Does -20 belong in whole numbers
1 answer:
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Answer:
1. The lawyer has 34 investors that contribute with $3,000 and has 26 investors that contribute with $6,000.
2. The jar has 26 nickels and 44 dimes that worth $5.70.
3. The concession stand has sold 1600 sodas and 1400 hotdogs
Step-by-step explanation:
For all the problems we are going to follow the same process that will consist on 1. Define the variables. 2. Formulate the system of two linear equations 3. Solve by the elimination method 4. Give the answer.
- First problem.
- Variables:
x = number of investors that contribute with $3,000
y = number of investors that contribute with $6,000
- System of equations.
First equation will be the result of adding the number of investors that will give us a total of 60 investors then:
x + y = 60
Second equation is the result of multypling the number of investors by its invest and adding between them to get the $258,000 they have raised:
3,000x + 6,000y = 258,000
The system will be:
x + y = 60
3,000x + 6,000y = 258,000
- Solve by the elimination method.
To cancel x we are going to multiply by -3000 in both sides of the first equation and we will leave the second equation the same but in the first row to make easier the calculations then:
3,000x + 6,000y = 258,000
(x + y ) (-3,000) = 60 (-3,000) <em> solve the multiplications </em>
3,000x + 6,000y = 258,000
<u>-3,000x - 3,000y = -180,000 </u><em> solve the operations</em>
0 + 3,000y = 78,000 <em>clear y</em>
<em>solve the division</em>
y = 26
For calculate x, replace the y value in the first equation and solve it
x + 26 = 60
x = 60 - 26
x = 34
- Answer
The lawyer has 34 investors that contribute with $3,000 and has 26 investors that contribute with $6,000.
- Second problem
- Variables:
x = number of nickels
y = number of dimes
- System of equations.
First equation will be the result of adding the number of nickels and dimes that will give us a total of 70 coins in the jar then:
x + y = 70
Second equation is the result of multypling the number of coins by its value and adding between them to get the $5.70 that the jar worth:
0.05x + 0.1 y = 5.70
The system will be:
x + y = 70
0.05x + 0.1 y = 5.70
- Solve by the elimination method.
To cancel x we are going to multiply by -0.05 in both sides of the first equation and we will leave the second equation the same but in the first row to make easier the calculations then:
0.05x + 0.1 y = 5.70
(x + y ) (-0.05) = 70 (-0.05) <em> solve the multiplications </em>
0.05x + 0.1 y = 5.70
<u>-0.05x - 0.05y = -3.50 </u><em> solve the operations</em>
0 + 0.05y = 2.20 <em>clear y</em>
<em>solve the division</em>
y = 44
For calculate x, replace the y value in the first equation and solve it
x + 44 = 70
x = 70 - 44
x = 26
- Answer
The jar has 26 nickels and 44 dimes that worth $5.70.
- Third problem.
- Variables:
x = number of sodas sold by $2
y = number of hotdogs sold by $3
- System of equations.
First equation will be the result of adding the number of sodas and hotdogs that is of 3000 then:
x + y = 3000
Second equation is the result of multypling the number of sodas and hotdogs by its price and adding between them to get the $7400 of the receipts:
2x + 3y = 7400
The system will be:
x + y = 3000
2x + 3y = 7400
- Solve by the elimination method.
To cancel x we are going to multiply by -2 in both sides of the first equation and we will leave the second equation the same but in the first row to make easier the calculations then:
2x + 3y = 7400
(x + y ) (-2) = 3000 (-2) <em> solve the multiplications </em>
2x + 3y = 7400
<u>-2x - 2y = -6000 </u><em> solve the operations</em>
0 + 1y = 1400 <em>clear y</em>
<em>solve the division</em>
y = 1400
For calculate x, replace the y value in the first equation and solve it
x + 1400 = 3000
x = 3000 - 1400
x = 1600
- Answer
The concession stand has sold 1600 sodas and 1400 hotdogs
Answer:
And rounded up we have that n=385
Step-by-step explanation:
Previous concepts
A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".
The margin of error is the range of values below and above the sample statistic in a confidence interval.
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
Solution to the problem
In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 99% of confidence, our significance level would be given by and
. And the critical value would be given by:
The margin of error for the proportion interval is given by this formula:
(a)
And on this case we have that and we are interested in order to find the value of n, if we solve n from equation (a) we got:
(b)
We can use as an estimator for p . And replacing into equation (b) the values from part a we got:
And rounded up we have that n=385