For a project in his Geometry class, Elijah uses a mirror on the ground to measure the height of his school building. He walks a distance of 8. 25 meters from the school, then places a mirror on flat on the ground, marked with an X at the center. He then steps 0. 8 meters to the other side of the mirror, until he can see the top of the school clearly marked in the X. His partner measures the distance from his eyes to the ground to be 1. 45 meters. How tall is the school? Round your answer to the nearest hundredth of a meter

Answer: Its B

Step-by-step explanation:

Answer: The width of the room is 36 feet and the length of the room is 48 feet.

Step-by-step explanation:

To solve this problem using elimination, you can set up a system of equations to represent the information given in the problem.

Let w be the width of the room, and let l be the length of the room. We are told that the length of the room is 12 feet longer than its width, so we can set up the equation:

l = w + 12

We are also told that half the perimeter of the rectangular floor is 72 feet. The perimeter of a rectangle is given by the formula:

Perimeter = 2 * (length + width)

Since half the perimeter is 72 feet, the full perimeter is 2 * 72 = 144 feet. Substituting the equation for the length of the room, we get:

144 = 2 * (w + 12 + w)

Combining like terms and solving for w, we get:

w = 36

Substituting this value back into the equation for the length of the room, we get:

l = 36 + 12 = 48

Therefore, the width of the room is 36 feet and the length of the room is 48 feet.

To solve this problem using substitution, we could start by solving for the width of the room in one of the equations, and then substituting that value into the other equation to solve for the length of the room.

For example, we could solve the equation l = w + 12 for w to get:

w = l - 12

Substituting this expression for w into the equation for the perimeter, we get:

144 = 2 * (l - 12 + l)

Combining like terms and solving for l, we get:

l = 48

Substituting this value back into the equation for the width of the room, we get:

w = 48 - 12 = 36

Therefore, the width of the room is 36 feet and the length of the room is 48 feet.

No, 1, 2, and 3 are not valid side lengths for a triangle. So 1, 2 and 3 cannot make a triangle.                                                                      

In order for a shape to be a triangle, the sum of the lengths of any two sides must be greater than the length of the third side. This is known as the triangle inequality theorem.                                                              

3 + 2 = 5 > 1

3 + 1 = 4 > 2

1 + 2 = 3 not greater than 3

So as 1 + 2 not greater than 3, these set of side lengths does not follow the theorem. Thus a triangle cannot be formed with sides of length 1, 2, and 3.

--The question is incomplete, answering to the question below--

" Can 1, 2 and 3 make the sides of a triangle?"

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The problem can be solved using algebra. Let's say the discount rate is x, then the price after discount is:

60000 (1 - x/100)

The price after VAT is:

60000 (1 - x/100) (1 + y/100) = 58986

Where y is the rate of VAT.

Rearranging the equation we get:

(1 - x/100) (1 + y/100) = 58986/60000

Multiply both sides by 100 to get rid of the fractions:

100 (1 - x/100) (1 + y/100) = 981

Expanding and grouping like terms, we get:

100 - x + 100y - xy = 981

We can see that x is in two terms, so we can move one side of the equation and get:

100 - x + 100y = 981 + x

x = (981 + x - 100 + 100y)/100 = (981 + xy - 100y)/100

Now we have x in only one term and we know the value of x is 10%, so we can substitute it:

10 + 10y = 9.81

Solving for y we can find that y = 0.81 or 81%

So the VAT rate is 81%

You can differentiate best time, worst time and average time of an algorithm like this:

Best time = fastest completion time with optimal inputs.

Worst time = slowest completion time, with pessimistic inputs.

Average time = arithmetic mean

The average-case complexity of an algorithm is the amount of a computational resource (typically time) used by the algorithm, averaged over all potential inputs, according to computational complexity theory. The worst-case complexity, which takes into account the algorithm's maximum complexity given all potential inputs, is frequently contrasted with it.

There are three main reasons to investigate average-case complexity. First off, while some problems may be insurmountable in the worst case, the inputs that cause this behaviour may only occasionally occur in practise, so the average-case complexity may be a better indicator of an algorithm's performance.

