Find the equation of the line that passes through (1,3) and is perpendicular to
y=2x-1.
Leave your answer in the form ax+by=c
Where a, b and c are integers.

a) The probability of being dealt a flush is approximately 0.00198, or about 0.2%.

b) The probability of being dealt one pair is approximately 0.422, or about 42.2%.

a. To find the probability of being dealt a flush, we need to first determine how many possible flush hands there are, and then divide that by the total number of possible hands. There are 4 suits in a deck of cards, so there are 4 ways to choose which suit the flush will be in.

Once we have chosen a suit, there are 13 cards of that suit, and we need to choose 5 of them. The number of ways to choose 5 cards from 13 is given by the combination formula: C(13,5) = 1287. Therefore, there are 4 x 1287 = 5148 possible flush hands.

The total number of possible hands is given by the combination formula for choosing 5 cards from a deck of 52: C(52,5) = 2598960. Therefore, the probability of being dealt a flush is 5148/2598960, which simplifies to approximately 0.00198, or about 0.2%.

b. To find the probability of being dealt one pair, we need to first determine how many possible one pair hands there are, and then divide that by the total number of possible hands. There are 13 denominations in a deck of cards, so there are 13 ways to choose which denomination will form the pair.

Once we have chosen a denomination, there are 4 cards of that denomination, and we need to choose 2 of them. The remaining 3 cards must each be a different denomination from the pair, so there are 12 denominations left to choose from, and 4 cards of each denomination.

We need to choose 3 of these 12 denominations, and then 1 card from each of those 3 denominations. The number of ways to choose 2 cards from 4 is given by the combination formula: C(4,2) = 6. The number of ways to choose 3 denominations from 12 is given by the combination formula: C(12,3) = 220.

The number of ways to choose 1 card from each of 3 denominations is 4 x 4 x 4 = 64. Therefore, the total number of possible one pair hands is 13 x 6 x 220 x 64 = 1,098,240. Dividing this by the total number of possible hands gives us the probability of being dealt one pair, which is 1,098,240/2598960, or approximately 0.422, or about 42.2%.

To learn more about probability click on,

https://brainly.com/question/13184490

#SPJ4

The number of times a variable appears in a data set is Known as Frequency.

Frequency

The frequency of a particular data is the number of times the data value appears. Denote the frequency of a data value by f. For example, if 5 students got an A in science, the frequency of an A score is considered to be 5.

Frequency distributions are used to tabulate the collected data. Data can be scores given by students, temperatures in different cities, scores scored in volleyball matches, and so on. After data is collected, it needs to be presented in a meaningful way for better understanding. Organize your data so that all characteristics are summarized in a table. This is called a frequency distribution.

Types of Frequency distribution:

1. Group frequency distribution: Use group frequency distribution tables to organize large numbers of observations or data. By doing so, we create class intervals to calculate the frequency of data belonging to a particular class interval.

2. Ungrouped Frequency Distribution:  In an ungrouped frequency distribution table, we record the exact frequency of individual data without classifying them.

Learn more about Frequency:

https://brainly.com/question/5102661

#SPJ4

Answer:

y=-2 over 1x+18

Step-by-step explanation:

Answer: To find out what Kelly's next score must be in order to obtain an average that is more than 88, we first need to find the current average of her scores. To do this, we add up her current scores and divide by the number of scores:

(79 + 89 + 86 + 93) / 4 = 337 / 4 = 84.25

Since the current average is 84.25, which is less than 88, Kelly must score higher than 88 on her next quiz to bring the average up to more than 88. To be specific, Kelly must score at least 89 on her next quiz.

Step-by-step explanation:

Percentage of the tickets were discount tickets is 36 %, if 144 out of 400 tickets sold were discount tickets.

Percentage is a number or ratio that can be expressed as a fraction of 100. According to the question, at an amusement park, 144 out of 400 tickets sold were discount tickets.

This means total number of tickets = 400

number of discount tickets = 144

we, have to find percentage of the tickets were discount tickets

Let the percentage be x

therefore x% of 400 = 144

              [tex]\frac{x}{100}[/tex] * 400 = 144

               x = 144 ÷ 4

               x = 36

so, percentage of the tickets were discount tickets is 36%

To know more about percentage

https://brainly.com/question/14127401

#SPJ4

The graph of the piecewise function is given by the image presented at the end of the answer.

A piecewise function is a function that has multiple definitions, according to it's input values.

The two definitions for this problem are given as follows:

For the values until x = 1, we have an increasing linear function, with intercept of y = -2, and finishes at the point (1,-1).

For the values greater than x = 1, the function is a linear function, starting at the point (1,-1), and decaying.

More can be learned about piecewise functions at https://brainly.com/question/19358926

#SPJ1

Check the picture below.

[tex]~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ Q(\stackrel{x_1}{-2}~,~\stackrel{y_1}{8})\qquad P(\stackrel{x_2}{6}~,~\stackrel{y_2}{2}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left(\cfrac{ 6 -2}{2}~~~ ,~~~ \cfrac{ 2 +8}{2} \right) \implies \left(\cfrac{ 4 }{2}~~~ ,~~~ \cfrac{ 10 }{2} \right)\implies (2~~,~~5)[/tex]

Answer: 1/m^2n^2

Step-by-step explanation: when dividing powers, we subtract.

so, the top would all cancel out

and we would be left with only m^-2n^-2.

to get rid of the negative we put the number into the denominator.

so m^-2n^-2 would become 1/m^2n^2.

Answer:

Student A is incorrect. Student b is correct.

Step-by-step explanation:

Yes, both students' evaluations of the expression are correct.

The product of a number by addition is equal to the total of the products of that number by each of the addends, according to the distribution property of multiplication.

Simplify the given expression 17(4 + 15) using the distributive property as:

17(4 + 15) = 17(19) = 323

Student A evaluates the expression by adding the product of 17 and 4 to the product of 17 and 15:

17(4) + 17(15) = 68 + 255 = 323

Thus, student A's evaluation is correct.

Student B evaluates the expression by determining the product of 17 and 19:

17(19) = 323

Thus, student B's evaluation is also correct.

Therefore, both students' evaluations are correct.

To learn about the distributive property here:

brainly.com/question/20754996

#SPJ2

The number of tots Rew has = X and X∈[0,5] or X(10,∝).

What is a number line?

A horizontal line with evenly spaced numerical increments is referred to as a number line. How the number on the line can be answered depends on the numbers present. The use of the number is determined by the question that it corresponds to, such as when graphing a point.

Let the number of tots Rew has = X.

It is given that Rew has either no more than 5 tots or more than 10 tots.

This means that the number of tots is either less than 5 or greater than 10.

which mean that X≤5 or X>10.

X∈[0,5] or X(10,∝)

The graph of the number line is attached below.

To learn more about graphing on the number line, refer to the link below:

https://brainly.com/question/27848910

#SPJ1

Y = -0.0063e0.16x + 99.97 is the exponential regression equation for the data, where x is the time in minutes and y is the temperature of the soup.

Calculate the x and y means in step one.

X's average: (0 + 10) / 2 = 5.

(95 + 88.5) / 2 = 91.75 is the mean of y.

Calculate the variance and covariance in step two.

(-5 6.5) + (5 -2.5) = 32.5 is the covariance.

X's variation is (5 0).

2 + (10 − 0)2 = 125

Calculate the regression coefficients in step three.

x = -32.5 / 125 = -0.26 where a = Covariance / Variance of x

Mean of x = 91.75 (-0.26 5) = 99.97 where b = Mean of y a Mean of x

Step 4: Compose the equation for exponential regression.

y = -0.0063e^0.16x + 99.97

Y = -0.0063e0.16x + 99.97 is the exponential regression equation for the data, where x is the time in minutes and y is the temperature of the soup. We must first determine the means of x and y before we can solve the problem. By summing the first and last values of x and dividing by 2, the mean of x is 5 and the mean of y is 91.75. (calculated by adding the first and last y values and then dividing by 2).

Calculating the covariance and variance comes next. The difference between each x and the mean of x is multiplied with the difference between each y and the mean of y to determine the covariance. By squaring the difference between each x and the mean of x, the variance of x is determined. The regression coefficients a and b can be determined when the covariance and variance have been computed.

Learn more about regression here

https://brainly.com/question/28178214

#SPJ4

Answer:

7.09

Step-by-step explanation:

s = r∅ = 7.09

s = (7 cm)(1.0123) = 7.086

58 deg x π/180 = 1.0123 radians

Answer:

CB ≈ 7.09 cm

Step-by-step explanation:

the length of arc CB is calculated as

AB = circumference of circle × fraction of circle

    = 2πr × [tex]\frac{58}{360}[/tex] ( r is the radius )

   = 2π × 7 × [tex]\frac{29}{180}[/tex]

  = [tex]\frac{14\pi (29)}{180}[/tex]

  ≈ 7.09 cm ( to 2 decimal places )

The value of x the width of the solar panel is 18.5.

If ABC is a triangle with AC as the hypotenuse and angle B with 90 degrees then we have Pythagoras theorem:

|AC|^2 = |AB|^2 + |BC|^2    

where |AB| = length of line segment AB. (AB and BC are rest of the two sides of that triangle ABC, AC being the hypotenuse).

We are given that;

Length of base of panel= 40feet

Other length = 12feet

Now,

Applying the pythagoras theorum;

|AC|^2 = |AB|^2 + |BC|^2  

|AC|^2= 12^2 + 14^2

|AC|^2= 144+196

AC= 18.5

Therefore, by Pythagoras theorem x will be equal to 18.5.

Learn more about Pythagoras theorem here:

https://brainly.com/question/12105522

#SPJ1

Answer:

Step-by-step explanation:

y = 2x:

This is an equation for a straight line in which "y" is proportional to "x" with a coefficient of 2. If you plot this line on a coordinate plane, it will have a slope of 2 and y-intercept of 0.

12 x 12:

This is a mathematical expression for finding the product of 12 and 12. The result is 144. In mathematical writing, it's usually written as "12 * 12 = 144".

Answer:

C

Step-by-step explanation:

Plug (5, -2) into the equation

2(5) - (-2) =

10 + 2 =

12

C is the answer

(5, -2) is the answer

Quadrilateral FGHI is a scalene quadrilateral as none of the sides equal to each other from calculated slopes and lengths.

Coordinates of the quadrilateral FGHI are,

F (-1,-8), G(-3,2), H(0,1) and I(2,7)

Slope of side lengths of FGHI are:

Slope FG = ( 2 + 8)/ (-3 + 1)

               = -5

Slope GH = ( 1 -2)/ (0 + 3)

                = -1/3

Slope HI = ( 7 -1)/ ( 2 -0)

              = 3

Slope IF = ( 7 + 8 )/ (2 + 1)

              = 5

Product of slopes of perpendicular lines = -1

FG is perpendicular to IF

GH is perpendicular to HI

Measure of side lengths are:

FG = √(2+8)² + (-3+1)²

     = √104

     = 2√26

GH =√(1-2)² + (0 +3)²

     = √10

HI = √(7-1)² + (2-0)²

    = √40

    =2√10

IF = √(7+8)² + (2+1)²

   = √234

   = 9√26

Therefore, the given quadrilateral is scalene quadrilateral concluded using slopes and lengths.

The above question is incomplete, the complete question is:

The points F (-1,-8), G(-3,2), H(0,1) and I(2,7) form a quadrilateral. Find the desired slopes and lengths, then fill in the words that BEST identifies the type of quadrilateral.

Slope of FG = __                            Length of FG = __

Slope of GH = __                            Length of GH = ___

Slope of HI= __                               Length of HI = ____

Slope of IF = __                               Length of IF = ____

Quadrilateral FGHI is ______

Learn more about quadrilateral here

brainly.com/question/29934291

#SPJ4

The inequality showing the maximum number of days he can rent a car is 10d ≤ 75.

The inequality expressions are the mathematical equations related by each other by using the signs of greater than or less than. All the variables and numbers can be used to make the equation of inequality.

Given that Passion has a budget of $75 and wants to rent a car for a trip. A fixed daily fee of 10 is charged.

The product of the number of days and the rent per day should be less than the amount he has.

The inequality mathematically can be written as:-

10t ≤ $75

Therefore, the inequality 10d ≤75 shows how many days he can rent an automobile for the most.

To know more about inequality follow

https://brainly.com/question/24372553

#SPJ9

Answer:

x=7/6

Step-by-step explanation:

add 2/3 to both sides

The expression that represents that number of items collected by Team A is a=2b+4.

Given that in a hunt, two teams collected a number of items for their teams. Now the items collected by team A is 4 more than the twice of the items collected by the team B. Let the items collected by team A be 'a' and the items collected by team B will be 'b'.

Now, team A collected items are 4 more than the doubled value of team B.

The expression that represents the items collected by the second team, that is Team A is:

a=2b+4

Therefore the expression that represents items collected by team A is a=2b+4.

Learn more about expressions:

https://brainly.com/question/13947055

#SPJ4

The required coordinates of B are (0, 6) for the given parabola.

The x-intercept is defined as an intercept that is located at the x-axis of the plane, is the location or coordinate from where the line crosses.

To determine the coordinates of B, we can use the information given in the problem.

A is an x-intercept, which means that the y-coordinate of A is 0, and it can be found by setting x = 0 in the equation for f(x).

The line AB is g(x) = 3x + 6. This line is a straight line and it is perpendicular to the x-axis at B, which means that the x-coordinate of B is 0.

Therefore, we can set x = 0 in both equations to find the y-coordinate of B.

For f(x), we have:

f(0) = a × 0² + b × 0 + c = c

For g(x), we have:

g(0) = 3 × 0 + 6 = 6

Since the line AB passes through the turning point B, we know that the y-coordinate of B is equal to both f(0) and g(0). Therefore, we have:

c = 6

So, the coordinates of B are (0, 6).

Learn more about the x-intercept here:

https://brainly.com/question/14180189

#SPJ9

The zeroes of 5x^4-26x^3-64x^2+9x-14 are -2, 7 ,  [tex]\frac{1+i\sqrt{19} }{10}[/tex]  and   [tex]\frac{1-i\sqrt{19} }{10}[/tex]  by Using the rational theorem.

f(x) = [tex]5x^{4} - 26x^{3} - 64x^{2} +9x -14[/tex]

Now, put x = -2

f(-2) = [tex]5(-2)^{4} - 26(-2)^{3} - 64(-2)^{2} +9(-2) -14[/tex]

f(-2) = 0

so, -2 is a zero of f(x)

or (x+2) is a factor of  [tex]5x^{4} - 26x^{3} - 64x^{2} +9x -14[/tex]

putting x = 7

f(7) = [tex]5(7)^{4} - 26(7)^{3} - 64(7)^{2} +9(7) -14[/tex]

f(7) = 0

so, (x-7) is a factor of  [tex]5x^{4} - 26x^{3} - 64x^{2} +9x -14[/tex]

Now (x+2)(x-7) would also be a factor so

Divide  [tex]5x^{4} - 26x^{3} - 64x^{2} +9x -14[/tex] by (x+2)(x-7)

or divide  [tex]5x^{4} - 26x^{3} - 64x^{2} +9x -14[/tex] by [tex]x^{2} -5x -14[/tex]

The quotient or other factor will be [tex]5x^{2} - x +1[/tex]

[tex]5x^{2} - x +1[/tex]

By factorizing  [tex]5x^{2} - x +1[/tex]

The other two zeroes are [tex]\frac{1+i\sqrt{19} }{10}[/tex] and  [tex]\frac{1-i\sqrt{19} }{10}[/tex]

To know more about polynomial

https://brainly.com/question/30503176

#SPJ4

Answer:

Step-by-step explanation:

i9 have no idea sorry

The diameter of a circle is 10 feet.

The circumference of a circle is the perimeter of the circle. It is the total length of the boundary of the circle. The circumference of a circle is the product of the constant π and the diameter of the circle.

Given that, the circumference of a circle is 31.4 ft.

We know that, circumference of a circle is 2πr

Now, 2πr=31.4

2×3.14×r=31.4

6.28r=31.4

r=31.4/6.28

r=5 feet

Then, diameter=2×radius =10 feet

Therefore, the diameter is 10 feet.

Learn more about the circumference here:

brainly.com/question/28757341.

#SPJ9

Answer:

-----------------------

Given measurements:

Bring all to same unit, grams, then compare;

Order them from smallest to largest:

Answer:

The order of the measurements from smallest to largest is:

Step-by-step explanation:

The three given measurements of mass are:

Therefore, to be able to order the three given measurements from smallest to largest, first convert them to the same unit of mass (grams):

⇒ 3,000 g = 3,000 g

⇒ 60,000 mg = 60,000 × 0.001 = 60 g

⇒ 1.5 kg = 1.5 × 1000 = 1,500 g

Therefore, the order of the measurements in grams from smallest to largest is:

So, the order of the measurements in their original units from smallest to largest is:

The M.A.S motion for two different time periods {T} = 2s and

{T} = 2/3s is calculated above.

The general equation is -

y{t} = A sin(ωt + Ф)

Given is a body describes an M.A.S according to the function -

{x} = 2 cos{(π/2)T+ π)r

Now -

For {T} = 2, we can write -

{x} = 2 cos{(π/2) x 2+ π)r

{x} = 2 cos{2π}r

{x} = 2 x 1 x r

{x} = 2r

For {T} = 2/3, we can write -

{x} = 2 cos{(π/2) x 2/3+ π)r

{x} = 2 cos{π/3}r

{x} = 2 x -0.33 x r

{x} = - 0.66r

Therefore, the M.A.S motion for two different time periods {T} = 2s and

{T} = 2/3s is calculated above.

To solve more questions on wave equations, visit the link below

https://brainly.com/question/1406081

#SPJ9

{Question in english -

a body describes an M.A.S according to what is specified.

x= 2 cos (π/2 T+π) r

Find its elements in:

T= 2

T= 2/3 sec

K=f/x}

After '2' hours, both Car A and Car B will be '20' miles from McDonald Middle School

What is a graph?

A diagram or pictorial representation that organises the depiction of data or values is known as a graph.

The relationships between two or more items are frequently represented by the points on a graph.

Given that, both the cars are traveling at a constant speed and given a graph showing the distance from The school in Y-axis and Time in X-axis

To find the point where the cars meet, We should look at the point of intersection of both the lines of Car A and Car B

We can see the point of intersection to be (2 hours, 20 miles)

i.e., After 2 hours, Both the cars are 20 miles from the school

To learn more about graphs, refer to the link below:

https://brainly.com/question/26865

#SPJ1

Answer:

= 74cm²

Step-by-step explanation:

Perimeter of a rectangle

[tex] = 2(l) + 2(w)[/tex]

therefore

= 2(18) + 2(19)

= 36 + 38

= 74cm².

Answer:

Step-by-step explanation:

Part A:

The actual length of the dining room is 120 inches and the percent error is -5%, which means that Rihana's measurement was too short. To find the length she measured, we need to add 5% to the actual length:

120 inches * (1 + (-5%)/100) = 120 inches * (1 - 0.05) = 120 inches * 0.95 = 114 inches

So Rihana measured the length of her dining room as 114 inches.

Part B:

To find the length that Rihana measured, we used the formula for calculating percent error:

measured length = actual length * (1 + (percent error)/100)

Since the percent error was negative (-5%), this means that Rihana's measurement was too short, so we subtracted the percent error from 100%. To do this, we added the negative percent error to 100%:

100% + (-5%) = 100% - 5% = 95%

So the measured length was 120 inches * 95% = 114 inches.

Aɳʂɯҽɾҽԃ Ⴆყ ɠσԃKEY ꦿ

The length of the dining room measured by Rihana with a -5%  percent error  is 114 inches.

What is a percent error?

The percent error is the distinction between the estimated value and the actual value in relation to the actual value. In other words, the relative error is multiplied by 100 to calculate the percent error.

A) Given the percent error as -5%.

The actual length = 120inches

Now error in measurement = 5% of 120 inches = 6 inches.

Since there is a negative sign in percent error, the measured value is 6 inches less than actual value.

Therefore the measured value = 120 - 6 = 114 inches.

B) We are given the actual length as 120 inches.

There is a -5% error in the measured value.

This means that the measured value is (5% of 120) inches less than actual value. It is identified as less because of the negative sign.

So the measured value is = 120 - 0.05*120 = 114 inches.

Therefore the length of the dining room measured by Rihana with a -5%  percent error is 114 inches.

To learn more about percent error, follow the link.

https://brainly.com/question/28771966

#SPJ1