What is the cost in dollars and cents for each chocolate bar?

The roots of the quadratic equation  x² + x + 2 = 0  is \(-1+\sqrt{-7} /2\) and\(-1-\sqrt{-7} /2\)

Roots: In mathematics, a solution to an equation, usually expressed as a number or an algebraic formula. The square root of a number is a value that can be multiplied by itself to give the original number. The square root of 9 is 3, because when 3 is multiplied by itself, you get 9.

given quadratic equation is,  x² + x + 2 = 0

to find the roots we have formula method ,

x=\(-b+\sqrt{b^2-4ac}\)\(/2a\)

x=\(-b-\sqrt{b^2-4ac}\)\(/2a\)

a=1, b=1 and c=2

sub the values in the above equation

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

x=\(-1-\sqrt{1-4(1)(2)} /2\)

x= \(-1+\sqrt{-7}/2\) and x=\(-1-\sqrt{-7} /2\) are the roots of the quadratic equation

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The derivative of f(g(x)) with respect to x is  f'(1/x).

The term derivative refers to a type of financial contract whose value is dependent on an underlying asset, group of assets, or benchmark.

Given that, g(x)=ln x

Differentiation of ln x = 1/x

Hence, The derivative of f(g(x)) with respect to x is  f'(1/x).

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To find the area bounded by the polar curve r=e^−θ/12 in the given sector, we use the formula A = ∫a b 1/z,2 dθ. Here, a=π/2 and b=π, and z=e^−θ/12. So, we have A = ∫π/2 π 1/(e^−θ/6) dθ. Therefore, the area of the region bounded by the polar equation r=e^−θ/12 in the sector π/2 ≤θ≤π is 1 - e^(-π/24).

To solve this integral, we use the substitution u=-θ/12, which gives us du/dθ = -1/12, or dθ = -12du. Substituting this and e^u for e^−θ/12, we get A = ∫−π/24 0 e^u * (-12)du.
Evaluating this integral, we get A = [e^u] from −π/24 to 0 = e^0 - e^(-π/24) = 1 - e^(-π/24). So, the area of the region bounded by the polar equation r=e^−θ/12 in the given sector is 1 - e^(-π/24).
In conclusion, the area of the region bounded by the polar equation r=e^−θ/12 in the sector π/2 ≤θ≤π is 1 - e^(-π/24).

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The most apt description of expected value is: The long-term average outcome of an experiment.

Expected value refers to the long-term average outcome of an experiment. It is a mathematical concept that represents the average value of a random variable over an infinite number of trials.

In other words, it is the sum of all possible outcomes of an experiment, weighted by their probability of occurring.

Expected value is a crucial concept in probability theory and statistics, as it helps in predicting the likely outcome of an experiment or event. It is often used in decision-making processes, such as in finance and insurance, to calculate the potential risks and rewards associated with different options.

The other options listed in the question are not correct definitions of expected value. The standard deviation is a measure of the variability or spread of a random variable, while the best result and median are specific values that may or may not be related to the expected value.

What you should expect to happen in an experiment every time may be related to the expected value, but it is not a precise definition.

Overall, expected value is a fundamental concept in probability theory and statistics that represents the long-term average outcome of an experiment or event.

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The value of 6x is 102.

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. LHS = RHS is a common mathematical formula.

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:

x=51/3

For 6x put x= 51/3 we get

6x = 6 x 51/3

6x = 2 x 51

6x = 102

Or, \(x^6\) = \((51/3)^6\)

\(x^6\) = 17,596,287,801 / 531,441

Hence, the value of 6x = 102.

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Based on the p-value approach, with a p-value of 0.0013, we reject the null hypothesis and conclude that the proportions are not equal to 0.40, 0.40, and 0.20. Using the critical value approach, since the test statistic (13.333) is greater than the critical value (9.210), we reject the null hypothesis and conclude that the proportions differ from 0.40, 0.40, and 0.20.

Based on the information, we can perform a goodness of fit test using the chi-square test statistic to determine if the observed proportions match the expected proportions.

(a) Using the p-value approach, the test statistic is calculated based on the observed and expected frequencies, which gives a value of 13.333.

The p-value associated with this test statistic is 0.0013. Since the p-value is less than the significance level of 0.01, we reject the null hypothesis.

Therefore, we can conclude that the proportions are not equal to 0.40, 0.40, and 0.20.

(b) Using the critical value approach, we compare the test statistic (13.333) to the critical values associated with the chi-square distribution with 2 degrees of freedom at a significance level of 0.01.

The critical values for the rejection rule are 9.210 and 0.010. Since the test statistic (13.333) is greater than the critical value (9.210), we reject the null hypothesis.

Thus, we conclude that the proportions differ from 0.40, 0.40, and 0.20.

In both approaches, we reject the null hypothesis, indicating that the observed proportions are significantly different from the expected proportions.

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Answer:

45

Step-by-step explanation:

f(4) = 3(4²) + 2(4) -1

f(4) = 48+8-1 or 55

h(5) = 3(5)-5

h(5) = 10

55-10=45

Answer:

‎

Step-by-step explanation:

‎

Triangle AED and triangle BEC have equal areas. The length of AE can be represented as 14 - x (since AC = 14). AE is equal to 10.

To find the length of AE, we can use the fact that triangle AED and triangle BEC have equal areas. Since the areas of two triangles with the same height are proportional to their base lengths, we can set up the following proportion:

Area of triangle AED / Area of triangle BEC = AE / EC

Let's denote EC as x (the length of EC). Then, the length of AE can be represented as 14 - x (since AC = 14).

Now, let's look at the given information about the lengths of the sides of the quadrilateral:

AB = 9

CD = 12

AC = 14

We can use the given information to find the lengths of the other sides of the quadrilateral:

BC = AC - AB = 14 - 9 = 5

AD = AC - CD = 14 - 12 = 2

Next, we can calculate the areas of triangle AED and triangle BEC using the lengths of their sides:

Area of triangle AED = (1/2) * AD * AE

Area of triangle BEC = (1/2) * BC * EC

Since the areas of the two triangles are equal, we can set up the following equation:

(1/2) * AD * AE = (1/2) * BC * EC

Plugging in the values we know:

(1/2) * 2 * (14 - x) = (1/2) * 5 * x

Simplifying the equation:

14 - x = (5/2) * x

Multiplying both sides by 2 to clear the fraction:

28 - 2x = 5x

Adding 2x to both sides:

28 = 7x

Dividing both sides by 7:

x = 4

Therefore, the length of EC is 4.

Since AE = AC - EC, we can calculate AE:

AE = 14 - EC = 14 - 4 = 10

So, AE is equal to 10.

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The complete question is:<Convex quadrilateral ABCD has AB = 9 and CD = 12. Diagonals AC and BD intersect at E, AC = 14 and triangle AED and triangle BEC have equal areas. What is AE?>

According to the inequality, Christopher would need to purchase 35 + 10s 75 sets of spoons to ensure that the restaurant has enough of them.

According to analysts, inequality promotes political dysfunction and slows down economic progress. Because wealthy households typically spend a smaller proportion of what they earn than do poorer households, concentrated earnings lower the amount of demand for goods and services. The economy may suffer if low-income families have fewer possibilities.

There are already 355 spoons available, but the eatery needs at least 75. Each set that is for sale includes 10 spoons.

Let s be the representation of each set. It will be demonstrated by:

35 + (10 × s) ≥ 75

35 + 10s ≥ 75

Collect like terms

10s ≥ 75 - 30

10s ≥ 45

Divide

s ≥ 45/10

s ≥ 4.5

The restaurant must have at least 5 sets.

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Answer: 10s + 355 >=755

s>=42

Step-by-step explanation:

The recursive definition for the amount of the blood pressure medicine in Hareem's bloodstream after n hours can be defined as :

a. a1=25, an= 0.40an-1 + 25

Base Case:

The initial amount of medicine in Hareem's bloodstream after 0 hours is 25 mg.

Recursive Step:

The amount of medicine in Hareem's bloodstream after n hours can be calculated by taking 60% of the amount of medicine in his bloodstream after (n-1) hours, and then adding 25 mg.

