WHAT INQUANLITY DESCRIBES THE SOLUTION OF 2Y< 8

The Var (X) for the random variable X with probability density function

f ₓ(x) = Cx² for |x| ≤ 1 is equal to 3/5.

Probability density function (pdf) :

f ₓ(x) = Cx² for |x| ≤ 1

            0 other wise

[tex]\int\limits^a_b {f(x)} \, dx = 1[/tex]

⇒ [tex]\int_{-1}^{1}Cx^{2}[/tex] = 1

⇒ C (x³ /3) [tex]|_{-1}^{1}[/tex] = 1

⇒ C/3 (  1 - (-1 )) = 1

⇒(2/3) C = 1

⇒ C = 3/2

Now,

E(x) = [tex]\int_{-1}^{1}x (3/2)x^{2}dx[/tex]

      = (3/2)[tex]\int_{-1}^{1}x^{3}dx[/tex]

      = ( 3/2) ( x⁴ /4 ) [tex]|_{-1}^{1}[/tex]

      = 0

Var (X) = [tex]\int_{-1}^{1}x^{2} (3/2)x^{2}dx[/tex] - [E(x)]²

           = (3/2) [tex]\int_{-1}^{1} x^{4}dx[/tex]  -0

           = (3/2) ( x⁵ /5 )[tex]|_{-1}^{1}[/tex]

           = (3/2 ) ( 1/5 + 1/5)

           = 3/5

Therefore, the Var (X) of the probability density function for the random variable X is equal to 3/5.

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Answer:

(-41)/6 or -6 5/6 as a mixed fraction

Step-by-step explanation:

Simplify the following:

1 + 2/3 - (8 + 1/2)

Put 8 + 1/2 over the common denominator 2. 8 + 1/2 = (2×8)/2 + 1/2:

1 + 2/3 - ((2×8)/2 + 1/2)

2×8 = 16:

1 + 2/3 - (16/2 + 1/2)

16/2 + 1/2 = (16 + 1)/2:

1 + 2/3 - ((16 + 1)/2)

16 + 1 = 17:

1 + 2/3 - 17/2

Put 1 + 2/3 - 17/2 over the common denominator 6. 1 + 2/3 - 17/2 = 6/6 + (2×2)/6 + (3 (-17))/6:

6/6 + (2×2)/6 + (3 (-17))/6

2×2 = 4:

6/6 + 4/6 + (3 (-17))/6

3 (-17) = -51:

6/6 + 4/6 + (-51)/6

6/6 + 4/6 - 51/6 = (6 + 4 - 51)/6:

(6 + 4 - 51)/6

6 + 4 = 10:

(10 - 51)/6

10 - 51 = -(51 - 10):

(-(51 - 10))/6

| 5 | 1

- | 1 | 0

| 4 | 1:

Answer:  (-41)/6

The equation used is 3 (x - 5) = 60, the cost of each rashguard at full price is $25

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

Given;

Price of rash guard on sale =$5

Number of rashguard miguel purchased= 3

Now, Let the full price of each rashguard be x,

Rashguards sell for $5 less than full price;

x - 5

Miguel purchases 3 rashguards and pays a total of $60;

3 (x - 5) = 60

x - 5 = 60 / 3

x - 5 = 20

x = 20 + 5

x = 25

Therefore, the algebraic solution for x will be 25;

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The radial distances from the center (-3, -2), to the points on the circumference (0, -6), and (a, 0), found using the distance formula, indicates that a = -3 ± √21

The distance between points (x₁, y₁), and (x₂, y₂), on the coordinate plane, can be found using the formula; d = √((x₂ - x₁)² + (y₂ - y₁)²).

The coordinates of the center of the circle = (-3, -2)

The coordinates of the locations (on the circumference of the circle), through which the circle passes = (0, -6) and (a, 0)

Therefore the distances between points (0, -6) and (-3, -2) and (a, 0) and (-3, -2) are the same;

The distance from (0, -6) to (-3, -2) = The distance from (a, 0) to (-3, -2)

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

25 = a² + 6·a + 9 + 4 = a² + 6·a + 13

a² + 6·a + 13 = 25 (symmetric property)

a² + 6·a + 13 - 25 = 0

a² + 6·a - 12 = 0

a = (-6 ± √(6² - 4×1×(-12)))/(2×1) = (-6 ± √(84))/2

a = (-3 ± √(21))

a ≈ 1.58 and a ≈ -7.58

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The critical region for a hypothesis test consists of outcomes that have a very low probability if the null hypothesis is true. This means that if the null hypothesis is true, these outcomes should not occur. The critical region is used to decide when to reject the null hypothesis and accept the alternative hypothesis.

