Question 6 of 10
Which is the best estimate of the circumference of this circle?
3
OA. 18 units
OB. 42 units
OC. 3 units
O D. 6 units

The total profit P in terms of x can be expressed as

P(x) =  (a - c) (a/(x-c) + b(95-x))

The selling price that will maximize profit is the positive constant, a in dollars.

To find the selling price that will bring a maximum profit, we need to find the derivative of the profit function P(x) and set it equal to 0.

The profit function P(x) is given by P(x) = nx - nc,

where n is the number of backpacks sold and c is the cost to manufacture and distribute each backpack.

Substituting the given expression for n into the profit function gives:

P(x) = (a/(x-c) + b(95-x))x - c(a/(x-c) + b(95-x))

P(x) = (a - c) (a/(x-c) + b(95-x))

To find the selling price that will maximize profit, we need to find the critical points of P(x) by taking the derivative of P(x) with respect to x and setting it equal to 0:

P'(x) = (a - c) (-a/(x - c)² - b) = 0

Thus P'(x) = 0 at c = a or (x - c)² = -a/ b

a and b are positive constants, so -a/ b is negative but (x - c)² is never negative, so it is not a possible solution.

So only solution is c = a, that is for maximum profit selling price, c should be equal to the positive constant, a.

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Fencing that Luke and Seth did each buy is 72 feet

Using the information given, you can set up and solve the system of equations. Let x be the length of Seth's garden.

Seth's garden is square, so it has four times the perimeter.

The perimeter of Luke's garden is a rectangle of length x + 3 feet and width x/2 feet, so 2(x + 3) + 2(x/2).

We also know that Luke and Seth should buy the same amount of fences. So:

4x = 2(x + 3) + 2(x/2)

Solving this equation for x gives x = 6 feet.

So Seth's yardage is 6 feet and Luke's yardage is 9 feet.

So the fence required for Seth's garden is 46 = 24 feet

and the fence required for Luke's garden is 2(9) + 2(9/2) = 29 + 2*4.5 = 36 + 9 = 45 It's feet.

So the total fencing required is 24 + 45 = 72 feet.

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Answer:

f(8) = -68

Step-by-step explanation:

f(x) = -x² - 2x + 12

f(8) = ?

We just need to put 8 in for the x and solve it

f(8) = -(8)^2 -2(8) + 12

f(8) = -64 -16 +12

f(8) = -80 + 12

f(8) = -68

function f(x) = 75 - 4.5 w.

where w = number of weeks.

this question is related to function and solution is as follows,

The owner of a mall Restaurant bought rice = 75 kg

Each week, the restaurant use rice = 4. 5 kg

so we have to make an equation of function by which we can find out the remaining rice after w number of weeks,

f(x) = 75 - 4.5 w

where ,w = number of weeks

example, find out rice after 6 weeks

number of weeks (w) = 6

put it in the function,

f(x) = 75 - 4.5(6)

f(x) = 75 - 27

f(x) = 48.

so the function is ,f(x) = 75 - 4.5 w.

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Therefore , the solution of the given problem of linear equation comes out to be  it is not a linear equation in two variables.

A linear model is the one that satisfies the algebraic formula y=mx+b. m is the y-intercept, while B is the slope. The foregoing sentence is sometimes referred to as a "mathematical expression having two variables" both y and x are different factors. Bivariate linear equations are two-variable linear equations. There are several uses for linear equations: , all result in zero. An equation is said to be linear if its formula is y=mx+b, where m denotes the slope and b the y-intercept. Y=mx+b is the formula for an equation, where m stands for the slopes and b for the y-intercept.

Here,

Given : 2x + 3 =0

thus,

To find that it is linear equation in two variable is given  equation

As,

We can see there is only one variable that is x.

So , it is not a linear equation in two variables.

Therefore , the solution of the given problem of linear equation comes out to be  it is not a linear equation in two variables.

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Total cost of Painting and tileing is for the cuboidical community hall is  $2172.

A three-dimensional form called a cuboid contains six faces, twelve edges, and eight vertices. It differs from a cube in that a cuboid's faces are entirely rectangular in shape whereas a cube's faces are square. A cuboid has three dimensions: length, breadth, and height.

Properties of a Cuboid are :

There are 6 faces, 12 edges, and 8 vertices on a cuboid.

All of the cuboid's faces have rectangular shapes.

The cuboid's opposing edges are parallel to one another.

The dimensions of a cube are length, breadth, and height.

All of the angles created at the cuboid's vertices are 90 degrees.

Surface area of 4 walls and Ceiling is = 40*3*2 + 15*3*2 + 40*15 = 930

Surface area of the floor is 40 *15 = 600

10 lt of tin covers 25

1  can be covered by 10/25 lt

930  can be covered by (10/25) * 930 = 372 lt.

Total cost of Painting is $372.

1  of floor tiles cost $3

600  of floor tiles will cost 3*600 = $ 1800

Total cost of Painting and tileing is for the cuboidical community hall is $ 372 + 1800 = $2172.

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Answer:

  1/2log₂(a-1) -log₂(9)

Step-by-step explanation:

You want the expanded form of log₂(√(a-1)/9).

The relevant rules of logarithms are ...

  log(a^b) = b·log(a)

  log(a/b) = log(a) -log(b)

The rules are applicable for any base.

  [tex]\log_2{\dfrac{\sqrt{a-1}}{9}}=\log_2{(\sqrt{a-1})}-\log_2{(9)}=\boxed{\dfrac{1}{2}\log_2{(a-1)}-\log_2{(9)}}[/tex]

Heyyyyyyyy how u doing I. Doing good how abt yo self

The area of the semi-circle with the radius of 4.1 mm, round to the nearest tenth is 52.8 mm²

The area of the semi-circle will be calculated by the formula -

Area = 1/2πr², where r is the radius of the circle.

Keep the values in formula to find the value.of area of semi circle

Area = 1/2×3.14×4.1²

Performing multiplication on Right Hand Side of the equation to find the area of the semi-circle

Area = 52.78 mm²

Round off the nearest tenth

Area = 52.8 mm²

Thus, the area of semi-circle with mentioned radius is 52.8 mm².

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The coordinates of K = (0, -7.5) and the scale factor is 8/5.

Consider the following figure of triangles.

△BOK and ΔPOS.

Since △BOK∼ ΔPOS, the sides of △BOK and ΔPOS must be in proportion. (from definition of triangle similarity)

i.e., OP / OB = OS / OK = PS/BK

Consider an equation,

OP / OB = OS / OK

From the diagram:

OP = 8, OB = 5, OS = 12

Substitute these values in above equation.

8/5 = 12/OK

OK = 60/8

OK = 7.5

We can observe that OK is the distance of point K from origin 'O'

So, the coordinates of K would be (0, -7.5)

And the scale factor is 8/5.

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The arithmetic expression may be used to get the formula T = (11 + w)/4, which is the distance Kane runs in a training session after w weeks.

Every training session, Kane begins out by running 3 miles, and he has a plan to improve that distance by 1/4 mile each week.

The number of weeks is w.

The arithmetic progression may be used to calculate an expression that displays the distance Kane runs during a training session after w weeks.

T = A + (n-1)d is the formula for the nth term in an arithmetic operation, where an is the first term, which is 3, d is the difference between two consecutive terms, which is, is the last term, and n is the total number of terms.

We get, T = (11+w)/4

This is the expression to show the distance Kane runs in a training session after w weeks.

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Complete question - Kane is training for a marathon. He starts by running 3 miles during every training session each week plans to increase the distance of his runs by 1/4 mile. Let w be the number of weeks. Write and expression to show the distance Kane runs in a training session after w weeks

The function rule to represent the total amount earned with Option A and earned with Option B are f(x) = 100 + 10x and f(x) = (1/100) * 2^x.

What is the function rule?

The function rule is the relationship between the input or domain and the output or range. A relation is a function if and only if there exists one value in the range for every domain value.

