If y, p and q vary jointly and p is 14 when y and q are equal to 2, determine q when p and y are equal to 7

Answer:

2/3-4x+7-2=-9.x+5/6

2/3+7/1-2/1-5/6=-9.x+4x

12+126-36-15/18=-5x

87/18=-5x

29/6=-5x

29/6÷5=-5x÷5

29/6*1/5=-5x÷5

29/30=-x

-29/30=x

-0.9667=x

Answer:

\(3.9\) × \(10^9\)

Step-by-step explanation:

To find out the standard form we simply have to look at the first digits in the number greater than 0 and count how many digits are after it!

Example:

The number we are given is 3900000000.

We can see that the first digit greater than 0 is the 3 and we put a decimal point there, so now we count how many digits there are after it.

Which is 9!!

This means our answer is \(3.9\) × \(10^{9}\)

Hope this helps, have a lovely day! :)

Answer

Trapezoids

Step-by-step explanation:

Squares are not trapazoids.

rho.buses 12342476512457

Answer:

D - All rational numbers are integers.

Step-by-step explanation:

This is because integers is a subcategory of rational numbers, so there are other rational numbers that aren't integers.

Hi there, here's your answer:

Given \(g(x) = -x-4\)

To find \(g(-2)\)

Substituting -2 in place of x:

\(-(-2) - 4 = 2-4 = -2\)

∴ \(g(-2) = -2\)

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Answer:

11 hours as a cashier

and 2 hours as a teacher

11 x 8 = 88

6 x 2 = 12

88 + 12 = 100

Step-by-step explanation:

Answer: The rate should normally be in

Gallons per Minute. But here, it might have to be "Pool per Hour" since the total volume is not given.

With two hoses taking 12 minutes, the rate is 5 pools per hour.

Step-by-step explanation:

Take the time to fill with two hoses, double that to get the time for two hoses with equal rates. 24 minutes. But one takes 10 minutes more, so split that. 24 + 5 is 29 minutes. 10 less is 19 minutes. Or try 27 and 17.

If you assume a typical kiddie pool 4 ft diameter and 1 ft deep, not quite full, that would hold around 84 gallons.

84÷12 = 7 gallons per minute.

84÷ 17 = about 4.9 gpm

84 ÷ 27= 3.1 gpm

So 16 and 6 might be possible times to try for realistic rates.

I realize this is not a complete answer, but it might help.

Answer:

Step-by-step explanation:

wouldn't it be 12  meters? is this isn't what you need ill figure it out and edit this

The partial derivative (∂∇∂P)T for the Van der Waals gas is given by

\(\[ \left( \frac{\partial (\frac{\partial P}{\partial V})}{\partial T} \right)_T \]\)

To determine the partial derivative\((\(\frac{\partial (\frac{\partial P}{\partial V})}{\partial T}\))\) for the Van der Waals gas, we can start by applying the product rule of differentiation. Let's break down the given equation:

\(\((P + \frac{a}{V^2})(V - b) = RT\)\)

Expanding the equation, we have:

\(\(PV - Pb + \frac{a}{V} - \frac{ab}{V^2} = RT\)\)

Rearranging the terms, we get:

\(PV + \frac{a}{V} = RT + Pb + \frac{ab}{V^2}\)

Now, let's differentiate both sides of the equation with respect to volume (\(V\)) while keeping the temperature (\(T\)) constant. Using the chain rule, we obtain:

\(\(\frac{\partial}{\partial V}(PV) + \frac{\partial}{\partial V}(\frac{a}{V}) = \frac{\partial}{\partial V}(RT + Pb + \frac{ab}{V^2})\)\)

Differentiating each term separately:

\(\(P + \frac{-a}{V^2} = 0 + \frac{dP}{dV}b - \frac{2ab}{V^3}\)\)

Simplifying the equation:

\(\(\frac{dP}{dV} = \frac{a}{V^2} + \frac{2ab}{V^3} - \frac{Pb}{V}\)\)

Finally, we need to differentiate the obtained expression for \(\frac{dP}{dV}\) with respect to temperature (\(T\)) while holding volume (\(V\)) constant. This will give us the partial derivative we are looking for:

\(\(\left(\frac{\partial (\frac{\partial P}{\partial V})}{\partial T}\right)_T = \left(\frac{\partial}{\partial T}\right)_V (\frac{a}{V^2} + \frac{2ab}{V^3} - \frac{Pb}{V})\)\)

Since \(V\) is held constant, the partial derivative of \(\frac{dP}{dV}\) with respect to \(T\) is zero. Therefore, we can conclude that:

\(\(\left(\frac{\partial (\frac{\partial P}{\partial V})}{\partial T}\right)_T = 0\)\)

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The price that is 3rd standard above the mean, if the mean is $10000  and the standard deviation is $500 is $18500.

Mean is a measurement of a probability distribution's central tendency along the median and mode. It also goes by the name "anticipated value."

Given:

The mean, m = $17000,

The standard deviation, σ = $500

Calculate the 3rd standard deviation as shown below,

3rd standard deviation  = mean + 3 × standard deviation

3rd standard deviation = 17000 + 3 × 500

3rd standard deviation = 17000 + 1500

3rd standard deviation = $18500

Therefore, the price that is 3rd standard above the mean, if the mean is $10000  and the standard deviation is $500 is $18500.

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i don't speak russian bro

The generating function B(x) for the sequence bₙ = ∑[k=0 to n] (k³ - k) is B(x) = (1 - (n + 1)xⁿ + nxⁿ⁺¹)/(1 - x)².To find the generating function A(x) for the sequence aₙ = n³ - n for n≥0.

We can manipulate the geometric series formula.

We have:
∑[infinity] xⁿ = 1/(1 - x)
Taking the derivative of both sides with respect to x,

we get:
d/dx (∑[infinity] xⁿ) = d/dx (1/(1 - x))
Using formal power series manipulations, we differentiate each term individually:
∑[infinity] n xⁿ⁻¹ = 1/(1 - x)²
Now, we multiply both sides by x:
x * ∑[infinity] n xⁿ⁻¹ = x/(1 - x)²
Simplifying, we have:
∑[infinity] n xⁿ = x/(1 - x)²
Therefore, the generating function A(x) for the sequence

aₙ = n³ - n is A(x) = x/(1 - x)².

To find the generating function B(x) for the sequence

bₙ = ∑[k=0 to n] (k³ - k) for n≥0,

we can use the formula for the sum of a geometric series:
∑[k=0 to n] xⁿ = (1 - xⁿ⁺¹)/(1 - x)
Differentiating both sides with respect to x,

we get:
d/dx (∑[k=0 to n] xⁿ) = d/dx ((1 - xⁿ⁺¹)/(1 - x))
Using formal power series manipulations,

we differentiate each term individually:
∑[k=0 to n] n xⁿ⁻¹ = (1 - (n + 1)xⁿ + nxⁿ⁺¹)/(1 - x)²

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(a) Pₙ = (1/6) * (1 - Pₙ₋₁) + (5/6) * Pₙ₋₁

This is the difference equation that we needed to prove.

(b) The difference equation and obtain an explicit formula for Pn,

Pₙ = (1 + 4Pₙ₋₁) / 6

Expressions that are equivalent serve the same purpose regardless of appearance. When we employ the same variable value, two algebraic expressions that are equivalent have the same value.

To prove the given difference equation for Pₙ , let's break it down into two parts: the case where the nth throw results in a six and the case where it does not.

(a) Case: The nth throw results in a six

In this case, we need to consider the previous (n-1) throws to determine the probability of having an even number of sixes. Since the (n-1)th throw cannot be a six, the probability of having an even number of sixes in (n-1) throws is Pₙ₋₁.

Now, for the nth throw to be a six, we have a probability of 1/6. Therefore, the probability of having an even number of sixes in n throws, given that the nth throw is a six, is (1/6) * (1 - Pₙ₋₁).

This is because (1 - Pₙ₋₁) represents the probability of having an odd number of sixes in (n-1) throws.

(b) Case: The nth throw does not result in a six

In this case, we still need to consider the previous (n-1) throws to determine the probability of having an even number of sixes.

Since the nth throw does not result in a six, the probability of having an even number of sixes in (n-1) throws remains the same, which is Pₙ₋₁.

Now, for the nth throw to not result in a six, we have a probability of 5/6. Therefore, the probability of having an even number of sixes in n throws, given that the nth throw does not result in a six, is (5/6) * Pₙ₋₁.

Combining the probabilities from both cases, we get:

Pₙ = (1/6) * (1 - Pₙ₋₁) + (5/6) * Pₙ₋₁

This is the difference equation that we needed to prove.

To solve the difference equation and obtain an explicit formula for Pn, we can rearrange the equation:

6Pₙ = 1 - Pₙ₋₁ + 5Pₙ₋₁

6Pₙ = 1 + 4Pₙ₋₁

Pₙ = (1 + 4Pₙ₋₁) / 6

Now, we can use this recursive formula to find explicit values for Pₙ. We start with P₀, which represents the probability of having an even number of sixes in 0 throws (which is 1):

P₀ = 1

Then, we can use the recursive formula to calculate P₁, P₂, P₃, and so on, until we reach the desired value of Pₙ.

Hence,

(a) Pₙ = (1/6) * (1 - Pₙ₋₁) + (5/6) * Pₙ₋₁

This is the difference equation that we needed to prove.

(b) the difference equation and obtain an explicit formula for Pn,

Pₙ = (1 + 4Pₙ₋₁) / 6

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To balance the line by choosing the assignable task with the longest task time first, you need to follow these steps. Determine the task times for each assignable task in the line.

Identify the assignable task with the longest task time. Assign that task to the first station in the line. Calculate the remaining cycle time by subtracting the task time of the assigned task from the total cycle time.
Repeat steps 2-4 for the remaining assignable tasks, considering the updated cycle time after each assignment.

Task A has the longest task time, so it is assigned to the first station. After each assignment, the cycle time is updated by subtracting the task time of the assigned task.  Task B is assigned to the second station, and Task C is assigned to the third station. Since Task C has a task time of 1.2 minutes, the remaining cycle time becomes 0. After that, Task D and Task E are not assigned any task time because the remaining cycle time is already 0. The specific values will depend on the actual task times and cycle time in your scenario.

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By following these steps, you will be able to balance the line by choosing the assignable task with the longest task time first. The final answer will be the completed table with all the relevant information.

To balance the line by choosing the assignable task with the longest task time first, we need to follow certain steps and fill in the table accordingly.

Step 1: Determine the cycle time.

Given that the cycle time is 2.3 minutes, we will use this value as a reference for balancing the line.

Step 2: List the tasks and their task times.

Create a table with columns for tasks and task times. List all the tasks that need to be performed on the line and their respective task times.

Step 3: Sort the tasks in descending order.

Sort the tasks in descending order based on their task times, with the longest task time at the top and the shortest at the bottom.

Step 4: Calculate the number of operators required for each task.

Starting from the top of the table, divide the task time by the cycle time. Round up the result to the nearest whole number to determine the number of operators needed for each task.

Step 5: Calculate the balance delay.

For each task, calculate the difference between the number of operators required and the number of operators available. This represents the balance delay for each task.

Step 6: Fill in the table.

Fill in the table with the tasks, task times, number of operators required, and balance delay for each task.

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Answer:

C. Approximately normal

Step-by-step explanation:

We know that when we have,  np≥10, and  n(1−p)≥10, and both of these are true, where n is the sample size, and p is the sample of proportions, the sampling proportions of sample distributions, will be normal in shape.

Expected successes : np=125(0.88)=110≥10

Expected failures : n(1−p)=125(1−0.88)=15≥10

The inequality of the temperatures where yeast will NOT thrive is T < 90°F or T > 95°F

from the question, we have the following parameters that can be used in our computation:

Yeast thrives between 90°F to 95°F

For the temperatures where yeast will not thrive, we have the temperatures to be out of the given range

Using the above as a guide, we have the following:

T < 90°F or T > 95°F.

Where

T = Temperature

Hence, the inequality is T < 90°F or T > 95°F.

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The correct answer is c.

The interpretation of the coefficient $0.03 in the regression of textbook retail price (PRICE) on number of pages in the book (LENGTH) is: As the length of the book increases by one page, the estimated price increases by $0.03 on average. Therefore, the correct answer is c.

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Answer:

The value of M₁₁ is -6.

Step-by-step explanation:

The minor, \(M_{ij}\) is the determinant of a square matrix, say P, formed by removing the ith row and jth column from the original square matrix, P.

The matrix provided is as follows:

\(A=\left[\begin{array}{ccc}7&9&-3\\3&-6&5\\4&0&1\end{array}\right]\)

The matrix M₁₁ is:

Remove the 1st row and 1st column to form M₁₁,

\(M_{11}=\left|\begin{array}{cc}-6&5\\4&0\end{array}\right|\)

Compute the value of M₁₁ as follows:

\(M_{11}=\left|\begin{array}{cc}-6&5\\4&0\end{array}\right|\)

       \(=(-6\times 1)-(5\times 0)\\\\=-6-0\\=-6\)

Thus, the value of M₁₁ is -6.

This would be written out as:

\(2y \times 3 + 4 \times 3\)

Answer:

2y x 3 + 4 x 3 is your written expression but it would equal = 6y + 12

Let A be a vector and n be a unit vector in a fixed direction. The scalar projection of A onto n can be represented as:

An = A . n = ||A||cos(θ),

where θ is the angle between vectors A and n.

The projection of A onto a plane perpendicular to n can be represented as:

A - (An) = A - (||A||cos(θ))n = ||A||sin(θ)nₜ,

where nₜ is a unit vector perpendicular to n.

Combining these two results, we have:

A = (An) + (A - (An)) = (||A||cos(θ))n + ||A||sin(θ)nₜ

By doing so, it is demonstrated that a vector A may be written as the product of its scalar projection along a unit vector n and its projection onto a plane perpendicular to n. This breakdown of a vector is helpful for looking at its parts from various angles.

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Answer:

here is an an example

Step-by-step explanation:

Let x = the width of the rectangle

P = 2l + 2w

2(40) + 2x ≤ 150

80 + 2x ≤ 150

2x ≤ 70

x ≤ 35 cm

Answer:

Answer:

-35π/18 radians

Step-by-step explanation:

The SUV's speed before the collision would be greater than 40 m/s

Let's assume the initial speed of the SUV is denoted by V (the value we're trying to find). The momentum of the car before the collision can be calculated as the product of the car's mass (m₁) and its speed (40 m/s), which is given as 40m1. Similarly, the momentum of the SUV before the collision is given by the product of its mass (m₂) and its speed (V), which is Vm₂.

Since the two vehicles come to a halt, the total momentum after the collision is zero. Therefore, the sum of the momenta of the car and the SUV before the collision must also be zero:

40m₁ + Vm₂ = 0

Since the car's mass (m₁) and the SUV's mass (m₂) are not given, we cannot solve for the actual values. However, we can still determine the relationship between the speeds of the car and the SUV before the collision. By rearranging the equation, we can solve for V:

V = -40m₁/m₂

From the equation, we can see that the speed of the SUV before the collision (V) is directly proportional to the speed of the car (40 m/s) and inversely proportional to the mass ratio of the car (m₁) to the SUV (m₂). The negative sign indicates that the SUV was traveling in the opposite direction to the car.

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Answer:

Transitive property of congruence

Step-by-step explanation:

If two shapes are congruent to the third shape, then all the shapes are congruent to each other.

I hope my answer helps you.

Answer:

Transitive property of congruence

Step-by-step explanation:

The transitive property of congruence states that two objects that are congruent to a third object are also congruent to each other.

The final conclusion is that the data suggest the population mean retirement age for small business owners is not significantly younger than 64 at the α = 0.01 level.

For this study, we should use a t-test for a population mean. The null and alternative hypotheses would be: H0: μ ≥ 64 (The population mean retirement age for small business owners is greater than or equal to 64). H1: μ < 64 (The population mean retirement age for small business owners is less than 64). To calculate the test statistic, we need to find the sample mean and sample standard deviation: Sample mean (xbar) = (64 + 59 + 67 + 58 + 54 + 63 + 54 + 63 + 62 + 56 + 59 + 67) / 12 = 61.833. Sample standard deviation (s) = 4.751. The test statistic (t) can be calculated using the formula t = (xbar - μ) / (s / sqrt(n)), where n is the sample size.  t = (61.833 - 64) / (4.751 / sqrt(12)) ≈ -1.685 (rounded to 3 decimal places) .

To find the p-value, we would compare the test statistic to the t-distribution with (n-1) degrees of freedom. Since the sample size is small (n = 12), we should refer to the t-distribution. The p-value can be determined by looking up the t-value (-1.685) and degrees of freedom (n-1 = 11) in a t-table or using statistical software. Let's assume the p-value is approximately 0.0637 (rounded to 4 decimal places). Since the p-value (0.0637) is greater than the significance level (α = 0.01), we fail to reject the null hypothesis. Therefore, there is insufficient evidence to conclude that the population mean retirement age for small business owners is younger than 64 at the α = 0.01 level of significance. Thus, the final conclusion is that the data suggest the population mean retirement age for small business owners is not significantly younger than 64 at the α = 0.01 level.

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The blanks can be filled as,
4/5x - 1/4x = 11

11/20x = 11

20/11(11/20x) = 20/11(11)

x = 20

The problem at hand is focused on finding the solution to a linear equation that has only one variable. To solve such an equation, one must use algebraic methods to isolate the variable and determine its value. First, we need to simplify the left-hand side of the equation:

4/5x - 1/4x = 11

(16/20x) - (5/20x) = 11 (finding a common denominator)

(11/20x) = 11 (combining like terms)

To solve for x, we isolate x on one side of the equation by multiplying both sides by the reciprocal of 11/20:

(20/11)(11/20)x = (20/11)(11)

x = 220/11

Simplifying:

x = 20

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--The complete question is, Fill in the blanks with appropriate calculations,
4/5x - 1/4x = 11

blank/20x = 11

blank/blank(blank/20x) = blank/blank(11)

x = blank--

Chevrolet owners are more loyal than owners of different cars, at least based on this sample of 870 Chevrolet owners.

In order to determine if Chevrolet owners are more loyal than owners of different cars, we need to conduct a hypothesis test. Our null hypothesis (H0) would be that there is no significant difference in loyalty between Chevrolet owners and owners of different cars, while our alternative hypothesis (Ha) would be that Chevrolet owners are more loyal. To test this, we can use a one-sample proportion test, since we are comparing the proportion of Chevrolet owners who would buy another Chevrolet (56%) to the proportion of the general consumer population who are loyal to their automobile manufacturer (47%). Using a significance level of 0.05, we can calculate the test statistic and p-value. Our test statistic is: z = (0.56 - 0.47) / √((0.47 × 0.53) / 870) = 4.71
Our p-value is then calculated as the probability of obtaining a z-value of 4.71 or higher:
p = P(Z ≥ 4.71) ≈ 0
Since our p-value is less than 0.05, we reject the null hypothesis and conclude that there is evidence to support the alternative hypothesis. Therefore, we can say that Chevrolet owners are more loyal than owners of different cars, at least based on this sample of 870 Chevrolet owners.

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Answer:

4

Step-by-step explanation:

9:8 = 4x+2:4x

36x = 32x + 16

x = 4

Answer:

Father:42

Son:18

Step-by-step explanation:

Present ages are father 48–6= 42

son = 24 ‘6 = 18

Answer:

Step-by-step explanation:

A \(45^\circ - 45^\circ - 90^\circ\) triangle is special -- it's a square cut in half diagonally.

The legs (sides that form the 90 degree angle) are both equal.

The hypotenuse is the leg multiplied by the square root of 2.

\(\text{hypotenuse}=\text{side}\sqrt{2}\)

So \(x=24\sqrt{2} \approx 33.9\)