Help me please!!!!!!!!

Required polynomial in the form p(x) is: \(\[f(x)=\boxed{x^3-2x^2+4x-3+\frac{5}{x-1}}\]\)

We are given the following polynomial: \(\[f(x)=\frac{x^4-3x^3+2x^2-7x-2}{x-1}\]\)

To perform polynomial long division we divide the highest degree terms of the numerator and denominator. Then we write the quotient and remainder on top of each other and multiply the denominator of the original problem with the quotient to check if the answer is correct.

Let's start with the highest degree terms.

\(\[\begin{array}{r r c r r} &x^3 &-2x^2 &+4x &-3\\ \cline{2-5} x-1 & x^4 &-3x^3&+2x^2&-7x&-2 \\ & \underline{x^4} &-\underline{x^3} & & & \\ & & -2x^3 & +2x^2 & & \\ & & \underline{-2x^3} & +\underline{2x^2} & & \\ & & & 0x^2 & -7x & \\ & & & & -7x & +7 \\ & & & & \underline{-7x} & +\underline{7} \\ & & & & & \boxed{5} \\ \end{array}\]\)

Therefore, the required polynomial in the form p(x) is:\(\[f(x)=\boxed{x^3-2x^2+4x-3+\frac{5}{x-1}}\]\)

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Answer:

Below.

Step-by-step explanation:

15y + 12x = 18

5y + 4x = 6

The  second equations is the first times 3 so they are basically the same.

Infinite Solutions.

2x+ 3y= 12

-6y= 4x-24          Rearranging the second equation:

-4x - 6y = -24      Multiplying the first equation by 2:

4x + 6y = 24      

- we see that the last equation is -1 * previous equation.

So there are infinite solutions.

The given fractions have equal value, so Liam is correct.

Equivalent fractions are defined as fractions that have different numerators and denominators but the same value. For example, 2/4 and 3/6 are equivalent fractions because they are both equal to 1/2. A fraction is part of a whole. Equivalent fractions represent the same part of a whole.  

Liam is claiming that the fraction -(5/12) is equivalent to 5/-12.

Thus, we can say that:

The fraction  -(5/12) can be described as the opposite of a positive number divided by a positive number. A positive number divided by a positive number always results in a positive quotient and its' opposite is always negative.

The fraction 5/-12 can be described as a positive number divided by a negative number which always results in a negative quotient

The fractions have equal value, so Liam is correct

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The point (7, -π/2) in polar coordinates corresponds to the rectangular coordinates (0, -7), representing a point on the negative y-axis.

In polar coordinates, a point is represented by its distance from the origin (r) and its angle from the positive x-axis (θ). For the given point (7, -π/2), the distance from the origin is 7 units (r = 7), and the angle is -π/2 radians.

To convert this point to rectangular coordinates, we can use the following formulas:

x = r * cos(θ)

y = r * sin(θ)

Applying these formulas to the given values, we get:

x = 7 * cos(-π/2)

y = 7 * sin(-π/2)

The cosine of -π/2 is 0, and the sine of -π/2 is -1, so we can substitute these values into the formulas:

x = 7 * 0 = 0

y = 7 * (-1) = -7

Therefore, the rectangular coordinates for the point (7, -π/2) are (0, -7). This represents a point on the negative y-axis, where the x-coordinate is 0 and the y-coordinate is -7.

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Answer:

y=\(\frac{1}{3}\)x+8

Answer:

A.

Step-by-step explanation:

Convex polygon

A polygon is a figure that has no curved lines. A convex polygons has no "caves."

In this instance, answer choices B, C, and D all have curved lines which means that they aren't polygons. Additionally, as an example of a concave polygon, answer choice D creates a sort of "cave."

Therefore, answer choice A is a convex polygon.

Hope this helps!

The probability of winning the car in this Monty Hall problem with 6 doors is 83.33%.

In this scenario, there are 6 doors, with 1 car behind one of them and goats behind the other 5. You pick a door, and the host opens 4 other doors revealing goats. You always switch to the last remaining door.

1. Initially, there is a 1/6 chance you picked the car and a 5/6 chance you picked a goat.

2. If you picked a goat (5/6 probability), the host will open the other 4 doors with goats, leaving the car behind the last remaining door. In this case, switching will win you the car.

