Answer:
B
Step-by-step explanation:
Givens
a^2 + b^2 = c^2
a = 4x
b = x + 2
c = 3x + 4
Solution
(4x)^2 + (x + 2)^2 = (3x + 4)^3 Remove all the brackets.
16x^2 + x^2 + 4x + 4 = 9x^2 + 24x + 16 Collect like terms on the left
17x^2 + 4x + 4 = 9x^2 + 24x + 16 Subtract the terms on the right
8x^2 - 20x - 12 = 0
This factors into
(4x - 12)(2x + 1)
There are 2 answers
4x - 12 = 0
4x = 12
x = 12/4
x = 3
or
2x + 1 = 0
2x = - 1
x = - 1/2
You have to look at x = -1/2 carefully. The problem is that 4x = 4*(-1/2) = - 2 which is not possible in Euclidean Geometry.
So the only answer is x = 3
The red figure is smaller so it is a reduction.
To find the scale factor divide the length of the smaller shape by the length of the larger shape:
9/15 this can be reduced to 3/5
Other Federalists claimed that the new government could not violate the people's rights because it only had limited powers. However, most state legislatures refused to ratify the Constitution without the Bill of Rights being added to the document.
Answer:
Option A
The p-value is less than the significance level of 0.05 chosen and so we reject the null hypothesis H0 and can conclude that the proportion of the subjects who have the necessary qualities is less than 0.2.
Step-by-step explanation:
Normally, in hypothesis testing, the level of statistical significance is often expressed as the so-called p-value. We use p-values to make conclusions in significance testing. More specifically, we compare the p-value to a significance level "α" to make conclusions about our hypotheses.
If the p-value is lower than the significance level we chose, then we reject the null hypotheses H0 in favor of the alternative hypothesis Ha. However, if the p-value is greater than or equal to the significance level, then we fail to reject the null hypothesis H0
though this doesn't mean we accept H0 automatically.
Now, applying this to our question;
The p-value is 0.023 while the significance level is 0.05.
Thus,p-value is less than the significance level of 0.05 chosen and so we reject the null hypothesis H0 and can conclude that the proportion of the subjects who have the necessary qualities is less than 0.2.
The only option that is correct is option A.
