Answer:
3 years old is Joshua.
Step-by-step explanation:
Let y represents the age of Grandpa Collins and x represents the age of grandson Joshua.
As per the given statement: Grandpa Collins is 2 years more than 25 times as his grandson Joshua.
"25 times as his grandson Joshua" means 25x
"2 years more than 25 times as his grandson Joshua" means 25x +2
⇒ y = 25x + 2 ......[1]
Also, it is given : Grandpa Collins is 77 years old
⇒ y = 77 years
Substitute y =77 in [1] to solve for x;
77 = 25x + 2
Subtract 2 from both sides of an equation:
77 -2 =25x+2 -2
Simplify:
75 = 25x
Divide both sides by 25, we get;
Simplify:
3 = x
Therefore, the age of Joshua is, 3 years old.
Answer:
PR = 5 because LP + PR = LR according to the Segment Addition Postulate, and 7 + 5 = 12 using substitution
Step-by-step explanation:
The naming of the segments suggests that point P is between L and R, so that ...
LP + PR = LR
This corresponds to the last choice.
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<em>Comments on the alternate interpretation</em>
On the other hand, if point L is between P and R, then the segments are PL and LR. The Segment Addition Postulate would tell you that ...
PL + LR = PR
The Reflexive Property of Congruence would tell you that PL = LP. The Substitution Property would tell you LP can be substituted into this equation, making it ...
LP + LR = PR
and by the commutative property, ...
LR + LP = PR.
Multiple properties of addition and congruence are involved with this interpretation, which more or less matches the third choice. That is, the simple explanation of answer choice 3, by itself, is insufficient to explain why the length of PR should be considered to be 19, not 5.
#1. look at the individual probability first.
A dice has 6 sides. The numbers > 2 are {3, 4, 5, 6}. So the chance of rolling a number > 2 is 4/6 or 2/3 simplified.
Multiples of 3 on a dice are {3, 6}. So the chance of rolling a multiple of 3 is 2/6 or 1/3 simplified.
Rolling a dice is an independent event, like flipping a coin the previous roll does not have an effect on the outcome of the next roll. So when you see the word AND connecting the outcomes, you multiply them.
Prob of rolling >2 AND then multiple of 3 = (2/3)*(1/3)
= 2/9
#2. The total socks in the drawer: 8+8+4= 20 socks
The probability of first drawing a blue sock is 8/20 or 2/5 simplified.
Since the question does not say the socks are put back in the drawer, the total number of socks and number of blue socks decrease by 1 after the first draw. This makes the next draw dependent on the first.
The probability of drawing a blue sock is then: 7/19
because there's a blue sock missing.
Probability of drawing blue sock AND then a blue sock (without replacement)
= (2/5)*(7/19)
= 14/95
Janine’s error is that she incorrectly counted the spaces that point C has shifted. Focusing on point C like Janine did, to get to point C’ you would need to shift 3 units to the left and 5 units down. This would make the new translation rule (x-3, y-5) to get from triangle ABC to triangle A’B’C’.
