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Answer:

\(3x^3y^2\:+1\div 9y=3x^3y^2+\frac{1}{9}y\)

Step-by-step explanation:

Given the expression

\(3x^3y^2\:+1\div9y\)

According to the order of operation with respect to PEMDAS

so

Thus, the expression becomes

\(3x^3y^2+\frac{1}{9}y\)

There are no like terms involved in the expression.

The expression is very much simplified.

Thus:

\(3x^3y^2\:+1\div 9y=3x^3y^2+\frac{1}{9}y\)

The area of a semi circle is 19.25

We know that,

Area of semicircle = 1/2(πr²)

Therefore,

19.25 = 1/2 * 22/7 * r²

19.25 = 22/14 * r²

19.25 * 14/22 = r²

269.5/22 = r²

12.25 = r²

r = √12.25

r = 3.5 cm

Thus, The radius of the given semicircle is 3.5 cm

Therefore,

Diameter of the given circle = 2 * Radius

Diameter = 2 * 3.5 = 7 cm

Hence, The diameter of the given circle is 7 cm

Answer:

The answer would be team D as their range is 24.

Step-by-step explanation:

Team A: range of 27

Team B: Range of 32

Team C: Range of 27

Team D: Range of 24

Team D has the lowest range found by subtracting the larger number 46 by the smaller number 22.

Answer:

23

Step-by-step explanation:

X - 15 =8

+ 15 +15

15+8=23

23-15=8

X =23

Parameters are the values that are computed from a complete census, which are considered to be precise and valid measures of the population. So, option(b) is right one.

In statistics, a population parameter is a number that identifies an entire group of people or population. This should not be confused with arguments in other forms of mathematics that refer to values that remain constant for a mathematical function. Note that the population parameter is not a statistic, it refers to data for a sample or group of the population. With good research, we can get statistics that accurately estimate the population. Statistics is a numerical measure described with sample data. Therefore, the parameter is a numerical description of the characteristic of population.

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Complete question:

Values that are computed from a complete census, which are considered to be precise and valid measures of the population, are referred to as:

a) statistic

b) parameters

Answer:

34 weeks

Step-by-step explanation:

Hello!

We can set up an equation to solve for the number of weeks.

Let w = the number of weeks he is saving up.

The equation is \(315 = 115 + 10w - 140\)

He needs to save up for 34 weeks.

Answer:

21?

Step-by-step explanation:

just divide 105 by 5?

the full question wasn't here so I just guessed what u were trying to say

Answer:

grinding points

Step-by-step explanation:

\(\boxed{\sf a(b+c)=ab+ac}\)

\(\\ \sf\longmapsto 6(x+y)\)

\(\\ \sf\longmapsto 6(x)+6(y)\)

\(\\ \sf\longmapsto 6x+6y\)

The number of non-degenerate triangles that can be formed is 10, which is the final answer.

What is the combination?

Combinations are a way to count the number of ways to choose a subset of objects from a larger set, where the order of the objects does not matter.

There are a total of 20 triangles that can be formed by connecting three of the points given below as vertices, without any three points being co-linear.

To see why, we can count the number of ways to choose 3 points out of 5.

This can be calculated using the combination formula:

\(nCr = n! / r!(n-r)!\)

where n is the total number of points, and r is the number of points we want to choose.

So for this case, we have:

5C₃ = 5! / 3!(5-3)! = 10

However, we must exclude any degenerate triangles formed by three co-linear points.

There are no three co-linear points in the given set, so we do not need to subtract any cases from our total.

Therefore, the number of non-degenerate triangles that can be formed is 10, which is our final answer.

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Mukat gets 40, Usha gets 8

Step-by-step explanation:

Mukat = 5 × Usha

After Mukat gives Usha 16 books ,Usha gets (16 + initial number of books) and Mukat gets (5 × Usha - 16)

Then Mukat = final number of books for Usha

5 × Usha - 16 = Usha + 16

(5 × Usha ) - Usha = 16+16

4 × Usha = 32

Usha = 8 i.e her number of books.

Mukat = 5×8=40.

I HOPE IT'S OK

Answer: 3/4

Step-by-step explanation:

Slope=rise/run

We rise 3

We run 4

3/4

The probability that Yasmin will not be offered a coupon on at least one of the days she visits the website will be;

⇒ 0.9375

The term probability refers to the likelihood of an event occurring

Given that;

The probability that a visitor is offered a coupon (p) = 50%

Now,

Since, The probability that a visitor is offered a coupon (p) = 50%

Hence, The probability that he gets coupon all 4 days is,

⇒ p (4) = p⁴

⇒ p (4) = (50%)⁴

⇒ p (4) = 0.0625

Hence, By using the complement rule, the probability that he is not offered a coupon at least one day is,

⇒ p' = 1 - 0.0625

⇒ p' = 0.9375

Thus, The probability that Yasmin will not be offered a coupon on at least one of the days she visits the website = 0.9375

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Answer:

the answer is 1 whole and 1/2

Step-by-step explanation:

1 and 1/2

Renee could use place-value patterns to check her answer by observing that 2.5 miles jogged for 4 days is equivalent to 2.5 × 4 = 10 miles.

This calculation shows that the sum of the individual jog distances matches the total distance she calculated for the week, confirming the accuracy of her answer. The place-value pattern allows her to multiply the distance per day by the number of days to obtain the total distance, providing a method of cross-checking her calculation.

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Answer:

x = 6

Step-by-step explanation:

Using Pythagoras' identity in the right triangle.

The square on the hypotenuse is equal to the sum of the squares on the other 2 sides , that is

x² + 8² = 10²

x² + 64 = 100 ( subtract 64 from both sides )

x² = 36 ( take square root of both sides )

x = \(\sqrt{36}\) = 6

The value of x, in the image given is calculated by applying the intersecting chords theorem, which is: x = 16.

The Intersecting Chords Theorem, also known as the Ptolemy's Theorem, states that in a circle, if two chords intersect, then the product of the lengths of the segments of one chord is equal to the product of the lengths of the segments of the other chord.

In mathematical terms, if two chords, AB and CD, intersect at point E inside a circle, then:

AE × EB = CE × ED

Applying the theorem, we have:

5(x) = (x - 6)8

5x = 8x - 48

5x - 8x = -48

-3x = -48

x = 16

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Answer:

B

Step-by-step explanation:

Answer:

Step-by-step explanation:

this is a cuboid

Volume = Length × Width × Height.

4 * 3 * 3 = 36 cubic units

Answers:

The tangent of angle R is given as follows:

\(\tan{R} = \frac{\sqrt{47}}{17}\)

The three trigonometric ratios are the sine, the cosine and the tangent of an angle, and they are obtained according to the formulas presented as follows:

For the angle R, we have that:

Hence the tangent is given as follows:

\(\tan{R} = \frac{\sqrt{47}}{17}\)

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Answer:

Step-by-step explanation:

a^6 = a * a * a * a * a * a You can break this into groups of 2 and groups of three.

Groups of 3

a^6 = a * a * a * a * a * a

what that means is that you have 2 groups of 3 which can be written as (a^3)^2 which means that this number is a perfect square.

Groups of 2

a^6 = a * a * a * a * a * a

What this means is that you have (a^2)^3 which is three groups of 2 members. The answer is that you have a perfect cube each member of which is a^2

a) The sine function represents the y-coordinate of a point on the unit circle, given the angle in radians. Starting at the positive x-axis, 3π/2 radians takes us three-quarters of the way around the circle in the clockwise direction, ending at the negative y-axis. Therefore, sin(3π/2) = -1.
b) Similarly, -π radians takes us halfway around the circle in the clockwise direction, ending at the negative x-axis. Therefore, sin(-π) = 0.
c) The cosine function represents the x-coordinate of a point on the unit circle, given the angle in radians. 3π/2 radians takes us three-quarters of the way around the circle in the clockwise direction, ending at the negative y-axis. Therefore, cos(3π/2) = 0.
d) -π/2 radians takes us a quarter of the way around the circle in the clockwise direction, ending at the negative y-axis. Therefore, cos(-π/2) = 0.
e) The tangent function represents the ratio of the sine to the cosine of an angle. 4π radians takes us twice around the circle, ending at the positive x-axis. At this point, the cosine is 1 and the sine is 0, so tan(4π) = 0/1 = 0.
f) -π radians takes us halfway around the circle in the clockwise direction, ending at the negative x-axis. At this point, the cosine is -1 and the sine is 0, so tan(-π) = 0/-1 = 0.

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Answer:

Step-by-step explanation:

1) 3/4x = 1/2       2) 2x = 3/11        3) 1 1/2 x = 12      4) 1/5x = 1/6

   x = 1/2 * 4/3         x = 3/11 * 1/2       3/2x = 12             x = 1/6 *5/1

    x = 2/3                   x = 3/22              x = 12 * 2/3       x = 5/6

                                                               x = 4*2

                                                               x= 8

5) 5x = 15/21           6) 2/3 x  = 3/2

    x = 15/21 *5               x = 3/2 * 3/2

    x = 75/21                  x =9/4

    x = 3.5                      x = 2.25

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Answer:

48

Step-by-step explanation:

This is a simple Trigonometry problem

cos(x) = 4/6

cos^-1(4/6) =  48.18 = 48

Answer:

\( \cos(x) = \frac{4}{6} \\ \cos(x) =(0.66666666667)\\ x = { \cos (0.66666666667) }^{ - 1} \\ x = (48.18968510422)\)

Answer:

In linear algebra, a coefficient matrix is a matrix consisting of the coefficients of the variables in a set of linear equations.

Step-by-step explanation:

the matrix is used in solving systems of linear equations

The total weights of the two animals is  11. 92 × 10² Ibs

In order to determine the total weights, we take the following steps:

The weight of the animals are given as;

Now, let's add the weights:

= 5. 12 × 10² + 6. 8 × 10²

Add the values

= 11. 92

It is important to note that the powers are similar and should be written as one

We then have the sum to be;

= 11. 92 × 10² Ibs

Thus, the total weights of the two animals is  11. 92 × 10² Ibs

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Answer: the Correct answer is 1.2 x 10^3

Step-by-step explanation: You add 5.12 and 6.8 and get 11.92 x 10^2

you then need to round up to 12 and move the decimal up for scientific notation 1.2 x 10^3

The correct answer is 1.2 x 10^3

please give Branliest

The coordinates of triangle U'V'W' include U'(8, 3), V'(4, -8) and W'(-8, -6) and this is represented by graph A shown in the image attached below.

A transformation can be defined as the movement of a point on a cartesian coordinate from its original (initial) position to a new location.

In Geometry, there are different types of transformation and these include the following:

Based on the information provided, triangle UVW would be rotated counterclockwise through an angle of 270 degree at origin to produce triangle U'V'W', we have:

\(\left[\begin{array}{ccc}0&1\\-1&0\end{array}\right]\)

Therefore, the image of triangle UVW would be given by this matrix:

\(\left[\begin{array}{ccc}0&1\\-1&0\end{array}\right]\) \(\left[\begin{array}{ccc}-3&8&6\\8&4&-8\end{array}\right]\)

Image = \(\left[\begin{array}{ccc}8&4&-8\\3&-8&-6\end{array}\right]\)

Based on the image above, we can logically deduce that the coordinates of triangle U'V'W' include U'(8, 3), V'(4, -8) and W'(-8, -6) and this is represented by graph A shown in the image attached below.

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Answer:

hi friend

Step-by-step explanation:

a.we get, `A = √(2α³/π)`.

b.`⟨H⟩ = (3/4)hω - (h²/4ma²)` where `a = α/√(mω/h)`.

c.we can say that the variational principle is valid in this case.

(a) Let's find the normalization constant A.

We know that the integral over all space of the absolute square of the wave function is equal to 1, which is the requirement for normalization.  `∫⟨ψ|ψ⟩dx= 1`

Hence, using the given trial wavefunction, we get, `∫⟨ψ|ψ⟩dx = ∫ |A/(x^2+α²)|²dx= A² ∫ dx / (x²+α²)²`

Using a substitution `x = α tan θ`, we get, `dx = α sec² θ dθ`

Substituting these in the above integral, we get, `A² ∫ dθ/α² sec^4 θ = A²/(α³) ∫ cos^4 θ dθ`

Using the identity, `cos² θ = (1 + cos2θ)/2`twice, we can write,

`A²/(α³) ∫ (1 + cos2θ)²/16 d(2θ) = A²/(α³) [θ/8 + sin 2θ/32 + (1/4)sin4θ/16]`

We need to evaluate this between `0` and `π/2`. Hence, `θ = 0` and `θ = π/2` limits.

Using these limits, we get,`⟨ψ|ψ⟩ = A²/(α³) [π/16 + (1/8)] = 1`

Therefore, we get, `A = √(2α³/π)`.

Hence, we can now write the wavefunction as `ψ(x) = √(2α³/π)/(x²+α²)`.  

(b) Using the wave function found in part (a), we can now determine the expectation value of energy using the time-independent Schrödinger equation, `Hψ = Eψ`. We can write, `H = (p²/2m) + (1/2)mω²x²`.

The first term represents the kinetic energy of the particle and the second term represents the potential energy.

We can write the first term in terms of the momentum operator `p`.We know that `p = -ih(∂/∂x)`Hence, we get, `p² = -h²(∂²/∂x²)`Using this, we can now write, `H = -(h²/2m) (∂²/∂x²) + (1/2)mω²x²`

The expectation value of energy can be obtained by taking the integral, `⟨H⟩ = ⟨ψ|H|ψ⟩ = ∫ψ* H ψ dx`Plugging in the expressions for `H` and `ψ`, we get, `⟨H⟩ = - (h²/2m) ∫ψ*(∂²/∂x²)ψ dx + (1/2)mω² ∫ ψ* x² ψ dx`Evaluating these two integrals, we get, `⟨H⟩ = (3/4)hω - (h²/4ma²)` where `a = α/√(mω/h)`.

(c) Since we have an approximate ground state wavefunction, we can expect that the expectation value of energy ⟨H⟩ should be greater than the true ground state energy.

Hence, the value obtained in part (b) should be greater than the true ground state energy obtained by solving the Schrödinger equation exactly.

Therefore, we can say that the variational principle is valid in this case.

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Answer:

Approximately 0.1894 or 18.94% of the population is less than 10.0.

Step-by-step explanation:

On use the z-score formula and the standard normal distribution.

a. To compute the z-value associated with 14.3, we use the formula:z = (x - μ) / σWhere:

x = 14.3 (the value)

μ = 12.2 (mean)

σ = 2.5 (standard deviation)

Substituting the values:

z = (14.3 - 12.2) / 2.5

z = 2.1 / 2.5

z ≈ 0.84

Therefore, the z-value associated with 14.3 is approximately 0.84.

b. To obtain the proportion of the population between 12.2 and 14.3, we need to get the area under the standard normal distribution curve between the corresponding z-scores.

Using a standard normal distribution table or a calculator, we can find the area associated with each z-score.The z-value for 12.2 can be calculated using the same formula as in part a:

z1 = (12.2 - 12.2) / 2.5

z1 = 0 / 2.5

z1 = 0

The z-value for 14.3 is already known from part a: z2 ≈ 0.84.

Now, we obtain the proportion by subtracting the area associated with z1 from the area associated with z2:

Proportion = Area(z1 < z < z2)

Using a standard normal distribution table or a calculator, we obtain:

Area(z < 0) ≈ 0.5000 (from the table)

Area(z < 0.84) ≈ 0.7995 (from the table)

Proportion = 0.7995 - 0.5000

Proportion ≈ 0.2995

Therefore, approximately 0.2995 or 29.95% of the population is between 12.2 and 14.3.

c. To obtain the proportion of the population less than 10.0, we need to get the area under the standard normal distribution curve to the left of the corresponding z-score.Using the z-score formula:z = (x - μ) / σ

Where:

x = 10.0 (the value)

μ = 12.2 (mean)

σ = 2.5 (standard deviation)

Substituting the values:

z = (10.0 - 12.2) / 2.5

z = -2.2 / 2.5

z ≈ -0.88

Now, we obtain the proportion by looking up the area associated with z ≈ -0.88 using a standard normal distribution table or a calculator:

Area(z < -0.88) ≈ 0.1894 (from the table)

Therefore, approximately 0.1894 or 18.94% of the population is less than 10.0.

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