Danton is rolling a fair six-sided die, each face with a number 1-6. He rolls 20 times and gets a “4” 6 times. What is the theoretical probability of rolling a 4 on this die?

A quadratic polynomial with integer coefficients is,
p(x) = x² + 6x + (17√21)/49.

A quadratic equation is an algebraic expression in the form of variables and constants.

A quadratic equation has two roots as its degree is two.

Given, The roots of the quadratic equation is x = 2/7, ± √21/7.

Let, p(x) = x² + bx + c.

p(x) = (x + 2/7 + √21/7)(x - 2/7 + √21/7).

p(x) = x² - (2/7)x + (√21/7)x + (2/7)x - (4/49) + 2√(21/49) + (√21/7)x - 2√21/49 + 21/49.

p(x) = x² + 2(√21/7)x + 21/49 - 4/49.

p(x) = x² + {(2√21)x}/7 + 17/49.

p(x) = x² + (42/7)x + (17√21)/49.

p(x) = x² + 6x + (17√21)/49.

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the real vector space of all continuous real-valued functions on the interval [0,1] is infinite-dimensional.

A vector space, also known as a linear space, is a collection of vectors that have been put together and multiplied ("scaled") by integers known as scalars. Real numbers are frequently seen as being scalars. Scalar multiplication by rational numbers, complex numbers, etc., on the other hand, seldom occurs. The term "subspace" refers to a vector space that is enclosed within another vector space. Each subspace is a vector space in and of itself, but it also has a definition in relation to another (bigger) vector space. We'll soon find out that there are a lot of different subspaces from earlier parts that we already know about.

We prove this theorem by contradiction.

(i.e. Suppose the vector space has finite dimension and we show that contradiction)

Suppose dimension vector space with finite dimension

Let, dim v = N, then N vector is linearly independent.

And Any (N + 1) vectors 1, x, x²,......, xⁿ cannot to be linearly independent, for we know that any linearly independent elements in a vector space with dimension N has size ≤ N.

Such that (N + 1) vectors 1, x, x²,......, xⁿ must be linearly independent.

The there elements exists Scalars a(j) ∈ R (0 ≤ i ≤ N), Not all Zero,

so that, a₁ + a₂²x + a₃x²+.......+ a^(N)x^(N) = 0; x ∈ [0,1]

∑a(i) x^(i) = 0 , x ∈ [0,1]

This is contradiction because any non-zero polynomial of degree N cannot be equal zero for all x ∈ [0,1].

Hence the real vector space for all continuous real-valued functions on the interval [0,1] which is infinite dimensional.

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A ray will always have one starting point before it may or may not diverge to produce other rays.

A ray is a geometric figure that consists of a part of a line that starts from a starting point and extends infinitely in one direction. It is represented by an arrow and has only one endpoint, with the other end extending without bounds. In mathematical terms, a ray can be described as half-line.

In geometry, there are two types of rays:

Opposite Rays: These are two rays that have the same endpoint and extend in opposite directions from that endpoint.

Same-side Rays: These are two rays that have the same endpoint and extend in the same direction from that endpoint, but do not overlap.

In optics, a third type of ray is often considered, which is:

Light Ray: This is a type of ray that travels in a straight line and carries energy, including electromagnetic radiation in the form of light.

Generally, all rays have one starting point and may or may not diverge to produce other rays.

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The value of the equation is A = 5/3

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

Substituting the values in the equation , we get

A = ( 25 ^ 1/2 ) / ( 27 ^ 1/3 )   be equation (1)

On simplifying the equation , we get

A = √25 / ∛27

The value of √25 = 5

And , the value of ∛27 = 3

Substituting the values in the equation , we get

A = 5/3

So , the value of A = 1.66667

Hence , the equation is A = 5/3

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Answer:

35%

Step-by-step explanation:

The remaining portion of the sheet from the overall length is 10.16 units.

In mathematics, a fraction is used to denote a portion or component of the whole. It stands for the proportionate pieces of the whole. Numerator and denominator are the two components that make up a fraction. The numerator is the number at the top, and the denominator is the number at the bottom. The denominator specifies the total number of equal parts in the whole, whereas the numerator specifies the number of equal parts that were taken.

