Clayton wonders what types of sports the students at his school like to play. So, he plans to ask a small sample of them. Pick all the ways of sampling the students that would produce a representative sample.

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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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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For the functions g (x) = 5 x - 2 and h (x) = x² + 1, the value of the composite function g o h (a) will be 5 a² + 3.

We are given the functions:

g (x) = 5 x - 2

h (x) = x² + 1

We first need to find the composite function g o h (x).

So, we get that:

g o h (x) = g ( h (x) )

g o h (x) = 5 ( x² + 1 ) - 2

g o h (x) = 5 x ² + 5 - 2

g o h (x) = 5 x² + 3

Now, we need to find the value of the composite function for x = a. So, we get that:

g o h (x = a) = 5 (a)² + 3

g o h (a) = 5 a² + 3

Therefore, for the functions g (x) = 5 x - 2 and h (x) = x² + 1, the value of the composite function g o h (a) will be 5 a² + 3.

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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

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

Answer:

11

Step-by-step explanation:

Answer:

11

Step-by-step explanation:

Plug in x and y values into the equation

Multiply

Add

Answer:

Step-by-step explanation:

$1.20 dollars

Answer:

1+4=5 23×21=44 44-3=41

Step-by-step explanation:

ANSWER= LOL

Answer:

(4, 2 )

Step-by-step explanation:

y = x - 2 → (1)

y = - 0.5x + 4 → (2)

substitute y = x - 2 into (2)

x - 2 = - 0.5x + 4 ( add 0.5x to both sides )

1.5x - 2 = 4 ( add 2 to both sides )

1.5x = 6 ( divide both sides by 1.5 )

x = 4

substitute x = 4 into (1)

y = 4 - 2 = 2

solution is (4, 2 )

Answer:

Hyperbole

Hope this helps :)

Step-by-step explanation:

This is because she is exaggerating, and hyperoble is when someone exaggerates. She will not really die if she didn't get a job.

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:

You can't. You must be a trusted helper.

Answer:

just message them by messaging them

[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]

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]

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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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 jogging speed of the jogger is 6 miles/hour.

Given that:-

Distance from home to park = 12 miles

Distance from park tp home from a different route = 18 miles

It is also given that the time taken to reach home from park is 1 hour longer than the number of hours taken to reach park from home.

We have to find the speed of the jogger.

Let the time taken by jogger to reach park from home be t hours.

Hence, according to the data given in the question,

Time taken by jogger to reach home from park is (t+2) hours.

We know that,

Speed = distance/time

We know that the speed of jogger in each route is same.

Hence, we can write,

12/t = 18/(t+1)

2/t = 3/(t+1)

2(t+1) = 3t

2t+2 = 3t

t = 2 hours.

Hence, speed of the jogger = 12/2 = 6 = 18/(2+1) = 18/3.

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She needs to locate the squares of the integers between 7.1 and 7.2 in order to estimate √51.

Finding an integer's square root is the inverse of squaring an integer. A number's square value is obtained by multiplying it by itself, whereas the square root of a number can be discovered by looking for a number that, when squared, produces the original value. It follows that a× a = b if "a" is the square root of "b." Every number has two square roots, one of a positive value and one of a negative value because the square of any number is always a positive number.

In the question given to us,

look at the table, we know

(7.1)² = 50.41 and (7.2)² = 51.84

So, (7.1) < √51 < 7.2 { estimate }

They should therefore determine the squares of the numbers between 7.1 and 7.2.

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The complete question is :

Meredith is trying to estimate √51 She uses this table of values:

What should she do next to find √51 to the nearest hundredth?

A. She should find the average of 7. 1 and 7. 2.

B. She should find the squares of numbers between 7. 2 and 7. 3.

C. She should find the squares of numbers between 7. 1 and 7. 2.

D. She should estimate that √51 is 7. 20.

The perimeter of the rectangle in it simplest form is 8x - 10.

The perimeter of a rectangle can be found as follows:

perimeter of a rectangle = 2(l + w)

where

Therefore,

length = 3x - 7

width = x + 2

perimeter of a rectangle = 2(3x - 7 + x + 2)

perimeter of a rectangle = 2(3x + x - 7 + 2)

perimeter of a rectangle = 2(4x - 5)

perimeter of a rectangle = 8x - 10

Therefore, the perimeter of the rectangle in it simplest form is 8x - 10.

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One strategy to eliminate a variable is by multiplying the first equation by 5 and the second equation by 2 and then adding the resulting equations or by multiplying the first equation by 3 and the second equation by 7 and then adding the resulting equations

From the question, we are to determine the strategies that would eliminate a variable in the given system of equations

The given system of equations is

-7x + 2y = 5

3x - 5y = -5

We can eliminate the variable y multiplying the first equation by 5 and the second equation by 2

That is,

5 × [-7x + 2y = 5

2 × [3x - 5y = -5

--------------------------

-35x + 10y = 25

6x - 10y = -10

------------------------

-29x = 15

Also,

We can eliminate the variable x by multiplying the first equation by 3 and the second equation by 7

That is,

3 × [-7x + 2y = 5

7 × [3x - 5y = -5

-------------------------

-21x + 6y = 15

21x - 35y = -35

---------------------

-29y = -20

Hence, one strategy is by multiplying the first equation by 5 and the second equation by 2 and then simplify by adding

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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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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:

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

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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Answer:4.5 hours, 4 hours and 30 minutes, 4 and a half hours

Step-by-step explanation: you are averaging, so you add all of the numbers together and divide that by the number of numbers.

3+6=9, 9 divided by 2=4.5

Answer:

2hours

Step-by-step explanation:

let windows = x

Mrs. Saunders can clean one-third of the windows in an hour = x/3

daughter can clean one-sixth of the windows in an hour = x/6

so,

x/3+x/6 = 1

thus, x = 2

mother and daughter together can clean the windows in 2 hours

Answer:

5

Step-by-step explanation:

5b+3.79

The derivative of a polynomial is the sum of the derivatives of its terms. The derivative of a constant term is 0. The derivative of ax^n is nax^n−1 .

5b^1-1

Subtract 1 from 1.

5b^0

For any term t except 0, t^0 = 1

5×1

For any term t, t×1=t and 1t=t.

5

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:

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

$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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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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