find the first four terms of the infinite series expansion of the given function f(x)=(1 + 2x)^3/2

Using Combination,

Total 12 possible subsets containing three different numbers can be selected from the set {89, 95, 99, 132, 166, 173} so that the sum of the three numbers is even.

We have given a set say S which contains 6 elements, S = {89, 95, 99, 132, 166, 173}

we want to select three numbers from S such that sum of these is even .

To have an even sum with three numbers, we must add either E+O+O, or E + E + E

where O ---> an odd number

E ---> an even number.

Since there are not three even numbers in the given set, case E+E+E is not possible. Thus, we must choose two odd numbers, and one even number.

There are 2 choices for the even number.

There are 4 choices for the first odd number. There are 3 choices for the last odd number. But the order in which we pick these 2 numbers doesn't matter, so this overcounts the pairs of odd numbers by a factor of 2. Thus, we have ⁴C₂ = 4×3/2 = 6 choices for a pair of odd numbers.

In total, there are 2 choices for an even number, and 6 choices for the odd numbers,

Hence, the total of 2×6 = 12 possible choices for a 3-element set that has an even sum.

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Answer:

8

Step-by-step explanation:

Answer:

he has 8 bags of gummy bears

Step-by-step explanation:

if you look at the graph the solution is at (4,8)

where four equals the amount of bags of chocolate he has and eight equals the amount of gummy bears he has

Answer:

100%

Step-by-step explanation:

Since 56/56 employees at the sports shop work part time, that means 100% of them do, or all of them.

Answer:

\(\sf \left(\dfrac{1}{11},\dfrac{3}{11}\right)\)

Step-by-step explanation:

The orthocenter is the point of intersection of the altitudes of a triangle.

(The altitude is the line that passes through the vertex and is perpendicular to the side opposite the vertex).

**Refer to attached diagram**

DC, EA and FB are the perpendicular lines drawn from the three vertices D, E and F.

\(\sf Let\:(x_1,y_1)=D\implies(x_1,y_1)=(1,3)\)

\(\sf Let\:(x_2,y_2)=E\implies (x_2,y_2)= (-1,0)\)

\(\sf Let\:(x_3,y_3)= F\implies (x_3,y_3)=(2,-1)\)

G (x, y) is the intersection point of the three altitudes of the triangle, i.e. the orthocenter.

To find the point of intersection (orthocenter), we need to create linear equations for the altitudes, then equate them to find the point of intersection.

We only need to work with 2 altitudes.

Calculate the slopes of two sides of the triangle.

\(\sf \implies Slope\:of\:EF=\dfrac{y_3-y_2}{x_3-x_2}=\dfrac{-1-0}{2-(-1)}=-\dfrac{1}{3}\)

\(\sf \implies Slope\:of\:DF=\dfrac{y_3-y_1}{x_3-x_1}=\dfrac{-1-3}{2-1}=-4\)

As the slopes of the altitudes are perpendicular to the slopes of the sides:

\(\textsf{Slope of DC}=\sf \dfrac{-1}{\textsf{slope of EF}}=\dfrac{-1}{-\frac{1}{3}}=3\)

\(\textsf{Slope of EA}=\dfrac{-1}{\textsf{slope of DF}}=\sf \dfrac{-1}{-4}=\dfrac{1}{4}\)

Using point D (1, 3) and the slope of DC to create a linear equation for DC using the point-slope form of a linear equation:

\(\sf \implies y-y_1=m(x-x_1)\)

\(\sf \implies y-3=3(x-1)\)

\(\implies \sf y=3x\)

Using point E (-1, 0) and the slope of EA to create a linear equation for EA using the point-slope form of a linear equation:

\(\sf \implies y-y_1=m(x-x_1)\)

\(\sf \implies y-0=\dfrac{1}{4}(x-(-1))\)

\(\sf \implies y=\dfrac{1}{4}x+\dfrac{1}{4}\)

To find the x-value of the point of intersection (the orthocenter), equate the equations and solve for x:

\(\implies \sf 3x=\dfrac{1}{4}x+\dfrac{1}{4}\)

\(\implies \sf \dfrac{11}{4}x=\dfrac{1}{4}\)

\(\implies \sf 11x=1\)

\(\implies \sf x=\dfrac{1}{11}\)

To find the y-value of the point of intersection (the orthocenter), substitute the found value of x into the equation for line DC:

\(\implies \sf y=3\left(\dfrac{1}{11}\right)\)

\(\implies \sf y=\dfrac{3}{11}\)

Therefore, the orthocenter is at point:

\(\sf \left(\dfrac{1}{11},\dfrac{3}{11}\right)\)

The formula L[e^(a+b)t] = (s-a) + ib / ((s-a)^2 + b^2) can be derived using Euler's formula. This can be written as [(s - a) / ((s - a)^2 + b^2)] + [ib / ((s - a)^2 + b^2)], which matches the desired result.

