There were 81 people sitting in a school auditorium of which
2 answers:
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Answer:
Probability that Adam and Ella will be selected:
Step-by-step explanation:
Probabilities
The probability of a random event E to occur is a real number between 0 and 1, both inclusive, where 0 indicates an impossible event and 1 a sure event. There are many techniques to compute probabilities depending on the particular situation and distribution.
This question will be solved by simple calculations and logic, given its simplicity. We know the middle school chess club has 5 members: Adam, Bradley, Carol, Dave, and Ella. Two of them are going to be selected at random to participate in the county chess tournament. We can calculate the number of different ways it can be done without any restriction. It's called the sample space.
The sample space of this event is the combination of 5 members regardless of their position. If {a,b,c,d,e} are the five members, then the possible combinations are {ab,ac,ad,ae,bc,bd,be,cd,ce,de}. Notice that there are only 10 possibilities because the combination ab is the same as ba since it's the same team for the tournament.
We can see there is only one combination of two specific letters out of 10. If a=Adam and e=Ella, only one combination is ae, the other 9 don't include both members, so the probability is
Work the information to set inequalities that represent each condition or restriction.
2) Name the variables.
c: number of color copies
b: number of black-and-white copies
3) Model each restriction:
i) <span>It takes 3 minutes to print a color copy and 1 minute to print a black-and-white copy.
</span><span>
</span><span>3c + b
</span><span>
</span><span>
</span><span>ii) He needs to print at least 6 copies ⇒ c + b ≥ 6
</span><span>
</span><span>
</span><span>iv) And must have the copies completed in no more than 12 minutes ⇒</span>
3c + b ≤ 12
<span />
4) Additional restrictions are c ≥ 0, and b ≥ 0 (i.e. only positive values for the number of each kind of copies are acceptable)
5) This is how you graph that:
i) 3c + b ≤ 12: draw the line 3c + b = 12 and shade the region up and to the right of the line.
ii) c + b ≥ 6: draw the line c + b = 6 and shade the region down and to the left of the line.
iii) since c ≥ 0 and b ≥ 0, the region is in the first quadrant.
iv) The final region is the intersection of the above mentioned shaded regions.
v) You can see such graph in the attached figure.
2) Name the variables.
c: number of color copies
b: number of black-and-white copies
3) Model each restriction:
i) <span>It takes 3 minutes to print a color copy and 1 minute to print a black-and-white copy.
</span><span>
</span><span>3c + b
</span><span>
</span><span>
</span><span>ii) He needs to print at least 6 copies ⇒ c + b ≥ 6
</span><span>
</span><span>
</span><span>iv) And must have the copies completed in no more than 12 minutes ⇒</span>
3c + b ≤ 12
<span />
4) Additional restrictions are c ≥ 0, and b ≥ 0 (i.e. only positive values for the number of each kind of copies are acceptable)
5) This is how you graph that:
i) 3c + b ≤ 12: draw the line 3c + b = 12 and shade the region up and to the right of the line.
ii) c + b ≥ 6: draw the line c + b = 6 and shade the region down and to the left of the line.
iii) since c ≥ 0 and b ≥ 0, the region is in the first quadrant.
iv) The final region is the intersection of the above mentioned shaded regions.
v) You can see such graph in the attached figure.
Answer:
option: b is correct.
( b.Yes, because both figures are rectangles and all rectangles are similar )
Step-by-step explanation:
Yes, the rectangle EFGH is a result of dilation of rectangle ABCD with a center of dilation at the origin.
Also The scale factor of the dilation is greater than one as the image is bigger than the pre-image i.e. there is a stretch.
The scale factor could be calculated by the ratuio of the sides of the image to the pre-image rectangle.
Rectangle ABCD: Its vertices have coordinates A(-3,3), B(3,3), C(3,0) and D(-3,0).
Now consider rectangle EFGH: Its vertices have coordinates E(-4,4), F(4,4), G(4,0) and H(-4,0).
Hence the scale factor is:
Hence the scale factor is: 4/3.
Also
∠A=∠B=∠C=∠D=∠E=∠F=∠G=∠H=90°
( When a shape is dilated the two shapes are similar.And similar shapes have equal interior angles , corresponding sides are proportional ).
Hence option: b is correct.
( b.Yes, because both figures are rectangles and all rectangles are similar )