true or false let a be a real square matrix. if a is diagonalizable then a is symmetric

Answer:

-2, -1/2, 0, 1/4

Step-by-step explanation:

As an = n - 3

when n = 1

then we get

a = 1 - 3

a = -2

when n = 2

then we get

2a = 2 - 3

2a = -1

a = -1/2

when n = 3

then we get

3a = 3 - 3

3a = 0

a = 0

when n = 4

then we get

4a = 4 - 3

4a = 1

a = 1/4

so the first four terms of the sequence are: -2, -1/2, 0, 1/4

Answer:

Step-by-step explanation:

Sol'n,

The base length of //gm is let to be "b" and the height can be let as "h"

so ,acc to q,

b = h+7

or , h= b-7...(i)

and, the area is 120 sq. ft

Now, Area= b * h

or, 120=b (b-7) {from eqn (i)}

or, 120= b^2- 7b

or, b^2-7b-120=0

Now if we just continue on using mid term factorization,

we get b as 15 or -8 ft and since it cant be negative the base is 15 ft

Finally, the height becomes h=15-7=8 ft...  

Answer:

c. There is no ideal debt-equity ratio, because it varies as per the industry.

Step-by-step explanation:

Answer:

Step-by-step explanation: im ok at these i beleve its Y = 4'2

The probability that someone who buys 3 packages will return exactly 1 of them is approximately 0.2448, or 24.48%.

Let's start by calculating the probability of finding at most 1 defective diskette in a single package. We can use the binomial distribution formula for this:

P(X ≤ 1) = P(X = 0) + P(X = 1) = (0.99)¹⁰ + 10(0.01)(0.99)⁹

The first term represents the probability of finding 0 defective diskettes in the package, and the second term represents the probability of finding exactly 1 defective diskette in the package. We can use the formula for combinations to calculate the second term: 10 choose 1.

Using a calculator, we can simplify this expression to:

P(X ≤ 1) = 0.9044

Now, let's consider the three packages. We want to find the probability that exactly one of them will be returned. This means that two of the packages will have at most 1 defective diskette, and one of them will have more than 1 defective diskette.

We can use the binomial distribution again to calculate this probability. Let's define a success as a package with at most 1 defective diskette, and a failure as a package with more than 1 defective diskette. The probability of success is 0.9044, as we calculated earlier, and the probability of failure is 1 - 0.9044 = 0.0956.

Using the binomial distribution formula, we can calculate the probability of exactly one failure in three trials:

P(X = 1) = (3 choose 1)(0.0956)¹(0.9044)²

Using a calculator, we can simplify this expression to:

P(X = 1) = 0.2448 or 24.48

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Answer:

1/6 × P(B) = 1/8, so P(B) = 3/4 = .75

Answer:

Step-by-step explanation:

a. To compute M₁ for y = f(x) on the interval [2, 5], we need to divide the interval into n = 3 subintervals of equal width Δx = (5 - 2)/3 = 1. Then, we can evaluate f(x) at the endpoints and midpoints of the subintervals to get the heights of the corresponding rectangles.

The values of Ax and the locations of the subintervals are:

Ax = Δx [f(2) + f(3) + f(4)] = 1[22 + 25 + 28] = 75

The sketch of the function and the rectangles is shown below:

            |

            |      ___

            |     |   |

            |     |   |

            |     |___|

_____________|___________

   2   3   4   5

b. The area of the region bounded by y = f(x) and the x-axis on [2, 5] is given by the definite integral:

∫[2,5] f(x) dx

= ∫[2,5] (3x + 4) dx

= [3/2 x^2 + 4x] from 2 to 5

= (3/2 (5)^2 + 4(5)) - (3/2 (2)^2 + 4(2))

= 37.5

c. The values computed in (a) and (b) turn out to be the same because the function f(x) = 3x + 4 is a linear function, which means that the area under the curve between any two points is the same as the area of the corresponding trapezoid with height equal to the average of the function values at those points. This is true regardless of the number of subintervals used in the approximation.

If we use a number different than n = 4 and compute M, we will get a different value for the area approximation. However, if the function is continuous and integrable on the interval, the exact area will still be given by the definite integral.

L4 and R4 will not have the same value as the exact area of the region found in (b) because they use the left and right endpoints of each subinterval to determine the height of the corresponding rectangle, which can overestimate or underestimate the true area. M4, on the other hand, uses the midpoint of each subinterval, which tends to give a better approximation to the true area.

To prove this identity, we start with Fermat's Little Theorem, which states that if p is a prime number and a is any integer coprime to p, then a^(p-1) ≡ 1 (mod p).

Using this theorem, we can rewrite the given identity as a^(p-1) * a(p-2) ≡ 1 (mod p^2).

Next, we can multiply both sides by a to get a^(p-1) * a(p-1) ≡ a (mod p^2).

Since a and p are coprime, we can use Euler's Totient Theorem, which states that a^φ(p) ≡ 1 (mod p) where φ(p) is the Euler totient function. Since p is prime, φ(p) = p-1, so a^(p-1) ≡ 1 (mod p).

Using this result, we can rewrite our identity as a^(p-1) * a(p-1) * a^-1 ≡ a^(p-1) ≡ 1 (mod p), which implies that a^(p-1) ≡ 1 (mod p^2).

Therefore, we have proven the identity a p(p−1) ≡ 1 (mod p 2 ), where a is coprime to p, and p is prime.

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Answer:

a- Joe worked 45 hours and is paid at a rate of $14.10 per hour for the first 40 hours and $21.15 per hour for the additional 5 hours. So, his gross pay for this pay period is:

40 hours x $14.10/hour = $564.00

5 hours x $21.15/hour = $105.75

Total gross pay = $564.00 + $105.75 = $669.75

b- Social security tax is 6.2% of gross pay. So, Joe's Social security deduction is:

$669.75 x 6.2% = $41.51

c- Medicare tax is 1.45% of gross pay. So, Joe's Medicare Tax deduction is:

$669.75 x 1.45% = $9.71

d- Joe’s Total Deductions for this pay period are:

$61.12 (Federal Tax) + $21.03 (State Tax) + $6.01 (City Tax) + $4.12 (Retirement Insurance) + $1.31 (Disability Insurance) + $13.05 (Medical Insurance) + $5.46 (Dental Insurance) = $112.10

e- Joe’s Total Deductions for this pay period are $112.10.

f- Joe pays $13.05 for Medical Insurance each weekly pay period. To calculate his annual premium, we can use the following formula:

Annual premium = Weekly premium x Number of weeks in a year

Weekly premium = $13.05

Number of weeks in a year = 52

Annual premium = $13.05 x 52 = $678.60

The correct answer is C. Systematic sampling because it is the mechanical sampling of one unit at a certain number of units in a certain order.

In statistical sampling, there is a methodology called systematic sampling wherein items or individuals are picked from a larger population regularly at predetermined intervals.

The reason this method exists is to analyze the smaller representative sample as it's overly ambitious to assess the entire population. It involves computing the interval at which the samples must be taken.

To compute such an interval, all one has to do is divide the size of the population with the desired sample size to get the answer.

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The price of an adult ticket is $10 and the price of a student ticket is $9.

An equation is a mathematical statement that shows that two expressions are equal. It usually contains variables, constants, and mathematical operations. The equal sign (=) is used to indicate that the expressions on both sides of the equation are equal.

Let "a" be the price of an adult ticket and "s" be the price of a student ticket. We can set up two equations based on the given information:

Equation 1: [tex]10a + 2s = 118[/tex] (from the first day of ticket sales)

Equation 2: [tex]6a + 12s = 168[/tex](from the second day of ticket sales)

We can use the elimination method to solve for one of the variables. Let's multiply Equation 1 by -6 and add it to Equation 2:

[tex]-60a - 12s = -708[/tex] (multiplying Equation 1 by -6)

[tex]6a + 12s = 168[/tex](Equation 2)

[tex]-54a = -540[/tex]

Dividing both sides by -54 gives us:

a = 10

Now we can substitute a = 10 into either Equation 1 or Equation 2 to solve for s. Let's use Equation 1:

[tex]10a + 2s = 118\\10(10) + 2s = 118\\100 + 2s = 118\\2s = 18s = 9[/tex]

Therefore, the price of an adult ticket is $10 and the price of a student ticket is $9.

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Option B is correct, the inequality which represents the  length of segment AB is greater than  length of segment AD is 9x-16>1.5x+42

The given rectangle is ABCD.

The length of segment AB is 9x-16 units

The length of segment AD is 1.5x+42 units

We have to find the inequality which represents the  length of segment AB is greater than  length of segment AD

> is the symbol used to represent greater than

AB>AD

9x-16>1.5x+42

Hence, option B is correct, the inequality which represents the  length of segment AB is greater than  length of segment AD is 9x-16>1.5x+42

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The statement that correctly describes how to show the relationship between the exterior angle and the interior angles using tracing paper is A. Trace ∠2. Move the paper so that ∠2 and ∠3 are adjacent angles. Then trace ∠3. Place the paper on top of ∠1 to show that ∠2 and ∠3 together are the same size as ∠1.

Instructing to trace ∠2 first, move the paper so that ∠2 and ∠3 are placed alongside one another. Then, succeeding the action taken beforehand, trace ∠3. Subsequently, rest the paper atop ∠1 in order to signify that, when combined, ∠2 and ∠3 possess an equivalent measure in comparison with ∠1.

Reason for this is based on the exterior angle adjacent to angle 2 being labeled inclusively as 1. As stated within the Exterior Angle Theorem, the magnitude of an exterior angle of a triangle shares equal dimensions to the aggregate measurement of its remote interior angles.

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Answer:

1) 93 2) 42 3) 135

Step-by-step explanation:

Angle CDE is 93 degrees because it's a supplementary angle. A straight line is equal to 180 degrees. So, you'd just do 180-87. This same rule applies for angle DEC where 180-138 is equal to 42. Then to find angle ECD, you'd do 93+42+x=180. Since a triangle is equal to 180 degrees.

Answer:

41.08 grams.

Step-by-step explanation:

79 * 0.52

The change in thermal energy is 75.06 kJ.

To calculate the change in thermal energy, we need to use the specific heat capacity of water, which is 4.184 J/(g°C).

First, we need to calculate the change in temperature:

ΔT = 90°C - 12°C

ΔT = 78°C

Next, we can calculate the change in thermal energy:

ΔQ = m × c × ΔT

where m is the mass of water and c is the specific heat capacity of water.

ΔQ = 230 g × 4.184 J/(g°C) × 78°C

ΔQ = 75060.96 J or 75.06 kJ (rounded to two decimal places).

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a) Margine of error for the proportion of all U.S. adults who think things are on the wrong track for 95% confidence is 0.019.

b) Correct answer is B. One is 95% confident that the observed proportion of adults that responded "Wrong Track" is within ±0.019 of the population proportion.

a) To calculate the margin of error for the proportion of all U.S. adults who think things are on the wrong track for 95% confidence, we can use the following formula:

ME = z√((p(1-p))/n)

Where:

z = the z-score associated with the desired level of confidence (in this case, 1.96 for 95% confidence)

p = the proportion of adults in the sample who said things are on the wrong track

n = the sample size

Using the percentages provided in the question, we can calculate the sample proportion:

p = % of adults who said things are on the wrong track / 100

p = % / 100 = %

So, p =

We don't have the sample size, but we can assume it's large enough (at least 30) to use the normal distribution approximation. Therefore, we can use the percentages directly to calculate the margin of error:

ME = 1.96√((0.490.51)/n)

ME = 1.96√(0.2499/n)

ME = 1.96(0.499/n¹/²)

ME = 0.019

Hence the margine of error is 0.019.

b) The margin of error means that if we were to conduct the same survey many times and calculate a 95% confidence interval for the proportion of all U.S. adults who think things are on the wrong track using each sample, we would expect the true population proportion to be within ±0.019 of the sample proportion in 95% of the intervals.

Therefore, the correct answer is B. One is 95% confident that the observed proportion of adults that responded "Wrong Track" is within ±0.019 of the population proportion.

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The graph of the exponential function 2(0.5)^x is given by the image presented at the end of the answer.

An exponential function is defined as follows:

y = ab^x.

In which:

The function for this problem is defined as follows:

y = 2(0.5)^x.

Meaning that when x = 0, y = 2, and for each increase of 1, the numeric values are halved, and hence the points are given as follows:

(0,2), (1,1), (2,0.5), (3, 0.25), (4, 0.125).

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The density of the rocks in the backyard is  0.2 g/sq.ft.

First, we need to find the total area covered by the 5 small rocks, which is 5 x 20 = 100 square feet

Then, we can subtract this from the total area of the backyard to find the area that is not covered by rocks

600 - 100 = 500 square feet

Next, we need to find the total mass of the rocks

5 x 20 = 100 grams

Finally, we can find the density by dividing the total mass by the total volume, which is the area not covered by rocks

Density = 100 grams / 500 square feet = 0.2 grams per square foot

Therefore, the density of the rocks in the backyard is 0.2 grams per square foot.

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--The given question is incomplete, the complete question is given

" Karie's backyard has an area of 600 square feet. She is covering the area with 5 small rocks of area 20 square feet. mass of each rock is 20 gram

What is the density of the rocks in the backyard?"--

The discount on the game console is 15.89% of the selling price.

To find the discount as a percentage of the selling price, we first need to calculate the discount amount. This can be found by subtracting the selling price from the original price:

Discount = Original Price - Selling Price

Discount = $428 - $360

Discount = $68

Next, we can calculate the discount as a percentage of the selling price by dividing the discount amount by the selling price and multiplying by 100:

Discount % = (Discount / Selling Price) * 100

Discount % = ($68 / $428) * 100

Discount % = 0.1589 * 100

Discount % = 15.89%

Therefore, the discount on the game console is 15.89% of the selling price.

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The proof that the identity; 1/(cscΘ+1) + 1/(cscΘ-1) = 2sec²ΘsinΘ is detailed as follows.

Start by using the identity csc(θ) = 1/sin(θ) and simplifying the left-hand side of the equation:

1/(csc(θ)+1) + 1/(csc(θ)-1)

= 1/(1/sin(θ)+1) + 1/(1/sin(θ)-1)

= sin(θ)/(1+sin(θ)) + sin(θ)/(1-sin(θ))

= sin²(θ)/(1-sin²(θ))

= sin²(θ)/cos²(θ)

= (sin(θ)/cos(θ))²

= sec²(θ)

Now substitute this expression into the left-hand side of the equation:

1/(csc(θ)+1) + 1/(csc(θ)-1) = sec²(θ)

2sec²(θ)sin(θ) = 2(sin(θ)/cos(θ))²sin(θ)

= 2sin³(θ)/cos²(θ)

= 2sin(θ)/cos(θ)

= 2sec(θ)sin(θ)

Therefore, it is shown that both sides of the equation are equal, and the identity is proved:

1/(csc(θ)+1) + 1/(csc(θ)-1) = 2sec²(θ)sin(θ)

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Answer:

Step-by-step explanation:

You want to know if the given distance calculations are correct (true) or not (false).

The distance between the animals at different coordinates is the absolute value of the difference of the coordinates.

The distance is ...

  |(-38 1/2) -(-84 1/4)| = 45 3/4 . . . . True

The distance is ...

  |-145 -(-84 1/4)| = 60 3/4 ≠ 229 3/4 . . . . False

The distance is ...

  |(18 3/4) -(-38 1/2)| = 57 1/4 . . . . True

The distance is ...

  |(18 3/4) -(-145)| = 163 3/4 ≠ 126 3/4 . . . . False

__

Additional comment

Since we're using the absolute value function, the order in which the subtraction occurs is immaterial. In the first two calculations we subtracted the location of the second animal from the first. In the last two calculations, this order was reversed. The correct distance is found either way.

If you don't use the absolute value function, you want to subtract the smaller coordinate from the larger. This will always give a positive result.

As a rule, distance and length are always positive. Displacement or position can be negative.

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Answer: the cost of the sketch notebook is $4.85.

Step-by-step explanation:

The length of side J is approximately 33 cm as per the law of sines.

We can use the law of sines to solve for the length of side JH, which is opposite the known angle at vertex J:

sin(116°)/JH = sin(5°)/ 340

First, we can simplify the equation by cross-multiplying:

JH × sin(116°) = 340 × sin(5°)

Then, we can solve for JH by dividing both sides by sin(116°):

JH = (340 × sin(5°)) / sin(116°)

JH = 32.9696

JH ≈ 33 to the nearest tenth.

The length of side J is 33 cm to the nearest tenth.

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The complete question:

In triangle HIJ, h = 340 cm, m∠J=116°, and m∠H=5°. Find the length of j, to the nearest 10th of a centimeter.

The weight of a beagle that is 1 standard deviation below average is 22 pounds, the weight of a beagle that is 1 standard deviation above average is 28 pounds, and approximately 68% of the data falls within the range of 22 to 28 pounds.

If the weights of beagles are approximately normally distributed with a mean weight of 25 pounds and a standard deviation of 3 pounds, we can use the empirical rule to determine the weight of a beagle that is 1 standard deviation below average and 1 standard deviation above average.

According to the empirical rule, approximately 68% of the data falls within 1 standard deviation of the mean. Therefore, the weight of a beagle that is 1 standard deviation below average would be:
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25 - (1 x 3) = 22 pounds

Similarly, the weight of a beagle that is 1 standard deviation above average would be:

25 + (1 x 3) = 28 pounds

Thus, we can expect the weights of approximately 68% of beagles to fall within the range of 22 to 28 pounds.

The normal distribution is a bell-shaped curve that is symmetrical around the mean. In this case, the mean weight of beagles is 25 pounds, which is the highest point on the curve. As we move away from the mean, the probability of encountering a particular weight decreases. One standard deviation away from the mean covers a large proportion of the data, but as we move further away, the proportion decreases rapidly.

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Answer: A. Graph A

this is the answer because yes

The graph A shows the positive white line, this is because the line cuts across both the x- axis and that of the y- axis

The maximum amoumt of milk that can be added to the container after 2 pails been emptied in it is 64 litres based on numerical-operations.

What are numerical-operations?

In mathematics, the terms addition, subtraction, multiplication, and division refer to the four basic operations that involve manipulating numbers.  Numerical operations include fundamental mathematical operations such addition, subtraction, multiplication, and division as well as other operations that are indicated by symbols:, >, =.

Given that the total capacity of container= 80 L

Also given that one pail holds milk of capacity= 8L

if two pails are emptied in the container,

Capacity of milk in container= 2 x capacity of each pail.

                                               = 2 x 8

                                               = 16 L

Milk in container after two pails been emptied= 16 L

Maximum amount of milk that can be still added = 80 L - 16 L

                                                                                 = 64 L

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The cost of buying the annuity today would be $1,061,733.29. (option b).

An annuity is a type of investment that provides a regular stream of income for a fixed period or for the rest of an individual's life.

To calculate the cost of buying the annuity, we need to use the present value formula. The present value of an annuity is the amount that needs to be invested today to provide a fixed stream of cash flows in the future. The formula for the present value of an annuity is:

PV = PMT x [1 - (1 + r)⁻ⁿ] / r

where PV is the present value, PMT is the annual payment, r is the interest rate per period, and n is the number of periods.

Using the given values, we can plug them into the formula as follows:

PV = $86,000 x [1 - (1 + 0.0725)⁻³⁰] / 0.0725

PV = $1,061,733.29

Therefore, Option b is the correct answer.

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[tex]\textit{exponential form of a logarithm} \\\\ \log_a(b)=y \qquad \implies \qquad a^y= b \\\\[-0.35em] ~\dotfill\\\\ \log(49)=y\implies \log_{10}(49)=y\implies 1.690196\approx y \\\\\\ \log_{10}(49)\approx 1.690196\implies \stackrel{\textit{then we can say}}{10^{1.690196}\approx 49}[/tex]

The constant term (36) represents the initial height of the ball, in feet, when it was thrown into the air.

In mathematics, a coefficient is a constant factor that appears in front of a variable or a term in an algebraic expression.

For example, in the expression 5x²  + 3x - 2, the coefficients are 5, 3, and -2. The coefficient 5 is in front of the variable x² , the coefficient 3 is in front of x, and the coefficient -2 is a constant term.

The function h(t) = −16t² + 48t + 36 models the height of a ball, in feet, at t seconds after being thrown into the air.

The coefficient of the t²  term (-16) represents the acceleration due to gravity, which is constant at approximately 32 feet per second squared. The negative sign indicates that the acceleration is directed downwards, opposing the motion of the ball.

The coefficient of the t term (48) represents the initial velocity of the ball, in feet per second, when it was thrown into the air. Since the coefficient is positive, the ball was thrown upwards.

The constant term (36) represents the initial height of the ball, in feet, when it was thrown into the air.

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