Algebra

I am going to assume you have a cylindrical tank. The base of a cylindical tank is a circle. The circumference of a circle is 2*Pi*r or Pi*d. So, the circumference of your tank would be Pi*12 ~= 37.7'

MEAN

[x(1) + x(2) + x(3) + x(4) + x(5) + x(6] / 6 = 9

Hence

[x(1) + x(2) + x(3) + x(4) + x(5) + x(6] = 54

RANGE ; x(6) - x(1) = 4

x(6) = 4 + x(1)

MEDIAN ; (x(3)+ x(4)) / 2 = 9

Hence x(3) + x(4) = 18

Substitute

[x(1) + x(2) + 18 + x(5) + x(1) + 4 ] = 54

2x(1) + x(2) + x(5) = 32

Assume x(2) = x(5) for Mode.

Then by substitution

2x(1) + 2x(2) = 32

2(x)1) + x(2)+ = 32

x(1) + x(2) = 16

So x)1) + x(2) = 6 + 10 (max. range) 7+9 or 8+8

Hence

x(1) = 7

x(2) = 9

x(3) = 9

x(4) = 9

x(5) = 10

x(6) = 10

The equation of a line can be expressed in slope-intercept form as ( y = mx + b ), where ( m ) is the slope and ( b ) is the y-intercept. Given a y-intercept of 75 and a slope (rate) of 75, the equation of the line is ( y = 75x + 75 ).

The square root of 3 is greater than 1.7 but less than 1.8. Specifically, its approximate value is about 1.732. Therefore, the square root of 3 is greater than any number less than 1.732.

Rearrange the terms into their rank order.

Already done!!! 63,65,66,75

For an EVEN number of terms; there are four terms here, and four is an even number.

You take the middle two terms, which are ,65, & 66. and find the mid-point between them, Which is 65.5

Hence ' 65.5 ' is the MEDIAN term.

NB If you have an ODD number of terms, 5 in this case, e,g, 63,65,66,66,75. Then you select the absolute middle term, which is ' 66 '.

I'm sorry, but I cannot access specific pages from books, including the Punchline Algebra book B. However, I can help with algebra concepts or problems if you provide more details or context!

To solve this problem, let ( x ) be the ounces of the 13% alcohol solution and ( y ) be the ounces of the 42% alcohol solution. We have two equations:

1. ( x + y = 58 ) (total volume)
2. ( 0.13x + 0.42y = 0.15(58) ) (total alcohol content)

Solving these equations, we find ( x = 24 ) ounces of the 13% solution and ( y = 34 ) ounces of the 42% solution.

x^(3) X x^(5) = x^(3+5) = x^(8)

Remember the coefficient 'x' MUST remain the same for both numbers.

NNB

x^(3) X y(5) is NOT allowed , because the coefficients 'x' & 'y' are different.

This multiplication is expressed as x^(3)y^(5). The indices are NOT added.

The power of '1/3' is another way of expressing the 'cube root'.

Hence 8^(1/3) = 2

Remember

2x2x2 = 8 .

2^(3) 8

Hence

8^(1/3) = 2

(-1/4)^(3) =

-1/4 x -1/4 x -1/4 =

(+)1/16 x -1/4 = -1/64 = -0.015625

(-4)^(4) = (+)256

-4x-4x-4x-4 = (+)16X (+)16 = 256

(256^(1/3))^(4) =

256^(4/3) =

256^(1.3333...... =

1625.498674..... ( The answer)

NB 256 raised to the power of 1/3 , means the 'cube root'. The answer is then raised to the fourth power.

However, under the rules for indices you can muktiply the indices together.

NNB Here are the indices rules.

a^(n) X a^(m) = a^(n+m)

a^(n) / a^(m) = a^(n - m)

(a^( n ))^(m) = a^(nm)

In all cases THE COEFFICIENT 'a' must be the same.

256^(1/4) = '4'

Remember

4x4x4x4 = 256

Hence the fourth root is '4'.

The equation (3v + x = w) represents a linear relationship between the variables (v), (x), and (w). In this equation, (w) is the sum of three times the variable (v) and the variable (x). To isolate any variable, you can rearrange the equation accordingly, such as solving for (x) by subtracting (3v) from both sides, giving (x = w - 3v).

To calculate simple interest, you use the formula: Interest = Principal × Rate × Time. For a principal of $200, an interest rate of 4% (or 0.04), and a time period of 1 year, the calculation would be: $200 × 0.04 × 1 = $8. Therefore, the simple interest earned in one year is $8.

To solve the expression (9x^0 y - 3), first recognize that (x^0) equals 1 for any non-zero (x). Therefore, the expression simplifies to (9y - 3). To further simplify or solve, you would need a value for (y) or additional equations if you are solving for (y).

It seems there might be a typographical error in your question, particularly with the functions you've provided. If ( f(x) = x^2 + 1 ) and ( g(x) = x - 4 ), to find the equivalent values, you would typically need to evaluate either ( f(g(x)) ) or ( g(f(x)) ). Please clarify your question so I can provide a more accurate response!

This is Simultaneous equ'ns.

3x + 5y = -1

2x -5y = 16

Add the two eq'ns. This will eliminate 'y'

Hence

5x = 15

x = 3

When x = 3 , substitute into either eq'n to yimnd 'y'.

Hence

3)3) + 5y = -1

9 + 5y = -1

5y = -10

y = -10/5 = -2

So the solution in ( x,y) form is ( 3, -2).

35

y = x/2 + 1

This is a line of the form y = mx + c

When c = 1 it passes through the y-axis at y = 1

When m= 1/2 ( 0.5) it has a gradient of 1/2 )0.5) . For every two places along in 'x', you go up one place in 'y'.

So to plot two point

s

When x = 1 ; y = 1/2 + 1 = 3/2 ( 1,3/2)

When x - 2 ; y = 2/2 + 1 =. 1 + ` = 2 (2,2)

et seq.,

The line y = x is a straight line of gradient '1' passing through the origin (0,0)

The line/curve y = x^(2) is 'bowl' shaped curve(parabola). with varying gradients, and just touching the origin (0,0).

Pythagoras was a Classical Greek mathematician , who intorduced his famous eq;'n to western civilisation. .

He lived in about 500 BC on the island of Samos ( now in modern Greece).

Her a pre=Socratean philosopher and mathematician .

The expression (x^3 + 1) can be factored using the sum of cubes formula, which states that (a^3 + b^3 = (a + b)(a^2 - ab + b^2)). Here, (a = x) and (b = 1). Thus, the factorization of (x^3 + 1) is ((x + 1)(x^2 - x + 1)).

Form left to right:

(14): Ten trillion

(13): One trillion

(12): Hundred billion

(11): Ten billion

(10): One million

(9): Hundred million

(8): Ten million

(7): One million

(6): Hundred thousand

(5): Ten thousand

(4): Thousand

(3): Hundred

(2): Ten

(1): Unit

The expression "five squared" refers to the mathematical operation of raising the number five to the power of two, which is written as (5^2). This calculation results in (5 \times 5 = 25), not 52. The confusion may arise from the notation, but 52 is simply the number fifty-two and does not have a direct correlation to "five squared."