2. Andrew made an error in determining the polynomial equation of smallest degree whose roots are 3, 2+2i and .

Review Andrew’s work, identify the error and correct all work from that point forward that is affected by this error. Include at least one sentence explaining his error. Use proper mathematical vocabulary, appropriately
(x-3)(x+2+2i)(x+2-2i)=0
(x-3)(x^2+4x+8)=0
x^3+x^2-4x-24=0)

Answer:  70

Step-by-step explanation:

easy addition

Repeated measures study is a technique used in statistics that involves taking multiple measures from the same individual or group. The major concern with a repeated-measures study is the possibility of carry-over effects.

What is a repeated-measures study?A repeated-measures study is a design used in statistics, where all the members of a given sample group are evaluated on two or more occasions. In other words, the repeated-measures study can be viewed as a test-retest design.In this type of study, participants undergo a specific treatment or intervention, and then their responses or measurements are evaluated at various intervals to examine any effects of the intervention. The repeated measures are then compared, and statistical tests are used to determine whether there are any significant differences in the results.

The possibility of carry-over effects: When conducting a repeated-measures study, the possibility of carry-over effects is a major concern. This occurs when the effects of the first treatment are still present when the second treatment is applied, resulting in an unintended impact on the second set of results. For example, if an experimental group is treated with a medication and then evaluated, and the same group is treated with a different medication and then evaluated, the results may be influenced by the residual effects of the first medication.

A carry-over effect can result in an inaccurate representation of the study's effect and can decrease the validity of the results. As a result, researchers must establish an appropriate washout period to reduce the impact of the carry-over effects before conducting a repeated-measures study.

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Using Chebyshev's Inequality, the lower bound for the number of signals that need to be sent so that the total number of errors are within 10% of the expected number of errors with at least 95% probability is 846.

Chebyshev's Inequality states that for any random variable X with finite mean μ and variance σ², the probability that X deviates from μ by more than k standard deviations is at most 1/k².

In other words,

P(|X-μ| ≥ kσ) ≤ 1/k².

In this problem, we know that the number of errors follows a Poisson distribution with a mean of 36 errors, which means that the mean and variance are both 36.

Let X be the total number of errors in n signals. We want to find the smallest value of n such that

P(|X-μn| ≥ 0.1μn) ≤ 0.05,

where μn = nμ is the expected number of errors in n signals.

Using Chebyshev's Inequality, we have

P(|X-μn| ≥ 0.1μn) ≤ σ²/[0.1²μn²] = σ²/[0.01μ²n²] = 1/25,

where σ² = 36 is the variance of X.

Therefore, we need to solve the inequality

1/25 ≤ 0.05,

which implies n ≥ 846. Hence, the lower bound for the number of signals that need to be sent is 846.

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The position value, r(t) is equals to the (t³/6)k + 2j and velocity value, v(t) is equals to ( t²/2 )k + 4i , for a(t) = tk, v(0) = 4i, r(0) = 2j.

Acceleration is defined as the rate of change of the velocity of an object with respect to time. Accelerations are vector quanty.

a = dv/dt

We have the following informations are available,

Initial velocity, v(0) = 4i

Initial position, r(0) = 2j

Acceleration at any time "t",

a(t) = tk

we have to determine the value of v(t) and r(t).

As we know, a(t) = dv(t)/dt = tk

integrating the above equation ,

v(t) = ∫tk dt = ( t²/2 )k + c

at t = 0 , v(0) = 0 + c = 4i ( since, v(0) = 4i

=> c = 4i

So, v(t) = ( t²/2 )k + 4i

Also, velocity is calculated by derivative of postion (r) with respect to time.

=> v(t) = dr(t) /dt

=> r(t) = ∫ v(t) dt

=> r(t) = ∫ ( t²/2 )k dt

integrating value of the right hand side,

r(t) = ( t³/2×3 )k +d

= (t³/6)k + d

At t = 0, r(0) = (0/6)k + d

=> r(0) = d = 2j

so, r(t) = (t³/6)k + 2j

Hence, the required position and velocity are

(t³/6)k + 2j and ( t²/2 )k + 4i.

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The related sample design can be a useful approach for many research questions, but researchers need to carefully consider the design of their study and choose the best approach for their specific research question.

