suppose that shoe sizes of american women have a bell-shaped distribution with a mean of 8.11 and a standard deviation of 1.46 . using the empirical rule, what percentage of american women have shoe sizes that are between 5.19 and 11.03 ?

Answer:

1. angle C= angle C , angle D= angle B , angle A= angle E

side CD= side CB, side DA= side BE, side AC= BC

2. angle G= angle J , angle H= angle K , angle J = angle G

side GH= side JK, side HJ= side KG, side JG= side GJ

The Corresponding sides and angles are shown below.

Congruent figures have sides that are the same length and angles that are the same measurement. In other terms, two figures are said to be congruent when they are superimposed upon one another. Even when they are flipped or rotated, they perfectly fit on top of one another.

Given:

1. In ΔCDA and Δ CBE

CD= CB

DA = BE

AC = EC

Angles

<CDA= <CBE

<DCA= <BCE

<CAD= <CEB

2. In GHJ and Δ JKG

GH= JK

HJ = KG

GJ = JG

Angles

<GHJ= <JKG

<HGJ= <KJG

<GJH= <JGK

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By assuming and solving with the rectangle measurements, we get the equation, 2x^2 + 6x - 33 = 0.

Follow the steps below to reach the answer:

A region of 11 cm2 divides the two rectangles A and B.

Rectangle A has a length of x cm.

Rectangle B has a length of (x+3) cm.

Form an equation in x and demonstrate that it simplifies when given the fact that rectangle A's width is 2 cm bigger than rectangle B's width:

2x^2 + 6x - 33 = 0

Rectangle A's length and area being x and 11, respectively, results in the following for rectangle A's width: 11 / x

Rectangle B's length is equal to x + 3 and its area is equal to 11, hence its width is as follows: 11 / (x + 3)

Given that width of the rectangle, A is 2 cm Larger than the width of rectangle B, we obtain: 11/x =  (11/ ( x + 3 ) ) + 2

In addition, based on the situation, we get

11/x - 11/ (x+3) = 2 cm

Let this be equation (1)

The main challenge at hand is to change this equation into the quadratic equation's standard form.

It is obtained by multiplying both sides of equation (1) by x*(x+3). As a result, you will get,

11*(x+3) - 11x = 2x*(x+3)

11x + 33 - 11x = 2x^2 + 6x

2x^2 + 6x - 33 = 0.

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Answer: y=3x-8

Step-by-step explanation:

           - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

\(\blue{\textsf{\textbf{\underline{\underline{Question:-}}}}\)

          What is the equation of the line in slope intercept form if its slope is 8 and its y-intercept is -3?

\(\blue{\textsf{\textbf{\underline{\underline{Answer:-}}}}\)

y=8x-3

\(\blue{\textsf{\textbf{\underline{\underline{How to solve:-}}}}\)

Slope Intercept form, as the name implies, has slope & intercept in its equation.

It looks like y=mx+b, where "m" is the slope and "b" is the y-intercept.

To determine the equation of the line, we need to write the value of m, which in this case is 8, in lieu of m:-

y=8x+b

Same with the y-intercept:-

\(\tt{y=8x+(-3)}\)

Which simplifies to

\(\tt{y=8x-3}\)

               - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

I am, honestly, slightly confused by the question wording, so here is what I think you need! :D

We can start by listing multiplies for each:

3:

3, 6, 9, 12, 15, 18, etc

4:

4, 8, 12, 16, 20, 24, etct

We can see that the least common denominator will be 12.

Answer:

\(\frac{1}{3}=\frac{x}{12}=\frac{4}{12}\)

\(\frac{1}{4} =\frac{x}{12} =\frac{3}{12}\)

If you need to multiply them:

\(\frac{4}{12} *\frac{3}{12} = \frac{12}{144} = \frac{1}{12}\)

But you do not need to use a least common denominator for multiplying and can go straight to this:

\(\frac{1}{3} *\frac{1}{4} =\frac{1}{12}\)

Hope this helps, have a nice day!  

The probability of flipping a heads on the coin and rolling a 5 on the die is 1/12 if a coin is flipped and die is rolled once.

The sample space for the coin toss is  {H,T}, so there are two possible outcomes. The favorable one is  H.

The probability of flipping a heads on the coin is equal to 1/2.

Die has six faces, meaning six possible outcomes, but we’re only interested in one of those outcomes: that roll of a 5. That means that only 1 in 6 outcomes is desirable and we can write it as  1/6

The probability of rolling a 5 on the die is equal to 1/6.

Since a coin is flipped and die is rolled independently, the joint probability is a product of above probabilities.

Therefore, the probability of flipping a heads on the coin and rolling a 5 on the die equals

\(\frac{1}{2} \times \frac{1}{6}\\= \frac{1}{12}\)

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If the number of calories in one serving of various cereals are 110, 98, 140, 145, 150, 90, 150, 140 and 120, then the 95% confidence interval for the average number of calories in cereal is (109.2457, 144.7544).

As per the question statement, the number of calories in one serving of various cereals are 110, 98, 140, 145, 150, 90, 150, 140 and 120,

And we are required to determine the following:

(a) 95% confidence interval for the average number of calories in cereal

(b) If the average is 115 calories or not.

Here, given that sample size, (n = 9)

And we know that, [Mean (M) = {(Σx)/n}],

That is, Mean [(M) = (1143/9)],

Or, [(M) = 127]

Also, we know that, Standard Deviation (s) = [{√Σ(xi - M)²}/(n - 1)]

Or,  (s) = [{√Σ(xi - 127)²}/(9 - 1)]

Or, [(s) = 23.0976]

Now solving for part (a) at 95% confidence interval,  (α = 0.05)

Or, [d = (n - 1) = (9 - 1) = 8]

And, (t-critical) = t[(α/2),d] = t(0.025, 8)

Also, (t-critical) = (±2.306)... [given in the students t-distribution table]

Therefore, the 95% confidence interval (CI) for (μ) goes as,

CI = [(M) ± {(t-critical) * (s/√n)}]

Or, CI = [127 ± {(2.306) * (23.0976/ √9)}]

Or, [CI = (127 ± 17.7543)]

Or, [CI = (109.2457, 144.7544)]

And for part (b), since 115 lies in the range of 95% confidence interval for the average number of calories in our concerned cereal, we cannot reject 115 calories as the average.

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Answer:

2 - 15 = -13

Step-by-step explanation:

Use the website, Math w a y or Desmos! It helps!

Answer: 65 inches

Step-by-step explanation:

11ft and 11inches/11 is  13 so the longest is 65 inches

Answer:

15m long

Step-by-step explanation:

The expression is twice the sum of four and a number is 2(4 + n). Then the correct option is A.

Simplification is to make something easier to do or understand and to make something less complicated.

The condition is given as "twice the sum of four and a number".

Let the number be n. Then according to the condition, we have

The sum of four and a number (n) will be

4 + n

And the number is twice. Then the expression will be

2 × (4 + n)

Thus, the expression is 2 × (4 + n). Then the correct option is A.

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Jill can pay a maximum of $192 for a bedspread.

Jill wants to mark up the price of the bedspread by 30%, so she needs to pay at least 250 / 1.3 = $192 for it. If she pays more than $192, she will not be able to make a 30% profit.

Jill wants to mark up the price of the bedspread by 30%. This means that she wants to sell it for 1.3 times the price she pays for it.

The maximum price that customers are willing to pay is $250.

If Jill pays more than $192 for the bedspread, she will not be able to sell it for $250 and make a 30% profit.

Therefore, the most that Jill can pay for the bedspread is $192.

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Jill can pay a maximum of $192 for a bedspread.

Jill wants to mark up the price of the bedspread by 30%, so she needs to pay at least 250 / 1.3 = $192 for it. If she pays more than $192, she will not be able to make a 30% profit.

Jill wants to mark up the price of the bedspread by 30%. This means that she wants to sell it for 1.3 times the price she pays for it.

The maximum price that customers are willing to pay is $250.

If Jill pays more than $192 for the bedspread, she will not be able to sell it for $250 and make a 30% profit.

Therefore, the most that Jill can pay for the bedspread is $192.

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In order for the characteristics of a sample to be generalized to the entire population, the sample should be representative of the population. This means that the sample should be selected in a way that each member of the population has an equal chance of being included in the sample. Additionally, the sample should be sufficiently large to minimize sampling error and ensure that the results are statistically significant.

So, to summarize, the sample should be:

1. Randomly selected from the population.

2. Representative of the population.

3. Sufficiently large to yield reliable results.

By meeting these criteria, we can make valid inferences and generalize the findings from the sample to the entire population.

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The correct answer is:

**C) 0.28**

The sum of deviations refers to the sum of the differences between individual data points and the mean of the dataset. In any dataset, the sum of deviations from the mean will always equal 0.

This is because, when calculating the mean, you sum all the data points and then divide by the number of data points. The mean represents the "middle" or "balance" point of the dataset. When you add up the differences between each data point and the mean, the positive and negative deviations will cancel each other out, resulting in a sum of 0.

So, any non-zero value for the sum of deviations is impossible. In this case, 0.28 is the only non-zero value.

Answer:

When a pair of parallel lines is cut with another line, known as an intersecting transversal, it creates pairs of angles with special properties.

Step-by-step explanation:

CORRESPONDING ANGLES are equal

<1 and <5 <2 and <6 <4 and <8 <3 and <7

ALTERNATE INTERIOR ANGLES are equal

<3 and <5 <2 and <8

ALTERNATE EXTERIOR ANGLES are equal

<1 and <7 <4 and <6

VERTICALLY OPPOSITE ANGLES are equal

<5 and <7 <6 and <8 <1 and <3 <2 and <4

COINTERIOR ANGLES are supplementary, meaning adding their measurements together will give you 180°

<2 and <5 <3 and <8

the angle between 0 and 2π that is coterminal with 17π/4 is π/4.

To find the angle between 0 and 2π that is coterminal with 17π/4, we need to find an equivalent angle within that range.

Coterminal angles are angles that have the same initial and terminal sides but differ by a multiple of 2π.

To determine the coterminal angle with 17π/4, we can subtract or add multiples of 2π until we obtain an angle within the range of 0 to 2π.

Starting with 17π/4, we can subtract 4π to bring it within the range:

17π/4 - 4π = π/4

The angle π/4 is between 0 and 2π and is coterminal with 17π/4.

what is equivalent'?

In mathematics, the term "equivalent" is used to describe two things that have the same value, meaning, or effect. When two mathematical expressions, equations, or statements are equivalent, it means that they are interchangeable and represent the same mathematical concept or relationship.

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Answer:

40

Step-by-step explanation:

divide 320 by 8 and get 40 cause ratio is 1:8 so answer is 40:320

When the quiz score is expected to be 98, the corresponding x-value, which represents the number of hours spent on homework, is approximately 5.125 hours.

What is the linear equation in two variables?

A linear equation in two variables is an equation of the form:

ax + by = c

where x and y are variables, a, b, and c are constants, and a and b are not both zero. The graph of a linear equation in two variables is a straight line, and any point on the line satisfies the equation.

The given equation is:

y = 8x + 57

where y is the quiz score and x is the hours spent on homework.

To find the meaning of the x-value when y = 98, we can substitute y = 98 into the equation and solve for x:

98 = 8x + 57

Subtracting 57 from both sides, we get:

41 = 8x

Dividing both sides by 8, we get:

x = 5.125

when the quiz score is expected to be 98, the corresponding x-value, which represents the number of hours spent on homework, is approximately 5.125 hours. This suggests that students who spend around 5 hours and 7.5 minutes on homework per week can expect to score around 98 on their weekly quiz.

Therefore, when the quiz score is expected to be 98, the corresponding x-value, which represents the number of hours spent on homework, is approximately 5.125 hours.

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Answer:

80

Step-by-step explanation:

Since the quadrilaterals are similar, corresponding angles are congruent.

m<A = m<F

m<F + 100° + 60° + 120° = 360°

m<F = 80°

z = m<F = 80°

Answer: 80

Answer:

1 the vertex point if there are no other angles at the vertex that be confused.

2 three letters with the vertex as the center letter and the other letters representing points from each side.

3 a small number if one is given in the angle.

Answer:

Three Ways to Name an Angle:

1) By its Vertex

2) By the Three Points of the Angle (The Middle Point Must Be the Vertex)

3) By a Letter or Number Written Within the Opening of the Angle.

Step-by-step explanation:

Answer:

1) Se siembra cinco doceavas partes del terreno con claveles rojos y amarillos, 2) Se siembra siete doceavas partes del terreno con claveles blancos.

Step-by-step explanation:

El enunciado se encuentra incompleto. La pregunta faltante es:

2 ¿Qué parte del terreno corresponde a los claveles blancos?

1) Sea \(A\) el área total sembrada con los tres tipos de claveles. Entonces, las áreas sembradas con claveles rojos y claveles amarillos son \(\frac{1}{6}\cdot A\) y \(\frac{1}{4} \cdot A\), respectivamente.

El área sembrada con claveles rojos y amarillos se obtiene al sumar las áreas correspondientes, es decir:

\(x = \frac{1}{6}\cdot A + \frac{1}{4}\cdot A\)

\(x = \left(\frac{1}{6}+\frac{1}{4}\right)\cdot A\)

\(x = \left(\frac{4+6}{24} \right)\cdot A\)

\(x = \frac{10}{24}\cdot A\)

\(x = \frac{5}{12}\cdot A\)

Se siembra cinco doceavas partes del terreno con claveles rojos y amarillos.

2) El área sembrada con claveles blancos se obtiene al sustraer el área obtenida en el punto anterior del área total. Esto es:

\(x = A - \frac{5}{12}\cdot A\)

\(x = \left(1-\frac{5}{12} \right)\cdot A\)

\(x = \left(\frac{12}{12}-\frac{5}{12} \right)\cdot A\)

\(x = \left(\frac{12-5}{12} \right)\cdot A\)

\(x = \frac{7}{12}\cdot A\)

Se siembra siete doceavas partes del terreno con claveles blancos.

Answer:

Step-by-step explanation:

>:C

According to the question  ⅆyⅆx at the point (2,8) is -12/103.

We start by implicitly differentiating the given equation with respect to x:

3x^2 + 13y(dy/dx) = dy/dx

Now we substitute the values x = 2 and y = 8:

3(2)^2 + 13(8)(dy/dx) = dy/dx

12 + 104(dy/dx) = dy/dx

Simplifying, we get:

104(dy/dx) - dy/dx = -12

(104-1)(dy/dx) = -12

103(dy/dx) = -12

dy/dx = -12/103

what is equation?

In mathematics, an equation is a statement that asserts the equality of two expressions. An equation typically consists of two expressions separated by an equal sign, with one expression on each side. The expressions may contain variables, which are quantities that can vary or take on different values. Solving an equation involves finding the values of the variables that make the equation true.

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The initial population at time t = 0 was 0.39 while the size of the bacteria population after 4 hours was 6553600

An equation is an expression that shows the relationship between two or more numbers and variables.

Let y represent the bacteria population at time t. a represent the initial population at t = 0. Since the doubling period of a bacteria population is 10 minutes, hence:

\(y=a(2)^\frac{t}{10}\)

At time t = 110 minutes, the bacterial population was 800. Hence:

\(800=a(2)^\frac{110}{10} \\\\a = 0.39\)

At 4 hours (240 minutes):

\(y=0.39(2)^\frac{240}{10} =6553600\)

The initial population at time t = 0 was 0.39 while the size of the bacteria population after 4 hours was 6553600

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4 quarts in a gallon, 8 quarts in 2 gallons, so 32.40 divided by 8 is $4.05..

each quart cost 4 dollars and 5 cents

Step-by-step explanation:

The price per quart will be $4.05.

Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both. Addition, subtraction, multiplication, and division are all possible mathematical operations.

It should be noted that 4 quarts are in a gallon. Therefore, since the 2-gallon container of laundry detergent costs $22.00. The price per quart will be:

= $22.00 / (4 × 2)

= $4.05

The price is $4.05.

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Answer:

4n - 1

Step-by-step explanation:

The expression is

As we know that

a + (n - 1)d

where

a denotes the first term

n denotes the nth term

And, d denotes the difference

Now

3 + (n - 1) 4

3 + 4n - 4

4n - 1

Understanding the history of credit provides valuable insights that can shape our perspective on credit cards and other forms of debt. History highlights the evolution and purpose of credit, leading to a more informed approach to personal finance.

**Exploration of the history of credit** reveals that it has played a crucial role in economic development throughout civilizations. From ancient societies engaging in barter systems to the introduction of coins and paper money, credit emerged as a means to facilitate trade and commerce. Over time, lending practices evolved, giving rise to concepts like interest, collateral, and promissory notes.

By studying this history, we can recognize that credit is a powerful tool when used responsibly. It allows individuals and businesses to access funds, invest in opportunities, and manage financial needs. However, it also highlights the potential pitfalls and risks associated with excessive debt.

Understanding the historical context enables us to approach credit cards and other forms of debt with caution and mindfulness. We realize that **credit card debt** is essentially borrowing money that needs to be repaid, often with interest. It prompts us to consider factors such as interest rates, repayment terms, and fees associated with credit cards. This awareness empowers us to make informed decisions, comparing different options, and selecting the most suitable financial products.

Furthermore, historical knowledge of credit reminds us to prioritize responsible financial practices. It encourages us to budget effectively, live within our means, and avoid accumulating excessive debt. Recognizing the potential consequences of mismanaging credit inspires us to develop strategies for debt reduction, such as making regular payments, minimizing interest charges, and seeking professional advice when necessary.

In conclusion, understanding the history of credit influences our perspective on credit cards and other forms of debt. It reminds us of the significance of responsible financial management, enabling us to approach credit with a balanced mindset. By considering historical context, we can make informed decisions, select appropriate financial products, and adopt strategies to maintain a healthy financial position.

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The unconditional mean E(Y) of the autoregressive model AR(1) is 10.5.

To compute the unconditional mean E(Y) of the autoregressive model AR(1) given by 1.05 + 0.9Y + ε, we can use the property of linearity in expectation and solve for the mean value.

The model can be rewritten as:

Y = (1.05 + ε) / (1 - 0.9)

Since ε follows a normal distribution with mean 0 and variance 0.01, we know that E(ε) = 0.

Using the linearity of expectation, we can compute the unconditional mean E(Y) as follows:

E(Y) = E((1.05 + ε) / (1 - 0.9))

= (1.05 + E(ε)) / (1 - 0.9)

= 1.05 / (1 - 0.9)

= 1.05 / 0.1

= 10.5

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Answer:

134

Step-by-step explanation:

On solving the equation Ý = 140 + (-0.0667)X, the value for blood pressure is obtained as 129.328 mm Hg.

What is an equation?

A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("=").

The equation is given as Ý = 140 + (-0.0667)X.

An amount of medication of 160 mg is found to result in a blood pressure of 127.74 mm Hg.

Here the value of X is X = 160.

The predicted blood pressure will be -

Ý = 140 + (-0.0667)160

Ý = 140 - 10.672

Ý = 129.328

The predicted blood pressure value is 129.328 mm Hg.

Here the predicted blood pressure value 129.328 mm Hg is greater than the actual blood pressure value 127.74 mm Hg.

Therefore, the observed value will be below the regression line.

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Significant independent variables makes a good regression model.

A reasonable high R-squared score makes sense if your regression model includes independent variables that are statistically significant. According to the statistical significance, shifts in the dependent variable are correlated with changes in the independent variables.

Accordingly, a high R-squared value shows that your model adequately accounts for the variation in the dependent variable.

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