if you played this game 559 times how much would you expect to win or lose? round your answer to two decimal places. losses must be expressed as negative values.

The maclaurin expansion for function eˣ  is 1 + x + x²/2 + x³/6 + x⁴/24 + .....

A function's expansion series, which provides the function's derivatives' sum, is known as a Maclaurin series.

Series [f, x, 0, n] can be used to find a function's Maclaurin series up to order n.

When x = 0, it is a specific example of the Taylor series. The series of Maclaurin is provided by

[tex]f(x) = f(x_0) + f(x_0)(x - x_0) + \frac{f"(x_0)}{2!}(x - x_0)^2 + . . .[/tex]

The formula for maclurin series is :

[tex]f(x) = \sum^{\infty}_{n=0} \frac{f^n (x_0)}{n!} (x-x_0)[/tex]

Where,

f(xo), f’(xo), f’‘(xo)……. are the successive differentials when xo = 0.

Maclaurin expansion for the function eˣ

Firstly , We will derivate the function

f(x) = eˣ

=> f'(x) = e⁰ = 1

=>  f''(x) = e⁰ = 1

=> f'''(x) = e⁰ = 1

and so on

Upon evaluation of all derivatives at x = 0, we obtain the value 1.

Moreover, f(0)=1, so we can deduce that the expansion of the Maclaurin Series as

=> eˣ = 1 + x + x²/2 + x³/6 + x⁴/24 + .....

The given question is incomplete , I answered the question in general according to the knowledge

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The Probability of both Zack and Lucy missing the target will be 0.48

Let the probability of Lucy and Zack missing the target be = P(L) and  P(Z), respectively. So, If the probabilities of Zack and Lucy missing the target are as follows-

P(L) = 0.6 and

P(Z) = 0.8

then, the probability of both Lucy and Zack missing the target will be,

P(L) × P(Z) i.e.

0.6×0.8 = 0.48

Probability is basically a method to find out the possibility of likelihood of a certain outcome. In mathematics, it was introduced by Pierre and Cardano in the seventeenth century.

The complete question is-

The probabilities of Lucy and Zack hitting or missing the target are given in the following image. As per that, what will be the probability of both Lucy and Zack missing the target?

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The use of analysis of variance rather than a t-test for the null hypothesis claims more than two populations.

Analysis of Variance (ANOVA) is a statistical component used to evaluate variances throughout the method (or average) of various groups. A variety of eventualities use to decide if there's any distinction among the method of various groups. Student's t-test is used to compare means between two His groups and ANOVA is used to compare means between three or more His groups. ANOVA first obtains the common t-test. A significant t-test for the ANOVA test indicates at least one pair for which the mean difference was statistically significant.

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No, Then the matrix has three columns and the eigenspaces' sum of dimensions is zero. The eigenspace's dimensions and the number of columns must add up to be equal.

A matrix is a rectangular arrangement of a collection of numbers into a fixed number of rows and columns. When the elements are arranged in a matrix horizontally, it forms the rows of a matrix. When the elements are arranged in a matrix vertically, it forms the columns of a matrix.

A matrix, also spelled "matrices," is a rectangular table, array, or set of letters, numbers, or phrases that are arranged in rows and columns to represent a mathematical object or a property of such an entity.

There are three eigen-spaces, since A has three eigen values, the dimension of each of the eigen value is at least one as there is at least one non-zero eigen vector in them.

Therefore,

No, Then the matrix has three columns and the eigenspaces' sum of dimensions is zero. The eigenspace's dimensions and the number of columns must add up to be equal.

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Answer:

A

Step-by-step explanation:

Answer:

  C  2.35 x 10¹¹

Step-by-step explanation:

You want the number 235,000,000,000 written in scientific notation.

The exponent of 10 when a number is written in scientific notation is the same as the exponent of 10 for the most significant digit when the number is written in expanded form using exponents.

  235,000,000,000 = 2×10¹¹ +3×10¹⁰ +5×10⁹ +0×10⁸ +... +0

The place value multiplier for the most-significant digit is 10¹¹, so this is the multiplier when the number is written in scientific notation.

