According to cell theory, all cells come from:

A.
water.
B.
soil.
C.
chemical reactions.
D.
pre-existing cells.

The Hindu-Arabic numeral system is superior to other numeral systems because of its invention of the number 0. This allows for the representation of the concept of nothingness or absence, which allows for the development of more advanced mathematical operations such as negative numbers and decimal fractions.

The two purposes of numerals or digits are to show the cardinal value (how many) and to show the place value (10s, 100s, 1000s). The cardinal value is the actual quantity of a number, while the place value is the position of a digit in a number, which determines its value in relation to other digits.

The natural numbers are the numbers used in a counting process and do not include 0. They include the numbers 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, and so on to infinity. The principle of closure is the idea that certain operations, such as addition and multiplication, will always result in a natural number when performed on natural numbers. However, subtraction and division do not result in natural numbers in all cases.

Integers are positive and negative numbers that start at 0 and expand infinitely in both directions. They are closed under addition, multiplication, and subtraction. However, division is not closed under integers.

Rational numbers are numbers that can be expressed as the quotient of two integers. Irrational numbers are non-terminating, non-repeating decimals.

The three axioms of equality are the reflexive property (A = A), the symmetric property (if A = B, then B = A), and the transitive property (if A = B and B = C, then A = C).

The commutative property states that the order of the numbers does not affect the result in operations such as addition and multiplication. The associative property states that the grouping of numbers does not affect the result in operations such as addition and multiplication. The distributive property states that multiplication can be distributed over addition.

The unity element for multiplication is the number 1, which serves as the identity element for multiplication. The zero element for addition is 0, which serves as the identity element for addition. Dividing by 0 is an error and not allowed.

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A vertical stretch of scale factor 2, followed by a translation of 4 units left and 1 unit down is written as:

g(x) = 2*f(x + 4) - 1

For a general function f(x), a vertical stretch of scale factor K is written as:

g(x) = K*f(x).

Horizontal translation:

For a general function f(x), a horizontal translation of N units is written as:

g(x) = f(x + N).

Vertical translation:

For a general function f(x), a vertical translation of N units is written as:

g(x) = f(x) + N.

So, if we start with a function f(x) and we stretch it vertically with a scale factor of 2, we get:

g(x) = 2*f(x)

Then we translate it 4 units left:

g(x) = 2*f(x + 4)

Then we translate 1 unit down:

g(x) = 2*f(x + 4) - 1

This is the equation for the transformation.

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Answer:

[C] 44°

Explanation:

Equation: x + 46 = 90

Subtract 46 From Both Sides

x + 46 - 46 = 90 - 46

x = 44

A possible amount for the median of the distribution is $22.50.

The histogram of the distribution of the amounts of the orders shows a roughly symmetrical distribution with a single peak, and most of the amounts falling between $15 and $30.

To identify the possible amount for the median of the distribution, we need to find the middle value in the ordered data set. Since the data set has an odd number of observations, the median is simply the middle observation.

There are a total of 91 observations, so the middle observation would be the 46th value when the data set is ordered. Looking at the histogram, we can see that the value corresponding to the 46th observation falls between $20 and $25. Therefore, a possible amount for the median of the distribution is $22.50.

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To create a histogram, use the data in the frequency table to plot dollar amounts on the x-axis and frequencies on the y-axis. The shape of the distribution can be determined by examining the histogram. To find a possible median, arrange the dollar amounts in order and find the middle value.

(a-i) To create a histogram, we will use the data in the frequency table. We will plot the dollar amounts on the x-axis and the corresponding frequencies on the y-axis. Each bar in the histogram will represent a range of dollar amounts.

(a-ii) The shape of the distribution of amounts can be determined by looking at the histogram. It may be symmetric, skewed to the left or right, or have other shapes like bimodal or uniform.

(b) To identify a possible amount for the median, we need to arrange the dollar amounts in ascending order and find the middle value. If our set has an even number of values, we find the average of the two middle values.

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19.25  scale factor did jennie use to go from polygon ccc to polygon ddd if Polygon ccc has an area of 777 square units.

What is polygon and examples?

A polygon is a closed shape with straight sides. Rectangles, triangles, hexagons, and octagons are all examples of polygons. The word polygon comes from the Greeks, like most terms in geometry, which they invented. It simply means many (poly) angles (gon).

The area of polygon D is given by:

Ad = k ^ 2 * Ac

Where,

k: scale factor

Ac: area of polygon C

Substituting the values we have:

Ad = (1/2) ^ 2 * (77)

Ad = (1/4) * (77)

Ad = 19.25 square unit

the area of Polygon D is: 28

Ad = 19.25 square units

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Answer:

The values of \(a\) and \(b\) are \(5\) and \(-\frac{15}{7}\), respectively.

