Step-by-step explanation:
km²
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A function assigns the values. The correct option is C, x=-6.
<h3>What is a Function?</h3>
A function assigns the value of each element of one set to the other specific element of another set.
A.) When the value of x is -12,
f(-12) = 2/3(-12) + 7 = -1
g(-12) = 2(-12) + 15 = -9
B.) When the value of x is -9,
f(-9) = 2/3(-9) + 7 = 1
g(-9) = 2(-9) + 15 = -3
C.) When the value of x is -6,
f(-6) = 2/3(-6) + 7 = 3
g(-6) = 2(-6) + 15 = 3
D.) When the value of x is -3,
f(-9) = 2/3(-3) + 7 = 5
g(-9) = 2(-2) + 15 = 11
Hence, the correct option is C, x=-6.
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Answer:
a) 48.408
b) 1.235
Step-by-step explanation:
a)
The average hardness value xbar can be computed as
xbar=sum of values/number of values
xbar=(46.5+46.9+49.4+50.3+49.8+48.8+47+47.7+48.3+49.4+47.8+49)/12
xbar=580.9/12
xbar=48.408 (rounded to 3 decimal places).
The average hardness value is 48.408.
b)
The standard deviation hardness value s can be computed as

x x-xbar (x-xbar)
²
46.5 -1.90833 3.64174
46.9 -1.50833 2.27507
49.4 0.99167 0.98340
50.3 1.89167 3.57840
49.8 1.39167 1.93674
48.8 0.39167 0.15340
47.0 -1.40833 1.98340
47.7 -0.70833 0.50174
48.3 -0.10833 0.01174
49.4 0.99167 0.98340
47.8 -0.60833 0.37007
49.0 0.59167 0.35007
Total 16.7692




s=1.235 (rounded to 3 decimal places)
The standard deviation hardness value is 1.235.
Answer:
114 units²
Step-by-step explanation:
The opposite sides of a parallelogram are congruent, so
AB = CD , that is
13x - 7 = 5x + 9 ( subtract 5x from both sides )
8x - 7 = 9 ( add 7 to both sides )
8x = 16 ( divide both sides by 8 )
x = 2
Then
5x + 9 = 5(2) + 9 = 10 + 9 = 19
3x = 3(2) = 6
The area (A) of a parallelogram is calculated as
A = bh ( b is the base and h the perpendicular height ), thus
A = 19 × 6 = 114 units²