Scale Factor (K) = (new length/measure)/ (original length/measure)
for x-coordinate = 8/2 = 4
for y-coordinate = 16/4 = 4
K=4, expansion
K is the representation of "scale factor". Scale factor is the ratio of the lengths involved of the similar figures. It can be used to identify the kind of dilation, whether it is contraction or expansion. If the Scale Factor is greater than 1, then that means expansion and if it is less than 1, then it signifies contraction.
Answer:
The other side was decreased to approximately .89 times its original size, meaning it was reduced by approximately 11%
Step-by-step explanation:
We can start with the basic equation for the area of a rectangle:
l × w = a
And now express the changes described above as an equation, using "p" as the amount that the width is changed:
(l × 1.1) × (w × p) = a × .98
Now let's rearrange both of those equations to solve for a / l. Starting with the first and easiest:
w = a/l
now the second one:
1.1l × wp = 0.98a
wp = 0.98a / 1.1l
1.1 wp / 0.98 = a/l
Now with both of those equalling a/l, we can equate them:
1.1 wp / 0.98 = w
We can then divide both sides by w, eliminating it
1.1wp / 0.98w = w/w
1.1p / 0.98 = 1
And solve for p
1.1p = 0.98
p = 0.98 / 1.1
p ≈ 0.89
So the width is scaled by approximately 89%
We can double check that too. Let's multiply that by the scaled length and see if we get the two percent decrease:
.89 × 1.1 = 0.979
That should be 0.98, and we're close enough. That difference of 1/1000 is due to rounding the 0.98 / 1.1 to .89. The actual result of that fraction is 0.89090909... if we multiply that by 1.1, we get exactly .98.
Answer:
Part A: The null hypothesis failed to be rejected.
Part B: The null hypothesis failed to be rejected.
Step-by-step explanation:
We have an hypothesis test with null and alternative hypothesis H0: p = 0.5 versus Ha: p > 0.5, which has the test statistic z=1.15.
Part A: If the significance level is 0.05, the conclusion depends on the P-value.
If the P-value is below 5%, the null hypothesis is rejected.
The P-value for this right-tailed tes and z=1.15 is:
The P-value is bigger than the significance level, so the effect is not significant and the null hypothesis is failed to be rejected.
Part B: In this case, the significance level is 0.01 and, as the alternative hypothesis is defined with an unequal sign, the test is two-tailed.
This changes the way we calculate the P-value, as we need to compute the two tails.
The P-value is:
The P-value is bigger than the significance level, so the effect is not significant and the null hypothesis is failed to be rejected.
6*5=30
8*2=16
30+16=46
The test was worth 46 total points
Answer:
0.07894. . .
Step-by-step explanation:
