5/6 - 4/9 what is the answer to this equation ???

Hello! In order to determine if the equation has a solution, we need to check if the determinant of the matrix A is equal to zero. The equation in question is given by Ax = b, where A is the coefficient matrix, x is the variable matrix, and b is the constant matrix.

If A is an invertible matrix, then its determinant is not equal to zero. Hence, the equation will have a solution. To find x, we can use the inverse of A. The solution is given by x = A^(-1) * b, where A^(-1) is the inverse of A.

To summarize:
1. Calculate the determinant of matrix A.
2. If the determinant is not equal to zero, the equation has a solution.
3. Find the inverse of A, denoted as A^(-1).
4. Compute the solution using x = A^(-1) * b.

Remember to substitute the actual matrices A and b into the equation to find the specific solution.

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Rn = 1/n^3 * Σ(i^2) from i=1 to n can be expressed as the sum Rn using summation notation

Riemann sum for the area under the curve of the function f(x) = x^2 on the interval (0,1). Right-Riemann sum Rn was 1/n^3(1^2+2^2+3^3+...+n^2).

A series can be represented in a compact form, called summation or sigma notation. The Greek capital letter, ∑ , is used to represent the sum.

To express the sum Rn using summation notation, you can write it as follows:

Rn = 1/n^3 * Σ(i^2) from i=1 to n

This notation means you're summing the squares of i (i^2) for each value of i from 1 to n, and then multiplying the result by 1/n^3.

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Y-intercept - 4

Slope - 3

Slope intercept form - y=3x + 4

Hope it's correct and it helped:)

The P-value in each of the given situations for testing the null hypothesis H₀: p = 0.6 using a z-test can be determined as follows:

A. Hₐ: p > 0.6, z = 1.47: The P-value is the probability of observing a z-score greater than 1.47, which can be found by calculating the area under the standard normal curve to the right of 1.47.

B. Hₐ: p < 0.6, z = -2.70: The P-value is the probability of observing a z-score less than -2.70, which can be found by calculating the area under the standard normal curve to the left of -2.70.

C. Hₐ: p ≠ 0.6, z = -2.70: The P-value is the probability of observing a z-score less than -2.70 or greater than 2.70, which can be found by calculating the sum of the areas under the standard normal curve to the left of -2.70 and to the right of 2.70.

D. Hₐ: p < 0.6, z = 0.25: The P-value is the probability of observing a z-score less than 0.25, which can be found by calculating the area under the standard normal curve to the left of 0.25.

To determine the P-value, we need to calculate the corresponding areas under the standard normal curve based on the given z-scores. The P-value represents the probability of observing a z-score as extreme or more extreme than the given value, assuming the null hypothesis is true.

By using standard normal distribution tables or statistical software, we can find the probabilities associated with the given z-scores. These probabilities represent the P-values for each scenario, providing a measure of evidence against the null hypothesis.


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Answer:

a. The stem-and-leaf plot shows data for two different schools, but it does not give us information on which school is Bay Side and which school is Seaside. Assuming the first column is Bay Side and the second column is Seaside, the measures of center for each school are:

Bay Side: median = 6, mode = 5 and 6

Seaside: median = 5, mode = 5

b. The measures of variability for each school are:

Bay Side: range = 8 - 2 = 6, IQR = Q3 - Q1 = 8 - 5 = 3

Seaside: range = 8 - 0 = 8, IQR = Q3 - Q1 = 8 - 1 = 7

c. If you are interested in a smaller class size, Seaside School is a better choice as it has a smaller median and range compared to Bay Side School.

a. The adjusted average for food can be calculated using the following spreadsheet formula:

=SUM(B2:G2)-B2-E2-F2-G2-C7

This formula adds up all the food expenses for the months of July, August, October, and November, and subtracts the September and December expenses, which were not included.

b. Using the formula above, the adjusted average for food is $725.

c. The adjusted average for electricity can be calculated using the following spreadsheet formula:

=SUM(B11:F11)-C11

This formula adds up all the electricity expenses for the months of July, August, October, and November, and subtracts the September expenses, which were not included.

d. Using the formula above, the adjusted average for electricity is $132.

