Don't understand this question

"The eigenvalues of the square of two matrices are not necessarily equal to the square of the eigenvalues of each of the matrices". The statement is incorrect.

Eigenvalues of the square of two matrices (A*B) are not necessarily equal to the square of the eigenvalues of each matrix (A and B).

In general, eigenvalues of the product of two matrices do not follow the same relationship as their individual eigenvalues.

In fact, there is no simple relationship between the eigenvalues of a matrix and the eigenvalues of its square. The eigenvalues of a matrix and its square can be different, and even if they are the same, their relationship is not necessarily as simple as taking the square root.

However, if the two matrices commute, meaning A*B = B*A, their eigenvalues may exhibit some specific relationships, but this is not guaranteed in all cases.

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Answer:

Never second guess yourself

Step-by-step explanation:

James will fully clear the loan after approximately 12 years when the remaining balance reaches zero.

To determine the number of years it will take for James to fully clear the loan, we need to calculate the remaining balance after each payment and divide the initial loan amount by the annual payment until the remaining balance reaches zero.

The loan amount is 9000 euros, and James pays off 770 euros each year. Since the interest is charged at a rate of 3% of the original amount per annum, the interest for each year will be \(0.03 \times 9000 = 270\) euros.

In the first year, James pays off 770 euros, and the interest on the remaining balance of 9000 - 770 = 8230 euros is \(8230 \times 0.03 = 246.9\)euros. Therefore, the remaining balance after the first year is 8230 + 246.9 = 8476.9 euros.

In the second year, James again pays off 770 euros, and the interest on the remaining balance of 8476.9 - 770 = 7706.9 euros is \(7706.9 \times 0.03 = 231.21\) euros. The remaining balance after the second year is 7706.9 + 231.21 = 7938.11 euros.

This process continues until the remaining balance reaches zero. We can set up the equation \((9000 - x) + 0.03 \times (9000 - x) = x\), where x represents the remaining balance.

Simplifying the equation, we get 9000 - x + 270 - 0.03x = x.

Combining like terms, we have 9000 + 270 = 1.04x.

Solving for x, we find x = 9270 / 1.04 = 8913.46 euros.

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In order for the exponential function and the tangent line to be equivalent at a certain point, their function values and their first derivatives must be equal at that point.

At a given point, if the function values of an exponential function and its tangent line are equal, it means that they have the same value and slope at that point.

This requires that their first derivatives at that point are equal. The first derivative of an exponential function is also an exponential function, so the derivative of the tangent line must also be an exponential function with the same slope as the original function.

Therefore, the two functions must have the same first derivative at that point. This condition is necessary for the two functions to be equivalent at that point.

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This is the general solution to the homogeneous differential equation.

To find the general solution to the homogeneous differential equation:

d^2y/dt^2 - 18(dy/dt) + 145y = 0

We can assume a solution of the form `y(t) = e^(rt)` and substitute it into the differential equation. This leads to the characteristic equation:

r^2 - 18r + 145 = 0

We can solve this quadratic equation to find the roots `r1` and `r2`. Once we have the roots, we can construct the general solution using the formulas:

y1(t) = e^(r1t)

y2(t) = e^(r2t)

Given that `y1(0) = 0` and `y2(0) = 1`, we can determine the specific values of `r1` and `r2` that satisfy these conditions. Let's solve the characteristic equation first:

r^2 - 18r + 145 = 0

Using the quadratic formula `r = (-b ± √(b^2 - 4ac))/(2a)`, we have `a = 1`,

`b = -18`, and `c = 145`. Substituting these values into the quadratic formula, we get:

r = (18 ± √((-18)^2 - 4(1)(145))) / (2(1))

Simplifying further:

r = (18 ± √(324 - 580)) / 2

r = (18 ± √(-256)) / 2

Since the discriminant is negative, we have complex roots:

r = (18 ± 16i) / 2

r = 9 ± 8i

Therefore, the roots are `r1 = 9 + 8i` and `r2 = 9 - 8i`.

Now we can write the general solution:

y(t) = c1 * y1(t) + c2 * y2(t)

Substituting the values for `y1(t)` and `y2(t)`:

y(t) = c1 * e^((9 + 8i)t) + c2 * e^((9 - 8i)t)

This is the general solution to the homogeneous differential equation.

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Given data:

Sensitivity of the third stage device = 0.5 V/N

The accuracy of the instrument is specified as: ±0.4% FSD or ±1% of the reading, whichever is greater. Force applied to the system is 11.3 V on the 30V range. The new sensitivity is 0.7 V/N, and the voltmeter is switched to the 15V range.i. Range of the applied force:Given that, the instrument displays 11.3 V on the 30V range.Since the voltage is proportional to the force, hence, we can say that the voltage is directly proportional to force.

We can also use the voltage formula,Voltage = K * Force where K is the constant of proportionality.

So, V1/F1 = V2/F2 where V1 and F1 are initial voltage and force, and V2 and F2 are final voltage and force.Let's assume the range of force applied is F, and the range of voltage is 30 V.Then, 0.5 = 30 / K, K = 60 N/VWhen the force applied is F, we have:V = K * FGiven that the voltage reading is 11.3 V.Then,F = V/K= 11.3/60= 0.188 Nii. New voltage reading:New sensitivity of the system = 0.7 V/NThe voltmeter is switched to the 15V range.In this case, we can calculate the range of force, which will be measurable by the new range of voltage.Let's assume the new range of force applied is F2, and the range of voltage is 15 V.Then, 0.7 = 15 / K, K = 21.43 N/VWhen the force applied is F2, we have:V = K * F2Let's assume the new voltage reading is V2.Now, we can find F2 as:F2 = V2 / KThe maximum force that can be applied for the new voltage reading is:F2 = 15 / 21.43= 0.7 NSo, the new voltage reading now lies in the range of 0-15 V.

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The weakest base is C5H5N (pyridine) with Kb = 1.7 × 10^(-9). The correct answer is C.

The strength of a base is determined by its ability to accept or donate a pair of electrons. In general, a stronger base has a higher tendency to accept or donate electrons compared to a weaker base.

In the given options, the bases are characterized by their Kb values. Kb (base dissociation constant) represents the equilibrium constant for the reaction of a base with water to form the corresponding conjugate acid and hydroxide ions.

Comparing the Kb values provided:

A smaller Kb value indicates a weaker base because it corresponds to a lower concentration of hydroxide ions in solution. Therefore, in this case, C5H5N (pyridine) with a Kb value of 1.7 × 10^(-9) is the weakest base among the given options. The correct answer is C.

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The given expression is a simplified algebraic equation: (1/2) * a^2 - 3b + 2c. It represents a combination of variables a, b, and c with their respective coefficients.

Utilizing symbols and operations, an algebraic equation illustrates the equivalence or inequivalence of two expressions. These generated expressions may hold variables that have varying values.

The premise centered around calculus is to arrive at a solution by acquiring the correct value(s) of these variable(s), ultimately fulfilling the outlined specification in the problem. Algebraic equations can range from uncomplicated linear problems to elaborate polynomials and trigonometric functions.

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Answer:

The constant term is 240. A constant term represents a fixed value. In other words, a term that does not change.

Step-by-step explanation:

In the polynomial expression given, the first and second terms are dependent of x, which means whatever the value x is, the terms will change. For example, if x = 2, we have -7(4) + 32(2) + 240. As you can see the constant never changes because it does not rely on a variable; it is constant.

9514 1404 393

Answer:

  Will’s Wrapping Company needs 9,980 mm^2 of paper to wrap the chocolate bar.

Step-by-step explanation:

The formula for the area of a rectangular prism can be written ...

  A = 2(LW +H(L+W))

  A = 2(90·50 +3.5(90 +50)) = 2(4500 +3.5(140)) = 2(4990)

  A = 9980 . . . square millimeters

Answer:

\(\frac{1}{343}\)

Step-by-step explanation:

Using the rule of exponents

\(a^{-m}\) ⇔ \(\frac{1}{a^{m} }\) , then

\(7^{-3}\)

= \(\frac{1}{7^{3} }\) = \(\frac{1}{343}\)

Answer:

D. Neither.

Step-by-step explanation:

y = 7x + 2.

I am not sure what you want to find, but I assume you put the coordinates into the equation and find whether they fit.

A. (3, 15).

y = 7 * 3 - 2 = 21 - 2 = 19

y is not equal to 19, so A does not work.

B. (-1, -10).

y = 7 * -1 -2 = -7 - 2 = -9

y is not equal to -9, either, so B does not work.

C. A combination of the two coordinates, which we know do not work.

D. Neither. Neither of the coordinates work, so this is the answer.

Hope this helps!

Answer:

neither

Step-by-step explanation:

y=7x-2    for (3,15)

y=7(3)-2

y=19 not solution

(-1.10)

y=-7-2=-9 not a solution

Answer:

the answer is 30% of the workers have output more than 70 units.

Step-by-step explanation:

Answer: I believe the answer is 25%.

Answer:

The approximate value of the scale is 1:67

or the actual value without approximation is 1: 66 2/3 ( 66 while number , two over three)

Step-by-step explanation:

Here, we want to figure out the scale in inches of the drawing to the actual object.

The actual object is 500 ft by 700 ft

while the drawing is 90 inches by 126 inches

Mathematically, we know that 12 inches = 1 foot

So the actual object will be;

500(12) by 700(12)

= 6000 inches by 8400 inches

Now let’s make a division to get the scale;

6000/90 by 8400/126

we get 66.67 as answers on both ends

This is approximately equal to 67

So the scale we have here is 1:67

A page frοm a fictiοn bοοk is therefοre much thicker than a page frοm a dictiοnary.

Three-dimensiοnal space is measured by vοlume; tο vοlumize is tο make fuller. The area between sides is thick; tο thicken wοuld be tο widen.

We can cοmpare the thicknesses οf the narrative bοοk's and the dictiοnary's pages by assuming that they are bοth made frοm the same size and substance:

Each page frοm the tale bοοk is 3.5 × 10⁻² centimeters thick.

A dictiοnary page has a thickness οf 6 × 10⁻³ centimeter.

We must represent the thicknesses using identical units in οrder tο directly cοmpare them. The fοllοwing fοrmula can be used tο cοnvert a stοry bοοk page's thickness frοm millimeters:

1 centimeter = 10 millimeters

Therefοre, 3.5 - 10⁻² centimeter = (3.5 x 10) - (10⁻² x 10) millimeters

= 35 - 0.1 millimeters

= 34.9 millimeters

Nοw we can cοmpare the thicknesses directly:

The thickness οf a page frοm the stοry bοοk is 34.9 millimeters.

The thickness οf a page frοm the dictiοnary is 6 x 10⁻³ centimeter = 0.06 millimeters.

Therefοre, a page frοm the stοry bοοk is much thicker than a page frοm the dictiοnary.

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Complete question:

A page from a story book has a thickness of 3.5 x 10⁻²centimeter and a page from a dictionary has a thickness of 6 x 10⁻³.  Which book has a thicker page?

Answer:

Jake has 30 cars

Step-by-step explanation:

3 times 10 equals 30

Answer:

Step-by-step explanation:

\(17. (a^{m})^{n}=a^{m*n}\\\\a^{m}*a^{n}=a^{m+n}\\\\-3k^{2}*(4k^{5})^{3}=-3k^{2}*4^{3}*k^{5*3}\\\\ = -3k^{2}*64*k^{15}\\\\= (-3)*64*k^{2+15}\\\\= - 192k^{17}\)

\(19. \dfrac{a^{m}}{a^{n}}=a^{m-n}\\\\\\\dfrac{(-7p^{4})*(-8p^{5})}{2p^{3}}= \dfrac{(-7)*(-8)*p^{4}*p^{5}}{2p^{3}}\\\\\\=(-7)*(-4)*p^{4+5-3} \\\\= 28p^{6}\\\)

\(20)\dfrac{15a^{16}b^{11}}{(3a^{4}b^{2})^{3}}=\dfrac{15a^{16}b^{11}}{3^{3}*a^{4*3}*b^{2*3}}\\\\\\=\dfrac{15a^{16}b^{11}}{27*a^{12}*b^{6}}\\\\=\dfrac{5*a^{16-12}*b^{11-6}}{9}\\\\\\=\dfrac{5a^{4}b^{5}}{9}\)

Total savings after 7 weeks : $140

Total savings after w weeks : $(70 + 10w)

Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.

Given is a phrase : Taub is saving up to buy a new bicycle. She already has $70 and can save an additional $10 per week using money from her after school job.

Taub will have a total of -

70 + 7 x 10 = $140

The expression that represents the amount of money Taub would have saved in [w] weeks is -

y = 70 + 10w

Therefore -

Total savings after 7 weeks : $140

Total savings after w weeks : $(70 + 10w)

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Answer:

The skeleton is 1150 yrs old.

Step-by-step explanation:

To get this answer you would take 5750 and divide by 5 because the problem say 1/5th. This would give you the equation 5750/5 = 1150.

Answer:

The third one

Step-by-step explanation:

A linear relationship would create a straight line when graphed therefore the answer is the third one

Option D. Doing inferential statistics. Inferential statistics is the process of using sample statistics to draw conclusions about population parameters.

This involves making inferences about a population based on data collected from a sample, and using statistical methods to estimate the true values of population parameters, such as the mean or proportion.

Descriptive statistics, on the other hand, involves summarizing and describing the characteristics of a sample or population, without making any inferences about the larger population.

Calculating the confidence level and finding the significance level are important components of inferential statistics, as they help to assess the accuracy and reliability of the estimates made based on the sample data. However, these are not the primary processes involved in using sample statistics to draw conclusions about population parameters.

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The process of using sample statistics to draw conclusions about population parameters is called: group of answer choices

A. Calculating the confidence level.

B. Calculating descriptive statistics.

C. Finding the significance level.

D. Doing inferential statistics.

use sin

sin(50) = x/6

sin(50) x 6 = x

x = ~4.5963

The five number summary for the set of data is given as follows:

The first step in constructing the five number summary is showing the entire data-set, which is defined from the frequency table, which gives the number of times that each observation appears.

The entire data-set is given as follows:

8, 8, 9, 10, 10, 11, 11, 11, 12, 12, 12, 12, 13, 14, 16.

From this, we already have that:

The data-set has 15 values, which is an odd cardinality, thus the median is the middle element, which is of 11.

Then the data-set can be divided into two halves, as follows:

Then the quartiles are obtained as follows:

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Answer:

5.1

Step-by-step explanation:

To solve this equation I will use the formula a²+b²=c². For these terms I will represent the missing value as the variable a. The equation should be renewed as this: a²+6.4²=8.2², simplified: a²+40.96=67.24. I will now subtract 40.96 from 67.24 to get "a" by itself, as of which now I have a²=26.28. Next I square root both values: √a² =√26.28. The final answer is "a"= 5.1264022471905, otherwise, when rounded, "5.1". Hopefully this helps. A word of advice, when a problem gives you two values for a triangle, always refer to the equation a²+b²=c², as you will always find the missing value. Also remember that the legs cannot be of greater value than the hypotenuse which is the diagonal line. The hypotenuse is always "c".

Answer:

x=16

Step-by-step explanation:

The length AC of the triangle ABC is approximately 12.083 centimeters.

The law of sine is a relationship between the sides and the angles of the triangle, which is defined below:

AB / sin C = AC / sin B = BC / sin A

Where:

First, determine the measure of angle C:

AB / sin C = BC / sin A

sin C = (AB / BC) · sin A

sin C = (8.2 / 13.5) · sin 81°

C ≈ 36.865°

Second, determine the measure of angle B:

B = 180° - A - C

B = 180° - 81° - 36.865°

B = 62.135°

Third, determine the length of side AC:

AC / sin B = BC / sin A

AC = BC · (sin B / sin A)

AC = 13.5 · (sin 62.135° / sin 81°)

AC ≈ 12.083 cm

The length AC is approximately equal to 12.083 centimeters.

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As the sample size rises, the sample distribution approaches a normal distribution.

The sample distribution approaches a normal distribution as the sample size grows. The sampling distribution's mean equals the population's mean if the number of consecutive samples is "infinite".

The Gaussian distribution is the official name for the normal distribution. However, the word "normal" was coined in the nineteenth century after a scientific inquiry revealed that numerous natural events appeared to "deviate from normal" from their typical values.

In his 1889 work Natural Inheritance, naturalist Sir Francis Galton popularized the notion of normal variability as the standard curve.

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Answer: 7%

(Hope this is right.)

Step-by-step explanation:

Let's solve this using the information we have and an equation.

Shane: $32,000 - (Given)

Theresa: 18,000+14x, if x=1,160 - (Given)

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

Step two: (Theresa) 14(1,160) =16,240 (Algebra)

Step three: (Theresa) 18,000+16,240=34,240 (Algebra, given.) - cost of Theresa's car.

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

Finally,

They're asking for how much more she paid for her car as a percentage of what Shane paid.

34,240-32,000=2,240 and

2,240/32,000=0.07

0.07x100=7

Answer 7% more than what Shane paid.

Answer:

1228 is your answer

Step-by-step explanation: