A sample of 15 small bags of the same brand of candies was selected. Assume that the population distribution of bag weights is normal. The weight of each bag was then recorded. The mean weight was 2 ounces with a standard deviation of 0.12 ounces. The population standard deviation is known to be 0.1 ounce.


a. σ =________

b. sx =________

The slope of a line parallel to the line x + 5y = 9 is; Choice B: -1/5

The slope of parallel lines from line geometry are equal.

The given parallel line equation is; x + 5y = 9:

Hence, it follows that the two lines have equal slopes.

By rewriting the equation to take the slope-intercept form of straight lines, it follows that;

On this note, the slope of the parallel lines is; -1/5

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Maria has $22,000 invested in account A and $8,000 invested in account B.

Let's begin by setting up a system of equations to solve for the amount Maria has invested in each account. Let x be the amount invested in account A and y be the amount invested in account B. Since Maria has a total of $30,000 invested in both accounts, we can write the first equation as:

x + y = 30,000

Next, we can write an equation to represent the total annual interest earned from both accounts:

0.045x + 0.038y = 1,294

Now, we can use the substitution method to solve for x and y. We'll rearrange the first equation to solve for x:

x = 30,000 - y

Then, we'll substitute this value of x into the second equation:

0.045(30,000 - y) + 0.038y = 1,294

Simplifying the equation gives:

1,350 - 0.045y + 0.038y = 1,294

Combining like terms and isolating y gives:

0.007y = 56

y = 8,000

Now, we can substitute this value of y back into the first equation to solve for x:

x = 30,000 - 8,000

x = 22,000

So, Maria has $22,000 invested in account A and $8,000 invested in account B.

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The geometric figures which could be this three-dimensional figure are:

A cross section can be defined as an exposed surface or shape that is formed when a cut is made through a three-dimensional figure.

In this scenario, the geometric figures which could be this three-dimensional figure are:

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According to the given equation, the solution is f = 19

What is an equation?

An equation is a mathematical statement that shows that two expressions are equal. It consists of two sides separated by an equals sign (=).

We can start by simplifying the expression inside the parentheses:

f - (13 - 2) = f - 11

Then, we can rewrite the original equation using this simplified expression:

8 = f - 11

To solve for f, we want to isolate it on one side of the equation. We can do this by adding 11 to both sides:

8 + 11 = f - 11 + 11

19 = f

Therefore, the solution is:

f = 19

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Answer:

Sebastian is going to choose design elements that include color, pattern, font, and image for the design of a sweatshirt for his dance team. There are 10 colors, 14 patterns, 12 fonts, and 9 images for him to choose from. (He will choose only one of each.)

How many different sweatshirt designs are possible?

Step-by-step explanation:

It's 4320

The solution to the system of equations is x = -1, y = -6.

What is a system of equations?

A system of equations is a set of two or more equations that are to be solved together, where the solutions must satisfy all the equations in the system. A system of equations can involve one or more variables and can be expressed in different forms, such as linear equations, quadratic equations, or any other type of equations.

The goal of solving a system of equations is to find the values of the variables that satisfy all of the equations in the system. Depending on the type and complexity of the equations, there are different methods that can be used to solve the system, such as substitution, elimination, or matrix methods.

For example, a system of two linear equations with two variables x and y can be written in the form:

a₁x + b₁y = c₁

a₂x + b₂y = c₂

where a₁, b₁, c₁, a₂, b₂, and c₂ are constants. To solve this system of equations, we need to find the values of x and y that satisfy both equations simultaneously.

Systems of equations can arise in various contexts, including in mathematics, physics, engineering, economics, and other fields. They are used to model and solve a wide range of problems that involve multiple variables and constraints.

To solve the system of equations by the method of subtraction, we need to eliminate one of the variables (x or y) by subtracting one equation from the other.

Given the system of equations:

Y=6x

2x-7y=40

We can use the first equation to express y in terms of x:

y = 6x

Substituting this expression into the second equation, we get:

2x - 7(6x) = 40

Simplifying and solving for x, we get:

2x - 42x = 40

-40x = 40

x = -1

Now that we have found the value of x, we can substitute it back into either equation to find the value of y. Using the first equation:

y = 6x = 6(-1) = -6

Therefore, the solution to the system of equations is x = -1, y = -6.

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Answer:

not detectable

Step-by-step explanation:

Firstly the question is not clear and the second thing is that the given information don't seem to be enough for calculation

\(~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\\ P=\textit{original amount deposited}\dotfill & \$5000\\ r=rate\to 5\%\to \frac{5}{100}\dotfill &0.05\\ t=years\dotfill &3 \end{cases} \\\\\\ I = (5000)(0.05)(3) \implies I = 750\)

Performing a Chi-Square test is a statistical tool used to determine if there is a significant difference between observed and expected data. The test helps to analyze categorical data by comparing observed frequencies to the expected frequencies. The p-value in a Chi-Square test refers to the probability of obtaining the observed results by chance alone.

If a p-value lower than 0.01 is obtained in a Chi-Square test, it means that the results are statistically significant. In other words, there is strong evidence to reject the null hypothesis, which states that there is no significant difference between the observed and expected data. This means that the observed data is not due to chance alone, but rather to some other factor or factors.

The mean, or average, is not directly related to the Chi-Square test or the p-value. The Chi-Square test is specifically used to determine the significance of the observed data. However, the mean can be used as a measure of central tendency for continuous data, but it is not applicable to categorical data.

In conclusion, obtaining a p-value lower than 0.01 in a Chi-Square test means that there is strong evidence to reject the null hypothesis, and that the observed data is statistically significant.

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Answer:

$54.01

Step-by-step explanation:

All you have to do is $300.00-$245.99 .

Answer:

(800 x 9) + (10 x 9)

Step-by-step explanation:

Find out what 810 x 9 is:

810 x 9 = 7290

Then see which expression has the same answer. Personally I'd check all of them, but luckily the first expression is the correct one so you don't need to go through the rest (since it only asks for one correct expression):

(800 x 9) = 7200

(10 x 9) = 90

7200 + 90 = 7290

Answer:
45.2x0.784

Step-by-step explanation:

This problem equals 35.4368, which has four decimal points

The value of the expression (8 1/5 + 4 1/5) - (6 6/8 - 6 2/4) is 243/20.

Let's simplify the addition within the parentheses:

8 1/5 + 4 1/5 = (8 + 4) + (1/5 + 1/5) = 12 + 2/5 = 12 2/5

Next, let's simplify the subtraction within the parentheses:

6 6/8 - 6 2/4 = (6 - 6) + (6/8 - 2/4) = 0 + (3/4 - 1/2) = 0 + 1/4 = 1/4

Now, we can substitute the simplified terms back into the original expression:

(8 1/5 + 4 1/5) - (6 6/8 - 6 2/4) = 12 2/5 - 1/4

To subtract mixed numbers, we need to find a common denominator. The common denominator for 5 and 4 is 20. Converting both terms:

12 2/5 = 12 * 5/5 + 2/5 = 60/5 + 2/5 = 62/5

1/4 = 1 * 5/5 * 5/20 = 5/20

Now we can subtract:

62/5 - 5/20 = (62 * 4)/(5 * 4) - 5/20 = 248/20 - 5/20 = (248 - 5)/20 = 243/20

Therefore, the value of the expression (8 1/5 + 4 1/5) - (6 6/8 - 6 2/4) is 243/20.

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Answer: A-(-3,-2)   B-(-1,-4)    C-(1,1)    D-(-4,4)     E-(-2,1)     F-(0,2)    G-(4,0)

Step-by-step explanation

The required 45-45-90 degree triangle is shown, where each of the two acute angles is 45 degrees and the length of the hypotenuse is equal to the length of each leg multiplied by the square root of 2.

A right-angled triangle, also known as a right triangle, is a triangle in which one of its interior angles measures exactly 90 degrees. The side opposite the right angle is called the hypotenuse, and the other two sides are called the legs.

Here,
o construct a 45-45-90 degree triangle with leg AB, we can follow these steps:

The resulting triangle will have sides AB, BC, and AC, where AB and BC are equal in length and AC is the hypotenuse.

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The required dimensions are solved using linear pair and vertical angle to get the result as

The value of x and y is calculated using linear pair theorem, the theorem implies that

solving for x

(3x + 5) + (x + 15) = 180

3x + x + 5 + 15 = 180

collecting like terms

4x = 180 - 15 - 5

4x = 160

x = 40

solving for y

(y + 20) + (4y - 15) = 180

y + 4y + 20 - 15 = 180

collecting like terms

5y = 180 - 20 + 15

5y = 175

y = 35

Angle AED

= 3x + 5

= 3 * 40 + 5

= 125 degrees

Angle AED = angle CEB = 125 degrees (vertical angles)

Angle DEB

= x + 15

= 40 + 15

= 55 degrees

Angle DEB = Angle AEC = 55 degrees (vertical angles)

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Answer:

PL = 9

PN = 5√5

Step-by-step explanation:

8/12 = 6/PL

8PL = 72

PL = 9

PN² = 10² + 5² = 100 + 25 = 125

PN = √125 = 5√5

Answer:

The

Step-by-step explanation:

x

=

√

11

−

7

,

−

√

11

−

7

Decimal Form:

x

=

−

3.68337520

…

,

−

10.31662479

…

Answer:

i believe the answer would be B

Step-by-step explanation:

Answer:

2/3 or 2:3

Step-by-step explanation:

If 6 out of 10 students completed the homework then 4 out of 10 students did not complete the homework.

So the answer is 4/6 but we are not done yet.

The 4 comes from people who didn't do it and the 6 comes from people who did.

Since its asking the ratio of students who did not do their homework to those who did the 4 comes first.

As I said we are not done yet since we have to simplify.

4/6=2/3

So the answer is 2/3 or 2:3

Answer:

3:5

Step-by-step explanation:

Using the midpoint method, the price elasticity of demand is approximately -0.67.

To calculate the price elasticity of demand using the midpoint method, we'll use the following formula:

Price Elasticity of Demand (Ed) = (% change in quantity demanded) / (% change in price)

First, let's find the percentage changes:

% change in quantity demanded = ((New Quantity Demanded - Old Quantity Demanded) / Midpoint of Quantities) * 100
= ((80 - 100) / ((100 + 80) / 2)) * 100
= (-20 / 90) * 100
= -22.22%

% change in price = ((New Price - Old Price) / Midpoint of Prices) * 100
= ((7 - 5) / ((5 + 7) / 2)) * 100
= (2 / 6) * 100
= 33.33%

Now, let's plug the values into the formula:

Ed = (-22.22% / 33.33%)
= -0.67

So, the price elasticity of demand is approximately -0.67.

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The equation of the line in slope-intercept form is y = (-2/3)x + (16/3).

We know that the slope of the line that passes through the given points (5, 2) and (2, 4) is equal to -2/3. By using the point-slope form of a line, we can find the equation of the line as (y - 2) = (-2/3)(x - 5). Multiplying both sides by 3, we get,3y - 6 = -2x + 10.

Now, we rearrange the terms of the above equation to obtain the standard form of the equation of the line, which is 2x + 3y = 16. The slope-intercept form of the equation of a line is y = mx + b, where m is the slope and b is the y-intercept.

To convert the standard form equation of the line to the slope-intercept form, we isolate y and write the equation as y = (-2/3)x + (16/3). Therefore, the equation of the line in slope-intercept form is y = (-2/3)x + (16/3).

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Answer:

The distance between X and Z is approximately 114.9 km

Step-by-step explanation:

The given parameters are;

The distance of Y from X = 75 km

The bearing of Y from X = 200°

The bearing of Z from Y = 150°

The bearing of Z from X = 180°

In triangle XYZ, we have;

∠YZX = 180° - (130° + 20°) = 30°

By sine rule, we have;

(75 km)/sin(30°) = XZ/(sin(130°))

XZ = sin(130°) × (75 km)/sin(30°) ≈ 114.9 km

The distance between X and Z ≈ 114.9 km. to one decimal place.

Program State Model describes a precise mathematical description of the semantics of an executing program.

This model is used to illustrate how the program executes and to determine its behavior. It is composed of three components: states, transitions, and actions. A program state is a snapshot of the program's state at a particular point in its execution. It includes the values of variables and other resources. Transitions are the changes that occur between states, and are caused by the execution of instructions. Finally, actions are the operations that are performed by the program as it transitions from one state to the next. All of these components together provide a mathematical model for understanding the behavior of a program.

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The chance that the hospital will run out of sleeping pills on any given day is 0.5000 (or 0.5000 with four decimal places).

To calculate the chance that the hospital will run out of sleeping pills on any given day, we can use the normal distribution and Z-score.

First, let's calculate the Z-score using the formula:

Z = (X - μ) / σ

Where:

X = consumption rate per day (1,155 pills)

μ = average consumption rate per day (1,155 pills)

σ = standard deviation (81 pills)

Z = (1,155 - 1,155) / 81

Z = 0

Now, we need to find the probability associated with this Z-score. However, since the demand for sleeping pills can be considered continuous and not discrete, we need to calculate the area under the curve from negative infinity up to the Z-score. This represents the probability of not running out of sleeping pills.

We discover that the region to the left of a Z-score of 0 is 0.5000 using a basic normal distribution table or statistical software.

To find the probability of running out of sleeping pills, we subtract this probability from 1:

Probability of running out of sleeping pills = 1 - 0.5000

Probability of running out of sleeping pills = 0.5000

Therefore, on any given day, the hospital has a 0.5000 (or 0.5000 with four decimal places) chance of running out of sleeping tablets.

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k(9) = 2(9)^2 - 3√9

= 2(81) - 27

= 162 - 27

= 135

If k(x) = 2x^2 - 3√x then k(9) is equal to 2(9)^2 - 3√9 which simplifies to 2(81) - 27 = 162 - 27 = 135 1