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3 years ago

Simplify the expression.

Mathematics

2 answers:

astra-53 [7]3 years ago

8 0

$a^{\log_a b}=b\\\\12^{\log_{12}24}=24$

Pachacha [2.7K]3 years ago

8 0

Answer:

The correct answer option is A) 24.

Step-by-step explanation:

We are given the following log expression and we are to simplify it:

$1 2 ^ { log _ { 1 2 } } ^ { 2 4 }$

Here, we are going to apply the rule for solving a log problem:

$a^{log_a^{(b)}$ $= b$

So if $1 2 ^ { log _ { 1 2 } } ^ { 2 4 }$ , then it would be equal to 24.

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Wires manufactured for use in a computer system are specified to have resistances between 0.11 and 0.13 ohms. The actual measure

Marina CMI [18]

Answer:

a) $P(0.11$

And we can find this probability with this difference and with the normal standard table or excel:

$P(-1.11$

b) $P(0.11 < \bar X < 0.13)$

And we can use the z score defined by:

$z = \frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n}}}$

And using the limits we got:

$z = \frac{0.11-0.12}{\frac{0.009}{\sqrt{4}}}= -2.22$

$z = \frac{0.13-0.12}{\frac{0.009}{\sqrt{4}}}= 2.22$

And we want to find this probability:

$P(-2.22< Z$

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".

Part a

Let X the random variable that represent the resitances of a population, and for this case we know the distribution for X is given by:

$X \sim N(0.12,0.009)$

Where $\mu=0.12$ and $\sigma=0.009$

We are interested on this probability

$P(0.11$

And the best way to solve this problem is using the normal standard distribution and the z score given by:

$z=\frac{x-\mu}{\sigma}$

If we apply this formula to our probability we got this:

$P(0.11$

And we can find this probability with this difference and with the normal standard table or excel:

$P(-1.11$

Part b

We select a sample size of n =4. And since the distribution for X is normal then we know that the distribution for the sample mean $\bar X$ is given by:

$\bar X \sim N(\mu, \frac{\sigma}{\sqrt{n}})$

And we want this probability:

$P(0.11 < \bar X < 0.13)$

And we can use the z score defined by:

$z = \frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n}}}$

And using the limits we got:

$z = \frac{0.11-0.12}{\frac{0.009}{\sqrt{4}}}= -2.22$

$z = \frac{0.13-0.12}{\frac{0.009}{\sqrt{4}}}= 2.22$

And we want to find this probability:

$P(-2.22< Z$

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3 years ago

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At the end of summer all sandals are marked down by 70%. If a pair of sandals originally cost $19.50, how much will it cost at t

aleksley [76]

70 percent off 19.50 would mean getting a discount of 13.65, so the final price of the sandals by the end of the summer should be 5.85

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3 years ago

- m + 62m2 + 1200 simplified

Gekata [30.6K]

3(41x+400) simplified = 123x+1200

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What is -3/8 - (1/6)

Mrac [35]

Remove parentheses.

-3/8 -1/6

Find the Least Common Denominator (LCD) of 3/8, 1/6. In other words, find the Least Common Multiple (LCM) of 8,6.

LCD=24

Make the denominators the same as the LCD.

- 3x3/8x3 - 1x4/6x4

Simplify. Denominators are now the same

-9/24 - 4/24

Join the denominators

-9-4/24

Simplify

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3 years ago

A complex shape with measurements 10 feet, 4 feet, 7 feet, 5 feet, 3 feet, 9 feet.

Archy [21]

Answer:

Add each side to get perimeter so your total is 38ft

Step-by-step explanation:

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2 years ago

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