HELPPPPPPPPPP ITS DUEEEEEEEEEEEEEEEE

The eigenvalues in terms of α are (7 + sqrt(49 - 16α)) / 4 and (7 - sqrt(49 - 16α)) / 4, in increasing order. There are no critical values.

The given coefficient matrix is [[7/4, 3/4], [α, 7/4]]. To find the eigenvalues, we need to solve the characteristic equation det(A - λI) = 0, where A is the coefficient matrix, I is the identity matrix, and λ is the eigenvalue.

Expanding the determinant, we get:(7/4 - λ)(7/4 - λ) - (3/4)(α) = 0

Simplifying and rearranging, we get: λ^2 - (7/2)λ + (49/16) - (3/4)α = 0

Using the quadratic formula, we get: λ = (7 ± sqrt(49 - 16α)) / 4

Therefore, the eigenvalues in terms of α are (7 + sqrt(49 - 16α)) / 4 and (7 - sqrt(49 - 16α)) / 4, in increasing order.

To find the critical values of α where the qualitative nature of the phase portrait changes, we need to examine the sign of the eigenvalues. If both eigenvalues are real and have the same sign, the phase portrait consists of either a stable node or a stable spiral. If both eigenvalues are real and have opposite signs, the phase portrait consists of either a saddle or an unstable node. If both eigenvalues are complex conjugates with positive real part, the phase portrait consists of a stable focus, and if both eigenvalues are complex conjugates with negative real part, the phase portrait consists of an unstable focus.

From part a), we know that the eigenvalues are (7 + sqrt(49 - 16α)) / 4 and (7 - sqrt(49 - 16α)) / 4. To determine the critical values of α where the nature of the phase portrait changes, we need to set each eigenvalue equal to zero and solve for α.

Setting (7 + sqrt(49 - 16α)) / 4 = 0, we get sqrt(49 - 16α) = -7, which is not possible since the square root of a real number is always non-negative. Therefore, there are no critical values of α where the nature of the phase portrait changes. Alternatively, we can examine the sign of the discriminant, which is 49 - 16α. If the discriminant is positive, the eigenvalues are real and have opposite signs, indicating a saddle or an unstable node. If the discriminant is zero, one of the eigenvalues is zero, indicating a degenerate case. If the discriminant is negative, the eigenvalues are complex conjugates with non-zero real part, indicating a stable focus or a stable spiral. In this case, the discriminant is always positive or zero, since α can take any value. Therefore, there are no critical values of α where the nature of the phase portrait changes.

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b. The system has a unique solution when k is not equal to -2 or 10.

c. The system has infinitely many solutions when k = 10.

d. The system has no solution when k = -2.

The augmented system for the system is:

[1 0 2 -2]

[1 1 k  2]

[3 k  -2 2]

The system to have a unique solution, the rank of the coefficient matrix must be equal to the rank of the augmented matrix.

Using row reduction to reduce the augmented matrix to echelon form, we get:

[1 0 2 -2]

[0 1 k+2 4]

[0 0 (k-10)/(k+2) 10]

So, the system has a unique solution when k is not equal to -2 or 10.

The system to have infinitely many solutions, the rank of the coefficient matrix must be less than the rank of the augmented matrix, and the last row of the echelon form of the augmented matrix must be all zeros.

This occurs when:

(k-10)/(k+2) = 0

which happens when k = 10.

So, the system has infinitely many solutions when k = 10.

The system to have no solution, the last row of the echelon form of the augmented matrix must have a non-zero constant on the right-hand side.

This occurs when:

(k-10)/(k+2) ≠ 0

True for all values of k except k = -2. So, the system has no solution when k = -2.

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(a) The augmented matrix for the system is: [1   0   2  |  -2] [1   1   k  |  2] [3   k   -2 |  2] (b) The system has a unique solution when the determinant of the coefficient matrix is nonzero.

In this case, the determinant is 2k + 3. Therefore, the system has a unique solution for any value of k except k = -3/2. (c) The system has infinitely many solutions when the determinant of the coefficient matrix is zero, and the system is consistent (i.e., the right-hand side of each equation is consistent with the others).

In this case, when k = -3/2, the determinant becomes zero, and the system has infinitely many solutions.

(d) The system has no solution when the determinant of the coefficient matrix is zero, and the system is inconsistent (i.e., the right-hand side of at least one equation is inconsistent with the others). In this case, there are no specific values of k that make the system inconsistent.