Hypothesis testing is a process used in statistics to determine whether a certain claim or hypothesis is valid. It involves collecting data, analyzing the data, and making decisions based on the analysis of the data. The goal of hypothesis testing is to either reject or accept a null hypothesis, which is an assumption that there is no relationship between two measured phenomena. Hypothesis testing can also be used to compare two groups or to determine the effectiveness of a treatment or intervention.

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Yes, if function f(x) = 5, then f is defined for all x, including x = 1.

Yes, f is defined for every x, including x = 1, if f(x) = 5. And if f is defined at x = 1, then f(1) = 5. The equation f(x) = 5 means that the function f takes on the value 5 for all x, so if the function is defined at x = 1, its value at that point must be 5.

The term "function" refers to a relationship between a set of inputs and outputs. To put it simply, a function is a relationship between inputs where each input is associated to exactly one output.

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Answer:  to label the point D on the number line, you can represent it as a real number and write it alongside the number line with an arrow pointing to its corresponding position. For example:

----|-----D---->|------

Where "D" is the label for the point and the arrow indicates its position on the number line.

Step-by-step explanation:

The line of reflection would be x+y =4, Hence the correct option is C.

The equation of a line's standard form is given as follows:

[tex]y = mx+c[/tex]

Where m is the slope and c is the y-intercept of the line.

The slope can be determined by

[tex]m =\dfrac{(y_2 - y_1)}{(x_2 - x_1)}[/tex]

Now, Along its diagonals should be reflected in order to reflect it back to itself.

The diagonals will pass through the points [tex]A(3, 1)[/tex] and [tex]C( 1,3)[/tex]

Hence, The slope of the line is,

[tex]m =\dfrac{(y_2 - y_1)}{(x_2 - x_1)}[/tex]

[tex]m =\dfrac{(3 - 1)}{(1 - 3}[/tex]

[tex]m =\dfrac{(2)}{(- 2)}[/tex]

[tex]m = - 1[/tex]

Hence, The equation of the line AC,

[tex](y - y_1) = m(x-x_1)[/tex]

It passes through the point (1,3)

[tex](y - 3) = -1( x-1 )[/tex]

[tex]y - 3 = -x +1[/tex]

[tex]y +x =4[/tex]

Therefore, Option C is true.

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The probability that a bag of chip is lower than 9.07 oz of weight is 0.1587.

A continuous probability distribution for a real-valued random variable is called a normal distribution or a Gaussian distribution.

An example of a continuous probability distribution is the normal distribution, in which the majority of data points cluster in the middle of the range while the remaining ones taper off symmetrically toward either extreme. The distribution's mean is another name for the center of the range.

The normal distribution defines how a variable's values are distributed, just like any probability distribution does. Because it properly depicts the distribution of values for many natural occurrences, it is the most significant probability distribution in statistics.

the mean of the data = 9.12 oz

The SD = 0.05 oz

The probability of the bag to be less than 9.07 oz

x = 9.07

z = x - mean / SD = 9.07 - 9.12/0.05 = - 1

for z = -ve

Ф(z) = 1 - Ф(-z) = 1 - Ф(1) = 1 - 0.8413 = 0.1587

The probability that a bag of chip is lower than 9.07 oz of weight is 0.1587.

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The simplified dorm of the expression [tex]\frac{\sqrt{15}}{5\sqrt{48}}\times\frac{\sqrt{48}}{\sqrt{48}}[/tex] is √720/240.

We know there are two types of radicals one is surds when the number has been raised by such power that it is greater than zero and less than one,

The other type of radicals are indices where a number is raised to such power that is greater than one.

Given, A radical expression [tex]\frac{\sqrt{15}}{5\sqrt{48}}[/tex].

Therefore,

[tex]\frac{\sqrt{15}}{5\sqrt{48}}\times\frac{\sqrt{48}}{\sqrt{48}}[/tex].

= (√15×√48)/(5×48).

= √720/240 or √720×(1/240).

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Answer:

A = 20, therfore B = 180

Step-by-step explanation:

Technically it's 17 but that is a really awkward scale so I had to round up. This really annoys me because if there was one more box you could had the scale 15 and it would've looked so much nicer but unfortunate you're short one

The subgroups of S6 include the following abelian groups: Z₁, Z₂, Z₃, Z₆, Z₂ x Z₂, and Z₃ x Z₂

A subgroup of a group is isomorphic to another group if there is a bijective homomorphism between the two groups, meaning there is a one-to-one correspondence between their elements that preserves the group operation. In this case, the subgroup of S6 (the symmetric group on 6 elements) is isomorphic to one of the abelian groups.

