\(log10(3 \times 2)\)
​

Solution:

Given that the initial cost price of the jewelry is $2,200.

The rate at which it decreases each year is 12%.

Thus, the exponential decay function is;

The graph of the function is;

From the graph;

CORRECT OPTION:

The value of \(x_5\), rounded to the nearest decimal place using Newton's method of approximation is 1.466.

The correct answer is option B.

To find the value of \(x_5\)using Newton's method of approximation, we need to iterate the following formula:

\(x_(_n_+_1_) = x_n - f(x_n) / f'(x_n)\)

where f'(x) represents the derivative of the function f(x). Let's calculate the values step by step.

Given function: f(x) = \(x^3 - x^2 - 1\)

Step 1: Find the derivative of f(x)

f'(x) = \(3x^2 - 2x\)

Step 2: Initialize the starting value

\(x_0\)= 1

Step 3: Calculate \(x_1\)

\(f(x_0) = f(1) = (1^3) - (1^2) - 1 = 1 - 1 - 1 = -1\)

\(f'(x_0) = f'(1) = (3(1^2)) - (2(1)) = 3 - 2 = 1\)

\(x_1 = x_0 - f(x_0) / f'(x_0)\)

   = 1 - (-1) / 1

   = 2

Step 4: Calculate \(x_2\)

\(f(x_1) = f(2) = (2^3) - (2^2) - 1 = 8 - 4 - 1 = 3\)

\(f'(x_1) = f'(2) = (3(2^2)) - (2(2)) = 12 - 4 = 8\)

\(x_2 = x_1 - f(x_1) / f'(x_1)\)

   = 2 - 3 / 8

   = 1.625

Step 5: Repeat the process until we reach \(x_5\)

Performing the calculations for \(x_3, x_4, andx_5\), we find:

\(x_3\) ≈ 1.465

\(x_4\) ≈ 1.466

\(x_5\)≈ 1.466

After applying Newton's method of approximation to the function f(x) = \(x^3 - x^2 - 1,\)starting with,\(x_0 = 1,\) we iteratively calculated the values of \(x_1, x_2, x_3, x_4, and x_5\). The final approximation, \(x_5\), is approximately 1.466 when rounded to the nearest decimal place. This aligns with option B as the correct answer.

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Answer:

60 degrees

Step-by-step explanation:

it has to be.

Answer:

it's D

Step-by-step explanation:

got it right edge 2021

The probability that among the first two songs played, exactly 1 of the 4 songs you like is played is 0.452 or 45.2%.

Probability is a measure of the likelihood of an event occurring. It is a numerical value between 0 and 1, where 0 represents an impossible event and 1 represents a certain event. The probability of an event is calculated by dividing the number of favorable outcomes by the total number of possible outcomes.

There are 4 songs that you like out of the 14 total songs, so the probability of selecting a song that you like on the first draw is 4/14.

On the second draw, the probability of selecting a song that you like is 3/13, since there are now 3 songs that you like out of the remaining 13 songs.

The probability of selecting exactly 1 of the 4 songs you like in the first two draws is given by:

P(exactly 1 like in first two draws) = (4/14) ×(10/13) + (10/14) × (4/13) = 0.452

Therefore, the probability that among the first two songs played, exactly 1 of the 4 songs you like is played is approximately 0.452 or 45.2%.

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The ratios are;

Sin θ =  5/6

Cos θ = √11/6

Tan θ =  5√11/11

Sec  θ =  6√11/11

Cosec  θ = 6/5

Cot θ =  √11/5

These trigonometric ratios are used to relate the angles of a right triangle to the lengths of its sides

We can see that the hypotenuse is obtained from;

x =√\((10)^2 + (2\sqrt{} 11)^2\)

x = √100 + 44

x = 12

Then;

Sin θ = 10/12 = 5/6

Cos θ =  2√11/12

= √11/6

Tan θ = 10/2√11

= 20√11/44

= 5√11/11

Sec  θ =  1/Cos  θ

=  6/√11

= 6√11/11

Cosec  θ = 1/Sin

 θ = 6/5

Cot θ = 1/tan θ

= 11/ 5√11

= 55√11/275

= √11/5

Sinβ = 2√11/12

= √11/6

Cos β = 10/12

= 5/6

Tan β = 2√11/10

= √11/5

Sec β = 6/5

Cosec β = 6√11/11

Cot β = 5√11/11

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Your A and C look correct if I were to do it your B needs to move

A transformation would accomplish this include the following: C. a rotation 180° counterclockwise about the origin.

In Mathematics and Geometry, the rotation of a point 180° about the origin in a clockwise or counterclockwise direction would produce a point that has these coordinates (-x, -y).

Furthermore, the mapping rule for the rotation of a geometric figure 180° counterclockwise about the origin is given by this mathematical expression:

(x, y)                                            →            (-x, -y)

Coordinates of point X (0, 4)  →  Coordinates of point Y = (0, -4)

Coordinates of point X (1, 3)  →  Coordinates of point Y = (-1, -3)

In conclusion, we can logically deduce that this transformation rule (x, y) → (-x, -y) would map Figure X onto Figure Y.

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The y-values of the quadratic equation for x = {1, 2, 3, 4} are {5, 11, 19, 29}.

What is quadratic equation?

A quadratic equation is a type of polynomial equation of degree 2, which means it contains a variable raised to the second power (i.e., x²). It has the standard form of ax² + bx + c = 0, where a, b, and c are constants and x is the variable. The coefficient a cannot be equal to zero, as this would result in a linear equation.

Quadratic equations can have one or two real solutions, depending on the discriminant (b² - 4ac) of the equation. If the discriminant is greater than zero, the equation has two real solutions. If the discriminant is equal to zero, the equation has one real solution. If the discriminant is less than zero, the equation has no real solutions (but has two complex solutions).

To find the y-values of the quadratic equation y = x² + 3x + 1 for x = {1, 2, 3, 4}, we simply substitute each value of x into the equation and evaluate.

For x = 1, y = 1² + 3(1) + 1 = 5.

For x = 2, y = 2² + 3(2) + 1 = 11.

For x = 3, y = 3² + 3(3) + 1 = 19.

For x = 4, y = 4² + 3(4) + 1 = 29.

Therefore, the y-values of the quadratic equation for x = {1, 2, 3, 4} are {5, 11, 19, 29}.

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Answer:

The correct answer is a.

Step-by-step explanation:

The sequence is: 2 3 E 4 5 I 6 8 We can notice that there are numbers and letters alternating in the sequence. The numbers are increasing, and the letters seem to be vowels in alphabetical order. So, the next value should be a letter (vowel) after I, which is O. The correct answer is a.

The numeric value of the function f(x) = 14/[3 + ae^(kx)] at x = 2 is given as follows:

f(2) = 0.172.

The function for this problem is defined as follows:

f(x) = 14/[3 + ae^(kx)]

When x = 0, y = 2, hence we can obtain the coefficient a as follows:

2 = 14/(3 + a)

6 + a = 14

a = 8.

Hence:

f(x) = 14/[3 + 8e^(kx)]

When x = 1, y = 1/2, hence the coefficient k is given as follows:

0.5 = 14/(3 + 8e^k)

1.5 + 4e^k = 14

4e^k = 12.5

e^k = 12.5/4

k = ln(12.5/4)

k = 1.14.

Hence:

f(x) = 14/[3 + 8e^(1.14x)]

Then the numeric value of the function at x = 2 is given as follows:

f(2) = 14/[3 + 8e^(1.14(2))]

f(2) = 0.172.

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For the statement "If a polygon lacks right angles, then it is a parallelogram.", the counter example is -

Option A : a right triangle

What is a parallelogram?

A quadrilateral with two sets of parallel sides is referred to as a parallelogram. In a parallelogram, the opposing sides are of equal length, and the opposing angles are of equal size. Additionally, the interior angles that are additional to the transversal on the same side.

A counterexample for a conditional statement is an example that satisfies the hypothesis (the first part of the statement) but does not satisfy the conclusion (the second part of the statement).

In this case, the statement is "If a polygon lacks right angles, then it is a parallelogram."

A right triangle is a polygon that lacks right angles, but it is not a parallelogram.

Therefore, a right triangle is a counterexample for this statement.

A square, a regular hexagon, and a rectangle all have right angles, so they are not counterexamples for this statement.

Therefore, the triangle is the counterexample.

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Answer:

C= 14.14 yd

Step-by-step explanation:

The circumference of a circle is equal to the equation

C = 2πr

Since the diameter is 4.5, the radius is 2.25.

Plug the radius into the equation, and solve.

C=2π(2.25)

C= 6.283185307(2.25)

C= 14.137

C= 14.14 yd

I hope this helps!

This function written in vertex form include the following: A. f(x) = (x –1)² – 7.

In Mathematics, the axis of symmetry of a quadratic function can be calculated by using this mathematical equation:

Axis of symmetry = -b/2a

Where:

a and b represents the coefficients of the first and second term in the quadratic function.

For the given quadratic function f(x) = x² – 2x – 6, we have:

a = 1, b = -2, and c = -6

Axis of symmetry, Xmax = -b/2a

Axis of symmetry, Xmax = -(-2)/2(1)

Axis of symmetry, Xmax = 2/2

Axis of symmetry, Xmax = 1.

Next, we would determine vertex as follows;

f(x) = x² – 2x – 6

f(x) = 1² – 2(1) – 6

f(x) = -7.

Now, we can write quadratic function in vertex form;

f(x) = a(x - h)² + k

f(x) = (x - 1)² - 7

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Complete Question:

The image shows a geometric representation of the function f(x) = x² – 2x – 6 written in standard form.

What is this function written in vertex form?

f(x) = (x –1)² – 7

f(x) = (x +1)² – 7

f(x) = (x –1)² – 5

f(x) = (x +1)² – 5

Answer: What is the commutative property of addition? To “commute” means to move around or travel. According to the commutative property of addition, changing the order of the numbers we are adding, does not change the sum. Here's an example of how the sum does NOT change, even if the order of the addends is changed and The commutative property of multiplication

states that when two numbers are being multiplied, their order can be changed without affecting the product.

Step-by-step explanation: Have a blessed day hopefully this helped!

Answer:

the second one

Step-by-step explanation:since i helped can i have brainlist please :D

Answer:

20%

Step-by-step explanation:

there are about millions of multinational and national companies which are working for the better Gross National Product(GNP).

The United States is super power and has multiple resources to maintain itself  and the over all economic system. As, there are about millions of multinational and national companies which are working for the better Gross National Product(GNP). As, there is agriculture, car manufacturer, and the military industry for improving and adding the value to the over all GNP of the United States.

The Oil and gas sector is the one major factor for the development of the United State's GNP(Gross National Product). As, the exports of the region is well known to be very high and generates more revenue for the over all system as well.    

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The property you are referring to is called the associative property of multiplication. According to this property, when multiplying three numbers, the grouping of the numbers does not affect the result. In other words, you can change the grouping of the factors without changing the product.

In the equation you provided: 3x(5x7) = (3x5)7

The associative property allows us to group the factors in different ways without changing the result. So, whether we multiply 5 and 7 first, or multiply 3 and 5 first, the final product will be the same.

Answer:

The slope is 0

Step-by-step explanation:

The area of the triangle is 47.91 units²

When all three sides of the triangle are known we can use Heron's formula. Consider the triangle ABC with sides a, b, and c has shown in the image.

Heron’s formula is:

Area =√s(s−a)(s−b)(s−c)

where,

a, b, c are the side length of the triangle

s is the semi-perimeter. s = (a+b+c)/2

In this case:

Using the knowledge of the radius of a circle. We can say:

a = BC = 3 + 9 = 12 units

b = AC = 5 + 3 = 8 units

c = AB = 5 + 9 = 14 units

s = (a+b+c)/2

s = (12+8+14)/2

s = 34/2

s = 17 units

Area = √s(s−a)(s−b)(s−c)

Area = √17(17−12)(17−8)(17−14)

Area = √17(5)(9)(3)

Area = √2295

Area = 47.91 units²

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Using translation concepts, the sequence that is used to obtain the translated image is:

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.

For all the vertices, the transformations follow the given pattern:

In the step (x,y) -> (-x,y), the function is reflected over the y-axis. Then, in step (-x,y) ->  (-x + 1, y), the function is shifted right one unit.

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Answer:

324pi

Step-by-step explanation:

V of sphere = 4/3 x pi x r^3

V of cone = pi x r^2 x h x 1/3

4/3 x pi x 6^3 = 288 pi

pi x 6^2 x 15 x 1/3 = 180 pi

since the sphere is cut in half = 288/2 = 144

144 pi + 180 pi = 324 pi

Answer: Let 5/9=□/54

Clearly shows 54=(9×6)

Now multiply the numerator by 6 also

∴5 / 9 = (5 \times 6) / (9 \times 6) = 30 /54$$

Hence, 30/54 is the equivalent fraction of 5/9 having denominator 54

(ii) Let 5/9=35/□

Clearly shows 35=(5×7)

Now multiply the denominator by 7 also

∴5/9=(5×7)/(9×8)=35/63

Hence, 35/63 is the equivalent fraction of 5/9 having numerator 35

Step-by-step explanation:

Answer:

lien earned 29950, husband earned 28650

Step-by-step explanation:

you subtract 1300 from the total then divide by 2 and add the 1300 to liens half.

Answer:

x = 84 , y = 168

Step-by-step explanation:

\(Sin 60 = \frac{opposite side}{hypotenuse}\\\\ \frac{\sqrt{3}}{2}= \frac{AB}{BC}\\\\ \frac{\sqrt{3}}{2} = \frac{84\sqrt{3}}{y}\\\\Cross\ multiply ,\\\\y*\sqrt{3} =2*84 \sqrt{3}\\\\y= \frac{2*84*\sqrt{3}}{\sqrt{3}}\\\\y=168\)

\(Cos\60 = \frac{adjacent}{hypotenuse}\\\\ \frac{1}{2}= \frac{AC}{BC}\\\\ \frac{1}{2}= \frac{x}{168}\\\\ \frac{1}{2}*168=x\\\\x= 84\)

Your analysis is correct. Here's a summary:

If it is sunny, then it is 80° Fahrenheit. (Original statement)

Converse: If it is 80° Fahrenheit, then it is sunny. (Valid)

If it is 80° Fahrenheit, then it is sunny. (Original statement)

Converse: If it is sunny, then it is 80° Fahrenheit. (Valid)

If it is not sunny, then it is not 80° Fahrenheit. (Original statement)

Converse: If it is not 80° Fahrenheit, then it is not sunny. (Invalid)

Counterexample: A day that is not 80° Fahrenheit and not sunny (e.g., 70° and cloudy).

If it is 80° Fahrenheit, then it is sunny. (Original statement)

Converse: If it is sunny, then it is 80° Fahrenheit. (Invalid)

Counterexample: A day that is 80° Fahrenheit and cloudy.

In cases 1 and 2, the original statements and their converses are valid because the relationship between "sunny" and "80° Fahrenheit" holds in both directions. However, in cases 3 and 4, the converses are invalid because there are counterexamples where the second part of the statement (either "not 80° Fahrenheit" or "cloudy") does not necessarily imply the first part ("not sunny" or "80° Fahrenheit").