Answer:
x = 5.75
Step-by-step explanation:
4^(x+7) = 8^(2x-3)
But; 4^(x+7) = 2^2(x+7)
8^(2x-3) = 2^3(2x-3)
2^2(x+7) = 2^3(2x-3)
Since the bases are the same;
2(x+7) = 3(2x-3)
2x + 14 = 6x -9
14 + 9 = 6x - 2x
23 = 4x
x = 23/4
<u>x = 5.75</u>
Supposing a normal distribution, we find that:
The diameter of the smallest tree that is an outlier is of 16.36 inches.
--------------------------------
We suppose that tree diameters are normally distributed with <u>mean 8.8 inches and standard deviation 2.8 inches.</u>
<u />
In a normal distribution with mean
and standard deviation
, the z-score of a measure X is given by:
- The Z-score measures how many standard deviations the measure is from the mean.
- After finding the z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X.<u>
</u>
<u />
In this problem:
- Mean of 8.8 inches, thus
. - Standard deviation of 2.8 inches, thus
.
<u />
The interquartile range(IQR) is the difference between the 75th and the 25th percentile.
<u />
25th percentile:
- X when Z has a p-value of 0.25, so X when Z = -0.675.




75th percentile:
- X when Z has a p-value of 0.75, so X when Z = 0.675.




The IQR is:

What is the diameter, in inches, of the smallest tree that is an outlier?
- The diameter is <u>1.5IQR above the 75th percentile</u>, thus:

The diameter of the smallest tree that is an outlier is of 16.36 inches.
<u />
A similar problem is given at brainly.com/question/15683591
The reflex angle is the other angle
see image below
so
reflex=360-angle
reflex=360-60=300
reflex angle=300
The answer is 7 and 4/ 7+4+11 and 7-4=3!
Answer:
45
Step-by-step explanation:
AEF is a similar triangle to ABC. that means it has the same angles, and the sides (and all other lines in the triangle) are scaled from the ABC length to the AEF length by the same factor f.
now, what is f ?
we know this from the relation of AC to FA.
FA = 12 mm
AC = 12 + 28 = 40 mm
so, going from AC to FA we multiply AC by f so that
AC × f = FA
40 × f = 12
f = 12/40 = 3/10
all other sides, heights, ... if ABC translate to their smaller counterparts in AEF by that multiplication with f (= 3/10).
the area of a triangle is
baseline × height / 2
aABC = 500
and because of the similarity we don't need to calculate the side and height in absolute numbers. we can use the relative sizes by referring to the original dimensions and the scaling factor f.
baseline small = baseline large × f
height small = height large × f
we know that
baseline large × height large / 2 = 500
baseline large × height large = 1000
aAEF = baseline small × height small / 2 =
= baseline large × f × height large × f / 2 =
= baseline large × height large × f² / 2 =
= 1000 × f² / 2 = 500 × f² = 500 ×(3/10)² =
= 500 × 9/100 = 5 × 9 = 45 mm²