Help please!

Provide a counterexample to the statement below:

"Supplementary angles are never congruent"

A 3x3 matrix, the rank can be 0, 1, 2, or 3, depending on the values of the entries in the matrix.

The rank of a matrix is the number of linearly independent rows or columns in the matrix.  The rank of a 3x3 matrix can be found by performing row reduction to obtain an echelon form, and then counting the number of non-zero rows.

For example, let's consider the following 3x3 matrix:

a11 a12 a13

a21 a22 a23

a31 a32 a33

Performing row reduction, we can obtain an echelon form:

a11 a12 a13

0   a22' a23'

0   0    a33'

Here, a22' and a33' represent the pivots of the matrix, and the number of non-zero rows in the echelon form is equal to the rank of the matrix.

Therefore, for a 3x3 matrix, the rank can be 0, 1, 2, or 3, depending on the values of the entries in the matrix.

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Answer:

\(9. \: \boxed{ \tt{x = 7}} \\10. \: \boxed{ \tt{x = 6}} \)

Step-by-step explanation:

\(quest \: 9 \to \\ \frac{5 + x}{32} = \frac{9}{33 - 9} \\ 24(5 + x) = (32)(9) \\ 5 + x = \frac{(32)(9)}{24} \\ 5 + x = 12 \\ x = 12 - 5 \\ \boxed{ x = 7} \\ \\ quest \: 10 \to \: \\ \frac{30 - (4x - 4)}{4x - 4} = \frac{18 - 12}{12} \\ \frac{34 - 4x}{4x - 4 } = \frac{6}{12} = \frac{1}{2} \\ 2(34 - 4x) = 4x - 4 \\ 68 - 8x = 4x - 4 \\ 68 + 4 = 4x + 8x \\ 72 = 12x \\ x = \frac{72}{12} = 6 \\ \boxed{x = 6}\)

Once we find Q(t), we can substitute it back into the expression for y_p(t) to get the particular solution of the differential equation.

To find a particular solution of the differential equation y(4) − y = g(t), we can use the method of undetermined coefficients. This method assumes that the particular solution has the same form as the forcing function g(t).

Let's assume that the forcing function is of the form g(t) = P(t)e^t, where P(t) is a polynomial. Then, we can guess that the particular solution is of the form y_p(t) = Q(t)e^t, where Q(t) is also a polynomial.

Now, let's find the derivatives of y_p(t):

y_p(t) = Q(t)e^t

y'_p(t) = (Q'(t) + Q(t))e^t

y''_p(t) = (Q''(t) + 2Q'(t) + Q(t))e^t

y'''_p(t) = (Q'''(t) + 3Q''(t) + 3Q'(t) + Q(t))e^t

y''''_p(t) = (Q''''(t) + 4Q'''(t) + 6Q''(t) + 4Q'(t) + Q(t))e^t

Substituting these derivatives into the differential equation, we get:

(Q''''(t) + 4Q'''(t) + 6Q''(t) + 4Q'(t) + Q(t))e^t - Q(t)e^t = P(t)e^t

Simplifying and canceling the exponential terms, we get:

Q''''(t) + 4Q'''(t) + 6Q''(t) + 3Q'(t) = P(t)

Now, we can use integration by parts to find a formula for Q(t) in terms of integrals of P(t):

Q(t) = (1/3) ∫∫∫[P(t) - 6Q''(t) - 12Q'(t) - 8Q(t)] dt

We can repeat this process of integration by parts until we get a formula for Q(t) in terms of integrals of P(t) only. Once we find Q(t), we can substitute it back into the expression for y_p(t) to get the particular solution of the differential equation.

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Answer:

which cost which table??

We have a sample of size =8 and x has a Normal distribution is not appropriate to use t procedures to make inferences about μ using x¯x¯

It would not be appropriate to use t procedures to make inferences about μ using x¯x¯ in the case .We have a sample of size = 20 and x has a right-skewed distribution with an outlier. The reason is that t procedures assume that the data follows a normal distribution or approximately normal distribution. In this case, with a right-skewed distribution and an outlier, the assumption of normality may be violated. Outliers can significantly affect the mean and potentially bias the results. In such cases, non-parametric methods or transformations may be more appropriate for making inferences about the population mean.