Step-by-step explanation:

The absolute value of x minus one is equal to two. Therefore, x must be either one greater than two (x = 3) or one less than two (x = 1).

One less than x results in a value of two in absolute terms. As a result, x minus 1 has an absolute value of 2, which is a positive number. The separation of an integer from zero is its absolute value. As a result, x minus 1 is two units from zero in absolute terms. As x minus one has an absolute value of two, its real value must either be two or a negative two. That is to say, x must either be one more than two (x = 3) or one less than two (x = 1).In order to confirm this, let's look at a few examples. If x = 3, then |x - 1| = |2 - 1| = |1| = 1 which is not equal to two. Therefore, x = 3 is not the answer we are looking for. On the other hand, if x = 1, then |x - 1| = |1 - 1| = |0| = 0 which is not equal to two. Therefore, x = 1 is also not the answer we are looking for. The only two possible solutions for the equation |x - 1| = 2 are x = 3 and x = 1. Therefore, the result of |x - 1| = 2 is that x must be either one greater than two (x = 3) or one less than two (x = 1)

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Answer:

5.04 seconds

Step-by-step explanation:

According to the graph :

Observe the end points on x axis of the parabola

They are

Time is x axis

So total time

Answer:

a₃₅ = 182

Step-by-step explanation:

There is a common difference d between consecutive terms, that is

d = 17 - 12 = 22 - 17 = 5

This indicates the sequence is arithmetic with n th term

\(a_{n}\) = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Here a₁ = 12 and d = 5 , then

a₃₅ = 12 + (34 × 5) = 12 + 170 = 182

the answer is the first one it is less likely he will turn left

Answer:

Hello!

Since 1 pound of deli turkey cost $6.20, 0.75 pound of turkey would cost $4.65. So it would be $1.55 per 0.25 pound of deli turkey. Hope this helps.

Step-by-step explanation:

The polynomial expression which represents the value of the account at the end of three years is 1000x³ + 300x² + 500x

Interest earned per year, x = 1 + r

First year :

Year end balance = 1000 × x = 1000x

Second year :

Year end balance = (1000x + 300)x = 1000x² + 300x

Third year :

Year end balance = (1000x² + 300x + 500)x = 1000x³ + 300x² + 500x

Therefore, the expression which represents the value of the account at the end of three years is 1000x³ + 300x² + 500

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If in a survey, 200 college students were asked whether they live on campus and if they own a car, 55% of college students in the survey don't own a car.

To find the percent of college students who don't own a car, we need to add up the number of students who don't own a car and divide it by the total number of students in the survey. In this case, the total number of students in the survey is 200.

From the table, we can see that there are 88 students who live on campus and don't own a car, and 22 students who don't live on campus and don't own a car. So the total number of students who don't own a car is 88 + 22 = 110.

To find the percentage, we divide the number of students who don't own a car by the total number of students in the survey and then multiply by 100 to get the percentage:

Percentage of students who don't own a car = (110/200) x 100% = 55%

When working with percentages, we need to divide the number we are interested in by the total and then multiply by 100 to get the percentage.

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The length of the entire tunnel is 127.88 meters by using cosine law or formulae.

Here we can use the formulae of cosine when two sides a and b and angle between then is given we can apply it.

\(c^{2} =a^{2} +b^{2} -2ab cos (\alpha )\)

Let us take surveyor as point A

one end of the tunnel denoted by point B

other end of the tunnel denoted by point C.

The length of AB is 101 meters

length of AC is 120 meters.

Measure of angle at point A = 42° + 28° =70°

Now lets find the length of tunnel

=\(\sqrt{(120^{2})+(101^{2})-2.(120)(101) cos (70) }\)

=\(\sqrt{14400+10201-24240(0.34)}\)

=\(\sqrt{24601-8246}\)

\(\sqrt{16355}\)

=127.88 meters.

Hence the length of the entire tunnel is 127.88 meters.

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Answer:

18

Step-by-step explanation:

Equation 9 x 4 / 2 = 18

First do 9 x 4 which is 36

Next do 36 / 2 which is 18

Also the "/" is another way to say to divide

Answer:

b I guess

what is that at the bottom?

We can see that the expression (p q) (q → r p) (p r) is true only for the first combination of truth values (p=T, q=T, r=T).