Second, tools and techniques to create challenging problems are provided by average-case complexity analysis. These tools and techniques can be used in fields like derandomization and cryptography.

Third, average-case complexity enables the most effective algorithm in practise to be distinguished from algorithms with equivalent best case complexity.

What is average case complexity

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[tex]24x+15=25x+45[/tex]

Subtract 25x from both sides:

[tex]24x+15-25x=25x+45-25x[/tex]

[tex]-x+15=45[/tex]

Subtract 15 from both sides:

[tex]-x+15-15=45-15[/tex]

[tex]-x=30[/tex]

Divide both sides by -1(to remove negative from variable):

[tex]\dfrac{-x}{-1} =\dfrac{30}{-1}[/tex]

[tex]\fbox{x = -30}[/tex]

Answer:

[tex] \sf \: x = - 30[/tex]

Step-by-step explanation:

Now we have to,

→ find the required value of x.

The equation is,

→ 24x + 15 = 25x + 45

Then the value of x will be,

→ 24x + 15 = 25x + 45

→ 24x - 25x = 45 - 15

→ -x = 30

→ [ x = -30 ]

Hence, the value of x is -30.

Answer:

y(2-10)2(12+3x)...

Step-by-step explanation:

first make groups of the numbers

y2 with 10 y they both have y in common

so you can write it as y(2-10)

after 24 with 6x they both have 2in common (2×12=24)

so you can write it as 2(12+3x)

and you can do the rest with the same technique

The correct option is (a) 48.

In algebra, an equation is a statement of equality between two expressions. These expressions can be numbers, variables, or a combination of both.

In the equation:

b/4 = 12, the variable b is on one side of the equation and the value 12 is on the other side.

To find the value of b that makes the equation true, we need to isolate the variable b on one side of the equation.

In this case, we can do this by multiplying both sides of the equation by 4.

This cancels out the denominator of the fraction on the left side, and we get,

b = 12*4= 48.

This means that when b is equal to 48, the equation b/4 = 12 is true.

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Step-by-step explanation:  12 - 14 is 2 years

                                               14 - 15 is 1 year

                                               15 - 17 is 3 years

I would say the rang is 1 -3 years apart

Hope this helps any

Answer:

infinity/undefined (both are acceptable)

Undefined is actually the best answer in college but your answer key might put it as infinity.

Step-by-step explanation:

Observe that the x coordinates of the two points are exactly the same at 12.

This reduces the possibility of the line being a horizontal or a vertical line.

Imagine, if x coordinates is always the same, it means that you are only varying y and that happens when you move up and down the graph.

Hence, the line is a straight vertical line. (Line equation: x = 12)

Gradient/Slope of a vertical line = infinity/undefined.

The slope of the given line is Undefined

The slope of the line when two points in the line is given is given by

m=(y₂-y₁)/(x₂-x₁)

The points are (12,0) and (12,9)

m=(9-0)/(12-12)

  = 9/0

  =Undefined

The slope of the line is Undefined

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Answer:

send the picture clearly i will help uou surely

Answer:

1. y-2=2/3(x-1) slope: y=2/3x+4/3 standard: 2x-3y=-4

Step-by-step explanation:

According to question we can say that 1% percent of people are ambidextrous.

A percentage in mathematics is a figure or ratio that is stated as a fraction of 100. The abbreviations "pct.," "pct," and "pc" are also occasionally used. It is frequently denoted using the percent symbol "%," though. The amount of percentages has no dimensions. With a denominator of 100, percentages are basically fractions. To show that a number is a percentage, place a percent symbol (%) next to it. For instance, if you correctly answer 75 out of 100 questions on a test (75/100), you receive a 75%. To compute percentages, divide the amount by the total and multiply the result by 100. The percentage is calculated using the formula (value/total) x 100%.

Let 'x' represent the percentage of left-handed people.

Let y represent the percentage of right-handed people.

Let z represent the percentage of ambidextrous people.

x = y/100

100x = y

y/100 = 9( x/100 + z/100)

y = 9x + 9Z

10x = 9x + 9z

x = 9z

x+y+z = 100

11x + x/9 = 100

100x/9 = 100

x = 9

z = 1%

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The slope of the line is 3 and the y-intercept is -5.

The slope of a line is the coefficient of the x term (in this case, 3). To calculate the y-intercept, we can plug in x = 0 and solve for y. Doing this, we get y = 0 + 3(0) + 5 = -5. Therefore, the slope is 3 and the y-intercept is -5.

The slope of a linear equation is found by looking at the coefficient of the x term. In this case, the coefficient of the x term is 3, so the slope of the line is 3. To find the y-intercept, we can plug in x = 0 into the equation and solve for y. Doing this, we get y = 0 + 3(0) + 5 = -5, so the y-intercept is -5. Therefore, the slope of the line is 3 and the y-intercept is -5. This equation is therefore a linear equation with a slope of 3 and a y-intercept of -5.

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The number of gloves selected for each cases is 11 and 19 gloves respectively.

How is selection done?

In mathematics, most of the times selection is done using permutation and combination.

Putting things or numbers in order is known as a permutation.

Combinations are a means to choose items or numbers from a collection of items or groups of items without regard to their order.

Given,

       Total black gloves = 5 left hand+ 5 right hand

       Total brown gloves = 3 left hand + 3 right hand

        Total gray gloves = 2 left hand + 2 right hand

Now to find the least number of gloves for the given conditions, we start with the worst condition.

a) To get at least one matching pair, we first consider no matching pair, which is (5 +3+2) gloves of only left only or right only hand of each colour.

Now to make one pair, we need to select only one glove of the opposite hand of any colour.

Therefore to get atleast one matching pair, smallest number of gloves to be selected = 5 + 3 + 2 + 1 = 11 gloves

b) In this case also we start with worst case.

   For no matching pair of each colour we have to take 10 black gloves, 6 brown gloves and  2 gray gloves of any one hand.

Therefore to get matching pair of each colour, we have to take one more gray glove.

Therefore to get atleast one matching pair of each colour, smallest number of gloves to be selected = 10 + 6 + 2 + 1 = 19 gloves.

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Step-by-step explanation: To solve this equation, you'll need to use the order of operations to determine the correct sequence of steps to follow. The order of operations is a set of rules that specifies the order in which calculations should be performed in a math problem. It helps to prevent ambiguity and ensures that all calculations are performed consistently.Here is the order of operations:Perform any calculations inside parentheses or brackets first.Perform all multiplications and divisions, working from left to right.Perform all additions and subtractions, working from left to right.Using this order, we can solve the equation as follows:3.5 x 4 + 11 x 2.2 = 14 + 11 x 2.2

3.5 x 4 + 11 x 2.2 = 14 + 24.2

3.5 x 4 + 11 x 2.2 = 38.2Therefore, the solution to the equation is 38.2.

Using BODMAS,

B-Bracket

O-Of

D-Division

M-Multiplication

A-Addition

S-Subtraction

Multiplication comes first before addition, so

3.5×4=17

+

11×2.2=24.2

17+24.2=41.2

The probability that the mean thickness in these 16 measurements x is farther than 3 units away from the target value is 0.15 + 0.15 = 0.30 which corresponds to the answer B) 0.32.

What is the Central Limit Theorem?

The central limit theorem states that if you have a population with mean μ and standard deviation σ and take sufficiently large random samples from the population with replacement, then the distribution of the sample means will be approximately normally distributed.

We can use the Central Limit Theorem to determine that the sampling distribution of the mean thickness of a random sample of size 17 from a population with a mean of 200 units and a standard deviation of 12 units will be approximately normal with a mean of 200 units and a standard deviation of (12 units)/√17 = 2.8 units.

Given that the mean thickness in these 17 measurements x is farther than 3 units away from the target value, we can use the standard normal table to find the probability.

Let's call X = mean thickness,

if X > 203, we have P(X>203) = P(Z> (203-200)/2.8) = P(Z>1.071) = 0.15

if X < 197, we have P(X<197) = P(Z< (197-200)/2.8) = P(Z<-1.071) = 0.15

Hence, the probability that the mean thickness in these 16 measurements x is farther than 3 units away from the target value is 0.15 + 0.15 = 0.30 which corresponds to the answer B) 0.32.