Given that the overall length of the sheet is 18 5/ 8 = 149 / 8.

The two pieces removed are:

8 1/2 =17/ 2 and

7 9/16 = 121 / 16 inches.

The sawcut removed 1/16.

For two pieces we have two saw cuts thus, 2(1/16) = 1/8 inches.

The remaining portion is:

R = 149 / 8 - 17/2 - 121/6 - 1/8

R = 447 - 204 - 484 - 3 / 24

R = 10.16

Hence, the remaining portion of the sheet is 10.16 units.

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Therefore , the solution of the given problem of test statistics comes out to be Since the p-value is less than the level of significance of 0.01, we reject the null hypothesis.

The Z-statistic, which demonstrates that the ordinary normal balanced hypothesis is true, has been used as the statistic for anything resembling a Z-test. Let's say you run two separate X-y tests with a 0.05 level of significance, and the results show that you got a 2.5 R t. (also a Z-value). The p-value variable for this Z-value is 0.0124.

Here,

a) State the null hypothesis [tex]H_{0}[/tex] and the alternative hypothesis H1.

[tex]H_{0}[/tex]: p = 0.70 (proportion has not changed)

H1: p ≠ 0.70 (proportion has changed)

(b)

Since we are testing for a proportion and have sample size n = 250, we can use the normal distribution to approximate the sampling distribution of the sample proportion. Therefore, we will use the z-test statistic.

(c)

z = (p' - p) / √(p(1-p)/n)

p' = 154/250 = 0.616

z = (0.616 - 0.70) / √(0.70(1-0.70)/250)

z = -2.759

(d)

The p-value is the probability of observing a z-score as extreme as -2.759 or more extreme under the null hypothesis. Since this is a two-tailed test, we need to find the area in both tails of the standard normal distribution.

p-value = P(Z ≤ -2.759) + P(Z ≥ 2.759)

p-value = 0.0058 + 0.0058

p-value = 0.0116

(e)

Since the p-value is less than the level of significance of 0.01, we reject the null hypothesis. We can conclude that there is sufficient evidence to suggest that the proportion of high school seniors who believe that "getting rich" is an important goal has changed.

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The population of the town X in 2020 is given by the equation

A = 2,88,654

A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, %

The difference between an exact value and an approximation to it is the approximation error in a data value. Either an absolute error or a relative error might be used to describe this error.

Percentage change is the difference between the measured value and the true value , as a percentage of the true value

Percentage change =( (| Measured Value - True Value |) / True Value ) x 100

Given data ,

Let the population of the town X in 2020 be A

Let the percentage of increase be represented as r

Now , the equation will be

The initial population of Town X be A = 220,000

The increased population in 10 years be B = 252,000

So , the percentage change = [ ( B - A ) / A ] x 100

Substituting the values in the equation , we get

The percentage change r = [ ( 252,000 - 220,000 ) / 220,000 ] x 100

On simplifying the equation , we get

The percentage change r = [ 32,000/220,000 ] x 100

The percentage change r = 0.1454545 x 100

The percentage change r = 14.545 %

Now , the population of the town X in 2020 = ( 14.545 + 100 )% x increased population in 10 years

On simplifying the equation , we get

The population of the town X in 2020 A = ( 114.545 )% x 252,000

The population of the town X in 2020 A = 2,88,654.544

Hence , The population of the town X in 2020 A = 2,88,654

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The required standard deviation for the given data set is 4.38.

The standard deviation reveals the degree of data skewedness. It gauges how far away from the mean each observed value is. Approximately 95% of values in any distribution will be within two standard deviations of the mean.

To calculate the standard deviation of this sample, we'll follow these steps:

Find the mean of the sample:

mean = (1 + 3 + 3 + 7 + 10 + 12) / 6 = 6

Subtract the mean from each value in the sample to find the deviations:

deviations: -5, -3, -3, 1, 4, 6

Square the deviations:

squared deviations: 25, 9, 9, 1, 16, 36

Sum the squared deviations:

sum of squared deviations = 25 + 9 + 9 + 1 + 16 + 36 = 96

Divide the sum of squared deviations by the number of values minus one:

sum of squared deviations / (n - 1) = 96 / (6 - 1) = 96 / 5 = 19.2

Take the square root of the result from step 5 to get the standard deviation:

standard deviation = [tex]\sqrt{(19.2)}[/tex] = 4.38

So, the standard deviation of this sample is 4.38.

