A reflection in a line maps point B(3, - 1) to point B(11, - 1) . What is the equation of the line of reflection?​

The algebraic expression is h - 21 = 62

If we let "h" be Holly's original height,

The phrase "Holly's height decreased by 21 is 62" can be translated into an algebraic expression as:

h - 21 = 62

This equation represents the relationship between Holly's original height and her current height, after a decrease of 21 units.

We can solve for h by adding 21 to both sides of the equation:

h - 21 + 21 = 62 + 21

h = 83

Hence, Holly's original height was 83 units.

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The area of an equilateral triangle is 16√3 m² and the perimeter of an equilateral triangle is 24 m.

In an equilateral triangle, median, angle bisector and altitude for all sides are all the same and are the lines of symmetry of the equilateral triangle. The area of an equilateral triangle is √3/4 ×a².

From the given figure, side of the equilateral triangle is 8 m.

Now, area of an equilateral triangle is

√3/4 ×8²

= √3/4 ×64

= 16√3 m²

The perimeter of an equilateral triangle is 3a.

Now, the perimeter is 3×8

= 24 m

Therefore, the area of an equilateral triangle is 16√3 m².

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a) The x-range of a unit square is from o to 1 and y-range is also from 0 to 1

Sample space = {(x, y)} , 0≤x≤1,  0≤y≤1.

So, sample space associated with this random experiment is

{(x, y)} , 0≤x≤1,  0≤y≤1.

b) From the given data,

Sample space for A : {1, 3, 5, 7, 9, 11,...}

Sample space for B: {5, 10, 15, 20, 25,...}

Therefore, the sample space for A∩B will be the set of all odd natural numbers divisible by 5 which is

{5, 15, 25, 35,....}

c) First letter is the capital letter = 26 Possibilities

then four digits = 9*10*10*10

two lower case letters = 26*26

Total possible ways = 26*9*10*10*10*26*26

= 15,81,84,000 ways.

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Complete question:

Suppose a point is to be selected at random from the unit square. Write the sample space associated with this random experiment. 2. Let S = {0, 1, 2, 3, 4, ...), A = the set of odd natural numbers, and B = the set of natural numbers divisible by 5. What is the set An B? 3. A computer password consists of two lowercase letters followed by a capital letter and four digits. Find the total number of possible passwords.

The value of the right triangle cos d = 15/17 and cos c = 8/17.

Simply put, trigonometric functions—also referred to as circular functions—are the functions of a triangle's angle. This means that these trig functions provide the relationship between the angles and sides of a triangle. Sine, cosine, tangent, cotangent, secant, and cosecant are the fundamental trigonometric functions.

Given that, the value of tan c = 15/8 and the value of sin d = 8/17.

From the trigonometric functions we can conclude that:

Opposite side to c = 15

Adjacent side to c = 8

Hypotenuse = 17

Opposite side to d = 8

Adjacent side to d = 15

The values of cos d is:

cos d = Adjacent side to d / Hypotenuse = 15/17

cos c = Adjacent side to c / Hypotenuse = 8/17

Hence the value of the right triangle cos d = 15/17 and cos c = 8/17.

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The total amount of interest earned at the end of 2 years is $60.

1. Calculate the interest earned in one year:

Interest = Principal × Rate × Time

Interest = 600 × 0.05 × 1

Interest = $30

2. Multiply the interest earned in one year by the number of years:

Total interest = 30 × 2

Total interest = $60

The total amount of interest earned at the end of 2 years is $60. This amount was earned by taking the principal amount of $600 and multiplying it by the rate of 5%, and then multiplying that product by the number of years, which in this case is 2. This calculation can be expressed as:

Total interest = Principal × Rate × Time

Total interest = 600 × 0.05 × 2

Total interest = $60

the complete question is :

An account earns simple annual interest. $600 at 5% for 2 years. How much interest will be earned on $600 invested at 5% simple annual interest for 2 years?

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The probability of getting both the marbles to be red will be 4/25.

Probability is a number that indicates the likelihood of an event occurring. Probability is defined as the ratio of favorable outcomes to all outcomes.

Probability = Number of favorable outcomes / Number of samples

Given that two red and three black marbles are in a bag. If Abby takes a marble out of the bag without looking, puts it back, and then draws another marble.

The probability of getting red in the first draw,

P = 2 / 5

Now the marble is returned and again the probability of getting the red marble is,

P = 2 / 5

The probability of getting both the marbles red will be,

Pb = ( 2/ 5 ) x ( 2 / 5 )

Pb = 4 / 25

Therefore, there is a 4/25 chance that both marbles will be red.

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a) The probability that the second person chosen is also a boy is; 13/28

b) The probability that both students chosen are girls is; 5/18

The parameters given in the question are;

Total number of students in the class = 28 students

Number of boys in class = 13 students

Number of girls = 28 - 13 = 15 students

a) Probability of the first student being selected as a boy is;

P(First is boy) = 13/28

b) The probability that both students chosen are girls is;

P(both girls) = (15/28) * (14/27) = 5/18

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The difference between the amount Anna ate and the amount she gave to her brother can be found by subtracting 3/8 from 5/8. This can be expressed as an equation by writing 5/8 - 3/8 = x, where x is the difference.

5/8 - 3/8 = x

5/8 = 5 ÷ 8

= 0.625

3/8 = 3 ÷ 8

= 0.375

0.625 - 0.375 = x

= 0.25

Therefore, the difference between the amount Anna ate and the amount she gave to her brother is 0.25.The difference between the amount Anna ate and the amount she gave to her brother can be found by subtracting 3/8 from 5/8. This can be expressed as an equation by writing 5/8 - 3/8 = x, where x is the difference. To solve this equation, we first need to convert the fractions into decimal values. 5/8 is equal to 5 divided by 8, which is equal to 0.625. 3/8 is equal to 3 divided by 8, which is equal to 0.375. We can then subtract 0.375 from 0.625 to get the difference. This gives us 0.25, which is the difference between the amount Anna ate and the amount she gave to her brother. Therefore, the answer to the equation 5/8 - 3/8 = x is x = 0.25.

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The of association represented in the graph is positive linear association.

option C

A positive correlation is a statistical relationship between two variables such that as one variable increases, the other variable also increases, and as one variable decreases, the other variable decreases as well.

In other words, positive correlation means that as the value of one variable goes up, the value of the other variable also goes up, and vice versa. The correlation is said to be positive because both variables move in the same direction.

The strength of the correlation can be measured using a correlation coefficient, which ranges from -1 to 1. A correlation coefficient of 1 indicates a perfect positive correlation, while a correlation coefficient of 0 indicates no correlation.

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The simplified expression after factoring numerator and denominator is (x + 7) / x.

We can start by factoring the numerator and denominator of the first fraction:

x^2 - 49 = (x + 7)(x - 7)

The denominator can also be factored using the quadratic formula or by factoring as a product of two binomials:

x^2 - 4x - 21 = (x - 7)(x + 3)

So, the first fraction can be simplified as:

(x + 7)(x - 7)/[(x - 7)(x + 3)]

We can cancel out the (x - 7) factor in the numerator and denominator, leaving:

(x + 7)/(x + 3)

Next, we can simplify the second fraction by canceling out the common factor of (x + 3) in both the numerator and denominator:

(x + 3)/x

Putting it all together, we get:

[(x + 7)/(x + 3)] * [(x + 3)/x] = x + 7 / x

Therefore, the simplified expression is (x + 7) / x.

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____The given question is incorrect, the correct question is given below:

The numerator should be expanded and simplified. The denominator should be either expanded or factored.

Simplify (x^2-49)/(x^2-4x-21)*(x+3)/x

There are 840 ways for the person to get 6 fives, 3 ones, and 1 two in 10 rolls of a six-sided die.

To calculate the number of ways to roll 6 fives, 3 ones, and 1 two in 10 rolls of a six-sided die, we can use the formula for combinations with repetition.

The number of ways to choose 6 rolls to be fives out of 10 is given by the combination formula:

C(10, 6) = 10! / (6! * (10 - 6)!) = 210

Similarly, the number of ways to choose 3 rolls to be ones out of the remaining 4 rolls is:

C(4, 3) = 4! / (3! * (4 - 3)!) = 4

Finally, there is only one way to choose the remaining roll to be a two.

Therefore, the total number of ways to roll 6 fives, 3 ones, and 1 two in 10 rolls of a six-sided die is:

210 * 4 * 1 = 840.

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Using the fractional value of blue paint to white paint, the number of pints of blue paint Fatina used to paint her bedroom walls is 3.12 pints.

A fractional value is a proportional quantity of the whole value.

Fractional values are depicted in decimals, fractions, or percentages.

The total quantity of white and blue paints used on the bedroom walls = 7.8 pints

The fraction of the white paint = 3/5

The fraction of the blue paint = 2/5 (1- 3/5)

2/5 of 7.8 = 3.12 pints

Thus, proportionately, we can conclude that the blue paint Fatina used was 3.12 pints.

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Kathy uses 3.12 pint of white paint to paint her bedroom walls

Total amount of paint ( Blue and white paint)= 7.8 pints

Amount of  blue paint=3/5 x 7.8 = 4.68Pints

amount of white paint = Total amount of paint - amount of blue  paint

= 7.6 pints - 4.68 pints

=3.12 pint of white paint

In conclusion, she uses 3.12 pint of white paint  to paint her bedroom walls

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The sum Given it can seen that according to the closure property of Rational numbers  the addition of two rational numbers will sum up to a rational number provided that the rational numbers ≠ 0 and a set of rational number is closed under the closures property rule i.e x + y = y + x.

What is Closure Property of Integers ?

Closure Property of Integers states the sum or subtraction of two integers always gives an integer.

Rational number is defined as a number that can be made by dividing two integers.

Using the definition of rational and expanding the property, we can conclude that the sum of two rational numbers will result in a rational number.

using the closure property and based on the sum given, the addition of two rational numbers will sum up to a rational number provided that the rational numbers ≠ 0 and a set of rational number is closed under the closures property rule i.e x + y = y + x

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Answer: No

Step-by-step explanation:

Valid only for numbers less than 40.

P(40) = 412 which is not a prime number

For four variables the required number of system of linear equations are at least option d. 4 equations.

Therefore, if there are four variables in the system of linear equations then we should have option d. 4 equations.

The above question is incomplete , the complete question is:

If we have four variables, then how many equations will we have in our system of linear equations?

a. 5       b. 2      c. 3     d. 4

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answer:     12          

explanation:

The values of x, y and z are;

x. x = 60° y = 55°

xi. x = 68° y = 56° z = 56°

xiii. x = 40° y = 50°

xiv. x = 40° y = 50°

A triangle is a 3-sided polygon that has three edges and three vertices. The most important property of a triangle is that the sum of the internal angles of a triangle that always equals 180 degrees. This property is called angle sum property of triangle.

x. x = 60° (corresponding angles are equal)

y + 65° + 60° = 180° (Sum of angles in a triangle equals 180°)

y + 125° = 180°

y = 180° - 125°

y = 55°

xi. y = 56° (corresponding angles are equal)

y = z = 56° (angles in equal sides of a triangle are equal)

x + 56° + 56° = 180° (Sum of angles in a triangle equals 180°)

x + 112° = 180°

x = 180° - 112°

x = 68°

xiii. x + 140° = 180° (sum of angles on a straight line equals 180°)

x = 180° - 140°

x = 40°

y + 90° + 40° = 180° (sum of angles in a triangle equals 180°)

y + 130° = 180°

y = 180° - 130°

y = 50°

xiv. y + 130° = 180° (sum of angles on a straight line equals 180°)

y = 180° - 130°

y = 50°

x + 90° + 50° = 180° (sum of angles in a triangle equals 180°)

x + 140° = 180°

x = 180° - 140°

x = 40°

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In all together, Clara ate 20 nuts.

A system of equations is a set of one or more equations involving a number of variables.

The solutions to systems of equations are the variable mappings such that all component equations are satisfied—in other words, the locations at which all of these equations intersect.

Given that Clara snacked on a mix of almonds and pecans. She ate 3 almonds for every 1 pecan. Clara ate 10 more almonds than pecans.

Let the number of pecans be x and the number of almonds is y.

We can write the system of equations as:

y = 3x

y = x + 10

Equating the value of {y}, we get -

3x = x + 10

2x = 10

x = 5          ...(1)

y = x + 10 = 15

y = 15         ...(2)

x + y = 15 + 5 = 20

Therefore, in together, Clara ate 20 nuts.

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To add a single edge to a graph to create an Euler path, we must connect two existing vertices with an odd degree.

In graph theory, an Euler path is a path that visits every edge of a graph exactly once. However, not all graphs have an Euler path. If a graph has an Euler path, it must have either zero or two vertices with an odd degree. In this scenario, we are given a graph and are asked to add a single edge to create an Euler path.

To add a single edge to the graph, we must connect two existing vertices that have an odd degree. This is because adding a new vertex would change the degree of the graph and potentially affect the existence of an Euler path. Therefore, we must carefully consider the degree of each vertex before adding the edge.

Let's consider a graph:

     A

    / \

   B---C

  / \ / \

 D---E---F

In this graph, vertices B, E, and F have an odd degree. To create an Euler path, we must connect two of these vertices with a new edge. Let's choose B and E, and add the edge (B, E) to the graph.

    A

    / \

   B---C

  / \ / \

 D---E---F

Now, the graph has only one vertex with an odd degree, which is C. This means that the graph has an Euler path that starts at C, visits every edge exactly once, and ends at A.

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you forgot to put the question

Answer: The simple interest will be 20%.

Step-by-step explanation:

we know the simple interest of borrowed amount is:

S.I.= (P x R x T)/100 ..... (i)

where P⇒ Principal amount

R⇒ rate of interest

T⇒ time

and

total Pays Back amount = Principal amount + S.I.

Hence S.I. = Pays Back amount - Principal amount

Now, as per the question: Clinton pays back Double of the amount hi borrowed. Means

if Principal amount = P

then Pays Back amount = 2P ⇒ S.I.= P

Rate of Interest = R

and Time = 5 years

P= (P x R x 5)/100

R= 100/5

R = 20%

Therefore, the simple interest is 20% annually.

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The standard function for F(x)=4(x+6)2+5, will be f(x)=8x+53.

What is the definition of a function?

A function is defined as a connection between a set of inputs and a single output. A function is a link between inputs that corresponds to exactly one output. Every function has a domain, a co-domain, and a range. A function is often denoted as f(x), where x represents the input. The general representation of a function is y = f(x).

There are several types of functions in mathematics. Here are a few examples:

An injective function or a one to one function exists when there is a mapping for a range for each domain between two sets.

Surjective functions, also known as Onto functions, are employed for transferring more than one element from domain to range.

A polynomial function is a function composed of polynomials.

Functions that may be used to inverse another function are known as inverse functions.

Now,

Given function is F(x)=4(x+6)2+5

=(4x+24)2+5

=8x+48+5

=8x+53

hence,

          The standard function for F(x)=4(x+6)2+5, will be f(x)=8x+53.

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As a result, no particular postulate can be used to demonstrate their congruence due to a lack of adequate data. So "None" is the correct response.

If two figures share the same form, congruent corresponding angles (which means the angles in the same locations of each shape are the same), and identical scale factors, they are said to be "similar figures." Equal scale factors signify a matched ratio between the lengths of their respective sides.

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Answer: None

Step-by-step explanation: I Just did it

The systems of equations in slope intercept form is

y = -6x + 110

y = 9x + 54

When you know the slope of the line to be investigated and the given point is also the y intercept, you can utilise the slope intercept formula, y = mx + b. (0, b). The y value of the y intercept point is denoted by the symbol b in the formula.

As, We know Slope-intercept form is

y = mx + b

where b is the starting value and m is the change per day.

Farmer Quect started with 110 rews on his farm. Every hour he destroyed 6 more of them.

So, the Equation to show the Situation

y = -6x + 110

and, Farmer Mimstone started with 54 rews on her farm. Every hour she collected 9 more of them.

So, the Equation to show the Situation

y = 9x + 54

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Answer:

Step-by-step explanation:

600 secs=600/60 mins=10 mins

9 mins= 9 mins

Therefore, 9 mins : 600 secs

                =9 mins : 10 mins

                =9:10

Answer:

  36 bottles

Step-by-step explanation:

You want to know the number of bottles that must be painted and sold in order to make a profit of $120, given that 3 bottles can be purchased for $11, and each bottle can be sold for $7.

The profit on each bottle is the difference between its cost and what it is sold for. The cost of 1 bottle is 1/3 of the cost of 3 bottles.

  profit = selling price - purchase price

  profit = $7/bottle - ($11/(3 bottles)) = $(21/3 -11/3)/bottle = $(10/3)/bottle

To make a profit of $120, you need n bottles such that ...

  (10/3)n = 120

  n = 36 . . . . . . . . . multiply by 3/10

The club needs to buy, paint, and sell 36 bottles to raise $120.

Answer:

10%

Explanation:

You increased it by 5% twice, which is basically 5+5 or 5x2 which equals 10

The difference between the amount Anna ate and the amount she gave to her brother can be found by subtracting 3/8 from 5/8. This can be expressed as an equation by writing 5/8 - 3/8 = x, where x is the difference.

5/8 - 3/8 = x

5/8 = 5 ÷ 8

= 0.625

3/8 = 3 ÷ 8

= 0.375

0.625 - 0.375 = x

= 0.25

Therefore, the difference between the amount Anna ate and the amount she gave to her brother is 0.25.The difference between the amount Anna ate and the amount she gave to her brother can be found by subtracting 3/8 from 5/8. This can be expressed as an equation by writing 5/8 - 3/8 = x, where x is the difference. To solve this equation, we first need to convert the fractions into decimal values. 5/8 is equal to 5 divided by 8, which is equal to 0.625. 3/8 is equal to 3 divided by 8, which is equal to 0.375. We can then subtract 0.375 from 0.625 to get the difference. This gives us 0.25, which is the difference between the amount Anna ate and the amount she gave to her brother. Therefore, the answer to the equation 5/8 - 3/8 = x is x = 0.25.

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The complete question is

Anna ate 5 8 of an orange and gave the other 3 8 to her brother. Which equation can be used to find the difference between the amount Anna ate and the amount she gave her brother?

The approximate value of f(4.5) is 550000.

Exponents are used in exponential functions, as the name suggests. But take note that an exponential function does not have a constant as its base and a variable as its exponent (A function is a power function rather than an exponential function if its base is a variable and its exponent is a constant).

From the given graph, the coordinate points are (0, 1000000), (1, 900000) and (2, 810000)

We know that, f(x)=mx+c

Here, (0, 1000000) and (1, 900000)

Now, m=(900000-1000000)/(1-0)

m=-100000/(1-0)

m=-100000

Substitute b=-100000 and (x, y)=(0, 1000000) in y=mx+c

1000000=-100000(0)+c

c=1000000

Substitute m=-100000 and c=1000000 in y=mx+c, we get

y=-100000x+1000000

The approximate value of f(4.5)

Now, y=-100000(4.5)+1000000

y=550000

Therefore, the approximate value of f(4.5) is 550000.

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By examining the shape and degree of association on the scatter plot, we can gain insights into the nature of the relationship between the variables and make predictions about their behavior in the future.

A scatter plot is a graphical representation of a set of data that shows the relationship between two variables.

The type of association between the two variables can be identified by the shape of the scatter plot. If the points on the plot form a linear pattern, then the association is said to be linear. If the points on the plot form a curved pattern, then the association is said to be nonlinear.

The degree of association between the two variables can be determined by the strength of the correlation coefficient, which is a measure of how closely the points on the scatter plot follow a linear pattern. The correlation coefficient ranges from -1 to 1, where a correlation coefficient of 1 indicates a perfect positive linear association, a correlation coefficient of -1 indicates a perfect negative linear association, and a correlation coefficient of 0 indicates no association between the two variables.

In this scenario, if the scatter plot shows a linear pattern and the correlation coefficient is positive, it means that there is a positive association between the amount of time the player spent practicing and the number of points he scored in the game.

On the other hand, if the correlation coefficient is negative, it means that there is a negative association between the two variables, which implies that the more time the player spent practicing, the lower the number of points he scored in the game.

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