For Option A, the total amount earned can be represented by the function:

f(x) = 100 + 10x

where x is the number of days in February (x = 28 for a standard non-leap year)

For Option B, the total amount earned can be represented by the function:

f(x) = (1/100) * 2^x

where x is the number of days in February (x = 28 for a standard non-leap year)

the above function will be in cents, to get dollar values divide it by 100.

hence, the function rule to represent the total amount earned with Option A and earned with Option B are f(x) = 100 + 10x and f(x) = (1/100) * 2^x.

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Answer: 7 13/15

Step-by-step explanation:

First of, you have to get your common denominator, as it's impossible without one.

The closest common denominator is 15, and it will ask you for a simplified version.

Multiply the 2/3 in 5 2/3 by 5 on both sides to get 5 10/15

Multiply the 1/5 in 2 1/5 by 3 on both sides to get 2 3/15

Then add up your sum.

5 10/15+2 3/15=7 13/15

Answer:

7 13/15

Step-by-step explanation:

5 2/3+2 1/5

We need to get a common denominator for the fraction

3*5 = 15

2/3 *5/5 = 10/15

1/5 * 3/3 = 3/15

5 10/15 + 2 3/15 = 7 13/15

The equation of the line in fully simplified intersect is y = mx + b

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On solving the provided question, we can say that the equation of the expression is given by y = 6x + 50

Equations with graphs as the unknowns are known as graph equations. The concept of isomorphism is one of the key issues in graph theory. When are two graphs identical, we inquire? Different graph equations may be used to express the aforementioned graphs.

A mathematical statement that has a "equal to" symbol between two expressions with equal values is called an equation. as in 3x + 5 Equals 15, for instance. Equations come in a variety of forms, including linear, quadratic, cubic, and others.

A mathematical expression with an equals sign is referred to as an equation. Algebra is widely used in equations. When performing calculations but unsure of the precise amount, algebra is utilized. A lot of specialists, such as air traffic controllers, architects, computer programmers, and carpenters, employ equations on a daily basis.

From the table we can see that if the equation be

y = mx + c

for x = 0 y = 50

c = 50

again from x = 1 and y = 56

m = 6

So the equation of the expression is given by y = 6x + 50

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You now have the total length for the remaining 2 sides. This number divided by 2 is the width.

When given an area of A and a length of h, its width w is equal to A/h.

Its width is w = P/2h if you have the perimeter P and length h.

If you know the length h and the diagonal d, you can calculate the width using the formula w = (d2h2).

The height, area, diagonal, or perimeter of your rectangle are the two measurements that the width of a rectangle calculator uses to calculate the width of your rectangle. We'll also demonstrate various formulas for calculating the width of a rectangle based on the information at hand. The width of a rectangle can be determined in a variety of ways, depending on the information at hand. 

A=w×h

P=(w+h)×2

d = w 2 +h 2

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Nevaeh's score in Exam A of 850, where the mean and standard deviation are 550, and 100, indicates, using the z-score, that in Exam B with a mean and standard deviation of 36 and 10, respectively, her score should be 66.

A z-score is an indication of the number of standard deviations, a data point is from the mean.

The score Nevaeh earned in Exam A, x₁ = 850

The mean score for Exam A, μ₁ = 550

The standard deviation for Exam A, σ₁ = 100

The mean score for Exam B, μ₂ = 36

The standard deviation for Exam B, σ₂ = 10

A quantity that can be used to evaluate Nevaeh's score for Exam A is the z-score, which can be expressed as follows;

[tex]z = \dfrac{x - \mu}{\sigma}[/tex]

Nevaeh's z-score for Exam A is therefore;

[tex]z = \dfrac{850 - 550}{100} =3[/tex]

Nevaeh's performance on Exam B in order for her to do equivalently well as she did on Exam A is obtained by using a z-score of 3 for her performance in Exam B as follows;

[tex]z = 3 = \dfrac{x_2 - 36}{10}[/tex]

3 × 10 = x₂ - 36

30 = x₂ - 36

x₂ = 30 + 36 = 66

Nevaeh's score on Exam B should be 66 in order for her to perform equivalently well as she did in Exam A

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Since the circumference of the base is given, the radius can be calculated as r = (circumference / 2π) and the volume as V = πr2h. The volume of the cylinder is therefore approximately 628.3 cubic centimeters.

1. Calculate the radius of the base of the cylinder. The circumference of the base is 167 centimeters. Rearranging this gives

r = C / 2π. Therefore,

r = (167 / 2π)

= 26.6 cm.

2. Calculate the volume of the cylinder. The formula for volume is V = πr2h. Therefore,

V = π(26.6)2 * 5

= 628.3 cubic centimeters.

or

r = (167 / 2π) = 26.6 cm

V = π(26.6)2 * 5 = 628.3 cubic centimeters

To calculate the volume of the cylinder, the radius of the base must first be calculated. This can be found by using the formula C = 2πr, where C is the circumference and r is the radius The circumference of the base of the cylinder is 167 centimeters, so the radius can be calculated as r = (167 / 2π) = 26.6 cm. The volume of the cylinder can then be calculated using the formula V = πr2h, where h is the height of the cylinder. In this case, the height is 5 centimeters, so the volume is V = π(26.6)2 * 5 = 628.3 cubic centimeters. This is the closest measurement to the volume of the cylinder.

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Answer:  To solve this problem, we can use the fact that a cubic centimeter of osmium has a mass of about 23 grams and the information provided about the chemist's amount of osmium.

First, we can divide the total mass of osmium by the mass of a cubic centimeter of osmium to find out how many cubic centimeters of osmium the chemist has. The equation would look like this:

2,530 grams / 23 grams/cubic centimeter = 110 cubic centimeters

So, the chemist has approximately 110 cubic centimeters of osmium.

It's worth mentioning that an exact value would require additional information as 23 grams per cc is an approximate value and also any impurities or loss of material in the sample also effect the total mass.

Step-by-step explanation:

A horizontal line is a line extending from left to right. When you look at the sunrise over the horizon you are seeing the sunrise over a horizontal line. The x-axis is an example of a horizontal line.

Now, According to the question:

What is a Horizontal Line?

Horizontal lines are also known as sleeping lines. In coordinate geometry, horizontal lines are those lines that are parallel to the x-axis. In geometry, we can find horizontal line segments in many shapes, such as quadrilaterals, 3d shapes, etc. In real life, we can find horizontal lines on the steps of the staircase, planks on the railway tracks, etc.

The x-axis is an example of a horizontal line.

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The algebraic sequence of 1,4,7,10 is aₙ = 3n - 2

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

1,4,7,10

In the above sequence, we can see that 3 is added to the previous term to get the current term

Using the above as a guide,

So, we have the following representation

aₙ = aₙ₋₁ + 3

Also, we have

a = 1 i.e. the first term

d = 3 i.e he common difference

When represented explicitly, we have

aₙ = a + (n - 1) * d

So, we have

aₙ = 1 + (n - 1) * 3

Evaluate the products

aₙ = 3n - 2

Hence, the explicit formula is aₙ = 3n - 2

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In question 1;

The student multiplied without flipping the second expression.

In second question;

The negative should only be distributed to the numerator.

In third question,

3/2 should be remove from the x - value which make the expression undefined.

In fourth student;

Neither student is correct.

In fifth question,;

Sarah didn't cancel incorrectly in step 3.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

In question 1;

The expression is,

⇒ x² + 2x - 3 / (x² - 3x - 10) ÷ (2x + 12) / (8x + 16)

= (2x³ + 16x² + 18x - 36) / (8x³ - 8x² - 128x - 100)

Cleary, The student multiplied without flipping the second expression.

In question 2;

⇒ (-2y - 2) / (y² + 2y - 8) - (y - 1) / (2 - y)

⇒ (-2y - 2) / (y² + 2y - 8) + (-y + 1) / (-2 + y)

Clearly, The negative should only be distributed to the numerator.

In Question 3;

The student make mistake is ''3/2 should be remove from the x - value which make the expression undefined.''

In fourth student;

Neither student is doing correct solution.

In fifth question,;

Sarah didn't cancel incorrectly in step 3.

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The half-life of caffeine in the body is approximately 5-6 hours, not 666 hours. Given this information, we can calculate the latest time Charlotte can drink a 222-ounce shot of espresso that contains 80mg of caffeine and still have no more than 2020mg of caffeine in her system at 11pm.