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Answer:

No the graph is not correct.  The point of intersection is (-3, 4)

Points on line y = x + 7  are  (-3, 4)  (0, 7) and (2, 9)

Points on line y = -1/3x +3  are (-3, 4) (0, 3) and (-6, 5)

Step-by-step explanation:

y = x + 7              do not change

y = -1/3x + 3        substitute into the top equation and solve for x

-1/3x + 3 = x + 7

       -3  =      -3    

-1/3x    =   x + 4  

- x      =   -x        

-1  1/3x =   4

 - 4/3x  = 4            Changed -1 1/3x to -4/3x

   x    =  4/ -4/3

  x =  -3

  y = x + 7

  y = -3 + 7

 y = 4                         Point of intersection is (-3, 4)  

Answer:

  arc AB = 68°

Step-by-step explanation:

You want the measure of arc AB whose parts are arc AE and EB with inscribed angles ADE = 11° and EDB = 23°.

The measure of angle ADB is the sum of the measures of its parts:

  ∠ADB = ∠ADE +∠EDB

  ∠ADB = 11° +23° = 34°

The measure of an inscribed angle is half the measure of the arc it subtends. This means the arc measure is twice the inscribed angle measure.

  arc AB = 2 × ∠ADB = 2 × 34°

  arc AB = 68°

Answer:

200.5ft²

Step-by-step explanation:

According to my calculation this is the answer ..

The recommended rule to sequence the jobs for minimum flow time is the EDD (Earliest Due Date) rule.

The EDD rule prioritizes jobs based on their due dates, where jobs with earlier due dates are given higher priority. By sequencing the jobs in order of their due dates, the goal is to minimize the total flow time, which is the sum of the time it takes to complete each job.

In this case, applying the EDD rule, the sequence of jobs would be as follows:

D (Due on Friday 10th June)

F (Due on Tuesday 14th June)

E (Due on Wednesday 15th June)

C (Due on Friday 17th June)

G (Due on Thursday 16th June)

H (Due on Saturday 18th June)

A (Due on Monday 13th June)

B (Due on Monday 20th June)

By following the EDD rule, we aim to complete the jobs with earlier due dates first, minimizing the flow time and ensuring timely delivery of the orders.

Therefore, the recommended rule for sequencing the jobs in this scenario is the EDD (Earliest Due Date) rule.

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If after hip surgery, your physical therapist tells you to slowly return to walking. The number of  weeks it will be before you are up to 45 minutes of walking per day is: c. 9.

Since the therapist suggests walking for 5 minutes each day for the first week and increasing that time by 5 minutes per day each week thereafter.

Hence,

You will  tend to need 9 weeks to reach 45 minutes of walking per day which are:

Week 1: 5 minutes

Week 2: 10 minutes

Week 3: 15 minutes

Week 4: 20 minutes

Week 5: 25 minutes

Week 6: 30 minutes

Week 7: 35 minutes

Week 8: 40 minutes

Week 9: 45 minutes

The total number of weeks are 9 weeks.

Therefore the correct option is C.

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Answer:

7

Step-by-step explanation:

hope this works :)

consecutive numbers means 2 numbers next to eachother like 8 and 9 or 3 and 4

product means basically the result of numbers multiplying together, e.g. the product of 8×9 = 72

so if you use trial and error you will find 6 × 7 = 42 and since mav is older she must be 7 years old

Answer:

mav is 7

Step-by-step explanation:

let justin's age be n then mav is n + 1 and the product is

n(n + 1) = 42

n² + n = 42 ( subtract 42 from both sides )

n² + n - 42 = 0 ← in standard form

(n + 7)(n - 6) = 0 ← in factored form

equate both factors to zero and solve for n

n + 7 = 0 ⇒ n = - 7

n - 6 = 0 ⇒ n = 6

since n > 0 then n = 6

mav is n + 1 = 6 + 1 = 7

Marvin will make 10 equal installments of $12 each to pay off the remaining balance of the watch.

