Answer:
See below.
Step-by-step explanation:
a.
The first figure has 1 square. The second figure has a column of 2 squares added to the left. The third figure has a column of 3 squares added to the left. Each new figure has a column of squares added to the left containing the same number of squares as the number of the figure.
b.
Figure 10 has 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 = 55 squares.
c.
The formula for adding n positive integers starting at 1 is:
1 + 2 + 3 + ... + n = n(n + 1)/2
For figure 55, n = 55.
n(n + 1)/2 = 55(56)/2 = 1540
d.
Let's use the formula set equal to 190 and solve for n. If n is an integer, then we can.
n(n + 1)/2 = 190
n(n + 1) = 380
We know that 380 = 19 * 20, so n = 19.
Answer: yes
e.
Use the formula above,
S = n(n + 1)/2, where S is the sum.
f.
n(n + 1) = 1478
38 * 39 = 1482
37 * 38 = 1406
Anthony's OT pay will be $118.875 and his overall pay will be $752.875.
Number of hours Anthony has to work in a week = 5 × 8 = 40 hours.
He worked for = 47.50 hours.
Overtime = 47.50 hours - 40 hours = 7.50 hours
Pay per hour = $15.85 / hour
Overtime pay (OT pay) = $15.85 × 7.50 = $118.875
Overall pay = $15.85 × 47.50 = $752.875
Therefore, Anthony's OT pay is $118.875 and his overall pay is $752.875.
Learn more about overtime pay here -
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Given that 4000 items are checked in one month, let the number of detective items be represented as y.
Quality control finds on average that 0.026% of the items in the factory are detective. This implies that
When 4000 items are checked, we have the number of detective items to be evaluated as
Hence, the number of detective items is 1.04.
Olate the variable by dividing each side by factors that don't contain the variable.
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