Answer:
9 cm²
Step-by-step explanation:
Two wires are attached 6 feet up a tree and 3 feet from the base of the tree. About how much TOTAL wire was used?
We solve the above question, using the Area of a Triangle
Area = 1/2 × Base × Height
Area = 1/2 × 3 × 6
Area = 9 cm²
Therefore, the total wore that was used was 9cm² of wire
Step-by-step explanation:
Given - In selecting a sulfur concrete for roadway construction in regions that experience heavy frost, it is important that the chosen concrete has a low value of thermal conductivity in order to minimize subsequent damage due to changing temperatures. Suppose two types of concrete, a graded aggregate and a no-fines aggregate, are being considered for a certain road. The table below summarizes data on thermal conductivity from an experiment carried out to compare the two types of concrete.
Type ni xi si
Graded 42 0.486 0.187
No-fines 42 0.359 0.158
To find - a. Formulate the above in terms of a hypothesis testing problem.
b. Give the test statistic and its reference distribution (under the null hypothesis).
c. Report the p-value of the test statistic and use it to assess the evidence that this sample provides on the scientific question of difference in mean conductivity of the two materials at the 5% level of significance.
Proof -
a.)
Hypothesis testing problem :
H0 : There is significant difference between mean conductivity for the graded concrete and mean conductivity for the no fines concrete.
H1 : There is no significant difference between mean conductivity for the graded concrete and mean conductivity for the no fines concrete.
b)
Test statistic :




⇒Z(cal) = 3.3687
Z(tab) = 1.96
As Z (cal) > Z(tab)
So, we reject H0 at 5% Level of significance
p-value = 0.99962
Hence
There is significant difference in mean conductivity at the two materials.
Answer:
the answer is no
Step-by-step explanation:
It only shows that one pair of lines are parallel but not both are. Parallelograms have two pairs of parallel lines.
Answer:
The 90% confidence interval for population mean is 
Step-by-step explanation:
From the question we are told that
The sample mean is 
The confidence level is 
The sample size is 
The standard deviation
Now given that the confidence level is 0.90 the level of significance is mathematically evaluated as


Next we obtain the critical value of
from the standardized normal distribution table. The values is 
The reason we are obtaining critical values for
instead of that of
is because
represents the area under the normal curve where the confidence level 1 -
(90%) did not cover which include both the left and right tail while
is just considering the area of one tail which is what we required calculate the margin of error
Generally the margin of error is mathematically evaluated as

substituting values


The 90% confidence level interval is mathematically represented as

substituting values



Answer:
x= 9
y=-12.5
Step-by-step explanation:
3x+2y = 2×2
2x+2y =-7×3
6x+4y =4
- 6×+6y =-21
-2y =25
y=-12,5
2x+2(-12,5)= -7
2x+-25= -7
2x= -7+25
2x/2=18/2
x= 9