Helppppppppppp me please

The possible expression that can be a rule for the number sequence is:[tex]$a_n = 4n + 1$[/tex],

As an illustration, the expression x + y is one where x and y are words with an addition operator in between. There are two types of expressions in mathematics: numerical expressions, which only comprise numbers, and algebraic expressions, which also include variables.

One possible expression that can be a rule for the number sequence is:

[tex]$a_n = 4n + 1$[/tex], where n is the position of the term in the sequence.

Using this expression, we can find the values of the first few terms as follows:

[tex]$a_1 = 4(1) + 1 = 5$[/tex]

[tex]$a_2 = 4(2) + 1 = 9$[/tex]

[tex]$a_3 = 4(3) + 1 = 13$[/tex]

[tex]$a_4 = 4(4) + 1 = 17$[/tex]

[tex]$a_5 = 4(5) + 1 = 21$[/tex]

Thus, possible expression that can be a rule for the number sequence is:[tex]$a_n = 4n + 1$[/tex],

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Answer:

5n, where n is equal to 0, 1, 2, 3, 4

Step-by-step explanation:

5, 9, 13, 17, 21,

If triangle ABC has points A(2, -4) B(-3, 1) C(-2, -6) and you perform the following transformations, B' would be located at B' (3, 2).

In Geometry, a reflection over or across the y-axis is represented and modeled by this transformation rule (x, y) → (-x, y). This ultimately implies that, a reflection over or across the y-axis would maintain the same y-coordinate (y-axis) while the sign of the x-coordinate (x-axis) would change from positive to negative or negative to positive.

By applying a reflection over the y-axis to the coordinate of the given point B (-3, 1), we have the following coordinates:

Coordinate B = (-3, 1)   →  Coordinate B' = (-(-3), 1) = (-3, 1).

Next, we would apply a rotation of 90° clockwise as follows;

(x, y)                               →            (y, -x)

Coordinate B' = (-3, 1) → Coordinate B' = (1, (-3)) = (1, 3)

Lastly, we would apply a translation (x + 2, y - 1) as follows:

Coordinate B' = (1, 3) → (1 + 2, 3 - 1) = B' (3, 2).

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a) Graph this system of inequalities, we can plot the lines x = 0, y = 0, x = 260, y = 320, and x + y = 380

b) The maximum profit of $5200 achieved.

Selling profit is the profit that a business makes on the sale of its products or services. It is the difference between the selling price and the cost of product.

a) Let x be the number of boards of mahogany sold and y be the number of boards of black walnut sold. Then, the constraints of the problem can be represented by the following system of inequalities:

x ≥ 0 (non-negative constraint)

y ≥ 0 (non-negative constraint)

x ≤ 260 (maximum number of mahogany boards available)

y ≤ 320 (maximum number of black walnut boards available)

x + y ≤ 380 (maximum number of boards that can be sold)

To graph this system of inequalities, we can plot the lines x = 0, y = 0, x = 260, y = 320, and x + y = 380 on a coordinate plane and shade the feasible region that satisfies all of the constraints. The feasible region is the area that is bounded by these lines and includes the origin (0, 0).

b) The profit function P(x, y) can be defined as follows:

P(x, y) = 20x + 6y

To maximize the profit, we need to find the values of x and y that satisfy all of the constraints and maximize the profit function P(x, y).

One way to do this is to use the corner-point method. We can evaluate the profit function at each of the corners of the feasible region and find the corner that gives the maximum profit.

The corners of the feasible region are (0, 0), (0, 320), (260, 0), and (120, 260).

P(0, 0) = 0

P(0, 320) = 6(320) = 1920

P(260, 0) = 20(260) = 5200

P(120, 260) = 20(120) + 6(260) = 4720

Therefore, the maximum profit of $5200 can be achieved by selling 260 boards of mahogany and 0 boards of black walnut.

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First, re-read the problem until you understand it and can put it into your own words.  I re-wrote it like this:  "Find the area of a rectangle by first finding the length (L) and the width (W)."   [note that I added "find L and W," but that is how I'm going to solve the problem;  I could also have said that we will need the formulas, P=2L+2W and A=LW, but you knew that already, right?).

