a number is 3 1/3 greater than another. If the sum of the numbers is doubled, the result is 19 1/2. What is the smaller number

Twenty five heat lamps are connected in a greenhouse so, that when one lamp fails, another takes over immediately (only one lamp

olga55 [171]

Answer:

P = 0.006

Step-by-step explanation:

Given

n = 25 Lamps

each with mean lifetime of 50 hours and standard deviation (SD) of 4 hours

Find probability that the lamp will be burning at end of 1300 hours period.

As we are not given that exact lamp, it means we have to find the probability where any of the lamp burning at the end of 1300 hours, So we have

Suppose i represents lamps

P (∑i from 1 to 25 ( $X_i$ > 1300)) = 1300

= P( $X^{'}$ > $\frac{1300}{25}$ ) where $X^{'}$ represents mean time of a single lamp

= P (Z> $\frac{52-50}{\frac{1}{\sqrt{25}}}$ ) Z is the standard normal distribution which can be found by using the formula

Z = Mean Time ( $X^{'}$ ) - Life time of each Lamp (50 hours)/ (SD/ $\sqrt{n}$ )

Z = (52-50)/(4/ $\sqrt{25}$ ) = 2.5

Now, P(Z>2.5) = 0.006 using the standard normal distribution table

Probability that a lamp will be burning at the end of 1300 hours period is 0.006

4 0

3 years ago

What is the argument of -5\sqrt{3}+ 5i?

Shtirlitz [24]

Answer:

150 degrees

Step-by-step explanation:

Graphing the complex number we see the angle terminates in the second quadrant. This means the argument, the angle, will be between 90 degrees and 180 degrees.

So if we create a right triangle with that point after graphing it. We see the height of that triangle is 5 because that is the imaginary part. The base of that triangle has length $5\sqrt{3}$ . The problem is this doesn't give us any part of the angle we want, but it does give us the complementary of the part of the angle that is in second quadrant.

Let's find the complementary angle.

So the opposite side of the complementary angle is 5.

The adjacent side of the complementary angle is $5\sqrt{3}$ .

$\tan(\theta)=\frac{5}{5\sqrt{3}}$

$\tan(\theta)=\frac{1}{\sqrt{3}}$

$\theta=\tan^{-1}(\frac{1}{\sqrt{3}})$

$\theta=30$

So 90-30=60.

The answer therefore 60+90=150.

4 0

3 years ago

1.Phone company A charges $20 a month and $0.10 per minute of phone calls. Phone Company B charges

Shtirlitz [24]

I might be wrong but I think it's 50 minutes.

$0.10 x 50min = $5

$20 + $5 = $25

$0.20 x 50min = $10

$15 + $10 = $25

So, it's 50 minutes.

7 0

3 years ago

If a → b is true, then ~a → b is also true.

Rasek [7]

Answer:

False

Step-by-step explanation:

To determine whether the statemaent "If $a\Rightarrow b$ is true, then $\neg a\Rightarrow b$ is also true" holds, you can form the truth table:

$\begin{array}{ccccc}a&b&a\Rightarrow b&\neg a&\neg a\Rightarrow b\\1&1&1&0&1\\1&0&0&0&1\\0&1&1&1&1\\0&0&1&1&0\end{array}$

When the result of the column $a\Rightarrow b$ takes value 1 (true), the result of the column $\neg a\Rightarrow b$ is not always 1, then the statement is false.

7 0

3 years ago

I need help with these

IrinaVladis [17]

Let x be the number.
"twelve decreased by twice a number" ---> 12 - 2x
"8 times the sum of number and 4" ---> 8(x + 4)
12 - 2x = 8(x + 4)
12 - 2x = 8x + 32 (distributive property)
12 = 10x + 32 (add 2x to both sides)
-20 = 10x (subtract 32 from both sides)
x = -2 (divide both sides by 10)

6 0

3 years ago

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