A recursive rule for a geometric sequence is a1=
4
9

;an=3an−1.

What is the explicit rule for this sequence?

ANSWER:

4
9

(3n−1) just took the test

To plot the above linear regression on a graph, follow the procedures outlined below.

You may use the following steps to plot the supplied data on a graph:

1) Create an x- and y-axis coordinate plane.

2) Label the x-axis with the numbers 1 through 13 (to represent the 13 data points).

3) Label the y-axis with a suitable scale that encompasses the data's greatest and lowest values (e.g., 0 to 2200 with 200 increments).

4) For each point, try to find  the associated x -value on the x-axis and the corresponding y-value on the y- axis, and then place a point at the intersection of the two values.

For example, if the first point is (1, 1000), you would identify the x-axis point labeled "1" and the y-axis point labeled "1000" and add a point at it  intersection.

5) based  on the pattern in the data, connect the points of the coordinares using  a line or a curve. Because the data appears to increase gradually with some fluctuations in this case, a line connecting the points would be appropriate.

After plotting the data on the graph, you may study the pattern and draw inferences about the data's trend over time. Please see the attached sample graph.

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The conjecture that can be made about the other number is option A: the other number is odd.

Let's assume that the two even numbers are x and y. Then, we can write their sum as x + y = 2a, where a is some even number.

Now, let's consider the sum of 6 and another number, which we can represent as 6 + z, where z is some unknown number. If this sum is even, then we can write it as 2b, where b is some even number.

So, we have the equations:

x + y = 2a (since the sum of two even numbers is even)

6 + z = 2b (since the sum of 6 and another number is even)

We can subtract 6 from both sides of the second equation to get:

z = 2b - 6

Now, we can substitute this expression for z into the first equation:

x + y = 2a

And we get:

x + y + z - 2z = 2a

x + (y + z) - 2z = 2a

x + (2b - 6) - 2z = 2a

x + 2b - 2z - 6 = 2a

This equation tells us that x + 2b - 2z - 6 is an even number (since 2a is even). Since x and 2b are even, the expression -2z - 6 must also be even. Therefore, -2z must be even. This means that z is odd (since an even number minus an even number is even, and -6 is even).

So, we can conclude that the other number (z) is odd. Option A is the correct answer.

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The index forms are simplified to;

1. [tex]5^6^\sqrt{2}[/tex]

2.[tex]3^5\sqrt{3}[/tex]

3.  [tex]2^2^\sqrt{25}[/tex]

It is important to note the following about the rules of index forms;

From the information given, we have that;

[tex]5^\sqrt{2}[/tex] × [tex]5^\sqrt{50}[/tex]

Add the exponents, we have;

[tex]5^\sqrt{2} ^+ 5\sqrt{2}[/tex]

Then, we have;

[tex]5^6^\sqrt{2}[/tex]

2. [tex]3\sqrt{12}[/tex] × [tex]3^\sqrt{27}[/tex]

We have;

[tex]3^2^\sqrt{3} + 3\sqrt{3}[/tex]

Add the exponents

[tex]3^5\sqrt{3}[/tex]

3. [tex]2^2^\sqrt{25}[/tex]

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The vector u+v can be represented as < √85, -41.19° >, which is obtained by adding vector u marked on the y-axis from 0 to 6 and vector v marked on the x-axis from 0 to -7 on a coordinate plane.

To add vectors on the coordinate plane. The vector u is marked on the y-axis from 0 to 6, and the vector v is marked on the x-axis from 0 to -7.

To add them, we start at the tail of u and move horizontally to the left by 7 units (since v has a negative x-component) and then vertically up by 6 units (since u has a positive y-component) to reach the head of the resulting vector. This gives us the vector u+v.

So, the vector u+v can be represented as

Magnitude √(6^2 + 7^2) = √85

Direction atan(6/(-7)) = -41.19 degrees (measured counterclockwise from the positive x-axis)

Notation < √85, -41.19° >

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Let H: X – Y be a mapping. The set Y is called the codomain of the mapping H: X – Y.

In mathematics, a mapping or function H: X – Y is a relation between two sets, where the set X is called the domain and the set Y is called the codomain.

The mapping H assigns each element in X to a unique element in Y. The codomain of the mapping H is the set Y, which contains all the possible outputs that can be obtained from the mapping.

It represents the range of the mapping H and provides a reference set for the outputs of the function. The actual range of the function may be smaller than the codomain, depending on the elements in X that are mapped to.

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18.2

Step-by-step explanation:

AB² =AC² + CB² -2(AC)(CB)CosA

X²=(17)² + (10)² - 2 (17)(10) Cos80

x² = 289 + 100- 340 cos 80

x= √289+100-340cos80

x= 18.2

Among the given options, V [tex]57^\circ[/tex]   is the closest estimate for the measure of the other acute angle.

To find the measure of the other acute angle, we can use the fact that the sum of the angles of a triangle is 180°. Let x be the measure of the other acute angle. Then we have:

[tex]x + 32.9^\circ + 90^\circ = 180^\circ[/tex]

Simplifying the equation, we get:

[tex]x = 180^\circ - 32.9^\circ - 90^\circ[/tex]

[tex]x = 57.1^\circ[/tex]

So the exact measure of the other acute angle is [tex]57.1^\circ.[/tex]

Therefore, Among the given options, V [tex]57.1^\circ.[/tex] is the closest estimate for the measure of the other acute angle.

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The minimum value of the data set is 10.5.

Box plots are an effective graphical tool used to display a summary of a dataset. They provide a visual representation of the minimum and maximum values, quartiles, and outliers of the data. They are commonly used in statistics and can provide valuable insights into a dataset.

Now, let's consider the box plot in question. The box plot is labeled "Volunteer Service Hours" and it has four quartiles, each marked by a horizontal line. The first quartile (Q1) is marked at 13, the second quartile (Q2) is marked at 16.5, the third quartile (Q3) is marked at 20, and the fourth quartile (Q4) is marked at 23, with the end of the box extending to 27.

The minimum value of the data set can be found at the lower whisker of the box plot.

The lower whisker represents the minimum value that is not an outlier.

In this box plot, we do not see any outliers, so the minimum value of the dataset is represented by the lower end of the whisker, which is located at 10.5.

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Answer:

Step-by-step explanation:

(-2-3)-(4-5)+ (−1+6)−(−9+8)

-5-4+5-1+6+9-8

-9+4+15-8

-5+7

2

There are 4 + 5 + 7 + 8 = 24 buttons in total.

After the cat knocks 2 buttons onto the floor, there are 22 buttons remaining on the table. The probability that the first button knocked onto the floor is blue or red can be calculated as follows:

P(blue or red) = P(blue) + P(red)

P(blue or red) = 4/24 + 5/24

P(blue or red) = 9/24

P(blue or red) = 3/8

Therefore, the probability that the button on the floor was blue or red is 3/8 or 0.375.Answer:

Step-by-step explanation:

The coordinates for the centroid of the triangle is (0, 2.67)

The centroid of a triangle is the place where the three medians of the triangle meet or intersect.

To find the centroid of the triangle, we use the formula

(x₁ + x₂ + x₃)/3 , (y₁ + y₂ + y₃)/3

We add all the x coordinates together and divide by 3, we also do the same for the y coordinates.

It becomes x = (-4 + 0 + 4)/3  

y = (8 + 2 + (-2))/3

Therefore, the centroid is (0, 2.67)

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Answer:

120

Step-by-step explanation:

25% is equal to 1/4. If you divide 30 by 1/4 you get 120. To check this, if you multiply 120 by 1/4 you get 30.

Answer: 120

Step-by-step explanation:

In order to find the missing value, divide the provided value by the percentage as follows:

30 / 0.25 = 120

This can be double-checked by plugging the number into the statement afterwards: 25% of 120 is 30, which is true

The probability that both events A and B will occur is 1/3 or approximately 0.3333.

To find the probability of both events A and B occurring, we need to calculate the individual probabilities of each event and then multiply them together.

Event A: The first die is a 4 or less.

In a standard six-sided die, there are four outcomes (1, 2, 3, 4) that satisfy this condition. Out of the six possible outcomes, four are favorable, so the probability of event A is 4/6 or 2/3.

Event B: The second die is even.

In a standard six-sided die, there are three even outcomes (2, 4, 6) out of the six possible outcomes.

Therefore, the probability of event B is 3/6 or 1/2.