To write this recursive definition in mathematical notation:

M(n) = 25 mg, if n = 1

M(n) = 40 mg, if n = 6

M(n) = M(n-1) + (60% * M(n-1)), if n > 6

This recursive definition represents the amount of the blood pressure medicine in Hareem's bloodstream after n hours. The base case sets the initial amount of medicine, and the recursive step calculates the amount of medicine at each hour by taking 60% of the previous amount and adding 25 mg.

The correct option is a. a1=25, an= 0.40an-1 + 25

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Answer:

x <= 9

Step-by-step explanation:

x -15 <= -6

+15. +15

x <=9

To construct a 3×3 matrix, not in echelon form, whose columns span ℝ³, we can choose three linearly independent vectors as the columns of the matrix.

To demonstrate that the constructed matrix has the desired property of spanning ℝ³, we can construct a specific example. Let's consider the matrix A:

A = [[1, 0, 0],

[0, 1, 0],

[0, 0, 1]]

In this case, A is a 3×3 matrix with three columns [1, 0, 0], [0, 1, 0], and [0, 0, 1]. Each column represents a standard basis vector in ℝ³.

To show that the columns of A span ℝ³, we need to demonstrate that any vector in ℝ³ can be expressed as a linear combination of the columns of A.

Let's consider an arbitrary vector x = [x₁, x₂, x₃]ᵀ in ℝ³. We can express x as a linear combination of the columns of A:

x = x₁[1, 0, 0] + x₂[0, 1, 0] + x₃[0, 0, 1]

Simplifying this expression, we get:

x = [x₁, x₂, x₃]ᵀ

Thus, we have shown that any vector x in ℝ³ can be expressed as a linear combination of the columns of the matrix A. Therefore, the columns of A span ℝ³.

Note: It is important to emphasize that there are many possible matrices that can be constructed to satisfy the given condition. The example provided here is just one of the many valid choices

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Answer:

A solution of the system of equation given in the question is;

(2) x = 7 and y = 23

Step-by-step explanation:

The given system of equation are;

2·x + 3·y = 83...(1)

y = 2·x + 9...(2)

Substituting the value of y = 2·x + 9 from equation (2) into equation (1) gives;

2·x + 3·y = 2·x + 3 × (2·x + 9) =  83

∴ 2·x + 6·x + 27 = 83

8·x = 83 - 27 = 56

x = 56/8 = 7

x = 7

By substituting the value of x = 7 derived above into equation (1), we have;

y = 2·x + 9

Where;

x = 7

y = 2 × 7 + 9 = 14 + 9 = 23

y = 23.

Answer:

Amount after 22 year = $484.80 (Approx.)

Step-by-step explanation:

Given:

Amount deposit in bank = $150

Double in year = 13 year

Find:

Amount after 22 year

Computation:

A = P[1+r]ⁿ

Amount after 13 year = 2 x 150

Amount after 13 year = $300

300 = 150[1+r]¹³

2 = [1+r]¹³

Rate of interest = 5.477%

Amount after 22 year

A = P[1+r]ⁿ

Amount after 22 year = 150[1+5.477%]²²

Amount after 22 year = $484.80 (Approx.)

When a relationship is plotted on a graph, a linear relationship results in a straight line; a nonlinear relationship, on the other hand, results in a curve.

There are a total of four components in a time series model.

Trend, Seasonal, Cyclical, and Error.

Seasonal Component is a wavelike pattern that is repeated throughout a time series and has a recurrence period of at most one year.

Cyclical Component is a wavelike pattern within the time series that repeats itself throughout the time series and has a recurrence period of more than one year.

Error Term represents the changes in time series data that are unpredictable and can't be associated with a seasonal , cyclical component.

Trend Component is the long-term increase or decrease in a variable being measured over time.

When a relationship is plotted on a graph, a linear relationship results in a straight line; a nonlinear relationship, on the other hand, results in a curve.

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As per the given curvature, the value of PC is 1785.68 and PT is 1787.55

Curvature:

In statistics, curvature means amount by which a curve deviates from being a straight line, or a surface deviates from being a plane.

Given,

PI is at station (20 00), the radius of curvature is 800 feet, and the angle of curvature is 30 degrees.

Here we need to determine the value of PC and PT.

According to the given value, the tangent distance is calculated as,

=> T = 800 x tan (30/2)

=> T = 800 x 0.2679

=> T = 214.32

Now, the value of PC is calculated as,

PC = PI - T

=> PC = 2000 - 214.32

=> PC = 1785.68

And the value of PT is calculated as,

PT =  PC + L

=> PT = 1785.68 + (100 x (30/1600))

=> PT = 1785.68 + 1.875

=> PT = 1787.55

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Chi-square test is a statistical test for categorical data. It is used to determine whether your data are significantly different from what you expected. There are two types of Pearson’s chi-square tests:

1. The chi-square goodness of fit test is used to test whether the frequency distribution of a categorical variable is different from your expectations.

2. The chi-square test of independence is used to test whether two categorical variables are related to each other.

Both of Pearson’s chi-square tests use the same formula to calculate the test statistic, chi-square (Χ2):

X^2=E{(O-E)^2}{E}} where,

Χ2 is the chi-square test statistic

Σ is the summation operator (it means “take the sum of”)

O is the observed frequency

E is the expected frequency

The larger the difference between the observations and the expectations (O − E in the equation), the bigger the chi-square will be. To decide whether the difference is big enough to be statistically significant, you compare the chi-square value to a critical value.

Chi square test is often useful in following situations -

1. if we want to check a hypothesis between two or more categorical variables.

2. The sample was randomly selected from the population.

3. There are a minimum of five observations expected in each group or combination of groups.

So, the Chi square test is used for checking the value of categorical data.

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1) The equal expressions are I and III

2) The value of the expression is 3 41/80

An absolute value expression is a mathematical expression that represents the distance of a number from zero, regardless of the sign of the number. The absolute value of a number is always positive, so an absolute value expression represents a positive number or zero.

The absolute value of a number x is denoted by |x| and is defined as follows:

|x| = x, if x is positive or zero

|x| = -x, if x is negative

Since -/x/ = -x then this are the equal expressions.

\(a^2/a + 1 + a + 1/a^2\)

Then;

\(4^2/4 + 1 + 4 +1/4^2\)

16/5 + 5/16

= 3 41/80

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Given the provided coordinates of the points, The shape that is formed is a parallelogram because the slopes of the opposite sides are same.

In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction. Divide the difference in elevation between two points by the distance between them to find the percent slope, then multiply the result by 100. The term "rise" refers to the difference in elevation between two sites. The run is the separation between the points. Percent slope is therefore equal to (rise / run) x 100.

A coordinate system in geometry is a method for determining the precise location of points or other geometrical objects on a manifold, such as Euclidean space, using one or more numbers, or coordinates.

slope between (1,1) and (4,4),

m1 = 4-1/4-1 =3/3 =1

slope between (4,-2) and (7,1),

m2= 1+2/7-4 = 3/3 =1

m1=m2

similarly, slope between (1,1) and (4,-2),

m3= -2-1/4-1 = -3/3 =-1

slope between (7,1) and (4,4)

m4= 1-4/7-4 = -3/3 =-1

m3=m4

So, slopes of opposite sides are same that means they are parallel, The shape is parallelogram.

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The ratio of the number of empty tables to the total number of tables is 3:22.

What is the ratio?

A ratio is a comparison of two quantities, often expressed as a fraction or in the form "a to b" (where a and b are numbers). Ratios can be used to compare different types of quantities, such as the number of boys to the number of girls in a classroom, or the amount of sugar to the amount of flour in a recipe.

The total number of tables at Manny's Italian Restaurant is:

total number of tables = number of full tables + number of empty tables = 57 + 9 = 66

The ratio of the number of empty tables to the total number of tables is:

number of empty tables : total number of tables = 9 : 66

This ratio can be simplified by dividing both numbers by their greatest common factor, which is 3:

number of empty tables : total number of tables = 3 : 22

Therefore, the ratio of the number of empty tables to the total number of tables is 3:22.

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Answer:

3,8,11

Step-by-step explanation:

if line d was parallel there might be more but it is not so the only ones that are congruent are 3,8 and 11

Step-by-step explanation:

(3*4+1) / 4. * (2*5+3) / 5

= 13/ 4 * 13 /5

= 169/20

Answer:

(8 9/20)(x)

Step-by-step explanation: