If p(x) = 5(x^2 +1) + 16, what is the value of p(11)?
A. 622
B. 736
C. 626
D. 690​

 The rational root theorem, also known as the rational zero theorem or the rational root test, holds that a single-variable polynomial with integer coefficients has rational roots if and only if constant term and leading coefficients are both divisible by the root's numerator and denominator, respectively.

    A theorem that is applied to polynomial roots is known as the rational root theorem or the rational zero test. The values of the variable that bring the polynomial to zero are known as the roots. Since the number of exact roots for a particular polynomial is always equal to the degree of the polynomial, we can determine this information from the polynomial's degree.

     For a linear polynomial, there is only one root, for instance. The number of zero roots in a cubic polynomial is three, whereas the number of  zero roots in a quadratic polynomial is two.

   f(x)=aₙxⁿ+aₙ₋₁xⁿ⁻¹+aₙ₋₂xⁿ⁻²+a₂x²+a₁x+a₀  where the coefficients aₙ to a₀ are all integers.

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A theorem that is applied to polynomial roots is known as the rational root theorem or the rational zero test. The values of the variable that bring the polynomial to zero are known as the roots. Since the number of exact roots for a particular polynomial is always equal to the degree of the polynomial, we can determine this information from the polynomial's degree.

f(x)=aₙxⁿ+aₙ₋₁xⁿ⁻¹+aₙ₋₂xⁿ⁻²+a₂x²+a₁x+a₀  where the coefficients aₙ to a₀ are all integers.

Linear equations are one-degree equations, it is formulated as: ax + by + c = 0.

A linear equation has the following standard form: ax + by + c = 0.

Here, variables x and y and constants a, b, and c are used.

Also, a ≠ 0, and b ≠ 0.

For linear equations, the slope-intercept formula is: y=mx+b

Where m stands for the line's slope and b represents the y-intercept.

The three types of linear equations are point-slope, slope-intercept, and standard form.

When an algebraic equation is graphed, it always produces a straight line since each term has an exponent of 1 or 0. This type of equation is known as a linear equation.

Steps are -

Step 1: Always begin by separating the variable y from the inequality's left side.

Step 2: Replace the symbol for inequality with that for equality.

Step 3: In the xy plane, graph the boundary line from step 2. You are creating the boundary line that would divide or cut the xy-plane into two sections in this stage.

Step 4: Shading one side or area of the boundary line is the final step.

Step 5: Use this optional step to check or confirm that you have shaded the boundary line's side appropriately.

So, the region of the coordinate plane where the inequality is satisfied is shown by a linear inequality.

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When X and Y axes are rotated through an angle θ to form X' and Y' axes, then the relation between the axes and the angle is given by,

[tex]\rm{X=X'\cos\theta-Y'\sin\theta}[/tex]

[tex]\rm{Y=X'\sin\theta+Y'\cos\theta}[/tex]

Then x and y are replaced in terms of x' and y' as,

[tex]\rm{x=x'\cos\theta-y'\sin\theta}[/tex]

[tex]\rm{y=x'\sin\theta+y'\cos\theta}[/tex]

Here θ = π/6. Then,

[tex]\rm{x=x'\cos\left(\dfrac{\pi}{6}\right)-y'\sin\left(\dfrac{\pi}{6}\right)=\dfrac{x'\sqrt3-y'}{2}}[/tex]

[tex]\rm{y=x'\sin\left(\dfrac{\pi}{6}\right)+y'\cos\left(\dfrac{\pi}{6}\right)=\dfrac{x'+y'\sqrt3}{2}}[/tex]

We are asked to find the transformed equation for,

[tex]\longrightarrow\rm{P:x^2+2\sqrt3\,xy-y^2=2a^2}[/tex]

We will give substitutions for x and y to find it.

