A local pizza parlor has the following list of toppings available for selection. The parlor is running a special to encourage patrons to try new combinations of toppings. They list all possible three-topping pizzas (3 distinct toppings) on individual cards and give away a free pizza every hour to a lucky winner. Find the probability that the first winner randomly selects the card for the pizza topped with ham, artichoke hearts, and pepperoni.

By Using Pythagorean Theorem, the value of x is 6.2 units.

Pythagorean Theorem:

In mathematics, the Pythagorean Theorem or Pythagorean Theorem is the fundamental relationship in Euclidean geometry between the three sides of a right triangle. It states that the area of ​​a square whose side is the hypotenuse (opposite the right angle) is equal to the sum of the areas of the squares on the other two sides. This theorem can be written as an equation for the lengths of sides a, b and hypotenuse c and is often called the Pythagorean equation.

                              a² +b² =c²

Now,

By using the Pythagorean theorem:

Hypotenuse² =  Perpendicular² + Base²

Now,

In the Δ ABD

As given

DB² = DA² + AB²

As given

DB = 13 units

AB = 9 units

Putting values in the above

13² = 9²+ DA²

169 - 81 = DA²

88 = DA²

Now,

In ΔABC

AB² = AC² + CB²

(As given AB = 9 units , CB = x)

9² = AC² + x²

AC ² = 81 - x²

Now in ΔADC.

AD² = AC² + DC ²

As

AC ² = 81 - x²

DC = 13 - x

AD = [tex]\sqrt{88}[/tex]

(√88)² = 81 -x² +( 13 - x²)

By using the formula (a + b)² = a² + b² + 2ab

    88 = 81 - x² + 13²- 2 × 13 × x + ²

⇒ 88 = 81 - x² + 13² - 26x + x²

⇒ 88-81 - 169 = -26x

⇒ 88-250 =-26x

⇒ -162 = - 26x

x = 6.2 (Approx.)

Therefore the value of x is 6.2 units.

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Answer:

Hope this helps you

Step-by-step explanation:

3x+8y=27   (0,9) .... look at picutre

It will take 1274  revolutions to cover 1200 meters

The circumference (or) perimeter of a circle = 2πr units. The area of a circle = πr2 square units. Where r is the radius of the circle. The circumference of the circle or the perimeter of the circle is the measurement of the boundary of the circle. Whereas the area of the circle defines the region occupied by the circle.

Given here: The diameter of a child's bicycle wheel is 12 inches.

The diameter of the wheel is 12 inches=0.30 m

∴ circumference=3.14 ×0.3

                           =0.942

Therefore the number of revolutions are = 1200/0.942

                                                                    = 1274

Hence, It will take 1274  revolutions

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Answer:

its 1254 revolutions

Step-by-step explanation:

you multiply 39.3701 by 1200 which gives 47,244.12 and you multiply 12 by 3.14 and that gives 37.68 so you then divide 47,244.12 by 37.68 which will give you a very long decimal including 1253 which becomes rounded to 1254

Answer: D. 1254 revolutions

2 students did not attend the Sports Day.

In mathematics, a fraction is used to denote a portion or component of the total. It stands for the proportionate pieces of the whole. The numerator and denominator are the two components that make up a fraction.

Given that,

Total number of students in a class = 24

Total number of students chosen for drills = 7/14 = 7/14 *24 = 12

Total number of students chosen for various races = 4/16 = 4/16 *24 = 6

Total number of students chosen for gymnastics= 1/6= 1/6* 24 = 4

Thus, the Total number of students participating in sports day = 12+6+4 = 22

Hence, the Total number of students that did not attend sports day= 24 - 22 = 2

Therefore, 2 students did not attend the Sports Day

Correct question: Out of a class of 24 students, 7/14 of the total students were chosen for drills, 4/16 of the total students were chosen for various races, and 1/6 of the total took part in gymnastics. The rest of them did not attend the Sports Day.

i) How many students did not attend the Sports Day?

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The general equation to find centre of a circle is ( x - h )^2 + ( y - k )^2 = r^2, where ( h, k ) is the center and r is the radius.

The location of a moving point on a plane such that its separation from a stationary point on the plane remains constant or fixed is described as a circle. The centre of the circle is the name given to the fixed point

A circle's centre and radius make up its 2D shape. Knowing the circle's centre and radius allows us to draw any circle. The number of radii that a circle can have is unlimited. The intersection of all the radii constitutes the centre of a circle. It is also known as the centre of the circle's diameter.

The general equation of a circle is another name for the centre of circle formula. If the radius is r, the center's coordinates are (h,k), and any point on the circle is (x,y), the centre of the circle formula is as follows:

(x - h)2 + (y - k)2 = r2

2 = r2

Also known as center of the circle equation. we'll use this formula to determine a circle's equation or centre.

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The measure of central tendency that is likely to vary least between the first and second samples of 30 scores is the median.

The median is less affected by outliers and variations in the sample compared to the mean and mode, making it less likely to vary between samples.

The median is a measure of central tendency that represents the middle value of a dataset when it is ordered by value. It is a robust statistic, which means that it is not easily affected by outliers or variations in the sample. This is because the median only looks at the middle value of a dataset, and does not take into account the values of the entire dataset, unlike the mean.

The mode, on the other hand, is the value that appears most frequently in a dataset. It is affected by variations in the sample because it is based on the frequency of values. A different sample of the same population may have a different distribution of values, resulting in a different mode.

The mean is the sum of all the values in a dataset divided by the number of values. It is affected by outliers, as a single large or small value can greatly affect the mean. In small samples, the mean can be affected by small variations in the sample.

In conclusion, since the median is based only on middle value of the sample, it is less affected by variations in the sample and outliers, making it less likely to vary between samples.

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Answer:

X < 5, or 5 > X

Step-by-step explanation:

Open up the parenthesis on the left side

-8 < 32 - 8x

Isolate -8x

- 8 - 32 < -8x
We can rewrite the inequality to make it easier to solve

-8x > -8 - 32

-8x > -40

Now solve for X, keep in mind you must switch the inequality sign when dividing by negatives

x < 5

The dimensions of the rectangle will be -

x {length} = 39 ft

y {width} = 15 ft

The area of a rectangle is -

Area = Length x Breadth

A = L x B

Given is the perimeter of a rectangle is 108 ft. Also the length is 24 ft more than the width.

We can write the length is equivalent to -

x {length} = y {width} + 24

The perimeter will be -

2(x + y) = 108

x + y = 54

y + 24 + y = 54

2y = 30

y {width} = 15 ft

Then, we can write the length as -

x {length} = 15 + 24 = 39

x {length} = 39 ft

Therefore, the dimensions of the rectangle will be -

x {length} = 39 ft

y {width} = 15 ft

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Since x is 1 and BD=7x -10, BC = 4x-29, and CD=5x-9, the values of BD, BC, and CD are 4 and 21, respectively.

An introduction to mathematics tool is the number line, which is a visual depiction of real numbers. It is a representation of an intensity line. Each precise figure is taken to symbolize a point on the real number, and each precise figure is taken to indicate a point. On a number line, distances between increments are equal. A train's values can only be answered in the way that is specified by those numbers. The question that coincides with the number will define how it is used. B: Speak your mind.

given

BD = BC + CD

7x - 10 = 4x-29 + 5x-9

x = 2

Since x is 1 and BD=7x -10, BC = 4x-29, and CD=5x-9, the values of BD, BC, and CD are 4 and 21, respectively.

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Answer:

No, the sides of a right triangle must obey the Pythagorean theorem, which states that the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. In this case, 8^2 + 15^2 = 64 + 225 = 289, which is not equal to 17^2 = 289. Therefore, 8cm, 15cm, and 17cm do not form a right triangle.

Step-by-step explanation:

To expand or contract, we say something has "dilated. Every point's coordinates in the initial triangle are multiplied by the scale factor if it is 2, which multiplies each point's coordinates by 2.

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y-axis 6 5 4 3 2 1 x=ax S 4 -3 2  -1 1 2 3 4 5 6 -1 -2.    

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A transformation modifies the parent function's graph.

The graph of a parent function is changed by a transformation. Transformations come in three different flavors: translations, reflections, and dilations.

A point, line, or geometric object can be changed in four different ways that are all collectively referred to as transformations. The pre-image is the shape of the object as it was originally, and the transformed shape of the object is termed the image.

Making pictures or replicas of an object is part of transformation geometry. You are introduced to transformation geometry in grade 9 through the use of translation, reflection, dilation, and rotation.

The foundation of the problem transformation approach is the notion that, if we are unable to address the given problem directly, we will move it to a setting where we can do so. The method's fundamental component is how the problem is broken down into smaller tasks.

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Answer:

1 [tex]\frac{3}{4}[/tex] inches per hour

Step-by-step explanation:

10 [tex]\frac{1}{6}[/tex] ÷ 6

10.5 ÷ 6 = 1.75

1.75 is the same as 1 [tex]\frac{3}{4}[/tex]

The account balance at the end of the month is $-1.04.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that Josiah's monthly bank statement showed the following deposits and withdrawals: $94.57, -−$87.78, -−$16.36, -−$64.92, $10.73 If Josiah's balance in the account was $62.72 at the beginning of the month.

The balance after the end of the withdrawal and deposits will be,

Account balance = $62.72 + $94.57−$87.78−$16.36−$64.92 + $10.73

Account balance = $-1.04

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C. Obtuse Angle refers to an angle whose measure is between 90 degrees and 180 degrees.

An acute angle measure less than 90 degrees, a right angle is exactly 90 degrees and a straight angle is 180 degrees.

0.5( -3)(-2x - 1/3+ 4 + 8x) and -1.5(12x -7) expressions are not equivalent

given that

first expression = 0.5( -3)(-2x - 1/3+ 4 + 8x)  and

second expression =-1.5(12x -7)

In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context. Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.

now we need to solve the first expression

0.5 (-3)(-2x - 1/3+ 4 + 8x)

= 0.5 (-3)(-1/3 + 4 + 6x)

= -1.5(6x + 11/3)

first expression is not equivalent to second expression

0.5( -3)(-2x - 1/3+ 4 + 8x) ≠ 1.5(12x -7)

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the answer is 22 only because I said so and that mean I’m right

Answer:

The y-intercept is the vertical line (population of butterflies)

Answer:

C

Step-by-step explanation:

[tex]-12<4x \leq 8 \\ \\ -3<x \leq 2[/tex]

Answer:

[C] x > -3 and x ≤ 2

Step-by-step explanation:

[tex]\mathrm{Given:}-9 < 4x+3\leq 11[/tex]

[tex]\mathrm{{If}\:a < u\le \:b\:\mathrm{then}\:a < u\quad \mathrm{and}\quad \:u\le \:b}[/tex]

[tex]-9 < 4x+3\quad \mathrm{and}\quad \:4x+3\le \:11[/tex]

[tex]\mathrm{solving\;the\;first\;one}:-9 < 4x+3[/tex]

[tex]\mathrm{Switch\:sides}[/tex]

[tex]4x+3 > -9[/tex]

[tex]\mathrm{subtract\;3\;from\;both\;sides}:\\4x > -12[/tex]

[tex]\mathrm{Divide\:both\:sides\:by\:}4\\\\\frac{4x}{4} > \frac{-12}{4}[/tex]

[tex]x > -3[/tex]

[tex]\mathrm{Now\;with\;the\;second\;one}:4x+3\le \:11[/tex]

[tex]\mathrm{subtract\;3\;from\;both\;sides}:\\4x\le \:8[/tex]

[tex]\mathrm{Divide\:both\:sides\:by\:}4[/tex]

[tex]\frac{4x}{4}\le \frac{8}{4}[/tex]

[tex]x\le \:2[/tex]

Therefore, the answer is [C] x > -3 and x ≤ 2

RevyBreeze~

Answer: Kaye is 4 years old

Step-by-step explanation:

Paula is 10 less than thrice of Kaye's age. two years from now, Paula's age is twice Kaye's present age. how old is Kaye now?  Let Kaye's age now be x years Paula is 10 less than thrice of Kaye's age =3x-10   TWO YEARS LATER  Paula,s age = (3x-10)+2 = 3x-8 3x-8 =x 2x=8 x=4  Kaya,s age = 4 years

his pay check equation will be f(x) = 11.25x + 20

The anti-federalist assumed that using the constitution will increase the oppression of the people by those in power but regardless, the constitution was ratified

The Anti-Federalists were a group of individuals who opposed the ratification of the Constitution. They believed that the Constitution granted too much power to the central government and did not adequately protect the rights of individual states and citizens. They argued that the Constitution should include a bill of rights to safeguard individual liberties and that the government should be more closely modeled after the Articles of Confederation. Additionally, some Anti-Federalists believed that the Constitution would lead to the rise of an aristocracy and the oppression of the common people. Despite their opposition, the Constitution was ultimately ratified in 1788 with the support of Federalists.

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Answer:

x = √22

Step-by-step explanation:

This is a right triangle.

In right triangles the sum of square value of legs is equal to the square value of hypotenuse:

[tex]( { \sqrt{11}) }^{2} + ( \sqrt{11} {)}^{2} = {x}^{2} [/tex]

[tex]11 + 11 = {x}^{2} [/tex]

√22 = x

Answer:

(-127)-62-(-15)

Open the bracket

-127-62+15

Bodmas rule(addition first)

-127-47=-174

Since the globe is in a shape of a sphere, the radius of the globe with a given volume of 904.78 in.³ is equal to 6 in .

The sphere is a three-dimensional form that is sometimes referred to as a circle's second cousin. A sphere is a solid form that is circular, without borders. Examples of spherical shapes include a playing ball, a balloon, and even light bulbs.

The formula for calculating the volume of a sphere is given by,

Volume of a sphere (V) = [tex]\frac{4}{3} \pi r^{3}[/tex] .

Where [tex]\pi[/tex] = 3.14 and r is the radius of the sphere.

Given information in the question,

volume of a sphere(V) = 904.78 in.³

Radius (r) = ?

To find the radius of the sphere, using the formula for volume of sphere,

Volume of a sphere (V) = [tex]\frac{4}{3} \pi r^{3}[/tex] .

or, 904.78 =  [tex]\frac{4}{3} \pi r^{3}[/tex]

Therefore, r = 6 in.

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The above computation is called a Long Division Method of carrying out Mathematical Division.

The original question form above requires that the student divides 896 by 29. When using the long division method, 896 is called the Dividend while 29 is the Divisor.

30 is the Quotient while 26 is the remainder. Thus, 896 divided by 29 will yield 30 with a remainder of 26.

The way it works is:

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Answer: X=4

Step-by-step explanation:

.5x=-x+6

1.5x=6

x=4

Answer: $3.20

Step-by-step explanation:

We have

15-mile stretch = $0.60

80-mile stretch = x

Cross Multiply

15 × x = 80 × $0.60

x = 80 × $0.60/15

x = $3.20

Hence, the cost to drive an 80-mile stretch is $3.20