Felipe planted some seeds for a science project. One of his plants grew 6 2/7 inches in the first week, and then it grew 5 11/14
1 answer:
Answer:
<em>The plant grew </em><em> inches</em>
Step-by-step explanation:
<u>Operations with Fractions</u>
Felipe planted seeds for a science project. One of the plants grew 6 2/7 inches in the first week and 5 11/14 inches in the second week.
We are required to find the total growth during the two weeks. We have to find the sum of:
Let's convert both fractions to improper form:
Adding the integers:
Now we find the LCM of 7 and 14 is 14, thus:
Rewriting as a mixed number:
The plant grew inches
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Answer:
the P matrix you are looking for is P=(1/) · [[1 1 0 0],[1 -1 0 0],[0 0 1 1],[0 0 1 -1]]
Step-by-step explanation:
Answer:
For an orthogonal diagonalization of any matrix you have to:
1º) Find the matrix eigenvalues in a set order.
2º) Find the eigenvectors of each respective eigenvalues.
Tip: You can write the matrix A like A = D P
3º) D is the diagonal matrix with each eigenvalue (in order) in the diagonal.
4º) Write P as the normalized eigenvectors in order (in columns).
Tip 2: Remember, ·P = I, so if A =
D P, then:
P A = P
D P
= I D I = D
So the P we are looking for is the of the diagonalization.
Tip 3: In this case, A is a block matrix with null nondiagonal submatrixes, therefore its eigenvalues can be calculated by using the diagonal submatrixes. The problem is reduced to calculate the eigenvalues of A₁₁ = A ₂₂ = [[5 3],[3 5]]
Solving:
1º)the eigenvalues of A₁₁ are {8,2}, therefore the D matrix is
2º) the eigenvectors of A₁₁ are P₈= {[1 1]T} P₂= {[1 -1]T}, therefore normalizing the eigenvectors you obtain P = (1/) · [[1 1 0 0],[1 -1 0 0],[0 0 1 1],[0 0 1 -1]] (you can see that P =
in this case).
As said in "tip 2": P A = P
D P
= I D I = D
So the P obtained is the one you are looking for.
Answer:
The probability that all three have type B+ blood is 0.001728
Step-by-step explanation:
For each person, there are only two possible outcomes. Either they have type B+ blood, or they do not. The probability of a person having type B+ blood is independent of any other person. So we use the binomial probability distribution to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
In which is the number of different combinations of x objects from a set of n elements, given by the following formula.
And p is the probability of X happening.
The probability that a person in the United States has type B+ blood is 12%.
This means that
Three unrelated people in the United States are selected at random.
This means that
Find the probability that all three have type B+ blood.
This is P(X = 3).
The probability that all three have type B+ blood is 0.001728