. So

$P(X = 5) + P(X \leq 4) = 1$

We want $P(X \leq 4)$

$P(X \leq 4) = 1 - P(X = 5)$

$P(X = 5) = C_{5,5}.(0.95)^{5}.(0.05)^{0} = 0.7738$

$P(X \leq 4) = 1 - P(X = 5) = 1 - 0.7738 = 0.2262$

There is a 22.62% probability that at least one valve fails to open.

5 0

3 years ago

The data below gives the number of books that 15 students checked out of the school library in one month. Make a frequency table

Alex

Answer: See the explanation below.

A frequency table is a way to organize data. We create bins (intervals) to collect the data. Then, we give the frequency (number) of data values in each interval.

Here is an example of how you could sort this data.

Interval: Frequency:
0 - 1 7
2 - 3 7
4 - 5 1

4 0

4 years ago