  2.35×10¹¹

The formula for calculating it is perimeter of the rectangle = 2(length + width), meaning that it is equal to twice the sum of its length and width.

Given that,

We have to find which equation perfectly describes the ABCD rectangle's perimeter? How do you determine a rectangle's length and width given its perimeter?

We know that,

The total length of a rectangle's outer boundary is known as its perimeter. The formula for calculating it is perimeter = 2(length + width), meaning that it is equal to twice the sum of its length and width.

The sum of a rectangle's boundary lengths on all sides is known as its perimeter. A rectangle's perimeter is a linear measurement that can be expressed in metres, feet, inches, or yards. Let's first comprehend the two fundamental characteristics of a rectangle.

A rectangle has four 90° angles.

The diagonals of a rectangle are all of the same length.

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Hence, the equation of the line is [tex]y=-4x-22[/tex].

What is the line of equation?

The equation of a line in a two-dimensional coordinate system is an equation including terms containing variables [tex]x[/tex] and [tex]y[/tex] separately with degree [tex]1[/tex].

Here given that,

The equation of the line passing through the point [tex](2,-14)[/tex] and having a slope [tex]-4[/tex].

Using the formula of line of slope

[tex]y=mx+c[/tex]

where [tex]m[/tex] is the slope.

Here,

[tex]m=-4\\x=2\\y=-14[/tex]

So,

[tex]y=mx+c\\-14=-4(2)+c\\\\-14=8+c\\\\c=-14-8\\\\c=-22[/tex]

Hence, the equation of the line is [tex]y=-4x-22[/tex].

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Based on the probability concept, the population is number of children in gymnastic class is 5 and the parameter is mean number of steps taken by the 5 children.

Probability:

In math probability  deals with the occurrence of a random event and the value is expressed from zero to one.

Given,

Suppose that there are 5 children in a gymnastics class.

One day, they count the number of steps each person takes while walking on their hands until they lose balance and come down.

The mean number of steps these children took while walking on their hands is 20 steps.

Here we need to find the the population and parameter.

Based on the given question,

We know that the parameters are descriptive measures of an entire population and their values are usually unknown because it is infeasible to measure an entire population.

Therefore, you can take a random sample from the population to obtain parameter estimates.

Similarly, for the population could simply be referred to as the total number or set of similar objects or subjects related to a certain study or research.

Here the given scenario described above, the area of interest is a particular gymnastic class, therefore all individuals or children belonging to this particular gymnastic class makes up the population.

And then the parameter on the other hand are statistical metrics, values or calculations derived from the population figure or information.

So, the mean value of steps obtained from the step counts of the population data is called the parameter.

And the parameter is a value that describes a characteristic of an entire population, such as the population mean.

Therefore, the population mean and standard deviation are two common parameters.

=> Population = number of children in gymnastic class = 5.

=> Parameter = mean number of steps taken by the 5 children.

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The height of the wall the brace reached is 8 feet.

Pythagorean theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

We have,

Height of the wall the brace reached = x

Now,

10² = 6² + x²

100 = 36 + x²

x² = 100 - 36

x² = 64

x = 8

Thus,

The brace reached 8 feet of the wall.

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23

Step-by-step explanation:

The answer is 23 because it is closer to the 0

Answer: the answer is 141

Step-by-step explanation:

bro its not that hard the guy up top is a bum just add all the angles together thats the answer and remember the formula is (n-2)180 for INTERIOR i wrote it in caps cuz some of yall goofy fr

The commission rate is 20% and the base pay is $41,000.

The total pay is the sum of the base pay and the total commission earned.

Total pay = base pay + commission

Total pay = base pay + (percentage commission x sales)

The equations that represents the information in the question are:

a + 50,000b = 51,000 equation 1

a + 100,000b = 61,000 equation 2

The elimination method would be used to determine the required values:

Subtract equation 1 from equation 2:

50,000b = 10,000

b = 10,000 / 50,000

b = 0.2 = 20%

Substitute for b in equation 1:

a + (50,000 x 0.2) = 51,000

a + 10,000 = 51,000

a = 51,000 - 10,000

a = 41,000

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Hence, the current yield is [tex]1212.897[/tex]

What is the calculation?

A calculation is a deliberate mathematical process that transforms one or more inputs into one or more outputs or results.

Here given that,

Leah Long bought one bond of Vick Company for [tex]147[/tex]. The original bond was [tex]8.25 10[/tex].

So,

[tex]8.2510(147)=1212.897[/tex]

Hence, the current yield is [tex]1212.897[/tex]

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The value of the function at -4 is f(-4) = -14.

What is the value of a function?

When the variables and constants in a mathematical expression are given values, the outcome of the computation it describes is the expression's value. The quantity that the function assumes for these argument values is the value of a function, given the value(s) assigned to its argument(s).

Given:

f(x) = 2x - 6

We have to find the value of f(-4).

So, plug x = -4 in the above equation.

Above equation becomes,

f(-4) = 2(-4) - 6

f(-4) = -8 - 6

f(-4) = -14

Hence, the value of the function at -4 is f(-4) = -14.

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The older computer takes 8 minutes to send out the email on its own.

Combining objects and counting them as one big group is done through addition. In arithmetic, addition is the process of adding two or more integers together. Addends are the numbers that are added, and the sum refers to the outcome of the operation.

Let , the older computer works at the rate of x.

According to the condition,

then the rate of work of newer computer is x/2.

And the combined work of both the computer = x/2 + x = 3x/2

It means that  3x = 12

then x = 4

Hence, x =8of the job per minute.

It means the older computer will make the entire job in 84 minutes.

Therefore, the older computer takes 8 minutes to send out the email on its own.

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Answer:

$5809.17

Step-by-step explanation:

Using the formula for continuous compound interest [tex]P(t)=Pe^{rt}[/tex] We can plug in our values [tex]P(t)=5000e^{0.03*5}[/tex] and solve.

Of the following, the option which is not a polynomial is 1/x+2. (Option D)

In mathematics, a polynomial refers to an expression consisting of indeterminates and coefficients, that only includes basic arithmetic operations of addition, subtraction, multiplication, and positive-integer powers of variables. In other words, it is a mathematical expression of one or more algebraic terms each of which consists of a constant multiplied by one or more variables raised to a nonnegative integral power. The general form of a polynomial is a + bx + cx^2. Hence, it is identified by noting which expressions contain only the operations of addition, subtraction, multiplication, and non-negative integer exponents. The non-polynomial expressions will be the expressions which contain other operations such as 1/x+2.

Note: The question is incomplete. The complete question probably is: Which of the following is not a polynomial (a) 3x+5 (b) 3y³-4y² +2y (c)x³-3 d) 1/x+2

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The number of ice cubes that  Gregory could use in all is; 15

Algebraic word problems are defined as the questions that require translation of sentences into equations, and thereafter solving those equations. The variable in these usually represents an unknown quantity in a real-life scenario.

We are told that Greg gave a glass of water to each person at dinner. He put more than 2 ice cubes in each glass. Each glass had the same number of ice cubes.

More than 2 ice cubes tells us that there would be 3 cubes or 5 cubes especially when we consider the size of an ice cube.

Now from the given options, we see that only 15 is the number divided equally by 3 and 5.

Therefore, the total number of ice cubes will be 15.

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The missing options are;

A. 13

B. 15

C. 17

D. 19

Using the concept of ratio, the month of February had a better ratio in sales compared to January

The ratio is defined as the comparison of two quantities of the same units that indicates how much of one quantity is present in the other quantity.

This is the process of comparing two quantities against one another to determine their ratio against each other.

In the question given;

January = 10 minivans, 20 sedans

The ratio of minivans to sedan = 10 / 20 = 1/2

The ratio of minivans to sedan in January = 1/2

February = 15 minivans, 25 sedans

The ratio of minivans to sedans  = 15/25 = 3/5

The month of February has the highest ratio

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The probability mass function of the sample mean of x1, ... , xn, then the

Expectation [tex]E[X][/tex] = 1 and Variance [tex]Var[X][/tex] = 4.9

To find the expected value, E(X), or mean μ of a discrete random variable X, simply multiply each value of the random variable by its probability and add the products. The formula is given as E(X)=μ=∑xP(x).

var(X)=∑(x−μ)2pX(x), where the sum is taken over all values of x for which pX(x)>0. So the variance of X is the weighted average of the squared deviations from the mean μ, where the weights are given by the probability function PX(x) of X.

Given that,

The probability mass function of the sample mean of x1, ... , xn,

p{x = 0} = 0.2, p{x = 1} = 0.3, p{x = 3} = 0.5

when (a) n = 2; (a) n = 3

Expectation is defined as

[tex]E[X][/tex] = ∑ˣ [tex]x P(X =x)[/tex]

We have

[tex]E[X][/tex] = ∑   [tex]x P(X =x)[/tex]

           [tex]x[/tex]∈(2,3)

[tex]E[X][/tex] = [tex]P(X =0)+2P(X=1)+3P(X=3)[/tex]

[tex]E[X][/tex] = 0.2 + 0.3 + 0.5

[tex]E[X][/tex] = 1

Variance is defined as

[tex]Var[X][/tex] = E[(X-[tex]E[X]^{2}[/tex]]

[tex]Var[X][/tex] = [tex]E[X^{2}][/tex] - [tex](E[X])^{2}[/tex]

We get

[tex]E[X]^{2}[/tex] = [tex]1^{2} P[X=0]+2^{2} P[X=1]+3^{2} P[X=2][/tex]

[tex]E[X]^{2}[/tex] = 0.2 + 4(0.3) + 9(0.5)

[tex]E[X]^{2}[/tex] = 0.2 + 1.2 + 4.5

[tex]E[X]^{2}[/tex] = 5.9

Variance is defined as

[tex]Var[X][/tex] = [tex]E[X^{2}][/tex] - [tex](E[X])^{2}[/tex]

[tex]Var[X][/tex] = 5.9 - [tex]1^{2}[/tex]

[tex]Var[X][/tex] = 5.9 - 1

[tex]Var[X][/tex] = 4.9

Therefore,

The probability mass function of the sample mean of x1, ... , xn, then the

Expectation [tex]E[X][/tex] = 1 and Variance [tex]Var[X][/tex] = 4.9

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There is not enough evidence to conclude that the company is putting less than 16 ounces into the salads.

At the null hypothesis, it is tested if there is not enough evidence that the mean is less than 16 ounces, hence:

[tex]H_0: \mu \geq 16[/tex]

At the alternative hypothesis, it is tested if there is enough evidence that the mean is less than 16 ounces, hence:

[tex]H_1: \mu < 16[/tex]

We have a left-tailed test, as we are testing if the mean is less than a value, with a significance level of 0.025 and 9 - 1 = 8 df, hence the critical value is of:

t = -2.306.

Hence the conclusion, considering the test statistic t, is reached as follows:

The equation to calculate the test statistic is presented as follows:

[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]

In which:

From the given sample, the values of these parameters are given as follows:

[tex]\overline{x} = 13.84, \mu = 16, s = 3.285, n = 9[/tex]

Hence the test statistic is of:

[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]

[tex]t = \frac{13.84 - 16}{\frac{3.285}{\sqrt{9}}}[/tex]

t = -1.97 -> not enough evidence.

The problem asks for the conclusion regarding the test of the hypothesis.

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Answer:

Step-by-step explanation:

The answer is (i)Yes the given relation is a function ,

(ii) the domain is Z and range is 2Z ,

(iii) the inverse is S₁⁻¹ = {(x,y) | x,y∈ Z : x = y/2 }

In the question ,

it is given that ,

the relation is S₁ = {(x,y) | x,y∈ Z : y = 2x }

Part(i)  ,

We can say that Yes , the given relation is a function because for each

x ∈ Z , there exists a unique y ∈ Z .

Part(ii)

since the variable  x , y ∈ Z , the input variable is x ,

so , the domain of the function will be Z , and

the Range of the function will be = 2Z .

Part(iii) ,

Since the given function is bijective function ,

the function will have an inverse .

given y = 2x ,

the inverse ⇒ x = y/2 .

so , the inverse function is S₁⁻¹ = {(x,y) | x,y∈ Z : x = y/2 } .

There fore , the relation is a function whose domain is Z and range is 2Z n and the inverse is S₁⁻¹ = {(x,y) | x,y∈ Z : x = y/2 } .

The given question is incomplete , the complete question is

For given relation , please answer the following questions (briefly justify your answers).

(i) Is the relation a function ?

(ii) If the relation is a function, what are its domain and image ?

(iii) Is the inverse a function ? If so, what is the inverse function ?

The relation is given as : S₁ = {(x,y) | x,y∈ Z : y = 2x }

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The graph of the piece-wise function in this problem is given by the image shown at the end of the answer.

A piece-wise function is a function that has different definitions, based on which interval the input value of the function belongs to.

In this problem, the function has three definitions, given as follows:

Hence the graph is defined as follows:

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Step-by-step explanation:

this is a structure of medians in the main triangle.

the center point X divides each median into parts in the ratio 2:1, with X being twice as far from the originating vertex than from the midpoint of the connected side.

so, RX is twice as long as XV.

RV = 54.

RX : XV = 2:1

that means RV consists of 2+1 = 3 equal parts. 2 of these parts are RX, and one part is XV.

how long is one part ?

54/3 = 18.

RX = 2×18, and XV = 1×18

XV = 18

The required measure of the XV in the triangle is 18.

The Median is defined as the line joining the vertex of a triangle to the midpoint of the facing side of the triangle.

Triangle RST is given, which consists of median RV, TU, and SW. All the median of the triangle intersects at X.

Now, the property triangle states that the point of intersection of the median(i.e centroid) X divides the median in the ratio of 2:1,

So,XV = 1 / 3 of RV and RX = 2/3 of RV,

Now,

XV = RV/3
XV = 54 / 3
XV = 18

Thus, XV = 18.

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Answer:

B) 11

Step-by-step explanation:

Let n = a number

2n - 7 = 15  Add 7 to both sides

2n - 7 + 7 = 15 + 7

2n = 22  Divide both sides by 2

[tex]\frac{2n}{2}[/tex] = [tex]\frac{22}{2}[/tex]

n = 11

Answer:

B. 11

Step-by-step explanation:

2a - 7 = 15

2a = 15 + 7

2a = 22

a = 22/2

a = 11

Check:

2*11 - 7 = 15

22 - 7 = 15

By simplifying the equation we can get 5y²+2y+0.4.

An equation is said to be a formula that express the equality of two expressions. These two expressions on either side of the equal sign are called the "left side" and "right side" of the equation. We usually assume that the right-hand side of the expression is zero. This can be compensated for by subtracting the right side formula from the two side formulas, so there is no loss of generality.

The equation is representing direct proportion is, by the commenting them with equal sign.

4y²+4.1+7y-3.7-5y+y²

Reorder and gather like terms-

(1.4y²+y²)+(4.1-3.7)-(7y-5y)

Collect coefficients of likes terms

(1.4+1)y²+(4.1-3.7)-(7y-5y)×y

Calculate the sum or difference we can get

2.4y²+0.4+2y

Rewrite the expression

2.4y²+2y+0.4

Thus this is the correct answer .

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Answer: (x + 1)^2 + (y - 3)^2 = 65

Step-by-step explanation:

Answer: (x+1)²+(y-3)²=89

Step-by-step explanation:

An equation of a circle: (x-a)²+(y-b)=R²

The center of a circle is (-1,3), hence a=-1    b=3

(x-(-1))²+(y-3)=R²

(x+1)²+(y-3)²=R²    (1)

Substitute the coordinate (7,-2) belonging to the circle into equation (1):

(7+1)²+(-2-3)²=R²

8²+(-5)²=R²

64+25=R²

89=R²

Thus, R²=89

Hence,

(x+1)²+(y-3)²=89

72 mph = 105.6 ft/second

In order to convert any value from mph the following formula can be referred to:

speed in miles per hour x  5,280 = speed in foot per second

Therefore when 72 miles per hour is converted to foot per second would equal to the following value:

105.6 feet per second

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