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VARVARA [1.3K]
3 years ago
11

Simplify the expressions. i^23

Mathematics
1 answer:
masha68 [24]3 years ago
8 0

Answer:

-i

Step-by-step explanation:

i^0=1

i^1=i

i^2=-1

i^3=-i

i^4=1

This repeats so we want to see how many 4 factors of i there is in i^(23) which is 5 with a remainder of 3.

So i^(23)=i^3=-i.

i^(23)=i^(5*4+3)=(i^4)^5 * (i^3)=(1)^5 * (-i)=1(-i)=-i.

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The denominator of a fraction is two more than the numerator. If both numerator and denominator are decreased by six, the simpli
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Answer:

\dfrac{40}{42}

Step-by-step explanation:

Let the numerator of the fraction=x

Since the denominator of a fraction is two more than the numerator.

Denominator=x+2

The fraction is therefore:

\dfrac{x}{x+2}

If both numerator and denominator are decreased by six, the fraction becomes:

\dfrac{x-6}{x+2-6}

The simplified result is \dfrac{17}{18}

Therefore:

\dfrac{x-6}{x+2-6}=\dfrac{17}{18}\\$Next, we solve for x\\Cross multiply\\18(x-6)=17(x+2-6)\\18(x-6)=17(x-4)\\Expand the bracket\\18x-108=17x-68\\Collect like terms\\18x-17x=-68+108\\x=40

Substituting x=40 into the initial fraction

\dfrac{x}{x+2}=\dfrac{40}{40+2}=\dfrac{40}{42}

Therefore, the original fraction is \dfrac{40}{42}

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3 years ago
Javier participated in a local hot dog-eating contest. The graph below shows the number of hot dogs he ate. What is Javier's ave
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Hypothesis testing on samples with fewer than 30 participants can be carried out by using the t-value for the corresponding leve
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Answer: true

Step-by-step explanation:

Z-tests are statistical calculations that can be used to compare the population mean to a sample mean The z-score is used to tellsbhow far in standard deviations a data point is from the mean of the data set. z-test compares a sample to a defined population and is typically used for dealing with problems relating to large samples (n > 30). Z-tests can also be used to test a hypothesis. Z-test is most useful when the standard deviation is known.

Like z-tests, t-tests are used to test a hypothesis, but a t-test asks whether a difference between the means of two groups is not likely to have occurred because of random chance. Usually, t-tests are used when dealing with problems with a small sample size (n < 30).

Both tests (z-tests and t-tests) are used in data with normal distribution (a sample data or population data that is evenly distributed around the mean).

3 0
3 years ago
In Neil's city, the temperature is 72.6 degrees and is rising 1.3 degrees each hour. In Sheppard's city, the temperature is 80.4
klio [65]

Answer:

2.5 hours

Step-by-step explanation:

Given that :

Temperature in Neil's city :

72.6° and rising by 1.3° per hour

Temperature in Sheppard's city :

80.4° and dropping by 1.82° per hour

In how many hours will the temperature in Neil's city be no less than the temperature in Sheppard's city

Let number of hours = h

Hence, Neil city :

72.6 + 1.3h

Sheppard city:

80.4 - 1.82h

72.6 + 1.3h ≥ 80.4 - 1.82h

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Answer:

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Step-by-step explanation:

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