A movie theater is offering a special summer pass. Passholders pay $8 per movie for the first 5 movies and watch additional movi

Response: 4.4

Detailed breakdown:

Answer and explanation:

Algebra revolves around the fundamental idea of using letters known as variables to represent quantities, which allows for solving for unknown values. Essentially, algebra involves transitioning from what is known to what is unknown to ascertain those unknown results. For instance, if we know a specific item was purchased twice but we're unsure of its price, we can denote this unknown price as 2a or 2p, depending on the selected variable. If the total spending for those items is, say, $50, we can set up the equation 2a = $50, which leads us to find that the cost per item is $25.

Algebra can also manifest itself in expressions, commonly referred to as algebraic expressions, which can be incorporated into equations, such as the previously mentioned 2a = $50. These expressions may take forms like 2a + 3b, where a and b designate the costs of different products that were acquired in quantities of 2 and 3, respectively.

The likelihood of all sprinklers functioning properly in a fire stands at 0.0282. This was determined via the Binomial probability distribution since the activation of sprinklers occurs independently. There are two potential outcomes: they either function correctly or they do not. The binomial distribution is used to calculate the probabilities over multiple trials. The resulting equation b(x; n, P) = P(X=x) considers the number of successes, probability of success in a singular attempt, and the number of trials involved. The computations conclude with the probability being reflected as 0.0282.

10-3 or 10+(-3), these two forms should be helpful.

Answer:

The Mean Absolute Deviation (MAD) for her dataset is 4.

Detailed explanation:

Vivian collected data from local cyclists to find the typical miles they rode daily.

Her recorded figures are shown below:

7, 10, 13, 4, 12, 21, 10, 3

= 10

            Data point          Distance from mean

                                           

1                   7                           7 - 10   =     | -3 |     = 3

2.                10                           10 - 10  =     | 0 |       = 0

3.                13                           13 - 10  =     | 3 |     = 3

4.                4                             4 - 10    =    | -6 |    = 6

5.               12                            12 - 10   =    | 2 |     = 2

6.               21                            21 - 10   =    | 11 |   = 11

7.               10                            10 - 10   =    | 0 |     = 0

8.               3                             3 - 10   =    | -7 |   = 7

                                               

Calculating the total distance gives us 3 + 0 + 3 + 6 + 2 + 11 + 0 + 7 = 32

Thus, MAD = = 4

The Mean Absolute Deviation of this data reflects an average variation of 4 miles that cyclists ride daily.