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Answer:
1) The determinant = 65
2) The determinant = 152
Step-by-step explanation:
Let us show how to find the determinant of a matrix
You can find the determinant of this Matrix
by using this rule
Determinant = a(en - fm) - b(dn - fg) + c(dm - eg)
Let us use this rule with the given matrices
1)
The determinand = 1[(5)(2) - (0)(1)] - (-1)[(2)(2) - (0)(-3)] + 3[(2)(1) - 5(-3)]
= 1[10 - 0] - (-1)[4 - 0] + 3[2 - (-15)]
= 1[10] + 1[4] + 3[2+15]
= 10 + 4 + 3[17]
= 10 + 4 + 51
= 65
The determinant = 65
Let us do the second one
2)
The determinand = -1[(1)(2) - (0)(1)] - (-8)[(9)(2) - (0)(4)] + 2[(9)(1) - 1(4)]
= -1[2 - 0] - (-8)[18 - 0] + 2[9 - 4]
= -1[2] + 8[18] + 2[5]
= -2 + 144 + 10
= 152
The determinant = 152
Answer:
The values of k are 2/3 and -1
Step-by-step explanation:
Product of zeros = αβ= constant / coefficient of x^2 = 4/k
Sum of zeros =α+β = - coefficient of x / coefficient of x^2= -4/k
Given
Consider a= α and b= β
can be written as
if we add
in the above equation.
Putting values of αβ and α+β
The values of k are 2/3 and -1
Answer:
Step-by-step explanation:
Hello!
You have the math and writing SAT scores of twelve students.
There are two variables of interest X₁: Math SAT score of a student. and X₂: Writing the SAT score of a student.
These two variables aren't independent since both of them represent data corresponding to the same student, meaning, that the math and writing scores belong to the same students and not to two separate groups of students.
This is an example of paired samples, to make the statistical test you have to establish a third variable, this variable will be the difference between the other two:
Xd= X₁-X₂
Xd: "Difference between the Math and Writing SAT scores of a student.
This variable has a normal distribution Xd~N(μd;σd²)
a. Using a .05 level of significance and test for a difference between the population mean for the math scores and the population mean for the writing scores? Enter negative values as negative numbers. Round your answer to two decimal places.
The parameter of interest is μd is the population mean of the difference between the math and writing SAT scores of the students.
The hypotheses are:
H₀: μd=0
H₁: μd≠0
α: 0.05
The test statistic is a t-student for dependent samples and it's rejection region is two-tailed.
What is the p-value? Round your answer to four decimal places.
The p-value for this test is: 0.0394
The p-value is less than the level of significance, the decision is to reject the null hypothesis.
b. What is the point estimate of the difference between the mean scores for the two tests?
The sample mean for the variable "difference" is X[bar]d
You can calculate the point estimate of the sample mean of the variable Xd using two ways.
1) You calculate all the differences between the pairs of scores, add them and divide them by the sample size
X[bar]d= ∑di/n
∑di= 300
n=12
X[bar]d= 300/12= 25
2) You can calculate the sample mean for each variable and then calculate the difference between the two sample means
X[bar]₁= ∑X₁/n
∑X₁= 6168
X[bar]₁= 6168/12= 514
X[bar]₂= ∑X₂/n
∑X₂= 5868
X[bar]₂= 5868/12= 489
X[bar]d= X[bar]₁-X[bar]₂ = 514 - 489= 25
What are the estimates of the population mean scores for the two tests?
Math test X[bar]₁= 514
Writing test X[bar]₂= 489
Which test reports the higher mean score?
The Math test reports a higher mean score.
I hope it helps!