[tex]\small\text{$\longrightarrow\rm{P':\left(\dfrac{x'\sqrt3-y'}{2}\right)^2+2\sqrt3\left(\dfrac{x'\sqrt3-y'}{2}\right)\left(\dfrac{x'+y'\sqrt3}{2}\right)-\left(\dfrac{x'+y'\sqrt3}{2}\right)^2=2a^2}$}[/tex]

Simplify this equation to get,

[tex]\small\text{$\longrightarrow\rm{P':(x')^2-(y')^2=a^2}$}[/tex]

Hence the transformed equation is,

[tex]\longrightarrow\rm{\underline{\underline{x^2-y^2=a^2}}}[/tex]

A prism is a solid with many plane faces that define its perimeter; two of these faces, known as the ends, are congruent parallel plane polygons, while the other two, known as the side faces, are parallelograms.

A prism is a polyhedron with two parallel polygonal bases. A prism is an optical element that is transparent and has polished, flat surfaces that refract light. The lateral faces tie together the two polygonal bases. Most of the lateral faces are rectangular. Sometimes, it could even be a parallelogram.

The formula for calculation of prism are as bellow,

The surface area of a prism = (2×Base Area) +Lateral Surface Area

The volume of a prism =Base Area× Height

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Yes, both the rates i.e. 24 laps in 6 minutes and 72 laps in 18 minutes are equivalent.

The unit rates for equivalent rates are the same. Similar to equivalent ratios, equivalent rates can be calculated by multiplying or dividing the numerator and denominator by the same amount.

When two expressions can be reduced to a single-third expression or when one of the expressions can be written in the same way as the other, they are said to be equivalent. When values are replaced for the variable and both expressions yield the same result, you may also tell if the two expressions are equal.

To determine whether the rates are equivalent, we need to compare the number of laps completed per unit of time. In the first case, the rate is 24 laps in 6 minutes, which is equal to 4 laps per minute. In the second case, the rate is 72 laps in 18 minutes, which is also equal to 4 laps per minute. Since both rates are equal to 4 laps per minute, the rates are equivalent.

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The rates of 24 laps in 6 minutes and 72 laps in 18 minutes are equal, therefore yes.

Equivalent rates have the same unit rates. Equivalent rates can also be determined by multiplying or dividing the numerator and denominator by the same number, just like equivalent ratios.

Two expressions are considered to be equivalent if one of them can be written in the same way as the other or if they can both be condensed to a single-third expression. You may also tell if two expressions are equivalent if, when the values for the variable are changed, both expressions provide the same outcome.

In order to determine whether the rates are similar, we must compare the number of laps completed per unit of time. The pace in the first scenario is 4 laps per minute, or 24 laps done in 6 minutes. When 72 laps are completed in 18 minutes, the rate is similarly 4 laps per minute. Due to the fact that they both equal 4 laps per minute, their rates are equal.

Answer:

value of Johnny's investments today, at age 50, is approximately 18.39 dollars.....................

Step-by-step explanation:

To find the present value of Johnny's investments, you will need to use the formula for continuous compound interest:

where PV is the present value, A is the final amount, r is the annual interest rate, and t is the number of years.

Solving this equation gives a present value of approximately 18.39 dollars. This means that the value of Johnny's investments today, at age 50, is approximately 18.39 dollars, given the original investment amount and the interest rate.

It is important to note that this calculation assumes that the interest is compounded continuously, which means that the interest is compounded infinitely often over the course of the year. This results in a slightly higher present value than if the interest were compounded annually or quarterly.

the 4 parallel line rules are Alternate angles are equal. ...Co-interior angles add to 180° ...Vertically opposite angles are equal. ...Angles on a line add to 180°

What are the 4 parallel line rules?

Working with angles in parallel lines

Corresponding angles are equal. A line cutting across two parallel lines creates four pairs of equal corresponding angles, as in the diagram below: ...

Alternate angles are equal. ...

Co-interior angles add to 180° ...

Vertically opposite angles are equal. ...

Angles on a line add to 180°

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The required equation for the given case is obtained as y = -0.2x + 5.

The slope of a straight line is the tangent of the angle formed by it with the positive x axis as the reference. The negative slope indicates the rate of decrease while the positive shows the rate of increase.

The given problem can be solved as follows,

The general form of slope-intercept equation for a line is y = mx + c.    

From the given data the slope can be calculated as,

m = Difference of miles ÷ Difference of minutes  

   = (2 - 4) ÷ (15 - 5) = -1/5

Now, substitute m = -1/5 in y = mx + c to obtain,

y = -1/5x + c

Substitute y = 4 and x = 5 to get,

4 = -1/5 × 5 + c

=> c = 5

Thus, the required equation becomes as y = -1/5x + 5 or y = -0.2x + 5.

Hence, the equation that models Ye's distance from home, y, in terms of minutes, x is given as  y = -0.2x + 5.

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5 turning points are in the graph of the polynomial function given in the picture.

Given that,

We have to find how many turning points are in the graph of the polynomial function given in the picture.

We know that,

Turning points are places on a graph where the direction of the line switches from upward to downward and downward to upward

The graph's direction is changing at five separate points, and those points are:

(-5,6) ,(-3,-3) ,(0.5,0.5) ,(3,2.5) ,(5,5)

Therefore, 5 turning points are in the graph of the polynomial function given in the picture.

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The function Y = -3 is a linear function.This means that the graph of the function will be a straight line.

This is because the equation has only one variable (Y) and the change in Y is directly proportional to the change in the independent variable, in this case X.

To prove that the function is linear, we can use the formula y = mx + b, where m is the slope and b is the y-intercept. In this case, the slope is 0, as the line is horizontal, and the y-intercept is -3. Thus, we can calculate the equation as follows:

y = 0x + (-3)

y = -3

Therefore, we can conclude that the function Y = -3 is a linear function.

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We can find sample mean by:

Sample Mean = Sum of terms [tex]\div[/tex] Number of Terms

We can find range by:

Range = Highest Value (H) - Lowest Value (L)

Sample mean:

Sample mean represents the measure of the center of the data. Any population's mean is estimated using the sample mean.

An average value found in a sample is termed the sample mean. the sample mean so calculated is used to find the variance and thereby the standard deviation.

Sample Mean = Sum of terms [tex]\div[/tex] Number of Terms

[tex]& =\frac{\sum x i}{n} \\& =\frac{\left(x_1+x_2+x_3+\ldots+x_n\right)}{n}[/tex]

Range:

The range formula determines the difference between the highest and the lowest values in a given set of numbers.

In distribution, the large range means higher variability whereas the small range means low variability.

The range formula includes the other aspects of statistics such as mean, median, and mode. Hence, the formula to calculate the range is:

R = Highest Value (H) - Lowest Value (L)

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How do you find the sample mean and range?

The provided collection of observations has a standard deviation of 2.8581.

The standard deviation in statistics is a measure of the degree of variation or dispersion in a set of values. A low standard deviation implies that the values are close to the set's mean, whereas a high standard deviation shows that the values are spread out over a larger range. A large standard deviation indicates that the data is widely dispersed (less dependable), whereas a low standard deviation indicates that the data is tightly grouped around the mean (more reliable).

Here,

n=9

sum=45

mean=5

variance=sum(xₙ-mean)/n

=(1-5)/9+.........+(9-5)/9

=60/9

=6.67

standard deviation=√(6.67)

=2.581

The standard deviation of given set of observation is 2.8581.

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Algebra is offered in Grade 7 as a preparatory subject for algebra in higher grades.

In the United States, a middle school mathematics course that is typically taught in the 7th or 8th grade is known as pre-algebra. Its goal is to get students ready for the study of algebra. Algebra is often covered in grades 8 and 9.

Pre-algebra serves as an intermediate step following arithmetic and aids pupils in getting over some conceptual obstacles. Students learn that an equals sign indicates that two sides are equivalent and can be combined, as opposed to only being the question's response as it is in fundamental arithmetic.

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Answer:

In geometry, the formula for base area is dependent on the shape. Chart below is correct :)

Step-by-step explanation:

Answer: 1/(16^13)

Step-by-step explanation: Another way of rewriting this would be

(8 - xy + x)^(2-3y). Plugging in numbers, this results to

[8 - (-2)(5) + (-2)]^[2 - 3(5)]

which can then be simplified to

(8+10-2)^(-13) = 16^(-13) = 1/(16^13) which has a pretty big number in the denominator

A whole number higher than one that cannot be divided exactly by any other whole number than itself and one is a prime number. So the smallest 8 prime numbers are: 2,3,5,7,11,13,17,19.

A whole number higher than one that cannot be divided exactly by any other whole number than itself and one is a prime number.

Complete numbers, the range of numbers that includes zero and natural numbers, not a decimal or fraction.

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The confidence interval of p+/-E is 0.555+/-0.444

A confidence interval is often represented as the estimated value plus and minus the margin of error.

Let the mid-point of the interval be 'p'

Therefore,'

[tex]p=\frac{0.111+0.999}{2} =0.555[/tex]

Now,

The error term 'E' is the distance between 'p' and the end of the interval.

[tex]E=\frac{0.999-0.111}{2} =0.444[/tex]

So finally we get, the answer as

p+/-E = 0.555+/-0.444

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The slope of function f(x) is of -1, while the slope of function g(x) is of zero. Thus, the function g(x) has a greater slope.

Given a table of values, the slope of a linear function is given by the rate of change of the output variable y relative to the input variable x.

From the table of function f(x), we have that when x increases by 2, y decays by 2, hence the slope of the function is given as follows:

m = -2/2 = -1.

From the graph, the slope is also given by the change in y divided by the change in x.

The graph at the end of the answer shows a constant line, meaning that y remains constant even when x changes, thus the change in y is of zero, meaning that the slope of function g(x) is of zero.

The graph of function g(x) is given by the image shown at the end of the answer.

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The sample data does not provide strong support for the claim that the mean salary offer for mathematics and statistics graduates of this university is greater than the national average of $62,915.

At the null hypothesis, it is tested if there is not enough evidence that the mean is greater than 62915, that is:

[tex]H_0: \mu \leq 62915[/tex]

At the alternative hypothesis, it is tested if there is strong evidence that the mean is greater than 62915, that is:

[tex]H_1: \mu > 62915[/tex]

We have a right-tailed test, as we are testing if the mean is greater than a value.

The critical value for a right-tailed test, using the t-distribution, with a significance level of 0.05(standard) and 50 - 1 = 49 df, is of:

t = 1.6766.

Hence the decision is taken as follows:

The equation for the test statistic is presented as follows:

[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]

In which:

The parameters for this problem are given as follows:

[tex]\overline{x} = 63400, \mu = 62915, s = 3900, n = 50[/tex]

Hence the test statistic is of:

t = (63400 - 62915)/(3900/square root(50))

t = 0.88.

0.88 < 1.6766, hence it does not provide strong evidence.

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Answer:

7 1/11, 71/10, 7.166, 8.19

Step-by-step explanation:

71/10, 7 1/11, 7.166, 8.19

71/10 = 7.1

7 1/11 = 78/11 = 7.09

So, the order from least to greatest is: 7 1/11, 71/10, 7.166, 8.19

It’s discriminant is zero, so it has one real solution statement is true for  x²-2x +1=0.

A quadratic equation is a second-order polynomial equation in a single variable x , ax²+bx+c=0. with a ≠ 0 .

The given quadratic equation is x²+1=2x

This can also be written as x²-2x +1=0

a=1, b=-2 and c=1

The expression b² − 4ac is called the discriminant, and can be used to determine whether the solutions are real, repeated, or complex.

(-2)² − 4(1)(1)=4-4

b² − 4ac= 0

A discriminant of zero indicates that the quadratic has a repeated real number solution.

It’s discriminant is zero, so it has one real solution.

Hence, It’s discriminant is zero, so it has one real solution statement is true for  x²-2x +1=0.

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Answer: 0

Step-by-step explanation:

slope = Δy/Δx

slope = (17-17)/(3-8) = 0

As per the linear equation, the value of correlation coefficient we have identified that option (a) is correct.

The term linear equation refers in which the highest power of the variable is always 1 and it is also known as a one-degree equation.

Here we have given that Nadeem keeps track of the number of times he visits the library and the number of books he checks out.

And we need to find the correlation if you model his data with a linear equation

While we looking into the given question, we have identified that Nadeem keeps track of the number of times he visits the library and the number of books he checks out.

And based on the given details we have identified the following values from the given tables,

=> ∑xy = 285

=> ∑x = 33

=> ∑y = 51

=> y = 8.5

=> x = 5.5

=> ∑x² = 199

=> ∑x·∑y = 33×51

=> (∑x)² = 1,089

=> (∑y)² = 51

Therefore, the value of b is calculated as,

=> [(6 x 285) - (33 x 51)] / [6 x 199 - 1089]

=> 0.2571

And the value of a is calculated as,

=> 8.5 - 0.2575 × 5.5 = 7.08575

Then the correlation coefficient, r, is calculated as,

=> r = [(6 x 285) - (33 x 51)] / √[6 x 199 - 1089 x 6 x 471 - 51²]

When we simplify this one then we get,

=> r = 0.176

Based on the value of correlation coefficient we have identified that option (a) is correct.

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The required mean of the values 20 and 40 is 30.

The total of all numbers multiplied by the total number of values yields the mean (also known as the arithmetic mean, which varies from the scaling factor) of a dataset.

The term "average" is frequently used to describe this central trend measurement.

So, we have the values:

20, 40

Mean formula: Sum of terms / Number of terms

Obtain mean using the formula as follows:

Mean: Sum of terms / Number of terms

Mean: 60/2

Mean: 30

Therefore, the required mean of the values 20 and 40 is 30.

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The average temperature on Saturday was 62.6 °F, then the actual temperature will be equal to 17 °C.

The four fundamental operations of arithmetic are addition, subtraction, multiplication, and division of two or even more items.

Included in them is the study of integers, especially the order of operations, which is important for all other areas of mathematics, notably algebra, data management, and geometry.

As per the given information in the question,

The temperature on Saturday was 62.6 F

Then, the actual temperature will be,

C = 5/9(F -32)

C = 5/9(62.6 - 32)

C = 5/9(30.6)

= 17 °C

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The concept of zero as a number and not merely a symbol for separation was developed by ancient Indian mathematicians as early as the 7th century CE, where it was used to represent the null set, or void in mathematics. However, the invention of zero as a number is attributed to Indian mathematician Brahmagupta in 628 CE.

The concept of zero as a number was developed by ancient Indian mathematicians in the 7th century CE. It was used to represent the null set, or void in mathematics. This concept was further developed by Indian mathematician Brahmagupta in 628 CE. He is credited with the invention of zero as a number and not merely a symbol for separation. Brahmagupta used zero to represent both positive and negative numbers, and developed rules for calculations with zero. This allowed mathematicians to develop the operations of arithmetic and algebra. Today, zero is an integral part of mathematics, and is used in many fields such as calculus and analysis. The invention of zero as a number is credited to Brahmagupta, and it is one of the most influential contributions to mathematics

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Answer:

Answer is below

Step-by-step explanation:

1st Identity:[tex]a^{2} + 2ab + b^{2}[/tex]

2nd Identity: [tex]a^{2} - 2ab + b^{2}[/tex]

3rd Identity:([tex]a-b)(a+b)[/tex][tex]= a^{2} - b^{2}[/tex]

The height of the pyramid BC is equal to 14 units if The base of a solid oblique pyramid is an equilateral triangle with a base edge length of 14 units

We have a right angled triangle BAC

Using the trigonometric formula

The tangent here = 45°

The opposite side, h (this is the side that is facing the angle)

The adjacent = 14°

This is due to the fact AD=DC=AC

When we put the values into the formula:

Tan 45= 1

When we cross multiply,

14*1 = h

Therefore the height of the pyramid BC is 14 units.

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The ordered pair that is a solution to both equations is the solution of such a system graph.

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Answer:

(s-50)+(s-30)=s+25 {sum of interior angles is equal to exterior angle}

s-50+s-30=s+25

2s-s=25+50+30

s=105