Euler's formula states that e^(ix) = cos(x) + isin(x), where i is the imaginary unit. We can use this formula to express a complex exponential function, e^(a+ib)t, in terms of real trigonometric functions. Starting with e^(a+ib)t, we can rewrite it as e^(at) * e^(ibt). Using Euler's formula, we can express e^(ibt) as cos(bt) + isin(bt). Substituting this back into the equation, we have e^(at) * (cos(bt) + isin(bt)). To find the Laplace transform of this expression, we need to integrate it with respect to t. Since the Laplace transform is defined for positive t values, we assume a > 0. The Laplace transform of e^(at) is given by 1 / (s - a), where s is the complex variable in the Laplace domain. Multiplying the Laplace transform of e^(at) by (cos(bt) + isin(bt)), we obtain (cos(bt) + isin(bt)) / (s - a). To simplify further, we rationalize the denominator by multiplying the numerator and denominator by (s - a) conjugate, which is (s - a) - ib. Expanding the numerator, we have (cos(bt)(s - a) + isin(bt)(s - a)) / ((s - a)^2 + b^2). Rearranging the terms, we get [(s - a)cos(bt) + isin(bt)(s - a)] / ((s - a)^2 + b^2). Finally, separating the real and imaginary parts, we have [(s - a)cos(bt) / ((s - a)^2 + b^2)] + [isin(bt)(s - a) / ((s - a)^2 + b^2)]. This can be written as [(s - a) / ((s - a)^2 + b^2)] + [ib / ((s - a)^2 + b^2)], which matches the desired result.

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Answer:

4x-18

Step-by-step explanation:

-6(-x +  3)–2x

first u expand =6x-18-2x

then u add up the like terms

Answer:

6x+-18-2x

6x+2x+18

8x+18

Step-by-step explanation:

If the cost for 10 ounce of organic blueberry is $2. 70, the cost of 30 ounce of organic blueberry is represented by the equation x = 20y + 2.70 where y is the cost in dollars for one ounce of organic blueberry.

As x is the cost in dollar for 30 ounce of organic blueberry. For y is the cost in dollars for one ounce of organic blueberry, then

x = 30y + c

where c is the fixed cost

We know for 10 ounce of organic blueberry it costs $2.70. That is

2.70 = 10y + c

c = 2.70 - 10y

So x = 30y + 2.70 - 10y

x = 20y + 2.70

-- The question is incomplete, the complete question is as follows--

"The cost for 10 ounce of organic blueberry is $2. 70 which equation can be used to determine x the cost in dollars, for 30 ounces of organic blueberries.?"

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Answer:

Step-by-step explanation:

You can do this using a small equation.

120% x = 96                    Change 120% to a decimal

120/100 * x = 96             Multiply by 100

120x = 96 * 100

120x = 9600                   Divide by 120

x = 9600/120

x =  80

Look what you got. 20% more than 80 is 96. x is smaller than 96.

If you take 20/100 * 80 = 16

if you add 16 to 80, you  get 96

Answer:

x = 80

Step-by-step explanation:

120 % of x = 96

or, 120/ 100 × x = 96 change percentage to 100 and devide

or, 6 / 5 × x = 96

or, 6x / 5 =96. multiply 6 and x

or, 6x = 96 × 5. change devide sign to multiply

or, 6x = 480. multiply

or, x = 480 / 6. change multiply sign to devide

therefore, x = 80

hope this answer will help you.

have a great time

Hey there!

-8/-4

= 8/4

= -8 ÷ -4

= 8 ÷ 4

= 2

Therefore, your answer is:

Option B. 2

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

Since they need to find the weight of their suitcases to make sure they meet airline regulations. the units that they should use Kg.

Airport passengers are often needed to put only at least a single baggage any time in the check-in self-service so that the baggage can be checked and identified.

Note that the Maximum Weight per piece is said to be 50 lb/23 kg and the Maximum Dimensions is said to be 45 linear inches or 115 cm (including the length + width + height)

Therefore, Since they need to find the weight of their suitcases to make sure they meet airline regulations. the units that they should use Kg.

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See full question below

Maria and Jose, students at Mississippi Valley State University, are going to study abroad in Spain. They need to find the weight of their suitcases to make sure they meet airline regulations. What units should they use?

If line CE is 3/8ths of line CD, we can make the equation 3/8x = line CD (which is also, in units, 16). Moving 3/8ths to the other side, we end up with x = 6. Point C is -9, and -9 + 6 = -3. So, Point E is -3.

To solve a first order linear equation, we can use an integrating factor to make the left side of the equation into the product of the integrating factor and the dependent variable. The integrating factor is given by μ(x)=exp(∫p(x)dx).

Given the equation xy′+(1+4x)y=10x^2−4x, we can find the integrating factor by first identifying p(x) and then finding the integral of p(x). In this case, p(x)=-(1+4x)/x. So, the integrating factor is:

μ(x)=exp(∫-(1+4x)/xdx)=exp(-∫(1/x)dx-∫(4)dx)=exp(-ln|x|-4x)=x^(-1)e^(-4x)

Now we can multiply both sides of the equation by the integrating factor to get:

x^(-1)e^(-4x)(xy′+(1+4x)y)=10x^2e^(-4x)−4xe^(-4x)

This simplifies to:

(ye^(-4x))′=10x^2e^(-4x)−4xe^(-4x)

Now we can integrate both sides of the equation to find the general solution:

ye^(-4x)=∫(10x^2e^(-4x)−4xe^(-4x))dx+C

Using integration by parts and the arbitrary constant C, we can find the general solution:

y(x)=e^(4x)(-5/8x^2e^(-4x)-1/4xe^(-4x)+1/16e^(-4x)+C)

To solve the initial value problem with y(1)=3−4, we can plug in the initial values and solve for the arbitrary constant C:

3−4=e^(4)(-5/8e^(-4)-1/4e^(-4)+1/16e^(-4)+C)

-1=(-5/8-1/4+1/16)+Ce^(4)

C=(-1+5/8+1/4-1/16)e^(-4)=(-1/8)e^(-4)

So the solution to the initial value problem is:

y(x)=e^(4x)(-5/8x^2e^(-4x)-1/4xe^(-4x)+1/16e^(-4x)+(-1/8)e^(-4))

Using the properties of exponents, we can simplify the solution to get:

y(x)=-5/8x^2-1/4x+1/16+(-1/8)e^(4x-4)

This is the solution to the initial value problem.

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a)The radius of convergence is R = |-2 - (-πi)| = |-2 + πi| = √(2^2 + π^2) ≈ 3.146.b)The radius of convergence is R = |1 + i - i| = |1| = 1. c)The radius of convergence is R = |1 + i - i| = |1| = 1.

The radius of convergence of a Taylor series centered at a point z0 is the distance from z0 to the nearest singularity of the function.

(a) The function sinz/e^z has singularities at z = kπi for any integer k, and the nearest singularity to z0 = -2 is at z = -πi. Therefore, the radius of convergence is R = |-2 - (-πi)| = |-2 + πi| = √(2^2 + π^2) ≈ 3.146.

(b) The function 1/cosz' has singularities at z = (k + 1/2)π for any integer k, which are equidistant from z0 = 0. Therefore, the radius of convergence is R = π/2.

(c) The function z^2+1/(z−i) has a singularity at z = i, which is the nearest singularity to z0 = 1 + i. Therefore, the radius of convergence is R = |1 + i - i| = |1| = 1.

Note that these radii of convergence only guarantee convergence within the radius; the series may converge or diverge at the boundary.

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Answer:

B

Step-by-step explanation:

Answer:

25/6 pizzas are needed. (4 1/6)

Step-by-step explanation:

25 x 1/6 is 4 1/6

Answer:

the square root of 1 is 1. hope this helps

Answer:

70 ft²

Step-by-step explanation:

ratio of their same side is 6/10 = 3/5

area ratio will be square of this so,

are of small traingle will be,

195 × (3/5)²= 195 × 9/25= 70.2

Answer:

-------------------------

Use the formula for standard deviation:

where:

From the question, we know that Maya's height is 52 inches, which is 1 standard deviation below the mean.

Plug in these values into the formula and solve for μ:

Therefore, the mean height for females is 55 inches.

according to question the mean height is 55 inches.

We know that Maya's height, 52 inches, is 1 standard deviation below the mean. Let's use the formula for standard deviation to write an equation:

z = (x - μ) / σ

where z is the number of standard deviations from the mean, x is the height of the person (in this case, Maya's height), μ is the mean height, and σ is the standard deviation.

We know that z = -1 (since Maya is 1 standard deviation below the mean), x = 52, and σ = 3. Plugging these values into the equation, we get:

-1 = (52 - μ) / 3

Multiplying both sides by 3, we get:

-3 = 52 - μ

Subtracting 52 from both sides, we get:

-55 = -μ

Dividing both sides by -1, we get:

μ = 55

what is number?

A number is a mathematical object used to represent quantity, value, or magnitude. It can be represented in many ways, such as numerals, words, or symbols. Numbers can be classified into various types, such as natural numbers, whole numbers, integers, rational numbers, and irrational numbers, depending on their properties and characteristics. In mathematics, numbers are used for various purposes, such as counting, measuring, computing, and solving problems in various fields, such as science, engineering, economics, and statistics.

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The values of a and b for the probability density function are a = 56 and b = 216.

According to the given information, the mean daily spending by Americans earning over $90,000 per year was $136 per day, and the probability density function is given by f(x) = 0.00625 for a ≤ x ≤ b.

To find the values of a and b for the probability density function, we can use the formula for the mean of a uniform distribution:

mean = (a + b)/2

Substituting the given mean value of $136 into the formula, we get:

136 = (a + b)/2

Multiplying both sides of the equation by 2, we get:

272 = a + b

Rearranging the equation, we get:

b = 272 - a

Now, we can use the formula for the area under the probability density function, which is equal to 1:

∫_a^b f(x) dx = 1

Substituting the given probability density function and the value of b into the formula, we get:

∫_a^(272-a) 0.00625 dx = 1

Simplifying the integral, we get:

0.00625(272 - 2a) = 1

Dividing both sides of the equation by 0.00625, we get:

272 - 2a = 160

Rearranging the equation, we get:

2a = 112

Dividing both sides of the equation by 2, we get:

a = 56

Substituting the value of a back into the equation for b, we get:

b = 272 - 56 = 216

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Step-by-step explanation:

\(x - 6 < - 4\)

\(x - 6 + 6 < - 4 + 6\)

\(x < 2\)

Answer:

NO

Step-by-step explanation:

\(4x^{2} -4x+1=0\\(2x-1)(2x-1)=0\\x=1/2\)

Answer:

AB= 94

Step-by-step explanation:

43+43= 86

180-86= 94

The solution of the system of equations is \(\[x=3,\text{ }y=0,\text{ and }z=2\]\).

As per data the system of linear equations,

\(\[ \left\{\begin{array}{c} x+2 y+3 z=9 \\ 2 x-y+z=8 \\ 3 x-z=3 \end{array}\right. \] 1)\)

Write the system in the matrix form \(\( A . X=B \)\)

We know that the matrix form of the system of linear equations is as follows.

\(\[A. X = B\]\)

Where

\(\[A=\begin{pmatrix} 1 & 2 & 3 \\ 2 & -1 & 1 \\ 3 & 0 & -1 \end{pmatrix}\[X=\begin{pmatrix} x \\ y \\ z \end{pmatrix}\]\)

and

\(\[B=\begin{pmatrix} 9 \\ 8 \\ 3 \end{pmatrix}\]2)\)

To solve the system, we can use row reduction method.

\(\[\begin{pmatrix} 1 & 2 & 3 & 9 \\ 2 & -1 & 1 & 8 \\ 3 & 0 & -1 & 3 \end{pmatrix}\]\)

Applying the elementary row operations

\(\[R_{2}\to R_{2}-2R_{1}\]\)

and

\(\[R_{3}\to R_{3}-3R_{1}\]\)

we get,

\(\[\begin{pmatrix} 1 & 2 & 3 & 9 \\ 0 & -5 & -5 & -10 \\ 0 & -6 & -10 & -24 \end{pmatrix}\]\)

Now applying the elementary row operations

\(\[R_{3}\to R_{3}-(6/5)R_{2}\]\)

we get,

\(\[\begin{pmatrix} 1 & 2 & 3 & 9 \\ 0 & -5 & -5 & -10 \\ 0 & 0 & -1 & -2 \end{pmatrix}\]\)

Now, we need to apply back substitution method. Using the third row, we can get the value of z as z = 2.

Now, using the second row,

\(\[-5y - 5z = -10\]\\\-5y - 5(2) = -10\]\)

Solving this equation, we get y = 0.

Finally, using the first row, we can get the value of x as

\(\[x + 2y + 3z = 9\]\\x = 3\]\)

Hence, the solution of the system of equations is \(\[x=3,\text{ }y=0,\text{ and }z=2\]\).

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The coin is flipped at least 52 times in order to obtain a 99% confidence interval of width of at most . 18 for the probability of flipping a head.

Hence, Option F is correct answer.

In a sample with a number n of people surveyed with a probability of a success of π , and a confidence level of (1-α), we have the following confidence interval of proportions.

\(\pi\) ± z\(\sqrt{\frac{\pi \p(1-\pi )}{n} }\)

z is the z-score that has a pvalue of \(1-\frac{\alpha }{2}\)

Since, the coin is fair, so \(\pi =0.5\).

The margin of error is:

\(M=z\sqrt{(\frac{\pi (1-\pi )}{n} )}\)

99% confidence level:

So \(\alpha =0.01\) ,z is the value of Z that has a p value of 1-\(\frac{0.01}{2}\)=0.995,

so Z= 2.575

We have to flip the coin in order to obtain a 99% confidence interval of width of at most 18 for the probability of flipping a head at least n times.

n is found when M=0.18 .

So

M=\(z\sqrt{\frac{\pi (1-\pi )}{n} }\)

\(0.18=2.575\sqrt{\frac{0.5*0.5}{n} }\)

\(0.18\sqrt{n} =2.575*0.5\)

\(\sqrt{n}=\frac{2.575*0.5}{0.18}\)

\(\sqrt{n} ^{2} =(\frac{2.575*0.5}{0.18} )^{2}\)

n = 51.16

Thus, we have to flip the coin at least 52 times.

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Answer: 1/6

Step-by-step explanation: Have a blessed day

The maximum clearance of the underpass ahead is 12 feet and 6 inches.

Based on the information provided, the sign indicates that there is an underpass ahead with a clearance of 12 feet and 6 inches. The sign further mentions that the train in question is also 12 feet and 6 inches long, and it highlights the presence of a narrow median, which is only 6-12 inches wide.

In this context, the sign serves as a warning to drivers approaching the underpass. The clearance measurement of 12 feet and 6 inches informs drivers of the maximum height of vehicles that can safely pass through the underpass without any risk of collision. Since the train length matches the clearance, it implies that vehicles longer than the underpass clearance may not be able to pass through safely if the train is present.

The mention of a narrow median emphasizes the limited space available between the opposing lanes of traffic. With a width of only 6-12 inches, the median may not provide sufficient room for larger vehicles to maneuver, particularly when encountering oncoming traffic or passing through the underpass while the train is present.

Overall, the sign conveys important information regarding the underpass clearance, the train length, and the narrow median, all of which should be considered by drivers to ensure safe passage through the upcoming area.

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The sign indicates the clearance height of an underpass, warns of a narrow median, and mentions the length of a train.

The sign in question is indicating that there is an underpass ahead with a clearance of 12 feet and 6 inches. This means that any vehicle taller than that would not be able to pass through without hitting the underpass ceiling. Additionally, the sign mentions that the train itself is also 12 feet and 6 inches long, so it is important for drivers to be cautious and aware of the height restrictions. The narrow median mentioned refers to the strip of land or barrier between lanes, which in this case is only 6-12 inches wide.

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The volume of the pyramid is B) 192ft

The volume of a pyramid can be calculated utilizing the condition:

V = (1/3) * base region * height...........(1)

In the case of a square pyramid, the base area is given by the condition:

base area = (edge length)²

Thus, in this issue, we have:

base area = (6 ft)² = 36 ft²

height = 16 ft (given)

Substituting these values into the condition for the volume of a pyramid ( equation (1) ), we get:

V = (1/3) * 36 ft² * 16 ft

V = 192 cubic feet

In this way, the volume of the pyramid is 192 cubic feet.

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The function f(x) = -√(x - 4) is a power function but not a polynomial.

To find whether the function f(x) = -√(x - 4) is a power function, a polynomial, both, or neither.

The function f(x) = -√(x - 4) is a power function since it can be written in the form f(x) = x^n, where n is a real number. In this case, n = 1/2, so the function is f(x) = -(x - 4)^(1/2).

However, f(x) = -√(x - 4) is not a polynomial because polynomials are functions with the form f(x) = a_nx^n + a_(n-1)x^(n-1) + ... + a_1x + a_0, where a_n, a_(n-1),..., a_1, and a_0 are constants and n is a non-negative integer. Since the exponent in f(x) = -√(x - 4) is 1/2 (a non-integer), it is not a polynomial.

In conclusion, f(x) = -√(x - 4) is a power function but not a polynomial.

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