factorise 9x^2 + 3x^3

The proportional relationship between x and y is shown by the table:

x   7  14  28   35

y  1     2    4     5

A connection among two factors that changes proportionally is referred to as a proportional relationship. If y=kx, where k is just the proportionality constant, can be used to represent two quantities, x and y, then they are said to be proportional.

From the given options, consider the table:

x   7  14  28   35

y  1     2    4     5

As per proportional relationship.:

y=kx

k = y/x (must be same in all cases)

k = 1/7

k = 14/2 = 1/7

k = 4/28 = 1/7

k = 5/35 = 1/7

As all the k value for the given values of x and y are found equal.

Thus, the proportional relationship between x and y is shown by the table:

x   7  14  28   35

y  1     2    4     5

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The parametric equations graph as a portion of a parabola. The initial point is (5,0), and the terminal point is (3,4). The vertex of the parabola is (2,9). Arrows are drawn along the parabola to indicate motion right to left.

Parametric equations are a way of expressing a set of equations that define the coordinates of a point in terms of a third variable (parameter) that varies over a certain range. In the given problem, the parametric equations:

x(t) = 2 - t

y(t) = (t+3)²

To visualize the graph of these equations, we can substitute different values of t and plot the corresponding points (x(t), y(t)) on a coordinate plane. Since t ranges from -4 to 0, we can choose a few values of t such as t=-4, t=-2, and t=0 to get the corresponding points.

When plotted these points, a portion of a parabola that opens upwards. The vertex of the parabola is at the point (3, 4) where x=2-t and y=(t+3)² intersect. The initial point of the graph is when t=-4, which gives the point (6, 1) and the terminal point is when t=0, which gives the point (2, 9). The arrows are drawn along the parabola to indicate the direction of motion, which is from right to left in this case.

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Step-by-step explanation:

first of all, remember, the sum of all angles in a triangle is always 180°.

now, we see that both bottom angles are 45°.

that means

180 = 45 + 45 + top-angle

90° = top-angle

aha ! we are dealing with a right-angled triangle, that is also isoceles (both legs are equally long, because the angles with the baseline are equal).

via Pythagoras

c² = a² + b²

where "c" is the Hypotenuse (the side opposite of the 90° angle), "a" and "b" are the legs.

in our case both legs are 7×sqrt(2) units long.

so,

baseline² = (7×sqrt(2))² + (7×sqrt(2))² = 49×2 + 49×2 =

= 98 + 98 = 196

baseline = sqrt(196) = 14 units

x is now the height of this triangle, and because of the isoceles form, it splits the baseline exactly in half.

so, one side of the baseline from x is 14/2 = 7 units.

and now Pythagoras for that sub-triangle :

(7×sqrt(2))² = 7² + x²

98 = 49 + x²

49 = x²

x = sqrt(49) = 7 units

the area of the triangle is

baseline × height / 2

in our case

14 × 7 / 2 = 7×7 = 49 units²

The volume of the triangular prism as shown in the attached image is 30 cm³.

To find the volume of a triangular prism, we need to multiply the area of the triangular base by the height of the prism.

The area of the triangular base can be found using the formula:

Area = (1/2) × base × height

In this case, the base is 5 cm and the height is 4 cm, so the area of the triangular base is:

Area = (1/2) × 5 cm × 4 cm = 10 cm²

The height of the prism is 3 cm.

Therefore, the volume of the triangular prism is:

Volume = Area of triangular base × height

= 10 cm² × 3 cm

= 30 cm³

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The system of equations defined is:

x = 2y

x*0.05 + y*0.10 = 1.40

First we need to define the variables:

x = number of nickels

y = number of dimes.

Now we can find the equations, we know that he has twice as many nickels as dimes, then:

x = 2y

We also know that Tristan has $1.40 then we can write:

x*0.05 + y*0.10 = 1.40

So the system of equations is:

x = 2y

x*0.05 + y*0.10 = 1.40

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Yes, Jalen is correct because the rectangle has a perimeter of 20 inches with the smaller side measuring 3 inches and the longer side of the rectangle had to be 7 inches.

