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igomit [66]
2 years ago
11

A certain company sells tea in loose leaf and bagged form, and in five flavors: Darjeeling, earl grey, chamomile, peppermint, an

d orange pekoe. The company packages the tea in boxes that contain either 8 ounces of tea of the same flavor and the same form, or 8 ounces of tea of 4 different flavors and the same form. If the order in which the flavors are packed does not matter, how many different types of packages are possible
Mathematics
1 answer:
ANTONII [103]2 years ago
7 0

Answer:

- 20

Step-by-step explanation:

Given that,

Flavors of tea = 5

Types of packaging = 2

So,

No. of possibilities = 5 * 2

= 10

A.T.Q.,

4 from 5 total flavors will be included in the variety pack, the number of available choices = 5C4

= 5 choices

Since 5 choices are probable for each form, The total in two forms would be 5 * 2 = 10.

Therefore,

Total no. of different packs can be possible = 10 + 10

= 20

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Find the value of x such that 365 based seven + 43 based x = 217 based 10.
Pepsi [2]

We need to find the base x in the following equation:

365_7+43_x=217_{10}

First, lets convert 365 from base 7 to base 10. This is given by

365_7=3\times7^2+6\times7^1+5\times7^0

where the upperindex denotes the position of eah number. This gives

\begin{gathered} 365_7=3\times49+6\times7+5\times1 \\ 365_7=147+42+5 \\ 365_7=194_{10} \end{gathered}

that is, 365 based 7 is equal to 194 bases 10.

Now, lets do the same for 43 based x. Lets convert 43 based x to base 10:

43_x=4\times x^1+3\times x^0

where again, the superindex 0 and 1 denote the position 0 and 1 in the number 43. This gives

43_x=(4x+3)_{10}

Now, we have all number in base 10. Then, our first equation can be written in base 10 as

194_{10}+(4x+3)_{10}=217_{10}

For simplicity, we can omit the 10 and get

194+4x+3=217

so, we can solve this equation for x. By combining similar terms. we have

197+4x=217

and by moving 197 to the right hand side, we obtain

\begin{gathered} 4x=217-197 \\ 4x=20 \end{gathered}

Finally, we get

\begin{gathered} x=\frac{20}{4} \\ x=5 \end{gathered}

Therefore, the solution is x=5

8 0
10 months ago
I need help with all of these I don’t get it
pochemuha
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sleet_krkn [62]
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____ [38]

Answer:

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