Topic: Using the rational theorem to find all zeros of a polynomial
Question: 5x^4-26x^3-64x^2+9x-14

The value of the expressions are;

a. 2x² + 6

b. 3x² - 6x + 2x -6

c. y = 3

d. x = 2

From the information given, we have

a. 2x(x + 3)

expand the bracket

2x² + 6

b. (3x + 2)(x-3)

expand the bracket

3x² - 6x + 2x -6

c. 4y -2(6-y) = 6

expand the bracket

4y - 12 + 2y = 6

collect like terms

6y = 18

Then,

y = 3

d.  x(2x-4)= (2x + 1)(x-2)

expand bracket

2x² - 4x = 2x² - 4x + x - 2

collect like terms

x = 2

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The probability of having at most 8 clear days in Juneau, 14 or more in Hilo, 20 or more in Phoenix, 18 or less in Las Vegas, and between 5 and 10 in Seattle is 0.7608, 0.7367, 0.4672, 0.9590, and 0.5385, respectively.

1. P(r≤8) = P(r=0) + P(r=1) + P(r=2)+ P(r=3)+ P(r=4)+ P(r=5)+ P(r=6)+ P(r=7)+ P(r=8)= 0.7608

2. P(r≥14) = 1 - P(r≤13) = 1 - (P(r=0) + P(r=1) + P(r=2)+ P(r=3)+ P(r=4)+ P(r=5)+ P(r=6)+ P(r=7)+ P(r=8)+ P(r=9)+ P(r=10)+ P(r=11)+ P(r=12)+ P(r=13))= 0.7367

3. P(r≥20) = 1 - P(r≤19) = 1 - (P(r=0) + P(r=1) + P(r=2)+ P(r=3)+ P(r=4)+ P(r=5)+ P(r=6)+ P(r=7)+ P(r=8)+ P(r=9)+ P(r=10)+ P(r=11)+ P(r=12)+ P(r=13)+ P(r=14)+ P(r=15)+ P(r=16)+ P(r=17)+ P(r=18)+ P(r=19))= 0.4672

4. P(r≤18) = P(r=0) + P(r=1) + P(r=2)+ P(r=3)+ P(r=4)+ P(r=5)+ P(r=6)+ P(r=7)+ P(r=8)+ P(r=9)+ P(r=10)+ P(r=11)+ P(r=12)+ P(r=13)+ P(r=14)+ P(r=15)+ P(r=16)+ P(r=17)+ P(r=18)= 0.9590

5. P(5≤r≤10) = P(r=5) + P(r=6) + P(r=7)+ P(r=8)+ P(r=9)+ P(r=10)= 0.5385

The probability of having at most 8 clear days in Juneau, 14 or more in Hilo, 20 or more in Phoenix, 18 or less in Las Vegas, and between 5 and 10 in Seattle is 0.7608, 0.7367, 0.4672, 0.9590, and 0.5385, respectively.

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Answer:

1. 11π/6

2. 43π/18

3. -π/4

4. - 43π/18

5. 23π/6

6. 25π/18

Step-by-step explanation:

A full circle has a measure of 360° in degrees and 2π radians in radians.

Since a full circle has a measure of 2π radians, then half a circle has a measure of π radians, and a quarter circle has a measure of π/2 radians.

1. 2π - π/6 = 11π/6

2. 61π/36 - π/2 = 61π/36 - 18π/36 = 43π/18

3. 5π/4 - π = π/4; -π/4

4. -36π/18 - 7π/18 = -43π/18

5. 2π + π + 5π/6 = 23π/6

6. 36π/18 - 11π/18 = 25π/18

If 5 1/2 ounce of mango has 17 1/2 grams of sugar and 4 ounces of pineapple has 25 grams of sugar, We will be having 7 grams of sugar for one ounce of mango and 6 1/4 grams of sugar for one ounce of pineapple.

The problem states that we have 5 1/2 ounces of mango with 17 1/2 grams of sugar, and 4 ounces of pineapple with 25 grams of sugar. We are asked to determine the grams of sugar per ounce for each type of food. To determine the grams of sugar per ounce for each type of food, we can use the following calculations:

For mango: 5 1/2 ounces is equivalent to 11/2 + 1/2 = 2 ounces + 1 ounce/2, so we have 17 1/2 grams of sugar in 2 1/2 ounces of mango. To find the grams of sugar per ounce, we can divide 17 1/2 by 2 1/2, which gives us 7 grams of sugar per ounce of mango.

For pineapple: 4 ounces of pineapple has 25 grams of sugar. To find the grams of sugar per ounce, we can divide 25 by 4, which gives us 6 1/4 grams of sugar per ounce of pineapple.

Therefore, the grams of sugar per ounce for mango and pineapple are 7 and 6 1/4, respectively.

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Complete question is:

5 1/2 ounce of mango has 17 1/2 grams of sugar and 4 ounces of pineapple has 25 grams of sugar. Determine the grams of sugar for ounce for each type of food​.

Answer: look at the image for the answer and the solution

Step-by-step explanation:

Answer: 18.84

Step-by-step explanation:

because the radius is 3, the diameter is 6. And the circumference is C=pi(d).In this case, C=3.14(6), and 3.14*6=18.84

What does this problem ask for:

 --> which statement is sufficient to prove that:

     ∠ADB ≅ ∠ABD

Let's separate this image into two triangles: ΔADC and ΔABC

   --> prove that these triangles are congruent

       --> thus proving that: ∠ADB ≅ ∠ABD

Let's consider what evidence we have:

             --> thus: ∠ADC = ∠ABC

The minimum information that we have:

  --> prove that one pair of sides on both triangles are congruent

      --> based on the SSA Triangle Formula

             --> Two triangles that have two sides and one angle that are

                   equal, are therefore congruent

Based on the choices given:

 --> if DA = BA or DA is congruent to BA

  --> then ΔADC = ΔABC

Thus:

--> ∠ADC = ∠ABC

Answer: DA is congruent to BA

Answer:

The value of z is 58    

Step-by-step explanation:

The mean is the average of a set of numbers.  Mean = (sum of the numbers)/(the number of numbers).

We are told that the mean of x+y+z is = 55.  

We can wriote this as:

 55 = (x+y+z)/3

We learn that x+y = 107.  So lets enter that number for x + y:

 55 = (x+y+z)/3

55 = ((x+y)+z)/3    

55 = ((107)+z)/3           [Substitution]

55 = (107+z)/3

165 = 107+z               [Multiply both sides by 3]

z = 58                       [Simplify]

CHECK:

Is the mean of x, y, and z 55?

55 = (x+y+z)/3  ?

55 = ((107)+z)/3 ?   [Since we know x+y = 107]

55 = ((107)+58)/3 ?  [Since z=58]

55 = (165)/3)  ?

55 = 55  YES  The value of z is 58    

The solution is, x= StartFraction t Over 4 + 2 EndFraction, is equivalent to 4 x = t + 2.

An equation can be stated  a  mathematical statement that is made up of two expressions connected by an equal sign.  In its normal form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal.

here, we have,

given that,

4 x = t + 2

or, x = (t + 2) /4

or, x = t/4 + 2/4

or, x = t/4 + 2

Hence, The solution is, x= StartFraction t Over 4 + 2 EndFraction, is equivalent to 4 x = t + 2.

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In a simple linear regression model we use the normal quantile plot of the residuals to evaluate if it is reasonable to assume the error term come from a normal distribution.

In a simple linear regression model, the normal quantile plot of the residuals is a graphical tool used to assess the normality assumption of the error term (also known as the residual). The error term represents the difference between the actual value of the dependent variable and the predicted value by the model.

Assuming that the error term follows a normal distribution is important for various reasons. Firstly, the normal distribution is a very common assumption in statistics, and many statistical methods rely on it. Secondly, a normal distribution of the error term is essential for making reliable predictions and for computing valid confidence intervals.

The normal quantile plot of the residuals compares the distribution of the residuals against a theoretical normal distribution. The plot consists of a straight line if the residuals are normally distributed. However, if the plot shows deviations from the straight line, it indicates non-normality in the residuals.

If the normality assumption is not satisfied, we need to explore the reasons for the non-normality and consider alternative methods to analyze the data, such as non-parametric methods.

Therefore, the normal quantile plot of residuals is an essential diagnostic tool in simple linear regression, as it allows us to evaluate the assumption of normality and make appropriate adjustments to the model.

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Answer:

34

Step-by-step explanation:

The absolute value of a real number [tex]a[/tex] is [tex]a[/tex] when [tex]a[/tex] ≥ 0, or −[tex]a[/tex] when [tex]a[/tex] < 0. The absolute value of −34 is 34.

Hope it helps and have a great day! =D

There are System A has 0 solutions and System B has 1 solution.

A solution to an equation is a number that can be substituted for the variable to provide a true number statement.

System A:

Line 1: y = (1/2)x

Line 2: y = (1/2)x - 1

System B:

Line 1: y = -x - 1

Line 2: y = -2x - 1

Using these equations, we can determine the number of solutions for each system:

System A has two lines that do not intersect (they are parallel), so it has no solutions.

System B has two lines that intersect at a single point, so it has one solution.

Therefore, System A has 0 solutions and System B has 1 solution.

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The null hypothesis statement is that the population is equal to the value mentioned in the claim:

[tex]H_{0} =P=75%=0.75[/tex]=[tex]\frac{75}{100}[/tex]=[tex]0.75[/tex].

[tex]H_{0} =P < 0.75[/tex]

The claim can be supported by either the null hypothesis or the alternative hypothesis. The null hypothesis states that the population proportion is the same as the value specified in the claim. If the null hypothesis is the assertion, then the alternative hypothesis statement is the antithesis of the null hypothesis.

[tex]H_0} =P < 0.75[/tex]

A hypothesis is a well-informed, logically-supported guess about the answer to a scientific question. Although it is the experiment's anticipated outcome, it does not constitute experimental proof. The information obtained may or may not be supported, depending on the information received. Simple hypotheses simply state the relationship between two independent and dependent variables. Examples: If you stay up late, you will feel fatigued the next day.

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The perimeter of one square which combined with other to form a rectangle of 288 cm² is 12 cm.

The area of rectangle is given by the formula -

Area = length × width

Now we know that all the sides of square are same. Also, the identical squares have been kept side by side. So, let us represent one dimension of square with b. Thus, length of rectangle will be (b + b)

Length of rectangle = 2b

Width of rectangle will be b. Now, finding the value of b first.

288 = 2b×b

Performing multiplication

2b² = 288

b² = 288/2

Performing division

b² = 144

b = ✓144

Taking square root

b = 12 cm

The perimeter of one square = 2(length + width)

Perimeter of one square = 2 ( 12 + 12)

Perimeter = 2 × 24

Performing multiplication

Perimeter = 48 cm

Thus, perimeter of one square is 48 cm.

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5 to the power of one sixth (5¹/⁶) will be equal to square root of the cube root of 5.

What is the definition of square root?

The square root of a number is a value that, when multiplied by itself, yields the original number. The square root is the opposite of squaring a number. As a result, squares and square roots are ideas that are connected.

If x is the square root of y, it is denoted as x=√y, or the same equation may be expressed as x² = y. √" is the radical symbol used to symbolise the numerical root here. When a positive number is multiplied by itself, it represents the number's square. The square root of a positive number yields the original value.

Now,

Given that square root of the cube root of 5 i.e. √∛5=?

=√5¹÷³

=5¹/²*¹/³

=5¹/⁶

hence,

          5 to the power of one sixth (5¹/⁶) will be equal to square root of the cube root of 5.

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The conclusion is that the bag filling machine appears to be working correctly at this setting.

Based on the information provided, the manufacturer conducted a hypothesis test to determine if the bags are underfilled at the 420 gram setting. The null hypothesis (H0) is that the bags are not underfilled, while the alternative hypothesis (H1) is that the bags are underfilled.

Since the manufacturer failed to reject the null hypothesis at the 0.01 level of significance, this means that there is not enough evidence to support the claim that the bags are underfilled at the 420 gram setting. In other words, the bag filling machine appears to be working correctly at this setting.

It's important to note that the conclusion may change if the sample size or the level of significance is different. Additionally, other factors such as the accuracy of the measuring device used or the consistency of the banana chips themselves may also impact the results.

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Answer: [tex]5x^{2} +6x[/tex][tex]-4[/tex]

Step-by-step explanation:

Synthetic division

Probability that only one of the two failure modes will occur over the life of the building is 0.11

The probability for failure of building

P (Failure) = P(C U E)

                 =  P(C) -  P(E) - P(CUE) - P(C|E)P(E)

Substitute 0.05 for P(C) 0.1 for P(E) and 0.2 for PC/E) in equation to find the probability for failure.

P(failure) = P(CUE)

                        = 0.05 +0.1 -0.2 x 0.1

                        = 0.13

Probability that only one of the two failure modes will occur over the life of the building

P(CE U EC) = P(ČE) + P(EC)

                   = P(C U E) - P(EC)]

                   = P(CUE) - P(C|C)P(E)

Substitute 0.13 for P(CUE) 0.1 for P(E) and 0.2 for P(CIE) in equation (3) to find P(CE UĒC).

P(CE U EC) - 0.13 - (0.2 x 0.1)

= 0.11

Hence,

Probability that only one of two failure modes will occur over the life of the building is 0.11.

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If administrators at International University are curious how students' GAs after their first year compare to their high school GPs. The correct answer is: C. We cannot assume independence between the high school GPAs in the sample.

The GPAs of the students in the sample at the end of their first year at the university are likely to be correlated with their high school GPAs, as students with higher high school GPAs are likely to perform better in university as well.

Thus, the high school GPAs of the students in the sample are not independent of each other, and using the formula for the standard deviation of the sample would not be appropriate in this situation.

Therefore the correct option is C.

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The correct question is:

Administrators at International University are curious how students' GPAs after their fist year compare to their high school GPAs. They plan on taking an SRS of 80 of the 900 freshmen to look up their high school GPAs. They plan to look at the difference between the mean high school and the mean university GPA for students in the sample at the end of their first year. Why is it not appropriate to use the formula for the standard deviation of

The samples are not independent of each other.

We cannot assume independence between the university GPAs in the sample.

We cannot assume independence between the high school GPAs in the sample.

The samples are independent of each other.

Answer: A

Step-by-step explanation:

The sample is sampling the high school GPA and college GPA of the same students meaning the samples are not independent.

The formula possible formula for the trigonometric function whose values are in the following table is  y = 6 x sin(π/2 * x) - 4.

Trigonometric functions are described as the periodic functions which denote the relationship between angle and sides of a right-angled triangle.

The formula for a trigonometric function is typically written as :

y = a sin (bx + c) + d

where a, b, c, and d are constants which tells us  the amplitude, frequency, phase shift, and vertical shift of the function, respectively.

From the above table,  the amplitude = 6,

the frequency is 2π/4 = π/2

the phase shift = 0, and

the vertical shift = -4.

Therefore, we can write  the formula for the function as Y = 6 * sin(π/2 * x) - 4.

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Answer:

Step-by-step explanation:Class Trip Fund Calculation

The class figured out that if the percent increase is 99% from the beginning of the year, the class will have enough money for every student to go on the field trip. How much money will the class need to raise for every student to go

To calculate the amount of money that the class needs to raise, you can use the formula for calculating the amount after a percent increase:

amount = original amount + (original amount * percent increase / 100)

Let's assume that the original amount is x. After a 99% increase, the new amount will be:

x + (x * 99 / 100) = x * 199 / 100

So, to find the original amount, you can set up an equation:

x * 199 / 100 = amount needed for the field trip

And then solve for x:

x = amount needed for the field trip * 100 / 199

So, the class needs to raise an amount equal to the amount needed for the field trip * 100 / 199 to have enough money for every student to go on the field trip.

The percentage K 25 that is 25 t, can be found to be 1 % .

The relationship between K and t is such that 1 K has 100 t.

This means that K 25 in terms of t, would be:

= 25 x 100

= 2, 500 t

The percentage of K that is 25 t is therefore :

= 25 / 2, 500

= 1 / 100

= 0. 01

= 1 %

In conclusion, when given the values K 25 and 25 t, then 25 t would be  1 % of K 25.

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Answer:

One pecan cheesecake = $9

One apple cheesecake = $20

Step-by-step explanation:

This is a system of equations problem, so we can set up these equations (Note: p = pecan cheesecake cost | a = apple cheesecake cost):

8p + 12a = 312

9p + 6a = 201

Now, we can solve the system of equations. Below is an example of using the elimination method to solve the system:

1.    8p + 12a = 312 --> -4p - 6a  = -156        

     9p + 6a = 201  -->  9p + 6a = 201

2.                                  5p         = 45

3.                                    p         = 9

4.  8(9) + 12a = 312

    72   + 12a = 312

              12a = 240

                 a = 20

1. We try to make one of the terms equal to the negative version of the other term to eliminate that term; here, I am eliminating "a". To do this, find a multiple of one of the equations where one of the terms is the negative version of the other term. In other words, divide/multiply the equation by a number so one of the terms in the equation is the negative version of the term in the other equation (I divided the first equation by -2 so 12a becomes -6a, the negative version of 6a in the second equation.

2. Next, add the two equations' corresponding terms

(-4p + 9p = 5p; -6a + 6a = 0; -156 + 201 = 45)

3. Simplify the equation (5p = 45; p = 45/5; p = 9)

4. Substitute the term you found back into one of the equations to find the other term.

Answer:

The answer is 26

Step-by-step explanation:

The correct classification of the statements is: False, True, False, True.

What is Function ?

Function can be defined in which it relates an input to output.

The point of symmetry on f-¹(x) is (4,6).

False. The point (4,6) is not on the graph of f-¹(x), so it cannot be the point of symmetry. We can verify that the function is not symmetric with respect to any vertical or horizontal line.

The domain of f-¹(x) is (-∞,4).

True. The cube root function is defined for all real numbers, so the expression inside the cube root must be nonnegative. Therefore, (z - 4) / 5 ≥ 0, which implies that z ≥ 4. This means that the domain of f-¹(x) is (-∞,4].

The graphs of f¹(x) and f(x) are reflections across the x-axis.

False. The graphs of f¹(x) and f(x) are not reflections across the x-axis. We can plot the functions to see that they have different shapes and are not symmetric with respect to the x-axis.

The range of f¹(x) is (-∞,∞).

True. The cube root function is defined for all real numbers, so f-¹(z) can take any real value. This means that the range of f¹(x) is (-∞,∞).

Therefore, the correct classification of the statements is: False, True, False, True.

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Answer:

135

Step-by-step explanation:

The max value is where the far right point of the "whisker" is.

Answer:

[tex]49[/tex]

Step-by-step explanation:

[tex]\frac{US}{UD}=\frac{UT}{UC} \implies US=\frac{(56)(14)}{16}=49[/tex]

Answer:

6°

Step-by-step explanation:

Two angles are called complementary if the sum of their measures equals to 90°:

The complementary angle of 84° = 90° - 84°

                                                       = 6°

Answer:   6

Step-by-step explanation:

The complementary angle means the sum of two angles equal to 90. Let x be the other angle.

x + 84 = 90

       x = 6

The solution to the system of given linear equations is x = 0 and y = 2.

The equation is defined as a mathematical statement that has a minimum of two terms containing variables or numbers that are equal.

The system of equations is given in the question, as follows:

2x + 2y = 4  .....(i)

8x - 2y = -4  .....(ii)

To eliminate y, add the two equations together:

2x + 8x = 4 - 4

10x = 0

Solve for x:

x = 0

Now that we have x, we can substitute it back into one of the original equations to find y:

2x + 2y = 4

2(0) + 2y = 4

2y = 4

y = 4/2

y = 2

Thus, the solution is x = 0 and y = 2.

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Given that AC bisects ∠BCD, the complete flowchart proof is given below:

One of the first areas of mathematics is geometry, along with arithmetic. It is concerned with spatial characteristics like the separation, shape, size, and relative placement of objects.

A geometer is a mathematician who specializes in geometry.

GIven the shape in the image, the flowchart proof has been completed above.

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