The angle represents the phase shift, determined by the initial conditions of the experiment or the position of the weight at t

Frequency distribution graphs, exponential graphs, logarithmic graphs, trigonometric graphs, and statistical graphs are among the six types of graphs (such as bar, pie, and line graphs).

A straightforward two-dimensional graph is created when a vertical and horizontal line join at the origin. The y axis is vertical whereas the x axis is horizontal. In simple line graphs, the x and y axes are split into regularly spaced sections and assigned integer values.

There are eight main categories of graphs: linear, power, quadratic, polynomial, and they are all used to organise how information is presented.

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a. The equation that represents the number of inches y you have knitted after x days will be y = 4x.

b. The inches you have knitted after 7 days will be 28 inches.

c. After 30 days, you'll have knitted 100 inches.

From the information, you're You are knitting a blanket at a rate of 4 inches per day and after 4 days, you have knitted 16 inches.

The equation that represents the number of inches y you have knitted after x days will be:

y = 4 × x

y = 4x

The inches you have knitted after 7 days will be:

= 7 × 4

= 28 inches.

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Note that the expression that is equivalent to 8x² ∛375x + 2∛3x⁷, if x ≠ 0 is:  42x²∛3x (Option B). Even if x = 0, then none of the answers would apply because the expression would automatically = 0.

To prove the above lets us factor and rewrite the radicand in exponential form as follows:

8x² ∛(5³ * 3x) + 2∛(3x⁶ * x)

Rework the expression using

ⁿ√ab = ⁿ√a * ⁿ√b:8x² * ∛5³ * ∛3x + 2∛x⁶ * ∛3x

Simplify the expression 8x² * 5∛3x + 2x² ∛3x

Multiply the monomials to get:
40x² ∛3x+2x²∛3x; Taking the coefficients for the like terms we have:

(40 + 2)x² ∛3x

Calculate the sum to get 42x²∛3x

Thus the simplified version of  8x² ∛375x + 2∛3x⁷, if x ≠ 0 is: 42x²∛3x

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Full Question:

Select the correct answer. Which expression is equivalent to 8x² ∛375x + 2∛3x⁷, if x ≠ 0

A) 42x³

B) 42x²∛3x

C) 10x⁴∛125x

D) 10x²∛125x³

The margin of error of the intervals 11.13 < μ < 15.03 is 1.95

In order to get the margin of error, we would first have to find the samole mean.

The sample mean x = the upper limit + lower limit / 2

the upper limit = 15.03

The lower limit = 11.13

Then we would have: 15.03 + 11.13 / 2

= 26.16 / 2

= 13.08

Then the margin of error would be

upper limit - sample mean

= 15.03 - 13.08

= 1.95

The margin of error is given as 1.95

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The number of solutions for the system of equations x - 2y = 0 and 3x + 4y = 20 is one.

For the given pair of equations x − 2y = 0 and 3x + 4y = 20;

a₁/a₂ = 1/3

b₁/b₂ = -2/4 = -1/2

c₁/c₂ = 0/-20 = 0

As the given pair of linear equation satisfies a₁/a₂ ≠ b₁/b₂​​,

The graph of these equations will be a pair of lines intersecting at a unique point, which is the solution of the given pair of equations.

Let's verify this by calculating the solution of the given system

x = 2y     eqn(1)

3x + 4y = 20     eqn(2)

Now, put the value of x in eqn(2), we get

3 × 2y + 4y = 20

10y = 20

y = 2

Now, put the value of y in eqn(1), and we get

x = 2 × 2 = 4

Thus, the solution is x = 4, y = 2.

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The concept of the oldest prime numbers is an ancient one and has been known since ancient times. The ancient Greeks were the first to systematically study prime numbers

The largest and oldest data collection in mathematics is prime numbers. What is it about them that has intrigued mathematicians for millennia?

They were very much aware of the existence of prime numbers and the fundamental theorem of arithmetic, the statement that every positive integer greater than 1 can be represented uniquely as the product of primes. So, it is hard to determine the oldest prime number known, but it's been studied throughout human history.

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Recursive sequence would produce the sequence 2,-6, 34 is a1 = 2 and an = 2an-1 - 4

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Therefore , the solution of probability problem In the absence of digit usage restrictions, 1000000 postcodes are possible, as are 900000 when the first integer cannot be 9.

The ratio of all possible outcomes to all outcomes in a large group of equally as likely alternatives that result in a specific event determines how likely it is for that event to occur. A branch of mathematics that studies probability a situation or occurrence that is likely to occur the characteristic or state of just being likely of range 0 to 1.

Here ,

1) If there aren't any digit restrictions, there are 1000000 zip codes, or 10*10*10*10*10.

2) 9*10*10*10*10=900000 is the maximum number of postal codes that could exist if the initial number is not 7.

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1. The statement that is false is: If two figures have the same shape, then they are congruent.

2. The dashed line appears to be a line of symmetry.

When two or more shapes have their length of sides and measure of internal angles to be equal, then it can be inferred that they are congruent. But shapes can be similar, but not congruent.

A line of symmetry is a straight line drawn in such a way that it divides a given shape into two equal parts. So that a shape may have more than one line of symmetry.

From the given questions, we can deduce that;

1. If two figures are similar, they may not be congruent. So that the statement that is false among the given option is A. If two figures have the same shape, then they are congruent.

2. Considering the dashed line drawn through the shape, it appears that it is a line of symmetry.

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Answer:

B. 2x² + 11

Step-by-step explanation:

(f - g)(x) means:

f(x) - g(x)

We've been given what each of these is equal to, so substitute that in:

3x² + 2 - (x² - 9)

Simplify. Don't forget to distribute that minus in the middle to both terms in x² - 9

3x² + 2 - x² + 9

Next, combine like terms.

2x² + 11

The possible algebraic equations, obtained based on the algebraic expressions in the question are;

1. [tex]\frac{x}{8} = y[/tex]

2. 15 - n = m

3. 25 + x = y

An algebraic expression is a collection of numbers and variables that are combined together, but without indicating the value indicated by the collection.

What is an algebraic equation?

An algebraic equation is a mathematical statement that expresses the equivalence of two expressions.

The algebraic expressions can be presented as follows;

1. Some number divided by 8

Let x represent the number divided by 8, and let y represent the result when x is divided by 8. The variables x and y can be defined based on the details in the question

The equation with x as the number and y as the result can be presented as follows;

2. n less than 15

The expression n less than 15 is; 15 - n

Let m represent the value of the expression; 15 - n, an algebraic equation based on the details is therefore;

3. 25 more than a number

Let x represent the number, we get

25 more than a number = 25 + x

The y represent the result or value of the expression 25 + x, we get the following algebraic equation;

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Answer:

Below

Step-by-step explanation:

5 out of ( 5 + 2) vehicles are cars     5 / 7 are cars

5/7 * 56 = 40 cars

Answer:

The power is 15 watts.

Step-by-step explanation:

It is equivalent to:

0.02012 mechanical horsepowers

0.02039 metric horsepowers

0.02011 electrical horsepowers

0.001529 boiler horsepowers

All the equations in which z = 5 are a solution are given as follows:

A. 8 = z + 3.

D. 12z = 60.

E. 12 + z = 17.

The first equation is defined as

8 = z + 3.

Isolating the variable z, applying the subtraction operation, which is the inverse of the addition, the solution is given as follows:

z = 8 - 3

z = 5.

The second equation is given as follows:

z - 1 = 6.

Applying the addition operation, which is the inverse of the subtraction, the solution is given as follows:

z = 7.

The third equation is given as follows:

20 = 40z

Applying the quotient operation, which is the inverse of the multiplication, the solution is given as follows:

z = 20/40

z = 0.5.

The fourth equation is given as follows:

12z = 60.

Applying the quotient operation, which is the inverse of the multiplication, the solution is given as follows:

z = 60/12

z = 5.

The fifth equation is defined as

12 + z = 17.

Isolating the variable z, applying the subtraction operation, which is the inverse of the addition, the solution is given as follows:

z = 17 - 12

z = 5.

The equations are given by the image presented at the end of the answer.

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we can find the total volume of material that makes up the ball by subtracting the volume of the hollow space from the volume of the sphere:

V = 20,834 cm^3 - 19,848.44 cm^3

= 985.56 cm^3

Volume is a measure of the amount of space occupied by an object or a substance. It is typically measured in units such as cubic meters (m^3), cubic centimeters (cm^3), or cubic feet (ft^3).

Diameter is a measure of the distance across the widest part of a circular object, such as a circle or a sphere. It is equal to twice the radius of the object and is typically measured in units such as millimeters (mm), centimeters (cm), or inches (in). It is a linear measurement.

To find the total volume of material that makes up the ball, we need to find the volume of the sphere and then subtract the volume of the hollow space in the center.

We can begin by calculating the volume of the sphere using the formula for the volume of a sphere:

V = (4/3) * pi * r^3

Where V is the volume, pi is approximately 3.14, and r is the radius of the sphere.

The outer diameter of the ball is 50 cm, so the radius of the sphere is (50/2) = 25 cm.

Substituting these values into the formula, we get:

V = (4/3) * 3.14 * (25 cm)^3

= (4/3) * 3.14 * 15,625 cm^3

= 20,834 cm^3

Next, we need to find the volume of the hollow space in the center of the ball, which is the same as the volume of a smaller sphere with a radius of (25 cm - 1.25 cm) = 23.75 cm.

So the volume of the hollow space is :

V = (4/3) * pi * (23.75 cm)^3

= (4/3) * 3.14 * (23.75 cm)^3

= 19,848.44 cm^3

Finally, we can find the total volume of material that makes up the ball by subtracting the volume of the hollow space from the volume of the sphere:

V = 20,834 cm^3 - 19,848.44 cm^3

= 985.56 cm^3

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Answer: $1.4

Step-by-step explanation:

let the price before the increase be x

1.2*x = 1.68

x=1.68/1.2 = 1.4

Price before increase = $1.4

Answer:

[tex]\Huge \boxed{\boxed{\textbf{False}}}[/tex]

Step-by-step explanation:

A quadrilateral must have four right angles in order to be a rectangle, not simply one. A quadrilateral with a single right angle, however, can take on a wide range of shapes, like a right angled triangle or an irregular quadrilateral. A shape having multiple sides and one right angle, for example, could be an irregular quadrilateral.

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________________________________________________________

A unbiased estimator is a statistic that accurately reflects the population mean, μ. A statistic is unbiased when the mean of its sampling distribution is equal to μ.

Mathematically, this can be expressed as:

E(x) = μ

Where E(x) is the expected value of x and μ is the population mean.

This means that if we take a sample from a population and calculate the mean from that sample, the expected value of that mean should be equal to the population mean. This can be seen in the following example:

Let's say we have a population with a mean of 30. We take a sample of size 5 from this population and calculate the sample mean, x. The expected value of x should be equal to 30. We can calculate this using the formula:

E(x) = ∑xi/n

Where xi are the values in the sample and n is the sample size.

For our example, E(x) = (30 + 30 + 30 + 30 + 30) / 5 = 30

This shows that x is an unbiased estimator of μ.

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The option that illustrates the truth value of the given conditional statement is; T T → T

A conditional statement is considered to be true when the antecedent and consequent statements are both true or if the antecedent is false. When the antecedent is false, it means that the truth value of the consequent does not matter; the conditional will always be true.

We are given the conditional statements at;

If 5 = 3 + 2, then 3 + 2 = 5

Now, a conditional statement, signified by t f which means true and false, is an if-then statement with t being a hypothesis and f being an inference. The statement that illustrates the truth value is T T → T because 5 = 3 + 2 which is true and 3 + 2 = 5 which is also true.

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The main difference between the 2D and 3D coordinate systems is that the 3D coordinate system adds a third axis (Z) to the two axes of the 2D coordinate system.

A coordinate system is a two-dimensional or three-dimensional system which is used to identify the location of a point or object in the space. It is represented by a set of axes, which are perpendicular and equally spaced from each other to form a grid-like structure. The coordinates of a point or object are determined by the intersection of the two or three axes. Common coordinate systems used in mathematics and science include the Cartesian, polar, and spherical coordinate systems.

A 2D coordinate system is a system in which two axes (X and Y) are used to define a point in a two-dimensional space. This system is used to describe the position of a point in relation to the origin, which is located at the intersection of the two axes. The two axes form a coordinate plane, which provides a visual representation of the system.

A 3D coordinate system is a system in which three axes (X, Y, and Z) are used to define a point in a three-dimensional space. This system is used to describe the position of a point in relation to the origin, which is located at the intersection of the three axes. The three axes form a coordinate space, which provides a visual representation of the system.

This third axis allows points in the 3D coordinate system to be represented in the third dimension. Additionally, the 3D coordinate system provides a more detailed representation of points, as it can represent points in all three dimensions.

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The slope of a line perpendicular to the line whose equation is x - 2y = 14 is -2

What is the equation of straight line ?

The equation of straight line is

y = mx + b

where m is slope of the straight line .

Given ,

The equation is x - 2y = 14 .

So, the equation in slope-intercept form would be 2y = x -14,

which then becomes y = 0.5x - 7

giving a slope of -0.5.

The slope of the perpendicular line is a negative reciprocal,

so 0.5 is the same as (1/2), so the positive reciprocal of that is -2,

meaning the slope of the perpendicular line will be -2.

Hence, The slope of a line perpendicular to the line whose equation is x - 2y = 14 is -2

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value of x is greater than or equal to half.

A mathematical expression shows the unequal comparison between two or more terms.

Inequalities can be greater than, less than, greater than or equal and less than or equal.

The difference of x and one third is greater than or equal to one third of x.

The statement can be written as x -1/3 ≥ x1/3

                                                 x -1/3 ≥ x/3

                              x - x/3 - 1/3 ≥ x/3- x/3 [ subtract x/3 from both parts]

                         2x/3 - 1/3 ≥ 0

             now add 1/3 on both parts

        we get, 2x/3 -1/3 + 1/3 ≥1/3

                      2x/3 ≥ 1/3

                   2x ≥ 1

                     x ≥1/2

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Answer:below

Step-by-step explanation:

y=1/3x

1/216 as a power of 6 is 6^-3. The solution has been obtained by using the concept of exponents.

What is an exponent?

A number's exponent demonstrates how many times we are multiplying a given number by itself. For instance, 2^4, indicates that we are multiplying 2 itself by four times. 2*2*2*2 is its expanded form. The power of a number is another name for an exponent. A whole number, fraction, negative number, or decimal are all acceptable.

We are given 1/216 which is to be written as a power of 6.

We know that 216 is the cube of 6.

This means that 216 can be written as 6^3.

Also, 1/n is written as n^-1

So, 1/216 can be written as 6^-3.

Hence, 1/216 as a power of 6 is 6^-3.

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Using formula of midpoint of a line, the endpoint have coordinates of (-29, 10)

The midpoint of a line is a point that divides the line into two equal parts. The coordinates of the midpoint can be found by taking the average of the x-coordinates of the endpoints and the average of the y-coordinates of the endpoints.

The formula of midpoint of a line is given as

M(x, y) = (x₂ + x₁) / 2, (y₂ + y₁) / 2

-21, 8 = (x₂ + x₁) / 2, (y₂ + y₁) / 2

For x - coordinate;

-21 =  (x₂ + x₁) / 2

-21 = -13 + x₁ / 2

-21 * 2 = -13 + x₁

-42 = -13 + x₁

x₁ = -42 + 13

x₁ = -29

For y - coordinate

8 = (y₂ + y₁) / 2

8 = (6 + y₁) / 2

16 = 6 + y₁

y₁ = 16 - 6

y₁ = 10

The endpoint is (-29, 10)

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Consequently, (3, 5/2) is the answer to the equations 5x+y=3 and 5x+y=2. Either conditional solutions or identities are categories for equations.

Its simplest form is thought to be the number's smallest equivalent fraction. How to determine the simplest form. Look for shared factors in the denominator and numerator. A fractional number can be checked to discover if it is a prime number. A statement having two quadrilateral and an equal sign in the middle is referred to as a mathematical equation. Every variable's degrees are listed in descending order in the general form of any equation. The formula for a linear equation is x + b = 0. The general form of a two-variable linear equation is an x + b y + c = 0. (or something similar). Either conditional solutions or identities are categories for equations. An identity holds true for whatever value of the variables.

given

5x + y = 3

5x + y = 2

x = y-3/ 5

y - 3 +y = 2

2y = 5

y = 5/2

x = 3

Consequently, (3, 5/2) is the answer to the equations 5x+y=3 and 5x+y=2.

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Answer:

$1223.75

Step-by-step explanation:

40 times $22.25 = $890

$22.25 times 1.5 to get overtime pay = $33.375

$33.375 times 10 hours overtime = $333.75

$890 + $333.75 = $1223.75

Answer:

12,800

Step-by-step explanation:

20% of 20000 is 4000

20000-4000=16000

20% of 16000 is 3200

16000-3200=12,800

Answer:

It would take her 22 minutes to text 143 words.

Step-by-step explanation:

First, you take 91 and divide that by 14.

You then get 6.5

Then you divide. 143/6.5

You then get 22.

Guadalupe can text 143 words in 22 minutes.

The ratio can be defined as the number that can be used to represent one quantity as a percentage of another. Only when the two numbers in a ratio have the same unit can they be compared. Ratios are used to compare two objects.

Given, Guadalupe can text 91 words in 14 minutes.

Since,

Guadalupe can text 91 words in =  14 minutes.

Thus, Guadalupe can text 1 word in  =  14/91 minutes.

So, Guadalupe can text 143 words in =  14*143/91 minutes.

Guadalupe can text 143 words in = 22 minutes.

Therefore, in 22 minutes, Guadalupe can text 143 words.

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