Question:
The admission fee at a carnival is $3.00 for children and $5.00 for adults. On the first day 1,500 people enter the fair and $5740 is collected. How many children and how many adults attended the carnival?
Answer:
Number of children and adults attended the carnival are 880 and 620 respectively
Step-by-step explanation:
Given:
The admission fee at a carnival for children = $3.00
The admission fee at a carnival for adults = $5.00
Number of people entered the fare on first day= 1500
Total amount collected on the first day = $5740
To Find:
Number of children and adults attended the carnival =?
Solution:
Let
The number of children be x
The number of adults be y
The we know that on the first day the total number children visited the fare was 1500
x + y = 1500
x = 1500 - y------------------------------(1)
Also the total fare collected was $5740
x(3) + y(5) = 5740
3x + 5y = 5740-------------------(2)
Substituting (1) in (2),
3 (1500 - y) + 5y = 5740
4500 -3y + 5y = 5740
-3y + 5y = 5740 - 4500
2y = 1240
![y = \frac{1240}{2}](https://tex.z-dn.net/?f=y%20%3D%20%5Cfrac%7B1240%7D%7B2%7D)
y = 620 adults
From 1 ,
x = 1500 - 620
x =880
This is a problem on hypothesis testing on the difference of two dependent means. To solve for this one, the difference for each pair should be solved.
After it, the mean and standard deviation of the differences should also be calculated. Then, we state the null and alternative hypotheses.
The null hypothesis is
![H_{0}: \mu_d=0](https://tex.z-dn.net/?f=H_%7B0%7D%3A%20%5Cmu_d%3D0)
The alternative hypothesis is
![H_a: \mu_d\ \textgreater \ 0](https://tex.z-dn.net/?f=H_a%3A%20%5Cmu_d%5C%20%5Ctextgreater%20%5C%200)
These are the required hypotheses <span>to see whether the number of graffiti incidents declined. </span>
Answer:
£108
Step-by-step explanation:
the rule of the simple interest is:
I=PRT
P=£1800 R=0.02 T=3
I=1800×0.02×3
I=£108
Answer:
x^2 + y^2 + 2xy
Step-by-step explanation:
Use the FOIL method.
Multiply the first terms: x•x=x^2
Multiply the outer terms: x•y=xy
Multiply the inner terms: y•x=xy
(alphabetical order)
Multiply the last terms: y•y=y^2
Combine like terms:
x^2 + y^2 + xy + xy
x^2 + y^2 + 2xy