True or false: A 5Ã5 real matrix has an even number of real eigenvalues

10.59 is the value of the given side b.

In our case, we know that side A has a length of 15 units and is opposite angle A, which measures 27 degrees.

Using the sine rule, we can write:

b/sin(27°) = 15/sin(40°)

To find the value of b, we can rearrange the equation:

b = (15 * sin(27°)) / sin(40°)

evaluate the trigonometric functions and calculate b:

b ≈ 10.59

Therefore, using the sine rule of the triangle, we find that the value of side b is approximately 10.59 units.

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The proportion of 12-ounce bags that contain more than the advertised 12 ounces of chips is 0.

The proportion of 12-ounce bags that contain more than the advertised 12 ounces of chips can be determined by finding the area under the normal distribution curve to the right of the mean.

To find this proportion, we can use the z-score formula:
z = (x - mean) / standard deviation

In this case, we want to find the proportion of bags that contain more than 12 ounces, so x = 12 ounces.

z = (12 - 12.5) / 0.2
z = -2.5 / 0.2
z = -12.5

Next, we need to find the cumulative probability associated with the z-score. We can use a standard normal distribution table or a calculator to find this probability.

Looking up the z-score of -12.5 in the table or using a calculator, we find that the cumulative probability is approximately 0.

Therefore, the proportion of 12-ounce bags that contain more than the advertised 12 ounces of chips is 0.

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Answer:

4.31 r 1

Step-by-step explanation:

We have to divide $17.25 into 4. 17.25 ÷ 4 = 4.31 r 1. Asnwer: every potato chip bag cost 4 dollars with 31 cents, with a penny (value: 0.01) to spend.

Answer: 1/4

Step-by-step explanation:

Reword the problem. It says what is the probability of landing on 2 or 1. That is 2 possibilities out of 8 so 2/8 = 1/4

The equation (v²* r) / (2g) represents the object's mass, m.

To solve for the object's mass, m, in the equation v = (2gm)/r, we can rearrange the equation to isolate the variable m.

1. Start with the equation v²= (2gm)/r.
2. Multiply both sides of the equation by r to eliminate the denominator: v² * r = 2gm.
3. Divide both sides of the equation by 2g: (v² * r) / (2g) = m.

The equation (v²* r) / (2g) represents the object's mass, m. This is the  answer to the question.

To further understand the equation, let's break it down. The equation v² = (2gm)/r is derived from the principle of escape velocity, which is the minimum velocity needed for an object to escape the gravitational pull of the Earth.

In the equation, v represents the velocity of the object, r is the distance from the center of the Earth to the object, and g is the acceleration due to gravity. The constant g is approximately 9.8 m/s².

By solving for the object's mass, we can determine the mass required for the object to have a specific velocity at a given distance from the Earth's center.

In conclusion, to find the object's mass (m) in the equation v² = (2gm)/r, you can use the formula (v² * r) / (2g). This equation allows you to calculate the mass of an object required to achieve a certain escape velocity at a given distance from the Earth's center.

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Answer:

175.62

Step-by-step explanation:

39.2•448=17561.6

17561.6/100=175.616

=175.62

The slope of the tangent to the parametric curve at the indicated point is -1 + πcos(πt)

Given parametric equations:

x = t + cos(πt)

y = -t + sin(πt)

To find the slope of the tangent, we need to differentiate x and y with respect to t.

Differentiating x with respect to t:

dx/dt = d/dt(t + cos(πt))

= 1 - πsin(πt) [Using the chain rule]

Differentiating y with respect to t:

dy/dt = d/dt(-t + sin(πt))

= -1 + πcos(πt)

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Answer:

  C.  142°

Step-by-step explanation:

You want the angle between vectors u=3i+√3j and v=-2i-5j.

There are a number of ways the angle between the vectors can be found. For example, the dot-product relation can give you the cosine of the angle:

  u•v = |u|·|v|·cos(θ) . . . . . . where θ is the angle of interest

You can find the angles of the vectors individually, and subtract those:

  u = |u|∠α

  v = |v|∠β

  θ = α - β

When the vectors are expressed as complex numbers, the angle between them is the angle of their quotient:

  \(\dfrac{\vec{u}}{\vec{v}}=\dfrac{|\vec{u}|\angle\alpha}{|\vec{v}|\angle\beta}=\dfrac{|\vec{u}|}{|\vec{v}|}\angle(\alpha-\beta)=\dfrac{|\vec{u}|}{|\vec{v}|}\angle\theta\)

This method is used in the calculation shown in the first attachment. The angle between u and v is about 142°.