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The equation y = 2x - 8, best describes the relationship between the corresponding values of x and y shown in the table.

A linear equation is defined as an equation in which the highest power of the variable is always one.

The table is given in the question, as follows:

x : -2    0    1     4

y : -12  -6   -3    6

Option C,  y = 3x - 6, best describes the relationship between the corresponding values of x and y shown in the table. This can be seen by plugging in the x values from the table into the equation and observing that it yields the corresponding y values.

So substitute the values of x = 4 and  y = 6 in the equation  y = 3x - 6, and we get

6 = 3(4) - 6

6 = 12 - 6

6 = 6

Hence, the correct answer would be option (C).

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The question seems incomplete, the missing part has been below:

Which equation best describes the relationship between the corresponding values of x and y shown in the table?

x : -2    0    1     4

y : -12  -6   -3    6

A. y = x - 10

B. y = 2x - 8

C. y = 3x - 6

D. y = x2 - 8

The state withholding tax for the unmarried person Mary Smith is 6.76.

When paying rent, commissions, or fees for professional services at rates specified by current tax laws, the taxpayer is required to withhold tax, which is also known as retention tax.

A tax determined using the tables or computation methods prescribed by the Secretary must be deducted and withheld from all wages paid by an employer, unless otherwise specified in this section.

Withholding taxes are paid by employers to the IRS on behalf of the employee. The amount collected is applied as a credit to the employee's yearly income tax liability. If too much money is withheld, the employee gets a tax refund; if not enough, the employee might have to pay the IRS.

So that the state withholding tax for the unmarried person Mary Smith is 6.76.

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The triangles are congruent by the AAS property.

A closed quadrilateral has four sides, four vertices, and four angles. It is a form of a polygon. In order to create it, four non-collinear points are joined. Quadrilaterals always have a total internal angle of 360 degrees.

Given a parallelogram ABCD,

with diagonal BD

to prove ΔABD ≅ ΔCDB

so AD ║ BC (because ABCD is a parallelogram)

so BD works as the transverse line between AD and BC,

similarly, AB and DC

so ∠ADB = ∠CBD (alternate interior angles are congruent)

AB ║ CD (because ABCD is a parallelogram)

so ∠ABD = ∠CDB (alternate interior angles are congruent)

DB = DB (common side)

ΔABD ≅ ΔCDB by AAS property

Hence triangles are congruent by AAS property.

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The greater the magnitude of the measurement, the greater the uncertainty in the measurement.

The accuracy of these measurements is often of great importance, but it is important to keep in mind that there is always some degree of uncertainty inherent in any measurement.

This uncertainty can arise from a number of sources, including the limitations of the measuring tools, the skill and experience of the person making the measurement, and the conditions under which the measurement is taken.

One way to describe the relationship between measurement uncertainty and the magnitude of the measurement is through the use of exponential functions.

An exponential function is a mathematical relationship between two variables, in which one variable changes at a rate that is proportional to its current value.

In the case of measurement uncertainty, the exponential function describes the relationship between the uncertainty in a measurement and the magnitude of the measurement.

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Answer:

  see attached

Step-by-step explanation:

You want the boxes of the pyramid shown filled with mixed numbers such that each box is the sum of the two numbers below it.

As the example shows, each box is filled with the difference between the box above and the one adjacent. Work must necessarily proceed from the top down.

As you know, the difference of fractions can be computed as ...

  [tex]\dfrac{a}{b}-\dfrac{c}{d}=\dfrac{ad-bc}{bd}[/tex]

Of course the number 1 can be written in terms of denominator d as ...

  1 = d/d

This can be used to adjust the integer and fractional parts so both are positive.

We will use subscripts rc to indicate the row and column of a box, counting rows from the top down.

  [tex]X_{22}=12\dfrac{3}{4}-8\dfrac{2}{3}=(12-8)+\left(\dfrac{3}{4}-\dfrac{2}{3}\right)=4\dfrac{9-8}{12}=\boxed{4\dfrac{1}{12}}\\\\\\X_{31}=8\dfrac{2}{3}-2\dfrac{4}{5}=(8-2)+\left(\dfrac{2}{3}-\dfrac{4}{5}\right)=6\dfrac{10-12}{15}=\boxed{5\dfrac{13}{15}}\\\\\\X_{33}=4\dfrac{1}{12}-2\dfrac{4}{5}=(4-2)+\left(\dfrac{1}{12}-\dfrac{4}{5}\right)=2\dfrac{5-48}{60}=\boxed{1\dfrac{17}{60}}[/tex]

  [tex]X_{41}=5\dfrac{13}{15}-1\dfrac{5}{9}=(5-1)+\left(\dfrac{13}{15}-\dfrac{5}{9}\right)=4\dfrac{39-25}{45}=\boxed{4\dfrac{14}{45}}\\\\\\X_{43}=2\dfrac{4}{5}-1\dfrac{5}{9}=(2-1)+\left(\dfrac{4}{5}-\dfrac{5}{9}\right)=1\dfrac{36-25}{45}=\boxed{1\dfrac{11}{45}}\\\\\\X_{44}=1\dfrac{17}{60}-1\dfrac{11}{45}=(1-1)+\left(\dfrac{17}{60}-\dfrac{11}{45}\right)=\dfrac{51-44}{180}=\boxed{\dfrac{7}{180}}[/tex]

__

Additional comment

In a couple of places the denominators have a common factor.

For example, 13/15 and 5/9 have denominators that have a common factor of 3: 15=3·5 and 9=3·3. When we did the cross multiplication to find the difference, we divided the cross products by that common factor so the resulting fraction would be in lowest terms.

That is, we used 13·9/3 = 39 and 15·5/3 = 25 for the numerator values, and 15·9/3 = 45 for the denominator value.

You will also recognize that 6+(-2/15) became 5+13/15 by using 6 = 5+15/15.

Many calculators and spreadsheets can perform arithmetic on mixed numbers and give a mixed number result. (That is how we checked our work.)

The answers for the asked probabilities, are a) P(boys only) = 6/100, b) P(not boys only) = 94/100 and c) 20

Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true.

Given that, a random list of 100 numbers and the assignations 0-4 to represent girls and 5-9 to represent boys,

a) Based on the results of the simulation, what is the experimental probability that a group will include only boys?

Answer :- 6 of the numbers simulate groups of all boys: 7579, 6577, 5697, 9675, 5656, 6658. So, the experimental probability of a group being all boys is 6/100 = 0.06

b) Based on the results of the simulation, what is the experimental probability that a group will not contain four boys?

Answer :- The other 94 groups do not include only boys.

The probability that the group will not contain four boys is

1 -6/100 = 94/100 = 0.94

c) Based on the results of the simulation, if 224 groups are formed, about how many of them would you expect to contain all girls?

Answer :- 9 of the groups contain all girls. Based on these results, we would expect,

9/100 × 224 ≈ 20

Therefore, 20 groups to contain all girls.

Hence, the answers are a) P(boys only) = 6/100, b) P(not boys only) = 94/100 and c) 20

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The question is incomplete, so I solved for,

Use the following random list of 100 numbers and the assignations 0-4 to represent girls and 5-9 to represent boys to answer the question below. 3199 9288 1023 1130 0809 1770 6231 7538 8927 4761 7258 7111 0209 0916 1450 9848 4654 7579 6150 3093 9608 0061 4014 9501 0382 3052 2385 9074 1664 6551 6577 1811 3454 5870 1277 5056 1063 5697 9141 4120 9181 1343 0168 3693 0463 4842 1704 3774 4908 4161 6404 9675 2518 3988 4268 6083 0636 9634 5295 5656 1918 3133 6831 8393 6363 2452 1531 1638 1317 2279 9395 0702 2091 5269 0422 0275 3373 1424 1958 0356 5163 0743 6658 6257 2772 0570 4522 2665 0890 3560 5549 2238 2172 9715 9741 4975 6617 9034 4441 8220 Based on the results of the simulation, what is the experimental probability that a group will include only boys? Based on the results of the simulation, what is the experimental probability that a group will not contain four boys? Based on the results of the simulation, if 224 groups are formed, about how many of them would you expect to contain all girls? Round your answer to the nearest number of groups.

Answer:

see below

Step-by-step explanation:

d= original price

so d−0.25d = full price less 25%

0.75d is the same - paying (1-25%) = 75% of original price

Answer:

Y=5−2y/3

x=1−y/3

hope that helps

The slope of the given line ( 2 / x ) + ( 3 / y ) = 0 which is calculated by solving the equation is equal to ( - 3 / 2).

A line's slope is defined as the ratio of the change in y coordinate to the change in x coordinate.

The net change in y-coordinate is represented by Δy and the net change in x-coordinate is represented by Δx.

Hence, the expression for the change in y-coordinate with respect to the change in x-coordinate is,

m = y/x = y/x = change in y/change in x

where "m" represents a line's slope.

Furthermore, the slope of the line can be shown as

tan θ = Δy/Δx

So, tan θ to be the slope of a line.

As given in the question,

Given equation of the line is equal to ( 2 / x ) + ( 3 / y ) = 0

Simplify the given equation to get the slope intercept form :

( 2 / x ) + ( 3 / y ) = 0

⇒ ( 2 / x ) = - ( 3 / y )

⇒ 2y = -3x

⇒ y = ( - 3 / 2 ) x + 0  __(1)

Standard slope intercept form of the line is given by :

y = mx + c  __(2)

Where m is the slope of the line

Compare (1) and (2) to get the slope of the line we get,

Slope of the line 'm' = ( - 3 / 2 )

Therefore, the slope of the given line by simplify the equation

( 2 / x ) + ( 3 / y ) = 0 in slope intercept form is equal to ( - 3/2).

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Answer: One way to check Abby's solution using a number line and counting on is as follows:

Start at 5 2/5 on the number line.

Subtract 2 1/2 by counting left 2 and a half units.

Check if the result is 2 9/10.

If the result of the subtraction is 2 9/10, then Abby's solution is correct. If not, then the solution is incorrect and needs to be re-evaluated.

Using this method, we can visually see the subtraction and verify the result.

Step-by-step explanation:

The coordinates of the vertex points of the triangle rotated through 180° about the origin, are (-1, -2), (-4, -2), and (-4, -4)

The drawing of the image of the triangle rotated through 180°, created using MS Excel is attached

A rotation transformation is one in which points on the figure to be rotated are turned about a center of rotation, following a circular path.

The coordinates of the vertices of the triangle are; (1, 2), (4, 2), and (4, 4)

The coordinates of the image following rotation of a point (x, y) 180°, about the origin is the point (-x, -y)

Therefore, the coordinates of the image of the triangle following the rotation are;

Rotation of the point (1, 2) 180° ⇒ (-1, -2)

Rotation of the point (4, 2) 180° ⇒ (-4, -2)

Rotation of the point (4, 4) 180° ⇒ (-4, -4)

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The pie chart for the data representing the expenditures of the family is given by the image presented at the end of the answer.

A pie chart is constructed in pizza format, considering the percentages of each input data in the problem.

A percentage is calculated as the division of the number of desired outcomes by the number of total outcomes, and then multiplied by 100%.

The total expenditures for the family are given as follows:

2000 + 1000 + 2500 + 2000 + 12000 + 10000 = 29500.

The percentages for the data-set in this problem is given as follows:

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Answer:

Quadrant II

Step-by-step explanation:

[tex]2i-10[/tex] can be written as [tex]-10+2i[/tex], which shows a 10-unit transformation to the left of the real axis and a transformation of 2 units up on the imaginary axis. Hence, this would be in Quadrant II.

The increase in the price of crude oil was 10% in March, and then again by 10% in September. Let the original price be $x, then after the first 10% increase in March, the new price is 1.1x. After the 10% increase in September, the new price is 1.1(1.1x) = 1.21x.

So, the price increased from $x to $1.21x, which is an increase of $0.21x. Since the final price is $72.60, we can set up the equation:

$1.21x = $72.60

Solving for x, we get:

x = $60

Therefore, the original price was $60 and the increase was $12.60. The percent increase is then:

(12.60/60) x 100% ≈ 21%

So the total percent increase in the price of crude oil in 2018 was approximately 21%, which is option D.

