Answer:
Two possible lengths for the legs A and B are:
B = 1cm
A = 14.97cm
Or:
B = 9cm
A = 12cm
Step-by-step explanation:
For a triangle rectangle, Pythagorean's theorem says that the sum of the squares of the cathetus is equal to the hypotenuse squared.
Then if the two legs of the triangle are A and B, and the hypotenuse is H, we have:
A^2 + B^2 = H^2
If we know that H = 15cm, then:
A^2 + B^2 = (15cm)^2
Now, let's isolate one of the legs:
A = √( (15cm)^2 - B^2)
Now we can just input different values of B there, and then solve the value for the other leg.
Then if we have:
B = 1cm
A = √( (15cm)^2 - (1cm)^2) = 14.97
Then we could have:
B = 1cm
A = 14.97cm
Now let's try with another value of B:
if B = 9cm, then:
A = √( (15cm)^2 - (9cm)^2) = 12 cm
Then we could have:
B = 9cm
A = 12cm
So we just found two possible lengths for the two legs of the triangle.
We keep the 2x^2 because we can only subtract something from that if it also is squared. From there, we subtract the 7x from 2x^2-11. Since there is no previous x's in the 2x^2-11, we just make it -7x. So, without even continuing the problem, we see that A) is the correct answer because it is the only one with -7x.
The confidence interval formula is computed by:
Xbar ± Z s/ sqrt (n)
Where:
Xbar is the mean
Z is the z value
S is the standard deviation
N is the number of samples
So our given are:
90% confidence interval with a z value of 1.645
Sample size 40, 45
Mean 180, 179
Standard deviation 2, 4
So plugging that information in the data will give us a
confidence interval:
For 1:
Xbar ± Z s/ sqrt (n)
= 180 ± 1.645 (2 / sqrt (40))
= 180 ± 1.645 (0.316227766)
= 180 ± 0.520194675
= 179.48, 180.52
For 2:
Xbar ± Z s/ sqrt (n)
= 179 ± 1.645 (4 / sqrt (45))
<span>= 179 ± 1.645 (0.596284794)</span>
therefore, the answer is letter b
Answer:
Option 2
Step-by-step explanation:
(12) - 2 = 10
(11) - 2 = 9
0 x 4 = 0
1 x 4 = 4
