Answer:
and then we have:
Step-by-step explanation:
From the info given by the problem we need an integer defined as the smallest positive integer that is a multiple of 75 and have 75 positive integral divisors, and we are assuming that 1 is one possible divisor.
Th first step is find the prime factorization for the number 75 and we see that
And we know that 3 =2+1 and 5=3+2 and if we replace we got:
And in order to find 75 integral divisors we need to satisify this condition:
such that 
For this case we have two prime factors important 3 and 5. And if we want to minimize n we can use a prime factor like 2. The least common denominator between 2 and 4 is LCM(2,4) =4. So then the need to have the prime factors 2 and 3 elevated at 4 in order to satisfy the condition required, and since 5 is the highest value we need to put the same exponent.
And then the value for n would be given by:
and then we have:
Answer:
Step-by-step explanation:
The sum of two irrational numbers is always still irrational.
5√3 + 6√5 is still going to be irrational. You cannot find two such numbers adding to rational.
Answer:
Step-by-step explanation:
We are given that
Sophomores=13
Juniors=12
Seniors=8
Male sophomores=5
Female sophomores=6
Male seniors=4
We have to find the probability of randomly selecting a junior or a senior.
Total persons=13+12+8=33
Let A=Seniors
B=Juniors
Probability,P(E)=
Using the formula of probability
Hence, the probability of selecting a junior or senior=
7(p)
p=3
7(3)
the answer is 21.
Answer:
one point
Step-by-step explanation:
A system of two linear equations will have one point in the solution set if the slopes of the lines are different.
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When the equations are written in the same form, the ratio of x-coefficient to y-coefficient is related to the slope. It will be different if there is one solution.
- ratio for first equation: 1/1 = 1
- ratio for second equation: 1/-1 = -1
These lines have <em>different slopes</em>, so there is one solution to the system of equations.
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<em>Additional comment</em>
When the equations are in slope-intercept form with the y-coefficient equal to 1, the x-coefficient is the slope.
y = mx +b . . . . . slope = m
When the equations are in standard form (as in this problem), the ratio of x- to y-coefficient is the opposite of the slope.
ax +by = c . . . . . slope = -a/b
As long as the equations are in the same form, the slopes can be compared by comparing the ratios of coefficients.
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If the slopes are the same, the lines may be either parallel (empty solution set) or coincident (infinite solution set). When the equations are in the same form with reduced coefficients, the lines will be coincident if they are the same equation.
