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3 years ago

Multiplication in exponential notation

2 answers:

6 0

Multiplication and Division. Quantities with exponents can be multiplied and divided easily if they have the same base. Since all number in scientific notation have base 10, we can always multiply them and divide them. To multiply two numbers in scientific notation, multiply their coefficients and add their exponents.

ivolga24 [154]3 years ago

6 0

Okay, examples of Multiplication in exponential notation:

2 * 2 * 2 = 2³

3 * 3 = 3²

The way it works is that you look at how many factors of a number there are (How many times you see the same number multiplied by its self in a row) and take that number and put it in smaller form, to the top right of the original number. That is called an exponent.

There were three twos multiplied by each other, so I put an exponent of 3 next to a two, the exponent means that the 2 is multiplied by its self 3 times. Same with the 3 to the 2ed power. There were two threes, and so I put a 2 as the exponent of 3.

So 2³ = 2 * 2 * 2 = 8.

We get 8 because 2 * 2 is 4, then multiply 4 by 2, we get 8. Once you break it down, exponents can become really simple! Just keep practicing! I hope that this helped!

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I need help with this Pythagorean Theorem word problem

frez [133]

Answer:

10.63.

Step-by-step explanation:

First we need to understand pythagorean theorem that is,

Hypotenuse^2=perpendicular^2+base^2.

=7^2+8^2.

=49+64

=113.

Hypotenuse^2=113.

Square root both sides.

Hypotenuse=10.63.

5 0

3 years ago

Mathematic equation <br> solve q <br> 11=8(3q-1)

pickupchik [31]

24q-8=11 (use distributive property)
24q= 11+8
24q = 20
q= 20/24
q= 0.8

4 0

2 years ago

Read 2 more answers

Memory module consists of 9 chips. The device is designed with redundancy so that it works even if one of its chips is defective

soldier1979 [14.2K]

Answer:

a) $P[C]=p^n$

b) $P[M]=p^{8n}(9-8p^n)$

c) n=62

d) n=138

Step-by-step explanation:

Note: "Each chip contains n transistors"

a) A chip needs all n transistor working to function correctly. If p is the probability that a transistor is working ok, then:

$P[C]=p^n$

b) The memory module works with when even one of the chips is defective. It means it works either if 8 chips or 9 chips are ok. The probability of the chips failing is independent of each other.

We can calculate this as a binomial distribution problem, with n=9 and k≥8:

$P[M]=P[C_9]+P[C_8]\\\\P[M]=\binom{9}{9}P[C]^9(1-P[C])^0+\binom{9}{8}P[C]^8(1-P[C])^1\\\\P[M]=P[C]^9+9P[C]^8(1-P[C])\\\\P[M]=p^{9n}+9p^{8n}(1-p^n)\\\\P[M]=p^{8n}(p^{n}+9(1-p^n))\\\\P[M]=p^{8n}(9-8p^n)$

$P[M]=(0.999)^{8n}(9-8(0.999)^n)=0.9$

This equation was solved graphically and the result is that the maximum number of chips to have a reliability of the memory module equal or bigger than 0.9 is 62 transistors per chip. See picture attached.

d) If the memoty module tolerates 2 defective chips:

$P[M]=P[C_9]+P[C_8]+P[C_7]\\\\P[M]=\binom{9}{9}P[C]^9(1-P[C])^0+\binom{9}{8}P[C]^8(1-P[C])^1+\binom{9}{7}P[C]^7(1-P[C])^2\\\\P[M]=P[C]^9+9P[C]^8(1-P[C])+36P[C]^7(1-P[C])^2\\\\P[M]=p^{9n}+9p^{8n}(1-p^n)+36p^{7n}(1-p^n)^2$

We again calculate numerically and graphically and determine that the maximum number of transistor per chip in this conditions is n=138. See graph attached.