how many pounds of chamomile tea that costs 18.20 per pound must be mixed with 12lb of orange tea that costs 12.25 per pound to make a mixture that costs 14.63 per pound


Answer 1

8 pounds of chamomile tea must be mixed to make a mixture that costs 14.63 per pound.              

Step-by-step explanation:

We are given the following in the question:

Chamomile tea:

Unit cost = 18.20 per pound

Amount = x pounds

Total cost =

18.20* x = 18.20x

Orange tea:

Unit cost = 12.25 per pound

Amount = 12 pounds

Total cost =

12.25* 12 = 147

Total mixture:

Unit cost = 14.63 per pound

Amount = (12+x) pounds

Total cost =

14.63* (12+x) = 175.56 + 14.63x

We can write the equation that cost of mixture is equal to cost of chamomile tea and orange tea.

18.20x + 147 = 175.56 + 14.63x\n\Rightarrow 18.20x- 14.63x = 175.56-147\n\Rightarrow 3.57x = 28.56\n\Rightarrow x = 8

Thus, 8 pounds of chamomile tea must be mixed to make a mixture that costs 14.63 per pound.

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If I had 60 units needed and units per case was 14 how many cases and additional units I got


The additional number of units required is 10 units.

Given that:

Total number of units needed = 60 units

Total number of units per case = 14

How to find the total number of cases required for the given question?

So, the total number of cases required=Number of units needed / number of units per case.

Number of cases required = 60/14 = 4.285 (this means that 5 cases are required as 4 cases won't be up to 60 units)

With 5 cases, we have exceeded the required units needed :

Additional units will be : (14×5) - 60

Additional units = 70 - 60 = 10 units

Therefore, the additional number of units required is 10 units.

To learn more about the unitary method visit:



4 with a remainder of 4

Step-by-step explanation:

60 divided by 14 is 4 with a remainder of 4

Morgan is 23 years old. Her grandfather is 4 times as old. How old is her grandfather?



92 years old

Step-by-step explanation:

Multiply 23 by 4


So Morgan's grandfather is 92 years old

Hope this helps :)

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Step-by-step explanation:


My soccer team has 16 players. I have to choose a starting lineup of a goalie and 10 regular players (the regular players are interchangeable). How many different starting lineups can i choose? *the answer is not 4368*




Step-by-step explanation:

We want to find out how many ways we can choose 10 players among 15 players (since the goalie is not interchangeable)

The number of different lineups you can have can be found by using combination:

^(15)C_(10) = (15!)/((15 - 10)! 10!)\n \n= (15!)/(5! * 10!) \n\n= 3003

There are 3003 different lineups that can be chosen.

Final answer:

To determine the number of starting lineups, we use combinations in probability. We first choose a goalie from 16 players, then 10 regular players from the remaining 15, giving us 48048 unique lineups.


This problem can be solved by using the concept of combinations in probability and statistics. The formula for combinations is C(n, k) = n! / [k!(n-k)!], where n is the total number of items, k is the number of items to choose, and ! denotes factorial, which is the product of all positive integers up to that number.

Firstly, we need to choose a goalie. There are 16 players, so the number of ways to choose a goalie is C(16, 1) = 16.

After choosing the goalie, we are left with 15 players. Then we need to choose 10 players to fill in the rest of the team. Thus, the number of ways to choose the 10 regular players is C(15, 10).

The total number of unique starting lineups is then the product of these two results. Hence, the solution would be C(16, 1) * C(15, 10) = 16 * 3003 = 48048 different starting lineups.

Learn more about Combinations here:


11 coommon factor of​


1? Isn’t it like a prime number

C= 7/6 (k-17)

Solve for k. ​



The brainliest!

Step-by-step explanation:

c= 7/6k- 17(7/6)

6/7c = k - 17

k = 6/7c+17

Suppose that X is a random variable with probability function x 0 1 2 3 4 5 P(x) 0.00032 0.0064 0.0512 0.2048 0.4096 0.32768 and that the random variable Y = 9X2 − 36X + 4. (a) What is the range of Y ? (b) Calculate P{Y = 4}. (c) Calculate P{Y = 0}.


(a) For each value of X we have:

X=0\quad\Rightarrow\quad Y=4\n\nX=1\quad\Rightarrow\quad Y=-23\n\nX=2\quad\Rightarrow\quad Y=-32\n\nX=3\quad\Rightarrow\quad Y=-23\n\nX=4\quad\Rightarrow\quad Y=4\n\nX=5\quad\Rightarrow\quad Y=49

so the range of Y = {-32, -23, 4, 49}




Y cannot equal 0, so