Which point is located at -1 3/8?

The Mean Value Theorem states that if a function f is continuous on the interval [a,b] and differentiable on (a,b), then there exists at least one c in the interval (a,b) such that


f'(c) = (f(b) - f(a)) / (b - a)

For the function f(x) = x/x+2, we can set
f(a) = a/a+2 and f(b) = b/b+2

Therefore, the equation we need to solve is:
(b/b+2 - a/a+2) / (b - a) = c/(c+2)

After rearranging, we get:
(b-a)c + 2(a-b) = 0

Solving this, we find that c = 2(b-a) / (a-b)

Therefore, the values of c that satisfy the Mean Value Theorem for the given function f(x) = x/x+2 are c = 2(b-a) / (a-b).

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Answer:

6

Step-by-step explanation:

The two triangles are similar which means the the two length is parallel

.°., the Length of the smaller triangle=6

Answer:

216÷4=54

Step-by-step explanation:

we have to divide the bulb he fixed in per room by how many he fixes I guess so

Answer: He can fix in a total of 54 rooms which makes 216 bulbs fixed by him.

Step-by-step explanation:

4 bulbs are present in = 1 room

thus, 216 bulbs are present in = 216/4 = 54 rooms

So, he fixes 54 rooms in total

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Answer:

Step-by-step explanation:

To construct an infinite set of sets of natural numbers such that all of their pairwise symmetric differences are infinite, we can define the following sequence of sets:

S_1 = {1, 2, 3, ...}

S_2 = {2, 3, 4, ...}

S_3 = {1, 3, 5, ...}

S_4 = {2, 4, 6, ...}

S_5 = {1, 4, 7, ...}

S_6 = {2, 5, 8, ...}

...

In general, S_n is the set of natural numbers that are congruent to n mod 2. For example, S_1 is the set of all odd natural numbers, S_2 is the set of all even natural numbers, and so on.

To show that all of their pairwise symmetric differences are infinite, we can consider any two distinct sets S_n and S_m. Without loss of generality, assume that n < m. Then, the symmetric difference between S_n and S_m is the set of natural numbers that are congruent to n or m mod 2, but not both:

S_n Δ S_m = {k ∈ N : (k ≡ n mod 2) XOR (k ≡ m mod 2)}

Since n < m, we can see that every other natural number is in this set, and therefore it is infinite. Hence, the sequence {S_n} is a set of sets of natural numbers such that all of their pairwise symmetric differences are infinite

In the given right triangle the length of side a is approximately 9.92 units.

A right triangle is a variety of triangles with a 90-degree angle (a right angle). The junction of the triangle's two legs, or the sides that meet at a right angle, creates this angle. The hypotenuse, which is always located opposite the right angle, is the third side of a right triangle.

A key characteristic of right triangles is the Pythagorean theorem, which asserts that the square of the hypotenuse is equal to the sum of the squares of the two legs of a right triangle.

We can use the trigonometric ratios of sine, cosine, and tangent to solve for the missing side of a right triangle. Since we are given the measure of one acute angle and the length of the side opposite that angle, we can use the tangent ratio:

tan A = opposite/adjacent

tan 51° = a/8

Multiplying both sides by 8:

a = 8 tan 51°

Using a calculator, we find that:

a ≈ 9.92

Therefore, the length of side a is approximately 9.92 units.

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Answer:

Step-by-step explanation:

half the base times the height

The solution to the system of equations is x =5 and y = -6

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

12x + 9y = 6

7x + 6y = −1

Multiply (2) by 1.5

So, we have the following representation

12x + 9y = 6

10.5x + 9y = −1.5

Subtract the equations to eliminate y

1.5x = 7.5

So, we have

x = 5

Recall that

12x + 9y = 6

So, we have

60 + 9y = 6

This gives

9y = -54

Divide

y = -6

SO, the value of y is -6

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The value of y in the regular dodecagon is 8°

What is Dodecagon?

Dodecagon is is a closed figure that has 12 sides and 12 angles. It has 12 vertices, each of which is connected to two sides.

What is Regular Dodecagon?

Regular Dodecagon is has all 12 sides of equal length and all angles of equal measure. It is a 12-sided polygon that is symmetrical.

To find the interior angle ,

= (n - 2)180° where the sides is 12

= (12-2)180°

= 1800°

= 1800/12  = 150°

i.e, each angle of the dodecagon = 150°

To determine this,

17y + 14° = 150°

17y = 150° - 14°

17y = 136°

y = 136°/17

y = 8°

Therefore, the value of y = 8°

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The supplies expense to be reported on the income statement for the year can be calculated using the formula:

Supplies expense = Beginning supplies balance + Supplies purchased during the year - Ending supplies balance

Substituting the given values, we get:

Therefore, the supplies expense to be reported on the income statement for the year is $3,050.

~ Zeph

The total annual income from both investment is

(14x -65000)/100

Interest is the price you pay to borrow money or the cost you charge to lend money. Interest is most often reflected as an annual percentage of the amount of a loan. This percentage is known as the interest rate on the loan.

I = x× 9/100

I = 9x/100

(13000 - x) × 5/100

= (65000-5x)/100

therefore the total amount annual income

= 9x /100 - (65000-5x)/100

= (9x+5x-65000)/100

= (14x - 65000)/100

therefore the total annual income = (14x -65000)/100

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In a case whereby a  person invested $13,000, part of the money, x, was placed in a stock that paid 9% annual interest the total annual income from both investments, I, as a function of x is I= [ 0.14X+12350 ]

The Amount that was invested =$13,000

Then the Profitable Investment which was givden as 9% can be expressed as =  [ X(1.09) ]

Then from the question we can see the Negative Investment, which is -5% and can be expressed as = [ (13,000-X)(1-0.05) ]

The we can sum up as

I= [ X(1.09) ]+ [ (13000-X)(0.95) ]

This can be simplified as

I= [ 1.09X-0.95X+12350 ]

I= [ 0.14X+12350 ]

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Answer:

are you trying to find the derivative if so the answer will be 0

Step-by-step explanation:

Answer:

Step-by-step explanation:

no because they don't have the same dominator

The correct sketch is B

The liquid range of water refers to the temperature range at which water exists as a liquid. At standard atmospheric pressure (1 atm), the liquid range of water is from 0 degrees Celsius to 100 degrees Celsius, or from 32 degrees Fahrenheit to 212 degrees Fahrenheit.

This means that water can exist as a liquid within this temperature range, but if the temperature falls below 0 degrees Celsius or rises above 100 degrees Celsius, it will freeze into a solid or boil into a gas, respectively.

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Answer: The value of a=29/23 and b=124/23

Step-by-step explanation:

Given equations are,

2b-3a=7       _(1)

3b+7a=25     _(2)

Multiplying (1) by 7

14b-21a=49

Multiplying (2) by 3

9b+21a=75

solving the above equations,

14b-21a=49

9b+21a=75

23b      =124

b=124/23

Substituting the value of b in eq. (1)

a=29/23

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Answer:

D. If an experiment is​ blinded, then any effect arising from psychological factors should affect all groups equally.

Answer: 16

Step-by-step explanation:

Since each bicycle has 2 wheels, this means 2 wheels times 8 bicycles. with comes out to 16 wheels

Answer:

16

Step-by-step explanation

If each bicycle has 2 wheels, we would multiply 2 wheels times 8 bicycles and we would get 16 wheels altogether.

Using the unitary method, we found that the cost of packing the unit weight of the chocolate box is  [tex]\frac{x^2}{4(x+2)}[/tex] , for x ≥ 3.

What is meant by the unitary method?

The unitary approach is a strategy for problem-solving that involves first determining the value of a single unit, and then multiplying that value to determine the required value. Recognizing the units and values is crucial when using the unitary technique to a problem.

Always write the items that need to be computed on the right side and the things that are known on the left side to simplify things.

The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.

Given,

  The cost of packing a box of chocolates = 1/4 * x²

 where x  = Number of chocolates and x ≥ 3 for one box.

Weight of a box of chocolates = x + 2

We are asked to find the cost of packing 1 unit weight of chocolates.

This can be found using the unitary method.

Cost of unit weight = Cost of packing a whole box / Total weight of the box.

                                = (1/4 * x²) / (x + 2)

                                 = [tex]\frac{x^2}{4(x+2)}[/tex] , for x ≥ 3

Now in the figure below, we are given four options.

