Solved on Dec 18, 2023

Find the missing values in the relative frequency table for the concession stand sales data. Solve for variables $a$ , $b$ , $c$ , $d$ , and $e$ to complete the table.

STEP 1

Assumptions
1. Each cell in the relative frequency table represents the proportion of total sales for a particular combination of concession stand item and beverage.
2. The 'Total' row and column represent the sum of the relative frequencies for that row or column.
3. The sum of all relative frequencies in the table should equal 1, as they represent the whole of the concession stand sales.

STEP 2

To find the value of $a$ , we need to use the total for the 'Soda' row. We know that the sum of the relative frequencies in this row is 0.36.
$0.17 + a + 0.05 = 0.36$

STEP 3

Now, solve for $a$ .
$a = 0.36 - 0.17 - 0.05$

STEP 4

Calculate the value of $a$ .
$a = 0.36 - 0.22$
$a = 0.14$

STEP 5

To find the value of $b$ , we look at the 'Total' column for 'Pizza'. The sum of the relative frequencies for 'Pizza' is 0.38.
$0.14 + b + 0.04 = 0.38$

STEP 6

Now, solve for $b$ .
$b = 0.38 - 0.14 - 0.04$

STEP 7

Calculate the value of $b$ .
$b = 0.38 - 0.18$
$b = 0.20$

STEP 8

To find the value of $c$ , we use the 'Water' row. We don't have the total for this row, but we can use the 'Total' column for 'Popcorn' to find it. We know that the sum of the relative frequencies for 'Popcorn' plus the known value for 'Nodrink' row (0.02) and 'Soda' row (0.05) should equal the total for the 'Popcorn' column.
$0.05 + c + 0.02 = Total\, for\, Popcorn$

STEP 9

Since we don't have the total for 'Popcorn', we can find it by subtracting the known totals for 'Hot Dog' and 'Pizza' from 1.
$Total\, for\, Popcorn = 1 - 0.45 - 0.38$

STEP 10

Calculate the total for 'Popcorn'.
$Total\, for\, Popcorn = 1 - 0.83$
$Total\, for\, Popcorn = 0.17$

STEP 11

Now we can solve for $c$ .
$0.05 + c + 0.02 = 0.17$

STEP 12

Solve for $c$ .
$c = 0.17 - 0.05 - 0.02$

STEP 13

Calculate the value of $c$ .
$c = 0.17 - 0.07$
$c = 0.10$

STEP 14

To find the value of $d$ , we use the 'Water' row. We now know the value of $c$ , so we can use the sum of the relative frequencies for 'Water'.
$0.23 + 0.20 + 0.10 = d$

STEP 15

Calculate the value of $d$ .
$d = 0.23 + 0.20 + 0.10$
$d = 0.53$

STEP 16

Finally, to find the value of $e$ , we use the 'Total' column for 'Hot Dog'. The sum of the relative frequencies for 'Hot Dog' is 0.45.
$0.17 + 0.23 + e = 0.45$

STEP 17

Now, solve for $e$ .
$e = 0.45 - 0.17 - 0.23$

STEP 18

Calculate the value of $e$ .
$e = 0.45 - 0.40$
$e = 0.05$
The missing values in the relative frequency table are as follows:
$\begin{array}{l} a = 0.14 \\ b = 0.20 \\ c = 0.10 \\ d = 0.53 \\ e = 0.05 \\ \end{array}$

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Find the missing values in the relative frequency table for the concession stand sales data. Solve for variables $a$ , $b$ , $c$ , $d$ , and $e$ to complete the table.

STEP 1

STEP 2

To find the value of $a$ , we need to use the total for the 'Soda' row. We know that the sum of the relative frequencies in this row is 0.36.
$0.17 + a + 0.05 = 0.36$

STEP 3

Now, solve for $a$ .
$a = 0.36 - 0.17 - 0.05$

STEP 4

Calculate the value of $a$ .
$a = 0.36 - 0.22$
$a = 0.14$

STEP 5

To find the value of $b$ , we look at the 'Total' column for 'Pizza'. The sum of the relative frequencies for 'Pizza' is 0.38.
$0.14 + b + 0.04 = 0.38$

STEP 6

Now, solve for $b$ .
$b = 0.38 - 0.14 - 0.04$

STEP 7

Calculate the value of $b$ .
$b = 0.38 - 0.18$
$b = 0.20$

STEP 8

STEP 9

Since we don't have the total for 'Popcorn', we can find it by subtracting the known totals for 'Hot Dog' and 'Pizza' from 1.
$Total\, for\, Popcorn = 1 - 0.45 - 0.38$

STEP 10

Calculate the total for 'Popcorn'.
$Total\, for\, Popcorn = 1 - 0.83$
$Total\, for\, Popcorn = 0.17$

STEP 11

Now we can solve for $c$ .
$0.05 + c + 0.02 = 0.17$

STEP 12

Solve for $c$ .
$c = 0.17 - 0.05 - 0.02$

STEP 13

Calculate the value of $c$ .
$c = 0.17 - 0.07$
$c = 0.10$

STEP 14

To find the value of $d$ , we use the 'Water' row. We now know the value of $c$ , so we can use the sum of the relative frequencies for 'Water'.
$0.23 + 0.20 + 0.10 = d$

STEP 15

Calculate the value of $d$ .
$d = 0.23 + 0.20 + 0.10$
$d = 0.53$

STEP 16

Finally, to find the value of $e$ , we use the 'Total' column for 'Hot Dog'. The sum of the relative frequencies for 'Hot Dog' is 0.45.
$0.17 + 0.23 + e = 0.45$

STEP 17

Now, solve for $e$ .
$e = 0.45 - 0.17 - 0.23$

STEP 18

Calculate the value of $e$ .
$e = 0.45 - 0.40$
$e = 0.05$
The missing values in the relative frequency table are as follows:
$\begin{array}{l} a = 0.14 \\ b = 0.20 \\ c = 0.10 \\ d = 0.53 \\ e = 0.05 \\ \end{array}$

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Find the missing values in the relative frequency table for the concession stand sales data. Solve for variables aaa, bbb, ccc, ddd, and eee to complete the table.

STEP 1

STEP 2

To find the value of aaa, we need to use the total for the 'Soda' row. We know that the sum of the relative frequencies in this row is 0.36.0.17+a+0.05=0.360.17 + a + 0.05 = 0.360.17+a+0.05=0.36

STEP 3

Now, solve for aaa.a=0.36−0.17−0.05a = 0.36 - 0.17 - 0.05a=0.36−0.17−0.05

STEP 4

Calculate the value of aaa.a=0.36−0.22a = 0.36 - 0.22a=0.36−0.22a=0.14a = 0.14a=0.14

STEP 5

To find the value of bbb, we look at the 'Total' column for 'Pizza'. The sum of the relative frequencies for 'Pizza' is 0.38.0.14+b+0.04=0.380.14 + b + 0.04 = 0.380.14+b+0.04=0.38

STEP 6

Now, solve for bbb.b=0.38−0.14−0.04b = 0.38 - 0.14 - 0.04b=0.38−0.14−0.04

STEP 7

Calculate the value of bbb.b=0.38−0.18b = 0.38 - 0.18b=0.38−0.18b=0.20b = 0.20b=0.20

STEP 8

STEP 9

Since we don't have the total for 'Popcorn', we can find it by subtracting the known totals for 'Hot Dog' and 'Pizza' from 1.Total for Popcorn=1−0.45−0.38Total\, for\, Popcorn = 1 - 0.45 - 0.38TotalforPopcorn=1−0.45−0.38

STEP 10

Calculate the total for 'Popcorn'.Total for Popcorn=1−0.83Total\, for\, Popcorn = 1 - 0.83TotalforPopcorn=1−0.83Total for Popcorn=0.17Total\, for\, Popcorn = 0.17TotalforPopcorn=0.17

STEP 11

Now we can solve for ccc.0.05+c+0.02=0.170.05 + c + 0.02 = 0.170.05+c+0.02=0.17

STEP 12

Solve for ccc.c=0.17−0.05−0.02c = 0.17 - 0.05 - 0.02c=0.17−0.05−0.02

STEP 13

Calculate the value of ccc.c=0.17−0.07c = 0.17 - 0.07c=0.17−0.07c=0.10c = 0.10c=0.10

STEP 14

To find the value of ddd, we use the 'Water' row. We now know the value of ccc, so we can use the sum of the relative frequencies for 'Water'.0.23+0.20+0.10=d0.23 + 0.20 + 0.10 = d0.23+0.20+0.10=d

STEP 15

Calculate the value of ddd.d=0.23+0.20+0.10d = 0.23 + 0.20 + 0.10d=0.23+0.20+0.10d=0.53d = 0.53d=0.53

STEP 16

Finally, to find the value of eee, we use the 'Total' column for 'Hot Dog'. The sum of the relative frequencies for 'Hot Dog' is 0.45.0.17+0.23+e=0.450.17 + 0.23 + e = 0.450.17+0.23+e=0.45

STEP 17

Now, solve for eee.e=0.45−0.17−0.23e = 0.45 - 0.17 - 0.23e=0.45−0.17−0.23

STEP 18

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Find the missing values in the relative frequency table for the concession stand sales data. Solve for variables $a$ , $b$ , $c$ , $d$ , and $e$ to complete the table.

To find the value of $a$ , we need to use the total for the 'Soda' row. We know that the sum of the relative frequencies in this row is 0.36.
$0.17 + a + 0.05 = 0.36$

Now, solve for $a$ .
$a = 0.36 - 0.17 - 0.05$

Calculate the value of $a$ .
$a = 0.36 - 0.22$
$a = 0.14$

To find the value of $b$ , we look at the 'Total' column for 'Pizza'. The sum of the relative frequencies for 'Pizza' is 0.38.
$0.14 + b + 0.04 = 0.38$

Now, solve for $b$ .
$b = 0.38 - 0.14 - 0.04$

Calculate the value of $b$ .
$b = 0.38 - 0.18$
$b = 0.20$

Since we don't have the total for 'Popcorn', we can find it by subtracting the known totals for 'Hot Dog' and 'Pizza' from 1.
$Total\, for\, Popcorn = 1 - 0.45 - 0.38$

Calculate the total for 'Popcorn'.
$Total\, for\, Popcorn = 1 - 0.83$
$Total\, for\, Popcorn = 0.17$

Now we can solve for $c$ .
$0.05 + c + 0.02 = 0.17$

Solve for $c$ .
$c = 0.17 - 0.05 - 0.02$

Calculate the value of $c$ .
$c = 0.17 - 0.07$
$c = 0.10$

To find the value of $d$ , we use the 'Water' row. We now know the value of $c$ , so we can use the sum of the relative frequencies for 'Water'.
$0.23 + 0.20 + 0.10 = d$

Calculate the value of $d$ .
$d = 0.23 + 0.20 + 0.10$
$d = 0.53$

Finally, to find the value of $e$ , we use the 'Total' column for 'Hot Dog'. The sum of the relative frequencies for 'Hot Dog' is 0.45.
$0.17 + 0.23 + e = 0.45$

Now, solve for $e$ .
$e = 0.45 - 0.17 - 0.23$