Samuel has 1 cup of rubbing alcohol and will use the entire amount. He plans to store the cleaning solution in containers that each hold a maximum of 6 cups. How many containers does he need.

Answer:

If h>0 , the graph of the base function shifts to the right. If h<0 , the graph of the base function shifts to the left. The function y=logb(x)+k y = l o g b ( x ) + k is the base function y=logb(x) y = l o g b ( x ) shifted vertically by k .

Step-by-step explanation:

There are mainly two types of logarithmic functions - common logarithm and natural logarithm.

Common logarithm (log): The logarithm function with base 10, it is represented as log10(x) or simply log(x) if the base is not specified.

Natural logarithm (ln): The logarithm function with base e (approx 2.718), it is represented as ln(x)

These two logarithmic functions are the most commonly used and have many applications in mathematics, physics, engineering, and other sciences. They are inverse functions of the exponential functions (10^x and e^x) respectively.

Additionally, there are other types of logarithms, such as logarithms with bases other than 10 or e, for example log2(x) which is logarithm with base 2, it is used in information theory and computer science.

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Answer:

30.25

Step-by-step explanation:

This is because y is the square of x

The solution for the system of equations as given in the task content is; x = 1 and y = 7.

It follows from the task content that the solution for the given system of equations is to be determined.

On this note, since the given equations can be written as;

-5x + 2y = 9

y = 7x

Therefore, by substitution of y for 7x in the first equation; we have;

-5x + 2 (7x) = 9

-5x + 14x = 9

9x = 9

x = 9/9 = 1

Hence, since y = 7x; y = 7 (1) = 7.

Ultimately, the solution for the system of equations is such that; x = 1 and y = 7.

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The end behavior for f(x)=x^5 is asymptotic growth to positive infinity as x approaches positive infinity and asymptotic growth to negative infinity as x approaches negative infinity.

Asymptotic growth is a term used to describe the behavior of a function as it approaches a certain value, usually infinity. In mathematics, an asymptotic function is one that grows or shrinks towards a certain point without ever actually reaching it. In other words, it approaches a limit without bound. Asymptotic growth is often used to describe the rate of growth of a function as its input values approach infinity. It is also used to describe the rate at which a function expands or contracts as its argument approaches a certain point. Asymptotic growth is a useful concept in many areas of mathematics, from calculus to number theory.

This is because x^5 becomes increasingly larger as the absolute value of x increases, resulting in an ever-growing value of f(x).

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Answer:

x=1/3

Step-by-step explanation:

= 5/x - 4/×=3

= 1/x=3/1

= 1=3×

= x=1/3

To write 21600000 in standard form, we need to move the decimal point to the left or right so that there is only one non-zero digit to the left of the decimal point.

21600000 in standard form would be written as 2.16 x 10^7. Standard form, also known as scientific notation, is a way of expressing a number in a compact and efficient manner. It is typically used for very large or very small numbers. To write a number in standard form, the decimal point is moved so that there is only one non-zero digit to the left of the decimal point.

The number of places the decimal point is moved is indicated by a power of 10. In the case of 21600000, the decimal point is moved 7 places to the left, giving us 2.16 x 10^7. This notation makes it easy to compare numbers of different magnitudes, and it simplifies calculations involving large or small numbers. It is commonly used in scientific, engineering and mathematical fields. A standard form is a useful tool for expressing numbers in a clear and concise way.

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In mathematics, a linear combination is any expression of the form ax + by, where a and b are constants, that are created from a set of terms by multiplying each term by a constant and adding the results.

The linear equations can be solved through the given steps-

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Answer:

[tex]\boxed{\sf{30.5 \times 10^{10}\;km^3}}[/tex]

Step-by-step explanation:

Volume of Lake Erie

[tex]\sf {= 25 \times 1.22 \times 10^{10} \\\\= 30.5\times 10^{10} \;km^3}[/tex]

The people who went to the concert will be 53 Adults and 39 Children respectively.

We will solve this problem with the help of a Binomial equation.

Let the number of adults is X and the number of children is Y.

Our first equation will be =

X + Y = 92

The total cost for adults is $3 and for Children is $2.25.

The total receipt for the concert is $246.75.

Our second equation will be =

3X + 2.25Y = 246.75

From equation 1, we get

X + Y = 92

X = 92-Y

Substitute this in equation second equation, and we get

3(92-Y) + 2.25Y = 246.75

276 - 3Y + 2.25Y = 246.75

-0.75Y = 246.75 - 276

-0.75Y = -29.25

Y = 39

So, our number of Children is 39.

Putting the value of Y in the first equation, we get:

X = 92 - 39 = 53

So, our number of adults is 53.

Therefore 53 Adults and 39 Children went to the concert respectively.

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The inverse function of the power of two functions is the binary logarithm, sometimes known as log base 2.

Given,

For each real number n, according to the general logarithm, can be expressed as an exponential function.

n = aˣ

The logarithm form is written as follows: Log base 2 is the power to which 2 must be raised to obtain the value of n.

logₐ n = x

Here, "a" is a base that is a positive real integer, and "x" is an exponent. For each real number x, the formulas for log base 2 functions are provided as;

x = log₂ n

That is equivalent to,

2ˣ = n

The base 0 logarithm and negative logarithms are not defined by the real number system.

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10) Using the equation 98.4 = (12.3)8, it costs $12.30 (cost per unit) per uniform.

11) Using the equation 26.70 = k6, the cost of one bag of apples (unit rate) is $4.45.

The unit rate is the quotient of the total cost divided by the number of items contained.

The unit rate is the same as the average or mean of a data set.

We describe the unit rate as the slope of a linear equation.

The unit rate shows the constant rate of change in an equation.

The total cost of 8 uniforms = 98.4 = (12.3)8

The cost per uniform = 12.30 (98.4/8)

The total cost of 6 bags of apples = 26.70

The cost per unit = 4.45 (26.70/6)

Thus, the unit rate or cost is also described as the variable unit cost.

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Solve x^2+3x+2=0

[tex]x_{1} = -1\\x_{2} = -2[/tex]

The first is to use the quadratic formula

x= (-b±[tex]\sqrt[{} ]{b^{2} -4ac}[/tex]) ÷ 2a

Once in standard form, identify a, b, and c from the original equation and plug them into the quadratic formula.

[tex]x^{2} +3x+2 = 0[/tex]

Where,

a = 1

b = 3

c = 2

So,

x = (-b±[tex]\sqrt[{} ]{b^{2} -4ac}[/tex]) ÷ 2a

  = (-3±[tex]\sqrt[]{3^{2}-4.1.2 }[/tex]) ÷ 2.1

The next step is to simplify numbers.

x= (-3±1) ÷ 2

The next step is separate it into two equations: one with the plus sign and the other with the minus sign.

x = (-3+1) ÷ 2

and

x = (-3-1) ÷ 2

Then,

[tex]x_{1}[/tex] = (-2)÷2 = -1

Or,

[tex]x_2}[/tex] = (-4)÷2 = -2

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the dilatation of the quadrilateral ABCD, where the vertices' coordinates are [tex]A (x1,y1), B (x2,y2), C (x3,y3),D(x4,y4){}[/tex] is written as: with scale factor k.

A(,3,8), B(6,-8), C(-6,-6) and D are the vertices of the quadrilateral ABCD (-3,4) Establish the rhombic shape of ABCD.

A polygon with four sides exactly is referred to as a quadrilateral. The fact that a quadrilateral has exactly four vertices and four angles is also implied by this.

Each diagonal is parallel to the other. It is therefore a rhombus. The diagonals of the parallelogram are a rectangle, rhombus, and square since they are congruent and perpendicular to one another. A rhombus is ABCD.

[tex]A(x1,y1){}[/tex]⇒[tex]A'(kx1,ky1){}[/tex]

[tex]B(x2,y2){}[/tex]⇒[tex]B'(kx2,ky2){}[/tex]

[tex]C(x3,y3){}[/tex]⇒[tex]C'(kx3,ky3){}[/tex]

[tex]D(x4,y4){}[/tex]⇒[tex]D'(kx4,ky4){}[/tex]

Therefore, a dilated quadrilateral A'B'C'D"s vertices would have the coordinates [tex]A'(kx1,ky1), B'(kx2,ky2), C'(kx3,ky3), and D(kx4,ky4){}[/tex]

It should be noted that "k" could have an integer, decimal, or fractional value.

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The area of mathematics known as algebra aids in the representation of circumstances or problems as mathematical expressions.

Given data :

1. We split it into the following:

[tex]\sqrt{4*6}[/tex]

Now, we use the radical rule which states that,

[tex]\sqrt{ab} = \sqrt{a} *\sqrt{b}[/tex] a,b > 0

So, we get,

[tex]\sqrt{4}[/tex] [tex]\sqrt{6}[/tex]

= 2[tex]\sqrt{6}[/tex]

2. We split it into the following:

[tex]\sqrt{12*9}[/tex]

Now, we use the radical rule which states that,

[tex]\sqrt{ab} = \sqrt{a} *\sqrt{b}[/tex] a,b > 0

So, we get,

[tex]\sqrt{12}[/tex] [tex]\sqrt{9}[/tex]

= 6 [tex]\sqrt{3}[/tex]

3.  √7 . √14 =

  = √7 . √7 .√2

     = 7.√2

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The Arc AB = (π * r * 38) / 180.

What is central angle?

A central angle is the angle formed when two radii intersect at the center of a circle.

Since chord CB is a diameter of the circle, angle B is a right angle and measures 90 degrees. Arc AB is half the circumference of the circle, so its measure is equal to half the circumference times the ratio of the central angle to the total central angle (360 degrees) of the circle.

Let r be the radius of the circle. Then the circumference is 2 * π * r and the measure of arc AB is:

Arc AB = (1/2) * 2 * π * r * (angle B / 360)

Arc AB = (π * r * angle B) / 180

Arc AB = (π * r * 38) / 180

Therefore, Arc AB would be (π * r * 38) / 180.

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Yes, the given coordinates X(1,-3), Y(6,1), Z(2,2) are the vertices of a triangle.

1. Calculate the distance between the points X and Y using the distance formula:

d = √[(x2 - x1)2 + (y2 - y1)2]

d = √[(6 - 1)2 + (1 - (-3))2]

d = √[52 + 42]

d = √25 + 16

d = √41

d = 6.4

2. Calculate the distance between the points Y and Z using the distance formula:

d = √[(x2 - x1)2 + (y2 - y1)2]

d = √[(2 - 6)2 + (2 - 1)2]

d = √[(-4)2 + 12]

d = √16 + 12

d = √28

d = 5.3

3. Calculate the distance between the points Z and X using the distance formula:

d = √[(x2 - x1)2 + (y2 - y1)2]

d = √[(1 - 2)2 + (-3 - 2)2]

d = √[(-1)2 + (-5)2]

d = √1 + 25

d = √26

d = 5.1

Since each side of a triangle must have a length greater than 0, and the distances calculated above are all greater than 0, then the given coordinates X(1,-3), Y(6,1), Z(2,2) are the vertices of a triangle.

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-9km is the  displacement for the changes in position from -4km to 5km.

The length along a line or line segment between two points on the line or line segment.

Distance=√(x₂-x₁)²+(y₂-y₁)²

We have to find the displacement for the the following changes in position

-4km to 5km.

Displacement is defined as the change in position of an object. It is a vector quantity and has a direction and magnitude.

-4-5

=-9 km is the displacement.

Hence, -9km is the  displacement for the changes in position from -4km to 5km.

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The system of equations x + 2y = 3, 2x + 4y = 15 is an example of no solution.

If (a₁/a₂) = (b₁/b₂) ≠ (c₁/c₂), then there will be no solution. This sort of system of equations is called an inconsistent pair of linear equations. If we plot the graph, the lines will be parallel, and the system of equations has no solution.

Given equations are x + 2y = 3

2x + 4y = 15

a₁ = 1, b₁ = 2, c₁ = -3

a₂ = 2, b₂ = 4, c₂ = -15

a₁/a₂ = 1/2

b₁/b₂ = 1/2

c₁/c₂  = 1/5

a₁/a₂ = b₁/b₂ ≠ c₁/c₂

So, the system of equations has no solution.

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Answer:

13/30

Step-by-step explanation:

Answer:

b = 11

Step-by-step explanation:

2(3b + 6) = 78 (divide both sides by 2 )

3b + 6 = 39 ( subtract 6 from both sides )

3b = 33 ( divide both sides by 3 )

b = 11

Answer:

2(3b+6) = 78

6b+ 12 = 78

Subtract 12 from both sides

6b+ 12 = 78

6b+12-12=78-12

6b = 66

b = 11

Answer:

perfect square trinomials

Step-by-step explanation:

Comes from (a+b) ^2

Answer:

Step-by-step explanation:

8kg = 8000 grams

New Ratio = 8000:800:4000

Reduced = 20:2:10

Reduced even more = 10:1:5

HOPE THIS HELPED!

The equation (2/3)x = 9/8 represents the question "How many 2/3's are in 9/8?" because it shows that the unknown number of 2/3's (represented by x) multiplied by 2/3 equals 9/8.

What is the equation?

The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that is equal.

The following equation represents the question "How many 2/3's are in 9/8?" because it shows that the unknown number of 2/3's (represented by x) multiplied by 2/3 equals 9/8.

(2/3)x = 9/8

To find out how many 2/3's are in 9/8, you would need to solve for x by dividing both sides of the equation by 2/3.

⇒ x = (9/8)/(2/3)

⇒ x = (9/8) × (3/2)

⇒ x = 27/16

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Answer:

a group of 4 people can be selected in 35 ways

let's put both fractions using the same denominator by multiplying each top and bottom by the other's denominator.

[tex]-\cfrac{1}{8}\cdot \cfrac{11}{11}\implies \boxed{-\cfrac{11}{88}}\hspace{15em}-\cfrac{2}{11}\cdot \cfrac{8}{8}\implies \stackrel{\textit{\LARGE \checkmark}}{\boxed{-\cfrac{16}{88}}}[/tex]

well, let's take a looksie above, on the positive side of the number line, 16/88 is larger than 11/88, however, on the negative side, the closer to "0", the larger, for that matter -1 is a much larger number than -1,000,000.

So, -11/88 is closer to 0 on the negative side, and because of that, is larger than -16/88 that is farther from 0.

Answer:

n = - 8

Step-by-step explanation:

0.4n = 4 + 0.9n ( subtract 0.9 from both sides )

- 0.5n = 4 ( divide both sides by - 0.5 )

n = - 8

The number of teams who took less than 40 minutes to complete the game is 34 teams

0 ≤ t < 20 = 6

time greater than or equal to 0 less than 20 minutes

20 ≤ t < 40 = 28

time greater than or equal to 20 minutes less than 40 minutes

40 ≤ t < 60 = 12

time greater than or equal to 40 minutes less than 60 minutes

60 ≤ t < 80 = 7

time greater or equal to 60 minutes less than 80 minutes

The number of the team who took less than 40 minutes to complete the game are;

0 ≤ t < 20 = 6

20 ≤ t < 40 = 28

So,

6 + 28 = 34 teams

Hence, 34 teams took less than 40 minutes to complete the game.

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The equation is [tex]\rm y = 3 \times \left (0.5 \right)^{t/88}[/tex]. Then the amount remaining after 8 years and 12 years will be 2.8168 grams and 2.729 grams, respectively.

Let a be the initial value and x be the power of the exponent function and b be the factor.

The exponent is given as

y = a(b)ˣ

The function is given below.

[tex]\rm y = a \left (0.5 \right)^{t/88}[/tex]

A scientist is studying a 3-gram sample. Then the function is written as,

[tex]\rm y = 3 \times \left (0.5 \right)^{t/88}[/tex]

The amount of plutonium-238 remaining after 8 years will be given as,

[tex]\rm y = 3 \times \left (0.5 \right)^{8/88}[/tex]

y = 3 × 0.9389

y = 2.8168 grams

From the graph, the amount remaining after 12 years will be 2.729 grams.

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