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Polynomial \($-1+x^3-\frac{1}{3} x^3$\) and its conventional form, \(x^5-\frac{x^2}{3}-1$$\) , are both used.

\($$-1+x^5-\frac{1}{3} x^2=x^5-\frac{x^2}{3}-1$$\)

steps

\($$-1+x^5-\frac{1}{3} x^2$$\)

\(\begin{aligned}& \frac{1}{3} x^2=\frac{x^2}{3} \\& =-1+x^5-\frac{x^2}{3}\end{aligned}\)

rephrase in proper grammar

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

The term "polynomial" refers to a mathematical statement of one or more algebraic terms in which the variables are all of non-negative integer powers. Variables, fixed values, and exponents are all present in the terms. The degree 'n' standard form polynomial is Standard form is one method of expressing a polynomial. You must consider each term's degree in order to write any polynomial in standard form.

Next, list each phrase in order of degree, left to right, highest to lowest. An expression that solely uses the operations of addition, subtraction, multiplication, and non-negative integer exponentiation of variables is said to be a polynomial. Variables, which are sometimes known as indeterminates, and coefficients make up a polynomial.

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Answer:

I hurried  wat

Step-by-step explanation:

wAT

Step-by-step explanation:

to add 8% the simplest operation is to multiply the basic amount by 1.08.

so,

£9.45 = original price × 1.08

original price = £9.45/1.08 = £8.75

the price before the increase was £8.75.

The measure of the side MR is given as 20

We have to first find the value of the angle

∠TQR = 180 - (35 + 25)

= 180 - 60

= 120 degrees

180 - 120 = 60 degrees

angle TPR  = 90 degrees

next we have to find ∠PTQ

= 180 - (90 + 60)

= 180 - 150

= 30 degrees

given that TMN = TQR

TNP = PTQ

So if TMN = 35 degrees since TQR = 35 degrees

PTQ = 30, so TNP = 30 degrees

The measure of QR = 4 since MN = 4

NP = pq

np = 6

Hence the measure of MR

= 4 + 6 + 6 + 4

= 20

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Answer:

0 and undefined

Step-by-step explanation:

The electric field for a nonconducting plate with a charge per unit area of 9 located at z < 0 is zero, for 0 < z < 4.75 cm is \(2.16 \times 10^4 N/C\) directed in the positive z-direction, and for z > 4.75 cm is \(2.16 \times 10^4 N/C\) directed in the negative z-direction.

When z < 0, the plate is located below the second plate, resulting in the cancellation of electric field contributions due to the opposite charges on the plates. Therefore, the electric field is zero in this region.

For 0 < z < 4.75 cm, the electric field can be calculated using the formula E = σ / (2ε₀), where σ is the charge per unit area and ε₀ is the permittivity of free space. Substituting the given values, we find the electric field to be \(2.16 \times 10^4 N/C\) directed in the positive z-direction.

For z > 4.75 cm, the electric field is again given by E = σ / (2ε₀), but this time the charge per unit area is negative. Therefore, the electric field is \(2.16 \times 10^4 N/C\) directed in the negative z-direction.

In summary, the electric field for z < 0 is zero, for 0 < z < 4.75 cm is \(2.16 \times 10^4 N/C\) in the positive z-direction, and for z > 4.75 cm is \(2.16 \times 10^4 N/C\) in the negative z-direction.

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Answer:

60

Step-by-step explanation:

x and 2x are co - interior angles, sum of co - interior angles is 180,

x + 2x = 180

3x = 180

x = 180 / 3

x = 60

The last two rows of the table should be completed as follows:

Input   Output

8       22.80

10      28.50

An algebraic expression is a mathematical phrase that contains numbers, variables, and operations. It is used to represent a single quantity or value, and can be written in terms of one or more variables.

The rule given is an algebraic expression, x, which is the input, multiplied by 2.85, which is the output. Using this information, we can determine the cost of 10 muffins.

To find the cost of 10 muffins, we can use the algebraic expression given. First, we will multiply 10, the number of muffins, by 2.85, the cost of one muffin. This gives us a total of 28.50. Therefore, the cost of 10 muffins is 28.50.

Using this same rule and process, we can also determine the cost of any number of muffins. For example, if we want to know the cost of 15 muffins, we can simply multiply 15 by 2.85, giving us a total of 42.75.

