What is a simpler form of
5n(3n³−n²+8) ?

Answer:

x = 18

Step-by-step explanation:

The "Angle Bisector" Theorem says that an angle bisector of a triangle will divide the opposite side into two segments that are proportional to the other two sides of the triangle.

So, 20/8 = (4x + 3)/30

8(4x + 3) = 20(30)

32x + 24 = 600

32x = 576

x = 18

Answer:

(-1,2) i think

Step-by-step explanation:

Answer: D

Step-by-step explanation: As we can see, D is the only one that has matching inputs, but those inputs have separate outputs. If they don't have the same output, it is not a function

Hope this helps :)

Step-by-step explanation:

1st expression

= px^4 + px

= px ( x³ + 1 )

= px ( x + 1) (x² - x + 1)

2nd expression

= qx³ - qx

= qx ( x² - 1 )

= qx ( x + 1) ( x - 1)

HCF = x ( x + 1)

Hope it will help :)❤

*see attachment for the diagram given

Answer:

Volume of the toy = 68 in.³

Step-by-step explanation:

The equation to find the volume of the toy = volume of the wooden rectangular prism - volume of the triangular prism removed form the center

Volume of the toy = (L*W*H) - (½*bhl)

Where,

L = 8 inches

W = 3 inches

H = 3 inches

b = 1 inch

h = 1 inch

l = 8 inches

Plug in the values into the equation

Volume of the toy = (8*3*3) - (½*1*1*8)

Volume = 72 - 4

Volume of the toy = 68 in.³

Answer:

x= 24

Step-by-step explanation:

5x=20*6

x=120/5

x=24

Hope this helps! Plz mark as brainliest! :)

Step-by-step explanation:

3 Area of lateral = 3 ( bh ) = 12.2 XIO +7.04X12.2 +7.04x 12.2 = 122+85.888+85.888 = 293.776

293.776 approximate to 288

Group A parallelogram, Group B Quadrilateral.

Answer: Parallelogram and Quadrilateral.

The  two ways of classifying shapes are: Parallelogram and Quadrilateral.

There are different ways to classify an item.

Quadrilaterals can be known by;

It is a polygon with four sides.

Since rectangle is known to be a parallelogram that has four right angles.

A trapezoid is regarded as a quadrilateral with only one pair of parallel sides.

And Parallelograms are known to be shapes that has four sides with only two pairs of sides that are known to be parallel.

So we conclude that Group A parallelogram, and Group B Quadrilateral.

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Answer:

The car was traveling for 1.5 hours.

Step-by-step explanation:

Given that distance d, in kilometers, that a car travels at a speed of 80 km per hour , for t hours, is given by the equation d=80t.

Here wee need to find the time if the car has gone 120 kilometers.

That is

            d = 120 km

we need to find t.

            d=80t

           120 = 80 x t

The car was traveling for 1.5 hours.

Answer:

3n + 2

Step-by-step explanation:

−n+(−4)−(−4n)+6

-n - 4 + 4n + 6

3n + 2

Answer:

7 is the answer

Step-by-step explanation:

Because 6x + 3 -8 + x = x is 6

Answer:

The answer your looking for is, C.

We have: u''(x) = ƒ(x)cot(x) - 2u'(x)cot(x).Thus, we can find a particular solution of this differential equation by using variation of parameters.

Let G(x) = ƒ(s)sin(x - s) ds.

Then, by the product rule, we have: G' = ƒ(s)cos(x - s) ds - ƒ(s)sin(x - s) ds, and G'' = -ƒ(s)sin(x - s) ds - ƒ(s)cos(x - s) ds. Hence, we have:G'' + G = ƒ(s)sin(x - s) ds - ƒ(s)cos(x - s) ds + ƒ(s)sin(x - s) ds = ƒ(s)sin(x - s) ds = G.

So, G is indeed a solution of y'' + y = ƒ(x).Next, we will use variation of parameters to find a second solution of the same differential equation.

Let us suppose that we have another solution of the form y = u(x) sin(x).

Then, y' = u(x)cos(x) + u'(x)sin(x), and y'' = - u(x)sin(x) + 2u'(x)cos(x) + u''(x)sin(x).

Substituting these into the differential equation, we get:- u(x)sin(x) + 2u'(x)cos(x) + u''(x)sin(x) + u(x)sin(x) = ƒ(x)2u'(x)cos(x) + u''(x)sin(x) = ƒ(x)

Dividing by sin(x), we get:2u'(x)cot(x) + u''(x) = ƒ(x)cot(x).

Now, let us assume that the second solution is of the form y = u(x)sin(x), where u is a function to be determined.

Then, we have: y' = u(x)cos(x) + u'(x)sin(x) and y'' = - u(x)sin(x) + 2u'(x)cos(x) + u''(x)sin(x).

Substituting these into the differential equation, we get: - u(x)sin(x) + 2u'(x)cos(x) + u''(x)sin(x) + u(x)sin(x) = ƒ(x)2u'(x)cos(x) + u''(x)sin(x) = ƒ(x)

Dividing by sin(x), we get:2u'(x)cot(x) + u''(x) = ƒ(x)cot(x).

Hence, we have: u''(x) = ƒ(x)cot(x) - 2u'(x)cot(x).Thus, we can find a particular solution of this differential equation by using variation of parameters.

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A uniform solid disk with a mass of 2.91 kg and a radius of 0.200 m is rotating about a fixed axis perpendicular to its face with an angular frequency of 5.94 rad/s.

The angular frequency of an object rotating about a fixed axis represents the rate at which it completes one full revolution in radians per second. In this case, the disk has an angular frequency of 5.94 rad/s.

The moment of inertia of a uniform solid disk rotating about its axis can be calculated using the formula:

I = (1/2) * m * [tex]r^2[/tex]

where I is the moment of inertia, m is the mass of the disk, and r is the radius of the disk. Substituting the given values, we have:

I = (1/2) * 2.91 kg * [tex](0.200 m)^2[/tex]= 0.0582 kg·[tex]m^2[/tex]

The moment of inertia is a measure of an object's resistance to changes in rotational motion. In this case, the disk's moment of inertia is 0.0582 kg·[tex]m^2[/tex].

The angular frequency, moment of inertia, and mass of the disk are related by the equation:

I * ω = L

where ω is the angular frequency and L is the angular momentum. Rearranging the equation, we can solve for the angular momentum:

L = I * ω = 0.0582 kg·[tex]m^2[/tex] * 5.94 rad/s = 0.3456 kg·[tex]m^2[/tex]/s

Therefore, the angular momentum of the rotating disk is 0.3456 kg·[tex]m^2[/tex]/s.

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Answer:

c I think but I am not sure but I hope you have a good day

Answer:

32

Step-by-step explanation:

Answer:

32

Step-by-step explanation:

This should help

Answer:

Seven cups of canned apples are required to make apple pie recipe

Step-by-step explanation:

The weight of one canned apple is 0.45 pounds

Weight of total canned apple required to make the apple pie recipe is 3 pounds.

Total number of cups of canned apples required

[tex]= \frac{3}{0.45} \\= \frac{300}{45} \\= \frac{20}{3} \\[/tex]

So approximately seven cups of canned apples are required to make apple pie recipe

Step-by-step explanation:

[tex] \frac{ - 48 + 6}{ - 7} + ( - 3)( - 4)( - 2) \\ = \frac{ - 42}{ - 7} + 12( - 2) \\ = 6 + ( - 24) \\ = 6 - 24 \\ = - 18[/tex]

Answer:

A or D

Step-by-step explanation:

The sum of the squared deviation for the given sample data (23, 27, 35, 44) is 212.00.

In statistics, the squared deviation is calculated by subtracting each data point from the mean and then squaring the result. The sum of these squared differences gives us a measure of how much the individual data points vary from the mean.  

Find the sum of squared deviations, we first calculate the mean of the data set. In this case, the mean is found by adding up all the values (23 + 27 + 35 + 44) and dividing the sum by the number of data points (4).

The mean turns out to be 32.25.Next, we subtract the mean from each data point:

(23 - 32.25) = -9.25

(27 - 32.25) = -5.25

(35 - 32.25) = 2.75

(44 - 32.25) = 11.75

Then, we square each of these differences:

(-9.25)² = 85.56

(-5.25)² = 27.56

(2.75)² = 7.56

(11.75)² = 138.06

Finally, we sum up these squared deviations:

85.56 + 27.56 + 7.56 + 138.06

= 212.00

Therefore, the sum of the squared deviations is 212.00 (rounded to two decimal places).

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Therefore, the variance of the time it takes for someone to finish a bowl of ramen is 4.6875.

Given, The moment generating function of the time it takes for someone to finish a bowl of ramen is

M(t)= 1/ (1−0.05t​)1​,t<0.05 We have to find the variance of the time it takes for someone to finish a bowl of ramen.

The variance of the random variable can be calculated by the formula Variance = M''(0) - [M'(0)]^2 where M(t) is the moment generating function of the random variable M'(t) is the first derivative of M(t)M''(t) is the second derivative of M(t)

We need to find M''(t) and M'(t)M(t) = 1/(1 - 0.05t)M'(t) = [0.05/(1 - 0.05t)^2]M''(t) = [0.1/(1 - 0.05t)^3] Now, at t = 0, M(0) = 1, M'(0) = 1.25, M''(0) = 6.25 Variance = M''(0) - [M'(0)]^2 Variance = 6.25 - (1.25)^2 Variance = 6.25 - 1.5625 Variance = 4.6875

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Given: The time it takes for someone to finish a bowl of ramen can be modeled by a random variable with the following moment generating function: M(t)= 1/ (1−0.05t​)1​,t<0.05. The variance of the time it takes for someone to finish a bowl of ramen is 400.

The moment generating function of a random variable is defined as [tex]$M(t) = \mathbb{E}(e^{tX})$[/tex] for all t in an open interval around 0 which X is a random variable.

We are given that the moment generating function of the random variable T is given by:

[tex]$$M(t)= \frac{1}{1-0.05t} ,\ t < 0.05$$[/tex]

The [tex]$n^{th}$[/tex] derivative of M(t) at 0 is given by:

[tex]$$\frac{d^n}{dt^n} M(t) \biggr|_{t=0} = \mathbb{E}(X^n)$$[/tex]

We differentiate $[tex]M(t)$[/tex] with respect to $t$ to get [tex]$$M'(t) = \frac{0.05}{(1 - 0.05t)^2}$$[/tex].

Differentiating [tex]$M'(t)$[/tex] with respect to [tex]$t$[/tex] we get [tex]$$M''(t) = \frac{2(0.05)^2}{(1-0.05t)^3}$$[/tex].

Differentiating [tex]$M''(t)$[/tex] with respect to [tex]$t$[/tex] we get [tex]$$M'''(t) = \frac{6(0.05)^3}{(1-0.05t)^4}$$[/tex].

Substituting t = 0, we get [tex]$$M'(0) = \frac{1}{0.05} = 20$$[/tex]

[tex]$$M''(0) = \frac{2}{(0.05)^3} = 800$$[/tex]

[tex]$$M'''(0) = \frac{6}{(0.05)^4} = 4800$$[/tex]

Using the following formula to calculate the variance of X: [tex]$$Var(X) = \mathbb{E}(X^2) - [\mathbb{E}(X)]^2$$[/tex], where [tex]$$\mathbb{E}(X^2) = M''(0) = 800$$[/tex].

[tex]$$[\mathbb{E}(X)]^2 = [M'(0)]^2 = 400$$[/tex]

Hence, we get:$$Var(X) = 800 - 400 = \boxed{400}$$.

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Answer:

Below :)

Step-by-step explanation:

Least/Minimum: 0

Greatest/Maximum: 6

Median: 2

Lower Quartile Range: 1

Upper Quartile Range: 3

Find median:

0, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 6

Find Lower Quartile:

0, 1, 1, 1, 1, 1, 1, 2, 2, 2

Find Upper Quartile:

2, 2, 3, 3, 3, 3, 4, 4, 4, 6

In a normal distribution, approximately 68% of scores fall between the z-scores of -1.00 and +1.00.

In a standard normal distribution, which has a mean of 0 and a standard deviation of 1, the Empirical Rule (also known as the 68-95-99.7 Rule) applies. According to this rule, approximately 68% of the data falls within one standard deviation from the mean.

Since the z-scores represent the number of standard deviations a particular value is away from the mean, a z-score of -1.00 represents one standard deviation below the mean, and a z-score of +1.00 represents one standard deviation above the mean. Therefore, using the Empirical Rule, we can conclude that approximately 68% of scores fall between these two z-scores (-1.00 and +1.00).

This percentage represents the central portion of the distribution that is within one standard deviation from the mean, providing a useful measure of the spread and concentration of data in a normal distribution.

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The point (-10, 1) in Cartesian-Coordinates can be represented in polar coordinates as approximately (10.05, 3.0416 radians).

To convert the point (-10, 1) from Cartesian-Coordinates to polar coordinates, we can use the formulas:

r = √(x² + y²)

θ = arctan(y / x)

We know that, the point is (-10, 1), we substitute the values into the formulas:

We get,

r = √((-10)² + 1²) = √(100 + 1) = √101 ≈ 10.05, and

The point lies in second-quadrant, so, the angle is measured counterclockwise from the positive x-axis, which means it is between π/2 and π radians.

Therefore, The adjusted θ is : θ = π + arctan(1/-10) ≈ 3.0416 radians.

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We can conclude that the null hypothesis is rejected. There is sufficient evidence to support the claim that the mean cost in Utah hospitals is below the national mean of $1231.

H₀: μ ≥ 1231 (The mean cost in Utah hospitals is greater than or equal to the national mean)

Hₐ: μ < 1231 (The mean cost in Utah hospitals is below the national mean)

Given

The test statistic for a one-sample t-test is given by

t = (x - μ) / (σ / √n)

Substituting we have

t = (1103 - 1231) / (252 / √25)

≈ -6.103

To determine the critical value, we need to find the critical t-value at the 5% significance level with degrees of freedom

(df) equal to (n - 1)

= (25 - 1)

= 24.

Using a t-distribution table or calculator, the critical value is approximately -1.711.

Since the calculated test statistic (-6.103) is smaller than the critical value (-1.711) and falls into the critical region, we reject the null hypothesis.

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it's simple it's really easy so the answer is 2.0 1682

a. Matrix A is invertible when |A| = -m ≠ 0 then statement true.

b. The system AX = B has no solution when m = 0 and n ≠ 0 has a real number then statement true.

c. The system AX = B has an infinite number of solutions when m = n = 0 then statement true.

d. Columns of the augmented matrix (AB) are linearly independent when m ≠ 0 and n= 0 then statement true.

e. The system AX = 0 has a unique solution when m ≠ 0 then statement true.

f. At least one eigenvalue of the matrix A is zero when m = 0 then statement true.

g. Columns of the matrix A form a basis in R³ when m ≠ 0 then statement true.

Given that,

The augmented matrix of a system of linear equations AX = B was reduced to upper-triangular form so that

[A|B] = [tex]\left[\begin{array}{ccc}2&1&0 \ | \ 2\\0&-1&3 \ | \ 1 \\0&0&m \ | \ n\end{array}\right][/tex]

Where m and n are real numbers.

We know that,

a. We have to prove matrix A is invertible.

For A to be invertible.

|A| ≠ 0

|A| is the determinant of the matrix A.

|A| = 2(-m) -1(0) + 0(0) = -m

Here, m is the real number.

So, |A| = -m ≠ 0

Therefore, Matrix A is invertible when |A| = -m ≠ 0 then statement true.

b. We have to prove the system AX = B has no solution.

When Rank[A|B] > Rank[A]

m = 0 and n ≠ 0 has a real number

Therefore, The system AX = B has no solution when m = 0 and n ≠ 0 has a real number then statement true.

c. We have to prove the system AX = B has an infinite number of solutions.

When m = n = 0, and Rank[A] < 3

Therefore, The system AX = B has an infinite number of solutions when m = n = 0 then statement true.

d. We have to prove columns of the augmented matrix (AB) are linearly independent.

When m ≠ 0 and m∈R and n= 0

Therefore, Columns of the augmented matrix (AB) are linearly independent when m ≠ 0 and n= 0 then statement true.

e. We have to prove the system AX = 0 has a unique solution.

When [tex]\left[\begin{array}{ccc}2&1&0 \\0&-1&3 \\0&0&m \end{array}\right]\left[\begin{array}{ccc}x\\y\\z\end{array}\right] =\left[\begin{array}{ccc}0\\0\\0\end{array}\right][/tex]

The equation are 2x + y = 0, -y + 3z = 0 and mz = 0

m ≠ 0 should be any real number except zero.

Therefore, The system AX = 0 has a unique solution when m ≠ 0 then statement true.

f. We have to prove at least one eigenvalue of the matrix A is zero.

When λ = 2, 1, m

m = 0 then eigen value is zero

Therefore, At least one eigenvalue of the matrix A is zero when m = 0 then statement true.

g. We have to prove columns of the matrix A form a basis in R³.

When m ≠ 0

Therefore, Columns of the matrix A form a basis in R³ when m ≠ 0 then statement true.

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