How many different 4 digit numerals can be written using the following 10 digits 1 3 3 4 4 5 5 6 6 9?

The two pair of linear equations are 2x+6y=30 and x+y=7.

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.

Each, x, table cover cost $2 and each, y, center piece cost $6.

Karl spent $30 decorating for the annual holiday party.

So, the equation is 2x+6y=30 --------(I)

Karl bought 7 items total.

Now, x+y=7 --------(II)

From equation (II), x=7-y

Substitute, x=7-y in equation (I), we get

2(7-y)+6y=30

14-2y+6y=30

14+4y=30

4y=16

y=4

Substitute y=4 in equation (II), we get

x=3

Therefore, the two pair of linear equations are 2x+6y=30 and x+y=7.

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Yes

We can use increasingly specific terms to describe numbers and categories they fit in such as rational and irrational numbers.

Rational Numbers

A rational number is defined as a number that can be written as a non-complex fraction. Another way to say this is that rational decimals will always either terminate or repeat. For example, if you have 0.333 repeating forever, that would be a rational number.

The number we are given, -1.63, terminates. Thus, it must be a rational number. Additionally, -1.63 can be written as [tex]-\frac{163}{100}[/tex], so it is a rational number.

Other Categories

As stated above, there are lots of categories numbers can fall into. Rational and irrational are extremely broad groups that all real numbers can fit into. Integers, whole numbers, and natural numbers are all more specific groups that include fewer and fewer numbers. Integers are all rational numbers that are not fractions or decimals. Whole numbers are all non-negative integers. Natural numbers are all non-zero whole numbers.

Answer:

First put a point on 2. That would be the y-intercept.

Then you will move 7 units down and move 2 units to right.

Step-by-step explanation:

This is most I can help you. I understand how you feel. I also was struggling with this topic too. Hope this helps. :)

Answer:The slope is 9, for every X value it goes up 9 times the Y value, so the Slope is 9

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

r=17/3

Step-by-step explanation:

Given -17=-3r

Divide both sides by -3

-17/-3=r=17/3

r=17/3

Hope this helps :)

Answer: The answer is -34 3/16

Step-by-step explanation:

−51/2 + 63/4(−41/4)

=−51/2 + −2583/16

= −2991/16

= -34 3/16

Answer:

Each DC cost $18.49.

Step-by-step explanation:

[tex](\frac{79.94 - 5.94)}{4}[/tex]  Subtract out the shipping cost of 5.98 from the total cost of $79.94 and divide that amount by 4.  That will get you 18.49 which is the cost of each DVD.

Answer:

270

Step-by-step explanation:

He read 45 pages an hour.  If we go back to hour 0, we would add 45 pages to 225

Answer:

270 pages

Step-by-step explanation:

In the attachment, we can see that Aiden read 45 pages per hour. Therefore, since he already read for an hour, we need to add 45 to 225

45+225=270

So, Aiden's book has a total of 270 pages.

Answer:

9

Step-by-step explanation:

What you do if first you draw your rectangle. You name length as x (as told in the question) and width as x-3 (since the width is 3 feet less). To obtain the area you have to do x × (x-3) because to find area you do length × width right.

So area is x(x-3) and it also tells you that area is 54 there

That's how you get x(x-3)=54

Now to solve it, you have to expand

x(x-3)=54

x²-3x-54 = 0 (you have to factorise this now)

(x+6) or (x-9) = 0

x = -6 or x = 9

As you can see you have two answers there. We have to eliminate the -6 because length can never be negative. The logic is simple, any length you take for example on a ruler (it has to be 0 or above) you can measure 1 feet, 2 feet, even 100 feet but you can't measure less than 0 right?

So the final answer is that x=9 and x represents the length

So length = 9

The total number of possible combinations would be 2,598,960.

The sample space for this experiment would be all possible combinations of 5 cards from a deck of 52 cards. This would include all possible combinations of 5 cards of the same suit (e.g. 5 spades, 5 hearts, etc.), all possible combinations of 4 cards of one suit and 1 card of another suit (e.g. 4 spades and 1 heart, 4 hearts and 1 spade, etc.), all possible combinations of 3 cards of one suit and 2 cards of another suit, and so on. The total number of possible combinations would be 2,598,960.

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The probability mass function (pmf) of x is:

                    = 0.0020      for x = 1

                    = 0.1459       for x = 2

P(X = x) {      = 0.8825       for x = 3

                    = 0.5883       for x = 4

                    = 0                otherwise

In this question we have been given that after shuffling a deck of 52 cards, a dealer deals out 5. let x = the number of suits represented in the five-card hand.

We need to find the pmf of x.

here, sample space n = 52,

and x = 5.

Let x = the number of suits represented in the five - card hand.

So, all possible outcomes for above event would be,

N = 52C5

N = 2598960

For x = 1 (all are spades)

Then the number of ways to get 5 spades would be 13C5 = 1287

so there are 1287 hands of 5S.

Since there are 4 suits, we multiply 1287 by 4C1

Then P(x = 1) = (4 * 1287)/2598960

                     = 0.0020

For x = 2 (only spades and hearts with at least one of each suit)

Then we can have 4S and 1H; 3S and 2H; 2S and 3H; or 1S and 4H.

And the number of possible outcomes would be,

(13C4 * 13C1) + (13C3 * 13C2) + (13C2 * 13C3) + (13C1 * 13C4)

= 2[(13C4 * 13C1) + (13C3 * 13C2)]

= 2(715 * 13 + 286 * 78)

= 63206

We're choosing 2 suits from the 4, so we multiply this by 4C2 = 6

Then P(x = 2) = (6 * 63206)/2598960

                     = 0.1459

For x = 3  (a hand with S, H, and clubs (C))

Then we can have 3S, 1H, and 1C; 1S, 3H, and 1C; 1S, 1H, and 3C; 2S, 2H, and 1C; 2S, 1H, and 2C; or 1S, 2H, and 2C.

Using combination formula,

3[(13C3 * 13C1 * 13C1) + (13C2 * 13C2 * 13C1)]

= 3 [(286 * 13 * 13) + (78 * 78 * 13)]

= 382278

We're choosing 3 suits from the 4, so we multiply this by 4C3 = 6

Then P(x = 3) = (6 * 382278)/2598960

                     = 0.8825

For x = 4  (2 spades ∩ one of each other suit)

For this case the possible outcomes would be,

13C2 * 13C1 * 13C1 * 13C1

= 78 * 13 * 13 * 13

= 171366

Then we can have 3S, 1H, and 1C; 1S, 3H, and 1C; 1S, 1H, and 3C; 2S, 2H, and 1C; 2S, 1H, and 2C; or 1S, 2H, and 2C.

Using combination formula,

3[(13C3 * 13C1 * 13C1) + (13C2 * 13C2 * 13C1)]

= 3 [(286 * 13 * 13) + (78 * 78 * 13)]

= 382278

Then P(x = 4) = (4 * 382278)/2598960

                     = 0.5883

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The complete question is:

After shuffling a deck of 52 cards, a dealer deals out 5. let x = the number of suits represented in the five-card hand.

(a) find the pmf of x.

[hint: p(1) = 4p(all are spades), p(2) = 6p(only spades and hearts with at least one of each suit), and p(4) = 4p(2 spades ∩ one of each other suit)](round your answers to five decimal places.)

The choice of method to the solution of the \pair of equations is substitution method.

In a pair of equations, we can use substitution method or any other method to solve the equations.

The given pair of equations is

y=-x+5 and

y=-x+3

The first thing is to write the two equations where the constant stays at the right hand side and the two variables stay at the left hand side tyo give

y+x = 5 and

y+x=3

Then we use substitution method to solve for x and y

In this case, make x the subject of the relation in equation 1

x=5-y

Then substitute x=5-y in equation 2

That is 2y = 5

then y = 2.2

Sibstitute y=2.2 in equation  to get x=5-2.2

Therefore the value of x=2.8

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On solving the provided question, we can say that - by the unitary method  price of the each drink will be $4

The unit technique is an approach to problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value. The unit method, to put it simply, is used to extract a single unit value from a supplied multiple. For instance, 40 pens would cost 400 rupees, or the price of one pen. The process for doing this may be standardized. a single country. anything that has an identity element. (mathematics, algebra) (Linear algebra, mathematical analysis, mathematics of matrices or operators) Its adjoint and reciprocal are equivalent.

here,

she spent $20  = on 5 cases

so of each will be 20/5 = $ 4

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The equation that represents the given word problem is y = 5 + 15x.

A mathematical definition of an equation is a claim that two expressions are equal and joined by the equal sign. It consists of coefficient, variable operator and constants.

Let the total charges be y and the number of hours be denoted by x.

It is given that for gas the flat fee is $5 this is represented as:

y = 5

Now, $15 per hour is represented as 15x, and the equation becomes:

y = 5 + 15x

Hence, the equation that represents the word problem is y = 5 + 15x

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Lilly is travelling at a faster speed.

Speed is the unit rate in terms of distance travelled by an object and the time taken to travel the distance.

Speed is a scalar quantity as it only has magnitude and no direction.

Given that,

Distance travelled by Spencer = 4/5 mile

Time taken to travel the distance = 1 1/3 minutes = 4/3 minutes

Speed = Distance / Time = (4/5) / (4/3) = 3/5 = 0.60 mile per minute

Distance travelled by Lilly = 3/4 mile

Time taken to travel the distance = 1 1/8 minute = 9/8 minutes

Speed = (3/4) / (9/8) = 2/3 = 0.67 mile per minute

Hence Lilly is travelling at a greater speed of  0.67 mile per minute.

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The segment lengths for this triangle are given as follows:

Similar triangles are triangles that share these two features given as follows:

There are three triangles in this problem, all of which are similar.

The length of segment PX can be obtained with triangles PQR and PXY, as follows:

PX/30 = 10/40

PX/30 = 1/4

4PX = 30

PX = 7.5.

The length of segment XQ is found applying the segment addition postulate, as follows:

PQ + XQ = 30

7.5 + XQ = 30

XQ = 22.5.

The length of segment XY can also be obtained with the similarity of triangles PXY and PQR, as follows:

XY/36 = 10/40

XY/36 = 1/4

4XY = 36

XY = 9.

The length of segment ZW is obtained with the similarity of triangles PZW and PQR, as follows:

ZW/36 = 24/40

ZW/36 = 0.6.

ZW = 36 x 0.6

ZW = 21.6.

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For the table, we have that the rate between the output and the input is given as follows:

12/3 = 16/4 = 28/7 = 32/8 = 4.

Meaning that this is a proportional relationship, and that one employee can help 4 customers, which is the constant of proportionality.

The graph has a constant slope and an intercept of zero, meaning that it also represents a proportional relationship, with the rate given as follows:

k = 8/1 = 8.

The data is given by the image presented at the end of the answer.

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The polygonal shape of the hexacontakaienneagon has 69 sides.

A polygon is a two-dimensional, closed form that is flat or planar and is limited by straight sides. Its sides are not curled. A polygon's edges are another name for its sides. The vertices (or corners) of a polygon are the places where two sides converge. Polygons include shapes like triangles, hexagons, pentagons, and quadrilaterals.

The hexacontakaienneagon shape's number of sides is indicated by the name. For instance, a triangle has three sides, whereas a quadrilateral has four. A two-dimensional closed figure with three or more straight sides is called a polygon. A polygon is any shape with straight edges, such as a triangle or rectangle. Figures with open sides or any curved sides are not considered to be polygons.

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No, we cannot. We must perform a t-test to determine whether or not the difference in the means is statistically significant.

We must perform a t-test to determine whether or not the difference in the means is statistically significant. First, we must calculate the difference in the means, which is

199 - 187

= 12.

Then, we must calculate the standard error of the difference in means, which is the square root of

(6^2/7 + 9^2/12).

Then, we must calculate the t-statistic, which is the difference in means divided by the standard error. Finally, we must compare the t-statistic to the critical t-value at the 0.01 level of significance. If the t-statistic is greater than the critical t-value, we can reject the null hypothesis that there is no difference in the means and conclude that the mean number of days before remission after treatment 1 is greater than the mean number of days before remission after treatment 2.

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The probability of (A, A) if two cards are randomly selected with replacement is B. one ninth.

It is important to note that probability is the chance that a particular thing or event will happen. It is the occurence of likely events.

In this situation, a set of 3 cards, spelling the word ADD, are placed face down on the table and we want to determine P(A, A) if two cards are randomly selected with replacement.

The probability will be:

P(A) × P(A)

= 1/3 × 1/3

= 1/9

In conclusion, the correct option is B.

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Answer:

(4.) 4(3 + 9)

(5.) 5(n + 7)

(6.) 7(11 + 3)

(7.) 8(5+n)

Step-by-step explanation:

(4.) The area of a rectangle is length * width.  Because there are two rectangles, the areas must be combined in order to find the total area.

The area of the first rectangle is 4*3 and the area of the second is 9*4 so the total area would be 4*3 + 4*9.  We can factor out the 4 and simply add the 9 and 3 to get area = 4(3 + 9).

(5.) The total area before using the distributive property is 5 * n + 5 * 7.  We factor out the 5 and add the n and 7 to get area = 5(n + 7)

(6.) We need two numbers whose product is 77 and two numbers whose product is 21. Also, one of the numbers must be the same (namely the width, since the width of both rectangles is equal and doesn't change).  

We can use 7*11 for the first rectangle and 7*3 for the second rectangle.  We factor out the 7 and add the 3 and 11 to get area = 7(3 + 11).

(7.) We need two numbers whose product is 5n and two numbers whose product is 40.  Like number 6, the width of both rectangles must be the same.  Since we already have 8 for the first rectangle, we can use 8 * n and 8 * 5.

We factor out the 8 and add the 5 and n to get 8(5 + n).

Answer:

20 months

Step-by-step explanation:

Define the variables:

Create an equation for the total costs of renting each apartment:

To calculate how many months it will take for the costs to be the same, substitute the equation for Apartment A into the equation for Apartment B and solve for m:

[tex]\implies 1000 + 1200m = 1500 + 1175m[/tex]

[tex]\implies 1000 + 1200m - 1175m = 1500 + 1175m - 1175m[/tex]

[tex]\implies 1000 + 25m = 1500[/tex]

[tex]\implies 1000 + 25m - 1000 = 1500 - 1000[/tex]

[tex]\implies 25m = 500[/tex]

[tex]\implies 25m \div 25 = 500 \div 25[/tex]

[tex]\implies m = 20[/tex]

Therefore, it will take 20 months for the costs to be the same.

Check by substituting m = 20 into both equations:

[tex]\begin{aligned}\textsf{Apartment A}: \quad c &= 1000 + 1200(20)\\ &= 1000 + 24000\\ &= 25000\end{aligned}[/tex]

[tex]\begin{aligned}\textsf{Apartment B}: \quad c &= 1500 + 1175(20)\\ &= 1500 + 23500\\ &= 25000\end{aligned}[/tex]

As the total cost for both apartments is $25,000 after 20 months, this proves that it will take 20 months for the costs to be the same.

Answer:

Slope (m) = 2
y = 2x

Step-by-step explanation:

Change in y / Change in x
-1 becomes 1 (positive)

1 + 1 = 2
1 - 5 = 4
4/2 = 2

y = 2x

Answer: y = -4

Step-by-step explanation:

Common factor

8x+4

4(2x +1)

∴ Solution is 4 (2x+1)

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The notes are £20 and £5. And the coins are £0.50 and £0.20.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

Nick buys some fruits for £25.70. There are eight distinct coin denominations in the euro series: 1, 2, 5, 10, 20, and 50 cents, as well as £1 and £2.

The number 25.70 is expanded. Then we have

£25.70 = £20 + £5 + £0.50 + £0.20

The notes are £20 and £5. And the coins are £0.50 and £0.20.

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False, sample evidence cannot prove that a null hypothesis is true.

Sample evidence can be used to infer whether a null hypothesis is true or not, but it cannot prove it to be true. The null hypothesis is a statement of no effect or no difference, and it is typically used as a starting point for statistical hypothesis testing. When sample data is collected, it is used to calculate a test statistic, which is then used to make a decision about the null hypothesis.

If the test statistic falls within the acceptance region, meaning that it is not unlikely to occur if the null hypothesis is true, then the null hypothesis is not rejected. However, if the test statistic falls in the rejection region, meaning that it is unlikely to occur if the null hypothesis is true, then the null hypothesis is rejected. The conclusion is that the sample evidence provides a probability that the null hypothesis is true or not, but it cannot prove it to be true.

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It will take approximately 6.5 years for the price of gasoline and oil to be equal.

To solve this problem, we need to set up a system of equations to represent the changing prices of gasoline and oil over time. Let "t" be the number of years that have passed.

The price of gasoline after "t" years is:

$2.27 - $0.03/2 months * 12 months/year * t years = $2.27 - $0.18t

The price of oil after "t" years is:

$0.45 + $0.05/6 months * 12 months/year * t years = $0.45 + $0.10t

To find the value of "t" for which the two prices are equal, we can set the two expressions equal to each other and solve for "t":

$2.27 - $0.18t = $0.45 + $0.10t

$1.82 = $0.28t

t = 6.5 years

Therefore, it will take approximately 6.5 years for the price of gasoline and oil to be equal.

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The two functions are not inverses of one another.

A relation is a function if it has only One y-value for each x-value.

The given two functions are F(x)=5x+2

G(x) = x-2/5

Now we need to verify whether these two are inverses of one another

F(G(x)=F(x-2/5)

=5(x-2/5)+2

=5x-2+2

=5x

Now G(F(x))=G(5x+2)

=5x+2-2/5

=5x+8/5

F(G(x) is not equal to G(F(x)).

Hence, the two functions are not inverses of one another.

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The value of angle x is 73⁰

You should be aware that a point where two or three straight lines intersect forms an angles.

The parameters that will help us to determine the value of x are

Line B is a straight line. then the sum of angles on a straight line is 180.

⇒110 + b = 180

Making b the subject we have

b = 180 - 110

This means that  b = 70°

Also, a = 52° (Opposite angles)

The sum of all interior angles of a triangle is 180.

This means that a + b + c = 180

substitute for a and b to get c

52 + 70 + c = 180

122 + c = 180

Making c the subject of the relation

c = 180 - 122

⇒c = 58°

On the other hand c + d + e = 180

Substitute for c and d to have 58 + 49 + e = 180

107 + e = 180

Making e the subject of the relation we have

e = 180 - 107

e = 73°

But x = e (opposite angles)

There the value of x is 73⁰

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