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Answer:

C

Step-by-step explanation:

There is no provided context for the question so I gave a logical answer therefore.

Answer:

Ik think that the first one is 5. im not sure tho

The type of sampling described, where the researchers intentionally select a sample with 50% straight and 50% LGBTQ+ respondents, is known as "disproportionate stratified sampling."

A. Disproportionate stratified sampling involves dividing the population into different groups (strata) based on certain characteristics and then intentionally selecting a different proportion of individuals from each group. In this case, the researchers are dividing the population based on sexual orientation (straight and LGBTQ+) and selecting an equal proportion from each group.

B. Availability sampling (also known as convenience sampling) refers to selecting individuals who are readily available or convenient for the researcher. This type of sampling does not guarantee representative or unbiased results and may introduce bias into the study.

C. Snowball sampling involves starting with a small number of participants who meet certain criteria and then asking them to refer other potential participants who also meet the criteria. This sampling method is often used when the target population is difficult to reach or identify, such as in hidden or marginalized communities.

D. Simple random sampling involves randomly selecting individuals from the population without any specific stratification or deliberate imbalance. Each individual in the population has an equal chance of being selected.

Given the description provided, the sampling method of intentionally selecting 50% straight and 50% LGBTQ+ respondents represents disproportionate stratified sampling.

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Answer:

54/324

Step-by-step explanation:

Multiply probability of first event (6/18) by probability of second (9/18), you can then simplify if you need to to 1/6 or leave it as 54/324

Answer:

The answer is letter B.

Solution:

(x+6)(x2−6x+36)

=(x+6)(x2+−6x+36)

=(x)(x2)+(x)(−6x)+(x)(36)+(6)(x2)+(6)(−6x)+(6)(36)

=x³−6x2+36x+6x2−36x+216

=x³+216

a. If you have 420 ml of blue, then you can make 1400 ml or 1.4 liters.

b. If you have 2.1 liters of paint, then you used 630 ml of blue.

What is the meaning of ratio?

An ordered pair of numbers a and b, written as a / b, is a ratio if b is not equal to 0. A proportion is an equation that sets two ratios at the same value.

Given that, to make a paint you need the ratio of Blue: green paint in a paint mix is 3:7.

Assume that, you have 3x blue paint and 7x green paint.

The total amount of paint is 3x + 7x = 10x

Again you have  420ml of blue.

Therefore,

3x = 420

x = 140.

Now putting x = 140 in  10x:

The total amount of paint is 10×140=1400 ml = 1.4 liters.

b.

You have 2.1 liters  = 2100 ml paint.

Therefore,

10x = 2100

x = 210.

Now putting x = 210 in 3x:

The amount of blue paint is 3×210 = 630 ml

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The 12th term of the given expression b(n)=−4−2(n−1)b is 4 -22 b .

We have given an expression b(n)=−4−2(n−1)b     ...(1)

In order to find 12th term put n = 12 in equation (1) , we get

  b(12) = 4 - 2(12-1)b

           = 4 -2(11)b

           = 4 -22b

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Answer:

addition property of equality. hope that helps!

Step-by-step explanation:

Answer:

addition property of equality

Step-by-step explanation:

The  C is perpendicular to AB

When using paper, the paper perpendicular te construct to is folded so that AB is divided equally and the two sides of. line AB will lie exactly on top of each other.

When using a reflective device to construct a live perpendicular to line AB, set One end of the device to coincide with point C, and then swing the other end of the device so that the reflection of line AB coincides with the midpoint of AB

The question is incomplete hence the complete question is shown here

Select the correct answer from the drop-down menu. Compare the steps for constructing a perpendicular line to line  through point  using a reflective device and using paper. , When using paper to construct the perpendicular line, the paper is folded so that and the two sides of line  will lie exactly on top of each other. When using a reflective dewice to construct a line perpendicular to line  , set one end of the device to coincide with , and then swing the other end of the device so the reflection of line  coincides with.

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Answer:

I toke the test, I think the first one is A and  B coincide

Step-by-step explanation:

Answer:

7 units

Step-by-step explanation:

You can just count the 7 units down the middle.

Answer: 0.5

Step-by-step explanation:

Given

Line passes through \((-10,-30), (0,-25), (10,-20), \text{and}\ (20,-15)\)

The slope of the line is

\(m=\dfrac{y_2-y_1}{x_2-x_1}\)

Taking any two points: (0, -25) and (20,-15)

Slope is

\(\Rightarrow m=\dfrac{-15-(-25)}{20-0}=\dfrac{10}{20}\\\\\Rightarrow m=0.5\)

The maximum number of chairs that can be made will be the minimum of 12, 15, and 11. That exists, 11 chairs can be made, limited by the number of available legs.

The study of probabilities, which are determined by the ratio of favorable occurrences to probable cases, is known as probability.

The maximum number of chairs that can be made will be the minimum of the number of parts divided by the number of parts required for each chair, as calculated across the various types of parts required.

seats: 12 available, used 1 per chair: 12/1 = 12 chairs possible

backs: 15 available, used 1 per chair: 15/1 = 15 chairs possible

legs: 44 available, used 4 per chair: 44/4 = 11 chairs possible

The maximum number of chairs that can be made will be the minimum of 12, 15, and 11. That exists, 11 chairs can be made, limited by the number of available legs.

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Answer:

Step-by-step explanation:

-4

Work Shown:

\(a_1 = -1 = \text{ first term} \\\\d = 0.5 = \text{ common difference} \\\\a_n = a_1 + d(n-1)\\\\a_n = -1 + 0.5(n-1)\\\\a_6 = -1 + 0.5(6-1)\\\\a_6 = -1 + 0.5(5)\\\\a_6 = -1 + 2.5\\\\a_6 = 1.5\\\\\)

Answer:

Based on the given information, we can conclude that the graph represents a quadratic function. The vertex of the parabola is located at (0, 9) and the function passes through several points including (-4, -7), (-3, 0), (3, 0), and (4, -7).

To find the equation of the function, we need to determine the value of "a" in the equation f(x) = ax^2 + bx + c. Since the vertex is located at (0, 9), we know that the x-coordinate of the vertex is 0. Therefore, we can use the vertex form of the equation, which is f(x) = a(x - 0)^2 + 9, or simply f(x) = ax^2 + 9.

Next, we can use one of the given points to solve for "a". Let's use the point (-3, 0).

0 = a(-3)^2 + 9

0 = 9a - 9

9 = 9a

a = 1

Therefore, the value of "a" in the equation of the function is B. 1.

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f(x) and g(x) are not closed under subtraction because when subtracted, the result will be a polynomial, the correct option is B.

A polynomial is a mathematical equation that solely uses the operations addition, subtraction, multiplication, and non-negative integer exponentiation of variables. Variables are sometimes known as indeterminate in mathematics. Majorly used polynomials are binomial and trinomial.

Given f(x) and  g(x) two polynomial functions in the standard form of the polynomial,

According to Closure Property, when something is closed, the output will be the same as the input.

The polynomials f(x) and g(x) can be seen in the image.

On subtracting the two polynomials, the output will be a polynomial and so it is closed under subtraction.

Therefore, The reason why f(x) and g(x) are not closed under subtraction is that the outcome of subtraction will be a polynomial, making option B the best choice.

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Complete question:

Answer:

(9,18)

Step-by-step explanation:

Given that the perimeter of the triangle APM is 152, and the angle PAM is a right angle. A circle of radius 19 with center O on AP is drawn so that it is tangent to AM and PM. We need to find the value of OP.

Here's how to solve the problem: We have to use the Pythagorean theorem in triangle APM.

Let AP = a,

PM = b, and

AM = c, then we have:

AP² + PM² = AM²

a² + b² = c²

Also, the radius of the circle is given as 19, and it is tangent to AM and PM. Therefore, the perpendicular distance from the center of the circle O to the line PM is equal to the radius 19. Let this distance be x.We have two similar right triangles, AOP and OPM. So, using the Pythagorean theorem in triangle AOP, we get:

OA² + AP² = OP²OP²

= OA² + a² Again, using the Pythagorean theorem in triangle OPM, we get:

OM² + PM² = OP²OP²

= OM² + b² Since the circle is tangent to AM at A, we have:

OA = r + AMOA = 19 + c

Now, substituting these values in the above two equations, we get:

OP² = (19 + c)² + a²

OP² = (19 + c)² + (152 - b)²

We have two equations for OP², so we can equate them:

(19 + c)² + a² = (19 + c)² + (152 - b)²

OM² + b² = (19 + c)² + (152 - b)²

Simplifying the first equation, we get:

a² = (152 - b)² Solving for b in this equation, we get:

b = 152 - a Substituting this value of b in the second equation, We have two equations for a and c, which we can solve using substitution:

a + b + c = 152

b = 152 - ac²

= a² - (152 - b)²

Substituting the value of b from the first equation in the second equation, Now, this is a quartic equation in OP², which can be solved using numerical methods. Using a calculator or software, we get:

OP² = 32009.5 or 17431.7 We take the positive value of OP:

OP = √32009.5

OP = 179.0449

Therefore, the value of OP is approximately equal to 179.0449.

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Answer:

Cone: 100ft^3

Sphere: 200ft^2

Step-by-step explanation:

Firstly, the volume of a cone is 1/3 of the volume of the cylinder. It's literally in the formula:

\(V_{cone} = \frac{h \pi r^2}{3}\\\textrm{As you can notice, }\pi r^2\textrm{ is the area of the base, like in the cylinder formula}\\\)

So we can just instantly tell that the volume of the cone is 100feet^3.

Not for the sphere - we can assume that if the height is the same, it's equal to two radiuses, or simply - to the diameter. Let's use the formula for the volume of a sphere, but substitute one of the radiuses with \(\frac{h}{2}\)

\(V_{sphere} = \frac{4\pi r^3}{3} = \frac{2\pi r^2 h}{3} = \frac{2h\pi r^2}{3} = 2\cdot V_{cone}\)

So we can instantly tell that the volume of the sphere is 200feet^3

The probability that the first applicant with advanced training in programming is found on the third interview is 0.625, or 62.5%.

The probability of finding the first applicant with advanced training in programming on the third interview can be determined using the concept of geometric probability.

Given that 75% of the applicants possess advanced training in computer programming, this means that the probability of an applicant having advanced training is 0.75. Since the applicants are selected at random from the pool, this probability remains constant for each interview.

To find the probability that the first applicant with advanced training is found on the third interview, we need to consider two scenarios:

Scenario 1: The first two applicants do not possess advanced training.
In this scenario, the probability of selecting an applicant without advanced training is 1 - 0.75 = 0.25.

Since the applicants are selected independently, the probability of this scenario occurring is (0.25)^2 = 0.0625 (0.25 raised to the power of 2).

Scenario 2: The first two applicants possess advanced training, but the third applicant does.

In this scenario, the probability of selecting an applicant with advanced training is 0.75. The probability of this scenario occurring is (0.75)^2 = 0.5625 (0.75 raised to the power of 2).

The probability of finding the first applicant with advanced training on the third interview is the sum of the probabilities from both scenarios:

Probability = Probability of Scenario 1 + Probability of Scenario 2
           = 0.0625 + 0.5625
           = 0.625

Therefore, the probability that the first applicant with advanced training in programming is found on the third interview is 0.625, or 62.5%.

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Answer:

50%

1 2 = 1 × 50 2 × 50 = 50 100 . . So the answer is 50%

please mark me as a brainalist

To create various plots of the symbolic function Z, given by Z = sin(/X+Y) X? +Y?, we can use different plotting functions in MATLAB. The three-dimensional plot can be generated using the "plot3" function, the fsurf plotting function can be used to create a three-dimensional surface plot, and the fcontour function can be used to create a contour map of Z.

To create a three-dimensional plot of Z, we can use the "plot3" function in MATLAB, which allows us to plot in three dimensions. This plot will show the relationship between the variables X, Y, and Z.

For a three-dimensional surface plot, the "fsurf" function can be employed. This function will generate a surface plot that illustrates the behavior of Z in a more detailed manner.

To create a contour map of Z, the "fcontour" function can be utilized. This function will produce a two-dimensional plot with contour lines representing the values of Z.

By employing the "subplot" function in MATLAB, we can combine all the plots into a single figure, allowing for easy visualization and comparison.

The symbolic function Z can be visualized using the "plot3" function for a three-dimensional plot, the "fsurf" function for a three-dimensional surface plot, and the "fcontour" function for a contour map. By utilizing subplots, all the plots can be combined into a single figure.

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