1. Find 10% of 20 1. Find 10% of 12.
1. Find 10% of 12.
1. Find 10% of 12.
1. Find 10% of 12.
1. Find 10% of 12.

Given:

The polynomial is

\(x(x-5)(2x+3)\)

To find:

The standard form of the polynomial and correct statement for the polynomial.

Solution:

Let, \(P(x)=x(x-5)(2x+3)\)

On multiplication, we get

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

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

\(P(x)=2x^3+3x^2-10x^2-15x\)

\(P(x)=2x^3-7x^2-15x\)

Here,

Constant term is 0, leading coefficient is 2, degree is 3 and number of terms is 3.

Therefore, the correct option is 2.

The statement which is true about the resulting polynomial is the leading coefficient is 2. Option 2 is correct.

In the standard form of the polynomial equation, the highest degree term is placed first. The order of a standard polynomial equation is decreasing power of variable of term.  

The standard form of the quadratic equation is,

\(ax^{n}+bx^{n-1}+cx^{n-2}......nx^{n-n}\\ax^{n}+bx^{n-1}+cx^{n-2}......nx^{0}\\ax^{n}+bx^{n-1}+cx^{n-2}......n\)

Here, (a,b,c and n) are the real numbers and x is variable.

The given expression in the problem is,

\((x)(x - 5)(2x + 3)\)

Simplify it further,

\((x)(x - 5)(2x + 3)\\(x^2-5x)(2x + 3)\\2x^3+3x^2-10x^2-15x\\2x^3-7x^2-15x\)

In the above expression, the highest degree of the polynomial is 3 and the coefficient of it is 2 which is the leading coefficient.

Hence, the statement which is true about the resulting polynomial is the leading coefficient is 2. Option 2 is correct.

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The eigenvalues and associated unit eigenvectors of the symmetric matrix the smaller eigenvalue has associated unit eigenvector is Ax = λx.

Symmetric matrix:

In algebra, symmetric matrix a square matrix that remains unaltered when its transpose is calculated.

Given,

Here we need to find the the eigenvalues and associated unit eigenvectors of the symmetric matrix the smaller eigenvalue has associated unit eigenvector and the larger eigenvalue has associated unit eigenvector.

Here the eigenvector is a vector that is associated with a set of linear equations.

And in the eigenvector of a matrix is also known as a latent vector, proper vector, or characteristic vector.

Therefore, those are defined in the reference of a square matrix.

So, the smaller eigenvalue has associated unit eigenvector is Ax is λx.

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Answer:

△E'L'M'

Step-by-step explanation:

-90° rotation = 270° rotation

Which maps (x,y) onto (y,-x)

L' (2,-3)

M' (7,-6)

E' (-3,-7)

The triangle with the lengths 2m, 5m and 6m is not a right triangle, as the lengths do not form a Pythagorean triple.

The Pythagorean Theorem states that for a right triangle, the length of the hypotenuse squared is equals to the sum of the squared lengths of the sides of the triangle.

The sum of the two smaller sides squared is given as follows:

2² + 5² = 4 + 25 = 29.

The square of the largest side is of:

6² = 36.

As 29 is different of 36, the Pythagorean Theorem is not respected, and thus the triangle is not a right triangle.

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Answer:

60 degrees

Step-by-step explanation:

This equation of the recipe can be represented as y = x + 5.5 and The constraints are x is ≥ 0 and y is ≥ 5.5.

A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.

Otto used 5.5 cups of whole wheat flour and x cups of white flour in the recipe.

The total amount of flour (y) = the total amount of whole wheat flour (5.5) + the total white flour (x).

Therefore, the equation is:

y = x + 5.5

The possible values are

x = 0 or greater to it since the minimum amount of white flour that can be added is 0.

y = 5.5 or greater to it since even if no

white flour is added the minimum total is 5.5.

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Answer: y=x+5.5; x is any real number greater than or equal to 0, and y is any real number greater than or equal to 5.5.