Step-by-step explanation:

There are mistakes in the statement, correct form is presented below:

\(5+\frac{\sqrt{3}}{7} + 2\sqrt{3} = a - b\cdot \sqrt{3}\).

By direct comparison we have the following system of equations:

\(a = 5\) (1)

\(\frac{\sqrt{3}}{7}+2\sqrt{3} = -b\cdot \sqrt{3}\) (2)

In (2) we solve for \(b\):

\(\left(\frac{1}{7}+2 \right)\cdot \sqrt{3} = -b\cdot \sqrt{3}\)

\(b = -\frac{15}{7}\)

The values of \(a\) and \(b\) are \(5\) and \(-\frac{15}{7}\), respectively.

it has gone up 4 lines and left -2 making it go for a (4,-2)

The area of the shaded region on the circle opposite to point C is approximately 9.76 square centimeters.

The area of the sector can be calculated using the formula:

Area of sector = (θ/360) x πr²

where r is the radius of the circle. In this case, r = 6 cm. To find θ, we can use trigonometry. We know that AC and BC are radii of the circle, so they are both equal to 6 cm. We also know that AB = 8 cm. Using the cosine rule, we can find the angle θ:

cos(θ) = (6² + 6² - 8²)/(2 x 6 x 6)

cos(θ) = 0.5 θ = cos⁻¹(0.5) θ = 60 degrees

Now we can substitute the values of θ and r into the formula for the area of the sector:

Area of sector = (60/360) x π x 6²

Area of sector = 18π cm²

Next, we need to find the area of the triangle ABC. We can use the formula for the area of a triangle:

Area of triangle = 0.5 x base x height

In this case, the base is AB = 8 cm, and the height is given by the perpendicular distance from point C to AB. We can find this distance using the sine rule:

sin(θ) = height/AC

sin(60) = height/6

height = 3√3 cm

Now we can substitute the values of the base and height into the formula for the area of the triangle:

Area of triangle = 0.5 x 8 x 3√3

Area of triangle = 12√3 cm²

Finally, we can find the area of the shaded region by subtracting the area of the triangle from the area of the sector:

Area of shaded region = Area of sector - Area of triangle

Area of shaded region = 18π - 12√3 Area of shaded region ≈ 9.76 cm²

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Answer:

Yes, because they both have two sets of parallel lines.

Hope that helps!

Step-by-step explanation:

Using the empirical rule, we know that for a normal distribution, approximately 68% of the data falls within one standard deviation of the mean, 95% falls within two standard deviations of the mean, and 99.7% falls within three standard deviations of the mean.

In this case, the mean is 56 and the standard deviation is 7. To find the number of phone calls between 35 and 77, we need to find how many standard deviations away from the mean these values are.

For 35: (35-56)/7 = -3

For 77: (77-56)/7 = 3

So the range we are interested in is 3 standard deviations below the mean to 3 standard deviations above the mean. Using the empirical rule, we know that approximately 99.7% of the data falls within this range.

Therefore, the approximate percentage of daily phone calls numbering between 35 and 77 is 99.7%.

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The limit of the given function is  π/2.

What is a limit?

A limit in mathematics is the value that a function gets closer to when the input gets closer to a certain value. Calculus and mathematical analysis are not possible without limits, which are also required to determine continuity, derivatives, and integrals.

Here, we have

Given: \(\lim_{(x,y) \to \pi, \pi /2} y sin(x-y)\)

We have to find the limit of the given function.

=  \(\lim_{(x,y) \to \pi, \pi /2} y sin(x-y)\)

Now, we substitute the value of each variable.

x = π and y = π/2

= y sin(x-y)

= π/2sin(π-π/2)

= π/2sinπ/2

= π/2sin(90°)   (∴sin90° = 1)

= π/2×1

= π/2

Hence, the limit of the given function is  π/2.

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The vectors v = 6i - 3j and w = i + 2j are orthogonal.

To determine if the vectors v and w are orthogonal, we need to find their dot product. If the dot product is 0, the vectors are orthogonal.

Here are the steps to find the dot product of v = 6i - 3j and w = i + 2j,

1. Identify the components of the vectors: v = (6, -3) and w = (1, 2)

2. Multiply the corresponding components of the vectors:

\((6 \times 1) + (-3 \times 2) = 6 - 6 \)

3. Add the products: 6 - 6 = 0 Since the dot product is 0, the vectors v = 6i - 3j and w = i + 2j are orthogonal.

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Correct question is " Are these vectors orthogonal? v = 6i - 3j and w = i+2j"

The function f(x) that satisfies the given functional equation is:

f(x) = 8 / (x³ + 1/x³) for all non-zero real values of x.

The functional equation is given as follows:

f(x)+5xf(1/x)=8x³

Substitute x with 1/x in the functional equation.

f(1/x) + 5(1/x)f(x) = 8(1/x)³

Multiply both sides of the equation by x³ to eliminate the denominators.

x³f(1/x) + 5xf(x) = 8

Rearrange the equation to isolate the terms involving f(x).

5xf(x) = 8 - x³f(1/x)

Substitute y = 1/x.

5xf(x) = 8 - (1/y)³f(y)

Multiply both sides of the equation by y³.

5xy³f(x) = 8y³ - f(y)

Substitute x = 1/y.

5(1/y)y³f(1/y) = 8y³ - f(y)

Simplify the left side of the equation.

5f(1/y) = 8y³ - f(y)

Substitute z = 1/y.

5f(z) = 8(1/z)³ - f(1/z)

Multiply both sides of the equation by z³ to eliminate the denominators.

5z³f(z) = 8 - z³f(1/z)

Rearrange the equation to isolate the terms involving f(z).

5z³f(z) + z³f(1/z) = 8

Combine the two terms on the left side of the equation.

(z³ + 1/z³)f(z) = 8

Divide both sides of the equation by (z³ + 1/z³).

f(z) = 8 / (z³ + 1/z³)

Therefore, the function f(x) that satisfies the given functional equation is:

f(x) = 8 / (x³ + 1/x³) for all non-zero real values of x.

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Answer:36%=9/25    17/50=34%   0.18=18%     1/4=0.25        Hope that helped:)

Step-by-step explanation:

The solution to the equation is

a) 24 / 25 = 0.96

b) 3/5 = 60 %

c) 9 / 50 = 0.18

26 % = 13 / 50

0.35 = 7 / 20

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is given by

a)

24 / 25

The value of the fraction A = 24/25 is

A = 0.96

Therefore , A = 24/25 = 0.96

b)

3/5

The value of the fraction A = 3/5

Multiply the numerator and denominator by 20 , we get

A = 3/5 x 20/20

A = 60 / 100

A = 60 %

Therefore , A = 3/5 = 60 %

c)

9/50

The value of the fraction A = 9/50

Multiply the numerator and denominator by 2 , we get

A = 3/5 x 2/2

A = 18 / 100

A = 0.18

Therefore , A = 9/50 = 0.18

d)

26 %

The value of the fraction A = 26 %

Convert the percentage A = 26 % into  fraction  , we get

A = 26/100

A = 13 / 50

A = 13/50

Therefore , A = 26 % = 13/50

e)

The value of the fraction A = 0.35

Convert the decimal A = 0.35 to fraction , we get

A = 35 / 100

Divide the numerator and denominator by 5 , we get

A = 7 / 20

Therefore , A = 0.35 = 7 / 20

Hence , the value of the equation A is

a) 24 / 25 = 0.96

b) 3/5 = 60 %

c) 9 / 50 = 0.18

26 % = 13 / 50

0.35 = 7 / 20

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The coordinates of B' are given as follows:

B'(12, -9).

A dilation is defined as a non-rigid transformation that multiplies the distances between every point in a polygon or even a function graph, called the center of dilation, by a constant factor called the scale factor.

The coordinates of B are given as follows:

B(4, -3).

The scale factor is given as follows:

k = 3.

Hence the coordinates of B' are given as follows:

B'(12, -9).

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The coordinates of B' include the following: D. (12, -9).

In Mathematics and Geometry, a dilation is a type of transformation which typically changes the dimensions (size) or side lengths of a geometric object, but not its shape.

This ultimately implies that, the dimensions (size) or side lengths of the dilated geometric object would increase or decrease depending on the scale factor applied.

In this scenario and exercise, we would have to dilate the coordinates of the pre-image (triangle ABC) by using a scale factor of 3 centered at the origin in order to determine B' as follows:

Coordinate B (4, -3)        →       (4 × 3, -3 × 3) = X' (12, -9).

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A function that satisfies the condition of having its square plus the square of its derivative equal to 1 is given by f(x) = sin(x).

The function f(x) = sin(x) has the property that its square, sin^2(x), is equal to 1 when added to the square of its derivative, \($\frac{d}{dx}\sin(x))^2 = \cos^2(x)$\).

This can be seen by directly evaluating the expression: \(sin^{2}(x) + cos^{2}(x) = 1\), which is a fundamental identity in trigonometry.

The sine function is periodic with a period of 2π, and its derivative, cosine function, also has the same period. This means that for any x, the function sin(x) and its derivative cos(x) will satisfy the given condition.

Geometrically, the sine function represents the y-coordinate of a point on the unit circle as the corresponding angle is varied. Its derivative, the cosine function, represents the rate of change of this y-coordinate with respect to the angle. The squares of the sine and cosine functions add up to 1, which is the square of the radius of the unit circle. This property is fundamental in trigonometry.

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The group that would best represent the sample population is; D: Every fifth person walking down the street in several different locations..

A sample population is simply a subset of the main population. Now, in this question we see that a poll is being taken on Wednesday to predict which movie will be the most popular at the city’s movie theaters the next weekend.

Now, since we are looking for sample population, the one that will best represent it will be Option D. This is because - Different locations through out the city at Different time has maximum randomness.

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Answer:

119.4 cm^2

Step-by-step explanation:

Area of a circle is \(\pi\) x radius^2, and the area of a rectangle is length * width. 11 cm x 12 cm = 132 cm^2 (rectangle's area). The circle's area would be \(\pi\) x 2^2 which would equal 12.56637061 cm^2 (left unrounded until the end). Then subtract 12.56637061 from 132 cm^2 and that would equal 119.4 cm^2 rounded to the tenth.

Answer:

20+2>50

Step-by-step explanation:

Answer:

15 roses

Step-by-step explanation:

20+2x≥50

-20     -20

2x≥30

2x/2≥30/2

x≥15

Answer: x = -7

Step-by-step explanation:

7 (x + 4) = -21

7x + 28 = -21

Subtract 28 from both sides

7x = -49

Divide both sides by 7

x = -7

Answer:

x = -7

Step-by-step explanation:

first distribute he 7 to get 7x + 28 = -21

then subtract 28 from both sides to get 7x = -49

lastly divide 7 from both sides to get x = -7

Michael’s child is going to college in 13 years. If he saves $ 7,000 a year at 9% compounded annually. Therefore,  the amount available for Peter's child education will be $147,330.55.

Given that Michael is saving $7,000 per year for his child's education which will occur in 13 years. If the interest rate is 9% compounded annually,

The problem of finding the amount of money Michael will have saved in 13 years is a compound interest problem.

In this case, the formula for calculating the future value of the annuity is: $FV = A[(1 + r)n - 1] / r

where: FV is the future value of the annuity, A is the annual payment,r is the annual interest rate, and n is the number of payments.

Using the above formula; the future value of Michael's savings is:

FV = 7000[(1 + 0.09)^13 - 1] / 0.09= 7000(1.09^13 - 1) / 0.09= 147,330.55

Therefore, the amount available for Peter's child education will be $147,330.55.

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Answer:

the mean is 14.8

the median is 14

the mode is 12

Step-by-step explanation:

hope this is what you were looking for and i hope it helps! :)

The solution to the system of equations is x = 1 and y = 1.

To solve the system of equations using substitution, we start by solving one equation for one variable and substituting it into the other equation. Given the system of equations:

1) 4x + 3y = 7

2) 3x + 5y = 8

We can solve equation 1 for x:

4x = 7 - 3y

x = (7 - 3y)/4

Now, substitute this expression for x into equation 2:

3((7 - 3y)/4) + 5y = 8

Simplify the equation:

(21 - 9y)/4 + 5y = 8

Multiply both sides by 4 to eliminate the fraction:

21 - 9y + 20y = 32

Combine like terms:

11y = 11

Divide both sides by 11:

y = 1

Now, substitute the value of y back into equation 1 to solve for x:

4x + 3(1) = 7

4x + 3 = 7

4x = 7 - 3

4x = 4

x = 1

Therefore, the solution to the system of equations is x = 1 and y = 1.

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Answer:

Additive Identity

Step-by-step explanation:

The additive identity is 0. Adding 0 to any number does not change the number

There is also a multiplicative identity which is 1. A number multiplied by 1 does not change the original number

Answer:

1.03% of 0.054=0.0005562

● < P=R " angles opp =sides"

●PQ =QR " Angles opposite = sides"

therefore PQR is an isosceles " 2 opp angles and sides are equal "

Are 5,040 different possible settings for the suitcase lock if all four digits have to be different.

For the first dial, there are 10 possible digits (0 to 9) that can be set. For the second dial, there are 9 remaining digits to choose from (since we cannot repeat the digit from the first dial). For the third dial, there are 8 remaining digits to choose from (since we cannot repeat any of the digits from the first two dials). Finally, for the fourth dial, there are 7 remaining digits to choose from.

Therefore, the total number of possible settings for the suitcase lock with all four digits different is:

10 × 9 × 8 × 7 = 5,040

There are 5,040 different possible settings for the suitcase lock if all four digits have to be different.

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The contribution of Arts and Crafts in our Culture is explained below .

The Art and Crafts represents a collective memory of society.

Through expressive outlets of Arts and craft such as paintings, sculptures, music, literature and other art forms, presents a better  historical fact-based records.

The Art expresses how it can be felt to exist in a particular time.

The Art is also communicative in nature because it helps people of  various cultures to understand and communicate with each other through songs, pictures and stories.

Folk Arts and Crafts are highly unique for specific cultures and Society and tell us about the history and rich traditions of a region.

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