Which equation shows an example of the associative property of addition?
a .(–4 + i) + 4i = –4 + (i + 4i)
b. (–4 + i) + 4i = 4i + (–4i + i)
c. 4i × (–4i + i) = (4i – 4i) + (4i × i)
d. (–4i + i) + 0 = (–4i + i)

Answer:

1/6

Step-by-step explanation:

because the dice is most likly a 6 sided dice but if you need to simplify then it would be 1/2

1) You will Rewrite both side by combining like terms. Thus, option D is correct.

2) Yes, they have same solution x = 2.

Balancing an equation in math typically refers to solving an equation for a specific variable. The goal is to isolate the variable on one side of the equation and simplify the other side. The steps for balancing an equation in math can vary depending on the type of equation, but here are some general steps to follow:

1) Identify the variable you want to solve for.

You have given:

5x - 2 + x = x - 4

Also

5x - x = x - 4

Here, as you can see x - 4 is common in both equation, (option D) Rewrite one side (or both) by combining like terms i.e. x - 4:

5x - 2 + x = 5x - x = x - 4

4x - 2  = 4x  = x - 4

4x - 4x - 2  = x - 4

- 2 = x - 4

4 - 2 = x

x = 2

Thus, You will Rewrite both side by combining like terms. Thus, option D is correct.

2) Yes, they have same solution x = 2

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The triangles KJL and GJL are not similar in figure 1 whereas in figure 2 the triangles RST and RPQ are similar by SSS similarity criteria.

The triangles are said to be similar if all the angles in one triangle are equal or congruent to the corresponding angles in another triangle and the sides are proportional. There are different criterias for similarity of triangles namely SSS, SAS, ASA/AAS and RHS. According to the criteria/rule

SSS(SIDE-SIDE-SIDE):two triangles are said to be similar if three sides of one triangle are proportional to the corresponding sides of another triangle.

SAS(SIDE-ANGLE-SIDE):The triangles are said to be similar if two sides are proportional and an included angle is congruent to the two sides and included angle of another triangle.

ASA(ANGLE-SIDE-ANGLE):The triangles are said to be similar if two angles are congruent and an included side is proportional  to the two angles and included side of another triangle.

RHS(RIGHT-HYPOTENUSE-SIDE):The triangles are said to be similar if one angle is right angle in both triangles, also the hypotenuse and any one side is proportional  to the hypotenuse and any one side of another triangle.

Q11)In ΔKJL and ΔGJH,

∠KJL = ∠GJH {vertically opposite angles}

But the sides aren't proportional to each other.

∴The given triangles are not similar.

Q12)Consider the triangles ΔRST and ΔRPQ ,

∠SRT = ∠PRQ {Common angle}

As we know that, =  { and }

By basic proportionality theorem, we can say that ST is parallel to PQ.

∴∠RST = ∠RPQ {corresponding angles} and

∠RTS = ∠RQP {corresponding angles}

All angles of ΔRST are congruent to corresponding angles of ΔRPQ.

The sides are proportional to each other:

RS= 35 units; RP= 35+14=49 units

ST=25 units; PQ=35 units

RT=30 units ; RQ=30+12=42 units

All three sides are proportional.

∴ ΔRST and ΔRPQ are similar by SSS.

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Step-by-step explanation:

A. To calculate the monthly payment, we can use the formula for a fixed-rate mortgage:

M = P * (r*(1+r)^n) / ((1+r)^n - 1)

where:

M = monthly payment

P = principal (amount borrowed) = $213,000

r = monthly interest rate = APR / 12 = 0.0375 / 12 = 0.003125

n = total number of payments = 30 years * 12 months/year = 360

Plugging in these values, we get:

M = 213000 * (0.003125*(1+0.003125)^360) / ((1+0.003125)^360 - 1)

M ≈ $988.32

So the monthly payment, rounded to the nearest 10th, is $988.30.

B. The total amount paid over the 30-year period would be the monthly payment multiplied by the total number of payments:

Total = M * n

Total = $988.30 * 360

Total = $355,788.00

So the total amount paid over 30 years would be $355,788.00.

C. To calculate the total interest paid over the 30-year period, we can subtract the principal from the total amount paid:

Total Interest = Total - P

Total Interest = $355,788.00 - $213,000

Total Interest = $142,788.00

So the total interest paid over the 30-year period would be $142,788.00.

Answer:

To solve this problem, we can use the Pythagorean theorem, which states that the sum of the squares of the two legs of a right triangle is equal to the square of the hypotenuse.In this case, the height of the monitor is one leg of the right triangle, and the width of the monitor is the other leg. The distance between opposite corners is the hypotenuse.Let w be the width of the monitor in inches. Then we have:w^2 + 18^2 = 30^2Simplifying and solving for w, we get:w^2 + 324 = 900

w^2 = 576

w = 24Therefore, the width of Mia's new monitor is 24 inches.

Step-by-step explanation:

Using the given secant line, we know that the required angle ∠a is 15° respectively.

A secant in geometry is a line that crosses a curve at least two different points.

The Latin verb secare, which means to cut, is where the word secant originates.

A secant crosses a circle at precisely two points in a case of circle.

The Latin word secant, which means to cut, is used in mathematics to define a line that passes through the points P and Q of any arbitrary curve whose equation is y=f(x).

So, we know that:

c = 55° and b = 25°

And, the formula is:

∠a = c - b/2

Now, insert values as follows:

∠a = c - b/2

∠a = 55 - 25/2

∠a = 30/2

∠a = 15°

Therefore, using the given secant line, we know that the required angle ∠a is 15° respectively.

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the probability of drawing a red, then a blue, and then a white marble is [tex]=\frac{7}{225}[/tex]

To find probability, we take the number of ways the specific event can occur and divide it by the number of ways any event can occur.

The probability of drawing a red marble is: (of red marbles) / (total # of marbles) = 3/(3 + 7 + 5) = 3÷15 = 1÷5.

The probability of drawing a blue marble is: ( of blue marbles) / (total # of marbles) = 5/(3 + 7 + 5) = 5÷15 = 1÷3.

The probability of drawing a white marble is: ( of white marbles) / (total # of marbles) = 7/(3 + 7 + 5) = 7÷15.

Now, we want these events to all to occur for us. So, we must multiply them by each other: (1/5) * (1/3) * (7/15)  [tex]=\frac{7}{225}[/tex]

Thus, the probability is [tex]=\frac{7}{225}[/tex]

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The image of the point (0,1) after a rotation of 270 degrees counterclockwise about the origin is the point (1,0).

What is trigonometry?

Trigonometry is a branch of mathematics that deals with the relationships between the sides and angles of triangles.

A rotation of 270 degrees counterclockwise about the origin corresponds to a transformation in which every point in the plane is rotated 270 degrees counterclockwise about the origin.

To find the image of the point (0,1) under this transformation, we can use the following formula for a counterclockwise rotation of a point (x,y) about the origin by an angle of θ:

x' = x cos(θ) - y sin(θ)

y' = x sin(θ) + y cos(θ)

Plugging in the values x = 0, y = 1, and θ = 270 degrees, we get:

x' = 0 cos(270°) - 1 sin(270°) = 0 - (-1) = 1

y' = 0 sin(270°) + 1 cos(270°) = 0 + 0 = 0

Therefore, the image of the point (0,1) after a rotation of 270 degrees counterclockwise about the origin is the point (1,0).

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The probability that the duration of rainfall at least 2 hours is 0.473,  at most 3 hours is 0.683, and between 2 and 3 hours is 0.156.

1. Find the rate parameter (λ):
λ = 1/2.725 ≈ 0.367
2. To find P(X ≥ 2):

P(X ≥ 2) = 1 - P(X < 2).

The (pdf) is:
P(X < x) = 1 - e^(-λx)
P(X < 2) = 1 - e^(-0.367 * 2) ≈ 0.527
P(X ≥ 2) = 1 - 0.527 ≈ 0.473
3. To find P(X ≤ 3):
P(X ≤ 3) = 1 - e^(-0.367 * 3) ≈ 0.683
4. To find P(2 ≤ X ≤ 3):
P(2 ≤ X ≤ 3) = P(X ≤ 3) - P(X ≤ 2) = 0.683 - 0.527 ≈ 0.156
The probability that  duration  at least 2 hours is 0.473,  at most 3 hours is 0.683, and between 2 and 3 hours is 0.156.

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The probability that the sample contains two rotten apples is 0.0612.

The sample of three apples can be selected in 14C3 (14 choose 3) ways and the probability that we select a rotten apple will be 2/14 and the probability of selecting an apple that is not rotten is 12/14.

Now we can apply the binomial distribution formula, to calculate the probability as follows,

P = (3 choose 2) × (2/14)² × (12/14)

P = (3! / (2! × 1!)) × (2/14)² × (12/14)

P = 3 × (1/49) × (12/14)

P = 0.06122449

So, the probability of selecting a sample of three apples in which 2 are rotten and one is not rotten is 0.0612 or approximately 6.12%.

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Christina will need 220 feet of fence to enclose her yard.

The perimeter of a form is the space surrounding its edge. Find the perimeter of various forms by summing the lengths of their sides.

To solve this, we need to calculate the perimeter of the rectangular yard:

Perimeter = 2 × (Length + Width)

Plugging in the given dimensions:

Perimeter = 2 × (60 ft + 50 ft)

Perimeter = 2 × (110 ft)

Perimeter = 220 ft

Christina will need 220 feet of fence to enclose her yard.

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Christina wants to fence in her rectangular yard. The length of her yard is 60 feet, and the width is 50 feet. How many feet of fence will she need to enclose the entire yard?

The parabola's equation is therefore for A: y  = 7x2 - 5$1.

As a result, the parabola's equation for B  is y = -1/2(x - 1)² + 4.

A parabola with vertex (h,k) has the basic equation y = a(x-h)² + k². In this instance, h=0 and k=-5 are equal because the vertex is at $(0,-5)$. Moreover, the parabola has a point at (-1 . 2). When we substitute these numbers in the general parabola equation, we obtain:

2 = a(-1-0)² -5

7 = a

The parabola's equation is therefore y = 7x2 - 5$1.

A cone and a plane perpendicular to its side cross to create a symmetrical open plane curve known as a parabola1. It is a U-shaped curve whose vertex and axis of symmetry characterise it. The line dividing the parabola into its two mirror counterparts is known as the axis of symmetry. The parabola's vertex is where the axis of symmetry intersects it.

A parabola's vertex is represented by the equation y = a(x - h)²+ k, where (h,k) represents the vertex. We may utilise the vertex version of the equation and substitute the values of h, k, and the x and y coordinates of the point to determine the equation of a parabola that passes through a particular point and has a certain vertex.

B.  Here, the vertex is (1, 4), and the point (5,-4). In the vertex form equation, we may therefore substitute h=1, k=4, x=5, and y=-4 to obtain:

-4 = a(5 - 1)²2 + 4 \s-8 = 16a

a = -1/2

As a result, the parabola's equation is y = -1/2(x - 1)² + 4.

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The distributive property allows us to distribute 4 to each term inside the parentheses, add the terms first, then distribute the result to x. It also allows us to distribute 6 to each term inside the parentheses, such as 6(x+y+z) = 6x + 6y + 6z.

The distributive property is a mathematical property that applies to operations, such as addition and multiplication, that involve two or more terms. The distributive property states that the result of multiplying a term by a sum or difference of terms is the same as multiplying each term inside the parentheses by the term outside the parentheses and then adding or subtracting the results.

1. Using the distributive property, we can distribute the 4 to each term inside the parentheses:

4(x+2) = 4x + 42 = 4x + 8

Therefore, the equivalent expression is 4x + 8.

2. Using the distributive property, we can add the terms inside the parentheses first, then distribute the result to x:

(6+8)•x = 14•x

Therefore, the equivalent expression is 14x.

3. Using the distributive property, we can distribute the 4 to each term inside the parentheses:

4(2x+3) = 42x + 43 = 8x + 12

Therefore, the equivalent expression is 8x + 12.

4. Using the distributive property, we can distribute the 6 to each term inside the parentheses:

6(x+y+z) = 6x + 6y + 6z

Therefore, the equivalent expression is 6x + 6y + 6z.

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The predicted number of green or yellow piece in 50 selection is 18

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

The number of candies

Where we have

Yellow or green = 6 + 3

Yellow or green = 9

Also, we have

Total = 25

So, we have

P(Yellow or green) = 9/25

In 50 selections, we have

Yellow or green = 9/25 * 50

Yellow or green = 18

Hence, the predicted times is 18

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The length of the two equal sides of the isosceles trapezoid is 11.3 millimeters.

What is trapezoid?

A trapezoid, also known as a trapezium in some countries, is a two-dimensional geometric shape with four sides. It is a quadrilateral that has at least one pair of parallel sides, which are called bases.

Let's start by labeling the sides of the isosceles trapezoid as follows:

The shorter base: b1 = 6.3 mm

The longer base: b2 = 16.1 mm

The two equal sides: s

We know that the perimeter P of the trapezoid is given by:

P = b1 + b2 + 2s

Substituting the values we have, we get:

45 mm = 6.3 mm + 16.1 mm + 2s

Simplifying this equation, we get:

22.6 mm = 2s

Dividing both sides by 2, we get:

s = 11.3 mm

Therefore, the length of the two equal sides of the isosceles trapezoid is 11.3 millimeters.

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Step-by-step explanation:

a) from n = 1 to 4 this equals

      -4       -4 (2/3)      -4 (2/3)^2    - 4 (2/3)^3

=      -4       - 8/3          - 16/9          - 32/27

b) converges  ===  since  common ratio, r= (2/3) is less than 1

c ) sum =  -4 / ( 1-r) =   -4 / (1- 2/3 ) =  -12    

The vertices of the ellipse are (-4,2) and (4,2), since these points lie on the major axis of the ellipse which is horizontal.

Two of the focuses given in the issue, (−4,2) and (4,2), are both situated on a similar even line. This implies that the significant hub of the oval should be level. Two different focuses given in the issue, (2,2) and (- 9,2), are likewise situated on this level line. Thusly, the focal point of the oval is the midpoint between the focuses (- 4,2) and (4,2), which is (0,2).

The other two focuses given in the issue, (−5,5) and (−5,−1), are situated on an upward line that goes through the focal point of the oval. This implies that the minor pivot of the oval should be vertical.

The vertices of the oval are the places where the significant hub meets the circle. Since the significant hub goes through the focuses (−4,2) and (4,2), the vertices of the oval are (- 4,2) and (4,2).

In this way, the vertices of the oval are (- 4,2) and (4,2).

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You can expect 95% of your customers to stay in your store between range of  39.7 minutes and 49.9 minutes.

To determine the range in which 95% of your customers would stay in your store, we will use the properties of a normally distributed data set with a mean of 44.8 minutes and a standard deviation of 2.6 minutes.
Identify the mean and standard deviation.
The mean is 44.8 minutes, and the standard deviation is 2.6 minutes.
Determine the z-score for a 95% confidence interval.
A 95% confidence interval corresponds to a z-score of 1.96. This means that 95% of the data lies within 1.96 standard deviations from the mean.
Calculate the range using the z-score, mean, and standard deviation.
To find the lower and upper limits of the range, we will multiply the standard deviation (2.6 minutes) by the z-score (1.96) and then subtract or add the result to the mean (44.8 minutes).
Lower limit: Mean - (Z-score × Standard deviation)
44.8 - (1.96 × 2.6) = 44.8 - 5.096 ≈ 39.7 minutes
Upper limit: Mean + (Z-score × Standard deviation)
44.8 + (1.96 × 2.6) = 44.8 + 5.096 ≈ 49.9 minutes
State the range in which 95% of customers would stay in the store.

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If there are 30 students in the class, then the number of students who play soccer but do not play basket-ball are 13 students.

The total-students in the class is = 30 students,

The Number of students who play basketball is = (2/5) × 30 = 12,

The Number of students who play soccer is = (7/10) × 30 = 21,

⇒ Number of basketball players who also play soccer = (2/3) × 12 = 8,

So, out of the 21 students who play soccer, 8 also play basketball.

To find the number of students who play soccer but not basketball, we can subtract the number of students who play both from the total number of soccer players:

⇒ 21 - 8 = 13 students play soccer but not basketball.

Therefore, the required number of students are 13 students.

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The answer is 3/20. By calculating the probability of selecting a female who plays the clarinet out of the total number of sophomores, we can get an accurate representation of the selection of the current sophomore class.

It is calculated by dividing the number of possible outcomes by the total number of possible outcomes.

This can be calculated by taking the number of females who play the clarinet (18) and dividing it by the total number of sophomores (120).

This gives us 18/120= 3/20.

This is the correct answer because it shows the probability of selecting a female who plays the clarinet out of the total number of sophomores. Option 1, 31/120, would show the probability of selecting a female or a clarinet player out of the total number of sophomores.

Option 3, 3/11, would show the probability of selecting a female who plays the clarinet out of the total number of female sophomores.

Option 4, 18/31, would show the probability of selecting a female out of the total number of clarinet players.

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The clοsest οptiοn tο the actual area οf the οbject is D. 64 square inches.

Area is a measure οf the amοunt οf space inside a twο-dimensiοnal shape, such as a square, rectangle, triangle, circle, οr any οther shape that has a length and a width. It is usually measured in square units, such as square inches, square feet, οr square meters.

Tο find the area οf the οbject, we need tο break it dοwn intο smaller shapes and add up their areas.

First, we can see that the οbject can be divided intο a rectangle with dimensiοns 8 inches by 4 inches (UWVZ), a triangle with base 4 inches and height 6 inches (VXY), and a trapezοid with bases 6 inches and 8 inches, and height 4 inches (WXYU).

The area οf the rectangle is:

A_rectangle = length × width = 8 in × 4 in = 32 square inches

The area οf the triangle is:

A_triangle = 1÷2 × base × height = 1÷2 × 4 in × 6 in = 12 square inches

The area οf the trapezοid is:

A_trapezοid = 1÷2 × (base1 + base2) × height = 1÷2 × (6 in + 8 in) × 4 in = 28 square inches

Therefοre, the tοtal area οf the οbject is:

A_οbject = A_rectangle + A_triangle + A_trapezοid

= 32 square inches + 12 square inches + 28 square inches

= 72 square inches

Therefοre, the clοsest οptiοn tο the actual area οf the οbject is D. 64 square inches.

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The value of angle C is 68°.

In geometry, complementary angles are two angles that add up to 90 degrees (a right angle). In other words, when two angles are placed adjacent to each other, and they form a right angle, they are considered complementary angles.

For example, if angle A is 40 degrees, then angle B, which is adjacent to angle A and together they form a right angle, is considered to be a complementary angle. Angle B would be 90 - 40 = 50 degrees.

Complementary angles can be found in many geometric shapes and objects, such as squares, rectangles, and triangles. In a right triangle, the two acute angles (the angles that are not the right angle) are always complementary.

Vertical angles are always congruent, which means that angle B is also 22°.

Since angle B and angle C are complementary, their sum is equal to 90°.

Thus, we can write the equation:

angle B + angle C = 90°

Substituting the known value of angle B, we get:

22° + angle C = 90°

Simplifying the equation, we get:

angle C = 90° - 22°

angle C = 68°

Therefore, the value of angle C is 68°.

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Equation of line: y = -3/4 x + 3. Here , slope m = -3/4 and y intercept is 3.

We need to knowing the slope of the line and indeed the intercept where the line crosses the y-axis in order to use the slope-intercept formula. Suppose a straight line with y-intercept b and slope m. For one straight line with slope "m" and y-intercept "b," the slope intercept program is designed is: y = mx + b.

Given coordinates are:

(2,3) and (4,0).

Slope m = (y2 - y1)/(x2 - x1)

m = (0 - 3)/(4 - 0)

m = -3/4

Equation of line:

y - y1 = m(x - x1)

y - 0 = -3/4(x - 4)

y = -3/4 x + 3

Here , slope m = -3/4 and y intercept is 3.

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Complete question:

Find the slope intercept equation of line passing through (2,3) and (4,0).

Answer:

I'm sorry your paper is not clear please retake the picture and again attached it

Step-by-step explanation:

Answer:

x=6 and x=−5.

The probability that Betty is first in line or Mary is last in line is (n^2 - n - 1)/n(n-1), as a function of n.

We can approach this problem by considering the probability of the complementary event, i.e., the probability that neither Betty is first in line nor Mary is last in line, and then subtracting this probability from 1 to get the probability we want.

The total number of ways the n kids can line up is n!, since there are n choices for the first person in line, n-1 choices for the second person, and so on down to 1 choice for the last person.

The number of ways in which neither Betty is first in line nor Mary is last in line is (n-2)!, since there are (n-2) choices for the first person in line (excluding Betty and Mary), (n-3) choices for the second person, and so on down to 1 choice for the second-to-last person.

Therefore, the probability that neither Betty is first in line nor Mary is last in line is

[(n-2)! / n!] = 1/n(n-1)

The probability we want is

1 - 1/n(n-1) = (n^2 - n - 1)/n(n-1)

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The given question is incomplete, the complete question is:

A class with n kids lines up for recess. The order in which the kids line up is random with each ordering being equally likely. There are two kids in the class named Betty and Mary. The use of the word “or” in the description of the events, should be interpreted as the inclusive or. That is “A or B” means that A is true, B is true, or both A and B are true.

What is the probability that Betty is first in line or Mary is last in line as a function of n? Simplify your final expression as much as possible and include an explanation of how you calculated this probability.

the missing dimension (diameter) of the cylinder is approximately 18.9 inches, rounded to the nearest tenth.

what is cylinder ?

A cylinder is a three-dimensional shape that consists of two parallel circular bases connected by a curved surface. It can be thought of as a tube or a can, and is a common shape found in many everyday objects such as soda cans, tubes, and pipes.

In the given question,

To find the missing dimension (diameter) of the cylinder, we can use the formula for the volume of a cylinder:

V = πr²h

where V is the volume of the cylinder, r is the radius of the cylinder, and h is the height of the cylinder.

Since the diameter (D) is twice the radius (r), we can also write:

V = π(D/2)²h

Simplifying this expression, we get:

V = πD²h/4

Multiplying both sides by 4/πh, we get:

D² = 4V/(πh)

Taking the square root of both sides, we get:

D = 2√(V/πh)

Substituting the given values, we get:

D = 2√(7433 in.³/π(14 in.))

D ≈ 18.9 in.

Therefore, the missing dimension (diameter) of the cylinder is approximately 18.9 inches, rounded to the nearest tenth.

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Therefore, there are 18 oranges in each box.

An equation is a mathematical statement that shows that two expressions are equal to each other. It typically consists of two sides separated by an equal sign (=), with mathematical expressions or variables on each side. Equations can be used to describe many different relationships and properties in mathematics, science, and engineering.

Here,

To represent the relationship described in the problem, we can use the following model or diagram:

4 boxes with b oranges per box, plus 1 free orange = 73 oranges in total

This can be written as the equation:

4b + 1 = 73

To solve for b, we need to isolate it on one side of the equation. We can start by subtracting 1 from both sides to get:

4b = 72

Then, we can divide both sides by 4 to get:

b = 18

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By answering the presented question, we may conclude that Therefore, Pythagorean the length of the third side of the triangle is [tex]2/\sqrt(5)[/tex]and the height is 4/5.

The Pythagorean theorem is a fundamental mathematical principle that describes the connection between the sides of a right triangle. It asserts that the sum of the squares of the other two sides' lengths equals the square of the hypotenuse's length (the side opposite the right angle). The mathematical theorem is as follows: c2 = a2 + b2 Where "c" denotes the hypotenuse length and "a" and "b" indicate the lengths of the other two sides, known as the legs.

Let's use the formula for the area of a triangle:

[tex]A = 1/2 * b * h2/5 = 1/2 * (6/5) * h\\h = 4/5\\a^2 = (6/5)^2 - (4/5)^2\\a^2 = 36/25 - 16/25\\a^2 = 20/25\\a^2 = 4/5\\[/tex]

[tex]a = \sqrt(4/5)\\a = 2/\sqrt(5)[/tex]

Therefore, the length of the third side of the triangle is [tex]2/\sqrt(5)[/tex]and the height is 4/5.

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On solving the provided question we can say that The amount of water lost is: [tex]V_lost = V1 - V2 = 346.36 cm^3 - 401.94 cm^3 = -55.58 cm^3[/tex]

A cylinder is a three-dimensional geometric shape made up of two parallel congruent circular bases and a curving surface connecting the two bases. The bases of a cylinder are always perpendicular to its axis, which is an imaginary straight line passing through the centre of both bases. The volume of a cylinder is equal to the product of its base area and height. A cylinder's volume is computed as V = r2h, where "V" represents the volume, "r" represents the radius of the base, and "h" represents the height of the cylinder.

[tex]V1 = \pi r^2h = \pi (3.5 cm)^2(9 cm) = 346.36 cm^3\\[/tex]

Next, let's calculate the volume of the ball:

The radius of the ball is 5/2 = 2.5 cm. The volume of the ball is:

[tex]V_ball = (4/3)\pi r^3 = (4/3)\pi (2.5 cm)^3 = 65.45 cm^3\\V_disp = V_ball = 65.45 cm^3\\h_new = 9 + (V_disp/\pi r^2) = 9 + (65.45 cm^3)/(\pi (3.5 cm)^2) = 10.77 cm\\V2 = \pi r^2h_new = \pi (3.5 cm)^2(10.77 cm) = 401.94 cm^3\\[/tex]

The amount of water lost is:

[tex]V_lost = V1 - V2 = 346.36 cm^3 - 401.94 cm^3 = -55.58 cm^3[/tex]

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