How many different 12-member juries can be chosen from a pool of 45 people

An equation is formed of two equal expressions. The value of the x in the two equation is x=t/(r+s) and x=15m/(ab-cd).

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

A.)

(rx + sx) / t = 1

Multiply both sides of the equating by t,

[(rx + sx)/ t] × t = 1 × t

rx + sx = t

Take x as the common factor from the left side of the equation,

x(r + s) = t

Divide both sides the sides of the equation by (r + s)

(r+s)x/(r+s) = t/ (r + s)

x = t/ (r + s)

B.)

abx - cdx = 15m

Take x as the common factor from left side of the equation,

x(ab - cd) = 15m

Divide both sides of the equation by (ab - cd)

(ab - cd)x / (ab - cd) = (15m)/(ab - cd)

x = 15m/(ab - cd)

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Answer:

3.458 × 10¹⁷

Explanation:

We multiply the amount of salt per liter, 3.5×10⁻², by the amount of sea water in the South China Sea, 9.88×10¹⁸:

(3.5×10⁻²)(9.88×10¹⁸)

Multiplication is commutative; this means we can switch around the numbers we are multiplying:

(3.5×9.88)(10⁻²×10¹⁸)

Multiplying the numbers in the first set of parentheses, we have 34.58.

To multiply the powers of 10, we use the product property; it states that if we multiply powers that have the same base, we add their exponents:

10⁻²×10¹⁸ = 10⁻²⁺¹⁸ = 10¹⁶

This gives us 34.58 × 10¹⁶.  In scientific notation, the decimal must be behind the first non-zero digit; this gives us 3.458.  When we move the decimal again, we add 1 to the exponent; this gives us 3.458 × 10¹⁷

The kilograms of salt in the South China Sea is required.

The amount of salt in the South China Sea is [tex]3.458\times 10^{17}\ \text{kg}[/tex]

The amount of salt in 1 liter of seawater is [tex]3.5\times 10^{-2}\ \text{kg}[/tex]

[tex]1\ \text{liter of seawater}=3.5\times 10^{-2}\ \text{kg of salt}[/tex]

The volume of seawater in the South China Sea is [tex]9.88\times 10^{18}\ \text{L}[/tex]

[tex]9.88\times 10^{18}\ \text{liters of seawater}=9.88\times 10^{18}\times 3.5\times 10^{-2}=3.458\times 10^{17}\ \text{kg}[/tex]

The amount of salt in the South China Sea is [tex]3.458\times 10^{17}\ \text{kg}[/tex]

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13x⁵y³z is the HCF of two given expressions.

The HCF (Highest Common Factor) of two or more numbers is the greatest number among all the common factors of the given numbers. The HCF or GCF of two natural numbers x and y is the largest possible number that divides both x and y without leaving any remainder.

The given expressions are 39x⁷y³z and 91x⁵y⁶z⁷.

Here, the numbers 39 and 91 divisible by 13.

The factor x⁵y³z can divide both the expressions

So, HCF of two given expressions is 13x⁵y³z

Therefore, the HCF is 13x⁵y³z.

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For c = 7, the expression 8x + cy is completely factored.

The correct answer is an option (b)

"It is a mathematical statement with a minimum two numbers or variables and at least one mathematical operation. "

For given example,

We have been given an expression 8x + cy

We need to find the value of c that would make the given expression completely factored.

For c = 2,

⇒ 8x + cy

= 8x + 2y

= 2(4x + y)                         ..............(Factor out common term)

This means c = 2 is not the required value.

For c = 12,

⇒ 8x + cy

= 8x + 12y

= 4(2x + 3y)                         ..............(Factor out common term)

This means c = 12 is not the required value.

For c = 16,

⇒ 8x + cy

= 8x + 16y

= 8(x + 2y)                         ..............(Factor out common term)

This means c = 16 is not the required value.

For c = 7,

⇒ 8x + cy

= 8x + 7y, which is completely factored

This means c = 7 is the required value of c.

Therefore, for c = 7, the expression 8x + cy is completely factored.

The correct answer is an option (b)

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A & B for sure! Hope this helps!!

Hello There!

Mode: Number that occurs most often in a set of numbers

-The mode would be 3-

The number 3 is the only number that occurs 5 times in the set of data. No other numbers appear more than that so our mode is 3.

Mason has 3 1/4 hours of driving remaining to reach Los Angeles.

To calculate the remaining time Mason needs to drive to reach Los Angeles, we subtract the time he has already driven from the total travel time. Mason's total drive time to Los Angeles is 10 1/2 hours, and he has driven for 7 1/4 hours already.

Firstly, we convert the mixed fractions to improper fractions for easy subtraction:

Total drive time: 10 1/2 hours = (10 * 2 + 1) / 2 = 21/2 hours

Time driven: 7 1/4 hours = (7 * 4 + 1) / 4 = 29/4 hours

Now, let's subtract the time driven from the total drive time:

(21/2) - (29/4) hours = (42/4) - (29/4) hours = 13/4 hours

Converting the improper fraction back to a mixed number, we get:

13/4 hours = 3 1/4 hours

Therefore, Mason has 3 1/4 hours remaining until he reaches Los Angeles.

To express sums as products, find the Greatest Common Factor (GCF) of each sum and factor it out, then use the Distributive Property to write the expression as a product.

To express the sums 20+35, 18+27, and 64+40 as products using the Greatest Common Factor (GCF) and the Distributive Property, we need to find the GCF of each pair of numbers and factor it out.

By applying the Distributive Property, we are effectively grouping the common factor outside of the parentheses and leaving the sum of the divided terms inside.

16.6 is a rational number

A rational number is a number that can be expressed as a ratio or a fraction of two integers

Examples of rational numbers are [tex]\frac{3}{7}[/tex], [tex]\frac{1}{2}[/tex]

16.6 can be expressed as [tex]16\frac{6}{10}[/tex] 0r [tex]16\frac{3}{5}[/tex]

An integer is a number without fractions or decimals

For example, integers are 2, 3, 0 - 1000

A whole number is a number that is a positive integer. It does not include negative numbers, fractions or decimals.

Examples are 1, 2, 10

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The surface area of a 3x3x1 rectangular prism is calculated using the formula Surface Area (SA) = 2(lw + lh + wh), resulting in a total surface area of 30 cm².

The surface area of a rectangular prism with dimensions 3x3x1 can be calculated using the formula for surface area of a cube, which is slightly modified for a rectangular prism. The formula is Surface Area (SA) = 2(lw + lh + wh), where 'l' is the length, 'w' is the width, and 'h' is the height of the prism. In this case, the length (l), width (w), and height (h) are 3 cm, 3 cm, and 1 cm respectively.

To calculate the SA:

The surface area of the 3x3x1 rectangular prism is thus 30 cm².

The surface area of a 3x3x1 cube is 54 square units.

To find the surface area of a 3x3x1 cube, we need to calculate the total area of all its faces.

Since the cube has six faces that are all identical squares, we can find the surface area by multiplying the length of one side of the square by itself, and then multiplying that result by 6.

Surface Area = 6 x (3 x 3)

= 6 x 9

= 54

Therefore, the surface area of a 3x3x1 cube is 54 square units.

Answer:

D. 2.4 x 10^10

<3 Enjoy,

    Dea

1mm = 0.001 meter

254 x 0.001 = 0.254 meters long