How many cubic centimetres of iron are there in an open box whose external dimensions are 36 cm, 25 cm and 16 cm, the iron being 2 cm thick throughout? If 1 cubic cm of iron weighs 15 g. find the weight of the open box in kg​

To solve many simultaneous linear equations, use the substitution method in algebra.

The algebraic technique for resolving multiple linear equations at once is called the substitution method. As the name implies, this method involves substituting a variable's value from one equation into another.

The first stage in the substitution approach is to determine any variable's value in terms of the other variable from one equation. If there are two equations, x+y=7 and x-y=8, for instance, we can deduce from the first equation that x=7-y. The substitution approach is applied in this manner as the first stage.

There are three steps in the substitution technique:

Therefore, the answer is x= -2 and y= -8.

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Using the provided data, We should consider the mid-value for the number of students and take the average of percentage to find the estimate number, The answer is 168.

Statistics is a branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organization of data. It is used to make decisions, predictions and gain knowledge from data. It involves using statistical methods to collect, summarize, and draw conclusions from data. It is used in various fields such as business, economics, social science, engineering, and medicine. It helps to make sense of complex data and make informed decisions.

In statistics, an estimate is a value that is calculated from a sample of data in order to approximate a population parameter. The most common examples of estimates are sample mean, sample proportion, sample standard deviation, and sample variance. These estimates are used to infer information about the population from which the sample was drawn. For example, an estimate of the population mean is calculated by taking the average of a sample of data and using that value to infer the value of the population mean.

mid-value of 500-600 = 550

average % = 30.5%

Athletes number = 30.5% of 550

=168

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To find the expected value of the sum of the numbers on the two selected pieces of paper, we need to calculate the probability of each possible outcome and then multiply that probability by the value of the outcome. The expected  value of the sum of the numbers on the two selected pieces of paper is 6.1625.

Therefore the answer is 6.1625.

The possible outcomes for the first bag are 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, each with a probability of 1/10.

The possible outcomes for the second bag are 20, 21, 22, 23, 24, 25, 26, 27, each with a probability of 1/8.

The possible outcomes for the sum of the numbers on the two selected pieces of paper are:

(1,20) ,(1,21) ,(1,22) ,(1,23) ,(1,24) ,(1,25) ,(1,26) ,(1,27)

(2,20) ,(2,21) ,(2,22) ,(2,23) ,(2,24) ,(2,25) ,(2,26) ,(2,27)

(3,20) ,(3,21) ,(3,22) ,(3,23) ,(3,24) ,(3,25) ,(3,26) ,(3,27)

...

(10,20) ,(10,21) ,(10,22) ,(10,23) ,(10,24) ,(10,25) ,(10,26) ,(10,27)

The expected value of the sum of the numbers on the two selected pieces of paper is the sum of the products of each possible outcome and its corresponding probability.

The probability of each outcome is (1/10) * (1/8) = 1/80

So the expected value of the sum of the numbers on the two selected pieces of paper is

(1 + 21)×(1/80) + (1 + 22)×(1/80) + (1 + 23)×(1/80) + (1 + 24)×(1/80) + .... + (10 + 27)×(1/80) = (21 + 22 + 23 + 24 + ... + 37)/80

= (20×17 + 1 + 2 + ... + 17)/80

= (340 + 17×(17 + 1)/ 2)/ 80

= (340 + 17×9)/ 80

= 6.1625

So the expected value of the sum of the numbers on the two selected pieces of paper is 6.1625

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Answer:

C And D

Step-by-step explanation:

94 Inches Is 7.8 Feet Tall & 79 Inches is 6.5 Feet Tall

Answer:

C and D

Step-by-step explanation:

You should start by changing the inches to feet

(there are 12 inches in foot [ 12 inch = 1 foot ])

A. 9 foot

B. 9.5

C. about 7 feet

D. about 6 feet

C and D are correct. Hope this helps!

The area of circle A to the area of circle B ratio is 100: 64, and the ratio of e: f is 13: 10.

The area of the circle is equal to the multiplication of the square of the circle's radius and π.

A = πr²

where 'r' is the radius

Circumference of circle A × 0.8 = circumference of circle B

So, taking r as the radius of A,

2πr =  circumference of circle A

2πr × 0.8 = circumference of circle B

So the radius of B is r × 0.8.

Now we can substitute that in the area equations :

Area of A = π×r²

Area of B = π × (r × 0.8)² = π × r² × 0.64

The circumferences of the A to B ratio is

Circumference of A : Circumference of B = (2 × π × r)/(2 × π × r × 0.8)

= 1: 0.8 = 100: 80,

The areas of circle A to circle B ratio is

Area of A : Area of B = (π × r²)/(π × r² × 0.64) = 1: 0.64 = 100: 64

e² = f² × 1.69

69% larger shows that f² is the 100% to which we must add 69% to obtain e². 100% + 69% Equals 169%, obtaining a factor of 1.69.

We have this equation:

e² = f² × 1.69

Apply the square root on both sides.

e = f × √(1.69) = f × 1.3

e/f = 1.3 = 1.3/1 = 13/10

the ratio e:f = 13: 10

Thus, the ratio of circle A's area to circle B's area is 100: 64 and the ratio of e: f is 13: 10.

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The equation of line is given by y = 13.45x - 7.95 where the slope of the line is m = 13.45 and y is the weight in kilograms , x is the number of months

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given data ,

Let the equation of line be represented as A

Now , the value of A is

The weight in kilograms = y

The number of months = x

Let the first point be represented as P = P ( 11 , 140 )

Let the second point be represented as Q = Q ( 1 , 5.5 )

Now , the slope of the line is given by

Slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Substituting the values in the equation , we get

Slope m = ( 140 - 5.5 ) / ( 11 - 1 )

Slope m = 134.5 / 10

Slope m = 13.45

Now , the equation of line is y - y₁ = m ( x - x₁ )

Substituting the values in the equation , we get

y - 140 = 13.45 ( x - 11 )

On simplifying the equation , we get

y - 140 = 13.45x - 147.95

Adding 140 on both sides of the equation , we get

y = 13.45x - 7.95

when x = 11 months

y = 13.45 ( 11 ) - 7.95

y = 147.95 - 7.95

y = 140 kilograms

Therefore , the value of A is y = 13.45x - 7.95

Hence , the equation is y = 13.45x - 7.95

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0.08/0.2 and 0.2/0.8 are not proportional.

A proportion is an equality of two ratios. We write proportions to help us establish equivalent ratios and solve for unknown quantities.

Given are two numbers, 0.08/0.2 and 0.2/0.8

Checking for if they are proportional or not,

0.08/0.2

Multiplying denominator and numerator by 100,

8/20 = 2/5

And,

0.2/0.8 = 1/4

Since, 0.08/0.2 ≠ 0.2/0.8

Hence, 0.08/0.2 and 0.2/0.8 are not proportional.

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Arranging cards with number -4, -2, -1, 5, 6, 8 making pair with the same total. Therefore, the pairs are (8,-4), (6,-2), (5,-1).

A pair is a hand that has two cards of same rank and three other cards that do not match any of these or each other. When comparing two similar hands, the hand with the higher pair wins – therefore 6-6-4-3-2 defeats 6-6-4-3-2. 5-5-A-K-Q.Some things, such as a pair of pants or a pair of scissors, contain two major sections that are the same size and form.

A 55-card deck with one 1, two 2s, three 3s, and so on up to ten 10s is used in the game. Shuffle the deck at the start of the game, then remove five cards from play without looking. Give each player one face-up card.

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On solving the question, by linear equation One bagel is 100*1.55 = 155 cents in dollars.

A linear equation is one that has the form y=mx+b in algebra. B is the slope, and m is the y-intercept.

A toast costs =  x dollars.

A bagel costs  = y dollars.

A muffin costs = z dollars.

It costs $3.15 for two pieces of toast and a bagel.

As a result, 2x + y = 3.15. To get the price of a bagel, we express x as a function of y,

2x = 3.15 —Y

x = -o.5y+ 1.575

It costs $3.30 for a bagel and a muffin.

Since x and z are functions of y,

—0.5y + 1.575 + + 3(3.3 — y) 9.15

—0.5y + 1.575 +2y + 9.9—3y = 9.15

—1.5y + 11.475 = 9.15

1.5y = 2.325

2.325

Y = 1.55

One bagel is 100*1.55 = 155 cents in dollars.

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A plot point example contains a point in a story that defines the turning point in the story.

A story's plot point is a crucial turning moment that occurs during the narrative. The tale and the characters may be developed and advanced using these ideas.

Plot points offer your tale movement by advancing the plot and dragging the reader along. 'A particularly crucial portion of a storyline of a work of fiction,' according to the definition of a plot point. Never undervalue the significance of your framework, even if your book is contemplative or literary.

An example of plot point is :

In a story about a young girl who is trying to save her village from an impending monster attack, the plot point may occur when the girl discovers an ancient artifact that gives her the power to defeat the monster. This event marks a significant turning point in the story, as it sets the stage for the girl to take on the monster and potentially save her village.

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The provided expression can be simplified in the form 2y4/x4 option ( B) Using the integer exponent characteristics,  = [x[tex]^\frac{1}{8}[/tex] . y⁸]  is the right answer.

In mathematics, integer exponents are exponents that fall under the integer category. It's possible for the number to be either positive or undesirable. The positive integer exponents in this example dictate how many times that base number must be multiplied by itself.

It's possible for the number to be either positive or undesirable. The positive integer exponents in this example dictate how many instances the base number must be multiplied by itself.

= [x[tex]^\frac{1}{4}[/tex] . y¹⁶][tex]^\frac{1}{2}[/tex]

= [x[tex]^\frac{1}{8}[/tex] . y⁸]

The provided expression can be simplified in the form 2y4/x4 option ( B) Using the integer exponent characteristics,  = [x[tex]^\frac{1}{8}[/tex] . y⁸]  is the right answer.

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Answer:

4 sweets per friend

Step-by-step explanation:

so first you want to minus 10 sweets since she ate 10 leaving her with 40 sweets. then she gives 8 sweets to her brother leaving her with 32 sweets left. If you divide the remaining sweets ( 32 ) by 8 you get 4 sweets per friend

The total weight of the loaves of bread remaining is 1.5 lbs

From the problem it can be deduced that'

There are 3.5 loaves of bread

each weighing 1.5 lbs

Anton's family eats 2.5 loaves of bread

the total weight of the loaves of bread that are left = ?

The loaves of bread that are left

= 3.5 loaves - 2.5 loaves

= 1 loaf

Since 1 loaf weighs  1.5 lbs the weight of the left over bread is 1.5 lbs

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The symbol ∑ (sigma) is used to represent the sum of a set of numbers. This is very important notation in statistics.

If a hypothesis is correct, a set of data's standard deviation serves as a gauge of how rare it is. Standard deviations are expressed in units called sigma, or, by physicists. The findings are progressively inconsistent with the hypothesis as the number of sigma increases. The word's derivation is derived from the Greek letter "sigma," which is used in statistics to measure how much a process deviates from its mean or goal.

To express the total of a set of data or the total of a function over a specified range, it is frequently used in statistics and probability. For instance, if X is a collection of numbers, the term ∑X would stand for the collection's total. The symbol is typically followed by a variable, such as I indicating the range of the sum, for example, ∑i=1 to n for the summing from i=1 to i=n. The index I is frequently used to identify the individual components of the set.

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The slope of a logarithmic graph depends on the type of logarithm used.

For a logarithmic function in the form y = log(b,x) where b is the base of the logarithm, the slope of the graph is undefined for x=0 and for x<0 because logarithmic functions are not defined in those cases.

For a natural logarithm, the slope is negative infinity at x=0 and positive for x > 0. As x increases, the slope becomes closer to zero.

For a common logarithm, the slope is negative infinity at x=0 and positive for x > 0. As x increases, the slope becomes closer to zero.

It's important to note that logarithmic functions are not linear functions, and therefore they do not have a constant slope, the slope of a logarithmic graph will change throughout the graph.

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Thus, 0 itself is the sole position at which [0,∞] and (0,∞] are separated. Since it is in [0,∞] the set is closed. Given that it is not in (0,∞), the set is open interval.

A (real) interval in mathematics is a collection of real numbers that includes all real numbers that fall within any two of the collection's numbers. For instance, the interval containing 0, 1, and all integers in between is the set of values x satisfying 0 x 1. The collection of numbers such that 0 x 1 and the collection of all real numbers are other examples of intervals.

the empty set, any singleton, the set of positive real numbers, the set of nonnegative real numbers, and (set of one element).

Because they are the most basic sets whose "length" (or "measure" or "size") is straightforward to define, real intervals are crucial in the theory of integration. The Borel measure and finally the Lebesgue measure result from extending the notion of measure to more intricate sets of real numbers.

