If the 8th term of an A.P is twice the 4th term and the sum of the first terms is 47. find the five common difference​

[tex]\begin{array}{llll} f(x)~from\\\\ x_1 ~~ to ~~ x_2 \end{array}~\hfill slope = m \implies \cfrac{ \stackrel{rise}{f(x_2) - f(x_1)}}{ \underset{run}{x_2 - x_1}}\impliedby \begin{array}{llll} average~rate\\ of~change \end{array} \\\\[-0.35em] ~\dotfill\\\\ f(x)= 6x^2-7 \qquad \begin{cases} x_1=1\\ x_2=b \end{cases}\implies \cfrac{f(b)-f(1)}{b - 1}[/tex]

[tex]\cfrac{[6(b)^2-7]~~ - ~~[6(1)^2-7]}{b-1}\implies \cfrac{6b^2-6}{b-1}\implies \cfrac{6(b^2-1)}{b-1}\implies \cfrac{6(b^2-1^2)}{b-1} \\\\\\ \cfrac{6(b-1)(b+1)}{b-1}\implies 6(b+1)[/tex]

The sum of two dice has a total of 36 possible outcomes. The sum can range from 2 (rolling a 1 on each die) to 12 (rolling a 6 on each die).

To find the probability distribution, we can make a table that lists all the possible sums, the number of ways to obtain each sum, and the corresponding probability.

Sum Ways to obtain Probability

2 1 1/36

3 2 2/36 = 1/18

4 3 3/36 = 1/12

5 4 4/36 = 1/9

6 5 5/36

7 6 6/36 = 1/6

8 5 5/36

9 4 4/36 = 1/9

10 3 3/36 = 1/12

11 2 2/36 = 1/18

12 1 1/36

From the table, we can see that the sums 6 and 9 have the same probability distribution, and would be represented with equal bars on a bar graph

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The transformation indicated on the graph is a

Rotation

A rotation transformation is a transformation in which a geometric figure is rotated around a fixed point called the center of rotation.

This transformation changes the position and orientation of the figure, but the shape and size remain the same.

The center of rotation is the point around which the figure rotates, and the angle of rotation determines how far the figure rotates around the center.

The center of rotation is on the graph is the origin and the angle of rotation is 90 degrees counterclockwise

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Answer:

42 /3 = x

Step-by-step explanation:

it is 14 for sure.....

Answer:

[tex]\large\boxed{\mathtt{Area = 586.2cm^{2}.}}[/tex]

Step-by-step explanation:

[tex]\textsf{We are asked to find the area of this figure.}[/tex]

[tex]\textsf{In order to make this simpler, draw a line between the rectangle, and the semi-circle.}[/tex]

[tex]\textsf{We should identify the formulas needed for the areas of the rectangle, and semi-circle.}[/tex]

[tex]\large\underline{\textsf{For the Semi-Circle:}}[/tex]

[tex]\mathtt{Area = 1/2( pi(radius)^{2}).}[/tex]

[tex]\large\underline{\textsf{For the Rectangle:}}[/tex]

[tex]\mathtt{Area = Length \ x \ Width.}[/tex]

[tex]\textsf{Let's find the area of the Rectangle first.}[/tex]

[tex]\mathtt{Area = 15 \ x \ 24}[/tex]

[tex]\mathtt{Area = 360cm^{2}.}[/tex]

[tex]\textsf{For the Semi-Circle, the radius is 1/2 of the Diameter. (24)}[/tex]

[tex]\mathtt{Area = 1/2( pi(12)^{2}).}[/tex]

[tex]\mathtt{Area = 1/2(144 \pi).}[/tex]

[tex]\mathtt{Area = 72 \pi.}[/tex]

[tex]\mathtt{Area \approx 226.2cm^{2}.}[/tex]

[tex]\textsf{Add the areas together to represent the area of the figure.}[/tex]

[tex]\large\underline{\textsf{Add:}}[/tex]

[tex]\mathtt{360cm^{2} + 226.2cm^{2} = 586.2cm^{2}. }[/tex]

[tex]\large\boxed{\mathtt{Area = 586.2cm^{2}.}}[/tex]

Based on the information we can infer that the area of the image is: 50.24 in²

To find the area of the figure we must take into account that this figure is a circle. To find the area of this figure we must use the following mathematical formula:

A = πr²

Then we must replace the values and find the result, the formula would look like this:

A = π4²

A=3.14*4²

A=3.14*16

A = 50.24in

According to the above, the area of the circle would be 50.24 in. Additionally, we learned the formula for circle area.

Note: This question is incomplete; here is the missing information:

Find the area of the figure below.

r = 4 in

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The width of a rectangle is 2 units less than the length. The area of the rectangle is 24 square units. The length of the rectangle is 6 units.

Let's denote the length of the rectangle as L and the width as W. According to the given information, the width is 2 units less than the length, so we can express this relationship as:

W = L - 2

The formula for the area of a rectangle is A = L * W, and in this case, the area is given as 24 square units. Substituting the values, we have:

24 = L * (L - 2)

Expanding the equation, we get:

24 = L^2 - 2L

Rearranging the equation and setting it equal to zero, we have:

L^2 - 2L - 24 = 0

We can now factor the quadratic equation:

(L - 6)(L + 4) = 0

Setting each factor equal to zero, we have two possible solutions:

L - 6 = 0 or L + 4 = 0

Solving each equation, we find:

L = 6 or L = -4

Since the length cannot be negative, the length of the rectangle is 6 units.

The length of the rectangle is 6 units.

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The slope of the equation -9x + 3y = 27 is greater and this line has a greater rate of change.

The pace at which one quantity changes in relation to another quantity is known as the rate of change function. Simply said, the rate of change is calculated by dividing the amount of change in one thing by the equal amount of change in another. In the slope-intercept form for a line, the rate of change m for a linear function is written as y=mx+b, whereas the rate of change of functions is defined as (f(b)-f(a))/b-a.

The standard equation of the line is given as:

y = mx + c

where, m is the slope of the line.

For the given equation of lines, transform them into standard equation:

-9x + 3y = 27

3y = 9x + 27

Divide both sides of the equation with 3:

y = 3x + 9

Here, the slope of the equation is 3.

For, -3x + 4y = 24

4y = 3x + 24

Divide both sides of the equation by 4:

y = 3/4x + 6

The slope of this line is 3/4.

Comparing the slope of the two lines we see that,

3 > 3/4

Hence, the slope of the equation -9x + 3y = 27 is greater and this line has a greater rate of change.

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The number of hamburger sold on Tuesday is 136.

On Tuesday, a local hamburger shop sold a combined total of 408

hamburgers and cheeseburgers. The number of cheeseburgers sold was

two times the number of hamburgers sold.

Therefore, the number of hamburger sold on Tuesday can be calculated as follows:

Let

x = number of hamburger

y  =number of cheeseburger

Therefore,

x + y = 408

2x = y

x + 2x = 408

3x = 408

divide both sides by 3

x = 408 / 3

x = 136

Therefore,

number of hamburger = 136

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The multiplicatiοn οf the cοmplex number is 13+19i.

Cοmplex numbers are the numbers that are stated in the fοrm οf a+ib where, a,b are real numbers and I is an imaginary number termed "iοta".

Cοmplex numbers allοw sοlutiοns tο all pοlynοmial equatiοns, even thοse that have nο sοlutiοns in real numbers. Mοre precisely, the fundamental theοrem οf algebra asserts that every nοn-cοnstant pοlynοmial equatiοn with real οr cοmplex cοefficients has a sοlutiοn which is a cοmplex number.

Here the given cοmplex number is ,

=> (7-2i)(1+3i)

Nοw simplifying the expression then,

=> [tex]7\times1+7\times3i-2i \times1 -2i \times3i[/tex]

=> 7+21i-2i-[tex]6i^2[/tex]

=> 7+19i -6(-1) [[tex]i^2=1[/tex]]

=> 7+19i+6

=> 13+19i

Hence the multiplication of cοmplex number is 13+19i.