A related sample can refer to a single sample that has been measured twice, or to two samples that have been matched. The advantages of using a related sample versus using two independent samples include greater statistical power, better control over extraneous variables, and fewer participants. Using two independent samples can also have some benefits, such as increased generalizability of results. However, researchers need to carefully consider the design of their study and choose the best approach for their specific research question. Here is an explanation in 130 words:Related sample designs are a type of experimental or quasi-experimental research design that involves two samples of participants, with some level of connection between the two samples. The two samples may be matched on certain variables, or they may be the same participants measured twice (repeated measures). This design can be used to test a hypothesis about the difference between two conditions or treatments, and it has some advantages over using two independent samples. One advantage is greater statistical power, as the related sample design can reduce error variance and increase the sensitivity of the statistical test. Another advantage is better control over extraneous variables, as the related sample design can reduce the impact of individual differences and other sources of variability. Finally, using a related sample design can reduce the number of participants required for a study, which can save time and resources.

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To convert a decimal number to binary, start by dividing by the highest binary place value and writing a 1 in that place value if the result is greater than 0. the converted values is 10111011, 10111011 , 10110101 , 11011101.

187:

Start with the binary place values equal to or less than the number: 128, 64, 32, 16, 8, 4, 2, 1.

Begin with the highest place value of 128 and subtract from 187. 187 - 128 = 59.

Since 59 is greater than 0, a 1 is placed in the 128 place value.

Next, subtract the next binary place value, 64, from 59. 59 - 64 = -5.

Since -5 is less than 0, a 0 is placed in the 64 place value.

Continue this process until all of the place values are filled.

The binary number for 187 is 10111011.

891:

Start with the binary place values equal to or less than the number: 512, 256, 128, 64, 32, 16, 8, 4, 2, 1.

Begin with the highest place value of 512 and subtract from 891. 891 - 512 = 379.

Since 379 is greater than 0, a 1 is placed in the 512 place value.

Next, subtract the next binary place value, 256, from 379. 379 - 256 = 123.

Since 123 is greater than 0, a 1 is placed in the 256 place value.

Continue this process until all of the place values are filled.

The binary number for 891 is 1110100011.

2014:

Start with the binary place values equal to or less than the number: 1024, 512, 256, 128, 64, 32, 16, 8, 4, 2, 1.

Begin with the highest place value of 1024 and subtract from 2014. 2014 - 1024 = 990.

Since 990 is greater than 0, a 1 is placed in the 1024 place value.

Next, subtract the next binary place value, 512, from 990. 990 - 512 = 478.

Since 478 is greater than 0, a 1 is placed in the 512 place value.

Continue this process until all of the place values are filled.

The binary number for 2014 is 10111011.

20486:

Start with the binary place values equal to or less than the number: 16384, 8192, 4096, 2048, 1024, 512, 256, 128, 64, 32, 16, 8, 4, 2, 1.

Begin with the highest place value of 16384 and subtract from 20486. 20486 - 16384 = 4102.

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Answer:

X<-3

Step-by-step explanation:

4 ( x - 1 ) > (1/2) ( 4 + 12x )

4x - 4 > 2 + 6x

-2 -4 > 6x - 4x

-6 > 2x

x < -3

Answer:

A= 80

B= 37

C= 13

D= ? not sure apologies, did this a long time ago.

Step-by-step explanation:

The solution to the equation \((\sum\limits^{\infty}_{i=1} \frac{1}{2^i}) + (\sum\limits^{\infty}_{i=1} \frac{9}{10^i}) + \sin^2(\theta) + \cos^2(\theta) + e^2\) is 10.3891

From the question, we have the following parameters that can be used in our computation:

\((\sum\limits^{\infty}_{i=1} \frac{1}{2^i}) + (\sum\limits^{\infty}_{i=1} \frac{9}{10^i}) + \sin^2(\theta) + \cos^2(\theta) + e^2\)

Using the following trigonometry ratio

sin²(x) + cos²(x) = 1

We have

\((\sum\limits^{\infty}_{i=1} \frac{1}{2^i}) + (\sum\limits^{\infty}_{i=1} \frac{9}{10^i}) + \sin^2(\theta) + \cos^2(\theta) + e^2 = (\sum\limits^{\infty}_{i=1} \frac{1}{2^i}) + (\sum\limits^{\infty}_{i=1} \frac{9}{10^i}) + 1 + e^2\)

The sum to infinity of a geometric series is

S = a/(1 - r)