Answer:  1.5

Step-by-step explanation: 4.05x3=12.15

                                             2.75x4.5=12.375  

4.5-3=1.5

Step-by-step explanation:

Next term is - 51

Use formula Tn=a+(n-1)d

a=the first term of the sequence which is - 15

d=the difference between the terms which is - 9

Substitute

Tn=-15+(n-1)(-9)

Tn=-15+9-9n

Tn=-9n-6

From this you will be able to generate all the terms in the pattern

If they say determine the 50th term just substitute 50 by n

Tn=-9(50)-6

Tn=-450-6

Tn=-456

These are the coordinates of the Vertices of the resulting triangle after performing the given transformations.the resulting vertices after the reflection and translation are: A'(-15, 8) B'(-4, 5) C'(-9, 6)

The triangle ΔABC and perform the given transformations, let's start by plotting the original triangle ΔABC on a graph:

Poin A: (10, 4)

Point B: (-1, 1)

Point C: (4, 2)

Now, let's reflect the triangle ΔABC by multiplying the x-coordinates of the vertices by -1:

Reflected Point A': (-10, 4)

Reflected Point B': (1, 1)

Reflected Point C': (-4, 2)

Next, let's use the given translation function (x, y) → (x - 5, y + 4) to translate the reflected triangle:

Translated Point A'': (-10 - 5, 4 + 4) = (-15, 8)

Translated Point B'': (1 - 5, 1 + 4) = (-4, 5)

Translated Point C'': (-4 - 5, 2 + 4) = (-9, 6)

Therefore, the resulting vertices after the reflection and translation are:

A'(-15, 8)

B'(-4, 5)

C'(-9, 6)

These are the coordinates of the vertices of the resulting triangle after performing the given transformations.

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In order to make 544 litres of petrol oil, require 204 litres of natural oil.

Any number of equal parts is represented by a fraction, which also represents a portion of a whole. When used in conversational English, a fraction indicates the number of components of a particular size, as in one-half, eight-fifths, and three-quarters.

Given that,

3 litres of natural oil for every 5 litres of synthetic oil,

If 544 litres have to be made then,

Add 3 + 5 = 8

So, 3/8 of 544 litres will be = 204 litres of natural oil

And, 5/8 of 544 litres will be =340 litres of synthetic oil

Therefore, in order to make 544 litres of petrol oil, require 204 litres of natural oil.

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Answer:

  -6 < x < 2

  see attached for a graph

Step-by-step explanation:

You want the solution to 3 > -x -3 > -5 expressed as an inequality and as a graph.

Multiplying by -1, we need to reverse the inequality symbols:

  -3 < x + 3 < 5

Now, we can subtract 3 to get the solution as an inequality.

  -6 < x < 2

The graph is in the attachment.

__

Additional comment

There are open circles at the boundary points because the "less than" (<) inequality means the boundary points are not included in the solution set.

Margin of Error = 1.96 * (6 / √10) ≈ 1.96 * 1.9 ≈ 3.72. So, the margin of error for the 95% confidence interval is approximately 3.72, rounded to 2 decimal places.

To find the margin of error, we first need to calculate the standard error:
standard error = sample standard deviation / square root of sample size
standard error = 6 / sqrt(10)
standard error = 1.8974
Next, we can use the formula for margin of error:
margin of error = critical value * standard error
Since we want a 95% confidence interval, our critical value is 1.96 (from a standard normal distribution table).
margin of error = 1.96 * 1.8974
margin of error = 3.72
Therefore, the margin of error for the mean customer satisfaction index is 3.72. Rounded to 2 decimal places, the answer is 3.72.

To calculate the margin of error for a 95% confidence interval, we will use the following formula:
Margin of Error = Z-score * (Sample Standard Deviation / √Sample Size)
In this case, the Z-score for a 95% confidence interval is 1.96, the sample standard deviation is 6, and the sample size is 10.
Margin of Error = 1.96 * (6 / √10) ≈ 1.96 * 1.9 ≈ 3.72
So, the margin of error for the 95% confidence interval is approximately 3.72, rounded to 2 decimal places.

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Answer:

25\(x^{2}\) - 30xy + 20xz + 9\(y^{2}\)  - 12yz + 4\(z^{2}\)

Step-by-step explanation:

We multiply it out.