To use the truth table method, we need to list all possible combinations of truth values for p, q, and r and then evaluate the expression (p q) (q → r p) (p r) for each combination.

If we find at least one combination that makes the expression true, then the expression is satisfiable; otherwise, it is unsatisfiable.

Let's start by listing all possible combinations of truth values for p, q, and r:

p | q | r

--+---+--

T | T | T

T | T | F

T | F | T

T | F | F

F | T | T

F | T | F

F | F | T

F | F | F

Next, we evaluate the expression (p q) (q → r p) (p r) for each combination of truth values:

p | q | r | (p q) (q → r p) (p r)

--+---+---+-----------------------

T | T | T |       T

T | T | F |       F

T | F | T |       F

T | F | F |       F

F | T | T |       F

F | T | F |       F

F | F | T |       F

F | F | F |       F

We can see that the expression (p q) (q → r p) (p r) is true only for the first combination of truth values (p=T, q=T, r=T). Therefore, the expression is satisfiable.

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The approximate area, in square feet, of the side panel is approximately 292.7 square feet. The correct option is A. 292.7.

To determine the approximate area, in square feet, of the side panel, use Heron's formula which is the square root of [s(s - a)(s - b)(s - c)] where s is the semiperimeter and a, b, and c are the side lengths of the triangle.

The first step to solving this problem is to calculate the semiperimeter of the triangle using the formula:

semiperimeter =  \((a + b + c) / 2\)

Given the dimensions of the triangular side panel for a roof as shown below, we can apply the Pythagorean theorem to find the length of the missing side (in red).

Triangle ABC

According to the Pythagorean theorem: a^2 + b^2 = c^25.4^2 + 8^2

= c^265.16 + 64

= c^2129.16

= c^2√129.16

= c11.37 ≈ 11.4 (rounded to one decimal place)

Therefore, the semiperimeter of the triangle is:

s = (5.4 + 8 + 11.4) / 2s

= 24.8

The area of the triangular side panel is approximately:

sqrt(s(s - a)(s - b)(s - c))

≈ sqrt(24.8(24.8 - 5.4)(24.8 - 8)(24.8 - 11.4))

≈ sqrt(24.8 × 19.4 × 16.8 × 13.4)

≈ sqrt(104947.9424)

≈ 323.72

≈ 292.7 square feet (rounded to one decimal place)

Therefore, the approximate area, in square feet, of the side panel is approximately 292.7 square feet. The correct option is A. 292.7.

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Based on the analysis, point D at (-7, 1) is the only solution to the system of inequalities y > -2x + 10 and y > (1/2)x - 2. Therefore, the correct answer is option d) D.

To determine which point is a solution to the system of inequalities y > -2x + 10 and y > (1/2)x - 2, we can test each point to see if it satisfies both inequalities.

a) Point E at (4, -2):

Substituting the coordinates into the inequalities:

-2 > -2(4) + 10 -> -2 > -8 + 10 -> -2 > 2 (False)

-2 > (1/2)(4) - 2 -> -2 > 2 - 2 -> -2 > 0 (False)

b) Point K at (2, 3):

Substituting the coordinates into the inequalities:

3 > -2(2) + 10 -> 3 > -4 + 10 -> 3 > 6 (False)

3 > (1/2)(2) - 2 -> 3 > 1 - 2 -> 3 > -1 (True)

c) Point B at (4, 7):

Substituting the coordinates into the inequalities:

7 > -2(4) + 10 -> 7 > -8 + 10 -> 7 > 2 (True)

7 > (1/2)(4) - 2 -> 7 > 2 - 2 -> 7 > 0 (True)

d) Point D at (-7, 1):

Substituting the coordinates into the inequalities:

1 > -2(-7) + 10 -> 1 > 14 + 10 -> 1 > 24 (False)

1 > (1/2)(-7) - 2 -> 1 > -3.5 - 2 -> 1 > -5.5 (True)

Based on the analysis, point D at (-7, 1) is the only solution to the system of inequalities y > -2x + 10 and y > (1/2)x - 2. Therefore, the correct answer is option d) D.

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Answer:

A.

Step-by-step explanation:

Count the arrows.  A has 1, B has 2, and C has 3.  D will have 4.  The pattern is also one vertical and one horizontal arrow being added alternately.