A graphing program can draw the vectors and measure the angle between them. This is shown in the second attachment.

__

Additional comment

The approach using the quotient of the vectors written as complex numbers is simply computed using a calculator with appropriate complex number functions. There doesn't seem to be any 3D equivalent.

The dot-product relation will work with 3D vectors as well as 2D vectors.

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Given equations are (5.1) z 4 +16=0 and z 3 −27=0.(5.1) z 4 +16=0z⁴ = -16z = 2 * √2 * i, 2 * (-√2 * i), -2 * √2 * i, -2 * (-√2 * i)Therefore, the roots of the equation are z = 2^(3/4) * i, 2^(1/4) * i, -2^(3/4) * i, -2^(1/4) * i.(5.2) z 8 −16i=0z⁸ = 16i z = 2^(1/8) * i, 2^(3/8) * i, 2^(5/8) * i, 2^(7/8) * i, -2^(1/8) * i, -2^(3/8) * i, -2^(5/8) * i, -2^(7/8) * i

Therefore, the roots of the equation are:

z = 2^(1/8) * i, 2^(3/8) * i, 2^(5/8) * i, 2^(7/8) * i, -2^(1/8) * i, -2^(3/8) * i, -2^(5/8) * i, -2^(7/8) * i. z 8 +16i=0z⁸ = -16i z = 2^(1/8) * i, 2^(3/8) * i, 2^(5/8) * i, 2^(7/8) * i, -2^(1/8) * i, -2^(3/8) * i, -2^(5/8) * i, -2^(7/8) * i

Therefore, the roots of the equation are:

z = 2^(1/8) * i, 2^(3/8) * i, 2^(5/8) * i, 2^(7/8) * i, -2^(1/8) * i, -2^(3/8) * i, -2^(5/8) * i, -2^(7/8) * i.

First of all, we need to know that a polynomial equation of degree n has n roots and they may be real or imaginary. Roots are also known as zeros or solutions of the equation.If the degree of the polynomial is n, then it can be written as an nth degree product of the linear factors, z-a, where a is the zero of the polynomial equation, and z is any complex number. Therefore, the nth degree polynomial can be factored into the product of n such linear factors, which are known as the roots or zeros of the polynomial.In the given equations, we need to find the roots of each equation. In the first equation (5.1), we have z⁴ = -16 and z³ = 27. Therefore, the roots of the equation:

z⁴ + 16 = 0 are:

z = 2^(3/4) * i, 2^(1/4) * i, -2^(3/4) * i, -2^(1/4) * i.

The roots of the equation z³ - 27 = 0 are:

z = 3, -1.5 + (3^(1/2))/2 * i, -1.5 - (3^(1/2))/2 * i.

In the second equation (5.2), we need to find the roots of the equation z⁸ = 16i and z⁸ = -16i. Therefore, the roots of the equation z⁸ - 16i = 0 are:

z = 2^(1/8) * i, 2^(3/8) * i, 2^(5/8) * i, 2^(7/8) * i, -2^(1/8) * i, -2^(3/8) * i, -2^(5/8) * i, -2^(7/8) * i.

The roots of the equation z⁸ + 16i = 0 are also the same.

Thus, we can find the roots of polynomial equations by factoring them into linear factors. The roots may be real or imaginary, and they can be found by solving the polynomial equation.

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In this scenario, the domain would be the set of all possible values for the amount of time it takes Sammy Speedster to drive from Houston to San Antonio. Since he is driving on a daily basis, the domain could be considered a continuous range from zero to some maximum value, perhaps 10 hours.

It's possible that Sammy could complete the trip in less than 3 hours if he were driving at a very high speed, but this would not be a common occurrence. Therefore, a reasonable domain could be considered to be between 3 and 10 hours.

The range, on the other hand, would be the set of all possible distances that Sammy could drive in the allotted time. Since we know that the distance is a constant 200 miles, the range would simply be 200 miles. It's possible that Sammy could drive more than 200 miles in a day if he were assigned additional routes, but this would not be relevant to this scenario.

