Which expression has a sum of one and two thirty sixths?

a
two ninths + three fourths
b
three ninths + two fourths
c
four ninths + two fourths
d
five ninths + two fourths

The parametric equation of the line10x - y = 20 is given as y = 2.5t - 5

parametric equation are equations where the dependent variable is expressed in terms of independent variable

say dependent variable y = f(t)

independent variable x = t

Given data

10x - 4y = 20

solution

10x - 4y = 20

10x - 20 = 4y

4y = 10x - 5

y = 2.5x - 5

where x = t

y = 2.5t - 5

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Step-by-step explanation:

Using simple interest, logan can use the equation:

amount × decimal multiplier = total

x × 1.15 = y

40.13  percentage of the bottles contain less than 32 oz of soda.

Mean (μ) = 32.3 oz

Standard Deviation (σ) = 1.2 oz

Threshold value (X) = 32 oz

We can use the standard normal distribution (Z-distribution) to calculate the cumulative probability.

First, let's standardize the threshold value using the formula

Z = (X - μ) / σ

Z = (32 - 32.3) / 1.2 Z ≈ -0.25

Next, we'll look up the cumulative probability corresponding to Z = -0.25 in the standard normal distribution table or use a calculator.

From the standard normal distribution table or calculator, we find that the cumulative probability for

Z = -0.25 is approximately 0.4013.

This means that approximately 40.13% of bottles contain less than 32 oz of soda.

Therefore, about 40.13% of the bottles contain less than 32 oz of soda.

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The Taylor polynomial of degree n = 4 for x near the point a = π/3 for the function cos(3x) is P4(x) = -1 - (9/2)(x - π/3)² - (81/24)(x - π/3)⁴

To find the Taylor polynomial of degree n = 4 for the function cos(3x) near the point a = π/3, we need to compute the derivatives of the function at point a and evaluate them.

First, let's find the derivatives of cos(3x):

f(x) = cos(3x)

f'(x) = -3sin(3x)

f''(x) = -9cos(3x)

f'''(x) = 27sin(3x)

f''''(x) = 81cos(3x)

Next, let's evaluate these derivatives at the point a = π/3:

f(π/3) = cos(3π/3) = cos(π) = -1

f'(π/3) = -3sin(3π/3) = -3sin(π) = 0

f''(π/3) = -9cos(3π/3) = -9cos(π) = -9

f'''(π/3) = 27sin(3π/3) = 27sin(π) = 0

f''''(π/3) = 81cos(3π/3) = 81cos(π) = -81

Now, let's write the Taylor polynomial of degree n = 4 using the derivatives at the point a = π/3:

P4(x) = f(a) + f'(a)(x - a) + (f''(a)/2!)(x - a)² + (f'''(a)/3!)(x - a)³ + (f''''(a)/4!)(x - a)⁴

Substituting the evaluated derivatives, we have:

P4(x) = -1 + 0(x - π/3) + (-9/2)(x - π/3)² + 0(x - π/3)³ + (-81/4!)(x - π/3)⁴

Simplifying further:

P4(x) = -1 - (9/2)(x - π/3)² - (81/24)(x - π/3)⁴

The Taylor polynomial of degree n = 4 for x near the point a = π/3 for the function cos(3x) is:

P4(x) = -1 - (9/2)(x - π/3)² - (81/24)(x - π/3)⁴

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Therefore, on average, a customer arriving during the morning rush would wait approximately 2.17 hours to be served.

To determine the average waiting time for a customer arriving during the morning rush at the coffee shop, we need to consider the arrival rate and the capacity of the shop.

Given that 100 customers per hour arrive at the coffee shop during the two-hour morning rush, and the shop has a capacity of 80 customers per hour, we can conclude that there will be more customers arriving than the shop can accommodate.

To calculate the average waiting time, we need to account for the time spent by customers who have to wait due to the shop being at full capacity. For simplicity, let's assume that customers arrive uniformly throughout the two-hour period.

During the first hour (8 a.m. to 9 a.m.), there will be 100 customers arriving, but the shop can only serve 80 customers. Therefore, 20 customers will have to wait for their turn to be served.

During the second hour (9 a.m. to 10 a.m.), again, 100 customers will arrive, but since the shop is already at full capacity, all 100 customers will have to wait for their turn.

In total, during the two-hour morning rush, there will be 20 customers who wait for one hour and 100 customers who wait for the entire two hours.

To calculate the average waiting time, we can sum up the waiting times and divide by the total number of customers:

Average waiting time = (20 * 1 hour + 100 * 2 hours) / (20 + 100) = (20 + 200) / 120 = 2.17 hours

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Answer:

I believe this is the answer you are looking for:

x3-6x2-7x

Step-by-step explanation:

a) The electric flux through each face of a cube with a point charge at its center is given by Φ = qL² / ε₀, where q is the magnitude of the charge, L is the side length of the cube, and ε₀ is the permittivity of free space.

b) If we have a cube with a different side length L1, the flux through a face of that cube would be Φ1 = qL1² / ε₀.

a) Electric flux through each face of the cube:

To calculate the electric flux through a surface, we use Gauss's Law, which relates the electric flux (Φ) to the enclosed charge (q_enc) by the equation Φ = q_enc / ε₀, where ε₀ is the permittivity of free space.

In this case, since the point charge is at the center of the cube, it is enclosed by each face of the cube. Therefore, the flux through each face will be the same. Let's calculate it.

The charge enclosed by each face is the magnitude of the point charge, q, since it is located at the center of the cube. Therefore, q_enc = q.

The area of each face of the cube is A = L², where L is the side length of the cube.

Now, substituting the values into the equation Φ = q_enc / ε₀, we get:

Φ = q / ε₀ * (1 face area)

= q / ε₀ * L²

Therefore, the electric flux through each face of the cube is Φ = qL² / ε₀.

b) Electric flux through a face with a different side length:

If we have a cube with a side length L1, we can use the same formula to calculate the flux through one face of the cube.

Using the equation Φ = qL² / ε₀, we substitute L1 for L:

Φ1 = qL1² / ε₀

So, the flux through a face of the cube with side length L1 is Φ1 = qL1² / ε₀.

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Complete Question:

A point charge of magnitude q is at the center of a cube with sides of length L.

a- What is the electric flux Φ through each of the six faces of the cube?

b- What would be the flux Φ1 through a face of the cube if its sides were of length L1?

Answer:

hypotenuse

Step-by-step explanation:

When you use the distance formula you are calculating the length of the hypotenuse of a right triangle.

When using the distance formula, you are making a right triangle whose hypotenuse connects two given points.

Answer: The blank would be hypotenuse if I’m not mistaken!

We need to use the concept of Pythagorean theorem. The value of x in the given triangle is 16.

The Pythagorean theorem, sometimes known as Pythagoras' theorem, is a basic relationship between a right triangle's three sides in Euclidean geometry. According to this rule, the areas of the squares on the other two sides add up to the area of the square whose side is the hypotenuse, or the side across from the right angle. This theorem can be expressed as the Pythagorean equation, which is an equation connecting the lengths of the sides a, b, and the hypotenuse c: [1]

a^{2}+b^{2}=c^{2},

So mark the given triangle as ABC in which B is right angled.

AC=24+x

Mark the height of the given triangle as BD and BD=14.

Now using pythagoras theorem,

    (BC)2=(CD)2 + (BD)2

     ⇒(BC)2=(24)2 + (14)2

      ∴(BC)2=772

Now after finding BC we need to find AB using pythagoras theorem.

     (AD)2 +(BD)2 =(AB)2

  ⇒(x)2 + (14)2 =(AB)2 - eq1

  ⇒ (AB)2 + (BC)2 = (24+x)2 - eq2

Substitute eq1 in eq2

⇒(x)2 + (14)2 + (BC)2 =(24+x)2

⇒(x)2 + 576 +772 = 576 + (x)2 + 48x

⇒772=48x

∴x=16.0833

x≈16.

We need to use the concept of Pythagorean theorem. The value of x in the given triangle is 16.

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Answer In the diagram, a = 47 m and angle a measures. 49°. ... 71.6 m. Cos luod. Nost. I 10 hod. "tan (49) = 1/2 x=tan 249). 47 x 64.1. X A ... 2. In the triangle shown, determine LA to the nearest degree. A. 6.7 1B) 9.0 ... triangle. The slanted sides are both 12 inches long and the bottom of the pad is 8 inches long. 11. ... RM 7.2 cm.:

Step-by-step explanation:

πr2 is an example of a (D) model.

Therefore, πr2 is an example of a (D) model.

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The complete question is given below:

Mia uses the formula πr2 to find the area of a circle. What is πr2 an example of?

A. a robot

B. a car

C. a telescope

D. a model

Answer:

8

Step-by-step explanation:

this is pretty simple, just an equation written out

800/100=8

Answer:

20000

Step-by-step explanation:

9600 = 80% after he gave 40% to his children

80%=4/5

9600 / 4 * 5 = 12000

12000 = 60% of the original

60%=3/5

12000 / 3 * 5 = 20000

a) To obtain the potential pressure drop in the wellbore, we can use the hydrostatic pressure equation.

The potential pressure drop is equal to the pressure gradient multiplied by the length of the wellbore. The pressure gradient can be calculated using the equation: Pressure gradient = (density of oil × acceleration due to gravity) × sin(θ), where θ is the deviation angle of the wellbore from horizontal flow. In this case, the pressure gradient would be (48 lbm/ft^3 × 32.2 ft/s^2) × sin(15°). Multiplying the pressure gradient by the wellbore length of 6,000 ft gives the potential pressure drop.

b) To determine the frictional pressure drop in the wellbore, we can use the Darcy-Weisbach equation. The Darcy-Weisbach equation states that the pressure drop is equal to the friction factor multiplied by the pipe length, density, squared velocity, and divided by the pipe diameter. However, to calculate the friction factor, we need the Reynolds number. The Reynolds number can be calculated as (density × velocity × diameter) divided by the oil viscosity. Once the Reynolds number is known, the friction factor can be determined. Finally, using the friction factor, we can calculate the frictional pressure drop.

c) To calculate the in-situ oil velocity, we need to consider the total volume of the pipe, including both oil and gas. The total pipe volume is calculated as the pipe cross-sectional area multiplied by the wellbore length. Subtracting the gas volume from the total volume gives the oil volume. Dividing the oil volume by the total time taken by the oil to flow through the pipe (converted to seconds) gives the average oil velocity.

d) The flow regime of the two-phase flow can be determined based on the oil and gas mixture properties and flow conditions. Common flow regimes include bubble flow, slug flow, annular flow, and mist flow. These regimes are characterized by different distribution and interaction of the oil and gas phases. To determine the specific flow regime, various parameters such as gas and liquid velocities, mixture density, viscosity, and surface tension need to be considered. Additional information would be required to accurately determine the flow regime in this scenario.

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The inequality that represents the legal driving speeds, s, in kilometers per hour is 45 >= s <= 70.

It should be noted that an inequality is simply used in mathematics to show that the expression or equation aren't equal.

From the information, the highway has a minimum speed limit of 45 miles per hour and a maximum speed limit of 70 miles per hour.

Therefore, the inequality that represents the legal driving speeds is 45 >= s <= 70.

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Answer:

x = − 10

Step-by-step explanation:

Let's solve your equation step-by-step.

4 ( x − 5 ) = 6x

Step 1: Simplify both sides of the equation.

4 ( x − 5 ) = 6x

( 4 ) ( x ) + ( 4 ) ( − 5 ) = 6x ( Distribute )

4x + − 20 = 6x

4x − 20 = 6x

Step 2: Subtract 6x from both sides.

4x − 20 − 6x = 6x − 6x

− 2x − 20 = 0

Step 3: Add 20 to both sides.

− 2x − 20 + 20 = 0 + 20 − 2x = 20

Step 4: Divide both sides by -2.

− 2x / − 2 = 20 / − 2

x = − 10

Answer:

(-3,-4)

Step-by-step explanation:

Carol has at least 7 garments in the dressing room.

Information given in the problem is

A store’s dressing room has a limit of 10 garments per customer

If Carol has at least 3 garments below the limit

the limit is 10 garments, this is the maximum number of clothes and Carol has 3 garments below the limit

we can conclude that Carol has at least

= 10 - 3

= 7

Carol has 7 garments in the dressing room.

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The one way to determine factors of x³  + 11x² – 3x – 33  will be \(x^2(x+11)-3(x+11)_\).

It is the method to separate the polynomial into parts and the parts will be in multiplication. And the value of the polynomial at this point will be zero.

The steps involved in the factorization are;

1. For each pair of parentheses, we create a common factor.

2. We use x2 as a common factor for the first parenthesis.

3. We use common factor 3 for the second parenthesis.

\(x^3 + 11x^2 - 3x -33 \\\\ x^2(x+11)-3(x+11)_\)

We will find the final solution as \(x^2(x+11)-3(x+11)_\).

Hence the one way to determine factors of x³  + 11x² – 3x – 33  will be \(x^2(x+11)-3(x+11)_\).

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the larger the sample, the more confidence you have when you generalize your sample findings to the population facts.

The larger the sample size, the more confidence you can have when you generalize your sample findings to the population facts. This is because larger sample sizes provide more accurate representation of the population facts due to the increased number of data points collected. As a result, the more data points you have, the more reliable your findings are in terms of representing the population facts. The larger the sample size, the more confidence you can have in generalizing the findings to the population facts.

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Answer:

Below in bold.

Step-by-step explanation:

To get g(f(x)) we replace the x in g(x) by f(x) and simplify:

g(f(x)) = (2x + 1) - 3

= 2x - 2.

A.  To ensure that the probability is at least 0.95 that the relative frequency estimate differs from 0.20 by less than 0.02, at least 7976 voters should be polled.

b. We find the z-score corresponding to a cumulative probability of 0.95 to be approximately 1.96.

n > 2401

a) Using the Chebyshev inequality, we can determine the minimum number of voters that should be polled to ensure that the probability is at least 0.95 that the relative frequency estimate differs from 0.20 by less than 0.02.

The Chebyshev inequality states that for any random variable X with mean μ and standard deviation σ, the probability of X deviating from the mean by k standard deviations is at least 1 - 1/k^2.

In this case, we want the relative frequency estimate to deviate from 0.20 by less than 0.02, which means we want the difference to be within 0.02 standard deviations of the mean. Since the relative frequency estimate is a sample proportion, its standard deviation can be approximated by sqrt(p(1-p)/n), where p is the true proportion (0.20) and n is the sample size.

We can set up the inequality as follows:

1 - 1/k^2 ≥ 0.95

Solving for k:

1/k^2 ≤ 0.05

k^2 ≥ 1/0.05

k^2 ≥ 20

Taking the square root of both sides:

k ≥ sqrt(20)

k ≥ 4.47

To ensure that the difference between the relative frequency estimate and 0.20 is within 0.02, we need k standard deviations to be less than 0.02. So, we have:

k * sqrt(p(1-p)/n) < 0.02

4.47 * sqrt(0.20(1-0.20)/n) < 0.02

Simplifying:

sqrt(0.20(1-0.20)/n) < 0.02/4.47

sqrt(0.16/n) < 0.00448

0.4/sqrt(n) < 0.00448

sqrt(n) > 0.4/0.00448

sqrt(n) > 89.29

n > 89.29^2

n > 7975.84

Therefore, to ensure that the probability is at least 0.95 that the relative frequency estimate differs from 0.20 by less than 0.02, at least 7976 voters should be polled.

b) Using the central limit theorem, we can determine the minimum number of voters that should be polled to ensure that the probability is at least 0.95 that the sample mean differs from 0.20 by less than 0.02.

According to the central limit theorem, the sample mean follows a normal distribution with mean μ and standard deviation σ/sqrt(n), where σ is the population standard deviation (unknown in this case), and n is the sample size.

To ensure that the difference between the sample mean and 0.20 is within 0.02, we can set up the following inequality:

z * (σ/sqrt(n)) < 0.02

Since the population standard deviation σ is unknown, we can use a conservative estimate by assuming the worst-case scenario, which is p(1-p) = 0.25. Therefore, σ = sqrt(0.25) = 0.5.

Using the standard normal distribution table, we find the z-score corresponding to a cumulative probability of 0.95 to be approximately 1.96.

1.96 * (0.5/sqrt(n)) < 0.02

0.98/sqrt(n) < 0.02

sqrt(n) > 0.98/0.02

sqrt(n) > 49

n > 49^2

n > 2401

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we are told that $400 is deposited in a bank account and that every month $200 is added. If "m" is the number of months then the total balance for a given number of months is given by:

In this case, the input variable is the number of months "m" and the output variable is the balance "b". The initial value is $400 and the rate of change is:

If you want the probability of randomly drawing a red marble to be 3/5, you need to add 13 red marbles.

The probability of drawing a red marble is equal to the quotient between the number of red marbles and the total number of marbles in the bag.

Initially, there are 12 red marbles and 32 in total, so if we add another x red marbles, we will have:

Then the probability will be:

p = (12 + x)/(32 + x)

And we want this to be 3/5, then we need to solve:

(12 + x)/(32 + x) = 3/5

(12 + x)*5 = 3*(32 + x)

60 + 5x = 96 + 3x

5x - 3x = 96 - 60

2x = 36

x = 36/2 = 13

x = 13

You need to add 13 red marbles.

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Methane (CH4) is an organic compound that is the simplest member of the hydrocarbon group. Each methane molecule is composed of one carbon atom and four hydrogen atoms. Carbon is the central atom in the molecule.

Methane is a colorless, odorless, and flammable gas that is lighter than air. Methane is a primary component of natural gas and is frequently found in oil wells.Methane has four single covalent bonds. Each hydrogen atom in the molecule shares one electron with the carbon atom.

As a result, carbon obtains four electrons, while hydrogen obtains one electron for each bond. Since carbon has four electrons in its outer shell and each hydrogen atom has one electron in its outer shell, the compound is electrically stable.

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You arrange 5 letters in 7893600 ways

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

Letters to use = 5

Total available letters = 26

The letters are distinct

This means that the letters cannot be repeated

So, we have

First = 26, Second = 25 ....... Fifth = 22

Using the above as a guide, we have the following:

Ways = 26 * 25 * 24 * 23 * 22

Evaluate

Ways = 7893600

Hence, the arrangement is 7893600

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The most spontaneous reaction at 298 K would be the one with the highest positive standard cell potential (E°cell) value. In this case, that would be reaction, a b c with an E°cell of 1.22 V.

A higher positive E°cell value indicates a greater tendency for the reaction to occur spontaneously in the direction of the products.

Conversely, a negative E°cell value indicates a tendency for the reverse reaction to occur spontaneously in the direction of the reactants. Therefore, reactions a) and b) are not spontaneous as their E°cell values are negative and positive, respectively, but much lower than reaction d). Reaction c) has a positive E°cell value but lower than reaction d), thus it would be less spontaneous than reaction d).

Therefore, option d is the correct answer.

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The perimeter of the square is 52 units.

In this question,

the points (1, -2) and (-4, 10) are adjacent vertices of a square.

We need to find the perimeter of the square

The side length of a square is the distance between given two points.

Let a be the side length of the square.

\(a=\sqrt{(-4-1)^2+(10-(-2)^2)}\\\\ a=\sqrt{25+144}\\\\ a=\sqrt{169}\\\\ a=13\)

The side length of the square is 13 units.

so, the perimeter of a square would be,

P = 4a

P = 4 × 13

P = 52 units

Therefore, the perimeter of the square is 52 units.

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Answer:

um u put numbers not triangle but also if u meant the numbers it would Correct

Step-by-step explanation:

Answer:

Yes it is

Step-by-step explanation:

Answer: g(f(10)) = g(√2x+5) = 6x-3

We need to substitute x = √2*10 + 5 into g(x) = 6x - 3

g(f(10)) = 6(√2*10 + 5) - 3 = 6√20 + 30 - 3 = 6√20 + 27

So g(f(10)) = 6√20 + 27.