Find the area of the SHADED figure. Pictures are not drawn to scale. Round answers to the nearest tenth.

We can rewrite the expressions by using exponent properties:

(225a¹⁰)/(5a²)² =  9a⁶

(x⁵/3)³*81x⁴ = 3x¹⁹

Here we need to use some exponent properties, these are:

(xᵃ)ᵇ = xᵃᵇ

xᵃ/xᵇ = xᵃ⁻ᵇ

Here we have the expression:

(225a¹⁰)/(5a²)²

We can rewrite the denominator as:

(5a²)² = 25a⁴

We can rewrite it as:

(225a¹⁰)/ 25a⁴ = (225/25)*(a¹⁰/a⁴) = 9*a¹⁰⁻⁴ = 9a⁶

The other expression is:

(x⁵/3)³*81x⁴

(x¹⁵/27)*81x⁴ = (x¹⁵*x⁴)*(81/27) = 3*x¹⁵⁺⁴ = 3*x¹⁹

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The compound proposition defined by implication is: If 2 · x + 5 = 5, then the value of x is 0.

Propositions are logical constructions that contains a truth value. Proposition can be simple or composite, that is, the result of combination between simple propositions by use of operators. In this case we find a composite proposition formed by two simple propositions and a logic operator (an implication):

α ⇒ β

Where:

If the antecedent is true, then the consequent must be true. If 2 · x + 5 = 5, then we must clear x within the equation to determine a value such as composite proposition becomes true:

2 · x + 5 = 5

2 · x = 0

x = 0

The statement presents several mistakes and is incomplete. Correct form is presented below:

Complete this proposition:

If 2 · x + 5 = 5, then the value of x is ___________.

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The 100th number of the sequence 1, 4, 7, 10..., is 298.

The given series 1, 4, 7, 10..., is an AP.

Arithmetic Progression (AP) is a sequence of numerals in order, in which the difference between any two consecutive digits is a constant value. A progression is a type of sequence for which it is possible to get a formula for the nth term.  

The Arithmetic Progression is the most generally used sequence in maths with easy-to-understand formulas. The nth-term formula of the AP (arithmetic progression) is

aₙ = a₁+ d(n-1)

Where

n = number of terms

a = first term

d = common difference

Here, n = 100, d = 3 and a₁ = 1

[tex]a_{100}[/tex] = 1 + 3(100-1)

[tex]a_{100}[/tex] = 1 + 3(99)

[tex]a_{100}[/tex] = 1 + 297

[tex]a_{100}[/tex] = 298

--The given question is incorrect, the correct question is

''If we count by 3's starting with 1, the following sequence is obtained: 1, 4, 7, 10..., what is the 100th number in this sequence?"--

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On solving the provided question, we can say that the equation representing the path of each kangaroo. x = 4ft and y = 11ft

An equation is a mathematical formula that connects two assertions using the equal sign (=) to denote equivalence. In algebra, an equation is a mathematical statement that establishes the equivalence of two mathematical expressions. For instance, an equal sign separates the components 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula is used to explain the connection between two sentences on either side of a letter. Frequently, there is just one variable, which is also the symbol. for example, 2x - 4 = 2.

equation

let X be kangaroo 1

and Y be kangaroo 2.

So the equation

X = 3ft + 1ft

while

Y = 5ft + 1ft +.5ft.

and now,

x = 4ft and y = 11ft

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Answer: 174

Step-by-step explanation: In the first year, the population of 32 goats increases by 71/10032 = 22.72 goats

So the population after 1 year would be 32+22.72 = 54.72 goats

In the second year, the population of 54.72 goats increases by 71/10054.72 = 38.9792 goats

So the population after 2 years would be 54.72+38.9792 = 93.69 goats

It's important to note that the answer provided (93) is the population after one year, not two years. The population after two years would be 174 goats.

Answer:

  2.4×10⁶

  2,400,000 in the US

Step-by-step explanation:

You want the value of the expression x²/y rounded to an appropriate precision when x=3.8×10⁵ and y=5.9×10⁴.

The attached calculator display shows the result to 2 significant figures, the appropriate for computation using values that have 2 significant figures.

  x²/y ≈ 2.4×10⁶

In the US, "standard form" would be the usual form in which numbers are written:

  x²/y ≈ 2,400,000

__

Additional comment

If you're working this out with pencil and paper, the value you want to compute is ...

  (3.8×10⁵)²/(5.9×10⁴) = (3.8²/5.9)×10¹⁰⁻⁴ = (144.4/59)×10⁶ ≈ 2.4×10⁶

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The limit exists, where limx→+∞ ex=+∞  and  limx→+∞ arctanx=π\2

This problem can be solved by dividing it into smaller parts.

Let f(x)=ex and g(x)=arctan(x)

The range of the function arctan(ex) is equal to the intersection of the ranges of f(x) and g(x).

Since the range of f(x) is [0,∞] and the range of g(x) is [−π/2,π/2], the intersection is [0,∞] ∩ [−π/2,π/2] or [0,π/2]

but the limit as x approaches infinity or limx→∞.

Since the highest number in the possible range is π/2, that is the limit as x approaches infinity.

if x is approaching negative infinity or limx→−∞, the answer would be the lowest value in the function's range. Therefore, it would be 0

So, as x→∞, ex→∞ so that, letting t=ex we have limx→∞ arctan(ex)=limt→∞ arctan(t)=π/2.

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A room classified as a group a-2 occupancy has dimensions of 60 feet by 80 feet and is in a sprinklered building. the minimum required separation distance from the nearest exit door is  r is 50 feet

This is determined by the occupancy type of the room, which is classified as a Group A-2 occupancy. According to the International Building Code, Group A-2 occupancies are those that involve assembly uses with an occupant load of 50 or more and with fixed seating. Therefore, the minimum required separation distance from the nearest exit door is 50 feet.  

To calculate this, I referred to the International Building Code (IBC) Chapter 10, which outlines the requirements for means of egress. Section 1020.1 of the IBC states that the required separation distance between an exit door and the nearest obstruction must be at least half the length of the maximum overall diagonal dimension of the room. Since the room has dimensions of 60 feet by 80 feet, the maximum overall diagonal dimension is 100 feet.

Therefore, half of this distance is 50 feet, which is the minimum required separation distance from the nearest exit door.   In addition, the IBC also requires that Group A-2 occupancies be sprinkled, which the room in question is. This means that there may be additional requirements for separation distances for the egress system depending on the specific type of sprinkler system being used.

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a room classified as a group a-2 occupancy has dimensions of 60 feet by 80 feet and is in a sprinklered building. what is the minimum required separation distance from the nearest exit door?

The number of such paths from (0,0) to (85,65) is C(150, 85).

What is co-ordinate ?

In mathematics, a coordinate is a pair of numerical values that represent a specific location on a two-dimensional surface, such as a graph, a map, or an image. The two values are usually referred to as the x-coordinate and the y-coordinate.

A path from (0,0) to (85,65) on the integer grid that starts at (0,0) and increments one coordinate by 1 and leaves the other unchanged at each step is equivalent to a sequence of 85 "right" steps and 65 "up" steps. The number of ways to arrange these steps is given by the binomial coefficient C(85+65, 85), which is the number of ways to choose 85 items (the "right" steps) from a set of 150 items (85 "right" and 65 "up" steps) without replacement and where order matters.

The general formula for the binomial coefficient is C(n, k) = n! / (k!(n-k)!), where n! is the factorial of n, i.e., the product of all integers from 1 to n, and k! is the factorial of k. Using this formula, we have:

C(150, 85) = 150! / (85!(150-85)!) = (150149148*...6665) / (858483*...1) = (150149148...6665) / (85!)

So, the number of such paths from (0,0) to (85,65) is C(150, 85).

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The solutions for the system of equations is the point (2, 2).

Linear equations are equation involving one or more expressions including variables and constants and the variables are having no exponents or the exponent of the variable is 1.

Given are two linear equations,

y = -x + 4 and

y = 2x - 2

First graph the lines.

For that, find two points on each equation and join them.

x = 0, then y = 4

y = 0, then x = 4

We have two points (0, 4) and (4, 0). Join these points to form the line.

x = 0, then y = -2

y = 0, then x = 1

We have two points (0, -2) and (1, 0). Join these points to form the line.

We have two equations, which are equal to each other.

-x + 4 = 2x - 2

-x - 2x = -2 - 4

-3x = -6

x = 2

y = -2 + 4 = 2

So the solution of the system of equations is the intersecting point of the two lines which is (2, 2).

Hence the solution of the system of equations is (2, 2).

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Answer:

Drawf planets orbit the Sun.

Dwarf planets are round.

Pluto is a dwarf planet.