In summary, a reasonable domain for Sammy's logbook would be between 3 and 10 hours, and the range would be a constant 200 miles.

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Answer:

intersecting lines will cross at the point

A stick has a length of 5 units and the stick is then broken at two points, chosen at random, then the probability that all three resulting pieces are shorter than 3 units is 16%.

Total length of the stick = 5 units

The stick is broken into pieces = 3

The equal length of the stick = 5/3

The equal length of the stick = 1.67

The probability that all three resulting pieces are shorter than 3 units = 2/5 × 2/5

The probability that all three resulting pieces are shorter than 3 units = 4/25

The probability that all three resulting pieces are shorter than 3 units = 0.16

The probability that all three resulting pieces are shorter than 3 units = 16%

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Test the claim that the proportion of people who own cats is significantly different than 70% at the 0.02 significance level. The p-value is 0.024.

The null and alternative hypotheses for the claim that the proportion of people who own cats is significantly different than 70% at the 0.02 significance level are:

H0: p = 0.7 (null hypothesis

)H1: p ≠ 0.7 (alternative hypothesis)

The test is a two-tailed test because the alternative hypothesis includes not equal to (<>) which means either p is less than 0.7 or greater than 0.7

Based on a sample of 500 people, 62% owned cats.

This means that the sample proportion, p = 0.62.

To calculate the p-value, we will use the z-test statistic.

The formula for calculating the z-test statistic is given as:

z = (p - P) / √(PQ/n) where P is the hypothesized proportion (P = 0.7), Q is the complement of P (Q = 1 - P), and n is the sample size.

Using the given values in the formula, we have; z = (0.62 - 0.7) / √(0.7 × 0.3 / 500) = -2.52

The p-value for a two-tailed test at 0.02 level of significance is obtained from the standard normal table.

The area in both tails beyond the z-score of 2.52 is 0.012.

Therefore, the p-value is:

p-value = 2 × 0.012 = 0.024

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Total number of five letter strings formed by A,B,C and D with repetitions allowed

={4x4x4x4x4 = 4 power 5 = 1024

Now, fix BAD in a string at one place then we have 2 more places to be filled with 4 letters, total number of such strings

=4x4=16

Here, BAD can be at any of the 3 positions,

Hence the total number of strings with BAD in it

= 3 x 16=48

Now, The total number of strings not containing BAD

=1024-48

=976

Using 26 letters, the number of 5-letter words that can be formed when the letters are different is determined as follows: 26P5 = 26 × 25 × 24 × 23 × 22 = 7883600 different words.

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1. The exponential form of the equation \(log_{x} 4 = - 2\) will be;

⇒ x⁻² = 4

2. The value of √e⁷/e⁵ will be;

⇒ e

3. The equivalent expression of 3 will be;

⇒ ln e³

What is an expression?

Expression in math is defined as the collection of the numbers, variables and functions by using signs like addition, subtraction, multiplication, and division.

Given that;

1. The expression is the equation \(log_{x} 4 = - 2\).

2. The equation is √e⁷/e⁵.

3. The number is 3.

Now,

The exponential form of the equation \(log_{x} 4 = - 2\) is calculated as;

\(log_{x} 4 = - 2\)

By the definition of logarithmic, we get;

4 = x⁻²

Hence, The exponential form of the equation \(log_{x} 4 = - 2\) will be;

⇒ x⁻² = 4

2. The equation is √e⁷/e⁵.

Solve as;

√e⁷/e⁵ = √ e ⁷ ⁻ ⁵

           = √ e²

           = e

Thus,  The value of √e⁷/e⁵ will be;

⇒ e

3. Since, by the definition of logarithmic;

\(ln_{e} e = 1\)

So, By option 1;

\(ln_{e} e^3\) = \(1 * 3\) = \(3\)

Thus, The equivalent expression of 3 will be;

⇒ ln e³

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6/10 is the fraction of days the cafetaria offered an apple as a fruit choice. The equivalent form of decimal is 0.6, the equivalent form of percentage is 60%, and the equivalent form of fraction is 3/5.

6/10 is equal to 3/5 because 3/5 is the simplified form of 6/10. To simplify the fraction, determine the greatest common factor (GCF) of the numerator 6 and the denominator 10 first.

