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3 years ago

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Assuming that Samir is equally likely to hit each of the 10 targets, what is the probability that he will miss at least one of t

hem?

1 answer:

hammer [34]3 years ago

7 0

Answer:40%

Step-by-step explanation:

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Determine if the given mapping phi is a homomorphism on the given groups. If so, identify its kernel and whether or not the mapp

shtirl [24]

Answer:

(a) No. (b)Yes. (c)Yes. (d)Yes.

Step-by-step explanation:

(a) If $\phi: G \longrightarrow G$ is an homomorphism, then it must hold

that $b^{-1}a^{-1}=(ab)^{-1}=\phi(ab)=\phi(a)\phi(b)=a^{-1}b^{-1}$ ,

but the last statement is true if and only if G is abelian.

(b) Since G is abelian, it holds that

$\phi(a)\phi(b)=a^nb^n=(ab)^{n}=\phi(ab)$

which tells us that $\phi$ is a homorphism. The kernel of $\phi$

is the set of elements g in G such that $g^{n}=1$ . However,

$\phi$ is not necessarily 1-1 or onto, if $G=\mathbb{Z}_6$ and

n=3, we have

$kern(\phi)=\{0,2,4\} \quad \text{and} \quad\\\\Im(\phi)=\{0,3\}$

(c) If $z_1,z_2 \in \mathbb{C}^{\times}$ remeber that

$|z_1 \cdot z_2|=|z_1|\cdot|z_2|$ , which tells us that $\phi$ is a

homomorphism. In this case

$kern(\phi)=\{\quad z\in\mathbb{C} \quad | \quad |z|=1 \}$ , if we write a

complex number as $z=x+iy$ , then $|z|=x^2+y^2$ , which tells

us that $kern(\phi)$ is the unit circle. Moreover, since

$kern(\phi) \neq \{1\}$ the mapping is not 1-1, also if we take a negative

real number, it is not in the image of $\phi$ , which tells us that

$\phi$ is not surjective.

(d) Remember that $e^{ix}=\cos(x)+i\sin(x)$ , using this, it holds that

$\phi(x+y)=e^{i(x+y)}=e^{ix}e^{iy}=\phi(x)\phi(x)$

which tells us that $\phi$ is a homomorphism. By computing we see

that $kern(\phi)=\{2 \pi n| \quad n \in \mathbb{Z} \}$ and

$Im(\phi)$ is the unit circle, hence $\phi$ is neither injective nor

surjective.

7 0

3 years ago

Write three division word problem solve and check with multiplication

babymother [125]

18 divided by 3... 3 times 6

14 divided by 7... 7 times 2

12 divided by 3 ... 3 x 4

5 0

2 years ago

Alguien puede ayudarme en esto

Montano1993 [528]

Lo siento, español no es mi primer lengua, pero trataré ayudar. ¿Qué significa L1, L2, y L3? No recuerdo.
Necesita multiplicar
x-3 • x+2
x-2 • x-1
Pero, obtendrías esto, y no ayudaría
x^2-6 = x^2+2
Es imposible resolver para x con eso.
Creo que la respuesta es e. no existe tal valor para x

7 0

3 years ago

How do you write 6.5 in word form

Cerrena [4.2K]

6.5 six and five tenths

7 0

2 years ago

I think of a number and add one fourth of it to half of it and the result is twelve. What is the number I thought of?

belka [17]

Suppose that the number u were thinking about is x thus :

$\frac{1}{4} x + \frac{1}{2} x = 12 \\$

Multiply both sides by 4

$4 \times ( \frac{1}{4} x + \frac{1}{2} x) = 4 \times 12 \\$

$x + 2x = 48$

$3x = 48$

Divide both sides by 3

$\frac{3x}{3} = \frac{48}{3 } \\$

$x = 16$

3 0

2 years ago