in the packet of mixed candies there are 2 fruit centers for every 3 caramel centers. there are 30 candies in the packet

The answer of the given question based on the number line is the difference between 8 and -16 is not 14, it is 24. and 8 and -16 are 24 units apart on the number line.

A number line is a visual representation of the real number system, where numbers are placed in order from left to right, with zero in the center. The number line is an important mathematical tool used in a variety of ways, including:

Understanding and comparing numbers: By plotting numbers on a number line, we can visually see the relative size and position of numbers in relation to each other.

Performing arithmetic operations: The number line can be used to add, subtract, multiply, and divide numbers.

Graphing functions: The number line can be used as the horizontal axis of a graph to plot functions and other mathematical relationships.

Actually, the difference between 8 and -16 is not 14, it is 24.

To find the difference between two numbers on a number line, you need to subtract the smaller number from the larger number. In this case, 8 is larger than -16, so we subtract -16 from 8:

8 - (-16) = 8 + 16 = 24

Therefore, 8 and -16 are 24 units apart on the number line.

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Answer:

31cm

Step-by-step explanation:

14 + 8 + 9 = 31

Make sure to add the cm on the end!

The perimeter of the triangle is 31cm.

The perimeter of the triangle with sides of length 14 cm, 8 cm and 9 cm is 31 cm. This can be calculated by simply adding up the length of each side. To explain, the perimeter of a triangle is the sum of the lengths of all three sides.

In this particular triangle, the length of side 1 is 14 cm, the length of side 2 is 8 cm and the length of side 3 is 9 cm. When we add these three lengths, we get the perimeter of the triangle: 14 cm + 8 cm + 9 cm = 31 cm.

In general, to calculate the perimeter of any triangle, we first have to identify the lengths of all three sides. Then, we simply add these lengths together to get the perimeter.

For example, if the triangle had sides of lengths 4 cm, 5 cm and 6 cm, then the perimeter would be 4 cm + 5 cm + 6 cm = 15 cm.

In conclusion, the perimeter of any triangle can be calculated by adding together the length of each side. In the case of the particular triangle in question, the perimeter is 31 cm.

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The events that are independent are,

1) Henry rolling a multiple of 2 and landing on a red portion of the spinner.

2) Two pairs of socks being randomly chosen from a drawer, Hayden choosing a black pair of socks, putting them on, and then choosing another black pair.

3) Olivia choosing an ace and the dart hitting the bull's-eye

1) Henry rolling a multiple of 2 and landing on a red portion of the spinner.

2) Two pairs of socks being randomly chosen from a drawer, Hayden choosing a black pair of socks, putting them on, and then choosing another black pair.

3) Olivia choosing an ace and the dart hitting the bull's-eye.

The other events are dependent because the outcome of the first event affects the outcome of the second event. Specifically

1) Sarah picking a number less than 5 and then picking an odd number. The second event depends on the outcome of the first event.

2) A number cube being rolled and a spinner being spun. The two events are independent of each other, but the outcomes of each event are not independent.

3) Two cards being randomly chosen from a standard deck, and Eliza choosing a jack, replacing it, and then choosing a black card. The outcome of the second event depends on the outcome of the first event, and the outcome of the first event affects the composition of the deck for the second event.

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The given question is incomplete, the complete question is:

Which events are independent? Check all that apply. Each number 1 through 10 is written on a slip of paper, placed in a hat, and randomly picked. Sarah picks a number less than 5, keeps it, and then picks an odd number. A number cube is rolled and a spinner is spun. Henry rolls a multiple of 2 and lands on a red portion of the spinner. Two cards are randomly chosen from a standard deck. Eliza chooses a jack, replaces it, and then chooses a black card. Two pairs of socks are randomly chosen from a drawer. Hayden chooses a black pair of socks, puts them on, and then chooses another black pair. A card is randomly chosen from a standard deck and a dart is randomly thrown. Olivia chooses an ace and the dart hits the bull’s-eye.

The geometric sequence is 9 + 2 + 20 = 29.

The smallest number the third term in the geometric sequence can be is 29.

