Triangle XYZ is drawn with vertices X(4, −5), Y(6, −1), Z(10, −8). Determine the line of reflection if Z′(10, 8).

y = 1

x = −8

y-axis

x-axis

Answers

Answer 1

Answer:

  (d)  x-axis

Step-by-step explanation:

You want the line of reflection that transforms Z(10, -8) to Z'(10, 8).

Line of reflection

The line of reflection is the perpendicular bisector of the segment between a point and its image.

Here, the segment ZZ' is on the vertical line x=10, so the bisector will be a horizontal line whose y-value is the average of the y-values of Z and Z':

  y = (-8 +8)/2 = 0/2 = 0

The line y=0 is the x-axis. The line of reflection is the x-axis.

__

Additional comment

Rather than go to the trouble of considering perpendicular bisectors, you can simply make use of your knowledge of reflection over the axes:

  (x, y) ⇒ (-x, y) . . . . reflection over the y-axis

  (x, y) ⇒ (x, -y) . . . . reflection over the x-axis   ←

  (x, y) ⇒ (-x, -y) . . . . reflection over both axes, or reflection across the origin

Answer 2

Answer:

 (d)  x-axis

Step-by-step explanation:


Related Questions

Find the perimeter and area of triangle ABC with altitude BD, given A(-5, 2) B(-3, 5), C(5, 2), and D (-3, 2).

Answers

Answer:

The perimeter of triangle ABC with altitude BD can be found by using the Distance Formula. The coordinates of the vertices are A(-5, 2), B(-3, 5), C(5, 2), and D(-3, 2). The perimeter is then calculated as the sum of the distances between each pair of points: P = AB + BC + CD + DA = 8.24 units. The area can be found using Heron's Formula, which gives an area of 6.00 units.

Step-by-step explanation:

The perimeter of triangle ABC with altitude BD can be found by using the Distance Formula. The coordinates of the vertices are A(-5, 2), B(-3, 5), C(5, 2), and D(-3, 2). Using the Distance Formula, the sides of the triangle can be calculated as follows: AB = √((-3 - (-5))² + (5 - 2)²) = √(8 + 9) = √17; BC = √((5 - (-3))² + (2 - 5)²) = √(8 + 9) = √17; and AC = √((-5 - 5)² + (2 - 2)²) = 0. Therefore, the perimeter of triangle ABC is AB + BC + AC = 17√2 units.

The area of triangle ABC can be found using Heron's Formula, which states that the area of a triangle is equal to the square root of s(s-a)(s-b)(s-c), where s is half of the perimeter and a, b, and c are the lengths of each side. In this case, s is half of 17√2 or 8.5√2 units. Plugging in these values into Heron's Formula yields an area for triangle ABC equal to 8.5√2 * 4 * 3 * 1.5√2 or 36√2 units squared.

Answer:

12 units

Step-by-step explanation:

AB^2 = [(-5) - (-2)]^2 + [(-2) - (-2)]^2 = 9

AB = 3

So similarly, BC = 5 and AC = 4

Hence, the perimeter = AB + BC + AC = 12 units

data set containing 36 sequential data points is divided into 9 quantiles. what is the maximum number of data points that falls below the second quantile?

Answers

the maximum number of data points that fall below the second quantile is 4.

4 data points.

Quantiles divide a set of data into four equal parts, each with an equal number of data points. In this case, 36 data points are divided into 9 quantiles, meaning each quantile contains 4 data points. Therefore, the maximum number of data points that fall below the second quantile is 4.

Quantiles divide a set of data into equal parts, each with an equal number of data points. The number of quantiles is determined by the total number of data points. For example, if there are 36 data points, then it is divided into 9 quantiles, each with 4 data points. The lower the quantile, the lower the value of the data points it contains. Therefore, the maximum number of data points that fall below the second quantile is 4.

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participants in a study on the effects of viagra are assigned to groups. one group receives a sugar pill (a zero dose of viagra) while the other group receives viagra. the number of erections over 30 days is recorded by participants in a journal. in this example, what is the independent variable?

Answers

Participants in a study on the effects of viagra are assigned to groups, the independent variable is The viagra.

In an algebraic equation, an independent variable is a variable whose values are not impacted by changes. It is claimed that the value of y is a function of the value of the independent variable (x), also known as the x value, and the value of y is known as the dependent variable, in an algebraic equation with two variables (x and y), if any value of x is related to any other value of y.

The alphabetic letter that conveys a numerical value or a number is known as a variable in mathematics. In algebraic equations, a variable is used to represent an unknowable quantity.

For these variables, any alphabet from a to z may be used. Most frequently, the variables "a," "b," "c," "x," "y," and "z" are utilised in equations.

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A rectangular lawn is 15 yards by 31 yards. It would cost $7.00 per yard to install a fence around the lawn. How much would it cost to put a fence around the lawn?

Answers

Answer:

$644

Explanation:

if the lawn is 15 yards wide and 31 yards tall, you need to figure out the perimeter. 15+15+31+31=92, so the perimeter of the yard is 92 yards. If it costs $7 per yard, then all you need to do from there is multiply 92 by 7, getting you 644. So it would cost $644 to install a fence around the lawn.

List the sample space of a fair, 7-sided number cube rolled while playing a board game.

S = {7}
S= {1,7}
S = {1, 2, 3 ,4, 5, 6, 7}
S = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

Answers

The sample space of a fair, 7-sided number cube rolled while playing a board game is,

S = {1, 2, 3, 4, 5, 6, 7}

The correct option is C.

What is sample space?

A sample space is a set of potential results from a random experiment. The letter "S" is used to denote the sample space. Events are the subset of potential experiment results. Depending on the experiment, a sample area could contain a variety of results.

Given:

7-sided number cube rolled while playing a board game.

The sample space is the collection of all the numbers.

So, the sample space is,

S = {1, 2, 3, 4, 5, 6, 7}

Hence, S = {1, 2, 3, 4, 5, 6, 7}.

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Guadalupe goes out to lunch. The bill, before tax and tip, was $11.25. A sales tax of 9% was added on. Guadalupe tipped 23% on the amount after the sales tax was added. What was the total cost of the meal, plus tax and tip? Round to the nearest cent.

Answers

Answer: $14.10

Step-by-step explanation:

11.25 * 9 = 101.25

101.25/100 = 1.0125

11.25 + 1.0125 = 12.2625

--
12.2625 * 26 = 282.0375

282.0375/100 = 2.820375

11.25 + 2.820375 = 14.070375
--

14.070375 rounded = 14.10

how to find 20.5% of 1850

Answers

Answer: make my answer brainliest

Step-by-step explanation:

379.25

RO
ROCK
each
Shirts on sale at concert!
uppose David has $65 to spend on his ticket and some shirts. He already
Dent $32.25 on his ticket and fee. Write an inequality that could be used
o find the maximum number of shirts he can buy.
hat is the maximum number of shirts he can buy?
He can buy a maximum of 2 shirts.

Answers

Answer: Let x be the number of shirts that David buys.

The cost of the shirts can be represented by the equation: $15x.

The total amount of money that David has spent can be represented by the equation: $32.25 + $15x.

Since David has a total of $65 to spend, we can write the inequality:

$32.25 + $15x ≤ $65

Solving for x, we get:

$15x ≤ $65 - $32.25 = $32.75

$15x ≤ $32.75

$x ≤ $32.75 / $15 = 2.183333

Since David can only buy a whole number of shirts, the maximum number of shirts that he can buy is 2.

So, the maximum number of shirts David can buy is 2.

Step-by-step explanation:

Translate The difference between a number squared and 14 is 50

Answers

Answer:

[tex]x^{2} - 14 = 50[/tex]

Step-by-step explanation:

Let x = Unknown number

Number squared = [tex]x^{2}[/tex]

Difference between the number squared and 14 is 50:

= [tex]x^{2} - 14 = 50[/tex]

= [tex]x^{2} = 14 + 50[/tex]

= [tex]x^{2} = 64[/tex]

(NOTE: It cannot be [tex]14 - x^{2} = 50[/tex] since:

[tex]x^{2} = 14 - 50[/tex] which would mean [tex]x^{2} = -36[/tex] and a square of a number CANNOT be a negative number)

Taking the square root of both sides to get rid of the square:

= [tex]x = \sqrt{64}[/tex]

= x = ±8

Estimate the circumference of the circular base of the object. Round to the nearest hundredth if necessary.


D battery with radius 0. 65 in.


circumference:__in.

Answers

The circumference of a D battery with 0.65 inches radius was found to be 4.14 inches.

To find the circumference of a circle, we can use the formula:

C = 2 * π* r

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

For the circular base of a D battery with a radius of 0.65 inches, the circumference can be calculated as follows:

C = 2 * π * 0.65

C = 2 * 3.14 * 0.65

C = 4.14

Rounding to the nearest hundredth, we get:

C = 4.14 inches

So, the estimated circumference of the circular base of the object is approximately 4.14 inches

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how many factors and terms are in the expression 4(8x + 5)

Answers

24x + 5 and 4 are the two variables in the equation.

What is a mathematical expression?

Mathematical expressions consist of at least two integers or factors, at least each math procedure, and a sentence. It's possible to multiply, divide, add, or remove with this mathematical procedure.

The expression 4(8x + 5) can be simplified using the distributive property of multiplication over addition as follows:

4(8x + 5) = 4×8x + 4×5 = 32x + 20

So the expression 4(8x + 5) has two terms: 32x and 20.

To find the factors of the expression, we can factor out the greatest common factor of 32 and 20, which is 4:

4(8x + 5) = 4×2×4x + 4×5 = 4(2×4x + 5)

So the expression has two factors: 4 and (2×4x + 5).

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Tonya saved $564 in one year. If she saved the same amount each month, how much did Tonya save in two months?​

Answers

On solving the provided question, we can say thatthe equations will be each moth will be 564/x = 564/12 = $47 and 2 moths will be = 47x = 47*2 = $94

What is equation?

A mathematical equation is a formula that joins two statements and uses the equal symbol (=) to indicate equality. A mathematical statement that establishes the equality of two mathematical expressions is known as an equation in algebra. For instance, in the equation 3x + 5 = 14, the equal sign places the variables 3x + 5 and 14 apart. The relationship between the two sentences on either side of a letter is described by a mathematical formula. Often, there is only one variable, which also serves as the symbol. for instance, 2x – 4 = 2.

Tonya saved $564 in one year.

the equations will be

each moth will be 564/x

= 564/12 = $47

2 moths will be = 47x = 47*2 = $94

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Which shows the solution of the combined inequality?

−1≤2−j<−5
Responses

Number line ranging from negative six to zero with a line beginning with an open point at negative five and ending with a closed point at negative one

Image with alt text: Number line ranging from negative six to zero with a line beginning with an open point at negative five and ending with a closed point at negative one

Number line ranging from negative six to zero with a line beginning with a closed point at negative five and ending with an open point at negative one

Image with alt text: Number line ranging from negative six to zero with a line beginning with a closed point at negative five and ending with an open point at negative one

Number line ranging from zero to six with a line beginning with a closed point at one and ending with an open point at five

Image with alt text: Number line ranging from zero to six with a line beginning with a closed point at one and ending with an open point at five

no solution

Answers

The correct option regarding the solution of the compound inequality is given as follows:

No solution.

How to solve the inequality?

The inequality for this problem is defined as follows:

−1≤2−j<−5

Hence the first condition is of:

j - 2 ≤ 1

j ≤ 3.

The second condition is of:

2−j<−5

j < -7

j > 7.

We have an and operation, meaning that the two conditions must be satisfied simultaneously.

A number cannot be simultaneously less or equal to 3 and greater than 7, hence the compound inequality has no solution.

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Florida has 8 less than 5 times the number of counties $a$ in Arizona.
Georgia has 25 more than twice the number of counties $f$ in Florida.

Answers

The expression which represents Arizona and Florida is 5a - 8 and 2f + 25 respectively.

How to write expressions?

Number of countries in Arizona= a

Number of countries in Florida= f

Florida:

5a - 8

Georgia:

2f + 25

Therefore, 5a - 8 and 2f + 25 represents the expression of each country respectively.

Complete question:

Write an expression for the number of counties in Georgia.

Florida has 8 less than 5 times the number of counties, a, in Arizona.

Georgia has 25 more than twice the number of counties, f, in Florida.

a. Write an expression for the number of counties in Florida.

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a drink costs 2 dollars. a taco costs 3 dollars. write a statement that assigns totalcost with the total meal cost given the number of drinks and tacos. ex: 4 drinks and 6 tacos yields totalcost of 26.

Answers

The equation or statement assigning total meal cost is total meal cost = cost of one taco × number of taco + cost of one drink × number of drink.

The word expression representing the complete transaction will be as follows -

The left hand side will have total cost and the right hand side will individual cost of each item. The individual cost of each item will further be states as -

Taco = The product of cost of one taco and number of tacos

Similarly, drinks = the product of cost of one drink and number of drinks

Forming the combined equation now -

total meal cost = cost of one taco × number of taco + cost of one drink × number of drink

Representing it according to example in Equation -

26 = 4 × 2 + 3 × 6

26 = 8 + 18

26 = 26

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write the following expression without negative exponents and without parentheses (-9x)^-2

Answers

The value of the expression is 1/(9x)^2

How to evaluate the expression

From the question, we have the following parameters that can be used in our computation:

(-9x)^-2

We can write the expression without negative exponents by using a fraction with a positive exponent:

(-9x)^-2 = 1/(-9x)^2

And without parentheses, this expression becomes:

1/(9x)^2

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kari is buying aa batters and d batteries. the store sells aa batteries in packs of 6 and d batteries in packs of 10. if kari wishes to buy the same number of aa and d batteries, what is the smallest number of each battery type that she can buy

Answers

Kari can buy 30 AA batteries and 30 D batteries. We used simple LCM for this solution.

To find the smallest number of each battery type that Kari can buy, we must find the least common multiple (LCM) of 6 and 10. The LCM is the smallest multiple that both numbers can divide into evenly. To find the LCM, we can list the multiples of each number until we find a common multiple. In this case, the LCM of 6 and 10 is 30. So, Kari can buy 30 AA batteries and 30 D batteries, which gives her an equal number of both battery types.

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Jackson has a coin collection consisting of quarters and dimes. The total value of his collection is $16.60​. His collection consists of five​ less quarters than three​ times the number of dimes. Using the variables q​ and d​ to represent the number of quarters in his collection and the number of dimes in his collection respectively, determine a system of equations that describes the situation.

Answers

The system of linear equations that describes the number and amount of coins that Jackson owns is: d - q = 5, 0.10 · d + 0.25 · q = 16.60, where q and d are the number of quarters and dimes.

How to construct a system of linear equations

In this problem we must construct a system of linear equations associated to number and amount of coins that Jackson owns. The procedure is shown below. First, determine the variables of the system:

q - Number of quarters

d - Number of dimes

Second, construct the system of linear equations:

Number of coins

d - 5 = q

d - q = 5

Amount of coins

0.10 · d + 0.25 · q = 16.60

Third, write the resulting system:

d - q = 5

0.10 · d + 0.25 · q = 16.60

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i need help comparing box plots

Answers

Answer:

Step-by-step explanation:

Box plots, also known as box-and-whisker plots, are a graphical representation of the distribution of a set of data. To compare two or more box plots, you should consider the following aspects:

Central Tendency: Compare the medians of the box plots to see if they are similar or if there are significant differences. If the medians are similar, it suggests that the central tendency of the data is similar.

Spread: Compare the ranges of the box plots to see if they are similar or if there are significant differences. If the ranges are similar, it suggests that the data has similar spread.

Outliers:the presence, frequency, and magnitude of outliers in each box plot. Outliers can significantly affect the central tendency and spread of the data, so they should be considered when comparing box plots.

Shape: Compare the shapes of the box plots to see if they are symmetrical or skewed. Symmetrical box plots suggest a normal distribution, while skewed box plots suggest a non-normal distribution.

Overlap: Compare the overlap between the box plots to see if there is significant overlap or if the data sets are mostly distinct. If the box plots overlap significantly, it suggests that there is some overlap between the data sets.

It's also important to keep in mind the context of the data when comparing box plots. For example, if the data sets being compared come from different populations, it may not be appropriate to compare them directly.

By considering these aspects, you can gain a better understanding of the similarities and differences between two or more box plots and make more informed comparisons.

HELP ITS EASY IM JUST LAZY ill give brainly If you add​ Natalie's age and​ Fred's age, the result is 39. If you add​ Fred's age to 4 times​ Natalie's age, the result is 84 . Write and solve a system of equations to find how old Fred and Natalie are.

Answers

Answer:

Natalie is 15 and Fred is 24.

Step-by-step explanation:

Let n = Natalie's age

Let f = Fred's age

n + f = 39

4n + f = 84 ⇒ multiply by -1 ⇒ -4n -f = -84

-4n - f = -84

  n + f = 39

-3n      = -45  Divide both sides by -3

n = 15

Natalie is 15.

Substitute 15 for n to solve for Fred's age:

n + f = 39

15 + f = 39  Subtract 15 from both sides

f = 24

Fred is 24.

If f(x)=2x+4, which graph represents f-1(x)

Answers

The graph of f-1(x) is (d)

How to determine the graph of f-1(x)

From the question, we have the following parameters that can be used in our computation:

f(x) = 2x + 4

This means that

y = 2x + 4

Swap x and y

So, we have

x = 2y + 4

Make y the subject

So, we have

y = 0.5x - 2

This equation is represented by graph (d)

Hence, the graph is (d)

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g let a and b be two events, and assume that 0 < p( b ) < 1. what is smallest value ( p( a | b ) p( not a | b ) )/2 might have?

Answers

The smallest value that (p(a|b) p(not a|b))/2 might have is 0.

The smallest value that (p(a|b) p(not a|b))/2 might have is 0. If p(a|b) = 0, then (p(a|b) p(not a|b))/2 = 0. This means that if event a does not occur, given that event b has already occurred, then the value of (p(a|b) p(not a|b))/2 will be 0.

On the other hand, if p(not a|b) = 0, then (p(a|b) p(not a|b))/2 = 0, which means that if the event, not a, does not occur given that event b has already occurred, then the value of (p(a|b) p(not a|b))/2 will also be 0. Therefore, the smallest value that (p(a|b) p(not a|b))/2 might have is 0.

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please help so hard due soon

Answers

Answer:

the answer I think is the 1st

Step-by-step explanation:

as the change (+4) is in y

not in x

A
When adding a constant to an equation, the only thing that changes is the y. Since you’re adding 4, you will move the equation up by 4 units.

7-2 Enrichment
Multiplying Polynomials
An architect is preparing to design an office building. She creates a sketch of the basic shape of the structure and
the relative dimensions of each piece shown. The angles in the sketch are all right angles. Find the volume of the structure using each approach. Draw lines on the sketches and record your expressions.

1. Divide the structure into two different rectangular
prisms. Add the volumes of the two prisms to create
an expression for the total
Volume

2. Divide the structure into three different rectangular
prisms. Add the volumes of the three prisms to create
an expression for the total volume.

3. View the structure as one prism with 2 equal sized prisms. Find the volume of the large prism and subtract the volumes of the smaller pieces to find the expression for the total volume!!

Thanks for helping!! (We are learning polynomials right now, like (2+x)^2 for clarification for the problems!!!) :)

Answers

The volume of the composite prism using the three methods is 4x^3 - 26x^2 -2x + 160

The volume using two prisms

From the question, we have the following parameters that can be used in our computation:

The composite figure

Using two prisms, we have the following dimensions

Rectangular prism 1: (x + 4) by (x - 5) by (x - 8)Rectangular prism 2: x by (x - 5) by (3x - 2)

The volume is the product of the dimensions

So, we have

Volume = (x + 4) * (x - 5) * (x - 8) + x * (x - 5) * (3x - 2)

Evaluate

Volume = 4x^3 - 26x^2 -2x + 160

The volume using three prisms

Here, we have the following dimensions

Rectangular prism 1: (x + 4) by (x - 5) by (x - 8)Rectangular prism 2: x by (x - 5) by (3x - 2 -x + 3)Rectangular prism 3: x by (x - 5) by (x - 3)

The volume is the product of the dimensions

So, we have

Volume = (x + 4) * (x - 5) * (x - 8) + x * (x - 5) * (3x - 2 - x + 3) + x * (x - 5) * (x - 3)

Evaluate

Volume = 4x^3 - 26x^2 -2x + 160

The volume as a single prism

In (a) and (b), we have

Volume = 4x^3 - 26x^2 -2x + 160

For the large prism, we have

Large = x * (x - 5) * (3x - 2)

Evaluate

Large = 3x^3 -17x^2 + 10x

Subtract 3x^3 -17x^2 + 10x from the total volume to get the smaller volume

Smaller = 4x^3 - 26x^2 -2x + 160 - (3x^3 -17x^2 + 10x)

Evaluate

Smaller = x^3 - 9x^2 - 12x + 160

Hence, the volume of the prism is 4x^3 - 26x^2 -2x + 160

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find two integers whose product is 136 such that one of the integers is seven less than three times the other integer

Answers

The two integers whose product is 136 are 17 and 8.

Let x be one of the integers. Then, the other integer is 3x - 7. The product of the two integers is given by:

x * (3x - 7) = 136

Expanding and solving for x, we get:

x^2 - 7x + 136 = 0

Using the quadratic formula, we can find the two solutions for x:

x = (-(-7) ± √([tex](-7)^2[/tex] - 4 * 1 * 136)) / (2 * 1)

x = (7 ± √(49 + 544)) / 2

x = (7 ± √593) / 2

Since x must be an integer, we round down the decimal to the nearest integer to get:

x = 8 or x = 9

Since x represents one of the integers, the other integer is 3x - 7, so:

3x - 7 = 3 * 8 - 7 = 17

Therefore, the two integers are 8 and 17, and their product is 136.

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Find total surface area of the cylinder whose radius is 3m and height is 6m...

Answers

The area is 169.65m² to get this A=2πrh+2πr2=2·π·3·6+2·π·32

A parachutist's rate during a free fall reaches 162 kilometers per hour. What is this rate in meters per second? At this rate, how many meters will the parachutist fall during 15 seconds of free fall? Do not round your answers.

Answers

Answer:

Below

Step-by-step explanation:

Using   162 km = 162000m   and  1 hour = 3600 s

162000 m / 3600s = 45 m/s

At constant 45 m/s :

  rate * time = distance

    45 m/s * 15 s = 675 m   in 15 seconds

Question content area top
Part 1
Suppose a compact disk​ (CD) you just purchased has tracks. After listening to the​ CD, you decide that you like of the songs. The random feature on your CD player will play each of the songs once in a random order. Find the probability that among the first songs played​ (a) you like 2 of​ them; (b) you like 3 of​ them; (c) you like all of them.

Answers

a) The probability that among the first songs played​  you like 2 of​ them

= 0.404

b)The probability that among the first songs played​  you like 3 of​ them

= 0.2246

c) The probability that among the first songs played​  you like all of​ them

= 0.0024

What is Combination?

Combinations are mathematical operations that count the number of potential configurations for a set of elements when the order of the selection is irrelevant.

Given:

Total tracks= 18

a) The probability that among the first songs played​  you like 2 of​ them

=  C(7 , 2) x C( 11, 3) /C(18, 5)

= 21 x 165 / 8568

= 0.404

b)The probability that among the first songs played​  you like 3 of​ them

= C(7 , 3) x C( 11, 2) /C(18, 5)

= 35 x 55 / 8568

= 0.2246

c) The probability that among the first songs played​ you like all of​ them

= C(7 , 5) x C( 11, 0) /C(18, 5)

= 0.0024

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what possible values can x % 10 evaluate to? (x is an integer). 0..9 means that possible values are 0, 1, 2, and so on up to 9. and so on.

Answers

The possible values of x % 10, where x is an integer, are integers between 0 and 9, inclusive, i.e. 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.

The modulo operation (represented by the percent symbol %) returns the remainder of the division of one number by another. For example, when x is divided by 10, the result of x % 10 is the remainder of that division.

Since 10 is a positive integer, when x is divided by 10, the result is always a non-negative integer. Furthermore, since the range of x is all integers, the result of x % 10 will always be less than 10.

Therefore, the possible x % 10 are integers in the range of 0 to 9, including 0 and 9. These are the remainders that can result from dividing x by 10. For example:

7 % 10 = 7

17 % 10 = 7

27 % 10 = 7

In all of these cases, the remainder is 7 when the number is divided by 10.

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Two friend shop for fresh fruit Elena buys a watermelon for 7.55 and 4 pounds of cherries Tonya buys a pineapple for $2.25 And 3 pounds of Cherries used the variable p to represent the price in dollars per pound of cherries 

Answers

Elena spent an amount of $4.10 + p more than Taniy.

What is the expression?

Expressions are defined as mathematical statements that have a minimum of two terms containing variables or numbers.

Let's represent the amount spent by Elena and Taniy as E and T, respectively. We know that:

E = 8.25 + 4p (since Elena bought a watermelon for $8.25 and 4 pounds of cherries for 4p)

T = 4.15 + 3p (since Taniy bought a pineapple for $4.15 and 3 pounds of cherries for 3p)

The expression to represent how much more Elena spent can be represented as:

E - T = (8.25 + 4p) - (4.15 + 3p)

Expanding the right side:

E - T = 8.25 + 4p - 4.15 - 3p

Combining like terms:

E - T = 4.10 + p

So Elena spent $4.10 + p more than Taniy.

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