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3 years ago

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Mathematics

1 answer:

a_sh-v [17]3 years ago

6 0

1. The three dots at the end of the number is called an ellipsis.
2. Since it doesn't terminate or repeat, the number is an irrational number.
3. When it can be written as a ratio, it is a rational number.
4. The decimal digits infinitely repeating is called a repeating decimal.
5. Ending decimal is another word for terminating decimal.
6. The fraction bar in which has numerator above and denominator below is a vinculum. Hope this helps!

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The mass of a proton is approximately 1.67 x 10−24, and the mass of an electron is approximately 9.11 x 10−28. Find the approxim

nataly862011 [7]

Answer:

≈ 1833

Step-by-step explanation:

To find ratio of proton mass to electron mass, we have to divide.

The numbers are given in scientific notation.

Let a number be $a*10^b$ and another be $c*10^d$ , when we divide, we will follow the rule shown below:

$\frac{a*10^b}{c*10^d}=(\frac{a}{c}*10^{b-d})$

Now, we use the information given to find the ratio:

$\frac{1.67*10^{-24}}{9.11*10^{-28}}\\=(\frac{1.67}{9.11}*10^{-24--28})\\=0.1833*10^4$

This means we can find the number by taking 4 decimal places to the right, so that would becomes:

$0.1833*10^4=1833$

The approximate ratio is 1833 [mass of proton is around 1833 times heavier than mass of electron]

7 0

3 years ago

Read 2 more answers

Suppose a geyser has a mean time between irruption’s of 75 minutes. If the interval of time between the eruption is normally dis

lesya [120]

Answer:

(a) The probability that a randomly selected Time interval between irruption is longer than 84 minutes is 0.3264.

(b) The probability that a random sample of 13 time intervals between irruption has a mean longer than 84 minutes is 0.0526.

(c) The probability that a random sample of 20 time intervals between irruption has a mean longer than 84 minutes is 0.0222.

(d) The probability decreases because the variability in the sample mean decreases as we increase the sample size

(e) The population mean may be larger than 75 minutes between irruption.

Step-by-step explanation:

We are given that a geyser has a mean time between irruption of 75 minutes. Also, the interval of time between the eruption is normally distributed with a standard deviation of 20 minutes.

(a) Let X = the interval of time between the eruption

So, X ~ Normal( $\mu=75, \sigma^{2} =20$ )

The z-score probability distribution for the normal distribution is given by;

Z = $\frac{X-\mu}{\sigma}$ ~ N(0,1)

where, $\mu$ = population mean time between irruption = 75 minutes

$\sigma$ = standard deviation = 20 minutes

Now, the probability that a randomly selected Time interval between irruption is longer than 84 minutes is given by = P(X > 84 min)

P(X > 84 min) = P( $\frac{X-\mu}{\sigma}$ > $\frac{84-75}{20}$ ) = P(Z > 0.45) = 1 - P(Z $\leq$ 0.45)

= 1 - 0.6736 = 0.3264

The above probability is calculated by looking at the value of x = 0.45 in the z table which has an area of 0.6736.

(b) Let $\bar X$ = sample time intervals between the eruption

The z-score probability distribution for the sample mean is given by;

Z = $\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }$ ~ N(0,1)

where, $\mu$ = population mean time between irruption = 75 minutes

$\sigma$ = standard deviation = 20 minutes

n = sample of time intervals = 13

Now, the probability that a random sample of 13 time intervals between irruption has a mean longer than 84 minutes is given by = P( $\bar X$ > 84 min)

P( $\bar X$ > 84 min) = P( $\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }$ > $\frac{84-75}{\frac{20}{\sqrt{13} } }$ ) = P(Z > 1.62) = 1 - P(Z $\leq$ 1.62)

= 1 - 0.9474 = 0.0526

The above probability is calculated by looking at the value of x = 1.62 in the z table which has an area of 0.9474.

(c) Let $\bar X$ = sample time intervals between the eruption

The z-score probability distribution for the sample mean is given by;

Z = $\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }$ ~ N(0,1)

where, $\mu$ = population mean time between irruption = 75 minutes

$\sigma$ = standard deviation = 20 minutes

n = sample of time intervals = 20

Now, the probability that a random sample of 20 time intervals between irruption has a mean longer than 84 minutes is given by = P( $\bar X$ > 84 min)

P( $\bar X$ > 84 min) = P( $\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }$ > $\frac{84-75}{\frac{20}{\sqrt{20} } }$ ) = P(Z > 2.01) = 1 - P(Z $\leq$ 2.01)

= 1 - 0.9778 = 0.0222

The above probability is calculated by looking at the value of x = 2.01 in the z table which has an area of 0.9778.

(d) When increasing the sample size, the probability decreases because the variability in the sample mean decreases as we increase the sample size which we can clearly see in part (b) and (c) of the question.

(e) Since it is clear that the probability that a random sample of 20 time intervals between irruption has a mean longer than 84 minutes is very slow(less than 5%0 which means that this is an unusual event. So, we can conclude that the population mean may be larger than 75 minutes between irruption.

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3 years ago

A mystery number is multiplied by 11 then 10 is subtracted from it to give you a result of 34. What is the mystery number?

klemol [59]

Answer:

Step-by-step explanation:

And let the missing number be x

We can solve using Algebra

11x - 10 = 34

11x = 34 + 10

11x = 44

x = 44/11

x = 4

For verification:

4(11) - 10 = 34

44 - 10 = 34

34 = 34

Hence, Proved

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2 years ago

Solve this using the substitution method please!! Y=425x+1139/Y=495x

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20 is jenna a ssjsjsn a ans s s s s s s s s s s s. S s s s s s s s. S ss. S s

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3 years ago

Describe how the value of the independent variable is related to the value of the dependent variable. Is the relationship additi

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The dependent value is determine by the value of the independent value. in other words, the dependent value is what you get when you take the independent value and substitute it in the original equation or situation. The relationship is multiplicative because you must first multiply the independent value in the equation where the x is before you can add or subtract to get your answer.

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3 years ago