At a baseball game, 45% of the fans are wearing jackets. Also, 30% of the fans are wearing baseball caps. Whether a fan is wearing a jacket is independent of whether the fan is wearing a baseball cap. What is the probability that a randomly selected fan is not wearing a jacket and is wearing a baseball cap?
A13.5%
B16.5%
C75%
85%​

Answer:

Halfway between x = 2 and x = 4 is x =3 , and halfway between y = 8 and

y = 6 is at y =7, so the midpoint is (3, 7) .

Step-by-step explanation:

In this problem, Alice's shopping duration, represented by the random variable H, can take values 1, 2, or 3 with equal probability.

The number of books she buys, represented by the random variable B, depends on her shopping duration. The joint distribution, marginal distribution, conditional distribution, and conditional expectation are calculated. The solution involves the chain rule, conditional probability, and Bayes' Theorem.

a) To find the joint distribution of B and H, we can use the chain rule. The joint distribution is given by P(B=b, H=h) = P(B=b | H=h) * P(H=h). Since P(B=b | H=h) = h^(-1) for b=1,...,h and P(H=h) = 1/3 for h=1,2,3, we have P(B=b, H=h) = (1/3) * (h^(-1)).

b) The marginal distribution of B can be obtained by summing the joint probabilities over all possible values of H. P(B=b) = Σ[P(B=b, H=h)] for h=1,2,3. Simplifying this expression, we get P(B=b) = Σ[(1/3) * (h^(-1))] for h=1,2,3. The marginal distribution of B is a probability mass function that assigns probabilities to each possible value of B.

c) To find the conditional distribution of H given that B=1, we use the definition of conditional probability. P(H=h | B=1) = P(H=h, B=1) / P(B=1). Using the joint distribution from part a), we have P(H=h | B=1) = [(1/3) * (h^(-1))] / P(B=1). To calculate P(B=1), we sum the joint probabilities over all possible values of H when B=1.

d) To find the expected number of hours Alice shopped conditioned on the event that she bought either 1 or 2 books, we use conditional expectation and Bayes' Theorem. Let E denote the expected number of hours conditioned on this event. We have E = E[H | B=1 or B=2]. Using the law of total expectation, we can express E as the sum of the conditional expectations E[H | B=1] and E[H | B=2], weighted by their respective probabilities. These conditional expectations can be calculated using the conditional distribution of H given B=1 (from part c).

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The number of bags of fiber stuffing needed to fill the cones is 52 bags.

Given:

Height (h) = 10 inches

Radius (r) = 4 inches

To calculate the number of bags of fiber stuffing needed to fill the ice cream cones, we first need to calculate the volume of a single cone ( cone + hemisphere) using its height and radius.

The volume of a cone can be calculated using the formula:

= (1/3) πr²h

The volume of a hemisphere can be calculated using the formula:

= (2/3) πr³

Substituting these values into the formula, we can find the volume of a single cone:

V = (1/3) π × 4² × 10 + (2/3)π × 4³

V = 167.5 + 134.04

V = 301.54

V ≈ 167.5516 cubic inches (rounded to 4 decimal places)

Now, to determine the number of bags of fiber stuffing needed, we divide the total volume of the cones by the volume that can be filled by a single bag of fiber stuffing:

Number of bags = Total volume of cones / Volume filled by a single bag

Total volume of cones = Volume of a single cone x Number of cones

Total volume of cones = 167.5516 cubic inches x 125 cones

Total volume of cones ≈ 37692.66 cubic inches (rounded to 2 decimal places)

Number of bags = 37692.66 cubic inches / 720 cubic inches (per bag)

Number of bags ≈ 52 (rounded to nearest whole number)

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Answer:

y = 5/3x + 31/3

=

5

3

x

+

31

3

Step-by-step explanation:

what i didn't submit this answer

Answer:

you have to divide ➗ the number

The formula for allocation deviation is as follows:σA = (w1σ1^2 + w2σ2^2 + … + wσn^2)^(1/2)σB = (w1σ1^2 + w2σ2^2 + … + wσn^2)^(1/2)

Here,

σ1 = 15%

σ2 = 10%

w1 = 50%,

w2 = 50%

Substituting the values in the above formula:

σA = (0.5 × 0.15^2 + 0.5 × 0.10^2)^(1/2)

= (0.0225 + 0.0100)^(1/2)

= 0.0158 = 1.58%σB

= (0.5 × 0.15^2 + 0.5 × 0.10^2)^(1/2)

= (0.0225 + 0.0100)^(1/2)

= 0.0158

= 1.58%

Hence, the correct option is

D. σ(A) = 14.14%;

σ(B) = 16.33%.

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Answer:

C. √2

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Pre-Calculus

Calculus

Step-by-step explanation:

Step 1: Define

y = sec(x)

x = π/4

Step 2: Differentiate

Step 3: Evaluate

Answer:

C and D

Step-by-step explanation:

If you mean x^2 (x squared), then C and D are both right.

Answer:

2 more

Step-by-step explanation:

you can only get 1 of everything 2 times

this is - the outfit she already made

3 - 1 = 2   - 1 = 1

7 - 1 = 6   - 1 = 5

4 - 1 = 3   - 1 = 2

2 - 1 = 1    - 1 = 0

By using exponent properties, we can see that the equivalent expressions are:

\(5*\sqrt{n^4} = 5*n^2\)

Here we need to use some rules for exponents and roots. Remember that:

\(\sqrt[n]{x} = x^{1/n}\)

We also will use that:

\((a^n)^m = a^{n*m}\)

Now we have the following expression:

\(5*\sqrt{n^4}\)

Particularly, the square root is equivalent to an exponent of 1/2, then we can write:

\(5*\sqrt{n^4} = 5*(n^4)^{1/2}\)

Using the second property we can rewrite:

\(5*(n^4)^{1/2} = 5*n^{4*1/2} = 5*n^2\)

So the equivalent expressions are:

\(5*\sqrt{n^4} = 5*n^2\)

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Answer:

33.5 units²

Step-by-step explanation:

We can see this figure as 2 shapes: a square and a triangle. The square measures 4 x 4, and it's area is 16. That leaves the triangle, which has half the area of a quadrilateral that measures 5 x 7. The area of the quadrilateral is 35, and the triangle has an area of 17.5, which is half of that. Adding them together, we get 33.5.

Answer:

33.5 unit²

it's a mixture of triangle and square.

draw a imaginary straight line across the figure from that line which has length of 3 units and now you can see the triangle and the square. Use the formula to find area of triangle and area of square and the sum of their area will be the area of this whole figure i.e 35.5 unit²

Answer:

If the scale factor is 1/800, it means that 1 cm on the scale drawing represents 800 cm or 8 meters in real life.

So, to find the actual distance between the house and the barn, we need to convert the distance on the scale drawing (4.8 cm) to meters and then multiply by the scale factor:

Actual distance = (Distance on scale drawing in cm) x (Conversion factor)

where the conversion factor is:

Conversion factor = (1 cm) / (100 cm/m) = 0.01 m/cm

Plugging in the values, we get:

Actual distance = (4.8 cm) x (0.01 m/cm) x (8 meters/1 cm) = 0.384 meters

Therefore, the actual distance between the house and the barn is 0.384 meters.

For the equation (x^2 - 16)^3 (x - 1)y" - 2xy' + y = 0, x = 0 is considered an ordinary point because the coefficients of the equation do not exhibit any irregular behavior, such as becoming infinite or undefined, at x = 0.

On the other hand, x = 1 is a singular point for this equation because at x = 1, the coefficient of y" becomes zero, leading to an irregular behavior. The uniqueness of linear first-order differential equations is guaranteed by the continuity of the partial derivative ∂f/∂y. This ensures that, under certain conditions, a unique solution exists for a given initial value problem.

y = xe^x is a solution to the differential equation y" - 2y' + y = 0, as when the derivatives of y = xe^x are substituted into the equation, it simplifies to 0, satisfying the given equation.

Finally, the differential equation y" + 2yy' + 3y = 0 is second-order linear because the equation involves the second derivative of y (y") and the equation can be expressed in the form ay" + by' + cy = 0, where a, b, and c are constants or functions of x. In this case, a = 1, b = 2y, and c = 3.

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Answer: y=6

Step-by-step explanation:

Data: y=3 and x=12

y=? and x=18

12/3=4 and 18/3=6

y=6

I hope this helps

If a scatterplot shows a non-linear relationship between the response and explanatory variable, several options can be considered depending on the purpose of the analysis and the nature of the data.

Here are some possible actions:

Transform the data: One common approach is to transform the data to make the relationship linear. For example, if the relationship appears to be exponential, taking the logarithm of the response variable might make it linear. Similarly, taking the square root, cube root, or inverse of one or both variables might also help.

Use a non-linear model: Another option is to fit a non-linear model that can capture the curvature in the relationship. There are many types of non-linear models, such as quadratic, cubic, exponential, logistic, or spline models. The choice of model depends on the shape of the curve and the underlying theory or hypothesis.

Resample or subset the data: If the non-linear relationship is driven by outliers, influential points, or a subset of the data, it might be helpful to resample or subset the data to remove them. For example, trimming the extreme values, bootstrapping the data, or stratifying the data by a third variable might help.

Explore alternative variables or interactions: If the non-linear relationship is due to an unobserved or omitted variable, it might be useful to explore alternative variables or interactions that could explain the pattern. For example, if the response is sales and the explanatory variable is price, adding a competitor's price or a marketing variable might improve the fit.

Use caution in interpretation: Finally, if the non-linear relationship persists after exploring the above options, it might be necessary to acknowledge the non-linearity and use caution in interpreting the results. Non-linear relationships can be more difficult to interpret and extrapolate, and the statistical inference might be more uncertain or sensitive to assumptions.

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The completion for the row of the table will be:

Grade 8

Dance club: 0.25

Hiking club: 0.75

Total : 1

Grade 9:

Dance club: 0.40

Hiking club: 0.60

Total : 1

The dance club for grade 8 will be calculated as:

= Number of dancers / Total number

= 5/20

= 0.25

The hiking club will be:

= 15/20

= 0.75

The dance club for grade 9 will be calculated as:

= Number of dancers / Total number

= 20/50

= 0.4

The hiking club will be:

= 30/50

= 0.6

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An unnormalized relation refers to a table in a relational database that contains more than one row. This means that there are duplicate rows in the table, which violates the rules of normalization.

Normalization is a process in database design that aims to eliminate data redundancy and ensure data integrity. It involves breaking down a database into multiple tables and defining relationships between them. By doing so, we can efficiently store and retrieve data while minimizing inconsistencies.

In an unnormalized relation, duplicate rows can lead to various problems. For example, it can result in data inconsistencies, as updating one instance of a row may not reflect changes in other duplicate rows. Additionally, it can cause unnecessary storage and maintenance overhead.

To normalize an unnormalized relation, we need to identify the functional dependencies in the table and create separate tables for related data. This helps organize the data and reduces redundancy.

In summary, an unnormalized relation is a table in a relational database that has duplicate rows. It is important to normalize such relations to ensure data integrity and efficiency.

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Answer:

Step-by-step explanation:

The standard form of this exponential function is

\(y=a(b)^x\) where a is the initial value and b is the growth rate. Our initial value is 490 and our growth rate is .2 so the equation is

\(y=490(.2)^x\)

Answer:

Last one is wrong

Step-by-step explanation:

It should be Slope then 1.00

Answer:

Your answer is D.

Step-by-step explanation:

If you need explanation ask me in comment

Answer: 13.8 m

Step-by-step explanation:

Given

From point A, angle of elevation is \(19^{\circ}\)

From point B which is 18 m closer, it changes to \(32^{\circ}\)

Suppose the height of tree is h

From figure, we can write

\(\Rightarrow \tan 32=\dfrac{h}{x}\\\\\Rightarrow h=x\tan 32^{\circ}\)

Similarly

\(\Rightarrow \tan19^{\circ}=\dfrac{h}{x+18}\\\\\Rightarrow h=(x+18)\tan 19^{\circ}\\\text{Substitute the value of h}\\\Rightarrow x\tan 32^{\circ}=x\tan 19^{\circ}+18\tan 19^{\circ}\\\Rightarrow x(\tan32^{\circ}-\tan 19^{\circ})=18\tan 19^{\circ}\\\\\Rightarrow x=\dfrac{18\tan 19^{\circ}}{\tan32^{\circ}-\tan 19^{\circ}}\\\\\Rightarrow x=22.09\approx 22.1\ m\)

Deduce the value of h

\(\Rightarrow h=22.092\times \tan 32^{\circ}\\\Rightarrow h=13.8\ m\)

Thus, the height of the tree is 13.8 m

Answer:

1.6c - 5

Step-by-step explanation:

Step 1: Distribute

-13 + 2.6c - c + 8

Step 2: Combine like terms

1.6c - 5

The angle 1 is 88 degree, 2 is 42 degree and the 3 is 113 degree.

We know that the sum of the angles of the triangle is 180, so in one triangle where the 3 angle is missing we can write as:

42 + 25 +  ∠3 = 180

∠3 + 67 = 180 ,

∠3 = 113°

now in the triangle where 1 and 2 angles are missing, we can say that ∠2 = 42° because of transversely equal angles:

so, ∠ 2 = 42°

now again for a triangle,

∠1 + 42 + 50 = 180

∠1 + 92 = 180

∠1 = 88°

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Precession is a phenomenon that refers to the gradual and continuous change in the orientation of the Earth's rotational axis over long periods of time.

This shift in the orientation of the axis of rotation results in changes in the position of the celestial pole with respect to the stars, which causes a shift in the apparent position of stars over time. The precession of the Earth's axis is caused by the gravitational forces of the Sun, Moon, and other planets in the solar system.
Precession is characterized by changes in the magnitude of the angle of tilt, which causes changes in the rate of the Earth's spin. As the axis of rotation moves, it causes the length of the day to change over time. Additionally, deviations in the circularity of the orbit also affect the precession of the Earth's axis.
Precession is a significant phenomenon in astronomy and has been observed for thousands of years. It has important implications for studies of astronomy, geology, and climate change. For instance, precession affects the timing of the seasons and has a significant impact on the Earth's climate. It also affects the orientation of the Earth's magnetic field, which has important implications for navigation and communication systems.
In conclusion, precession is the gradual change in the orientation of the Earth's rotational axis, caused by the gravitational forces of the Sun, Moon, and other planets. It results in changes in the magnitude of the angle of tilt, changes in the rate of Earth's spin, and deviations in the circularity of the orbit. Precession has significant implications for various fields of study, including astronomy, geology, and climate change.

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Tiffany's marginal utility of apples can be calculated by taking the derivative of her utility function with respect to apples (q). In this case, Uq = 3 + 10q. Therefore, her marginal utility of apples is 3 + 10q. Similarly, her marginal utility of kumquats can be calculated by taking the derivative of her utility function with respect to kumquats (q2). In this case, Uq2 = 5. Thus, her marginal utility of kumquats is a constant value of 5.

Tiffany's budget constraint can be represented by the equation 2q + 4q2 = 40, where q represents the pounds of apples and q2 represents the pounds of kumquats she purchases. By rearranging the equation, we get q = 20 - 2q2/5, which represents the trade-off between the two goods given her income.

Tiffany's marginal rate of substitution (MRS) is the ratio of the marginal utility of apples to the marginal utility of kumquats, i.e., MRS = (3 + 10q)/(5). Since the marginal utility of apples is linear, the MRS remains constant, indicating that Tiffany's indifference curves are linear as well.

To find Tiffany's optimal consumption bundle, we need to find the point where her budget constraint is tangent to an indifference curve. Since Tiffany's indifference curves are linear, they have a constant slope (MRS), and the optimal consumption bundle will occur where the slope of the budget constraint (the price ratio of apples to kumquats) equals the slope of the indifference curve (MRS). This point can be found by solving the equations simultaneously.

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Answer:

Step-by-step explanation:

2. (5-y) (-2y)

-10y + 2y^2

3. (-5v) (5-4v+5v^2)

-25v + 20v^2 -25v^3

4. 7y (y^2-y+5)

7y^3 - 7y^2 + 35y

There is no solution for two equations 2x – y = 7 and y = 2x + 3 .

What is an equation?

A statement that the values of two mathematical expressions are equal (indicated by the sign =).

Name different methods to solve the system of equations .

(1)The Graphing Method .

(2)The Substitution Method .

(3)The Linear Combination Method

(4)The Addition Method

(5)The Elimination Method.

(6)The Matrix Method .

The solution of two equations

2x – y = 7 and

y = 2x + 3

On solving the two equations by Subsitution Method ,we get

2x-(2x+3) =7

⇒2x-2x-3=7

⇒0 -3 =7

⇒-3 =7

But since the numbers are not equal ,so we conclude that

-3≠7

Hence ,as x gets canceled and y value is subsituted ,so as a result we get two numbers which are also not equal .

Hence,there is no solution for x and y .

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Corrected Question

What is the solution to the system of equations 2x – y = 7 and y = 2x + 3 ?

There is no solution for two equations 2x – y = 7 and y = 2x + 3 .

A statement that the values of two mathematical expressions are equal (indicated by the sign =).

Name different methods to solve the system of equations .

(1)The Graphing Method .

(2)The Substitution Method .

(3)The Linear Combination Method

(4)The Addition Method

(5)The Elimination Method.

(6)The Matrix Method .

The solution of two equations

2x – y = 7 and

y = 2x + 3

On solving the two equations by Substitution Method ,we get

2x-(2x+3) =7

⇒2x-2x-3=7

⇒0 -3 =7

⇒-3 =7

But since the numbers are not equal ,so we conclude that

-3≠7

Hence ,as x gets canceled and y value is substituted ,so as a result we get two numbers which are also not equal .

Hence, there is no solution for x and y .

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NOTE: The given question is incomplete on the portal. Here is the complete question.

QUESTION: What is the solution to the system of equations 2x – y = 7 and y = 2x + 3 ?

Recall that variability is a way of measuring how different are a set of numerical values from each other. So, in this case, we want to choose a question to which the answers from the sample are not different from each other. We are told that all apartments are identical, so if the question is referred to the characteristics of the apartments, we will get the same response.

From the given options, we can see that the only question referring to the characteristics of the apartments is how many bedrooms are in your apartment ?. Note that as the apartments are identical, the answer to this question would be the same number (let's say 3 as an example). So the variability of this set would be 0 as we only have one numerical value in the set.