5. A salesman bought a computer from a manufacturer. The salesman then sold the computer for


$15 600 making a profit of 25%. Unfortunately, he suffered a 5% loss due to damages when


assembling


a. What was his actual profit earnings? (10 marks)

The answer is 2, which represents the sum of the values of x for which f'(x) = 0.

To find the critical points of f(x), we need to find the derivative of f(x):

Setting f'(x) = 0 and solving for x, we get:

We can use the Rational Root Theorem to find possible rational roots of the equation. The possible rational roots are:

We can use synthetic division or long division to check which of these roots are actually roots of the equation. We find that the only real root is x = 5/4, and it has multiplicity 2.

The sum of the values of x for which f'(x) = 0 is simply the sum of the critical points of f(x). In this case, we only have one critical point: x = 5/4.

We first find the derivative of the given function and set it equal to zero to find the critical points. We use the Rational Root Theorem to find the possible rational roots of the equation, and then we use synthetic division or long division to check which of these roots are actually roots of the equation. In this case, we find that the only critical point of the function is x = 5/4 with multiplicity 2.

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Answer: 129275775.0

Step-by-step explanation:

129275775.0

whenever there is a whole number, the decimal is at the end of the number.

Answer:

h = 3/2

Step-by-step explanation:

Volume of cone formula: V = 1/3 π r²h

We are given volume and the radius so we can plug in those values

1/18π = 1/3 π (1/3)²h

1/18π = 1/3 π 1/9 h

Multiply the fractions on the right side:

1/18π = 1/27πh

Multiply both sides by reciprocal of 1/27 (which is 27)

3/2π = πh

Divide both sides by π

h = 3/2

Hope this helps!

Using FOIL, the simplified expression for the product of (3x-4)(6x-2) is c. 18x² - 30x + 8.

To simplify the product (3x-4)(6x-2) using FOIL, we follow the First, Outer, Inner, Last rule. Let's break down the process:

First: Multiply the first terms of both expressions:
(3x) * (6x) = 18x²

Outer: Multiply the outer terms of both expressions:
(3x) * (-2) = -6x

Inner: Multiply the inner terms of both expressions:
(-4) * (6x) = -24x

Last: Multiply the last terms of both expressions:
(-4) * (-2) = 8

Now, combine the results:
18x² - 6x - 24x + 8

Simplify by combining the like terms (middle terms -6x and -24x):
18x² - 30x + 8

The simplified product is 18x² - 30x + 8, which corresponds to option (c).

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The lower bound for the 95% confidence interval for the proportion of Android users who plan to get another Android phone is 0.463 .

It can be evaluated applying the formula

Lower Bound = Sample Proportion - Z-Score × Standard Error

Here

Sample Proportion
= 200/371 = 0.539

Z-Score = 1.96 (for a 95% confidence interval)

Standard Error = √[(Sample Proportion * (1 - Sample Proportion)) / Sample Size]
= √[(0.539 × (1 - 0.539)) / 371]
= 0.045
Therefore,

Lower Bound = 0.539 - 1.96 × 0.045 = 0.463
A confidence interval is a known as the specified range of values that is prone to contain an unknown population area with a certain degree of confidence.

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The solution of the inequality 4x-1 grater then -5 is x > -1

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

4x-1 grater then -5

Express properly

so, we have the following representation

4x - 1 > -5

Add 1 to both sides of the inequality

so, we have the following representation

4x > -4

Divide both sides by 4

x > -1

Hence, the solution of the inequality is x > -1

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The prediction that is not supported by the data is option B: "The number of non-fiction books sold on Friday will be two-and-a-half times the number of arts and crafts books sold on Friday."

We can see from the table that on Thursday, 7 sports and trivia books and 19 arts and crafts books were sold, for a difference of 12.

On Thursday, 13 non-fiction books and 19 arts and crafts books were sold. If we assume that the same ratio will hold on Friday, then we can predict that the number of non-fiction books sold will be (19/2)*2.5 = 23.75, which is not a whole number. Therefore, this prediction is not supported by the data.

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The prime number values of a, b and c that satisfy the equation a⁴ + b⁴ + c⁴ + 54 = 11abc are a = 3, b = 2, and c = 5.

Let's consider the equation a⁴ + b⁴ + c⁴ + 54 = 11abc. Due to the fact that the total of four even numbers is also even, the left-hand side is always even. As a result, since 2 is the only even prime, one of the factors a, b, or c must be 2 for 11abc to likewise be even.

Let's examine each instance,

Case 1: a = 2

Substituting a = 2 into the equation, we get,

16 + b⁴ + c⁴ + 54 = 22bc

b⁴ + c⁴ - 22bc + 38 = 0

Since b and c are primes, they must be odd. Let b = 3 and c = 5, we have,

3⁴ + 5⁴ - 2235 + 38 = 0

81 + 625 - 330 + 38 = 0

Case 2: b = 2

Substituting b = 2 into the equation, we get,

a⁴ + 16 + c⁴ + 54 = 22ac

a⁴ + c⁴ - 22ac + 70 = 0

Since a and c are primes, they must be odd. Let a = 3 and c = 5, we have,

3⁴ + 5⁴ - 2235 + 70 = 0

Case 3: c = 2

Substituting c = 2 into the equation, we get,

a⁴ + b⁴ + 16 + 54 = 22ab

a⁴ + b⁴ - 22ab + 70 = 0

However, for any odd number x, x⁴ mod 16 = 1, which means that a⁴ and b⁴ are both corrosponds to 1 mod 16. So, as the conclusion, a = 3, b = 2, and c = 5.

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Both vertical angles measure 90 degrees, and the adjacent angles each measure 90 degrees as well.
When two lines intersect at a point, we can use the properties of vertical and adjacent angles to set up and solve equations relating to their measures. This can help us find missing angles or verify that two angles are congruent.

When two lines intersect at a point, they form two angles. These angles are called vertical angles, and they are always congruent. In addition, the two lines also form two pairs of adjacent angles, each pair of which adds up to 180 degrees.

Let's consider an example to understand this concept better. Suppose we have two lines AB and CD that intersect at point P. If angle APD measures x degrees, then angle BPC also measures x degrees because they are vertical angles. Similarly, angle APB and angle CPD are adjacent angles, and their sum is 180 degrees. If angle APB measures y degrees, then angle CPD also measures y degrees.

Therefore, we can set up the following equation:

x + y = 180

This equation relates the measures of the adjacent angles formed by the two lines. We can solve for one variable in terms of the other by rearranging the equation:

y = 180 - x

This equation gives us the measure of one angle in terms of the measure of the other. We can substitute this expression into the equation for the vertical angles to get:

2x = 180

Solving for x, we find that x = 90.

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I'm sorry, but I cannot answer your question without a net or a description of the solid figure. Can you please provide more information or context?

To differentiate x^6y^9 with respect to x, we will use the product rule. The product rule states that the derivative of a product of two functions is the derivative of the first function multiplied with the second function, plus the first function multiplied with the derivative of the second function.

Step 1: Identify the functions
Function 1 (u): x^6
Function 2 (v): y^9

Step 2: Find the derivatives
u' (du/dx): Differentiate x^6 with respect to x, which gives 6x^5
v' (dv/dx): Differentiate y^9 with respect to x, which gives 9y^8 * (dy/dx) = 9y^8D (since D = dy/dx)

Step 3: Apply the product rule
d/dx (x^6y^9) = u'v + uv'
= (6x^5)(y^9) + (x^6)(9y^8D)
= 6x^5y^9 + 9x^6y^8D

So, the derivative of x^6y^9 with respect to x is 6x^5y^9 + 9x^6y^8D.

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Answer:

x=85

y=27

;)

Step-by-step explanation:

x+y=112

y=x-58

add 58 to the other side

58+y=x

Subtract y

x-y=58

x+y=112

Now if we add these we get

2x=170

x=85

Then if we substitute 85 in x+y=112

85+y=112

112

-85

____

27

Check your Answer on

y=x-58

27=85-58

27=27

This is the Answer

Please DM me if I should reexplain THANK YOU!

Hope this helps!

The 95 percent confidence interval for the population mean is $65.59 to $74.41.

To calculate a 95% confidence interval for the population mean, we will use the sample mean, population standard deviation, and sample size provided. The formula for the confidence interval is:

CI = X ± (Z * (σ / √n))

Where:
- X is the sample mean, $70.00
- Z is the Z-score for a 95% confidence interval, 1.96
- σ is the population standard deviation, $17.50
- n is the sample size, 60

CI = $70.00 ± (1.96 * ($17.50 / √60))

Calculate the margin of error:

Margin of Error = 1.96 * ($17.50 / √60) ≈ $4.41

Now, calculate the confidence interval:

Lower Limit = $70.00 - $4.41 ≈ $65.59
Upper Limit = $70.00 + $4.41 ≈ $74.41

So, the 95% confidence interval for the population mean is approximately $65.59 to $74.41.

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The two contradictory statements are "triangle LMN is a right triangle" and "triangle LMN is equilateral."

An equilateral triangle has all three sides and angles congruent. Therefore, if triangle LMN is equilateral, all angles in the triangle must be congruent and equal to 60 degrees. However, the statement "triangle LMN is a right triangle" implies the presence of a 90-degree angle, which contradicts the requirement for all angles to be 60 degrees in an equilateral triangle.

Additionally, the statement "angle L ≅ angle N" suggests that angles L and N are congruent. In an equilateral triangle, all angles are congruent, so if angles L and N are congruent, it further supports the claim that triangle LMN is equilateral.

In conclusion, the statement "triangle LMN is a right triangle" contradicts the statement "triangle LMN is equilateral" because a right triangle cannot be equilateral.

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Based on the above, the proportion of the population who said yes is  78%.

To be able to calculate the population proportion who said yes,  you  have to divide the number of students who said "Yes" by the total amount or number of students in the  whole population:

Hence it will be:

Population proportion who said yes = 741/950

= 0.78

= 78%

So, the proportion of the population who said yes is 0.78 or 78%.

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See text below



At a high school with 950 total students, the true opinions of the entire student body on whether they approve of the student council president are shown below. Follow the directions below to determine a confidence interval for a sample of size 125.

Population Yes 741, Population No 209,  Population Size 950

Population proportion who said yes: ---

Using one cigarette packet per day with the cost of $ 5.50 tax revenue would be raised from John's cigarette purchases is $9,636.

Tax revenue is the income received by the government from the taxation of individuals, businesses, and other entities.

Taxes are mandatory payments imposed on income, goods and services, property, and other items, which are collected by the government to finance public goods and services such as infrastructure, education, healthcare, and defense.  

To solve the given problem, assume the cost of a cigarette packet and find the total revenue that can be generated.

Here we have

There was a 10 percent tax on every pack of cigarettes John bought between the age of 22 and age 70

To calculate the tax revenue raised from John's cigarette purchases between ages 22 and age 70, we need to know how many packs of cigarettes he bought during that period.

Let's assume that John bought an average of one pack of cigarettes per day or 365 packs per year.

The difference Between the ages of 22 and age 70 = 70 - 22 = 48 years

Hence, John would have bought cigarettes for 48 years, so the total number of packs he bought would be:

365 packs/year x 48 years = 17,520 packs

If there were a 10% tax on each pack, the tax revenue would be:

0.10 x $5.50 (average cost of a pack of cigarettes in the US)

= $0.55 tax per pack

$0.55 tax per pack x 17,520 packs = $9,636 in tax revenue

This is an estimate, as it does not take into account any variations in the price of cigarettes over time or across different regions.

As for how much tax money could be used to reduce smoking rates, there are several options.

One possibility is to invest the revenue in smoking cessation programs and public health campaigns to educate people about the risks of smoking and help them quit.

The money could also be used to fund research into developing new treatments for tobacco addiction or to support medical research into the health effects of smoking.

Therefore  

Using one cigarette packet per day with the cost of $ 5.50 tax revenue would be raised from John's cigarette purchases is $9,636.

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To answer this question, we need to know the driver's reaction time. Let's assume the reaction time is 1.5 seconds, which is a typical average for most drivers.

To find how far the car traveled during the reaction time, we can use the formula:

distance = speed × time

Plugging in the given speed of 72.08 feet per second and the assumed reaction time of 1.5 seconds, we get:

distance = 72.08 ft/s × 1.5 s

distance = 108.12 ft

Therefore, the car traveled 108.12 feet during the driver's reaction time. Rounded to two decimal places, the answer is 108.12.

According to the given standard deviation, the engineer would need a sample size of at least 75 wires to estimate the mean length to within 0.025 feet with 99% confidence.

To estimate the mean length of the wires being cut, the engineer needs to determine the sample size needed to achieve a certain level of confidence and level of precision. In this case, the engineer wants to estimate the mean length to within 0.025 feet with 99% confidence. This means that there is a 99% chance that the true population mean falls within the estimated range.

To determine the sample size needed, the engineer can use a formula that takes into account the desired level of confidence, level of precision, and the standard deviation of the population. The formula is:

n = (z² x s²) / E²

Where:

n = sample size needed

z = z-score for desired level of confidence (99% = 2.58)

s = standard deviation of the population (0.15 feet)

E = level of precision (0.025 feet)

Plugging in the values, we get:

n = (2.58² x 0.15²) / 0.025²

n = 74.83 ≈ 75

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Answer:

To simplify the given expression:

(7/2 x 5/3) + (1/6 x 3/2) - (12/8 x 4/3)

Step 1: Simplify the fractions within the parentheses first.

(35/6) + (1/4) - (48/24)

Step 2: Find a common denominator for all three terms. The least common multiple of 6, 4, and 24 is 24.

(35/6 x 4/4) + (1/4 x 6/6) - (48/24 x 1/1)

Step 3: Simplify the numerators using the common denominator.

(140/24) + (6/24) - (48/24)

Step 4: Combine the like terms.

98/24 or 4 1/6

Therefore, the simplified form of the expression is 4 1/6.

The surface integral of the dot product between the vector field F = 3i + 3j + 4k and the unit normal vector of the surface S is equal to zero.

To use Stokes' theorem to find the flux of the vector field F = 3i + 3j + 4k across the surface S, which is the part of the plane 3x + 2y + z = 1 in the first octant and oriented upward.

Stoke's theorem statement is “the surface integral of the curl of a function over the surface bounded by a closed surface will be equal to the line integral of the particular vector function around it.” Stokes theorem gives a relation between line integrals and surface integrals.

First, we need to parametirize the curve C that bounds the surface S. Since S is in the first octant, x, y, and z are all non-negative.

The boundary C consists of three line segments: (i) from (0, 0, 0) to (1/3, 0, 0), (ii) from (1/3, 0, 0) to (0, 1/2, 0), and (iii) from (0, 1/2, 0) to (0, 0, 0). Next, calculate the curl of F, which is the cross product of the del operator and F:
curl(F) = (∂Fz/∂y - ∂Fy/∂z)i - (∂Fx/∂z - ∂Fz/∂x)j + (∂Fy/∂x - ∂Fx/∂y)k = (0 - 0)i - (0 - 0)j + (0 - 0)k = 0.

Since curl(F) = 0, the line integral of F over C is also 0.

According to Stokes' theorem, the flux of F across S equals the line integral of F over C, which we found to be 0.

Therefore, the flux of the vector field F = 3i + 3j + 4k across the surface S is 0.

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The volume of the largest right cylinder that fits in a sphere of radius 4 is 128π cubic units.

To find the volume, we need to understand that the cylinder that fits inside a sphere will have its height (h) equal to the diameter of the sphere (2r), and the cylinder's radius (r') will also be equal to the sphere's radius (r).

We can use the formula for the volume of a cylinder: V = π[tex]r^2^h[/tex], where π is pi (approximately 3.14), r is the radius, and h is the height.

Since the cylinder's height is equal to the sphere's diameter, which is 2r, the height of the cylinder is 2r. Therefore, we can write the volume of the cylinder as:

V = πr²(2r)

Simplifying this expression, we get:

V = 2π[tex]r^3[/tex]

To find the maximum volume of the cylinder that fits inside a sphere of radius 4, we need to maximize the volume by finding the maximum value of r. Since the radius of the cylinder is equal to the radius of the sphere, we have:

r = 4

Substituting this value into the formula for the volume of the cylinder, we get:

V = 2π[tex](4)^3[/tex]

V = 128π

Therefore, the volume of the largest right cylinder that fits in a sphere of radius 4 is 128π cubic units.

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Answer:

3/2

Step-by-step explanation:

f(x) = 2x+5

f-¹(x) = ?

to find f-¹(x)

let f(x) be y

y = 2x+5

then we'll make x the subject of formula

y-5 = 2x

x = y-5/2

change y to x and x to y

f-¹(x) = x-5/2

f-¹(8) = 8-5/2 = 3/2

The calculated value of X when Y equals four is four

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

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

y = kx

Where

k = constant of variation

When Y equals eight when X equals eight, we have

8k = 8

So, we have

k = 1

This means that the equation is

y = 1 * x

Evaluate

y = x

When the value of y is 4, we have

4 = x

This gives

x = 4

Hence, the value of X when Y equals four is four

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If FY varies directly as X, we can write the equation as:

FY = kX

where k is the constant of variation. To find the value of k, we can use the fact that "Y equals eight when X equals eight":

8 = k(8)

Simplifying this equation, we get:

k = 1

Now we can use this value of k to find the value of X when Y equals four:

4 = 1X

Solving for X, we find that

X = 4

Therefore, when Y equals four, X equals 4 as well...

In this prism, lateral Area =  858.54 m² and surface area = 890.54 m².

Firstly, we will find the lateral area of the prism by applying the formula:

Lateral  area = perimeter × height

Perimeter = sum of all the sides of prism

= 4 + 8 + 8.94  = 20.94 m

Lateral Area = 20.94 * 41  =  858.54 m²

Now, we have to find the surface area of the prism.

Surface area = Lateral Area + 2 × ( Base Area)

Base Area = the area of a triangle with sides 4, 8, and 8.94.

Now, we will calculate the area of the triangle

Firstly, we will find s for calculating the area of triangle and then apply the formula.

s = ( 4 + 8 + 8.94)/2 = 10.47 m

Area of triangle =  [tex]\sqrt{ (10.47 (10.47 - 4)(10.47 - 8)(10.47 - 8.94))}[/tex]

= [tex]\sqrt{(10.47 (6.47)(2.47)(1.53))}[/tex]

= 16 m²

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Correct question:

Use formulas to find the lateral area and surface area of the given prism. Round your answer to the nearest whole number. The figure is not drawn to scale. The bases are right triangles.

Hunter made a mistake in calculating the volume of the rectangular prism, hence he may have chosen the wrong formula.

The volume of a rectangular prism, with dimensions length, width and height, is given by the multiplication of these dimensions, according to the equation presented as follows:

Volume = length x width x height.

The dimensions for this problem are given as follows:

2m, 3m and 5m.

Hence the volume of the prism is given as follows:

V = 2 x 3 x 5

V = 30 m³.

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First, using the Pythagorean theorem, we get the hypotenuse = 12.

sin = opposite/hypotenuse = [tex]\frac{6\sqrt{3} }{12} = \frac{\sqrt{3} }{2}[/tex]

cos = adjacent/hypotenuse = [tex]\frac{6}{12} =\frac{1}{2}[/tex]

tan = opposite/adjacent = [tex]\frac{6\sqrt{3} }{6} = \sqrt{3}[/tex]

csc = hypotenuse/opposite = [tex]\frac{12}{6\sqrt{3} } =\frac{2}{\sqrt{3} }[/tex]

sec = hypotenuse/adjacent = [tex]\frac{12}{6} =2[/tex]

cot = adjacent/opposite = [tex]\frac{6}{6\sqrt{3} } = \frac{1}{\sqrt{3} }[/tex]

Answer:

I'm assuming that A and B are two different items, and you want me to work with the same data set for both items. Here are the calculations:

1. Mean price of milkshake:

To find the mean price of a milkshake, you need to add up all the prices and divide by the total number of prices:

(4 + 2 + 9 + 14 + 6) / 5 = 7

Therefore, the mean price of a milkshake is $7.

2. Median price of milkshake:

To find the median price of a milkshake, you need to put the prices in order from lowest to highest:

2, 4, 6, 9, 14

The median is the middle value. Since there are five values, the middle value is the third value, which is 6.

Therefore, the median price of a milkshake is $6.

3. Mode of price of milkshake:

To find the mode of the price of a milkshake, you need to find the price that appears most frequently in the data set. In this case, there is no price that appears more than once, so there is no mode.

Therefore, there is no mode for the price of a milkshake.

I hope that helps! Let me know if you have any further questions.

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14 revolutions per second can be expressed as 28π radians per second.

A radian is an angle whose corresponding arc in a circle is equal to the radius of the circle. A revolution is a full rotation, or a complete, 360-degree turn.

1 revolution per second is expressed as 2π radians per second.

To calculate the number of radians in 14 revolutions per second, we have to multiply 2π by 14.

14 revolutions per second = 14 * 2π

= 28π radians per second

Thus, the answer to the given question comes out to be 28 π radians per second

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The volume of the given cylinder is 84.78 cubic yards.

The first step to finding the volume of a cylinder is to use the formula V = πr^2h, where r is the radius of the cylinder (which is half of the diameter). So, to find the radius, we divide the diameter (which is 3 yards) by 2, giving us a radius of 1.5 yards. Then, we can plug in the values for radius (1.5), height (12), and π (3.14) into the formula to find the volume:

V = πr^2h
V = 3.14 x 1.5^2 x 12
V = 84.78 cubic yards

Therefore, the volume of the cylinder is 84.78 cubic yards.
Hi! To find the volume of a cylinder with a diameter of 3 yards and a height of 12 yards, the first step is to find the radius.

Step 1: Since the diameter is 3 yards, you can find the radius by dividing the diameter by 2. Radius = Diameter / 2. So, the radius is 1.5 yards.

Step 2: Now, you can find the volume of the cylinder using the formula: Volume = π × (radius^2) × height. In this case, Volume = π × (1.5^2) × 12.

Step 3: Calculate the volume: Volume = π × 2.25 × 12. Using the value of π as approximately 3.14, the volume becomes 3.14 × 2.25 × 12.

Step 4: Multiply the numbers: Volume ≈ 84.78 cubic yards.

So, the volume of the cylinder is approximately 84.78 cubic yards.

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she can add each number one by one , and whenever she needs to carry numbers over. She can add them to the already existing numbers. she cna check with a calculator