3. If you picked the car (1/6 probability), the host will still open 4 doors with goats, but switching would make you lose the car in this case.

Since you always switch, the probability of winning the car is the same as the probability of initially picking a goat, which is 5/6. So, the probability of winning the car is approximately 83.33%.

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Answer: 1 cup or 2 cups.

The buyer should purchase 87913 bales to ensure that he has at least 2000 bales that weigh 420 kilograms each.

For having a bale of 420 and above,

we calculate standard deviation using below information

(420 - 376 /22) = 0.02275 = 2.275% chance of having a bale of 420+ kg

To find out the number of bales to pe precise,

2000/0.02275 = 87912.1 so you'll need at the very least 87913 bales to be reasonably certain.

The standard deviation is a statistic that expresses how much variance or dispersion there is in a group of numbers. While a high standard deviation suggests that the values are dispersed throughout a wider range, a low standard deviation suggests that the values tend to be close to the established mean.

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a) The co-efficient of x⁴y³ = -241920

b) The coefficient of x²y⁷ =  900

What Does an Expression Coefficient Mean?

The expansion is given by the following formula:

(a + b)ⁿ = Σⁿₓ=₀(ⁿₓ) aⁿ⁻ˣ bˣ, where

(ⁿₓ) = n! / (n-x)! k! and n! = 1.2..3.....n.

a) (-3x+4y)⁷ = ⁷C₀ (-3x)⁷(4y)⁰ + ⁷C₁ (-3x)⁶(4y)¹ + ⁷C₂ (-3x)⁵(4y)¹ + ⁷C₃ (-3x)⁴(4y)³ + ⁷C₄ (-3x)³(4y)⁴ + ⁷C₅ (-3x)²(4y)⁵ + ⁷C₆ (-3x)¹(4y)⁶ + ⁷C₇ (-3x)⁰(4y)⁷

The co-efficient of x⁴y³ = 35x - 27x³ * 256y⁴

= -241920x³y⁴

Hence, the coefficient of x⁴y³ = -241920.

b) (5x - y)⁹ = ⁹C₀(5x)⁹(-y)⁰ + ⁹C₁(5x)⁸(-y)¹ + ⁹C₂(5x)⁷(-y)² + ⁹C₃(5x)⁶(-y)³ + ⁹C₄(5x)⁵(-y)⁴ + ⁹C₅(5x)⁴(-y)⁵ + ⁹C₆(5x)³(-y)⁶ + ⁹C₇(5x)²(-y)⁷ + ⁹C₈(5x)(-y)⁸ + ⁹C₉(5x)⁰(-y)⁹

The coefficient of x²y⁷ = 36 * 25x² * y⁷

= 900x²y⁷

Hence, the coefficient of x²y⁷ = 900.

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The correct answer is to achieve an overall alpha of 0.01, you would use an alpha level of 0.0025 for each of your tests.

To achieve an overall alpha of 0.01 when conducting multiple tests, you need to adjust the alpha level for each individual test to control for the familywise error rate (FWER). The most common approach for this adjustment is the Bonferroni correction.

The Bonferroni correction divides the desired overall alpha level (0.01) by the number of tests you are conducting. This adjustment ensures that the probability of making at least one Type I error across all tests (FWER) remains below the desired overall alpha level.

For example, if you are conducting four tests, you would divide 0.01 by 4:

Adjusted alpha level = 0.01 / 4 = 0.0025

Therefore, to achieve an overall alpha of 0.01, you would use an alpha level of 0.0025 for each of your tests.

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Answer:

A then B

Step-by-step explanation:

1440≈1,000, and 1,000=10^3

1000000/1440≈700, and 700≈1,000. 1,000=10^3

Answer: 3/52

Step-by-step explanation:

You want to pick a diamond jack, diamond queen or diamond king

There are only 3 of those so

P(DJ or DQ or DK) = 3/52        There are 3 of those out of 52 total

Answer:

x = 15

Step-by-step explanation:

\((\sqrt{4(x -5}) ^{2}\) = 40  If you square the square root of something, it would end up being itself.

4(x - 5) = 40

4x - 20 = 40  Add 20 to both sides

4x = 60  Divide both side by 4

x = 15

Answer:

\(\sqrt{4}(x-5)^2=40 \implies x=5 +2 \sqrt{5}, \quad x=5-2 \sqrt{5}\)

\(\sqrt{4(x-5)^2}=40 \implies x=-15, \quad x=25\)

Step-by-step explanation:

Given equation:

\(\sqrt{4}(x-5)^2=40\)

Simplify  √4 = 2 :

\(\implies 2(x-5)^2=40\)

Divide both sides by 2:

\(\implies (x-5)^2=20\)

Square root both sides:

\(\implies x-5=\pm \sqrt{20}\)

Simplify the right side of the equation:

\(\implies x-5=\pm \sqrt{4 \cdot 5}\)

\(\implies x-5=\pm \sqrt{4} \sqrt{5}\)

\(\implies x-5=\pm 2 \sqrt{5}\)

Add 5 to both sides:

\(\implies x=5 \pm 2 \sqrt{5}\)

Therefore, the solutions are:

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

Given equation:

\(\sqrt{4(x-5)^2}=40\)

Square both sides:

\(\implies 4(x-5)^2=1600\)

Divide both sides by 4:

\(\implies (x-5)^2=400\)

Square root both sides:

\(\implies x-5=\pm \sqrt{400}\)

\(\implies x-5=\pm 20\)

Add 5 to both sides:

\(\implies x=5-20=-15\)

\(\implies x=5+20=25\)

Therefore, the solutions are:

The probability distribution of the number of hours per day people are able to relax is constructed, and probabilities of relaxing more than 4 hours, between 2 to 6 hours, and not relaxing at all are 0.283, 0.767 and 0.068 respectively. The mean and standard deviation are 3.326 hours and 1.950 hours (approx.) respectively.

The probability distribution of X is:

X Frequency Probability

0 114                    0.068

1 156                    0.093

2 336                    0.201

3 251                     0.150

4 316                      0.189

5 231                     0.138

6 149                    0.089

7 33                    0.020

8 60                    0.036

      1676                     1.000

The probability that a person relaxes more than 4 hours per day is:

P(X > 4) = P(X = 5) + P(X = 6) + P(X = 7) + P(X = 8)

= 0.138 + 0.089 + 0.020 + 0.036

= 0.283

The probability that a person relaxes from 2 to 6 hours per day is:

P(2 ≤ X ≤ 6) = P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6)

= 0.201 + 0.150 + 0.189 + 0.138 + 0.089

= 0.767

The probability that a person does not relax at all is:

P(X = 0) = 0.068

The mean Mx is:

Mx = Σ(X * P(X))

= 00.068 + 10.093 + 20.201 + 30.150 + 40.189 + 50.138 + 60.089 + 70.020 + 8*0.036

= 3.326 hours

The standard deviation Ox is:

Ox = sqrt[Σ(X^2 * P(X)) - Mx^2]

= sqrt[(0^20.068)+(1^20.093)+(2^20.201)+(3^20.150)+(4^20.189)+(5^20.138)+(6^20.089)+(7^20.020)+(8^2*0.036) - 3.326^2]

= 1.950 hours (approx.)

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Answer:

The ratio of girls to total students is 12:30, which can be simplified to 2:5.

Step-by-step explanation:

You can express the ratio in different ways by using the same numbers, for example, you could say that for every 2 girls, there are 5 total students, or that for every 5 total students, 2 of them are girls.

If the stove is run on 120 V instead of 240 V, it would receive approximately 61.02 W of power.

To determine the power the stove would receive if it was run on 120 V instead of the normal 240 V, we can use the relationship between power, voltage, and current.

The power equation is given by:

P = V * I

Where:

P is the power (in watts)

V is the voltage (in volts)

I is the current (in amperes)

We can rearrange the equation to solve for the current:

I = P / V

Given that the stove requires 2,929 W to operate at 240 V, we can calculate the current at 240 V:

I1 = 2929 W / 240 V

Next, we can calculate the power at 120 V using the current at 240 V:

P2 = V2 * I1

Where:

V2 is the new voltage (120 V)

I1 is the current at 240 V

Substituting the values:

P2 = 120 V * (2929 W / 240 V)

Simplifying:

P2 = 14645 W / 240

Calculating the value:

P2 ≈ 61.02 W

Therefore, if the stove is run on 120 V instead of 240 V, it would receive approximately 61.02 W of power.

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Answer:

38

Step-by-step explanation:

6 times 5 =30

d=8

30+8-38

The given statement is "To construct a binomial distribution, it is necessary to know the total number of trials and the probability of success on each trial." true because to construct a binomial distribution, it is necessary to know the total number of trials and the probability of success on each trial.

The binomial distribution is a discrete probability distribution that describes the number of successes in a fixed number of independent trials, each with the same probability of success.

The parameters of a binomial distribution are n, the number of trials, and p, the probability of success on each trial. The distribution is then constructed by computing the probability of getting k successes in n trials, where k can be any integer from 0 to n.

The binomial distribution is widely used in many areas of statistics, including quality control, reliability engineering, and hypothesis testing. It is a fundamental concept in probability theory and serves as the basis for many other probability distributions.

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The researchers are investigating the perception of three-dimensional shapes on computer screens and specifically examining the components of a square figure or cube necessary for viewers to perceive details of the shape. They vary the stimuli to include fully rendered cubes, cubes with incomplete sides, and cubes with missing corner information. Four participants are recruited for an intense study, and their accuracy rates are measured across the three figure conditions. The trials are presented in different orders for each participant using a random-numbers table to determine unique sequences.

In this study, the researchers are interested in understanding how viewers perceive details of three-dimensional shapes on computer screens. They manipulate the stimuli by presenting fully rendered cubes, cubes with incomplete sides, and cubes with missing corner information. By varying these components, the researchers aim to identify which elements are necessary for viewers to accurately perceive the shape.

Four participants are recruited for an intense study, indicating a small sample size. While a larger sample size would generally be preferred for generalizability, intense studies often involve fewer participants due to the time and resource constraints associated with conducting a large number of trials. This approach allows for in-depth analysis of individual participant performance.

The participants are trained on how to detect subtle deformations in the shapes, which suggests that the study aims to assess their ability to perceive and discriminate fine details. After the training, the participants' accuracy rates are measured across the three different figure conditions, likely reported as a percentage of correctly identified shape details.

To minimize potential biases, the trials are presented in different orders for each participant, using a random-numbers table to determine unique sequences. This randomization helps control for order effects, where the order of presenting stimuli can influence participants' responses.

The researchers in this study are investigating the perception of three-dimensional shapes on computer screens. By manipulating the components of square figures or cubes, they aim to determine which elements are necessary for viewers to perceive shape details accurately. The study involves four participants, an intense study design, and measures accuracy rates across different figure conditions. The use of randomization in trial presentation helps mitigate potential order effects.

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Answer:

7x

Step-by-step explanation:

Answer:

7x

Step-by-step explanation:

4x+3x

4+3=7

add x, same answer of 7x

The area  rate of change of side of square is 8 cm/s;

dA/dt = 112 cm²/s;

Area = (r)²; where r is the side of square;

dA/dt = (dA/dr)(dr/dt);

dA/dr = 2r and dA/dt = 112 cm²/s;

Therefore; dr/dt = 112/2r at r = 7;

dr/dt = 112/14 = 8 cm/s;

Rate of change of side of square is 8 cm/s;

area is the quantity that expresses the extent of a area on the plane or on a curved floor. The location of a aircraft region or plane place refers to the location of a shape or planar lamina, at the same time as surface place refers to the vicinity of an open floor or the boundary of a 3-dimensional object.

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Answer:

The segment bisector of FG is HI because it splits it into two equal parts. Since point F to the bisector equals 33 and the bisector to point G is the same, that would also be 33. 33+33=66=FG

Step-by-step explanation:

The measurement of the line segment FG is 66 units.

We need to identify the segment bisector of FG and then find FG.

A segment bisector is a line, a ray, a line segment, or a point that cuts a line segment at the centre dividing the line into two equal parts. The word segment can also be referred to as line segment which means a segment is a part of the line that has fixed endpoints. The word bisect means cutting any object or line into two equal halves. Hence, a segment bisector is referred to as when two line segments bisect or cut each other at a point dividing the lines into equal halves.

From the given figure, HI is the bisector of the line segment FG.

Given that, 1/2 (FG)=33 units

⇒FG=66 units

Therefore, the measurement of the line segment FG is 66 units.

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a) The figure below shows the long-run model of a small open economy graphically that illustrates the impact of reducing the government's budget deficit on the exchange rate and the trade balance.

Axes are labeled in the diagram below. The vertical axis is the exchange rate and the horizontal axis is the trade balance. In the graph, "NX" represents the trade balance in the economy while "r" represents the real interest rate.

ii) The curvesThe curve labeled "NX" slopes downward because the trade balance declines as the real interest rate in the domestic economy increases. The curve labeled "r" is the positively sloping curve, representing the real interest rate in the economy.

iii) The initial equilibrium values The initial equilibrium is marked as point A in the diagram, with a trade balance of NX0 and a real interest rate of r0. The initial equilibrium exchange rate is marked by E0.iv) The direction the curves shift If the government cuts the budget deficit, it will reduce demand for funds, causing a decrease in the interest rate. This is illustrated by the r curve moving leftward to r1 in the graph. At the new interest rate, the trade balance will rise to NX1, as shown by the shift in the NX curve to the right. As a result of these changes, the exchange rate increases from E0 to E1.v) The new long-run equilibrium values The new long-run equilibrium is shown by point B in the graph. At point B, the exchange rate is higher at E1, and the trade balance is greater at NX1.b) The policy recommendation of Michel Camdessus will work based on the graphical analysis. When the government reduces its budget deficit, it reduces the demand for funds and, as a result, reduces the interest rate. As a result of the decrease in interest rates, investment in the economy will rise, raising output. An increase in output will increase demand for imports, reducing the trade balance. As a result, the exchange rate increases because a higher exchange rate reduces demand for exports, reducing the trade balance to the level at which saving equals investment in the economy.

Consequently, the policy recommendations of Michel Camdessus will work since the exchange rate and trade balance will both increase. The new long-run equilibrium will be reached at a higher exchange rate and trade balance in the long run, which will bring about more stability and sustainability.

Michel Camdessus recommended that the United States reduce its budget deficit in order to raise the exchange rate. The long-run model of a small open economy was used to illustrate graphically the impact of reducing the government's budget deficit on the exchange rate and the trade balance. The graphical analysis showed that if the government cuts the budget deficit, the exchange rate and trade balance will both increase. The new long-run equilibrium will be reached at a higher exchange rate and trade balance in the long run, which will bring about more stability and sustainability. Therefore, Mr. Camdessus's policy recommendation will work.

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Answer:

C. 8, H. 6x^2+43x+55

Step-by-step explanation:

You're looking for a value that will make x-2=6, since you add exponents. So W^8/W^-2 is equal to 1/W^6. Since 8-2=6.

A= length * width

(2x+11)(3x+5), foil it out by taking 2x(3x+5), then 11(3x+5).

6x^2+10x+33x+55, combine like terms

6x^2+43x+55

Answer:

26. H: \(6x^2+43x+55\)

Step-by-step explanation:

\(( 2x + 11 ) ( 3x + 5 )\)

\(6x^2+43x+55\)

To construct a 90% confidence interval for the average speed of cars on the highway with a margin of error no more than ±0.5 mph and a standard deviation of 7 mph, you must clock at least 339 cars.

Step 1: Identify the critical value (z-score) for a 90% confidence interval. This can be found in a standard z-table or using a calculator. The critical value for a 90% confidence interval is 1.645.

Step 2: Use the margin of error (E) formula to calculate the sample size (n):
E = (z * σ) / √n

Where E is the margin of error (0.5 mph), z is the critical value (1.645), σ is the standard deviation (7 mph), and n is the sample size.

Step 3: Rearrange the formula to solve for n:
n = (z * σ / E)^2

Step 4: Plug in the values and calculate the sample size:
n = (1.645 * 7 / 0.5)^2
n ≈ 338.89

Since the sample size must be a whole number, round up to the nearest whole number.

To construct a 90% confidence interval for the average speed of cars on the highway with a margin of error no more than ±0.5 mph and a standard deviation of 7 mph, you must clock at least 339 cars.

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Answer:

About 4 hours.

Step-by-step explanation:

To find the answer we will add both percentages of Watching TV and Homework.  8% + 13% = 21%.  Now we will divide 100 by 21 and we get 4 hours a day.

Answer:

below

Step-by-step explanation:

Rewrite the expression using the negative exponent rule  

b ^− n =1/ b^ n  . 1 x^ 7