Interval arithmetic is a broad numerical computing technique that automatically generates assured enclosures for arbitrary formulas, even in the presence of uncertainties, mathematical approximations, and arithmetic roundoff. Intervals are at the centre of this technique.

Therefore, 0 itself is the sole place at which [0,∞] and (0,∞] have a boundary. Due to its location in [0,∞] the set is closed. Since it is not in (0,∞), the set is unclosed.

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The length of the rectangle's shorter side is 6cm and the of the rectangle's longer side is 12cm.

What is perimeter?

The total length of a shape's boundary, as used in geometry, is referred to as the shape's perimeter. Adding the lengths of all the sides and edges that surround a shape yields its perimeter. It is calculated using linear length units like centimeters, meters, inches, and feet.

Given:

A rectangle has a perimeter of 36 cm and an area of 72 cm^2.

Let the length of the rectangle's shorter side is 'a' and

the length of the rectangle's longer side 'b'.

As the perimeter is 36 cm.

⇒ Perimeter = 2(a + b)

               36 = 2(a + b)

                18 = a+ b

                 a = 18 - b

Now the area of rectangle is 72cm^2.

⇒                   Area = ab

                         72 = (18 - b)*b

                         72 = 18b - b^2

      b^2 - 18b + 72 = 0

b^2 - 12b - 6x + 72 = 0

b(b - 12) - 6(b - 12) = 0

         (b - 12)(b - 6) = 0

(b - 12) = 0,    (b - 6) = 0

b = 12,   b = 6

When  b = 12   ⇒  a = 18 - 12 = 6

When  b = 6   ⇒  a = 18 - 6 = 12

Hence, the length of the rectangle's shorter side is 6cm and the of the rectangle's longer side is 12cm.

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The dilation of the circle with a scale factor 1/r and center at (a,b) will transform the circle into a point at (a,b).

A dilation is a transformation that results in an image with the same shape as the original but a different size. • An enlargement is a dilation that produces a larger image. • A reduction is a dilation that produces a smaller image.

To solve this we will use the transformation formula for a dilation with center (a,b) and scale factor

k, (x,y) --> (a + k(x-a), b + k(y-b)).

Substituting in our values, we get

(x,y) --> (a + (1/r)(x-a), b + (1/r)(y-b)).

Setting this equal to (a,b), we get

(a + (1/r)(x-a) = a, b + (1/r)(y-b) = b).

Solving for x and y gives x = a and y = b. Therefore, the dilation of the circle with a scale factor of 1/r and center at (a,b) will transform the circle into a point at (a,b).

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Answer:

Can you please show the picture

Step-by-step explanation:

The cost  of hiring a van for 5 days is $235.

In this question, we have been given an equation c = 10 + 45d that represents the cost in pounds of hiring a van for days.

here c = cost in pounds

d = number of days

We need to find the cost  of hiring a van for 5 days.

Substitute the value d = 5 in given equation.

c = 10 + 45d

c = 10 + (45 × 5)

c = 10 + 225

c = 235 dollars

Therefore, the cost for 5 days is 235 dollars

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Step-by-step explanation:

send the pic clearly i will help surely im sorry

Answer:

g>5

Step-by-step explanation:

Simply add 6 to both sides to get g>5

Logarithmic Functions

In mathematics, the logarithmic function is an inverse function to exponentiation

Domain and range of logarithmic functions

We know that is defined only when >0. So the domain is the set of all positive real numbers. We can see that can be either a positive or negative real number (or) it can be zero as well. Thus,  can take the value of any real number.

Note:

The domain of function = is >0 (or) (0,∞).

The range of any log function is the set of all real numbers ().

Logarithmic graph

We know that exponentials and functions are inversely proportional to each other, and so their graphs are symmetric concerning the line =. Also, note that =0 when =0 as =(1)=0 for any . Thus, all such functions have an -intercept of (1,0).  A logarithmic function doesn’t have a -intercept as 0 is not defined.

Properties of logarithmic graph

>0 and ≠1.

The logarithmic graph increases when >1 and decreases when 0<<1.

The domain is obtained by setting the argument of the function greater than 0.

The range is the set of all real numbers.

Graphing logarithmic functions

Before plotting the log function, just have an idea of whether you get an increasing curve or decreasing curve as the answer. If the >1 then the curve is increasing, and if 0<<1, then the curve is decreasing.

Here are the steps for graphing logarithmic functions:

Find the domain and range.

Find the vertical asymptote by setting the argument equal to 0. Note that a  function doesn’t have any horizontal asymptote.

Substitute some value that makes the argument equal to 1 and use the property (1)=0. This gives us the -intercept.

Substitute some value that makes the argument equal to the base and use the property ()=1 This would give us a point on the graph.

Connect the two points (from the last two steps) and extend the curve on both sides relative to the vertical asymptote.

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[tex]2(q+p)=1+5q\implies 2q+2p=1+5q\implies 2q+2p-5q=1 \\\\\\ 2q-5q=1-2p\implies q(2-5)=1-2p\implies -3q=-2p+1 \\\\\\ q=\cfrac{-2p + 1}{-3}\implies q=\cfrac{2}{3}p-\cfrac{1}{3}[/tex]

Answer:

Step-by-step explanation: 2(q+p)=1+5q

2q+2p=1+5q

2q-5q=1-2p

-3q=1-2p/:(-3)

q=-1/3+2/3 p

Answer:

7. .44

8. .009

Step-by-step explanation:

7. 44 ÷ 100 = .44

8. 9 ÷ 1000 = .009

A line's x-intercept as well as y-intercept are the points at which the x- and y-axes, respectively, are crossed.

Now, According to the question:

Let's know:

Definition of Intercept

The term "intercept" refers to the location where a line and curve crosses an graph's axis. The x-intercept would be the point at which the x-axis gets crossed. The y-intercept would be the point at which the y-axis becomes crossed.

The x- as well as y-axis intersection point gets what is meant when a line has an intercept. The y-axis was often taken into account if indeed the axis is also not stated. The letter "b" can be typically used to represent it.

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So A is a triangle, and B is a triangle, and C is a right triangle (or a right-angled triangle)

The Pythagorean Theorem states that the squares on the hypotenuse (the side across from the right angle) of a right triangle, or, in standard algebraic notation, a2 + b2, are equal to the squares on the legs.

A right triangle, also known as a right-angled triangle, right-perpendicular triangle, orthogonal triangle, or previously rectangled triangle, is a triangle with one right angle, or two perpendicular sides. The foundation of trigonometry is the relationship between the sides and various angles of the right triangle.

A. a = 8, b = 15, c = 17

We can use the Pythagorean theorem to determine the type of triangle:

c² = a² + b²

17² = 8² + 15²

289 = 64 + 225

289 ≠ 289

Therefore, this is not a right triangle.

B. a = 6, b= 15, c = 18

We can use the Pythagorean theorem to determine the type of triangle:

c² = a² + b²

18² = 6² + 15²

324 = 36 + 225

324 ≠ 324

Therefore, this is not a right triangle.

C. a = 7, b = 10, c = 12

We can use the Pythagorean theorem to determine the type of triangle:

c² = a² + b²

12² = 7² + 10²

144 = 49 + 100

144 = 144

Therefore, this is a right triangle.

So A is a triangle, and B is a triangle, and C is a right triangle (or a right-angled triangle)

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4 is the range of the data set in the given set.

The space between the highest and lowest values in a data collection is known as the range. Similar units to the data are used to quantify variability. Variability is increased with larger values. The range has several limitations but is the most straightforward statistical measure of dispersion to compute and comprehend.

This means that the range might alternatively be described as the distance between the highest and lowest observation.

In the given data set,

range = maximum frequency - minimum frequency

range = 5 - 1

range = 4

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The exponential function that best models this data is given as follows:

C. y = 80(0.75)^x + 20.

An exponential function, considering it's asymptote, is defined as follows:

y = a(b)^x + c.

In which the parameters are given as follows:

From the graph, the horizontal asymptote is at y = 20, hence the parameter c is defined as follows:

c = 20.

When x = 0, y = 100, hence the parameter a is obtained as follows:

100 = a(b)^0 + 20

a + 20 = 100

a = 80.

When x = 5, y = 40, hence the parameter b is obtained as follows:

40 = 80b^5 + 20

80b^5 = 20

b^5 = 1/4

b = (1/4)^(1/5)

b = 0.75. (approximately).

Hence the function is defined as follows:

y = 80(0.75)^x + 20.

Meaning that the correct option is given by option C.

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