Solve the inequality:
3x > 72-5х
x ≤ -9
x ≥ -9
x ≥ 9
x ≤ 9

Answer:

$$0.8^4=0.4096$$ Explanation: The introduction to logarithms and definition of it is explained in the first link. 0.8 is the base of both logarithm and exponent

Step-by-step explanation:

A function assigns the values. The profit-maximizing quantity of labour to hire is 15 workers.

A function assigns the value of each element of one set to the other specific element of another set.

Given the marginal revenue product, MRP = 40-(Q/10)

The cost of labour, WL = 10

The production function, Q = 20 L

For profit maximizing quantity of labour to hire where,

MRP = WL

40-(Q/10) = 10

40-(20L/10)=10

40-2L=10

-2L = 10-40

-2L=-30

L=15

Hence, the profit-maximizing quantity of labour to hire is 15 workers.

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a. The truth set for the predicate "6/d is an integer" with a domain of Z (the set of all integers) is the set of all integers that divide 6 evenly, which are {-6, -3, -2, -1, 1, 2, 3, 6}.

b. The truth set for the predicate "6/d is an integer" with a domain of Z+ (the set of all positive integers) is the set of all positive integers that divide 6 evenly, which are {1, 2, 3, 6}.

c. The truth set for the predicate "1 ≤ x2 ≤ 4" with a domain of R (the set of all real numbers) is the set of all real numbers between 1 and 4, including 1 and 4 themselves. So the truth set is [1, 4] .

d. The truth set for the predicate "1 ≤ x2 ≤ 4" with a domain of Z (the set of all integers) is the set of all integers whose square is between 1 and 4, including 1 and 4 themselves. So the truth set is {-2, -1, 1, 2}.

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Answer:

a 3 pound almonds is the best deal with the 5 pound bag of walnuts being the second and the 4 pounds of cashews is the worst deal

Step-by-step explanation:

the almonds cost 5.50$ a pound the 5 pound bag of walnuts cost 5.75$ dollars a pound and the 4 pound bag of cashews cost  6.20$ a pound    

The sum of 17.25 and 1.725, to the nearest integer, is 19.

First, let's add the two numbers together: 17.25 + 1.725 = 19.975

Next, we need to round the sum to the nearest integer. To do this, we need to look at the tenths place of the number. Since the tenths place is a nine, we need to round up to the nearest integer.

In this case, the nearest integer is 19.

To check our answer, we can add the two numbers together again using a calculator and confirm that the answer is 19.

To make sure we understand how to round to the nearest integer, let's look at another example. If we add 3.45 + 2.735, the sum is 6.185.

Looking at the hundredths place, we see that it is a five. Since five is greater than or equal to five, we need to round up to the nearest integer.

In this case, the nearest integer is 7.

To check our answer, we can add the two numbers together again using a calculator and confirm that the answer is 7.

In summary, to round a number to the nearest integer, we need to look at the tenths place. If the tenths place is greater than or equal to five, we round up to the nearest integer. If it is less than five, we round down to the nearest integer.

Therefore, the sum of 17.25 and 1.725, to the nearest integer, is 19.

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The sum of 17.25 and 1.725 is 18.975. To the nearest integer, this number is rounded up to 19.

Rounding to the nearest integer involves finding the closest whole number to a decimal or fractional number. When the decimal portion of a number is greater than or equal to 0.5, the number is rounded up to the next whole number. When the decimal portion of a number is less than 0.5, the number is rounded down to the previous whole number. In this case, the decimal portion of 18.975 is greater than 0.5, so the number is rounded up to 19.

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The units for weight are gram (g) and kilogram (kg). And extreme weights measured in tons (t).

The weight of an object determines how much of it is there, or how heavy it is. The perception of a bigger body is one of weight, like that of an elephant or a bus. Yet, a body that is lighter is described as being light. Light items include a feather, a leaf, and a bubble. Also, we might compare two or more objects to determine which is heavier or lighter. But the lighter and heavy one will always measured in gram (g) and kilogram (kg) itself. The lighter one will be in grams and the heavy one will be measured in kilograms. Kilo means 1000.

Therefore, the units are weight are g and kg.

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The production function given is P(t) = 27t + 12t^2 - t^3, where P(t) represents the total number of units produced by a worker in t hours of an 8-hour shift.

(a) To find the number of hours before production is maximized, we need to find the maximum value of the production function P(t). We can do this by finding the critical points of P(t) and determining whether they correspond to a maximum. Taking the derivative of P(t) with respect to t, we get P'(t) = 27 + 24t - 3t^2. Setting P'(t) equal to zero and solving for t, we find the critical points. In this case, the critical points are t = -3, t = 0, and t = 8. However, since the worker is only working an 8-hour shift, the valid solution is t = 8. Therefore, production is maximized after 8 hours.

(b) To find the number of hours before the rate of production is maximized (the point of diminishing returns), we need to find the maximum value of the production rate, which is the derivative of the production function, P'(t). Taking the derivative of P'(t) with respect to t, we get P''(t) = 24 - 6t. Setting P''(t) equal to zero and solving for t, we find t = 4 as the critical point. Therefore, the rate of production is maximized (point of diminishing returns) after 4 hours.

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Answer:

$\frac{10}{3}$ in by $\frac{14}{3}$ in by $\frac{10}{3}$ in.

Step-by-step explanation:

Let's denote the length of the box as $l$, the width as $w$, and the height as $h$. We are given that the original piece of cardboard has dimensions 10 in by 12 in, so we know that:

$$l + 2h = 10 \quad \text{and} \quad w + 2h = 12.$$

To find the dimensions of the box with the largest volume, we need to maximize the volume function, which is given by:

$$V(l,w,h) = lwh.$$

Using the equations above, we can express the volume in terms of just two variables, say $l$ and $h$:

$$V(l,h) = lwh = l(10-2h)h = 10h^2 - 2h^3.$$

Now we can use calculus techniques to find the maximum of this function. To do this, we need to find the critical points, which are the values of $h$ where the derivative of $V$ with respect to $h$ is zero or undefined.

Taking the derivative of $V$ with respect to $h$, we get:

$$V'(h) = 20h - 6h^2.$$

Setting this to zero to find the critical points, we get:

$$20h - 6h^2 = 0 \quad \Rightarrow \quad h(10 - 3h) = 0.$$

This equation has two solutions: $h = 0$ and $h = \frac{10}{3}$. We can check that $h=0$ corresponds to a minimum, and $h = \frac{10}{3}$ corresponds to a maximum by computing the second derivative of $V$ with respect to $h$:

$$V''(h) = 20 - 12h.$$

At $h=0$, we have $V''(0) = 20$, which is positive, so $h=0$ is a minimum. At $h=\frac{10}{3}$, we have $V''\left(\frac{10}{3}\right) = -8\frac{1}{3}$, which is negative, so $h=\frac{10}{3}$ is a maximum.

Therefore, the maximum volume is achieved when $h=\frac{10}{3}$. Using the equations we derived earlier, we can find the corresponding values of $l$ and $w$:

$$l = 10 - 2h = \frac{10}{3}, \quad w = 12 - 2h = \frac{14}{3}.$$

So the dimensions of the box with largest volume are $\frac{10}{3}$ in by $\frac{14}{3}$ in by $\frac{10}{3}$ in.

Answer:

-20/33

Step-by-step explanation:

y2 - y1 / x2 - x1

1/6 - (-1/4) / -5/16 - 3/8

5/12 / -11/16

= -20/33

The rate at which the water level in reservoir 1 drops can be calculated as follows:

Let the volume of reservoir 1 be V1, and the surface area be A1. The volume of water that is flowing out of reservoir 1 per minute is given by;

V = A1 x h

where h is the height of water that flows out of reservoir 1 per minute. Since the water level in reservoir 1 drops at a rate of 0.01 m/min, then the height of water that flows out of reservoir 1 per minute is 0.01 m/min. Therefore, the volume of water that flows out of reservoir 1 per minute is given by;

V = A1 x hV = A1 x 0.01 .

Assuming that the cross-sectional area of the pipe that connects the two reservoirs is the same as that of reservoir 1 (A1), then the volume of water that flows into reservoir 2 per minute is also given by;

V = A2 x h

where A2 is the surface area of reservoir 2.

Therefore, the rate at which the water level in reservoir 2 rises can be calculated as follows:

Let the volume of reservoir 2 be V2. The volume of water that flows into reservoir 2 per minute is given by;

V = A2 x hA1 x 0.01 = A2 x h = (A1 / A2) x 0.01

Since the height of water that flows out of reservoir 1 per minute is 0.01 m/min, then the height of water that flows into reservoir 2 per minute is (A1 / A2) x 0.01. Therefore, the rate at which the water level in reservoir 2 rises is given by;

(A1 / A2) x 0.01 m/min.

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Step-by-step explanation:

To find the angle between a line and the x-axis, we need to calculate the slope of the line first. The slope of a line passing through two points (x₁, y₁) and (x₂, y₂) is given by the formula:

m = (y₂ - y₁) / (x₂ - x₁)

Using the points (-2, 2) and (8, 9), we can substitute the values into the formula:

m = (9 - 2) / (8 - (-2))

= 7 / 10

= 0.7

The slope of the line is 0.7. The angle between the line and the x-axis can be found using the inverse tangent (arctan) function. The tangent of an angle is equal to the slope of the line, so we can write:

tan(θ) = 0.7

Taking the inverse tangent of both sides, we find:

θ = arctan(0.7)

Using a calculator, we can evaluate this to be approximately:

θ ≈ 35.87 degrees

Therefore, the angle between the line and the x-axis is approximately 35.87 degrees.

If Lina's father has a 15% off coupon, he will only have to pay 85% of the original cost. So the cost of the meal after the discount is:

Cost after discount = 85% of $20

Cost after discount = 0.85 x $20

Cost after discount = $17

Next, a 7% sales tax is applied to the cost after the discount:

Cost after tax = Cost after discount + (7% of Cost after discount)

Cost after tax = $17 + (0.07 x $17)

Cost after tax = $17 + $1.19

Cost after tax = $18.19

Therefore, Lina's father pays $18.19 for the meal after the discount and sales tax are applied.

Answer:

f(x)=|x-6|

Step-by-step explanation:

Translation is a shift. Opposite how many units it moved. In with the x because that's side to side. If it was not with the x, it's up and down.

The transformation of a function may involve any change. The equation of g(x) is |x-6|.

The transformation of a function may involve any change.

Usually, these can be shifted horizontally (by transforming inputs) or vertically (by transforming output), stretched (multiplying outputs or inputs), etc.

If the original function is y = f(x), assuming the horizontal axis is the input axis and the vertical is for outputs, then:

Horizontal shift (also called phase shift):

Vertical shift:

Stretching:

Given that the function f(x)=|x|, this function is needed to be translated 6 units to the right. Therefore, the new function can be written as,

g(x) = f(x-6)

      = |x - 6|

Hence, the equation of g(x) is |x-6|.

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Step-by-step explanation:

A parenthesis is used when the number next to it is NOT part of the solution set

   like :   all numbers up to but not including 3 .    

  Parens are always next to  infinity  when it is part of the solution set .

  A bracket is used when the number next to it is included in the solution set.

There are 25 yellow flowers in the bucket

The ratio of yellow flowers to the total number of flowers in a bucket is 5:9

There are a total of 45 flowers

The number of yellow flowers can be calculated as follows

= 5/9 × 45

= 25

Hence there are 25 yellows flowers

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Answer:

The better deal is $32.05/15 gal

Step-by-step explanation:

Divide:

56/25

=2.24

32.05/15

=2.13666667

=2.14

When U = 10, the value of n is 112.604.

We are given that the number n is the algebraic sum of two terms:

Term 1 varies directly as u.

Term 2 varies inversely as U².

Let's denote the first term as k1 u, where k1 is the constant of proportionality.

And let's denote the second term as k2/U², where k2 is another constant of proportionality.

We have,

When U = 2, n = 22.

When U = 8, n = 56.5.

So, Equation 1: n = k1u + k2/U²

Equation 2: 22 = k1(2) + k2/(2)²

Equation 3: 56.5 = k1(8) + k2/(8)²

Let's solve these equations to find the values of k1 and k2.

Equation 2 becomes: 22 = 2k1 + k2/4

Equation 3 becomes: 56.5 = 8k1 + k2/64

To eliminate k2, let's multiply Equation 2 by 64:

1408 = 128k1 + k2

Now we have two equations with two variables:

128k1 + k2 = 1408

8k1 + k2/64 = 56.5

Let's subtract Equation

120k1 = 1351.5

k1 = 1351.5 / 120

k1 = 11.2625

Substituting the value of k1 back into Equation 2:

22 = 2(11.2625) + k2/4

22 = 22.525 + k2/4

k2/4 = 22 - 22.525

k2/4 = -0.525

k2 = -2.1

Now we have the values of k1 and k2:

k1 = 11.2625

k2 = -2.1

Finally, we can find the value of n when U = 10 by substituting these values into Equation 1:

n = k1u + k2/U²

n = 11.2625(10) - 2.1/(10)²

n = 112.625 - 2.1/100

n = 112.625 - 0.021

n ≈ 112.604

Therefore, when U = 10, the value of n is 112.604.

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The answer is that Leola ran 6.2

Answer:

Step-by-step explanation:

Answer:

43+26=R

Step-by-step explanation:

43 is JFK's age

26 could be substituted for d, or difference

R is Reagan's age, 69

4.2 hours take to screen-print a batch of 14 shirts.

The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.

For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.

12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.

As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.

This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.

Given:

initial set-up time = 15 min

Additional time= 3 min

Total time to print T shirt= 15 + 3= 18 min

So, to print 14 T shirts the time will be taken

= 14 x 18

= 252 min

= 4.2 hours

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Answer:

57 minutes

Step-by-step explanation:

I just did it

A linear system with 3 equations and 4 variables by representing it with an augmented matrix and bringing the matrix to reduced row-echelon form can be solved.

A mathematical representation of a system based on the application of a linear operator is known as a "linear system" in systems theory. Ordinarily, compared to nonlinear systems, linear systems display much simpler features and properties. The automatic control theory, signal processing, and telecommunications all heavily rely on linear systems as a mathematical abstraction or idealisation.

Linear systems, for instance, are frequently used to model the propagation medium for wireless communication systems. An operator, H, that converts an input, x(t), into an output, y(t), a kind of black box description, can be used to describe a general deterministic system.

The superposition principle, or alternatively both the additivity and homogeneity properties, must be satisfied by a system to be considered linear, and only then.

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Answer:73

Step-by-step explanation:

45

+28

73

The inverse of the bus-admittance matrix is the bus-impedance matrix.

What is a bus-impedance matrix?

The bus impedance matrix is a square matrix that represents the electrical circuit that connects the network nodes.

The values of this matrix are the impedances of the branches that join the nodes, and they are known as self-impedance (diagonal elements) and mutual impedance (non-diagonal elements).

What is the difference between the bus impedance matrix and the bus admittance matrix?

The difference between the bus impedance matrix and the bus admittance matrix is that the bus impedance matrix has all the elements non-zero, while the bus admittance matrix has most of the elements zero.

In power systems, the bus impedance matrix is preferable over the bus admittance matrix since the former is a dense matrix while the latter is a sparse matrix.

Hence, the computational cost required for carrying out power flow analysis using the bus impedance matrix is lower as compared to the bus admittance matrix.

The Jacobian matrix is a square matrix that represents the derivatives of a vector function with respect to another vector. It is used for performing Newton Raphson power flow analysis.

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The bug changes direction at t = 4. This can be answered by the concept of velocity.

To determine when the bug changes direction, we need to find when its velocity changes sign from positive to negative. From the graph, we see that the bug's velocity is positive for t < 4 and negative for t > 4. Therefore, the bug changes direction at t = 4.

To verify this, we can look at the behavior of the bug's velocity as it approaches t = 4. From the graph, we see that the bug's velocity is increasing as it approaches t = 4 from the left, and decreasing as it approaches t = 4 from the right. This indicates that the bug is reaching a maximum velocity at t = 4, which is when it changes direction.

Therefore, the bug changes direction at t = 4.

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When subtracting several quantities, the number of decimal places in the result should match the quantity with the fewest decimal places or the highest level of precision for consistency and accuracy.

When performing subtraction, it is important to maintain consistency in terms of decimal places or precision. The number of decimal places in the result should match the quantity with the fewest decimal places among the numbers being subtracted.

For example, let's consider the following subtraction:

2.4567 - 1.23 = 1.2267

In this case, both numbers have four decimal places, so the result also has four decimal places.

However, if we have a situation like this:

3.45 - 1.236 = 2.214

In this case, the number being subtracted has three decimal places, so the result is rounded to three decimal places to maintain consistency.

The general principle is to consider the number with the fewest decimal places or the highest level of precision when determining the number of decimal places in the result of a subtraction operation. This ensures that the result is presented in a consistent and meaningful manner.

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The residual value for x = 1 is 0. To find the residual value for x = 1, we need to plug in x = 1 into the equation for the least squares regression line (lsrl) that we have been given. The equation for the lsrl is ŷ = 5.5x + 18.5.

So, when x = 1, we have:
ŷ = 5.5(1) + 18.5
ŷ = 24
This means that the predicted value of y for x = 1 is 24.
To find the residual value, we need to subtract the predicted value of y from the actual value of y for x = 1.
The actual value of y for x = 1 is 24 (according to the data given).
So, the residual value for x = 1 is:
residual = actual value of y - predicted value of y
residual = 24 - 24
residual = 0
Therefore, the residual value for x = 1 is 0.

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Answer: Option D (0.833)

Step-by-step explanation:

There are 6 possible outcomes when the arrow is spun, and 5 of those outcomes correspond to the arrow landing on a number greater than 10 (the numbers 11, 12, 13, 14, and 15).

Therefore, the probability of the arrow landing on a number greater than 10 is 5/6, or about 0.833