What does math's % mean?

In essence, percentages are fractions with a 100 as the denominator. We place the percent symbol (%) next to the number to indicate that the number is a percentage. For instance, you would have received a 75% grade if you answered 75 out of 100 questions correctly on a test (75/100).

We know that after 5-6 hours, the amount of caffeine in the body decreases by 50%. Therefore, in 11 hours, the amount of caffeine in the body would decrease by approximately 87.5%.

If we let x be the number of hours before 11pm that Charlotte can drink the espresso, then the amount of caffeine in her body at 11pm would be:

80mg * (1 - (87.5% ^ (x/5-6))) = 2020mg

Solving for x, we find that the latest time Charlotte can drink the espresso is approximately 6:30pm.

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Step-by-step explanation:

the center of the circle is (−3,5) and radius is 16 =

Answer:

0

Step-by-step explanation:

625 / 25 = 25

55g + 25 = 25

55g = 25 - 25

55g = 0

g = 0/55

g = 0

Answer:

[tex] \sf \: g = 0[/tex]

Step-by-step explanation:

Given equation,

→ 55g + 25 = 625 ÷ 25

Now the value of g will be,

→ 55g + 25 = 625 ÷ 25

→ 55g + 25 = 25

→ 55g = 25 - 25

→ g = 0 ÷ 55

→ [ g = 0 ]

Hence, the value of g is 0.

With a temporal complexity of O(n2) in the average and worst circumstances, and O(n) in the best case, Bubble Sort is a simple, reliable sorting algorithm.

A mathematical algorithm is a process that describes a series of steps that can be used to accomplish a mathematical computation. A typical illustration of a mathematical algorithm would be the step-by-step process used in long division. Integral calculus and differential calculus are the two varieties of calculus. These fields work together to let you calculate rate of change, a crucial component of many algorithms and programs. Particularly crucial are differential equations.

given

With a temporal complexity of O(n2) in the average and worst circumstances, and O(n) in the best case, Bubble Sort is a simple, reliable sorting algorithm.

The outer loop, in the worst case, executes O(n) times.

Therefore, bubble sort's worst-case time complexity is O(n x n) = O(n x n) (n2).

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A statement which is known as tautology is a type of compound statement in whose result is always the truth value. We don't take in consideration the other individual values in consideration , the result in tautology is always true.

It is one of the most significant part in logical mathematics if we need to find the most accurate answers or findings among a given group of answers.

In mathematics, tautology is used so as to ensure that the results which is obtained are true and exact and not false . A tautology is a compound statement and it will always returns true value. The result in tautology is always true, regardless of what the constituent parts are.

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Answer:

D)  (6.6, 7.4)

Step-by-step explanation:

Begin by finding the margin of error based on the given information.

[tex]\boxed{\begin{minipage}{7.3cm}\underline{Margin of Error formula}\\\\$\textsf{Margin of Error}= Z \times \dfrac{S}{\sqrt{n}}$\\\\where:\\\phantom{ww} $\bullet$ $Z =$ $Z$ score\\\phantom{ww} $\bullet$ $S =$ Standard Deviation of a population\\\phantom{ww} $\bullet$ $n =$ Sample Size\\\end{minipage}}[/tex]

Given:

The z-score for 95% confidence level is 1.96.

Therefore, to find the margin of error, substitute the values into the formula:

[tex]\implies \textsf{Margin of Error}= 1.96 \times \dfrac{1.3}{\sqrt{50}}[/tex]

[tex]\implies \textsf{Margin of Error}=0.360341...[/tex]

To find a reasonable range for the true mean number of hours a teenage spend on their phone, subtract and add the margin of error to the given mean of 7 hours:

[tex]\begin{aligned}\implies \textsf{Lower bound}&=7-0.360341...\\&=6.63965...\\&=6.6\;\; \sf (1\;d.p.)\end{aligned}[/tex]

[tex]\begin{aligned}\implies \textsf{Upper bound}&=7+0.360341...\\&=7.360341...\\&=7.4\;\; \sf (1\;d.p.)\end{aligned}[/tex]

Therefore, the reasonable range for the true mean is: