Math and Arithmetic

360.89 feet

11000 metres=6.8 miles

To solve the expression (12x - 5y - 20) using systems of equations with substitution, you would first need to have a system of equations that includes variables (x) and (y). You can solve one of the equations for one variable in terms of the other, then substitute that expression into (12x - 5y - 20). After substituting, you can simplify the expression to find its value based on the specific values of (x) and (y) from the original system of equations.

To convert 247.25 to a fraction, first separate the whole number and the decimal. The whole number is 247, and the decimal 0.25 can be expressed as ( \frac{25}{100} ), which simplifies to ( \frac{1}{4} ). Therefore, 247.25 can be written as ( 247 \frac{1}{4} ) or as an improper fraction, ( \frac{989}{4} ).

To find the product of a number using two different methods, you can first use the traditional multiplication approach, where you multiply the number by another directly. For example, to find the product of 4 and 5, you can simply calculate (4 \times 5 = 20). Alternatively, you can use addition by repeated summation, where you add 4 together five times: (4 + 4 + 4 + 4 + 4 = 20). Both methods yield the same result.

The starting five for Michigan's "Fab Five," which played in the early 1990s, consisted of Chris Webber, Jalen Rose, Juwan Howard, Jimmy King, and Ray Jackson. This talented group made a significant impact on college basketball, known for their style of play and swagger, as well as reaching the NCAA Championship game in 1992 and 1993. Their influence extended beyond the court, helping to popularize the baggy shorts and a more expressive style of play in the sport.

The quotient of thirty and the product of ten times a number can be expressed mathematically as ( \frac{30}{10x} ), where ( x ) represents the number. Simplifying this expression gives ( \frac{3}{x} ). This means that the quotient decreases as the value of ( x ) increases.

In a three-dimensional coordinate system, the x-axis typically runs horizontally, representing the horizontal dimension, while the y-axis runs vertically, representing the vertical dimension. The z-axis extends perpendicularly from the x-y plane, representing depth or height. Together, these axes define a 3D space where any point can be identified using coordinates (x, y, z).

90

50 to 90

Both are multiples of ;10;

So reduce by '10'.

Hence

5 : 9 :: 50 : 90

NB In mathematica the colon(:) mean 'as to'.

5 to 40

Both numbers are multiples of '5' So cancel down by '5'

Hence

5:40 :: 1:8

The ratio of 8 to 20 can be simplified by dividing both numbers by their greatest common divisor, which is 4. This gives us a simplified ratio of 2 to 5. Therefore, the ratio of 8 and 20 is 2:5.

To find the average of the numbers 20, 22, 23, 26, 26, and 27, first sum them up: 20 + 22 + 23 + 26 + 26 + 27 = 144. Then, divide the total by the number of values, which is 6. So, the average is 144 ÷ 6 = 24.

0.02 ft x 12 inches = 0.24 inches ~ 0.25 inches ( one quarter of an inch).

To convert feet to inches, you multiply the number of feet by 12, since there are 12 inches in a foot. Therefore, 10 feet of cloth equals 10 x 12, which equals 120 inches.

0

square root(4 raised to the fifth) = 32

By 'nesting'

Fifth root of 'x' is x^(1/5)

Then we 'nest' to the square root ( 1/2)

Hence

[x^(1/5]^(1/2) =

x^(1/10) or x^(0.1)

To calculate the volume of your cylindrical tank, use the formula: Volume = π × (radius²) × height. First, find the radius by dividing the diameter (42 inches) by 2, giving you a radius of 21 inches. Convert the dimensions to feet for easier volume calculations (86 inches = 7.17 feet; 21 inches = 1.75 feet). Then, calculate the volume in cubic feet and convert to gallons (1 cubic foot = 7.48 gallons): Volume = π × (1.75²) × 7.17 ≈ 61.56 cubic feet, which equals about 460.5 gallons.

The number of boxes that fit on a standard pallet depends on the size of the boxes and the pallet itself. A standard pallet typically measures 48 inches by 40 inches. For example, if you have boxes that are 12 inches by 12 inches, you could fit 16 boxes on a single layer of the pallet, assuming no space is wasted and the boxes are arranged efficiently. Adjustments must be made for different box sizes and stacking configurations.

To subtract using counters, start with a group of counters representing the minuend (the number you are subtracting from). Next, remove a number of counters equal to the subtrahend (the number you are subtracting). The remaining counters represent the difference, or the result of the subtraction. For example, if you have 5 counters and want to subtract 2, you would remove 2 counters, leaving you with 3 counters.

Our bodies bend in various ways due to the flexibility of our joints, muscles, and connective tissues. Joints, such as hinges in the knees and elbows or the ball-and-socket structure in the shoulders and hips, allow for a range of motion. Muscles and tendons facilitate movement by contracting and relaxing, enabling us to stretch, twist, and flex. Additionally, factors like age, fitness level, and overall health can influence our body's ability to bend and move.

To show that two numbers are proportional in an equation, you can demonstrate that their ratio remains constant. This can be done by rearranging the equation to express one number as a multiple of the other, or by showing that the cross-products of the ratios are equal. For example, if you have two pairs of numbers (a) and (b), and (c) and (d), you can verify proportionality by confirming that (a/b = c/d). If this equality holds, the numbers are proportional.

The Oakley Square Wire sunglasses typically feature a lens width of 57mm, a bridge width of 18mm, and temple length of 135mm. These dimensions may vary slightly depending on specific models or variations within the Square Wire line. The design is known for its lightweight and durable frame, making it suitable for various activities. Always check the specific product details for precise measurements.

To find when both lights change together, we first need to determine the least common multiple (LCM) of their change intervals. The first light changes every 28 seconds, and the second every 32 seconds. The LCM of 28 and 32 is 224 seconds. Therefore, both lights will change together again in 224 seconds.