Calculate the probability of each pen color by dividing the number of times each color was chosen by the total selections:
Red pens: 6 out of 30, which simplifies to 1/5
Blue pens: 10 out of 30, which simplifies to 1/3
Black pens: 14 out of 30, which simplifies to 7/15
To find the likelihood of first selecting a blue pen and then a red pen, multiply their individual probabilities:
(1/3) × (1/5) = 1/15
The resulting probability is 1/15.
There is clear favoritism present. However, it is crucial to examine not just how many women were promoted in comparison to men but also the rate of promotion within each group. In the case of men, 21 out of 24 received promotions, indicating a substantial rate of 87.5%. In contrast, for women, only 14 out of 24 were promoted, which is 58.3%, just over half. Therefore, we can conclude that there is a distinct bias favoring male employees.
The diagrams for parts A and C are included here. For part B, we have circle O. We begin by drawing two radii OA and OC, connecting points A and C to create chord AC. The radius intersects chord AC at point B, bisecting AC into equal segments AB and BC. This gives us two triangles, ΔOBA and ΔOBC, where OA equals OC (since they're radii), OB equals OB (by the reflexive property), and AB is equal to BC (as stated in the question). By applying the SSS triangle congruence criterion, we conclude that ΔOBA is congruent to ΔOBC, allowing us to deduce that ∡OBA equals ∡OBC, both measuring 90°. Thus, OB is perpendicular to AC. Moving on to part D, we again work with circle O and draw the two radii OA and OC, joining points A and C to create chord AC. The radius intersects AC at point B, where AB is perpendicular to AC, meaning ∡B equals 90°. We then consider the right triangles ΔOBA and ΔOBC, and given OA equals OC (the radii), and OB equals OB (reflexive property), we conclude through the HL triangle congruence that ΔOBA is congruent to ΔOBC. Consequently, we find BA equal to BC, thus OB bisects AC.
77%
I prefer using ratios and cross multiplication for scenarios like this. Divide the part (1001) by the whole (1300), and set that equal to x percent of 100 percent.
1001/1300 = x/100
100100 = 1300x
x = 77
