Answer:
10
Step-by-step explanation:
Answer:
(10, 5)
Step-by-step explanation:
Total money to spend = $60
Cost of each plate = $3
Cost of each candlestick = $6
Let number of plates bought = ![x](https://tex.z-dn.net/?f=x)
Let number of candlesticks bought = ![y](https://tex.z-dn.net/?f=y)
Total number of items to be bought = 15
Therefore, the first equation can be written as:
..... (1)
Total money spent on plates = Number of plates bought
Cost of each plate = $3![x](https://tex.z-dn.net/?f=x)
Total money spent on candlesticks = Number of candlesticks bought
Cost of each candlestick = $6![y](https://tex.z-dn.net/?f=y)
Second equation can be written as:
![3x+6y = 60](https://tex.z-dn.net/?f=3x%2B6y%20%3D%2060)
Dividing both sides with 3:
..... (2)
Subtracting (1) from (2):
![y = 5](https://tex.z-dn.net/?f=y%20%3D%205)
From equation (1) :
![x = 15-5\\\Rightarrow x = 10](https://tex.z-dn.net/?f=x%20%3D%2015-5%5C%5C%5CRightarrow%20x%20%3D%2010)
Number of plates bought = 10
Number of candlesticks bought = 5
Answer as ordered pair is: <em>(10, 5)</em>
-c^2(3c - 2) =
-3c^3 + 2c^2 <==
Answer:
31.35%
Step-by-step explanation:
<h3><u>Initial</u><u> </u><u>reading</u><u>:</u></h3>
In the box, there are:
- 6 Black pens
- 4 blue pens
- 7 red pens
Total number of pens in the box = 6 + 4 + 7
<u>= 17</u>
<em>If we count pens as outcomes the total number of possible outcomes are 17</em>.
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<h3><u>New</u><u> </u><u>reading</u><u>:</u></h3>
Clarissa takes out a black pen from the box.
That reduces the number of black pens by 1 which increases the total number of pens by 1 as well.
So now:
- Number of black pens = 6 - 1 =<u> 5 </u>
- Total number of pens = 17 - 1 =<u> </u><u>16</u><u> </u>
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
<h3><u>Probability</u><u>:</u></h3>
![\boxed{ \mathsf{probability = \frac{favorable \: outcomes}{total \: outcomes} }}](https://tex.z-dn.net/?f=%20%5Cboxed%7B%20%5Cmathsf%7Bprobability%20%3D%20%20%5Cfrac%7Bfavorable%20%5C%3A%20outcomes%7D%7Btotal%20%5C%3A%20outcomes%7D%20%7D%7D)
If we want her to pick up a black pen, and she ends up picking one. So, we can say that the outcome is in our favor.
That makes it,
- the number of favorable outcomes = number of black pens
= 5
- and total outcomes = Total number of pens
= 16
![\implies\mathsf{probability = \frac{5}{16} }](https://tex.z-dn.net/?f=%20%20%5Cimplies%5Cmathsf%7Bprobability%20%3D%20%20%5Cfrac%7B5%7D%7B16%7D%20%7D)
For showing it as some percent we'll just multiply the fraction by 100
![\implies \mathsf{ \frac{5}{16} \times 100 }](https://tex.z-dn.net/?f=%20%5Cimplies%20%5Cmathsf%7B%20%5Cfrac%7B5%7D%7B16%7D%20%5Ctimes%20100%20%7D)
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<h3><u>As</u><u> </u><u>a</u><u> </u><u>percent</u><u>:</u></h3>
![\implies \mathsf{ \underline{ 31.25 \: \% } }](https://tex.z-dn.net/?f=%20%5Cimplies%20%5Cmathsf%7B%20%5Cunderline%7B%2031.25%20%5C%3A%20%5C%25%20%7D%20%7D)