For the given system of linear equations to give an infinite number of solutions the value of k should be 2.
<h3>What is a Dependent Consistent System of equations?</h3>
A system of the equation to be a Dependent Consistent System the system must have multiple solutions for which the lines of the equation must be coinciding.
Given the two systems of linear equations,
2x + 3y = 4
(k+ 2)x + 6y = 3k+2
For any system of equations to have infinitely many solutions, the equation of the linear system must be in ratio, so that the lines of the equations overlap each other. Therefore, the ratio for the two of the given equations can be written as,
2/(k+2) = 3/6 = 4/(3k+2)
Solving the ratio to get the value of k,
2/(k+2) = 3/6
2/(k+2) = 1/2
2 × 2 = 1 × (k+2)
4 = k + 2
4 - 2 = k
k = 2
Hence, for the given system of linear equations to give an infinite number of solutions the value of k should be 2.
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Answer:
87.965 in.
Step-by-step explanation:
1) the formula of full arc is L=2π*r, the formula of the required 7π/4 is:
L=7π/4 *r;
2) according to the formula above:
L=7π*16/4=28π≈87,964594300514210676954014731826 (in).
Answer:
95%
Step-by-step explanation:
The Empirical rule, also the 68–95–99.7 rule, states that for a population that is approximately normal or symmetrical, nearly all of the data values will lie within three standard deviations of the mean;
68% of data values will fall within one standard deviation from the mean
95% of data values will fall within two standard deviation from the mean
99.7% of data values will fall within three standard deviation from the mean
From the graph given, we note that the weights 60 and 80 pounds fall within two standard deviations from the mean;
70 ± (2*5) = 70 ± 10 = (60, 80)
70 is the mean, 5 the standard deviation and 2 the number of standard deviations from the mean. From the Empirical rule we can conclude that the probability that a boxer weighs between 60 and 80 pounds is 95%
Answer:
The number y decreased by 12.
Step-by-step explanation:
Let x be the smallest odd number.
x+(x+2)+(x+4)=147
3x+6=147
x=47
therefore the smallest odd no. is 47.