To determine the unique solution, infinitely many solutions, or no solution for the system, we analyze the determinant of the coefficient matrix. If the determinant is nonzero, there is a unique solution. If the determinant is zero and the system is consistent, there are infinitely many solutions. If the determinant is zero and the system is inconsistent, there is no solution.

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A NORMAL distribution is a symmetrical probability distribution with a bell-shaped curve. It is also called a Gaussian distribution or a normal curve. This distribution is often used in statistics to represent a large number of natural phenomena, such as the distribution of height, weight, or IQ scores in a population.

The first deviation of a NORMAL distribution includes 68.2% of the data. This means that if we were to take a random sample of data from a normally distributed population, about 68.2% of the data would be within one standard deviation of the mean.

The second deviation includes 95.4% of the data. This means that about 95.4% of the data would be within two standard deviations of the mean.

The third deviation includes 99.7% of the data. This means that about 99.7% of the data would be within three standard deviations of the mean.

It is important to note that while these percentages hold true for a NORMAL distribution, they may not apply to other types of distributions.

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The equation can be used to find the distance she rides each evening is 5 ( 1.5 + 1.5 + x) = 25, the correct option is D.

Given'

Each morning Rin rides 1.5 miles to school and then rides home in the afternoon.

Later in the evening, she rides to the park and back home.

Over the 5 school days, she rides a total of 25 miles.

A solution of a system of equations is a list of numbers x, y, z,... that make all of the equations true simultaneously.

Let, 'x' miles be the total distance covered by her while going to the park and coming back home every evening.

The total distance covered by Rin while going to school and coming back is given by;

= 1.5 + 1.5 miles

Then,

The total distance that she rides every day will be;

= 1.5 + 1.5 + x

And she rides a total of 25 miles over 5 school days, so the equation that can be used to find the distance she rides each evening is given by;

5 ( 1.5 + 1.5 + x) = 25

Hence, the equation can be used to find the distance she rides each evening is 5 ( 1.5 + 1.5 + x) = 25.

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Answer:

Accumulation generally refers to the process of gradually collecting or gathering something over time. It can be used in various contexts and has different meanings depending on the subject matter. Here are a few common uses of the term "accumulation":

Financial context: In finance, accumulation refers to the process of acquiring wealth or assets over time. It can involve saving money, investing in stocks or real estate, or accumulating capital for business purposes.

Scientific context: In scientific research, accumulation often refers to the gradual buildup or increase of something, such as the accumulation of data, evidence, or knowledge. It implies the progressive growth or accumulation of measurable quantities or information.

Environmental context: In the environmental context, accumulation typically refers to the gradual buildup of substances or pollutants in an ecosystem or organism. For example, bioaccumulation refers to the process by which substances, such as toxins or heavy metals, accumulate in the tissues of living organisms over time.

Physical context: In physics, accumulation can refer to the process of collecting or gathering particles or objects in one place or area. For instance, snow accumulation refers to the gradual buildup of snowfall on the ground.

Overall, accumulation describes the act of gradually amassing or gathering something, whether it be wealth, data, substances, or other forms of accumulation, depending on the context.

Step-by-step explanation:

Answer:

the acquisition or gradual gathering of something.

"the accumulation of wealth"

a mass or quantity of something that has gradually gathered or been acquired.

plural noun: accumulations

"the accumulation of paperwork on her desk"

Step-by-step explanation:

Answer:

Step-by-step explanation:

The distance between two points can be found by using the formula

\(d = \sqrt{ ({x1 - x2})^{2} + ({y1 - y2})^{2} } \\\)

where

(x1 , y1) and (x2 , y2) are the points

From the question the points are

A(-3,-5) and B(-2,5)

The distance between them is

\( |AB| = \sqrt{ ({ - 3 + 2})^{2} + ({ - 5 - 5})^{2} } \\ = \sqrt{ {1}^{2} + ( { - 10})^{2} } \\ = \sqrt{1 + 100} \: \: \: \: \: \: \: \: \: \\ = \sqrt{101} \\ = 10.04987562...\)

We have the final answer as

Hope this helps you

Answer:

i think it is 10 but .-.

Step-by-step explanation:

i graphed it o.o

If we pick 23 fruits at random, then 7% of the time, their mean weight will be greater than 210.8 grams.