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Answer:

1872 cards

Step-by-step explanation:

1 cards=52

36×52

=1872 cards

Answer:

5:2

Step-by-step explanation:

5:2

5/2

2.5

4:5

4/5

0/8

Answer:

5:2 is greater

Step-by-step explanation:

a ratio is like a division or fraction, divide 5:2 and 4:5 and you will see that you have 2.5 and 0.8, so 5:2 is greater

$1500

Step-by-step explanation:

if $1000 is equal to 2 parts then .....1 part is given by 1000÷2 =500

so John's share is given by 3x500

1500

The quadratic equation is; x^2 -6x + 8 = 0

A quadratic equation is a mathematical equation of the form ax^2 + bx + c = 0, where x is the unknown variable, and a, b, and c are constants (numbers). The exponent of x in the equation is 2, which means it is a second-degree polynomial equation.

We know that the solution of  x^2- 3x + 2 = 0 is x = 2 and x = 1 hence;

α = 2, β = 1

We have that;

αβ^2 = 2

α^2β = (2)^2(1) = 4

The equation would now be;

x^2 - (2 + 4)x - (2 * 4) = 0

x^2 -6x + 8 = 0

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The length of the arc XY = 6.28yards

The area of shaded part = 12.57yards²

The arc length of a portion of a circle's circumference is the length of the curved line that makes up that portion of the circle. Formula:

Arc length = [tex]\frac{(angle subtended by the arc)}{360}[/tex] × (circumference of the circle)

Area of portion = [tex]\frac{(angle subtended by the arc)}{360}[/tex] × (area of circle)

Part 7: Given that, r = 4yards and Ф = 90°

So, The length of the arc XY = [tex]\frac{90^{o} }{360^{o} }[/tex] × 2π × 4yards = 2π = 6.28yards

The area of shaded part = [tex]\frac{90^{o} }{360^{o} }[/tex] × π × (4yards)² = 4π = 12.57yards²

Part 8: Given that, r = 19ft and Ф = 300°

So, The length of the arc ST = [tex]\frac{300^{o} }{360^{o} }[/tex] × 2π × 19ft = [tex]\frac{95}{3}[/tex]π = 99.48ft

The area of shaded part = [tex]\frac{300^{o} }{360^{o} }[/tex] × π × (19ft)² = [tex]\frac{1805}{6}[/tex]π = 945.09ft²

Part 9: Given that, r = 4inch and Ф = 315°

So, The length of the arc EF = [tex]\frac{315^{o} }{360^{o} }[/tex] × 2π × 4inch = 7π = 21.99inch≅22inch

The area of shaded part = [tex]\frac{315^{o} }{360^{o} }[/tex] × π × (4inch)² = 14π = 43.98inch²

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Answer:

16:24

Step-by-step explanation:

The ratio of boys to girls is 2 : 3

total of the ratio is 5

∴ fraction of the class are boys = 2/5

and  the girls=  3/5

Ratio of boys =( 2/5)×40=16

Ratio of girls=3/5  ×40 =24

The sοlutiοn οf the given prοblem οf unitary methοd cοmes οut tο be  there are 21 pοtential οutcοmes in the sample space.

One may use this cοmmοn cοnvenience, already-existing variables, οr all impοrtant elements frοm the οriginal Bishοp custοmizable questiοn that adhered tο a particular methοd tο achieve the gοal. If sο, there will be anοther chance tο get in tοuch with the οbject. If it dοesn't, all οf the crucial elements that make up an expressiοn prοοf οutcοme will be lοst.

Here,

Using the fοrmula fοr the number οf cοmbinatiοns, we can determine hοw many pοssibilities are pοssible in the sample space:

=> nCk = n!/(k!*(n-k))!

where k is the number οf οbjects being selected, and n denοtes the οverall number οf οbjects in the set.

As there are 7 marbles in the cοntainer, we want tο select 2 οf them, sο n = 7 and k = 2.

the sample space has the fοllοwing amοunt οf οutcοmes that cοuld οccur:

=> 7C2 = 7! / (2! * (7-2)!)

=>  21

Therefοre, when twο marbles are drawn frοm the given bag withοut a replacement, there are 21 pοtential οutcοmes in the sample space.

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Complete Question:

'You draw two marbles without replacement from bag containing three green marbles and four black marbles_ The number of possible outcomes in the sample space is'

Answer: √910 . 0.5 . 0.5= √227.5≈ 15.08.

Step-by-step explanation: The number x of correct guesses in n=910

trials is a binomial random variable with probably p= 0.5 of success. The standard deviation of such a variable is √np(1 -- p ). In this case, that's √910 . 0.5 . 0.5=√227.5≈ 15.08.

Such a variable would be well modeled by a normal distribution with mean np=  910 . 0.5= 455 and standard deviation √222.75 ≈ 15. using the 68-95.99.7 rule-of-thumb , about 68%  of the people who guessed on such a exam would score between 440 and 470, about 95% of such people would  score between 425 and 485, and about 99.7% of such people would score between 410 and 500

Answer:

We can simplify the expression as follows:

4^3 * 4^4 / 4^9

First, we can simplify the terms in the numerator by adding the exponents of 4:

4^3 * 4^4 = 4^(3+4) = 4^7

Now, we can substitute this value in the expression:

4^7 / 4^9

To divide powers with the same base, we can subtract their exponents:

4^(7-9) = 4^(-2)

Therefore, the simplified expression is:

4^3 * 4^4 / 4^9 = 4^(-2)

So, the final answer is 1/16 or 0.0625.

Answer:

the actual food cost is $20,000.

Step-by-step explanation:

To calculate the actual food cost, we need to use the following formula:

Actual Food Cost = Beginning Inventory + Purchases - Ending Inventory + Other Credits

Substituting the given values in the formula, we get:

Actual Food Cost = $12,000 + $20,000 - $14,000 + $2,000

Actual Food Cost = $20,000

Therefore, the actual food cost is $20,000.

In this case, the preferred alternative is Alternative 1, since it has a present value of $60,623.

An investment is the use of money to buy assets or take part in activities with the expectation of a financial gain or other benefit in the future. It can take many forms, such as purchasing shares, bonds, mutual funds, real estate, artwork, or antiques.

The present value of an investment can be calculated by taking the amount of the future cash flow and discounting it by an appropriate rate of return. In this case, the appropriate rate of return is 15%. The present value of Alternative 1 can be calculated by taking the total cash flows of $105,000 and discounting them by 15%:

Present Value of Alternative 1 = $105,000 / (1 + 0.15)3 + (1 + 0.15)7 = $60,623

The present value of Alternative 2 can be calculated in the same manner:

Present Value of Alternative 2 = $8,000 / (1 + 0.15)7 = $4,923

The discounted cash flow criterion states that the preferred alternative is the one with the higher present value. Therefore, in this case, the preferred alternative is Alternative 1, since it has a present value of $60,623 compared to the present value of Alternative 2, which is $4,923.

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Therefore , the solution of the given problem of function comes out to be [-3√x + 3√(x + h)] / h / √x√(x + h).

Every subject will be covered, including created and real locations as well as algebraic variable design, in the midterm test questions. a schematic illustrating the connections between various components that work together to produce the same outcome. A service is made up of many unique parts that work together to produce unique outcomes for each input.

Here,

A function's difference quotient, f(x), is provided by:

=> [f(x+ h) - f(x)] / h

where h denotes a slight modification to the x-value.

The difference quotient for the function f(x) = -3/x can be calculated as follows:

=> [f(x + h) - f(x)] / h

=> [-3/√(x + h) + 3/√x] / h (substituting x + h for x in the function)

=>  [-3√x + 3√(x + h)] / [h√x√(x + h)] (finding a common denominator and combining the terms)

=> [-3√x + 3√(x + h)] / h / √x√(x + h) (dividing by the denominator)

Therefore, the difference quotient of f(x) is:

=> [-3√x + 3√(x + h)] / h / √x√(x + h)

The difference fraction of f(x) is thus:

=> [-3√x + 3√(x + h)] / h / √x√(x + h)

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The value of a in the given parallelogram such that 2a + 27 and 59 are opposite angles is 16

Given the attached parallelogram

Opposite angles in a parallelogram are equal in measure.

This property is known as the "Opposite Angles Property" or "Alternate Angles Property" of a parallelogram.

So, we have

2a + 27 = 59

Evaluating the like terms, we have

2a = 32

Divide both sides by 2

a = 16

Hence, the value of a is 16

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Answer:

Abdul paid $0.50 per pound of rice ($12 divided by 24 pounds).

Answer:16

Step-by-step explanation:

10/p=5/8

can be shown as

1/p=5/80

p=80/5=18

Answer:

[tex]P=16[/tex]

Step-by-step explanation:

Given

[tex]\frac{10}{P} =\frac{5}{8}[/tex]

We can use cross multiplication to find the value of [tex]P[/tex].

Multiply the numerator of the first fraction by the denominator of the second fraction. Set this equal to the product of the denominator of the first fraction and the numerator of the second fraction.

Following these steps we can evaluate [tex]P[/tex].

[tex]10*8=5P[/tex]

Multiply [tex]10[/tex] by [tex]8[/tex].

[tex]80=5P[/tex]

Divide both sides of the equation by [tex]5[/tex]. [tex]P[/tex] cancels out on the right side.

[tex]\frac{80}{5} =\frac{5P}{5}[/tex]

[tex]\frac{80}{5} =P[/tex]

Divide [tex]80[/tex] by [tex]5[/tex].

[tex]16=P[/tex]

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The width of the book cover made by Meals for his brother is 40 cm.

An area is just a surface that is free of objects. With a shape's length and breadth, one may compute the area of the object. Measured in terms of feet (ft), yards (yd), inches (in), etc., length is a one-dimensional quantity. The size of a form, however, is a two-dimensional measurement. Because of this, it is measured in square units like square inches (in2), square feet (ft 2), square yards (yd2), etc. Corners and edges are present on the majority of items and forms. Calculating the area of a certain form takes into account the length and breadth of these edges.

The area of the rectangle is:

A = lw

Given that the area is 890 cm and the height is 22 1/4 cm.

890 = (22 1/4)w

22 1/4 = (4 * 22 + 1) / 4 = 89 / 4

890 = (89 / 4)w

w = 40

Hence, the width of the book cover is 40 cm.

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The complete question is:

Below given are the steps to copy the original triangle using only two of its sides and the included angle.

It is a fundamental geometric shape in mathematics and has many applications in science, engineering, and everyday life. They can be classified based on the lengths of their sides and the measures of their angles.

Using point E as the center, draw a circle with a radius equal to the length of n×CA that was calculated in part B.

Using point E as the vertex, draw a ray DE in the direction of one of the sides of the angle to be copied (in this case, ∠BCA).

Create an angle at point E that is equal to the measure of ∠BCA. To do this, place the point of a compass at point E and adjust the compass to the length of segment CA. Then, draw an arc that intersects both sides of the ray DE. Without changing the width of the compass, place the compass at point C and draw an arc that intersects the previous arc. Draw a line connecting point E to the intersection of the two arcs to create an angle that is equal to ∠BCA.

Draw ray ED' from point E through the intersection of the two arcs.

Locate the intersection of ray ED' and the circle drawn in step 1. Label this point F.

Draw a polygon through points D, E, and F to complete the copied triangle, which is ΔDEF.

The resulting triangle ΔDEF will be a copy of the original triangle, with side EF corresponding to the included angle and sides DE and DF corresponding to the sides used to construct the copy.

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The solution to the system of equations on the graph is (1, 5)

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

The graph

On the graph, we have two lines that intersect at a point

Using the above as a guide, we have the following:

The point of intersection of lines in a graph is the solution to the graph

In this case, they intersect at (1, 5)

So, the solution is (1. 5)

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Complete question

Given the system of equations represented by the graph

What is the solution?