Marvin is buying a watch from his brother for $170.

His brother offers him a payment plan where Marvin can make a $50 down payment and pay the remaining amount in 10 equal installments.

To calculate the amount of each installment, we first need to determine the remaining balance after the down payment.

Remaining balance = Total price of the watch - Down payment

Remaining balance = $170 - $50

Remaining balance = $120.

Since Marvin will pay the remaining balance in 10 equal installments, we can divide the balance by the number of installments to find the amount of each installment.

Amount of each installment = Remaining balance / Number of installments

Amount of each installment = $120 / 10

Amount of each installment = $12

Therefore, Marvin will make 10 equal installments of $12 each to pay off the remaining balance of the watch.

1In summary, Marvin will make a $50 down payment and then pay $12 per month for 10 months to complete the payment of the watch.

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Answer:

average rate of change = 2

Step-by-step explanation:

since f(x) is a linear function, then the slope is the measure of the average rate of change of f(x).

note the average rate of change is constant over any closed interval.

the equation of a linear function in slope- intercept form is

f(x) = mx + c ( m is the slope and c the y- intercept )

f(x) = 2x + 4 ← is in slope- intercept form

with slope m = 2

then average rate of change = 2

To solve the non-linear ODE y''' + 2/3 y' + (y')^2 = 0, we can use the method of power series. We assume that the solution has the form y(x) = ∑(n=0 to infinity) a_n x^n, and substitute this into the ODE to obtain a recurrence relation for the coefficients a_n.

Differentiating y(x) three times, we get y'(x) = ∑(n=1 to infinity) n a_n x^(n-1), y''(x) = ∑(n=2 to infinity) n(n-1) a_n x^(n-2), and y'''(x) = ∑(n=3 to infinity) n(n-1)(n-2) a_n x^(n-3).

Substituting these expressions into the ODE, we get:

∑(n=3 to infinity) n(n-1)(n-2) a_n x^(n-3) + 2/3 ∑(n=1 to infinity) n a_n x^(n-1) + (∑(n=1 to infinity) n a_n x^(n-1))^2 = 0

We can simplify this expression by shifting the index of the second sum by 2:

∑(n=3 to infinity) n(n-1)(n-2) a_n x^(n-3) + 2/3 ∑(n=3 to infinity) (n-2) a_(n-2) x^(n-3) + (∑(n=1 to infinity) n a_n x^(n-1))^2 = 0

Expanding the third term and collecting coefficients of x^(n-3), we get:

3a_3 + (8/3)a_4 + (13/3)a_5 + ... + [∑(k=1 to n-1) k a_k a_(n-k)] + ... = 0

This is the recurrence relation for the coefficients a_n. We can use this relation to compute the coefficients recursively, starting with a_0 = 1, a_1 = 0, and a_2 = 0. For example, to find a_3, we use the first term of the recurrence relation:

3a_3 = -[(8/3)a_4 + (13/3)a_5 + ...]

Then, to find a_4, we use the second term:

8/3 a_4 = -[(13/3)a_5 + ... + ∑(k=1 to 3) k a_k a_(4-k)]

And so on.

Once we have computed the coefficients, we can substitute them into the power series expression for y(x) and obtain the solution to the ODE.

However, we also need to check the convergence of the power series. Since the ODE is non-linear, it is not straightforward to determine the radius of convergence. We can use numerical methods to estimate the radius of convergence and check that it includes the interval [1, infinity] (where the boundary conditions are specified).

Overall, this is a difficult problem that requires advanced techniques in differential equations and numerical analysis.

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When P is not on the line l, the image and pre-image are: a. parallel.

In Geometry, a dilation is a type of transformation which typically transforms the dimensions or side lengths of a geometric object, without affecting its shape.

Generally speaking, a dilation is not a rigid transformation because it can preserve angle measure, orientation, perpendicular lines, betweenness of points, parallel lines, and collinearity in any geometric figure.

In conclusion, we can reasonably infer and logically deduce that the the image and pre-image are still parallel lines when P is not on the line l.

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The 9th term of the geometric sequence is 64.

The formula for the nth term of a geometric sequence is:

an = a1 * r^(n-1)

where a1 is the first term and r is the common ratio.

In this case, we are given that:

a6 = 8

r = 2

n = 9

To find the 9th term, we need to plug in the values into the formula:

a9 = a1 * r^(9-1)

We don't know a1, but we can find it using the 6th term:

a6 = a1 * r^(6-1)

8 = a1 * 2^5

a1 = 8 / 2^5

a1 = 8 / 32

a1 = 1/4

Now we can substitute a1 and r into the formula for the 9th term:

a9 = (1/4) * 2^(9-1)

a9 = (1/4) * 2^8

a9 = (1/4) * 256

a9 = 64

Therefore, the 9th term of the geometric sequence is 64.

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We are asked to find the probability of different scenarios when 37 students are randomly selected.By using the binomial probability formula and the appropriate ranges, we can calculate the probabilities.

(a) To find the probability that exactly 26 students need to take another math class, we can use the binomial probability formula:

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

where n is the number of trials, k is the number of successes, p is the probability of success, and (nCk) is the binomial coefficient. Plugging in the values, we get:

P(X = 26) = (37C26) * (0.69^26) * (0.31^(37-26))

(b) To find the probability that at most 27 students need to take another math class, we need to calculate the cumulative probability:

P(X ≤ 27) = P(X = 0) + P(X = 1) + ... + P(X = 27)

(c) To find the probability that at least 23 students need to take another math class, we can calculate the complement of the probability that fewer than 23 students need to take another math class:

P(X ≥ 23) = 1 - P(X < 23)

(d) To find the probability that between 20 and 25 students (including 20 and 25) need to take another math class, we need to calculate the cumulative probability:

P(20 ≤ X ≤ 25) = P(X = 20) + P(X = 21) + ... + P(X = 25)

By using the binomial probability formula and the appropriate ranges, we can calculate the probabilities for each scenario.

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The given expression has to be expanded and evaluated. The given expression is FA1 for\(L1 FA1 a a 1+ FA2 for L2 FA2 3 a CO b b b b b a a 2 a 4 OS + b.\)

\(FA3 for L1 + L2\):

It is given that FA1 for \(L1 = a + b, FA1 a a 1 = 2a\), FA2 for\(L2 = 3a + 4b, FA2 3 a CO b b b b b a a 2 a 4 OS = 3a + 5b\). Substituting the given values in the expression, we have:

\(FA3 for L1 + L2 = (FA1 for L1) (FA1 a a 1) + (FA2 for L2) (FA2 3 a CO b b b b b a a 2 a 4 OS) + b\)
\(FA3 for L1 + L2 = (a + b) (2a) + (3a + 4b) (3a + 5b) + b\)
\(FA3 for L1 + L2 = 2a2 + 3a2 + 15ab + 12b2 + 2ab + b\)
\(FA3 for L1 + L2 = 5a2 + 17ab + 12b2 + b\)
\(FA3 for L1 + L2 is 5a2 + 17ab + 12b2 + b.\)
FA1 for L1:

It is given that FA1 for\(L1 = a + b.\)

FA1 for L1 is a + b.

Answer:

FA3 for L1 + L2 is 5a² + 17ab + 12b² + b and FA1 for L1 is a + b.

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Answer:

Exact: 3,999,500,000

Estimate: 4,000,000,000

Step-by-step explanation:

(4)(10) = 40

(4 x 10)9 = 4,000,000,000

Notice that there are 9 zeros

_________________________________________

(5)(10) = 50

(5 x 10)5 = 500,000

Notice that there are 5 zeros

_________________________________________

4,000,000,000 - 50,000 = 3,999,500,000

He also added lettuce, tomatoes, and cheese. Kenneth also made sure to put plenty of condiments like mayonnaise and mustard on each sandwich.

Number is a mathematical entity used to represent a computer magnitude it can be symbol or a combination of simple you should in order to take quantity such as the two, five, seven, three or eight number are used to verify the context including counting measuring and computing.


Kenneth's family was excited to get to the beach. When they arrived, they set up their umbrellas and beach chairs and found a spot to settle down. After they were all settled, Kenneth passed out the sandwiches he had made. Everyone was satisfied with the delicious sandwiches Kenneth had created.

Kenneth's family enjoyed their day at the beach. They swam in the ocean, built sandcastles, and played volleyball. They even laid out and got a nice tan. As the day got hotter, Kenneth's family got hungrier. Fortunately, they still had the sandwiches Kenneth had made. Everyone was thankful for the delicious sandwiches that Kenneth had prepared for them.

After a fun day at the beach, Kenneth's family packed up their things and headed home. Kenneth was happy that he could provide for his family and make their day even better. He was grateful for the opportunity to make the sandwiches for his family and make their day at the beach even more enjoyable.

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Answer:

6.25 in

Step-by-step explanation:

25/3= 8.33

8.33*.75= 6.25

Operations of polynomials can be used to create new Polynomial models in a variety of real-world situations, from calculating total costs and profits to finding the total area and volume of composite figures and modeling the relationship between dependent variables.

Polynomial functions are widely used in many fields such as science, engineering, economics, medicine, and statistics, to model and predict real-world phenomena. Operations of polynomials can be used to create new polynomial models by adding, subtracting, multiplying, or composing polynomial functions.

In the following paragraphs, we will discuss each operation of polynomials and provide real-world examples of when it is necessary to use them to model real situations. Adding Polynomials:

When adding polynomials, we simply combine like terms to form a new polynomial function. In real-world situations, polynomial addition can be used to calculate the total number of a certain item that is made up of different parts or groups. For example, suppose that a company makes two types of products type A and type B, and each product has a different cost per unit. The total cost of producing both products can be modeled by adding two polynomials: C(x) = 3x² + 2x + 5 and D(x) = 2x² + 4x + 3, where C(x) represents the cost of producing type A and D(x) represents the cost of producing type B. The total cost of production can be found by adding the two polynomials: C(x) + D(x) = 5x² + 6x + 8.

Subtracting Polynomials: When subtracting polynomials, we simply distribute the negative sign and combine like terms to form a new polynomial function. In real-world situations, polynomial subtraction can be used to calculate the difference between two quantities. For example, suppose that a company produces two types of products, type A and type B, and each product has a different profit per unit. The difference in profit between the two products can be modeled by subtracting two polynomials: P(x) = 5x² + 3x - 2 and Q(x) = 3x² - 2x + 5, where P(x) represents the profit of type A and Q(x) represents the profit of type B. The difference in profit can be found by subtracting the two polynomials: P(x) - Q(x) = 2x² + 5x - 7.

Multiplying Polynomials: When multiplying polynomials, we use the distributive property to multiply each term of one polynomial by each term of the other polynomial and then combine like terms to form a new polynomial function. In real-world situations, polynomial multiplication can be used to calculate the total area or volume of a composite figure or object. For example, suppose that a company produces a rectangular box with length 2x + 1, width x + 2, and height x - 3. The total volume of the box can be modeled by multiplying the three binomials: V(x) = (2x + 1)(x + 2)(x - 3) = 2x³ - 9x² - 5x + 6.

Compose Polynomials: When composing polynomials, we use one polynomial as the input into the other polynomial and then simplify the resulting function to form a new polynomial function. In real-world situations, the polynomial composition can be used to model the relationship between two variables that are dependent on each other. For example, suppose that the population of a town is modeled by the polynomial function P(t) = 2t² - 5t + 10, and the average income per capita is modeled by the polynomial function I(p) = 3p² + 4p - 2, where t represents time in years and p represents the population of the town.

