Answer:
Step-by-step explanation:
a) H0: 
Ha: 
(Two tailed test at 5% significance level)
b) n=30
Mean difference = 
Std error of mean = 
b) Test statistic t = mean diff/std error = -1.552
df = 30-1 =29
p value=0.0657
c) Since p > 0.05 our signi. level, we accept null hypothesis.
There is no significant difference between the means.
d) Using critical value we find that test statistic is > critical value left
So accept H0
Answer:
x=37°
y=6
Step-by-step explanation:
(ASSUMING BD is a perpendicular bisector of AC, otherwise answers maybe be wrong)
Consider the triangle ABC:
AB is the same length as BC (marked), meaning ABC is an isosceles triangle.
Since ABC is isosceles, ∠BAC=∠BCA=53
All angles in a triangle add up to 180:
180=∠ABC + ∠BAC + ∠BCA
180= ∠ABC + 53 +53
∠ABC = 180 - 106
∠ABC = 74
Assuming BD bisects ∠ABC perfectly, x is half of ∠ABC.
x=74/2=37
If BD bisects AC perfectly, AD=DC=y=6
Answer:
They used 6 vans and 3 buses
Step-by-step explanation:
x + y= 9
13x + 40y= 198
x= 9 - y
13(9 - y) + 40y= 198
117 - 13y + 40y= 198
27y= 81
y= 3
9-3= 6
Answer:
80
Step-by-step explanation:
10- w = 90
w = 90 -10
w = 80
Answer:
tons of high steel and
tons of low steel
Step-by-step explanation:
Let x be the number of tons of high grade steel and y be the number of tons ow low grade steel needed.
In x tons of high grade steel there are
tons of iron
tons of magnese
In y tons of low grade steel there are
tons of iron
tons of magnese
NASA orders 500 tons of steel, so

and specifies that it must be in the proportion 80% iron and 20% magnese, so

From the first equation,

Substitute it into the second equation:
