pls help i will give 20 points

a) The binomial expansion of (1+12x)^1/2 is given by:

(1+12x)^1/2 = 1^1/2 + (1/2)(1^-1/2)(12x) + (1/2)(1^-1/2)(-1/2)*(12x)^2 + ...

Binomial expression: what is it?

A polynomial with only terms is a binomial. An illustration of a binomial is x + 2, where x and 2 are two distinct terms. Additionally, in this case, x has a coefficient of 1, an exponent of 1, and a constant of 2. As a result, a binomial is a two-term algebraic expression that contains a constant, exponents, a variable, and a coefficient.

The first four terms, in ascending powers of x, are:

1, (1/2)(12x), (1/8)(12x)^2, (1/16)*(12x)^3

b) To use x=1/36 in the expansion, you would substitute x=1/36 into the expansion, and keep only the terms up to x^3 (the fourth term in the expansion). This will give an approximation of the value of (1+12x)^1/2 when x=1/36.

This will be an approximation of √12 because x=1/36 corresponds to 12x = 1 and the initial value of the expansion is 1 + 12x .

We can use this approximation to approximate square root of 12 and also for other square roots by using appropriate x values.

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The percent discount is 18%.

Now, According to the question:

Based on the given condition:

Formulate:

(34 - 27.88) ÷ 34

Calculate the sum or difference:

= 6.12/34

Convert decimal into fraction:

[tex]=\frac{612}{\frac{100}{34} }[/tex]

Divide a fraction by multiplying its reciprocal:

[tex]\frac{612}{100}[/tex] × [tex]\frac{1}{34}[/tex]

Write as a single fraction:

= 612/ (100 × 34)

Cross out the common factor:

= 18/100

= 9/50

Multiply a number to both numerator and denominator:

[tex]\frac{9}{50}[/tex] × [tex]\frac{2}{2}[/tex]

= 18/100

Rewrite a fraction with denominator equals 100 to a percentage: 18%

Hence,  the percent discount is 18%.

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The next time that they have an appointment start at the same time is at  10:50 a.m.

Now, According to the question:

Ist Step

For the same time, take LCM of 20 and 35.

20 = 2 × 2 × 5

35 = 5 × 7

IInd Step

HCF (20, 35) = 2 × 2 × 5 × 7

HCF (20, 35) = 140

Hence, it will take the appointment after 140 minutes which equals to 2 hours 20 minute.

Now, from 8.30 am, the addition of the 2 hours 20 minute gives us 10:50 a.m. which is the next time that they have an appointment start at the same time.

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288 m³ is The Volume Of The Pyramid.

The space occupied inside an object's borders in three dimensions is referred to as its volume. It is sometimes referred to as the object's capacity.

Given, The base of the pyramid shown has a length of 9m and a width of 8m. The height of the pyramid is 12m.

Since, The Formula for the volume, V , of a pyramid is V = 1/3Bh ,

where B is the area of the base of the pyramid and h is the pyramid's height.

Since, Area of rectangle = Width *height

Thus, Area of the base = 9 * 8

Area of the base = 72 m²

So, the volume of pyramid (V) =  1/3Bh

the volume of pyramid (V) = 1/3 * 72 * 12

the volume of pyramid (V) =  288 m³

therefore, The Volume Of The Pyramid is 288 m³.

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The two mathematical expressions can be written as:-

2) . [ 23 + ( 14 ÷ 2 ) - 20 ] = 5

3) . [ 9² - ( 8 x 4 ) + 26 ] = 75

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

The two expressions will be solved as:-

For the first problem, the numbers are 23,2,14, and 20. The expression will be written as:-

[ 23 + ( 14 ÷ 2 ) - 20 ] = 5

[ 23 + 2- 20 ] = 5

[ 25 - 20 ] = 5

5 = 5

The numbers for the second expression are 8,26,9 and 4. The expression can be written as:-

[ 9² - ( 8 x 4 ) + 26 ] = 75

[ 81 - 32 + 26 ] = 75

[ 49 + 26 ] = 75

75 = 75

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The median of a sample will always equal the 50th percentile.

