An absolute value function with a vertex or 3,7

Answer:

the answer is 9

2,3,5,8,9,11

5+8

2= 9

The production level that minimizes the average cost per unit is x = 6.

This is a fourth-degree polynomial, which can be difficult to solve algebraically. However, we can use numerical methods (such as a graphing calculator or software) to find the value of y that minimizes the polynomial. We find that y ≈ 1.08025, which implies that x ≈ 1.1669. Therefore, the production level that minimizes the average cost per unit is x = 6 (rounded to the nearest integer). This can be verified by checking the second derivative of AC(x) to ensure that it is positive at x = 6, indicating a minimum point.

We first need to find the average cost per unit. This is given by the total cost divided by the number of units produced:
AC(x) = c(x) / x
Substituting c(x) into this equation, we get:
AC(x) = (5x - 8x - 2√x) / x
Simplifying this expression, we get:
AC(x) = (5 - 8/x - 2/x√x)
Now, we need to find the value of x that minimizes AC(x). To do this, we can take the derivative of AC(x) with respect to x and set it equal to zero:
dAC(x) / dx = -5/x^2 + 8/x^3 + 1/(x√x) = 0
Multiplying both sides by x^3√x, we get:
-5x√x + 8x^2 + √x = 0
Squaring both sides of this equation, we get:
25x^3 - 64x^4 + 16x = 0
Simplifying this expression, we get:
x(25 - 64x + 16√x) = 0
Since x cannot be zero, we must solve for the other factor:
25 - 64x + 16√x = 0
Squaring both sides of this equation, we get:
625 - 320x + 256x - 512√x = 0
Simplifying this expression, we get:
256x - 320x + 512√x = 625
Simplifying further, we get:
16x - 20x + 32√x = 25
Dividing both sides by 4, we get:
4x - 5x + 8√x = 25/
Substituting x = y^2, we get:
4y^2 - 5y^4 + 8y = 25/4
Multiplying both sides by 4, we get:
16y^2 - 20y^4 + 32y = 25
Dividing both sides by 5, we get:
3.2y^2 - 4y^4 + 6.4y = 5

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The area of the paperboard that remains after the cut-out has been made is 632 square inches.

To find the area of the paperboard that remains, we first need to determine the area of the entire paperboard. The area of a rectangle is calculated by multiplying its length by its width, so the area of the original paperboard is:
Area = Length x Width
Area = 34 in x 20 in
Area = 680 in²
Next, we need to calculate the area of the cut-out portion. The cut-out is a rectangle measuring 6 inches in length and 8 inches in width. The area of the cut-out can be found by multiplying its length by its width:
Area of cut-out = Length x Width
Area of cut-out = 6 in x 8 in
Area of cut-out = 48 in²
To find the area of the paperboard that remains, we need to subtract the area of the cut-out from the total area of the paperboard:
Area remaining = Total area - Area of cut-out
Area remaining = 680 in² - 48 in²
Area remaining = 632 in²

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Answer: 15.625 ft^3

Step-by-step explanation:

The volume of a cube is the side length cubed.

Therefore, the volume of this cube would be equal to 2.5^3

2.5^3 = 15.625 ft^3

The given statement in the form of inequality is given as -

c - 6 > 24.

An inequality is used to make unequal comparisons between two or more expressions. For example → ax + b > c

In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.

Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.

Given is the statement as -

"Six subtracted from c is greater than 24"

We can write the inequality as -

c - 6 > 24

Therefore, the given statement in the form of inequality is given as -

c - 6 > 24.

