(1 point) Rework problem 9 from section 2.4 of your text. Assume that 12 people, including the husband and wife pair, apply for 6 sales positions. People are hired at random. (1) What is the probability that both the husband and wife are hired? 210/924 (2) What is the probability that one is hired and one is not?

Answer:

A.10

Step-by-step explanation:

add all of them =48

48/5= 9.6

Answer:

Tip: $2.61

Total: $17.11

Step-by-step explanation:

tip = total cost * rate of tip

Add the tip to the original bill, that's the total.

I hope this helped.

Answer:

Step-by-step explanation:

B

The total mass of the stars in Pair X is 16 times the total mass of the stars in Pair Y. This means that Pair X has a significantly greater total mass compared to Pair Y.

To understand why, let's consider the relationship between orbital period and total mass in binary star systems. According to Kepler's Third Law of Planetary Motion, the square of the orbital period (T) is proportional to the cube of the semi-major axis (a) of the orbit. Since the separation of the pairs is identical, we can assume that the semi-major axes are the same for both pairs.

Given that the orbital period of Pair X is 4 times that of Pair Y, the square of the orbital period of Pair X (T_x^2) is 16 times the square of the orbital period of Pair Y (T_y^2). Since the semi-major axes are the same for both pairs, the ratio of the total masses (M_x/M_y) will be the square root of the ratio of the orbital periods (T_x/T_y). Therefore, (M_x/M_y) = sqrt(T_x/T_y) = sqrt(4) = 2.

This implies that the total mass of Pair X is 2 times the total mass of Pair Y. Since the total mass of Pair X is 16 times the total mass of Pair Y, we can conclude that Pair X has a total mass that is 16 times greater than Pair Y.

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Answer:

fart

Step-by-step explanation:

Answer:

10 groups

Step-by-step explanation:

because 30 divided by 3 is 10

Answer:

y - 5 = 3(x - 6)

Step-by-step explanation:

The equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b ) a point on the line

Here m = 3 and (6, 5 ) a point on the line , then

y - 5 = 3(x - 6) ← equation of line

Step-by-step explanation:

Since g(f(x))=x g ( f ( x ) ) = x , f−1(x)=2x f - 1 ( x ) = 2 x is the inverse of f(x)=12x f ( x ) = 1 2 x .

Replace f(x)f(x) with yy.

y=12xy=12x

Interchange the variables.

x=12yx=12y

Solve for yy.

Rewrite the equation as 12y=x12y=x.

12y=x12y=x

Multiply both sides of the equation by 22.

2⋅12⋅y=2⋅x2⋅12⋅y=2⋅x

Simplify 2⋅12⋅y2⋅12⋅y.

Cancel the common factor of 22.

Cancel the common factor.

2⋅12⋅y=2⋅x2⋅12⋅y=2⋅x

Rewrite the expression.

1⋅y=2⋅x1⋅y=2⋅x

Multiply yy by 11.

y=2⋅xy=2⋅x

Solve for yy and replace with f−1(x)f-1(x).

Replace the yy with f−1(x)f-1(x) to show the final answer.

f−1(x)=2xf-1(x)=2x

Set up the composite result function.

g(f(x))

The specific range depends on the material properties and the energy levels involved.

The minimum and maximum frequencies for the acoustic and optic modes depend on the specific system or material under consideration. However, I can provide some general information.

Acoustic Mode:

The acoustic mode refers to the propagation of sound waves or vibrations in a material. In a solid, the acoustic mode can have different types, such as longitudinal and transverse modes.

The minimum frequency for the acoustic mode is typically determined by the size and physical properties of the material. In general, it can be close to zero for macroscopic objects or materials with low elasticity.

The maximum frequency for the acoustic mode depends on factors such as the speed of sound in the material and the characteristic dimensions of the system. It can range from a few kilohertz to several gigahertz.

Optic Mode:

The optic mode is related to the interaction of light with a material. It typically refers to the vibrations of charged particles (such as electrons) in a solid or the oscillations of electric or magnetic fields associated with photons.

The minimum frequency for the optic mode is typically determined by the energy gap between electronic states in the material. For example, in a semiconductor, the minimum frequency is usually in the infrared range.

The maximum frequency for the optic mode is not strictly defined, as it can extend into the terahertz, infrared, visible, ultraviolet, X-ray, and even gamma-ray regions. The specific range depends on the material properties and the energy levels involved.

