Mathematics College

A display that shows how the values in a data set are distributed

Answers

Answer 1

Answer: Line Plot

Step-by-step explanation: A line plot is a display that shows how the values in a data set are distributed.

Answer 2

Answer: histogram

Step-by-step explanation:

Related Questions

Suppose a weather forecaster says the probability that it will rain on saturday is 2929​% and the probability that it will rain on sunday is 4040​%. from this​ information, is it possible to find the probability that it will rain on saturday or sunday​ (or both)? why or why​ not?

Answers

Yes because you are given both probabilities you can calculate the OR

If angle A is complementary to angle B, and angle B is supplementary to angle C, what is the measurement of angle C if angle A is 21 degree...

Answers

C = 111 degrees

Since A and B are complementary they add to 90. So we know that B must be 69 degrees. 

Since B and C are supplementary they add to 180. So we know that C must be 111. 

HELP FAST!! What is the volume of a right rectangular prism with a base that measures 4 in by 6 in. and a height of 7 in? A) 17 in.3. B) 51 in.3. C) 84 in.3. D) 168 in.3.

Answers

Hello!

What you need to do first is multiply 6 and 4 together. Once you've done that, you now have 24. You now need to multiply 24 by 7 to get 168. Now you have 168 in³ for your Volume.

I hope this helps!

Answer:

d

Step-by-step explanation:

What is the height of a triangle that has an area of 60 yd squared and a base with a length of 12 yd

Answers

the answer would be 0.4yd
The answer is:  " 10 yd. " . 
_______________________________________________________
The height of the triangle is:  " 10 yd " .
_______________________________________________________
Explanation:
_______________________________________________________
The formula for the area, "A", of a triangle is:

          →   " A = (b * h) / 2  " ; 

in which:  " A = area (in square units;  in this case;  "yd² " ; 
                       
                      = " 60 yd² " {given} ; 

                  "b = base length = 12 yd" {given} ; 

                  "h = [perpendicular] height ; for which we shall solve;
_______________________________________________________

 →  A = (b * h) / 2 ;  

 → Rearrange the equation to isolate "h" on one side of the equation; since we need to solve for "h" (height) ; 

→  Multiply each side of the equation by "2" ; 

→  2 * A = 2 * [ (b * h) / 2 ] ;

to get:

→  2A  = b * h ; 

↔  b * h = 2A ; 

Divide each side of the equation by "b" ; 
          to isolate "h" on one side of the equation; 

→  (b * h) / b  =  2A / b ; 

→  h = 2A / b ; 

Now, plug in our given values for "A" and "b" ;  
    to solve for "h" ; 

→  h = (2* 60 yd²) / (12 yd) ; 

         = (120 yd²) / (12 yd). 

         = 10 yd.

→  h = 10 yd.
_______________________________________________________
The answer is:  " 10 yd. " . 
_______________________________________________________
The height of the triangle is:  " 10 yd " .
_______________________________________________________

julie will build a rectangular pen for her dog against a barn. A wall from the barn will from one side of the pen. She has 32m of fencing to form the other three sides. She plans to build the pen so that it has its maximum possible area. What will be the dimensions of julie's pen?

Answers

The answer is 8 m by 16 m. I just answered this on my quiz.

the answer is 8 and 16

Can you please help me with this math problem

Answers

This question is nasty. It sounds like you should be finding area of the figure you see. I'll do that first, although I don't think it's the right answer. (But it might be).

Area Trapezoid = (b1 + b2) * h / 2
b1 = 8
b2 = 12
h = 5
Area Trapezoid = (8 + 12 ) * 5 / 2
Area Trapezoid = 20 * 5/2
Area = 50 square feet.

The problem is that no lumber yard will cut that for you without charging you. The practical answer is 12 * 5  = 60 square feet is what you will have to buy. Then you cut out the triangles for yourself.

This question is nasty. It sounds like you should be finding area of the figure you see. I'll do that first, although I don't think it's the right answer. (But it might be).


Area Trapezoid = (b1 + b2) * h / 2

b1 = 8

b2 = 12

h = 5

Area Trapezoid = (8 + 12 ) * 5 / 2

Area Trapezoid = 20 * 5/2

Area = 50 square feet.


The problem is that no lumber yard will cut that for you without charging you. The practical answer is 12 * 5  = 60 square feet is what you will have to buy. Then you cut out the triangles for yourself.



Which stem-and-leaf plot represents the data? 15, 16, 15, 48, 48, 63, 15, 29, 16, 30, 48 A stem-and-leaf plot with a stem value of 1 with a leaf value of 5, 5, 5, 5, 5, a stem value of 2 with a leaf value of 9, a stem value of 3 with a leaf value of 0, a stem value of 4 with a leaf value of 8, a stem value of 5, and a stem value of 6 with a leaf value of 3. Key: 1|5 means 15 A stem-and-leaf plot with a stem value of 1 with a leaf value of 5, 5, 6, a stem value of 2, a stem value of 3 with a leaf value of 0, and a stem value of 4 with a leaf value of 8, 8, 8. Key: 1|5 means 15 A stem-and-leaf plot with a stem value of 1 with a leaf value of 5, 5, 5, 6, 6, 6, 6, a stem value of 2 with a leaf value of 9, a stem value of 3 with a leaf value of 0, a stem value of 4 with a leaf value of 8, a stem value of 5, and a stem value of 6 with a leaf value of 3. Key: 1|5 means 15 A stem-and-leaf plot with a stem value of 1 with a leaf value of 5, 5, 5, 6, 6, a stem value of 2 with a leaf value of 9, a stem value of 3 with a leaf value of 0, a stem value of 4 with a leaf value of 8, 8, 8, a stem value of 5, and a stem value of 6 with a leaf value of 3. Key: 1|5 means 15

Answers

The stem and leaf plot that would be created would be the last choice.

Here is the data in order and the Stem and Leaf plot created:

15, 15, 15, 16, 16, 29, 30, 48, 48, 48, 63

Stem|Leaf
     1 | 5 5 5 6 6 
     2 | 9
     3 | 0
     4 | 8 8 8
     5 |
     6 | 3

Key:1|5 = 15

Options: A

A stem-and-leaf plot with a stem value of 1 with a leaf value of 5, 5, 5, 5, 5, A stem value of 2 with a leaf value of 9, A stem value of 3 with a leaf value of 0, A stem value of 4 with a leaf value of 8, A stem value of 5A stem value of 6 with a leaf value of 3.

Key: 1|5 means 15

Options: B

A stem-and-leaf plot with a stem value of 1 with a leaf value of 5, 5, 6, A stem value of 2, A stem value of 3 with a leaf value of 0, A stem value of 4 with a leaf value of 8, 8, 8.

Key: 1|5 means 15

Options: C

A stem-and-leaf plot with a stem value of 1 with a leaf value of 5, 5, 5, 6, 6, 6, 6, A stem value of 2 with a leaf value of 9, A stem value of 3 with a leaf value of 0, A stem value of 4 with a leaf value of 8, A stem value of 5, and a stem value of 6 with a leaf value of 3.

Key: 1|5 means 15

Options: D

A stem-and-leaf plot with a stem value of 1 with a leaf value of 5, 5, 5, 6, 6, A stem value of 2 with a leaf value of 9, A stem value of 3 with a leaf value of 0, A stem value of 4 with a leaf value of 8, 8, 8, A stem value of 5A stem value of 6 with a leaf value of 3.

Key: 1|5 means 15

Answer:

Options: D

A stem-and-leaf plot with a stem value of 1 with a leaf value of 5, 5, 5, 6, 6, A stem value of 2 with a leaf value of 9, A stem value of 3 with a leaf value of 0, A stem value of 4 with a leaf value of 8, 8, 8, A stem value of 5A stem value of 6 with a leaf value of 3.

Key: 1|5 means 15

Step-by-step explanation:

Given: 15, 16, 15, 48, 48, 63, 15, 29, 16, 30, 48

To plot a stem and leaf plot, first rearrange the observations in ascending order: 15, 15, 15, 16, 16, 29, 30, 48, 48, 48 , 63

Next, is to get the range of values

Low: 15

High = 63

Next, is to identify the stems

Using the range of 15 to 63, we need stems of 1, 2, 3, 4, 5 and 6

In tabular form, the stems are:

Stems ||

1  ||

2  ||

3  ||

4  ||

5  ||

6 ||

Next, is to fill in the leafs

Stem || Leaf

1 || 5 5 5 6 6

2 || 9

3 || 0

4 || 8 8 8

5 ||

6 || 3

Lastly, we write out our observations

1. The stem Value 1 has leaf values 5,5,5,6,6

2. The stem Value 2 has a leaf value 9

3. The stem Value 3 has a leaf value 0

4. The stem Value 4 has leaf Values 8,8,8

5. The stem Value 5 has no leaf

6. The stem Value 6 has leaf value 3

Comparing the observation with the options, option D represents the stem-and-leaf plot representation of 15, 16, 15, 48, 48, 63, 15, 29, 16, 30, 48  

Assume that X has a normal distribution, and find the indicated probability. The mean is μ= 15.2 and the standard deviation is σ = 0.9. Find the probability that X is greater than 16.1.

Answers

Answer:0.1587

Step-by-step explanation:

z = (x-μ)/σ

mean, μ= 15.2

standard deviation, σ = 0.9

To find the probability that x is greater than 16.1,

x = 16.1

z = (16.1-15.2)/0.9

= 1

Looking at the normal distribution table, the area covered by 0 to 1

=0.8413

Therefore, the probability that x is greater than 16.1, = 11- probability that x = 16.1

= 1-0.8413

= 0.1587

Simplify the expression (a^2b^5c^3)^4(a^3b^3)^3(a^2c)^2

Answers

 i think that's the answer   a^21b^29c^14
The simplified expression is shown below:

[tex]( a^{2} b^{5} c^{3} )^{4} ( a^{3} b^{3} )^{3} ( a^{2} c )^{2} \\ \\ =( a^{8} b^{20} c^{12} )( a^{9} b^{9} )( a^{4} c^{2} ) \\ \\ = a^{(8+9+4)} b^{(20+9)} c^{(12+2)} \\ \\ = a^{21} b^{29} c^{14} [/tex]

how can x2+3x+1=2x2+2x+3 be set up as a system of equations

Answers

For this case we can write the system of equations as two equations with two unknowns.
 We then define the following unknowns:
 incognitas: x and y.
 We write the system of equations:
 y = x2 + 3x + 1
 y = 2x2 + 2x + 3
 Answer:
 y = x2 + 3x + 1
 y = 2x2 + 2x + 3
Final answer:

The given equation can be converted into a system of equations by setting each side of the given equation to equal zero separately. The system of equations will then be x² - x + 2 = 0 and x² + 3x + 1 = 0.

Explanation:

The given equation, x²+3x+1=2x²+2x+3, can be set as a system of equations by getting each side of the equation to equal zero. Begin by subtracting the entire left-hand side of the equation from the right-hand side which gives us:

2x² + 2x + 3 - (x² + 3x + 1) = 0

This simplifies to x² - x + 2 = 0. That's your first equation.

Now, take the left-hand side of the original equation and set it equal to zero: x² + 3x + 1 = 0. That's your second equation. So the system of equations from the original equation are:

x² - x + 2 = 0 x² + 3x + 1 = 0

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Given that P = (-5, 5) and Q = (-13, 6), find the component form and magnitude of 2vector PQ

Answers

ANSWER

Component form:

[tex]\binom{ - 16}{2} [/tex]

2. Magnitude

[tex]2\sqrt{65} [/tex]

EXPLANATION

Given that P = (-5, 5) and Q = (-13, 6),

Vector PQ

[tex] = \binom{ - 13}{6} - \binom{ - 5}{5} [/tex]

[tex] = \binom{ - 13 + 5}{6 - 5} [/tex]

[tex] = \binom{ - 8}{1} [/tex]

2 vector PQ

[tex] = 2 \binom{ - 8}{1} [/tex]

[tex] = \binom{ - 16}{2} [/tex]

This is the component form.

The magnitude is given by

[tex] = \sqrt{ {x}^{2} + {y}^{2} } [/tex]

[tex] = \sqrt{ {( - 16)}^{2} + {2}^{2} } [/tex]

[tex] = \sqrt{256 + 4} [/tex]

[tex] = \sqrt{260} [/tex]

[tex] = 2\sqrt{65} [/tex]

Find the greatest common divisor of 100 and 254, using • prime factorization- • euclidean algorithm-

Answers

Via prime factorization:

[tex]100=10^2=2^2\cdot5^2[/tex]
[tex]254=2\cdot127[/tex]

of which the only common factor is a single power of 2, so [tex]\mathrm{gcd}(100,254)=2[/tex].

Via the Euclidean algorithm:

[tex]254=2\cdot100+54[/tex]
[tex]100=1\cdot54+46[/tex]
[tex]54=1\cdot46+8[/tex]
[tex]46=5\cdot8+6[/tex]
[tex]8=1\cdot6+2[/tex]
[tex]6=3\cdot2+0[/tex]

which means [tex]\mathrm{gcd}(100,254)=2[/tex], as expected.
Final answer:

The Greatest Common Divisor (GCD) of 100 and 254 can be found using Prime Factorization and the Euclidean Algorithm. Both methods produce a GCD of 2.

Explanation:

The student is asking for how to find the Greatest Common Divisor (GCD) of 100 and 254 using two different methods: Prime Factorization and the Euclidean Algorithm.

Prime Factorization: Start by writing down each number's prime factors. The prime factors for 100 are 2, 2, 5, 5 and the prime factors for 254 are 2, 127. The GCD is the product of the smallest power of each common prime number. In this case, the only common prime number is 2, so the GCD by prime factorization is 2.Euclidean Algorithm: This method begins with the larger number (254) and divides it by the smaller one (100). Write down the remainder (54). Then, divide the smaller number (100) by the remainder from the last step (54) to get a new remainder (46). The process is repeated until there is no remainder. The last non-zero remainder serves as the GCD. In this case, the process would continue as follows: 54 divided by 46 equals 1 remainder 8, then 46 divided by 8 equals 5 remainder 6, then 8 divided by 6 equals 1 remainder 2, then 6 divided by 2 equals 3, no remainder. Therefore, the GCD by Euclidean Algorithm is also 2.

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Determine the number of solutions the following system of equations will have: 1/3 y - 5 = 2x y = 15 + 6x

Answers

For this case we have the following system of equations:
 1/3 y - 5 = 2x
 y = 15 + 6x
 The equations are linearly dependent, that is, there is a scalar that allows us to write an equation as a linear combination of the other.
 We multiply the equation (1) by a scalar, which will be 3:
 3 * (1/3 y - 5) = 3 * (2x)
 Rewriting:
 y-15 = 6x
 y = 15 + 6x
 Answer:
 Therefore, if there is a solution, then there are infinite solutions.

hey can you please help me posted picture of question

Answers

The linear parent function is y = x

it has a slope equal to 1 and passes through the origin. All the other linear functions are derived from this parent function.

So, the correct answer to this question is option B

Use the given information to find the indicated probability. a and b are mutually exclusive. p(a) = .8, p(b) = .1. find p((a ∪ b)').

Answers

If [tex]A[/tex] and [tex]B[/tex] are mutually exclusive, then

[tex]\mathbb P(A\cup B)=\mathbb P(A)+\mathbb P(B)=0.8+0.1=0.9[/tex]

Then [tex]\mathbb P((A\cup B)')=1-\mathbb P(A\cup B)=0.1[/tex].

Anyone care to help with this please

Answers

The general equation is y = a sin(b[x+c]) + d, where a is the amplitude, b is the frequency, and d is the midline.
For the first equation, only one choice has a midline y = 4, which is h(x).
For the second equation, the first and fifth choices have midline y = 8, but the frequency of 2 only fits the fifth choice: q(x).
For the third equation, the midline of y = 1 only fits g(x).
The fourth equation has midline y = 2 and frequency of 4, which only fits the last choice, r(x).

6. Alice Correa bought three yards of cloth to make a dress. The cloth was on sale for $1.93 per yard. How much did Alice pay for the cloth if the sales tax was 5 percent? A. $5.79 B. $2.02 C. $6.08 D. $5.82

Answers

A: C. $6.08

$1.93 per yard x 3 yards = $5.79 before tax

5% sales tax means that there will be 0.05 added to the price of the product 

$5.79 x 1.05 = 6.0795 = $6.08

On a coordinate graph, points F (4,1), G (4,-1), H (-7,1) and J (-7,-1) are the vertices of a rectangle. What is the area of the rectangle?
PLEASE EXPLAIN HOW YOU GOT THE ANSWER!!!!

Answers

The sides of the rectangle are aligned with the coordinate axes, so the dimensions of the rectangle are easily determined to be 4 -(-7) = 11 units by 1 -(-1) = 2 units. As with any rectangle, the area is the product of length and width.

The area is 11*2 = 22 square units.

The price of an item has risen to $276 today. Yesterday it was $115. Find the percentage increase.

Answers

are you kidding me, bro? lol

276-115=131
131 divided by 276 = 0.47

0.47% increase
Final answer:

The student's question asked for finding the percentage increase in an item's price. This can be calculated by subtracting the initial price from the final price, dividing that difference by the initial price, and then multiplying the result by 100. In this case, the price of the item has increased by 140% from yesterday to today.

Explanation:

To find the percentage increase of the price of an item, we subtract the initial price from the final price, then divide that number by the initial price, finally multiply that result by 100 to obtain the percentage. In this case, the initial price of the item was $115, and the final price is $276.

Here's how the calculation works:

Subtract the initial price from the final price: $276 - $115 = $161. Divide the difference by the initial price: $161 / $115 ≈ 1.4. Multiply the result by 100 to get the percentage increase: 1.4 * 100 = 140%.

Therefore, the price of the item has increased by 140% from yesterday to today.

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A college cafeteria pays student cashiers $10.20 per hour. Cashiers earn an additional $1.30 per hour for each hour worked over 35 hours per week. A cashier worked 40 hours one week and 38 hours the second week. How much did this cashier earn in this two-week period?

Answers

First week: 40 hours

Total Earning = 40 x $10.20 + (40 - 35) x $1.30 = $414.50

Second Week: 38 hours
Total Earning = 40 x $10.20 + (40 - 38) x $1.30 = $410.60

Total for the two weeks = $414.50 +  $410.60 = $825.10

Answer: $825.10

Answer:

$806

Step-by-step explanation:

The regular earning of a cashier = $10.20 per hour

over 35 hours per week he gets = $10.20 + $1.30 per hour

                                                      = $11.50 per hour

He worked 40 hours in first week and 38 hours the second week.

His earnings in first week  = (35 × 10.20) + (5 × 11.50)

                                           = $357 + $57.5

                                           = $414.50

His earnings in second week = (35 × 10.20) + (3 × 11.50)

                                                 = $357 + $34.50

                                                 = $391.50

His total earnings in this two weeks = $391.50 + $414.50

                                                            = $806

His total earning was $806.

Cross section of a metal ingot is a trapezoid the cross section has an area of 39 square cm the top base of the cross section is 12 CM the length of the bottom base is 2 cm greater than the top base how tall is the Metal Ingot explain

Answers

The area of a trapezoid is given by the formula
  A = (1/2)(b₁ +b₂)×h
Fill in the given information and solve for h.
  39 cm² = (1/2)(12 cm +(12 cm +2 cm))×h
  39 cm²/(13 cm) = h = 3 cm

The height of the metal ingot is 3 cm.

Help Please..

Arrange from smallest to largest

0.2 , 0.06, 0.602, 0.026, 0.21

Answers

0.026, 0.06, 0.21, 0.2, 0.602

Given the following sets:
A={ 2, 4, 6, 8, 10}
B={ 3, 5, 7, 9}
C={ 2, 3, 5, 7}
N={ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

Match the following Unions and intersections to the correct set.

1.
What is A U C?

2.
What is A ∩ B?

3.
What is A ∩ N?

4.
What is B ∩ N?

5.
What is B U C?

{2, 3, 4, 5, 6, 7, 8, 10}


{2, 3, 5, 7, 9}


{ }


{3, 5, 7, 9}


{2, 4, 6, 8, 10}

Answers

A = {2, 4, 6, 8, 10}
B = {3, 5, 7, 9}
C = {2, 3, 5, 7}
N = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

1. A ∪ C = {2; 3; 4; 5; 6; 7; 8; 10}
2. A ∩ B = { } =Ø
3. A ∩ N = {2; 4; 6; 8; 10} = A
4. B ∩ N = {3; 5; 7; 9} =B
5. B ∪ C = {2; 3; 5; 7; 9}

Is a cubic inch is the space taken by a cube whose sides are 1 inch long?

Answers

Hello!

A cubic inch is the space taken by a cube that sides are 1 inch long

The answer is Yes or true

Hope this helps!

hey can you please help me posted picture of question

Answers

The correct answer is option B.

Solution is shown below

[tex]y= 4 x^{3} \\ \\ \frac{y}{4} = x^{3} \\ \\ \sqrt[3]{\frac{y}{4}} =x \\ \\ f^{-1}(y)= \sqrt[3]{\frac{y}{4}} \\ \\ f^{-1}(x)= \sqrt[3]{\frac{x}{4}} \\ \\ y^{-1}= \sqrt[3]{\frac{x}{4}} [/tex]
The correct answer is B

evaluate the following expressions 7/8 ×5/7 =

Answers

[tex]\dfrac{7}{8}\times\dfrac{5}{7}=\dfrac{\not7^1}{8}\times\dfrac{5}{\not7_1}=\dfrac{5}{8}[/tex]

A neighbor needs to put up a square fence around her garden to keep the deer out. If the area is 500 square feet, how much fence does she need to buy, rounded to the nearest tenth of a foot? Show your work.

Answers

Area of a square = length * width

And since it’s a square the length and width is the same amount

So width=length=L
500 ft^2=L*L=L^2

Square root both sides
Sqrt(500 ft^2) =L= 22.36067977

The neighbor needs to buy approximately 89.6 feet of fencing to surround her 500 square feet garden, which is a square. This is calculated by taking the square root of the area to find the length of one side and then multiplying by four to get the perimeter.

To determine how much fence the neighbor needs to buy to surround her square garden, we need to calculate the perimeter of the square. The area of a square is given by the formula Area = side × side or Area = side². Since the area is 500 square feet, we first find the length of one side of the square by taking the square root of the area:

Side = √Area = √500 ft²

The square root of 500 is approximately 22.4 feet. Now, we calculate the perimeter, which is the sum of all four sides of the square:

Perimeter = 4 × side = 4 × 22.4 ft = 89.6 ft

Rounded to the nearest tenth of a foot, the neighbor needs to buy approximately 89.6 feet of fencing to surround her garden.

Q and R are not mutually exclusive events. p (q) = 3/5 p(r) = 1/3 and p ( q and r)= 1/5 find P(Q or R).

Answers

Recall the inclusion/exclusion principle:

[tex]\mathbb P(Q\cup R)=\mathbb P(Q)+\mathbb P(R)-\mathbb P(Q\cap R)[/tex]

which means

[tex]\mathbb P(Q\text{ or }R)=\dfrac35+\dfrac13-\dfrac15=\dfrac{11}{15}[/tex]

The answer to this item is 23/32.

What is probability?

Probability is a measure of the likelihood of an event to occur. Many events cannot be predicted with total certainty.

Given that the events are not mutually exclusive the union of the probability of the events is calculated through the equation,

P(Q or R) = P(Q) + P(R) - P(Q and R)

Substituting the known values,

P(Q or R) = 3/5 + 1/3 - 1/5

Simplifying,

P(Q or R) = 11/15

Hence the answer to this item is 23/32.

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A population of protozoa develops with a constant relative growth rate of 0.8877 per member per day. on day zero the population consists of six members. find the population size after five days. (round your answer to the nearest whole number.) p(5) = members

Answers

The exponential equation for the number of protozoa can be written as ...
  p(t) = 6×1.8877^t

The population size when t=5 is then
  p(5) = 6×1.8877^5 ≈ 144 . . . . members

Solve the systems x ≡ 1 (mod 2), x ≡ 2 (mod 3). x ≡ 2 (mod 5), 2x ≡ 3 (mod 7), 3x ≡ 4 (mod 11). x ≡ 31 (mod 41), x ≡ 59 (mod 26).

Answers

Working with the relation of "congruence modulo" is a bit hard, so lets convert this congruence modulo relations to equations.

We know that '[tex]x=1(mod 2)[/tex]' means 2 divides '[tex]x-1[/tex]'. Keep in mind I can't add a three line "equality" symbol in Brainly...

The previous can be written with this statement:
[tex]x-1=2k[/tex]
In which '[tex]k[/tex]' is any integer.

From the previous equation is very easy to see that '[tex]x=2k+1[/tex]'.

We write the remaining congruence modulo relations as equations and solve for them in similar fashion: 
[tex] x_{1}-2=3k [/tex]
[tex] x_{2}-2=5k [/tex]
[tex] 2x_{3}-3=7k [/tex]
[tex] 3x_{4}-4=11k [/tex]
[tex] x_{5}-31=41k [/tex]
[tex] x_{6}-59=26k [/tex]

Now we solve for the x's, remember, k is any integer!
[tex] x_{1} =3k+2[/tex]
[tex] x_{2} =5k+2[/tex]
[tex] x_{3} = \frac{7k+3}{2} [/tex]
[tex] x_{4} = \frac{11k+4}{3} [/tex]
[tex] x_{5} =41k+31[/tex]
[tex] x_{6} =26k+59[/tex]
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