The energy balance for a continuous stirred tank reactor with an exothermic reaction is given by the equation ..pepAh dT dt -E RT fipep (T. -T.)+AH,Vk,e *CAo -UAH(T) -Teo) State the assumption on which this energy balance equation is based. Re-write the energy balance equation if this assumption was not made

a). The number of ways which the company can choose 4 workers from the list of employees is; 2,730 ways.

b). The number of ways the company can choose the workers if 2 labourers and 3 joiners are on holiday is; 700 ways.

It follows from the task content that the number of ways the company can choose 4 workers in each scenario be determined.

a). Since there are 3 labourers, 13 joiners, 10 electricians, and 7 plumbers.

The number of possible ways to choose 4 workers is; ³C₁ × ¹³C₁ × ¹⁰C₁ × ⁷C₁

= 3 × 13 × 10 × 7

= 2,730 ways.

b). Also, when 2 labourers and 3 joiners are absent, it follows that the selection space is now; 1 labourer, 10 joiners, 10 electricians and 7 plumbers.

The number of possible ways is therefore; ¹C₁ × ¹⁰C₁ × ¹⁰C₁ × ⁷C₁

= 1 × 10 × 10 × 7

= 700 ways.

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Answer:

c

Step-by-step explanation:

Answer:

3 because 4+4+4=14

Step-by-step explanation:

Answer:

3 times

Step-by-step explanation:

12 divided by 4 = 3

Answer:

In the 4% interest account, $3,000 was invested while in the 3.5% interest account, $2,000 was invested

Step-by-step explanation:

Here, we want to know the amount of money invested in each of the two accounts.

Let the amount invested be $x and $y for each of the two accounts

Since the total invested is $5,000

Mathematically;

x + y = 5000 •••••••(i)

Let’s now work with the interest

for the 4% account, interest will be;

4/100 * x = 4x/100

For the 3.5% account, interest will be;

3.5/100 * y = 3.5y/100

The total amount of interest earned is $190

Thus;

4x/100 + 3.5y/100 = 190

Multiply through by 100

4x + 3.5y = 19000 •••••••(ii)

So we have two equations to solve simultaneously

From i, x = 5000-y

Substitute this into ii

4(5000-y) + 3.5y = 19000

20000-4y + 3.5y = 19000

0.5y = 20,000-19,000

0.5y = 1,000

y = 1,000/0.5

y = $2,000

x = 5,000 - y = 5,000 - 2,000 = $3,000

9514 1404 393

Answer:

  angle BAC = 35°

Step-by-step explanation:

The measure of an inscribed angle is half the measure of the arc it intercepts. Arc BC is 70°, so inscribed angle BAC is half that, or 70°/2 = 35°.

_____

In this geometry, you can find angle BAC a couple of ways.

Any triangle inscribed in a semicircle is a right triangle. That is, AB is a diameter, so angle ACB intercepts half the circle (180°). Half that measure is 90°. Then angles ABC and BAC are complementary:

  angle BAC = 90° -55° = 35°

Answer:

8 in

Step-by-step explanation:

Area of a square = l×w

Since it is a square then l and w are equal to each other.

So we can instead just say l^2 = A

l^2 = 68.2

l = square root of 68.2

l = 8.26

O....M.....G.....?!

i am only in 6th grade....

but i could do it.....but i have no idea...

BIG OOOOOF!

The value of angle E  in the ΔDEF is 121°.

Given,

∠B = (96 + y)°

∠E = (6y - 29)°

EF = BC

AB = DE

AC = DF

Therefore, ΔABC ≅ ΔDEF

So, ∠ABC = ∠DEF or ∠B = ∠E

     96 + y = 6y - 29

      6y - y = 96 + 29

           5y = 125

             y = 125/5

             y = 25

∠E = 6y - 29

     = 6(25) - 29

     = 150 - 29

     = 121

Hence, ∠E = 121°.

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A table used to find the area under the standard normal distribution to determine the probability of a z-score being less than a given value.

A negative z-score table is a tool used in statistics to find the probability of a z-score being less than a certain value. A z-score is a measure of the number of standard deviations an observation or data point is above or below the mean of a dataset.

The standard normal distribution is a bell curve with a mean of zero and a standard deviation of one. The negative z-score table lists the area under the curve to the left of a negative z-score, which can be used to calculate probabilities. The table is used by finding the corresponding row and column for the desired z-score and reading the probability from the table.

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\(\large\underline{\sf{Solution-}}\)

\(\sf \dfrac{x + 1}{10} - \dfrac{3(x - 1)}{5} = 2\)

\(\sf\longmapsto \dfrac{x + 1}{10} - \dfrac{3x - 3}{5} = 2\)

\(\sf\longmapsto \dfrac{(x + 1) - 2(3x - 3)}{10} = 2\)

\(\sf\longmapsto \dfrac{x + 1 - (6x - 6)}{10} = 2\)

\(\sf\longmapsto \dfrac{x + 1 - 6x + 6}{10} = 2\)

\(\sf\longmapsto \dfrac{ - 5x + 7}{10} = 2\)

\(\sf\longmapsto - 5x + 7 = 20\)

\(\sf\longmapsto - 5x = 20 - 7\)

\(\sf\longmapsto - 5x = 13\)

\(\sf\therefore x = - \dfrac{13}{5} \)

Hence, the value of x will be -13/5 respectively.

\( \huge \boxed{\mathfrak{Question} \downarrow}\)

\(\frac{x + 1}{10} - \frac{3(x - 1)}{5} = 2 \\ \)

\( \large \boxed{\mathfrak{Answer \: with \: Explanation} \downarrow}\)

\(\frac { x + 1 } { 10 } - \frac { 3 ( x - 1 ) } { 5 } = 2 \\ \frac { x + 1 } { 10 } - \frac { 3 ( x - 1 ) } { 5 } = \frac{2}{1} \)

Take a look at the denominators. The denominators are 10, 5 & 1. Their LCM is 10. So, multiply the fractions on both the sides of the equation by 10.

\(\frac { x + 1 } { 10 } - \frac { 3 ( x - 1 ) } { 5 } = \frac{2}{1} \\ \frac{x + 1}{10} \times \frac{1}{1} - \frac{3x - 3}{5} \times \frac{2}{2} = \frac{2}{1} \times \frac{10}{10} \\ \frac{x + 1}{10} - \frac{6x - 6}{10} = \frac{20}{10} \)

Now cancel the denominators (as they have the same value) & take the numerators.

\(x + 1 - (6x - 6) = 20 \\ \)

Now, simplify it.

\(x + 1 - (6x - 6) = 20 \\ x + 1 - 6x + 6 = 20 \\ x - 6x + 1 + 6 = 20 \\ - 5x + 7 = 20 \\ - 5x = 13 \\ x = -\frac{13}{5} \\ \boxed{ \boxed{ \bf x = - \frac{13}{5} =\: - 2 \frac{3}{5} = - 2.6}}\)

__________________

Hope it'll help you!

ℓu¢αzz ッ

Answer:

4x+6y

Step-by-step explanation:

The percent equivalent to 66 over 165 is 40%.

Percentage is defined as the parts of a number per fraction of 100. We have to divide a number with it's whole and then multiply with 100 to calculate the percentage of any number.

So the percentage actually means a part per 100.

Percentage is usually denoted by the symbol '%'.

We have to calculate the percent of the numbers 66 over 165.

First divide 66 with 165. The multiply with 100 to get the required percentage.

(66 / 165) × 100 = 0.4 × 100 = 40%

Hence the required percentage is 40%.

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A(n) example is a specific case that is utilized to illustrate a broader concept, and it can take the form of factual occurrences, hypothetical scenarios, or personal experiences.

Examples operate as concrete proof that makes it easier to understand and put into practice abstract ideas. They offer concrete or fictitious examples that exemplify a broad topic, making it more straightforward for others to understand and relate to the underlying notion.

Examples make complex theories or concepts more understandable and relatable, promoting effective communication and improved comprehension across various subjects and disciplines.

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Answer: 31 m/s

Step-by-step explanation:

70 miles per hour = 112654 meters per 3600 seconds = 31.3 = 31 m/s

Answer:

The friends split the bill at 15.32$

Step-by-step explanation:

So to find how much each paid you would take the bill total and divide it by the amount of people in this case three

And for the equation it would be 45.96/3=15.32$

The equation to model the solution to the problem would be; 3x = 45.96. the friends split the bill at 15.32 dollars.

An equation is an expression that shows the relationship between two or more numbers and variables. A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be one degree.

Given that the dinner for Lorenzo and his 3 friends costs $45.96.

To determine how much each paid would take the bill total

Therefore, we will divide it by the number of people in this case three

3x = 45.96

x = 45.96/3

x  = 15.32$

And for the equation would be; 3x = 45.96

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Answer:

none (as shown) or

one if all uppercase letters

Step-by-step explanation:

A line of symmetry is a line you could place on a shape (usually a square, rectangle, triangle, etc, but here the "shape" is the word checkbook) which, if you folded the shape on the line, the two halves of the shape would exactly match each other.

"checkbook" does NOT have any lines of symmetry. BUT,

CHECKBOOK

does have a line of symmetry, horizontally, right thru the middle.

The Solution:

We want to find the equation of a line S, which passes through point (6,2).

Let the required equation of line S be

Where m = the slope of line S, and

We are told that line S is parallel to line r, which is, y = 56x + 1. This implies that both lines have the same slope (m).

So, to find the slope (m) of line S, we shall compare y=56x+1 to the general form of equation of a line as given below:

Comparing both equations below:

Substituting 56 for m, and the given point (6,2) in the formula above, we get

Clearing the bracket, we get

Thus, the equation of line r is: y = 56x - 334

To find what needs to be added subtract the two numbers:

19/21 - 11/21 = 8/21

You need to add 8/21 to 11/21 to get 19/21

Answer:

$7.1875

Step-by-step explanation:

$28.75 x .25=7.1875

You cannot compare two marginal distributions to see if the corresponding two are related . So, the statement is false .

The answer to the stated question is false . No , you cannot compare two marginal distributions to see if the corresponding two variables are related.

The given question is related to probability and statistics.

Coming to probability distribution , it is the mathematical function that gives the probabilities of occurrence of different possible outcomes for an experiment. It is a mathematical description of a random phenomenon in terms of its sample space and the probabilities of events.

The marginal distribution of a subset of a collection of random variables is the probability distribution of the variables contained in the subset. It gives the probabilities of various values of the variables in the subset without reference to the values of the other variables.

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The first partial derivative of a multivariable function measures the rate of change of the function with respect to one specific variable while holding other variables constant.

In the case of the function f(x, y) = 8x cos(xy), we will find the first partial derivatives with respect to x and y.

To find ∂f/∂x, we differentiate f(x, y) with respect to x while treating y as a constant. The derivative of 8x with respect to x is simply 8, and the derivative of cos(xy) with respect to x is -xy sin(xy) by applying the chain rule. Therefore, ∂f/∂x = 8 cos(xy) - 8xy sin(xy).

To find ∂f/∂y, we differentiate f(x, y) with respect to y while treating x as a constant. The derivative of 8x with respect to y is 0 since x is a constant, and the derivative of cos(xy) with respect to y is -x sin(xy) by applying the chain rule. Therefore, ∂f/∂y = -8xy sin(xy).

These first partial derivatives give us information about how the function f(x, y) changes with respect to x and y. The derivative ∂f/∂x tells us how the function changes as we vary x while keeping y constant. The derivative ∂f/∂y tells us how the function changes as we vary y while keeping x constant.

In summary, the first partial derivatives of f(x, y) = 8x cos(xy) are ∂f/∂x = 8 cos(xy) - 8xy sin(xy) and ∂f/∂y = -8xy sin(xy). These derivatives provide valuable information about the rate of change of the function with respect to each variable, allowing us to analyze its behavior in different directions in the x-y plane.

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Answer:

0.684

Step-by-step explanation:

if sam and his 18 classmates want to that is 19 and there are 13 brownies so divide the number of brownies by the number of people to get your answer

Answer:

0.7

Step-by-step explanation:

13/18=0.7

Answer:

D. 3/20

Step-by-step explanation:

12/80 can be dimplified to 3/20

The probability that jim will win = P(A) = 1/9

The area of mathematics known as probability deals with numerical descriptions of how likely it is for an event to happen or for a claim to be true. A number between 0 and 1 is the probability of an event, where, broadly speaking, 0 denotes the event's impossibility and 1 denotes its certainty.

The odds in favor of jim beating a friend at golf are =  1:8

Let A be the event that Jim beating a friend golf.

So,

according to ratio, it becomes

P(A)/P(A') = 1/8

P(A) = 1x

P(A')  = 8x

we know that :

P(A) + P(A') = 1

x + 8x = 1

9x = 1

x = 1/9

so that

P(A) = 1/9

P(A')  = 8/9

the probability that jim will win = P(A) = 1/9

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Answer:

H(10) Would be the time, in minutes the balloon spent in air . H(10) Means the balloon spent 10 minutes in air

Answer:(a) The smallest possible distance between the two towns would be 12km (the distance to Bergville) + 15km (the distance to Reddington) = 27km. The largest possible distance would be 12km + 15km + 1km (the margin of error for each distance being given to the nearest kilometer) = 28km.

(b) The possible difference in the distance the two walkers walk would be the difference in the distances given on the sign, which is 15km - 12km = 3km. However, this difference would also be affected by the margin of error of 1km for each distance given on the sign, so the possible difference in distance could range from 2km to 4km.

Answer:

Option 4

125 × 125

Step-by-step explanation:

5⁶ = 5 × 5 × 5 × 5 × 5 × 5 = 125 × 125

Thus, 5⁶ = 125 × 125

-TheUnknownScientist