In Mathematics and Geometry, the perimeter of a rectangle can be calculated by using this mathematical equation (formula);

P = 2(L + W)

Where:

By substituting the given side lengths into the formula for the perimeter of a rectangle, we have the following;

P = 2(3 + 7)

20 = 2(10)

20 = 20 (True).

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Answer:

x = 68

Step-by-step explanation:

X + 22 = 90 degrees

90 - 22 = 68 degrees

The number of different passwords, considering 2 digits and 2 letters, is given as follows:

A. 6,760,000.

B. 3,276,000.

The Fundamental Counting Theorem states that if there are m ways to do one thing and n ways to do another, then there are m x n ways to do both.

This can be extended to more than two events, where the number of ways to do all the events is the product of the number of ways to do each individual event, according to the equation presented as follows:

[tex]N = n_1 \times n_2 \times \cdots \times n_n[/tex]

The password is composed by:

With repetition, we have that:

Hence the number of passwords is given as follows:

10^4 x 26² = 6,760,000.

Without repetition, we have that:

Hence the number of passwords is given as follows:

10 x 9 x 8 x 7 x 26 x 25 = 3,276,000.

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The probability that at least 2 students feel like they can do better in their math class is E. 0.9130.

To find the probability that at least 2 students feel like they can do better, we need to calculate P(X >= 2). This can be done using the cumulative distribution function (CDF) of the binomial distribution:

P(X >= 2) = 1 - P(X < 2) = 1 - P(X = 0) - P(X = 1)

Using the binomial probability formula, we can calculate:

P(X = 0) = (5 choose 0) * 0.6^0 * 0.4^5 = 0.01024

P(X = 1) = (5 choose 1) * 0.6^1 * 0.4^4 = 0.07680

Therefore,

P(X >= 2) = 1 - 0.01024 - 0.07680 = 0.91296

Rounding this to four decimal places, we get: 0.9130

Therefore, the answer is option E: 0.9130.

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Answer:

B. 314 m²

Step-by-step explanation:

Area of circle = π · r²

r = 10 m

π = 3.14

Let's solve

3.14 x 10² = 314 m²

So, the area of the circle is B. 314 m²

Answer:

441cm^2

Step-by-step explanation:

84 divided by 4 is 21

21cm*21cm is 441cm^2

Answer:

Ok so we know it has to equal=180 right?

90+90=180

180/4

45

Approximately 15.87% of the bowlers in the Capital Three bowling tournament performed better than Dr. Baker.

Standard deviation (σ) = √(variance) = √(121) = 11

Now, we can calculate the z-score for Dr. Baker's average of 169 using the formula:

z = (X - μ) / σ

z = (169 - 158) / 11

z = 11 / 11

z = 1

Dr. Baker's z-score is 1, meaning his performance is one standard deviation above the mean.

The area to the left (or the cumulative probability) is approximately 0.8413

1 - 0.8413 = 0.1587

Approximately 15.87% of the bowlers in the Capital Three bowling tournament performed better than Dr. Baker.

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4[tex]\pi[/tex]/9 radians equals 80 degrees.

To convert a radian angle to a degree angle, multiply it by 180°/[tex]\pi[/tex]. To convert a degree angle to a radian angle, multiply it by [tex]\pi[/tex]/180°.

We utilize the conversion factor that 1 radian = 180/[tex]\pi[/tex] degrees to convert radians to degrees.

So we multiply 4[tex]\pi[/tex]/9 radians by the conversion factor to get degrees:

[tex]\\\frac{4\pi }{9} * \frac{180}{\pi } \\\frac{720}{9}[/tex]

On simplifying we get,

720 / 9 = 80 degrees

As a result, 4[tex]\pi[/tex]/9 radians equals 80 degrees.