To find the probability of both events occurring, we multiply the probabilities of each event:

[tex]P(A and B) = P(A) \times P(B) = (2/3) \times (1/2) = 1/3[/tex]

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The vertical shift and vertical shrink of the exponential function are 2 and 1/2 respectively and the graph of the function is attached below

A curve displaying an exponential function is known as an exponential graph. A curve with a horizontal asymptote and a rising or decreasing slope characterizes the graph of an exponential function. i.e., it begins as a horizontal line, grows or drops gradually, and then the growth or decay accelerates.

The vertical shift and vertical shrink of the function f(x) = 1/2(4 - eˣ) are 2 and 1/2

The vertical shift = 2

vertical shrink = 1/2

Kindly find the attached graph below

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Answer:

(x + 3)(x - 15)

Step-by-step explanation:

To factor the expression x^2 - 12x - 45, we need to find two numbers that multiply to -45 and add to -12. Let's use the method of decomposition to find these two numbers:

x^2 - 12x - 45

We need to find two numbers that multiply to -45 and add to -12. Let's try -15 and 3:

x^2 - 12x - 45 = x^2 - 15x + 3x - 45

Now we can group the first two terms and the last two terms:

x^2 - 15x + 3x - 45 = x(x - 15) + 3(x - 15)

We can see that both terms have a common factor of (x - 15), so we can factor this out:

x(x - 15) + 3(x - 15) = (x + 3)(x - 15)

Therefore, the expression x^2 - 12x - 45 can be factored as (x + 3)(x - 15).

Refer to the attachment ^-^

Hope Helpful ~

The length of the curve y = 5 - 4x, -2 ≤ x ≤ 2, is 4√(17).

To use the arc length formula, we need to find the derivative of the curve y = 5 - 4x:

y' = -4

Then, we can use the arc length formula:

L = ∫[a,b] √(1 + (y')^2) dx

where a and b are the limits of integration. In this case, a = -2 and b = 2.

L = ∫[-2,2] √(1 + (-4)^2) dx

= ∫[-2,2] √(17) dx

= √(17) * [x]_(-2)^(2)

= 4√(17)

So the length of the curve y = 5 - 4x, -2 ≤ x ≤ 2, is 4√(17).

To check this answer, we can note that the curve is a line segment with endpoints (-2, 13) and (0.75, 1), and we can calculate its length using the distance formula:

L = √((0.75 - (-2))^2 + (1 - 13)^2)

L = √(18.25 + 144)

L = √(162.25)

L = 4√(17)

This matches our previous answer, so we can be confident that the length of the curve is 4√(17).

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Answer: The answer is actually 12 pieces of vanilla cake.

The solutions  of the system of equations are (0, -6) and (7, 8)

Here we have the system of equations:

y=x^2−5x−6

y=2x−6

To solve this, we need to solve the equation:

x^2 - 5x - 6 = 2x - 6

x^2 - 7x = 0

x*(x - 7) = 0

We can see that the two solutions are:

x = 0

x = 7

Evaluating the line in these values we get:

y = 2*0 - 6 = -6

y = 2*7 - 6 = 8

Then the solutions are (0, -6) and (7, 8)

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Answer:

Each CD cost $14.90 before tax.

Step-by-step explanation:

Let's call the price of each CD before tax "x".

We know that Ashley bought 2 CDs, so the total cost before tax would be 2x.

We also know that the sales tax on each CD was $0.80, so the total sales tax for both CDs would be 2(0.80) = $1.60.

So the total cost including tax would be:

2x + 1.60 = 31.40

To solve for x, we can start by subtracting 1.60 from both sides:

2x = 29.80

Then, we can divide both sides by 2 to solve for x:

x = 14.90

The sine of the angle ANM is equal to 3/5 as the triangles are similar.

Given that the sine of angle ACB is equal to 3/5, line MN is parallel to BC and MN is midsegment of triangle ABC which implies that the triangles ABC and ANM are similar so;

sine ANM = 3/2 ÷ 5/2

sine ANM = 3/2 × 2/5

sine ANM = 3/5.

Therefore, the sine of the angle ANM is equal to 3/5 as the triangles are similar.

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The proportion relation obtained from the similar triangles indicates that the x/3 = 10/x

Similar triangles are triangles that have the same shape but their sizes may vary.

The proportion equation from the image based on the ratio of the corresponding sides of the similar right triangles can be found as follows;

The side x is the hypotenuse side of the smallest right triangle

The ratio x/3, is equivalent to the ratio of the hypotenuse side to the shortest side of the right triangle

The corresponding ratio in the medium triangle is ((x² - 3²) + 7²)/(x² - 3²)

((x² - 3²) + 7²)/(x² - 3²) = (x² + 40)/(x² - 3²)

The corresponding ratio in the large similar right triangle is (7 + 4)/x = 10/x

Therefore, the corresponding ratio is; x/3 = 10/x

The proportion is; x/3 = 10/x

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The answer to Monnor's problem is NOTA

For any quadratic equation of the form ax² + bx + c, the sum of roots is given by:

sum of roots = -b/a

In this case, x² - 7x + 5 = 0. Where a = 1 and b = -7. Thus:

sum of roots = -(-7)/1 = 7

Since Monnor must find the square of the sum of the roots of the equation, we have:

square of the sum of the roots = 7² = 49

Thus, the answer to Monnor's problem is NOTA

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The expression that represents the perimeter of the triangle is 18.4 + 8.7x + 7.5w.

The perimeter of a triangle is the sum of the lengths of its sides. Using the given expressions for the side lengths of the triangle, we can write the perimeter as:

(6.1w + 7.8) + (1.4w + 8.1) + (8.7x + 2.5)

Simplifying and combining like terms, we get:

7.5w + 11.2x + 18.4

Therefore, the expression that represents the perimeter of the triangle is 18.4 + 8.7x + 7.5w.

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The mean age of the U.S. presidents at inauguration is 54.7 years and the population standard deviation is approximately 5.7 years.

To find the mean and population standard deviation of the ages of the U.S. presidents at inauguration, we first need to calculate the sum of the ages and the number of presidents in the data set.

The sum of the ages is:

57 + 61 + 57 + 57 + 58 + 57 + 61 + 54 + 68 + 51 + 49 + 64 + 50 + 48 + 65 + 52 + 56 + 46 + 54 + 49 + 50 + 47 + 55 + 55 + 54 + 42 + 51 + 56 + 55 + 51 + 54 + 51 + 60 + 62 + 43 + 55 + 56 + 61 + 52 + 69 + 64 + 46 + 54 + 47 = 2,405

There are 44 presidents in the data set.

Therefore, the mean age is:

mean = sum of ages / number of presidents = 2,405 / 44 = 54.7

To find the population standard deviation, we first need to calculate the sum of the squared deviations from the mean:

(57 - 54.7)² + (61 - 54.7)² + ... + (47 - 54.7)² = 3,391.5

Then, we divide the sum of squared deviations by the number of presidents and take the square root:

population standard deviation = √(3,391.5 / 44) ≈ 5.7

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Answer:

30 and 10

Step-by-step explanation:

Main concepts:

Concept 1.  Geometric Sequence

Concept 2. Common ratio

Concept 3. Finding the next terms

Concept 1.  Geometric Sequence

Geometric sequences are a specific type of sequence with a pattern where a specific number is multiplied to each term to get the next term.

For instance, a completely different geometric sequence 1,2,4,8,16,... is geometric because you multiply any term by 2 to get the next term.

Concept 2. Common ratio

In a geometric sequence, this number that you can multiply by to get the next term (in the "1,2,4,8,16,..." example, the number 2) is called the common ratio because taking the ratio of two sequential terms of the sequence (dividing two terms in a row) always gives the same answer:

This process of finding ratios will yield a common ratio only if the sequence is a Geometric Sequence.

Concept 3. Finding the next terms

Since we're told that the sequence we're given in the question is a Geometric sequence, it must have a common ratio (otherwise, it wouldn't be a geometric sequence).

Find the common ratio by dividing sequential terms:

270/810 = 1/3

90/270 = 1/3

So, for the sequence in the question, the common ratio is 1/3.  Each term is multiplied by 1/3 to get the next term in the sequence.  (This is equivalent to dividing each term by 3 to get the next term in the sequence, if you prefer division and/or to avoid fractions)

So, to get the next two terms in the sequence, multiply by the common ratio:

90 * 1/3 = 30

30 * 1/3 = 10

So, the next two terms of the sequence are 30 and 10

The triangles which are congruent are P and Q. So, the correct answer is A).

Triangles are congruent if they have the same shape and size. This means that all corresponding angles and sides are equal. In this case, we can use the side lengths to determine which triangles are congruent.

Triangle P and Q have the same side lengths, so they are congruent (A). Triangle Q and R do not have the same side lengths, so they are not congruent (not B). Triangle R and S do not have the same side lengths, so they are not congruent (not C).

Triangle S and P do not have the same side lengths, so they are not congruent (not D). Therefore, the answer is A. Triangles P and Q are congruent.

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--The given question is incomplete, the complete question is given

" 8.G.1.2 A mathematical puzzle uses four triangles with the dimensions show below. Which of the following triangles are congruent? A. P and Q B. Q and R C. R and S D. S and P "--

Tyler will need a amount of  79,200 grams (or 79.2 kilograms) of glitter to cover the prism completely.

To calculate the amount of glitter needed to cover the prism completely, we first need to find the total surface area of the prism.

The prism consists of five faces: two rectangular faces with dimensions 18 m x 10 m, two triangular faces with base 18 m and height 10 m, and one rectangular face with dimensions 18 m x 25 m.

The total surface area of the prism can be calculated by adding the areas of all the faces together:

Total Surface Area = 2(18 m x 10 m) + 2(0.5 x 18 m x 10 m) + 18 m x 25 m

Total Surface Area = 360 m² + 180 m² + 450 m²

Total Surface Area = 990 m²

Given that 80 g of glitter is needed to cover each m², we can now calculate the total amount of glitter needed:

Total Glitter = Total Surface Area x Glitter per m²

Total Glitter = 990 m² x 80 g/m²

Total Glitter = 79,200 g

Therefore, Tyler will need 79,200 grams (or 79.2 kilograms) of glitter to cover the prism completely.

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The order of the equations from least number of solutions to greatest number of solutions is: C, B , and A.

In algebra, an expression is made up of several numbers, variables, and mathematical operations including addition, subtraction, multiplication, and division. One expression is, for instance, 3x + 2y - 5.

In algebra, an equation is a claim that two expressions are equal to one another. Often, it asks us to determine the value of a variable that would make the equation true.

Equation A:

4x + 12 = 2(2x + 3) + 6

4x + 12 = 4x + 12

This equation has infinitely many solutions, as 0 = 0 is always true.

Equation B:

5(x - 1) = 3(x + 7)

5x - 5 = 3x + 21

2x = 26

x = 13

This equation has one solution, which is x = 13.

Equation C:

2x - 4 = 2(x + 18)

2x - 4 = 2x + 36

-4 = 36

This equation has no solutions.

Hence, the order of the equations from least number of solutions to greatest number of solutions is: C, B , and A.

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Using some logarithm properties we will get the expanded expression:

log(y^10) = 10*ln(y)/ln(10)

So there are two logarithm properties that we can use here, these are:

logₙ(x) = ln(x)/ln(n)

and:

logₙ(x^a) = a*logⁿ(x)

Now let's go to our expression, it is:

log(y^10)

Using the second property we can remove the exponent, then we will get:

log(y^10) = 10*log(y)

Now we can use the first rule, remember that log(x) has a base of 10, then we can write:

10*log(y) = 10*ln(y)/ln(10)

That is the expession expanded.

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The value of the constant term k in the exponential model of the bacteria population is k ≈ 0.0972

An exponential function is one in which the input variable is part of the exponent of the expression for the function.

The function for the population of the bacteria indicates;

[tex]P(t) = \frac{22,000 }{1 + 1.2\cdot e^{(-k\cdot t)}}[/tex]

The population of the bacteria after t = 1 hour is P(1) = 10,532

Therefore;

[tex]P(1) = \frac{22,000 }{1 + 1.2\cdot e^{(-k\times 1)}} = 10,532[/tex]

[tex]1 + 1.2\cdot e^{(-k\times 1)} = \frac{22,000}{10,532}[/tex]

[tex]1.2\cdot e^{(-k\times 1)} = \frac{22,000}{10,532} - 1[/tex]

[tex]e^{(-k\times 1)} = \frac{\frac{22,000}{10,532} - 1}{1.2}[/tex]

Taking the natural logarithm of both sides, we get;

[tex]\ln (e^{(-k\times 1)}) = \ln (\frac{\frac{22,000}{10,532} - 1}{1.2})[/tex]

[tex]\ln (e^{(-k)}) = \ln (\frac{\frac{22,000}{10,532} - 1}{1.2})[/tex]

[tex]\ln (e^{(-k)}) = -k = \ln (\frac{\frac{22,000}{10,532} - 1}{1.2})[/tex] ≈ -0.0972 (rounded to 4 decimal places)

-k ≈ -0.0972

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