A desktop world globe has a volume of about 1386 cubic inches. The radius of Earth is approximately equal to the radius of the globe raised to the 10 th power. Find the radius of Earth. (Hint: Use the formula V=⁴/₃πr³ for the volume of a sphere.)

Step-by-step explanation:

2x-4 > 8 or 3x-1 < -10

Grouping the like terms

2x > 8 +4 or 3x < -10 +1

2x > 12 or 3x < -9

2x > 12 3x < -9

2 2 3 3

x > 6 or x < -3

The expressions represents “the difference between a number and eleven” is (n - 11) while, for the second case, the one statement which does not represent the same concept, among the four options provided is "a number minus five".

As per question statement, we are provided with two separate questions, first one requiring us to determine the expressions represents “the difference between a number and eleven”, while the second one requiring us to determine the one statement which does not represent the same concept, among the four options provided.

Considering the first case, the statement “the difference between a number and eleven”, considering the number to be "n" can be mathematically expressed as [tex](n - 11)\\[/tex]. Hence, the correct answer is [tex](n - 11)\\\\[/tex].

Coming to the second case, considering the number to be "n",

Option (A) is "a number minus five" which when mathematically stated becomes [tex](n-5)[/tex]

Option (B) is "five more than a number" which when mathematically stated becomes [tex](n+5)[/tex]

Option (C) is "the sum of a number and five" which when mathematically stated becomes [tex](n+5)[/tex]

And, option (D) is "a number increased by five" which when mathematically stated becomes [tex](n+5)[/tex].

That is, Option (B), (C) and (D) all belong to the same concept. Hence, the one statement which does not represent the same concept, among the four options provided is "a number minus five".

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Answer:

10

Step-by-step explanation:

it us a right triangle so we can use the equation

a^2 + b^2 = c^2

6^2 + 8^2 = c^2

36 + 64 = c^2

100 = c^2

10 = c

After rounding off the whole number it becomes 12,346.

According to the statement

We have to find that the value of the whole number.

So, For this purpose, we know that the

The whole numbers are the numbers without fractions and it is a collection of positive integers and zero.

From the given information:

The given number is a 12,345.6789

Then

We know that the

Rounding off means a number is made simpler by keeping its value intact but closer to the next number. It is done for whole numbers etc.

The number

12,345.6789

Its round off to the

12,346

Because when the number greater than 5 comes after the point then while rounding off we increased the number by 1.

So, After rounding off the whole number it becomes 12,346.

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The inverse function is written as  [tex]f^{-1}(x)[/tex] =x³+15x²+75x+125 and the inverse is a function.

The inverse of a function is defined as the opposite function . Ideally we use a function to map the dependent variable y based on the independent variable x. Inverse function is the relation which defines the value of x depending on a particular value of y.

For an inverse function the domain of the function changes to the range and vice-versa.

Mathematically for a function defined as y=g(x) where g(x) is a polynomial of x . We solve the equation for x in terms of y.

Given function is g(x)=∛x-5

Therefore it can be written as

y= ∛x-5

or, y+5=∛x

Cubing both sides we get:

(y+5)³=(∛x)³

or, y³+15y²+75y+125=x

or, x=y³+15y²+75y+125

So the inverse function can be written as:

[tex]f^{-1}(x)[/tex]=x³+15x²+75x+125 and the inverse function exists.

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f(2) is -8

According to the question,

Given that,

f(x)=2x-3x^2

Substitute x = 2 into f(x) = 2x-3x^2

f(2)=2x-3x^2

f(2)=2x2 - 3x [tex]2^{2}[/tex]

f(2)= 4 - 3 x 4

f(2)= 4 - 12

f(2)= - 8

In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an ‘equal’ sign. The most basic and simple algebraic equations consist of one or more variables in math.

Example of an Equation:

4y + 2 = 18

4×2 + 3x − 28 = 0

9m = 49.5

Equation Types

Algebra considers two prominent families of equations, namely polynomial equations and linear equations. Polynomial equations with one variable can be written in P(x) = 0, where P is a polynomial, and ax + b = 0 is the general form of linear equations. Here, a and b are parameters. We can practice geometric or algorithmic methods from linear algebra or mathematical analysis to solve these equations. Also, there are different types of equations, such as:

Linear equations

Quadratic equations

Cubic equations

Quartic equations

Differential equations

Parametric equations

Equation of a line

The standard form of the equation of a line is A x + By + C = 0. The slope-intercept form of an equation is y = mx + b, where m is the slope of the line and b is the y-intercept. However, there are various types of equations to represent lines.

Equation of x-axis

Generally, we say that the equation of the x-axis equation is of the form y = 0. However, we can also write the x-axis equation as x = c where c is constant.

The x-axis comprises all the real values of x, although the value of y is equal to 0 on the complete x-axis.

Thus, x can be recognised as constant and y as 0.

In the coordinate system representation, we can represent any point on the x-axis as (c, 0), where c is any real number.

Therefore, the x-axis formula will be x= c + y

Here,

c = constant

y = 0

The x-axis formula is x = c, where c is constant.

Equation in One Variable

The equation in one variable means the equation containing only one variable. Let’s have a look at the below equations.

17 – 9 = 8

x + 4 = 4y + 22z

4x2 + 3x – 7 = 0

The three examples above represent equations that propose equality (could be true or not) between two expressions.

The first equation does not contain any variable.

The second equation has three different variables, such as x, y and z. Thus, it is a multivariate equation.

The third equation contains only one variable, i.e. x.

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Answer:

[tex]\frac5{12}[/tex]

Step-by-step explanation:

[tex]\frac34 - \frac13\\\\\to \frac34 \times \frac33 - \frac13 \times \frac44\\\\\to \frac9{12} - \frac4{12}\\\\\to \frac{9 - 4}{12} \to \frac5{12}[/tex]

We need to know about logarithm to solve this problem. The answer of the given algorithm is -4.

Logarithm is the exponent that a base needs to be raised to get a certain number. There are a few rules of algorithm, log a + log b can be written as log ab, log a- log b can be written as log a/log b. When a number whose logarithm is being calculated is raised to a power, the power can be multiplied to the log itself. In this question we have to find the logarithm of 625 with base 1/5. To find the logarithm of this number we need to first write 625 in terms of 1/5, the log of number same as base is equal to 1.

[tex]log_{\frac{1}{5} } 625=-log_{\frac{1}{5} } (\frac{1}{5} )^{4} =-4log_{\frac{1}{5} } \frac{1}{5} =-4[/tex]

Therefore we found out the logarithm of 625 with base 1/5 to be -4.

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If PQR is similar to WXY and PQ=12 cm and WX=9 cm and the area of WXY is 72cm², then the area of PQR is equal to 128 cm².

The area of PQR can be determined by first finding the scale factor. The scale factor in mathematics can be defined as the ratio of the length of a side of one figure (which in this case is a triangle) to the length of the side of a similar figure.

Therefore, the scale factor = 9 / 12

Now by using theorem 61,

area ΔWXY / area ΔPQR = (9/12)²

As the area of WXY = 72cm², therefore;

72 / area ΔPQR = 81 / 144

81 (area ΔPQR) = 144 × 72

81 (area ΔPQR) = 10,368

area ΔPQR = 10,368 / 81

area ΔPQR = 128 cm²

Hence, the area of PQR is calculated to be 128 cm².

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Answer:

length = 23 inches , width = 4 inches

Step-by-step explanation:

let width be w then length l = 2w + 15

the perimeter P is calculated as

P = 2l + 2w

given P = 54 , then

2(2w + 15) + 2w = 54

4w + 30 + 2w = 54

6w + 30 = 54 ( subtract 30 from both sides )

6w = 24 ( divide both sides by 6 )

w = 4

l = 2w + 15 = 2(4) + 15 = 8 + 15 = 23

the length is 23 inches and width is 4 inches

California   has the greatest area of each state.

What does a math area mean?

So, we know that

         Montana  =    5 * 9 =  45 grids

California  = 15 + 16 + 14 + 6 = 51 grids

                          45 < 51

California   has the greatest area .

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The solution for the equation ln 5 x=4 is 10.92.

ln 5 x=4

5 x = [tex]e^{4}[/tex]

x = 10.92

A formula would be 3x - 5 = 16, for instance. When this equation is solved, we discover that the value of the variable x is 7.

The point-slope form, standard form, and slope-intercept form are the three main types of linear equations.

A formula that expresses the connection between two expressions on each side of a sign. Typically, it has a single variable and an equal sign.

Two expressions joined by the equals symbol ("=") form an equation. The "left hand side" and "right hand side" of the equation are the expressions on either side of the equals sign. The right side of an equation is frequently considered to be zero.

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After direct variation y = 2 when x = -3.

So,

The initial statement is y = kx

Then to find y when x = -3.

When x = -3:

Therefore, y = 2 when x = -3.

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Answer: i think that it is 2/-6

Step-by-step explanation:

Answer:

[tex]y10 = - 5[/tex]

The statement "15.7 is less than 15.245 because 15.27 has fewer digits after the decimal point than 15.245" is false

The statement is given as

15.7 is less than 15.245 because 15.27 has fewer digits after the decimal point than 15.245

When comparing greater and lesser values, we do not make use of the number of digits in them

Instead, we compare the values

Though, 15.7 is less than 15.245 but the reason is that 15.27 has lesser value than 15.245

Hence, the statement "15.7 is less than 15.245 because 15.27 has fewer digits after the decimal point than 15.245" is false

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Answer:

Step-by-step explanation:

Recursive formula is used to represent the terms using the previous term of the sequence.

Using the explicit equation find the first two terms and their difference:

The recursive formula for this sequence is:

Answer:

0.14*10⁻¹ seconds

Step-by-step explanation:

3 × 10⁸ = 30*10⁷

Then:

4.2*10⁷ / 30*10⁷ = 4.2/30 = 0.14

0.14 = 1.4*10⁻¹ seconds

The Lateral Surface Area of a Right triangular prism is given by:

= (a + b + c) × h

= (ah + bh +ch)

where a, b and c are the dimensions of base and h is the height of the Right triangular prism.

The given dimensions of base are:

a = 5 cm

b = 2.5 cm

c = 5.6 cm

The height of the Right triangular prism is 8 cm.

Now, the Lateral Surface Area of a Right triangular prism will be

= (5 + 2.5 + 5.6) × 8

= (40 + 20 + 44.8)

= 104.8 [tex]cm^{2}[/tex]

Therefore, the Lateral Surface Area of the Right triangular prism is 104.8 [tex]cm^{2}[/tex].

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The slope of the line that passes through (-4, 2) and (-5, 0), in simplest form is calculated as: 2.

The slope of a line (m) = change in y/change in x = y2 - y1/x2 - x1 or rise/run of the line.

Given the following points on the line:

(-4, 2) = (x1, y1)

(-5, 0) = (x2, y2)

Substitute the values into m = y2 - y1/x2 - x1:

Slope (m) of the line = (0 - 2) / (-5 - (-4))

Slope (m) of the line = (-2) / (-5 + 4)

Slope (m) of the line = -2/-1

Slope (m) of the line = 2

Thus, the slope of the line that passes through (-4, 2) and (-5, 0), in simplest form is calculated as: 2.

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$6208.86 amount should be put into an account that pays 5.2% annual interest compounded.

It is given that a student wants to save $ 8000 for college in five years having interest 5.2% annual interest compounded .

Putting [tex]A=\$8000 , \ r= 5.2\% , \ t=5 \ years[/tex] in equation (1) , we get

  [tex]8000=P(1+\frac{5.2}{100} )^5\\\\8000=P(1+0.052)^5\\\\8000=P(1.052)^5\\\\8000=1.28848P\\\\P=\$6208.86[/tex]

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Answer:

The square root of 400 is represented by √400, where ‘√’ represents a radical and a radicand represents its value. It is rational to multiply 400 by 20, which is 20. Simple prime factorization or long division can be used to find the square root. Taking the square root of 400, we get √400 = ±20

Step-by-step explanation:

Answer:

b = a² - 6

Step-by-step explanation:

a = [tex]\sqrt{b+6}[/tex] ← square both sides to clear the radical

a² = b + 6 ( subtract 6 from both sides )

a² - 6 = b

Answer:

Point G

Step-by-step explanation:

It is point G because since you mirrored it and flipped it, you need to flip figure one and if you move it to where figure two is, in the same place, the new point R is where point G is, so G corresponds to R

The inequality expression 6 <= x < 15 to represent the statement "a number is at least 6 and less than 15"

Expressions are mathematical statements that are represented by variables, coefficients and operators

The mathematical statement is given as

a number is at least 6 and less than 15.

Represent the number with x

So, we have

x is at least 6 and less than 15.

At least 6 means greater than or equal 6

So, we have

x >= 6

Less than 15

So, we have

x < 15

When the above expressions are combined, we have

6 <= x < 15

Next, we plot the inequality expression 6 <= x < 15 to represent the statement "a number is at least 6 and less than 15"

See attachment for the inequality expression

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Answer: I don't know if this is scientific notation, but I got 900 gallons.

Step-by-step explanation:

1.5 x 10 = 15

15 x 60 = 900

(I used 60 because there's 60 seconds in one minute)

The equation has just two solutions, which are 11 and 7.

While the inequality will have a range of solutions, which is:

7 ≤ w ≤11

That is the difference.

Here we have an inequality:

|w - 9| ≤ 2

And an equation:

|w - 9| = 2

To solve these we can start by solving the equation, it gives two equations:

w - 9 = 2

w - 9 = -2

With these we can get two solutions for w,:

w = 2 + 9 = 11

2 = -2 + 9 = 7

Then the equation has just two solutions, which are 11 and 7.

While the inequality will have a range of solutions, which is:

7 ≤ w ≤11

That is the difference between the two.

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Answer:  9v=162

Step-by-step explanation:

If you need the answer, Victors height is 18.

9v = 162

/9       /9

V = 18

Step-by-step explanation:

we are given a variable of victors height as v

according the expression

9 × v = 162

9v = 162

divide both sides by 9

v = 18

Answer:

160π

Step-by-step explanation:

The surface area of a right circular cylinder can be calculated using the following equation:

[tex]\boxed{\mathrm{Surface \ area = }2 \pi rh + 2 \pi r^2}[/tex] ,

where h is the height and r is the radius of the base of the cylinder.

We are told that the rod is 16 inches tall, therefore h = 16. We are also told that the radius of the base is 4 inches, therefore r = 4. Using this information along with the formula above, we can calculate the surface area of the metallic rod:

Surface area = [tex](2 \times \pi \times 4 \times 16) + (2 \times \pi \times (4)^2)[/tex]

                     = [tex]128\pi + 32\pi[/tex]

                     = [tex]\bf 160\pi[/tex]

Therefore the surface area of the metallic rod is 160π.

Answer:

[tex]144\pi \: or \: 145\pi[/tex]

SA to cylinder is

[tex]2\pi \: rh + \pi \: r {}^{2} [/tex]

=2

[tex] 2 \times \pi \times r \\ \times h + \pi \times r {}^{2} [/tex]

2

[tex]2\pi \times 4 \times 16 + \pi \times 4 \times 4[/tex]

answer =

[tex]144\pi \: to \: 145\pi[/tex]

Answer:

11

Step-by-step explanation:

Answer:

11

Step-by-step explanation:

Plug in x and y values into the equation

Multiply

Add

[tex]~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{2}~,~\stackrel{y_1}{19})\qquad (\stackrel{x_2}{32}~,~\stackrel{y_2}{y})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ \stackrel{d}{34}=\sqrt{(32-2)^2 + (y-19)^2}\implies 34^2=(32-2)^2 + (y-19)^2 \\\\\\ 1156=30^2 +(y-19)^2\implies 1156=900 + (y-19)^2\implies 256=(y-19)^2 \\\\\\ \pm\sqrt{256}=\pm\sqrt{(y-19)^2}\implies \pm 16=\pm (y-19)\implies \mp 16 =y - 19 \\\\\\ \mp 16 + 19 = y\implies y= \begin{cases} 3\\ 35 \end{cases}[/tex]