is this relation a function?

The sum of the first 4 terms of the binomial expansion of (0.9 + 0.081)³ is approximately 0.9441.

The binomial expansion formula is given by:

[tex](a + b)^n = nC_0 \times a^n \times b^0 + nC_1 \times a^{(n-1)} \times b^1 + nC_2 \times a^{(n-2)} \times b^2 + ... + nC_n \times a^0 \times b^n[/tex]

where nCk is the binomial coefficient, which is equal to n! / (k! * (n-k)!) for k = 0, 1, 2, ..., n.

Here, we have a = 0.9 and b = 0.081, and we want to find the sum of the first 4 terms, which means we need to find:

(0.9 + 0.081)⁰ + (0.9 + 0.081)¹ + (0.9 + 0.081)² + (0.9 + 0.081)³

Using the binomial expansion formula with n = 3, we get:

(0.9 + 0.081)³ = 3C0 x 0.9³ x 0.081^0 + 3C1 x 0.9² x 0.081¹ + 3C2 x 0.9¹ x 0.081² + 3C3 x 0.9⁰ x 0.081³

Simplifying each term, we get:

1 x 0.729 x 1 + 3 x 0.81 x 0.081 + 3 x 0.9 x 0.006561 + 1 x 0.000531441

= 0.729 + 0.19683 + 0.0177117 + 0.000531441

= 0.944076141

Therefore, the sum of the first 4 terms of the binomial expansion of (0.9 + 0.081)³ is approximately 0.9441 (rounded to 4 decimal places).

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Answer:

ok

Step-by-step explanation:

later

On solving the provided question we can say that by percentage y = $1900(77/100)t

A percentage in mathematics is a figure or ratio that is stated as a fraction of 100. The abbreviations "pct.," "pct," and "pc" are also occasionally used. It is frequently denoted using the percent symbol "%," though. The amount of percentages has no dimensions. With a denominator of 100, percentages are basically fractions. To show that a number is a percentage, place a percent symbol (%) next to it. For instance, if you correctly answer 75 out of 100 questions on a test (75/100), you receive a 75%. To compute percentages, divide the amount by the total and multiply the result by 100. The percentage is calculated using the formula (value/total) x 100%.

In 2005, a laptop computer was purchased for 81900. Each year since, the resale value has decreased by 23%. Let t be the number of years since Let Y be the value of the laptop computer, in dollars. Write an exponential function showing the relationship between Y and

t. value of laptop in 2005 81900 decrease in resale \/aIUe each year

23 77% resale value of laptop after each year = 100

resale value after one x $1,900

Now, Hence relation between value of the laptop computer and time is

y = $1900(77/100)t

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Answer: 20% of the class is girls.

6/30 = 0.2

0.2=20%

Answer:8

Step-by-step explanation:

100*0.08

you would buy 8 cupcakes

Answer:

1960g remaining

Step-by-step explanation:

2kg=total amount of tea

40g=amount of tea taken

Thus, covert 2kg to gram

2×1000=2000g

amount of tea remaining=total amount of tea –amount of tea taken

x=2000–40

x=1960g remaining

With a constant speed Robert took 20 minutes paddle.

The speed formula can be defined as the rate at which an object covers some distance. Speed can be measured as the distance travelled by a body in a given period of time. The SI unit of speed is m/s.

Given that, Robert paddled at a constant speed and travels 3/4 of a mile in 15 minutes.

We know that, Speed = Distance/Time

Speed = 3/4 ÷15/1

= 3/4 × 1/15

= 1/20 miles per minutes

Now, distance = 1 mile and speed =1/20 miles per minutes

1/20 = 1/Time

Time = 20 minutes

Therefore, with a constant speed Robert took 20 minutes paddle.

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Federal Deposit Insurance Corporation, programs were parts of FDR's New Deal.

Social security is the protection that a society provides to individuals and households to ensure access to health care and to guarantee income security, particularly in cases of old age, unemployment, sickness, invalidity, work injury, maternity or loss of a breadwinner.

here, we have,

One of Franklin D. Roosevelt's most well-known and widespread programmers, Social Security was first introduced in 1935. One of the New Deal initiatives that helped the nation emerge from the Great Depression and recover its assets and wealth as well as give the economy new life was Social Security.

In order to help the aged and disabled better support themselves while they were unable to work, Social Security established safety net protections.

The Social Security programmed and Fannie Mae, or The Federal National Mortgage Association, both still exist today, despite the fact that the majority of the New Deal policies were abandoned when the United States entered World War II. After World War II, Fannie Mae contributed to funding and fueling the housing boom for soldiers coming home.

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Answer:

See below

Step-by-step explanation:

The derivative function f' is the slope of the function at any given 'x'

A) f ' = 8 x^3 - 24 x^2

B ) put in x = -1 and compute   8 ( -1)^3 -24(-1)^2 = -8 - 24 = - 32 slope

C)  we know the slope (-32) and the x coordinate (-1)   put this value of x into the original equation to find y = 2(1^4) - 8(-1)^3 + 6 = 16

   so point slope form of the line is

       y - 16 = -32 (x - -1)    re-arrange:

       y = -32x -16

D) where slope (f ') = 0 the slope is 0 and thus the tangent line is horizontal      8x^3 - 24x^2 = 0    

                         8x^3 = 24x^2

                           8x = 24

                             x = 3  

Answer: We can use the formula for compound interest to calculate the total amount in each account after 2 years.

Account 1: A = P * (1 + r/n)^(nt)

where P = $1,200, r = 2.7%, n = 365 (days/year), t = 2 years.

Substituting the values into the formula, we get:

A = $1,200 * (1 + 0.027/365)^(365 * 2) = $1,200 * (1.0007365)^(365 * 2)

Account 2: A = P * (1 + r)^t

where P = $1,000, r = 3.9%, t = 2 years.

Substituting the values into the formula, we get:

A = $1,000 * (1 + 0.039)^2 = $1,000 * (1.039)^2

Comparing the two amounts, we see that Account 1 has a higher return. The final amount in Account 1 is $1,268.27 and the final amount in Account 2 is $1,079.61.

Step-by-step explanation:

Answer:

Step-by-step explanation:

Using the Pythagorean Theorem, we know the hypotenuse is 2[tex]\sqrt{26}[/tex]

sin = Opp/hyp ----> [tex]\frac{5}{2\sqrt26}[/tex]

csc = hyp/opp -----> [tex]\frac{2\sqrt{26} }{5}[/tex]

cot = adj/opp -------> [tex]\frac{7}{5}[/tex]

Answer:

see attached

Step-by-step explanation:

The Schrödinger equation, sometimes called the Schrödinger wave equation, is a partial differential equation. It uses the concept of energy conservation (Kinetic Energy + Potential Energy = Total Energy) to obtain information about the behavior of an electron bound to a nucleus.

see attached

Answer:

[tex]\hat{H} \Psi=E \Psi[/tex]

Step-by-step explanation:

[tex]\hat{H}[/tex]= the total energy of a system in all aspects. this includes both potential and kinetic energy.

[tex]\Psi[/tex]= wave function. if I remember right the wave function is exactly that, the function in which the wave is behaving, reflected on a graph.

[tex]E[/tex]= energy

P(Female) = 111, P(Car) = 132, P(Female | truck) = 19 P(Truck | female)

Probability is a branch of math which deals with finding out the likelihood of the occurrence of an event. Probability measures the chance of an event happening.

From the image in the question,

P(Female) = 92 + 19

= 111

P(Car) = 40 + 92

= 132

P(Female | truck) = 19

P(Truck | female) = 19

The events "Female" and "Truck" are dependent

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Answer I think Ann is 36 and Denny is 12 Im not for sure but thats what i got

Step-by-step explanation:

D i.e. {C, T, U, -, *} is the minimal complete set of relational algebra operations.

What is relational algebra?

Relational Algebra is a query language that takes a Relation as input and returns another Relation as output. Relational algebra provides the theoretical basis for relational databases and SQL. The necessary column data for a relation is projected via projection.

Now,

As Five basic operations in relational algebra are : Selection, Projection, Cartesian product, Union, and Set Difference and all these are present in

{C, T, U, -, *}.

Hence,

            D i.e. {C, T, U, -, *} is the minimal complete set of relational algebra operations.

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87 is the test score is 1.2 standard deviations above the mean.

Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.

Given that scores on a standardized test are normally distributed with a mean of 105 and standard deviation of 15.

We need to find the test score is 1.2 standard deviations above the mean

1.2 standard deviations is 1.2×15 =18

So 105-18=87

87 is the score that is 1.2 standard deviations from the mean.

Hence, 87 is the test score is 1.2 standard deviations above the mean.

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Answer: Let X be the number of tables that ordered chips and salsa. Then, 7X tables did not order chips and salsa. So, X + 7X = 108, which simplifies to 8X = 108. Dividing both sides by 8, we have X = 13.5.

Since X must be a whole number, we round down to get X = 13 tables ordered chips and salsa.

Step-by-step explanation:

with no missing powers, meaning including any "stepping down" values, anyhow, let's do so

[tex]3x^3-70\implies \boxed{\begin{array}{llll} 3x^3+0x^2+0x^1 + 0x^0 - 7 \\\\\\ 3x^3+0x^2+0x^1 - 7 \end{array}}[/tex]

now, notice, the others were there all along, however their coefficient is 0, thus anything times 0 goes poof, however they were there all along.

some folks like to use the 1st form there, I usually use the 2nd form, but both are acceptable.

Answer:

(a) 44%

(b) 32%

Step-by-step explanation:

(a) In order to find the percentage of students that prefer comedies, we can add up divide the sum of the total number of students who prefer comedies (Twice/month or less + Thrice/month or more) by the total number of students.  

Then, we can multiply this number by 100 to find the percentage:

[tex](\frac{45+21}{150})*100\\ (\frac{66}{150})*100\\ 44[/tex]

(b) To find the percentage of students who visit the movies three times a month or more, we can divide the sum of the total number of students who visit the movies three times a month or more by the total number of students.

Like before, we can multiply this number by 100 to find the percentage:

[tex](\frac{21+27}{150})*100 \\(\frac{48}{150})*100\\ 32[/tex]

The Inferential statistics is given below.

Statistics is the science concerned with developing and studying methods for collecting, analyzing, interpreting and presenting empirical data.

Given is to discuss the statistical inference.

Therefore, the Inferential statistics is given above.

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The given assertion states that the length of BD in its simplest radical version is 7/√2.

A triangle is indeed a 3-sided shape that is occasionally (though not frequently) referred to as the trigon. There are three edges and three angles in every triangle, some of which could be the same.

Since BD is an altitude of the right triangle ABC, we can use the Pythagorean Theorem to find the length of BD. First, let's determine the size of AC:

AC² = AD * DC = 7 * 5 = 35

When we square the two edges, we obtain:

AC = √35

Now, we can use the fact that BD is an altitude to write:

BD = (AC * AD) / hypotenuse

where hypotenuse is the length of BC.

Using the Pythagorean Theorem, we can find the length of BC:

BC² = AC² + AB²

Since triangle ABC is a right triangle, we have AB = BC, so we can write:

BC² = AC² + BC²

Simplifying, we get:

BC² / AC² = 2

When we square the two edges, we obtain:

BC / AC = √2

Multiplying both sides by AC, we get:

BC = AC * √2 = √35 * √2 = √70

Now, we can substitute the values of AC, AD, and BC into the formula for BD:

BD = (AC * AD) / BC = (√35 * 7) / √70 = 7 / √2

Therefore, the length of BD in simplest radical form is 7 / √2.

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Answer:

z=0.13 or z=-2/15

Step-by-step explanation:

First you must simply the fraction into a decimal, leaving us with 1.2 and 1.3. Then you subtract 1.3 from 1.2. Leaving us with z=0.13 or in fraction form,

z= -2/15

The page numbers of the book are 147 and 148.

Consecutive numbers are numbers that follow each other in order. They have a difference of 1 between every two numbers.

In a set of consecutive numbers,the mean and the median are Equal. If n is a number, then n, n+1, and n+2 would be consecutive numbers.

Given,

Left and right page numbers of a book are consecutive integers.

Sum of both integers = 295

Let x is left integer then right integer is x + 1

Equation becomes

x + x + 1 = 295

2x + 1 = 295

2x = 295 - 1

x = 294/2

x = 147

Left integer = 147,

Right integer = 147 + 1 = 148

Hence, 147 and 148 are the page numbers of the book.

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The value of the side x is 6. Option D

It is important that we know the six different trigonometric identities in mathematics.

These identities are;

We have the sides are;

Hypotenuse side = x

Opposite side = y

Angle = 30

Adjacent side = 3

Then,

cos 60 = 3/x

Find the value

x = 6

Hence, the value is 6

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The answer of the questions:

a) The surface is an ellipsoid,

(b) If the equation is changed to x² - y² + z² = 4, the graph is still an ellipsoid, and

(c) If the equation is changed to x² + y² + 2y - z² = 3, the graph is not an ellipsoid anymore,

What is an ellipsoid?

An Ellipsoid is a closed surface on which all plane cross sections are either ellipses or circles. An ellipsoid is symmetrical about three mutually perpendicular axes that intersect at the center.

(a)

x = k:

Trace: Circle in the x-z plane

Identification: Circle

y = k:

Trace: Circle in the y-z plane

Identification: Circle

z = k:

Trace: Circle in the x-y plane

Identification: Circle

The surface is an ellipsoid, which is a 3-dimensional surface that is the result of stretching or compressing a sphere along different axes.

(b)

If the equation is changed to x² - y² + z² = 4, the graph is still an ellipsoid, but it is rotated so that its axis is the x-axis.

(c)

If the equation is changed to x² + y² + 2y - z² = 3, the graph is not an ellipsoid anymore, and its shape cannot be determined from the equation alone.

This is because the equation contains a linear term (2y) that makes it non-quadratic.

To find the shape of the surface, a more in-depth analysis would be required.

Hence, the answer of the questions:

a) The surface is an ellipsoid,

(b) If the equation is changed to x² - y² + z² = 4, the graph is still an ellipsoid, and

(c) If the equation is changed to x² + y² + 2y - z² = 3, the graph is not an ellipsoid anymore,

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The total amount of money in the bag is M = $ 2.98

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as M

Now , the value of M is

Let the total amount of money in the bag be M

The number of coins in the bag = 50 coins

The number of pennies = 12 % of coins

So , the number of pennies = ( 12/100 ) x 50 = 6 pennies

The number of dimes in the bag = 44 % of the coins

The number of dimes in the bag = ( 44/100 ) x 50 = 22 dimes

The number of nickels = 8 + number of pennies = 8 + 6

The number of nickels = 14 nickels

The remaining number of coins are quarters

On simplifying the equation , we get

So , the number of quarters = 50 - 6 - 22 - 14 = 8 quarters

And , the value of 6 pennies = $ 0.06

The value of 22 dimes = $ 0.22

The value of 14 nickels = $ 0.70

The value of 8 quarters = $ 2.00

Therefore , the total amount in the bag = $ 2.00 + $ 0.70 + $ 0.22 + $ 0.06

The total amount of money in the bag = $ 2.98

Hence , the total money in the bag is $ 2.98

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Answer:

To find the number of cats Carly can feed, divide the total weight of cat food by the weight of cat food used per cat.

2.85 lbs ÷ 0.19 lbs/cat = 15 cats

Therefore, Carly can feed 15 cats.

The derivative of a composite function is given by the chain rule: the fifth derivative of fog(x) depends only on the second and fourth derivatives of f.

d(fog(x))/dx = df/d(g(x)) * d(g(x))/dx

The fifth derivative of fog(x) can be calculated by taking the derivative five times:

d^5(fog(x))/dx^5 = d^5f/d(g(x))^5 * (dg(x)/dx)^5 + 5 * d^4f/d(g(x))^4 * d^2g(x)/dx^2 * (dg(x)/dx)^3 + 10 * d^3f/d(g(x))^3 * (dg(x)/dx)^2 * (d^2g(x)/dx^2)^2 + 10 * d^2f/d(g(x))^2 * (dg(x)/dx) * (d^3g(x)/dx^3) + 5 * df/d(g(x)) * (d^4g(x)/dx^4)

Since g'(x) is constant, dg(x)/dx is also constant, and its derivative is 0. Therefore, all the terms with derivatives of g(x) higher than 1 are 0, leaving us with:

d^5(fog(x))/dx^5 = 5 * d^2f/d(g(x))^2 * (dg(x)/dx)^2 * d^2g(x)/dx^2 + 5 * df/d(g(x)) * d^4g(x)/dx^4

Since g'(x) is constant, dg(x)/dx and d^2g(x)/dx^2 are also constant, and can be replaced by their values. Therefore, the fifth derivative of fog(x) depends only on the second and fourth derivatives of f.

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