Solve the following equations and check your answer.
6x+2=9x+14​

The largest possible assigned cycle time for the production line is 2.7 minutes, while the smallest possible assigned cycle time is 0.9 minutes.

In line balancing, the goal is to allocate the tasks evenly across the production line to achieve maximum efficiency. The largest possible assigned cycle time is determined by the task with the longest duration. In this case, the task with a duration of 2.7 minutes sets the upper limit for the cycle time. If all tasks were assigned the same cycle time, it would take at least 2.7 minutes to complete one cycle of the production line.

On the other hand, the smallest possible assigned cycle time is determined by the sum of the task durations. In this case, the sum of all task times is 6.4 minutes. By dividing this total time by the number of workstations or operators in the production line, we can determine the smallest possible assigned cycle time.

Since there are no constraints mentioned about the number of operators, we assume a single operator. Therefore, the smallest possible assigned cycle time would be 6.4 minutes divided by 1, which equals 6.4 minutes. However, it is worth noting that this cycle time is not realistic or practical for an operator to achieve.

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Answer:

1000 cm²

Step-by-step explanation:

Given:

Formula:

\(\text{Volume = Length} \times \text{Width} \times \text{Height}\)

Substitute the length, width, and the height of the prism to determine the volume of the prism.

\(\implies \text{Volume = 10} \times 12.5 \times 8\)

Simplify the right hand side of the equation, as needed;

\(\implies \text{Volume = 10} \times 12.5 \times 8\)

\(\implies \text{Volume =}\ 125 \times 8\)

\(\implies \boxed{\text{Volume =}\ 1000 \ \text{cm}^{2} }\)

Therefore, the volume of the prism is 1000 cm².

C

C is the answer. It is the only one that gives y when you input x.

Answer:

Your answer is C :)

Y = 3^x + 2.

You just substitute this into any of the functions. If you need more clarification I can help :)

Answer:

21/4

Step-by-step explanation:

(5 * 4) + 1

20 + 1

21/4

9514 1404 393

Answer:

  -8

Step-by-step explanation:

If α and β are roots of x^2 +5x +a = 0, then we must have ...

  (x -α)(x -β) = x^2 +5x +a

  x^2 -(α+b)x +αβ = x^2 +5x +a

Then ...

  α + β = -5

Together with the other relation between the roots, we have a system of equations in α and β.

Using the above to write an expression for β, we get ...

  β = -α -5

Substituting this into the given relation, we have an equation for α:

  2α +5(-α -5) = -1

  -3α -25 = -1 . . . . . . eliminate parentheses

  -24 = 3α . . . . . . . . add 3α +1

  -8 = α

The root α is equal to -8.

There are 60 students in the class.

They were all born in 1999. No two students in the class have the same birthday date.

Therefore, there are approximately 1.146 x 10^98 ways that no two students in the class have the same birthday date.

Summary: There are 60 students in the class who were all born in 1999. We want to find the total number of ways that no two students in the class have the same birthday date. We use the permutations formula and let n = 365 and k = 60 to get P(365, 60) = 1.146 x 10^98. Therefore, there are approximately 1.146 x 10^98 ways that no two students in the class have the same birthday date.

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Step-by-step explanation:

f(-4) = 13 - 5(-4)

= 13 + 20

= 33

Answer:

answes is 33

hopes rhis helps

The marginal propensity to consume (MPC) for Australia in 2021, when total income (Y) is 10, is 0.3.

The consumption function for Australia in 2021 is given as C = 0.0052 + 0.3Y + 20, where C represents the total consumption and Y represents the total income. To calculate the MPC, we need to determine how much of an increase in income is consumed rather than saved. In this case, when Y = 10, we substitute the value into the consumption function:

C = 0.0052 + 0.3(10) + 20

C = 0.0052 + 3 + 20

C = 23.0052

Next, we calculate the consumption when income increases by a small amount, let's say ΔY. So, when Y increases to Y + ΔY, the consumption function becomes:

C' = 0.0052 + 0.3(Y + ΔY) + 20

C' = 0.0052 + 0.3Y + 0.3ΔY + 20

To find the MPC, we subtract the initial consumption (C) from the new consumption (C') and divide it by the change in income (ΔY):

MPC = (C' - C) / ΔY

MPC = (0.0052 + 0.3Y + 0.3ΔY + 20 - 23.0052) / ΔY

Simplifying the equation, we can cancel out the terms that don't involve ΔY:

MPC = (0.3ΔY) / ΔY

MPC = 0.3

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The common difference of the arithmetic sequence is d = 3.

What is an Arithmetic sequence?

An arithmetic progression, also referred to as an arithmetic sequence, is a set of numbers where each term following the first is derived by adding a fixed constant number to the term before it.

To solve this problem, we can use the formula for the nth term of an arithmetic sequence. The formula is as follows:

an = a1 + (n - 1)d

Where an is the sequence's nth term, a1 is the first term, d is a common difference, and n is the number of terms we want to discover:

We know that a1 = 10 and a4 = 19. By entering these numbers into the formula, we obtain:

          a4 = a1 + (4 - 1)d

          19 = 10 + 3d

In order to find d, we can divide by 3 after subtracting 10 from both sides:

          9 = 3d

          d = 3

Therefore, the common difference of the arithmetic sequence is d = 3.

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The values of integrals  ∫cos² x/2 dx = 1/2 (x + sin x) + C.

We can use the identity cos 2θ = 1 - 2 sin²θ to rewrite sin² x/2 in terms of cos x/2:

sin² x/2 = 1 - cos² x/2

Now, let's evaluate the integral of sin² x/2:

∫sin² x/2 dx = ∫(1 - cos² x/2) dx

Let u = cos(x/2), then du/dx = -1/2 sin(x/2) dx, and we have:

∫(1 - cos² x/2) dx = ∫(1 - u²) (-2 du) = 2∫(u² - 1) du

= 2(u³/3 - u) + C = 2(cos³(x/2)/3 - cos(x/2)) + C

Therefore, ∫sin² x/2 dx = 2(cos³(x/2)/3 - cos(x/2)) + C.

Similarly, we can use the identity cos 2θ = 2 cos²θ – 1 to rewrite cos² x/2 in terms of cos x:

cos² x/2 = (1 + cos x)/2

Now, let's evaluate the integral of cos² x/2:

∫cos² x/2 dx = ∫(1 + cos x)/2 dx

= 1/2 ∫(1 + cos x) dx

= 1/2 (x + sin x) + C

Therefore, ∫cos² x/2 dx = 1/2 (x + sin x) + C.

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Answer:

2.5 is greater than 2.

They are not equal

2.5 is in between 2 and 3

Since 3 is greater than 2, and 2.5 is in between them, 2.5 is greater than 2.

We can observe that the expression xyz + xyz + xyz + xyz simplifies to 4xy + 4z.

The given sum-of-products expansion in three variables can be represented using Karnaugh maps (K-maps). The K-map for this expression consists of eight cells corresponding to all possible combinations of the three variables (x, y, z). Each cell represents a minterm of the expression. Since the given expression has four identical terms (xyz), these terms can be combined to simplify the K-map.

The K-map for the given expression xyz + xyz + xyz + xyz in three variables (x, y, z) can be drawn as follows:

```

  zy   00  01  11  10

 --------------------

 x  0 |  4   0   0   0

    1 |  0   4   4   4

```

In the above K-map, the values in each cell represent the number of occurrences of the corresponding minterm. Since the expression has four identical terms (xyz), each term contributes to four cells in the K-map. Therefore, each cell containing the term xyz is assigned a value of 4.

By examining the K-map, we can observe that the expression xyz + xyz + xyz + xyz simplifies to 4xy + 4z. This simplification is possible by grouping the cells with a value of 4 and identifying the corresponding minterms. Hence, the simplified form of the expression is 4xy + 4z.

Note that K-maps are useful graphical tools for simplifying Boolean expressions and can help identify common patterns and simplify complex expressions.


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The two-digit number is 34.

Zero, a positive natural number, or a negative integer denoted by a minus sign are all examples of integers. The inverse additives of the equivalent positive numbers are the negative numbers. The boldface Z is a common way to represent the set of integers in mathematical terms.

If p and q are integers and q is not equal to 0, then the number is in the form of p/q and is said to be rational. Among the rational number examples are 1/3, 2/4, 1/5, 9/3, and so on.

The given information can be translated into the following equation:

(10x + y) + (2x - y - 1) = 13

Where x is the tens digit and y is the units digit.

Solving for x and y, we get:

x = 3 and y = 4

So the number is 34.

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The convolution integral y(t) = x(t) * h(t) for the given pair of signals x(t) and h(t) can be computed as follows:

y(t) = ∫[x(τ) * h(t - τ)] dτ

1) x(t) = δ(t) and h(t) = δ(t - 2) * (t - 1)

The convolution integral becomes:

y(t) = ∫[δ(τ) * δ(t - τ - 2) * (τ - 1)] dτ

To evaluate this integral, we consider the properties of the Dirac delta function. When the argument of the Dirac delta function is not zero, the integral evaluates to zero. Therefore, the integral simplifies to:

y(t) = δ(t - 2) * (t - 1)

The convolution result y(t) is equal to the shifted impulse response h(t - 2) scaled by the factor of (t - 1). This means that the output y(t) will be a shifted and scaled version of the impulse response h(t) at t = 2, delayed by 1 unit.

In summary, for x(t) = δ(t) and h(t) = δ(t - 2) * (t - 1), the convolution integral y(t) = x(t) * h(t) simplifies to y(t) = δ(t - 2) * (t - 1).

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Answer:

itz 5.5

Step-by-step explanation:

i just got it right

The expressions when simplified are -9 - 2i and x = ±8i

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

(6 -7i) - (8 - 5i) - 7

When evaluated, we have

(6 -7i) - (8 - 5i) - 7 = -9 - 2i

Here, we have

6x² = -384

Divide by 6

x² = -64

Take the square roots

x = ±8i

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Answer:

B: -2

Step-by-step explanation:

The value of c does lim f(x) x -> c not exist is -2, the correct option is B.

A one sided limit will not exist when it is outside the domain of the function.

The domain of a function is composed by the set of all the input values of the function, hence on the graph it is given by the values of x.

We are given that;

f(x) x -> c

Now,

The domain is then given as follows:

-6 ≤ x ≤ 8.

To the left of -6, the function is not defined, hence the one-sided limit that does not exist is given as follows:

lim x -> -6^- f(x).

=-2

Therefore, by limits the answer will be -2.

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Answer:

-1

Step-by-step explanation:

I'm pretty sure this is right

Answer:

19 miles per hour

Step-by-step explanation:

Answer:

Lets do this step by step

Step-by-step explanation:

I hope this helps

Answer:

-14

Step-by-step explanation:

To solve for x, you would first need to add 10 to both sides. Then you would get -3x-10+10=32+10. Then we simplify that to get, -3x=42. Then, you would divide both sides by -3, to get x=-14

Answer:

Hey there! The answer to your question is below.

Step-by-step explanation:

The answer would be f(4) = -11, g(x) = 2    x = 0

I attached a picture below, sorry for my bad handwriting.

By xBrainly

Answer:

1st and 3rd are functions, 2nd and 4th are not functions

Step-by-step explanation:

Answer:

Function : 1 , 3

Not a Function : 2 , 4

Step-by-step explanation:

Using the vertical line test for the first two, and the last two you are able to tell because each input (x) can only have one output (y).

Answer:

\(684\:\mathrm{cm^2}\)

Step-by-step explanation:

The area of any triangle is equal to \(A=\frac{1}{2}\cdot a\cdot b\cdot \sin C\), where \(a\) and \(b\) are two sides of a triangle and \(C\) is the angle between them.

Plugging in given values, we have:

\(A=\frac{1}{2}\cdot 27\cdot 82\cdot \sin 162^{\circ}=\boxed{684\:\mathrm{cm^2}}\)

Answer:

342

Step-by-step explanation:

see image

The sets of transformations that result in the same image when performed in any order are:

Translation, dilation with center (0,0)

Two translations

In mathematics, a transformation refers to a process that changes the size, shape, position, or orientation of a geometric figure or an object in a coordinate plane or space. There are several types of transformations, such as translation, rotation, reflection, and dilation, which are used to alter the original figure to create a new one that is similar or congruent to the original. Transformations are used in geometry, algebra, and other branches of mathematics to study and understand various properties of geometric shapes and objects.

Here,

For the first set, if we perform a translation followed by a dilation with center (0,0), the result will be the same as if we perform the dilation first followed by the translation. This is because the dilation does not change the direction of the translation, and the center of dilation is at the origin, so the translation is unaffected.

For the second set, any two translations can be combined to form a single translation, so the order in which they are performed does not matter.

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Answer:

a

Step-by-step explanation:

The number to complete the square is 64 and the factored expression is (x - 8)²

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

y² - 16y

Take the coefficient of y

k = -16

Divide by 2

k/2 = -8

Square both sides

(k/2)² = 64

This means that the number to add to the expression is 64

When the expression is factored, we have

(x - 8)²

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Answer: p=25%

Step-by-step explanation:We have a sample of 100 clients.

To find the probability that a randomly selected customer chooses a cold drink, we must first count how many people in the sample chose cold drinks.

The table shows that cold drinks were

8 small, 12 medium and 5 large.

Then the number of cold drinks was:

The probability that the customer ordered a small given that he or she ordered a hot drink is 67%.

Probability is simply the possibility of getting an event. Or in other words, we are predicting the chance of getting an event.

The value of probability will be always in the range from 0 to 1.

Given a table which shows the number of orders of coffee by first 100 customers.

Out of it,

Total number of orders which are hot = 5 + 48 + 22 = 75

Number of orders which are small out of the total hot drinks = 5

Probability = 5/75 = 0.6667 = 66.67% ≈ 67%

Hence the required percent is 67%.

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In a case whereby letters in the word bubble are arranged in a row the number of unique arrangements that are there  in the letters is 120.

From the question we were given the word, bubble  which can be recognized as 6! arrangements  however we know that the  3 B’s are interchangeable, from the word which is to be arranged, and we can see that there are 6 letters all together in the word and can be arranged as;

6!/3!

= 720/6

= 120

Hence, we can conclude the arangement here is 120 unique wayas.

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The lifecycle cost of the clothes washer is $1,032.68.

The lifecycle cost of the clothes washer is $1,104.20. Here's how to compute it:Given:Energy consumed by the clothes washer = 198 kWhPrice of the washer = $389Lifetime of the washer = 14 yearsEnergy price in the city = 8 cents per kWhMaintenance cost = $17 per yearFormula: Lifecycle cost = (purchase price + (energy price x energy consumed) + (maintenance cost x lifetime)) / lifetimeLet's substitute the given values in the formula:Lifecycle cost = ($389 + ($0.08 x 198 kWh) + ($17 x 14)) / 14Lifecycle cost = ($389 + $15.84 + $238) / 14Lifecycle cost = $642.84 / 14Lifecycle cost = $45.92 (rounded to two decimal places).

The lifecycle cost of the clothes washer is $45.92 per year. To find the total lifecycle cost, multiply it by the lifetime of the washer:Total lifecycle cost = $45.92 x 14Total lifecycle cost = $643.68Add the initial cost of the washer to get the final answer:Final answer = $643.68 + $389Final answer = $1,032.68 (rounded to two decimal places)

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In a hypothesis, when the t value is 7.14 and the critical value is 6.10, the decision that should be made is to reject the null hypothesis.

It should be noted that a hypothesis is simply used to get information about a certain thing.

In this case, in a hypothesis, when the t value is 7.14 and the critical value is 6.10, the decision that should be made is to reject the null hypothesis.

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