The probability of the complement of an event is ____ less than the probability of the event itself.
A. Not enough information provided to answer the question.
B. Sometimes
C. Always
D. Never

Answer:

Number of granola bars that Josh gave to each of his friend =3

Number of fruit drinks that Josh gave to each of his friend =4

Step-by-step explanation:

Number of granola bars with Josh = 42

Number of fruit drinks with Josh = 56

He wants to give the same number of granola bars and fruit drinks to each friend.

To find : Number of granola bars and fruit drinks Josh give to each friend.

First, find HCF of 42 and 56 .

[tex]42=2\times 3\times 7\,,\,56=2^3\times 7[/tex]

Therefore, HCF ( 42, 56 ) = Highest common factor of 42 and 56 = 14

Number of granola bars that Josh gave to each of his friend = Number of granola bars with Josh / HCF ( 42, 56 )

= 42/14 = 3

Number of fruit drinks that Josh gave to each of his friend =  Number of fruit drinks with Josh / HCF ( 42, 56 )

= 56/14 = 4

3x-82 = x-6

subtract 1 x from each side

2x -82 = -6

add 82 to each side

2x = 76

divide both sides by 2

x = 76/2 =38

x = 38

Check:

3(38)-82 = 38-6

3*38 = 114, 114-82 =32 and 38-6 = 32 32 = 32 TRUE

1st piece = x

2nd piece = x+2

3rd piece = x+2+3 = x+5

37 = x +x+2 + x+5 =

37 = 3x+7

30=3x

x = 30/3 = 10

 1st piece = 10 inches

 2nd piece = 10+2 = 12 inches

 3rd piece = 10+5 = 15 inches

Adding a negative number on a number line is equivalent to subtracting the absolute value of that number. Thus, 56+(−116) = -60, 34+(−212) = -178 and 1.3+(−2.4) = -1.1

When you are adding a negative number on a number line, you are essentially performing a subtraction operation. Let's look at the three problems you've posted:

1. 56+(−116): Start at positive 56 on the number line and then move 116 steps to the left because we're adding a negative number. Your final position will be -60. So, 56+(−116) equals -60.

2. 34+(−212): Similarly, start at 34 on the number line and move 212 spaces to the left which results a value of -178. Therefore, 34 + (-212) = -178.

3. 1.3+(−2.4): Starting at 1.3 on the number line, if we move 2.4 steps to the left we end up at -1.1. So, 1.3 + (-2.4) = -1.1

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The geometric plane is two-dimensional since there are two variables.

A geometric plane is a plane which is a flat surface.

The general equation of a plane is :

ax + by + c = 0

Here x and y are variables.

Since there are two variables, the plane is two dimensional.

Or in other words, there are two directions for the plane.

So the geometric plane is two-dimensional.

Learn more about Geometric plane here :

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1x+5 2x+10 3x+15 4x+20 5x+25

Step-by-step explanation:

To write expressions equivalent to 20x + 100, we can use factoring, distributing, and properties of equality. Examples include 4(5x + 25), 10(2x + 10), and three other variations, all of which maintain the original value of the expression.

To write five expressions equivalent to 20x + 100, we can apply various mathematical techniques such as factoring, distributing, adding/subtracting terms, or using properties of equality. Here are five different equivalent expressions:

The equivalence of these expressions to 20x + 100 remains intact because they are simply restructured using basic algebraic principles without changing the value.

Answer:

The value of the equation is [tex]x=\frac{12-y}{5+4k}[/tex].

Step-by-step explanation:

Consider the provided equation.

[tex]12-5x-4kx=y[/tex]

We need to solve the provided equation for x.

Subtract 12 both side.  

[tex]12-12-5x-4kx=y-12[/tex]

[tex]-5x-4kx=y-12[/tex]

Take -x common as shown:

[tex]-x(5+4k)=y-12[/tex]

Divide both sides by 5+4k.

[tex]-x=\frac{y-12}{5+4k}[/tex]

[tex]x=\frac{-y+12}{5+4k}[/tex]

[tex]x=\frac{12-y}{5+4k}[/tex]

Hence, the value of the equation is [tex]x=\frac{12-y}{5+4k}[/tex].

The formula V=lWh is solved for W by dividing both sides of the equation by lh, providing the solution W = V / lh. This is a simple algebraic operation used for isolating the variable we're solving for, which is W in this case.

The question asks to solve for the variable, W, in the formula V =lWh, where V represents volume, l represents length, h represents height, and W is the width we are solving for. To isolate W, you need to perform some algebraic operations. Let's go step by step:

Remember, in algebra, the main goal is to isolate the variable we're trying to find on one side of the equation, which in this case is W.

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Answer:

x^2 + 3x - 2 - (2x^2 - x + 6) =

x^2 + 3x - 2 - 2x^2 + x - 6 =

-x^2 + 4x - 8

the answer is 8

To make a 16-gallon mix that costs $14 per gallon from a paint costing $19 per gallon and a thinner costing $3 per gallon, you need approximately 11.56 gallons of paint and 4.44 gallons of thinner.

This is a problem of Mathematics, specifically Systems of Equations. Let's denote the amount of paint as P (in gallons) and the amount of thinner as T (in gallons). We are looking for the values of P and T that satisfy these two conditions:

This gives us two equations,

Now, you can subtract the first equation from the second to solve for P,

18P = 208, therefore P = 208/18 = 11.56 gallons. Substitute P = 11.56 into the first equation to solve for T, T = 16 - 11.56 = 4.44 gallons. So, approximately 11.56 gallons of paint and 4.44 gallons of thinner should be mixed to get the desired 16-gallon mixture.

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To find the amounts of paint and thinner needed to make a $14 per gallon mix by mixing two different-priced liquids.

Mathematically, this problem can be solved using a system of equations.

Let x be the gallons of paint and y be the gallons of thinner. We have two equations based on the given information:

Solving this system of equations will give you the amounts of paint and thinner that need to be mixed to achieve a $14 per gallon mix.

Answer:

3 g/ml

Step-by-step explanation:

After the marble was introduced into the graduated bottle, the volume change from 10 ml to 12.5 ml, this means that 12.5 - 10 = 2.5 ml is the volume occupied by the marble.

The mass of a marble is 7.5 g.

Density is defined as follows:

density  = mass / volume =

Replacing with the measures:

density = 7.5/2.5  =  3 g/ml