It's important to note that these frequency ranges are general guidelines and can vary depending on the specific system or material being studied.

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Answer:

$2.20

Step-by-step explanation:

40% converted to decimal is 0.4.

$5 × 0.4 = $2

10% converted to decimal is 0.1.

Because the tax is increasing the price by a percentage you add a 1 to the 0.1.

1.1 × $2 = $2.20

Answer:

$3.30

Step-by-step explanation:

40% of $5 = $2

Therefore, discounted price of candy is $5 - $2 = $3.

10% sales tax = 1.1 x $3 = $3.30

Answer: $3.30

Answer:

x=-2

Step-by-step explanation:

Isolate the variable by dividing each side by factors that don't contain the variable

Answer:

\((\sqrt[3]{729} )^{3}\) + 24 can be simplified to 753.

Step-by-step explanation:

If you take the root of a number to a specific number, then square that by the same number you took the root by, then you will have the same number you started with. In this case, \(\sqrt[3]{729}\) equals 9, and \(9^{3}\) equals 729, so \((\sqrt[3]{729} )^{3}\) equals 729. 729 + 24 = 753, so that is the simplified answer.

Among the provided functions, the ones that approach positive infinity as x approaches negative infinity are:

- f(x) = 2x^5

- f(x) = 6x^8 + 9x^6 + 32

- f(x) = -x + 8x^4 + 248

To determine which functions approach positive infinity as x approaches negative infinity, we need to analyze the leading terms of the functions. The leading term dominates the behavior of the function as x becomes very large or very small.

Let's examine each function and identify their leading terms:

1. f(x) = 2x^5

The leading term is 2x^5, which has a positive coefficient and the highest power of x.

As x approaches negative infinity, this term becomes very large and positive, indicating that f(x) approaches positive infinity.

2. f(x) = 9x + 100

The leading term is 9x, which has a positive coefficient but a lower power of x compared to the constant term 100.

As x approaches negative infinity, the leading term becomes very large and negative, indicating that f(x) approaches negative infinity, not positive infinity.

3. f(x) = 6x^8 + 9x^6 + 32

The leading term is 6x^8, which has a positive coefficient and the highest power of x.

As x approaches negative infinity, this term becomes very large and positive, indicating that f(x) approaches positive infinity.

4. f(x) = -8x^3 + 11

The leading term is -8x^3, which has a negative coefficient and the highest power of x.

As x approaches negative infinity, this term becomes very large and negative, indicating that f(x) approaches negative infinity, not positive infinity.

5. f(x) = -10x + 5x + 26

Combining like terms, we have f(x) = -5x + 26.

The leading term is -5x, which has a negative coefficient but a lower power of x compared to the constant term 26.

As x approaches negative infinity, the leading term becomes very large and positive, indicating that f(x) approaches negative infinity, not positive infinity.

6. f(x) = -x + 8x^4 + 248

The leading term is 8x^4, which has a positive coefficient and the highest power of x.

As x approaches negative infinity, this term becomes very large and positive, indicating that f(x) approaches positive infinity.

Therefore, the correct choices are:

- f(x) = 2x^5

- f(x) = 6x^8 + 9x^6 + 32

- f(x) = -x + 8x^4 + 248

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The matrix that shows the prices in U.S. dollars is:

[1.81  6.32  0.56 0.36]

Here we have a simple row matrix which can be written as:

[80  280  25  16]

You can see this as a row vector or something like that, notice that if we multiply this by an scalar, we just need to multiply each element by an scalar.

Now, we know that:

1 dollar = 44.32 Nu

then:

1 Nu = (1/44.32) dollars.

So to get the matrix in dollars, just multiply each number by (1/44.32), then we will get:

(1/44.32)*[80  280  25  16] = [80/44.32  280/44.32  25/44.32  16/44.32]

= [1.81  6.32  0.56 0.36]

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Answer:

be chill bro but which subject is this

100 : 110 : 121 is the ratio must they invest money at 10% per annum compounded yearly so that each gets same sum at the age of their retirement

percentage, a relative value indicating hundredth parts of any quantity.

Given,

Let P, R and S are three persons with ages 26 years, 27 years and 28 years

We need to find the ratio must they invest money at 10% per annum compounded yearly so that each gets same sum at the age of their retirement

x(11/10)ⁿ=y(11/10)ⁿ⁻¹=3(11/10)ⁿ⁻²

x.121/100=y.11/10=3

x/100=y/110=3/121

Hence,  100 : 110 : 121 is the ratio must they invest money at 10% per annum compounded yearly so that each gets same sum at the age of their retirement

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To visualize this transformation, imagine a rectangle with vertices at and (0,2). Applying the transformation (x,y) →  \((3x,3y)\) to each vertex, we get a new rectangle with vertices at   \((0,0), (3,0), (3,6),\) and \((0,6)\), which is three times the size of the original rectangle.

Algebraic representations can take many forms, including equations, inequalities, functions, and matrices. These representations provide a powerful tool for analysing complex systems and deriving meaningful insights from them.

The algebraic representation \((x,y) (3x,3y)\) describes a dilation transformation, specifically an enlargement or stretch by a scale factor of 3 in both the x and y directions.

This means that every point in the original figure is multiplied by 3 in both the x and y directions, resulting in a larger, similar figure.

To visualize this transformation, imagine a rectangle with vertices at  \((0,0), (1,0), (1,2),\)  and   \((0,2).\) Applying the transformation (x,y) → (3x,3y) to each vertex, we get a new rectangle with vertices at \((0,0), (3,0), (3,6),\)  and (0,6), which is three times the size of the original rectangle.

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Answer:

10

Step-by-step explanation:

30 x 1/3 = 10

aka if you do something 30 times and every 3 times it happens you do it 10 times.

Answer:

\( \boxed{ \bold{ \huge{ \boxed{ \sf{84.5}}}}}\)

Step-by-step explanation:

Given data :

89 , 74 , 100 , 86 , 74 , 67 , 86 , 72 , 60 , 93 , 83 , 86

Arranging the data in ascending order, we have,

60 , 67 , 72 , 74 , 74 ,83 , 86 , 86 , 86 , 89 , 93 , 100

Here, n ( total no.of observation ) = 12

Now, finding the position of media :

\( \boxed{ \sf{position \: of \: median = ( \frac{n + 1}{2} ) ^{th} \: item}}\)

⇒\( \sf{ (\frac{12 + 1}{2} ) ^{th} item}\)

⇒\( \sf{( \frac{13}{2} ) ^{th} item}\)

⇒\( \sf{ {6.5}^{th} item}\)

6.5 th item is the average of 6 th and 7 th items.

Again,

\( \sf{median = \frac{ {6}^{th \: item} + {7}^{th} item}{2} }\)

⇒\( \sf{ \frac{83 + 86}{2} }\)

⇒\( \sf{ \frac{169}{2} }\)

⇒\( \sf{84.5}\)

Hope I helped!

Best regards!!

The correct answer is d. the zeros are neither positive nor negative. The student included these in the interval over which the function is positive, which is incorrect.

The statement indicates that the zeros of the function are neither positive nor negative. This means that the function changes sign at the zeros, crossing the x-axis from either the positive side to the negative side or vice versa.

If the student included these zeros in the interval over which the function is positive, it would be incorrect because the function should be positive on one side of the zero and negative on the other side.

Similarly, if the student included these zeros in the interval over which the function is negative, it would also be incorrect because the function should be negative on one side of the zero and positive on the other side.

The correct statement is d. the zeros are neither positive nor negative. The student including these zeros in the interval over which the function is positive is incorrect. The function changes sign at the zeros, and it is important to consider both the positive and negative intervals correctly when determining the intervals of positivity and negativity for the function.

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Answer:

10.3

Step-by-step explanation:

a^2 + b^2 = c^2

3.9^2 + b^2 = 11^2

b^2 = 121 - 15.21

b = 10.3

Answer:

10.3

Step-by-step explanation:

We use the pythagorean theorem. (a^2+b^2=c^2)

3.9^2 + b^2 = 11^2

3.9^2 = 15.21

11^2 = 121

15.21 + b^2 = 121

Subtract 15.21 from both sides

b^2=105.79

Take the square root of both sides

b = 10.28

10.28 is closest to 10.3 and it is also rounded to 10.3, therefore 10.3 is the answer.

Liam’s profits after six years will be \($46,637.44\).

The formula to calculate the amount of profits after six years is given by:

Final Profits = Initial Profits x (1 + Appreciation Rate)^Years

In this case, Liam's profits after six years can be calculated as:

Final Profits = \($43,200 x (1 + 1.2%)^6\)

Final Profits = \($43,200 x 1.07722\)

Final Profits = \($46,637.44\)

Therefore, Liam’s profits after six years will be \($46,637.44\).

The formula used to calculate the profits after six years is useful for predicting the amount of profits Liam will earn in the future given a certain appreciation rate. This can help Liam make more informed decisions about his business and plan for the future.

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Answer:

option 1 and option 2 should be correct

To determine the speed at which Peter traveled from A to C via B in 3 hours, we will first calculate the total distance and then divide it by the time. Here's a step-by-step explanation:

1. Calculate the total distance: Add the distance from A to B (137km) and the distance from B to C (115km).
Total distance = 137km + 115km = 252km

2. Calculate the time taken: Peter traveled this total distance in 3 hours.

3. Calculate the speed: Divide the total distance by the time taken.
Speed = Total distance / Time taken
Speed = 252km / 3 hours

4. Calculate the result:
Speed = 84 km/h

So, Peter was traveling at a speed of 84 km/h during his journey from A to C via B in 3 hours.    

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The probability that she selects the route of three specific capitals is 97290/1.

The probability that she selects the route of three specific capitals can be calculated by taking the total number of possible routes and dividing it by the total number of routes that involve the three specific capitals. To calculate the total number of possible routes, multiply the number of states (47) by the number of routes that could be selected from each state (2). This gives 94 total possible routes.

47 x 46 x 45 ways = 97290 ways

= 1/97290

Now, calculate the number of routes that involve the three specific capitals. Since the president is selecting three states, the total number of routes will be 3. Therefore, the probability that she selects the route of three specific capitals is 3/94, which can be simplified to 97290/1.

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To find the probability that the sample proportion of Republicans will be greater than 60% in a sample of 447447 voters, we need to use the concept of sampling distributions and the normal approximation to the binomial distribution.

To calculate the probability, we can use the normal approximation to the binomial distribution since the sample size is large (447447) and the proportion of Republicans in the population is given (56%).

First, we calculate the mean and standard deviation of the sampling distribution. The mean (μ) is equal to the proportion of Republicans in the population (56%) and the standard deviation (σ) is determined using the formula: σ = sqrt((p * (1 - p)) / n), where p is the proportion of Republicans and n is the sample size.

Next, we standardize the sample proportion of 60% using the formula: z = (x - μ) / σ, where x is the sample proportion we want to find the probability for. In this case, x is 60%.

Finally, we use a standard normal distribution table or a statistical calculator to find the probability corresponding to the standardized value of z. The probability will be the area under the curve to the right of the standardized value.

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The 2nd order Taylor's expansion of f(x, y) at (0, 0) is simply 2x + 2y.

To find Taylor's expansion of the function f(x, y) = 2x + 2y at the point (0, 0) up to the 2nd order, we need to compute the partial derivatives and evaluate them at (0, 0).

First, let's calculate the first-order partial derivatives:

∂f/∂x = 2

∂f/∂y = 2

Next, we need to evaluate these partial derivatives at (0, 0):

∂f/∂x evaluated at (0, 0) = 2

∂f/∂y evaluated at (0, 0) = 2

Now, let's compute the second-order partial derivatives:

∂²f/∂x² = 0 (since the derivative of a constant is zero)

∂²f/∂y² = 0 (since the derivative of a constant is zero)

∂²f/∂x∂y = 0 (since the order of differentiation doesn't matter for this function)

Evaluating the second-order partial derivatives at (0, 0):

∂²f/∂x² evaluated at (0, 0) = 0

∂²f/∂y² evaluated at (0, 0) = 0

∂²f/∂x∂y evaluated at (0, 0) = 0

Now, we can write the 2nd order Taylor's expansion of f(x, y) at (0, 0):

f(x, y) ≈ f(0, 0) + (∂f/∂x)(0, 0) * x + (∂f/∂y)(0, 0) * y + (1/2)(∂²f/∂x²)(0, 0) * x² + (1/2)(∂²f/∂y²)(0, 0) * y² + (∂²f/∂x∂y)(0, 0) * xy

Substituting the evaluated derivatives, we have:

f(x, y) ≈ 0 + 2x + 2y + (1/2)(0)(x²) + (1/2)(0)(y²) + (0)(xy)

Simplifying further, we obtain:

f(x, y) ≈ 2x + 2y

Therefore, the 2nd order Taylor's expansion of f(x, y) at (0, 0) is simply 2x + 2y.

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Answer:

0.051

Step-by-step explanation: