Se consideran los vectores u (-3,2) y v (5,1). Calcula gráficamente y utilizando las coordenadas del vector w= 2u – v

1287 combinations are a way to calculate the total outcomes of an event where order of the outcomes does not matter.

You win the jackpot if you match all six numbers. You receive a lesser fixed prize if you partially match some of the numbers.

Divide the number of winning lottery numbers by the total number of available lottery numbers to discover the probability of winning any lottery. Use the formula if the numbers are picked from a set and the order of the numbers is unimportant.

To find the winning combination we use the following formula

n !/ r!( n – r ) !

Where n = total number of to be drawn

r = the number which are drawn

In this question, n = 13, and r = 5

from the formula

13 !/5!( 13 – 5 ) !

= 13! / 5! 8!

= 13*12*11*10*9*8! / 5*4*3*2*1*8!

= 154,440 / 120

= 1287

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The linear function expressed by the table is y = -1x + 4.

What is a linear function?

A linear function is a type of mathematical function that represents a linear relationship between two variables, often represented by x and y. The general form of a linear function is y = mx + b, where m is the slope of the line and b is the y-intercept (the point at which the line crosses the y-axis). Linear functions are also called lines.

To find the equation of the line from a table of values, you can use the slope-intercept form, y = mx + b

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

In order to find the slope 'm' we use the following formula:

m = (change in y)/(change in x) = (y2 - y1) / (x2 - x1)

Here,

m = (-2 - 2) / (2 - (-2)) = (-4)/4 = -1

The slope is -1, which means that for every one-unit increase in x there's a corresponding one-unit decrease in y.

To find the y-intercept, you can use one of the points from the table and substitute the x and y values into the equation

y = mx + b

So now we know that m = -1,

plugging the first point (x,y) = (-2,2) in the equation

2 = -2 - b

b = 4

So the equation of the line is y = -1x + 4

Hence, the linear function expressed by the table is y = -1x + 4.

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The provided expression can be simplified in the form 2y4/x4 option ( B) Using the integer exponent characteristics,  = [x[tex]^\frac{1}{8}[/tex] . y⁸]  is the right answer.

In mathematics, integer exponents are exponents that fall under the integer category. It's possible for the number to be either positive or undesirable. The positive integer exponents in this example dictate how many times that base number must be multiplied by itself.

It's possible for the number to be either positive or undesirable. The positive integer exponents in this example dictate how many instances the base number must be multiplied by itself.

= [x[tex]^\frac{1}{4}[/tex] . y¹⁶][tex]^\frac{1}{2}[/tex]

= [x[tex]^\frac{1}{8}[/tex] . y⁸]

The provided expression can be simplified in the form 2y4/x4 option ( B) Using the integer exponent characteristics,  = [x[tex]^\frac{1}{8}[/tex] . y⁸]  is the right answer.

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Answer:

The answer is 11

Step-by-step explanation:

The answer is 11 because you need to add the sides up that the points are on point P is 5 Point Q is 3 and point R is 3 5+3 is 8 8+3 is 11

Answer:

19.56

Step-by-step explanation:

PR = [tex]\sqrt{3^{2} + 3^{2} }[/tex] = [tex]\sqrt{18}[/tex] = 3[tex]\sqrt{2}[/tex]

RQ = [tex]\sqrt{5^{2} +5^{2} }[/tex] = [tex]\sqrt{50}[/tex] = 5[tex]\sqrt{2}[/tex]

QP = [tex]\sqrt{8^{2} +2^{2} }[/tex] = [tex]\sqrt{68}[/tex] = 2[tex]\sqrt{17}[/tex]

Perimeter = sum of the sides = 3[tex]\sqrt{2}[/tex] +  5[tex]\sqrt{2}[/tex] +  2[tex]\sqrt{17}[/tex] = 19.56

Break the triangle PQR into 3 right triangles, with each leg being a hypotenuse.  Then you can use the Pythagorean theorem to find the length of each leg.  Add them all together to get the perimeter.

In essence, a perfect square is produced when two equal integers are multiplied by one another.

Squaring an integer produces perfect squares. For instance, the number 81 is a perfect square since it can be calculated by squaring 9: 99=81. Due to the fact that 12 is squared to produce 144, 144 is a perfect square. Because 13 is squared to produce 169, 169 is a perfect square. Language of Mathematics. Informally: The result is known as a square number, a perfect square, or simply "a square" when an integer (a "whole" number), whether positive, negative, or zero, is multiplied by itself. So all square numbers are 0, 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, and so forth.

given

In essence, a perfect square is produced when two equal integers are multiplied by one another.

Due to the fact that you are multiplying two equal integers (5 and 5) by one another, 25, it is a perfect square. The result of a number being multiplied by itself is referred to as the square of the number.

In the case when m and n are both natural numbers, m is a perfect square if m = n2. A perfect square is produced when two perfect squares are added together.

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Response is $6.40, a proportion is the relationship or equivalence between two ratios or fractions.

While the denominator of a percentage is always 100, a proportion is the relationship or equivalence between two ratios or fractions. Both proportion and percentage can be expressed as fractions.

A percentage is an equation in which two ratios are made equal to one another.

Out of a possible 100, the percentage is given.

Because 32 ounces is the difference between 128 and 96, making it 1/3 of 96, we can divide $4.80 by 3 to get $1.60, then add $1.60 to $4.80 to get $6.40.

Response is $6.40, a proportion is the relationship or equivalence between two ratios or fractions.

The complete question is,

It cost $4.80 for a 96-ounce bottle of orange juice. How much should be charged for a 128-ounce container in order to equalize the unit rates of the two sizes? Describe your thought process.

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Hence proved that FG = IJ with CPCT theorem for ΔGHF ≅ ΔJHI by SAS Congruency rule.

Triangle congruence: Two triangles are deemed to be congruent if all three of their corresponding sides and angles have the same magnitude. Slides, rotations, flips, and turns can be used to make these triangles appear identical. They would be in alignment if they were moved. Congruence is represented by the letter "≅".

When two figures are similar to one another in terms of their size and shape, this is what mathematicians mean by congruence. It can be demonstrated that two triangles are congruent using four congruence rules in general. Finding all six dimensions is necessary, though.

Given that,

GH ≅ JH

FH ≅ HI

And,

∠GHF = ∠JHI

Therefore,

ΔGHF ≅ ΔJHI (SAS Congruency)

∴ FG = IJ (CPCT theorem)

Hence proved that FG = IJ with CPCT theorem for ΔGHF ≅ ΔJHI by SAS Congruency rule.

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The numerical coefficient of xy in the given expression -7xy is -7.

The numerical coefficient of an expression is a number that is multiplied by a variable or a product of variables. The coefficient is the number that appears in front of a variable or a product of variables. In the case of a constant term, the coefficient is the constant itself.

For example, in the expression 3[tex]x^2[/tex] + 4x - 5, the numerical coefficient of [tex]x^2[/tex] is 3, the numerical coefficient of x is 4, and the numerical coefficient of the constant term -5 is -5.

Here, in the expression -7xy, the numerical coefficient of xy is -7.

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The complete question is -

What is the coefficient of XY in the expression - 7xyz?

The solution to the system of equations is x = 4 and y = 5.

3x + 2y = 7

y = 3x - 11

Substitute 3x - 11 for y in the first equation:

3x + 2(3x - 11) = 7

Simplify:

3x + 6x - 22 = 7

Combine like terms:

9x - 22 = 7

Add 22 to both sides:

9x = 29

Divide both sides by 9:

x = 29/9

x = 4

Change x in the second equation to 4:

y = 3(4) - 11

Simplify:

y = 12 - 11

y = 1

The solution to the system of equations is x = 4 and y = 1.

The solution to the system of equations 3x + 2y = 7 and y = 3x - 11 is x = 4 and y = 1. To solve this system, we first substituted 3x - 11 for y in the first equation. We then simplified the equation and combined like terms to get 9x - 22 = 7. We then added 22 to both sides, divided both sides by 9, and got x = 29/9 which is x = 4. We then substituted 4 for x in the second equation, simplified, and got y = 1. Thus, the solution to the system of equations is x = 4 and y = 1.

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Answer: 7

Step-by-step explanation:

There are 60 different ways of choosing a meal for this wedding.

There were five distinct main courses available for selection.

There are a total of 15 possible main dish and salad combinations when ordering these 5 distinct main meals together with any one of the 3 available salads.

A total of 60 distinct main dishes, salads, and dessert combinations are conceivable by ordering one of the four potential deserts for each of the 15 various main meals and salad combinations.

60 distinct main dishes might be purchased since.

There are 60 different ways of choosing a meal for this wedding

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Answer:

y = [tex]\frac{1}{3}[/tex] x - 6

Step-by-step explanation:

9y - 3x = -54

We want in the form

y = mx + b

9y - 3x = -54  Add 3x to both sides

9y - 3x + 3x =  3x - 54

9y = 3x - 54   Divide all the way through by 9

[tex]\frac{9y}{9}[/tex] = [tex]\frac{3x}{9}[/tex] - [tex]\frac{54}{9}[/tex]

y = [tex]\frac{3}{9}[/tex] x - 6

We can simplify [tex]\frac{3}{9}[/tex] ÷ [tex]\frac{3}{3}[/tex] = [tex]\frac{1}{3}[/tex]

y = [tex]\frac{1}{3}[/tex] x - 6

The solution to the system of linear equations 3x + 2y = 14 and 5x + y = 32 is (x, y) = (6, 10).

3x + 2y = 14

5x + y = 32

Subtracting 3x from both sides of the first equation:

2y = 14 - 3x

Substituting this into the second equation:

5x + (14 - 3x) = 32

Simplifying:

8x = 18

x = 18/8

x = 2.25

This x value is substituted into the first equation.:

2y = 14 - 3(2.25)

2y = 14 - 6.75y

= 7.25

The solution is (x, y) = (2.25, 7.25)

The solution to the system of linear equations 3x + 2y = 14 and 5x + y = 32 is (x, y) = (2.25, 7.25). To solve the system, we first subtracted 3x from both sides of the first equation and then substituted this into the second equation. After simplifying, we obtained a value of x, which we then substituted into the first equation to obtain a value of y. This gave us the solution (x, y) = (2.25, 7.25).

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Answer:

Step-by-step explanation:

Let the costs of 1 t - shirt and 1 pair of pants be 'x' and 'y' respectively then:

Case 1 --> 8x + 5y = 220 ----------(1)

Case 2 --> 5x + y = 112 ----------(2)

Multiplying equation (2) by 5:

8x + 5y = 220

25x + 5y = 560 ------(3)

Subtracting equation (1) from equation (3) we get :

17x = 340

x = 20

Putting x in (2):

5 x 20 + y = 112

y = 12

therefore, cost of each t-shirt is 20 rupees and the cost of each pair of pants is 12 rupees

An expression that represents the total cost of an order of n number of tickets: 35n + 15

Let n be the number of tickets to a concert.

Let C be the cost for the tickets

Given that the tickets to a concert are $35 each.

So, by unitary method the cost of n number of tickets would be,

n × 35

And the cost for the tickets would be,

C = 35n

In addition to the cost for the tickets ordered, there is a $15 processing charge per order.

So, the cost for the tickets would be,

C = 35n + 15

This is the required expression.

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The complete question is:

Tickets to a concert are $35 each. In addition to the cost for the tickets ordered, there is a $15 processing charge per order.

Write an expression that represents the total cost of an order of n number of tickets.​

Answer:

absolute deviation means distance between each data value and the mean of the data set.

Step-by-step explanation:

(MAD)

or

(Average)

1) Number of 200 notes = 17,923,275

Number of 100 notes = 35,846,550

Number of 50 notes = 71,693,100

Number of 20 notes = 179,232,750

2) Number of 200 notes = 428,800

Number of 100 notes = 857,600

Number of 50 notes = 1,715,200

Number of 20 notes = 4,288,000

3) Number of 200 notes = 733,685

Number of 100 notes = 1,467,370

Number of 50 notes = 2,934,740

Number of 20 notes = 7,336,850

4) Number of 200 notes = 27,778,135

Number of 100 notes = 55,556,270

Number of 50 notes = 111,112,540

Number of 20 notes = 277,781,350

5) Number of 200 notes = 38,885

Number of 100 notes = 77,770

Number of 50 notes = 155,540

Number of 20 notes = 388,850

Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications. For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.

Given that;

Ghana credits 200,100,50 and 20 notes.

Now,

Since, Ghana credits 200,100,50 and 20 notes.

1) Hence, To credit the amount 3584655000,

Number of 200 notes = 3584655000/200 = 17,923,275

Number of 100 notes =3584655000/100 = 35,846,550

Number of 50 notes =3584655000/50 = 71,693,100

Number of 20 notes = 3584655000/20 = 179,232,750

2) To credit the amount 85760000;

Number of 200 notes = 85760000/200 = 428,800

Number of 100 notes = 85760000/100 = 857,600

Number of 50 notes = 85760000/50 = 1,715,200

Number of 20 notes = 85760000/20 = 4,288,000

3) To credit the amount 146737000;

Number of 200 notes = 733,685

Number of 100 notes = 1,467,370

Number of 50 notes = 2,934,740

Number of 20 notes = 7,336,850

4) To credit the amount 5555627000;

Number of 200 notes = 27,778,135

Number of 100 notes = 55,556,270

Number of 50 notes = 111,112,540

Number of 20 notes = 277,781,350

5) To credit the amount 7777000;

Number of 200 notes = 38,885

Number of 100 notes = 77,770

Number of 50 notes = 155,540

Number of 20 notes = 388,850

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The value of x in 2(5x)=14 is 1 2/5.

A mixed fraction is one that is represented by both its quotient and remainder. A mixed fraction is, for instance, 2 1/3, where 2 is the quotient and 1 is the remainder. An amalgam of a whole number and a legal fraction is a mixed fraction.

When converting a mixed fraction to an improper fraction, the denominator and the whole number are multiplied, the product is added to the numerator, and the sum is written as the numerator and denominator.

2(5x) = 14

10x = 14

x = 14/10

Simplify the fraction, by turning it into a mixed number.

x = 1 4/10

Simplify the equation by dividing it by 2, so that it is in simplest form.

x = 1 2/5

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The rule for the given set of data is y = 3x - 1.

The relationship between dependent and independent variables, expressed as an equation, is referred to as a function rule. In order to calculate the value of the dependent variable, say y, in terms of the independent variable, say x, one must follow a specific function rule.

A function rule can be defined as the procedure that transforms an input value into an output in plain English.

Lets put two of the points in slope formula

y - y₁ = m(x - x₁)

29 - (-13) = m(10 - ( -4))

42 = m14

m = 42/14

m = 3

Now lets make the equation

y - 29 = m(x - 10)

y = 3x - 30 + 29

y = 3x - 1

Thus, the rule for the given set of data is y = 3x - 1.

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One side of the square has a length of 10 cm.

The triangle $ABC$ is a right triangle and it has one leg of length 6 cm and one leg of length 8 cm. Using the Pythagorean theorem, we can find the length of the hypotenuse:

c^2 = a^2 + b^2

c = √(a^2 + b^2)

c = √(6^2 + 8^2)

c = √(36 + 64)

c = √(100)

c = 10

So the hypotenuse of triangle $ABC$ has a length of 10 cm.

The square has one side on the hypotenuse of the triangle $ABC$ and a vertex on each of the two legs of the triangle $ABC$. Since the square is on the hypotenuse of the triangle, one side of the square has the same length as the hypotenuse of the triangle, which is 10 cm.

Therefore, one side of the square has a length of 10 cm.

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Answer:

[tex] \frac{7}{8} \times \frac{4}{5} = \frac{7 \times 1}{2 \times 5} \\ = \frac{7}{10} [/tex]

16 full days will be covered by the 785.7 pounds of food.

A single unit's value can be determined from the values of multiple units, and multiple units' values can be determined from the values of single units using the unitary technique.

We typically utilize this technique for math calculations.

This approach will be helpful to you while tackling problems involving ratio and proportion, algebra, geometry, etc.

We are able to locate the missing value using the unitary technique.

This technique allows us to calculate both the value of multiple units from the value of a single unit and the value of single unit from the value of multiple units.

According to our question-

1 pound of food will last = 1/48.5 day

Pounds equal 785.7*(1/48.5) = 785.7

= 785.7/48.5

= 16.2

Only full days will be counted, therefore

We'll only count up to 16.

So, the 785.

16 days will pass after 7 days.

The 785.7 pounds of food will therefore be plenty for 16 full days.

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The residual of the given situation is 0.8

The residual for each observation is the difference between predicted values of y (dependent variable) and observed values of y.

Given that, The grade can be modelled by the equation y = 0.66x + 33.3, where y is the student's grade as a percentage and x is the number of days that the student attended class. We are asked to find residual if student who was in attendance for 75 days and has a grade of 82%,

Finding the actual value,

y = 0.66 × 75 + 33.3

y = 82.8

The predicted value = 82

Residual = actual y value − predicted y value

Therefore,

Residual = 82.8-82 = 0.8

Therefore, y = 0.8

Hence, the residual of the given situation is 0.8

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Answer: ummm B

Step-by-step explanation:

Answer: B

Step-by-step explanation: To make his special energy drink Jerome uses 8 cups of water and 3 cups of drink mix. So the ratio of drink mix to water is 3:8.

The length of the rectangle's shorter side is 6cm and the of the rectangle's longer side is 12cm.

What is perimeter?

The total length of a shape's boundary, as used in geometry, is referred to as the shape's perimeter. Adding the lengths of all the sides and edges that surround a shape yields its perimeter. It is calculated using linear length units like centimeters, meters, inches, and feet.

Given:

A rectangle has a perimeter of 36 cm and an area of 72 cm^2.

Let the length of the rectangle's shorter side is 'a' and

the length of the rectangle's longer side 'b'.

As the perimeter is 36 cm.

⇒ Perimeter = 2(a + b)

               36 = 2(a + b)

                18 = a+ b

                 a = 18 - b

Now the area of rectangle is 72cm^2.

⇒                   Area = ab

                         72 = (18 - b)*b

                         72 = 18b - b^2

      b^2 - 18b + 72 = 0

b^2 - 12b - 6x + 72 = 0

b(b - 12) - 6(b - 12) = 0

         (b - 12)(b - 6) = 0

(b - 12) = 0,    (b - 6) = 0

b = 12,   b = 6

When  b = 12   ⇒  a = 18 - 12 = 6

When  b = 6   ⇒  a = 18 - 6 = 12

Hence, the length of the rectangle's shorter side is 6cm and the of the rectangle's longer side is 12cm.

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Answer:

b:  5x-4y+31=0

Step-by-step explanation:

Let's look for an equation of the form y=mx+b, where m is the slope and b the y-intercept (the value of y when x=0).

We are given the slope, m, as (5/4), so we can write:  y = (5/4)x+b.

To find b, just enter the given point, (-3,4), into the above equation and solve for b:

 y=(5/4)x + b

 4=(5/4)(-3) + b   for (-3,4)

 4 = -(15/4)+b

 4 + (15/4) = b

 4 + (3 3/4) = b

b = 7 3/4

The equation becomes y = (5/4)x + 7 3/4

Also written as:  y = (5/4)x + (31/4)

To match this with one of the options, let's multiply by 4 to remove the two fractions:

   y = (5/4)x + (31/4)

   4y = (5)x + (31)

Rearrange so that the expression is = 0:

4y-5x-31 = 0

Now multiply by -1:   -4y+5x+31=0

Rearrange and this will match option b:  5x-4y+31=0

Answer: Based on the survey results, we can calculate the number of ice cream cones to sell for each flavor by multiplying the percentage of the flavor by the total number of ice cream cones to be sold.

Mint: 10% of 300 ice cream cones = 0.1 * 300 = 30 ice cream cones

Strawberry: 25% of 300 ice cream cones = 0.25 * 300 = 75 ice cream cones

Chocolate chip: 15% of 300 ice cream cones = 0.15 * 300 = 45 ice cream cones

Vanilla: 50% of 300 ice cream cones = 0.5 * 300 = 150 ice cream cones

So, based on the survey results, you should sell 30 ice cream cones of Mint flavor, 75 ice cream cones of Strawberry flavor, 45 ice cream cones of Chocolate chip flavor, and 150 ice cream cones of Vanilla flavor.

It's worth mentioning that the sum of the percentages provided, 10+25+15+50 = 100%. Which means that it is a proper survey and the total number of ice cream cones you expect to sell is equal to the survey results.

Step-by-step explanation:

Based on the survey results flavors sold at the sporting event are, 30 mint ice creams, 75 Strawberry icecreams, 45 Chocolate chip icecreams, and 150 Vanilla icecreams.

A percentage is a value per hundredth. Percentages can be converted into decimals and fractions by dividing the percentage value by a hundred.

The number of different types of ice creams can be obtained as follows,

10% - Mint.

= (10/100)×300.

= 30.

25% - Strawberry.

= (25/100)×300.

= 75.

15% - Chocolate chip.

= (15/100)×300.

= 45.

50% - Vanilla.

= (50/100)×300.

= 150.

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Step-by-step explanation:

Regular decagons have two additional identifying properties: 10 exterior angles of 36° , summing to 360° 10 interior angles of 144° , summing to 1,440°

Each interior angle of a regular dodecagon is equal to 150°. Each exterior angle of a regular dodecagon is equal to 30°. 30×12= 360

The p-value of the test statistic is calculated as follows:

0.6386.

At the null hypothesis, it is tested if the mean is actually of 48.3 miles per gallon, that is:

[tex]H_0: \mu = 48.3[/tex]

At the alternative hypothesis, it is tested if the mean is different of that, hence:

[tex]H_1: \mu \neq 48.3[/tex]

The population standard deviation is known, hence the z-distribution is used to obtain the test statistic.

The equation is given as follows:

[tex]z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

In which:

The parameters for this problem are given as follows:

[tex]\overline{x} = 48.2, \mu = 48.3, \sigma = \sqrt{6.76} = 2.6, n = 150[/tex]

Hence the test statistic is obtained as follows:

[tex]z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

[tex]z = \frac{48.2 - 48.3}{\frac{2.6}{\sqrt{150}}}[/tex]

z = -0.47.

The p-value is found using a z-distribution calculator, with a two-tailed test, as we are testing if the mean is different of a value, with z = -0.47, hence it is of:

0.6386.

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Answer:

To drain the tank to the right level, you need to remove 859 - 635 = <<859-635=224>>224 gallons.

So you need to work for 224 / 56 = <<224/56=4>>4 minutes.

Step-by-step explanation: