Divide decimals 1.52 / 1.9

Yesterday, James sold $29 worth of cookies and chocolate at his store. He sells cookies for $5 a box, and chocolate for $2 a bar

MAXImum [283]

Answer:

he sold 4 boxes of cookies and 3 chocolate bars

Step-by-step explanation:

5+5+5+5 = 20 3+3+3 = 9 so add 20+9 = 29

8 0

3 years ago

A. -4,0,2<br> B. -2,0,4<br> C. -5,0,17<br> D. -17,0,5

Lostsunrise [7]

Answer:

You have three

-4,0, and 2 or the answer choice A

Step-by-step explanation:

3 0

2 years ago

Let f(x)=5x3−60x+5 input the interval(s) on which f is increasing. (-inf,-2)u(2,inf) input the interval(s) on which f is decreas

o-na [289]

Answers:

(a) f is increasing at $(-\infty,-2) \cup (2,\infty)$ .

(b) f is decreasing at $(-2,2)$ .

(c) f is concave up at $(2, \infty)$

(d) f is concave down at $(-\infty, 2)$

Explanations:

(a) f is increasing when the derivative is positive. So, we find values of x such that the derivative is positive. Note that

$f'(x) = 15x^2 - 60
$

So,

$
f'(x) \ \textgreater \ 0
\\
\\ \Leftrightarrow 15x^2 - 60 \ \textgreater \ 0
\\
\\ \Leftrightarrow 15(x - 2)(x + 2) \ \textgreater \ 0
\\
\\ \Leftrightarrow \boxed{(x - 2)(x + 2) \ \textgreater \ 0} \text{ (1)}$

The zeroes of (x - 2)(x + 2) are 2 and -2. So we can obtain sign of (x - 2)(x + 2) by considering the following possible values of x:

-->> x < -2
-->> -2 < x < 2
--->> x > 2

If x < -2, then (x - 2) and (x + 2) are both negative. Thus, (x - 2)(x + 2) > 0.

If -2 < x < 2, then x + 2 is positive but x - 2 is negative. So, (x - 2)(x + 2) < 0.
If x > 2, then (x - 2) and (x + 2) are both positive. Thus, (x - 2)(x + 2) > 0.

So, (x - 2)(x + 2) is positive when x < -2 or x > 2. Since

$f'(x) \ \textgreater \ 0 \Leftrightarrow (x - 2)(x + 2) \ \textgreater \ 0$

Thus, f'(x) > 0 only when x < -2 or x > 2. Hence f is increasing at $(-\infty,-2) \cup (2,\infty)$ .

(b) f is decreasing only when the derivative of f is negative. Since

$f'(x) = 15x^2 - 60$

Using the similar computation in (a),

$f'(x) \ \textless \ \ 0 \\ \\ \Leftrightarrow 15x^2 - 60 \ \textless \ 0 \\ \\ \Leftrightarrow 15(x - 2)(x + 2) \ \ \textless \ 0 \\ \\ \Leftrightarrow \boxed{(x - 2)(x + 2) \ \textless \ 0} \text{ (2)}$

Based on the computation in (a), (x - 2)(x + 2) < 0 only when -2 < x < 2.

Thus, f'(x) < 0 if and only if -2 < x < 2. Hence f is decreasing at (-2, 2)

(c) f is concave up if and only if the second derivative of f is positive. Note that

$f''(x) = 30x - 60$

Since,

$f''(x) \ \textgreater \ 0
\\
\\ \Leftrightarrow 30x - 60 \ \textgreater \ 0
\\
\\ \Leftrightarrow 30(x - 2) \ \textgreater \ 0
\\
\\ \Leftrightarrow x - 2 \ \textgreater \ 0
\\
\\ \Leftrightarrow \boxed{x \ \textgreater \ 2}$

Therefore, f is concave up at $(2, \infty)$ .

(d) Note that f is concave down if and only if the second derivative of f is negative. Since,

$f''(x) = 30x - 60$

Using the similar computation in (c),

$f''(x) \ \textless \ 0 
\\ \\ \Leftrightarrow 30x - 60 \ \textless \ 0 
\\ \\ \Leftrightarrow 30(x - 2) \ \textless \ 0 
\\ \\ \Leftrightarrow x - 2 \ \textless \ 0 
\\ \\ \Leftrightarrow \boxed{x \ \textless \ 2}$

Therefore, f is concave down at $(-\infty, 2)$ .

3 0

3 years ago

Alice purchased 4 1⁄2 kilograms of olive oil for $27. What is the price per kilogram?

vitfil [10]

Hi!

We will solve this using ratios, like this:

4 1/2 = 4,5 kg of olive oil for 27 $

1 kg of olive oil for x $

_____________________________

x = (27*1)/4,5

x = 27/4,5

x = 6 $ per kilogram

Hope this helps!

8 0

3 years ago

There are several ways you might think you could enter numbers in WebAssign, that would not be interpreted as numbers. N.B. Ther

Vikki [24]

Answer:

a) $1.56e^{-9}$

b) -4.99

d) 1.9435

Step-by-step explanation:

We are given certain rule to identify number. We have to identify from the entries that can be interpreted as numbers.

a) 1.56e-9

This a number as there are no spaces, no comma, no units.

b) -4.99

This a number as there are no spaces, no comma, no units.

c) 40O0

This is not a number as 0 is substituted by O.

d) 1.9435

This a number as there are no spaces, no comma, no units.

e) 1.56 e-9

This is not a number as it contains a space.

f) $2.59

This is not a number as it contains a dollar sign.

g) 3.25E4

This is not a number as it contains alphabet.

h) 5,000

This is not a number as there is a comma in the given.

i) 1.23 inches

This is not a number as it contains a unit.

5 0

3 years ago