This is because when you add 2 to the second term and 20 to the third term of the three-term arithmetic sequence with a first term of 9,

the third term of the geometric sequence is 9 + 2 + 20 = 29.

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a) The rate of change of the drug's concentration at 50 minutes is 1.7 mg/min.

b) The rate of change of the drug's concentration at 85 minutes is 0.2 mg/min.

c) The drug's concentration is decreasing at 115 minutes.

a) The central difference approach can be used to calculate the rate of medication change after 50 minutes.

f'(x) = (f(x+h) - f(x-h))/2 × h    ....(1)

As per the question, we have h = 10 and x = 50

Substitute the values of h = 10 and x = 50 in (1),

f'(40) = (f(50+10) - f(50-10))/2 × 10

f'(40) = (89-55)/20

f'(40) = 1.7 mg/min

b) For the rate of change of concentration at 85 minutes:

Here, f(80) = 111 mg and f(90) = 113.

The concentration at 90 minutes is 113 mg.

Rate of change = (f(90) - f(80)) / h

= (113 - 111) /10

= 2 / 10

= 0.2 mg/min

c) Since the concentration at 120 minutes (68 mg) is lower than the concentration at 110 minutes (103 mg), the drug's concentration is decreasing.

Therefore, the drug's concentration is decreasing at 115 minutes.

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If the first and last pages of a document must be printed in color, and only two printers can print in color, then there are a total of 4⁹⁹ ways that 100 pages can be assigned for printing to four printers.

The fundamental principle of counting says that if there are p ways to do one thing and q ways to do another thing, then there are p×q ways to do both things. Number of printers that is able to print in color = 2

Number of colors printed by printers = 2

We have to determine the number of ways are there for the 100 pages to be assigned to the four printers. Now, consider there are no restrictions. Let's break this problem into two parts. First, we have to print 2 pages in color and there are only two color printers. So, number of ways to print the first and the last page of the document = 2²

= 4

Number of remaining pages of document = 98

Number of avaliabile printers = 4

Now, second part, we have only 98 pages (out of 100 pages, 2 colors pages are already printed). Each of these 98 pages can be assigned to a printer in 4 ways. So, number of ways to print remaining 98 pages of document = 4⁹⁸.

Using the counting principle, number of ways for printing the 100 pages by four printers = 2² × 4⁹⁸

= 4 × 4⁹⁸ = 4⁹⁹

Hence, required number of ways are 4⁹⁹.

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The frequency table shows that there is a relationship between buying a hot dog and buying a drink at a baseball game. The huge 70.2% is evidence of this.

The frequency table is meant to show the relationship between variables. Of all the values provided, the relationship with the highest percentage is 70.2%.

This shows that the number of people who purchased a hot dog while also purchasing a drink constituted the highest number. None of the figures come close to this one. So, there is a strong relationship between the variables.

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a pie chart would be an effective way to quickly and easily understand the distribution of time spent on different course subjects.

For visualizing the percentage distribution of different course subjects, a pie chart would be the most suitable type of chart. Pie charts are ideal for displaying the relative proportions of different categories or groups as slices of a circular pie. Each slice of the pie represents a proportion of the whole, which in this case would be the total time spent on all course subjects during homework sessions. The size of each slice will correspond to the percentage of time spent on each course subject. Therefore, a pie chart would be an effective way to quickly and easily understand the distribution of time spent on different course subjects.

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The altitude of the plane at the George Washington Bridge is approximately 0.2095 miles (or 1,106 feet) above sea level, plus whatever the height of the bridge is.

Altitude refers to the height of an object or location above a specific reference point, usually the Earth's sea level. In aviation, altitude is often used to describe the height of an aircraft above sea level, and is measured in feet or meters.

Trigonometry is a branch of mathematics that deals with the relationships between the sides and angles of triangles. It involves the study of trigonometric functions, which are functions of an angle, and are used to relate the angles and sides of a right triangle.

In the given question,

To solve this problem, we need to use trigonometry and the fact that the plane descended at a 2° angle. Let's assume that the altitude of the plane at the George Washington Bridge is h feet.

Using trigonometry, we know that the tangent of the angle of descent is equal to the difference in altitude divided by the horizontal distance traveled. In this case, we have:

tan(2°) = (h - e) / 6

To solve for h, we need to isolate it on one side of the equation. Multiplying both sides by 6, we get:

6 tan(2°) = h - e

Adding e to both sides, we get:

h = 6 tan(2°) + e

We can use a calculator to find the tangent of 2°, which is approximately 0.03492. Substituting this value and the given distance of 6 miles into the equation, we get:

h = 6(0.03492) + e

h = 0.2095 + e

Therefore, the altitude of the plane at the George Washington Bridge is approximately 0.2095 miles (or 1,106 feet) above sea level, plus whatever the height of the bridge is.

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Answer:

5) 59.7 in

6) 39.0 mi

7)

8) 50.3 mi

Step-by-step explanation:

5) C = [tex]\pi (19)[/tex]

C = 59.7 in

6) C = [tex]2\pi (6.2)[/tex]

C = 39.0 mi

7) RADIUS IS CUT OFF

use C = [tex]2\pi r[/tex]

8) C = [tex]2\pi (8)[/tex]

C = 50.3 mi

We can claim that after answering the above question, the As a result, the triangular prism has a volume of 240 cubic centimetres.

A prism is a polyhedron with an n-sided polygonal basis, a second base that is a shifted copy of the first base, and n extra faces (necessarily all parallelograms), with two connecting the corresponding sides of the base. All cross sections that are parallel to the base are translations of it. A prism is a two-sided, solid, three-dimensional object with two faces. It has the same cross-sections, flat sides, and similar bases. Faces of a prism are parallelograms or rectangles with no bases. A prism is a refracting item that is homogeneous, solid, and transparent, contained by two planes that are obliquely oriented to one another. A typical prism has two triangular faces and three parallel rectangular faces. They are made of either glass or metal.  

To calculate the volume of a triangular prism, multiply the area of the triangular base by the prism's height.

Triangle area = 1/2 * base * height

Triangle area = 1/2 * 8 cm * 6 cm

Triangle area = 24 cm2

We must now determine the prism's height. The diagram shows that the prism has a height of 10 cm.

Finally, the volume of the triangular prism can be calculated by multiplying the area of the triangle base by the prism's height:

Prism volume = base area * The prism's height

Prism volume = 24 cm2 * 10 cm

Prism volume = 240 cm3

As a result, the triangular prism has a volume of 240 cubic centimeters.

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The quotient of 3.013 × [tex]10^{8}[/tex] and 6.55 × [tex]10^{5}[/tex] expressed in scientific notation is equal to 0.46 × [tex]10^{3}[/tex].

In Mathematics, a quotient is a mathematical expression that is simply used to represent the division of a number (numerator) by another number (denominator).

Generally speaking, any numerical data (number) can be written in scientific notation as shown below:

a × [tex]b^n[/tex]

Where

Next, we would rewrite the given numerical data (number) in scientific notation by dividing by 6.55 × [tex]10^{5}[/tex] as follows:

Scientific notation = 3.013 × [tex]10^{8}[/tex]/(6.55 × [tex]10^{5}[/tex])

Scientific notation = 0.46 × [tex]10^{8-5}[/tex]

Scientific notation = 0.46 × [tex]10^{3}[/tex].

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Yes, it is possible to have a c2 strictly convex function on a compact domain that is not also strongly convex.

Let's have a look at the following details of it.

A strictly convex function is a function whose Hessian matrix is positive-definite for all arguments. As a result, if f is differentiable and convex, it is strictly convex if and only if its Hessian matrix is positive-definite for all arguments.

The Definition of Strong Convexity: A function is said to be strongly convex if it meets the following criteria:
Let C be a convex subset of a Hilbert space H, and let f:C→ℝ be a continuously differentiable function. There is a positive constant μ such that, for all x,y∈C: f(y)≥f(x)+⟨∇f(x),y−x⟩+μ/2‖y−x‖2

Thus, it is clear from the above-mentioned definitions that it is possible to have a c2 strictly convex function on a compact domain that is not also strongly convex.

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The angle of rotation in standard form is 251.5651 degrees.

The length of arc S is approximately 20.94 feet.

If the point (-1, -3) is on the circle x² + y² = 10, then we can substitute these values for x and y in the equation to obtain:

(-1)² + (-3)² = 10

1 + 9 = 10

So, the point (-1, -3) satisfies the equation of the circle.

To find the angle of rotation in standard form, we need to use the formula:

tan(θ) = y/x

where θ is the angle of rotation.

In this case, x = -1 and y = -3, so we have:

tan(θ) = (-3)/(-1)

tan(θ) = 3

θ = tan⁻¹(3)

Using a calculator, we find:

θ ≈ 1.2490 radians or 71.5651 degrees

To express in standard form, add 180 degrees to the angle in order to obtain an angle between 0 and 360 degrees:

θ ≈ 71.5651 + 180 ≈ 251.5651 degrees

To find the length of an arc S given the radius r and the central angle θ, we use the formula:

S = (θ/360) x 2πr

In this case, r = 15 ft and θ = 1.396 radians

Substituting the values:

S = (1.396/2π) x 2π(15 ft)

S ≈ 1.396 x 15 ft

S ≈ 20.94 ft

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Complete question:

Consider the point (-1, -3), which is on the circle x² + y² = 10. Find the angle of rotation in standard form

Find the length of the arc S when r = 15 ft and θ = 13.96°

According to the question, "Suppose we randomly select 5 cell-phone owners. What is the probability that all 5 of them find themselves checking their phone for messages, alerts, or calls even when they don't notice their phone ringing or vibrating?"The formula for finding the probability of an event is:P(E) = number of favorable outcomes/number of total possible outcomes.The given data in the question states that 67% of cell-phone owners find themselves checking their phone for messages, alerts, or calls even when they don't notice their phone ringing or vibrating.

Therefore, the probability of any cell-phone owner checking their phone when it is not ringing or vibrating is:P(E) = 67/100 = 0.67To find the probability of 5 cell-phone owners checking their phones when they are not ringing or vibrating, we have to use the multiplication rule of probability. [tex]P(E₁∩E₂∩E₃∩E₄∩E₅) = P(E₁) × P(E₂) × P(E₃) × P(E₄) × P(E₅)P(E₁∩E₂∩E₃∩E₄∩E₅) = 0.67 × 0.67 × 0.67 × 0.67 × 0.67P(E₁∩E₂∩E₃∩E₄∩E₅) = 0.2197[/tex]

Therefore, the probability that all 5 of them find themselves checking their phone for messages, alerts, or calls even when they don't notice their phone ringing or vibrating is approximately 0.2197 or 22%.

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Using empirical rule, the approximate percentage of daily phone calls numbering between 42 and 52 is 68%.

A statistical principle known as the empirical rule, also known as the three-sigma rule or 68-95-99.7 rule, holds that with a normal distribution, virtually all observed data will lie within three standard deviations (denoted by ) of the mean or average (denoted by ).

The empirical rule specifically states that 68% of observations will fall inside the first standard deviation, 95% will fall within the first two standard deviations, and 99.7% will fall within the first three standard deviations.

Mean = 47

SD = 5

Using Empirical Formula ,approximate percentage of daily phone calls numbering between 42 and 52

Normal Distribution has bell shape curve

The Empirical Rule states that in  a normal distribution

68% of the data falls with in one standard deviation ( -1 to 1)

95%  of data falls with in two standard deviations, and  (-2 to 2)

99.7% of data falls with in three standard deviations from the mean. (-3 to 3)

z score = ( Value - mean)/SD

Calculate z score for 60

Z = (42 - 47)/5

Z = -1

Calculate z score for 66

Z = (52 - 47)/5

Z =  1

As data lies between -1 and 1 hence with in one standard deviation from the mean Hence using Empirical data approximate percentage of daily phone calls numbering between 42 and 52  is 68%.

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Answer: 239

Step-by-step explanation:

Darius wrote 2 integers 256 and -17. The question is asking you to solve how much larger is 256 than -17. This means you will subtract 256 by -17 which will give you 239 (256-17). The answer remains positive because 256 is larger

Hope this helps

Answer: They are exactly 273 places away.

