AB= 6 cm, AC = 12 cm
Calculate the length of CD.
Give your answer to 3 significant figures.
C
D
55°
12 cm
B 6 cm

Given, the   Probability   Density Function: f(x)=(6/27)x(3−x) for 0≤x≤3

To determine the Expected Value of demand, E(x), we use the formula; E(x) = ∫x f(x)dx

For the probability Density function given ;f(x)=(6/27)x(3−x) for 0≤x≤3E(x) = ∫x f(x)dx= ∫[0,3] x (6/27)x(3−x) dx= (6/27) ∫[0,3] x²(3−x) dx= (6/27) [∫[0,3] 3x² dx - ∫[0,3] x³ dx]= (6/27) [(3x³/3) - (x⁴/4)] [0,3]= (6/27) [(27-81/4)]= (6/27) [(108-81)/4]= (6/27) (27/4)= 1/4

Therefore, the expected value of demand is 1/4To determine the Standard Deviation of demand,

We use the formula; SD(x) = √Var(x) where, Var(x) = ∫(x - E(x))² f(x) dx SD(x) = √[∫(x - E(x))² f(x)dx]Var(x) = ∫(x - E(x))² f(x)dxVar(x) = ∫[0,3] (x - 1/4)² (6/27)x(3−x) dx= (6/27) ∫[0,3] (x - 1/4)² (3−x) dx= (6/27) [∫[0,3] (x - 1/4)² (3) dx - ∫[0,3] (x - 1/4)² x dx]= (6/27) [9∫[0,3] (x² - 1/2x + 1/16) dx - ∫[0,3] (x³ - 1/2x² + 1/16x) dx]= (6/27) [9(27/4 - 1/2(3)/2 + 1/16(3)) - (81/4 - 1/2(3²)/2 + 1/16(3²)/2)]= (6/27) [(243/4 - 9/2 + 3/16) - (81/4 - 9/4 + 9/32)]= (6/27) [(243/4 - 9/2 + 3/16) - (81/4 - 9/4 + 9/32)]= (6/27) (24.53)= 1.46

Therefore, the standard deviation of demand is 1.46

To determine the probability that x is within one standard deviation of the mean,

We use the formula P(μ - σ < X < μ + σ) = ∫f(x)dx

Where,μ = E(x) = 1/4σ = SD(x) = 1.46P(μ - σ < X < μ + σ) = ∫[μ - σ, μ + σ] f(x)dx= ∫[1/4 - 1.46, 1/4 + 1.46] (6/27)x(3−x) dx= (6/27) ∫[-1.21, 1.96] x(3−x) dx= (6/27) [(3x²/2 - x³/3)] [-1.21, 1.96]= (6/27) [(3(1.96)²/2 - 1.96³/3) - (3(-1.21)²/2 - (-1.21)³/3)]= (6/27) (3.56 + 1.17)= 1.06

Therefore, the probability that x is within one standard deviation of the mean is 1.06.

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Answer:

Q1: 3/72

Q2: 6 inches

Step-by-step explanation:

What is the unit rate for inches per yard on this blueprint?

First convert 1 1/5 yards to inches, so that becomes 216/5 inches.

To keep things consistent, let's convert the 1 4/5 inches to an improper fraction: 9/5 inches.

The question asks for inches per yard, so we substitute in the values:

\(\frac{\frac{9}{5} }{\frac{216}{5} }\)

and simplify: 3/72

If fence B is 4 yards long, how long is fence B on the blueprint?

Convert 4 yards to inches (to comply to the ratio above): 144 inches

The ratio is inches to yards, so substitute in the value:

\(\frac{3}{72} = \frac{x}{144}\)

and solve: 6 inches

Answer:

Option A

Step-by-step explanation:

The median is the value that lies in the middle of the data when the data set is ordered.

It is also the value that separates the higher half of the dataset from the lower half of the dataset.

Answer:

B

Step-by-step explanation:

Answer:

morning - 40

afternoon - 85

Step-by-step explanation:

The bus traveled 40 miles in the morning and 85 miles in the afternoon.

The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.

The school bus traveled five miles more on a field trip in the afternoon than it did in the morning. If the journey was 125 kilometers long

Let x the distance traveled by bus in the morning.

As per the given condition, we can get the equation shown below:

⇒ x + 2x + 5 = 125

⇒ 3x + 5 = 125

⇒ 3x = 120

⇒ x = 40

In the afternoon, the bus traveled 2x + 5 miles.

Now substitute the value of x in the equation for the afternoon miles to include:

⇒ 2 × 40 +5 = 85

Therefore, the bus traveled 40 miles in the morning and 85 miles in the afternoon.

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The accumulated value of the annuity, considering quarterly payments of $575 for 17 years with a nominal interest rate of 13% per year compounded quarterly, is approximately $75,473.08. To find the accumulated value of an annuity, we can use the formula for the future value of an ordinary annuity:

Accumulated Value = Payment * [(1 + interest rate)^n - 1] / interest rate

Payment (PMT) = $575

Nominal Interest Rate (r) = 13% or 0.13

Number of periods (n) = 17 years * 4 quarters per year = 68 quarters

Substituting the values into the formula, we have:

Accumulated Value = $575 * [(1 + 0.13/4)^68 - 1] / (0.13/4)

Calculating the exponent:

(1 + 0.13/4)^68 ≈ 7.9936

Now we can calculate the accumulated value:

Accumulated Value = $575 * (7.9936 - 1) / (0.13/4) ≈ $75,473.08

Therefore, the accumulated value of the annuity, considering quarterly payments of $575 for 17 years with a nominal interest rate of 13% per year compounded quarterly, is approximately $75,473.08.

The annuity payments are made at the beginning of each quarter, and the interest is compounded quarterly. The formula calculates the accumulated value by summing up the future values of each payment over the specified time period.

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Answer:

\(2\sqrt[3]{3}\)

explanation:

\(\rightarrow \sf 24^{\frac{1}{3}}\)

\(\rightarrow \sf \sqrt[3]{24}\)

\(\rightarrow \sf \sqrt[3]{2*2*2*3}\)

\(\sf \rightarrow \left(2^3\cdot \:3\right)^{\frac{1}{3}}\)

\(\sf \rightarrow 2\cdot \:3^{\frac{1}{3}}\)

\(\sf \rightarrow 2\sqrt[3]{3}\)

Answer:

Step-by-step explanation:

24^(1/3)

=(8*3)^(1/3)

=(8)^(1/3)*(3)^(1/3)

=(2^3)^(1/3)*3^(1/3)

=2*(3)^(1/3)

or \(2\sqrt[3]{3}\)

Thus,  the proof of the identity cos^2(5x) - sin^2(5x) = cos(10x) involves the use of the double angle formula for cosine. This identity is useful in solving various problems related to trigonometry.

To prove the trigonometric identity cos^2(5x) - sin^2(5x) = cos(10x), we will use the double angle formula for cosine.

This formula states that cos(2θ) = cos^2(θ) - sin^2(θ). We can rewrite our identity as:
cos^2(5x) - sin^2(5x) = cos(2 * 5x)

Using the double angle formula, we get:
cos^2(5x) - sin^2(5x) = cos(10x)

This proves the given trigonometric identity.

To understand this identity better, let's break it down.

The left-hand side of the identity consists of two terms, cos^2(5x) and sin^2(5x).

These terms are known as the Pythagorean identity and state that cos^2(θ) + sin^2(θ) = 1.

We can rewrite cos^2(5x) as 1 - sin^2(5x) using this identity.

Substituting this value in the given identity, we get:
1 - sin^2(5x) - sin^2(5x) = cos(10x)

Simplifying this equation, we get:
cos^2(5x) - sin^2(5x) = cos(10x)

Therefore, we have successfully proven the given trigonometric identity.

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The magnitude of the expected shortfall at a 95% confidence level is not provided. Please provide the necessary information to calculate the expected shortfall.

The expected shortfall at a specific confidence level, we need additional information, such as the distribution of returns or loss data. The expected shortfall, also known as conditional value-at-risk (CVaR), represents the average value of losses beyond a certain threshold.

Typically, the expected shortfall is calculated by taking the average of the worst (1 - confidence level) percent of losses. However, without specific data or parameters, it is not possible to determine the magnitude of the expected shortfall at a 95% confidence level.

To calculate the expected shortfall, we would need a set of data points representing returns or losses, as well as a specified distribution or methodology to estimate the expected shortfall. Please provide the necessary details so that the expected shortfall can be calculated accurately.

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i just got some free money off of you kid

Answer:

455

Step-by-step explanation:

I answered first, but forgot to answer here.

The total number of combinations of sandwiches possible is 360.

A local sub shop offers five different breads, four different meats, three different cheeses, and six different vegetables. You can choose one bread and any number of the other items.

To find the total number of combinations of sandwiches possible, we can use the multiplication rule.The multiplication rule states that if there are m ways to do one task and n ways to do another task, then there are m × n ways to do both tasks.

Similarly, if there are m ways to do one task, n ways to do another task, and p ways to do a third task, then there are m × n × p ways to do all three tasks.

To apply the multiplication rule to this problem, we can multiply the number of options for each component:Breads: 5 optionsMeats: 4 optionsCheeses: 3 optionsVegetables: 6 options

To find the total number of combinations, we can multiply the number of options for each component:5 × 4 × 3 × 6 = 360Therefore, there are 360 possible combinations of sandwiches.

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Answer:

    The correct answer is: (Line segment E F)

Answer:

30+y

Step-by-step explanation:

Answer:

He didn't include a parenthesis around 5+y

Step-by-step explanation:

The variables of the test statistic may be determined to be \($s _1$\), \($s _2$\), \($n_ 1, n _2$\), t, which is the t - distribution test statistic, and \($x _1, x _2$\), which is the mean of the two samples.

When the variances of the two groups are not equal, pooled standard deviation estimations cannot be used. As an alternative, we must determine the standard error for each group separately. The variables of the test statistic may be determined to be \($s _1$\), \($s _2$\), \($n_ 1, n _2$\), t, which is the t - distribution test statistic, and \($x _1, x _2$\), which is the mean of the two samples.

The formula for this type of test statistic is given by -

\($t=\frac{x_1-x_2}{\sqrt{\frac{s_1^2}{n_1}+\frac{x_2}{n_2}}}$$\)

Here, the variables can be defined as below -

\($s_1^2, s_2^2=$\) variance of two samples

\($n_1, n_2=$\) respective sizes of the two samples

t = t - distribution test statistic

\($x_1, x_2=$\) Mean of the two samples

As a result, the variables of the test statistic can be determined to be \($s _1, s _2$\), which represents the variance of two samples, \($n _1, n _2$\), which represents the size of the two samples, t, which represents the t-distribution test statistic, and \($x _1, x _2$\), which represents the mean of the two samples.

The complete question is:

The formula for the test statistic used for a two sample test of means where the population variances are unknown and unequal is:

t = X1−X2√s12/n1+s22/n2X1-X2s12/n1+s22/n2

Match the variables to their description.

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The arc length is π units and the sector area is 3π/2 unit²

The formula for the length of arc is given by:

L = θ * r

where r is the radius and  θ is the central angle

L = π/3 × 3

L = π units or L = 22/7 = 3.14 units

The formula for the area of sector is given by:

A = 1/2 × r² × θ

where r is the radius and  θ is the central angle

A =  1/2 × 3² × π/3

A =  1/2 × 9 × π/3

A = 3π/2 unit² or A = 3/2 × 22/7 = 4.71 unit²

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Answer:

Hi

Step-by-step explanation:

The expression was reduced to it's lowest expression or term or we say we found the common factor amongst them

Answer:

1/2 .............

Step-by-step explanation:

hope this helped

Answer:

the 92nd term of the arithmetic sequence is 731 because the common difference between them is 8.

x = 0 and Reduced cost = -4: This combination is not possible for decision variable x and its corresponding reduced cost.

Based on the complementary slackness condition in linear programming, the values of the decision variable x and its corresponding reduced cost can provide insights into the feasibility and optimality of the solution.

In the given scenarios:

x = 20 and Reduced cost = -4:

This combination is possible as a non-zero value of x with a negative reduced cost indicates that x is a non-basic variable and has a potential to increase in order to improve the objective function value.

x = 0 and Reduced cost = -4:

This combination is not possible because if x is a non-basic variable with a reduced cost of -4,

it implies that increasing x from zero would improve the objective function value, violating the complementary slackness condition.

x = 0 and Reduced cost = 0:

This combination is possible as x can be a basic variable with a reduced cost of zero,

indicating that it is at its lower bound and does not need to change.

x = 20 and Reduced cost = 0:

This combination is possible as a non-zero value of x with a reduced cost of zero implies that x is a non-basic variable and has already reached its upper bound,

so it does not need to change to improve

the objective function value.

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Answer:

4x+12

Step-by-step explanation:

hereeeeere you go?!

Answer:

4x + 12

Step-by-step explanation:

Answer:

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

Using triangle inequality theorem, we get two options:

1) x is the longest side, then:

2) x is the shortest side, then:

Combine the two options to get, x is between 2 and 22, or:

This is the first choice.

Answer:

\(Ratio = 7:6\)

Step-by-step explanation:

Given

Initially

\(Joe = 12oz\) -- coffee

\(JoAnn = 12oz\) -- coffee

Joe drank 2oz coffee; So, we have:

\(Joe = 12oz - 2oz\)

\(Joe = 10oz\) --- coffee

Joe added 2oz cream; So, we have:

\(Joe = 10oz\) --- coffee     \(Joe = 2oz\) --- cream

JoAnn added 2oz cream and stirred. So, we have:

\(Joe = 12oz\) --- coffee     \(JoAnn = 2oz\) --- cream

\(Total = 14oz\)

JoAnn drank 2oz from the drink; the amount of drink JoAnn drank is:

\(JoAnn = \frac{Cream}{Total}\)

\(JoAnn = \frac{2}{14}\)

\(JoAnn = \frac{1}{7}\)

Amount of cream left is:

\(Amount = [1- \frac{1}{7}] *2\)

Take LCM

\(Amount = [\frac{7-1}{7}] * 2oz\)

\(Amount = \frac{6}{7} * 2oz\)

\(Amount = \frac{12}{7}oz\)

So, we have:

\(Joe = 2oz\) --- cream

\(JoAnn = \frac{12}{7}\) cream

The ratio is:

\(Ratio = 2:\frac{12}{7}\)

Multiply by 7

\(Ratio = 14:12\)

Divide by 2

\(Ratio = 7:6\)

Answer:

13 hours

Step-by-step explanation:

605/11=55

715/55=13

Answer:

x = 100

Step-by-step explanation:

180 = 46 + 34 + x

180 = 80 + x

100 = x

Cofunction pairs are shifted by π/2 radians (90 degrees) from each other.

Cofunction pairs are shifted by π/2 radians (90 degrees) from one another. It means that the value of one function at an angle is equal to the other function at that angle plus π/2 radians.

For example, the sine function and cosine function are cofunctions, and they are shifted by π/2 radians from each other. The same is true for other cofunction pairs such as tangent and cotangent, and secant and cosecant.

This means that the value of the sine function at a certain angle is equal to the cosine function at that angle plus π/2 radians (90 degrees), and vice versa. Similarly, the same for value of the tangent function, secant function at a certain angle.

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Answer:

0.1

Step-by-step explanation:

Just take 24/24 which is 1 and move the decimal one place to the left because there is an extra 0 on the denominator

Answer:

3(3a+4)

Step-by-step explanation:

Answer:

I think you cannot add 9a + 12 because 12 does not have a letter in tonces, it will stay the same

Step-by-step explanation:

Answer:

a = 5

Step-by-step explanation:

let's label the triangle as a, b and c

where b is the hypotenuse and c is the adjacent of the hypotenuse a to be the height.

from the formula

a² + c² = b²

we substitute the values to find a

so,

a² + 12² = 13²

but we don't know "a" so we make it stand alone by grouping liked terms.

a² = 13² - 12²

a² = 25

we need "a" not "a²" so we take the square root of both sides to get rid of "a²" leaving "a"

\( \sqrt{ {a}^{2} } = \sqrt{25} \)

and the answer will be

a = 5

a. Second partial derivatives of f(x, y):

∂²f/∂x² = 12x^2

∂²f/∂y² = -2x

∂²f/∂x∂y = -2y

b. Second partial derivatives of g(x, y):

∂²g/∂x² = (2y^2 - x^2)/(x^2 + y^2)^2

∂²g/∂y² = (2x^2 - y^2)/(x^2 + y^2)^2

∂²g/∂x∂y = (-4xy)/(x^2 + y^2)^2

c. Second partial derivatives of h(x, y):

∂²h/∂x² = -sin(ex+y) * (ex+y)^2 + cos(ex+y)

∂²h/∂y² = -sin(ex+y) * (ex+y)^2 + cos(ex+y)

∂²h/∂x∂y = -sin(ex+y) * (ex+y)^2 + cos(ex+y)

(a) First partial derivatives of f(x, y):

∂f/∂x = 4x^3 - y^2

∂f/∂y = -2xy + 1

Second partial derivatives of f(x, y):

∂²f/∂x² = 12x^2

∂²f/∂y² = -2x

∂²f/∂x∂y = -2y

(b) First partial derivatives of g(x, y):

∂g/∂x = (2x)/(x^2 + y^2)

∂g/∂y = (2y)/(x^2 + y^2)

Second partial derivatives of g(x, y):

∂²g/∂x² = (2y^2 - x^2)/(x^2 + y^2)^2

∂²g/∂y² = (2x^2 - y^2)/(x^2 + y^2)^2

∂²g/∂x∂y = (-4xy)/(x^2 + y^2)^2

(c) First partial derivatives of h(x, y):

∂h/∂x = cos(ex+y) * ex+y

∂h/∂y = cos(ex+y) * ex+y

Second partial derivatives of h(x, y):

∂²h/∂x² = -sin(ex+y) * (ex+y)^2 + cos(ex+y)

∂²h/∂y² = -sin(ex+y) * (ex+y)^2 + cos(ex+y)

∂²h/∂x∂y = -sin(ex+y) * (ex+y)^2 + cos(ex+y)

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