(5x - 3y + 2z) * (5x - 3y + 2z)

5x*5x + 5x*-3y + 5x*2z - 3y*5x - 3y*-3y -3y*2z + 2z*5x +2z * -3y +2z *2z

25\(x^{2}\) - 15xy + 10xz - 15xy + 9\(y^{2}\) - 6yz + 10xz - 6yz + 4\(z^{2}\)

Add like terms

25\(x^{2}\) - 15xy - 15xy + 10xz + 10xz + 9\(y^{2}\) - 6yz - 6yz + 4\(z^{2}\)

25\(x^{2}\) - 30xy + 20xz + 9\(y^{2}\)  - 12yz + 4\(z^{2}\)

Answer: n = 35/71

Step-by-step explanation:

35 - 2n = 69n

We can add 2n to both sides:

35 = 71n

We can divide both sides by 71:

n = 35/71

Answer:

To find the area, you have to multiply the length times the width

Step-by-step explanation:

Answer:

The area of this rectangle is 6 square units.

Step-by-step explanation:

Multiply the width (8/3 inches) by the height (9/4 inches) to get the rectangle area:

 8       9

----- * -----

  3      4

                        8 * 9

This results in ----------    which itself reduces to 6.  

                          4 * 3

The area of this rectangle is 6.

Answer:

I would but there's no image

Using the fundamental counting principle, it is found that there are 24 different combinations she can wear.

The sweaters and the pants are independent, and this is why the fundamental counting principle is used.

Fundamental counting principle:

States that if there are p ways to do a thing, and q ways to do another thing, and these two things are independent, there are p*q ways to do both things.

Thus:

T = 6 * 4 = 24

There are 24 different combinations.

A combination in mathematics is a selection of items from a fixed that have amazing members, making the order of selection irrelevant (not like permutations). For instance, given a set of three fruits—say let's an apple, an orange, and a pear—one can choose between three combinations: an apple and a pear, an apple.

A hard and fast S's ok aggregate is, more precisely, a subset of S's ok amazing components. As a result, two combinations are equal if and best if each contains the same players. (The ties between the people in each group are not considered.)

(n/k) ={ n(n - 1) . . . (n – k + 1)}/{k(k - 1) . . . 1}

n!/{k!(n - k)!}

k > n.

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The height of the wall where the ladder reaches will be 23.6 feet.

It's a form of a triangle with one 90-degree angle that follows Pythagoras' theorem and can be solved using the trigonometry function.

Trigonometric functions examine the interaction between the dimensions and angles of a triangular form.

Avery leans a 24-foot ladder against a wall so that it forms an angle of 80° with the ground.

The height of the wall where the ladder reaches is given as,

\(\text{sin 80}^\circ \sf =\dfrac{h}{24}\)

\(\sf h = 24 \times \text{sin 80}^\circ\)

\(\sf = 24 \times \text{0.9848}\)

\(\sf h = 23.63\thickapprox\bold{23.6 \ feet}\)

The height of the wall where the ladder reaches will be 23.6 feet.

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The value of x in the equation is x = -1 and x = -4.67

From the question, we have the following parameters that can be used in our computation:

3x^2 + 13x + 4 = 0

This is a quadratic equation that can be solved using the quadratic formula:

x = (-b ± √(b² - 4ac)) / 2a

where a = 3, b = 13, c = 4

So, we have

x = (-13 ± √(13² - 4 * 3 * 4)) / 2 * 3

x = (-17 ± √(169 +- 48)) /6

x = (-17 ± 11) /6

Expand

x = (-17 + 11)/6 and x = (-17 - 11)/6

Evaluate

x = -1 and x = -4.67

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Creation

There is no other way

The total cost  of he meat with tax and tip is $ 22.42

To calculate the total cost with tax and tip, we need to follow these steps:

multiply the meal cost by the tip rate. when  the tip rate is 18%, we have:

Tip amount = $19.00 * 0.18 = $3.42

Add the meal cost, sales tax, and tip amount to get the total cost:

Total cost = Meal cost + Sales tax + Tip amount

= $19.00 + $3.42

= $ 22.42

Therefore, the total cost with tax and tip is $22.42

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To solve the given inequality, first we have to simplify the given inequality.38 < x + 10 After simplification we get, 38 - 10 < x or 28 < x.

The correct option is B.

The given inequality is 38 < 4x + 3 + 7 - 3x. Simplify the inequality38 < x + 10  - 4x + 3 + 7 - 3x38 < -x + 20 Combine the like terms on the right side and simplify 38 + x - 20 < 0 or x + 18 < 0x < -18 + 0 or x < -18. The given inequality is 38 < 4x + 3 + 7 - 3x. To solve the given inequality, we will simplify the given inequality.

Simplify the inequality38 < x + 10  - 4x + 3 + 7 - 3x38 < -x + 20 Combine the like terms on the right side and simplify 38 + x - 20 < 0 or x + 18 < 0x < -18 + 0 or x < -18. Combine the like terms on the right side and simplify38 + x - 20 < 0 or x + 18 < 0x < -18 + 0 or x < -18.So, the answer is  x > 28. In other words, 28 is less than x and x is greater than 28. Hence, the answer is x > 28.

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Answer:

y+1=-3(x+2)

Step-by-step explanation:

point-slope form is the formula y-y1=m(x-x1), where (x1, y1) is a point and m is the slope

we are given a point (-2, -1) and a slope of -3

all we really need to do is substitute the given into the formula

remember: since the formula gives subtraction, we're going to be subtracting, even though we have negative numbers

substitute -2 as x, -1 as y and -3 as m

y--1=-3(x--2)

we can simplify this equation:

y+1=-3(x+2)

Hope this helps!

Answer:

0.54

Step-by-step explanation:

sin 105 / 2 = sin 15 / b

b = sin 15 / 0.48296

b = 0.54

Probability of choosing the biased coin if you won a prize is 0.30

Let "B" be the event of selecting biased coin and "H" be the event of getting head.

P(B) = 0.5

P(getting head when coin was biased) = 100% - 78%

= 22% = 0.22

Using conditional Probability that biased coin was selected given that you have won the prize that is getting head

we have to calculate ,

P(B | H ) = P(B∩H)/P(H)

here , P(B∩H) = P(biased coin selected and getting head) = 0.5 × 0.22

and P(H) = P(getting head)

P(getting head when coin was biased) + P(getting head when coin was unbiased) = 0.5 × 0.22 + 0.5 × 0.5

putting all together ,

P(B | H ) = P(B∩H)/P(H) = 0.5 × 0.22 / 0.5 × 0.22 + 0.5 × 0.5

cancelling 0.5 from numerator and denominator

= 0.22 / 0.5+ 0.22

= 0.22 / 0.72 = 22/72

=0.30

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Answer:

g=4.6

Step-by-step explanation:

5g-11=12

5g=23

g=4.6

There is a 16% probability that the individual actually had the disease given a positive test result.

The probability that the individual had the disease can be calculated as follows:

Let A = Event of testing positive and actually having the disease

Let B = Event of testing positive but not actually having the disease

We are looking for P(A|B), which is the probability of actually having the disease given a positive test result.

Using Bayes' Theorem, we have:

P(A|B) = P(A) * P(B|A) / P(B)

Bayes' theorem is a mathematical formula used in probability theory to calculate the probability of an event based on prior knowledge of conditions that might be related to the event.

It states that the conditional probability of an event A given event B is equal to the product of the probability of event B and the conditional probability of event A given event B, divided by the probability of event B. The formula is represented as P(A|B) = P(B|A) * P(A) / P(B).

Where:

P(A) = 1/500 (probability of having the disease)

P(B|A) = 0.95 (probability of a correct positive result given that the individual has the disease)

P(B) = P(B|A) * P(A) + P(B|A') * P(A') (probability of a positive test result)

= 0.95 * 1/500 + 0.01 * 499/500 (probability of a false positive result given that the individual does not have the disease)

Plugging in the values, we have:

P(A|B) = (1/500) * 0.95 / [0.95 * 1/500 + 0.01 * 499/500] = 0.16 or 16%

Therefore, there is a 16% probability that the individual actually had the disease given a positive test result.

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