It is known that the number of subgroups of a finite group is bounded above by the number of its elements, so there are only finitely many possible subgroups of S6 to consider. The most common abelian groups are the cyclic groups Zₙ, and any group that is isomorphic to a direct sum of cyclic groups is also abelian.

It is known that the subgroups of S6 include the following abelian groups: Z₁, Z₂, Z₃, Z₆, Z₂ x Z₂, and Z₃ x Z₂. These are the only abelian groups that can be isomorphic to subgroups of S6. Note that there may be non-abelian subgroups of S6 as well.

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Thus, the solution of the inequality is x > -4 or x < 0.

The graph of the solution is option B.

An inequality is a relationship that makes a non-equal comparison between two numbers or other mathematical expressions e.g. 2x > 4

Because of absolute sign | |, the inequality |x+2l <2 can be written as:

x+2 <2 or -(x+2) <2

For x+2 <2:

x+2 <2

x < 2-2

x < 0

For -(x+2) <2:

-(x+2) <2

-x - 2 < 2

-x < 2+2

-x < 4

x > -4

Thus, the solution is x > -4 or x < 0.

The graph of the solution is option B because x > -4 or x < 0 can be written as -4<x<0, which shows the value of x is between -4 and 0.

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The value of constant a is 2.45.

To find the value of the constant a, we need to make sure that the pdf (probability density function) is properly normalized. The pdf must satisfy the following property:

∫[a, ∞] f(x) dx = 1

In this case, we have pdf:

∫[a, ∞] (12/x^3) dx = 12∫[a, ∞] (1/x^3) dx

= 12 [-1/(2x^2)]ₐ∞

= 12 * (1/(2a^2))

= 6/ a²

Therefore, to ensure that the integral is equal to 1, we need:

6/ a² = 1

Solving for a:

a^2 = 6

a = ±√6

Since x is always positive, we have a = √6 ≈ 2.45.

So, the constant a is equal to 2.45.

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The true statement is (c). The coefficients of x^n and y^n are both equal

From the question, we have the following parameters that can be used in our computation:

(x + y)^n

When the above expression is expanded, we have

(x + y)^n = x^n + ..... + y^n

See that the coefficients of x^n and y^n is 1

This means that they have equal coefficient of 1

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Therefore , the solution of the given problem of triangle comes out to be sides are a = 10 and b=5√3.

Due to their four sides or more, triangles are considered polygons. It has a straightforward, geometric form. A triangle is a square angle formed by the letters ABC. A singular rectangle or square is produced by Euclidean geometry when the sides are still not collinear. Triangles are polygons because they have three sides and three corners. Where three sides of a triangle come together are its corners. A triangle's angles sum up to 180 degrees.

Here,

Given :

A right triangle is :

=> 5 , b and a

has 30 degree angle .

=> Sin 30° = 5/a

=> 1/2 = 5/a

=> a = 10

Thus,

Using pythagoras theorem ,

=> 10² = 5² + b²

=> 100 -25 = b²

=>  b² = 75

=> b = 5√3

Thus , sides comes out to be a = 10 and b=5√3

Therefore , the solution of the given problem of triangle comes out to be sides are a = 10 and b=5√3.

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The substantive audit sampling technique uses a statistical sampling approach is Sampling or MUS.

Sampling is a powerful tool in auditing as it allows the auditor to make conclusions about the population without having to test all the transactions, balances or data.

Substantive audit sampling refers to the use of samples in an audit process to make conclusions about a population of transactions, balances or other data.

There are three main substantive audit sampling techniques: Stratified Sampling, Attribute Sampling and Monetary Unit Sampling.

Monetary Unit Sampling or MUS is a statistical sampling approach that focuses on the monetary value of transactions.

The auditor will select a sample of transactions and calculate the expected deviation rate.

This technique is used when the auditor is focused on testing material balances and ensuring that they are correct.

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Using the area of the rectangle and circle, the shaded area is equal to 6.88 squared units

To determine the area of the shaded region, we can simply find the area of the rectangle and the area of the circle.

The formula of area of the rectangle;

Assuming the width is half the length

Area of rectangle = length * width

Area of rectangle = 8 * 4

Area of rectangle = 32 squared units.