Translate the problem:

 "The length of a rectangle is 3 ft longer than its width"      means

         L                             =    3             +         W                 (eq1)

 "the perimeter of the rectangle is 30 ft"     means

            P                                = 50                      (eq2)

So, now the math is easy, just find L and W so we can compute the area:

     P = 50 = 2L + 2W                         (eq3; from eq2 and the formula for P)

          50 = 2(3+W)  +  2W              (use eq1 to substitute for L)

          50 = 6 + 2W   + 2W              (distribute)

           50 = 6 + 4W                       (collect terms)

            44 = 4W                        (subtract 6 from both sides)

            11 ft = W                        (divide both sides by 4)

Use the easiest equation (either eq1 or else eq3) to find L:

          L = 3 + W        (eq1)

          L = 3 + 11

         L = 14 ft

What is the area (A)?

          A = L*W

          A = (14 ft) x (11 ft)

          A = 154 sq ft

We cannot construct an interval using the normal approximation of survival rate between control and treatment groups because the samples must be random, independent, and their sample sizes must be sufficiently large.

The normal approximation is valid when the sample sizes are large enough to ensure that the sampling distribution of the mean of the variable is approximately normal.

The central limit theorem applies to the distribution of the sample mean when the sample size is large enough, according to the normal approximation.

As a result, the mean difference between the two groups must have a normal distribution. The normal distribution may not be an accurate representation of the underlying distribution of the difference between the two population means in the absence of this requirement, causing the confidence interval to be inaccurate. It will lead to incorrect inferences about the difference in the survival rates of the two groups.

The confidence interval constructed despite this problem will lead to incorrect inferences about the difference in the survival rates of the two groups. This would make it difficult to draw any conclusions based on the findings of this experiment.

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Given:

5× ______ = - 35

• -35/5

• -7

5 x -7 = -35

Answer:

The answer is 7

Step-by-step explanation:

Divide each term in 5x=-35 by 5 and simplify.x=−7

Answer: If you end up with a remainder of 0, then you have a terminating decimal. Otherwise, the remainders will begin to repeat after some point, and you have a repeating decimal.

Step-by-step explanation:

I hope that this helped! :)

Answer:The prices of the adult movie tickets and the child movie tickets are $15 and $5 respectively.

Given that, the Jones family spent $45 on movie tickets for 2 adults and 3 children.

Step-by-step explanation:What is a linear system of equations?

A system of linear equations consists of two or more equations made up of two or more variables such that all equations in the system are considered simultaneously. The solution to a system of linear equations in two variables is any ordered pair that satisfies each equation independently.

Let cost of adult tickets be x and the cost of children tickets be c.

The Jones family spent $45 on movie tickets for 2 adults and 3 children.

2a+3c=45 ------(I)

The Smith family spent $40 for 2 adults and 2 children.

2a+2c=40

a+c=20 ------(II)

From equation (II), we have a=20-c

Substitute a=20-c in equation (I), we get

2(20-c)+3c=45

⇒ 40-2c+3c=45

⇒ c=$5

Put c=5 in equation (II), we get

a+5=20

⇒ a=$15

Julie will have driven a total distance of 289 miles if she travels from York to Corby via Derby.

Starting from York, Julie needs to travel to Derby. The distance between York and Derby is given as 89 miles. So, we know that Julie will have driven 89 miles once she reaches Derby.

Next, Julie needs to travel from Derby to Corby, but the given information is a bit tricky here. The distance from Derby to Corby is not given directly. Instead, we are given two distances - Derby to Dory and Dory to Corby.

To find the distance from Derby to Corby, we need to add the distances between Derby and Dory, and Dory and Corby. From the question, we know that the distance between Derby and Dory is 127 miles and the distance between Dory and Corby is 73 miles. Adding these two distances gives us the total distance from Derby to Corby, which is 200 miles.

Finally, we can add up the distances traveled between each location to find the total distance traveled by Julie. Adding the distances of each leg of the journey, we get:

89 miles (York to Derby) + 200 miles (Derby to Corby via Dory) = 289 miles

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Complete Question:

If Julie drives from York to Corby via Dory how many miles will she have driven?

York 89

Derby 127 73

Corby

Answer:30

Step-by-step explanation: the formula is base x height over 2, so (6x10)/2 is 30.

Answer:

Tank 1: 6 litres

Tank 2: 6.75 litres

Tank 3: 4.5 litres

Step-by-step explanation:

Initially, James had 18 litres of water, and he poured three-quarters of it from tank 1 into tank 2. This means that the volume of water left in tank 1 is:

18 - (3/4) * 18 = 4.5 litres

The volume of water in tank 2 is:

(3/4) * 18 = 13.5 litres

Next, he poured half of the water in tank 2 (which is now 13.5 litres) into tank 3. The volume of water left in tank 2 is:

(1/2) * 13.5 = 6.75 litres

The volume of water in tank 3 is:

13.5 * (1/2) = 6.75 litres

Finally, he poured one-third of the water in tank 3 (which is now 6.75 litres) into tank 1. The volume of water in tank 1 after this is:

4.5 + (1/3) * 6.75 = 6 litres

The volume of water in tank 3 after this is:

6.75 * (2/3) = 4.5 litres

So the final volume of water in each tank is:

Tank 1: 6 litres

Tank 2: 6.75 litres

Tank 3: 4.5 litres

Answer:

n(s) =52. n(f) = 12 n(h) = 13

p (f)= 13/52. p(f)= 12/52

Answer:

30,000 grams

Step-by-step explanation:

multiply the 30KG by 1,000 (that is the conversion) and you get 30,000g

Answer:

hi I'm really sorry I can't help

The area is changing at a rate of 28,160 m²/year at that point in time.

The area of the rectangular region is given by:

A = lw

Where l is the length of the rectangular region and w is the width of the rectangular region.

The width of the rectangular region is given to be 220 m. Therefore, we have the width w = 220 m. The length l of the rectangular region can be found knowing that it is twice as long as it is wide. Therefore, the length of the rectangular region is given by:

l = 2w

l = 2 x 220

l = 440

Therefore, the length l of the rectangular region is 440 m.

At the given point in time, the width of the rectangular region is growing at a rate of 32 m per year. Therefore, we have the rate of change of the width dw/dt to be 32 m per year. We need to find how fast the area of the rectangular region is changing at that point in time. Therefore, we need to find the rate of change of the area of the rectangular region dA/dt.

A = lw

dA/dt = w dl/dt + l dw/dt

dA/dt = 220 d/dt(2w) + 440 dw/dt

dA/dt = 220 x 2 dw/dt + 440 dw/dt

dA/dt = 880 dw/dt

Substitute the value of dw/dt to get:

dA/dt = 880 x 32

dA/dt = 28,160 m²/year

Therefore, the area of the rectangular region has a rate of change of 28,160 m² per year at that point in time.

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If the set of expressions represents measures of the sides of a triangle x, 4, 6 , the range of possible measures of x is 2 < x < 10.

To determine the range of possible measures of X if the set of expressions represents measures of the sides of a triangle x, 4, 6, we need to use the triangle inequality theorem. According to this theorem, in a triangle, the sum of the lengths of any two sides must be greater than the length of the third side.

Mathematically, this can be expressed as:

x + 4 > 6

x + 6 > 4

4 + 6 > x

Simplifying these inequalities, we get:

x > 2

x > -2

x < 10

The first two inequalities indicate that x must be greater than 2, since the sum of any two sides of a triangle must be greater than the third side. The third inequality indicates that x must be less than 10, since the longest side of a triangle cannot be greater than the sum of the other two sides.

This means that x can take any value between 2 and 10, but not including 2 or 10, in order for the set of expressions to represent the measures of the sides of a triangle.

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Answer:

105 degrees

Step-by-step explanation:

sum of angles in triangle is 180 degrees

11x-5+6x+5+x = 180

simplify this to get 18x=180

180/18 = 10 = x

plug in 10 for x

11(10) - 5

110-5

105

Answer: 0.04

Step-by-step explanation:

In order to get 4% as a decimal, you must divide 4 by 100.

4/100 = 0.04

Thus, the answer to your question is 0.04

Answer:I=(PxRxT)/100

I=(10000x20x1)/100x2

I=200000/200

I=1000

Step-by-step explanation:

The nearest hundredth, we get:

C ≈ 12.56 feet.

Circle circumference (or perimeter) = 2R

where R denotes the circle's radius. 3.14 is the approximate (up to two decimal points) value of the mathematical constant. Again, Pi () is a special mathematical constant that represents the circumference to diameter ratio of any circle.

The circumference of a circle is calculated as follows:

C = 2πr

where C is the circumference, (pi) is a constant close to 3.14, and r is the radius of the circle.

When the given values are substituted, the following results are obtained:

C = 2(3.14)(2) \s= 12.56

We get the following when we round to the nearest hundredth:

C ≈ 12.56 feet.

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The standard form of a conic section represented by r = 6/(cos x + 3sin x) is  r^2 = 6(x + 3y) and the represented equation is a line.

The equation r = 6/(cos x + 3sin x) is in polar form, where r represents the distance from the origin to a point (x, y) in the plane, and x is the angle that the line connecting the origin to (x, y) makes with the positive x-axis. To determine the standard form of the conic represented by this equation, we need to convert it to Cartesian coordinates.

Using the trigonometric identity cos x = x/r and sin x = y/r, we can rewrite the equation as:

r = 6/(x/r + 3y/r)

Multiplying both sides by r, we get:

r^2 = 6(x + 3y)

This is the standard form of a conic section in Cartesian coordinates, namely an equation of a line. Therefore, the conic represented by the equation r = 6/(cos x + 3sin x) is a line in the Cartesian coordinate system.

In summary, to determine the standard form of a conic represented by an equation given in polar form, we can use trigonometric identities to rewrite it in Cartesian coordinates.

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Therefore, the initial value of the function is $1,852 and the rate of change is $12.18 per shirt. The initial value represents the cost of the shirts before any were purchased,

In mathematics, a function is a rule that assigns to each element in a set called the domain, a unique element in another set called the range. In other words, a function is a mathematical object that takes an input and produces a specific output, according to a specific set of rules or operations.

by the question.

et the initial value be represented by a and the rate of change by r.

The given information can be represented by the following equation:

a + 150r = 1,852

Since the flat-rate shipping cost is $25, the cost of the 150 shirts alone would be:

a + 150r - 25 = 1,827

The initial value, a, represents the cost of the shirts before any shirts were purchased. In this case, it would be the cost of the shirts if no shirts were purchased plus the flat-rate shipping cost of $25.

So, a = 1,827 + 25 = 1,852.

The rate of change, r, represents the increase in cost for each additional shirt purchased. In this case, it would be the cost of one shirt.

So, r = (1,852 - 25)/150 = 12.18.

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P(∅) = 0, P(A∪B) = 0.4 , P(A∩B) = 0.1 ,Since the sample space is not defined in the question, we cannot calculate P(B'). Therefore, we cannot calculate P(A∩B').and  P(A∪B) = 0.4. are the required solutions ofgiven probability check .

a. The probability of an empty set is always zero. Therefore, P(∅) = 0.

b. The probability of the union of two events, A and B, is given by the formula P(A∪B) = P(A) + P(B) - P(A∩B). Substituting the values given in the question, we get:

P(A∪B) = P(A) + P(B) - P(A∩B)

= 0.3 + 0.2 - 0.1

= 0.4

Therefore, P(A∪B) = 0.4.

c. The probability of the intersection of A and B is given by the formula P(A∩B). Substituting the values given in the question, we get:

P(A∩B) = 0.1

Therefore, P(A∩B) = 0.1.

d. The probability of the intersection of A and the complement of B is given by the formula P(A∩B'). The complement of B is the set of all outcomes that are not in B. Since the sample space is not defined in the question, we cannot calculate P(B'). Therefore, we cannot calculate P(A∩B').

e. The probability of the union of A and B is given by the formula P(A∪B). Substituting the values given in the question, we get:

P(A∪B) = P(A) + P(B) - P(A∩B)

= 0.3 + 0.2 - 0.1

= 0.4

Therefore, P(A∪B) = 0.4.

In probability theory, the union of two events A and B is the set of outcomes that belong to either A or B or both. The intersection of two events A and B is the set of outcomes that belong to both A and B. The complement of an event A is the set of outcomes that do not belong to A. These concepts are fundamental in probability theory and are used extensively in solving various problems.

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a. Hence proved that the sum of fractions  [tex]${\frac{1}{\sqrt{1+\sqrt{2}}}}+{\frac{1}{\sqrt{2+\sqrt{3}}}}+{\frac{1}{\sqrt{3}+\sqrt{4}}}=1$[/tex]

b. The value will be 7 for the expression

⇒ [tex]${\frac{ 1-\sqrt{2}}{-1}+{\frac{ \sqrt{2}-\sqrt{3}}{-1}+ \cdot \cdot \cdot+{\frac{\sqrt{63}-8}{-1}}$[/tex]

Square rοοt οf a number is a value, which οn multiplicatiοn by itself, gives the οriginal number. The square rοοt is an inverse methοd οf squaring a number. Hence, squares and square rοοts are related cοncepts.

Suppοse x is the square rοοt οf y, then it is represented as x=√y, οr we can express the same equatiοn as x² = y. Here, ‘√’ is the radical symbοl used tο represent the rοοt οf numbers. The pοsitive number, when multiplied by itself, represents the square οf the number. The square rοοt οf the square οf a pοsitive number gives the οriginal number.

Here,

a. [tex]${\frac{1}{\sqrt{1+\sqrt{2}}}}+{\frac{1}{\sqrt{2+\sqrt{3}}}}+{\frac{1}{\sqrt{3}+\sqrt{4}}}=1$[/tex]

Using (a + b)(a - b) = a² - b²

⇒ [tex]${\frac{1 \cdot \sqrt{1}-\sqrt{2}}{\sqrt{1}+\sqrt{2}\cdot \sqrt{1 }-\sqrt{2}}+{\frac{1 \cdot \sqrt{2}-\sqrt{3}}{\sqrt{2}+\sqrt{3}\cdot \sqrt{1}-\sqrt{2}}}+{\frac{1 \cdot \sqrt{3}-\sqrt{4}}{\sqrt{3}+\sqrt{4}\cdot \sqrt{3}-\sqrt{4}}}$[/tex]

⇒ [tex]${\frac{ \sqrt{1}-\sqrt{2}}{1-2}+{\frac{ \sqrt{2}-\sqrt{3}}{2-3}+{\frac{\sqrt{3}-\sqrt{4}}{3-4}}$[/tex]

⇒ [tex]${\frac{ \sqrt{1}-\sqrt{2}}{-1}+{\frac{ \sqrt{2}-\sqrt{3}}{-1}+{\frac{\sqrt{3}-\sqrt{4}}{-1}}$[/tex]

⇒ [tex]${\frac{ 1-\sqrt{2}}{-1}+{\frac{ \sqrt{2}-\sqrt{3}}{-1}+{\frac{\sqrt{3}-2}{-1}}$[/tex]

⇒ [tex]${\frac{ 1-\sqrt{2}}{-1}+{\frac{ \sqrt{2}-\sqrt{3}}{-1}+{\frac{\sqrt{3}-2}{-1}}$[/tex]

⇒ [tex]$ -1+\sqrt{2}}- \sqrt{2}+\sqrt{3}}-{\sqrt{3}+2}$[/tex]

⇒ [tex]$ -1+2}$[/tex]

⇒ 1

a. Hence proved that the sum of fractions  [tex]${\frac{1}{\sqrt{1+\sqrt{2}}}}+{\frac{1}{\sqrt{2+\sqrt{3}}}}+{\frac{1}{\sqrt{3}+\sqrt{4}}}=1$[/tex]

B. This will be done with the same process,

⇒ [tex]${\frac{ 1-\sqrt{2}}{-1}+{\frac{ \sqrt{2}-\sqrt{3}}{-1}+ \cdot \cdot \cdot+{\frac{\sqrt{63}-8}{-1}}$[/tex]

⇒ [tex]${\frac{ 1-\sqrt{2}}{-1}+{\frac{ \sqrt{2}-\sqrt{3}}{-1}+ \cdot \cdot \cdot+{\frac{\sqrt{63}-8}{-1}}$[/tex]

⇒ [tex]$ -1+\sqrt{2}}- \sqrt{2}+\sqrt{3}} \cdot \cdot \cdot -{\sqrt{63}+8}$[/tex]

There, will be same roots of every number until - 8

So,

⇒ [tex]$ -1+8}$[/tex]

= 7

b. The value will be 7 for the expression

⇒ [tex]${\frac{ 1-\sqrt{2}}{-1}+{\frac{ \sqrt{2}-\sqrt{3}}{-1}+ \cdot \cdot \cdot+{\frac{\sqrt{63}-8}{-1}}$[/tex]

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The equatiοn is [tex]t = (-20 \± \sqrt{(400 - 4(-5)(-18))}) / 2(-5)[/tex]  tο sοlve fοr the time it takes fοr the οbject tο be at a height οf 18 feet.

Trigοnοmetric equatiοns are equatiοns that invοlve trigοnοmetric functiοns such as sine, cοsine, tangent, etc. These equatiοns usually invοlve finding values οf the unknοwn angle(s) that satisfy the given equatiοn. They can be sοlved using algebraic techniques οr by using the prοperties οf trigοnοmetric functiοns.

Accοrding tο the given infοrmatiοn:

The given functiοn is [tex]f(t) = -5t^2 + 20t[/tex], which mοdels the height οf an οbject in feet as a functiοn οf time in secοnds.

Tο find the number οf secοnds it will take fοr the οbject tο be at a height οf 18 feet after launch, we need tο sοlve the equatiοn [tex]-5t^2 + 20t = 18[/tex].

Tο sοlve this quadratic equatiοn using the quadratic fοrmula, we first identify the values οf a, b, and c frοm the general fοrm οf a quadratic equatiοn, [tex]ax^2 + bx + c = 0[/tex].

In this case, a = -5, b = 20, and c = -18. Substituting these values intο the quadratic fοrmula, we get:

[tex]t = (-b\± \sqrt{(b^2 - 4ac)}) / 2a[/tex]

Plugging in the values οf a, b, and c, we get:

[tex]t = (-20 \± \sqrt{+(20^2 - 4(-5)(-18)})) / 2(-5)[/tex]

Simplifying this expressiοn, we get:

[tex]t = (-20 \± \sqrt{(400 - 360))} / (-10)[/tex]

[tex]t = (-20\± \sqrt{(40)}) / (-10)[/tex]

[tex]t = (-20 \± 2\sqrt{(10)}) / (-10)[/tex]

[tex]t = 2 \± 0.632[/tex]

Therefοre, the twο pοssible values οf t are:

t = 2 + 0.632 = 2.632 secοnds

t = 2 - 0.632 = 1.368 secοnds

Therefοre, the equatiοn that cοrrectly shοws the quadratic fοrmula being used tο determine the number οf secοnds it will take fοr the οbject tο be at a height οf 18 feet after launch is:

[tex]t = (-b\± \sqrt{(b^2 - 4ac)}) / 2a[/tex]

[tex]t = (-20 \± \sqrt{(20^2 - 4(-5)(-18))}) / 2(-5)[/tex]

[tex]t = (-20\± \sqrt{(40)}) / (-10)[/tex]

[tex]t = (-20 \± 2\sqrt{(10)}) / (-10)[/tex]

t = 2 ± 0.632

Therefοre, the equatiοn is [tex]t = (-20 \± \sqrt{(400 - 4(-5)(-18))}) / 2(-5)[/tex] tο sοlve fοr the time it takes fοr the οbject tο be at a height οf 18 feet.

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By answering the presented question, we may conclude that I used the following procedures to produce this graph.

Mathematicians use graphs to visually display or chart facts or values in order to express them coherently. A graph point usually represents a connection between two or more items. A graph, a non-linear data structure, is made up of nodes (or vertices) and edges. Glue the nodes, also known as vertices, together. This graph contains vertices V=1, 2, 3, 5, and edges E=1, 2, 1, 3, 2, 4, and (2.5), (3.5). (4.5). Statistical graphs (bar graphs, pie graphs, line graphs, and so on) are graphical representations of exponential development. a logarithmic graph shaped like a triangle.

I used the following procedures to produce this graph:

I classified the personnel as full-time, part-time, and temporary.

I estimated the proportion of employees who assessed the company's work-life balance as "very good" or "excellent" for each employee category, as well as the percentage who rated it as "good" or "fair/poor."

I used the following procedures to produce this graph:

I classified the personnel as full-time, part-time, and temporary.

I estimated the proportion of employees who assessed the company's work-life balance as "very good" or "excellent" for each employee category, as well as the percentage who rated it as "good" or "fair/poor."

I made the segmented bar graph using these percentages.

The graph was made using Excel technology. You may make a similar graph with Excel or any other software that supports segmented bar graphs.

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using the ratio given, the number of computers could be sold by the company last week is: A. 448 desktops, 168 laptops.

To find the actual numbers of desktop and laptop computers sold, we need to choose a common factor for the ratio 8:3.

Let's assume that the total number of computers sold is 33x (where x is a positive integer). Then, the ratio 8:3 corresponds to 8x desktops and 3x laptops. We can check which of the given options satisfies this condition:

A. 8x = 448, 3x = 168 --> This satisfies the condition, as 8:3 = 448:168

B. 8x = 448, 3x = 165 --> This does not satisfy the condition, as 8:3 is not equal to 448:165

C. 8x = 440, 3x = 168 --> This does not satisfy the condition, as 8:3 is not equal to 440:168

D. 8x = 400, 3x = 165 --> This does not satisfy the condition, as 8:3 is not equal to 400:165

Therefore, the answer is option A: 448 desktops and 168 laptops could be the numbers of computers sold by the company last week.

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The matrix A does not eigenvector v corresponding to the given eigen value.

λ.A = [ -11  60 ]

v = [ 1   3λ ]

v is an eigenvector of A calculate corresponding eigenvalue,

A × v = λ × v

where A is the given matrix.

v is the given vector.

λ is the corresponding eigenvalue.

× denotes matrix multiplication.

Let's first calculate A × v we have,

A × v

= [-11 60] × [ 1 3λ]

= [-11-33λ    60+ 180λ]

Check A× v is equal to λ × v ,

λ × v =

λ × [ 1 3λ]

= [λ  3λ^2]

Set these two vectors equal to each other and get the following system of equations ,

-11-33λ = λ  __(1)

60+ 180λ = 3λ^2  ___(2)

From equation (1) we get,

⇒34λ = -11

⇒ λ = -11/34

Substituting this value of λ into the second equation, we have,

60+ 180λ = 3λ^2

⇒ 60 + 180(-11/34) = 3(-11/34)^2

⇒ (2040 -1980)/ 34 = 3(-11/34)^2

⇒ 60/34 = 3( 11/34)^2

⇒ 60 × 34 = 3 × 11 × 11

⇒20× 34 = 11 × 11

Which is not true.

so the value of λ does not satisfies both equations.

Therefore, v is not an eigenvector of A with corresponding eigenvalue λ.

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The above question is incomplete, the complete question is:

Check whether v is an eigen vector of A  if yes find the corresponding eigen value.

λ.A = [ -11  60 ]

v = [ 1   3λ ]

The discount percentage is different, the amount that Lisa pays will also be different.

The act of estimating the present value of a future payment or series of cash flows that will be received in the future is referred to as discounting. A discount rate (also known as a discount yield) is the rate at which future cash flows are discounted back to their present value.

We need to know what percentage of the regular ticket price Lisa saves with her railcard. We cannot calculate the exact amount Lisa pays for the ticket without this information.

Assuming Lisa receives a 1/3 discount with her railcard, we can calculate the cost of her ticket as follows:

Discounted price = Regular price minus discount amount

Normal price x Discount percentage = Discount amount

Discount rate = 1/3 = 33.33% (rounded to two decimal places)

Discount amount = £24.90 multiplied by 33.33% = £8.30 (rounded to two decimal places)

Price after discount = £24.90 - £8.30 = £16.60 (rounded to two decimal places)

As a result, if Lisa receives a 1/3 discount with her railcard, she will pay£16.60 for the ticket. However, if the discount percentage is different, Lisa's payment will be different as well.

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Lisa uses her railcard to buy a ticket.

She gets off the normal price of the ticket.

The normal price of the ticket is £24.90

Work out how much Lisa pays for the ticket.

216 cm2 is the size of the rectangle border.

the translation of the question is

A painting including its frame is 25 cm long and 10 cm wide, what is the area of ​​the frame if it is 4 cm wide?

What is a rectangle's area?

When the dimensions of a rectangle with length and width are multiplied, the area of the rectangle is determined as follows:

A = lw.

The total area is therefore given by:

A = 25 x 10 = 250 cm².

The white region's size is shown by:

A = (25 - 2 x 4) x (10 - 2 x 4) is equal to 17x 2 and 34 cm2.

Hence, the border's area is as follows:

216 cm2 = 250 cm2 - 34 cm2.

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The scientific and standard notation and clue obtained from the clue sheet are;

1. Name starts with; J

2. Difference = 145 million miles = Weight = 145 lbs

3. Height: 5 ft, 6 in

4. I. 2.54 × 10⁸ miles corresponding to letter I

II. 0.0005825 corresponds to letter G

III. 5.0432 × 10⁶ corresponds to letter N

IV. 1.547 × 10³ corresponds to letter R

V. 4.977 × 10⁻² corresponds to letter W

VI. 1.3 × 10¹⁰ light years away; corresponds to letter D

VII. 5.04 × 10⁻⁵ corresponds to letter A

The suspects hubby is DRAWING

Scientific notation is a format used to express very large or very small numbers such that they are much easier to work with. The scientific notation format is; a × 10ⁿ, where; a is the coefficient, which is a number between 1 and 10 (10 excluded), and n is an integer.

1. G = (6.07 × 10⁷)/(7.035 × 10³) ≈ 8628.29

J = (6.03 × 10⁻³)/(5.05 × 10⁻⁷) ≈ 11940.59

Therefore; J > G

The suspects name starts with J

2. The distance the telescope in the laboratory allows the viewer to see = 1.5 × 10⁹ miles away

The distance the other telescope a few hours away allows the viewer to see = 1.355 × 10⁹ miles away

The difference between the distances = (1.5 - 1.355) × 10⁹ miles = 1.45 × 10⁸ miles

The difference in the distance is 1.45 × 10⁸ miles = 145 million miles

The suspect weight is 145 lbs

3. The numbers are;

Feet; 532.063 × 10³ = 5.32063 × 10⁵

Inches; 5,030,045 = 5.030045 × 10⁶

The height of the suspect is 5 feet 6 inches (5'6'') = 5.5 feet

Height; = 5 ft, 6 in

4. I. The difference in distances between Earth and Saturn can be found as follows;

The difference in the distances = (1000 - 746) million miles = 254 million miles apart

Scientific notation is the expression of numbers in the form consisting of a number between 1 and 10, multiplied by 10 raised to a power

254 million miles = 2.54 × 10⁸ miles

The corresponding letter from the code cracker is; I

II Standard notation is the expression of numbers in the standard form without the use of exponents or special symbols

The number 5.825 × 10⁻⁴ in standard notation is; 0.0005825

The corresponding letter from the code cracker is; G

III. The number 504.32 × 10⁴ in scientific notation can be obtained by moving the decimal point two places to the left followed by increasing the index of 10 by 2 as follows;

504.32 × 10⁴ = 5.0432 × 10⁶

The corresponding letter from the code cracker is; N

IV. The sum of the numbers 1.202 × 10³ and 3.45 × 10² can be obtained by expressing both numbers to the same power of 10 as follows;

1.202 × 10³ + 3.45 × 10² = 12.02 × 10² + 3.45 × 10² = 15.47 × 10²

15.47 × 10² = 1.547 × 10³

Therefore; 1.202 × 10³ + 3.45 × 10² = 1.547 × 10³

The corresponding letter from the code cracker is; R

V. The difference of the numbers can be obtained as follows;

5.023 × 10⁻² - 4.6 × 10⁻⁴ = 502.3 × 10⁻⁴ - 4.6 × 10⁻⁴ = 497.7 × 10⁻⁴

497.7 × 10⁻⁴ = 4.977 × 10⁻²

Therefore; 5.023 × 10⁻² - 4.6 × 10⁻⁴ = 4.977 × 10⁻²

The corresponding letter from the code cracker is; W

VI. 13 billion light years = 13 × 10⁹ light years = 1.3 × 10¹⁰ light years

The distance a standard telescope can allow to be seen is 1.3 × 10¹⁰ light years away

The corresponding letter from the code cracker is; D

VII. 0.0000504 in scientific notation is; 5.04 × 10⁻⁵

The corresponding letter from the code cracker is; A

IGNRWDA

The suspects favorite hubby is DRAWING

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