A carton of one dozen eggs costs $1.92. What is the unit price of each egg?

The minimum value of the expression log_a(x)+log_x(x) is 2 because the minimum value of each term is 1.

It is another way to represent the power of numbers, and we say that 'b' is the logarithm of 'c' with base 'a' if and only if 'a' to the power 'b' equals 'c'.

[tex]\rm a^b = c\\log_ac =b[/tex]

We have:

1 < a ≤ x

We have an expression:

[tex]\rm log_a(x)+log_x(x)[/tex]

We know,

[tex]\rm log_aa = 1[/tex]

[tex]\rm log_a(x)+1[/tex]

If a = x

Then, [tex]\rm log_a(x)=1[/tex]

We cannot find the function value less than 1 because it goes infinitely in a negative direction.

So the minimum value of the expression:

= 1 + 1

= 2

Thus, the minimum value of the expression log_a(x)+log_x(x) is 2 because the minimum value of each term is 1.

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Answer:

This is impossible.

Step-by-step explanation:

The interior angle of a regular polygon is equal to

[tex] \frac{180(n - 2)}{n} [/tex]

where n is the number of sides.

Setting this equal to 180°,

[tex] \frac{180(n - 2)}{n} = 180 \\ \\ \frac{n - 2}{n} = 1 \\ \\ n = n - 2 \\ \\ 0 = - 2[/tex]

which is false.

Answer:

(x+2)(x-3)(x+3) this is ans

Answer:

a. (x + 2)

Step-by-step explanation:

x^2(x + 2) - 9(x + 2)

(x + 2)(x^2 - 9)

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

Therefore the answer is (x + 2)

Answer:

0.00893 feet elevation per 1 foot distance.

Step-by-step explanation:

The hill reaches an elevation of 250 ft (above sea level) over the course of 28,000 feet.  The average rate of change would be (250 ft)/(28,000 ft), or 0.00893 feet elevation/1 foot distance.

((0.00893 (feet up/foot distance))*(28,000 feet distance) = 250 feet  up (elevation).

The steps of student B are in the correct order but the steps of student A are in the incorrect order.

Lines that intersect at a right angle are named perpendicular lines. Lines that are always the same distance apart from each other are known as parallel lines and the lines that never intersect are known as parallel lines.

We have:

You are given AB and point C. Construct a line parallel to AB that passes through point C

The correct way to draw a parallel line to AB that passes through point C is:

The steps of student B are in the correct order but the steps of student A are in the incorrect order.

Thus, the steps of student B are in the correct order but the steps of student A are in the incorrect order.

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For the graphed function we can see:

For a function y = f(x), the domain is the set of the possible inputs "x" and the range is the set of the possible outputs "y".

In this case, we can see that in the right side we have a parabola, and on the left side a linear equation which increases up to the left (so it has a negative slope).

Then the domain will be the set of all real numbers.

Similar for the range, as we can see that on the left side, the line goes upwards, while on the right side, the parabola goes downwards. So this function has a range of all real numbers.

Then:

domain = set of all real numbers

range = set of all real numbers.

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A graph is a way to represent a lot of data in such a visual format. The graph for the given situation can be drawn as shown below.

A graph is a way to represent a lot of data in such a visual format that it is easy for the user to understand the complete information in one go. Usually, the line of the graph is a function that follows the graph.

The graph for the given situation can be drawn as shown below, where the x-axis represents the number of pounds of rice scooped and purchased from a bulk bin at the grocery store and the y-axis represents the total cost of the rice.

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Answer:

Given sequence in the table is a Geometric sequence and The sum for term 5 through term 11 in sigma notation is given by:

[tex]$\sum_{n=5} ^{\111} 2(-5)^n^-^1$[/tex]

Step-by-step explanation:

Geometric sequence - it is a sequence of non-zero numbers where each term after the first is found by multiplying the previous one by a fixed, non-zero number called the common ratio

here the given terms :

a1 = 2, a2 = -10, a3 = 50

you can see it is a geometric sequence as the ratio is constant  [tex]\frac{a2}{a1}{=}\frac{a3}{a2}{=}{-5}[/tex]

now the nth term for geometric sequence :

[tex]a_{n} {=}{a}{r}^{n-1}[/tex]

here,

now substituting the given values in the expression,

[tex]a_{n} {=}{2}{{(}-5}{)}^{n-1}[/tex]

we have to find the sum from term 5 to term 11,

therefore using sigma notation and putting n= 5 and n=11 at the below and above the sigma respectively,

[tex]$\sum_{n=5} ^{\111} 2(-5)^n^-^1$[/tex]    

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Answer:

No, it's not.

Answer:

The correct answer is True

Answer:

True

Step-by-step explanation:

Each branch of a tree diagram is the likelihood of that outcome happening. You multiply as you go along the branch.

Answer:

70

Step-by-step explanation:

180 minus 110 is 70

straight lines are 180 degrees

The product of 4 and 5g + 2.34 is 20g + 9.36

The expressions are given as:

4 and 5g + 2.34

As a product expression, we have:

4 * (5g + 2.34)

Evaluate the product

20g + 9.36

Hence, the product of 4 and 5g + 2.34 is 20g + 9.36

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The solution of the equation 4p – [(2p – 3) / 2] = 6 with variable p will be 1.5.

The solution of the equation means the value of the unknown or variable.

The equation is given below.

4p – [(2p – 3) / 2] = 6

On simplifying, we have

(8p – 2p + 3) / 2 = 6

               6p + 3 = 12

                     6p = 9

                       p = 1.5

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Answer:

telmhtkhknrkh

Step-by-step explanation:

eg

Answer:

4.08x^2

Step-by-step explanation:

Answer:

4y^2

Step-by-step explanation:

least common denominator is 4y^2

The permutation equation [tex]^{n+1}P_3 - ^nP_3= 3 * ^nP_2[/tex] is true for all integers n ≥ 3

We have:

[tex]^{n+1}P_3 - ^nP_3= 3 * ^nP_2[/tex]

Apply the following permutation formula

[tex]^{n}P_r = \frac{n!}{(n- r)!}[/tex]

So, we have:

[tex]\frac{(n + 1)!}{(n + 1 - 3)!} - \frac{n!}{(n - 3)!} = 3 * \frac{n!}{(n - 2)!}[/tex]

Evaluate the difference

[tex]\frac{(n + 1)!}{(n - 2)!} - \frac{n!}{(n - 3)!} = 3 * \frac{n!}{(n - 2)!}[/tex]

Expand

[tex]\frac{(n + 1)!}{(n - 2)(n - 3)!} - \frac{n!}{(n - 3)!} = 3 * \frac{n!}{(n - 2)(n - 3)!}[/tex]

Multiply through by (n - 3)!

[tex]\frac{(n + 1)!}{(n - 2)} - n! = 3 * \frac{n!}{(n - 2)}[/tex]

Expand

[tex]\frac{(n + 1) * n!}{(n - 2)} - n! = 3 * \frac{n!}{(n - 2)}[/tex]

Divide through by n!

[tex]\frac{(n + 1)}{(n - 2)} - 1 = \frac{3}{(n - 2)}[/tex]

Take the LCM

[tex]\frac{n + 1 - n + 2}{(n - 2)} = \frac{3}{(n - 2)}[/tex]

Evaluate the like terms

[tex]\frac{3}{(n - 2)} = \frac{3}{(n - 2)}[/tex]

Both sides of the equations are the same.

Hence, the permutation equation [tex]^{n+1}P_3 - ^nP_3= 3 * ^nP_2[/tex] is true for all integers n ≥ 3

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The ordered pair that represents a function is {(0,0),(1,10),(10,4),(-1,-7)}.

A set of ordered pairs that defines a function will be the one that has exactly one y-value that assigned to every x-value. This means that none of its x-values can have two corresponding y-values.

All the sets of ordered pairs don't have exactly one y-value that corresponds to each of its x-value except {(0,0),(1,10),(10,4),(-1,-7)}.

Thus, we can say that the ordered pair that represents a function is {(0,0),(1,10),(10,4),(-1,-7)}.

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Answer:

b6,4

Step-by-step explanation:

becust tehf sdj

The equation of the line will be y = [tex]\dfrac{1}{5}x + \dfrac{12}{5}[/tex]

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

First, we need to find the equation of the line that is given:

We can use the formula,

[tex]m = \dfrac{y_1 - y_2}{x_1-x_2}[/tex]

[tex]m=\dfrac{-3-(-4)}{0-(-5)}=\dfrac{1}{5}[/tex]

So the equation for this line is  

y = (1/5) x - 3

This means that the equation for the line we are trying to find has a slope of as well

Let's put the points in the equation and try to find the y-intercept:

2 = [tex]\dfrac{1}{5}[/tex] ( -2 ) + b

[tex]\dfrac{15}{5} = b[/tex]

So the final equation for the line we are trying to find is y = [tex]\dfrac{1}{5}x + \dfrac{12}{5}[/tex]

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The linear relation of the height as a function of the number of weeks is:

y = 0.5*x

A general linear relation is written as:

y = a*x + b

Where a is the slope.

If we know that the line passes through two points (x₁, y₁) and (x₂, y₂), then the slope is:

[tex]a = \frac{y_2 - y_1}{x_2 - x_1}[/tex]

In this case, we have the points of the form (week, height).

(4, 2)

(6, 3)

(8, 4)

If we use any two of these we can get the slope, so using the first two:

a = (3 - 2)(6 - 4) = 1/2 = 0.5

y = 0.5*x + b

To get the value of b, we can use the first point, it says that when x = 4, we have y = 2, then:

2 = 0.5*4 + b

2 = 2 + b

0 = b

Then the linear relation of the height as a function of the number of weeks is:

y = 0.5*x

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Answer:

$3,272

Step-by-step explanation:

Continuous Compounding Formula

[tex]\large \text{$ \sf A=Pe^{rt} $}[/tex]

where:

Given:

Substitute the given values into the formula and solve for A:

[tex]\sf \implies A=2600e^{(0.023 \times 10)}[/tex]

[tex]\sf \implies A=2600e^{0.23}[/tex]

[tex]\implies \sf A=3272.360026...[/tex]

Therefore, the value of the account after 10 years is $3,272 to the nearest dollar.

The simplified form of the expression has a numerator (x + 9)(2x + 1) and the denominator (x + 7) and the expression doesn't exist at (x = 9).

The given expression is:

= [(3x² - 27x)/(2x² + 13x - 7)]/(3x/4x² - 1)

Firstly, factorize the expression 4x² - 1.

4x² - 1 = (2x - 1)(2x + 1)

Then, factorize 2x² + 13x - 7.

2x² + 13x - 7 = 2x² + 14x - x - 7

2x(x + 7) - 1(x + 7)

= (2x - 1)(x + 7)

Then, factorize the equation 3x² - 27x.

3x² - 27x = 3x(x - 9)

The factorized terms will be substituted into the equation. This will be:

= [3x(x - 9)/(2x - 1)(x + 7)] / 3x[(2x - 1)(2x + 1)]

= (x + 9)(2x + 1)/(x + 7)

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Answer: Domain: (-∞, 0) U (0, ∞)

Step-by-step explanation:

[tex]\frac{12}{x} *-8x^{3}[/tex]

[tex]=-96x^2[/tex]

Domain: (-∞, 0) U (0, ∞)

Answer:

894.035793467 or roughly 894

Step-by-step explanation:

I square rooted it by using a calculator, and by working it out on paper.