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4 years ago

Let F be a field, and suppose a EF, a *0. Prove that a has a unique multiplicative inverse.

Mathematics

1 answer:

bezimeni [28]4 years ago

6 0

Answer with Step-by-step explanation:

Let F be a field .Suppose $a\in F$ and $a\neq 0$

We have to prove that a has unique multiplicative inverse.

Suppose a has two inverses b and c

Then, $ac=1,ab=1$ where 1 =Multiplicative identity

$ac=ab$

$c=b$ (cancel a on both sides)

Hence, a has unique multiplicative inverse.

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An economy pack of highlighters contains 12 yellow, 6 blue, 4 green, and 3 orange highlighters. An experiment consists of random

Serhud [2]

Answer:

The probability of choosing a blue or yellow highlighter when one yellow highlighter is picked is 17/25.

Step-by-step explanation:

Here, according to the question:

Total number of yellow highlighters = 12

Total number of blue highlighters = 6

Total number of green highlighters = 4

Total number of orange highlighters = 3

So, the total number of highlighters = 12 + 6 + 4 + 3 = 25

Let E1 : Event of selecting a yellow highlighter.

P(E1) = $\frac{\textrm{Total number of yellow highlighters}}{\textrm{Total Highlighters}}$ = $\frac{12}{25}$

Let E2 : Event of selecting blue or yellow highlighter ONCE yellow highlighter is selected.

So, the total yellow highlighters left after selecting one = 12 -1 = 11

Also, the number of blue highlighter = 6

So, the TOTAL FAVORABLE options to E2 = 6+ 11 = 17

P(E2) =

$\frac{\textrm{Total number of yellow + Blue highlighters}}{\textrm{Total Highlighters}}$ = $\frac{17}{25}$

Hence, the probability that a blue or yellow highlighter is selected given that a yellow highlighter is selected is 17/25.

7 0

3 years ago

Tasha invests $5,000 annually at 6% and an additional $5,000 annually at 8%. Thomas invests $10,000 annually at 7%. Which statem

Setler79 [48]

Answer:

B is correct.

Step-by-step explanation:

Compound Interest Formula:

$V(t)=P(1+\frac{r}{n})^{nt}$

Tasha invests in two ways

Case 1:

Principal P=$5,000
Rate of Interest r=0.06
Time t=t
n=1

$V(t)=5000(1+0.06)^t$

$V(t)=5000(1.06)^t$

Case 2:

Principal P=$5,000
Rate of Interest r=0.08
Time t=1
n=1

$V(t)=5000(1+0.08)^t$

$V(t)=5000(1.08)^t$

Total amount yield by Tasha = $5000[(1.06)^t+(1.08)^t]$

Thomas Investment

Principal P=$10,000
Rate r= 0.07
t=t
n=1

Total amount yield by Thomas = $10000(1.07)^t$

Now we make table for Tasha and Thomas different value of t

t Tasha Thomas

1 $10,700 $10,700

2 $11,450 $11,449

3 $12,254 $12,250

4 $13,115 $13,108

In table we can see Tasha investment will yield more from Thomas.

Thus, Tasha’s investment will yield more over many years because the amount invested at 8% causes the overall total to increase faster.

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3 years ago

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kupik [55]

Answer: next point would be (12,-6)

Step-by-step explanation:

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3 years ago

Given: 5x - 6y = 0, What is the x-intercept?

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Alan has 90 apple tree he has 90 apples and each apple tree how many apples does he have in all?

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Answer:

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