25% because 21 is a quarter of 84. And 21 times 4= 84, so 21 is 25% of 84.
Answer:
58
Step-by-step explanation:
As there are 12 teams in the league and each teams plays every other team twice per season. so, the total number of matches in the league will be 132.
let the matches won by home team = 'x'
given,
number of matches drawn = 34
matches won by the away team = x - 18
Now, according to the question,
⇒ total matches = matches drawn + matches won by home team + matches won by away team
⇒ 132 = 34 + x + x -18
⇒ x = 58
x = # of balcony seats
y = # of orchestra seats
We have to create a system of equations to solve this problem
x + y = 256
$8x + $12y = $2,716
We will solve this system of equations by elimination.
Multiply the first equation by -8
-8x - 8y = -2048
8x + 12y = 2716
Let's add the equations together
0 + 4y = 668
Simplify the left side
4y = 668
Divide both sides by 4
y = 167
We can subtract 167 from 257 to get the number of balcony seats.
257 - 167 = 90 balcony seats
There are 167 orchestra seats and 90 balcony seats
Answer:
Step-by-step explanation
Hello!
Be X: SAT scores of students attending college.
The population mean is μ= 1150 and the standard deviation σ= 150
The teacher takes a sample of 25 students of his class, the resulting sample mean is 1200.
If the professor wants to test if the average SAT score is, as reported, 1150, the statistic hypotheses are:
H₀: μ = 1150
H₁: μ ≠ 1150
α: 0.05
![Z= \frac{X[bar]-Mu}{\frac{Sigma}{\sqrt{n} } } ~~N(0;1)](https://tex.z-dn.net/?f=Z%3D%20%5Cfrac%7BX%5Bbar%5D-Mu%7D%7B%5Cfrac%7BSigma%7D%7B%5Csqrt%7Bn%7D%20%7D%20%7D%20~~N%280%3B1%29)

The p-value for this test is 0.0949
Since the p-value is greater than the level of significance, the decision is to reject the null hypothesis. Then using a significance level of 5%, there is enough evidence to reject the null hypothesis, then the average SAT score of the college students is not 1150.
I hope it helps!