To solve this problem, we need to use the Central Limit Theorem, which states that the sampling distribution of the means of a random sample from any population will be approximately normally distributed if the sample size is large enough.

In this case, since we are picking 23 fruits at random, we can assume that the sampling distribution of the mean weight of the fruits will be approximately normal with a mean of 204 grams and a standard deviation of 16/sqrt(23) grams.

To find the weight of the fruits such that their mean weight will be greater than a certain amount 7% of the time, we need to find the z-score associated with that probability using a standard normal distribution table. The z-score can be calculated as:

z = invNorm(0.93) = 1.475

where invNorm is the inverse normal function. This means that the weight of the fruits such that their mean weight will be greater than this amount 7% of the time is:

x = 204 + 1.475*(16/sqrt(23)) = 210.8 grams (rounded to one decimal place)

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Answer:

-44!

Step-by-step explanation:

I’m going to try and explain this the best way possible through a keyboard:

14+(-22)-14-22

I usually work from left to right with these kinda problems, it helps me stay organized.

The rule for adding integers is when the signs are different you always subtract and take the sign of the LARGER number…

With that being said,

14+-22=-8

Then re write the problem

-8-14-22

Subtracting integers with different sign calls for the KCF method (keep the first number the same, change the sign, flip the second number:

Working one step at a time left to right…

-8+-14 (just add normally and keep the sign)

-22-22

Again using the kcf method,

-22+22=

-44

Hope that helps!

The woman has €123,750 left after paying taxes.

To calculate how much the woman has left after paying taxes, we need to determine her taxable income and then subtract the tax amount.

The woman earns €150,000 per annum and is allowed a tax-free pay of €45,000. This means that her taxable income is the difference between her total income and the tax-free allowance:

Taxable Income = Total Income - Tax-Free Pay

= €150,000 - €45,000

= €105,000

Next, we need to calculate the tax amount based on the taxable income. The woman pays 25 cents per euro as tax on her taxable income, which can be expressed as a tax rate of 25%.

Tax Amount = Tax Rate * Taxable Income

= 0.25 * €105,000

= €26,250

Finally, we can determine the amount the woman has left after paying taxes by subtracting the tax amount from her total income:

Amount Left = Total Income - Tax Amount

= €150,000 - €26,250

= €123,750

Therefore, the woman has €123,750 left after paying taxes.

It is important to note that tax calculations can vary depending on the specific tax laws and regulations in a particular jurisdiction. The above calculation assumes a tax rate of 25% and does not take into account any additional deductions or credits that may apply.

It is always advisable to consult with a tax professional or refer to the tax laws in the relevant jurisdiction for accurate and up-to-date information regarding tax calculations.

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Answer:

I think 36 for child and 18 for adult

Step-by-step explanation:

A cost function is a mathematical formula used to chart how production expenses will change at different output levels. Hence, \(25\) child tickets are sold and adults are \(15\).

What is the cost?

A cost function is a mathematical formula used to chart how production expenses will change at different output levels. In other words, it estimates the total cost of production given a specific quantity produced.

Let \(y\) be the number of child tickets sold

Then, \(40-y\) be the number of adults tickets sold

Each ticket costs $\(3\) and there are \(y\) child so it is of the form

\(3\)×\(y=3y\)

So, \(40-y\) tickets sold and each costs $\(5\), so it`s the cost is \(5(40-y)\).

\(3x+5(40-y)=150\\3y+200-5y=150\\200-2y=150\\-2y=150-200\\-2y=-50\\2y=50\\y=25\)

Hence, \(25\) child tickets are sold and adults are \(15\).

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Answer:

There will be sufficient evidence to conclude. A further explanation is provided below.

Step-by-step explanation:

The given values are:

\(\sigma=1.8\)

\(\alpha=0.05\)

\(n=10\)

As we know,

\(\bar{x}=\frac{\Sigma x_i}{n}\)

  \(=\frac{71.5}{10}\)

  \(=7.15\)

The standard deviation will be:

⇒  \(s=\sqrt{\frac{1}{n-1} \Sigma(x_i- \bar{x})^2 }\)

On substituting the values, we get

⇒     \(=\sqrt{\frac{1}{10-1} [(6.5-7.15)^2+...(7.7-7.15)^2]}\)

⇒     \(=\sqrt{\frac{1}{9} [(6.5-7.15)^2+...(7.7-7.15)^2]}\)

⇒     \(=0.477\)

According to the question,

Hypotheses:

\(H_o: \sigma=1.8\)

\(H_a: \sigma<1.8\)

The test statistic will be:

⇒ \(X^2=\frac{(n-1)s^2}{\sigma^2}\)

⇒       \(=\frac{(10-1)\times 0.477^2}{1.8^2}\)

⇒       \(=\frac{2.0477}{3.24}\)

⇒       \(=0.632\)

Thus the above is the correct response.

Answer:The slope of the given line is -4

Step-by-step explanation:

The average rate of change of the function f(x) on the interval [0,2] is -0.25

we can use the formula for average rate of change, which is:

\($$\frac{f(b)-f(a)}{b-a}$$\)

where a and b represent the endpoints of the interval and f(a) and f(b) represent the corresponding function values.

In this case, a = 0, b = 2, and f(x) = 3/(2x + 2).

So, we have:

\($$\frac{f(2)-f(0)}{2-0}$$$$=\frac{\frac{3}{2(2)+2}-\frac{3}{2(0)+2}}{2-0}$$$$=\frac{\frac{3}{6}-\frac{3}{2}}{2}$$$$=\frac{\frac{1}{2}-\frac{3}{2}}{2}$$$$=\frac{-1}{4}$$$$=-0.25$$\)

Therefore, the average rate of change of the function f(x) on the interval [0,2] is -0.25. This means that the function is decreasing on the interval [0,2].

The average rate of change of the function f(x) on the interval [0,2] is -0.25. This indicates that the function is decreasing on the interval. The formula for average rate of change is: (f(b) - f(a))/(b - a). We can plug in the values of a, b, and f(x) into this formula to find the average rate of change.

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Answer:

After 4 minutes

Step-by-step explanation:

After 1 min: Ant 1 is 9.75 mm underground. Ant 2 is 14.5 mm underground.

After 2 min: Ant 1 is 9.5 mm under. Ant 2 is at 14 mm under.

After 3 min: Ant 1 is 9.25 mm under.

After 4 min: Ant 1 is 9 mm under. Ant 2 is 13.5 mm under.

Ant 2 is now closer to the surface than Ant 1.

Answer:

119 inches

Step-by-step explanation:

cos 42° = \(\frac{b}{160}\)

b = 160 × cos 42° ≈ 119 in.

Answer:

6 Miles

Step-by-step explanation:

\(\frac{1}{8} *8=1\\\\\frac{5}{2}*8= \frac{40}{2}=20\)

This means Peter walks a mile every 20 minutes.

Thus, peter can walk 3 miles in 60 minutes

If peter can walk 3 miles in 60 minutes, he can walk 6 miles in 120 minutes

The hypotheses for the test are H₀: σ₁² = σ₂² and H₁: σ₁² ≠ σ₂². This is a two-tailed test to assess if there is a difference in the standard deviations of sound levels between the areas designated as "casualty doors" and operating theaters. The claim being investigated is whether or not there is a difference in the standard deviations.

The hypotheses for the test are:

H₀: σ₁² = σ₂² (There is no difference in the standard deviations of the sound levels between the areas designated as "casualty doors" and operating theaters.)

H₁: σ₁² ≠ σ₂² (There is a difference in the standard deviations of the sound levels between the areas designated as "casualty doors" and operating theaters.)

This hypothesis test is a two-tailed test because the alternative hypothesis is not specifying a direction of difference.

To substantiate the claim that there is a difference in the standard deviations, we will conduct a two-sample F-test at a significance level of 0.10, comparing the variances of the two groups.

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Answer:

k=2

Step-by-step explanation:

2x+y=1 (1)

(1)×2: 4x+2y= 2

The y-intercept of both lines must be the same as if the y-intercept is different, it will have no solutions instead of infinite solutions. In order to achieve infinite solutions, both lines must be on the same points and have same gradient and same y-intercept.

Hence, k= 2

Answer: k=2

Step-by-step explanation:

If the two equations 2x+y=1, 4x+2y=k have infinite number of solutions, it means that the two equations are dependent and represent the same line. To check this, we can find the ratio of the coefficients of x and y in the two equations:2/4 = 1/2

1/2 = k/1

From the first ratio, we can see that the coefficient of x in the second equation is twice that of the first equation.

Similarly, the coefficient of y in the second equation is twice that of the first equation. Therefore, the second equation is just a multiple of the first equation.Solving the first equation for y, we get y = 1-2x. Substituting this into the second equation, we get:4x + 2(1-2x) = k

4x + 2 - 4x = k

2 = k

Therefore, the value of k is 2.

Answer:

SAS,

Step-by-step explanation:

2 sides and the included angle.

According to the population growth law, the size of a population grows exponentially over time, with a growth rate proportional to population size. If the population doubling time is t, then the population size P can be written as:

\(P = P_0 * 2^{t/t_d)}\)

where P_0 is the initial population size, t is the time elapsed, and t_d is the doubling time.

To find the time it will take for the population to increase to 3 times its original population size, we can set \(P = 3P_0\) and solve for t:

\(3P_0 = P_0 * 2^{t/t_d}\)

Dividing both sides by \(P_0\) gives:

\(3 = 2^{t/t_d}\)

Taking the logarithm of both sides (using any base) gives:

\(log(3) = log(2^{t/t_d} )\)

Using the logarithmic identity

\(log(a^b) = b*log(a),\)

we can rewrite this as:

\(log(3) = (t/t_d)*log(2)\)

Solving for t, we get:

\(t = t_d * (log(3)/log(2))\)

Substituting \(t_d\) = 6 hours (given in the problem), we get:

\(t = 6 * (log(3)/log(2)) hours\)

Simplifying using the change of base formula

\((log(a)/log(b) = log_b(a))\), we get:

\(t = 6 * log_2(3)\) hours

Therefore, the answer is (f) None of the above.

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Correct question should be

Click on image for question

Answer:

10: -11n^5

12: 6k^2 -6k+7

Step-by-step explanation:

Ok so what your gonna do is add or subtract the ones with the same exponent.

so -15+4= -11 since they are both n^5 you can add them so your answer is:

-11n^2

now you have 8k^2-k-5k+7-2k. so you are gonna rearrange them so the same exponents are together.(keep the sign in front in front, if no sign it is positive)

8k^2-2k^2-5k-k+7

add like exponents

6k^2-6k+7

The terminal ray of α falls in the third quadrant (where cosine is negative), we can conclude that: cos(α) = -3/5.

Trigonometry is a branch of mathematics that deals with the relationships between the sides and angles of triangles. It is used to calculate the lengths of sides and angles in triangles, and to solve problems involving angles, distances, and heights. The three primary trigonometric functions are sine, cosine, and tangent, which describe the ratios of the sides of a right triangle. Other trigonometric functions include cosecant, secant, and cotangent, which are the reciprocals of the primary trig functions. Trigonometry has many applications in science, engineering, and technology, including astronomy, physics, navigation, and surveying.

Here,

Since the reference angle of α has a sine value of 4/5, we can use the Pythagorean identity sin²(θ) + cos²(θ) = 1 to find the cosine of the reference angle:

cos²(θ) = 1 - sin²(θ)

= 1 - (4/5)²

= 1 - 16/25

= 9/25

Taking the square root of both sides gives us:

cos(θ) = ± √(9/25)

= ± (3/5)

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If A=18 cm, N=23.5 ft, R=2.6 in, K=34.5 m and H=9 mm, The volume of cube H using the side length is 729 cubic millimeters.

The side length of each cube is as follows:

A=18 cm

N=23.5 ft

R=2.6 in

K=34.5 m

H=9 mm

The formula to find the volume of a cube is given as:

Volume of cube = side³

Let's substitute the given side length in the formula to find the volume of each cube.

1. For cube A with side length of 18 cmVolume of cube A = side³= 18³= 5832 cubic cm

Therefore, the volume of cube A is 5832 cubic cm.

2. For cube N with side length of 23.5 ft

Volume of cube N = side³= (23.5)³= 12812.375 cubic feet

Therefore, the volume of cube N is 12812.375 cubic feet.

3. For cube R with side length of 2.6 in

Volume of cube R = side³= (2.6)³= 17.576 cubic inches

Therefore, the volume of cube R is 17.576 cubic inches.

4. For cube K with side length of 34.5 m

Volume of cube K = side³= (34.5)³= 420175.125 cubic meters

Therefore, the volume of cube K is 420175.125 cubic meters.

5. For cube H with side length of 9 mm

Volume of cube H = side³= (9)³= 729 cubic millimeters

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Answer x= 18 y=-39

Step-by-step explanation: