1. Use properties of logarithms with the given approximations to evaluate the expression. Use logb2=0.693 and/or logb6=1.792 to find logb12.2. Complete parts (a) and (b). a. Write the inverse of y=8x in logarithmic form. b. Graph y=8x and its inverse and discuss the symmetry of their graphs.3. 2log2^15 EVALUATEUse properties of logarithms with the given approximations to evaluate the expression.loga3≈0.477andloga5≈0.699.Use one or both of these values to evaluate loga27.Write as a single logarithm. Assume that variables represent positive numbers.5log2x+2log2zOn the basis of data for the years 1918 through1997, the expected life span of people in a country can be described by the functionf(x)=12.576ln x+17.088 years, where x is the number of years from1905 to the person's birth year. What does this model estimate the life span to be for people born in 1941?This model estimates that the life span for people born in1941 is

The popcorn container can hold 432 cubic inches of popcorn.First, we need to find the volume of the popcorn container. The formula for the volume of a square pyramid is:

Volume = (1/3) * base area * height

To find the base area, we need to first find the area of one of the square sides. Since each side measures 6 inches, the area of one square side is:

Area = side length^2 = 6^2 = 36 square inches

Since the popcorn container is a square pyramid, it has four identical square sides, so the total base area is:

Base area = 4 * 36 square inches = 144 square inches

Now we can plug in the values for the base area and height into the formula for volume:

Volume = (1/3) * 144 square inches * 9 inches

Volume = 432 cubic inches

So the popcorn container can hold 432 cubic inches of popcorn.

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The coordinate of points of the image are:

A' = (-1, 1), B' = (1, 1) and C' = (1, -1)

To dilate the preimage about the origin using a scale factor of 1/3, we can use the following formula:

image coordinate = scale factor * preimage coordinate

Substituting the values, we get:

A' = 1/3 * (-3, 3)

A' = (-1, 1)

B' = 1/3 * (3, 3)

B' = (1, 1)

C' = 1/3 * (3, -3)

C'  = (1, -1)

Thus, the coordinate of points of the image are A' = (-1, 1), B' = (1, 1) and C'  = (1, -1)

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The fraction of the material that each strip represents is 1/12 of a yard.

Susan bought 1/3 of a yard of material to use for the border for the blanket. She cut the material into 4 same-size strips. The problem is asking for the part of a whole yard that each strip represents.

Since Susan has 1/3 of a yard of material and she cut it into 4 same-size strips, we can use division to find the fraction of the material that each strip represents.

Therefore, the fraction of the material that each strip represents is 1/3 ÷ 4.

To divide fractions, we multiply the first fraction by the reciprocal of the second fraction.

The reciprocal of 4 is 1/4, so we can rewrite the expression as:

1/3 ÷ 4 = 1/3 × 1/4

Now we can multiply the fractions:

1/3 × 1/4 = 1/12

Therefore, each strip represents 1/12 of the whole yard of material.

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[tex]\huge\text{Hey there!}[/tex]

[tex]\mathsf{(3\times10^6) + (5\times10^7)}\\\mathsf{= (3\times10\times10\times10\times 10\times10\times10) + (5\times 10\times10\times10 \times 10\times10\times10 \times 10)}\\\mathsf{= (3\times 100\times100\times100) + (5\times100\times100\times100\times10)}\\\mathsf{= (3\times10,000\times100) + (5\times10,000\times1,000)}\\\mathsf{= (3\times1,000,000) + (5\times10,000,000)}\\\mathsf{= (3,000,00) + (50,000,000)}\\\mathsf{= 3,000,000 + 50,000,000}\\\mathsf{= 53,000,000}\\\mathsf{= 5.3\times10^7}[/tex]

[tex]\huge\text{Therefore your answer should be:}\\\huge\boxed{\mathsf{5.3\times10^7}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

The differential equation with initial conditions describing the motion is F = -k * (s(t) + 5) - 6g and the displacement of the mass from its equilibrium position as a function of time s(t) = (3 * r2 * e^(r1*t)) / (r2 - r1) + (3 * r1 * e^(r2*t)) / (r1 - r2)

The differential equation for the motion of the mass is given by Newton's Second Law, F = ma:

F = -k * (s(t) + 5) - 6g

where k is the spring constant, s(t) is the displacement from the equilibrium position, and g is the acceleration due to gravity. The initial conditions are s(0) = 3 and s'(0) = 0, since the spring is initially stretched an additional 3 cm and released from rest.

We can rearrange the equation to get:

s''(t) + (k/6) * s(t) = -5k/6 - g

This is a second-order linear homogeneous differential equation with constant coefficients. The general solution is:

s(t) = C1 * e^(r1*t) + C2 * e^(r2*t)

where r1 and r2 are the roots of the characteristic equation:

r^2 + (k/6) * r = -5k/6 - g

Using the quadratic formula, we get:

r1,2 = -(k/12) ± √((k/12)^2 + 5k/6 + g)

We can find the values of C1 and C2 by applying the initial conditions:

s(0) = C1 + C2 = 3

s'(0) = C1 * r1 + C2 * r2 = 0

Solving for C1 and C2, we get:

C1 = (3 * r2) / (r2 - r1)

C2 = (3 * r1) / (r1 - r2)

Substituting back into the general solution, we get:

s(t) = (3 * r2 * e^(r1*t)) / (r2 - r1) + (3 * r1 * e^(r2*t)) / (r1 - r2)

This is the displacement of the mass from its equilibrium position as a function of time.

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Answer: x-3

Step-by-step explanation: if Martin's age is unknown and we have to use x for it, you could only plug in x-3 to figure out Jennifer's age. And if we have to write an expression for Connor's age it would be x*2

martin = x years

jennifer = x - 3

The volume of this cylinder is equal to 7,771.5 cubic millimeter

In Mathematics, the volume of a cylinder can be calculated by using this formula:

Volume of a cylinder, V = πr²h

Where:

Since the radius of the base is 15 mm and the height of this cylinder is 11 mm, the volume of the cylinder in cubic millimeter can be calculated as follows;

Volume of a cylinder, V = 3.14 × 15² × 11

Volume of a cylinder, V = 3.14 × 2,475

Volume of a cylinder, V = 7,771.5 cubic millimeters.

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Answer:

I really want to help you!

Factored completely:

2x2(−x−2)(x−7)

Step-by-step explanation:

Answer:

The final answer is 18-2 = which is 16

Step-by-step explanation:

x =3

y =2

6(3) -2

Then do 18-2

You have to multiply 6 and 3, after that, subtract by 2

Just substitute your value in!

Answer:

16

Step-by-step explanation:

6x - y =

6 * 3 - 2 =

18 - 2 =

16

The length οf the thermοmeter is 16 1/4 inches.

Any instrument that measures temperature οr a thermal diffusivity is called a thermοmeter (the degree οf hοtness οr cοldness οf an οbject). Twο crucial cοmpοnents make up a thermοmeter:

(1) a temperature sensοr that changes in respοnse tο changes in temperature (fοr example, the mercury-in-glass thermοmeter's bulb οr an infrared thermοmeter's pyrοmetric sensοr);

(2) a way tο translate this change intο a specific number (e.g. the visible scale that is marked οn a mercury-in-glass thermοmeter οr the digital readοut οn an infrared mοdel). In technοlοgy, business, meteοrοlοgy, medicine, and scientific research, thermοmeters are frequently used tο track prοcesses.

Tο find the length οf the thermοmeter, we need tο add the distance abοve the water tο the distance belοw the water.

Distance abοve water: 3/4 inch

Distance belοw water: 31/2 inches

The tοtal length οf the thermοmeter:

3/4 + 31/2 = 6/8 + 124/8 = 130/8 = 16 1/4 inches

Therefοre, the length οf the thermοmeter is 16 1/4 inches.

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Answer:

need brainly point

Step-by-step explanation:

[  1  -0.0004    -0.00202    |  0.0404 ] [  0   1         -0.00020828 |  6] this is the Gauss Jordan elimination method step by step of the given linear equation.

The Gauss Jordan elimination method is a systematic way of solving a system of linear equations by performing elementary row operations on an augmented matrix. The augmented matrix is formed by combining the coefficients and constants of the linear equations.

The given system of linear equations can be written in matrix form as:

[  99  -0.04  -0.2  |  4  ]

[ -0.1  0.97   0    |  6  ]

[ -0.2  -0.01  0.96 |  3  ]

The goal of the Gauss Jordan elimination method is to transform the augmented matrix into reduced row echelon form, which is a unique form that represents the solution of the system of linear equations.

The following steps outline the Gauss Jordan elimination method to solve the given system of linear equations:

Step 1: Begin with the first column and eliminate the coefficients below the first row by using row operations.

Divide the first row by 99 to make the leading coefficient equal to 1:

[  1   -0.0004  -0.00202  |  0.0404  ]

[ -0.1  0.97     0        |  6       ]

[ -0.2 -0.01     0.96     |  3       ]

Add 0.1 times the first row to the second row:

[  1   -0.0004  -0.00202  |  0.0404 ]

[  0   0.9704  -0.000202 |  6.00404]

[ -0.2 -0.01     0.96     |  3      ]

Add 0.2 times the first row to the third row:

[  1   -0.0004  -0.00202  |  0.0404 ]

[  0   0.9704  -0.000202 |  6.00404]

[  0   -0.00018  0.960396 |  3.00808]

Step 2: Continue with the second column and eliminate the coefficients below the second row by using row operations.

Divide the second row by 0.9704 to make the leading coefficient equal to 1:

[  1  -0.0004    -0.00202    |  0.0404 ]

[  0   1         -0.00020828 |  6.18377]

[  0  -0.00018    0.960396   |  3.00808]

Add 0.00018 times the second row to the third row:

[  1  -0.0004    -0.00202    |  0.0404 ]

[  0   1         -0.00020828 |  6.18377]

[  0   0.0000324  0.96052174|  3.01998]

Step 3: Continue with the third column and eliminate the coefficients above the third row by using row operations.

Divide the third row by 0.96052174 to make the leading coefficient equal to 1:

[  1  -0.0004    -0.00202    |  0.0404 ]

[  0   1         -0.00020828 |  6]

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The value of x in the triangle is 2√3

Right triangles are triangles with one angle measuring 90 degrees.

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

The triangle

From the triangle, we have the following equation

x/2 = 6/x

Cross multiiply the equation

So, we have the following representation

x^2 = 12

Take the square roots of both sides

So, the equation becomes

x = 2√3

Hence, the value of x is 2√3

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The correct option is D. Inequality. The expression -9 > 2x is an inequality, meaning it shows a relationship between two values that are not necessarily equal.

In this case, it indicates that -9 is greater than 2 times x. To solve the inequality, we would need to isolate x on one side of the inequality symbol. We can start by dividing both sides by 2, which gives us -4.5 > x. This means that any value of x that is less than -4.5 would satisfy the inequality. Therefore, the solution set for this inequality is all real numbers less than -4.5.

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Full question:

Which word BEST describes 9(2x+6y)

A Constant

B. Equation

c. Expression

D. Inequality

A repeated-measures experiment comparing two treatment conditions, the t statistic has a df of 31. 32 subjects participated in this study.

A matched-subjects experiment produced a t statistic with a df of 17.

34 subjects participated in this study.

Both a repeated-measures experiment and a matched-subjects experiment share the following characteristics when used to compare two treatment conditions:

1. They both use the same t statistic.
2. The researcher computes difference scores to compute a t statistic.
3. The researcher must compute an estimated standard error for the mean difference score to compute a t statistic.

For a repeated-measures experiment comparing two treatment conditions, the t statistic has a df of 31.

The number of subjects that participated in this study is 32 because the degrees of freedom (df) for a repeated measures experiment is calculated as (number of subjects - 1),

so 31 + 1 = 32.

A matched-subjects experiment produced a t statistic with a df of 17.

In this case,

the number of subjects that participated in the study is 34 because the degrees of freedom (df) for a matched-subjects experiment is calculated as (number of pairs - 1),

since there are two subjects in each pair, 17 + 1 = 18 pairs, which means 18 * 2 = 34 subjects.

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the area of the figure will be 15cm²

What is square?

Having four equal sides, a square is a quadrilateral. There are numerous square-shaped objects in our immediate environment. Each square form may be recognized by its equal sides and 90° inner angles. A square is a closed form with four equal sides and interior angles that are both 90 degrees. Numerous different qualities can be found in a square.

We are given that rajiv wishes to make a cube without lid with cardboard.

the area will be = area of square+area of rhombus

area of square = 3² = 9 cm²

area of rhombus = 2cm * 3cm =6cm²

The total area will be 15cm²

Hence the area of the figure will be 15cm²

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Answer:

watch sean delete this LOL IMAGINE HAVING TO DO THAT BC YOU SUK

the area of the figure will be 15cm²

What is square?

Having four equal sides, a square is a quadrilateral. There are numerous square-shaped objects in our immediate environment. Each square form may be recognized by its equal sides and 90° inner angles. A square is a closed form with four equal sides and interior angles that are both 90 degrees. Numerous different qualities can be found in a square.

We are given that rajiv wishes to make a cube without lid with cardboard.

the area will be = area of square+area of rhombus

area of square = 3² = 9 cm²

area of rhombus = 2cm * 3cm =6cm²

The total area will be 15cm²

Hence the area of the figure will be 15cm²

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Step-by-step explanation:

In response to the query, we can state that Therefore, the area of the base of the triangular pyramid is 21 square inches.

A pyramid is a polygon in mathematics, formed by connecting points referred to as bases and polygonal vertices. For each hace and vertex, a triangle called a face is formed. a cone with a polygonal form. A pyramid with a floor and n pyramids has 2n edges, n+1 vertices, and n+1 vertices. Each pyramid is dual in itself. Pyramids can be seen in three dimensions. The vertex, the intersection of a pyramid's flat tri face and polygonal base, is where they come together. The base and apex are connected to form a pyramid. Triangle faces that connect to the top are formed by the edges of the base.

volume of a triangular pyramid

V = (1/3) * Base Area * Height

65 = (1/3) * Base Area * 9.75

Area = 65 / (1/3) / 9.75

Area = 21

Therefore, the area of the base of the triangular pyramid is 21 square inches.

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Answer: The difference between 125 million dollars and 312.5 million dollars is, 187.5 Million Dollars.

Answer:

Step-by-step explanation:

The sine model is y=10 sin(1/30 t) + 30.  The 30 represents default distance from the ground, and the ten is required to represent the length of the blades.  Every 30 seconds, one rotation completes, so t must be multiplied by 1/30.

Answer:

[tex]\mbox{\large y = -\dfrac{3}{5}x - 4}[/tex]

Step-by-step explanation:

The given equation is
[tex]\mbox{\large 6x + 10y = - 40}[/tex]

The slope-intercept form of the equation of a line is
[tex]y = mx +b[/tex]

where
m = slope

b = y-intercept

Subtract 4x from both sides of [tex]\mbox{\large 6x + 10y = - 40}[/tex]

[tex]6x - 6x + 10y = - 6x-40\\\\\rightarrow \quad 10y = -6x - 40\\\\\text{Divide both sides by 10}\\\rightarrow \quad \dfrac{10y}{y} = -\dfrac{6}{10}x - \dfrac{40}{10}\\\\y = -\dfrac{6}{10}x - 4\\\\\dfrac{6}{10} = \dfrac{3}{5}\\\\\text{Equation of the line in slope-intercept form is: }\\\\y = -\dfrac{3}{5}x - 4[/tex]

The third side of the given Pythagorean triple-right-angled triangle is 32.02 units.

As per the formula pertaining to the Pythagorean triple-right-angled triangle, we have the:

h = √{(a)^2+(b)^2} .........(i),

Where, (h) = Third side of a Pythagorean triple-right-angled triangle,

(a) = First side of a Pythagorean triple-right-angled triangle = 20 units

(b) = Second side of a Pythagorean triple-right-angled triangle = 25 units

Substituting the values in equation (i), we get:

h = √{(20)^2+(25)^2} units,

or, h = √(1025) units,

or, h = 32.015 units = rounded off to 32.02 units.

Hence the third side of the given Pythagorean triple-right-angled triangle is 32.02 units.

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The area of the rectangle is 31/3 square centimeters or 10 1/3 square centimeters as a mixed number.

To find the area of the rectangle, we need to multiply its length by its width.

First, we need to convert the mixed numbers to improper fractions:

Length = 5 1/6 cm = (6 × 5 + 1)/6 = 31/6 cm

Width = 2 2/7 cm = (7 × 2 + 2)/7 = 16/7 cm

Now, we can multiply the two fractions to get the area of the rectangle:

Area = length × width

= (31/6 cm) × (16/7 cm)

= (31 × 16) / (6 × 7) cm²

= 496/42 cm²

= 248/21 cm²

We can simplify this fraction by dividing both the numerator and denominator by their greatest common factor (GCF), which is 8:

248/21 cm² = (8 × 31)/ (8 × 3) cm²

= 31/3 cm²

= 10 1/3 cm²

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Answer: 34

Step-by-step explanation:

based on the given conditions , formulate

[tex]\sqrt{16^2+30^2}[/tex]

x= [tex]\sqrt{(16)^2f(30)^2}[/tex]

x= [tex]\sqrt{256+900}[/tex]

x= [tex]\sqrt{11 56}[/tex]

x=  34

A. x+x+11 is the expression can be best simplified for equation 2x+11

A statement that establishes the equivalence of two expressions is known as an equation in mathematics. It has two sides containing expressions on each, each separated by the equals symbol (=).

For example, the equation x + 2 = 5 asserts that the expression on the left side, x + 2, is equal to the expression on the right side, 5. This equation can be solved for the variable x, by subtracting 2 from both sides, to obtain x = 3, which is the value that satisfies the equation.

Given equation 2x+11

2x can be written as x+ x

So, expression can be written as

x+x+11

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The car's value will decrease at rate of 1/5.

Rate refers to the ratio between two quantities with different units. For example, if you travel 100 miles in 2 hours, your rate of speed would be 50 miles per hour (mph).

From the graph, we have the following:

1: At mileage (x) = 20,000 miles, value of car (y) = $12000

2: At mileage (x) = 40,000 miles, value of car (y) = $8000

Rate = (y2 - y1)/(x2 - x1)

Rate = (8000 - 12000)/(40000 - 20000)

Rate = -1/5

Thus, the car's value will decrease at rate of 1/5.

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Complete Question

Check attached image

The resultant force on the box, along with it's direction, is given as follows:

5N Down.

The resultant force on the box is obtained as the vector sum of all the forces in the box.

The forces are given as follows:

The horizontal forces are the same force in opposite directions, hence the horizontal forces are of zero.

The sum of the vertical forces is given as follows:

5 - 10 = -5N.

As the sum is negative, the direction is in the down direction, hence the resultant force is of -5N down.

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In linear equation, 103000  is the minimum acceptable settlement on a case on which the attorney spent 110 hours.

What in mathematics is a linear equation?

An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.

                           Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.

Let x be the amount settlement.

  amount he earn from client = 175 * 110

                                         = 19250

     amount he earn from settlement = x * 25/100  = x/4

        according to given condition

                         19250 + x/4 ≥ 45000

                     x/4 ≥ 45000 - 19250

                    x/4 ≥ 25750

                    x ≥ 25750 * 4

                     x ≥ 103000

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Answer:

1.65

Step-by-step explanation:

The first number is 1.95, to find the rest we must keep subtracting 0.15 from the previous.

1.95-0.15 = 1.8 (second number)

1.8-0.15 = 1.65 (third number)

Above, we find our answer with the 3rd number.