Answer:
M∠DEC equals 123º.
Step-by-step explanation:
The sum of a triangle's three angles always equal 180º. The exterior angle, x, equals the two non-adjacent interior angles.
180 - {(x - 45)+(x - 12)} = m∠DEC
m∠DEC + x = 180
<u>(x - 45) + (x - 12) = x</u>
Solving for x:
(x - 45) + (x - 12) = x
x - 45 + x - 12 = x Remove parenthesis
2x - 57 = x Combine like terms
2x = x + 57 Add 57 to both sides
<u>x = 57</u><u> Subtract x from both sides</u>
Finding m∠D:
x - 45 = ?
<u>57 - 45 = </u><u>12º </u>
Finding m∠C:
x - 12 = ?
<u>57 - 12 = </u><u>45º </u>
<em>** </em><em>(Checking x: 12 + 45 = 57) </em><em>**</em>
<em>Finding </em>m∠DEC:
AC is a straight line, and because straight lines are equivalent to 180º, we subtract 57 from 180:
180 - 57 = 123º
Hope this helps,
❤<em>A.W.E.</em><u><em>S.W.A.N.</em></u>❤
Answer:
0.1
Step-by-step explanation:
Take paranthesis away.
5.6-3.2-2.3
subtract 3.2 from 5.6
2.4-2.3=0.1
Hope it helps1
Answer:
76
Step-by-step explanation:
4^2 x 5^2 - 18^2
PEMDAS is our acronym for order of operations: Parentheses, exponents, multiplication, division, addition, subtraction.
Since we have no parentheses, we'll calculate the numbers and exponents (PEMDAS) first. "to the power of 2" is also called "squared" and means multiplying that number by itself.
(4x4) x (5x5) - (18x 18)
=16 x 25 - 324
Now we multiply: (PEMDAS)
= 400 - 324
then subtract: (PEMDAS)
=76
Answer:
Step-by-step explanation:
Given that a statistics teacher taught a large introductory statistics class, with 500 students having enrolled over many years.
Mean = 78 and std dev =10
Next time, sample size n was reduced to 25
For smaller sample size the mean was found to be = 83
The teacher wanted to know if teaching a smaller class was more effective and students performed better
ie comparison of two means of two samples should be done with different sample sizes but same teacher.
Hence hypothesis should be:

where x denotes the I sample and Y the second with 25 students.
Answer:
y = 40 x = 80
Step-by-step explanation:
520 = 3.25x + 6.5y x+y=120
x+y=120
x = 120-y
520 = 3.25(120-y)+6.5y
520 = 390-3.25y+6.5y
520 = 390+3.25y
130=3.25y
Divide each side by 3.25
40 = y
x = 120-y
x = 120-(40)
x = 80