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The resultant output of  the given question is 7 by 2 is 14.

This is because 7 multiplied by 2 is equal to 14

When you multiply two numbers, the result is the product of the two numbers. In this case, 7 multiplied by 2 is equal to 14.

Mathematicians use the process of multiplication to calculate the product of two or more given numbers. It is a fundamental mathematical operation in maths that is frequently utilised in everyday life. When we need to combine groups of similar sizes or values , we utilise multiplication.

Hence the correct answer to the given question is 14 .

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Step-by-step explanation:

I have to assume the equations are

4x + y = 13

(1/2)y = -2x + 5

let's bring both of them into a "y = ..." form :

y = -4x + 13

y = -4x + 10

now we see that both equations are lines with the same slope but different y-intersect.

so, they are parallel but not identical.

therefore, there are 0 solutions. the lines will never intersect and have no point in common.

I believe this is correct.

A is: -4, -6, 2

B is: -4, 6

Answer:

-4 and 12 are the zeros of the quadratic.

Step-by-step explanation:

What value does X need to be so (x+4) is 0? -4

What value does X need to be so (x-12) is 0? 12

11 students could sell 1870 cookies.

A statement, at least two variables or integers, and one or more arithmetic operations make up a mathematical expression. This mathematical operation enables the multiplication, division, addition, or subtraction of numbers.

Combining numbers, variables, and operators to represent something's value is known as a mathematical expression. Setting two expressions equal to one another creates an equation, a mathematical statement.

An expression is a collection of numbers, variables, and functions (such as addition, subtraction, multiplication or division etc.) Expressions and phrases are similar in certain ways. Language phrases can comprise actions on their own, but they do not make up complete sentences.

=  10 X 17

=  170 X 11

= 1870

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Inverse operations, such as addition and subtraction, multiplication and division, are pairs of mathematical operations where one operation reverses the effect of the other. The term "inverse" refers to the reciprocal of a number, i.e., x - 1 = 1 / x. One results from multiplying a number by its reciprocal, or inverse.

Inverse operations, such as addition and subtraction, multiplication and division, are pairs of mathematical operations where one operation reverses the effect of the other. The term "inverse" refers to the reciprocal of a number, i.e., x - 1 = 1 / x. One results from multiplying a number by its reciprocal, or inverse.

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Answer:

Step-by-step explanation:

ASA requires that both triangles have two angles and the included side to be congruent.

We have one side and an adjacent angle and need the second angle adjacent to the marked side to be congruent as well

It is the ∠BAC of ΔABC and ∠DPF of ΔPDF or simply ∠A and ∠P.

Answer: The scale factor is a ratio that compares the dimensions of an object to a copy of that object. To find the scale factor from the original picture to the copy, you can divide the length of the copy by the length of the original.

In this case, the length of the original picture is 8 feet and the length of the copy is 1/2 a foot.

So the scale factor is:

1/2 a foot / 8 feet = 1/16

This means that the copy is 1/16 the size of the original. This means that, for each inch or foot on the original, the same length on the copy is 1/16 of that length.

It's also common to express scale factor as a ratio or a fraction of the original, which in this case is 1/16

It's worth mentioning that you could use this same method to find the scale factor for any other dimension of the picture, such as width, height and so on.

Step-by-step explanation:

Answer:

7:15 ,2 weeks=14 days and 30 days divide by 2 = 7 and 15 put them to a ratio and you'll get 7:15.

The area of the garden whose length and width as given in the task content is; 30 (x + 2) square units.

It follows from the task content that the expression which represents the area of the garden plot whose dimensions are as given.

Recall that Area, A = length × width.

Therefore, since length = 6 (√(x + 2)) units

The width = (5 √(x + 2) ) units

Hence, the area of the garden plot as required in the task content is; 6 (√(x + 2)) × ( 5 √(x + 2) )

= 30 (x + 2) square units

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