Jackie is planning a party. She has a budget of $5000 to
spend on the party. Food costs $70 per person. The party
hall, where the party will take place, charges $1500 to rent
out. What is the most people she can invite to the party?

x/2 = -0.73

To solve for x multiply both sides by 2:

x = -1.46

Therefore, the probability of getting exactly 4 calls between 8:00 AM and 9:00 AM is approximately 0.1755, rounded to four decimal places.

To calculate the probability of getting exactly 4 calls between 8:00 AM and 9:00 AM, we need to use the Poisson distribution formula. The Poisson distribution is commonly used to model the number of events occurring in a fixed interval of time or space. In this case, the mean (λ) is given as 5. The formula for the Poisson distribution is:

P(X = k) = (e*(-λ) * λ\(^k\)) / k!

Where:

P(X = k) is the probability of getting exactly k calls

e is the base of the natural logarithm (approximately 2.71828)

λ is the mean number of calls (given as 5)

k is the number of calls (in this case, 4)

k! is the factorial of k

Let's calculate the probability using the formula:

P(X = 4) = (e*(-5) * 5⁴) / 4!

P(X = 4) ≈ 0.1755

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We need to add 81 as the constant term to the binomial (n² - 18n) so that the resulting trinomial is a perfect square, and factorization of that resulting trinomial will be (n - 9).

As per the question statement, we are provided with a binomial (n² - 18n),

And we are required to add a proper constant to the above mentioned binomial so that the resulting trinomial is a perfect square, and then factorise the resulting trinomial.

To answer question, first we need to know the standard form of expanding a perfect square into a trinomial, which goes as,

[(a - b)² = {(a)² + (b)² - (2 * a * b)]

Here, if we compare our concerned binomial (n² - 18n), or, [(n)² - (2 * n * 9)], with the above mentioned standard expansion of a perfect square into a trinomial, we get, (a = n) and (b = 9), and the (b²) term is missing.

Adding [(b²) = (9²) = 81] which is a constant term, to our concerned binomial (n² - 18n), we get, (n² - 18n + 81),

Or, [(n)² + (9)² + (2 * n * 9)],

Which is a trinomial and matches with the standard expansion of a perfect square into a trinomial, and hence,

[(n² - 18n + 81) = (n - 9)²]

That is, we need to add 81 as the constant term to the binomial (n² - 18n) so that the resulting trinomial is a perfect square, and factorization of that resulting trinomial will be (n - 9).

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B alone could do the work in D) 6 days.

Let's assume that A and B together can complete the work in x days. According to the question, we know that:

1/x = 1/3 (since they can complete the work in 3 days)

Solving for x, we get x = 3.

Now, we know that A and B worked together for 2 days. So, the amount of work done in those 2 days is:

2/x = 2/3

This means that the remaining work that needs to be done is:

1 - 2/3 = 1/3

We also know that B alone can complete the work in y days. So, the amount of work B can do in 2 days is:

2/y

Therefore, the remaining work that A needs to do is:

1/3 - 2/y

We also know that A and B together can complete the work in 5 days (after B left). So, we have:

1/x + 1/y = 1/5

Substituting the value of x, we get:

1/3 + 1/y = 1/5

Solving for y, we get y = 6.

Therefore, B alone could do the work in 6 days.

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The value of the population proportion of people from Hawaii who exercised for at least 30 minutes a day 3 days a week cannot be determined from the given information alone. This is because we only have the sample proportions from Vermont and Hawaii.

However, we can use the sample proportions from Vermont and Hawaii to make inferences about the population proportions with some level of confidence. We can use statistical tests such as hypothesis testing and confidence intervals to estimate the population proportions within a certain range.

For example, if we conduct a  with a significance level of 0.05, we can test the null hypothesis that the population proportion of people from Hawaii who exercise for at least 30 minutes a day 3 days a week is equal to the sample proportion of 62.2%. If the test results in a p-value less than 0.05, we can reject the null hypothesis and conclude that the population proportion is likely different from 62.2%. On the other hand, if the test results in a p-value greater than 0.05, we cannot reject the null hypothesis and conclude that the population proportion is likely similar to 62.2%.

Alternatively, we can construct a confidence interval for the population proportion using the sample proportion, sample size, and a chosen confidence level (e.g. 95%). The confidence interval will give us a range of values within which the true population proportion is likely to fall. For example, a 95% confidence interval for the population proportion of Hawaii could be calculated as 0.622 ± 1.96 * sqrt((0.622 * (1 - 0.622)) / 100), which gives us a range of 0.529 to 0.715. This means that we are 95% confident that the true population proportion of people from Hawaii who exercise for at least 30 minutes a day 3 days a week falls within this range.

In summary, while we cannot determine the exact value of the population proportion from the given information, we can use statistical tests and confidence intervals to estimate it with some level of confidence.

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Answer: Richard is 29 and Teo is 9.

Step-by-step explanation: Use Substitution

Replace x with -2 and solve:

A) -2 + -2 = -4 which is not less than or equal to -8

B) 2 + -2 = 0, this is greater than or equal to -8

C) -2 + -2 = -4, this is not less than -8

D) 2 + -2 = 0, this is not greater than 8

Answer: B is true

Answer:

\(1\)

Step-by-step explanation:

\({(4.51) }^{0} = 1\)

hope this helps you.

Answer:

-58

Step-by-step explanation:

8*3*-2=-48

-48-2*5=-58

This is the answer to your problem

Answer: M= 3.75

Step-by-step explanation:

Answer:

-90

Step-by-step explanation:

Answer:

m = 4

Step-by-step explanation:

m−10+6m=10+2m

7m-10=10+2m

Subtract 2m from both sides

5m-10=10

Add 10 to both sides

5m=20

Divide both sides by 5

m=4

Answer:

m=4

Step-by-step explanation:

m − 10 + 6m = 10 + 2m

7m - 10 = 10 + 2m   (subtract 2m from both sides)

7m - 10 - 2m = 10

5m - 10 = 10   (add 10 to both sides)

5m = 10 + 10

5m = 20  (divide both sides by 5)

m = 20/5

m = 4

Answer:

Step-by-step explanation:

92-8

the incorrect answer is step 4

The missing step in solving the inequality 4(x – 3) + 4 < 10 + 6x is step 6: The division property of inequality: x > -9

The missing step in solving the inequality 4(x – 3) + 4 < 10 + 6x is step 6: The division property of inequality.

After step 4, which is -2x < 18, we need to divide both sides of the inequality by -2 to solve for x.

However, since we are dividing by a negative number, the direction of the inequality sign needs to be reversed.

Dividing both sides by -2:

-2x / -2 > 18 / -2

This simplifies to:

x > -9

Therefore, the correct answer is x > -9.

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The given system of equation:

y = -x + 7 (1)

y = 2x + 7 (2)

Apply substitution method to solve for x & y

Substitute the value of y from the equation(2) into equation(1)

y = 2x + 7

-x + 7 = 2x + 7

7 - 7 = 2x + x

3x = 0

x = 0

Now, susbtiute the value of x = 0, in the equation (1)

y = - x + 7

y = -(0) + 7

y = 7

So, the solution of the system of equation is : (x, y) = (0, 7)

Answer : (x,y) = (0,7)

The graph will be :

Answer:

Im pretty sure it is

1 1/2 sq ft per hour

3/4 in 2/4

Double it

1 2/4 in 1

Simplifies to 1 1/2

The unit rate that fertilizer cover is 3/2 square foot.

The unitary technique involves first determining the value of a single unit,  followed by the value of the necessary number of units.

For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.

12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.

As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.

This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.

Given:

A fertilizer covers 3/4 square foot in 1/2 hour.

So, unit rate fertilizer covers

= 3/4 x 2

= 3/2 square foot.

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Answer:

A≈603.19in²

Step-by-step explanation:

sorry if it's wrong

Answer:

603.19

Step-by-step explanation:

Answer: 16−32

Step-by-step explanation:

(2−4)⋅8

1) Reorder terms  (2−4) ⋅8 = 8(2−4)

2) Apply the distributive law  

8(2−4)= 8 . 2m -8 . 4

3) Simplify

8 . 2m -8 . 4 = 16m-32

The image of the triangle RST when rotated 90° counterclockwise around the origin is (-15,5), (-15,15) and (-5,10)

The coordinates of RST are given as:

R = (5,15)

S = (15,15)

T = (10,5)

The rule of 90° counterclockwise around the origin is:

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

So, we have:

R' = (-15,5)

S' = (-15,15)

T' = (-5,10)

Hence, the image of the triangle when rotated 90° counterclockwise around the origin is (-15,5), (-15,15) and (-5,10)

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Using quantifiers; a) ∀ student ∈ this class, ∃ exactly 2 mathematics classes ∈ this school that the student has taken and b) ∃ person, ∀ country ∈ the world (country ≠ Libya), the person has visited that country.

a) "Every student in this class has taken exactly two mathematics classes at this school."

In this statement, we have two main quantifiers:

Universal quantifier (∀): This quantifier denotes that we are making a statement about every individual student in the class. It indicates that the following condition applies to each and every student.

Existential quantifier (∃): This quantifier indicates the existence of something. In this case, it asserts that there exists exactly two mathematics classes at this school that each student has taken.

So, when we combine these quantifiers and their respective conditions, we get the statement: "For every student in this class, there exists exactly two mathematics classes at this school that the student has taken."

b) "Someone has visited every country in the world except Libya."

In this statement, we also have two main quantifiers:

Existential quantifier (∃): This quantifier signifies the existence of a person who satisfies a particular condition. It asserts that there is at least one person.

Universal quantifier (∀): This quantifier denotes that we are making a statement about every individual country in the world (excluding Libya). It indicates that the following condition applies to each and every country.

So, when we combine these quantifiers and their respective conditions, we get the statement: "There exists at least one person who has visited every country in the world (excluding Libya)."

In summary, quantifiers are used to express the scope of a statement and to indicate whether it applies to every element or if there is at least one element that satisfies the given condition.

Therefore, Using quantifiers; a) ∀ student ∈ this class, ∃ exactly 2 mathematics classes ∈ this school that the student has taken and b) ∃ person, ∀ country ∈ the world (country ≠ Libya), the person has visited that country.

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There is no element a in the prime field of order,GF(5^n) with a² = 2 when n is odd. Therefore, 2 is not a square in GF(5^n) for odd n.

To prove that 2 is not a square in GF(5^n) when n is odd, we can use proof by contradiction. Suppose there exists an element an in GF(5^n) such that a² = 2. We can write an as a polynomial in GF(5)[x], where the coefficients are elements of GF(5). Since a² = 2, we have (a² - 2) = 0.

Now, consider the field GF(5^n) as an extension of GF(5). The polynomial x² - 2 is irreducible over GF(5) because 2 is not a quadratic residue modulo 5. Therefore, if a² = 2, it implies that x² - 2 has a root in GF(5^n).

However, this contradicts the fact that the degree of GF(5^n) over GF(5) is odd. By the degree extension formula, the degree of GF(5^n) over GF(5) is equal to the degree of the irreducible polynomial that defines the extension, which is n. Since n is odd, the degree of GF(5^n) is also odd.

Hence, we have reached a contradiction, proving that there is no element a in GF(5^n) with a² = 2 when n is odd. Therefore, 2 is not a square in GF(5^n) for odd n.

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The ordered pair that represents a point that is inside the perimeter of the figure is  (3\(\frac{1}{2}\), 3\(\frac{1}{2}\)).

The correct option is H.

Coordinates are a pair of integers (Cartesian coordinates), or occasionally a letter and a number, that identify a certain place on a grid, often referred to as a coordinate plane.

Given:

A shape in the coordinate plane.

From the given choices,

the ordered pair (3\(\frac{1}{2}\), 3\(\frac{1}{2}\)).

The other points lie outside the perimeter of the shape.

