Are the expressions -0.5(3r+ 5) and -1.5r+2.5 equivalent? Explain why or why not.

The probability density function (pdf) of X, denoted as f(x; 0), is

f(x; 0) = (8 + 1) x^2 (0 + 1) x for 0 ≤ x ≤ 1, and 0 otherwise.

The probability density function (pdf) represents the likelihood of a random variable taking on different values. In this case, X represents the proportion of allotted time that a randomly selected student spends working on a certain aptitude test.

The given pdf, f(x; 0), is defined as (8 + 1) x^2 (0 + 1) x for 0 ≤ x ≤ 1, and 0 otherwise. Let's break down the expression:

(8 + 1) represents the coefficient or normalization factor to ensure that the integral of the pdf over its entire range is equal to 1.

x^2 denotes the quadratic term, indicating that the pdf increases as x approaches 1.

(0 + 1) x is the linear term, suggesting that the pdf increases linearly as x increases.

The condition 0 ≤ x ≤ 1 indicates the valid range of the random variable x.

For values of x outside the range 0 ≤ x ≤ 1, the pdf is 0, as indicated by the "otherwise" statement.

Hence, the pdf of X is given by f(x; 0) = (8 + 1) x^2 (0 + 1) x for 0 ≤ x ≤ 1, and 0 otherwise.

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Yes, if a figure can be rotated 360° to be mapped onto itself, it is considered to have rotational symmetry.

This is because a 360° rotation means that the figure will return to its original position, making it symmetrical. Rotational symmetry is a type of symmetry where a figure can be rotated about a central point and still look the same. The degree of rotational symmetry depends on the number of times a figure can be rotated to match its original appearance. Therefore, if a figure can be rotated 360° and maintain its original appearance, it is said to have rotational symmetry of degree 1. This is true regardless of the size, orientation, or position of the figure. Yes, a figure that can be rotated 360° to be mapped onto itself is considered to have rotational symmetry. Rotational symmetry occurs when an object can be rotated around a central point and still appear the same as its original position. In the case of a 360° rotation, the figure returns to its initial configuration, confirming its rotational symmetry.

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\(f(x) =4 x {}^{3} - 4x {}^{2} - 16x + 16\)

\(divide \: by \: x - 2\)

\(4x {}^{2} \: into \: (x - 2) = 4x {}^{3} - 8x {}^{2} \)

\(g(x) = 4x {}^{2} - 16x + 16\)

\(4x \: into \: (x - 2) = 4x {}^{2} - 8x\)

\(z(x) = - 8x + 16\)

\( - 8 \: into \: (x - 2) = - 8x + 16 \\ no \: remainder\)

\(f(x) = (x - 2)(4x {}^{2} + 4x - 8)\)

\(f(x) = 0 \\ x - 2 = 0 \: \: \: \: \: \: \: \: \: 4x {}^{2} + 4x - 8 = 0 \\ \)

\(x = \frac{ - 4 + \sqrt{4 {}^{2} - 4(4)( - 8) } }{2(4)} = \frac{ - 4 + \sqrt{144} }{8} = \frac{ - 4 + 12}{8} = 1\)

\(x = 2\)

\(x = \frac{ - 4 - 12}{8} = \frac{ - 16}{8} = - 2\)

Answer: B

Step-by-step explanation:

Edge 2023

Check the picture below.

let's noticed the distances from one to the next value in the dataset, let's notice the distance on the last one.

The constant of proportionality is 2.02.

According to the concept of proportion, two ratios are in proportion when they are equal.

Two ratios or fractions are equal when an equation or a declaration to that effect is utilised. A mathematical comparison of two numbers is called a proportion. According to proportion, two sets of provided numbers are said to be directly proportional to one another if they increase or decrease in the same ratio. "::" or "=" are symbols used to indicate proportions.

Given:

Four dozen gourmet donuts cost a total of $96.96.

So, if y be the total cost of the donuts and x be the number of donuts.

then the proportionality is

y= kx

k= y/x

k = 96.96 / (4 x 12)

k= 96.96/ 48

k= 2.02

Hence, the constant of proportionality is 2.02.

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Answer:

25b+7 should be the answer

Answer:

A

Step-by-step explanation:

The angle's radian value is 0.16 radians, and the circle's radius is 30 units.

Given,

Arc length of a circle = 5 units

Subtends an area of 75 square units

We know,

θ = Arc length / radius

θ = 5 / r radians

Now,

The total area of the circle = πr²

Which makes its radius 2π

∴ 2π radians = πr²

  1 radian = πr²/2π

θ radians = πr²/2π * θ

Given,

πr²/2π * θ = 75

πr²/2π * 5/r = 75

5r/2 = 75

5r = 150

r = 150/5

r = 30 units

Now,

θ = 5 / r radians

  = 5 / 30

  = 0.16 radians

Hence, the radius of the circle is 30 units and the radian measure of the angle is 0.16 radians.

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Answer:

6.1

Step-by-step explanation:

because the 3 is below 5 so it sticks to 1

Using the square formula, the value of (1+i)^4 is -4.

The square formula is the algebraic identity which is used to find the square or difference of the sum of two terms. The square of sum of the two terms and can be calculated by multiplying the binomial by itself. The general form of square formula to find the square of the sum of two terms is given by: (a + b)^2 = a^2 + 2ab + b^2 where a and b are variables.

The given expression can be rewritten as binomial with exponent:

((1 + i)^2)^2

Using the square formula to find the square of the sum of two terms to the (1 + i)^2. Hence,

(1 + i)^2 = 1 + 2i + i^2

As 'i' iota is the square root of negative 1, i^2 = -1

1 + 2i -1 = 2i

Therefore,

(2i)^2 = 4i^2 = 4*-1 = -4

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Answer:

They are 12, 13, 14 and 15.

Step-by-step explanation:

If the least integer is x, then:

x + x + 1 + x + 2 + x + 3 = 54

4x + 6 = 54

4x = 48

x = 12.

Answer:

1.03x larger

Step-by-step explanation:

i cant say this is correct, because i know some teachers have different preferred types of answers. but from what i learned that should be the answer.

Answer:8x104=832      8x101= 808

              so, 32 - 8= 24 8x104 is 24 bigger than 8x101

Step -by-step explanation:

pls mark as brainliest

The expected value of the estimator equals the true parameter.

The estimator  is calculated as the intercept of the linear regression model.

It represents the average difference between the predicted values and the actual values of the dependent variable, given a fixed value of the independent variable.

If the estimator is unbiased, the expected value will be equal to the true parameter. .

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Answer: The volume is 5 cm^3

Step-by-step explanation:

v= lwh

v= 4/1 * 1/2* 5/2

v= 20 /4

v= 5

Answer:

the answer is attached to the picture

Answer:

The probability is 1/2 because 3/6 numbers are even.

Step-by-step explanation:

the product of x and a factor not depending on x

What is quadratic equation

it's a second-degree quadratic equation which is an algebraic equation in x. Ax2 + bx + c = 0, where a and b are the coefficients, x is the variable, and c is the constant term, is the quadratic equation in its standard form. A non-zero term (a 0) for the coefficient of x2 is a prerequisite for an equation to be a quadratic equation. The x2 term is written first, then the x term, and finally the constant term is written when constructing a quadratic equation in standard form. In most cases, the numerical values of letters a, b, and c are expressed as integral values rather than fractions or decimals.

The equation given 3x(m-6n)²

This expression contains two factors:

1 factor: 3x

2 factor: (m-6n)²

Hence the product of x and a factor not depending on x.

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To determine the placement of 4.7 on a number line between two decimals, 4/7 should be placed between the pair of decimals 0.57 and 0.58 on a number line.

The number 4.7 falls between the integers 4 and 5, so we need to find the decimal values that come after 4 and before 5.  The decimal value that comes after 4 is 4.1, and the decimal value that comes before 5 is 4.9.
1. Convert the fraction 4/7 to a decimal.
2. Identify the two consecutive decimals on the number line that the converted decimal falls between.

Step 1: Convert 4/7 to a decimal.
To do this, divide the numerator (4) by the denominator (7):
4 ÷ 7 ≈ 0.5714 (rounded to 4 decimal places)

Step 2: Identify the two consecutive decimals.
Now, we know that 0.5714 is the decimal equivalent of 4/7. To determine the pair of decimals on the number line, we can see that 0.5714 falls between 0.57 and 0.58.

So, 4/7 should be placed between the pair of decimals 0.57 and 0.58 on a number line.

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The theoretical probability that the family has two dogs or two cats is 25% (1), one coin can simulate the cats and another the dogs (2), and the possible frequencies are 25, 30, 20, 25 (2).

To begin, there are four possible theoretical outcomes:

Based on this, the probability that a family has two cats or two dogs is 1/4 = 0.25 or 25%. (1)

Then, the coins can be used to simulate this situation if one side of the coin represents the cat and the other side represents the dog (2)

Finally, some possible frequencies are  25, 30, 20, 25. Remember that the theoretical frequency is 25 but in real life this can vary.

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Answer:

Step-by-step explanation:

Triangle MNP is a right triangle with the following values:

Interior angles of a triangle sum to 180°. Therefore:

m∠M + m∠N + m∠P = 180°

m∠M + 58° + 90° = 180°

m∠M + 148° = 180°

m∠M = 32°

To find the measures of sides MN and NP, use the Law of Sines:

\(\boxed{\begin{minipage}{7.6 cm}\underline{Law of Sines} \\\\$\dfrac{a}{\sin A}=\dfrac{b}{\sin B}=\dfrac{c}{\sin C}$\\\\\\where:\\ \phantom{ww}$\bullet$ $A, B$ and $C$ are the angles. \\ \phantom{ww}$\bullet$ $a, b$ and $c$ are the sides opposite the angles.\\\end{minipage}}\)

Substitute the values into the formula:

\(\dfrac{MN}{\sin P}=\dfrac{NP}{\sin M}=\dfrac{PM}{\sin N}\)

\(\dfrac{MN}{\sin 90^{\circ}}=\dfrac{NP}{\sin 32^{\circ}}=\dfrac{8}{\sin 58^{\circ}}\)

Therefore:

\(MN=\dfrac{8\sin 90^{\circ}}{\sin 58^{\circ}}=9.43342722...\)

\(NP=\dfrac{8\sin 32^{\circ}}{\sin 58^{\circ}}=4.99895481...\)

To find the perimeter of triangle MNP, sum the lengths of the sides.

\(\begin{aligned}\textsf{Perimeter}&=MN+NP+PM\\&=9.43342722...+4.99895481...+8\\&=22.4323820...\\&=22.43\; \sf units\; (2\;d.p.)\end{aligned}\)

Answer:

a = 16

Step-by-step explanation:

6 = \(\frac{a}{4}\) + 2 ( subtract 2 from both sides )

4 = \(\frac{a}{4}\) ( multiply both sides by 4 to clear the fraction )

4 × 4 = a , that is

a = 16

The diameter of the basketball is increasing at a rate of 0.24 inches per second when the radius is 1 inch.

Let's denote the radius of the basketball as r and the volume of the basketball as V. The volume of a sphere can be calculated using the formula V = (4/3)π\(r^3\).

Given that the basketball is being filled with air at a rate of 6 \(in^3\)/sec, we can write dV/dt = 6. Since the basketball is a perfect sphere, the radius and the diameter are related by the equation D = 2r, where D is the diameter.

To find how fast the diameter is increasing, we need to find dD/dt. Since D = 2r, we have dD/dt = 2dr/dt.

We can find dr/dt by differentiating the volume formula with respect to time. Taking the derivative of both sides of V = (4/3)π\(r^3\), we get dV/dt = 4π\(r^2\)(dr/dt).

Substituting the given value of dV/dt and the known value of r (1 inch), we can solve for dr/dt.

6 = 4π\((1^2)\)(dr/dt)

6 = 4π(dr/dt)

dr/dt = 6/(4π)

Finally, substituting this value into dD/dt = 2dr/dt, we get dD/dt = 2(6/(4π)) = 3/(2π) ≈ 0.477 inches per second.

Therefore, when the radius is 1 inch, the diameter of the basketball is increasing at a rate of approximately 0.477 inches per second.

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Answer:

a) 8/20 = 8 is the total of the girls and 20 is the total of the kids

b)2/20 = 2 is the total of girls that are left handed and 20 is the total of the kids

By permutation and combination, Maximum 171 number of different  2 - person teams are possible.

Provide an example of permutation and combination?

An arrangement of things in a specific order is referred to as a permutation. In this arrangement, the components or components of sets are organized in a linear or sequential order.

                       As an illustration, set A=1,6 has the permutation 2, which is 1,6,1. Permutations include the arrangement of individuals, digits, numbers, alphabets, letters, and colors. Combinations include things like choosing a menu, cuisine, clothing, a subject, and a team.

Total number of ways to choose different 2 person out of 19 person.

                     = ¹⁹C₂

              = 19!/2! (19 - 2)!

              =  19!/2!   17!

             = 19 * 18 * 17!/2 * 1 * 17!

            = 19 * 7

              = 171

Hence, maximum 171 number of different  2 - person teams are possible.

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The variance of a sample or a population cannot be negative. This means that option c, negative, is the correct answer.

Variance is a statistical measure that quantifies the dispersion or spread of data points around the mean. It tells us how much the individual data points deviate from the average. The variance is always a non-negative value because it is calculated by summing the squared differences between each data point and the mean, divided by the total number of data points.
If the variance were negative, it would imply that the sum of the squared differences between each data point and the mean is less than zero. However, this is not possible because squared differences are always positive or zero.
On the other hand, options a, zero, and d, less than 1, are incorrect. The variance can be zero if all the data points in the sample or population are the same, indicating no dispersion. Additionally, the variance can be any positive value, including values less than 1.
To summarize, the variance of a sample or a population cannot be negative, making option c, negative, the correct answer.

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Answer:

D

Step-by-step explanation:

In the photos above

The solution to the given differential equation 2xy(dy/dx) = y², with the initial condition y(2) = 3, is y = (27 * e⁽ˣ⁻²⁾\()^{1/4}\).

To solve the given differential equation

2xy(dy/dx) = y²

We will use separation of variables and integrate to find the solution.

Start with the given equation

2xy(dy/dx) = y²

Divide both sides by y²:

(2x/y) dy = dx

Integrate both sides:

∫(2x/y) dy = ∫dx

Integrating the left side requires a substitution. Let u = y², then du = 2y dy:

∫(2x/u) du = ∫dx

2∫(x/u) du = ∫dx

2 ln|u| = x + C

Replacing u with y²:

2 ln|y²| = x + C

Using the properties of logarithms:

ln|y⁴| = x + C

Exponentiating both sides:

|y⁴| = \(e^{x + C}\)

Since the absolute value is taken, we can remove it and incorporate the constant of integration

y⁴ = \(e^{x + C}\)

Simplifying, let A = \(e^C:\)

y^4 = A * eˣ

Taking the fourth root of both sides:

y = (A * eˣ\()^{1/4}\)

Now we can incorporate the initial condition y(2) = 3

3 = (A * e²\()^{1/4}\)

Cubing both sides:

27 = A * e²

Solving for A:

A = 27 / e²

Finally, substituting A back into the solution

y = ((27 / e²) * eˣ\()^{1/4}\)

Simplifying further

y = (27 *  e⁽ˣ⁻²⁾\()^{1/4}\)

Therefore, the solution to the given differential equation with the initial condition y(2) = 3 is

y = (27 * e⁽ˣ⁻²⁾\()^{1/4}\)

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Answer:

hi my name is ais

Step-by-step explanation:

1624#I don't care

Answer:

The temperature of the oven after 6 minutes is 125 degrees and after 10 minutes its 165 degrees.

Step-by-step explanation:

10 x 6 = 60

60+65=125

10 x 10 = 100

100+65=165

Answer:

3 miles

Step-by-step explanation:

if she can run at a constant speed for 30 minutes, then it is 3 miles. But, if there is some reason that she cannot run at the same rate as she did for one mile, the answer is unknown.

The man’s son. Since the man has no brothers and the father of the man in the photograph is the man’s father’s son, the father of the man in the photograph must be the man. That means that the man in the photograph is the man’s son.