On solving the first option we get the above equation as follows.

[tex]\frac{1}{4} x - \frac{1}{2} + \frac{1}{x+2}[/tex]  

Taking LCM and making the same denominator for all.

[tex]\frac{x(x+2) - 2(x+2) +4 }{4(x+2)} = \frac{x^2+2x-2x-4+4}{4(x+2)} = \frac{x^2}{4(x+2)}[/tex]

Therefore using the unitary method, we found that the cost of packing the unit weight of the chocolate box is  [tex]\frac{x^2}{4(x+2)}[/tex] , for x ≥ 3.

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The value of the composition of functions are

a) f o g ( 5 ) = 1315

b) g o f ( 5 ) = 59

Evaluation of a function at the value of another function is known as Composition of function. A function composition is a process in which two functions, f and g, form a new function, h, in such a way that h(x) = g(f(x)). This signifies that function g is being applied to the function x. So, in essence, a function is applied to the output of another function.

Given data ,

Let the value of the the function be f ( x ) = x² + 6x

Let the value of the function g ( x ) = x + 4

Now , the composition of functions is given by

f o g ( 5 ) is given by

g ( 5 ) = 5 + 4 = 9

So , the value of f ( 9 ) = ( 9 )² + 6 ( 9 ) = 81 + 54 = 135

Therefore , the value of f o g ( 5 ) = 135

Now , the composition of functions is given by

g o f ( 5 ) is given by

f ( 5 ) = ( 5 )² + 6 ( 5 ) = 25 + 30 = 55

Now , the value of g ( 55 ) = 55 + 4 = 59

Therefore , the value of g o f ( 5 ) = 59

Hence , the composition of functions are solved

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The standard error tells us how much we can expect the sample proportion to vary from the true proportion in repeated samples of the same size. Option (d) correctly states that "In samples of size 100 from this school, the sample proportion of students who bring a reusable water bottle from home typically varies by about 0.048 from the true proportion." This means that if we were to take many samples of 100 students from the same school and calculate the proportion of students who bring a reusable water bottle from home in each sample, about 95% of the sample proportions would fall within +/-0.048 of the true proportion.

The correct option is (d) "In samples of size 100 from this school, the sample proportion of students who bring a reusable water bottle from home typically varies by about 0.048 from the true proportion."

The standard error of the sample proportion can be calculated using the formula:

SE = √[p*(1-p) / n]

where p is the sample proportion and n is the sample size.

In this case, the sample proportion is 37/100 = 0.37 and the sample size is 100. Plugging in these values, we get:

SE = sqrt[0.37*(1-0.37) / 100] = 0.048

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The value of the variable x and y will be 1.5 and -2.5, respectively. Then the value of the expression (x + y) will be negative 1.

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

here, we have,

A system of equations is given below.

x = -2y - 3.5       ...1

-5x + 3y = -15    ...2

From equations 1 and 2, then we have

-5(-2y - 3.5) + 3y = -15

10y + 17.5 + 3y = - 15

13y = -32.5

y = - 2.5

Then the value of the variable 'x' is calculated as,

x = - 2(-2.5) - 3.5

x = 5 - 3.5

x = 1.5

Then the value of the expression (x + y) is calculated as,

x + y = 1.5 + (-2.5)

x + y = 1.5 - 2.5

x + y = - 1

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Refer to the attached image.

The mean age of the 12 students is approximately 17.02 years, the variance is 37.41, and the standard deviation is approximately 6.117 years.

The statistic is the study of mathematics that deals with relations between comprehensive data.

Here,
To calculate the mean, variance, and standard deviation of the ages of the 12 students, we first need to find the sum of the ages:

Sum = 16 + 17 + 18 + (16/0.5) + 17 + 18 + 19 + 17 + 17 + 13 + (17/2/2) + 16

= 16 + 17 + 18 + 32 + 17 + 18 + 19 + 17 + 17 + 13 + 4.25 + 16

= 204.25

Mean = Sum / Number of students = 204.25 / 12 ≈ 17.02 years

To calculate the variance, we need to subtract the mean from each age, square the differences, add up the squares, and divide by the number of students minus one:

Variance = [ (16 - 17.02)² + (17 - 17.02)² + ... + (16 - 17.02)² ] / (12 - 1)

= [ 0.16 + 1.96 + ... + 0.16 ] / 11

= 37.41

Finally, we can calculate the standard deviation by taking the square root of the variance:

Standard deviation = √(Variance) ≈ 6.117

Therefore, the mean age of the 12 students is approximately 17.02 years, the variance is 37.41, and the standard deviation is approximately 6.117 years.

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Answer:

$2700

Step-by-step explanation:

The x-coordinate of the vertex can be found using the formula:

x = -b/2a

where a = -6 and b = 360, so we have:

x = -360/(2*(-6)) = 30

Therefore, the company will maximize its profit by selling 30 units of the product.

p(x) = -6x^2 + 360x - 2500

(x = 30 )

p(30) = -6(30)^2 + 360(30) - 2500 = 2700

So, the maximum profit for the company is $2700.

Answer:  a

Step-by-step explanation:

karabee kailash

David's opportunity cost of producing 1 pound of watermelon is 4 pounds of zucchini, whereas Morgan's opportunity cost of producing 1 pound of watermelon is 3 pounds of zucchini. Because David has a higher opportunity cost of producing watermelon than Morgan, Morgan has a comparative advantage in the production of watermelon, and David has a comparative advantage in the production of zucchini.

What is opportunity cost?

Opportunity costs are the possible advantages that a person, investor, or company forgoes while deciding between two options. Opportunity costs are by definition invisible, making it simple to ignore them.

The best input combinations to achieve the highest level of output are displayed on the production potential frontier.

The individual who has a lower opportunity cost in output than another individual enjoys a comparative production advantage.

David's watermelon production -

54 units watermelon = 216 units zucchini

1 unit watermelon = 216/54 units zucchini

1 unit watermelon = 4 units zucchini

Morgan's watermelon production -

108 units watermelon = 324 units zucchini

1 unit watermelon = 324/108 units zucchini

1 unit watermelon = 3 units zucchini

Morgan has absolute advantage in production of Zucchini and Morgan has also absolute advantage in production of watermelon.

Therefore, David's opportunity cost of 1 pound of watermelon is 4 pound of Zucchini and Morgan's opportunity cost of 1 pound of watermelon is 3 pound of Zucchini.

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Answer:

there is an error in the question. if you compute ac - ab = 4 you get -2x+4 =4 that leads to x=0.

if so, ab = -6 and this is not allowed.

Therefore, 11/2 + 3/4 expressed as a fraction is 25/4.

A fraction is a number that represents a part of a whole. It is represented as a ratio of two numbers, the numerator and the denominator, separated by a horizontal line. The numerator represents the number of parts, while the denominator represents the total number of parts that make up the whole. Fractions can be expressed in different forms, including proper fractions, improper fractions, and mixed numbers. A proper fraction is a fraction where the numerator is less than the denominator. An improper fraction is a fraction where the numerator is greater than or equal to the denominator. A mixed number is a combination of a whole number and a proper fraction.

Here,

5 1/2+3/4

5 1/2=5*2+1/2

=11/2

11/2+3/4

To add 11/2 and 3/4, we need to find a common denominator. The smallest common multiple of 2 and 4 is 4, so we can rewrite 11/2 as an equivalent fraction with a denominator of 4:

11/2 = (11/2) x (2/2) = 22/4

Now we can add the two fractions:

11/2 + 3/4 = 22/4 + 3/4

To add the two fractions, we add the numerators and keep the same denominator:

= (22 + 3)/4

= 25/4

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This is a valid example of stringing arguments together using conditional statements.

The first statement establishes a conditional relationship between Martin shooting the sheriff and Martin shooting first.

The second statement also establishes a conditional relationship, but this time between Martin using his best pistol and Martin shooting first.

By combining the two conditional statements, we can conclude that if Martin didn't use his best pistol, then he didn't shoot first.

This follows from the fact that not using his best pistol would mean Martin didn't shoot first (according to statement 2), and if he didn't shoot first, then he couldn't have shot the sheriff (according to statement 1).

Therefore, the conclusion of the argument, which is that if Martin didn't use his best pistol, then he didn't shoot the sheriff, follows logically from the two conditional statements.

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Answer:

Hope the picture helps! <3

Step-by-step explanation: