geologists have an interest in the structure and the history of the earth. a geologist can go back in time by drilling deep into the ground, retrieving a core sample, estimating the ages of the various layers, and examining the composition. a timeline can be built of the entire area from where the core sample was drilled. a geologist may retrieve several core samples to confirm the history of the earth's structure in that sampled area. mountains, lakes, and unstable ground can easily impede a simple random sampling of a desired geographical area, therefore what is the most realistic sampling method that represents the actual drillings, comparisons, and scientific examinations of several core samples within the same geographical area?

Answer:Acute Angle

Step-by-step explanation:

What is a 15 degree angle called? Acute Angle – Acute Angle An acute angle is an angle that is more than 0° but less than 90°. Common examples of acute angles include: 15°, 30°, 45°, 60°, etc.

Annabelle has collected approximately 213.7 grams of the trace element.

What is the volume of a cylinder?

The volume of a cylinder can be calculated using the formula V=πr2(h). When determining the volume of a cylinder, you are simply finding the area of the circular base shape and then multiplying this by the height.

The container has the shape of a right cylinder, so the volume of the cylinder can be found by using the formula for the volume of a cylinder: V = πr^2 * h

Where r = radius , h = height, and π = 3.14

So, the volume of the container is:

V = 3.14 * 8.6^2 * 16.5 = 3.14 * 73.96 * 16.5 = 2959.18 cm^3

Now we can use this volume and the proportion of the trace element given in the problem to find the approximate amount of trace element Annabelle has collected:

0.072 g/cm^3 * 2959.18 cm^3 = 213.7 grams

Hence, Annabelle has collected approximately 213.7 grams of the trace element, rounded to the nearest tenth.

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The value k = 6 satisfies both equations Kx + 3y − (K − 3) = 0 and 12x + Ky − K = 0.

A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept.

An equation that depicts a straight line on a graph is said to be linear. The "line" in the name of the equation will help you remember this. Regular Form. Standard forms for linear equations look like this: Ax + By = C.

A linear equation has the form y = mx + b in the slope-intercept notation. X and Y are the variables in the equation. The values m and b represent the line's slope (m) and the value of y when x is 0. (b).

Given

Kx + 3y −(K − 3) = 0

Comparing with [tex]$a_1 x+b_1 y+c 1=0$[/tex]

[tex]$$\therefore \mathrm{a}_1=\mathrm{k}, \mathrm{b}_1=3, \mathrm{c}=-(\mathrm{k}-3)$$[/tex]

12x + ky - k = 0

Comparing with [tex]$a_1 x+b_1 y+c 1=0$[/tex]

[tex]$$\therefore a_1=12, b_1=k, c=-k$$[/tex]

Since equation has infinite number of solutions

So, [tex]$\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}$[/tex]

substitute the values in the above equation, we get

[tex]$\frac{\mathrm{k}}{12}=\frac{3}{\mathrm{k}}=\frac{\mathrm{k}-3}{\mathrm{k}}$$[/tex]

simplifying the equation, we get

[tex]$\frac{\mathrm{k}}{12}=\frac{3}{\mathrm{k}}$$[/tex]

[tex]$$\mathrm{k}^2=12 \times 3$$[/tex]

[tex]$$\mathrm{k}^2=36$$[/tex]

[tex]$$\mathrm{k}=\pm 6$$[/tex]

[tex]$\frac{3}{\mathrm{k}}=\frac{\mathrm{k}-3}{\mathrm{k}}$$[/tex]

simplifying the equation, we get

[tex]$$3 \mathrm{k}=\mathrm{k}(\mathrm{k}-3)$$[/tex]

[tex]$$\mathrm{k}=\pm 6$$[/tex]

[tex]$\frac{3}{k}=\frac{k-3}{k}$$[/tex]

[tex]$$3 \mathrm{k}=\mathrm{k}(\mathrm{k}-3)$$[/tex]

simplifying the equation, we get

[tex]$$3 k=k^2-3 k$$[/tex]

[tex]$$\mathrm{k}^2-3 \mathrm{k}-3 \mathrm{k}=0$$[/tex]

[tex]$$k^2-6 k=0$$[/tex]

[tex]$$\mathrm{k}(\mathrm{k}-6)=0$$[/tex]

k = 0, 6

Therefore, k = 6 satisfies both equations.