The relationship between population and income can be modeled by composing the two polynomial functions: I(P(t)) = 3(2t² - 5t + 10)² + 4(2t² - 5t + 10) - 2, which simplifies to I(P(t)) = 12t⁴ - 98t³ + 262t² - 262t + 28.

In conclusion, operations of polynomials can be used to create new polynomial models in a variety of real-world situations, from calculating total costs and profits to finding the total area and volume of composite figures and modeling the relationship between dependent variables.

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The rate of change in the area of the circle is 22 cm²/s when the radius of the circle is increasing at a rate of 0.5 cm/s.

It is half of the diameter of the circle or sphere. The radius is commonly denoted by the letter "r".

The area of a circle is given by the formula A = πr², where A is the area and r is the radius.

If the radius is increasing at a rate of 0.5 cm, then the rate of change of the radius with respect to time is dr/dt = 0.5 cm/s.

Using the chain rule of differentiation, we can find the rate of change of the area with respect to time:

dA/dt = dA/dr * dr/dt

By varying the area formula, we can determine dA/dr:

dA/dr = 2πr

Plugging in the values of r and dr/dt, we get:

dA/dt = (2πr)(0.5) = πr

At the initial radius of 7cm, the rate of change in the area is:

dA/dt = π(7) = 22/7 * 7 = 22 cm²/s

Therefore, the rate of change in the area of the circle is 22 cm²/s when the radius of the circle is increasing at a rate of 0.5 cm/s.

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Answer:

  (a)  15 -18i

Step-by-step explanation:

You want the simplified form of the expression -2i(5- i) + (17- 8i).

For many purposes, the value i in a complex number can be treated in the same way a variable would be treated. When simplifying an expression involving i, any instances of i² can be replaced with the real value -1.

  -2i(5- i) + (17- 8i) = -10i +2i² +17 -8i

  = -2 +17 +(-10 -8)i

  = 15 -18i

__

Additional comment

Your scientific or graphing calculator can probably help you evaluate such expressions.

Hello! To solve completing by the square, we have to follow some steps:

Now, we have to add the same value in both sides (square):

If we factorize the first part of this expression, we can obtain:

Notice that we obtained the same expression, and now we know the value of the square. So, let's rewrite the first expression and replace the squares by 4:

The procedure the researcher will use is called stratification sampling.

A stratified sample is created by separating a population into similar subpopulations (strata) and taking a representative sample from each. Stratified sampling is used by researchers to ensure that specific subgroups are represented in their samples. Additionally, it helps them estimate the characteristics of each group precisely. This method is used in many surveys in order to better understand the differences between subpopulations. The term stratified sampling is also used to refer to stratified random sampling.

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Answer:

75%

Step-by-step explanation:

Answer:

75/300= 1/4 or 25% (A)

Step-by-step explanation:

75 women own a blue car.

300 people were surveyed.

The remainder would be 12 as per the remainder theorem if the function P is defined by P(x) = x³ +7x² - 26x - 72.

A polynomial is defined as a mathematical expression that has a minimum of two terms containing variables or numbers. A polynomial can have more than one term.

Let   P(x) = x³ +7x² - 26x - 72  ...(i)

Divisor = (x+9)

Apply remainder theorem,

x + 9 = 0

x = -9

Substitute the value of x = -9 in equation (i),

⇒ P(-9) = (-9)³ +7(-9)² - 26(-9) - 72

⇒ P(-9) = (-729) +7(81) - 234 - 72

⇒ P(-9) = -729 + 567 - 234 - 72

⇒ P(-9) = -468

Therefore, the remainder would be -468.

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The measure of DE, given that Triangle ABC is similar to Triangle DEF, is 53. 09 units .

To find the measure of DE, you need to use the corresponding sides of BC and EF to find the scale factor that shows the difference in the sizes of corresponding sides.

The scale factor is:

= 31 / 8

= 3. 875

Now, since the value of the corresponding side of AB is 13.7 units, the measure of DE would be :

= 13. 7 x 3. 875

= 53. 09 units

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