use mental math to complete the pattern(5×6^3=5__6__? Can you help me with the two blank spaces

The coordinate of point R after the rotation is determined as = ( - 4, 7).

option A.

A rotation is a transformation that turns the figure in either a clockwise or counterclockwise direction.

You can turn a figure 90°, a quarter turn, either clockwise or counterclockwise. When you spin the figure exactly halfway, you have rotated it 180°. Turning it all the way around rotates the figure 360°.

When a figure is rotated 180 degrees, each point of the figure is moved to a new position that is exactly opposite its original position with respect to a fixed center of rotation.

The initial coordinate of point R = ( 4, 7),

The new coordinate of point R after the rotation = ( - 4, 7)

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A variable is a characteristic or attribute that can take on different values. It is an observable and measurable property of an object or phenomenon, which can be used to describe and analyze it.

Parameters are used in inferential statistics to make conclusions about a population based on a sample of data.

(a) If you decide to select based on proportion of 10% from each group, the number of patients selected from each group would be: Group A = (10/100) x 100 = 10 patients Group B = (10/100) x 30 = 3 patients Group C = (10/100) x 30 = 3 patients.

(b) The classified groups can be named as follows: Group A = 10 years of education or less Group B = More than 10 years but less than or equal to 20 years of education Group C = More than 20 years of education.

(c) The sampling method employed in the selection process was stratified sampling. Stratified sampling is a type of probability sampling technique where the population is divided into homogeneous subgroups or strata, and the researcher selects a simple random sample from each subgroup or stratum.

The researcher chooses a proportion of participants from each subgroup to represent the population as a whole, which allows for more precise estimates of the population parameters than simple random sampling.

The sample is selected randomly from the stratified sample, which ensures that the sample is representative of the population.

A variable is a characteristic or attribute that can take on different values. It is an observable and measurable property of an object or phenomenon, which can be used to describe and analyze it.

Variables are used in research to test hypotheses, determine relationships between different phenomena, and make predictions about future outcomes.

A parameter is a numerical summary of a population, which describes a characteristic of the population. It is an unknown constant that can only be estimated from a sample of data.

Parameters are used in inferential statistics to make conclusions about a population based on a sample of data.

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Answer:

a) the sample size is 400

b) 95% confidence Interval for p is ( 0.0286, 0.0714 )

Step-by-step explanation:

Given the data in the question;

sample size n = 400

x = 20

p = x / n = 20 / 400 = 0.05

q = 1 - p = 1 - 0.05 = 0.95

a)

n = 400

Hence, the sample size is 400

b) 95% confidence Interval for p;

At 95% confidence interval,

significance level ∝ = 1 - 95% = 1 - 0.95 = 0.05

∝/2 = 0.05 / 2 = 0.025

so, Z critical Value ; \(Z_{\alpha /2\) = 1.96  { from table }

So for Confidence Interval for p;

⇒ p' ± \(Z_{\alpha /2\)√( p'q' / n )

we substitute

⇒ 0.05 ± 1.96√( (0.05 × 0.95 ) / 400 )

⇒ 0.05 ± 1.96√( 0.00011875 )

⇒ 0.05 ± 1.96 × 0.010897

⇒ 0.05 ± 0.021358

⇒ ( 0.05 - 0.021358 ), ( 0.05 + 0.021358 )

⇒ ( 0.0286, 0.0714 )

Therefore, 95% confidence Interval for p is ( 0.0286, 0.0714 )

Answer:

A=x2 - 2x -35

Step-by-step explanation:

x+5 x-7

The solution is Option D.

The area of the rectangle is A = x² - 2x - 35

What is the Area of a Rectangle?

The area of the rectangle is given by the product of the length of the rectangle and the width of the rectangle

Area of Rectangle = Length x Width

Given data ,

Let the area of the rectangle be represented as A

Now , the value of A is

The length of the rectangle L = x + 5

The width of the rectangle is W = x - 7

And ,

The area of rectangle = L x W

Substituting the values in the equation , we get

The area of rectangle = Length of rectangle x Width of rectangle

The area of rectangle = ( x + 5 ) ( x - 7 )

On simplifying the equation , we get

The area of rectangle A = x ( x - 7 ) + 5 ( x - 7 )

The area of rectangle A = x² - 7x + 5x - 35

The area of rectangle A = x² - 2x - 35

Therefore , the value of A is x² - 2x - 35

Hence , the area of rectangle is x² - 2x - 35

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The Great Lakes are the world's largest group of freshwater lakes by total area and second-largest by total volume.

The Great Lakes, also known as the Great Lakes of North America or the Laurentian Great Lakes are a series of large interconnected freshwater lakes with sea-like characteristics in North America's mid-east region that connect to the Atlantic Ocean via the Saint Lawrence River.

Superior, Michigan, Huron, Erie, and Ontario are the names of five lakes that are located on or near the Canada-United States border. Lakes Michigan and Huron are joined hydrologically at the Straits of Mackinac. The Great Lakes Waterway allows for modern water travel.

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Answer:

4x^2 - 1 = 0

Step-by-step explanation:

x = 1/2, x = -1/2

2x = 1, 2x = - 1

2x - 1 = 0, 2x + 1 = 0

( 2x - 1 )( 2x + 1 ) = 0

4x^2 - 1 = 0

Each silver bead costs $0.50, and each green bead costs $1.

Let's assume the cost of each silver bead is 's' dollars, and the cost of each green bead is 'g' dollars.

According to the given information, the necklace requires 25 silver beads and 15 green beads, and the bracelet requires 10 silver beads and 5 green beads.

The total cost of the necklace beads is $27.50, and the total cost of the bracelet beads is $10.

Using this information, we can set up the following system of equations:

25s + 15g = 27.50 (Equation 1)

10s + 5g = 10 (Equation 2)

We can solve this system of equations using any appropriate method, such as substitution or elimination.

Let's use the elimination method to solve the system:

Multiplying Equation 2 by 3, we get:

30s + 15g = 30 (Equation 3)

Subtracting Equation 3 from Equation 1:

25s + 15g - (30s + 15g) = 27.50 - 30

-5s = -2.50

s = 0.50

Now, substituting the value of s into Equation 2:

10(0.50) + 5g = 10

5 + 5g = 10

5g = 5

g = 1

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Answer:

The ANOVA table and the solution are attached below

The perimeter of the rectangular Panto will be 38 meters.

It is important to note that the perimeter of a rectangle is calculated as:

= 2(length + width)

In this case, Cassandra has a rectangular Panto in her backyard the painter is 12.74 m long and 5.45 m wide.

We are told to convert the dimensions to the nearest whole numbers. This will be 13m and 6m. Therefore, the perimeter will be:

= 2 (length + width)

= 2 13 + 6)

= 2(19)

= 38m.

The perimeter is 38m.

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Answer:

-2 - 24i

Step-by-step explanation:

a + bi + (7 - 3i) + (5 + 9i) + 13i = 10 - 5i

a + bi + 7 + 5  - 3i + 9i + 13i = 10 - 5i

                a + bi  + 12  + 19i = 10 - 5i

                         a + bi          = 10 - 5i - 12 - 9i

                                 a + bi = 10 - 12 - 5i - 9i

                                 a + bi = -2 - 24i

Answer:

A. 3x+12

Step-by-step explanation:

8x+3-5x+9

8x-5x=3x

3+9=12

then put them together

3x+12

answer= A

The function that describes the area of the rectangle in terms of one of the sides is A = 12L - L².

The perimeter of the rectangle is given as 24. Therefore, the area in terms of one of its side will be:

A = L(24 - 2L)/2

A = L(12 - L)

A = 12L - L²

The length side for the maximum area will be 6 and 6. The maximum area of the rectangle will be:

= 6 × 6

= 36

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Answer:

Among the four choices, \((x + 5)\) is the only one that is not a linear factor of this polynomial function.

Step-by-step explanation:

Let \(a\) denote some constant. A linear factor of the form \((x - a)\) is a factor of a polynomial \(f(x)\) if and only if \(f(a) = 0\) (that is: replacing all \(x\) in the polynomial \(f(x) \!\) with the constant \(a\!\) would give this polynomial a value of \(0\).)

For example, in the second linear factor \((x - 2)\), the value of the constant is \(a = 2\). Verify that the value of \(f(2)\) is indeed \(0\). (In other words, replacing all \(x\) in the polynomial \(f(x) \!\) with the constant \(2\) should give this polynomial a value of \(0\!\).)

\(\begin{aligned}f(2) &= 2^3 - 5\times 2^2 - 4 \times 2 + 20 \\ &= 8 - 20 - 8 + 20 \\ &= 0 \end{aligned}\).

Hence, \((x - 2)\) is indeed a linear factor of polynomial \(f(x)\).

Similarly, it could be verified that \((x - 5)\) and \((x + 2)\) are also linear factors of this polynomial function.

Rewrite the first linear factor \((x + 5)\) in the form \((x - a)\) for some constant \(a\): \((x + 5) = (x - (-5))\), where \(a = -5\).

Calculate the value of \(f(5)\).

\(\begin{aligned}f(5) &= (-5)^3 - 5\times (-5)^2 - 4 \times (-5) + 20 \\ &= (-125) - 125 + 20 + 20 \\ &= -210\end{aligned}\).

\(f(5) \ne 0\) implies that \((x - (-5))\) (which is equivalent to \((x + 5)\)) isn't a linear factor of this polynomial function.

Answer (let x be the number):

5x - 40 = x + 8

I hope this helps!

The number in the equation 5n - 40 + 8 = n is 8.

A numerical expression is formed by numbers and their operation.A numerical expression can also be constructed from given statements.

We can also construct numerical expression form real life scenarios.

According to to the question statement 40 subtracted from five times a number is 8 more than the number and we have to form an numerical expression.

Let the number be 'n'.

∴ 5n - 40 + 8 = n

5n - n = 40 - 8.

4n = 32.

n = 32/4.

n = 8.

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Answer:

17.93

Step-by-step explanation:

y= 2.11x+5.27

x= the # of years

y=total

2000---->2006, six years have past

y=2.11(6)+5.27

y=17.93

Heuristic is 0 for every city Heuristic is 1 for every city Selecting an inadmissible heuristic has a -50% penalty.

To find the shortest path to a destination city from a start city using roads (e.g., traveling from Arad to Bucharest) using A* search, the following heuristics are admissible:

Manhattan distance ("go first east/west and then north/south") between a city and start city.

Euclidean distance ("as the crow flies") between a city and destination city.

Euclidean distance ("as the crow flies") between a city and start city.

Manhattan distance ("go first east/west and then north/south") between a city and destination city.

The following heuristics are inadmissible:

Twice the Euclidean distance ("as the crow flies") between a city and destination city.

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The polynomial, f(x) = x² + 4·x - 1, has a value of -5 when x = -2

A polynomial consists of terms comprising of variables and numbers with positive integer indices with operations including additions, subtractions, multiplications.

The specified polynomial is f(x) = x² + 4·x - 1

The point at which the polynomial is evaluated is; x = -2

The value of the specified polynomial at x = -2 is therefore;

f(-2) = (2)² + 4 × (-2) - 1 = -5

The polynomial can also be evaluated by graphing polynomial and finding the point of intersection of the line x = -2 and the graph of the polynomial as follows;

The attached graph created with MS Excel, indicates that at the point x = -2 (represented by the point where the vertical line, x = -2, intersects the polynomial, x² + 4·x - 1) is the point where, f(x) = -5

The value of the polynomial, f(x) = x² + 4·x - 1, when x = -2 is -5.

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The line of best fit for the set of data in this problem is given as follows:

y = 0.613x + 4.142.

To find the regression equation, which is also called called line of best fit or least squares regression equation, we need to insert the points (x,y) of the data-set in the calculator.

The points for this problem are given as follows:

(-2, 2.9), (-3.5, 2), (1.4, 4.8), (-4.2, 1.5), (0,4), (2.8, 6), (-1.5, 3.5).

Inserting these points into a calculator, the line of best fit is given as follows:

y = 0.613x + 4.142.

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Answer: Hope this helps ;) don't forget to rate this answer !

Step-by-step explanation:

Another way to write the compound inequality y + 3 ≥ 2 and y + 3 ≤ 6 is to use the "and" symbol to connect the two inequalities:

2 ≤ y + 3 ≤ 6

This compound inequality can also be written using the "interval notation," which represents a range of values that a variable can take:

[2, 6]

This notation means that the solution set for the compound inequality is the set of all values of y that are greater than or equal to 2 and less than or equal to 6. In other words, the solution set is all values of y that lie within the closed interval from 2 to 6, including 2 and 6 themselves.

For example, if y is 3, the compound inequality is satisfied because 3 is within the interval [2, 6]. If y is 7, the compound inequality is not satisfied because 7 is not within the interval [2, 6].

The number of each type of ad that the department can run each month are:

TV Ads = 32

Radio Ads = 12

News Ads =  20

x = number of tv ads

y = number of radio ads

z = number of news ads

Two formulas are indicated.

x + y + z = 64

1000x + 200y + 600z = 46400

they want as many tv ads as radio and news ads combined.

equation for that is x = y + z

since x = y + z, replace x with y + z in both equations to get;

y + z + y + z = 64

1000 * (y + z) + 200 * y + 600 * z = 46400

combine like terms and simplify to get:

2y + 2z = 64

1000y + 1000z + 200y + 600z = 46400

combine like terms again to get:

2y + 2z = 64

1200y + 1600z = 46400

Solving simultaneously gives:

y = 12

z = 20

Thus:

x = 12 + 20

x = 32

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The volume of the cone is 13 cm³. option D

To determine the volume of the cone, we have that;

The formula for calculating the volume of a cone is expressed as;

Volume = (1/3)πr ²√(L ² - r ²).

Such that;

Substitute the values, we have;

Volume = 1/3 × 3.14 ² × √(25 - 9)

Find the squares, we get;

Volume, V = 1/3 × 9. 86 × √16

Find the square root

Volume, V = 1/3 × 9.86 × 4

Volume, V = 13 cm³

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Answer:

100 GROUPS OF TEN

Step-by-step explanation:

THERE IS 1000 ML IN 1L

A quadrilateral with one pair of parallel side is a D) Trapezium

Given :

A quadrilateral with one pair of parallel side is.

we know that ,

Trapezium :

A trapezium is a convex quadrilateral with exactly one pair of opposite sides parallel to each other.

The trapezium is a two - dimensional shape that appears as a table when drawn on a sheet of paper.

In Euclidean Geometry, a quadrilateral is defined as a polygon with four sides and four vertices.

so a trapezium also has four sides, four angles and four vertices.

Area of trapezium = 1/2 * ( a+ b ) h

where a and  b are bases

and h is height of altitude.

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For given polygon, the value of x is 61°

In this question we have been given a polygon with five sides.

We have been given the five interior angles of the polygon.

We need to find the value of x.

From given figure, we can observe that the given polygon is nothing but a pentagon.

We know that the sum of all interior angles of the pentagon is 540°

⇒ 107° + 144° + 138° + x° + 90° = 540°

⇒ 479° + x° = 540°

⇒ 479° + x° - 479° = 540° - 479°

⇒ x = 61°

Therefore, for given polygon, the value of x is 61°

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The expression is true for all values of a between 0 and -5 (inclusive)

What is an expression?

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a complete sentence. Any one of the following mathematical operations can be used. A sentence has the following structure: Number/variable, Math Operator, Number/Variable is an expression.

The expression is given as:

|a+5|= -5–a

The absolute value expression is always positive.

So, we have:

a +5 = -5 -a or -5 - a = -5 - a

For the expression a +5 = -5 -a we have:

a + a = -5 - 5

Evaluate like terms

2a =- 10

Divide both sides by 2

a = -5

For the expression -5 - a = -5 - a, we have:

0 = 0

So, we have:

0 = 0 or a = -5

This means that, the expression is true for all values of a between 0 and -5 (inclusive)

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Step-by-step explanation:

here u gggggggggggggggoooo

Answer:

x = 4, y = 2 or (4, 2)

Step-by-step explanation:

Given :-

2x + 3y = 14 -(1)

 x +  3y = 10 -(2)

To Find :-

x and y

Solving :-

Subtract (2) from (1).

=> x =  4

Substituting value of x in Equation 2 :-

4 + 3y = 10

3y = 6

=> y = 2

Solution :-

x = 4, y = 2

Answer:

the median value of the given data set is 30

Step-by-step explanation:

The computation of the median value is as follows:

27,28,28,29,29,29,30,30,30,31,31,31,33,34

There are 14 entries

So the mid value is 30

Hence the median value of the given data set is 30

Answer:

30

Step-by-step explanation:

The relationship between the related rates dp/dt and dV/dt is -1.3kV^-2.3

Given :

When a certain polyatomic gas undergoes adiabatic expansion, its pressure p and volume V satisfy the equation pV^1.3 = k, where k is a constant. Find the relationship between the related rates dp/dt and dV/dt.

p * V^1.3 = k

divide by v^1.3 on both sides

p *  V^1.3 /  V^1.3 = k /  V^1.3

p = k /  V^1.3

p = k *  V^-1.3

differentiate with respect to t on both sides

dp / dt = -1.3kV^-1.3 - 1 dv / dt

dp / dt / dv / dt = -1.3kV^-2.3

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