Step-by-step explanation:

If a number is larger than another number then you need to subtract it to get the distance. In this case, you look at the subtraction to see how far away they are.

Hope this helps!

Have a blessed day!

By using Central Limit Theorem, the distribution of to-go orders per hour over 700 random hours at a restaurant with a rate of 10 per hour can be approximated by a normal distribution with a mean of 10 and a standard deviation of 0.119.

The distribution of the average number of to-go orders per hour over 700 random hours can be approximated by the Central Limit Theorem (CLT). In this case, the population mean (μ) is 10 to-go orders per hour, and the population standard deviation (σ) can be calculated using the Poisson distribution formula:

σ = sqrt(μ) = sqrt(10) ≈ 3.162

The sample size (n) is 700, which is larger than 30, so we can use the CLT to approximate the distribution of the sample means. The mean of the sample means is equal to the population mean, which is 10 to-go orders per hour. The standard deviation of the sample means (also called the standard error) is equal to:

SE = σ / sqrt(n) = 3.162 / sqrt(700) ≈ 0.119

Therefore, the distribution of the average number of to-go orders per hour over 700 random hours is approximately normal with a mean of 10 and a standard deviation of 0.119

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Thus, the explicit formula for the simple interest sequence A(n) = P + (n-1)(i.P) is: A(n) = P * (1 + i * (n-1)).

Simple interest is a method of calculating interest on a loan or investment where interest is charged only on the initial principal amount. In simple interest, the interest rate is applied to the original principal amount, and the interest earned remains the same throughout the entire term of the loan or investment.

by the question.

The formula for a simple interest sequence A(n) = P + (n-1) (i.P) represents the value of an investment that earns simple interest over n periods, where:

A(n) is the value of the investment after n periods.

P is the principal or initial investment

i is the interest rate per period as a decimal fraction (e.g. 0.05 for 5%)

n is the number of periods

To derive the explicit formula for A(n), we can use the formula for simple interest:

I = P * i * n

where I am the total interest earned over n periods. We can then express A(n) as:

A(n) = P + I

Substituting the expression for I, we get:

A(n) = P + P * i * (n-1)

Simplifying, we can factor out P to get:

A(n) = P * (1 + i * (n-1))

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Answer: She has 10$ to save

Step-by-step explanation:

Elsia has 30$ to start her week. She spent 10 on food and drink, (30-10=20) 5 on entertainment, (20-5=15), and 5 on Misc. things. (15-5=10). This means that the answer is 10.

Steps:

30-10=20

20-5=15

15-5=10

I hope it helped! :D

The government rectangular survey consisting SW 1/4, NE 1/4, and NW 1/4 of Section 13 in Blendon Township covers 480 acres.

We have,

In the Government Rectangular Survey System, a section is a square tract of land measuring 1 mile by 1 mile, covering an area of 640 acres.

Each section is divided into quarters.

If we consider the SW 1/4, NE 1/4, and NW 1/4 of Section 13 in Blendon Township, the total acreage can be calculated as follows:

SW 1/4:

This represents one-fourth of the section.

The SW 1/4 of Section 13 is 640 acres / 4 = 160 acres.

NE 1/4:

The NE 1/4 of Section 13 is also 160 acres.

NW 1/4:

The NW 1/4 of Section 13 is 160 acres.

To find the total acreage, add up the individual acreages:

160 acres (SW 1/4) + 160 acres (NE 1/4) + 160 acres (NW 1/4)

= 480 acres

Therefore,

The government rectangular survey consisting SW 1/4, NE 1/4, and NW 1/4 of Section 13 in Blendon Township covers 480 acres.

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The empirical rule states that approximately 95% of the population lies within 2 standard deviations of the mean for a normal distribution, but you found that the z-scores that mark off the middle 95% of the standard normal distribution are -1.96 and 1.96. This does not represent a contradiction, and I will explain why is it so ?

The empirical rule, also known as the 68-95-99.7 rule, is a useful guideline to help us understand the proportions of data in a normal distribution. According to this rule, about 68% of the data falls within 1 standard deviation, 95% within 2 standard deviations, and 99.7% within 3 standard deviations. However, it is essential to note that the empirical rule is a simplified approximation.

On the other hand, the z-scores that you calculated, -1.96 and 1.96, are more precise values based on the actual standard normal distribution. These values come from a more accurate calculation using the cumulative distribution function (CDF) of the normal distribution, which gives the exact probability for any given range of z-scores.

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x is the base of given right angled triangle, which is calculated as 7 using the Pythagoras theorem.

The Pythagorean theorem, the well-known geometric theorem states that the sum of the squares across the sides of a right triangle equals the square across the hypotenuse (opposite the right angle) – or in general algebraic notation a² + b² = c².

It has long been associated with the Greek mathematician and philosopher Pythagoras (c. 570-500/490 BC), but is actually much older. His four clay tablets in Babylonia, circa 1900 BC to his 1600. Using a very precise calculation of the square root of 2 (the length of the hypotenuse of a right-angled triangle with legs equal to 1) and a special list of integers known as Pythagorean triples, we acquire some knowledge of theorems, indicate and fill them. This phrase is mentioned in his Baudhayana Sulba-sutra of India written between 800 BC and his 400 AD. written.

Given,

DF = 24

DE = 25

Using Pythagoras theorem:

Hypotenuse² = Base² + Perpendicular²

25² = x² + 24²

x² = 25² - 24²

x² = 625 - 576

x² = 49

x = √49

x = 7

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The area of the figure rounded to the nearest square meter is 97 m². So correct option is A.

With five equal sides and five equal angles, a regular pentagon is a polygon. In other words, a regular pentagon's sides and angles are all congruent. It is a closed, two-dimensional object that is categorized as a sort of polygon since it is constructed of straight line segments.

Regular pentagons have a number of distinctive features, including:

A regular pentagon has 108 degree internal angles that are all equal.

A standard pentagon's outside angles are all 72 degrees in angle.

A regular pentagon is divided along its diagonals into three smaller triangles, two of which are congruent.

Regular pentagons are prevalent in a variety of fields, including geometry, architecture, and the arts.

First, you would need to determine the side length of the regular hexagon. This can be done using the radius of the circumscribed circle, which is given as 5 meters. The side length of the hexagon can be calculated using the formula:

s = r * √(3)

where s is the side length and r is the radius of the circumscribed circle. Plugging in the given value for r, we get:

s = 5 * √(3)

simplifying, we get:

s ≈ 8.7 meters

Next, you would need to calculate the area of one of the congruent triangles. This can be done using the formula:

A = (1/2) * b * h

where A is the area of the triangle, b is the base, and h is the height. The base of the triangle is equal to one side of the hexagon, which we just calculated to be approximately 8.7 meters. To find the height, we can draw an altitude from one vertex of the triangle to the opposite side, creating a 30-60-90 right triangle. The height is equal to the shorter leg of this triangle, which can be calculated using the formula:

h = (1/2) * s * √(3)

Plugging in the value for s, we get:

h ≈ 7.5 meters

Now we can calculate the area of one of the triangles:

A = (1/2) * 8.7 * 7.5 ≈ 32.6 square meters

Finally, we can calculate the total area of the figure by adding the area of the hexagon to three times the area of one of the triangles:

A = 6 * (s²) * √(3)/4 + 3 * A

Plugging in the values we calculated, we get:

A ≈ 96.9 square meters

Rounding to the nearest square meter, we get:

A ≈ 97 square meters

Therefore, the answer is A. 97 m².

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As a result, (x, y) = is the answer to a set of equations. (-17, -3). There aren't an endless number of answers because there is a single one.

The meaning of an equation in algebra is a mathematical assertion that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two expressions 3x + 5 and 14, which are split by the 'equal' symbol.

The statements that are true about this system of equations are:

The x-variable will be eliminated when adding the system of equations.

There are infinitely many solutions to the system of equations.

To eliminate the x-variable, we can add the two equations as follows:

(2x - 7y) + (-2x + 11y) = -13 + 1

Simplifying the left-hand side and the right-hand side gives:

4y = -12

Dividing both sides by 4 yields:

y = -3

Substituting y = -3 into either of the original equations gives:

2x - 7(-3) = -13

Simplifying this equation yields:

2x + 21 = -13

Subtracting 21 from both sides yields:

2x = -34

Dividing both sides by 2 yields:

x = -17

Therefore, the solution to the system of equations is (x, y) = (-17, -3). Since there is a unique solution, there are not infinitely many solutions.

The statement "The sum of the system of equations is 4y = -12" is false since the sum of the equations does not simplify to that expression.

The statement "x = 17" is false since the correct solution is x = -17.

The statement "The y-variable will be eliminated when adding the system of equations" is false since adding the equations only eliminated the x-variable.

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The number of ways to form an 8-person committee with 4 men and 4 women is 9,180. The number of ways to form a committee with at least 2 men is 70,320. The number of ways to form a committee with more women than men is 7,620. This can be solved by the concept of  Permutation and Combination.

If the committee must contain four men and four women, there are 7,425 ways to form the committee. If there must be at least two men, there are 58,275 ways to form the committee. If there must be more women than men, there are 26,207,700 ways to form the committee.

To find the number of ways to form a committee with four men and four women, we can use combinations. The number of ways to choose 4 men out of 12 is 495, and the number of ways to choose 4 women out of 15 is 1,365.

To get the total number of ways, we can multiply these numbers:

495 x 1,365 = 7,425.

To find the number of ways to form a committee with at least two men, we need to consider two cases: 2 men and 6 women, and 3 men and 5 women. For the first case, we can choose 2 men out of 12 in 495 ways, and 6 women out of 15 in 5,005 ways. For the second case, we can choose 3 men out of 12 in 2,190 ways, and 5 women out of 15 in 3,003 ways.

To get the total number of ways, we can add these numbers:

495 x 5,005 + 2,190 x 3,003 = 58,275.

To find the number of ways to form a committee with more women than men, we can use a different approach. We can count all the possible committees with 1 man, 2 men, 3 men, and 4 men, and then subtract the committees that have more men than women. There are 15 ways to choose 1 man, 330 ways to choose 2 men, 3,960 ways to choose 3 men, and 12,870 ways to choose 4 men.

To count the committees with more men than women, we can use the complement rule. This means we need to count the committees with 4 men and 0, 1, 2, or 3 women, the committees with 3 men and 0 or 1 women, the committees with 2 men and 0 women, and the committee with 1 man and 0 women.

Adding these numbers gives us the total number of committees with more women than men:

15 + 330 + 1,320 + 2,772 + 330 + 15 = 26,207,700

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The volume of the container is 91125 cubic meters.

What is volume?

A measurement of three-dimensional space is volume. It is frequently expressed numerically using SI-derived units, as well as different imperial or US-standard units. Volume and the definition of length are related.

A sphere is the most basic and typical form of a three-dimensional shape. A sphere's radius is the simplest parameter to measure. The radius of the sphere is used to determine its volume.

Given the edge of a cube is 45 meters.

The formula of volume is V = s³.

The volume of the container is

45³

= 91125 cubic meter.

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The area of the equilateral triangle is 36√3 square units

What is area of the equilateral triangle?

Area of an equilateral triangle is equal to(√3/4)a², where an is the length of the triangle's side.

In an equilateral triangle, the center, the centroid, and the circumcenter coincide.

The distance between the center and a vertex is 6cm, which is also the radius of the circumcircle.

The side length is [tex]6(3)^{1/2}[/tex], which is twice the length of the radius.

So, the radius of the circumcircle is 6 cm, and the length of each side of the equilateral triangle is 12 cm.

The area of an equilateral triangle with side length s is given by:

A = (s² * √3) / 4

Substituting s = 12, we get:

A = (12² * √3) / 4

= 36√3

Therefore, the area of the equilateral triangle is 36√3 square units.

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Answer:

15.556

Step-by-step explanation:

The length of the diagonal of a square is equal to the length of one side of the square multiplied by the square root of 2

22=x√2

Answer:

-45

Step-by-step explanation: