Linear Algebra
Solve systems of equations using row reduction method
PLEASE do all part a-g Thank you!

x₁ +4x₂+2x₂=0
Given 2x₁ +5x₂+x3=0 (1)
3x1+6x2=0
(a) Write system (1) into augmented matrix_form
(b) Without using a calculator, reduce the augmented matrix to reduced row echelon form (rref). ▲ write out all elementary row operations in sequence order ▲
(c) Identify all basic variables and free variables.
(d) Find the general solutions of system (1). What is the role of free variable ?
(e) Write the solution of system (1) as parametric vector form.
(f) True or False? "This system of equations has unique solution (2, -1, 1)." why yes or why no.
(g) With the aid of a graphic calculator, solve system (1). Specify the calculator model, show formulas setup and answers.

Answer:

length= 5+ 12= 17

Step-by-step explanation:

will take width as x

then the length is x+12

perimeter = x+ x+12+x+x+12= 44

=4x= 44-24= 36

x= 20/4

x= 5

Answer:

2.34

Step-by-step explanation:

9.36÷4 =2.34

you divide on 4as showen

A. The probability that one selected subcomponent is longer than 122 cm can be found by calculating the area under the normal distribution curve to the right of 122 cm. We can use the z-score formula to standardize the value and then look up the corresponding probability in the standard normal distribution table.

z = (122 - μ) / σ = (122 - 100) / 5.6 = 3.93 (approx.)

Looking up the corresponding probability for a z-score of 3.93 in the standard normal distribution table, we find that it is approximately 0.9999. Therefore, the probability that one selected subcomponent is longer than 122 cm is approximately 0.9999 or 99.99%.

B. To find the probability that the mean length of three randomly selected subcomponents exceeds 122 cm, we need to consider the distribution of the sample mean. Since the sample size is 3 and the subcomponent lengths are normally distributed, the distribution of the sample mean will also be normal.

The mean of the sample mean will still be the same as the population mean, which is 100 cm. However, the standard deviation of the sample mean (also known as the standard error) will be the population standard deviation divided by the square root of the sample size.

Standard error = σ / √n = 5.6 / √3 ≈ 3.24 cm

Now we can calculate the z-score for a mean length of 122 cm:

z = (122 - μ) / standard error = (122 - 100) / 3.24 ≈ 6.79 (approx.)

Again, looking up the corresponding probability for a z-score of 6.79 in the standard normal distribution table, we find that it is extremely close to 1. Therefore, the probability that the mean length of three randomly selected subcomponents exceeds 122 cm is very close to 1 or 100%.

C. If we want to find the probability that all three randomly selected subcomponents have lengths exceeding 122 cm, we can use the probability from Part A and raise it to the power of the sample size since we need all three subcomponents to satisfy the condition.

Probability = (0.9999)^3 ≈ 0.9997

Therefore, the probability that if three subcomponents are randomly selected, all three of them have lengths that exceed 122 cm is approximately 0.9997 or 99.97%.

Based on the given information about the normal distribution of subcomponent lengths, we calculated the probabilities for different scenarios. We found that the probability of selecting a subcomponent longer than 122 cm is very high at 99.99%. Similarly, the probability of the mean length of three subcomponents exceeding 122 cm is also very high at 100%. Finally, the probability that all three randomly selected subcomponents have lengths exceeding 122 cm is approximately 99.97%. These probabilities provide insights into the performance of the automatic machine in terms of producing longer subcomponents.

To know more about probability follow the link:

https://brainly.com/question/251701

#SPJ11

The average score of all students, calculated by taking a weighted average based on the number of students in each group, is 38. The overall performance is slightly below the group averages.

The average score of students in the first, second, and third groups are 39, 32, and 43, respectively. There are 24 students in the first group, 26 students in the second group, and 27 students in the third group.

To find the average score of all students, we need to take a weighted average of the scores in each group, with the number of students in each group as the weights.

Here's how to do it: First, we calculate the total number of students:24 + 26 + 27 = 77. Then, we calculate the total score across all students: 39*24 + 32*26 + 43*27 = 936 + 832 + 1161 = 2929

Finally, we divide the total score by the total number of students to get the average score:2929/77 = 38. The average score of all students is 38.

This means that the overall performance of all the students is slightly below the average of the scores in each group.