The GCF of 6 and 10 is 2. Therefore, you divide the numerator and the denominator by 2 to get the simplified form, like this: \(\frac{6}{10}=\frac{6\div 2}{10\div 2}=\frac{3}{5}\).

You can convert 6/10 to a decimal using long division:

      0.6  

10 / 6 0

      6 0   -

         0

6 divided by 10 is equal to 0.6. This is the decimal form of the fraction 6/10.

Finally, to get the percentage form, you can multiply the fraction by 10/10: \(\frac{6}{10}=\frac{6}{10}\times \frac{10}{10}=\frac{60}{100}=60\%\).

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Answer:

B. 28 + 14 = x

Step-by-step explanation:

Susie bought 14 dolls this week. Last week she had 28 dolls. determine how many dolls Susie has now.

using this info we know that we must find the sum of both numbers.

Hence, Answer B has the correct equation

When an inequality is multiplied or divided by a negative number, the inequality sign will flip, meaning it will change its direction. For example, if you have a > b and you multiply or divide both sides by a negative number, the inequality will become a < b. This is because the relationship between the values reverses when multiplied or divided by a negative number.

Explanation:

When an inequality is multiplied or divided by a negative number, the direction of the inequality sign is flipped. This is because multiplication or division by a negative number, results in a reversal of the order of the numbers on the number line.

To see why this happens, consider the following example:

Suppose we have the inequality x < 5. If we multiply both sides of this inequality by -1, we get -x > -5. Notice that we have flipped the inequality sign from "<" to ">". This is because multiplying by -1 changes the sign of x to its opposite, and also changes the sign of 5 to its opposite, resulting in a reversal of the order of the numbers on the number line.

Similarly, if we divide both sides of the inequality x > 3 by -2, we get (-1/2)x < (-3/2). Here, we have again flipped the inequality sign from ">" to "<". This is because dividing by a negative number also changes the order of the numbers on the number line.

In general, if we have an inequality of the form a < b or a > b, where a and b are real numbers, and we multiply or divide both sides by a negative number, we obtain:

If we multiply by a negative number, the inequality sign is flipped. For example, if a < b and c < 0, then ac > bc.

If we divide by a negative number, the inequality sign is also flipped. For example, if a > b and c < 0, then a/c < b/c.

Therefore, it is important to be mindful of the signs of the numbers involved when performing operations on inequalities. If we multiply or divide by a negative number, we must flip the direction of the inequality sign accordingly.

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B) Given

Set y=65 and solve for x, as shown below

Then, solve the quadratic equation using the quadratic formula,

The function is not valid for negative values of x; therefore, the solution can only be x=7.05065 which can be rounded to x=7. Furthermore, x=7 corresponds to the year 2001. The answer to part B is 2001.

The level of significance in hypothesis testing is the probability of: c. rejecting a true null hypothesis. In hypothesis testing, the critical value is:
a. a number that establishes the boundary of the rejection region.

Probability is a branch of mathematics in which the chances of experiments occurring are calculated. It is by means of a probability, for example, that we can know from the chance of getting heads or tails in the launch of a coin to the chance of error in research. In statistics , a null hypothesis is a statement that one seeks to nullify with evidence to contrary most commonly it is a statement that the phenomenon being studied produces no effect on makes no difference.

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Answer:x+(-4)=12 the answer is 8

Step-by-step explanation:

Answer:

can you please explain the different way

Step-by-step explanation:

Answer:

31 years

Step-by-step explanation:

65000*(1.07) ^31 is around $529000

however, 65000*(1.07) ^30 is around $491000

so you would need 31 years to gain more than $500,000.

It will take approximately 30 years to reach $500,000 in savings with an investment that earns an average of 7% per year.

To determine the number of years it will take to reach $500,000 in savings with an investment that earns an average of 7% per year, we can use the given investment model equation: y = 65000(1.07)ˣ.

We need to find the value of x, which represents the number of years.

Setting y = $500,000, we can solve for x:

500,000 = 65,000(1.07)ˣ

500,000/65,000 = (1.07)ˣ

100/13 = (1.07)ˣ

To solve for x, we take the logarithm of both sides:

ln 100/13 = ln (1.07)ˣ

ln 100/13 = x ln (1.07)

x = (ln 100/13)/(ln (1.07))

x = 30

Therefore, it will take approximately 30 years to reach $500,000 in savings with an investment that earns an average of 7% per year.

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The solution to the equations obtained using inverse trigonometric function values are;

1. x ≈ 0.65

4. x ≈ 0.95

Trigonometric functions indicates the relationships between the angles in a right triangle and two of the sides of the triangle. Trigonometric functions are periodic functions.

The value of x is obtained from the inverse trigonometric function of the output value of the trigonometric function, as follows;

The inverse function for sine is arcsine

The inverse function for cosine is arccosine

The inverse function for the tangent of an angle is arctangent

1. sin(x) = 0.6051

Therefore; x = arcsine(0.6051) ≈ 0.65 radians

The value of x in the interval [0·π, 2·π] is x ≈ 0.65

4. tan(x) = 1.3972

Therefore, x = arctan(1.3972) ≈ 0.95

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Answer:

-20z² + 13z - 2.

Step-by-step explanation:

hello !

you use the F.O.I.L method to multiply these two. first, you multiply the first terms, which are:

(-4z)(5z) = -20z²

then, the outside terms, which are:

(-4z)(-2) = 8z

then, the inside terms, which are:

(1)(5z) = 5z

then, lastly, the last terms, which are:

(1)(-2) = -2

Therefore, we get:

-20z² + 8z + 5z - 2.

combine like terms, and the answer is:

-20z² + 13z - 2.

The triangles ΔKLM and ΔEFG can be proven similar using both SSS and SAS similarity theorems.

In this question, we need to determine whether the triangles can be proven similar using the SSS or SAS similarities theorems.

For given diagrams,

the ratio of the corresponding sides is:

KM/EG = 8/24

            = 1/3

KL/EF = 6/18

          = 1/3

and ML/GF = 5/15

                  = 1/3

The sides of both triangles is proportional .

So by SSS similarity theorem, we have ΔKLM ≈ ΔEFG

Also, ML/GF = 1/3

∠L ≅ ∠F

KL/EF = 1/3

So by SAS similarity theorem, we have ΔKLM ≈ ΔEFG

Therefore, the triangles can be proven similar using both SSS and SAS

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The figure associated to given question is as shown below.

Answer:

C - 768cm for Plato

Step-by-step explanation:

From the given bar graph, the average number of students who are afraid of spider and snakes is of 15.

A bar graph shows the absolute frequency of each observation in the data-set, that is, the number of times that each variable is observed.

Hence, in the context of this problem, from the bar graph on the image, the number of students that are afraid of each thing are:

The average between two values is given by the sum of the two values divided by two.

Hence, the average number of students who are afraid of spiders and snakes is calculated as follows:

M = (18 + 12)/2 = 30/2 = 15.

The bar graph is missing and is given by the image at the end of the answer.

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Answer:

15

Step-by-step explanation:

got it right on quiz

(a) Find the dual of the LP.Primal problem isminimize \($b_1y_1+C_1x_1+...+C_nx_n$\) subject to \($a_{11}x_1+a_{12}x_2+...+a_{1n}x_n \leq\) \(b_1$...$a_{m1}x_1+a_{m2}x_2+...+a_{mn}x_n \leq b_m$ and $x_1, x_2,\)..., x_n\(\geq 0$\)

Let us find the dual of the above primal problem.

Dual problem ismaximize \($b_1y_1+...+b_my_m$\)subject to \($a_{11}y_1+a_{21}y_2+...+a_{m1}y_m \leq\)\(C_1$...$a_{1n}y_1+a_{2n}y_2+...+a_{mn}y_m \leq C_n$\)

and\($y_1, y_2, ..., y_m \geq 0$\)

(b) Find the standard form of the LP and dual.Standard form of the primal problem isminimize \($b_1y_1+C_1x_1+...+C_nx_n$\)subject to \($a_{11}x_1+a_{12}x_2+...+a_{1n}x_n +s_1 = b_1$...$a_{m1}x_1+a_{m2}x_2+...+a_{mn}x_n +s_m = b_m$\) and\($x_1, x_2, ..., x_n, s_1, s_2, ..., s_m \geq 0$\)

Standard form of the dual problem ismaximize \($b_1y_1+...+b_my_m$\)subject to \($a_{11}y_1+a_{21}y_2+...+a_{m1}y_m \leq 0$...$a_{1n}y\)

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