Answer:
16 dimes
Step-by-step explanation:
He already has 7, and got 9 more, so we can add 7 and 9
7+9 =16
So, Dan has 16 dimes now
Hope this helps! :)
Answer:
Step-by-step explanation:
In this problem, we have the following linear equations:
y=3x+5
y=ax+b
We know that a linear equation is an equation for a line. In a system of linear equations, two or more equations work together.
1. What values for a and b make the system inconsistent?
A system is inconsistent if and only if the lines are parallel in which case the system has no solution. This is illustrated in the first Figure bellow. Two lines are parallel if they share the same slope. So, the system is inconsistent for:
a=3
for any value of b
2. What values for a and b make the system consistent and dependent?
A system is consistent if and only if the lines are the same in which case the system has infinitely many solutions. This is illustrated in the second Figure bellow. So, the system is consistent and dependent for:
a=3 and b=5
Answer:
(A) Set A is linearly independent and spans . Set is a basis for .
Step-by-Step Explanation
<u>Definition (Linear Independence)</u>
A set of vectors is said to be linearly independent if at least one of the vectors can be written as a linear combination of the others. The identity matrix is linearly independent.
<u>Definition (Span of a Set of Vectors)</u>
The Span of a set of vectors is the set of all linear combinations of the vectors.
<u>Definition (A Basis of a Subspace).</u>
A subset B of a vector space V is called a basis if: (1)B is linearly independent, and; (2) B is a spanning set of V.
Given the set of vectors , we are to decide which of the given statements is true:
In Matrix , the circled numbers are the pivots. There are 3 pivots in this case. By the theorem that The Row Rank=Column Rank of a Matrix, the column rank of A is 3. Thus there are 3 linearly independent columns of A and one linearly dependent column. has a dimension of 3, thus any 3 linearly independent vectors will span it. We conclude thus that the columns of A spans .
Therefore Set A is linearly independent and spans . Thus it is basis for .
Answer:
B
Step-by-step explanation:
Here, we are to give the reason why we would reject the null hypothesis during the hypothesis testing.
In considering whether to accept the null hypothesis or reject the null hypothesis, we have to take into consideration two things.
The p-value and the alpha value. The p-value refers to the probability which is directly obtainable from the standard score which is referred to as the z-score while the alpha refers to the level of significance.
Now, when the p-value is less than alpha, we simply reject the null hypothesis and accept the alternative hypothesis. In a case however, we have the value of p greater than or equal to the significance level alpha, we simply accept the null hypothesis in this case.
The question asks for a rejection case and this can happen only when the p-value is less than the level of significance alpha
<h2>189 boys is 54%</h2><h2>x is 46%(100-54)</h2><h2>Cross multiply:</h2><h2>189*46%=54%*x</h2><h2>86.94=0.54x</h2><h2>x=161</h2><h2>189 boys 161 girls</h2><h2>350 altogether</h2><h2>Hope this helps plz hit the crown :D</h2>