For more questions on average score

https://brainly.com/question/13832161

#SPJ8

Answer:

A. 5 PM

Step-by-step explanation:

5 PM if they woke up at 7 AM as teens under 16 cannot work more than 9 hours

Answer:

the answer is C - 9:00 pm I guess

Given that profits decrease by 13.8% when the degree of operating leverage (DOL) is 3.8.

The decrease in sales is: We have to determine the percentage decrease in sales Let the percentage decrease in sales be x.

Degree of Operating Leverage (DOL) = % change in Profit / % change in Sales3.8

= -13.8% / x Thus, we have: x

= -13.8% / 3.8

= -3.63%Therefore, the decrease in sales is 3.63%.Hence, the correct option is C) 3.63%. Percentage decrease in sales = % change in profit / degree of operating leverage

= 13.8 / 3.8

= 3.63% The percentage decrease in sales is 3.63%.

To know more about profits, visit:

https://brainly.com/question/29987711

#SPJ11

Answer:

\(y = mx + c \\ - 3 = - 2( - 6) + c \\ c = - 15 \\ y = - 6x - 15\)

Answer:

x = 20

Step-by-step explanation:

x° + 2x° + (x + 10)° = 90° ( complementary angles)

(4x + 10) ° = 90°

4x + 10 = 90

4x = 90 - 10

4x = 80

x = 80/4

x = 20

Answer:

20°

Step-by-step explanation:

#thanks me late,thankyou

Answer:

300

Step-by-step explanation:

25% of 240 is 60.

Answer: The first three odd prime numbers are 3, 5, and 7. A number is a multiple of two but not three of these prime numbers if it is divisible by two of them, but not the third.

To find the number of numbers between 1000 and 2000 that are multiples of two but not three of the first three odd prime numbers, we can count the number of multiples of each pair of prime numbers and subtract the number of multiples of all three prime numbers.

There are 200 multiples of 3 and 5 between 1000 and 2000 (200 numbers for each, for a total of 200 * 2 = 400). There are 133 multiples of 3 and 7 between 1000 and 2000 (133 numbers for each, for a total of 133 * 2 = 266). There are 80 multiples of 5 and 7 between 1000 and 2000 (80 numbers for each, for a total of 80 * 2 = 160). There are no multiples of all three prime numbers between 1000 and 2000.

Thus, the total number of numbers between 1000 and 2000 that are multiples of two but not three of the first three odd prime numbers is 400 + 266 + 160 = 826.

Step-by-step explanation:

Let the number of pants bought be p and the number of shirts bought be s

• Each pant costs $8.99 and ,p, pants would cost

• Each shirt costs $3.99 and ,s, shirts would cost

The total budget is at max $60, so we can write the inequality:

-------------->>>>>>>>>>>>> First, let's find the s-intercept by putting p = 0:

Rounding to a whole number,

-------------->>>>>>>>>>>>> Then, let's find the p-intercept by putting s = 0:

Answer: 1. 35 5/6 - 4 1/2

2. 1 5/8 - 2/3

3. 1 5/8 + 2/3

4. 35 5/6+4 1/2

Step-by-step explanation:

1. E=Eli. J=Jamison

E=J+4 1/2

35 5/6=J+4 1/2

J=35 5/6 - 4 1/2

2. s=cups of strawberries

b=cups of blueberries

m=more cups of b than s

m=b-s

m=1 5/8 - 2/3

3. o=original length of patio.

i=increase in length of patio

t=total length of patio after increase.

o+i=t

1 5/8 + 2/3=t

4. p=pine tree. a=palm tree. i=inches taller

p+i=a

35 5/6+4 1/2=a

Answer:

10.8 kilometers

Step-by-step explanation:

Perimeter of a triangle equation is P (perimeter)= a+b+c

put 32.4 of the left side of the equation as it is the answer for the perimeter and replace and and b with your first 2 side legnths like this

32.4= 10.8+ 10.8+c

Now we must solve for the unknown side legnth c. To do this we must simplify the right side of the equation first by adding 10.8+ 10.8

32.4= 21.6+c

Now we can subtract 21.6 from the left side to solve for c

10.8=c

Therefore the third side is 10.8 kilometers

Answer: 10.8 km

Step-by-step explanation:  A triangle has three sides:  a, b, and c

The perimeter is a+b+c and is a total of 32.4 km.   We know a=10.8 km and b = 10.8 km.

