Which product of prime polynomials is equivalent to 3x^4 - 81x?
a) 3x(x − 3)(x2 – 3x - 9)
b) 3x(x − 3)(x2 + 3x + 9)
c) 3x(x - 3)(x - 3)(x + 3)
d) 3x(x − 3)(x + 3)(x + 3)

We can prove that the statement is false by contradiction, as if a triangle had two obtuse angles, the sum of the measures of the internal angles of the triangle would be greater than 180º.

To prove an statement by contradiction, we must simply take an statement that either accepts the statement (true) or rejects (false).

An angle is classified as obtuse if it has a measure that is greater than 90º.

The sum of the measures of the internal angles of a triangle is of 180º, hence if the triangle had two obtuse angles, then the sum of the measures of the internal angles of the triangle would be greater than 180º.

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Answer:

Answer:

pretty sure its 10 i might be wrong

Step-by-step explanation:

Answer:

x = -2 | y = -6
x = 1 | y = 6
x = 2 | y = 10

Step-by-step explanation:

Answer:

Graph C

Step-by-step explanation:

Answer:

Yes, they both have a volume of 339.12 inches cubed.

Step-by-step explanation:

To calculate the volume of an oblique cylinder is very simple, we must multiply π (Pi = ~ 3.14) by the radius to the power of two and then multiply by the height. In this case the height forms a 90 degree angle from the opposite base to the position of the base, but outside of it.

Volume = π × Radius² × Height

The formula for the volume of a regular cylinder or an oblique cylinder is the same, if we imagine a stack of poker chips (forming a cylinder), even when we tilt the chips to one side (forming an oblique cylinder) the volume remains the same.

Now using this information, we must find the volumes of both cylinders.

For the oblique cylinder:
Given

Using the formula,

The volume would be 339.29 m³

Now solving for the other cylinder:

V=πr²h=π·32·12≈339.29201

Rounded, the answer would be 33.29 m³

This therefore proves that they both have the same volume.

Answer:Less energy

Step-by-step explanation:Because if you don't have alot of energy in you you'll be tired and cant move that much if that makes since.

Answer is  b. Less Energy is not a benefit of increased physical activity.

Physical activity refers to all movement including during leisure time, for transport to get to and from places, or as part of a person's work.

here, we know that,

not a benefit of increased physical activity is Less Energy.

Because if you don't have a lot of energy in you you'll be tired and cant move that much if that makes since.

Hence, Answer is  b. Less Energy is not a benefit of increased physical activity.

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Megan have total 1,071 stamps.

The concept used in this problem is multiplication, specifically using it to find the total number of stamps by multiplying the number of pages by the number of stamps per page. Additionally, it also uses the concept of addition to find the total number of stamps by adding the number of stamps on full pages to the number of stamps on half-full pages.

as given, Megan keeps her stamps in a book that can hold 17 on each page. she has 56 pages full of stamps. So,

Megan has 56 pages * 17 stamps per page = 952 stamps on full pages.

and 14 pages that are only half full. So,

She has 14 pages * (half of 17 stamps per page) = 14 pages * 8.5 stamps per page = 119 stamps on half-full pages.

Therefore, Megan has 952 stamps + 119 stamps = 1,071 stamps in total.

hence, Megan have total 1,071 stamps.

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Answer:

Yes

Step-by-step explanation:

1 piece per week can be written as a 1:1 ratio

Answer:

15

Step-by-step explanation:

EZZZZZZZZZZZZZZZZZZZZZZZZZ

Answer:

15

Step-by-step explanation:

hdhfddd gotta sg themselves when's high

Answer:

Step-by-step explanation:

To find the general solution to the given differential equation y^(4) + 2y" + y = 3 + cos(2t), we can follow these steps.Therefore, the correct option is:

o y = c_1cost + c_2sint + t(c_3cost + c_4sint) + 3 + (1/9)sin(2t)

1. Start by finding the complementary function by assuming y = e^(rt), where r is a constant:

  Substitute this assumption into the differential equation:

  r^4e^(rt) + 2r^2e^(rt) + e^(rt) = 0

  Simplify the equation:

  e^(rt)(r^4 + 2r^2 + 1) = 0

2. Solve the equation r^4 + 2r^2 + 1 = 0 to find the roots:

  Let's substitute u = r^2:

  u^2 + 2u + 1 = 0

  (u + 1)^2 = 0

  u + 1 = 0

  u = -1

  Substitute back u = r^2:

  r^2 = -1

  r = ±i

  Therefore, the roots of the equation are r = ±i.

3. Based on the roots, the complementary function is:

  y_c = c_1cos(t) + c_2sin(t) + c_3cos(t) + c_4sin(t)

       = (c_1 + c_3)cos(t) + (c_2 + c_4)sin(t)

4. To find a particular solution, guess a form that matches the non-homogeneous term:

  y_p = At^2 + B + Ccos(2t) + Dsin(2t)

5. Take derivatives of y_p and substitute them into the differential equation to solve for the coefficients A, B, C, and D.

6. Substituting the values of A, B, C, and D back into the particular solution y_p, we get:

  y_p = t^2 + 3 + (1/9)cos(2t) + (1/9)sin(2t)

7. The general solution is the sum of the complementary function and the particular solution:

  y = y_c + y_p

    = (c_1 + c_3)cos(t) + (c_2 + c_4)sin(t) + t^2 + 3 + (1/9)cos(2t) + (1/9)sin(2t)

Therefore, the correct option is:

o y = c_1cost + c_2sint + t(c_3cost + c_4sint) + 3 + (1/9)sin(2t)

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Answer:

Total length in inches - 126 inches

Total length in feet = 10.5 feet

Total length in yards = 3.503 yards

Step-by-step explanation:

Given the dimension of the ribbon by the three friends given as;

Carol- 42 in.

Tino- 2.5 feet

Baxter- 1.5 yards

Express feet in inches

1 feet = 12inches

2.5 feet = 12*2.5

25feet = 30inches

Express yard in inches

1 yard = 36inches

1.5yard = 36(1.5)

1.5yard = 54inches

Take the sum in inches

Sum in inches = 42 + 30 + 54

Sum in inches = 126inches

Convert dimensions to feet

42inches to feet = 42/12 = 3.5 feet

1.5yards to feet = 1.5*3 = 4.5 feet

Take the sum in feet

Sum in feet = 3.5 + 4.5 + 2.5

Sum in feet = 10.5feet

Convert dimensions to yards

42inches to yards = 42/36 = 1.17 yards

2.5 feet to yards = 0.833yards

Take the sum in yards

Sum in yards = 1.5 + 1.17 + 0.833

Sum in yards = 3.503yards

Solving the question asked, we can say: If you win tonight, your odds of winning the next game are \($58.33\%$\). After that, if you lose, you have a \($38.88 \%$\) chance of winning the game.

Probability theory is a branch of mathematics that measures the probability that an event or statement is true. The probability of an event is a number between 0 and 1, with approximately 0 indicating that the event is unlikely and 1 indicating that it is certain. Probability is a numerical representation of the disease that a particular event will occur. Another way to express probability is as a percentage from 0% to 100% or 0 to 1. Proportion of occurrences in the complete set of equally likely possibilities leading to a particular occurrence compared to the total number of outcomes.

\($$\begin{aligned}& (2 / 3+1 / 2) / 2=X \\& 1,666 / 2=X \\& 0.58333=X \\& ((2 / 3+1 / 2 / 2) x 2 / 3=X \\& 0.58333 x 0.666=X .3888=X\end{aligned}$$\)

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Answer:

\(832 \sqrt{13} \)

Step-by-step explanation:

This question means

\(4 \sqrt{13} \times 4 \sqrt{13} \times 4 \sqrt{13} \)

Lets solve it in simplest way

\((4 \sqrt{13} {)}^{3} \)

\(64 \times \sqrt{13} \times \sqrt{13} \times \sqrt{13} \)

\(64 \times \sqrt{139} \times \sqrt{13} \)

\(64 \times 13 \times \sqrt{13} \)

\(832 \sqrt{13} \)

I hope u like it ‍❤️‍

cooment me for any question

The volume of the right prism include the following: 8,640 in³.

In Mathematics and Geometry, the volume of a rectangular prism can be calculated by using the following formula:

Volume of a rectangular prism = L × W × H

Where:

Next, we would determine the area of the triangle at the base of the right prism as follows:

Base area = 1/2 × ( 36 × 12)

Base area = 1/2 × 432

Base area = 216 in².

Now, we can calculate the the volume of this right prism:

Volume = base area × height

Volume = 216 × 40

Volume = 8,640 in³.

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Answer:

24a^9b^4

Step-by-step explanation:

you would multiply 4a^2 and 24^a^7b^3.

Answer:

24 a ^9 b^4

Step-by-step explanation:

Area of a rectangle using the following formula: Area of a rectangle = length or width x square root of (the square of the diameter - the square of the length or the square of the width)

The interquartile range (IQR) is a measure of the spread or variability of the middle 50 percent of the data.

The interquartile range (IQR) is a statistical measure that describes the spread or dispersion of the middle 50 percent of the data. It is calculated as the difference between the third quartile (Q3) and the first quartile (Q1) of a dataset.

The quartiles divide a dataset into four equal parts, each representing 25 percent of the data. The first quartile (Q1) represents the lower boundary of the middle 50 percent, while the third quartile (Q3) represents the upper boundary of the middle 50 percent. The IQR captures the range of values within this middle range.

By focusing on the middle 50 percent of the data and excluding the extreme values, the interquartile range provides a measure of variability that is less affected by outliers or extreme values. It is commonly used in descriptive statistics and data analysis to understand the spread and distribution of a dataset, particularly when the data is not symmetrically distributed or contains outliers.

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Answer:

y = 130

Step-by-step explanation:

(4x+8) + (3x-19) + (x+7) = 180

4x + 8 + 3x - 19 + x + 7 = 180

(4x + 3x + x) + (8 -19 + 7) = 180

8x - 4 = 180

8x -4 +4 = 180 +4

8x = 184

8x/8 = 184/8

x = 23

3(23) - 19 = 50

50 + y = 180

180 - 50 = y

y = 130

It is false as the left and right ends of the normal probability distribution extend indefinitely, approaching but never touching the horizontal axis.

The statement is false because the left and right ends of the normal probability distribution do not extend indefinitely. In reality, the normal distribution is defined over the entire real number line, meaning it extends infinitely in both the positive and negative directions. However, as the values move further away from the mean (the center of the distribution), the probability density decreases. This means that although the distribution approaches but never touches the horizontal axis at its tails, the probability of observing values extremely far away from the mean becomes extremely low. Thus, while the distribution theoretically extends infinitely, the practical probability of observing values far from the mean decreases rapidly.

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The answer to the integral 0∫π/3 cos⁴xsinx dx using a u-substitution is -5/24 - √3/24, or approximately -0.315.To use a u-substitution to evaluate 0∫π/3 cos⁴xsinx dx, we will use the following steps:

Step 1: Choose a u-substitution that simplifies the integral. In this case, we will let u = cosx, which will allow us to rewrite the integral as 0∫1 u⁴(1-u²)du.

Step 2: Substitute the expression for u into the integral, and simplify. Using the substitution u = cosx, we have:

0∫π/3 cos⁴xsinx dx = 0∫1 u⁴(1-u²)du

Step 3: Evaluate the integral using standard integration techniques. Integrating u⁴(1-u²) with respect to u, we get:

∫ u⁴(1-u²)du = (1/5)u⁵ - (1/3)u³ + C

Step 4: Evaluate the integral from 0 to 1 using the substitution u = cosx. Substituting back, we have:

0∫π/3 cos⁴xsinx dx = (1/5)cos⁵x - (1/3)cos³x ∣₀ᴰ³/₃

Evaluating this expression at the limits of integration, we get:

(1/5)(cos⁵(π/3) - cos⁵(0)) - (1/3)(cos³(π/3) - cos³(0))

Simplifying, we get:

(1/5)(27/64 - 1) - (1/3)(3√3/8 - 1)

= -1/120 (27 - 64) - √3/24 + 1/3

= -5/24 - √3/24

Therefore, the answer to the integral 0∫π/3 cos⁴xsinx dx using a u-substitution is -5/24 - √3/24, or approximately -0.315.

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When the population standard deviation is unknown and the sample size is less than 30, we need to use the t-distribution to compute a confidence interval for the mean, and we should consult a t-table to find the appropriate t-value based on the degrees of freedom and the desired level of confidence.

When the population standard deviation is unknown and the sample size is less than 30, we need to use the t-distribution to compute a confidence interval for the mean.

The t-distribution is similar to the standard normal distribution, but with heavier tails, and it is used when the population standard deviation is unknown.

To compute the confidence interval for the mean using the t-distribution, we need to find the appropriate t-value from a t-table. The t-table provides critical values for different degrees of freedom and levels of confidence.

The degrees of freedom for a t-distribution with a sample size of n is (n-1). For example, if we have a sample size of 20, the degrees of freedom would be 19.

To find the appropriate t-value from the t-table, we need to know the degrees of freedom and the desired level of confidence. For example, if we have a sample size of 20 and want to calculate a 95% confidence interval, we would look for the t-value with 19 degrees of freedom and 0.025 (0.05/2) in the middle of the table. This t-value would be used in the formula to calculate the confidence interval for the mean.

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Answer:

$1.08

Step-by-step explanation:

Answer:

2,033-993.50= 1039.50/74.25= 14

Step-by-step explanation:

not sure the exact equation but p would be 14 and you'd do something similar to that shown above

607 students must there be to guarantee that there are two students with the same professor who earned the same fnal examination score

We use Pigenhole principle to solve this problem.

We know the Pigenjole principle states that if y number of items are put into z number of containers, with y > z, then it means that that at least one container must definitely contain more than one item.

Here, the possible scores are from 0 to 100 with both inclusive.

So, the number of possible scores = 101.

Now,  there are two students with the same professor who earned the same final examination score.

The number of students would be = 101 + 1

                                                     = 102

For each student there are 6 professors.

so the possible combination for a score would  be = 6

So, the number of students must there be to guarantee that there are two students with the same professor who earned the same fnal examination score: (6 × 101) + 1 = 607

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Answer:

x

Explanation:

Let cost of leash = y

14.26 - y = x

Hope this helps and have a great day :)

And please mark me brainliest if you can :)

34% of the data in a normal distribution is more than 1 standard deviation above the mean.

In a normal distribution, about 68% of the data falls within one standard deviation above or below the mean. This means that roughly 34% of the data falls one standard deviation above the mean.

To be more precise, we can use the empirical rule or the 68-95-99.7 rule, which states that:

Approximately 68% of the data falls within one standard deviation of the mean.

Approximately 95% of the data falls within two standard deviations of the mean.

Approximately 99.7% of the data falls within three standard deviations of the mean.

Therefore, if we assume that the normal distribution is perfectly symmetrical, we can estimate that roughly 34% of the data falls more than one standard deviation above the mean.

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The equation of the plane that contains the given points is: -2x - y - 3z = -3. The equation of the plane that contains the points (3, 0, -1), (-2, -2, 3), and (2, 1, -2) can be determined using the concept of normal vectors.

In order to find the equation of a plane, we need to determine its normal vector. To find the normal vector, we can calculate the cross product of two vectors formed by the given points.

Let's consider the vectors formed by the points (3, 0, -1) and (-2, -2, 3) as  v₁ and v₂, respectively. The cross product of v₁ and v₂ will give us the normal vector of the plane.

v₁ = (-2-3, -2-0, 3-(-1)) = (-5, -2, 4)

v₂ = (2-3, 1-0, -2-(-1)) = (-1, 1, -1)

By taking the cross product of v₁ and v₂, we get the normal vector N of the plane:

N = v₁ x v₂ = (-5, -2, 4) x (-1, 1, -1) = (-2, -1, -3)

Now, we have the normal vector N = (-2, -1, -3). We can use this normal vector and any one of the given points (let's take (3, 0, -1)) to find the equation of the plane using the general form of the plane equation:

Ax + By + Cz = D

Substituting the values, we get:

-2x - y - 3z = D

By substituting the coordinates of (3, 0, -1) into the equation, we can determine the value of D:

-2(3) - (0) - 3(-1) = -6 + 0 + 3 = -3

Therefore, the equation of the plane that contains the given points is:

-2x - y - 3z = -3

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Answer:

a

Step-by-step explanation:

sin G=(opposite side)/hypotenuse=x/z