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BabaBlast [244]
3 years ago
13

I need help with this, it's due in 15 mins-

Mathematics
1 answer:
LiRa [457]3 years ago
3 0

Answer:

Mean: 3.5263157894737

Median: 3

Mode: 3

Step-by-step explanation: The mode is 3 because the mode is for which number pops up the most, which is 3.

I got the median by crossing out 8 from the left and the right of the number set and got 3 as the last number.

I got the mean by adding up all the numbers and divided it by the amount of numbers in the set.

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Let g' be the group of real matricies of the form [1 x 0 1]. Is the map that sends x to this matrix an isomorphism?
aliina [53]

Yes. Conceptually, all the matrices in the group have the same structure, except for the variable component x. So, each matrix is identified by its top-right coefficient, since the other three entries remain constant.

However, let's prove in a more formal way that

\phi:\ \mathbb{R} \to G,\quad \phi(x) = \left[\begin{array}{cc}1&x\\0&1\end{array}\right]

is an isomorphism.

First of all, it is injective: suppose x \neq y. Then, you trivially have \phi(x) \neq \phi(y), because they are two different matrices:

\phi(x) = \left[\begin{array}{cc}1&x\\0&1\end{array}\right],\quad \phi(y) = \left[\begin{array}{cc}1&y\\0&1\end{array}\right]

Secondly, it is trivially surjective: the matrix

\phi(x) = \left[\begin{array}{cc}1&x\\0&1\end{array}\right]

is clearly the image of the real number x.

Finally, \phi and its inverse are both homomorphisms: if we consider the usual product between matrices to be the operation for the group G and the real numbers to be an additive group, we have

\phi (x+y) = \left[\begin{array}{cc}1&x+y\\0&1\end{array}\right] = \left[\begin{array}{cc}1&x\\0&1\end{array}\right] \cdot \left[\begin{array}{cc}1&y\\0&1\end{array}\right] = \phi(x) \cdot \phi(y)

8 0
3 years ago
How could you estimate the difference of 6.52 and 6.520
borishaifa [10]
They are equal because no matter how many zeroes are the decimal point and all the numbers so  6.900000000000000 and 6.9 are equal.
3 0
3 years ago
Read 2 more answers
The first side of a triangle measures 4 in. less than the second side, the third side is 3 in. more than the first side, and the
Firdavs [7]

Answer:

\boxed{\frac{23}{3} ~in} or \boxed{7,7~in}

.

Step-by-step explanation:

Suppose, the first side is a, the second side is b, and the third side is c. So:

→ a = s - 4

→ b = s

→ c = (s - 4) + 3

→ a + b + c = 15

First step, find the value of s

a + b + c = 15

(s - 4) + s + (s - 4) + 3 = 15

3s - 5 = 15

3s = 15 + 5

3s = 20

s = \frac{20}{3}

So, the third side is

c = (s - 3) + 4

c = s + 1

c = \frac{20}{3} + 1

c = \frac{23}{3}

.

Happy to help :)

5 0
3 years ago
Read 2 more answers
a baby weights 7 pounds at birth. the table shows the birth weight after each month of life, up to six months​
BigorU [14]

Answer:

they are adding by 7 because 6 +7=13

6 0
2 years ago
Serena is the manager at the coffee shop .the amount of money she earns is represented by the equation m= 21h , where h is the a
shutvik [7]
21 - 13.50= 7.50

so based on what your question is asking, Serena makes $7.50 more than Gabe per hour.
8 0
3 years ago
Read 2 more answers
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