The attached graph illustrates the region. The centroid's coordinates are (5/3, 1). The centroid's coordinates are determined by averaging the coordinates of the area; Oₓ = (Aₓ+Bₓ+Cₓ)/3 = (0+1+4)/3 = 5/3 and O(y) = (A(y) + B(y) + C(y)) = (0+3+0)/3=3/3=1.
A)
4(q - 10) = 76..... Tim earned 4 points for each correct answer, totaling 76 points. He got 10 answers right less than the total number of questions on the test.
b)
q = 10 + 76/4
q = 29
Thus, the overall number of questions on Tim's math test amounted to 29.
Part a) When a page is scaled down to 80%, how much enlargement is necessary to bring it back to its original size?
Let
x---------> the percent enlargement
Given the original size is 100%
This means:
x*80%=100%
x=(100%/80%)
x=1.25--------> 1.25=(125/100)=125%
Thus,
The answer to Part a) is
The percent enlargement required is 125%
Part b) Estimate how many successive copies of a page are needed to make the final copy less than 15% of its original size.
Since the photocopy machine reduces sizes to 80% of the original
Therefore:
Copy N 1
0.80*100%=80%
Copy N 2
0.80*80%=64%
Copy N 3
0.80*64%=51.2%
Copy N 4
0.80*51.2%=40.96%
Copy N 5
0.80*40.96%=32.77%
Copy N 6
0.80*32.77%=26.21%
Copy N 7
0.80*26.21%=20.97%
Copy N 8
0.80*20.97%=16.78%
Copy N 9
0.80*16.78%=13.42%-------------> 13.42% < 15%
Therefore,
The answer to Part b) is
The necessary number of copies to achieve this is 9
Answer:
The photographer sold 72 small photos and 54 large photos.
Step-by-step explanation:
We can create a system of equations based on the details provided. Let X represent small photos and Z represent large photos.
It is given that the total number of photos sold is 126:
X + Z = 126
Additionally, she generated $2,250 from selling specific amounts of small and large photos, stated as:
$2,250 = $11X + $27Z
From the first equation, we know X=126-Z. Substituting this into the second equation gives:
2,250 = 11(126-Z) + 27Z
2,250 = 1,386 - 11Z + 27Z
2,250 - 1,386 = 16Z
864 = 16Z
Z = 864/16
Z = 54, which indicates the number of large photos sold. To find X:
X = 126 - Z
X = 126 - 54
X = 72, representing the small photos sold.
Lacking information on the proportion, we will assume the sample proportion is 0.50
thus,
p = 0.50
The margin of error is set at 10 percentage points. This indicates that the error on either side of the population proportion is 5%, so E = 0.05
z = 1.645 (Z value for a confidence level of 90%)
The calculation for the margin of error when estimating population proportions follows:
Consequently, 271 students need to be part of the sample.