Answer:a,c,d

Step-by-step explanation:

edge 2023

The linear equation in slope-intercept form from the given description is

c = 9.25x + 4.50.

In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction.

The standard form of slope-intercept form:

y = mx + b,

where m is the slope and b is the y-intercept.

The cost c, of instant camera film is $9.25 per box, x, plus $4.50 in shipping.

That means,

c = 9.25x + 4.50

Therefore, the linear equation is c = 9.25x + 4.50.

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Answer:

x = 9

Step-by-step explanation:

the intersecting secants theorem states that IH * IS = IF * IT

here, x = IH

x * 16 = 8 * (10+8)

16x  = 144

divide both sides by 16 to get x

x = 9

Answer: 2 meters

Step-by-step explanation:

[tex]\frac{20.8 \text{ m}}{10.4 \text{ min}}=2[/tex]

Answer: 2 Meters

Step-by-step explanation: 20.8 divided by 10.4 is 2

The length of the side XY for the given triangles is 3 units.

Congruent figures and shapes are those that may be reversed or rearranged such that they match up with other figures and shapes. These shapes can be produced by mirroring these forms.

A closed polygon known as a triangle has three line segments that cross at each of its three angles.

Given two triangles,

ΔHIJ and ΔXYZ

and both are congruent,

ΔHIJ ≅ ΔXYZ

for congruent triangles the measure of sides and angles are equal,

we find that,

YZ ║ IJ, HI ║ XY and XZ ║ HJ

so YZ = IH = 4 units

HI = XY = 3 units

XZ = HJ = 5 units

Hence the length of XY is  3 units.

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The specific heat shows that Substance Y has more atoms per gram than substance W.

Specific heat:

Specific heat is a property of a substance that describes how much heat energy is required to raise the temperature of a certain amount of that substance by one degree. It is typically measured in units of joules per gram per degree Celsius (J/g°C).

Different substances have different specific heats. For example, water has a relatively high specific heat of 4.18 J/g°C, which means that it takes a lot of heat energy to raise the temperature of water by one degree. This is why water is often used as a coolant or in air conditioning systems, as it can absorb a large amount of heat energy without experiencing a significant temperature change.

Therefore, the specific heat shows that Substance Y has more atoms per gram than substance W.

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There's still a 5.48% chance that you'd find that the average of their 64 wages is $6.90 or less so to assume that the wage rate of the ethnic group is equivalent to that of a random sample of workers from those employed in the service industry is not valid.

If the true mean of this group's wages is also $7.00 and the standard deviation is $0.50, then the average of a sample of n workers has the same mean and a standard deviation of (pop. stan. dev. / √n).

In this case, the sample average is a random variable with a mean of $7.00 and a standard deviation of $0.50/√64 = 0.0625.

If a random variable has a normal distribution with a mean $7.00 and st. dev. $0.0625, then the probability of observing it as $6.90 or less is:

P[sample mean < 6.90] = P[z < (6.90 - 7.00)/0.0625] = P[z < -1.6] = 0.0548.

In other words, it could be the case that there's no discrimination against ethnic workers, and there's still a 5.48% chance that you'd find that the average of their 64 wages is $6.90 or less.

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The slope formula, when two points are on a line, the Slope-intercept formula, Point-slope formula, are the 3 types of slope formulas.

The slope of a line is defined as the change in the y coordinates with respect to the change in the x coordinate of that line.

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of the line in the coordinate plane.

Slope formula:  m = (y₂ - y₁) / (x₂ - x₁), when two points on a line,

Slope-intercept formula: y = mx + b, the slope, and y-intercept of a line

Point-slope formula: y - y1 = m(x - x1), the slope of a line and a point on the line.

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Number line of integers from 1 to 30:

   |    5    |    10    |    15    |    20    |    25    |    30

   |    1    2    3    4    5    6    7    8    9    10    11    12

   |    13   14   15   16   17   18   19   20   21   22   23   24

   |    25   26   27   28   29   30

Examples of comparing integers:

5 is less than 10

15 is greater than 10

Examples of querrainging integers:

The square of 9 is 81

The cube of 3 is 27

Examples of counters:

I gained 2 pounds of weight

I lost 3 pounds of weight

Examples of addition of integers:

5 + 10 = 15

-3 + 8 = 5

Answer:

A triangle is a right angle triangle if and only if the Pythagorean theorem holds true for the sides of the triangle. The Pythagorean theorem states that in a right angle triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

In this case, we can call the side opposite the right angle the hypotenuse, and the other two sides the legs. According to the information given, the hypotenuse is AC, and the legs are AB and BC.

So, we can use the Pythagorean theorem to check if this triangle is a right angle triangle:

AC^2 = AB^2 + BC^2

26^2 = 10^2 + 25^2

676 = 100 + 625

676 = 725

This equation does not hold true, so the triangle is not a right angle triangle.

The required value of the given function is (f ⋅ g)(4) = 130.

The function is defined as a mathematical expression that defines a relationship between one variable and another variable.

The functions are given in the question, as follows:

f(x)=3x+1 and g(x)=x²-6

(f ⋅g)(x) is the composition of the functions f and g, which means f(x) × g(x).

(f ⋅ g)(x) = f(x) × g(x)

So, substituting x = 4:

(f ⋅ g)(4) = f(4) × g(4)

= (3 × 4 + 1)×(4² - 6)

= 13 × 10

= 130

So, (f ⋅ g)(4) = 130.

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Answer:

Step-by-step explanation: if 9p to the 3rd power is what I think it means the answer is 1458 if the 9 just means 9 then the answer is 18

The percentage for Utah is 9.0%.

The collection of data is gathered and chosen from a statistical population with the use of some prescribed techniques in both statistics and quantitative methodology. Data sets may be divided into two categories: sample and population.

All the components of the data set are included in the population, which also contains quantifiable qualities like mean and standard deviation.

A sample is made up of one or more observations that are taken from the population, and a statistic is what makes a sample quantifiable. The act of sampling is the selection of a sample from a population.

Thus, The percentage for Utah is 9.0%.

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Hi!

y = m x + c is the slope intercept form of a line whose slope is m and

y intercept is c. Hence

y=x/2+5

LCM

y=x+10/2

2y=x+10

x-2y+10=o

Required equation of the line is x - 2 y +10 = 0

The values in b are compared with the true volume. And we conclude that b is precise and accurate.

Accuracy determines how closely measured values match the actual value. The degree to which two measured values are inside a certain range, or how closely they agree, is called precision.

First calculate the mean of a, b, and c. We get, the mean of a is 87.63, the mean of b is 87.06, and the mean of c is 87.77.

From the values in "a", we can tell there is no good agreement between the given values, and just one (87.1) value is near to the true value. So a is neither precise nor accurate.

From the values in "b", we can tell these given values are reasonably close to the true value and exhibit good agreement. So b is precise and accurate.

From the values in "c", we can tell there is a considerable agreement between the given values but they are not very close to the true value. So c is precise but not accurate.

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Answer:

The sunflower is 28 inches tall after 9 weeks

The sunflower is 2w + 10 tall after w weeks

Step-by-step explanation:

We know

The sunflower was 10 inches tall, growing at a rate of 2 inches per week. Let's T represent the tall of the sunflower; we have the equation

t = 2w + 10

How tall would the sunflower be after 9 weeks?

t = 2(9) + 10

t = 28 inches

How tall would the sunflower be after w weeks?

t = 2(w) + 10

t = 2w + 10

So,

The sunflower is 28 inches tall after 9 weeks

The sunflower is 2w + 10 tall after w weeks

Answer:

x = 2

Step-by-step explanation:

To solve, you have to get the variable to only be on one side by subtracting from one side.

Therefore , the solution of the given problem of unitary method comes out to be Points equal 5020 for each life.

The unitary strategy is a way of solving problems that involves first figuring out how much of a single model there is, then multiplying that value to achieve the solution. Simply described, the unit technique is used to retrieve a single program value from a supplied many. As an example, 40 pens cost 400 rupees ($1.01), or Rs. It's possible that the procedure utilized to do this will be regulated. a single country. Anything has a distinguishing feature. Its capable of integrating and reciprocal are equal (mathematics, algebra).

Here,

There are 5 enemies.

Each adversary is worth 3012 points.

Total points: 15060 (or 3012 multiplied by 5)

There are 3 lives left.

Points for every life equal?

Points per life are calculated as follows: total points / quantity of life = 15060/3

Points equal 5020 for each life.

Therefore , the solution of the given problem of unitary method comes out to be Points equal 5020 for each life.

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Answer:

Boon Li spent 7/12 of his money altogether.

Answer:

(0, 9)

Step-by-step explanation:

y = 9 is the same as (0, 9)