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Mathematics

1 answer:

earnstyle [38]3 years ago

7 0

Answer:

Step-by-step explanation:

Trust me

S=5

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Evaluate 11 C4 and 1 P4

Svet_ta [14]

Answer:

Step-by-step explanation:

11C4 = 11! / (7!*4!) = 11 * 10 * 9 * 8 * 7!/ 7! * 4!

11C4 = 11*10 * 9 * 8 / 24

11C4 = 11*10 * 3

11C4 = 330

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You can't do the second one. Permutations and Combinations always give an answer greater than 1 and integers.

7 0

4 years ago

Let A = { x ∈ R : x 2 − 5 x + 4 ≤ 0 } , B = (3 , 5), and C = (3 , 4]. Show that A ∩ B = C . (Recall, you must show two separate

kolbaska11 [484]

Answer:

You can proceed as follows:

Step-by-step explanation:

First solve the quadratic inequality $x^{2}-5x+4\leq 0$ . To do that, factorize, then we have that $(x-4)(x-1)\leq 0$ . This implies that

$x-1\leq 0\, \text{and}\, x-4\geq 0$

$x-1 \geq 0\, \text{and}\, x-4\leq 0$

In the first case the solution is the empty set $\emptyset$ . In the second case the solution is the interval $1\leq x \leq 4$ . Now we have that

$A=[1,4]$

$B=(3,5)$

$C=(3,4]$ .

To show that $A\cap B\subseteq C$ consider $x\in A\cap B$ . Then $1\leq x \leq 4\, \text{and}\, 1$ , this implies that $3$ , then $x\in C$ . Now, to show that $C\subseteq A\cap B$ consider $x\in C$ , then $3$ , then $1\leq x \leq 4\, \text{and}\, 3$ , then $x\in [1,4] \, \text{and}\, x\in (3,5)$ , this implies that $x\in A\cap B$ .