12 Work out an expression for the nth term for each sequence.b,20,19.8,19.6,19.4​

The number of tablets that should be taken each day by the patient who needs Synthroid is 1 tablet.

To find the number of tablets of Synthroid that should be taken, you convert the requirements from micrograms ( μg ) to milligrams ( mg).

1 milligram = 1, 000 micrograms ( μg )

25. 0 μg in milligrams is therefore:

= 25 / 1, 000

= 0. 025 mg

This means that the number of tablet to take is:

= Mg requirement / Mg of tablet

= 0. 025 / 0. 025

= 1 tablet

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The 80th percentile is also known as the upper quartile. To find the 80th percentile for a set of data, you need to first arrange the data in numerical order. The 80th percentile is the value below which 80% of the data falls.

The required details for upper quartile in given paragraph

For example, if you have a set of red blood cell counts for women as follows:

3.4, 3.5, 3.6, 3.7, 3.8, 3.9, 4.0, 4.1, 4.2, 4.3

You can arrange the data in numerical order as follows:

3.4, 3.5, 3.6, 3.7, 3.8, 3.9, 4.0, 4.1, 4.2, 4.3

To find the 80th percentile, you need to find the value below which 80% of the data falls. In this case, 80% of the data is 8 values, so the 80th percentile is the 8th value in the list, which is 4.1.

Therefore, the 80th percentile for the red blood cell counts for women in this example is 4.1.

The 50th percentile, or median, is the value that divides the data into two equal parts. The 20th percentile, or lower quartile, is the value below which 20% of the data falls.

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Answer:

6.25 seconds

Step-by-step explanation:

Using the the equation

h = 100t − 16t^2

The ball hits the ground, when h = 0, solving below equation:

100t − 16t^2 = 0

4t(25 - 4t) = 0

t = 0 seconds, this is the starting point when ball was hit

25 - 4t = 0 ⇒ 4t = 25 ⇒ t= 25/4 = 6.25 seconds later the ball hits the ground

Answer:

x = 16

Step-by-step explanation:

We are given the equation:

\( \displaystyle \large{10x + 8 = 11x - 8}\)

First, subtract both sides by 10x.

\( \displaystyle \large{10x - 10x+ 8 = 11x - 10x - 8} \\ \displaystyle \large{8= x- 8}\)

Then add both sides by 8 to isolate x-term.

\( \displaystyle \large{8 + 8= x- 8 + 8} \\ \displaystyle \large{16 = x}\)

And we're done! The value of x is 16.

Out of the 30, 15 students brought snacks

From the question, we have it that out of the 30 students, only 3/6 bought

The number that brought snacks can be calculated by multiplying the fraction with the number of students

Mathematically, we have this as;

Iris should use an income value of approximately $3,137.50 when making her budget.

When making her budget as a freelancer, Iris should use an income value that reflects her average earnings over the past four months. By calculating the average income, Iris can have a more stable and reliable estimate for her budget planning.

To determine the average income, Iris needs to add up the total income earned over the four months and divide it by the number of months. Summing up the income values, we get:

$2700 + $4600 + $3550 + $1700 = $12,550

Next, dividing the total income by four (the number of months), we find:

$12,550 / 4 = $3,137.50

Therefore, Iris should use an income value of approximately $3,137.50 when making her budget. This average value allows her to account for fluctuations in her monthly income and provides a more accurate representation of her earning potential.

It is important for Iris to consider her expenses and financial goals when budgeting. By using the average income, she can create a budget that balances her income and expenses, allowing her to allocate funds appropriately for various needs such as bills, savings, investments, and personal expenses.

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The probable question may be:

Iris is a working freelancer and has been tracking her monthly income for the last four months, which are $2700, $4600, $3550, and $1700. What income value should she use when making her budget?

Answer:

gebiz hadi bir ben kusura siz

Step-by-step explanation:

sneidmd

Answer:

Step-by-step explanation:

To solve this you need the Law of sines

a, b, c are the sides opposite to angles A, B and C respectively

Applied to the given triangle we have one side given, the opposite angle to be found.

Answer:c

Step-by-step explanation is va cuz when your multiply:

Answer:

\(\sqrt[6]{2}\left(\cos\left(\frac{3\pi}{4}\right)+i\sin\left(\frac{3\pi}{4}\right)\right)\)

Step-by-step explanation:

The analysis is as attached below.

we have the equation

the parent function is

so

the transformations of the parent function to the given equation are

1) Reflection over x-axis

the rule is

(x,y) -------> (x,-y)

so

2) vertical compress by factor of 3

3) shift down 5

therefore

the answer is

The solution to the differential equation \(2^{\sqrt{x}}\frac{dy}{dx} = cosce(ln(y))\) is,

\(\frac{y sin(ln(y))}{2} - \frac{y cos(ln(y))}{2} = C - \frac{2 ln(2) \sqrt{x} + 2}{ln^2(2)2^{\sqrt{x}}}\).

Any equation with at least one ordinary or partial derivative of an unknown function is referred to as a differential equation.

The given differential equation is \(2^{\sqrt{x}}\frac{dy}{dx} = cosce(ln(y))\).

Now, multiplying both sides by dx we,

\(2^{\sqrt{x}}dy = cosce(ln(y))dx\).

Dividing both sides by \(2^{\sqrt{x}}\) we have,

\(sin(ln(y))dy = \frac{dx}{2^{\sqrt{x}}}\).

\(\[ \int sin(ln(y))dy = \int \frac{dx}{2^{\sqrt{x}}}\).

\(\frac{y sin(ln(y))}{2} - \frac{y cos(ln(y))}{2} = C - \frac{2 ln(2) \sqrt{x} + 2}{ln^2(2)2^{\sqrt{x}}}\).

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Answer:

C

Step-by-step explanation:

The answer is the orange one because pie * radius^2 leads to the area of the circl.e

The dimensions of the room are approximately 5.87 meters by 7.63 meters.

Let's assume the width of the room is "x" meters.

According to the problem, the length of the room is 1.3 times the width, so the length would be 1.3x meters.

The perimeter of a rectangle is calculated by adding the lengths of all four sides. In this case, the perimeter is given as 27 meters.

Perimeter = 2(length + width)

Substituting the values we know:

27 = 2(1.3x + x)

Simplifying:

27 = 2(2.3x)

27 = 4.6x

Dividing both sides by 4.6:

x = 27 / 4.6

x ≈ 5.87

The width of the room is approximately 5.87 meters.

To find the length, we can multiply the width by 1.3:

Length = 1.3 * 5.87 ≈ 7.63

The length of the room is approximately 7.63 meters.

Therefore, the dimensions of the room are approximately 5.87 meters by 7.63 meters.

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Given that 16 families went on a trip and the cost of the trip was Rs. 2,16,352.The amount paid by each family is to be determined by unitary method Hence each family paid Rs.13522

Now, let's solve this by using the method of unitary method. To find the cost of 1 family trip, we will divide the total cost of the trip by the number of families.2,16,352 / 16 = 13,522 So, the cost of the trip per family is Rs. 13,522.Hence, each family paid Rs. 13,522 for the trip.

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Answer:

Step-by-step explanation

1. The total cost of the trip for all 16 families is Rs 2,16,352.
2. To find out how much each family paid, we need to divide the total cost by the number of families: Rs 2,16,352 ÷ 16.
3. When we do the division, we get the result: Rs 13,522.

Now let's check if this result is correct:

1. If each family paid Rs 13,522 for the trip, then the total cost for all 16 families would be: 16 × Rs 13,522 = Rs 2,16,352.
2. This is exactly the same as the total cost given in the problem statement.

So we have shown that each family paid **Rs 13,522** for the trip

Each bag contains 20 pennies and we have 6 such bags.

A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.

From the given information let the number of pennies in each bag is 'x'

and we have 6 such bags.

Therefore, The equation can be formed as,

6(10 + x) = 180.

60 + 6x = 180.

6x = 180 - 60.

6x = 120.

x = 120/6.

x = 20.

So, The number of pennies in each bag is 20.

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SOLUTION

The empirical rule, also referred to as the three-sigma rule or 68-95-99.7 rule, is a statistical rule which states that for a normal distribution, almost all observed data will fall within three standard deviations (denoted by σ) of the mean or average (denoted by µ).

In particular, the empirical rule predicts that 68% of observations falls within the first standard deviation (µ ± σ), 95% within the first two standard deviations (µ ± 2σ), and 99.7% within the first three standard deviations (µ ± 3σ).

The image below shows a sketch of the distribution following the empirical rule

a) 99.7% of the widget lies between 3 standard deviations to the right and left of the mean.

99.7% of the widget lies between 31 oz and 85 oz.

b) The percentage of the widget weights that lies between 40 and 85 ounces is calculated thus:

The answer is 97.35%

c)

The answer is 84%

Answer:

\(x+8=7*10\)

Step-by-step explanation:

Sum of X and 8: \(x+8\)

Product of seven and 10: \(7*10\)

Put them together:

\(x+8=7*10\)

9514 1404 393

Answer:

  12/x^5

Step-by-step explanation:

The fractions are multiplied in the usual way. The applicable rule of exponents is ...

  (x^a)(x^b) = x^(a+b)

__

  \(\dfrac{3}{x^2}\cdot\dfrac{4}{x^3}=\dfrac{3\cdot4}{x^2\cdot x^3}=\dfrac{12}{x^{2+3}}=\boxed{\dfrac{12}{x^5}}\)

Answer:

\(16a^6x^4y^2\)

Step-by-step explanation:

To simplify this expression, use the exponent rule stating that when an exponent is put to an exponent, the exponent values are multiplied (e.g., \((x^2)^2 = x^{2 \cdot 2} = x^4\))

Using that rule, we get:

\((-4x^2ya^3)^2 = (-4)^2 \cdot x^{(2 \, \cdot \, 2)} \cdot y^2 \cdot a^{(3 \, \cdot \, 2)}\).

This can be simplified to

\(16 \cdot x^4 \cdot y^2 \cdot a^6\),

which can be written as:

\(16a^6x^4y^2\)

using the commutative property of multiplication.

Answer:

x = 5

y = 1

Step-by-step explanation:

2x - y = 9

3x + 4y = 19

We multiply the first equation by 4

8x - 4y = 36

3x + 4y = 19

11x = 55

x = 5

Now we put 5 in for x and solve for y

2(5) - y = 9

10 - y = 9

-y = -1

y = 1

Let's Check the answer

2(5) - 1 = 9

10 - 1 = 9

9 = 9

So, x = 5 and y = 1 is the correct answer.

Answer: B

Step-by-step explanation:

Substitution method

solve the equation for Y by putting the variable on the left. -3 = y - 2x would become y = 2x - 3

Plug Y into the top equation. 2(2x - 3) + 6 =4x

4x - 6 + 6 = 4x

Combine like terms

4x - 0 = 4x

4x = 4x

Infinite Solutions

Answer:

  A) (256/3)√2 ≈ 120.68 units³

  B) 64√3 ≈ 110.85 units²

  C 64(1+√3) ≈ 174.85 units²

Step-by-step explanation:

The dimensions used in the usual formulas for area and volume are not given, so it can work reasonably well to start by finding them.

Each face is an equilateral triangle with side length 8, so the slant height is the altitude of that triangle: 8(√3/2) = 4√3.

The height of the pyramid is the vertical leg of a right triangle with hypotenuse equal to the slant height (4√3) and horizontal leg equal to half the base side length. The height is found from the Pythagorean theorem:

  a² +b² = c²

  b = √(c² -a²) = √((4√3)² -4²) = 4√2

The pyramid with all sides of length 8 has height 4√2 and slant height 4√3.

__

The volume is ...

  V = 1/3s²h . . . . . . where s is the side length, and h is the height

  V = 1/3(8²)(4√2) = (256/3)√2 ≈ 120.68 . . . . cubic units

__

The lateral area is the total area of the 4 triangular faces, so is ...

  LA = 4(1/2)(bh) = 2(8)(4√3) = 64√3 ≈ 110.85 . . . . square units

h is the slant height in this formula

__

The total surface area is the sum of the base area and the lateral area. The base area is the square of the side length.

  SA = 8² +64√3 = 64(1+√3) ≈ 174.85 . . . . square units

Given:

Given a figure.

Required: Area of the shaded figure

Explanation:

The shaded figure can be split into two: a rectangle, triangle

The area of the shaded region is the sum of thH area of the triangleeand the area of the rectangie.

First, find the areg of thh triangle.

t of the triangle = 2 units

Base ength of te triangle = 8 units

Area of th triangle

Find the area of the rectangle.

Length of the rectangle = 4 units

Width of the rectangle = 6 units

Area of thereactanle

The expression (1 - x)(125 + 80y) gives us the final cost for Hector after applying the coupon, taking into account the surfboard rental fee and the fee per hour for the surfing classes with the instructor.

(1 - x): This represents the remaining percentage after applying the coupon. If the coupon offers a discount of x percent, then (1 - x) represents the percentage of the total cost that Hector has to pay.

(125 + 80y): This represents the original cost without any discounts or coupons. The term 125 represents the surfboard rental fee, and 80y represents the fee per hour that Hector works with the instructor (where y is the number of hours).

(1 - x)(125 + 80y): Multiplying the two terms together gives us the cost after applying the coupon. The expression (1 - x)(125 + 80y) represents the product of the remaining percentage after the coupon and the original cost.

Therefore, the expression (1 - x)(125 + 80y) gives us the final cost for Hector after applying the coupon, taking into account the surfboard rental fee and the fee per hour for the surfing classes with the instructor.

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Answer:

5/96

Step-by-step explanation:

Fraction used to buy new books = 5/8

Amount for book money = 1/12 of amount of adult novels

Part used for adult movies = 1/12 * 5/8

Part used for adult movies = 5/96

Hence the  part of the budget that went towards buying young adult novels is 5/96

The polynomial with the given zeros is:;

P(x) = (300/108)*x*(x + 1)*(x - 1)*(x - 3/2)

Remember that if a polynomial has the zeros a, b, c, and d, then we can write it as:

P(x) = K*(x - a)*(x - b)*(x - c)*(x - d)

Where K is a coefficient.

Here the zeros are 0, -1, 1, 3/2

Then we can write:

P(x) =K*(x - 0)*(x + 1)*(x - 1)*(x - 3/2)

P(x) =K*x*(x + 1)*(x - 1)*(x - 3/2)

We also know that when x = -3, P(x) = 300

Then we can write:

300 = K*(-3)*(-3 + 1)*(-3 - 1)*(-3 - 3/2)

300 = K*(-3)*(-2)*(-4)*(-9/2)

300 = K*108

300/108 = K

Then the polynomial is:

P(x) = (300/108)*x*(x + 1)*(x - 1)*(x - 3/2)

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Answer:

231.04

Step-by-step explanation:

Answer:

229.14

Step-by-step explanation:

If I am incorrect in my reasoning, please let me know so that I can plan better for my future answers. Have an amazing day.

The distance between the pair of points (-6, -5) and (2, 0) is √89.

To find the distance between the two points (x₁, y₁) and (x₂, y₂), we use the distance formula, according to which the distance d is shown as:

d = √((x₂ - x₁)² + (y₂ - y₁)²).

In the question, we are asked to find the distance between the pair of points (-6, -5) and (2, 0).

We take (x₁, y₁) = (-6, -5), and (x₂, y₂) = (2, 0).

Using the distance formula,

d = √((x₂ - x₁)² + (y₂ - y₁)²),

and substituting the values of x₁, y₁, x₂, and y₂, we get:

d = √((2 - (-6))² + (0 - (-5))²),

or, d = √((2 + 6)² + (0 + 5)²),

or, d = √(8² + 5²),

or, d = √(64 + 25),

or, d = √89.

Thus, the distance between the pair of points (-6, -5) and (2, 0) is √89.

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