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Licemer1 [7]
3 years ago
5

Luis and Sara both open savings accounts at the same bank. Luis opens his account with $125 and deposits $60 per week. Sara open

s her account with $50 and increases the amount by 4% per week. Which account has a greater average rate of change between 10 and 20 weeks?
A. Luis's account has a smaller average rate of change than Sara's account between 10 and 20 weeks.
B. Sara's account has a greater average rate of change than Luis' account between 10 and 20 weeks.
C. Luis's account has a greater average rate of change than Sara's account between 10 and 20 weeks.
D. Sara's and Luis's accounts have the same average rate of change between 10 and 20 weeks.
Mathematics
2 answers:
Tanya [424]3 years ago
8 0

Answer:

luis account a

Step-by-step explanation:

it is trust me

frez [133]3 years ago
7 0

Answer:

Luis's account has a greater average rate of change than Sara's account between 10 and 20 weeks.

Step-by-step explanation:

An exponential function means a curved line while a linear function is a straight line.

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A bag of trail mix weighs 2 lb. By weight, 20% of the bag is oats. How many pounds is the oats portion of the trail mix? (a) Wri
posledela
Answer: 0.4 pounds of the trail mix is oats.

To find the answer, you can set up a proportion. We can use the percent proportion below.

part/whole = percent/100

x/2 = 20/100

To solve this you cross multiply and divide.

100x = 40
x = 0.4
3 0
3 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&#10;\\&#10;\\ \Leftrightarrow 30x - 60 \ \textgreater \  0&#10;\\&#10;\\ \Leftrightarrow 30(x - 2) \ \textgreater \  0&#10;\\&#10;\\ \Leftrightarrow x - 2 \ \textgreater \  0&#10;\\&#10;\\ \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 &#10;\\ \\ \Leftrightarrow 30x - 60 \ \textless \  0 &#10;\\ \\ \Leftrightarrow 30(x - 2) \ \textless \  0 &#10;\\ \\ \Leftrightarrow x - 2 \ \textless \  0 &#10;\\ \\ \Leftrightarrow \boxed{x \ \textless \  2}

Therefore, f is concave down at (-\infty, 2).
3 0
3 years ago
Translate the figure 2 units left and 7 units down.
STALIN [3.7K]

The translation of the given figure will have vertices, <u>A'(1,2),</u> <u>B'(3,2),</u> <u>C'(3,-5),</u> and <u>D(-1,-3)</u> from the initial vertices A(3,9), B(5,9), C(5,2), and D(1,4). The figure is attached.

In the question, we are asked to translate the given figure 2 units left and 7 units down.

In the translation, the left-right movement implies the change in the x-coordinate, whereas the up-down movement implies the change in the y-coordinate.

For any point P(x, y) the given rule says that after translation,

P(x, y) becomes P'(x - 2, y - 7).

The coordinates of the given figure are:

A(3,9), B(5,9), C(5,2), and D(1,4).

After translation, these points can be shown as:

A(3,9) becomes A'(1,2).

B(5,9) becomes B'(3,2).

C(5,2) becomes C'(3,-5).

D(1,4) becomes D'(-1,-3).

Thus, the translation of the given figure will have vertices, <u>A'(1,2),</u> <u>B'(3,2),</u> <u>C'(3,-5),</u> and <u>D(-1,-3)</u> from the initial vertices A(3,9), B(5,9), C(5,2), and D(1,4). The figure is attached.

Learn more about translations at

brainly.com/question/1400185

#SPJ9

7 0
2 years ago
Garne Problem med
Citrus2011 [14]

Total distance the rover need to travel ​is D = 1miles .

<u>Step-by-step explanation:</u>

We have , Garne Problem med   . A rover needs to travel mile to reach its destination  traveled mile. a rover needs to travel 5/8 mile to reach its destination it has already travel 3/8 miles . We need to find that  how much farther does the rover need to travel ​ , Let's do it step by step:

First , rover has already traveled 3/8 miles , Let total distance to be traveled by rover is D :

⇒ D = \frac{3}{8} + d , where d is distance left to cover .

Now, rover need to travel 5/8 miles more to reach destination :

⇒ D = \frac{3}{8} + d , where d is distance left to cover  , So d = \frac{5}{8}

⇒ D = \frac{3}{8} + d

⇒ D = \frac{3}{8} + \frac{5}{8}

⇒ D = \frac{3+5}{8}

⇒ D = \frac{8}{8}

⇒ D = 1miles

∴ Total distance the rover need to travel ​is D = 1miles .

8 0
3 years ago
A point that has a positive x-coordinate and a positive y-coordinate is located in which quadrant?
zhuklara [117]
Quadrant I or QI

This is tough to explain but here I go
If x and y is positive, it's QI
If x is negative and y is positive it's QII
If x and y are negative, it's QIII
If x is positive and y is negative It's QIV

So the answer is C
Hopes this helps :D
5 0
3 years ago
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