Answer:
66
Step-by-step explanation:
Use the formula for the mean of a set of numbers:
sum of the numbers
average = --------------------------------
count of numbers
Here we know that the average mark was 68, so we can write:
75 + 62 + 84 + 53 + x
average = 68 = ----------------------------------
5
or 274 + x
68 = -------------------
5
Solving for x, we multiply both sides by 5: 340 = 274 + x.
Subtracting 274 from both sides effectively isolates x:
340 = 274 + x
- 274 -274
------------------------
66 = x
The fifth student's mark was 66.
Answer:
Step-by-step explanation:
Looking at the given graph, the slope of the line is expressed as
Slope = (y2 - y1)/(x2 - x1)
y2 = 19.5
y1 = 9.5
x2 = 6
x1 = 1
Slope = (19.5 - 9.5)/(6-1)
Slope = 10/5 = 2
The successive terms is increasing by 2
The formula for the nth term of an arithmetic sequence is expressed as
Tn = a + (n - 1)d
Where
a is the first term of the sequence
n is the number of terms in the sequence.
d is the common difference.
From the information given,
a = 9.5
Tn = an
d = 2
The explicit rule for the arithmetic sequence will be
an = 9.5 + 2(n-1)
The waitress earns $425 weekly.
Work:
Use proportions.
x 4
------- = ------
4,200 100
4,200 x 4 = 16800
100 multiply x = 100x
16800 divided by 100 = 168
Commission = $168
Base salary = $257
$168 + $257 = $425
Answer: 27x²yz + 3xz² - 2xy - 2y²z + 2yz²
<u>Step-by-step explanation:</u>
Use the distributive property.
3xz(9xy + z) - 2yz(x + y - z)
= 3xz(9xy) + 3xz(z) -2yz(x) -2yz(y) -2yz(-z)
= 27x²yz + 3xz² -2xy -2y²z +2yz²