The complete question is:

For what value of K will the following pair of linear equations have infinitely many solutions?

Kx + 3y −(K − 3) = 0

12x + Ky − K = 0

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The triangles are similar triangles. and the scale factor of triangle UVW to triangle XYZ is 7

What is triangle ?

triangle can be defined in which it contains three sides , three angles and the sum of three angles is always is 180 degrees.

How to determine the scale factor

From the given figure, we have the following corresponding side lengths:

UW = 2

XZ= 14

The scale factor of UVW to XYZ is then calculated using:

Scale factor = XZ/UW

Substitute known values

Scale factor = 14/2

Divide

Scale factor = 7

Hence, the scale factor of triangle UVW to triangle XYZ is 7

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Answer:

f(x) increases from -9 to -0.5 and from 3 to 5.

Step-by-step explanation:

See the attached graph.

Answer:

the answer 446600 ,nice to be of help to u

On the graph above, the input when f(x) = -5 is equal to -2.

Mathematically, the point-slope form of a straight line can be calculated by using this mathematical expression:

y - y₁ = m(x - x₁) or y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)

Where:

Next, we would determine the linear equation representing the line and passes through the points (-1, -2) and (1, 4) by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)

y - (-2) = (4 - (-2))/(1 - (-1))(x - (-1))

y + 2 = 6/2(x + 1)

y = 3(x + 1) - 2

y = 3x + 3 - 2

y = 3x + 1

When y = -5, the input value (x) can be calculated as follows;

y = 3x + 1

-5 = 3x + 1

3x = -5 - 1

3x = -6

x = -6/3

x = -2.

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The correct statement is D. Yoni CANNOT dunk the basketball because the discriminant of 0 = -16t² + 10t - 2.5 is negative.

The discriminant of a quadratic equation is the value that is inside the square root sign of the equation,

in this case: b²-4ac.

Given that

h(t) = -16t² + 10t

Height = 2.5

We have

-16t² + 10t = 2.5

This gives

0 = -16t² + 10t - 2.5

In this case, the discriminant of the equation 0 = -16t² + 10t - 2.5 is negative, which means that there are no real roots.

This means that Yoni will not reach the height of 2.5 feet because the equation has no real solutions, so he cannot dunk the basketball

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Answer:

Option B) 803.84in²

Step-by-step explanation:

We know the formula to find the area of a circle is listed as,

[tex]A = \pi r^{2}[/tex]

But over here the diameter is only given

that means we have to find the radius which is,

[tex]r = \frac{32}{2}[/tex]

[tex]r = 16in[/tex]

Now we can find the area of a circle which is,

[tex]A = 3.14X(16)^{2}[/tex]

[tex]A = 803.84in^{2}[/tex]

Hence , Option B) is the correct answer

Answer:

Option D

Step-by-step explanation:

As per your question, cos θ = 3/10

tanθ = √(sec²θ - 1) = √((1/cos²θ) - 1)

Put the value of cos θ, √(1/(9/100) - 1 = √(100/9 - 1) = ±√91/9 = -√91/3 (tan θ is negative in the third quadrant.)

So, option D is the correct answer.

Answer: C- Opposite sides are parallel. (Same distance apart)

Hope this helps :)

The three numbers which are in the ratio 1:2:3 and whose sum of the cubes is 4500 are 5, 10, and 15.

As given in the question,

Let us consider three number which are in the ratio 1: 2 : 3 be,

y, 2y , and 3y.

As per given condition:

Sum of their cubes = 4500

⇒x³ + (2x)³ + (3x)³ = 4500

⇒ x³ ( 1 + 8 + 27 ) = 4500

⇒36x³ = 4500

⇒ x³ = 4500/36

⇒x³ = 125

⇒ x = ∛125

⇒ x = 5

⇒2x = 10

⇒3x = 15

Therefore, three numbers which are in the given ratio are given by 5, 10, 15.

The above question is incomplete, the complete question is :

Three numbers are in the ratio 1:2:3 and the sum of their cubes is 4500. Find the numbers.

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The polynomial identities and proofs are mathematical statements that show that two algebraic expressions are equal. They can be used to simplify equations or to prove certain properties of polynomials.

For example, to prove x^2 + 2x + 1 = (x + 1)^2, you can factor the left side and expand the right side. This will show that x^2 + 2x + 1 = x^2 + 2x + 1 and thus the two polynomials are equal.

x^2 + 2x + 1

= (x + 1) (x + 1)

= x^2 + 2x + x + 1

= x^2 + 3x + 1

= (x + 1)^2

To prove that x^2 + 2x + 1 = (x + 1)^2, we first factor the left side x^2 + 2x + 1 and expand the right side (x + 1)^2. This will give us two equations: x^2 + 2x + 1 and x^2 + 3x + 1. From here, we can observe that both equations are identical, and thus the two polynomials are equal. This can be further verified by noting that the left side is the result of squaring x + 1, and the right side is the square of x + 1. Therefore, x^2 + 2x + 1 is equal to (x + 1)^2.

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15+5x<55 is inequality represents the name of movie tickets he can buy.

A relationship between two expressions or values that are not equal to each other is called 'inequality.

Given that Alan saved 55$.

He has already spent 15$.

Alans plans to spend 5$ on a movie ticket each month.

We have to write the  inequality which represents the name of movie tickets he can buy.

15+5x<55

Here x represents the number of movies he can watch

5x<30

x<6

Hence, 15+5x<55 is inequality represents the name of movie tickets he can buy.

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When a number under the root sign contains no square factors, it is considered to be a radical in its simplest form. The number y = 2

The expression x = 2

The number y = 2

Trigonometry is the study of the correlations between triangle angles and side lengths.

Sine, cosine, tangent, cosecant, sec, and cotone are the six trigonometric functions.

Suppose the angle is such that

opposite/hypotenuse = sin

neighboring / hypotenuse = cos

tan = opposite or nearby

Tan equals sin and cos.

cosec = 1 / sin

Sec = 1 / Cos

Cot = 1 + Tan

given the data,

Let ABC be the triangle.

The angles inside the triangle ABC are 45°, 45°, and 90°. The triangle ABC is a right-angled triangle.

Now, based on the illustration,

trigonometric relationships

tan θ = x / √2

Now , θ = 45°

In this case, x = 2.

Moreover, using trigonometric relationships,

base2 plus length2 = hypotenuse2

y = √ ( √2 )² + ( √2 )²

y = √4

y = 2

Consequently, x has a value of 2.

The number y = 2

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The k represents a vertical shift (how far up, or down, the graph has shifted from y = 0).

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Latoya swims 7 kilometers per hour if there were no currents.

Latoya's speed without the current can be calculated by adding the speed she swam against the current (S-c) to the speed of the current (c). Since she swam the same distance at the same time in both cases, we know that (S-c) * t = S * t. Therefore, S = (S-c) + c. We know that the rate of the current is c = 2 Km/h and she swam 5 Km against the current, so (S-c) = 5 Km/t and S * t = 15 Km.

By substituting the values, we get S = (5 + 2) Km/t = 7 Km/t.

Complete question :

Latoya swam 5 kilometers against the current in the same amount of time it took her to swim 15 kilometers with the current. The rate of the current was 2 kilometers per hour. How fast would Latoya swim if there were no currents?

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The unique solution system is given by the intersection of two lines .

When the line intersects at a point the value of the function becomes zero and also intersecting lines meet at only one point.

Hence this type of system have a unique solution.

The condition of the unique solution is

a1/a2[tex]\neq[/tex]b1/b2

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The interest earned in a savings account after 12 months on a balance of $1000, with an interest rate of 1.5% APY compounded yearly, is $15.00.

A savings account is a type of bank deposit account that typically pays interest and allows customers to access their funds at any time. Savings accounts are a safe, convenient way to store money, and they offer a variety of benefits, including allowing customers to earn interest on their deposits, access their funds quickly and securely, and take advantage of certain tax benefits.

This is calculated by multiplying the principal balance ($1000) by the interest rate (1.5%) and then multiplying by the number of years (12). Therefore, the interest earned is calculated as follows:
$1000 x 1.5% x 12 = $15.00.

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This is a sequence of numbers where each number is determined by the number that comes before it.

a(1) = 1, a(2) = 2, a(3) = -1, a(4) = -4, a(5) = 7

b(1) = 1, b(2) = -1, b(3) = -3, b(4) = -5, b(5) = -7

c(1) = 1, c(2) = 3, c(3) = 7, c(4) = 15, c(5) = 31

d(1) = 1, d(2) = 2, d(3) = 5, d(4) = 26, d(5) = 677

f(1) = 1, f(2) = 3, f(3) = 6, f(4) = 11, f(5) = 18

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Answer:

8/21

Step-by-step explanation:

2/7 ÷ 3/4 =

= 2/7 × 4/3

= 8/21

The coordinates of K are (3, 1).

What is the coordinate point?

The coordinates of a point are a pair of numbers that define its exact location on a two-dimensional plane. Recall that the coordinate plane has two axes at right angles to each other, called the x and y-axis. The coordinates of a given point represent how far along each axis the point is located.

Point K is 1/n of the way from J(4,5) to L(0,-7). To find the coordinates of K, we can use the concept of linear interpolation.

Given two points J(x1,y1) and L(x2,y2) and a value of t, such that 0<=t<=1, the coordinates of the point K(x,y) that is t of the way from J to L is given by:

x = (1-t)x1 + tx2

y = (1-t)y1 + ty2

In this case, we know that n=4 and t = 1/4.

So the x and y coordinates of K are:

x = (1-1/4)x1 + (1/4)x2 = (3/4)x1 + (1/4)x2 = (3/4)(4) + (1/4)(0) = 3

y = (1-1/4)y1 + (1/4)y2 = (3/4)y1 + (1/4)y2 = (3/4)(5) + (1/4)(-7) = 1

Hence, the coordinates of K are (3, 1).

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The angle-side connection theorem states that angle E in triangle DEF is equal to angle F.

Since a triangle has three sides and three vertices, it is a polygon. It is a fundamental geometric shape. Triangle ABC is the moniker given to a triangle that has vertices A, B, and C. When the three points are not collinear, a singular plane and triangle are found in Euclidean geometry. A triangle is a polygon if it has three sides and three corners. The points where the three sides meet are known as the triangle's corners.

given

The length of every triangle side is proportional to the size of the angles that are directly across from them, according to the angle-side relationship theorem.

Thus,

Angle F = (61 + 58)/180 (sum of triangle)

F = 61 degree angle

Since mE = 61 degrees, F and E are therefore congruent to one another.

It follows that the sides that are perpendicular to each angle will also be parallel to one another.

The angle-side connection theorem states that angle E in triangle DEF is equal to angle F, which also implies that the sides that are opposite one other are congruent.

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To find out how many people watching the parade are adults, we can subtract the number of children from the total number of people.

524 people - 178 children = 346 adults

So, 346 people watching the parade are adults.

Answer:

To find out how many people watching the parade are adults, we have to subtract the number of children from the total number of people.

Total number of people watching the parade: 524

Number of children watching the parade: 178

524 - 178 = 346

Therefore, 346 people watching the parade are adults.

No, 7 is a number, not an algebraic expression.

No, 7 is a number, not an algebraic expression. An algebraic expression is a combination of numbers, variables, and mathematical operations (such as +, -, x, /) that can be evaluated to a single numerical value. Examples of algebraic expressions include 2x + 3 and 4y - 7.

Algebraic expressions can also contain exponents and roots, and can be combined using arithmetic operations. Algebraic expressions are used in many mathematical and scientific fields, and are fundamental to understanding advanced mathematical concepts such as algebra, calculus and more.

Therefore, No, No, 7 is a number, not an algebraic expression.

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The largest possible value of n can be calculated using factorials and the largest value would be 3628800

The concept of factorials is used to calculate the value of n.

Factorials are defined as mathematical expression that is the product of the given number down to 1. It is denoted with the symbol n! which means that if n is given as 5, then its factorial would be =5×4×3×2×1 = 120.

Factorial of n!= nx(n-1)(n-2)........x2x1

Factorials are used in mathematics or statistics to denote the possibilities of an event in an outcome.

The total numbers of the two groups = 10

The factorials of 10! = 10×9×8×7×6×5×4×3×2×1

= 3,628,800.

Therefore, The largest possible value of n can be calculated using factorials and the largest value would be 3628800

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