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Complete question:

attach in the image form

Answer:

B

Step-by-step explanation:

Pretty sure this is B. The height of your parents is the clearest way to determine how tall someone you'll be, and usually, your shoe size depends on your height. You can see this in real life. Shaq has huge feet because he's a huge guy.

A makes no sense. C might, but this will only apply to really small children. And D makes no sense either. So B is the best choice.

Answer:

C. age of the student is likely to be the answer

Answer:

-9.5.

Step-by-step explanation

To find a reasonable value for n, we need to use the given data points and the equation of the line. We can plug in any pair of x and y values into the equation and solve for m or b. For example, using (4, 2), we get:

2 = m(4) + b

Solving for b, we get:

b = 2 - 4m

Now we can plug in another pair of x and y values, such as (7, 4.5), and use the value of b we just found:

4.5 = m(7) + 2 - 4m

Solving for m, we get:

m = 0.5

Now we have the slope and the y-intercept of the line. The equation is:

y = 0.5x + 2 - 4(0.5)

Simplifying, we get:

y = -1.5x + 4

To find n, we need to plug in x = 9 and solve for y:

y = -1.5(9) + 4

y = -9.5

Answer: the answer is 4

Step-by-step explanation: good luck

Answer:

I would say probability.

The angle of depression that the paper airplane is flying down at 55. 78 degrees

Note that the different trigonometric identities in mathematics are;

These identities also have their ratios are;

sin θ = opposite/hypotenuse

cos θ = adjacent//hypotenuse

tan θ = opposite/adjacent

From the information given, we have;

Using the cosine identity

Adjacent = 9 feet

Hypotenuse = 16 feet

Substitute the values

cos θ = 9/ 16

divide the values

cos θ = 0. 5625

θ = 55. 78 degrees

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Answer:

55.8° (nearest tenth)

Step-by-step explanation:

The angle of depression is the angle between the horizontal line of sight at the top of the treehouse and line of sight to the sandbox (the flight path of the paper airplane). (See attached diagram).

To find the angle of depression, we can use the cosine trigonometric ratio. The cosine of an angle is equal to the ratio of the length of the side adjacent the angle to the length of the hypotenuse.

[tex]\boxed{\begin{minipage}{9 cm}\underline{Cosine trigonometric ratio} \\\\$\sf \cos(\theta)=\dfrac{A}{H}$\\\\where:\\ \phantom{ww}$\bullet$ $\theta$ is the angle. \\ \phantom{ww}$\bullet$ $\sf A$ is the side adjacent the angle. \\\phantom{ww}$\bullet$ $\sf H$ is the hypotenuse (the side opposite the right angle). \\\end{minipage}}[/tex]

In this case, the length of the side adjacent the angle of depression is equal to the distance between the base of the tree and the sandbox, so A = 9 ft. The hypotenuse is the distance the airplane flies through the air, so H = 16 ft.

Substitute these values into the cosine ratio and solve for θ:

[tex]\cos (\theta)=\dfrac{9}{16}[/tex]

[tex]\theta=\cos^{-1}\left(\dfrac{9}{16}\right)[/tex]

[tex]\theta=55.7711336...^{\circ}[/tex]

[tex]\theta=55.8^{\circ}\; \sf (nearest \; tenth)[/tex]

Therefore, the angle of depression that the paper airplane is flying down at is 55.8° (nearest tenth).

The greatest common factor (GCF) of the polynomial 12x²9x is 3x, therefore option B is correct.

The Greatest Common Factor (GCF) of a polynomial is the largest factor that all of the terms in the polynomial have in common.

To find the GCF, we need to find the largest factor that both terms have in common. Both terms have a factor of 3x, so that is the greatest common factor. Factoring out 3x from each term gives:

12x²9x = 3x(4x)3(3x) = 3x(4x3)

So the GCF of 12x²9x is 3x.

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According to the information provided, HI = 20, the triangle can be categorised by sides that are as follows:

A collection of numbers or "terms" is called a sequence. Examples of terms are 2, 5, and 8. Some sequences can be made endlessly lengthy by taking advantage of a particular pattern they follow. Use the example of 2,5,8 and add 3 to continue the sequence.I have a code that tells me where to look for words in a sequence. A collection of objects in a peculiar order is called a sequence (or event) in mathematics. . It resembles a set in that it contains pieces (also called elements or terms). The entire, perhaps infinite number of ordered objects are referred to as the sequence's length. the act of placing two or more items in a logical order. Chronological.

We need further details regarding the triangle's side lengths in order to identify whether the cylinder is scalene, isosceles, etc equilateral. The cylinder with HI = 20 appears to have no relationship to the sides with lengths values 10, 6, & 8.

Given that the material after "b" contains symbols and numerals that do not make sense together, it can be incomplete or improperly structured. If you would kindly submit a thorough and correctly formatted inquiry, I would be pleased to assist you with sorting the triangle according to its sides or to offer any other information you might require.

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According to the given condition. The inequality that matches this graph is option B) x ≥ -5.

An inequality equation is a mathematical statement that compares two expressions using an inequality symbol such as < (less than), > (greater than), ≤ (less than or equal to), or ≥ (greater than or equal to).

The inequality that matches this graph is option B, "x ≥ -5". The graph represents a solid dot at x = -5 and a shaded region to the right of x = -5, including x = -5. This means that x can take on any value greater than or equal to -5, so the inequality can be written as x ≥ -5.

Therefore, According to the given condition. The inequality that matches this graph is option B) x ≥ -5.

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1. the APR for this loan is 6%.

2.  the unearned interest is $118.83.

3.  the monthly payment necessary to amortize the $80,000 mortgage at 6% annual interest for 25 years is $506.69.

APR = (finance charge / loan amount) / number of years * 100%

In this scenario, the loan amount is $2400 and the finance charge is $288. Since it's a two-year loan, the number of years is 2

APR = (288 / 2400) / 2 * 100%

APR = 0.06 * 100%

APR = 6%

b.

Number of payments = 4 years * 12 months/year = 48

If the loan is paid off in 3 years instead of 4 years, the number of payments made is:

Number of payments made = 3 years * 12 months/year = 36

Substituting these values into the formula, we get:

Unearned interest = (1426 / 48) * (48 - 36)

Unearned interest = $118.83

3.

To find the monthly payment necessary to amortize a mortgage, we need to use the formula:

M = P * (r / (1 - (1 + r)^(-n)))

where M is the monthly payment, P is the principal (loan amount), r is the monthly interest rate, and n is the total number of payments (in months).

In this scenario, the loan amount is $80,000, the annual interest rate is 6%, and the loan term is 25 years. To find the monthly interest rate, we divide the annual interest rate by 12 (since there are 12 months in a year):

Monthly interest rate = 6% / 12 = 0.005

To find the total number of payments, we multiply the number of years by 12:

Number of payments = 25 years * 12 months/year = 300

Substituting these values into the formula, we get:

M = 80000 * (0.005 / (1 - (1 + 0.005)^(-300)))

M ≈ $506.69

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Here are the answers to the above questions:

To calculate the locator and percentile, we need to first arrange the scores in ascending order:

6, 8, 11, 12, 14, 17, 20, 34, 36, 38, 47, 48, 49

a) To calculate the locator for the 52nd percentile, we use the following formula:

Lp = (p/100) * (N + 1)

where Lp is the locator for the pth percentile, p is the percentile we are interested in, and N is the total number of scores.

For the 52nd percentile, p = 52 and N = 13. Substituting these values into the formula, we get:

L52 = (52/100) * (13 + 1) = 6.72

Therefore, the locator for the 52nd percentile is 6.72.

b) To determine the 52nd percentile, we need to find the score corresponding to the locator L52. Looking at the ordered list of scores, we see that the score at position 6 is 17 and the score at position 7 is 20. Since the locator L52 falls between positions 6 and 7, we can use linear interpolation to estimate the 52nd percentile:

P52 = (7 - L52) / (7 - 6) * 50 + (L52 - 6) / (7 - 6) * 50

P52 = (7 - 6.72) / (7 - 6) * 50 + (6.72 - 6) / (7 - 6) * 50

P52 = 38 + 0.48 * 50

P52 = 61.4

Therefore, the 52nd percentile is approximately 61.4.

c) To find the percentage of scores that are above the 52nd percentile, we subtract the 52nd percentile from 100:

100 - 52 = 48

Therefore, approximately 48% of the scores in the dataset are above the 52nd percentile.

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Step-by-step explanation:

a1 = 2

a2 = 10

d = a2 - a1 = 10 - 2 = 8

a15 = a + 14d = 2 + 14(8) = 2 + 112 = 114

Answer:

2, 10, 18, 26, 34, 42, 50, 58, 66, 74, 82, 90, 98, 106, 114

Step-by-step explanation:

all you do is add 8 each time

By using the partial sum of series is

[tex]a_{n} = 5^{(-n-1) } - (n+1)5^{(-(n+1))}[/tex]

and summation n=1 to infinity of [tex]a_{n}[/tex] is =6 .

To obtain the formula for the nth term of the series and its total, we must first discover the formula for the series' general term.

The formula for the series' nth partial sum is as follows:

[tex]sn = 6 - n*5^{-n}[/tex]

The nth term of the series can be obtained by subtracting the (n+1)th and nth partial sums, i.e.,

a = sn+1 - sn

When we substitute the formula for sn, we get:

[tex]a_{n} = [6 - (n+1)5^{(-(n+1))} ] - [6 - n5^{(-n)} ]\\a_{n} = 5^{(-n-1) } - (n+1)5^{(-(n+1))}[/tex]

As a result, the formula for the series' nth term is:

[tex]a_{n} = 5^{(-n-1) } - (n+1)5^{(-(n+1))}[/tex]

To calculate the series total, take the limit of the nth partial sum as n approaches infinity:

lim(n->inf) lim(n->inf) sn [6 - n*5^(-n)]

lim(n->inf) [n*5(-n)] = 6

= 6 - 0

= 6

As a result, the series' sum is 6.

As a result, the formula for the nth term in the series is:

[tex]a_{n} = 5^{(-n-1) } - (n+1)5^{(-(n+1))}[/tex]

And the series' total is:

a = sum(n=1 to inf) = 6

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Answer:

Let s be the number of smartphones.

81 = .45s, so s = 180

Answer:

36.45

Step-by-step explanation:

You make 45 into a percentage, which is 0.45%. Then, multiply 0.45 by 81 and you get 36.45. Hope this helps! And if you’re incorrect I deeply apologize. I tried my best and I’m 95% sure that I’m correct.

Therefore , the solution of the given problem of probability comes out to be  z-score from a typical normal distribution.

Any considerations technique's fundamental objective is to determine the likelihood that a claim is true or that a particular incident will take place. Any number range from one to one, when 0 traditionally signifies a percentage and 1 typically implies the degree of certainty, can be used to represent chance. A probability illustration shows the likelihood that a particular event will occur.

Here,

The formula for the standard error of the mean (SEM), which is as follows:

=> SEM = the standard deviation / √(sample size).

We can enter these numbers into the SEM calculation to determine the SEM given that the standard deviation of the tariff rates is $1200 and the sample size is 400:

=> SEM=$1200/√(400)

=> $1200/20 =$60

It is possible to calculate the z-score for a $80 departure from the mean with a $60 SEM as follows:

=>  z = (80 - 0) / $60 = 1.3333

Now that we have the probability corresponding to the z-score of 1.3333,

we can look up the cumulative distribution function (CDF) of the standard normal distribution using a z-table or a statistical calculator.

The CDF depicts the likelihood that a random variable will occur is less than or equal to a certain z-score from a typical normal distribution.

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