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docker41
18 days ago
8

The number of users of a cell tower in a small, developing town increased by a factor of 1.5 every year from 2010 to 2019. The f

unction below shows the number of cell tower users, f(x), after x years from the year 2010:
f(x) = 5,000(1.5)x

Which of the following is a reasonable domain for the function?

A.2,010 ≤ x ≤ 2,019
B.0 ≤ x ≤ 5,000
C.0 ≤ x ≤ 9
D.All positive integers
Mathematics
2 answers:
zzz [9K]18 days ago
7 0

Answer:

Option C) 0 \leq x \leq 9

Step-by-step explanation:

In the question, we have that:

From 2010 to 2019, the number of users of a cell tower rose by a factor of 1.5 each year.

f(x) = 5000(1.5)^x

where f(x) represents the users of the cell tower, and x stands for the years since 2010.

The task requires us to identify the domain of this function.

We define the domain of a function as the set of x values for which the function is valid.

In this case, the function relates to the number of users between the years 2010 and 2019, thus it is relevant for the years 2010 through 2019.

Here, x represents the count of years since 2010.

So, in 2010, x = 0 and in 2019, x = 9.

Therefore, the domain for the function is:

0 \leq x \leq 9

tester [8.8K]18 days ago
3 0

Answer:

B

Step-by-step explanation:

In the provided statement, there is a function indicating the quantity of users of a cell tower, f(x), over the years from 2010 to 2019. To address the question, we need to recall that the domain comprises all possible values that the variable (in this case, x) can take for the function to be valid.

Consequently, since the function relates to years, and "x" stands for the timeframe from 2010 (beginning) to 2019 (end), it follows that the domain spans between these two points.

Thus, the correct answer is:

B. 0 ≤ x ≤ 5,000

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Svet_ta [9500]
You can acquire 42 cookies through 12 different combinations. The first method involves purchasing 2 packs of 21 (21x2 = 42). The second consists of acquiring 1 pack of 21 alongside 3 packs of 7 (21 + 3x7 = 42). The third way is to buy 1 pack of 21 and 21 individual cookies (21 + 21 = 42). The fourth option combines 1 pack of 21, 1 pack of 7, and 14 single cookies (21 + 7 + 14 = 42). The fifth strategy includes 1 pack of 21, 2 packs of 7, and 7 individual cookies (21 + 14 + 7 = 42). The sixth way is to opt for 6 packs of 7 (7x6 = 42). The seventh option is to purchase 5 packs of 7 along with 7 individual cookies (7x5 + 7 = 42). For the eighth method, you can buy 4 packs of 7 and 14 single cookies (7x4 + 14 = 42). The ninth way is to get 3 packs of 7 with 21 single cookies (7x3 + 21 = 42). The tenth consists of acquiring 2 packs of 7 plus 28 individual cookies (7x2 + 28 = 42). The eleventh strategy involves 1 pack of 7 and 35 single cookies (7 + 35 = 42). Lastly, the twelfth method is simply buying 42 individual cookies (42 = 42).
4 0
9 days ago
Emma earns $6 each time she mows the lawn and $8 per hour for babysitting. She is saving up to buy a new pair of jeans that cost
zzz [9080]

Answer:

The illustration provided shows the graph

Step-by-step explanation:

Let

x ------> number of times Emma cuts the grass

y ------> hours Emma spends babysitting

it is known that

6x+8y\geq 48 ------> represents the inequality of the scenario

The solution is the shaded region above the solid line where both x and y are positive

The equation for the solid line is represented as 6x+8y=48

The slope of the line is negative m=-\frac{3}{4}

The y-intercept is at the point (0,6) (the y-value when x is zero)

The x-intercept is at (8,0) (the x-value when y equals zero)

therefore

The illustration provided shows the graph

6 0
18 days ago
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The area of the postcard is 24 square inches. What is the width b of the message (in inches)?
Leona [9271]
Area of a rectangle = length x width
For this postcard:
length = 4 in
width = (3+b) in
area = 24 in^2

Substitute into the area formula:
24 = 4 x (3+b)
24 = 12 + 4b
24 - 12 = 4b
12 = 4b
b = 3 in

Therefore:
the length of the postcard = 4 inch
the width of the postcard = b+3 = 3 + 3 = 6 inch
4 0
1 month ago
How much profit was generated by the sales of gold label and black label combined?
lawyer [9240]
The profit produced by combining sales of gold label and black label equals the total of their individual profits. From the table \begin{array}{ccc}&\text{Number of bottles sold}&\text{Average profit (per bottle)}\\\text{Gold label}&1,000&\$2.75\end{array} you find the gold label's profit 1,000\cdot \$2.75=\$2,750. and similarly from another table \begin{array}{ccc}&\text{Number of bottles sold}&\text{Average profit (per bottle)}\\\text{Black label}&2,000&\$1.50\end{array} find the black label's profit 2,000\cdot \$1.50=\$3,000.. Adding these yields \$2,750+\$3,000=\$5,750.. Thus, option 5 is the correct choice.
8 0
1 month ago
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Students have organized
tester [8842]

Answer:

Part A. At least 6 hours

Part B. In less than 2.5 hours, Elijah will fall behind Mercedes

Part C. In over 2.5 hours, Elijah will lead Aubrey

Step-by-step explanation:

D = distance

v = speed

t = time

Formula connecting D, v, and t:

D=v\cdot t

Part A.

Steve's speed: v=3.5\ mph

Distance: a minimum of 21 miles

Time: unknown, so

3.5\cdot t\ge 21\\ \\35t\ge 210\ [\text{Multiplied by 10}]\\ \\t\ge \dfrac{210}{35}\\ \\t\ge \dfrac{30}{5}\\ \\t\ge 6

It would require Steve a minimum of 6 hours to traverse at least 21 miles on Day 1.

Part B.

Mercedes's speed: v_M=2.4\ mph

Elijah's speed: v_E=3.2\ mph

Elijah's Distance walked: D_E miles

Mercedes's Distance walked: D_M miles

Time: x hours

Mercedes is 2 miles ahead, therefore

D_E=3.2x\\ \\D_M=2.4x+2

Elijah will trail behind until

D_E

In 2.5 hours, Elijah will close the gap on Mercedes, and in less than 2.5 hours, Elijah will trail behind her.

Part C.

Aubrey's speed: v_M=3\ mph

Elijah's speed: v_E=3.2\ mph

Elijah's Distance walked: D_E miles

Aubrey's Distance walked: D_A miles

Time: x hours

At the beginning of Day 3, Elijah starts from Mile 42, while Aubrey begins at Mile 42.5.

D_E=42+3.2x\\ \\D_A=42.5+3x

Elijah will be ahead of Aubrey when

D_E>D_A\\ \\42+3.2x> 42.5+3x\\ \\3.2x-3x>42.5-42\\ \\0.2x>0.5\\ \\2x>5\ [\text{Multiplied by 10}]\\ \\x>\dfrac{5}{2}\\ \\x>2.5\ hours

In 2.5 hours, Elijah will surpass Aubrey, and after more than 2.5 hours, Elijah will outpace Aubrey.

4 0
1 month ago
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