10.8 km + 10.8 km + c = 32.4 km

21.6km + c =  32.4 km

c = 10.8 km

picture one x=8 and y=4

picture two x=-18 and y=-10

picture three x=7 and y=8

give me 5 stars so i will get a crown

Answer:

5

Cinco es en quince 3 veces igualmentes, 1 vez es uno sobre tres de  15.

Answer:

36

Step-by-step explanation:

A dentist bought 9 bags of prizes for his patients.

Each of the bags has 12 prizes

The first step is to calculate the total number of prizes

= 9 × 12

= 108 prizes

Since the prizes will be shared equally in 3 boxes then the number of prizes in each box can be calculated as follows

= 108/3

= 36

Hence the number of prizes in each of the 3 boxes is 36

The number of terms increase and we will compare it with another series whose sum we know that whether it is finite or infinite. Let us first simplify the expression:√j / (j + 3)

= (√j / (j + 3)) * (√j / √j)

= j / (j√j + 3√j)

= j / (√j(j + 3))∑(-1)j is an alternating series that is decreasing for all positive integer j, so the alternating series test can be used to show that it converges.

Also, √j / (j + 3) > 0 for all j > 0, so the absolute value of the terms of the series is equal to the terms themselves. We can then use the comparison test with the series 1 / √j to show that the series converges. The given series is,Σ(-1) j √j / (j + 3)j = 1 To check convergence or divergence of the given series,

√j / (j + 3) = (√j / (j + 3)) * (√j / √j)

= j / (j√j + 3√j)

= j / (√j(j + 3))

Now, using the Alternating Series Test, the absolute value of the terms of the series is √j / (j + 3) > 0 for all j > 0, so the absolute value of the terms of the series is equal to the terms themselves. We can then use the comparison test with the series 1 / √j to show that the series converges. Therefore, the series is convergent.

To know more about expression visit:

https://brainly.com/question/30721594

#SPJ11

Probability: P(education beyond high school but not a bachelor's degree) = (number of young adults with education beyond high school but not a bachelor's degree) / (total number of young adults).

The probability that a randomly chosen young adult has some education beyond high school but not a bachelor's degree would be:

P(education beyond high school but not a bachelor's degree) = (number of young adults with education beyond high school but not a bachelor's degree) / (total number of young adults)

where "number of young adults with education beyond high school but not a bachelor's degree" refers to the count of individuals in the population who meet this criteria, and "total number of young adults" refers to the count of all individuals in the population who are considered young adults.

The formula calculates the probability of a certain event by dividing the number of favorable outcomes by the total number of possible outcomes. In this case, the event is a randomly chosen young adult having some education beyond high school but not a bachelor's degree. The numerator, "number of young adults with education beyond high school but not a bachelor's degree," represents the favorable outcomes, while the denominator, "total number of young adults," represents all possible outcomes.

By dividing the favorable outcomes by the total number of possible outcomes, we get the probability of the event occurring, which is a value between 0 and 1. The closer the value is to 1, the higher the probability that the event will occur. The closer the value is to 0, the lower the probability that the event will occur. This formula allows us to quantify the likelihood of an event occurring in a population based on the available data.

Learn more about probability here:

https://brainly.com/question/14289833

#SPJ4

Answer:

24

Step-by-step explanation:

dont exaclty have an explanations - its just the calculations

To determine if the bolts vary by more than the required variance, we can conduct a hypothesis test. The null hypothesis (H₀) states that the variance of the bolts is equal to or less than the required variance (σ² ≤ 0.025), while the alternative hypothesis (H₁) states that the variance is greater than the required variance (σ² > 0.025).

Next, we need to determine the critical value(s) of the test statistic. Since we are testing for variance, we will use the chi-square distribution. For a one-tailed test with α = 0.01 and 14 degrees of freedom (n-1), the critical value is 27.488.

Now, we can compare the test statistic to the critical value. The test statistic is calculated as (n-1) * s² / σ², where n is the sample size (15), s² is the sample variance (0.1587²), and σ² is the required variance (0.025).

If the test statistic is greater than the critical value, we reject the null hypothesis and conclude that the bolts vary by more than the required variance. Otherwise, we fail to reject the null hypothesis.

