The following dotplot shows the centuries during which the 111111 castles whose ruins remain in Somerset, England were constructed. Each dot represents a different castle. According to the 1.5.IQR rule for outliers, how many high outliers are there in the data set?

On solving the provided question, we can say that - here in graph Between the lowest number, which is 0, and the highest value, which is 5, there is a range. The range is therefore -9=y=5.

Graphs are visual representations or charts used in mathematics to methodically express data or values. A relationship between two or more objects is frequently represented by a point on a graph. A non-linear data structure called a graph is made up of nodes, or vertices, and edges. Connect the nodes, also known as vertices. This graph comprises a set of vertices V= 1, 2, 3, 5, and a set of edges E= 1, 2, 1, 3, 2, 4, and (2.5), (3.5), (4.5). Statistics graphs (bar charts, pie charts, line charts, etc.) Exponential diagrams. triangle graph, a logarithmic graph

There is a range between the minimum value, which is 0, and the greatest value, which is 5. Thus, the range is -9=y=5.

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Answer:

y = -3x +20

Step-by-step explanation:

Equation of line: y =mx + b

Where m is the slope and b is the y-intercept.

3x + y = 17

Write the above equation in y = mx +b form.

      y = -3x + 17

m = -3

Parallel lines have same slope.

So, slope of the required line is (-3).

     y = -3x + b

This line is passing through (4,8). Substitute in the above equation and find the value of 'b'.

       8 = -3*4 + b

        8 = -12 + b

  8 + 12 = b

          b = 20

Equation of the line:

               [tex]\sf \boxed{ y = -3x + 20}[/tex]

The value for the blanks after calculating the as per the given data is found to be as 4 and 9 respectively.

On solving the question we will get the answer of the final blank as 0.

The question can be rephrased as ,

__x 9 - __ x 4 = ___ - ___ = ___.

Now if we will place 4 in first blank and 9 in second blank we will get the result as follows,

4 x 9 - 9 x 4 = 36 - 36 = 0

Therefore , we will get our desired answer.

A relationship between two quantities or, more broadly, two mathematical expressions that asserts that the quantities have the same value or that the expressions reflect the same mathematical object is referred to as equality.

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The value u > -16 that makes the inequality 5u > -80 is true.

In mathematics, "inequality" refers to a relationship between two expressions or values that are not equal to each other. To solve the inequality, you may multiply or divide each side by the same positive number, add the same amount to each side, take the same amount away from each side, and more. You must flip the inequality sign if you multiply or divide either side by a negative number.

Given:

We have the inequality,

5u > -80

To find the solution set of the inequality;

Divide by 5 to both sides,

5u/5 > -80/5

u > -16.

That means, the inequality is true for u > -16.

Therefore, the inequality is true for u > -16.

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The dimensions length is 10 feet, width is 10 feet and height is 5 feet and the smallest possible surface area is 300 square feet.

Volume=lbh

lbh=500 cubic feet

h=500/lb

Surface area S=lb+2bh+2lh...(1) {rectangular tank has no top}

S=lb+2b(500/lb)+2l(500/lb) {substituting the value of h in 1}

S=lb+1000/l+1000/b { partially differentiating S with respect to l and b}

for S to be minimum dS/dl=0 and dS/db=0

dS/dl= b-1000/l^2

dS/dl=0

b=1000/l^2...(2)

dS/db= l-1000/b^2

dS/db=0

l=1000/b^2

l=1000/(1000/l^2)^2 {substituting the value of b from 2}

l=(1000 x l^4)/(1000000)

1000000/1000=l^4/l

1000=l^3

l=10  feet

b=1000/l^2

b=1000/100=10  feet

lbh=500

h=500/(10x10(

h=5  feet

S=10x10+2x5x10+2x10x5

S=300 square  feet

Length is 10 feet, width is 10 feet and height is 5 feet and the smallest possible surface area is 300 square feet of the  rectangular tank.

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For the given expression, x has a value of 6.5.

A sentence qualifies as a mathematical expression if it comprises one or more mathematical operations, at least two numbers, or variables.

A number is 6 times larger than the other number, x, by a factor of 2.

The equation x/2 + 6 in mathematics represents this claim.

Here, we have the equation:

-3(4x - 5) = 2(1 - 5x)

Find the value of x by solving the expression:

-3(4x - 5) = 2(1 - 5x)

-12x + 15 = 2 - 10x

-2x = -13

x = -13/-2

x = 13/2

x = 6.5

Therefore, for the given expression, x has a value of 6.5.

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Correct question:

What value of x satisfies the equation -3(4x - 5) = 2(1 - 5x)?

Answer:

X=8

Step-by-step explanation:

Step 1: Simplify both sides of the equation.

17x−30+7x+18=180

17x+−30+7x+18=180

(17x+7x)+(−30+18)=180(Combine Like Terms)

24x+−12=180

24x−12=180

Step 2: Add 12 to both sides.

24x−12+12=180+12

24x=192

Step 3: Divide both sides by 24.

X=8

Enchanted Rock State Natural Area is located at latitude 30.506130 and longitude -98.820064. The geographic coordinates of Enchanted Rock State Natural Area in Fredericksburg, United States, are 30° 30' 22.068" N and 98° 49' 12.2304" W. Enchanted Rock State Natural Area falls under the Mysterious Sites category.

The standard datum used by default for GPS devices used for commercial and recreational purposes is WGS84. GPS users are advised to always verify the datum of the maps they are utilising.

WGS 84, also known as the datum, is now in use by US forces.

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Answer:

The tower is 113 meters.

Step-by-step explanation:

We are given a pole and a tower that both create a shadow.

Hence, the figures made are triangles.

If you draw the figure (attached to this response), you can see the two triangles are similar triangles.

⭐What are similar triangles?

The length of the height of the pole (3.2) corresponds to the length of the height of the tower (x).

The length of the shadow of the pole (1.32) corresponds to the length of the shadow of the tower (46.75).

Therefore, our two ratios are:

[tex]\frac{3.2}{x}[/tex] and [tex]\frac{1.32}{46.75}[/tex]

A proportion is when you set two ratios equal to each other:

[tex]\frac{3.2}{x} = \frac{1.32}{46.75}[/tex]

To solve for x, cross multiply by multiplying the opposite parts of the fraction together.

[tex]\frac{3.2}{x} = \frac{1.32}{46.75}\\46.75(3.2) = 1.32x\\149.6 = 1.32x\\\\113 = x[/tex]

∴ The tower is 113 meters tall!

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The pairs of alternate interior angles are <5<4 and <6<3

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On solving the provided question, we can say that - the radicals are as follows be = 3x^2|y| sqrt(7x)  

The square root or nth root symbol is called a radical. Expressions with square roots are referred to as root expressions. A radical's radicand is a number or phrase that appears there. The radicals 7, 2y+1, and so on are examples. The following phrases can also be used to describe radicals: Radical equations are equations contained within of radicals. The term "root expression" refers to the expression found inside the square root. Examples of radical representations are the numbers 2, 372, 2x+7, and 41p.

here,

the radicals will be - 7xy ∛(xy^2)

and   3x^2|y| sqrt(7x)  

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Therefore after using the Pythagorean Theorem and the properties of chords in a circle we got 626 when m+n is divided by 1000.

The Pythagorean theorem, sometimes known as Pythagoras' theorem, is a basic relationship between a right triangle's three sides in Euclidean geometry. According to this statement, the areas of the squares on the other two sides add up to the size of the square whose side is the hypotenuse.

The longest side of a right-angled triangle, or the side across from the right angle, is called the hypotenuse.

Let M and N be the midpoints of chords AB and CD, respectively.

Let X and Y be the foot of the perpendicular from P to chord AB and CD respectively.

Since X,Y are on the circle and P is the midpoint of XY,

OP = PX = PY = radius = 25

Now, using the Distance Formula:

(XM)^2 + (YN)^2 = (12)^2

By the Pythagorean Theorem, on triangle PXN and PYM,

(25)^2 + (YN)^2 = (PN)^2 = (14/2)^2 and

(25)^2 + (XM)^2 = (PX)^2 = (30/2)^2

OP^2 = 625 = 25^2

thus m+n = 625 + 1 = 626

and remainder when m+n is divided by 1000 is 626 % 1000 = 626

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The amount of money which the chef spends on steak as calculated from the data given is found to be $412.50.

Now as we know that ,

for a meal of 12 meals the chef uses 3 pounds.

Therefore , for a meal of 250 meals the chef uses x pounds

Now , we will solve this proportion.

x=(250 meals*3 pounds)/12 meals

= 62.5 pounds

Now , cost of steaks = 6.60 dollars.

Therefore cost of 62.5 pounds of steaks will be ,

62.5 pound x $ 6.60/pound

=  $ 412.50

A comparison between two numbers is called a proportion. If two sets of provided numbers increase or decrease in the same ratio, then the ratios are said to be directly proportional to each other.

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A) Amaire have more money than Jermaine after 10 years.

B) By [tex]5.387*10^{11}[/tex]% Amaire has more money than Jermaine.

What is compound interest?

The interest charged on a loan or deposit is known as compound interest. It is the idea that we employ the most frequently on a daily basis. Compound interest is calculated for an amount based on both the principal and cumulative interest.

Amare and Jermaine has initial amount = $1000

Amare spend his money that pays 2.25% compounded daily.

where are Jermain invest his money that pays 2.25% compounded annually.

Formula of Compound interest that compounded daily

final amount = [tex]A(1+\frac{r}{365})^{365t}[/tex]

where A is initial amount and t is time in years .

final amount after 10 years

final amount = [tex]1000(1+\frac{2.25}{365})^{365*10}[/tex]

final amount = 1000×[tex]1.00616^{3650}[/tex]

final amount = 1000×5.51×[tex]10^{9}[/tex]

final amount  = $5.51 ×[tex]10^{12}[/tex]

Formula of Compound interest that compounded annually

final amount = [tex]A(1+\frac{r}{100})^{t}[/tex]

where A is initial amount and t is time in years .

final amount after 10 years

final amount = [tex]1000(1+\frac{2.25}{1000})^{10}[/tex]

final amount = 1000×[tex]1.00225^{10}[/tex]

final amount = 1000×1.0227

final amount  = $1022.7

Part A :

Amare has more money after 10 years.

part B :

percent more money = [($5.51 ×[tex]10^{12}[/tex] - 1022.7)/1022.7]*100=[tex]5.387*10^{11}[/tex]%

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No, the segments will not form a triangle based on the line segments provided.

For three line segments to form a triangle, they must satisfy the triangle inequality theorem. The triangle inequality theorem states that for any triangle, the sum of the lengths of any two sides of the triangle must be greater than the length of the third side.

This is because if the sum of the lengths of any two sides is less than or equal to the third side, it would not be possible to form a triangle with those side lengths, as the two shorter sides would not be able to reach the longer side to form the triangle.

In this case, the sum of the two shorter segments (12 units + 10 units) is 22 units, which is less than the measure of the longest segment (18 units). Therefore, the three segments will not form a triangle.

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The equation that represents the relationship of x number of badges to y dollars is y = 9x.

What is an equation?

A mathematical statement called an equation displays the equality of two mathematical expressions. Variables, coefficients, exponents, arithmetic operators, equal signs, and constants are some of the components that make up an equation.

 An equation is said to be linear if the maximum power of the variable is consistently 1.

Let the number of badges be x and the cost of x number of badges be y.

From the question, we know that for 48 badges, the cost is $432.

So the cost of one badge = 432/48 = $9

Now the cost of x number of badges = $(9x)

We mentioned in the beginning that the cost of x number of badges is y

Therefore the equation that represent the relationship of x badge to y dollars is,

        y = 9x

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y = 3/2x - 9/2

The equation of the line that passes through the points (4,-3) and (2,0) can be found using the point-slope form of a linear equation. The point-slope form of a linear equation is y-y1=m(x-x1), where m is the slope of the line and (x1,y1) is a point on the line.

To calculate the slope, we will use the formula m = (y2-y1)/(x2-x1). In this equation, (x1,y1) = (4,-3) and (x2,y2) = (2,0). Substituting these values into the slope formula, we get m = (0-(-3))/(2-4) = 3/(-2) = -1.5.

Now that we have the slope, we can plug the point (4,-3) and the slope (-1.5) into the point-slope form of a linear equation to get y-(-3)=-1.5(x-4). Simplifying this equation, we get y+3=-1.5x+6, which is the equation of the line that passes through the points (4,-3) and (2,0).

1.3338 is the likelihood, The probability of anything occurring is known as probability.

The probability of anything occurring is known as probability. To determine probability, divide the total number of possible outcomes by the number of possible ways an event could occur.

The likelihood or chance that a specific event will occur is represented by a probability. Both proportions between 0 and 1 and percentages between 0% and 100% can be used to describe probabilities.

Explanation:

Mean (m) = 25

The standard deviation is 13

Sample size (n) is 95.

Chance that x will fall between 22 and 27.

Zscore = x - mean / s / n

If x = 22, Zscore is equal to (22 - 25) / (13/95).

For x = 27, Zscore is equal to (27 - 25) / (13/95) / n = 13 / 95, which is 1.3338.

1.3338 is the likelihood.

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Determine what a, b, and c are worth. the quadratic formula in writing. After that, enter the values for a, b, and c. Simplify.

A quadratic polynomial in a single variable is represented by the expression x ax2+bx+c=0, which is a quadratic equation. a 0. Since it is a second order polynomial, the Fundamental Theorem of Algebra guarantees that it has at least one solution. Simple or difficult solutions are both possible. The term "quadratic equation" refers to an equation that is quadratic. It must square at least one word, according to this indication. One of the common solutions for quadratic equations is the formula "ax2 + bx + c = 0." where the variables "X" are undefined and are numerical coefficients or constants a, b, and c.

given

steps are

Find out what a, b, and c are worth.

Quadratic formula: write it down.

Add the values of a, b, and c after that. Simplify.

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Answer:

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

According to the two-tangent theorem, two tangent segments drawn to one circle from the same external point are congruent.

That is:

We have EF = 10 units, it means EG is also 10 units.

The perimeter of triangle EHP is:

We can substitute:

Then the perimeter is:

Answer: x= 23

Step-by-step explanation:

Let's start by using the provided information to formulate an equation.

Kelly starts with $800 in her savings account, so this is the initial amount. She makes $340 per week, 15% of which is invested into her savings account for 8 weeks, so this information will form a rate. Kelly also withdrew (subtracted) 45 dollars 3 times. Now, let's form the equation.

y=8(.15·340)+800-45(3), where y=remaining balance after 8 weeks. Now, lets simplify the equation using Orders of Operations.

Simplify parenthesis first:

y=8(.15·340)+800-45(3)

y=8(51)+800-45(3)

Complete any multiplication:

y=8(51)+800-45(3)

y=408+800-135

Add and subtract from left to right; addition and subtraction are not separate steps and must be done in the same step, so we work left to right as to whichever comes first:

y=408+800-135

y=1208-135

y=1,073

Remember that y is the remaining balance after 8 weeks. This means that $1,073 dollars is the balance after 8 weeks.

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The account balance at the end of 8 weeks is $1073.

A percentage is a value per hundredth. Percentages can be converted into decimals and fractions by dividing the percentage value by a hundred.

Given, Kelly has a savings account with a beginning balance of $800 and she earns $340 per week.

Therefore, 15% of her weekly earnings for 8 weeks is,

= (15/100)×340×8.

= $408.

Again, She made $45 withdrawals 3 times, which is,

= 3×45.

= $135.

Therefore, The final amount in her account after 8 weeks is,

= $(800 + 408 - 135).

= $1073.

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Field goal stats include number of made/attempted, percentage made, average points scored per made, total points scored/attempted, and possibly rebounds, assists, turnovers.

FG (field goal) stats are a way of measuring an individual or team's performance in the sport of basketball. Generally, the stats will include the number of field goals made, the number of field goals attempted, the percentage of field goals made, the average number of points scored per field goal made, the total number of points scored, and the total number of points attempted. This data can be used to compare different players or teams, or to track a player or team's performance over time. Depending on the context, other stats such as rebounds, assists, and turnovers may also be included. This data can help coaches, scouts, and analysts make decisions and evaluate performance. Ultimately, it is important to use field goal stats in combination with other data and context to create an accurate picture of a player or team's performance.

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If at least one of $y_1, y_2$ is nonzero, then $\frac{y_2}{y_1}$ = $\frac{1}{4}$

If x is directly proportional to y, we can write this as x = ky for some constant k.

Since $\frac{x_1}{x_2} = 4$, we can write it as $x_1 = 4x_2$.

Now, substituting the value of $x_1$ in equation x = ky gives

$4x_2 = ky_1$.

Also, since x = ky, we can write $x_2 = ky_2$.

Now, we can substitute the value of $x_2$ in the equation $4x_2 = ky_1$

So, $4ky_2=ky_1$, which gives $\frac{y_2}{y_1} = \frac{1}{4}$

Therefore, $\frac{y_2}{y_1}$ = $\frac{1}{4}$ when x is directly proportional to y and $\frac{x_1}{x_2} = 4$.

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The value of a and b are respectively 15 and 17 respectively.

What are trigonometry ratios?

The trigonometric functions in mathematics are real functions that connect the right-angled triangle's angle to the ratios of its two side lengths. They are extensively employed in all fields of geometry-related study, including geodesy, solid mechanics, celestial mechanics, and many others.

Given that csc θ = 17/8 and cos θ = a/b.

The reciprocal of sin θ is csc θ.

Therefore,

1/sinθ = 17/8

or, sin θ = 8 /17

Applying the trigonometry identity cos²θ = 1- sin²θ

cos²θ = 1- (8/17)²

cos²θ = 1- 64/289

cos²θ = 225/289

cos θ = 15/17

The value of a is 15 and the value of b is 17.

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The best option regarding the solutions of the trigonometric equation presented in this problem is given as follows:

A. 60º + n360º, 300º + n360º.

The trigonometric equation for this problem is defined as follows:

[tex]\cos{x} - \sqrt{1 - 3\cos^2{x}} = 0[/tex]

Then, isolating the cosine, we have that:

[tex]\cos{x} = \sqrt{1 - 3\cos^2{x}}[/tex]

Applying the square for both sides, we have that:

cos²(x) = 1 - 3cos²(x).

4cos²(x) = 1.

cos²(x) = 1/4

cos²(x) = 0.25.

Applying the square root to both sides, we have that:

cos(x) = 0.5.

Meaning that the angle measures of x with the cosine of 0.5 are given as follows:

x = 60º, x = 300º.

(as the cosine is positive on the first and fourth quadrant).

One entire lap over the unit circle is equivalent to 360º, hence adding 360º n times to any of these solutions is also a solution to the trigonometric equation, meaning that option a is correct.

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The annual salary will be 49750

Gross salary would be the total amount of compensation that an employer or business pays an employee during their employment. The Cost of Company, as well as CTC, on the other hand, would represent the overall compensation of employees. The CTC seems to be an employee's gross pay, but their net compensation is how much they actually take home.

Now, According to the question:

Let x be the annual salary.

Then 10% of x+250 equates 0.1(x+250).

Thus, the bonus equates $5000, then we will get the equation:

0.1(250 + x) = 5000

Solving for 'x' we get:

250 + x = [tex]\frac{5000}{0.1}[/tex]

250 + x = 50000

x = 50000 - 250

x = 49750

CTC and gross salary are sometimes confused. But there is a distinction among the two. Before taxes, Employee Provident Fund (EPF) contributions, and gratuities deducted from the CTC, the amount paid to the employee would be known as their gross salary.

The complete question is this:

__"Ayesha earns a 10% bonus based on her annual salary plus the number of sales she makes. She made 250 and earned a $5,000 bonus last year. Write and solve an equation to find her salary last year__"

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Answer:

B) 81 and 20°

Step-by-step explanation:

In any triangle, the sum of the measures of the three angles is 180°. Therefore, if two angles in a triangle have measures of 79° and 81°, the third angle must have a measure of 180 - 79 - 81 = 20°. Therefore, the answer is B) 81 and 20°.

Answer:

B

Step-by-step explanation:

Answer:

I don't know I'm just a grade 6 girl

The positive value of the distance between the two objects

is [tex]r = +\sqrt \frac{GM_1M_2}{F_g}[/tex].

A quadratic equation is an algebraic expression in the form of variables and constants.

A quadratic equation has two roots as its degree is two.

Given, The formula to calculate the gravitational force between two objects

is [tex]F_g = \frac{GM_1M_2}{r^2}[/tex] where r is the distance between the objects M is the individual masses and G is the gravitational constant.

Solving for r would result in two values one positive and one negative and distance can not be negative so we want the positive value.

[tex]F_g = \frac{GM_1M_2}{r^2}[/tex].

[tex]r^2 = \frac{GM_1M_2}{F_g}[/tex].

[tex]r = \pm\sqrt \frac{GM_1M_2}{F_g}[/tex].

[tex]r = +\sqrt \frac{GM_1M_2}{F_g}[/tex].

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