whats the unit rate situation for 228 students in 12 classes

Answer:

Corresponding Angles Theorem

x = -5

Step-by-step explanation:

Since they are corresponding angles, they are equal to each other.

x + 105 = 100

x = -5

Answer

CIAD

Step-by-step explanation

The Pythagorean theorem states:

where a and b are the legs and c is the hypotenuse of a right triangle.

Applying this theorem to triangle 1:

Then, the first letter is C.

Applying the theorem to triangle 2:

Then, the second letter is I.

Applying the theorem to triangle 3:

Then, the third letter is A.

Applying the theorem to triangle 4:

Then, the fourth letter is D.

Answer:

Step-by-step explanation:

Answer: The radius of convergence, r, is 1. So the series converges for -1 < x < 1 and diverges for |x| ≥ 1.

Step-by-step explanation:

Here, we can use the ratio test.

Let's apply the ratio test to the given series:

|(n+1)^2 x^(n+1) 2*4*6*...*(2n)*(2n+2)/(n^2 x^n 2*4*6*...*(2n))| n->∞

Simplifying the expression, we get:

|(n+1)^2 / n^2| * |x| * |2n+2|/|2n| n->∞

Taking the limit as n approaches infinity, we get:

|(n+1)^2 / n^2| * |x| * |2n+2|/|2n| n->∞

Note that |2n+2|/|2n| = |n+1|/|n|, so we can simplify the expression in (1) to:

|(n+1)^2 / n^2| * |x| * |n+1|/|n| n->∞

Simplifying further, we get: |(n+1) / n| * |(n+1) / n| * |x| n->∞

Note that (n+1)/n approaches 1 as n approaches infinity, so we can simplify the expression to:

 1 * 1 * |x| n->∞

Therefore, the series converges if: |x| < 1 n->∞

Which means the radius of convergence, r, is 1. So the series converges for -1 < x < 1 and diverges for |x| ≥ 1.

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The projected error of this sample would be an understatement of $2,000.

Hence, the correct option is A.

Step 1. In a probability-proportional-to-size sample, the projected error can be determined by calculating the difference between the recorded amount and the audit amount, and then scaling it up to the population using the sampling interval.

Step 2. Given:

Sampling interval = $5,000

Recorded amount = $10,000

Audit amount = $8,000

Step 3. Projected error = (Audit amount - Recorded amount) * (Population size / Sample size)

Step 4. In this case, since it is mentioned that this is the only error discovered by the auditor, the sample size can be assumed to be 1.

Projected error = ($8,000 - $10,000) * (Population size / 1)

Step 5. Since the error is the difference between the recorded amount and the audit amount, and the audit amount is lower than the recorded amount, it indicates an understatement.

Therefore, the projected error of this sample would be an understatement of $2,000.

Hence, the correct option is A.

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Answer:

I believe the next time both bells will ring at the same time is at 6:30PM.

Step-by-step explanation:

If the bells toll together at 6:00PM, the next time they toll together again should be at 6:30PM.(this is just how it works in my mind) if you add 15 to 15,, you get 30, right? And if you add 10+10=10, you get 30, right? And since 30 is a common number that both 10 and 30 can go into,, and is the lowest number both can go into,, it has to be the answer.

To determine the test statistic for a hypothesis test, we need additional information such as the null hypothesis, alternative hypothesis, and the population parameters. The sample standard deviation alone is not sufficient to calculate the test statistic.

In hypothesis testing, we typically compare sample statistics to population parameters to make inferences about the population. The test statistic depends on the specific hypothesis test being conducted, such as a t-test or z-test, and the information provided about the population.

Therefore, without further details about the specific hypothesis test, null hypothesis, alternative hypothesis, and population parameters, it is not possible to determine the test statistic.

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The magnitude of charge q₂ as per the given charges and information is equal to approximately 59.72 μC.

q₁ = -25 μC (negative charge),

y₁ = +0.22 m (y-coordinate of q₁),

q₂ = unknown (charge we need to determine),

y₂= +0.34 m (y-coordinate of q₂),

q = +8.4 μC (charge at the origin),

F = 27 N (magnitude of the net electrostatic force),

Use Coulomb's law to calculate the electrostatic forces between the charges.

Coulomb's law states that the magnitude of the electrostatic force between two point charges is given by the equation,

F = k × |q₁| × |q₂| / r²

where,

F is the magnitude of the electrostatic force,

k is the electrostatic constant (k ≈ 8.99 × 10⁹ N m²/C²),

|q₁| and |q₂| are the magnitudes of the charges,

and r is the distance between the charges.

and the force points in the +y direction.

Let's calculate the distance between the charges,

r₁ = √((0 - 0.22)² + (0 - 0)²)

  = √(0.0484)

  ≈ 0.22 m

r₂ = √((0 - 0.34)² + (0 - 0)²)

   = √(0.1156)

   ≈ 0.34 m

Since the net force is in the +y direction, the forces due to q₁ and q₂ must also be in the +y direction.

This implies that the magnitudes of the forces due to q₁ and q₂ are equal, since they balance each other out.

Applying Coulomb's law for the force due to q₁

F₁= k × |q₁| × |q| / r₁²

Applying Coulomb's law for the force due to q₂

F₂= k × |q₂| × |q| / r₂²

Since the magnitudes of F₁ and F₂ are equal,

F₁ = F₂

Therefore, we have,

k × |q₁| × |q| / r₁² = k × |q₂| × |q| / r₂²

Simplifying and canceling out common terms,

|q₁| / r₁²= |q₂| / r₂²

Substituting the values,

(-25 μC) / (0.22 m)² = |q₂| / (0.34 m)²

Solving for |q₂|

|q₂| = (-25 μC) × [(0.34 m)²/ (0.22 m)²]

Calculating the value,

|q₂| = (-25 μC) × (0.1156 m² / 0.0484 m²)

     ≈ -59.72 μC

Since charge q₂ is defined as positive in the problem statement,

take the magnitude of |q₂|,

|q₂| ≈ 59.72 μC

Therefore, the magnitude of charge q₂ is approximately 59.72 μC.

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Answer:

Only part a; still haven't figured out b

Step-by-step explanation:

For a) the answers would be:

x: -5 0 3

y: -3 2 5

The equation says add y = x+2

Replace x with let's say -5, and we get y = -5+2

-5+2=-3

Answer: John is 29 years old and Jane is 36 years old.

Step-by-step explanation:

There are many parts to this problem, so let's start by defining John as x and Jane as y.

We know that the sum of their age 10 years ago was 55, which gives us x+y-10=55. The reason we put -10 is because of 10 years ago. If you think about it in terms of now, 10 years back is 55, so now they would be 65 years old. So we can have either x+y-10=55 or x+y=65. For simplicity, I will use x+y=65.

We also know that John is 7 years younger than Jane, which gives x=y-7.

Luckily, we have x defined for us, so we can directly substitute that into our equation.

\((y-7)+y=65\)         [combine like terms]

\(2y-7=65\)                [add both sides by 7]

\(2y=72\)                      [divide both sides by 2]

\(y=36\)

Now we know that y=36, we can plug that into either equations to find x.

\(x+36=65\)                [subtract both sides by 36]

\(x=29\)

This concludes that John is 29 years old and Jane is 36 years old.

Answer :

4x + 9y = 27

Explanation :

Multiply the equation with 9

9( y = -4x/9 + 3 )

9y = -4x + 27

4x + 9y = 27

The minimum score that assures a student an A in the midterm is 87.7.

Given that the average score of a midterm exam in a large class is 69.7 and the standard deviation is 18.0. Suppose that in order to get an A in the midterm, the student's score in the test has to be at least one standard deviation above the mean.

To find the minimum score that assures a student an A in the midterm, we use the following formula: Minimum score = Mean + 1(Standard Deviation). Substituting the given values in the above formula, Minimum score = 69.7 + 1(18.0)Minimum score = 87.7. Therefore, the minimum score that assures a student an A in the midterm is 87.7.

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Answer:

The answer is

Step-by-step explanation:

To find an equation of a line given a point and slope we use the formula

\(y - y_1 = m(x - x_1)\)

where

m is the slope

( x1 , y1) is the point

From the question the point is (-2,-2) and slope = 1/2

The equation of the line is

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

We have the final answer as

\(y = \frac{1}{2} x - 1\)

Hope this helps you

The correct formula for the revenue generated by the item is Revenue = 200p - 5p^2.

The revenue generated by the item can be calculated by multiplying the price (p) by the unit sales (200 - 5p). Therefore, the correct formula for the revenue generated by the item is:

Revenue = Price x Unit Sales
Revenue = p(200 - 5p)
Revenue = 200p - 5p^2

The revenue generated by the item is a quadratic function of the price (p). To find the maximum revenue, we need to differentiate the function with respect to p and set it equal to zero:

dRevenue/dp = 200 - 10p = 0
10p = 200
p = 20

Therefore, the maximum revenue is generated when the price of the item is $20. Substituting p = 20 in the revenue formula, we get:

Revenue = 200(20) - 5(20^2) = $2000

Hence, the correct formula for the revenue generated by the item is Revenue = 200p - 5p^2, and the maximum revenue is achieved when the price of the item is $20, generating a revenue of $2000.

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Answer:

sine=opposite/hypotenuse

sin52.2=x/150

sin0.790=x/150

x=118.5

Answer:

21/143

Step-by-step explanation:

If it was simplified into a decimal it would be .146853

Answer:

x=10

Step-by-step explanation:

5x+10+3x=90

8x+10=90

8x=80

x=10

:)

Answer:

x=5   x=3

Step-by-step explanation:

x^2 - 8x + 15 = 0

Factor

What 2 numbers multiply to 15 and add to -8

-5*-3 = 15

-5-3 = -8

(x-5)(x-3) =0

Using the zero product property

x-5 =0    x-3 =0

x=5   x=3

Answer:

x = -5

Evidence to support reasoning:

Answer:

34000cm or 340m

Step-by-step explanation:

We have to find total surface area.

dimensions of 1 wooden box =

l = 1m = 100cm

b = 80cm

h = 25cm

∴ In the case of 2 =

l = 100cm

b= 80cm

h  = 25 + 25 = 50cm

T.S.A = 2(lb + lh + bh)

= 2(100*80 + 100*50+ 80*50)

= 2(8000+5000+4000)

= 2*17000

= 34000cm

= 340m

To reach a concentration of 4% we need to evaporate 4 ounces of water.

We know that we have 16 ounces of water, such that the concentration of salt is of the 3%.

Then the mass of salt is:

m = (0.03)*16 oz = 0.48 oz

Now, the mass of water that we need to have such that 0.48oz of salt represents a concentration of 4% is M, and it is given by:

0.48oz = (0.04)*M

Solving for M:

M = (0.48 oz)/0.04 = 12oz

So, we need to go from 16 oz of water to 12 oz of water, this means that we need to evaporate 4 ounces of water.

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Answer:

1. 93 m is the length of the rectangular garden.

2. The width of the window is 72 cm.

Step-by-step explanation:

\(\left(\dfrac{3^8}{3^5} \right)^3\\\\\\=\left(3^{8-5}\right)^3\\\\=(3^3)^3\\\\=(3)^{3\cdot 3}\\\\=3^9\)

Solution

Consider the figure below

The figure above is an hexagon divided into 6 parts, each part being an equilateral tringle.

Thus, the answer is option C

The quadrilateral ABCD is a square.

To show  that a quadrilateral is a square, we need to show that all four sides are equal in length and that the angles are all right angles.

So let's calculate the distances between the given points like this

AB  = √((3-0) ² + (0 -4)²)

= √(9  + 16) =   √(25)

= 5

BC = √((7-3)² + (3-0)²)

= √(16 + 9)

= √(25) = 5

CD = √((4-7) ² + (7-3) ²)

= √(9 + 16)

= √(25)

= 5

DA = √ ((0-4) ² + ( 4- 7) ²)

= √(16 + 9)

= √(25)

= 5

This shows that all the sides are equal in lenght. Now, lets solve for the slopes.

mAB = (0-4)/(3-0)

= -4/3

m BC

= (3- 7)/(0-3)

= 4/3

mCD  = ( 7-4)/(3- 0)

= 3/3 = 1

mDA = (0-4)/(4-0)

= -4/4 = -1

Since the slopes of opposites sides are reciprocals thus, the quadrilateral ABCD is a Square.

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Complete question is below

What type of quadrilateral is A B C D ? Explain your reasoning.

Employees in the transportation and shipping industry today are required to know advanced math for several reasons. Here are some of the most important ones:

1. Efficiency: In the transportation and shipping industry, time is money. To maximize efficiency, workers need to be able to calculate distances, speeds, and travel times accurately.

This requires a solid understanding of advanced math concepts such as algebra, calculus, and trigonometry.

2. Safety: Transporting goods and people comes with risks. To ensure safety, employees need to understand the physics of motion, forces, and momentum.

This requires knowledge of advanced math concepts such as vectors, kinematics, and dynamics.

3. Technology: The transportation and shipping industry is becoming increasingly automated and technology-driven. Employees need to be able to understand and use complex algorithms, statistical models, and data analysis tools.

This requires advanced math skills such as statistics, probability theory, and linear algebra.

4. Regulations: The transportation and shipping industry is subject to a wide range of regulations, including safety standards, environmental laws, and trade policies.

Compliance with these regulations often requires complex calculations and data analysis. Advanced math skills are essential for navigating this regulatory landscape.

In summary, advanced math skills are essential for employees in the transportation and shipping industry to ensure efficiency, safety, technology adoption, and compliance with regulations.

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Answer:

y = 4x - 2 would be the equation

Line SY bisects angle PSR. To prove that line SY bisects angle PSR, we can use the property that an angle inscribed in a circle is half the measure of the intercepted arc. Here's the proof:

Since XY is a diameter, it subtends a 180-degree angle at any point on the circle. Therefore, angle QXY measures 180 degrees.

Angle PQY is an inscribed angle, and its measure is half the intercepted arc PQ. Similarly, angle YSR measures half the intercepted arc SR.

Since angle QXY is 180 degrees and angle PQY and angle YSR are half of their respective intercepted arcs, the sum of angles PQY and YSR must be 180 degrees.

Therefore, angle PQY and angle YSR are equal, and since angle PQY is congruent to angle PQS (as QX bisects angle PQR), it follows that angle YSR is congruent to angle PSR.

Hence, we have proved that line SY bisects angle PSR.

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