Answer:

Abby will earn $510 if she works 60 hours.

Step-by-step explanation:

8 hrs --> $68

1 hr --> 68 × 1/8 = $8.5

So, 60 hrs

= 8.5 × 60

= $510

(a) As we have shown that the differentiable function f decreases most rapidly at x in the direction opposite the gradient vector, that is, in the direction of −∇f(x).

(b) The direction in which f(x, y) = x³y − x²y³ decreases fastest at (4, -4) is the direction of the unit vector u = <-3/5, 4/5>.

To show that a differentiable function f decreases most rapidly at x in the direction opposite the gradient vector, we first need to define the directional derivative. The directional derivative of f at x in the direction of a unit vector u is denoted by Du f and is given by the dot product of the gradient vector ∇f(x) and u.

Du f = ∇f(x)·u

Now, we want to find the direction in which Du f is minimized. Let θ be the angle between ∇f(x) and u. Using the dot product formula, we have:

Du f = |∇f(x)| cos(θ)

where |∇f(x)| is the magnitude of the gradient vector. Since cos(θ) is maximum when θ = 0 (i.e., when u points in the same direction as ∇f(x)) and minimum when θ = π (i.e., when u points in the opposite direction of ∇f(x)), we can conclude that the direction in which f decreases most rapidly at x is opposite the gradient vector −∇f(x).

Now, let's apply this result to the function f(x, y) = x³y − x²y³ and find the direction in which it decreases fastest at the point (4, −4).

First, we need to find the gradient vector of f:

∇f(x, y) = <3x²y-2xy³, x³-3x²y²>

Evaluating at (4, -4), we have:

∇f(4, -4) = <192, -256>

The magnitude of the gradient vector is |∇f(4, -4)| = √(192² + (-256)²) = 320.

To find the direction of fastest decrease, we need to consider the opposite of the gradient vector:

−∇f(4, -4) = <-192, 256>

To make this a unit vector, we divide by its magnitude:

u = <-192, 256>/320 = <-3/5, 4/5>.

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Answer:

y is your answer

m is your rise/run

x is there for x

and b is your negative or positive y-intercept

Step-by-step explanation:

Answer:

21

Step-by-step explanation:

prim factors: 2, 3, 5, and 11

The sum of the prime factors of the number 330 is 21.

A natural number other than 1 whose only factors are 1 and itself is said to have a prime factor. In actuality, the first few prime numbers are 2, 3, 5, 7, 11, and so forth.

Given:

The number is 330

Factorize the above number,

330 = 1 × 2 × 3 × 5 × 11

Prime factors are = 2, 3, 5, 11

Calculate the sum of the prime factor

2 + 3 + 5 + 11 = 21

Therefore, the sum of the prime factors of the number 330 is 21.

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The correct answer is (d) The price must be replaced with a relative price, and the marginal values must be replaced with the corresponding Marginal Rates of Substitution.

When the value of a public good cannot be expressed in monetary terms, the Samuelson condition still holds, but some modifications are required. In this case, the per-unit price (p) used in the Samuelson condition needs to be replaced with a relative price, which represents the trade-off between the public good and other goods or services. Additionally, the marginal values (MV) of the public good need to be replaced with the Marginal Rates of Substitution (MRS), which measure the rate at which one person is willing to substitute the public good for another good.

Therefore, to determine the efficient level of the public good, the modified Samuelson condition uses a relative price and the corresponding Marginal Rates of Substitution.

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Answer:24

Step-by-step explanation:

g∘f(x) or g(f(x)) is equal to 27x + 43.

To find g∘f(x) or g(f(x)), we need to substitute the function f(x) into the function g(x).

Given:

f(x) = 3x + 4

g(x) = 9x + 7

To find g∘f(x), we substitute f(x) into g(x) as follows:

g(f(x)) = g(3x + 4)

Now, we substitute 3x + 4 for x in the function g(x):

g(f(x)) = 9(3x + 4) + 7

Expanding and simplifying:

g(f(x)) = 27x + 36 + 7

g(f(x)) = 27x + 43

Therefore, g∘f(x) or g(f(x)) is equal to 27x + 43.

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