Area of circle = πr²

r = radius of the circle

In this problem, the diameter of the circle is the width of the rectangle or rather, the diameter of the circle is half the length of the the rectangle.

d = 8 / 2 = 4 units

radius = diameter / 2

radius = 4 / 2 = 2 units

Substituting the values into the formula

A = πr²

A = 3.14 * 2²

A = 3.14 * 4

A = 12.56 squared units.

The non-shaded area = 2 * 12.56 = 25.12 squared units.

The shaded area = area of rectangle - non-shaded area

The shared area = 32 - 25.12

The shaded area = 6.88 squared units.

b.

The approximated area to the nearest tenth is 6.9 squared units

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36 motorcycles were repaired during the month.

To solve this problem, we can use the formula for the total number of wheels of a vehicle, which is equal to the number of vehicles multiplied by the number of wheels per vehicle. In this case, the number of wheels per vehicle is 4 since both autos and motorcycles have 4 wheels each. This formula can be expressed as: Wheels = Vehicles × Wheels per Vehicle.

We can substitute the given values of the total number of wheels (336) and the number of wheels per vehicle (4) into the formula, and solve for the number of vehicles (V): Wheels = Vehicles × Wheels per Vehicle → 336 = Vehicles × 4 → Vehicles = 336 ÷ 4 → Vehicles = 84.

Since we know that both autos and motorcycles were repaired, and the total number of vehicles was 84, we can use the information that 120 vehicles were repaired to solve for the number of motorcycles (M) that were repaired.

If the total number of vehicles was 84, and 120 vehicles were repaired, then the number of motorcycles that were repaired must be equal to the difference between the total number of vehicles and the total number of autos, which is 120 - 84 = 36.

Therefore, 36 motorcycles were repaired during the month.

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In the transformation ABC → A'B'C', the preimage of B' is B.

In Mathematics, a transformation can be defined as the movement of a point from its original (actual) position to a final (new) location. This ultimately implies that, when an object (pre-image) is transformed, all of its points would be transformed as well to form a new image.

Generally, there are four (4) major types of transformation and these include the following:

In this context, we can reasonably infer and logically deduce that corresponding vertices, points, or coordinates would be matched together in any type of transformation such as the following:

Point A → Point A'.

Point B → Point B'.

Point C → Point C'.

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By algebra properties, the radical equation [tex]3 \cdot \sqrt[4]{(x - 2)^{3}} - 4 = 20[/tex] has the following extraneous solution: x = - 14.

A solution for a radical equation is extraneous when result leads to an absurdity (i.e. 3 = 4). In this problem, we proceed to show how to solve a radical equation by means of algebra properties. First, write the entire radical equation:

[tex]3 \cdot \sqrt[4]{(x - 2)^{3}} - 4 = 20[/tex]

Second, use compatibility with addition:

[tex]3\cdot \sqrt [4]{(x-2)^{3}} = 24[/tex]

Third, use compatibility with multiplication:

[tex]\sqrt [4] {(x - 2)^{3}} = 8[/tex]

Fourth, use a relationship between powers and roots:

[tex](x - 2)^{\frac {3}{4}} = 8[/tex]

Fifth, elevate both sides to 4 / 3 to cancel exponent on left side:

[tex]x - 2 = 8^{\frac {4}{3}}[/tex]

Sixth, solve the power constant:

x - 2 ≈ ± 16

Seventh, apply absolute value properties:

x - 2 = 16 or x - 2 = - 16

Eighth, use compatibility with addition once again:

x = 18 or x = - 14

Ninth, check for extraneous solutions:

x = 18

[tex]3\cdot \sqrt [4]{(18-2)^{3}} = 24[/tex]

24 = 24

x = - 14

[tex]3\cdot \sqrt [4]{(- 14-2)^{3}} = 24[/tex]

NaN

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Answer:

Below

Step-by-step explanation:

First position   26 possibilities

 second    25

   third   24

       fourth  10

           fifth   9

              sixth 8          

     multiply all of these numbers together = 11 232 000 possible plates

In (a) and (d), the -1 is a reciprocal, as -1 is being multiplied by f(p) or f(p⁻¹) respectively, and the solutions for p are p = 2 and p = -7/3 respectively. In (b) and (c), the -1 is an inverse, as it is part of the inverse of f(p), and the solutions for p are p = 7 and p = 5/3 respectively.

(a) f(p) = 5 is not an inverse or a reciprocal. To solve for p, we can use the equation f(p) = 5 and solve for p. We do this by subtracting 2 from both sides of the equation to get 3p = 3, and then dividing both sides by 3 to get p = 1.

(b) f⁻¹(p) = 5 is an inverse and we can solve for p using the equation f⁻¹(p) = 5. To do this, we subtract 2 from both sides to get 3p = 3, and then divide both sides by 3 to get p = 1.

(c) (f(p))⁻¹ = 5 is a reciprocal and we can solve for p using the equation (f(p))⁻¹ = 5. To do this, we first divide both sides of the equation by 5 to get 1/f(p) = 1. Then, we multiply both sides by f(p) to get f(p) = 5. Finally, we subtract 2 from both sides to get 3p = 3, and then divide both sides by 3 to get p = 1.

(d) f (p⁻¹) = 5 is not an inverse or a reciprocal. To solve for p, we can use the equation f (p⁻¹) = 5 and solve for p. We do this by multiplying both sides of the equation by p⁻¹ to get f(p) = 5p⁻¹. Then, we subtract 2 from both sides to get 3p = 5p⁻¹ - 2, and then multiply both sides by 3 to get 9p = 5p⁻¹ - 6. Finally, we add 6 to both sides to get 9p + 6 = 5p⁻¹, and then divide both sides by 4 to get p = 1.

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The vertex form of given expression  y=9x² + 9x - 1  is y = 9 ( x + 1/2  )² - 13 / 4

What is Algebraic expression ?

Algebraic expression can be defined as the combination of variables and constants.

Given expression,

y = 9x² + 9x - 1

complete the square for 9x² + 9x - 1

Use the form ax²+ bx +c , to find the values of a,b,c

a = 9 b = 9 c = -1

Consider the vertex form of a parabola

a ( x+d )² + e

Find the value of d using the formula d = b / 2a

d = 9 / 2.9

d = 1 / 2

So, now we have to find the value of e suing the formula

e = c - b²  / 4a

e = -1 - 9*9 / 4*9

e = -13/ 4

Substitute the values a,d and e into the vertex form

9 ( x + 1/2  )² - 13 / 4

So,

y = 9 ( x + 1/2  )² - 13 / 4

Therefore, The vertex form of given expression  y=9x² + 9x - 1  is

y = 9 ( x + 1/2  )² - 13 / 4

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Answer:

3/4 of a lap

Step-by-step explanation:

You have to find the LCD (lowest common denominator)

That is 4, so your equation will be:

[tex]\frac{1}{4} + \frac{1}{2} = x\\\\\frac{1}{4} + \frac{2}{4} = x \\\\\frac{3}{4} = x[/tex]

The value of w is 5

Two figures are considered to be "similar figures" if they have the same shape, congruent corresponding angles (meaning the angles in the same places of each shape are the same) and equal scale factors.

Similar shapes are enlargements of each other using a scale factor. All the corresponding angles in the similar shapes are equal and the corresponding lengths are in the same ratio.

The ratio of the corresponding sides of similar shapes are equal.

Therefore 35/28 = w/8

w× 28 = 35 × 8

w = 35× 8/28

w = 5

therefore the value of w is 5

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The remaining side is 16.9 and remaining angles are 83.1 and 34.9.

The cosine formula to find the side of the triangle is given by:

c = √[a² + b² – 2ab cos C] Where a,b and c are the sides of the triangle.

Given:

m∠B = 62°, a = 11, and c = 19

Now, b² = a² + c² - 2ac cos B.

b = √ a² + c² - 2ac cos B

b = √ 11² + 19² - 2x 11  x 19 cos 62

b= 16.9

Now. a/ sin A = b/ sin B= c/ sin C

So, <C = arc sin ( c sin B /b)

<C = arc sin ( 19 sin 62 /16.9)

<C = 83.1

and, <A = arc sin ( a sin B /b)

<A = arc sin ( 11 sin 62 /16.9)

<A = 34.9

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The equation representing the relationship between the number of balls of dough (b) and the amount of flour (f) would be b = f / 2.5.

To find the relationship, we need to determine how much flour is used per ball of dough. We know that Cam uses 12 1/2 cups of flour to make 5 balls of dough, so we can calculate the amount of flour per ball of dough by dividing the total amount of flour by the number of balls of dough: 12 1/2 cups / 5 balls = 2 1/2 cups per ball.

Therefore, the equation representing the relationship between the number of balls of dough (b) and the amount of flour (f) would be: b = f / 2.5, where f is the amount of flour used in cups and b is the number of balls of dough.

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Answer:

25 degree

Step-by-step explanation:

23 - 25 = -2 degree

So, the temperature change is 25 degrees.

Answer: Alan would have to sell less than 540 boxes.

Step-by-step explanation: