Every month, Rachel gets a basic salary of $4000. She also gets a bonus of $200 for each policy she sells and a bonus of $50 for each client's compliant she resolves. Write an expression for her total salary for a month if she sells n policies an resolves x complaints

Answer:

0.625

Step-by-step explanation:

Answer:

0.625

Step-by-step explanation:

It is possible for a data set to have a more specific distribution, such as a normal distribution, which allows for a more accurate estimate of the percentage of data within certain standard deviations of the mean.

False.

Chebyshev's Theorem states that for any set of data, regardless of its distribution, at least 1-1/k^2 of the data will be within k standard deviations of the mean, where k is any positive integer greater than 1. In other words, at least 75% of the data will be within 2 standard deviations of the mean, not 95%.

For example, if we have a data set with a mean of 50 and a standard deviation of 10, Chebyshev's Theorem tells us that at least 75% of the data will be within 20 units of the mean (i.e. between 30 and 70). However, it is possible for a data set to have a more specific distribution, such as a normal distribution, which allows for a more accurate estimate of the percentage of data within certain standard deviations of the mean.

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It is possible for a data set to have a more specific distribution, such as a normal distribution, which allows for a more accurate estimate of the percentage of data within certain standard deviations of the mean.

False.

Chebyshev's Theorem states that for any set of data, regardless of its distribution, at least 1-1/k^2 of the data will be within k standard deviations of the mean, where k is any positive integer greater than 1. In other words, at least 75% of the data will be within 2 standard deviations of the mean, not 95%.

For example, if we have a data set with a mean of 50 and a standard deviation of 10, Chebyshev's Theorem tells us that at least 75% of the data will be within 20 units of the mean (i.e. between 30 and 70). However, it is possible for a data set to have a more specific distribution, such as a normal distribution, which allows for a more accurate estimate of the percentage of data within certain standard deviations of the mean.

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The expected population size after two generations is 216.

To calculate the expected population size after two generations using the given value of λ, we can use the formula:

\(Nt = N0 * lemda ^{t}\)

where Nt is expected population size after t generations,

N0 is the initial population size, and lemda (λ) is the geometric growth rate.

Here, initial population size is N0 = 150, and the growth rate is λ = 1.2. We want to find the expected population size after two generations, so t = 2.

Putting these values into the formula, we get:

\(Nt = 150 * (1.2)^{2} \\Nt = 150 * 1.44\\Nt = 216\)

Therefore, the expected population size after two generations is 216.

So, the correct answer is option (d) 216.

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Answer:

18

Step-by-step explanation:

From the rectangle, M O = NP

4x - 10 = 2x+4

4x-2x = 4 + 10

2x = 14

x = 14/2

x = 7

SInce MO and NP are the diagonal

Length of diagonal = 4x- 10

Length of diagonal = 4(7) - 10

Length of diagonal = 28 - 10

Length of diagonal = 18

hence the required length is 18

Answer:

Total number of chips = 720 Favorable cases = 720 - 568

Answer:

\(c(8) =29\)

Step-by-step explanation:

\(c(n) = -6 + 5(n - 1)\)

For 8th term (n=8)

\(c(8) = -6 + 5(8 - 1)\)

\(c(8) = -6 + 35\)

\(c(8) =29\)

The work required to lift the entire chain to the top of the building is 1,662.9 ft-lbs.

The work required to lift the chain to the top of the building is equal to the potential energy gained by the chain, which is given by

potential energy = mass × gravity × height

where mass is the mass of the chain, gravity is the acceleration due to gravity (32.2 ft/s^2), and height is the length of the chain (18 feet) since it is being lifted vertically.

First, we need to find the mass of the chain. We can use the fact that the weight of the chain is 93 pounds to find the mass using the formula

weight = mass × gravity

Rearranging this formula to solve for mass, we get

mass = weight / gravity

Substituting the given values, we get

mass = 93 pounds / 32.2 ft/s^2 = 2.89 slugs

Now we can calculate the potential energy of the chain using the formula

potential energy = mass × gravity × height

Substituting the values we have calculated, we get

potential energy = 2.89 slugs × 32.2 ft/s^2 × 18 feet = 1,662.9 ft-lbs

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Answer:

-21p - 7c

Step-by-step explanation:

Answer:

55

Step-by-step explanation:

Right on edge

Answer:

Step-by-step explanation:

55°

A rectangle is a rhombus =Sometimes

A parallelogram is a rectangle = Always

A quadrilateral is a pentagon = Never

Parallelogram is a quadrilateral that has two pairs of parallel sides.

In a parallelogram, opposite sides and angles are equal.

The adjacent angles add up to 180 degrees.

We have,

A rhombus has four equal sides and its opposite angles are equal.

A rectangle is a rhombus if the rectangle becomes a square.

So,

We can say that a rectangle is sometimes a rhombus.

A parallelogram is always a rectangle.

But not all rectangle is a parallelograms.

A quadrilateral has four sides.

A pentagon has 5 sides.

So,

A quadrilateral is never a pentagon.

Thus,

A rectangle is sometimes a rhombus.

A parallelogram is always a rectangle.

A quadrilateral is never a pentagon.

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Answer: use the algebric condistional process

Step-by-step explanation: this is sample only

Therefore, the surface represented by the given equation is a sphere centered at the origin with a radius of 6 units.

The given equation rho^2(sin^2(φ)sin^2(θ) + cos^2(φ)) = 36 represents a surface in spherical coordinates. Let's break down the equation to identify the surface:

ρ^2(sin^2(φ)sin^2(θ) + cos^2(φ)) = 36

Here, ρ represents the radial distance, φ is the polar angle, and θ is the azimuthal angle.

By analyzing the equation, we can see that it combines both the azimuthal and polar angles. The terms sin^2(φ)sin^2(θ) and cos^2(φ) involve both angles.

The equation ρ^2(sin^2(φ)sin^2(θ) + cos^2(φ)) = 36 describes a sphere centered at the origin with a radius of 6 units. The constant value of 36 indicates that the squared radial distance from the origin to any point on the surface is 36.

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Answer:

254.4

Step-by-step explanation:

if its 0.75 inch thick, then to get the radius you just times to thickness by 2 which gets 1.5.

6-1.5= 4.5

to get the radius you divide 4.5 by 2 which gets 2.25

and then put this in the formula you get=

V=πr2h=π·2.252·16≈254.469

so the answer is 254

edit:i might be wrong feel free to correct me

Answer: 254

Step-by-step explanation:

Answer: 0.20 Ω

Step-by-step explanation:

From the question, we are informed that a multi-cab starter motor has a current of 60.0 A and a voltage of 12 V. The resistance of the starter motor will be calculated thus:

Current (I) = 60.0A

Voltage (V) = 12V

Resistance = Unknown

Since Voltage = Current × Resistance

Therefore, Resistance = Voltage / Current

= 12/60

= 0.20 Ω

The resistance of the motor is 0.20 Ω

The resistance of the starter motor if a multi-cab starter motor has a current of 60.0 A and a voltage of 12V is 0.2 ohms

Based on the given question, for us to get the resistance of the starter motor, we will need to use Ohm's law.

According to the law, the current I passing through a conductor at constant temperature is directly proportional to the voltage "V". Mathematically;

V = IR

V is the voltage = 12V

I is the current = 60.0A

R is the resistance

Substitute the given parameters into the formula as shown:

12 = 60 R

R = 12/60

R = 1/5

R = 0/2

Hence the resistance of the starter motor if a multi-cab starter motor has a current of 60.0 A and a voltage of 12V is 0.2 ohms

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try A

Step-by-step explanation:

Answer:

\( \huge{ \boxed{ \bold{ \tt{ \angle \: UTQ \: and \: \angle \: RQO}}}}\)

Step-by-step explanation:

✎ The easiest way to think of a corresponding angles is ' F - pattern ' . In our case , \( \angle\) UTQ and ∠ RQO are corresponding angles as they makes F - Shape .

Hope I helped!

Have a wonderful time ! ツ

~TheAnimeGirl

Answer:

\(\frac{9}{100}\)

1/11.....................

If one of the longer sides of the Isosceles triangle is 6.3 centimeters, the length of the base is 3.1 centimeters.

Let's solve the problem step by step:

1. Identify the given information:

  - The triangle is isosceles, meaning it has two equal sides.

  - The two equal sides, labeled "a," are longer than the base, labeled "b."

  - The perimeter of the triangle is 15.7 centimeters.

  - One of the longer sides is 6.3 centimeters.

2. Set up the equation based on the given information:

  Since the triangle is isosceles, the sum of the lengths of the two equal sides is twice the length of the base. Therefore, we can write the equation:

  2a + b = 15.7

3. Substitute the known value into the equation:

  One of the longer sides is given as 6.3 centimeters, so we can substitute it into the equation:

  2(6.3) + b = 15.7

4. Simplify and solve the equation:

  12.6 + b = 15.7

  Subtract 12.6 from both sides:

  b = 15.7 - 12.6

  b = 3.1

5. Interpret the result:

  The length of the base, labeled "b," is found to be 3.1 centimeters.

Therefore, if one of the longer sides of the isosceles triangle is 6.3 centimeters, the length of the base is 3.1 centimeters.

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Using compatible numbers and adjusting them helps us to perform mental math and make calculations faster. This method also helps us to estimate answers and check if the actual answer is reasonable or not.

To find sums, I would prefer to use the method of using compatible numbers and adjusting. The reason behind this is that it can help me to perform mental calculations and solve mathematical problems faster.What are compatible numbers?Compatible numbers are numbers that are close to the actual numbers, but are easier to work with mathematically. They are rounded numbers that make it easier to perform mental math. Once we have the answer, we can adjust it to get the correct answer.To solve an addition problem using compatible numbers, we choose numbers close to the actual numbers in the problem. For example, if we are adding 45 and 32, we can round the numbers to 50 and 30. Then we add 50 and 30 to get 80, which is the compatible number sum. But this is not the actual answer because we rounded the numbers, so we need to adjust. We subtract 5 from 50 and add 3 to 30 to get 45 and 33, respectively. Then we add the adjusted numbers (45 and 33) to get the correct answer, which is 78.Using compatible numbers and adjusting them helps us to perform mental math and make calculations faster. This method also helps us to estimate answers and check if the actual answer is reasonable or not.

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Answer:

Step-by-step explanation:

The measures of the arcs AB and ABC and the area of the sectors they form are:

arc AB = 110° and sector area AB = 1050.35

arc ABC = 300° and sector area ABC = 4125

The area of a sector is calculated by multiplying the fraction of the angle for the sector divided by 360° and πr², where r is the radius.

measure of an arc is equal to the angle it substends at the center of the circle.

arc AB = 180 - 70 = 110

radius = 25/2 = 12.5

sector area AB = (110°/360°) × 22/7 × 12.5 × 12.5

sector area AB = 1050.35

arc ABC = 360 - 60 = 300

radius = 30/2 = 15

sector area ABC = (300°/360°) × 22/7 × 15 × 15

sector area ABC = 4125

Therefore, the measures of the arcs AB and ABC and the area of the sectors they form are:

arc AB = 110° and sector area AB = 1050.35

arc ABC = 300° and sector area ABC = 4125

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The required  cost of each shirt is $21.28.

A mathematical statement known as an equation is made up of two expressions joined together by the equal symbol. A formula would be 3x - 5 = 16, for instance. When this equation is solved, we discover that the value of the quantity x is 7.

The total cost of 3 identical shirts, including shipping, is $71.83. So we can write the equation as:

3s + 7.99 = 71.83

To solve for the cost of each shirt, we need to isolate the variable "s" on one side of the equation. We can start by subtracting 7.99 from both sides:

3s = 63.84

Then, we can divide both sides by 3:

s = 21.28

Therefore, the cost of each shirt is $21.28.

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The equation in percentage given by, $2.21 + 8% tax = $2.3868 rounds to $2.4 to the nearest tenth.

Given an equation,

$2.21 + 8% tax = $2.3868

This is an equation which relates the cost including the percentage of tax.

When 2.21 is added to the tax amount, we get $2.3868.

2.21 + (0.08 × 2.21) = 2.3868

Here it is not mentioned up to what decimal we have to round the figure.

If 2.3868 is rounded to the nearest whole number, it becomes 2.

If 2.3868 is rounded to the tenth, it becomes 2.4.

If 2.3868 is rounded to the hundredth, it becomes 2.39.

Hence the rounded amount to the nearest tenth is $2.4.

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The magnitude of the potential energy on the x-axis at a distance of 9.85 cm is approximately 0.01976 J.

To calculate the electric potential energy at a point on the x-axis, we need to consider the contributions from each point charge and sum them up. Let's perform the calculations using the given values and formulas:

Given:

\(\( Q = 8.07 \times 10^{-6} \, \text{C} \)\\\\\( d = 0.1 \, \text{m} \)\\\\\( x = 0.0985 \, \text{m} \)\\\\\( k \approx 8.99 \times 10^9 \, \text{Nm}^2/\text{C}^2 \)\)

1. Charge at \(\( y = +d = 10 \)\)cm:

\(\( r_1 = \sqrt{x^2 + d^2} = \sqrt{(0.0985 \, \text{m})^2 + (0.1 \, \text{m})^2} \)\\\\\( U_1 = (8.99 \times 10^9 \, \text{Nm}^2/\text{C}^2) \cdot (8.07 \times 10^{-6} \, \text{C})^2 / r_1 \)\)

2. Charge at y = 0 :

\(\( r_2 = x = 0.0985 \, \text{m} \)\\\\\( U_2 = (8.99 \times 10^9 \, \text{Nm}^2/\text{C}^2) \cdot (8.07 \times 10^{-6} \, \text{C})^2 / r_2 \)\)

3. Charge at \(\( y = -d = -10 \)\) cm:

\(\( r_3 = \sqrt{x^2 + d^2} = \sqrt{(0.0985 \, \text{m})^2 + (0.1 \, \text{m})^2} \)\\\\\( U_3 = (8.99 \times 10^9 \, \text{Nm}^2/\text{C}^2) \cdot (8.07 \times 10^{-6} \, \text{C})^2 / r_3 \)\)

Now, let's substitute the values and calculate:

\(\( r_1 = \sqrt{(0.0985 \, \text{m})^2 + (0.1 \, \text{m})^2} \approx 0.1399 \, \text{m} \)\\\\\( U_1 = (8.99 \times 10^9 \, \text{Nm}^2/\text{C}^2) \cdot (8.07 \times 10^{-6} \, \text{C})^2 / 0.1399 \, \text{m} \)\)

\(\( r_2 = 0.0985 \, \text{m} \)\\\\\( U_2 = (8.99 \times 10^9 \, \text{Nm}^2/\text{C}^2) \cdot (8.07 \times 10^{-6} \, \text{C})^2 / 0.0985 \, \text{m} \)\)

\(\( r_3 = \sqrt{(0.0985 \, \text{m})^2 + (0.1 \, \text{m})^2} \approx 0.1399 \, \text{m} \)\\\\\( U_3 = (8.99 \times 10^9 \, \text{Nm}^2/\text{C}^2) \cdot (8.07 \times 10^{-6} \, \text{C})^2 / 0.1399 \, \text{m} \)\)

To calculate the total potential energy, we need to sum up the individual potential energies:

\(\[ U_{\text{total}} = U_1 + U_2 + U_3 \]\)

Substituting the calculated values into the equation:

\(\[ U_{\text{total}} = U_1 + U_2 + U_3 \]\)

We have:

\(\ U_1 = (8.99 \times 10^9 \, \text{Nm}^2/\text{C}^2) \cdot (8.07 \times 10^{-6} \, \text{C})^2 / 0.1399 \, \text{m}]\\\\\\[ U_2 = (8.99 \times 10^9 \, \text{Nm}^2/\text{C}^2) \cdot (8.07 \times 10^{-6} \, \text{C})^2 / 0.0985 \, \text{m} \]\\\\\ [U_3 = (8.99 \times 10^9 \, \text{Nm}^2/\text{C}^2) \cdot (8.07 \times 10^{-6} \, \text{C})^2 / 0.1399 \, \text{m}]\\\\\)

Now, let's substitute the values and calculate the total potential energy:

\(\[ U_{\text{total}} = \left( \frac{{(8.99 \times 10^9 \, \text{Nm}^2/\text{C}^2) \cdot (8.07 \times 10^{-6} \, \text{C})^2}}{{0.1399 \, \text{m}}}\right) + \left( \frac{{(8.99 \times 10^9 \, \text{Nm}^2/\text{C}^2) \cdot (8.07 \times 10^{-6} \, \text{C})^2}}{{0.0985 \, \text{m}}}\right) + \left( \frac{{(8.99 \times 10^9 \, \text{Nm}^2/\text{C}^2) \cdot (8.07 \times 10^{-6} \, \text{C})^2}}{{0.1399 \, \text{m}}}\right) \]\)

Performing the calculations:

\(\[ U_{\text{total}} \approx 0.01976 \, \text{J} \]\)

The magnitude of the potential energy on the x-axis, at a distance of x = 9.85 cm, is approximately 0.01976 Joules. Please indicate the direction on your paper when you upload it.

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Chebyshev's theorem says that for any set of observations, the proportion of values that lie within k standard deviations of the mean is  1 - 1/k².

In statistics, Standard deviation is a measure of the variation of a set of values.

σ = standard deviation of population

N = number of observation of population

X = mean

μ = population mean

We know that Chebyshev's theorem states that for a large class of distributions, no more than 1/k² of the distribution will be k standard deviations away from the mean.

This means that 1 - 1/k² of the distribution will be within k standard deviations from the mean.

Lets k = 1.8, the amount of the distribution that is within 1.8 standard deviations from the mean is;

1 - 1/1.8² = 0.6914

= 69.14%

Hence, Chebyshev's theorem says that for any set of observations, the proportion of values that lie within k standard deviations of the mean is  1 - 1/k².

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Answer:

Step-by-step explanation:

The values of angles are written below,

a° = 121°

b° = 53°

c° = 87°

d° = 72°

The Inscribed Angle Theorem: This theorem states that the measure of an inscribed angle in a circle is equal to half the measure of the intercepted arc.

In other words, if an angle is formed by two intersecting chords in a circle, the measure of the angle is equal to half the sum of the measures of the arcs intercepted by the angle.

The values of angles are calculated as,

a = (2 x 108 ) - 9 5

a = 121°

b = 360 - ( 121 + 95 + 91 )

b = 53°

c = (121 + 53 ) / 2

c = 87°

d = ( 91 + 53 ) /2

d = 72°

Therefore, the values are a = 121°, b = 53°, c = 87°, and d = 72°.

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Answer:

12

Step-by-step explanation:

bc it is

The marginal probability distribution of Y1, the number of married executives among the three selected for promotion, needs to be found. Additionally, the conditional probabilities P(Y1 = 1 | Y2 = 2) and P(Y3 = 1 | Y2 = 1) need to be determined.

Finally, a comparison needs to be made between the marginal distribution derived in part (a) and the hypergeometric distribution with N = 9, n = 3, and r = 3.

(a) To find the marginal probability distribution of Y1, we need the joint probability distribution of Y1, Y2, and Y3. Once we have the joint distribution, we can sum the probabilities for each value of Y1 to obtain its marginal distribution.

(b) To find P(Y1 = 1 | Y2 = 2), we need to determine the conditional probability of Y1 being equal to 1 given that Y2 is equal to 2. This can be calculated using the joint probability distribution and applying the definition of conditional probability.

(c) To find P(Y3 = 1 | Y2 = 1), we need to determine the conditional probability of Y3 being equal to 1 given that Y2 is equal to 1. Again, this can be calculated using the joint probability distribution and the definition of conditional probability.

(d) To compare the marginal distribution derived in part (a) with the hypergeometric distribution with N = 9, n = 3, and r = 3, we need to calculate the probabilities of Y1 = 0, Y1 = 1, Y1 = 2, and Y1 = 3 using both distributions. The hypergeometric distribution represents the probability of getting a specific number of successes (married executives) in a sample of a specific size (3) from a population of a specific size (9) with a specific number of successes (3).

By comparing the probabilities obtained from the marginal distribution and the hypergeometric distribution, we can analyze the agreement or discrepancy between the two distributions.

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Using the area of rectangle, the dimensions of the rectangle with maximum area are 5√2 and 5/√2.

In the given question we have to find the dimensions of the rectangle with maximum area.

Given Semicircle Radius is 5.

As we know that standard equation of circle is \(x^2+y^2=a^2\)

a=5, so the equation is \(x^2+y^2=(5)^2\)

\(x^2+y^2=25\)

Therefore, Half circle y=\(\sqrt{25-x^2}\)

Area of Rectangle(A) =xy

Because Half of the rectangle is lies in first quadrant and half lies in second quadrant

Therefore,

Area of Rectangle(A) = 2xy

Now putting the value of y

Area(A) = 2x\(\sqrt{25-x^2}\)

Here we need to maximize the area of Rectangle, so find derivative and set equal to zero.

A'= \(\frac{d}{dx}(2x\sqrt{25-x^2})\)

A'= 2\([x\frac{d}{dx}\sqrt{25-x^2}+\sqrt{25-x^2}\frac{d}{dx}x]\)

A'= 2\([x\cdot\frac{-x}{\sqrt{25-x^2}}+\sqrt{25-x^2}\cdot1]\)

A'= 2\([\frac{-x^2}{\sqrt{25-x^2}}+\sqrt{25-x^2}]\)

A'= 2\((\frac{-x^2+25-x^2}{\sqrt{25-x^2}})\)

A'= 2\((\frac{25-2x^2}{\sqrt{25-x^2}})\)

For critical Number A' = 0

2\((\frac{25-2x^2}{\sqrt{25-x^2}})\) = 0

25-2x^2 = 0

2x^2=25

x^2=25/2

x=±√25/2

x=±5/√2

Therefore,

Base of the Rectangle = 2x

Base of the Rectangle = 2×5/√2

Base of the Rectangle = 5√2

and

height of rectangle = \(\sqrt{25-x^2}\)

height of rectangle = \(\sqrt{25-(5/\sqrt{2})^2}\)

height of rectangle = \(\sqrt{25-(25/2)}\)

height of rectangle = √(50-25)/2

height of rectangle = √25/2

height of rectangle = 5/√2

Hence, the dimensions of the rectangle with maximum area are 5√2 and 5/√2.

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