Algebra 1
1.1 Evaluating Expressions
Evaluate each using the values given.
1) z−5+ x; use x = 1, and z = -3

The real eigenvalues of the given matrix, once it has been diagonalized, are presented to its right as D = (7 0 0, 0 11 0, 0 0 11).

Learn about the dimensions and components of matrices by starting your first introduction. A rectangular grid of numbers organized into rows and columns is known as a matrix. Matrix A, as an illustration, has two rows and three columns. matrix, a collection of numbers lined up in rows and columns to create a rectangular array.  In addition to many other areas of mathematics, matrices have extensive applications in the fields of engineering, physics, economics, and statistics. It is so named because there is just one row, and a row matrix has the order 1 n as a result.

given

Eigen values ( λ )

| A - λI | = 0

=  ( 7 - λ ) ( 11 - λ ) ( 11 - λ ) =0

= λ = 7 , 11 , 11

eigen vector for λ = 7

( A - IB ) X = 0

= Let y = 1 , n1 = ( -1  1  0 )

eigen vector for λ = 11

( A - λI ) X = 0

n2 = ( 0 1 0 ) let n3= ( -2 0 1 )

D = ( 7 0 0 ,  0 11 0 , 0 0 11 )

The real eigenvalues of the given matrix, once it has been diagonalized, are presented to its right as D = (7 0 0, 0 11 0, 0 0 11).

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Answer:d

Step-by-step explanation:

Answer: i agree with the other guy ↑

Answer:

less than a mile is the answer

Answer:

35

Step-by-step explanation:

\(\frac{5}{6}\) m -5 < \(\frac{1}{2}\) m + 3  Subtract 1/2 from both sides.  Use the equivalent fraction 3/6

\(\frac{5}{6}\) m - \(\frac{3}{6}\) m -5 < \(\frac{3}{6}\) m - \(\frac{3}{6}\)m + 3

\(\frac{1}{3}\) m - 5 < 3   ( \(\frac{2}{6}\) ÷ \(\frac{2}{2}\) makes the equivalent fraction \(\frac{1}{3}\))  Add 5 to both sides

\(\frac{1}{3}\) m -5 + 5 < 3 -+ 5

\(\frac{1}{3}\) m < 8  Multiple both sides by3

\((\frac{3}{1})\) \(\frac{1}{3}\) m < (3)(8)       Another name for 3 is \(\frac{3}{1}\)

m < 24  The only number in the set that is greater than 24 is 35

Answer:

c. √7

Step-by-step explanation:

:)

Answer: c

Step-by-step explanation: I’m sm0rt :0

Answer:

C

Step-by-step explanation:

A. B . C

The more consistent the results given by repeated measurements, the higher the precision of the measurement procedure.

Precision refers to the degree of agreement or reproducibility among multiple measurements of the same quantity. When repeated measurements yield similar results with little variation, it indicates a high precision. This suggests that the measurement procedure has a low level of random error or uncertainty.

Precise measurements are valuable because they provide reliable and consistent information about the quantity being measured, allowing for more accurate comparisons, analyses, and conclusions. Precision is an important characteristic of any measurement procedure to ensure the reliability and validity of the obtained data.

Therefore, the more consistent the results given by repeated measurements, the higher the precision of the measurement procedure.

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The statistic used to determine the percentage variation in height is the coefficient of variation (CV).

In statistics, the coefficient of variation (CV) is a normalized measure of the dispersion of a probability distribution. The coefficient of variation is used to measure the relative variability of data with respect to the mean, and is calculated as the ratio of the standard deviation to the mean.

It is often expressed as a percentage, and is useful in comparing the variability of two or more sets of data measured in different units. Therefore, the coefficient of variation is used to determine the percentage variation in height.

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The value of x that makes 25x^2 + 70x + c a perfect square trinomial is c = 1225.

To make the quadratic expression 25x^2 + 70x + c a perfect square trinomial, we need to determine the value of c.

A perfect square trinomial can be written in the form (ax + b)^2, where a is the coefficient of the x^2 term and b is half the coefficient of the x term.

In this case, a = 25, so b = (1/2)(70) = 35.

Expanding (ax + b)^2, we have:

(25x + 35)^2 = 25x^2 + 2(25)(35)x + 35^2

= 25x^2 + 70x + 1225.

Comparing this with the given quadratic expression 25x^2 + 70x + c, we can see that c = 1225.

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Answer:

1 1/12

Step-by-step explanation:

3/4 + 1/3

Get a common denominator of 12

3/4 * 3/3 = 9/12

1/3 * 4/4 =4/12

9/12 + 4/12

13/12

12/12 + 1/12

1 1/12

Answer

The cost of 1 and (1/4) pounds of raspberries is $10.

Explanation

Anyeny bought (3/4) pounds of raspberries for $6.

What is the cost of 1 and (1/4) pounds of raspberries.

(3/4) pounds = $6

(5/4) pounds = x dollars

Creatin a mathematical relation by cross multiplying

(3/4) × x = (5/4) × 6

Hence, the cost of 1 and (1/4) pounds of raspberries is $10.

Hope this Helps!!!

Answer:

y=3x+3

Step-by-step explanation:

If \(y=x^m\) is a solution to the ODE

\(x^2 y'' - 7xy' + 15y = 0\)

then substituting \(y\) and its derivatives

\(y' = mx^{m-1} \text{ and } y'' = m(m-1)x^{m-2}\)

gives

\(m(m-1)x^2x^{m-2} - 7mxx^{m-1} + 15x^m = 0\)

\(m(m-1)x^{m} - 7mx^{m} + 15x^m = 0\)

\((m(m-1) - 7m + 15)x^{m} = 0\)

We ignore the trivial case of \(y=x^m=0\). Solve for \(m\).

\(m(m-1) - 7m + 15 = 0\)

\(m^2 - 8m + 15 = 0\)

\((m - 3) (m - 5) = 0\)

\(\implies \boxed{m=3} \text{ or } \boxed{m=5}\)

The expected number of federal inmates serving time for drug dealing out of the sample of 15 is approximately 8.3.

To solve these probability questions, we can use the binomial distribution formula, assuming that the selection of federal inmates follows a binomial distribution.

In this case:

The probability of success (p) is 55% or 0.55, as given in the question.

The number of trials (n) is 15, as 15 federal inmates are selected.

The number of inmates serving time for drug dealing (X) follows a binomial distribution.

(a) To find the probability that 13 or more inmates are serving time for drug dealing:

P(X ≥ 13) = P(X = 13) + P(X = 14) + P(X = 15) + ...

Using the binomial distribution formula:

P(X = k) = C(n, k) * p^k * (1 - p)^(n - k)

Using the formula to calculate the probabilities:

P(X ≥ 13) = P(X = 13) + P(X = 14) + P(X = 15)

= [C(15, 13) * 0.55^13 * (1 - 0.55)^(15 - 13)] + [C(15, 14) * 0.55^14 * (1 - 0.55)^(15 - 14)] + [C(15, 15) * 0.55^15 * (1 - 0.55)^(15 - 15)]

Calculating the probabilities and rounding to three decimal places:

P(X ≥ 13) ≈ 0.526

Therefore, the probability that 13 or more federal inmates out of the sample of 15 are serving time for drug dealing is approximately 0.526.

(b) To find the probability that 7 or fewer inmates are serving time for drug dealing:

P(X ≤ 7) = P(X = 0) + P(X = 1) + P(X = 2) + ... + P(X = 7)

Using the binomial distribution formula and calculating the probabilities:

P(X ≤ 7) = P(X = 0) + P(X = 1) + P(X = 2) + ... + P(X = 7)

= [C(15, 0) * 0.55^0 * (1 - 0.55)^(15 - 0)] + [C(15, 1) * 0.55^1 * (1 - 0.55)^(15 - 1)] + ... + [C(15, 7) * 0.55^7 * (1 - 0.55)^(15 - 7)]Calculating the probabilities and rounding to three decimal places:

P(X ≤ 7) ≈ 0.138

Therefore, the probability that 7 or fewer federal inmates out of the sample of 15 are serving time for drug dealing is approximately 0.138.

(c) To find the expected number of inmates serving time for drug dealing:

The expected number (E(X)) can be calculated using the formula:

E(X) = n * p

Using the given values:

E(X) = 15 * 0.55

Calculating the expected number and rounding to one decimal place:

E(X) = 8.3

Therefore, the expected number of federal inmates serving time for drug dealing out of the sample of 15 is approximately 8.3.

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The time taken to create the driveway is 7 hours 42 minutes

The dimensions of the rectangle tile = 3 inch by 5 inches

The area of the rectangle tile = Length × width

= 3×5

= 15 square inches

Time taken to position each rectangle = 6 minutes

The dimensions of the driveway = 2 foot by 4 foot

Convert the dimensions to inches

2 foot by 4 foot = 2×12 inches by 4×12 inches

= 24 inches by 48 inches

The area = Length × Width

= 24×48

= 1152 square inches

Number of tiles needed = Area of the driveway/ Area of the tile

= 1152/15

= 76.8

≈77 tiles

Time taken to create the drive way = Number of tile× Time taken to position each rectangle

= 77×6

= 462 minutes

= 7 hours 42 minutes

Hence, the time taken to create the driveway is 7 hours 42 minutes.

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Answer:

Step-by-step explanation:

There ought to be infinitely many solutions.

How many solutions can a system of 3 linear equations with 5 variables have?

There are infinitely many solutions. Assuming the 3 linear equations are linearly independent you have 2 free variables that can be chosen freely and depending on those two values you can find the 3 remaining variables as function of those two so for any choice of those two variables you can find a solution. If the equations are not linearly independent you have effectively only 1 or two equations so you can pick 4 or 3 variables freely and then the remaining variable or variables are function of these.

How do you solve a system of equations with 3 variables?
Simultaneous equations. Easy, if they are all linear. Possibly difficult otherwise. Basically pick 1 variable and 1 equation to rearrange so that variable is expressed in terms if the other 2. Then simplify. Now you have 2 equations in 2 variables. Repeat with the remaining 2 variables. When you have solved for the last variable, you can then substitute to solve for the second last. Then backtrack to the original substitution and solve that. General advice that works even for nonlinear equations.

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Answer: The solutions of the absolute value equation are given by:

x = -41 and x = 49.

What is the absolute value function?

The absolute value function is defined by:

|x| = x, x >= 0.

|x| = -x, x < 0.

The absolute value function measures the distance of a point x to the origin, that is, the distance to x = 0. From this, we get that |x| = a can mean either that:

x = a, or;

x = -a.

In this problem, the equation is given by:

Hence:

0.2|x - 4| = 9

|x - 4| = 45

The first possible solution is:

x - 4 = 45

x = 49.

The second possible solution is:

-x + 4 = 45

-x = 41

x = -41.

Hence the solutions are x = -41 and x = 49.

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Step-by-step explanation:

Answer:

1. (x + 8)(x + b) = x² + bx + 8x + 8b = x² + (b + 8)x + 8b

2. (3x - 2)(x - 2) = 3x² - 6x - 2x + 4 = 3x² - 8x + 4

3. (2x + 1)(x - 1) = 2x² - 2x + x - 1 = 2x² - x - 1

4. (a - b)(a² + ab + b²) = a³ - b³

5. (5x + 2)(6x³x²y - 1) = 30x^4 x²y + 12x³x²y - 5x - 2

Step-by-step explanation:

Answer:

1)  x^2 + (b+8)x + 8b

2)    3x^2 - 8x + 4

3)  2x^2 - x - 1

4)    a^3 - b^3

5)    30x^4 y - 10x + 12x^3 y - 4xy

Step-by-step explanation: The answer to (x + 8) (x + b) is x^2 + (b+8)x + 8b, which is found using the FOIL method.

The answer to (3x – 2) (x – 2) is 3x^2 - 8x + 4, which is also found using the FOIL method.

The answer to (2x + 1) (x – 1) is 2x^2 - x - 1, which is also found using the FOIL method.

The answer to (a - b) (a^2 + ab + b^2) is a^3 - b^3, which is found using the formula for the difference of cubes.

The answer to (5x + 2) (6x^3 x 2y - 1) is 30x^4 y - 10x + 12x^3 y - 4xy, which is found using the FOIL method.

Answer:

\(6\frac{13}{28}\)

Step-by-step explanation:

Add:

-Chetan K

Answer:

\( \frac { - 3}{5} \)

Answer:

othe large one is 234 i ran out of time sorry i didnt get  circleto t

Step-by-step explanation:

Answer:

347.04 m²

Step-by-step explanation:

Total surface area = central rectangular prism + (1/2 left + 1/2 right)cylinder

a = 2x(11x3+11x6+6x3) + (2xπx(6/2)²+2xπx(6/2)x3)

  = 234 + 113.04

  = 347.04

Answer:

Answer is above (In the image).

Step-by-step explanation:

I am not sure if that is what you were looking for. To convert it to decimals, just input the figures into your calculator.

In my opinion the best way to solve these equations are elimination, therefore I will be giving my answer in this way!

2x-y+8z=13 1️⃣

3x+4y+52=182️⃣

5x-2y-72=203️⃣

We first combine liked terms in equation 2 and 3.

2️⃣turns into 3x+4y=-34 let's call it 2️⃣'

3️⃣turns into 5x-2y=92 let's call it 3️⃣'

Then solve for x

3️⃣'*2

10x-4y=184

3️⃣+2️⃣

13x=150

x=150/13

Now substitute the x back into equation 2️⃣'

3*150/13+4y=-34

450/13+4y=-442/13

4y=-892/13

2y=-446/13

y=-223/13

Now we can substitute this back into 1️⃣ to solve for z

2*150/13- - 223/13+8z=169/13

523/13+8z=169/13

8z=-354/13

4z=-177/13

z=-177/52

This problem is kind of messy so let me restate my answer!

x=150/13

y=-223/13

z=-177/52

I really hoped this is correct and it helped, and would appreciate it if you give me brainlliest! If you have any more questions about my solution please ask me in the comments!

Answer:

$167.50

Step-by-step explanation:

Since the state pays 40% of the health insurance, Maggie will have to pay 100 - 40 = 60% of the insurance amount annually

60% = 0.6 decimal

So Maggie pays 0.6 x 6700 = $4,020

Maggie is paid semi-monthly ie 2 paychecks a month

In a year, there are 12 months so Maggie receives 24 paychecks annually

The total insurance amount of 4020 is split over 24 paychecks

So each paycheck deduction will be 4020/24 = $167.50

the answer is C, hope this helps.

Answer:

BELOW

Step-by-step explanation:

(Y, X)

Y=-1

X=1

*** ACCORDING TO MY SOLUTION THE ANSWER IS (-1,1)

a. The degrees of freedom (df) value for inference about the slope β​ is calculated as the total number of observations minus the number of predictors (excluding the intercept term).

Since the regression analysis has 9 observations, and assuming there is only one predictor (X variable), the df value would be 9 - 1 = 8.

b. To find the t-test statistic values that would give a​ P-value of 0.01 for testing H0​: β=0 against Ha​: β ≠​0, you can use t-distribution tables or statistical software.

Since we are conducting a two-tailed test with a desired significance level of 0.01, we need to find the critical t-values that divide the upper and lower tails, each containing 0.005 (0.01/2) probability.

Using a t-distribution table with 8 degrees of freedom, the critical t-value for a two-tailed test at a significance level of 0.01 is approximately ±3.355.

Therefore, the two t-test statistic values that would give a P-value of 0.01 for testing H0​: β=0 against Ha​: β ≠​0 are -3.355 and 3.355.

c. To find the t-score that should be multiplied by the standard error to calculate the margin of error for a 99% confidence interval for β​, we need to determine the critical value from the t-distribution.

Since we want a 99% confidence interval, we are looking for a critical value that leaves 0.005 probability in the upper tail of the t-distribution (0.01/2).

Using a t-distribution table with 8 degrees of freedom, the critical t-value for a 99% confidence interval is approximately 2.896. Therefore, you would multiply the standard error by 2.896 to find the margin of error for the 99% confidence interval for β​.

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