What is the slope of the line that passes through the points (-4,8) and (-14.8)?

A corporation must appoint a president, chief executive officer (CEO), chief operating officer (COO), and chief financial off

Zolol [24]

Answer:

(a) There are 32,760 different ways to appoint the officers.

(b) 3003 different ways can the committee be appointed.

(c) Probability of getting the five youngest of the qualified candidates is 0.00033.

Step-by-step explanation:

We are given that a corporation must appoint a president, chief executive officer (CEO), chief operating officer (COO), and chief financial officer (CFO). It must also appoint a planning committee with five different members.

There are 15 qualified candidates, and officers can also serve on the committee.

(a) The number of officers are 4, i.e; A president, chief executive officer (CEO), chief operating officer (COO), and chief financial officer (CFO).

There are 15 qualified candidates.

To find the number of ways to appoint the officers, we will use permutation because here the order of selecting the officer's matters.

So, the number of ways to appoint the officers = $^{15}\text{P}_4$

= $\frac{15!}{(15-4)!}$ { $\because ^{n}\text{P}_r = \frac{n!}{(n-r)!}$ }

= $\frac{15!}{11!}$ = 32,760 ways

(b) The number of committee numbers to appoint include five members.

There are 15 qualified candidates.

To find the number of ways in which the committee can be appointed, we will use combination because here the order of selecting the members doesn't matter.

So, the number of ways to appoint the committee = $^{15}\text{C}_5$

= $\frac{15!}{5! \times (15-5)!}$ { $\because ^{n}\text{C}_r = \frac{n!}{r! \times (n-r)!}$ }

= $\frac{15!}{5! \times 10!}$ = 3003 ways

(c) The probability of randomly selecting the committee members and getting the five youngest of the qualified candidates is given by;

Number of ways of selecting the committee = 3003

Selecting the five youngest of the qualified candidates = 1

So, the required probability = $\frac{1}{3003}$

= 0.00033

4 0

3 years ago

One leg in a right triangle is 11 m, and the hypotenuse measures 11√2 m. Find the length of the other leg.

ipn [44]

Answer:

$\boxed{11m}$

Step-by-step explanation:

Method #1: 45-45-90 Triangle

You can use the rules for a 45-45-90 triangle. These are:

→ Each 45-45-90 triangle is a right triangle with two additional 45° angles.

→ The triangle will have 2 legs, x, and one hypotenuse, x√2.

Therefore, because the problem gives values for one leg and the hypotenuse, the value for the one leg is equal to the value for the unsolved leg.

Method #2: Pythagorean Theorem

You can use the Pythagorean Theorem to solve for a missing side in a triangle. Please note, however, that the Pythagorean Theorem only works on right triangles.

The Pythagorean Theorem is defined as $a^{2} + b^{2} = c^{2},$ where a and b are both legs of the triangle and c is the hypotenuse.

Therefore, substitute the known value for a, 11, and the known value for c, 11√2. Then, evaluate each value to its power (except for b - it is unsolved) and simplify the equation with basic algebraic methods. Once your equation is down to $b^{2}= ?$ , you should take the square root of both sides of the equation to get the value for b.

$11^{2} +b^{2} =(11\sqrt{2} )^{2}\\121 + b^{2} = 242\\b^{2}=121\\b=11$

4 0

4 years ago

Please help 100 points and will mark brainliest!!!!!!!!

xz_007 [3.2K]

Answer:

x>3, on a number line, first draw a circle over the number , if the sign has equal to (≥ or ≤), fill in the circle. If the sign does not have equal to (> or <), leave the circle unfilled in.

Step-by-step explanation:

7 0

3 years ago

What is the domain and range of y=-1/4(x)

LenKa [72]

Domain: $(-\infty, \infty)$

Range: $(-\infty, \infty)$

Explanation:

The function is $y=-\frac{1}{4} x$

The domain of a function is the set of all input values for which the function is well defined. Generally, domain consists of all x-values of the function. Hence, the function $y=-\frac{1}{4} x$ is defined in the interval $(-\infty, \infty)$ .

The range of a function is the set of output values obtained by substituting the value of x in the function. Hence, the function $y=-\frac{1}{4} x$ is defined in the interval $(-\infty, \infty)$ .

6 0

3 years ago

A $120.00 pair of shoes at your nearby department store is marked up 4% and then is offered at 45% off. If sales tax is 13%, wha

S_A_V [24]

Answer:

$26

Step-by-step explanation:

0.8(X - 3) = 18.4

X - 3 = 23

X = 26

7 0

3 years ago