Nancy has a shelf over her bed where she keeps her four stuffed teddy bears. How many ways can she arrange the four bears?

CRITICAL THINKING A local zoo employs 36 people to take care of the animals each day. At most, 24 of the employees work full tim

k0ka [10]

We assume all employees are either full-time or part-time.

36 = 24 + 12

If the number of full-time employees is 24 or less, the number of part-time employees must be 12 or more. (Thinking, based on knowledge of sums.)

_____

You can write the inequality in two stages.

First, write and solve an equation for the number of full-time employees in terms of the number of part-time employees.
Then apply the given constraint on full-time employees. This gives an inequality you can solve for the number of part-time employees.

Let f and p represent the numbers of full-time and part-time employees, respectively.

... f + p = 36 . . . . . . given

... f = 36 - p . . . . . . . subtract p. This is our expression for f in terms of p.

... f ≤ 24 . . . . . . . . . given

... (36 -p) ≤ 24 . . . . substitute for f. Here's your inequality in p.

... 36 - 24 ≤ p . . . . add p-24

... p ≥ 12 . . . . . . . . the solution to the inequality

5 0

2 years ago

Given the function f(x) = −5x2 − x + 20, find f(3). −28 −13 62 64

Katyanochek1 [597]

Answer:

Option (a) is correct.

The value of given function $f(x)=-5x^2-x+20$ at x = 3 is -28

Step-by-step explanation:

Given : Function $f(x)=-5x^2-x+20$

We have to find the value of given function at x = 3

Consider the given function $f(x)=-5x^2-x+20$

Since, we have tof ind the value of function at x = 3

Put x = 3 in given function f(x)

$f(3)=-5(3)^2-(3)+20$

Simplify, we have,

$f(x)=-45-3+20=-28$

Thus, the value of given function $f(x)=-5x^2-x+20$ at x = 3 is -28

5 0

2 years ago

Read 2 more answers

An expression is well-defined if you can compute its value without any illegal operations. examples of expressions that are not

Gelneren [198K]

The given expression is $\frac{\sqrt{x + 1} + \sqrt{1 - x}}{\sqrt{x}}$

So, we have 3 square roots.
The number under a square root sign must be Non negative.
Beside that the denominator must be not equal zero.
For the term ⇒⇒⇒ $\sqrt{x}$
∴ x > 0 ⇒⇒⇒ x ∈ (0,∞)
For the term ⇒⇒⇒ $\sqrt{x+1}$
∴x+1 ≥ 0 ⇒⇒⇒ x ≥ -1 ⇒⇒⇒ ∴ x ∈ [-1,∞)
For the term ⇒⇒⇒ $\sqrt{1-x}$
∴ 1-x ≥ 0 ⇒⇒⇒ x ≤ 1 ⇒⇒⇒ x ∈ (-∞,1]

So, The values of x which make the expression well defined

∴ x ∈ { (0,∞) ∪ [-1,∞) ∪ (-∞,1] }

∴ x ∈ [-1,0) ∪ (0,1]

OR can be written as ⇒⇒ x ∈ [-1,1] - {0}

6 0

2 years ago

Celia bought a bag of 121212 goldfish for \$3$3dollar sign, 3.

muminat

Celia bought a bag of 12 goldfish for $3, Cost of 1 goldfish is $0.25 .

Step-by-step explanation:

The goldfish is a freshwater fish in the family Cyprinidae of order Cypriniformes. It is one of the most commonly kept aquarium fish. A relatively small member of the carp family, the goldfish is native to East Asia.

Here we have , Celia bought a bag of 12 goldfish for $3 . We need to find the cost of 1 goldfish . Let's find out:

Celia have a bag of 12 goldfish which cost her $3 . So , cost of 1 goldfish is equivalent to

⇒ $(1)\frac{12}{3}$