A 5 inch tall bamboo shoot doubles in height every 3 days. If the equation y=ab^x, where x is the number of doubling periods, represents the height of the bamboo shoot, what are the values of a and b?

After 8 weeks your accounts have the same balance.

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

You have $22 in your bank account and deposit $11.50 each week.

And, At the same time your cousin has $218 but is withdrawing $13 each week.

Let after x weeks your accounts have the same balance.

Hence, We can formulate;

⇒ $22 + $11.50x = $218 - $13x

Solve for x as;

⇒ 22 + 11.50x = 218 - 13x

⇒ 13x + 11.50x = 218 - 22

⇒ 24.50x = 196

⇒ x = 196 / 24.50

⇒ x = 8

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Answer:

Hence, the model that best represents the data is:

Step-by-step explanation:

We are given a table that  shows the estimated number of lines of code written by computer programmers per hour when x people are working.

We are asked to find which model best represents the data?

So for finding this we will put the value of x in each of the functions and check which hold true that which gives the value of y i.e. f(x) as is given in the table:

We are given 4 functions as:

A)

B)

C)

D)

We make the table of these values at different values of x.

x                  A                 B                C               D

2              66.66          49.3            52.5           50

4             94.57            71.44           106.3         104  

6             134.14           103.57         160.1          158

8             190.27          150.14          213.9         212

10           269.91           217.64         267.7         266

12           382.85          315.5           321.5          320.

Hence, the function that best represents the data is:

Option C.

y=26.9x-1.3

The exponential function gotten from the table is y = 34(1.204)ˣ

Exponential function

An exponential function is in the form:

y = abˣ

where y, x are variables, a is the initial value of y and b is the multiplier.

Let y represent the lines of code written by x people.

From the table using the points:

(2,50) and (12, 320)

At (2, 50):

50 = ab²   (1)

At (12, 320):

320 = ab¹²   (2)

From equation 1 and 2:

b = 1.204, a = 34

The exponential function gotten from the table is y = 34(1.204)ˣ

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Answer:

Answer is attached to steps.

Step-by-step explanation:

Those are the steps and the answer attached

The dimensions that give the maximum area is 5 cm by 5 cm.

Given:

The perimeter of this rectangle is 20 cm, and formula for perimeter is

P= 2(W+L)

P = 20 cm = 2W + 2L.  

Then W + L = 10 cm,

or W = (10 cm) - L.

The area of the rectangle is A = L·W, and is to be maximized.  

On substituting the values, we get A = L[ (10 cm) - L ], or A = 10L - L²

Note that this is the equation of a parabola that opens down.  With coefficients a = -1, b = 10 and C = 0, we find that the x-coordinate of the vertex (which is the x-coordinate of the maximum as well) is

x = -b / (2a).  Subbing 10 for b and -1 for a, we get:

x = -[10] / [2·(-1)] = 10/2, or 5.

This tells us that one dimension of the rectangle is 5 cm.

Since P = 20 cm = 2L + 2W, and if we let L = 5 cm, we get:

20 cm = 2(5 cm) + 2W, or

10 cm = W + 5 cm, or W = 5 cm.

Therefore, choosing L = 5 cm and W = 5 cm results in a square, which in turn leads to the rectangle having the maximum possible area.

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Answer:

5 cm by 5 cm

Step-by-step explanation:

The perimeter of this rectangle is 20 cm, and the relevant formula is

P = 20 cm = 2W + 2L.  Then W + L = 10 cm, or W = (10 cm) - L.

The area of the rectangle is A = L·W, and is to be maximized.  Subbing (10 cm) - L for W, we get A = L[ (10 cm) - L ], or A = 10L - L²

Note that this is the equation of a parabola that opens down.  With coefficients a = -1, b = 10 and C = 0, we find that the x-coordinate of the vertex (which is the x-coordinate of the maximum as well) is

x = -b / (2a).  Subbing 10 for b and -1 for a, we get:

x = -[10] / [2·(-1)] = 10/2, or 5.

This tells us that one dimension of the rectangle is 5 cm.

Since P = 20 cm = 2L + 2W, and if we let L = 5 cm, we get:

20 cm = 2(5 cm) + 2W, or

10 cm = W + 5 cm, or W = 5 cm.

Thus, choosing L = 5 cm and W = 5 cm results in a square, which in turn leads to the rectangle having the maximum possible area.

Answer:

He earned approximately $ 9.87 per hour.

Step-by-step explanation:

The given selling price of the lawn mower = $ 155.00

Since, His spending for the lawn = The cost price of the lawn + Spending in parts repair + Spending in polishing and paint

= $35.00 +$39.17 + $36.43

= $ 110.60

Thus, the profit he gain by selling = Selling price - His total spending

= 155.00 - 110.60

= $ 44.4

Since, the procedure took 4.5 hours,

His earning in 4.5 hours = $ 44.4

⇒ His earning in 1 hour = 9.86666666667 ≈ $ 9.87

Hence, he earned approximately $ 9.87 per hour.

Answer: The correct answer is $9.87. The person below forgot to round up their answer. Everything else they did is correct. Have a blessed day!