To learn more about Hypothesis test - brainly.com/question/29996729

#SPJ11

To determine if the bolts vary by more than the required variance, we can conduct a hypothesis test. The null hypothesis (H₀) states that the variance of the bolts is equal to or less than the required variance (σ² ≤ 0.025), while the alternative hypothesis (H₁) states that the variance is greater than the required variance (σ² > 0.025).

Next, we need to determine the critical value(s) of the test statistic. Since we are testing for variance, we will use the chi-square distribution. For a one-tailed test with α = 0.01 and 14 degrees of freedom (n-1), the critical value is 27.488.

Now, we can compare the test statistic to the critical value. The test statistic is calculated as (n-1) * s² / σ², where n is the sample size (15), s² is the sample variance (0.1587²), and σ² is the required variance (0.025).

If the test statistic is greater than the critical value, we reject the null hypothesis and conclude that the bolts vary by more than the required variance. Otherwise, we fail to reject the null hypothesis.

To learn more about Hypothesis test - brainly.com/question/29996729

#SPJ11

The correct option is option (b) . The statement that mean of the sampling distribution is same as the population parameters is not true .

Sampling Distribution:

A statistical sampling distribution is a type of probability distribution constructed by drawing a large number of random samples of a specified size from the same population. These distributions are useful for understanding how sample statistics vary from sample to sample. Mean of sampling distribution:

The distribution of the values of the sample mean (x- bar) in replicate samples is called the x -bar sampling distribution.

Central Limit Theorem :

For populations with finite mean μ and finite nonzero variance σₓ, the sampling distribution of the mean approaches a normal distribution with mean μ and variance σₓ/N, and for large N (sample size) become.

distribution is depends on sample size

Hence, the correct option is option (c) which gives the false or not true statement about mean of sampling distribution.

To learn more about sampling distribution of mean refer:

https://brainly.com/question/26952915

#SPJ4

Step-by-step explanation:

What type of line the picture represent

Answer:

30/13

Step-by-step explanation:

15/13x2

15/13x2/1

30/13

22 minutes is spent doing aerobics and 38 minutes doing stretching

Let x represent the amount of time spent doing aerobics, Let y represent the amount of time spent doing stretching.

Since the goal is to do a 60-minute workout, hence:

x + y = 60     (1)

Also, 416 calories needs to be burnt hence:

12x + 4y = 416    (2)

We need to solve equation 1 and 2 simultaneously; multiply equation 1 by 4 and subtract the result from equation 2, hence:

8x = 176

x = 22 minutes

Put x = 22 in (1)

22 + y = 60

y = 38 minutes

Therefore 22 minutes is spent doing aerobics and 38 minutes doing stretching.

Find out more at: https://brainly.com/question/16763389

Answer:

a

Step-by-step explanation:

Answer:

$450

Step-by-step explanation:

You want to calculate the interest on $3000 at 3% interest per year after 5 year(s).

The formula we'll use for this is the simple interest formula, or:

Where:

P is the principal amount, $3000.00.

r is the interest rate, 3% per year, or in decimal form, 3/100=0.03.

t is the time involved, 5....year(s) time periods.

So, t is 5....year time periods.

To find the simple interest, we multiply 3000 × 0.03 × 5 to get that:

The interest is: $450.00

Usually now, the interest is added onto the principal to figure some new amount after 5 year(s),

or 3000.00 + 450.00 = 3450.00.

The correct statement about step 3 include the following: C. When the equation -3x − 5y = -5 is subtracted from -10x + 5y = -60, a third linear equation, -13x = -65, is formed, and it has a different solution from the original equations.

In order to determine the solution to a system of two linear equations, we would have to evaluate and eliminate each of the variables one after the other, especially by selecting a pair of linear equations at each step and then applying the elimination method.

Given the following system of linear equations:

2x - y = 12                .........equation 1.

-3x - 5y = -5               .........equation 2.

By multiplying the equation 1 by -5, we have:

-5(2x - y = 12) = -10x + 5y = -60

By adding the two equations together, we have:

-3x - 5y = -5

-10x + 5y = -60

-------------------------

-13x = -65

Read more on elimination method here: brainly.com/question/28405823

#SPJ1