Using the compound interest formula, we can calculate that the original price was around $65.04 and the total increase in price across 2018 was about 11.6%. Therefore, none of the options provided are correct.

The question has to do with the concept of compound interest in Mathematics. In this case, the price of crude oil increased by 10% twice in the year. The compounded increase, however, is not just the sum of these two increases, which would be 20%. It's actually slightly more, because the second 10% increase is applied not to the initial price, but to the price that already had been increased by 10% in March.

To calculate the total increase, we can use the formula for compound interest, which is A =[tex]P(1 + r/n)^(^n^t^)[/tex], where A is the amount of money accumulated after n years, including interest, P is the principal amount (the initial amount of money), r is the annual interest rate (in decimal), n is the number of times that interest is compounded per year, and t is the time the money is invested for in years.

Considering the given scenario, and setting P as the unknown initial price of oil, r as 0.1 (10% expressed in decimal), t as 1 (since the increment happened twice within the same year), and n as 2 (since the increment happened twice). From the compound interest formula, we know that the final price $72.60 =[tex]P(1 + 0.10/2)^(^2^*^1^)[/tex]. Solving this equation for P, we find that P approximately equals $65.04, indicating the price at the start of the year.

Expressed in percentage terms, the total increase during 2018 is approximately (($72.60 - $65.04)/$65.04) * 100% = 11.6%. So, from the options given in your question, none is the correct answer.

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Answer:

A is the correct answer

Step-by-step explanation:

graph show it If you put a number in for x then you can see the different

Solving for x gives the axis of symmetry of quadratic equation, where the quadratic equation is given as: y = ax² + bx + c.

How is this determined?

The vertical line that passes through a parabola's vertex is the axis of symmetry, making the parabola's left and right sides symmetric. This line divides the graph of a quadratic equation into two mirror representations in order to make things simpler.

The line on the graph that separates the graph into two symmetrical sides and runs through the vertex of the parabola is known as the axis of symmetry of the parabola.

It is written as:

x = -b /2a.

Hence, for x = -b /2a. Solving for x gives the axis of symmetry of quadratic equation, where the quadratic equation is given as: y = ax² + bx + c.

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Answer:

1

Step-by-step explanation:

Evaluate. Write your answer as a fraction or whole number.

1/4 (4) = 1

3(t+4).

[tex]t+4[/tex]

[tex](t+4)[/tex]

For this, just write a 3 infront of the parenthesis to express the multiplicaition of the sum (t+4) by 3.

[tex]3(t+4)[/tex]

Final answer: [tex]3(t+4)[/tex].

The solution is, max no. of +ve real roots for is 2. &  max no. of -ve real roots is 1.

Descartes rule of signs says the max no. of +ve real roots

= no. of changes in sign of the coefficients of a polynomial.

here, we have,

the polynomial function P(x)=8x^3 +2x^2-14x+5

now,

so max no. of +ve real roots for

P(x)=8x^3 +2x^2-14x+5, which has 2 changes in sign of coefficients (8,2,-14,5)

i,e,  max no. of +ve real roots for is 2.

again,  P(-x)=-8x^3 +2x^2+14x+5

which has 1 changes in sign (-8,2,14,5)

i.e. max no. of -ve real roots is 1.

Hence, The solution is, max no. of +ve real roots for is 2. &  max no. of -ve real roots is 1.

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If the straw fits exactly into the box diagonally from the bottom left corner to the top right back corner, then the straw is √181 inches long.

In a right-angled triangle, the square of the hypotenuse side is equal to the sum of the squares of the other two sides, according to Pythagoras's Theorem.

Given:

A straw is placed inside a rectangular box that is 9 inches by 6 inches by 8 inches, as shown.

So, the diagonal of the base by the Pythagorean theorem,

c = √{(9)² + (6)²}

c = √117

Now, to find the value of d,

d = √{(√117)² + (8)²}

d = √181

Therefore,  the straw is √181 inches long.

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Answer: 35 mph

Step-by-step explanation:

      We will write this as a unit rate of miles per hour. To do this, we will divide the miles by the hours.

70 miles / 2 hours = 35 miles per hour