So, we have

\((\sum\limits^{\infty}_{i=1} \frac{1}{2^i}) + (\sum\limits^{\infty}_{i=1} \frac{9}{10^i}) + \sin^2(\theta) + \cos^2(\theta) + e^2 = \frac{1/2}{1 - 1/2} + \frac{9/10}{1 - 1/10} + 1 + e^2\)

So, we have

\((\sum\limits^{\infty}_{i=1} \frac{1}{2^i}) + (\sum\limits^{\infty}_{i=1} \frac{9}{10^i}) + \sin^2(\theta) + \cos^2(\theta) + e^2 = 1 + 1 + 1 + e^2\)

Evaluate the sum

\((\sum\limits^{\infty}_{i=1} \frac{1}{2^i}) + (\sum\limits^{\infty}_{i=1} \frac{9}{10^i}) + \sin^2(\theta) + \cos^2(\theta) + e^2 = 3 + e^2\)

This gives

\((\sum\limits^{\infty}_{i=1} \frac{1}{2^i}) + (\sum\limits^{\infty}_{i=1} \frac{9}{10^i}) + \sin^2(\theta) + \cos^2(\theta) + e^2 = 10.3891\)

Hence, the solution to the equation is 10.3891

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By comparing this solution to the given form In Z(t) = -A(ta + 7), we can see that A = To - Ta and ta + 7 = kt.

The heat-transfer processes occurring following the death of an individual can be described using a mathematical model. The body temperature decreases over time until it reaches the ambient temperature.

This can be represented by a first-order differential equation. By solving the differential equation, the temperature of the body as a function of time can be obtained. The solution takes the form of an exponential decay with a constant factor.

(a) The word equation for the heat-transfer processes following the death of an individual can be stated as follows: "The rate of change of body temperature with respect to time is proportional to the temperature difference between the body and the environment."

(b) To convert the word equation into a mathematical model, we make the following assumptions:

- The body and the environment are in thermal equilibrium initially.

- The body loses heat solely through conduction and radiation.

- The surrounding environment remains at a constant temperature.

Let T(t) represent the temperature of the body at time t, and Ta represent the ambient temperature. The mathematical model can be expressed as:

dT/dt = -k(T - Ta)

where dT/dt represents the rate of change of body temperature, and k is a constant that determines the rate of heat loss.

(c) (i) To find the temperature of the body as a function of time, we solve the differential equation:

dT/dt = -k(T - Ta)

By separating variables and integrating, we get:

∫(1 / (T - Ta)) dT = -k ∫dt

Solving the integral and applying initial conditions, we obtain:

ln|T - Ta| = -kt + C

where C is the constant of integration.

(ii) Assuming the individual dies at time t = 0 and the body is discovered at time t = ty, we can substitute these values into the solution obtained above:

ln|To - Ta| = -k(0) + C

ln|To - Ta| = C

Therefore, the solution can be written as:

ln|T(t) - Ta| = -kt + ln|To - Ta|

T(t) - Ta = e^(-kt + ln|To - Ta|)

T(t) = Ta + (To - Ta)e^(-kt)

By comparing this solution to the given form In Z(t) = -A(ta + 7), we can see that A = To - Ta and ta + 7 = kt.

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the probability of an archer hitting her target is 83%.The mean of x is 16.6 (16.6 targets hit).

The probability of the archer hitting her target is 83%. This means that for each shot she takes, the probability of her hitting her target is 0.83. Since she has 20 shots to take, the expected number of targets hit is 20 x 0.83, which is 16.6.

The mean of x, which is the number of targets hit, is therefore 16.6. This can be calculated by taking the probability of success (0.83) multiplied by the number of trials (20), which gives the expected value of 16.6.

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According to the information, we can infer that the number of ounces of water, x, that Will could have put in each cup is 8 ounces.

Will initially had a cooler filled with 144 ounces of water. After using 16 ounces to fill his water bottle, there were 144 - 16 = 128 ounces of water remaining in the cooler.

Will then took out 16 plastic cups for his teammates. Since the same amount of water was put in each cup, the remaining amount of water, 128 ounces, needs to be divided equally among the cups.

Dividing 128 ounces by 16 cups gives us 8 ounces of water for each cup.

So, Will could have put 8 ounces of water in each cup.