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{Question in english -

Six subtracted from c is greater than 24}

The last term is 300

The sum of all the terms is 15150.0

The average of all the terms is 151.5

Here is an example solution in Python that follows the given pseudocode:

# Prompt for and read the first term

first_term = int(input("Enter first term: "))

# Prompt for and read the common difference

common_difference = int(input("Enter common difference: "))

# Prompt for and read the number of terms

number_of_terms = int(input("Enter number of terms: "))

# Calculate the last term

last_term = first_term + (number_of_terms - 1) * common_difference

# Calculate the sum of all the terms

sum_of_terms = number_of_terms * (first_term + last_term) / 2

# Calculate the average of all the terms

average_of_terms = sum_of_terms / number_of_terms

# Display the results

print("The last term is", last_term)

print("The sum of all the terms is", sum_of_terms)

print("The average of all the terms is", average_of_terms)

If you run this code and enter the values from the sample run (first term: 3, common difference: 3, number of terms: 100), it will produce the following output:

The last term is 300

The sum of all the terms is 15150.0

The average of all the terms is 151.5

The program prompts the user for the first term, common difference, and number of terms. Then it calculates the last term using the given formula. Next, it calculates the sum of all the terms and the average of all the terms using the provided formulas. Finally, it displays the calculated results.

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Answer:

Starnes 2.9

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

y = - x + 10 → (1)

y = 7x + 2 → (2)

Substitute y = 7x + 2 into (1)

7x + 2 = - x + 10 ( add x to both sides )

8x + 2 = 10 ( subtract 2 from both sides )

8x = 8 ( divide both sides by 8 )

x = 1

Substitute x = 1 into either of the 2 equations and solve for y

Substituting into (2)

y = 7(1) + 2 = 7 + 2 = 9

solution is (1, 9 ) → B

In 2.22 years, there will only be 50,000 African penguins left.

Since the population of African penguins is cut in thirds every year, we can use the exponential decay model to describe its population as follows:

P(t) = P₀(1/3)^t

where P(t) represents the population after t years, and P₀ represents the initial population in 2000, which is 200,000.

So, the formula for the population of African penguins after t years is:

P(t) = 200,000(1/3)^t

To find how many years it will take for the population to be reduced to a certain number, we can plug in that number for P(t) and solve for t.

For example, if we want to find out how many years it will take for the population to be reduced to 50,000, we can write:

50,000 = 200,000(1/3)^t

Divide both sides by 200,000:

1/4 = (1/3)^t

Take the natural logarithm of both sides:

ln(1/4) = ln[(1/3)^t]

ln(1/4) = t ln(1/3)

Solve for t:

t = ln(1/4) / ln(1/3)

Using a calculator, we get t ≈ 2.22 years.

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The value of the union of sets A and B is, P(A ∪ B) is 0.64.

The union of two sets means the total elements in both the sets combined.

Given: sets P(A) = 0.38, P(B) = 0.83, and  intersection P(A ∩ B) = 0.57

We need to find the union of P(A ∪ B).

P(A ∪ B) = P(A) + P(B) - P(A ∩ B)

Let us substitute the given values in the formula.

P(A ∪ B) = P(A) + P(B) - P(A ∩ B)

=0.38+0.83-0.57

=1.21-0.57

=0.64

Therefore, the value of union of sets P(A ∪ B) is 0.64.

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Answer:

I don't understand ur question.

Step-by-step explanation:

Please there is no picture or complete

Answer:

f(x)= -3x² - 12x - 5

Step-by-step explanation:

-3(x+2)² + 7

-3(x+2)(x+2) + 7

(-3x-6)(x+2) + 7

-3x² - 6x - 6x - 12 + 7

-3x² - 12x - 5

Answer: 0 does not =29 and result means the effect of a sequence

Step-by-step explanation:

3(x-7) +9x= 4(3x+ 2)

3x -21 +9x= 12x +8

12x -21=12x +8

0 does not= 29

From the given data value of function f ' (- 10) is,

⇒ f ' (- 10) = 0.035

A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable and another variable.

Given that;

Table for the given data is shown.

Now, We have to find the value of f ' (- 10).

Since, - 10 is in between - 11 and - 9.

Hence, The slope given the value of f ' (- 10) as;

⇒ f ' (- 10) = (1.12 - 1.05) / (- 9 - (- 11))

⇒ f ' (- 10) = (0.07/2)

⇒ f ' (- 10) = 0.035

Thus, From the given data value of f ' (- 10) is,

⇒ f ' (- 10) = 0.035

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Answer:

The entrance is30 ft wide

Answer:

20 feet

Step-by-step explanation:

When graphing, we see that the length of the transverse axis is the shortest distance, which is a length of 20 feet from one wall to the other.

To make it simple, just subtract the age that you died to the age that you were born.

1730 - 1620 = 110

Which means that you would die at the age of 110 if you were born at 1620 and died on 1730.

Answer: 110 years

Step-by-step explanation:

theres 110 years between 1620 and 1730

$2816.80 is the raise

21 is 30% of 70

So, the probability that Mike will have to work overtime, given that it rains, is 0.056 or 5.6%.

To find the probability that Mike has to work overtime given that it rains, we will use conditional probability. We are given the joint probability of Mike working overtime and it raining (0.028) and the probability of rain (0.5).
Let A be the event of Mike working overtime, and B be the event of rain. We want to find the probability of A given B, or P(A|B). We can use the formula for conditional probability: P(A|B) = P(A and B) / P(B).
Plugging in the values we have:
P(A|B) = P(A and B) / P(B) = 0.028 / 0.5
Now, divide 0.028 by 0.5:
P(A|B) = 0.056
So, the probability that Mike will have to work overtime, given that it rains, is 0.056 or 5.6%.

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There is a 90° clockwise rotation about the origin followed by a dilation of scale factor of 0.5

Thus the correct option is C.

The first thing we can notice in the image is that the two figures have different orientations.

On the left side, we can see that the two "plane opposite sides" are oriented upwards and downwards, while on the left figure we can see that these sides are oriented "left and right"

Then there is a rotation of 90° to the right (this is actually called a rotaion of 90° clockwise) from 1 to 2.

Then, if you look at the bottom side of figure 1, you can see that the side measures 2 units.

If you look at the left side of figure 2 (it is the same one as the bottom side of image 1, remember that figure 2 is a rotation of figure 1) it measures one unit.

So there is a dilation of scale factor k such that:

k*2 = 1

k = 1/2 = 0.5

Then:

There is a 90° clockwise rotation about the origin followed by a dilation of scale factor of 0.5

Thus the correct option is C.

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Answer:

no I didn't but why ask ?

Step-by-step explanation:

brainiest pls

Answer:

it is typically 22 to 7

Step-by-step explanation:

if you divide 22 by 7 you get 3.142857143...

Answer:

  22/7

Step-by-step explanation:

You want to know a ratio commonly used as an alternative to 3.14 for an approximation to pi.

The value 3.14 as an approximation of pi is obtained by simply truncating the value to 2 decimal places. That makes the approximation lower than the actual value by about 0.0507%.

Rational approximations can be found from the expression of pi as a continued fraction. Truncating that fraction at various points gives the approximations ...

  22/7 . . . . high by about 0.0402%

  333/106 . . . . low by about 0.0026%

  355/113 . . . . . high by about 0.0000085%

22/7 is the most commonly used rational approximation of pi instead of 3.14.

__

Additional comment

The continued fraction is non-repeating. It starts ...

  \(3+\cfrac{1}{7+\cfrac{1}{15+\cfrac{1}{1+\cfrac{1}{292+\cfrac{1}{1+\dots}}}}}\)

The curve of intersection between the cylinder x^2 + y^2 = 1 and the plane y + z = 2 is a circle lying on the plane y + z = 2. The parametric equations for this curve are x = cos(θ), y = sin(θ), and z = 2 - sin(θ), where θ is the parameter representing points on the circle.

To find the parametric equations for the curve of intersection between the cylinder and the plane, we can start by parameterizing the cylinder using the angle θ. Since the equation x^2 + y^2 = 1 represents a circle in the x-y plane with radius 1, we can use θ as a parameter to represent points on this circle.

The parametric equations for the cylinder are:

x = cos(θ)

y = sin(θ)

z = 2 - y

Next, we substitute these equations into the plane equation y + z = 2 to determine the intersection points. By substituting y and z, we have sin(θ) + 2 - sin(θ) = 2, which simplifies to sin(θ) - sin(θ) = 0. This implies that the plane equation is satisfied for any value of θ.

Therefore, the intersection between the cylinder and the plane is the entire cylinder itself, lying on the plane y + z = 2. The parametric equations for the curve of intersection are x = cos(θ), y = sin(θ), and z = 2 - sin(θ).

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The statement that can be concluded from the triangle is A. RS/VU=ST/UT and ∠S≅∠U.

The Side-Angle-Side Similarity Theorem states that if two sides in one triangle are proportional to two sides in another triangle and the included angle in both are congruent, then the two triangles are similar.

In this problem the included angle is ∠S≅∠U, therefore side RS must be proportional to side VU  and side ST must be proportional to side UT

Hence, RS/VU=ST/UT.

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Answer:

Step-by-step explanation:

Given line h:

Dilated line is parallel to original, so will have same slope of -2

y-intercept will change by a scale factor of 4:

So the equation of the new line is:

Answer:

10

Step-by-step explanation:

each taco is 1.50$ 15$ divided by 1.50$ is 10

Answer:

He can buy 10 tacos with $15.

Step-by-step explanation:

You can do a cross multiplication process. Think in this way:

If he buys 4 tacos for $6, then how many tacos can he get in $15? When you do the cross multiplication process, you'll find that he can get 10 tacos with $15.

Answer:

Step-by-step explanation:

The slope of the line is -5, and the y-intercept is 250

Answer and Explanation:

Given:

Let's go ahead and chose different values of x and corresponding values of y;

When x = -2;

When x = -1;

When x = 0;

When x = 1;

When x = 5;

With the above values, we can go ahead and graph the function as seen below;

The domain of a function is the set of possible input values(x-values) for which the function is defined. On a graph, it is the set of x-values from left to right.

Looking at the given graph, we can see that the domain is;

The range of a function is the set of possible output values(y-values). It is the set of y-values from the bottom to the top of the graph.

Looking at the given graph, we can see that the range is;

i) The probability density function for the number of non-defective items in a sample of ten items picked at random is: P(X=x) =10Cx × 0.9ˣ × 0.1¹⁰⁻ˣ

ii) The probability of having none or all the ten items being non-defective

is: 0.3487.

Here, we have,

Probability that item is non defective (P)=0.90

q=1-0.90=0.1

n=10

i) let X be the number of non defective iteam

Probability function of this given by the binomial distribution formula

P(X=x)

=10Cx × 0.9ˣ × 0.1¹⁰⁻ˣ

ii)P( X=0 or X=10)=P(X=0)+P(X=10)

P(X=0)=10C0×0.9^0×0.1^10

=0.0000000001

P(X=10)=10C10×0.9^10×0.1^0

=0.3487

P(X=0 or X=10)=0.3487+0.0000000001

=0.3487

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The values of the missing sides are;

a.  x = 35. 6 degrees

b. x = 15

c. x = 22. 7 ft

d. x = 31. 7 degrees

To determine the values, we have;

a. Using the tangent identity;

tan x = 5/7

Divide the values

tan x = 0. 7143

x = 35. 6 degrees

b. Using the Pythagorean theorem

x² = 9² + 12²

find the square

x² = 225

x = 15

c. Using the sine identity

sin 29= 11/x

cross multiply the values

x = 11/0. 4848

x = 22. 7 ft

d. sin x = 3.1/5.9

sin x = 0. 5254

x = 31. 7 degrees

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