I need help with finding the area of a rectangle with a length of 3 feet and a width of 2 7/8

The required simplified value for the expression [tex]3^{-4}[/tex] is 1 / 81.

Given that,
To determine the simplified value of the expression [tex]3^{-4}[/tex] .

The process in mathematics to operate and interpret the function or expression to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication, and division,

Here,
[tex]3^{-4} = 1/3^4[/tex]

3 * 3 * 3 * 3 = 9 * 9 = 81

[tex]3^{-4} = 1 / 81[/tex]

Thus the required simplified value for the expression [tex]3^{-4}[/tex] is 1 / 81.

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To find the number of times the bacteria in petri dish A than petri dish B, let us divide.

So, number of times = [tex]\frac{Number of times bacteria in petri dish A}{Number of times bacteria in petri dish B}[/tex]

[tex]= \frac{1.08(10^{15} )}{2.7(10^{11} )}[/tex]

= 0.4 × [tex]10^{4}[/tex]

= 4000

Hence, the number of bacteria in petri dish A is 4000 times the number of bacteria in petri dish B.

Hence, slope = 3 and, y-intercept = 5.

Function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable.

Here, given that,

Avery and her friends attend a museum. It costs $5 to enter the main exhibit hall, with an added charge of $3 to view each special exhibit.

Avery writes an equation that models the total price of visiting the museum as a function of the number of special exhibits they view.

Now, let the function be,

f(x)= 3x+5  = the total price of visiting the museum

[where, x= special exhibit & 5=the main exhibit hall]

Let, y = f(x)

So, w get, y=3x+5

Hence, slope = 3

and, y-intercept = 5.

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The total length of the new highway, when complete, will be 57 miles.

The question states that 37 miles of a new highway have been completed and this distance is one mile less than two thirds of the entire length of the highway. To solve this problem, we need to write an equation using the given information and solve for the variable representing the total length of the highway.

Let's denote the total length of the highway as 'x'. According to the problem, two thirds of this length minus one mile equals 37 miles. Forming an equation, we can write (2/3)x - 1 = 37.

To solve for 'x', first add 1 to both sides of the equation to get rid of the '-1' on the left, that gives us (2/3)x = 38. After, to completely isolate 'x', multiply both sides of the equation by the reciprocal of 2/3, which is 3/2. Doing this results in 'x' = 38 * (3/2) = 57 miles.

Therefore, the new highway will be 57 miles long when complete.

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Final answer:

By applying the commutative property of addition and rearranging the numbers for easier mental calculation, the sum of 43 + 39 + 43 + 11 can be found to be 136.

Explanation:

The question asks to change the order and the grouping of the addends for easier mental calculation, and then to find the sum of 43 + 39 + 43 + 11. By understanding the commutative property of addition, which states that numbers can be added in any order without changing the sum, we can rearrange these numbers for easier addition.

To use mental math effectively, grouping numbers that make round numbers or those that are easier to add can simplify the process. Here, we can group 43 and 43, which are identical, and 39 and 11, which sum up to a round number.

Therefore, by rearranging:

43 + 43 = 86

39 + 11 = 50

Adding these sums together:

86 + 50 = 136

By changing the order and grouping of the addends, we find that the sum is 136.

The time it will take for an airplane to fly from London to Montreal at a speed of 550 mph covering a distance of 3300 miles is approximately 6 hours.

To find the time it will take for an airplane to fly from London to Montreal, we can use the equation for speed, which is:

Speed = Distance \u00f7 Time

Knowing that the plane can travel at a speed of 550 mph and the distance from London to Montreal is 3300 miles, we can rearrange the equation to solve for time:

Time = Distance \u00f7 Speed

Time = 3300 miles \u00f7 550 mph

After calculating, we find that:

Time = 6 hours

Therefore, it will take the airplane approximately 6 hours to fly from London to Montreal at a constant speed of 550 mph, ignoring any other factors such as wind or air traffic delays.

To find the time it will take, we can use the formula Time = Distance/Speed. In this case, it will take approximately 6 hours to fly from London to Montreal.

To find the time it will take to fly from London to Montreal, we can use the formula Time = Distance/Speed. In this case, the distance is approximately 3300 miles and the speed is 550 mph.

Plugging in the values into the formula, we get Time = 3300 miles / 550 mph = 6 hours. So, it will take approximately 6 hours to fly from London to Montreal.

Therefore, the time it will take to fly from London to Montreal is 6 hours.