(ii) Explain why a+b+c= 235°
This is a cornet maths question. How do I solve it

The net work output of the turbine in the ideal Brayton cycle is approximately -1593.11 kJ/kg.

To find the net work output of the turbine in an ideal Brayton cycle, we need to use the cold air standard assumptions. These assumptions include:

Given:

Initial temperature of air entering the turbine (T₁) = 1200 °C

Pressure ratio (P₂/P₁) = 7:1

Let's calculate the net work output using the following steps:

Step 1: Convert the initial temperature to Kelvin.

T₁ = 1200 °C + 273.15 = 1473.15 K

Step 2: Calculate the polytropic exponent (n) using the specific heat ratio (γ).

For air, γ ≈ 1.4 (approximately)

n = 1 / (γ - 1) = 1 / (1.4 - 1) = 1 / 0.4 = 2.5

Step 3: Calculate the temperature ratio (T₂/T₁) using the pressure ratio (P₂/P₁) and polytropic exponent (n) in turbine.

T₂/T₁ = (P₂/P₁)^((γ-1)/γ) = (7/1)⁰.⁴ ≈ 2.0736

Step 4: Calculate the final temperature (T₂) by multiplying it with the initial temperature.

T₂ = T₁ * (T₂/T₁)

= 1473.15 K * 2.0736

≈ 3051.74 K

Step 5: Calculate the net work output (W_net) using the isentropic turbine equation.

W_net = Cp * (T₁ - T₂)

Here, Cp is the specific heat at constant pressure for air. Assuming constant specific heat values for air:

Cp ≈ 1.005 kJ/kg·K (approximately)

W_net = 1.005 * (1473.15 - 3051.74) kJ/kg

W_net ≈ -1593.11 kJ/kg (negative sign indicates work extraction)

Therefore, the net work output of the turbine in the ideal Brayton cycle is approximately -1593.11 kJ/kg.

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Answer:

Step-by-step explanation:

First, put them in order.

5.3x+3.6x+9.8-8.14

Add 5.3x and 3.6x

8.9x

Subtract 8.14 from 9.8

1.66

\(\boxed{\underline{\bf \: ANSWER}}\)

977.834 can be defined as a rational number. Why? Well, 977.834 is not a non-terminating non-recurring/recurring number. Of it was, then it would have been an irrational number. Now, it can be a real number also because real numbers include all sorts of numbers whether it be fractions, decimals, roots, cubes etc. It's not an integer because integers don't include decimals or fractions numbers. So, the answers or options that are correct are

\( \sf \hookrightarrow \boxed{\sf\: rational \: number \: \: and \: real \: number}\)

________

Hope it helps.

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X is the amount of time individual waits at the courthouse to be called for service. X-bar is the mean wait time for a sample of individuals.

What is a random variable?

A random variable is a mathematical representation of a quantity or object that is affected by random events. It is a mapping or function from possible outcomes in a sample space to a measurable space, which is frequently real numbers.

Assume a committee is investigating whether there is excessive time waste in our judicial system. It is curious about the average amount of time people spend at the courthouse waiting to be called for jury duty. The committee polled 81 people who had recently served as jurors at random. The average wait time for the sample was 4 hours, with a standard deviation of 1.2 hours. In words, define the random variables X and.

X is the amount of time individual waits at the courthouse to be called for service. is the mean wait time for a sample of individuals.

The random variable X is the amount of time for which each of the prospective jurors waits at the courthouse before being called for service. is the mean wait time for the given sample of individuals. In the case given,

Hence, X is the amount of time individual waits at the courthouse to be called for service. X-bar is the mean wait time for a sample of individuals.

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actual cost is 950+23,500=24450

he sold them for 25000 so his profit is 25000-950-23500=550

Answer:

A cycle + A scooter

= 950 + 23,500

= 24,450

Profit = Sold - cost

= 25,000 - 24,450

= 550

So the profit is $550

Answer:

790

Step-by-step explanation:

19 3/4÷ 1/8=158

158*5 = 790

The company earned 68 billion dollars from 2008 to 2018.

According to the statement

we have given that the company's particular sales in expression are represented by (t² + 10t + 68)

And we have to find the constant terms in this expression which represent the sale of the company.

So, The given expression is (t² + 10t + 68)

From above expression it is clear that the it is in the form of Quadratic Equations.

So, The Quadratic equation, is an equation containing a single variable of degree 2. Its general form is ax^2 + bx + c = 0, where x is the variable and a, b,c are the known numbers and C is the Constant.

The general representation of Quadratic equation is

ax^2 + bx + c = 0  -(1)

and the given expression are

(t² + 10t + 68)  -(2)

After comparing both equations

Here C =68 = Constant.

So, 68 is the Constant term of the expression represent in terms of the context.

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Disclaimer: The question was incomplete. Please find the full content below.

Question:

A particular company's net sales, in billions, from 2008 to 2018 can be modeled by the expression t2 + 10t + 68, where t is the number of years since the end of 2008. What does the constant term of the expression represent in terms of the context?

The company earned 68 billion dollars from 2008 to 2018.

The company earned 68 billion dollars in 2008.

The company earned 10 billion dollars from 2008 to 2018.

The company earned 10 billion dollars in 2008.

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The minimum number of elements required for the construction of  a quadrilateral uniquely are 5 elements.

Explanation:

The minimum number of elements required for the construction of  a quadrilateral uniquely are  as follow:

Therefore, minimum 5 elements are required to construct a unique quadrilateral.

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Answer:

A,D,F

Step-by-step explanation:

if he drives 90 in 2 hours then in one hour its 45. 45 times 2 is 90. 45 times 3 is 135. 45 times 4 is 180. 45 times 5 is 225. 45 times 6 is 270. 45 times 7 is 315. and 45 times 8 is 360.

Answer:

To find f(4), we simply need to substitute 4 for x in the equation for f(x):

f(x) = -x + 2

f(4) = -(4) + 2

f(4) = -2

Therefore, f(4) = -2.

Step-by-step explanation:

Answer:

1

Step-by-step explanation:

1+1=2

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Calculate the rise between the two points and divide it by the difference in the horizontal direction to arrive at the answer (run).

An indication of how steep a line is is its slope. When calculating slope mathematically, "rise over run" is used (change in y divided by change in x). Calculate the rise over the run ratio of a line going through the points (-7,3) and (4, 2). With this in mind, the rise over run ratio of the line joining the two points is -1/11. Decide on the coordinates of two spots along the line.

Find the location of these two points' respective y-coordinate differences (rise). The difference between these two places' x-coordinates should be known (run). In order to calculate the difference in y-coordinates (rise/run or slope), divide it by the difference in x-coordinates. Rise is the quantity you gain or lose when moving from one location to another. That would result in a modification of the y values on the graph.

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Answer:

All three products were already rounded to the nearest 5g.

"Algebra made Easy" 450g

“Terrible Trigonometry" 95g

Wrapping 120g

867.107844 Is the maximum Jemima might have to pay to post the parcel.

Step-by-step explanation:

510 divided by 79 = 6.455g per 510g

665g total of products so divide 665 by 510 now to get 1.30392157g per weight which brings us to the maximum total of 867.107844

Answer:

-9

Step-by-step explanation:

you have to go left wards 6 times from -3

The correct answer is option C which is on the number line move 6 units left and stop at -9 the dolphin will now be at 9 feet below sea level.

A graph is the representation of the data on the vertical and horizontal coordinates so we can see the trend of the data.

It is given that a dolphin was swimming 3 feet below sea level. The number line shows the location of the dolphin. It then dove down 6 feet.

In the graph, we can see that from -3 point the 6 units left will be -9 point. Therefore the correct answer is option C which is on the number line move 6 units left and stop at -9 the dolphin will now be at 9 feet below sea level.

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Approximately 16% of the design is black.

Since the radius of each circle increases by 2 inches, the diameter of each circle increases by 4 inches. Thus, the diameter of the largest circle is 2 + 4(5) = 22 inches.

The area of each circle is proportional to the square of its radius, so the area of the smallest circle is π(\(2^2\)) = 4π square inches. The area of the second circle is π(\(4^2 - 2^2\)) = 12π square inches, the area of the third circle is π(\(6^2 - 4^2\)) = 20π square inches, and so on.

The total area of the design is the sum of the areas of all the circles, which is:

4π + 12π + 20π + 28π + 36π = 100π

The black area in the design consists of four quarter circles, each with a radius of 4 inches. The area of a one-quarter circle is:

(1/4)π(\(4^2\)) = 4π

So the total black area is 4 times this, or 16π.

The percent of the design that is black is:

(16π / 100π) x 100% ≈ 16%

Therefore, approximately 16% of the design is black.

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Concave hexagon with two pairs of congruent sides is:

   /\

   /  \

  /    \

 /      \

/        \

/_____\

\        /

\      /

 \    /

  \  /

   \/

A hexagon is a six-sided polygon. A concave hexagon is a hexagon with at least one interior angle greater than 180 degrees.

We can start with a regular hexagon, which has six congruent sides and six interior angles of 120 degrees each.

We can then extend two opposite sides of the regular hexagon outwards to create two pairs of congruent sides. The extended sides should not be parallel to each other, but rather at an angle, so that the resulting hexagon is concave.

Here is an example of a concave hexagon with two pairs of congruent sides:

   /\

   /  \

  /    \

 /      \

/        \

/_____\

\        /

\      /

 \    /

  \  /

   \/

In this hexagon, sides AB and CD are congruent, and sides EF and GH are also congruent. However, the angles at vertices A and H are greater than 180 degrees, making this a concave hexagon.

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1.  x² - 5x - 16 can be written as (x - 8)(x + 2).

2. 6an² - 3b²n² = n²(6a - 3b²).

3. This expression represents a perfect square trinomial, which can be factored as (2x - y)².

4. Combining like terms, we get -n³ - n² + n + 1 = -(n³ + n² - n - 1).

5. 17x³y⁴z⁶ = (x²y²z³)².

6. 12a²b³ = (2a)(6b³) = 12a6b³ = 12a⁷b³x⁶.

Let's simplify the given expressions:

Simplifying x² - 5x - 16:

To factorize this quadratic expression, we look for two numbers whose product is equal to -16 and whose sum is equal to -5. The numbers are -8 and 2.

Therefore, x² - 5x - 16 can be written as (x - 8)(x + 2).

Simplifying 6an² - 3b²n²:

To simplify this expression, we can factor out the common term n² from both terms:

6an² - 3b²n² = n²(6a - 3b²).

Simplifying 4x² - 4xy + y²:

This expression represents a perfect square trinomial, which can be factored as (2x - y)².

Simplifying n + 1 - n³ - n²:

Rearranging the terms, we have -n³ - n² + n + 1.

Combining like terms, we get -n³ - n² + n + 1 = -(n³ + n² - n - 1).

Simplifying 17x³y⁴z⁶:

To simplify this expression, we can divide each exponent by 2 to simplify it as much as possible:

17x³y⁴z⁶ = (x²y²z³)².

Simplifying 12a²b³:

To simplify this expression, we can multiply the exponents of a and b with the given expression:

12a²b³ = (2a)(6b³) = 12a6b³ = 12a⁷b³x⁶.

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Answer: e=−2

Step-by-step explanation:

jjjj

Answer:

e = 2

Step-by-step explanation:

Answer:

I attached the photo hoped it helped

Step-by-step explanation:

The values of x that provide meaningful predictions for the output value y are given as follows:

c. Prediction values are meaningful only for X-values in (or close to the range of the original data.

Regression equations are built from a sample of a data-set, and are used to model the entire data.

Depending on the behavior of the data, the regression equation can be linear, quadratic, logistic, exponential, and so on...

These regression equations are not valid for all values of the input x, some conditions are given as follows:

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Answer: \(f^{-1}(x)=\frac{\sqrt{x}-1}{2}\)

Step-by-step explanation:

Let \(f(y)=x\).

\(x=(2y+1)^2\\\\\pm \sqrt{x}=2y+1\\\\-1 \pm \sqrt{x}=2y\\\\y=-\frac{1}{2} \pm \frac{\sqrt{x}}{2}\)

Since the domain of the original function is the same as the range of the inverse, the rate of \(f^{-1}(x)\) is \(f^{-1}(x) \geq -1/2\). This means we consider the positive case.

\(\therefore f^{-1}(x)=\frac{\sqrt{x}-1}{2}\)

Answer:

4 gallons

Step-by-step explanation:

Say that g = the number of gallons of a 20% salt solution,

The first thing we want to do here is to convert each " percentage " into decimal form, to make things a bit simpler here.

( \(20(percent) = 0.20\)

( \(30( percent ) = 0.30\)

( \(25( percent ) = 0.25\)

Before this mixture takes place, the 20% salt solution is associated with g, the number of gallons of a 20% salt solution. Respectively the 30% salt solution is associated with 4 gallons. After mixing the two ( g and 4 ) the 25% salt solution should be associated with g + 4. We can therefore conclude the following equation -

0.20( g )+0.30( 4 ) = 0.25( g + 4 )

And now, let us solve for " g, "

0.2g + 1.2 = 0.25g + 1

- 0.2g       = - 0.2g

_________________

1.2 = 0.05g + 1

- 1  =          -  1

_________________

0.2 = 0.05g,

g = 4 gallons of a 20% salt solution

Answer:

  7

Step-by-step explanation:

We want to find the number 4-digit of positive integers n such that removing the thousands digit divides the number by 9.

__

Let the thousands digit be 'd'. Then we want to find the integer solutions to ...

  n -1000d = n/9

  n -n/9 = 1000d . . . . . . add 1000d -n/9

  8n = 9000d . . . . . . . . multiply by 9

  n = 1125d . . . . . . . . . divide by 8

The values of d that will give a suitable 4-digit value of n are 1 through 7.

When d=8, n is 9000. Removing the 9 gives 0, not 1000.

When d=9, n is 10125, not a 4-digit number.

There are 7 4-digit numbers such that removing the thousands digit gives 1/9 of the number.

Therefore, the total distance Gabe will paddle is 2x + 400 meters. The exact value of x depends on the width of the river, which is not provided in the given information.

To find the total distance Gabe will paddle, we need to consider the distance he will travel from Q to P, then from P to R, and finally from R back to Q.

First, let's consider the distance from Q to P. Since Gabe will paddle in a diagonal line across the river, this distance can be calculated using the Pythagorean theorem.

The length of the bridge (PR) is given as 400 meters, which is the hypotenuse of a right triangle. The width of the river can be considered as the perpendicular side, and the distance Gabe will paddle from Q to P is the other side. Let's call this distance x.

Using the Pythagorean theorem, we have:

x^2 + (width of the river)^2 = PR^2

Since the width of the river is not given, we'll represent it as w. Therefore:

x^2 + w^2 = 400^2

Next, let's consider the distance from P to R. Gabe will paddle along a route beside the bridge, which means he will travel the length of the bridge (PR) again. So, the distance from P to R is also 400 meters.

Finally, Gabe will paddle back from R to Q along the shore. Since he will follow the shoreline, the distance he will paddle is equal to the distance from Q to P, which is x.

To find the total distance, we add up the distances:

Total distance = QP + PR + RQ

= x + 400 + x

= 2x + 400

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The given functions are:

y = f(x) = - sin x + 2 and

y = g(x) = - 2cos x.

To sketch the graphs of these functions on the same set of axes, we need to construct a table of values and plot them on a coordinate plane.

Let's begin with function f(x).

Table of values for f(x):x f(x)0° 32° 1.87° 2.45° 2.83° 2.97° 2.85° 2.5° 1.95° 1.18° 0.3° 0°

The values of f(x) were obtained by substituting the corresponding values of x in the given function and evaluating the resulting expression.

Note that we chose values of x in increments of 30° to make it easier to plot the points on the graph.

However, any values of x within the given interval [0°; 180°] could be used.

Table of values for g(x):

x g(x)0° -20.00° -1.80° -1.17° -0.53° -0.13° 0.00° -0.13° -0.53° -1.17° -1.80° -2.00°

The values of g(x) were obtained in the same way as for f(x).

Note that the amplitude of f(x) is 1 and the amplitude of g(x) is 2.

Also, the period of both functions is 360° or 2π radians since they are both sin and cos functions respectively and the coefficient of x is 1.

Therefore, we can use these values to draw the graphs of the two functions on the same set of axes.

The graph of y = f(x) = - sin x + 2 and y = g(x) = - 2cos x for x is an element [0°; 180°] is shown below.

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Answer:

84

Step-by-step explanation:

The 4 part of the ratio relates to 48 girls, then

48 ÷ 4 = 12 ← value of 1 part of the ratio , then

3 parts = 3 × 12 = 36 ← number of boys

total number of students = 48 + 36 = 84

The units of weight of watermelon on the digital scale could be kilogram, gram and pounds.

According to the question,

We have the following information:

A watermelon is placed on a digital scale. The scale reads 10.5.

We know that there are several units of measurements for every physical quantity. For example, the units for measuring length are kilometers, meters, centimeters, feet, inches and many more.

In the same way, there are many units for measurements of weight. However, in most of the cases for the weight on a digital scale, it can be kilogram, gram or pound.

So, it could 10.5 kg or 10.5 g or 10.5 pounds.

Hence, the units of the weight of watermelon on the digital scale could be kilogram, gram and pounds.

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Answer:

She made $1230 more on printed shirts than plain shirts in 25 weeks.

Step-by-step explanation:

Hi,

Okay, I have to admit, this is pretty complicated. But, it's not impossible :) First things first, we know that the equation in the table is the number of shirts sold after W number of weeks. We know that we need to, first, find the total number of shirts sold in 25 weeks.

The equation for the plain shirts is 5w -4. Let's start with that.

Plugin 25 for w to find the total number of plain shirts sold after 25 weeks.

5w - 4

5(25) - 4

= 121

She sold 121 plain shirts after 25 weeks. But we're not done yet, we still have to see how much money she made after selling 121 plain shirts. To do this, we have to multiply the total number of plains shirts sold by 15. (we know that each plain short costs $15, that's why we're multiplying it by 121)

When you do this...

121 x 15

You get...

$1815

She got $1815 after 25 weeks just for selling plain shirts.

Now, let's find the total cost of printed shirts after 25 weeks.

The equation for the printed shirts if 8w + 3.

8w + 3

8(25) + 3

= 203

She sold 203 printed shirts in 25 weeks. Let's find the cost. Each printed shirt costs $15 so we need to multiply 203 by 15.

203 x 15

You get...

$3045

She made $3045 by selling printed shirts in 25 weeks.

Now, we have to subtract $3045 by $1815 to find how much more she made. You get...

3045 - 1815

= $1230

She made $1230 more on printed shirts than plain shirts in 25 weeks.

I really hope this helps :)

a. Simple interest: around 14.29 years.

b. Annual compound interest: about 5 years.

c. Continuous compound interest: roughly 4.95 years.



a. With a 14 percent simple interest rate, the time it takes for a sum to double can be calculated using the formula:Time = (100 / interest rate) * 2

In this case, the interest rate is 14 percent, so the time it takes for the sum to double is:Time = (100 / 14) * 2 = 14.29 years (approximately).

b. With a 14 percent interest rate compounded annually, the time it takes for a sum to double can be calculated using the compound interest formula:Time = log(2) / log(1 + (interest rate / 100))

Substituting the values, the time it takes for the sum to double is:

Time = log(2) / log(1 + (14 / 100)) = 5.00 years (approximately).

c. With a 14 percent interest rate compounded continuously, the time it takes for a sum to double can be calculated using the formula:

Time = ln(2) / (interest rate / 100)

Using the values, the time it takes for the sum to double is:

Time = ln(2) / (14 / 100) = 4.95 years (approximately).

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The probability of getting the color yellow when spinning a spinner with three equal sections colored red, white, and blue is 0%. Therefore, the correct answer is d) 0%.

Since the spinner has three equal sections colored red, white, and blue, and there is no section labeled yellow, it is not possible to obtain the color yellow when spinning the spinner. Each section has an equal chance of being landed on, but none of them represent the color yellow. Therefore, the probability of getting the color yellow is 0%. It's important to note that probability represents the likelihood of an event occurring, and in this case, the event of landing on the color yellow is not possible given the given information about the spinner. Therefore, the probability is 0%.

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