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3 years ago

Solve 1)3x-7=35? 2)22=7-3a 3)-d+7=3 4)2x+23=49 5)-c+2=5

2 answers:

8 0

$1)\\3x-7=35\\3x-7+7=35+7\\3x=42\\3x=3\cdot14\ /:3\\x=14\ \ \ \leftarrow\ \ \ Answer\\\\
2)\\22=7-3a\\22-22+3a=7-3a-22+3a\\3a=-15\\3a=3\cdot(-5)\ /:3\\a=-5\ \ \ \leftarrow\ \ \ Answer\\\\3)\\-d+7=3\\-d+7-7=3-7\\-d=-4\\d\cdot(-1)=4\cdot(-1)\ /:(-1)\\d=4\ \ \ \leftarrow\ \ \ Answer\\\\$

$4)\\2x+23=49\\ 2x+23-23=49-23\\2x=26\\2\cdot x=2\cdot 13\ /:2\\x=13 \ \ \ \leftarrow\ \ \ Answer\\\\ 
5)-c+2=5\\ -c+2-2=5-2\\ -c=3\\ c\cdot(-1)=-3\cdot(-1)\ /:(-1)\\c=-3 \ \ \ \leftarrow\ \ \ Answer$

astra-53 [7]3 years ago

7 0

$1)\ 3x-7=35\ \ \ |add\ 7\ to\ both\ sides\\\\3x=42\ \ \ \ |divide\ both\ sides\ by\ 3\\\\\boxed{x=14}\\-------------------------\\2)\ 22=7-3a\\\\7-3a=22\ \ \ \ |subtract\ 7\ from\ both\ sides\\\\-3a=15\ \ \ \ \ |divide\ both\ sides\ by\ (-3)\\\\\boxed{a=-5}\\--------------------------$

$3)\ -d+7=3\ \ \ \ \ |subtract\ 7\ from\ both\ sides\\\\-d=-4\\\\\boxed{d=4}\\---------------------------\\\\4)\ 2x+23=49\ \ \ \ \ \ |subtract\ 23\ from\ both\ sides\\\\2x=26\ \ \ \ \ \ |divide\ both\ sides\ by\ 2\\\\\boxed{x=13}\\---------------------------\\5)\ -c+2=5\ \ \ \ \ \ |subtract\ 2\ from\ both\ sides\\\\-c=3\\\\\boxed{c=-3}$

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Answer:

0.1353 = 13.53% probability that the lifetime exceeds the mean time by more than 1 standard deviations

Step-by-step explanation:

Exponential distribution:

The exponential probability distribution, with mean m, is described by the following equation:

$f(x) = \mu e^{-\mu x}$

In which $\mu = \frac{1}{m}$ is the decay parameter.

The probability that x is lower or equal to a is given by:

$P(X \leq x) = \int\limits^a_0 {f(x)} \, dx$

Which has the following solution:

$P(X \leq x) = 1 - e^{-\mu x}$

The probability of finding a value higher than x is:

$P(X > x) = 1 - P(X \leq x) = 1 - (1 - e^{-\mu x}) = e^{-\mu x}$

The mean time for the component failure is 2500 hours.

This means that $m = \frac{2500}, \mu = \frac{1}{2500} = 0.0004$

What is the probability that the lifetime exceeds the mean time by more than 1 standard deviations?

The standard deviation of the exponential distribution is the same as the mean, so this is P(X > 5000).

$P(X > x) = e^{-0.0004*5000} = 0.1353$

0.1353 = 13.53% probability that the lifetime exceeds the mean time by more than 1 standard deviations

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To solve this, we are going to use the surface are of a sphere formula: $A=4 \pi r^2$
where
$A$ is the surface area of the sphere
$r$ is the radius of the sphere

We know for our problem that $A=2122.64$ and $\pi =3.14$ , so lets replace those vales in our formula:
$A=4 \pi r^2$
$2122.64=4(3.14)r^2$
$2122.64=12.56r^2$
Now, we just need to solve our equation for $r$ :
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$r^2=\frac{2122.64}{12.56}$
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$r=+or- \sqrt{169}$
$r=13$ or $r=13$
Since the radius of a sphere cannot be a negative number, $r=13$ .

We can conclude that the radius of a sphere with surface area <span>2,122.64 </span> $in^2$ is 13 in.

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