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Kipish [7]
4 years ago
6

What is the value of the expression i^0 x i^1 x i^2xi^3xi^4

Mathematics
2 answers:
monitta4 years ago
5 0

Answer: The answer is - 1.

Step-by-step explanation: We are given to find the value of the given expression

E_c=i^0\times i^1\times i^2\times i^3\times i^4.

We know that 'i' is an imaginary unit and its value is √-1. So, we have

i^0=(\sqrt{-1})^0=1,\\\\i^1=i=\sqrt{-1},\\\\i^2=(\sqrt{-1})^2=-1,\\\\i^3=i^2.I=(-1)i=-\sqrt{-1},\\\\i^4=(i^2)^2=(-1)^2=1.

Therefore, the given expression becomes

E_c\\\\=i^0\times i^1\times i^2\times i^3\times i^4\\\\=1\times \sqrt{-1}\times(-1)\times({-\sqrt{-1}})\times 1\\\\=1\times (-1)\\\\=-1..

Thus, the answer is - 1.

Mars2501 [29]4 years ago
5 0

Answer:

The value of given expression is -1.

Step-by-step explanation:

We have to evaluate the following expression:

i^0\times i^1\times i^2\times i^3\times i^4

We know that:

i = \sqrt{-1}\\i^2 = -1\\i^3 = -i\\i^4 = 1

Putting the values in the expression:

i^0\times i^1\times i^2\times i^3\times i^4\\=1\times i\times -1\times -i\times 1\\= i^2\\= -1

Hence, the value of given expression is -1.

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What is the solution to the system of equations below? y=2/5x-3 and x=-10
mojhsa [17]

Answer:

The solution is (-10,-7)

Step-by-step explanation:

y=2/5x-3 and x=-10

We know x = -10

Substitute the second equation into the first equation to find y

y = 2/5 (-10) -3

y = -4 -3

y = -7

The solution is (-10,-7)

4 0
3 years ago
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Customers who purchase an aluminum-structured Audi A8 can order an engine in any of three sizes: 2.0L, 2.4L, and 2.8L. Of all Au
sergiy2304 [10]

Answer:

The probability that an Audi A8 car with 2.4L engine is selected given that the car failed emissions test taken within four years of purchase is 0.3589.

Step-by-step explanation:

Let's denote event as follows:

<em>A</em> = an Audi A8 car has a 2.0L engine.

<em>B</em> = an Audi A8 car has a 2.4L engine.

<em>C</em> = an Audi A8 car has a 2.8L engine.

<em>X</em> = an Audi A8 car failed emissions test taken within four years of purchase.

The information provided is:

P(A)=0.45\\P(B)=0.35\\P(C)=0.20\\P(X|A)=0.10\\P(X|B)=0.12\\P(X|C)=0.15

The probability that an Audi A8 car with 2.4L engine is selected given that the car failed emissions test taken within four years of purchase is:

P(B|X)=\frac{P(X|B)P(B)}{P(X)}

Compute the probability of an Audi A*8 car failed emissions test taken within four years of purchase as follows:

P(X)=P(X|A)P(A)+P(X|B)P(B)+P(X|C)P(C)\\=(0.45\times0.10)+(0.35\times0.12)+(0.20\times0.15)\\=0.117

Compute the value of P (B|X) as follows:

P(B|X)=\frac{P(X|B)P(B)}{P(X)}=\frac{0.35\times0.12}{0.117} =0.3589

Thus, the probability that an Audi A8 car with 2.4L engine is selected given that the car failed emissions test taken within four years of purchase is 0.3589.

4 0
4 years ago
Tiffany buys a basket of watermelons on sale for $9 before tax. The sales tax is 9% What is the total price Tiffany pays for the
Tamiku [17]
$0.81+$9.00=$9.81
Answer: $9.81

We know t<span>o find the total price, first find the amount of sales tax paid by multiplying the sales tax by the original price of the basket of watermelons.
</span><span>9%×$9=<span>?
</span></span>Percent means "out of one hundred," so <span><span><span><span>9% </span></span></span></span> is equivalent to <span>9/100 </span><span>which is also equal to 9 divided by 100.
9 divided by 100 is 0.09
</span>To find the amount of sales tax that must be paid, multiply <span><span>0.09 </span></span><span>by the original price.
So it would be 0.09*$9=$0.81
</span>
<span>To find the final price Tiffany paid, add the sales tax you just found to the original price.
$0.81+$9.00=$9.81
</span>To find the final price Tiffany paid, add the sales tax you just found to the original price.
5 0
3 years ago
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6.8% increase in $44,000
tatuchka [14]
(100+6.8=106.8%)
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4 years ago
There are approximately 3,000 bass in a lake. The population grows at a rate of 2% per year. Round answers to the nearest tenth.
Tamiku [17]

Answer:

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Step-by-step explanation:

If the population in year n is ...

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then the average rate of change from year 1 to year 4 is ...

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The average rate of change for years 1–4 is 62.4 bass per year.

For years 5–8, the rate of change is similarly computed:

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The average rate of change for years 5–8 is 67.6 bass per year.

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3 years ago
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