The median is the value in the middle of a data set, which means that 50% of the data points have a value less than or equal to the median, and 50% of the data points have a value greater than or equal to the median. The statistical median is the number in the middle of a series of numbers. To find the median, sort each number by size; the number in the middle is the median. The median is the value in the middle of a set of data. First, organize and sort the data in ascending order from smallest to largest. Divide the number of observations by two to find the midpoint value. If there are an odd number of observations, round that number up to the nearest whole number, and the value in that position is the median.

Here,

A sample's median will always equal the 50th percentile.

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Debts, or other outstanding bills or loans that must be repaid are called option B: Liabilities.

What is Debt?

Debt can be defined as the sum that the borrower owes the lender. A debt is an amount of money that has been borrowed for a set period of time and must be repaid, plus interest.

A liability is a debt that a person or business has, typically in the form of money. Through the transmission of economic benefits like money, products, or services, liabilities are eventually satisfied.

Liabilities are items that are listed on the balance sheet's right side and consist of debts including loans, accounts payable, mortgages, deferred income, bonds, warranties, and accumulated expenses.

Therefore, debts are a form of liability.

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Answer:

x = 2

Step-by-step explanation:

2x + 8 = -3.5x+19

2x = -3.5x + 11

5.5x = 11

x = 2

Let's check

2(2) + 8 = -3.5(2) + 19

4 + 8 = -7 + 19

12 = 12

So, x = 2 is the only correct answer.

Answer: (x + 3)^2 + (y + 8)^2 = 14pi^2

(x-h)^2 + (y-k)^2 = r^2

Step-by-step explanation:

( x1 + x2 /2 , y1 + y2 / 2 )

= ( -7 + 7 / 2 , 0 + 7 / 2 )

= ( 0, 3.5 )

Answer:

Slope:3/4

y-int: (0,5)

Step-by-step explanation:

Slope:

3x-4y=20

-3x        -3x

-4y=-3x+20

/-4     /-4

y=3/4x+5

So 5 would be y-int

A plausible lurking variable that could explain the cause and effect in the headline "Is Gluten the Culprit in Our Fight Against Obesity?" is overall diet.

It's possible that individuals who consume a diet high in gluten also consume a diet high in overall calories and processed foods, leading to weight gain and obesity. This would mean that it is not specifically gluten causing the obesity, but rather a combination of factors in the individual's diet.

A lurking variable is a variable that has a connection (e.g., may be correlated) with the response and the explanatory variable but is neither the explanatory variable nor the response variable.

Although it is not taken into account in the study, it might affect how the variables are related.

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Answer:

D is the one trust me man I do this all the time and good luck on your exam

Answer: To find r'(1), we need to use the chain rule of differentiation, which states that:

r'(x) = f'(g(h(x))) * g'(h(x)) * h'(x)

In this case, we know that:

h(1) = 2, g(2) = 4, h'(1) = 4, g'(2) = 4, and f '(4) = 7

Therefore:

r'(1) = f'(g(h(1))) * g'(h(1)) * h'(1) = f'(g(2)) * g'(2) * h'(1) = 7 * 4 * 4 = 112

So, the derivative of r(x) with respect to x at x = 1 is 112

Step-by-step explanation:

The expression using brackets is (3x)(x⁴) + (2)(2) = 26

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

7x5-4x5+16÷4=26

Express the superscripts in the expression properly

So, we have the following representation

7x⁵ - 4x⁵ + 16 ÷ 4 = 26

Evaluate the like terms

3x⁵ + 16 ÷ 4 = 26

Divide 16 by 4

3x⁵ + 4 = 26

Factorize and use brackets

(3x)(x⁴) + (2)(2) = 26

Hence, the expression is (3x)(x⁴) + (2)(2) = 26

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The size of each angle to draw the pie chart is given as follows:

The size of each angle in this problem is found applying the proportions.

First we obtain the relative frequency of each item, dividing the absolute frequency by 40.

Then we obtain the angle size, multiplying the relative frequency by 360º, which is the angle measure of the entire circumference of the pie chart.

Then the angle measures are obtained as follows:

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As per the unitary method, Gordon is correct because the Gordon would charge more than Ironing Palace

In math the term unitary method is defined as the value of a single unit and then find the value of more or fewer units by multiplying their quantity with the value of a single unit.

Here we have given that the total weight of these shirts is 9. 5 kg.

And here we have also given that each shirt weighs 190 g.

And Gordon charges £38 to iron these shirts.

And the charges in the Ironing Palace is 90p for each.

Here we have to use the unitary method to calculate the values for each of them,

The Total cost for Gordon is calculated as,

=> 38 x (9.5 / 0.19)

=> 1900

And the total cost for Ironing Palace is calculated as,

=> 90 x 9.5

=> 855

Therefore, while we looking into the values we have identified that Gordon is correct.

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Answer: The distance between the points (-4,7) and (-4,-5) is 12.

Step-by-step explanation:

To calculate the distance between two points, we apply the following formula:

[tex]\huge \boxed{\sf{d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2} }}[/tex]

The points are:

To solve the process is:

We substitute the points in the previous formula given, then

[tex]\huge \boxed{\sf{d=\sqrt{(-4-(-4))^2+(-5-7)^2 } }}[/tex]

[tex]\huge \boxed{\sf{d=\sqrt{0^2+(-12)^2 }=\sqrt{0+144} }}[/tex]

[tex]\huge \boxed{\sf{d=\sqrt{144}=12 }}[/tex]

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Joint and 2/3 survivor means that if the insured passes away, two of the beneficiaries will receive two-thirds of the insurance benefits, and the remaining third will be divided among all three beneficiaries.

Joint and 2/3 survivor is a settlement option for life insurance policies which means that when the insured passes away, two of the beneficiaries will receive two-thirds of the death benefits, while the remaining third will be divided equally among all three beneficiaries. This is beneficial because it ensures that two of the beneficiaries will receive the majority of the death benefits, while the remaining third will be split equally among all three. This provides a more secure financial future for the two beneficiaries receiving the most money as well as allowing the remaining third to be split equally, providing more financial security for all beneficiaries.

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The solution to the inequality |2x + 3| < 7 is x < 2 or x > -5.

What is inequality?

An inequality is a statement that compares two expressions and asserts that one is greater or less than the other. It can be represented using mathematical symbols such as <, >, ≤, ≥, ≠.

|2x + 3| < 7 is a type of absolute value inequality. The absolute value of a number is its distance from zero on the number line, and is always positive. So, |2x + 3| is the absolute value of 2x + 3, which is always greater than or equal to zero.

To solve this inequality, we need to consider two cases:

If 2x + 3 is greater than or equal to zero, we can drop the absolute value bars and solve the inequality as is:

2x + 3 < 7

2x < 4

x < 2

If 2x + 3 is less than zero, we need to reverse the inequality sign:

-2x - 3 < 7

-2x < 10

x > -5

Hence, the solution to the inequality |2x + 3| < 7 is x < 2 or x > -5.

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[tex]2~~,~~\stackrel{2\cdot \frac{5}{2}}{5}~~\stackrel{5\cdot \frac{5}{2}}{\cfrac{25}{2}}~~,~~...\hspace{5em}\stackrel{\textit{common ratio}}{r=\cfrac{5}{2}} \\\\[-0.35em] ~\dotfill\\\\ n^{th}\textit{ term of a geometric sequence} \\\\ a_n=a_1\cdot r^{n-1}\qquad \begin{cases} a_n=n^{th}\ term\\ n=\textit{term position}\\ a_1=\textit{first term}\\ r=\textit{common ratio}\\[-0.5em] \hrulefill\\ a_1=2\\ n=9\\ r=\frac{5}{2} \end{cases}[/tex]

[tex]a_9=2\left( \frac{5}{2} \right)^{9-1}\implies a_9=2\left( \frac{5}{2} \right)^8\implies a_9=2\left( \cfrac{390625}{256} \right) \\\\\\ a_9=\cfrac{390625}{128}\implies {\Large \begin{array}{llll} a_9=3051\frac{97}{128} \end{array}}[/tex]

Answer:

8 square units

Step-by-step explanation:

For a triangle,

area = base × height / 2

We need to identify a base and a height for this triangle, and then use them in the area formula above.

Use BC as the base.

A height of a triangle is usually inside the triangle, but not always.

The height of a triangle is a segment that is perpendicular to the a side, or the line containing a side, and intersects the opposite vertex.

In this case, for base BC, the height is a segment from point (-2, 2) to point A.  The length of the height is 4.

area = 4 × 4 / 2

area = 8 square units

The single discount of 45% is better than the successive discount of 30% and 20%.

Let us assume that the Maximum retail price = 100x

As in case 1,

The percentage discount is given as 45%

So, the value of the selling price of the item will be = (100-45)% of 100x

=55% of 100x = 55x ------(i)

Now in case 2,

The successive discount of 30% and 20% is given.

So, let us assume that the Maximum retail price = 100x

So, after giving the discount of 30%

The value of the selling price will be = (100-30)% of 100x

=70% of 100x = 70x

Now again giving the discount of 20%

Then the value of new selling price will be = (100-20)% of 70x

=80% of 70x = 56x ------(2)

In case (1) the selling price is 55x while in case 2 the selling price is 56x.

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It depends on the price of the article. A 45% single discount will always result in a larger price reduction than a 30% discount followed by a 20% discount on the same price.

However, the overall savings from the two different discount schemes may be the same if the price of the article is high enough. To determine which discount scheme is better, it is necessary to know the price of the article and calculate the total savings under both schemes.

For instance: For example, if we are considering the price of an article is Rs 100, then the successive percentage would be 30% and 20% for the discount, the price falls to Rs 56, whereas with a single 45%discount, the amount comes to Rs55.

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Answer:

Step-by-step explanation:

the new one will tell you be

The probability that exactly 14 adults have been vaccinated 0.49

Probability is a measure of the likelihood of an event to occur. Many events cannot be predicted with total certainty. We can predict only the chance of an event to occur i.e., how likely they are going to happen, using it. Probability can range from 0 to 1, where 0 means the event to be an impossible one and 1 indicates a certain event

the national center for health statistics (nchs) reports that 70% of us adults aged 65 and over have ever  vaccination

the pneumococcal vaccination rate applies to an independent random sample of 20 us adults aged 65

the probability that exactly 14 adults have been vaccinated

(14/20)*(70/100)

0.49

The probability that exactly 14 adults have been vaccinated 0.49

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Answer: the second, third and fifth options.

Step-by-step explanation:

When an equation is set up in a y=mx+b format, the slope is always equal to the value m.

The length of PQ in terms of MO if ∠POQ = 120° is PQ = -x * √3/3.

Let MO = x.

Since MO is perpendicular to plane α, MP and MQ form right angles with MO.

Using the Pythagorean Theorem, we have:

MP = x * tan(30°) = x * √3/3

MQ = x * tan(60°) = x * √3

Since ∠POQ = 120°, we have:

PQ = MP * 2 * cos(120°)

= 2 * x * √3/3 * -1/2

= -x * √3/3

Therefore, the length of PQ in terms of MO is PQ = -x * √3/3.

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The area of the trapezoid is 42.5 m².

A trapezium is a quadrilateral with four sides where two sides are parallel to each other.

We have,

Trapezoid:

Short base = 3 m

Height = 5 m

Large base.

= 4 + 3 + 7

= 14 m

Now,

Area of a trapezoid.

= 1/2 x (Short base + Large base) x h

= 1/2 x (3 + 14) x 5

= 1/2 x 17 x 5

= 42.5 m²

Thus,

Trapezoid area is 42.5 m².

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According to Bernoulli's theorem, the success rate for the situation is 0.7173.

In math Bernoulli's theorem is states that that random experiment with exactly two possible outcomes, "success" and "failure" in which the probability of success is the same every time the experiment is conducted.

In order to calculate p we must sum the possible permutations of getting 0 success of 10 trials, 1 success of 10 trials, and 2 successes of 10 trials, and divide this sum by the total possible subsets from 10 elements, then it can be written as,

=> P = (10 1) (10 2) (10 1) / 2¹⁰

When we simplify this one, then we get,

=> P = 56/1024

=> P = 0.0547

When we apply the value on Bernoulli's theorem, then we get,

=> B(340, 0.0547, 0) = ( 340 0 ) x (1/1024) x (1023/1024)³⁴⁰

When we simplify this one then we get,

=> B = 0.7173

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