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Answer:

105.2°

Step-by-step explanation:

Supplementary means the angles add up to 180. 180-74.5=105.2

Answer:

The answer is 15.2

Step-by-step explanation:

This is literally the EASIEST subject in math so all you do is subtract 90 - 74.8 easy peasy! That's middle school math lol.

The given polynomial  2x² + 3x - 4 is a (C) Trinomial polynomial.

Monomials have one term, binomials have two, trinomials have three, and polynomials have one or more terms.

Two monomials added together form a binomial.

It has two terms that contrast. (3x+1, x24x, 2x+y, or yy2) (bi suggests two). Three monomials added together form a trinomial.

A four-term polynomial is occasionally referred to as a "quadrinomial."

A polynomial with real coefficients is considered a real polynomial.

So, the expression we have is:

2x² + 3x - 4

We can count that here are 3 terms in the polynomial.

And when there are 3 terms in a polynomial, it represesnts a trinomial.

Therefore, the given polynomial  2x² + 3x - 4 is a (C) Trinomial polynomial.

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Step-by-step explanation:

Answer:

D. 4 And 8

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Answer:

B

Step-by-step explanation:

The main reason behind solving an equation system is to find the value of the variable that satisfies the condition of all the given equations true.

Solving system can be defined as solution set of a system of equations to the collection of all solutions. Solving the system also means finding all solutions with formulas involving some number of parameters.

There are three methods used to solve systems of equations such as:

Therefore the main reason behind solving an equation system is to find the value of the variable that satisfies the condition of all the given equations true.

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Answer:

x=1.3

Step-by-step explanation:

Answer:

3,696

Step-by-step explanation:

7x24x22 equals 3,696

24x7=168

168x22=3,696

To find the measure of angle C in triangle ABC, we can use the Law of Cosines, which states that for any triangle with sides a, b, and c and opposite angles A, B, and C:c^2 = a^2 + b^2 - 2abcos(C)In this case, we know that AB = 7, BC = 8, and AC = 9. Plugging these values into the Law of Cosines equation and solving for cos(C), we get:cos(C) = (7^2 + 9^2 - 8^2) / (2 * 7 * 9)

cos(C) = 0.6111111Taking the inverse cosine (cos^-1) of 0.6111111, we get the angle C:C = cos^-1(0.6111111)

C ≈ 51.96 degreesTherefore, to the nearest degree, m∠C ≈ 52 degrees.

Answer:

48°

Step-by-step explanation:

Use the Law of Cosines.

c² = a² + b² - 2ab cos C

7² = 8² + 9² - 2(8)(9) × cos C

49 = 145 - 144 cos C

-144 cos C = -96

cos C = 2/3

C = 48.196...°

Answer: 48°

To determine the minimum radius of the circle for the jet's loop, we need to calculate the centripetal acceleration at the lowest point and set it equal to the given limit of 6.5 g's.

Centripetal acceleration (ac) is given by the equation:

ac = (\(v^2\)) / r

Where:

ac = centripetal acceleration

v = velocity of the jet

r = radius of the circle

We need to convert the given speed from km/h to m/s for consistent units. Using the conversion factor 1 km/h = 0.2778 m/s:

v = 1250 km/h * 0.2778 m/s = 347.25 m/s

Now, we can rearrange the formula to solve for the radius:

r = (\(v^2\)) / ac

Substituting the values:

The acceleration due to gravity, g, is approximately 9.8 m/s^2.

r = (347.25 m/s)^2 / (6.5 * 9.8 m/s^2)

Calculating this:

r ≈ 1995.3 m

Rounded to two significant figures, the minimum radius of the circle for the jet's loop should be approximately 2000 m.

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To maximize the volume, squares of size 3 inches should be cut from each corner, resulting in a box with dimensions 12 inches by 24 inches by 3 inches, and a maximum volume of 972 cubic inches.

Let's assume that the side length of the squares to be cut is x inches. When the squares are cut from each corner, the resulting dimensions of the box will be (18-2x) inches by (30-2x) inches by x inches. The volume V of the box is given by V = (18-2x)(30-2x)x.

To find the value of x that maximizes the volume, we can take the derivative of V with respect to x, set it equal to zero, and solve for x. The critical point we obtain will correspond to the maximum volume.

Differentiating V with respect to x, we have dV/dx = -4x^3 + 96x - 540. Setting this equal to zero and solving for x, we find x = 3.

Substituting x = 3 back into the volume equation V = (18-2x)(30-2x)x, we can calculate the volume as V = (18-2(3))(30-2(3))(3) = 972 cubic inches.

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Answer:

2

Step-by-step explanation:

Answer:

I believe the answer is

P=4

Answer: 11p+10 = 5p+20  

Step-by-step explanation:

TV = 6ft

VS = 21

___________________

Ratio

wall/ Raf = 21/ 6

wall/ 4= 21/ 6

wall = 21*4/6 = 14

The wall is 14 ft high. ​

Jennie has 1.5 liters of soda left. if Jennie poured ¼ of a 2 liter bottle of soda into the punch bowl, she poured 2/4 or 1/2 of a liter into the bowl. This means she has 2 - 1/2 = 1.5 liters of soda left.

Sure! To find the amount of soda Jennie has left, we start with a 2 liter bottle. She poured ¼ of it into the punch bowl, which is equivalent to 2/4 or 1/2 liter. To calculate the remaining amount, we subtract the amount poured (1/2 liter) from the original amount (2 liters). So, 2 - 1/2 equals 1.5 liters. Therefore, Jennie has 1.5 liters of soda left after pouring ¼ of the 2 liter bottle into the punch bowl.

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Therefore, we have shown that the equation e(-x) * sin(x) = ln(x) has at least one solution on the interval [1, 2].

To show that the equation e(-x) * sin(x) = ln(x) has at least one solution on the interval [1, 2], we can use the Intermediate Value Theorem.

1. First, let's evaluate the left-hand side of the equation at the endpoints of the interval [1, 2]:
  - At x = 1: e(-1) * sin(1) ≈ 0.2447
  - At x = 2: e(-2) * sin(2) ≈ -0.2707

2. Next, let's evaluate the right-hand side of the equation at the endpoints of the interval [1, 2]:
  - At x = 1: ln(1) = 0
  - At x = 2: ln(2) ≈ 0.6931

3. Now, let's consider the values in between. We observe that e(-x) * sin(x) is a continuous function, and ln(x) is also continuous on the interval [1, 2].

4. By the Intermediate Value Theorem, since the left-hand side of the equation takes on values both greater than and less than the right-hand side on the interval [1, 2], there must be at least one solution for e(-x) * sin(x) = ln(x) on this interval.

Therefore, we have shown that the equation e(-x) * sin(x) = ln(x) has at least one solution on the interval [1, 2].

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As a result, we are unable to determine the age of a child who is 133 cm tall using the regression equation.

A statistical technique called linear regression is used to represent the connection between two variables, where one of the variables is the dependent variable and the other is the independent variable. Finding the best-fit line that depicts the connection between the two variables is the objective of linear regression. This enables us to make predictions or estimate values based on the known data.

given

These numbers allow us to determine a and b:

a = 0.997 (9.285 / 1.547) ≈ 5.977

b = 128.2 - 5.977 (8.02) ≈ 81.704

The regression equation is therefore y = 5.977 x + 81.704.

(ii) Based on the calculations made above, the Pearson's product-moment correlation coefficient, or r, has a value of roughly 0.997.

(b) We enter x = 9 into the regression equation to calculate an approximation of the height of a 9-year-old child:

As a result, we calculate that a 9-year-old kid will be roughly 134.6 cm tall.

We must resolve the regression equation for x in order to determine the age of a kid who measures 133 cm in height.

x = (y - b) / a

This calculation, though, would result in an illogically negative age. As a result, we are unable to determine the age of a child who is 133 cm tall using the regression equation.

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The complete question is:-  

The following table shows the mean height, y cm, of primary school children who are age x years old.

Age, x years Mean Height, y cm

6.25 7.35 8.5 9.25 10.75

115 121 129 136 140

The relationship between x and y can be modelled by the regression line of y on x with equation y = ax + b.

(a) (i) Find the value of a and the value of b.

(ii) Write down the value of Pearson's product-moment correlation coefficient, r.

(b) Use your regression equation from part (a)(i) to estimate the height of a child aged 9 years old.

(c) Explain why it is not appropriate to use the regression equation to estimate the age of a child who is 133 cm tall.

Answer:

First we make an equation for each company

4500 + 100.25t

t is going to be tons

the second company

3443 + 175.72t

Step-by-step explanation: