Which rule explains why these triangles are congruent

Given that the signal gets larger than 210 microvolts, there is a 2.335 % chance that it is also larger than 240 microvolts.

As, per the given question.

Gaussian random variable n (200, 256)

Part a: Probability that signal will exceed 240 micro volts.

P(x > 240) = 1 - P(x ≤ 240)

P(x > 240) = 1 - P(240 - 200)/16

P(x > 240) = 1 - P(2.5)

See p value for z = 2.5

P(x > 240) = 0.00621

Thus, Probability that signal will exceed 240 micro volts is 0.00621.

Part b:  larger than 210 micro volts.

P(x ≥ 240) | x ≥ 210) = P(x ≥ 240) / P(x ≥ 210)

P(x ≥ 240) | x ≥ 210) = 1 - P(240 - 200)/16 /  1 - P(210 - 200)/16

P(x ≥ 240) | x ≥ 210) = 0.00621 / 0.26599

P(x ≥ 240) | x ≥ 210) = 0.02335

Thus, for the signal gets larger than 210 microvolts, there is a 0.02335 percent chance that it is also larger than 240 microvolts.

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The probability that there is a continuous stripe encircling the cube is 3/16.

A single, thin stripe is painted from the center of one edge to the center of the other edge on each face of a cube. Each face's edge pairing is selected independently and at random.

For each of the cube's six faces, there are two possible stripe orientations, resulting in a total of 2 x 6 = 64 possible stripe permutations. Since there are three sets of parallel faces, the stripe orientation for the remaining faces is determined uniquely by the pair of faces that does not contribute to the encircling stripe. Additionally, there are two possible orientations for the stripe on each face that is non-contributing.

A continuous stripe surrounds the cube as a consequence of a total of

3 * 2 * 2 = 12 stripe variations.

The necessary probability is 12/64, which equals 3/16.

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I think you would just add 8 + 5, because if NO is the same length as MN, then the length from MN is 5 and NP makes up the rest of the line.

Answer: MP = 13

The dimensions of a rectangular box with a square base which has a volume of 12 cubic feet is a = 12^ 1/3, b = 12^ 1/3

Rectangular Box with Square base

Volume v = a²b = 12

S = Surface area = 2a² + 4ab

v = a²b = 12

b = 12/a²

S = 2a² + 4ab = 2a² + 4a(12/a²) =2a² + 48/a

S'(a) = 4a -48/a² = 0

4a³ = 48

a = 12^ 1/3

b = 12/a² = 12/12^ 2/3 = 12^ 1/3

Therefore, the dimensions of a rectangular box with a square base which has a volume of 12 cubic feet is a = 12^ 1/3, b = 12^ 1/3

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The equivalent fractions for 8/9 and 5/8 using the least common denominator are 8/9 = 64/72 and 5/8 = 45/72.

What is the Least Common Denominator?

The smallest number that can serve as a common denominator for a group of fractions is known as the least common denominator (LCD). The smallest number that may be used as the denominator to produce a group of comparable fractions that all have the same denominator is known as the lowest common denominator.

The given fractions are 8/9 and 5/8.

The denominators of these fractions are 8 and 9.

so Least Common Divisor(LCD) of 8 and 9 will be = 8 × 9

                                                                                   = 72.

so the equivalent fraction can be calculated as

for 8/9 = [tex]\frac{8*8}{9*8}[/tex]

           = 64/72

and for 5/8 = [tex]\frac{5*9}{8*9}[/tex]

                   = 45/72

Hence, the equivalent fractions are 64/72 and 45/72.

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Number of square tiles that are needed to fit the rectangular region are

(a)  30000 tiles and (b)  20000 tiles  .

In the question ,

it is given that

the side of the square tile is = 6 cm

so ,the area  of the square tile = 6*6= 36 cm²

Part(a)

the length of the rectangular region = 9m = 900 cm

the breadth of the rectangular region = 12m = 1200 cm

So, the area of the rectangular region = 900 * 1200 = 1080000 cm²

the number of tiles required = (area of rectangular region)/(area of tile )

= 1080000/36

= 30000

hence , 30000 tiles are needed.

Part(b)

the length of the rectangular region = 8m = 800 cm

the breadth of the rectangular region = 9m = 900 cm

So, the area of the rectangular region = 800 * 900 = 720000 cm²

the number of tiles required = 720000/36

= 20000

hence , 20000 tiles are needed .

Therefore ,Number of square tiles that are needed to fit the rectangular region are

(a)  30000 tiles and (b)  20000 tiles  .

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Answer:

  y = x² +8x -9

Step-by-step explanation:

You want the least-degree polynomial with roots 1 and -9, written in standard form.

Each root p means there is a factor (x-p). The two roots make the factored form of the polynomial be ...

  y = (x -1)(x +9)

Expanding this to standard form, we get ...

  y = x² +8x -9

__

Additional comment

A quadratic that has two roots, p and q, will have the standard form ...

  y = (x -p)(x -q) = x² -(p+q)x +pq

That is, the linear term coefficient is the opposite of the sum of the roots, and the constant is their product. This means you can write down the equation directly from the roots:

  y = x² -(1-9)x +(1)(-9) = x² +8x -9

The function rule for each are:

f(x) = -2x - 6

g(x) = 5x - 4

f(x) is less than g(x), in terms of slope, while in terms of y-intercept, f(x) is greater than g(x).

The rule of a function can be written in slope intercept form as, f(x) = mx + b, where the slope is m and the y-intercept is the value of b.

To write the function rule for f(x), substitute m = -2 and b = -6 into f(x) = mx + b:

f(x) = -2x - 6

Find the slope of the function g(x) whose graph is given:

Slope of g(x) = rise/run = 5/1 = 5

m = 5

The y-intercept is at y = -4, therefore b = -4.

To write the function rule for g(x), substitute m = 5 and b = -4 into g(x) = mx + b:

g(x) = 5x - 4

In terms of slope, f(x) is less than g(x)

In terms of y-intercept, f(x) is greater than g(x).

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Graph will shift in both horizontal and vertical direction by 4 units.

What is straight line?

An unending, one-dimensional figure with no width is a straight line. It consists of an infinite number of points connected on either side of a point. There is no curvature in a straight line. It might be angled, vertical, or horizontal.

What is general equation of a Straight Line?

The general equation of a straight line can be given as ax + by + c = 0, where

What do you mean by function?

A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output. Each function has a range, co-domain, and domain. The usual way to refer to a function is as fn(x), where x is the input.

We have function,

fn(x) = x + 5

when the graph is translated by 4 units, we can write it as;

g(x) = fn(x) + 4

the graph will shift in both horizontal and vertical direction by 4 units as it can be seen in the graph.

Therefore, graph will shift in both horizontal and vertical direction by 4 units.

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Answer:

X = 2, Y = 0

Step-by-step explanation:

Add the two equations together to cancel out -4y and +4y

leaving you with:

8x = 16

8x = 16

divide both sides of the equation by 8 to get x on its own (8x/8 = x, 16/8 =2)

leaving you with:

x = 2

substitute the value of x back into the equation to calculate y (it can be either equation, top or bottom):

8(2) - 4 y = 16

8 x 2 = 16

leaving you with:

16 - 4y = 16

subtract 16 from both sides to get 4y on its own

leaving you with:

-4y = 0

so y = 0, and x = 2

The first four terms in the sequence are 30, 90, 270 and 810 respectively.

We have that the nth term of the sequence is expressed as;

U = 10 × 3 ^n

Where;

n = number of terms

To determine the first terms, let's substitute the value of n as 1, we get;

U = 10 × 3^1

Multiply the values

U₁ = 30

The second terms, n = 2

U₂ = 10 × 3²

U₂ =  10 × 9

Multiply through

U₂ = 90

The third year, n = 3

U₃ = 10 × 3³

Find the cube of the value and multiply the values

U₃ = 270

The fourth year, n = 4

U₄ = 10 × 3^4

U₄ = 10 × 81

Multiply through

U₄ = 810

Thus, the numbers are 30, 90, 270, 810

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Answer: the answer would be 2

Step-by-step explanation: f(x) means that for every x you are going to multiply it by the value it gives you in this case it is 3.

2x3=6-4=2

The relationship between height and vertical jump is High positive correlation.

What is a correlation?

A statistical indicator of the relationship between the relative motions of two variables is the correlation. If the variables are correlated, a line or curve will be formed by the points. The points will touch the line more closely the better the correlation.

Main body:

To find the relation we need to draw a line passing closely to all the points , if we are able to draw such line , it has high positive correlation.

If the line doesn't pass through all points it has low positive correlation.

hence this has high positive correlation .

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Answer:

-positive

-linear

-strong

-no.

Step-by-step explanation:

edge 2023

The domain of the function d(t)=1/2t+6 is (-∞, ∞) and the range of the function is (-∞, ∞).

Similar to how we input different numbers into functions, we also receive new numbers as the outcome. The two main characteristics of functions are domain and range.

A function's domain and range are its constituent parts. A function's range is its potential output, whereas its domain is the set of all possible input values. Range, Domain, and Function. A is the domain and B is the co-domain if a function f: A  → B exists that maps every element of A to an element in B. 'b', where (a,b) R, provides the representation of an element 'a' under a relation R. The set of images is the function's range.

The domain of the function d(t)=1/2t+6 is given by

Domain: (-∞, ∞), {x|x ∈ R}

The range of the function is given by

Domain: (-∞, ∞) , {y|y ∈ R}

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The area of the figure created by Brianna is  [tex]33\frac{3}{4}[/tex] square feet.

Explain area in mathematics.

Area is a mathematical concept that expresses the size of a region on a planar or curved surface. The area of an open surface or the boundary of a three-dimensional object is referred to as the surface area or, it can be simply defined as the total amount of space occupied by a flat (2-D) surface or an object's shape.

Solution Explained:

A square with a side of 4 1/2 feet and two parallelograms with bases of 4 1/2 feet and heights of 1 1/2 feet make up the figure.

Therefore, the total area of the figure is
Area of Square + 2 X Area of Parallelogram
= (side)^2 + 2(b X h)
= (4 1/2)^2 + 2(4 1/2 X 1 1/2)
= 81/4 + 27/2    
=  135/4
= [tex]33\frac{3}{4}[/tex] square feet

Area of the figure is [tex]33\frac{3}{4}[/tex] square feet.

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The number of groups formed is 10 if we consider 5 cars in groups of 3.

Given, 5 cars in groups of 3, we can use the formula,

(5 3) = 5! / 3! × 2!

= 10

Permutation and combination are the various ways in which one can form a set that may be selected without any replacement. When the selection of a subset is where we use the permutation and when the ordering of the subset is there we use a combination.

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The length and width of the rectangle are 50 feet and 25 feet respectively, the product of which gives the area of the rectangle which is 1250 feet.

Given, 100 feet of fence to make a rectangular play area that is side by side with the wall of your house.

The perimeter of the rectangle is = 2x+2y, since the wall bounds from one side as given in the question perimeter changes to = x+2y.

Perimeter = x+2y

100 = x+2y

100 = 50+2y

2y = 50

y = 25

Using this we found the length and width of the rectangle which is equal to 50 feet and 25 feet respectively. The area which is the final answer comes out to be 1250 feet.

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The probability of selecting two students (a and b) randomly is found as 1/380.

The formula for evaluating the Probability is-

Probability = Favourable outcomes / Total outcomes.

As, per the given question.

Total number of students = 20.

The probability for selection of 'a' is 1/20.

Now, the total students left is 19.

Thus, the probability for selection of 'b' is 1/19.

The total probability for selection of both is -

Probability(a and b) = 1/20×1/19

Probability(a and b) = 1/380

Thus, the probability of selecting two students ( a and b) randomly is found as 1/380.

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Answer:

hello\\

Step-by-step explanation:

The speed at which raina can swim if there is no current is 3 km/hor 3 kilometers per hour.

Given that,

In the same length of time it took raina to swim kilometers with the river, she was able to swim 8 kilometers against it. The current flowed at a kilometer per hour rate.

Distance 1 * (Raina's velocity - current velocity) = Distance2 * (Raina's velocity + current velocity)

16 * (Raina's velocity - 1) = 8 * (Ivan's velocity + 1)

(16 * Raina's velocity) - 16 = (8 * Ivan's velocity) +8

8 * Raina's velocity = 24

Raina's velocity = 3 kilometers per hour

As a result, Raina can swim at a speed of 3 km/hr in the absence of a current.

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When the sum M+N is divided by 6 , the remainder is 8

The remainder is the amount "left over" after performing some computation. In arithmetic, the remainder is the integer "left over" after dividing one integer by another to produce an integer quotient (integer division). We always have remainder when the denominator is a factor of numerator.

For example 5/2, diving 5 with 2, 2 is not a factor of 5,

There are 2 2s in 5 with remainder 1.

M/6= x y/6

where is the factor and y is the remainder

therefore m/6= (6x+y)/6

y= 3,. m/6= (6x+3)/6

N/6= (6x+5)/6

therefore dividing both sides by 6

m= 6x+3

n= 6x+5

adding m and n

m+n= 12x+8

dividing m+n by 6

(m+n)/6 = (12x+8)/6

relating (12x+8)/6 with (6x+y)/6

y = 8

Therefore the remainder is 8

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The table of solutions for this quadratic equation (y = -2x²) include the following:

x                    y_

-2                  -8

-1                   -2

0                   -0

1                    -2

2                   -8

A graph of the solution of the given quadratic equation has been plotted in the image attached below.

In Mathematics, the graph of any quadratic equation or function always forms a parabola, which simply means a u-shaped curve. In order to determine the correct solutions to the given quadratic equation, we would have to substitute the x-values contained in the table into the quadratic equation.

At point x = -2, the y-value of this quadratic equation is given by:

y = -2x²

y = -2(-2)²

y = -2 × 4

y = -8

At point x = -1, the y-value for this quadratic equation is given by:

y = -2x²

y = -2(-1)²

y = -2 × 1

y = -2

At point x = 0, the y-value of this quadratic equation is given by:

y = -2x²

y = -2(0)²

y = -2 × 0

y = 0

At point x = 1, the y-value of this quadratic equation is given by:

y = -2x²

y = -2(1)²

y = -2 × 1

y = -2

At point x = 2, the y-value of this quadratic equation is given by:

y = -2x²

y = -2(2)²

y = -2 × 4

y = -8

In conclusion, we can logically deduce that the graph of this quadratic equation forms a downward parabola.

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The model which properly represent the information in given axioms is Cross geometry (+).

In the given question we have following information,

by using the above axioms we draw a geometry of Cross sign Geometry as seen above .

We can draw a line which contains three points and these points are only from given five points another line also follow this . this geometry follows all given axioms . The two lines intersect each other at a point . The point of intersection is one of point from five points . both of lines are linear and consists three points .

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The number of student like at least one kind of ice cream is given by (d) 275.

Let C be the student who like chocolate ice cream and P be the student who like Pistachio ice cream.

Now given that, n(C) = 145, n(P) = 150

Also given that, 123 students do not like neither chocolate or pistachio ice cream.

So, n(P' and C') = 123

The required number of student like at least one kind of ice cream is given by,

N = 398 - n(P' and C') = 398-123 = 275

Hence the correct option is (d).

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When charging $15 for a key chain, it is discovered that his maximum profit is $75 using the vertex of the quadratic function.

The vertex of a quadratic equation,

A quadratic equation is given by, [tex]ax^{2} +bx +c[/tex]

The vertex is given by [tex]A (x_{1} ,y_{1} )[/tex]

[tex]x_{1} = \frac{-b}{2a}\\ \\y_{1} = \frac{-b^{2} +4ac }{4a}[/tex]

Considering the coefficient a, we have that:

If a < 0, the vertex is a maximum point.

If a > 0, it will be a minimum point.

The function given is (x -10 ) (60 -3x)

f(x) = (x -10 ) (60 -3x)  = 60x -3[tex]x^{2}[/tex] -600 +30x = -3[tex]x^{2}[/tex] +90x -600

So, here a = -3, b = 90 and c = -600

So,

[tex]x_{1} = \frac{-b}{2a}\\ \\x_{1} = \frac{-90}{2*(-3)} = 15[/tex]

[tex]y_{1} = \frac{-b^{2} +4ac }{4a} = \frac{(-90)^{2} + 4*(-3)*(-600) }{4*(-3)} = 75[/tex]

Hence, He can make up to $75 in profit when he charges $15 for a key chain.

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Norman will measure the light pole to be 12 feet tall

Information from the question

Norman uses his sextant to measure the angle of elevation to be 36

5 feet from the ground. if he is 10 feet away from the light pole

how tall is the light pole = ?

The height of the light pole is calculated using SOH CAH TOA

The direction of movements describes a right angle triangle of

opposite = height of the light pole

adjacent = 10 feet away from the light pole

The height is is calculated using tan, TOA let the angle be x = 36

tan x = Opposite / Adjacent

tan 36 = opposite  / 10

opposite = tans 35 * 10

opposite = 7 feet

this is height 5 feet from the ground, so total height is calculated to be

5 + 7 = 12 feet

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The series expansion for e z 1 z up to z 5 is obtained by multiplying the Maclaurin series for e z and 1 1 z. For |z| 1, this series converges.

The Maclaurin series for e^z is:

e^z = 1 + z + z^2/2! + z^3/3! + z^4/4! + ...

The Maclaurin series for 1/1-z is:

1/(1-z) = 1 + z + z^2 + z^3 + z^4 + ...

Multiplying these two series together gives:

e^z/(1-z) = (1 + z + z^2/2! + z^3/3! + z^4/4! + ...)(1 + z + z^2 + z^3 + z^4 + ...)

= 1 + (1+z) + (z + z^2/2! + z^2) + (z^2/2! + z^3 + z^3/3!) + (z^3/3! + z^4 + z^4/4!) + ...

= 1 + z + 2z^2 + 3z^3 + 5z^4 + ...

This series converges for |z| < 1

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The statement about the given expression is described below.

A math expression consist numbers, variables and operators its operation addition, subtraction, multiplication, and division. The parts of the expression that are connected with addition and subtraction are considered as terms.

Expression, (a+b+c)(d+e+f)(a+b+c)(d+e+f) = (a +b+c)^2(d+e+f)^2

Thus, given expression has two factors which consist 3 terms.

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