△RST is dilated with the rule DT,1/3 (x, y), where the center of dilation is T(3, –2).
2 answers:
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System 1: The solution is (x, y) = (-4, 5)
System 2: The solution is
<em><u>Solution:</u></em>
<em><u>Given system of equations are:</u></em>
2x + 3y = 7 ------ eqn 1
-3x - 5y = -13 --------- eqn 2
We can solve by elimination method
Multiply eqn 1 by 3
6x + 9y = 21 ------ eqn 3
Multiply eqn 2 by 2
-6x - 10y = -26 ------- eqn 4
Add eqn 3 and eqn 4
6x + 9y -6x - 10y = 21 - 26
-y = -5
y = 5
Substitute y = 5 in eqn 1
2x + 3(5) = 7
2x + 15 = 7
2x = -8
x = -4
Thus the solution is (x, y) = (-4, 5)
<h3><em><u>Second system of equation is:</u></em></h3>8 - y = 3x ------ eqn 1
2y + 3x = 5 ----- eqn 2
We can solve by susbtitution method
From given,
y = 8 - 3x ----- eqn 3
Substitute eqn 3 in eqn 2
2(8 - 3x) + 3x = 5
16 - 6x + 3x = 5
3x = 16 - 5
3x = 11
Substitute the above value of x in eqn 3
y = 8 - 3x
Thus the solution is
Answer:
Probability that none of the 20 children in such a classroom would be unvaccinated is 0.055.
Step-by-step explanation:
We are given that a classroom of 20 children in one such area where 13.5% of children are unvaccinated.
If there are no siblings in the classroom, we are willing to consider the vaccination status of the 2020 unrelated children to be independent.
The above situation can be represented through binomial distribution;
where, n = number of trials (samples) taken = 20 children
r = number of success = none of the 20 children
p = probability of success which in our case is probability that
children are unvaccinated, i.e; p = 13.5%
<u><em>Let X = Number of children that are unvaccinated</em></u>
So, X ~ Binom(n = 20, p = 0.135)
Now, Probability that none of the 20 children in such a classroom would be unvaccinated is given by = P(X = 0)
P(X = 0) =
=
= 0.055
<em>Hence, the probability that none of the 20 children in such a classroom would be unvaccinated is 0.055.</em>
Answer:
Total number of dogs is 5.
Step-by-step explanation:
Cups of food each dog gets=
Here,each dog eats two-third cups of dog food.
Amount of dog food used=
A total of three and one-third cups of food is used up.
Let the number of dogs be x.
To find the number of dogs,divide total dog food used by the amount of dog food eaten by each dog.
Hence, x =
x =
x =5