Hence, the point is H: (3\(\frac{1}{2}\), 3\(\frac{1}{2}\)).

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If there is a positive correlation between x and y in a research study, then the regression equation y = bx + a will have a positive slope.

The positive correlation between x and y indicates that as the values of x increase, the corresponding values of y also tend to increase. In the regression equation, the coefficient b represents the slope of the line, which indicates the change in y for a unit change in x. Since there is a positive correlation, the slope (b) will be positive, indicating that as x increases, y will also increase.

what is slope?

Slope refers to the measure of how steep or flat a line is. In mathematics, the slope is defined as the ratio of the vertical change (change in y-coordinates) to the horizontal change (change in x-coordinates) between two points on a line. It represents the rate of change of the dependent variable (y) with respect to the independent variable (x).

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Only matrices of the same size can be added or subtracted.

A matrix is a rectangular array of numbers and is composed of rows and columns. In order to add or subtract matrices, the matrices must have the same number of rows and columns. If the matrices do not have the same size, they cannot be added or subtracted.

For example, if one matrix is a 2x3 matrix, the other matrix must also be a 2x3 matrix. Similarly, if one matrix is a 3x2 matrix, the other matrix must also be a 3x2 matrix. The numbers in each matrix may vary, but the size of the matrices must be the same for the operation to be valid.

When adding or subtracting matrices, the numbers in the same position (row and column) are added or subtracted. For example, if one matrix is [[1,2,3], [4,5,6], [7,8,9]] and the other matrix is [[2,4,6], [8,10,12], [14,16,18]], the resulting matrix would be [[3,6,9], [12,15,18], [21,24,27]].

Adding and subtracting matrices is a useful tool in mathematics and is often used to solve equations and simplify complex problems. It is important to remember that only matrices of the same size can be added or subtracted.

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The solution is 44 copies

The number of copies the copy machine makes in one minute is 44 copies

What is an Equation?

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 A

Now , the value of A is

The number of copies the copy machine makes = 231 copies

Time required by the to make 231 copies = 5 minutes 15 seconds

5 minutes = 5 x 60 seconds

5 minutes = 300 seconds

5 minutes 15 seconds = 300 + 15 seconds

5 minutes 15 seconds = 315 seconds

So , Time required by the to make 231 copies = 315 seconds

Now , number of copies in 1 minute = 60 x ( The number of copies the copy machine makes / Time required by the to make 231 copies )

Substituting the values in the equation , we get

Number of copies in one minute A = 60 x ( 231 / 315 )

Number of copies in one minute A = 60 x 0.733

Number of copies in one minute A = 44 copies

Therefore , the value of A is 44 copies

Hence , the number of copies is 44 copies

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Exercise caution when making predictions beyond the observed range of data, and consider factors such as data quality, model assumptions, and potential limitations.

To perform quadratic extrapolation of a time series, you can use a quadratic model to estimate or predict the value of z at a future time t+1. Here's how you can do it:

Collect your time series data up to time t and note down the corresponding values of z.

Fit a quadratic model to the available data points. The quadratic model has the form: z = at^2 + bt + c, where a, b, and c are coefficients that need to be determined.

Use regression techniques such as least squares regression to estimate the coefficients a, b, and c of the quadratic model using the available data.

Once you have the estimated coefficients, substitute the value t+1 into the quadratic model equation to predict the value of z at time t+1.

For example, if your quadratic model is z = 2t^2 + 3t + 1, and you want to predict the value of z at time t+1, you would substitute the value (t+1) into the equation:

z(t+1) = 2*(t+1)^2 + 3*(t+1) + 1

After evaluating this equation, you will obtain the predicted value of z at time t+1 based on the quadratic extrapolation of the time series.

It's worth noting that extrapolation carries some inherent uncertainty and assumes that the underlying patterns in the time series will continue in the future. Therefore, exercise caution when making predictions beyond the observed range of data, and consider factors such as data quality, model assumptions, and potential limitations.

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Answer:

i's 20 because it seems that it is the most successful