please helppppppp meee

According to Descartes' Rule of Signs, there is 1 positive real zero and 2 or 0 negative real zeroes of the polynomial.

Descarte's Rule of Signs determines the number of real zeros in polynomial functions.

This indicates that -

The number of positive real zeros in the polynomial function f(x) is less than or equal to an even number depending on the sign change of the coefficients.

The number of negative real zeros in f(x) is an even number equal to or less than the number of sign changes of the coefficients of f(-x) terms.

Here, the polynomial function is given as -

\(P(x)=x^{3}-x^{2} -x-5\) ----- (1)

We have to find out the number of positive and negative real zeros that  the given polynomial can have.

The given polynomial already has its variables in the descending powers. So, we can easily determine the number of sign changes in the coefficients of P(x).

So, the coefficients of the variables in P(x) are -

1, -1, -1, -5

From above, we see that -

There is a sign change in the first and second variable coefficients

There is no sign change in the second and third variable coefficients

There is no sign change in the third and fourth variable coefficients

According to Descartes' Rule of Signs, there can be exactly three positive real zeros or less than three but an odd number of zeros.

So, we can determine that the number of positive real zeroes of the given polynomial can be 1.

To find out the negative real zeroes of the given polynomial, we have to find out P(-x) and determine the sign changes in the variable coefficients of P(-x).

From equation (1), we can write P(-x) as -

\(P(x)=x^{3}-x^{2} -x-5\\= > P(-x)=(-x)^{3}-(-x)^{2} -(-x)-5\\= > P(-x)=-x^{3}-x^{2} +x-5\)----- (2)

So, the coefficients of the variables in P(-x) are -

-1, -1, +1, -5

From above, we see that -

There is no sign change in the first and second variable coefficients

There is a sign change in the second and third variable coefficients

There is a sign change in the third and fourth variable coefficients

According to Descartes' Rule of Signs, since there are two sign changes of the coefficient variables, there can be two negative real zeros or less than two but an even number of zeros.

So, we can determine that the number of negative real zeroes of the given polynomial can be 2 or 0.

Thus, according to Descartes' Rule of Signs, there is 1 positive real zero and 2 or 0 negative real zeroes of the polynomial.

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The true statements are:

The initial cost for manufacturing records is $454, regardless of the number of records ordered.

In addition to the initial cost, each record costs $0.90 to manufacture.

Each record costs a total of $454.90 to manufacture.

As according to the question the function f(x)= 454+0.9x gives the cost, in dollars, of manufacturing x vinyl records.

Hence the incorrect statements are:

"The initial cost for manufacturing records depend on the quantity ordered".

"in addition to the initial cost, each record costs $454 to manufacture".

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Historical scientists deal with falsification by rigorously analyzing evidence, using peer review and scholarly discourse, and revising hypotheses based on new discoveries and interpretations.



Historical scientists deal with falsification by employing rigorous methodologies and critical analysis of evidence. They strive to gather as much relevant data as possible to test hypotheses and theories. This is done through meticulous research, including the examination of primary sources, archaeological artifacts, historical records, and other forms of evidence. Historical scientists also engage in peer review and scholarly discourse to subject their findings to scrutiny and criticism.

The mechanism used by historical scientists to falsify hypotheses involves a combination of evidence-based reasoning and the application of established principles of historical analysis. They aim to construct coherent and logical explanations that are supported by the available evidence. If a hypothesis fails to withstand scrutiny or is contradicted by new evidence, it is considered falsified or in need of revision. Historical scientists constantly reassess and refine their hypotheses based on new discoveries, reinterpretation of existing evidence, and advancements in research techniques. This iterative process helps to refine our understanding of the past and ensures that historical knowledge remains dynamic and subject to revision.

Therefore, Historical scientists deal with falsification by rigorously analyzing evidence, using peer review and scholarly discourse, and revising hypotheses based on new discoveries and interpretations.

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Answer:

x = 5

Step-by-step explanation:

3x + 15 = 30  Subtract 15 from both sides of the equation

3x = 15  Divide both sides by 3

x = 5

Answer:

$31.104

Step-by-step explanation:

Given :

Regular price = $36

Discount on sale = 20%

Discounted price = (100-20)%*36=0.8*36 = $28.8

Sales tax rate = 8% ;

Tax on sale = 8% * $28.8 = 2.304

Final amount that will have to be paid :

Discounted price + tax on sale

$28.8 + $2.304

= $31.104

Answer:

Quadrant III

Step-by-step explanation:

hope it helps :-)

Answer:

neither the correct answer for this would be SAS

Step-by-step explanation:

Answer:The interior angle of a polygon is given by

The exterior angle of a polygon is given by

where n is the number of sides of the polygon

The statement

The interior of a regular polygon is 5 times the exterior angle is written as

Solve the equation

That's

Since the denominators are the same we can equate the numerators

That's

180n - 360 = 1800

180n = 1800 + 360

180n = 2160

Divide both sides by 180

n = 12

I).

The interior angle of the polygon is

The answer is

150°

II.

Interior angle + exterior angle = 180

From the question

Interior angle = 150°

So the exterior angle is

Exterior angle = 180 - 150

We have the answer as

30°

III.

The polygon has 12 sides

IV.

The name of the polygon is

Dodecagon

Step-by-step explanation:

Answer:

608 cm²

Step-by-step explanation:

base = 2ac²

base = 2x4x2²

base = 2x4x4

base = 32cm

height = base + 6cm

height = 32 + 6cm

height = 38cm

Area of triangle = ½ x base x height

Area = ½ x 32 x 38

Area = 1216/2

Area = 608 cm²

Therefore the area of the triangle is 608cm²

Answer:

hello the function graph is turned 90 degree like clock way.

All the plotted graphs represent functions whose inverse is also a function.

A function is a relation between a dependent and independent variable. We can write the examples of functions as -

y = f(x) = ax + b

y = f(x, y, z) = ax + by + cz

Given is to find the function whose inverse is also a function.

A one to one function is a type of function whose inverse is also a function. The linear equations are one to one functions. They are of the form {y} = ax + b. This means that all of the graphs plotted represent a  function whose inverse is also a function. So, we can conclude that all the plotted graphs represent the straight line, and all of them represent functions whose inverse is also a function.

Therefore, all the plotted graphs represent functions whose inverse is also a function.

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Answer:

x = 1/3

Step-by-step explanation:

64^2x+1 = 1024
4^3(2x+1) = 4^5

Since the bases are the same, two expressions are only equal if the exponents are also equal.

3 (2x + 1) = 5

Divided each term by 3

2x + 1 = 5/3

2x = 2/3

x = 1/3

We have to find the value of  `(sinθ+cosθ−tanθ)/(secθ+cscθ−cotθ)`

Let's find all trigonometric ratios:

We can say that:

\($$\tan \theta= \frac{opp}{adj}= \frac{-4}{3}$$$$\text\)

{Using the Pythagorean Theorem we can find the hypotenuse }

\($$$$\text{Hypotenuse = } \sqrt{(-4)^2+(3)^2}\)

\(= \sqrt{16+9}\)

= \(\sqrt{25}\)

=\(5$$$$\)

Substituting the values of sinθ, cosθ and tanθ in `

\(= \frac{\frac{3}{5} + \frac{-4}{5} - \frac{-4}{3}}{\frac{-4}{5} + \frac{5}{3} - \frac{-3}{4}}$$$$\)

\(=\frac{\frac{9}{15} + \frac{-12}{15} + \frac{20}{15}}{\frac{-16}{20} + \frac{25}{12} + \frac{3}{4}}$$$$\)

\(=\frac{\frac{17}{15}}{\frac{-14}{15}}$$$$\)

\(=-\frac{17}{14}$$\)

Therefore, \(`(sinθ+cosθ−tanθ)/(secθ+cscθ−cotθ)\)` is equal to

`-17/14` when `tanθ=−43` (Quadrant II).

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Step-by-step explanation:

36 because since theres 36 people each person gets one for each

The two steps for calculating the mean:

Add up all the values in the data set.

Divide this number by the number of values.

The mean of a dataset is the sum of all values divided by the total number of values. It’s the most commonly used measure of central tendency and is often referred to as the “average.”

There are two steps for calculating the mean \((\bar{x})\):

(1) Add up all the values in the data set.

Sum of all the observations of given data denoted by \(\sum x\)

(2) Divide this number by the number of values.

The total number of values of given data denoted by 'n'

Sample mean:

\($$\overline{x}= \frac{\sum x}{n} $$\)

Example: Find the mean step by step?

42, 13, 31, 87, 24, 58, 76, 69

Solution:

Step 1: Find the sum of the values by adding them all up.

\(\sum x=\) 42 + 13 + 31 + 87 + 24 + 58 + 76 + 69 = 400

Step 2: Divide the sum by the number of values

In the formula, n is the number of values in your data set. Our data set has 8 values.

\($$\overline{x}= \frac{\sum x}{n} $$\)

\($$\overline{x}=\frac{400}{8}\)

\($$\overline{x}\) = 50

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Answer: okay so you add all of the numbers in the data set and then divide by how many numbers there were in the set.

Step-by-step explanation:

On dividing the circumference and the diameter of our Jack-o-Lantern we will get π.

A Jack-o-Lantern can be considered spherical in shape.

The circumference of a #D shape is the intersection of the 3D shape with any plane passing through its center.

Hence the circumference of a jack-o-lantern will be the perimeter of the circle that has been cut through its center.

Let the radius of our Jack-o-lantern be r cm.

The formula of a circumference of a sphere is 2πr

where r is the radius of the sphere.

The diameter of a sphere is twice its radius.

Therefore, the diameter of our jack-o-lantern will be

2r cm.

By dividing the circumference and the diameter we get

2πr cm / 2r cm

= π

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Answer:

1, 2, 4

Step-by-step explanation:

Okay so all of these CAN be true, but the question asks which ones MUST be:

As long as you add or multiply both sides by the same amount,  that keeps them even. Subtraction and addition can change it though because we don’t know if it’s positive or negative.

I Hope this Helps!

Answer: (A)(B)(D)    

Step-by-step explanation:

hope this helps here is proof

The area of the polygon is solved to be  1044 squared cm

The area of the composite polygon is solved by dividing the object into two sections. Then adding up the areas

Section 1 has dimensions:

length * width = 46 * 14 = 644

section 2 has dimensions:

length = 46 - 21 = 25

width = 30 - 14 = 16

Area = 25 * 16 = 400

Area of the composite figure

section 1  + section 2

= 644 + 400

= 1044 squared cm

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After  solving the equation 5(X - C)  = D , for the given matrices , we get , the unknown matrix X is = \(\left[\begin{array}{ccc}5&9\\10&6\\6&8\end{array}\right]\) .

In the question ,

it is given that , the matrices are

A = \(\left[\begin{array}{ccc}7&3\\4&3\end{array}\right]\)   B = \(\left[\begin{array}{ccc}7&2\\7&2\end{array}\right]\)   C = \(\left[\begin{array}{ccc}3&3\\4&0\\0&8\end{array}\right]\)   and D = \(\left[\begin{array}{ccc}10&30\\30&30\\30&0\end{array}\right]\) .

and the equation is given as 5(X - C)  = D ,

and we have to find the value of unknown matrix X .

let the matrix X be = \(\left[\begin{array}{ccc}a&b\\c&d\\e&f\end{array}\right]\)

Substituting , the given matrices A , B , C and D in the equation 5(X - C)  = D ,

we get ,

5(X - C)  = D ,

5X - 5C = D ,

5\(\left[\begin{array}{ccc}a&b\\c&d\\e&f\end{array}\right]\) - 5\(\left[\begin{array}{ccc}3&3\\4&0\\0&8\end{array}\right]\) = \(\left[\begin{array}{ccc}10&30\\30&30\\30&0\end{array}\right]\)

5\(\left[\begin{array}{ccc}a&b\\c&d\\e&f\end{array}\right]\) = \(\left[\begin{array}{ccc}10&30\\30&30\\30&0\end{array}\right]\) - \(\left[\begin{array}{ccc}15&15\\20&0\\0&40\end{array}\right]\)

Simplifying further ,

we get ,

5\(\left[\begin{array}{ccc}a&b\\c&d\\e&f\end{array}\right]\) = \(\left[\begin{array}{ccc}25&45\\50&30\\30&40\end{array}\right]\)

Dividing both sides by 5 ,

we get ,

X = \(\left[\begin{array}{ccc}a&b\\c&d\\e&f\end{array}\right]\) = \(\left[\begin{array}{ccc}5&9\\10&6\\6&8\end{array}\right]\)

Therefore , the matrix X is = \(\left[\begin{array}{ccc}5&9\\10&6\\6&8\end{array}\right]\) .

The given question is incomplete , the complete question is

Solve the matrix equation for the unknown matrix X.

A = \(\left[\begin{array}{ccc}7&3\\4&3\end{array}\right]\)   B = \(\left[\begin{array}{ccc}7&2\\7&2\end{array}\right]\)   C = \(\left[\begin{array}{ccc}3&3\\4&0\\0&8\end{array}\right]\)   and D = \(\left[\begin{array}{ccc}10&30\\30&30\\30&0\end{array}\right]\) . the equation is

5(X - C)  = D .

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The distance between the refreshment stands is 440 feet

From the question, we are to determine how far apart are the refreshment stands in feet

From the given information,

The parade route is 3/4 mile long

and

There are refreshment stands at the beginning and end of the route. And there will also be 8 refreshment stands along the route.

This means there will be 10 refreshment stands in all.

If there are 10 refreshment stands in all, then there will be 9 spaces between the refreshment stands.

∴ The distance between any two refreshment stands will be

3/4 mile ÷ 9 = 3/36 mile = 1/12 mile

Now, we will convert this to feet

NOTE: 1 mile = 5280 feet

∴ 1/12 mile = 1/12 × 5280 feet

= 440 feet

Hence, the distance between the refreshment stands is 440 feet.

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Explanation

Let the length be l and width b W, Since the length of the rectangle is 3 m less than twice the width, we will have

Therefore, the area becomes

Logically, the width becomes

Answer: width = 6.5m

Therefore, the length becomes

Answer" lenght =10 m

Answer:

12 friends

Step-by-step explanation:

If we have 3 pizzas, each cut into slices of \(\frac{1}{4}\), then we have a total of \(3 \div \frac{1}{4} = 3\cdot\frac{4}{1} = 12\) slices.

This means that 12 friends can share the 3 pizzas.

Hope this helped!

Answer:

12 people

Step-by-step explanation:

If everyone is getting 1/4 of the pizza then that means there are 4 slices in each pizza

Answer:

56

Step-by-step explanation:

48 ounces would feed 6 people and if 16 oz is for two people than 8 oz is for one person. So, 48 plus 8 is 56.

Confidence Interval = 0.1703 ± 0.0222 Confidence Interval ≈ (0.1481, 0.1925)  We are 95% confident that the true proportion of student loan borrowers with loans totaling more than $40,000 for their undergraduate education falls between approximately 0.1481 and 0.1925.

To construct a confidence interval to estimate the population proportion, we can use the following formula:

Confidence Interval = Sample Proportion ± Margin of Error

First, let's calculate the sample proportion:

Sample Proportion = Number of borrowers with loans > $40,000 / Total number of borrowers

Sample Proportion = 218 / 1280 ≈ 0.1703

Next, we need to determine the margin of error. For a 95% confidence level, we can use the formula:

Margin of Error = Z * sqrt((Sample Proportion * (1 - Sample Proportion)) / n)

Where Z is the z-value corresponding to the desired confidence level (in this case, 95%), and n is the sample size.

For a 95% confidence level, the critical z-value is approximately 1.96.

Margin of Error = 1.96 * sqrt((0.1703 * (1 - 0.1703)) / 1280)

Margin of Error ≈ 0.0222

Now, we can construct the confidence interval:

Confidence Interval = 0.1703 ± 0.0222

Confidence Interval ≈ (0.1481, 0.1925)

We are 95% confident that the true proportion of student loan borrowers with loans totaling more than $40,000 for their undergraduate education falls between approximately 0.1481 and 0.1925.

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a. (i) 4/5 + 1/3 = 17/15
  (ii) 4/5 + 1/3 = 0.933 (Three-digit chopping)
  (iii) 4/5 + 1/3 = 0.933 (Three-digit rounding)
  (iv) Relative error in (ii) = |(17/15) - 0.933| / (17/15) = 0.039
      Relative error in (iii) = |(17/15) - 0.933| / (17/15) = 0.039

b. (i) 4/5 x 1/3 = 4/15
  (ii) 4/5 x 1/3 = 0.267 (Three-digit chopping)
  (iii) 4/5 x 1/3 = 0.267 (Three-digit rounding)
  (iv) Relative error in (ii) = |(4/15) - 0.267| / (4/15) = 0.272
      Relative error in (iii) = |(4/15) - 0.267| / (4/15) = 0.272

c. (i) (1/3-3/11)+3/20 = -11/220
  (ii) (1/3-3/11)+3/20 = -0.050 (Three-digit chopping)
  (iii) (1/3-3/11)+3/20 = -0.051 (Three-digit rounding)
  (iv) Relative error in (ii) = |(-11/220) - (-0.050)| / (-11/220) = 0.077
      Relative error in (iii) = |(-11/220) - (-0.051)| / (-11/220) = 0.068

d. (i) (1/3+3/11)-3/20 = 19/220
  (ii) (1/3+3/11)-3/20 = 0.086 (Three-digit chopping)
  (iii) (1/3+3/11)-3/20 = 0.086 (Three-digit rounding)
  (iv) Relative error in (ii) = |(19/220) - 0.086| / (19/220) = 0.554
      Relative error in (iii) = |(19/220) - 0.086| / (19/220) = 0.554

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16.

$12.99 - $3.95 = $9.04

Approximately 678 electrons move past the fixed reference point every t = 1.55 ps, given a current of i = -0.7 μA.

The current is defined as the rate of flow of electric charge, which is given by:

i = ΔQ/Δt

where ΔQ is the amount of charge that flows past a point in time Δt.

Solving for ΔQ, we have:

ΔQ = iΔt

Substituting the given values, we get:

ΔQ = (-0.7 μA) × (1.55 ps) = -1.085 × 10^-16 C

The negative sign indicates that the current is carried by electrons, which have a negative charge. The magnitude of the charge on a single electron is approximately 1.6 × 10^-19 C.

Therefore, the number of electrons that pass the fixed reference point in time t = 1.55 ps is given by:

n = ΔQ/e

where e is the charge on a single electron.

Substituting the values, we get:

n = (-1.085 × 10^-16 C) / (-1.6 × 10^-19 C) = 678.125

Rounding off to the nearest integer, we get:

n = 678

Therefore, approximately 678 electrons move past the fixed reference point every t = 1.55 ps, given a current of i = -0.7 μA.

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Answer:

y = 3/4x - 2 2/3

Step-by-step explanation:

Are there choices?

y = 3/4x + b

1/3 = 3/4(4) + b

1/3 = 3 + b, b = -2 2/3

y = 3/4x - 2 2/3

According to ADA guidelines, a ramp with a two-foot vertical rise should be at least 20 feet long.

This length allows for a gentle slope that is safe and accessible for individuals with mobility impairments, including those using wheelchairs or other mobility aids. The slope of the ramp should not exceed 1:12, which means that for every inch of vertical rise, the ramp should extend 12 inches horizontally.

The ADA guidelines are designed to ensure that individuals with disabilities have safe and accessible routes of travel in public spaces. Ramps with proper dimensions and slope ratios are critical for individuals with mobility impairments to access buildings and spaces that may not be accessible via stairs. Ramps should also be designed with non-slip surfaces, handrails, and other safety features to prevent accidents and ensure that all individuals can use them safely and comfortably.

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