Explain why the standard deviation of a set of data is always given as a positive number, but data points can have a negative overall standard deviation.

The curve of the graph would move closer to the y-axis for a > 4

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

f(x) = a(1/2)^x

Such that

a = 4

The graph of the function is added as an attachment

From the given parameters, we can see that the value of a is positive

This implies that an increment in the value of a would make the curve move closer to the y-axis

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Answer:

the highest (hcf) would be 6 , while lowest (lcm) is 5,040

The equation of the function g(x) will be √ [ (x) -  4 )].

A line that, in analytical geometry, is an asymptote of a curve is one where, as one or both of the x or y coordinates tend to infinity, the distance between the curve and the line approaches zero.

An asymptote of a curve is a line that is tangent to the curve at a point at infinity in projective geometry and related contexts.

Given that the function F(x) is √x and is horizontally stretched by a factor of 4 to form function g(x).

The equation of the stretched function can be written as:-

f(x) = √x

g(x) = √ [ (x) -  4 )]

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Answer:

option a is correct

Step-by-step explanation:

18 is the multiple of 3

so the first option is correct as 3 is multiplied with 6 to give 18

so the first number is multiple of second number

The equation 7x^4 = 56 can be rewritten as x^4 = 8. To find the real solutions of the equation, we take the fourth root of both sides:

What does a math equation mean?

Algebraically speaking, an equation is a statement that shows the equality of two mathematical expressions. For instance, the two equations 3x + 5 and 14, which are separated by the 'equal' sign, make up the equation 3x + 5 = 14.

x = ∛8 = 2.

So the real solutions of the equation are x = 2.

Note: since the fourth root of 8 is 2, we can check that the equation holds true. i.e 7*2^4 = 56

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The scale factor for the dilation from the quadrilateral EFGH to form DABC is the fraction 3/5.

Scale factor is the ratio between the scale of a given original object and a new object, which is its representation but of a different size either bigger or smaller.

Considering the coordinates (1/2, 3/4) and (3/10, 9/4) centered at the original, we will observe the the point 1/2 was increased by 3/5 to become 3/10 at the x–axis, that is;

1/2 × 3/5 = 3/10

Also, the point 3/4 was increased by 3/5 to become 9/20 at the y–axis, that is;

3/4 × 3/5 = 9/20

Therefore, 3/5 is the scale factor of the dilation for the quadrilateral EFGH to DABC.

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The value of the 7th term of the Geometric sequence is 6

A geometric sequence is a sequence of numbers that follows a pattern were the next term is found by multiplying by a constant called the common ratio, r.

An example of a Geometric sequence is 2, 4, 8, 16, 32, 64, …, where the common ratio is 2.

r is found by dividing the second term by first term.

The nth term of a geometric sequence is S(n) = ar^(n-1).

The common ratio in the sequence = 1458/4374 = 1/3

therefore S(7) = 4374×1/3^( 7-1)

= 4374× (1/3)⁶

= 4374/729

= 6

Therefore the value of the seventh term is 6

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The 100th prime number is 541.

Therefore the answer is 541.

Prime numbers are numbers that are divisible by only 1 and themselves. They are considered to be the "building blocks" of the natural numbers, and are important in number theory and other branches of mathematics.

Prime numbers are fundamental for number theory and have a lot of applications in cryptography, coding theory, and other areas of mathematics.

The first few prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23, and 29. The primes continue indefinitely, with no repeating pattern or predictable distribution. Finding the nth prime number is not an easy task, it requires knowledge of number theory and a lot of computational power.

In general, the nth prime number grows faster than any polynomial in n. The 100th prime number is larger than the 100th Fibonacci number (which is about 354) and smaller than the 100th triangular number (which is about 5050).

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In given word problem the number of cards Alan has is 13 and Number of cards Calvin has is 13.

What is word problem?

A math word problem is a question that is written as one or more sentences and asks students to use their mathematical understanding to solve an issue from "real world." In order  to understand the word problem, they must be familiar with the terminology that goes along with the mathematical symbols that they are used to.

Here , Let us take Number of card Alan has as A and Number of card bill has as B and Number of cards does Calvin has as C.

Now Alan has 11 less than 2 times the number of cards Bill has then,

=> A = 2B-11 ------------->1

And Calvin has 1 more than 1 times the number of cards Bill has then,

=> C =  B+1 ----------> 2

Here Alan and Calvin has same number of cards then

=> 1 = 2

=> 2B - 11 = B +1

=> 2B-B = 11+1

=> B = 12

Now put B= 12 into 1 then

=> A = 2(12)-11= 24-11 = 13

Now put B= 12 into 2 then

=> C = 12+1 = 13

Hence the number of cards Alan has is 13 and Number of cards Calvin has is 13.

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The polynomial 8X/Y has a coefficient of X of 8.

A polynomial is a mathematical statement made up of coefficients and indeterminates that uses only the operations addition, subtraction, multiplication, and powers of positive integers of the variables.

A coefficient in mathematics is a multiplicative factor in a polynomial term, a series term, or an expression. It is often a number, but it can also be any expression. They may also be referred to as parameters if the coefficients are variables in and of themselves.

In the above polynomial 8X/Y, the coefficient of X is 8.

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Answer:

5.099

Step-by-step explanation:

trust me

5.099 is the answer....

For the value of f (x) = 11, the value of x is

A relation between a set of inputs having one output each is called a function.

We have to given that;

The function is,

⇒ f(x) = -5x + 1

And, f (x) = 11

Now, We have;

⇒ f(x) = -5x + 1

Substitute f (x) = 11, we get;

⇒ 11 = - 5x + 1

⇒ 5x = - 11 + 1

⇒ 5x = - 10

⇒ x = - 2

Thus, The value of x = - 2

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The size of the cardboard piece required is 7627.0 in.

The formula for finding the size of a box is

2(L + W) + 8L + 8W = Perimeter of the cardboard piece

Where L = Length, W = Width

We need to find L and W to find the size of the cardboard piece.

7623 = 2(L + W) + 8L + 8W

7623 = 2L + 2W + 8L + 8W

7623 = 10L + 10W

7623/10 = L + W

762.3 = L + W

Let's take L = 500 and W = 262.3 (762.3 - 500 = 262.3)

Now we plug in the values of L and W in the original formula

2(500 + 262.3) + 8(500) + 8(262.3) = 7623

2(762.3) + 4000 + 2102.4 = 7623

1524.6 + 4000 + 2102.4 = 7623

7627.0 = 7623

Therefore, the size of the cardboard piece required is 7627.0 in.

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4/5 and 6/10 form a proportion.

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Answer:

y=2x+3

Step-by-step explanation:

See attached worksheet.

Guidelines are presented on how to both graphically and mathematically solve for the equation.  

Graphing:  Mark the the two given points and connect them with a ruler to form the line.  These same two points may be used to determine the slope, as is shown.  The slope is 2.  The line intersects the y axis at 3, so the y-intercept is 3.  Using the standard form of an equation, the line is y = 2x + 3, as is outlined in the attachment.

The same line is determined mathematically by using the same technique for calculating slope.  The value of the y-intercept may be found by using one of the two given points in the equation that has the slope of 2:

  y= 2x +b

Enter pont (-1,1), for example, and calculate the value of b. b = 3, (since 1 = 2*(-1)+ b, so b=3).

The equation of this line is y=2x+3

Answer:

[tex] \sf \: 12th \: term = 37[/tex]

Step-by-step explanation:

Common difference (d) is,

→ d = a2 - a1

→ d = -3 - (-7)

→ d = -3 + 7

→ [ d = 4 ]

Now the 12th term will be,

→ a1 + (d × (n - 1))

→ -7 + (4 × (12 - 1))

→ -7 + (4 × 11)

→ -7 + 44

→ 37 => 12th term

Hence, the answer is 37.

Answer:

Property

Step-by-step explanation:

The coordinates of the point after the transformation is (-7, -4)

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

(x, y) = (-4, 7)

Transformation involves changing the location and/or the size of a shape in a coordinate plane

A point rotating -90° about the origin will have its x-coordinate become its y-coordinate and its y-coordinate become its negative x-coordinate.

Hence, the point (-4, 7) will become (-7, -4) after rotating -90° about the origin.

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As per the unitary method, the number of soda bottles required to fill the 26 party bottle is approximately 104.

Unitary method in math is known as the method of finding the value of the required number of a quantity by first finding the value of the unit quantity

Here we have given that a barrel can fill up 72 soda can and the same barrel can fill up 18 party bottle.

Here we need to fill 26 party bottle, so it need the number of barrel as,

=> 1 barrel = 18 party bottles.

Then for 26 party bottle it need the following number of barrels,

=> 26/18

=> 1.44

Here we also know that a barrel can fill up 72 soda can.

So, if we have 1.44 barrel, then the number of soda bottle is calculated as,

=> 1.44 x 72

=> 103.68

Therefore, approximately 104 soda bottles are required.

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Answer:

18.03

Step-by-step explanation:

Its pretty easy actually,

50x100 When we put 50 correct out of 61 possible into our formula, we get this: (50/61) x 100 = 81.97%

so , 100-81.97 = 18.03

The slope of the line passing through the points is given by the equation Slope m = 15/11

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given data ,

Let the equation of line be represented as A

Now , the value of A is

Let the first point be represented as P = P ( 7 , 10 )

Let the second point be represented as Q = Q ( 18 , 25 )

Now , the slope of the line between the points is given by

Slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Substituting the values in the equation , we get

Slope m = ( 25 - 10 ) / ( 18 - 7 )

On simplifying the equation , we get

Slope m = 15/11

Hence , the slope of the line is m = 15/11

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The solution for given linear inequality will be x>11/2.

What are linear inequalities?

Inequality represents the mathematical expression in which both sides are not equal. If the relationship makes the non-equal comparison between two expressions or two numbers, then it is known as inequality in Maths. In this case, the equal sign “=” in the expression is replaced by any of the inequality symbols such as greater than symbol (>), less than symbol (<), greater than or equal to symbol (≥), less than or equal to symbol (≤) or not equal to symbol (≠). The different types of inequalities in Maths are polynomial inequality, rational inequality, absolute value inequality.

The symbols ‘<‘ and ‘>’ express the strict inequalities and the symbols ‘≤’ and ‘≥’ denote slack inequalities. A linear inequality seems exactly like a linear equation but there is a change in the symbol that relates two expressions.

e.g. y>x+2

Now,

Given linear inequality is

10<2x-1

i.e. x>11/2.

The number line is in image.

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Answer:

Step-by-step explanation: Substitute the values in the bracket (2,6). X =2. Y = 6. Do the same for the same question

Answer:

To find the final balance of an account earning interest compounded continuously, you can use the formula:

A = Pe^(rt)

where A is the final account balance, P is the initial principal (or starting) amount, r is the interest rate, and t is the time (in years) for which the interest is being calculated.

Substituting in the given values:

A = 550 * e^(0.066 * 10)

Therefore, the final balance would be approximately $1064.14.

Answer:

C)  $1064.14

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{8.5 cm}\underline{Continuous Compounding Formula}\\\\$ A=Pe^{rt}$\\\\where:\\\\ \phantom{ww}$\bullet$ $A =$ final amount \\\phantom{ww}$\bullet$ $P =$ principal amount \\\phantom{ww}$\bullet$ $e =$ Euler's number (constant) \\\phantom{ww}$\bullet$ $r =$ annual interest rate (in decimal form) \\\phantom{ww}$\bullet$ $t =$ time (in years) \\\end{minipage}}[/tex]

Given:

Substitute the given values into the continuous compounding formula and solve for A:

[tex]\implies A=550e^{0.066 \times 10}[/tex]

[tex]\implies A=550e^{0.66}[/tex]

[tex]\implies A=550(1.93479233...)[/tex]

[tex]\implies A=1064.13578...[/tex]

Therefore, the balance of the account after 10 years would be $1064.14.

The expression that is equal to the provided expression, x2+7x+8, is 5x/x2+2x-1.

In math, it is possible to multiply, divide, add, or subtract. The following sentence form describes an expression: (Mathematical Operator, Number or Variable, Expression) Numbers, variables, and operations make constitute a mathematical expression (such as addition, subtraction, multiplication or division etc.) Expressions and phrases can be compared.

given

expression = x²+7x+8/x²+2x-1

x²+8/x²+7x+2x-1

5x + 1/x2 + 2x -1

5x/x²+2x-1

The expression that is equal to the provided expression, x2+7x+8, is 5x/x2+2x-1.

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Answer:

4,6,8,12

Hope it helps because im not sure if its right

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Answer:

2

Step-by-step explanation:

There is x and no variable

The total words Cecilia types over a 4 minute period is 152 words

An equation is a mathematical expression that contains two or more numbers and variables linked together by mathematical operations such as exponents, multiplication, division, addition, subtraction and so on.

The slope intercept form of a linear equation is:

y = mx + b

where m is the slope and b is the y intercept.

Let y represent the total words that Cecilia types after x minutes.

Cecilia types at a speed of 38 words per minute. Hence:

y = 38x

After 4 minutes:

y = 38(4) = 152 word

The total words Cecilia types over a 4 minute period is 152 words

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A bivariate probability distribution is a statistical distribution that describes the joint probability of two random variables. It provides the probability of each combination of values for the two variables. In simple words, it's a way to model the joint probability of two variables and the relationship between them.

A bivariate probability distribution is represented by a probability density function (pdf) or a probability mass function (pmf) depending on whether the variables are continuous or discrete. The function gives the probability of a given pair of values of the two variables. Bivariate probability distributions are useful in understanding the relationship between two variables and can be used to make predictions or draw inferences. It can be visualized using a scatter plot, a contour plot or a 3D plot. It can also be used to calculate the covariance and correlation between the two variables.

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Complete question:

Describe Bivariate Probability Distribution.