if two events are complementary, they must also be mutually exclusive events. group of answer choices true false

distributive property

The unidentified term is 3m.

An equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Given that, an equation (x-0.2n)² = x-1.2mn+0.04n²

We know that, (a-b)² = a²-2ab+b²

Comparing the given equation with the above identity, we get,

a = x, b = 0.2n and 2ab = 1.2mn

Therefore, 2x×0.2n = 1.2mn

x = 3m

Hence, the unidentified term is 3m

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If the radius of the hole is 3 inches than the volume of the resulting solid is 410.29 in³    .

In the question ,

it is given that ,

the manufacturer drills a hole in the metal sphere that has radius of 5 inches ,

the radius of hole in sphere is 3 inches .

the volume of the metal sphere is = (4/3)×π×r³

= (4/3)×π×5³

= 523.33 in³

the volume of the hole of radius 3 inches is = (4/3)×π×3³

= 113.04 in³

So , the volume of the remaining solid is = 523.33 - 113.04

= 410.29 in³  .

Therefore , the Volume of the resulting solid is 410.29 in³    .

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Answer:

5x + 16

Step-by-step explanation:

First you have to distribute the 2 into the parentheses

2 times x is 2x

2 times 6 is 12

so now the equation is

2x + 12 + 3x + 4

add the 2x and 3x and that is 5

so now the equation is...

5x + 12 + 4

add 12 + 4 and that is 16

so now the answer is

5x + 16

By looking at the definition of mutually exclusive and independent event, the statement for both events are true.

A statistical term used to describe events that cannot occur concurrently is "mutually exclusive." It is frequently used to refer to circumstances in which the occurrence of one event takes precedence over the other. For instance, it is impossible for war and peace to exist together. They are therefore opposed to one another.

Events classified as independent do not depend on other events for their occurrence. For instance, if we toss a coin in the air and it lands on head, we can toss it again and this time it will land on tail. Both instances include independent occurrences of the two events.

(a) True. The given event is both mutually exclusive as well as independent

(b)True. The given event is both mutually exclusive as well as independent

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It will be 13min until there are 20 grams of the element remaining.

What is exponential decay?

The term "exponential decay" in mathematics refers to the process of a constant percentage rate reduction in an amount over time. It can be written as y=a(1-b)x, where x is the amount of time that has passed, and is the initial amount, b is the decay factor, and y is the final amount.

Here, we have

This is a compound decay problem, which goes by the formula:

F = P(1-r)ˣ

Where

F is the future amount (we want it to be 20)

P is the present amount (240 now)

r is the rate of decay per minute (17.4% = 17.4/100 = 0.174)

x is the time it takes (what we want to find)

Substitute all values in the formula and we get

20 = 240(1-0.174)ˣ

20 = 240(0.826)ˣ

0.0833 = 0.826ˣ

㏑0.0833 = ㏑0.826ˣ

㏑0.0833 = x ㏑0.826

x = ㏑0.0833/㏑0.826

x = 13

Hence, it will be 13min until there are 20 grams of the element remaining.

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The perimeter of the right triangle shown is given by the following option:

39 units.

The perimeter of a figure is composed by the sum of the lengths of the outer edges of the figure.

The sides of the right triangle in this problem are given as follows:

Then, applying the Pythagorean Theorem, the hypotenuse of the triangle is given as follows:

h² = 5² + 17²

h = square root(5² + 17²)

h = 17.7.

The hypotenuse is the third side length of the triangle, hence it's perimeter is calculated as follows:

5 + 17 + 17 = 39 units.

(I suppose there was a typing mistake on the options).

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Answer:

its D

Step-by-step explanation:

30

Answer:

congruence is compatibility or agreement while equal is the same or equivalent to one another.

Given graph is satisfied by System A.

Inequality refers to formulas or equations that define relationships (such as less than, larger than, etc.).

As for Type 1:

Consider the location (3,1) for y>2x.

1 > 6, which is false Hence Since the area opposite point (3,1) will satisfy the equation and since y > 2x and not y 2x, a dotted line will be drawn on the graph.

Consider (-3, -4) for x + 2y -8.

⇒ -3 + 2(-4) ≤ -8

Since x + 2y -8 and not x + 2y -8 is the correct equation, the area containing the points (-3, -4) will be included, and the line of the graph will be solid.

The presented figure is formed by these two equations.

Therefore, System A is accurate.

The Complete Question is inequality.

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Answer:

y= 3x + 5

Step-by-step explanation:

Some examples

(1,8)

8= 3 (1) + 5

8 = 3 + 5

8= 8

(2,11)

11= 3 (2) + 5

11= 6 + 5

11= 11

Answer:

0

Step-by-step explanation:

If it lies on the y line then it is horizontal. This means the slope is 0 and so is the x value.

Answer:

x ≥ 5

Step-by-step explanation:

5 + 2 (2x - 3) ≥ 3x + 4

5 + 4x - 6 ≥ 3x + 4

-1 + 4x ≥ 3x + 4

4x ≥ 3x + 5

x ≥ 5

So the valid bounding conditions for the sum of the subset problem are:

0 <= x[i] <= 1 (for all i such that 1 <= i <= n)

∑(w[i] * x[i]) <= m (for all i such that 1 <= i <= n)

The valid bounding condition for the sum of the subset problem is:

0 <= x[i] <= 1 (for all i such that 1 <= i <= n)

This means that each item can either be included in the subset (x[i] = 1) or not included in the subset (x[i] = 0).

The sum of the weights of the items in the subset should not exceed the maximum capacity constraint, m. So the bounding condition for the weight of the subset is:

∑(w[i] * x[i]) <= m (for all i such that 1 <= i <= n)

This means that the sum of the weights of the items in the subset should be less than or equal to the maximum capacity constraint.

So the valid bounding conditions for the sum of the subset problem are:

0 <= x[i] <= 1 (for all i such that 1 <= i <= n)

∑(w[i] * x[i]) <= m (for all i such that 1 <= i <= n)

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There is 20% decrease in the number of people who went to the pool over these four weeks.

What is percentage?

A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The proportion therefore refers to a component per hundred. Per 100 is what the word percent means. The letter "%" stands for it.

There is no dimension to percentages. As a result, it is known as a dimensionless number. When we say a number is 50% of anything, we mean that it is 50% of everything.

Attendance of pool in first week of July = 1120

In second week, 125 fewer people joined.

Thus, attendance in second week is = 1120-125 = 995

In third week, 130 more people joined.

Thus, attendance in third week is = 995+130 = 1125

In fourth week, 229 fewer people joined.

Thus, attendance in fourth week is = 1125-229 = 896

Difference of attendance in first and fourth week = 1120-896 = 224

Percentage decrease = (Decrease number/Initial number)×100%

= (224/1120)×100%

= 0.20×100%

= 20%

Thus, there has been a 20% decrease over the four weeks.

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4 inches is the rim's radius

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Answer: C. End of third day

Step-by-step explanation:

The question is asking when there will be 36 pieces left, so you start with the equation:

-6d + 54 = 36

Then, solve this equation:

-6d + 54 = 36

-6d = -18 (subtract 54 from both sides)

d = 3 (divide both sides by -6)

It will take 3 days until there are 36 pieces left, which is the end of the third day.

Answer:

2400

Step-by-step explanation:4152 is just 173% of d.

We create an equation d = 4152/1.73

after solving you get 2400.

Let x be the number of bags of food Rachel can buy, and let y be the number of toys she can buy.

We can write the linear inequality as follows:

8x + 4y ≤ 46

An inequality is a mathematical statement that shows the relative size of two values.

A linear inequality is an inequality that involves a linear expression, which is an expression that involves variables and constants, but no exponents or other mathematical operations. Linear inequalities are used to represent relationships between variables that are linear in nature.

This inequality can be rewritten as follows:

x + 0.5y ≤ 5.75

This inequality states that the number of bags of food (x) and half the number of toys (0.5y) must be less than or equal to 5.75, which is the amount of money Rachel has available to spend divided by the cost per bag of food.

Therefore, Rachel can buy x bags of food and y toys for her cats as long as the inequality 8x + 4y ≤ 46 (or x + 0.5y ≤ 5.75) is satisfied.

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Let x be the number of bags of food Rachel can buy, and let y be the number of toys she can buy.

We can write the linear inequality as follows:

8x + 4y ≤ 46

What is inequality?

An inequality is a mathematical statement that shows the relative size of two values.

What is linear inequality?

A linear inequality is an inequality that involves a linear expression, which is an expression that involves variables and constants, but no exponents or other mathematical operations. Linear inequalities are used to represent relationships between variables that are linear in nature.

This inequality can be rewritten as follows:

x + 0.5y ≤ 5.75

This inequality states that the number of bags of food (x) and half the number of toys (0.5y) must be less than or equal to 5.75, which is the amount of money Rachel has available to spend divided by the cost per bag of food.

Therefore, Rachel can buy x bags of food and y toys for her cats as long as the inequality 8x + 4y ≤ 46 (or x + 0.5y ≤ 5.75) is satisfied.

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The function, f(x) = -50 and g(x) = -17

A function is a relationship between a set of inputs and a set of potential outputs, where each input is associated to exactly one outcome.

Instance: f(x) = x/2 ("f of x equals x divided by 2")

we are given that f(x) = -3[tex]x^{2}[/tex] -2 and g(x) = 4x - 1

we need to find f(4) and g(-4)

f(4) = -3([tex]4^{2}[/tex]) - 2

f(4) = -3*16 - 2

f(4) = -48-2

f(4) = -50

g(x) = 4x - 1

g(-4) = 4 *-4 -1

g(-4) = -16-1

g(-4) = -17

The function f(x) = -50  and g(x) = -17

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The perimeter of the image is 70 meters and its area is 210 square meters.

The circumference of a shape is known as its perimeter. The lengths of all four sides must be added in order to get a rectangle's or square's perimeter. The sum of the lengths of all the sides in a rectangle is its perimeter, or P. A rectangle's opposite sides are equal, hence it has two equal lengths and two equal widths. The following formula is used to determine a rectangle's perimeter: Diameter is equal to the sum of the following dimensions: length, width, height, and width.

There are numerous practical uses for calculating the perimeter. The size of the fence needed to enclose a yard or garden is known as the calculated perimeter.

Area=(1/2)×base× height

=(1/2)×21×20

=210 square meters

Perimeter=a+ b+ c

=21+20+29

=70meters

Therefore, The perimeter of the image is 70 meters and its area is 210 square meters.

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Answer: Not a Question

Step-by-step explanation:

No question mark and not a math quiestion

The x-intercept has an ordered pair (-4, 0) and the y-intercept has an ordered pair(0,16).

In an alternative method, a linear polynomial over a field from which the coefficients are extracted is equalized to zero to produce a linear equation. The values that, when used as placeholders for the unknowns, result in the equality being true are the solutions to this kind of equation.

In this specific situation, where the variable is appropriately referred to as the unknown, the term "linear equation" frequently applies indirectly.

The Cartesian coordinates of a point on the Euclidean plane can be read as each solution in the case of two variables.

Given equation is:

-4x+y=16

For x-intercept, y=0

-4x+0=16

-4x=16

x= -4

The x-intercept has an ordered pair (-4, 0)

For y-intercept, x=0

-4(0)+y=16

y=16

The y-intercept has an ordered pair(0,16)

Therefore, The x-intercept has an ordered pair (-4, 0) and the y-intercept has an ordered pair(0,16).

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Answer:

d ≈ 8.5 units

Step-by-step explanation:

calculate the distance using the distance formula

d = [tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex]

with (x₁, y₁ ) = A (2, - 1 ) and (x₂, y₂ ) = B (- 4, 5 )

d = [tex]\sqrt{(-4-2)^2+(5-(-1))^2}[/tex]

   = [tex]\sqrt{(-6)^2+(5+1)^2}[/tex]

   = [tex]\sqrt{36+6^2}[/tex]

   = [tex]\sqrt{36+36}[/tex]

   = [tex]\sqrt{72}[/tex]

   ≈ 8.5 units ( to 1 decimal place )

The value of the side AC is 40 if the points  B, D, and F are midpoints of

the sides of ΔACE.

The midpoint theorem states that in order to determine the midpoints of a triangle's sides, "a line segment linking any two of its midpoints is said to be parallel to the triangle's third side and also half the length of the third side."

Divide the distance between the two endpoints by 2, then do it again. The two terminal x coordinates can alternatively be combined, then the result divided by two. Draw a line from a midway to the opposite corner. The centroid of a triangle is the point at where the three medians intersect.

Given,

The points B, D, F are midpoints of the sides of a triangle ACE.

And also given that,

EC =32 and DF=20, AC=?

So, FD=1/2(AC)

AC=2(FD)

AC=2(20)

AC=40

Therefore, the value of the side AC is 40 if the points  B, D, and F are

midpoints of the sides of ΔACE.

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x = 3 is the true solution to 2 ln e superscript ln 5 x baseline = 2 ln 15, using the concept of simplification.

Make something simpler by simplifying it. In mathematics, reducing an expression, fraction, or issue to a simpler form is referred to as simplification. With calculations and solutions, the problem is made simple.

In order to achieve consistency in efforts, costs, and time, procedures must be simplified. It gets rid of variation and variety that is superfluous, harmful, and unproductive. It is termed simplification to use and interpret the function in order to make it simpler or easier to grasp.

The equation can be simplified by using the fact,

ln(eˣ) = x

This gives,

2 ln(5x) = 2·ln(15)

Comparing arguments, we see that,

5x = 15

x = 3

Check if it is true or not:

2 ln(e^(ln(5·3))) = 2·ln(15)

2 ln(e^2.70805) = 2·2.70805

2 ln(15) = 5.41610

and,

2·2.70805 = 5.41610

So, it is true.

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Answer:

3/2

Step-by-step explanation:

slope = m = change in y/change in x OR y2-y1/x2-x1

change in y: -14 - -2= -12 (or -14 + 2, because two negatives make a positive)

change in x: -15- -7 = -8 (or -15+ 7 due to two negatives making a postive)

slope = -12/-8 = 3/2

Answer:

$1944

Step-by-step explanation:

18x12=216

216x$9=$1944

Answer:

£1944

Step-by-step explanation:

The area of the floor is 216 feet²

18 x 12 = 216

216 x 9 = 1944