How can you decide whether the domain of a function is discrete or continuous? Describe two real-life examples of functions: one with a discrete domain and one with a continuous domain.

Answer:

6 Apples

Step-by-step explanation:

There would be six apples and 2 oranges left over.

Hope this Helps!

:D

Answer:

I was kind of confused on this one but is it 15 apples?

Step-by-step explanation:

3, 6, 9, 12, 15

4, 8, 12, 16, 20

I think the answer is 15 apples.

The order would be DE < FD < EF. To order the sides of triangle ΔDEF from shortest to longest, you need to compare the lengths of the sides.

1. Determine the lengths of sides DE, EF, and FD.
2. Compare the lengths to find the shortest side.
3. Identify the next shortest side.
4. The remaining side will be the longest.

Once you have the side lengths, simply arrange them in ascending order (from shortest to longest) to answer your question. For example, if DE is 3 units, EF is 5 units, and FD is 4 units, the order would be DE < FD < EF.
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Answer:

I think it already is in standard form.

Step-by-step explanation:

Standard form means that a quadratic function is in the form \(ax^2+bx+c=y\).

In this case, a=-1, b=2, and c=4.

Answer:

28th

Step-by-step explanation:

4*7=28.

Answer:

x=1

Step-by-step explanation:

6x+5=11

6x=11-5

6x=6

x=1

Answer:

Step-by-step explanation:

let a number be x

first condition multiply the number by 6

therefore,

6×x

6x

second condition add 5 to that

therefore,

6x+5

last condition the number is equal to 11

therefore,

6x+5=11

\(first \: step \colon \: define\)

\(6x + 5 = 11\)

\(second \: step \colon \: \\ subtract \: 5 \: from \: both \: sides\)

\(6x + 5 - 5 = 11 - 5\)

\(6x = 6\)

\(last \: step \colon \\ divide \: both \: sides \: by \: 6\)

\( \frac{6x}{6} = \frac{6}{6} \)

Answer:

see below

Step-by-step explanation:

given function: \(Cos(x)=\frac{1}{3}\)

Cosine - (In a right triangle, the ratio of the length of the adjacent side to the length of the hypotenuse.)

#1: Take the inverse cosine of both sides of the equation to extract \(x\) from inside the cosine.

\(x=arccos\frac{1}{3}\)

#2: Evaluate

\(x=1.23095941\)

#3: The cosine function is positive in the first and fourth quadrants. To find the second solution, subtract the reference angle from \(2\)π to find the solution in the fourth quadrant.

\(x=2(3.14159265)-1.23095941\)

#4: Simplify the equation above.

- Multiply \(2\) by \(3.14159265\)

\(x=6.2831853-1.23095941\)

- Subtract \(1.23095941\) from \(6.2831853\)

\(x=5.05222588\)

#5: Find the period.

- The period of the function can be calculated using \(\frac{2\pi }{|b|}\).

\(\frac{2\pi }{|b|}\)

- Replace \(b\) with \(1\)  in the formula for period.

\(\frac{2\pi }{|1|}\)

#6: Solve the equation.

- The absolute value is the distance between a number and zero. The distance between \(0\) and \(1\) is \(1\).

\(\frac{2\pi }{1}\)

- Divide \(2\pi\) by \(1.\)

\(2\pi\)

The period of the \(cos(x)\) function is \(2\pi\) so values will repeat every \(2\pi\) radians in both directions.

\(x=1.23095941+2\pi n,5.05222588+2\pi n\), for any integer \(n\)

Answer:

5 : 7

Step-by-step explanation:

groom's side: 40

bride's side: 56

ratio groom to bride = 40/56 = 20/28 = 10/14 = 5/7

Answer: 5 : 7

Answer:

15 ft

Step-by-step explanation:

If every 1/4 of an inch is a foot, than every inch is 4 feet.

1 inch = 4ft

3 inches = 12ft

1/4 + 1/4 + 1/4 = 3/4

3/4=3 ft

12+3=15ft

The decrease in diameter of the bar due to the applied load is -0.005434905d and the final diameter of the bar is 1.005434905d.

A compressive load of 80,000 lb is applied to a bar with a circular section of 0.75 in diameter and a length of 10 in.

if the modulus of elasticity of the bar material is 10,000 ksi and the Poisson's ratio is 0.3.

We have to determine the decrease in diameter of the bar due to the applied load.

Let d be the initial diameter of the bar and ∆d be the decrease in diameter of the bar due to the applied load, then the final diameter of the bar is d - ∆d.

Length of the bar, L = 10 in

Cross-sectional area of the bar, A = πd²/4 = π(0.75)²/4 = 0.4418 in²

Stress produced by the applied load,σ = P/A

= 80,000/0.4418

= 181163.5 psi

Young's modulus of elasticity, E = 10,000 ksi

Poisson's ratio, ν = 0.3

The longitudinal strain produced in the bar, ɛ = σ/E

= 181163.5/10,000,000

= 0.01811635

The lateral strain produced in the bar, υ = νɛ

= 0.3 × 0.01811635

= 0.005434905'

The decrease in diameter of the bar due to the applied load, ∆d/d = -υ

= -0.005434905∆d

= -0.005434905d

The final diameter of the bar,

d - ∆d = d + 0.005434905d

= 1.005434905d

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The limit of the given function is  π/2.

What is a limit?

A limit in mathematics is the value that a function gets closer to when the input gets closer to a certain value. Calculus and mathematical analysis are not possible without limits, which are also required to determine continuity, derivatives, and integrals.

Here, we have

Given: \(\lim_{(x,y) \to \pi, \pi /2} y sin(x-y)\)

We have to find the limit of the given function.

=  \(\lim_{(x,y) \to \pi, \pi /2} y sin(x-y)\)

Now, we substitute the value of each variable.

x = π and y = π/2

= y sin(x-y)

= π/2sin(π-π/2)

= π/2sinπ/2

= π/2sin(90°)   (∴sin90° = 1)

= π/2×1

= π/2

Hence, the limit of the given function is  π/2.

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Answer:

look id k which ans u want I m telling both

#5 such number could be 0 becoz it is not whole integer or positive

#6 there could be many numbers like

8.67676767.....

or

8.111111111111

etc....

The ordered rational numbers representing the gauge readings from least to greatest are 19/10, 63/10, 78/10, 78/10, 13/1, 25/1, 2/1.

To represent the gauge readings as rational numbers, we can express them as fractions with a common denominator.

Given readings:

25 psi pressure

13 psi vacuum

6.3 psi vacuum

7.8 psi vacuum

1.9 psi vacuum

2 psi pressure

7.8 psi pressure

Expressed as rational numbers with a common denominator:

25 psi = 25/1

13 psi = 13/1

6.3 psi = 63/10

7.8 psi = 78/10

1.9 psi = 19/10

2 psi = 2/1

7.8 psi = 78/10

Now, let's order these rational numbers from least to greatest:

1.9 psi = 19/10

6.3 psi = 63/10

7.8 psi = 78/10

7.8 psi = 78/10

13 psi = 13/1

25 psi = 25/1

2 psi = 2/1

Ordered from least to greatest:

19/10, 63/10, 78/10, 78/10, 13/1, 25/1, 2/1

Therefore, the ordered rational numbers representing the gauge readings from least to greatest are 19/10, 63/10, 78/10, 78/10, 13/1, 25/1, 2/1.

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Miguel finish an 800-meter race first.

To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

We have to given that;

Miguel ran 80 meters in 20 seconds while Trina ran 40 meters in 15 seconds.

Hence, The speed of Miguel is,

⇒ Speed = Distance / Time

⇒ Speed = 80 / 20

⇒ Speed = 4 m/s

And, The speed of Trina is,

⇒ Speed = Distance / Time

⇒ Speed = 40/15

⇒ Speed = 2.67 m/s

Cleary, The speed of Miguel is faster than Trina.

Hence, Miguel finish an 800-meter race first.

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A. The work done is 300 ft-lbs when a 100 lb rock is lifted to a height of 3 ft.

To calculate the work done, we can use the formula: Work = force x distance x cos(Ф).In this case, the force is the force of gravity acting on the rock, which can be calculated using the formula:

force = m * g

where m is the mass of the rock and g is the acceleration due to gravity (32.17 ft/s^2).

force = 100 lb * 32.17 ft/s^2 = 3,217 ft-lbs

The distance is the height to which the rock is lifted, which is 3 ft.

The angle of the rock to the vertical is 90 degrees, so cos(90) = 0.

So,

Work = force x distance x cos(theta) = 3,217 ft-lbs * 3 ft * 0 = 300 ft-lbs

So, the work done is 300 ft-lbs.

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After evaluating the expression for x=0, the equation 13-6.5x = 13

⇒ 13-6.5(0)

⇒ 13 - 0

⇒ 13

To solve linear equations, utilize the steps that are provided below.

Lets take an example of solve z for 7z – (3z – 4) = 12

Here is no multiplication or division, so this will be easy to solve

⇒ 7z – (3z – 4) = 12

⇒ 7z – 3z + 4 = 12

⇒ 4z = 12 – 4

⇒ 4z = 8

⇒ z = 8/4

⇒ z = 2

See, that was so simple, using the mentioned methods, every linear equation can be solved easily.

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9514 1404 393

Answer:

  7. (x, y) = (0, 1)

  10. (x, y) ={((7+√97)/2, (-1-√97)/2) and ((7-√97)/2, (-1+√97)/2)

  6. (x, y) = (-3+√6, -1+√6) and (-3-√6, -1-√6)

Step-by-step explanation:

7. It is convenient to subtract the second equation from the first:

  (y) -(y) = (x^2 +5x +1) -(x^2 +2x +1)

  0 = 3x . . . . simplify

  0 = x . . . . . divide by 3

  y = 0 + 0 + 1 . . . . substitute x=0 into either equation

The solution is (x, y) = (0, 1). The first attachment shows this solution.

__

10. It can work to subtract the first equation from the second.

  (y) -(x +y) = (x^2 -8x -9) -(3)

  -x = x^2 -8x -12 . . . . simplify

  x^2 -7x = 12 . . . . . . . add x+12, swap sides

  x^2 -7x +49/4 = 12 +49/4 . . . . complete the square

  (x -7/2)^2 = 97/4 . . . . . . . . write as a square

  x -7/2 = (±√97)/2 . . . . . . .  square root

  x = (7±√97)/2 . . . . . add 7/2

  y = 3 -x = (-1±√97)/2 . . . . find corresponding y

Solutions are (x, y) = {((7+√97)/2, (-1-√97)/2), ((7-√97)/2, (-1+√97)/2)}. The second attachment shows the solution.

__

6. For this one, it can work well to subtract the first equation from the second.

  (y) -(y) = (x +2) - (-x^2 -5x -1)

  0 = x^2 +6x +3

Adding 6 to both sides completes the square.

  x^2 +6x +9 = 6

  (x +3)^2 = 6

  x +3 = ±√6

  x = -3±√6

  y = x +2 = -1±√6

Solutions are (x, y) = (-3+√6, -1+√6) and (-3-√6, -1-√6). The third attachment shows the solution.

_____

About completing the square

In general, completing the square starts with ...

  x^2 +ax = b

Then the square is completed by adding the square of a/2.

  x^2 +ax +(a/2)^2 = b + (a/2)^2

Then you can write the left side as a square.

  (x +a/2)^2 = (b +a^2/4)

Finally, take the square root and subtract the left-side constant.

  x = -a/2 ± √(b +a^2/4)

The binomial probability formula is used to calculate the probability of a specific number of successes in a fixed number of independent trials, where each trial can only result in success or failure. It is used to model situations where there are only two possible outcomes for each trial, and where the trials are independent and identically distributed.

The formula for binomial probability is:

\(P(x) = (n choose x) * p^x * (1 - p)^{n-x}\\\)

where P(x) is the probability of x successes in n trials, p is the probability of success on each trial, (n choose x) is the binomial coefficient which gives the number of ways to choose x successes from n trials, and (1 - p) is the probability of failure on each trial.

The binomial probability formula can be used in a variety of applications, such as:

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Answer:

The dependent variable is the number of plays he carries the ball.

The independent variable is the number of touchdowns he scores.

The dependent variable is the number of yards he gains.

Step-by-step explanation:

Tom's coach keeps track of the number of plays that Tom carries the ball and how many yards he gains. Select all the statements about independent and dependent variables that are true.

The dependent variable is the number of plays he carries the ball.

The independent variable is the number of plays he carries the ball.

The independent variable is the number of touchdowns he scores.

The dependent variable is the number of yards he gains.

The dependent variable is the number of touchdowns he scores.

y = kx

y = dependent variable. it is the variable that is explained by the dependent variable

x = is the variable that explains the dependent variable

Answer:

true

Step-by-step explanation:

if you rewrite \(sec\left(\frac{\pi }{2}\:-x\right)\) with trigonometric identities:

\(sec\left(\frac{\pi }{2}\:-x\right)\)    \(=\frac{1}{\sin \left(x\right)}\)

\(\frac{1}{\sin \left(x\right)}\)  \(=\csc \left(x\right)\)

so, yes,  \(sec\left(\frac{\pi }{2}\:-x\right)\)  \(=\csc \left(x\right)\)

hope this helps!!

For a normal distribution with mean 0 and standard deviation 1 the python line will be 0.627409464153

What is mean?

The sum of all values divided by the total number of values determines the mean (also known as the arithmetic mean, which differs from the geometric mean) of a dataset. It is known as the "average" and is the most widely used central tendency measure.

What is standard Deviation?

The term "standard deviation" (or "") refers to a measurement of the data's dispersion from the mean. A low standard deviation implies that the data are grouped around the mean, whereas a large standard deviation shows that the data are more dispersed.

Appropriate function and output are given below

import scipy.stats as st

print(st.norm.cdf(0.325,0,1)

0.627409464153

The python line will be 0.627409464153 for a normal distribution with a mean of 0 and a standard deviation of 1.

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The scale factor of the dilation of the triangles is 2

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

The similar triangles

The scale factor of the dilation is the division of the corresponding sides

So, we have

Scale factor = 6/3

When evaluated, we have

scale factor = 2

Hence the scale factor is 2

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The table that shows the growth rate of Plant 1 which is 4 cm/week, and the graph that gives the growth rate of Plant 2 as 2 cm/week gives the correct option as C;

C. I think that plant 1 grows more per day and I disagree with Aaliyah's reasoning

A proportional relationship between two variables is one in which one variable is a multiple of the other.

The possible table in the question is presented as follows;

Plant 1

The values on the graph are;

Plant 2

The rate, r1, of growth of Plant 1 is therefore;

r1 = 8 cm/(2 weeks) = 4 cm/week

The rate, of growth, r2, of plant 2 is found as follows;

r2 = 4 cm/(2 weeks) = 2 cm/week

Given that Plant 1 grows faster at 4 cm/week, than Plant 2, that grows at 2 cm/week, the correct statement is since Plant 1 grows 4 cm/week and Plant 2 grows 2 cm/week, Plant 1 grows more per day.

The correct option is therefore;

C. I think that plant 1 grows more per day and I disagree with Aaliyah's reasoning

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Answer:

12 for 9$

Step-by-step explanation:

Because you get more cans.

The likelihood of their next third child having additional digits of (six fingers on each hand and six toes on each foot) is 1/2.

For the given condition,

Because the father has the dominant feature as well as the mother is now in normal condition, there is a 50% chance that this deformity will be passed down to children.

Thus, the likelihood of their next (third) child having additional digits is 1/2.

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Answer:o understand the behaviour of a polynomial graphically all one one needs is the degree (order) and leading coefficient. This two components predict what polynomial does graphically as gets larger or smaller indefinitely. This called "end behavior". For example it easy to predict what a polynomial with even degree and +ve leading coefficient will do. All even polynomial have both ends of the graph moving in the same direction with direction dictated by the sign of leading coefficient. On the other hand odd power will get have the polynomial end points moving in opposite direction, with the leading coefficient dictating the direction.

Step-by-step explanation:To understand the behaviour of a polynomial graphically all one one needs is the degree (order) and leading coefficient. This two components predict what polynomial does graphically as gets larger or smaller indefinitely. This called "end behavior". For example it easy to predict what a polynomial with even degree and +ve leading coefficient will do. All even polynomial have both ends of the graph moving in the same direction with direction dictated by the sign of leading coefficient. On the other hand odd power will get have the polynomial end points moving in opposite direction, with the leading coefficient dictating the direction.

Step-by-step explanation:

The end behavior of a function f describes the behavior of the graph of the function at the "ends" of the x-axis. In other words, the end behavior of a function describes the trend of the graph if we look to the right end of the x-axis (as x approaches +∞ ) and to the left end of the x-axis (as x approaches −∞ ).

The molar composition of the product stream is: CO2: 68.65%, O2: 6.01%, and N2: 25.34%.

Given that a gas power plant combusts 600 kg of coal every hour in a continuous fluidized bed reactor that is at a steady state.

The composition of coal fed to the reactor is found to contain 89.20 wt% C, 7.10 wt% H, 2.60 wt% S, and the rest moisture.

Air is fed at 20% excess and that only 90.0% of the carbon undergoes complete combustion. The following are the answers to the questions that follow:

Calculate the air feed rate - The first step is to balance the combustion equation to find the theoretical amount of air required for complete combustion:

\(C + O2 → CO2CH4 + 2O2 → CO2 + 2H2OCO + (1/2)O2 → CO2C + (1/2)O2 → COH2 + (1/2)O2 → H2O2C + O2 → 2CO2S + O2 → SO2\)

From the equation, the theoretical air-fuel ratio (AFR) is calculated as shown below:

Carbon: AFR

1/0.8920 = 1.1214

Hydrogen: AFR

4/0.0710 = 56.3381

Sulphur: AFR

32/0.0260 = 1230.7692

The AFR that is greater is taken, which is 1230.7692. Now, calculate the actual amount of air required to achieve 90% carbon conversion:

0.9(0.8920/12) + (0.1/0.21)(0.21/0.79)(1.1214/32) = 0.063 kg/kg of coal

The actual air feed rate (AFR actual)

AFR × kg of coal combusted = 1230.7692 × 600

= 738461.54 kg/hour or 205.128 kg/s

The air feed rate is 205.128 kg/s or 738461.54 kg/hour.

Calculate the molar composition of the product stream

Carbon balance: C in coal fed = C in product stream

Carbon in coal fed:

0.892 × 600 kg = 535.2 kg/hour

Carbon in product stream

0.9 × 535.2 = 481.68 kg/hour

Carbon in unreacted coal = 535.2 − 481.68 = 53.52 kg/hour

Molar flow rate of CO2 = Carbon in product stream/ Molecular weight of CO2

= 481.68/(12.011 + 2 × 15.999) = 15.533 kmol/hour

Molar flow rate of O2:

Air feed rate × (21/100) × (1/32) = 205.128 × 0.21 × 0.03125 = 1.358 kmol/hour

Molar flow rate of N2:

Air feed rate × (79/100) × (1/28) = 205.128 × 0.79 × 0.03571 = 5.720 kmol/hour

Total molar flow rate:

15.533 + 1.358 + 5.720 = 22.611 kmol/hour

Composition of product stream: CO2: 15.533/22.611

0.6865 or 68.65%

O2: 1.358/22.611 = 0.0601 or 6.01%

N2: 5.720/22.611 = 0.2534 or 25.34%

Therefore, the molar composition of the product stream is: CO2: 68.65%, O2: 6.01%, and N2: 25.34%.

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The molar composition of the product stream is approximately:
- Carbon dioxide (CO2): 17.35%
- Water (H2O): 4.15%
- Sulfur dioxide (SO2): 0.19%
- Nitrogen (N2): 78.31%

To calculate the air feed rate, we need to determine the amount of air required for the complete combustion of carbon.

Calculate the moles of carbon in the coal:
  - The molecular weight of carbon (C) is 12 g/mol.
  - We know the weight percentage of carbon in the coal is 89.20 wt%.
  - Convert the weight percentage to mass: 600 kg * (89.20/100) = 534.72 kg of carbon.
  - Convert the mass of carbon to moles: 534.72 kg / 12 g/mol = 44.56 mol of carbon.

Calculate the stoichiometric amount of air required for complete combustion:
  - The balanced equation for the combustion of carbon is: C + O2 -> CO2.
  - From the balanced equation, we see that 1 mole of carbon requires 1 mole of oxygen (O2) for complete combustion.
  - Since air contains 21% oxygen, we can calculate the moles of air required: 44.56 mol * (1/0.21) = 212.17 mol of air.

Calculate the excess air:
  - We are given that air is fed at 20% excess. Excess air is the additional amount of air supplied beyond the stoichiometric requirement.
  - Calculate the excess air: 212.17 mol * (20/100) = 42.43 mol of excess air.
  - Total moles of air required: 212.17 mol + 42.43 mol = 254.60 mol.

Calculate the air feed rate:
  - We are given that the gas power plant combusts 600 kg of coal every hour.
  - The rate of coal combustion is equal to the rate of carbon combustion since only 90.0% of the carbon undergoes complete combustion.
  - Convert the rate of carbon combustion to moles: 44.56 mol/hour.
  - The air feed rate is the same as the moles of air required per hour: 254.60 mol/hour.

To calculate the molar composition of the product stream, we need to determine the moles of each component in the product stream.

Calculate the moles of carbon dioxide (CO2):
  - From the balanced equation, we know that 1 mole of carbon produces 1 mole of carbon dioxide.
  - The moles of carbon in the coal is 44.56 mol.
  - Therefore, the moles of carbon dioxide produced is also 44.56 mol.

Calculate the moles of water (H2O):
  - The weight percentage of hydrogen (H) in the coal is 7.10 wt%.
  - Convert the weight percentage to mass: 600 kg * (7.10/100) = 42.60 kg of hydrogen.
  - The molecular weight of water (H2O) is 18 g/mol.
  - Convert the mass of hydrogen to moles: 42.60 kg / 2 g/mol = 21.30 mol of hydrogen.
  - Since water contains 2 moles of hydrogen per mole of water, the moles of water produced is 21.30 mol / 2 = 10.65 mol.

Calculate the moles of sulfur dioxide (SO2):
  - The weight percentage of sulfur (S) in the coal is 2.60 wt%.
  - Convert the weight percentage to mass: 600 kg * (2.60/100) = 15.60 kg of sulfur.
  - The molecular weight of sulfur dioxide (SO2) is 64 g/mol.
  - Convert the mass of sulfur to moles: 15.60 kg / 32 g/mol = 0.4875 mol of sulfur.
  - Since sulfur dioxide contains 1 mole of sulfur per mole of sulfur dioxide, the moles of sulfur dioxide produced is 0.4875 mol.

Calculate the moles of nitrogen (N2):
  - Nitrogen is the remaining component in the air after combustion.
  - Since air contains 79% nitrogen, the moles of nitrogen is 79% of the moles of air: 254.60 mol * 0.79 = 201.03 mol.

Calculate the total moles in the product stream:
  - The total moles is the sum of the moles of carbon dioxide, water, sulfur dioxide, and nitrogen: 44.56 mol + 10.65 mol + 0.4875 mol + 201.03 mol = 256.72 mol.

Calculate the molar composition of the product stream:
  - The molar composition of each component is the moles of that component divided by the total moles, multiplied by 100 to get a percentage.
  - Carbon dioxide (CO2): (44.56 mol / 256.72 mol) * 100 = 17.35%
  - Water (H2O): (10.65 mol / 256.72 mol) * 100 = 4.15%
  - Sulfur dioxide (SO2): (0.4875 mol / 256.72 mol) * 100 = 0.19%
  - Nitrogen (N2): (201.03 mol / 256.72 mol) * 100 = 78.31%

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The perameter to find a cartesian equation of the curve is y^2 = 1 + x.

We are given that;

x=tan^2(theta)

y=sec(theta)

Now,

We need to solve for t in one equation and substitute it into the other equation. In this case, we have:

x = tan^2(t) y = sec(t)

Solving for t in the first equation, we get:

t = arctan(sqrt(x))

Substituting this into the second equation, we get:

y = sec(arctan(sqrt(x)))

Using the identity sec^2(t) = 1 + tan^2(t),

we can simplify this equation as:

y^2 = 1 + x

Therefore, by the given equation the answer will be y^2 = 1 + x

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