Determine if the scenario involves mutually exclusive events

You roll a fair six-sided die. The die shows an even number or a number less than three.
A) Not mutually exclusive
B) Mutually exclusive

The statement that justifies that ΔBAE ≅ Δ DAE is Side-Side-Angle Postulate. The best option from the statements given is "Classify A triangle". That is definition of a triangle.

The Side Side Angle Postulate states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent.

Between both triangles, here are the congruent sides and angles:

AB ≅ AD  - Given

AE  = EA - Reflexive Property. Note that AE is shared by both triangles so we have Two congruent sides.

AC ⊥ BD - that means ∠AEB = ∠AED = ∠BEC = ∠CED = 90°

(perpendicular bisector theorem)

A perpendicular bisector is a line segment that cuts another line segment at 90 degrees. A perpendicular bisector, in other terms, meets another line segment at 90° and splits it into two equal halves.

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Answer:

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There are 15 black pens out of total 80.

The probability of a black pen is:

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

The cylinder contains three areas, the top circle, the bottom circle, and the middle. The surface area of it is the sum of the three;

[tex]As = \pi r^{2} + \pi r^{2} + 2\pi r (h) \\[/tex]

or

[tex]As = 2\pi r^{2} + 2\pi r (h)[/tex]

where h is the height,

104[tex]\pi[/tex] = [tex]2 \pi (4)^{2} + 2\pi (4)(h)[/tex]

h = 9m

Answer:

Jurek is 8. His brother is 14

Step-by-step explanation:

let's call Jurek J, and let's call his brother B.

his brother is 6 years older than Jurek.

So, B = J + 6.

B + J = 22

(J + 6) + J = 22

2J + 6 = 22

2J = 16

J = 8

so Jurek is 8

B + J = 22, B = 22 - J = 22 - 8 = 14.

Brother is 14

The area of the larger square is 900% of the area of the smaller square.

Let's assume that the side of the smaller square is "s". Therefore, the area of the smaller square will be:

Area of smaller square = s²

Now, the sides of the square are increased by a scale factor of 3, which means that the new side length of the larger square will be 3s. The area of the larger square will be:

Area of larger square = (3s)² = 9s²

To find the percentage of the larger square with respect to the smaller square, we need to divide the area of the larger square by the area of the smaller square, and then multiply by 100:

(9s²/s²) x 100 = 900%

This means that the larger square is 9 times the area of the smaller square.

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Answer:

Three Hundred.

Fifty-four and eight tenths" can be expressed in expanded form as the sum of 54 (representing 50 + 4) and 0.8, which represents the decimal part.

To write the number "fifty-four and eight tenths" in expanded form, we can break it down into its individual place values and numerical components.

The number "fifty-four" can be broken down as follows:

The digit 5 represents the value of 50, which is 5 tens.

The digit 4 represents the value of 4, which is 4 ones.

So, "fifty-four" can be expressed as 50 + 4.

Next, we have "eight tenths". This can be expressed as 8/10 or simply 0.8 since each tenth is equal to 0.1.

Putting it all together, the number "fifty-four and eight tenths" can be written in expanded form as:

50 + 4 + 0.8

Simplifying further, we can combine the integer and decimal parts:

54 + 0.8

Therefore, the expanded form of "fifty-four and eight tenths" is 54 + 0.8.

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The only relation that is a function is the one in option C.

A relation maps elements from a set called the domain into elements of another set, called the range.

Particularly, if each of the elements in the domain is mapped to a single value in the range, then we have a function.

When we have a graph, we can do the vertical line thest, if a vertical line touches the graph more than once, then it is not a function, with that we can discard the two graphs in the left.

And for option D, we can see that the input 22 is mapped into two different values.

The remaining option, C, is the correct one.

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Answer:

96 cubic inches

Step-by-step explanation:

To calculate the empty space that will be left in the box once the book is inside, we need to find the difference between the volume of the box and the volume of the book.

Volume of the box:

20" x 12" x 2 1/2" = 600 cubic inches

Volume of the book:

18" x 3 1/2" x 8" = 504 cubic inches

Empty space in the box:

600 cubic inches - 504 cubic inches = 96 cubic inches

Therefore, there will be 96 cubic inches of empty space left in the box once Kylie puts the book inside.

The dot product of vectors a and b is option D. 30.

To find the dot product of two vectors, you need to multiply their corresponding components and then sum the results.

Let's calculate the dot product of vectors a = <5, 2> and b = <4, 5>:

a • b = (5 x 4) + (2 x 5)

= 20 + 10

= 30

Therefore, the dot product of vectors a and b is 30.

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If rectangular prism with a square base has a height of 17.2 cm and a volume of 24.768 cm², the side length of the square base is 1.2 cm.

Let's denote the side length of the square base as x cm. Then, the volume of the rectangular prism can be expressed as V = x² * 17.2 cm³, and its surface area can be expressed as S = 2x² + 4x * 17.2 cm².

We are given that the volume of the rectangular prism is 24.768 cm³, so we can write the equation:

x² * 17.2 cm³ = 24.768 cm³

Simplifying this equation, we get:

x² = 24.768 cm³ / 17.2 cm² = 1.44 cm²

Taking the square root of both sides, we get:

x = 1.2 cm

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A moving streaming service offers two types of subscriptions: a basic subscription and a premium subscription.

The moving streaming service provides customers with two distinct types of subscriptions to cater to their viewing preferences and needs. The first option is the basic subscription, which offers access to a limited selection of movies and TV shows. This subscription provides users with a basic streaming experience, allowing them to enjoy a range of popular titles at a lower cost.

On the other hand, the second option is the premium subscription, which provides subscribers with a more extensive and premium streaming experience. With the premium subscription, users gain access to a wider library of content, including exclusive movies, TV series, and original productions. Additionally, premium subscribers often enjoy additional features such as ad-free streaming, simultaneous streaming on multiple devices, and the ability to download content for offline viewing.

By offering these two subscription options, the moving streaming service aims to cater to a diverse range of users, providing them with flexibility and choice based on their preferences and budget.

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Answer:

84°

Step-by-step explanation:

opposite angles in a cyclic quadrilateral (4-sided shape) add up to 180.

c + 96 = 180

c = 180 - 96 = 84°

Answer:

A. the set of all points in a plane that are the same distance from a given point called the center

Step-by-step explanation:

Answer:

 y = 4.87x + 2.28 Is the answer

Step-by-step explanation:

( i see a little bit of part b but do not see the FULL QUESTION which is a problem and i cannot answer.. )

using a:

THE ULTIMATE LINEAR REGRESSION CACLAULTOR

yes it is the epic i get:

y = 4.87x + 2.28

Nothing more noting less ikr

y = 4.87x + 2.28 Being the answer

Answer:

Step-by-step explanation:

Based on the information, tere are 16224000 possible passwords.

There are 52 possible letters for the first two characters (26 uppercase and 26 lowercase).

There are 6 possible special characters for the third character.

There are 10 possible numbers for the last three characters.

We can use the Fundamental Counting Principle to calculate the number of possible passwords. The Fundamental Counting Principle states that if there are n ways to do one thing and m ways to do another thing, then there are n×m ways to do both things.

In this case, there are 52×52=2704 ways to choose the first two characters, 6 ways to choose the third character, and 10×10×10=1000 ways to choose the last three characters.

Therefore, there are 2704×6×1000

=16224000 possible passwords.

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The equation that could be used to represent the whole pizza is 4/8 + 2/8 = 6/8 = 3/4.

We are given that;

Pizza ate by children= 4/8

Pizza ate by Jonus= 2/8

Now,

4/8 + 2/8 + x = 1

where x is the fraction of the pizza that was saved for later. This equation shows that the sum of the fractions of the pizza that were eaten and saved is equal to 1, which represents the whole pizza. To solve for x, we can simplify the fractions and subtract them from both sides:

4/8 + 2/8 = 6/8 = 3/4

3/4 + x = 1

x = 1 - 3/4

x = 1/4

Therefore, the equation will be 4/8 + 2/8 = 6/8 = 3/4

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Answer:

2x^2-5x-12

Step-by-step explanation:

(2x+3)(x-4) can be simplified using the acronym FOIL, which stands for "first, outer, inner, last." This means that you multiply the first terms in each group, the the outer terms, then the inner terms, and lastly the last terms in  each group.

2x*x=2x^2

2x*-4=-8x

3*x=3x

3*-4=-12

Combine those and you get 2x^2-8x+3x-12. Combine like terms, and your final answer is 2x^2-5x-12

Function graph that has y- intercept of 3 is g(x) = 3[tex](\frac{1}{4}) ^{x}[/tex].

y- intercept will be 3 when we will put value of x = 0 and y will be 3 that graph will have y intercept 3

A) h(x) = 5[tex](2)^{x}[/tex]

when x = 0

Any number with zero power is always 1

h(x) = 5

B) h(x) = 5[tex](0.5)^{x}[/tex] + 0.5

when x = 0

h(x) = 5 + 0.5

h(x) = 5.5

C) g(x) = 3[tex](\frac{1}{4}) ^{x}[/tex]

when x = 0

g(x) = 3

Here we get y intercept as 3.

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Using a rule for exponents, we can simplify the expression and see that the correct option is B, 8.

Remember that when we have the quotient of two powers with the same base (like in this case, where the base is 2) the outcome will be a power of the same base, such that the exponent is equal to the difference between the other two exponents.

The rule is:

[tex]\frac{x^m}{x^n} = x^{m - n}[/tex]

Then we can use that to simplify the expression, we will get:

[tex]\frac{2^6}{2^3} = 2^{6 - 3} = 2^3 = 2*2*2 = 8[/tex]

We can see that the correct option is B.

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Answer:

[tex]\textsf{D)} \quad x=-\dfrac{\pi}{3}, 0, \dfrac{\pi}{3}, \dfrac{\pi}{2}[/tex]

Step-by-step explanation:

To find the solutions of the given trigonometric equation, begin by factoring out the common term sin 2x:

[tex]\begin{aligned}2 \sin 2x \cos x - \sin 2x & = 0\\\sin 2x(2 \cos x - 1)&=0\end{aligned}[/tex]

Set each factor equal to zero and solve for x using the unit circle.

[tex]\begin{aligned}\sin 2x & = 0\\2x & = \sin^{-1}(0)\\2x&=0+ 2\pi n, \pi + 2 \pi n\\ x&=\pi n, \dfrac{\pi}{2}+\pi n \end{aligned}[/tex]

[tex]\begin{aligned}2\cos x - 1 & = 0\\2 \cos x& = 1\\\cos x&=\dfrac{1}{2}\\x&=\cos^{-1}\left(\dfrac{1}{2}\right)\\x&=\dfrac{\pi}{3}+2\pi n, \dfrac{5\pi}{3}+2 \pi n\end{aligned}[/tex]

Therefore, the solutions in the given interval -π/2 < x ≤ π/2 are:

[tex]\boxed{x=-\dfrac{\pi}{3}, 0, \dfrac{\pi}{3}, \dfrac{\pi}{2}}[/tex]

Answer:

 r=5.9

Step-by-step explanation:  

Answer:

66.6 miles/hour

Step-by-step explanation

50/7.5 = 66.6

Answer:

20 square feet

Step-by-step explanation:

area of a triangle = (1/2) base x height

The "base" for this one gigantic triangle is the 'top' of the diagram - - - - it's the entire 3+7 = 10 side. (We can calculate the area of the whole thing at once. We don't have to do the left and the right halves separately!!!)

The height is 4.

So area = (1/2) base x height

= (1/2) * 10 * 4

= 20 square feet

Answer:

75 points ( more than?? you didn't add the drop-down list ) today's score.

Hope this helps!

Step-by-step explanation:

y = mx + b

y = 5x + b

(50) = 5(6) + b  -> b = 20

y = 5x + 20

If Carlos plays the game today for 0 min, he will get a score of 20 ( odd...  how is that possible )

But tomorrow, he plans to play for an extra 15 min, so he will get a score of 95 ( ( 5 × 15 ) + 20 ). The question asks for how much his score will change so his score will change by 75 points ( 95 - 20 ).

You could also just do 15 × 5 to get 75 :)

1260° is the sum of all interior angles of the given polygon.

Generally speaking, the measure of the angle at the center of a regular polygon is equal to 360 degrees.

The sum of the interior angles in a polygon can be calculated using the formula:

Sum of interior angles = (n - 2) * 180 degrees

In this formula, "n" represents the number of sides or vertices of the polygon.

In the given problem the number of sides is 9.

Thus,

Sum of all interior angle = (9-2)*180

The sum of all interior angles = 1260°

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The equivalent expression is 5 - 3x/2. Option D

Algebraic expressions are described as expressions that are made up of variables, their coefficients, factors and constants.

these algebraic expressions are also composed of mathematical operations. These operations includes;

From the information given, we have that;

1/ 4(8 - 6x + 12)

expand the bracket, we have;

Add the like terms

1/4(20 - 6x)

now, multiply the values, we have;

20 - 6x/4

Divide by the denominator

5 - 3x/2

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The complete question:

Simply the expression:

1/ 4(8 - 6x + 12)

The roots of the cubic function:

f(x)=  x³ + 3x² - x - 3

are x = 1, x= -1, x = -3

We want to find the roots of the function:

f(x)=  x³ + 3x² - x - 3

We know that x = 1 is a root, because f(1) = 0.

Then we can write that function as:

(x - 1)*(x - a)*(x - b)

Where a and b are the other two roots, then we need to solve:

x³ + 3x² - x - 3 = (x - 1)*(x - a)*(x - b)

Expanding the right side, we will get:

x³ + 3x² - x - 3 = x³ + (-a - b - 1)x² + (a + b + ab)x + (-ab)

Comparing like terms, we can see that:

(-a - b - 1) = 3

(a + b + ab) = -1

(-ab) = -3

The third equation gives:

ab = 3

Replacing that in the second one we get:

a + b + 3 = -1

a + b = - 1 - 3 = -4

a + b = -4

a = -4 - b

Replacing that in the relation above:

ab = 3

(-4 - b)*b = 3

-4b - b² = 3

b² + 4b + 3  = 0

The zeros of that function are:

[tex]b = \frac{-4 \pm \sqrt{4^2 -4*3*1} }{2*1} \\\\b = \frac{-4 \pm 2}{2}[/tex]

Then if b is the value when we take the positive sign:

b = (-4 + 2)/2 = -1

the value of a is:

a = -4 - b = -4 + 1 = -3

These are the other two roots.

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