The table showing the conversion of angle measure in degrees to angles in gradients is attached below.
In order to find the slope we divide the difference of two y-coordinates (or dependent variable which in this case is gradient measure) by the difference of two respective x-coordinates (or independent variable which in this case is degree measure).
For finding the slope we will use the first and the last point given in the table. So, the slope m will be given by:
So rounding of to nearest hundredth, the slope of line representing the conversion of degrees to gradients is 1.11
The easist way to find the vertex is to complete the square:
y=2x^2 +11x-6 => <span>y=2[ x^2 + (11/2)x + (11/2)^2 - (11/2)^2 ] - 6
This can be rewritten as
y = 2[(x+11/2)^2 ] -(121/4) - 24/4
y = 2 (x+11/2)^2 - 145/4
this is the equation in vertex form. The vertex is at (-11/2, -145/4).</span>
Answer:
Step-by-step explanation:
From the given information, we can compute the table showing the summarized statistics of the two alloys A & B:
Alloy A Alloy B
Sample mean

Equal standard deviation

Sample size

Mean of the sampling distribution is :

Standard deviation of sampling distribution:

Hypothesis testing.
Null hypothesis: 
Alternative hypothesis: 
The required probability is:
![P(\overline X_A - \overline X_B>4|\mu_A - \mu_B) = P\Big (\dfrac{(\overline X_A - \overline X_B)-\mu_{X_A-X_B}}{\sigma_{\overline x_A -\overline x_B}} > \dfrac{4 - \mu_{X_A-\overline X_B}}{\sigma _{\overline x_A - \overline X_B}} \Big) \\ \\ = P \Big( z > \dfrac{4-0}{1.2909}\Big) \\ \\ = P(z \ge 3.10)\\ \\ = 1 - P(z < 3.10) \\ \\ \text{Using EXCEL Function:} \\ \\ = 1 - [NORMDIST(3.10)] \\ \\ = 1- 0.999032 \\ \\ 0.000968 \\ \\ \simeq 0.0010](https://tex.z-dn.net/?f=P%28%5Coverline%20X_A%20-%20%5Coverline%20X_B%3E4%7C%5Cmu_A%20-%20%5Cmu_B%29%20%3D%20P%5CBig%20%28%5Cdfrac%7B%28%5Coverline%20X_A%20-%20%5Coverline%20X_B%29-%5Cmu_%7BX_A-X_B%7D%7D%7B%5Csigma_%7B%5Coverline%20x_A%20-%5Coverline%20x_B%7D%7D%20%3E%20%5Cdfrac%7B4%20-%20%5Cmu_%7BX_A-%5Coverline%20X_B%7D%7D%7B%5Csigma%20_%7B%5Coverline%20x_A%20-%20%5Coverline%20X_B%7D%7D%20%20%20%5CBig%29%20%5C%5C%20%5C%5C%20%3D%20P%20%5CBig%28%20z%20%3E%20%5Cdfrac%7B4-0%7D%7B1.2909%7D%5CBig%29%20%5C%5C%20%5C%5C%20%3D%20P%28z%20%5Cge%203.10%29%5C%5C%20%5C%5C%20%3D%201%20-%20P%28z%20%3C%203.10%29%20%5C%5C%20%5C%5C%20%5Ctext%7BUsing%20EXCEL%20Function%3A%7D%20%5C%5C%20%5C%5C%20%20%3D%201%20-%20%5BNORMDIST%283.10%29%5D%20%20%5C%5C%20%5C%5C%20%3D%201-%200.999032%20%5C%5C%20%5C%5C%200.000968%20%5C%5C%20%5C%5C%20%5Csimeq%20%200.0010)
This implies that a minimal chance of probability shows that the difference of 4 is not likely, provided that the two population means are the same.
b)
Since the P-value is very small which is lower than any level of significance.
Then, we reject
and conclude that there is enough evidence to fully support alloy A.
Assuming you want answer 3, which is simply stating to find the area of each rectangle, expressed by the equation A=width x length. Your answers are:
Old carpet: 15 sq ft.
New carpet: 60 sq ft.
Hope this helps!