Answer:
71
Step-by-step explanation:
in a triangle all the angles together equal 180°. So all you have to do is add 43 + 66=109 and then subtract that from 180
Answer:
b= 10 miles/hr and c= 5 miles/hr
Step-by-step explanation:
Let it's downstream and upstream speed be d and u respectively
also speed of the boat be b and speed of stream be c.
as per question d = 150/10= 15 miles/hr
and, u= 150/30= 5 miles/hr
also we know d= b+c = 15.....i and u = b-c= 5....ii
solving i and ii we get b= 10 miles/hr and c= 5 miles/hr
Hey there! I'm happy to help!
We have 24 total beads, and we have 6 red ones. This gives us a probability of 6/24, which simplifies to 1/4. However, we do this twice with replacement (we put the bead back, so the probability stays the same), so we multiply that probability twice to find the probability of it happening twice.
1/4×1/4=1/16
Therefore, the probability that both beads are red is 1/16.
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Answer:
(A) put the 7 in front of the log
log 6 (6)^7 = x
7 * log 6 (6) = x
7 * 1 = x
x = 7
Answer:
To get the highest scores, one needs to answer 4 computational problems and 8 graphical problems.
Step-by-step explanation:
Let x be the required number of computational problems one can answer
And y be the number of graphical problems one can answer.
- One cannot answer more than 12 questions in total
x + y ≤ 12
- Computational problems take 2 mins to answer and graphical problems take 4 mins to answer and there is a maximum of 40 mins for the quiz
2x + 4y ≤ 40
- Then finally, there 6 points associated with a computational problem and 10 points associated with a graphical problem and we want to maximize the number of points obtained from the test.
P(x,y) = 6x + 10y
So, the problem looks more like a linear programming problem to maximize
P(x,y) = 6x + 10y
subject to the constraints
x + y ≤ 12
2x + 4y ≤ 40
solving the constraint equations using the maximum values of the inequalities
x + y = 12
2x + 4y = 40
From the first eqn, x = 12 - y
Substituting into the second wan
2(12 - y) + 4y = 40
24 - 2y + 4y = 40
2y = 16
y = 8
x = 12 - y = 12 - 8 = 4
So, the solution of the equation of constraints, or even the graph of both constraint equation is
x = 4, y = 8
These represents the number of computational and graphical problems to maximally satisfy the constraints and maximize the required number of points.
Hope this Helps!!!