Five sixths of Forty two

The problem is a simple division process. We set up the equation where the number of buckets, B is calculated by the total quantity of paint in gallons, divided by how many gallons each bucket holds. Solving this equation, we discover that 30,000 gallons of paint can fill 6,000 buckets.

We can solve this problem by using a simple division process. Each bucket holds 5 gallons. So, if we have 30,000 gallons, we need to find out how many 5-gallon buckets this amount equals to.

If we denote the number of buckets by B, we can write an equation as follows:

5B = 30000.

To find B, we solve the equation by dividing both sides by 5: B = 30000/5

So, using a calculator, we find that B = 6000 buckets.

Therefore, the facility would be able to give away 6000 buckets of paint.

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Utilize trigonometric identities to find exact values without decimals:

To find the exact values of the given trigonometric expressions, we can use the trigonometric identity sine of the sum of angles: sin(A + B) = sinA x cosB + cosA  x sinB.

1. For the first expression, sin(96°)cos(264°) + cos(96°)sin(264°), using the identity, it simplifies to sin(96° + 264°), which equals sin(360°), and sin(360°) equals 0.

2. For the second expression, sin(258°)cos(33°) - cos(258°)sin(33°), applying the identity yields sin(258° - 33°), which is sin(225°), and sin(225°) simplifies to -√2/2.

Answer:58

Step-by-step explanation:

The rule for solving proportions is that the product of the means equals the product of the extremes. This method is used when dealing with categorical data in two categories.

The rule for solving proportions is this: The product of the means is equal to the product of the extremes (option B). When you have a proportion which is often written in the mathematically form 'a/b = c/d', you can use this rule. 'a' and 'd' are the extremes and 'b' and 'c' are the means. Therefore, the rule means that a*d (product of the extremes) is equal to b*c (product of the means).

In terms of identifying when you're dealing with a proportion problem, you're involved in this scenario when the data you're dealing with is of two categories like Yes or No, Success or Failure. This is typically when you're attempting to estimate a population proportion for example, the proportion of the population that smokes or will vote for candidate A.

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Answer:

is there another example i really need this..?

sorry if i took the points..

Answer: y minus 1.9 equals negative 1.8 open parentheses x plus 0.5 close parentheses.

Step-by-step explanation:

The point slope form of a line that has slope m and passes through (a,b) is given by :-

[tex](y-b)=m(x-a)[/tex]

Given : Slope = -1.8 and Point  (a,b) = (-0.5, 1.9)

Then, the point-slope form of a line that has a slope of -1.8 and passes through the point (-0.5, 1.9) will be :-

[tex](y-1.9)=-1.8(x-(-0.5))\\\\\Rightarrow\ (y-1.9)=-1.8(x+0.5)[/tex]

Hence, the correct option is y minus 1.9 equals negative 1.8 open parentheses x plus 0.5 close parentheses.

Possible rational roots: ±1,±2,±3,±4,±6,±12±1,±2,±3,±4,±6,±12

Actual rational roots: 1,−1,2,−2,−3

see attachments for all steps.

Final answer:

To find the height of the taller sign, we can use similar triangles and the concept of proportions and  the height of the taller sign comes out o be 12 feet.

Explanation:

To find the height of the taller sign, we can use similar triangles and the concept of proportions. The height of the shorter sign is given as 12 feet, and its corresponding shadow length is 25 feet. We can set up the proportion:

Height of taller sign / Length of its shadow = Height of shorter sign / Length of its shadow

Substituting the given values, we can solve for the height of the taller sign:

Height of taller sign = (Height of shorter sign / Length of its shadow) x Length of its shadow

Plugging in the values, we get:

Height of taller sign = (12 feet / 25 feet) x 25 feet

Height of taller sign = 12 feet

Therefore, the height of the taller sign is 12 feet.

We apply the Pythagorean theorem and differentiate it to relate the rates of the ladder's top slipping and the foot of the ladder moving away from the wall. Substituting given values in the differentiated equation gives us the speed at which the foot of the ladder is moving away.

In this problem, we are dealing with a right triangle formed by the wall, ground and the ladder acting as the hypotenuse. The rate at which the top of the ladder is descending and the height at which the rate needs to be calculated are given. This problem applies the concepts of related rates in calculus.

According to the Pythagorean theorem, for a right triangle, the sum of the square of the two shorter sides is equal to the square of the longest side (the hypotenuse). Here, we have  x² + y² = 15² where x is the distance of foot of the ladder from the wall and y is the height from the ground.

Differentiating both sides with respect to time (t),  we get 2x(dx/dt) + 2y(dy/dt) = 0. Solve this differentiation equation to find dx/dt, the speed of the foot of the ladder moving away from the wall while y is 13.

To solve this, plug y = 13, dy/dt (rate at which top of ladder is descending) = -4 ft/sec into the equation and solve for dx/dt.

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Answer:

3.38461

Step-by-step explanation:

The given number is 3.38461370132 and we have to round it to the nearest hundred-thousandth.

In order to round this number to nearest hundred-thousandth, we round the fifth number after the decimal point.

So, must see if the sixth digit is less than 5 or not. If it is five or greater than five then we add 1 to the previous digit otherwise it will not change.

The fifth digit is  1

And the sixth digit is 3 < 5

hence, we'll keep the 5th digit as it is.

So, when rounded to the nearest hundred-thousandth the number is 3.38461

I find it convenient to rearrange the numbers so that positive numbers are added, negative numbers are added, then the two sums are added. Of course, you can do it any way you like. Your calculator does not care about the order of the numbers you enter.

... = (1.4 +1.8) -(5.5 +1.73 +1.09)

... = 3.2 - 8.32

... = -5.12

A) -5.12

... = (1.4 +1.8) -(5.5 +1.73 +1.09)

... = 3.2 - 8.32

... = -5.12

- Prodixy ☕

To solve the equation 49x²+56x-64 = 0 by completing the square, we first convert it to the format (ax + b)² = c. It is found that a=1, b=4/7, and c=16/49. Hence, a+b+c = 381/147 or approximately 2.59183673469.

The equation to solve is 49x²+56x-64 = 0. By completing the square, we can rewrite the equation in the form (ax + b)² = c. To get to this form, Po first divided the entire equation by 49, giving x²+8/7x-64/49= 0. Following this, he then took half of the coefficient of x (which is 4/7), squared it (which is 16/49), and added it to both sides of the equation. This transforms the left-hand side of the equation into a perfect square giving us (x+4/7)²=16/49. Hence, we find that a=1, b=4/7, and c=16/49. Therefore a+b+c = 381/147 or approximately 2.59183673469.

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Answer:

B.No the graph fails the vertical line test.

Step-by-step explanation:

A function in math is a correspondence where to any given number there is a result and it has two variables that are dependent and independent, in this case, the vertical line test is a test done to determine if a graph is a function or not, in order to test if it is a function you just draw a vertical line, parallel to the Y-axis and if it touches more than one point in the X then it is not a function, in order for a graph to be a function there must only exist one value of Y for each X value.

Answer:

The common reasoning that can be use while solving a radical equation are shown below.

Step-by-step explanation:

Radical equations are the equations which contains radical expressions like [tex]\sqrt{x}\text{ and }\sqrt{x+2}[/tex], etc.

If a radical expression is defined as [tex]\sqrt{x}[/tex], then the sign [tex]\sqrt{}[/tex] is the radical and x is radicand.

The common reasoning that can be use while solving a radical equation are:

1. Isolate or separate the radical expression.

2. To remove radical square both sides of the equation.

3. After that solve the equation to find the unknown variable

4. Check the answer for solution or extraneous solution.

For example:

[tex]\sqrt{x+1}+1=x[/tex]

subtract 1 from both sides.

[tex]\sqrt{x+1}=x-1[/tex]

Taking square on both sides.

[tex]x+1=(x-1)^2[/tex]

On simplification we get

[tex]x+1=x^2-2x+1[/tex]

[tex]0=x^2-2x+1-x-1[/tex]

[tex]0=x^2-3x[/tex]

[tex]0=x(x-3)[/tex]

Using zero product property,

[tex]x=0,x-3=0\Rightarrow x=3[/tex]

Check the equation for x=0,

[tex]LHS=\sqrt{0+1}+1=1+1=2\neq 0=RHS[/tex]

Since LHS is not equal to RHS, therefore 0 is an extraneous solution.

Check the equation for x=3,

[tex]LHS=\sqrt{3+1}+1=2+1=3=RHS[/tex]

Since LHS is equal to RHS, therefore 3 is an solution.

Answer:

what is the reflection rule

Step-by-step explanation:

In mathematics, a reflection is a mapping from a Euclidean space to itself that is an isometry with a hyperplane as a set of fixed points; This set is called axis in 2 dimensions or plane in 3 dimensions of reflection.

Answer:  The number of general admission tickets that were sold is 148.

Step-by-step explanation:  Given that a total of 210 people attended the opening night of a School Musical, where students tickets cost $3 each while general admission tickets cost $7.50 each.

The total sales were $1,296.

We are to find the number of general admission tickets that were sold.

Let x and y represents the number of student tickets and the general admission tickets respectively that were sold.

Then, according to the given information, we have

[tex]x+y=210\\\\\Rightarrow x=210-y~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]

and

[tex]3x+7.50y=1296\\\\\Rightarrow 3(210-y)+7.50y=1296~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~[\textup{Using equation (i)}]\\\\\Rightarrow 630-3y+7.50y=1296\\\\\Rightarrow 4.50y=1296-630\\\\\Rightarrow 4.50y=666\\\\\Rightarrow y=\dfrac{666}{4.50}\\\\\Rightarrow y=148.[/tex]

Thus, the number of general admission tickets that were sold is 148.