If a₁ = 3 and an+1 = (an)² + 1 then find the value of a3.​

Jazmine has 80 quarts of lemonade, which is 5 times the amount Maliha has (16 quarts).

We are given that Maliha has 4 gallons of lemonade. To find out how much lemonade Jazmine has, we need to calculate 5 times the amount Maliha has.

To convert the gallons to quarts, we know that 1 gallon is equal to 4 quarts.

Therefore, Maliha has 4 x 4 = 16 quarts of lemonade.

Now, since Jazmine has 5 times as much lemonade as Maliha, we can calculate Jazmine's amount by multiplying Maliha's amount (16 quarts) by 5.

Jazmine's lemonade = 16 quarts x 5 = 80 quarts.

Hence, Jazmine has 80 quarts of lemonade.

This can be understood as follows:

Maliha's 4 gallons of lemonade can be converted to 16 quarts (4 gallons x 4 quarts/gallon). Jazmine, on the other hand, has 5 times as much lemonade as Maliha.

Therefore, we multiply Maliha's amount (16 quarts) by 5 to find Jazmine's amount, which equals 80 quarts.

It's important to note that 1 gallon is equal to 4 quarts, which is a conversion factor used to convert between the two units of measurement.

By applying this conversion factor, we can determine the amount of lemonade in quarts for both Maliha and Jazmine.

In conclusion, Jazmine has 80 quarts of lemonade, which is 5 times the amount of lemonade Maliha has (16 quarts).

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For any positive number b not equal to 1 and any number or variable n, note that when evaluated, logb(bⁿ) = n.

A positive number is any integer that signifies something other than zero. Positive numbers include natural or counting numbers such as 1,2,3,4,5, fractions such as 3/5 or 232/345, and decimals such as 44.3.

Given logb(bⁿ)  and b is any positive number, not equal to 1 and n is any number

If Logₓ ([tex]y^{z}[/tex]) = z * logₓ (y)

Then

Log[tex]_{b}[/tex] (bⁿ) = n * Log[tex]_{b}[/tex] (b)

If logₓ(y) = log[tex]_{z}[/tex](y) / log[tex]_{z}[/tex](x)

Then

Log[tex]_{b}[/tex] (b) =  log[tex]_{z}[/tex] (b)/log[tex]_{z}[/tex] (b) = 1

Therefore,

Log[tex]_{b}[/tex] (bⁿ)  = n * Log[tex]_{b}[/tex] (bⁿ)

= n x 1

= n

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Full Question:

Although part of your question is missing, you might be referring to this full question:

For any positive number b not equal to 1 and any number or variable n, evaluate the following expression.

logb(b^n) =

with logb being the base

Answer:6??

Step-by-step explanation:

The area of the triangle is 85 square units

The area of a triangle with vertices (x₁, y₁), (x₂, y₂) and (x₃, y₃) is given by:

A =  (1/2) [x₁(y₂ – y₃) + x₂(y₃ – y₁ ) + x₃(y₁ – y₂)]

Where:

B: (x₁, y₁) = (-8, 3)

O: (x₂, y₂) = (5, 4)

X: (x₃, y₃) = (-7, -10)

A =  (1/2) [x₁ (y₂ – y₃) + x₂(y₃ – y₁ ) + x₃(y₁ – y₂)]

A =  (1/2) [-8 (4 – (-10)) + 5(-10 – 3) + (-7)(3 – 4)]

A = (1/2) [-112 - 65 + 7]

A = 85 square units

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The decimal that represents the number of packs of loom bands that Natalie has is 7.57.

We can see that Natalie has 7 full packs of loom bands, which is a total of:

7*100= 700 loom bands

In addition, she has 57 other bands, making a total of:

700+57 =757 loom bands.

Now to find the decimal that represents the number of packs Natalie has, we need to divide the total number of loom bands by 100, since there are 100 bands in each pack. Thus, we have:

757 / 100 = 7.57

Therefore, the decimal that represents the number of packs of loom bands that Natalie has is 7.57.

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Answer:

Step-by-step explanation:

You want the quotient and remainder from division of (6x² +27x +17) by (x +4).

Synthetic division of a polynomial by a monic binomial is an easy way to perform the division without a lot of writing. The attachment pretty well describes the process.

The result is a quotient of 6x +3, and a remainder of 5.

__

Additional comment

A "monic" polynomial is one that has a leading coefficient of 1.

The number at upper left in the synthetic division tableau is the zero of the divisor. Using the negative of the divisor constant means we can add partial products, saving the confusion and error associated with subtraction.

The value of the expression 20 − 9 ÷ m × 2 × n  for m = 3 and n = 2 is 8

From the question, we have the following parameters that can be used in our computation:

20 − 9 ÷ m × 2 × n

The values of m and n are given as

m = 3 and n = 2

Substitute the known values in the above equation, so, we have the following representation

20 − 9 ÷ 3 × 2 × 2

Evaluate the quotient

So, we have

20 − 3 × 2 × 2

Evaluate the products

So, we have

20 − 12

Evaluate the difference

So, we have

8

Hence, the value of the expression is 8

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By using the BODMAS rule, Where

B stands for the bracket, O stands for of, D stands for division, M stands for multiplication, A stands for addition, and S stands for subtraction

so ,now

[tex][45-(25+8)]*18\\[/tex]

[tex][45-33]*18\\=216\\[/tex]

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Answer:

Step-by-step explanation:

[45- (25+8)] X 18 =

[45 - (25 + 8)] × 18 =

[45 - 33] × 18 =

12 × 18 =

216

The setting of a novel is important because it provides the reader with context on the time, place, and environment that the story takes place in.

It aids in setting the tone, showcasing personalities and tensions, and offering hints about the story's message.

One can establish an ambiance or emotional tone in a novel by means of its setting. One illustration can be seen in the book "The Great Gatsby" authored by F. Scott Fitzgerald uses the backdrop of the Jazz Age to generate a feeling of splendor and exhilaration.

The rapid tempo of the book mirrors the busy lives led by the characters, while the opulent festivities and luxurious habits of the affluent are employed to cultivate an air of indulgence and debauchery.

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The full question is:

On the importance of setting in the novel, comment on how it can be used to create a sense of realism, atmosphere, and meaning?

The value of x when the Richter scale rating is 7.9, rounded to the nearest whole number, is approximately 79,432,823.

The formula relating the Richter scale rating (r) and the intensity ratio (x) is r = log(x). To find the value of x when r is 7.9, we can rearrange the formula and solve for x,

x = 10ʳ

Substituting r=7.9 into the formula, we get,

[tex]x = log((10)^{7.9} )[/tex]

Using a calculator, we get,

x ≈ 79432823.09

Rounding this to the nearest whole number, we get,

x ≈ 79432823

Therefore, the value of x when the Richter scale rating is 7.9, rounded to the nearest whole number, is approximately 79,432,823.

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Complete question - What is the value of x when the Richter scale rating is 7.9 round your answer to the nearest

r=log x

r=rating of the earthquakes size on the Richter scale

x=ratio of earthquake intensity to a minimum level of intensity

Answer:

79632 cu ft

Step-by-step explanation:

The volume of a rectangular prism is length x width x height. We are given the values 158 ft by 80 ft by 6.3 ft. All we do is multiply all 3 values by each other, (158)(80)(6.3). The answer after multiplying is 79632 cubic feet.

Answer:

Let's denote the number of football games Tommy started as "f" and the number of baseball games he started as "b."

We're given two pieces of information:

Tommy has started a total of 109 RHS games:

f + b = 109 (Equation 1)

The number of baseball games he started was five less than twice the number of football games he started:

b = 2f - 5 (Equation 2)

We can solve this system of equations to find the value of "f," which represents the number of football games Tommy started.

Substitute Equation 2 into Equation 1:

f + (2f - 5) = 109

Combine like terms:

3f - 5 = 109

Add 5 to both sides:

3f = 114

Divide both sides by 3:

f = 38

Therefore, Tommy started 38 football games.

Step-by-step explanation:

Answer:

Step-by-step explanation:

Tommy started with 71

Answer: To plot ratios and rates as ordered pairs on the coordinate plane, you can follow these steps:

Understand the ratio or rate: Make sure you understand the meaning and value of the ratio or rate you are working with. A ratio compares two quantities, while a rate compares two quantities with different units.

Choose a coordinate system: Set up a coordinate system on the plane with an x-axis and a y-axis. Determine the range of values you want to plot on each axis based on the given ratio or rate.

Determine the values for the axes: Assign the x-axis and y-axis values based on the given ratio or rate. For ratios, you can assign the values of the ratio to the x and y axes directly. For rates, you will need to convert the rate into a ratio by choosing a unit for one of the quantities.

Plot the points: Use the values obtained from step 3 as the x and y coordinates for each ordered pair. Plot the points on the coordinate plane.

Connect the points (if applicable): If you have multiple points, you can connect them with a line to show the relationship between the ratios or rates.

Label the axes and title the graph (if applicable): Add labels to the x and y axes to indicate the quantities being compared. You can also add a title to the graph to describe the relationship being represented.

Step-by-step explanation:

Answer:

[tex]3 {x}^{2} - 15x - 18 = 0[/tex]

[tex] {x}^{2} - 5x - 6 = 0[/tex]

[tex](x + 1)(x - 6) = 0[/tex]

x = -1 or x = 6

The coordinates of the zeroes are (-1, 0) and (6, 0).

The value of the function [tex]\rm f (x) = \frac{18}{6} + 5e^{-0.1x}[/tex] at x = 6 will be 5.744.

Given that:

Function, [tex]\rm f (x) = \frac{18}{6} + 5e^{-0.1x}\ \ or \ \ f (x) = 3+ 5e^{-0.1x}\\[/tex]

A function is an assertion, concept, or principle that establishes an association between two variables. Functions may be found throughout mathematics and are essential for the development of significant links.

The value of the function at x = 6 is calculated as,

[tex]\rm f (x) = 3+ 5e^{-0.1\times 6}\\\\f (x) = 3+ 5e^{-0.6}[/tex]

Simplify the equation further, then we have

f(x) = 3 + 5 · 0.5488

f(x) = 3 + 2.744

f(x) = 5.744

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The value of the product of expression is,

⇒ m⁶n² + 3m³n - 40

We have to given that;

Expression is,

⇒ (m³n + 8) (m³n - 5)

Now, We can product the expression is,

⇒ (m³n + 8) (m³n - 5)

⇒ m⁶n² - 5m³n + 8m³n - 40

⇒ m⁶n² + 3m³n - 40

Thus, The value of the product of expression is,

⇒ m⁶n² + 3m³n - 40

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The area of the given figure is 12/25 cm²

According to the question, one grid represents 1/5 cm.

So, the dimensions of the shown rectangle are as follows:

Length of the rectangle = 4 grids = 4 × 1/5 cm = 4/5 cm

Width of the rectangle = 3 grids = 3 × 1/5 cm = 3/5 cm

As we know that the area of a rectangle is defined as the product of the length and width.

The area of the figure = Length of the rectangle × Width of the rectangle

The area of the figure = 4/5 cm × 3/5 cm

The area of the figure = 12/25 cm²

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The difference of the expression in scientific notation is 1.2 * 10⁸

From the question, we have the following parameters that can be used in our computation:

(5.6 * 10⁸) - (4.4 * 10⁸)

Factor out 10⁸ from the expression

So, we have

(5.6 * 10⁸) - (4.4 * 10⁸) = (5.6 - 4.4) * 10⁸

Evaluate the difference

(5.6 * 10⁸) - (4.4 * 10⁸) = 1.2 * 10⁸

Hence, the difference of the expression in scientific notation is 1.2 * 10⁸

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The probability that exactly 3 of those games were won by the colonies is 25%.

We are given that;

Number of colonies= 4

Number of games= 3

Now,

To find the probability of exactly 3 wins out of 4 games, we can use the binomial probability formula1:

P(X = 3) = nCx * p^x * q^(n-x)

where n is the number of trials (4 games), x is the number of successes (3 wins), p is the probability of success (0.5), q is the probability of failure (1 - p = 0.5), and nCx is the combination of n things taken x at a time.

P(X = 3) = 4C3 * 0.5^3 * 0.5^(4-3) P(X = 3) = (4! / (3! * (4-3)!)) * 0.125 * 0.5 P(X = 3) = (24 / (6 * 1)) * 0.0625 P(X = 3) = 4 * 0.0625 P(X = 3) = 0.25

Therefore, by the probability the answer will be 25%.

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The length of XY in the congruent triangle is 8 units.

'

Two triangles are said to be congruent if pairs of their corresponding sides and their corresponding angles are equal.

Therefore, the triangle XYZ is congruent to the triangle MNL.

Hence,

ΔXYZ ≅ ΔMNL

Therefore,

XY = MN

XZ = ML

YZ = NL

Hence,

XY = MN = 8 units

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The value of the variables will be 90° and 51°, respectively.

It is the close curve of an equidistant point drawn from the center. The radius of a circle is the distance between the center and the circumference.

The angle at the periphery will be 90 degrees if it is made by the largest chord which is the diameter. Then we have

x = 90°

The sum of the angles of the triangle will be 180 degrees. Then the value of 'y' is calculated as,

39° + x + y = 180°

39° + 90° + y = 180°

y = 51°

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The calculated dimensions of the sticker are 11 mm by 5 mm

From the question, we have the following parameters that can be used in our computation:

shape = rectangle

perimeter = 32 mm

Area = 55 square mm

Represent the dimensions of teh sticker with x and y

So, we have

Area = xy

Perimeter = 2(x + y)

substitute the known values in the above equation, so, we have the following representation

xy = 55

2(x + y) = 32

So, we have

xy = 55

x + y = 16

When x = 11 and y = 5, we have

11 * 5 = 55

11 + 5 = 16

Hence, the dimensions of the sticker are 11 mm by 5 mm

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Answer:

p(3) = 16

Step-by-step explanation:

to evaluate p(3) substitute x = 3 into p(x)

p(3) = 0.5(3 - 5)² + 14

      = 0.5(- 2)² + 14

      = 0.5(4) + 14

      = 2 + 14

      = 16

Answer:  C  y-1=7 (x+4)

Step-by-step explanation:

Point slope formula

y - y₁ =  m ( x - x₁ )        Where m= slope and (x₁ , y₁) is your point

Given:

point: (-4, 1); slope: 7

plug in to formula

y -  1 = 7 (x+4)

The average value of f(x) over the interval [-14, 14] is 0.

The average value of the function f(x) = 14 - |x| over the interval [-14, 14] we need to use the formula:

[tex]f_{ave[/tex] = (1/(b-a)) × integral(a to b) f(x) dx

a and b are the limits of integration.

a = -14 and b = 14.

So we have:

[tex]f_{ave[/tex] = (1/(14 - (-14))) × integral(-14 to 14) (14 - |x|) dx

Simplifying the integral get:

[tex]f_{ave[/tex] = (1/28) × integral(-14 to 0) (14 + x) dx + (1/28) × integral(0 to 14) (14 - x) dx

Evaluating the integrals get:

[tex]f_{ave[/tex] = (1/28) × [(14x + (x²)/2)|(-14 to 0) + (-14x + (x²)/2)|(0 to 14)]

[tex]f_{ave[/tex] = (1/28) × [(0 + 98) + (-196 + 98)]

[tex]f_{ave[/tex] = (1/28) × 0

f_ave = 0

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Answer:

32.6

3.26

0.326

Step-by-step explanation:

You could use long division or a calculator to get these quotients (answers to division problems) but, probably you're supposed to see the pattern of how the decimal moves when you divide by 1, 10, 100 (these are powers of 10)

● Divide by 1, decimal does not move

● Divide by 10, the decimal moves left one place

● Divide by 100, the decimal moves left two places

The seagull is approximately 47.86 feet above sea level, and the man's binoculars are approximately 46.25 feet away from the dolphin.

Let's denote the height of the seagull above sea level as "h" and the distance between the man's binoculars and the dolphin as "d."

For the seagull:

We have the angle of elevation as 27 degrees and the distance from the man's binoculars as 94 feet.

Using the tangent function, we can write:

tan(27 degrees) = h / 94

Solving for h, we have:

h = 94 × tan(27 degrees)

For the dolphin:

We have the angle of depression as 46 degrees and the distance from the man's binoculars as 44 feet (lenses level).

Using the tangent function, we can write:

tan(46 degrees) = h / d

Solving for d, we have:

d = h / tan(46 degrees)

Now, let's calculate the values:

h = 94 × tan(27 degrees) ≈ 47.86 feet

d = (47.86 feet) / tan(46 degrees) ≈ 46.25 feet

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To calculate the area of her rectangular quilt, Mrs. Kuhn needs to multiply the length and width of the quilt in inches. Since each quilt square is 4 inches long, the calculation for the area of the quilt is:

Area of quilt = Length of quilt x Width of quilt x (4 inches) ^2

Therefore, the correct calculation for Mrs. Kuhn to determine the area of her quilt is the product of 4 inches times the sum of the length and width of the quilt.