2 is a common sample in the 2 events, therefore they are not mutually exclusive.
What is probability ?Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has included probability to forecast the likelihood of certain events. The degree to which something is likely to happen is basically what probability means. You will discover the likelihood of outcomes for a random experiment using this fundamental probability theory, which is also applied to the probability distribution.
Two occurrences are mutually exclusive or disjoint in logic and probability theory if they cannot both occur at the same time. The results of a single coin toss, which can result in either heads or tails but not both, provide a clear illustration.
If we roll a dice which is fair
Events that we get to shw even are = {2, 4, 6}
Events that we get when getting less that 3 = {1, 2}
So, 2 is a common sample in the 2 events, therefore they are not mutually exclusive.
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Mr. Jonus ordered a pizza to take home. His children ate 4/8 of the pizza and
Mr. Jonus ate 2/8 of the pizza. The remaining pizza was saved for later. Which
equation could be used to represent the whole pizza?
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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a moving streaming service offers two types of subscriptions
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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here is my algebra 13 homework screenshot, can somebody help me QUICKK PLS
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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A toy ball can be modeled as a sphere. Jeriel measures its diameter as 21.9 cm. Find
the ball's volume in cubic centimeters. Round your answer to the nearest tenth if
necessary.
Answer:
Step-by-step explanation:
Select the correct answer.
Which statement best defines a circle?
OA the set of all points in a plane that are the same distance from a given point called the center
OB. the set of all points that are the same distance from a given point called the center
OC points in a plane that surround a given point called the center
OD. the set of all points in a plane that are the same distance from each other surrounding a given point called the center
Reset
Next
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:
If f(1) = 0, what are all the roots of the function f (x) = x cubed + 3 x squared minus x minus 3? Use the Remainder Theorem.
The roots of the cubic function:
f(x)= x³ + 3x² - x - 3
are x = 1, x= -1, x = -3
How to find the roots of the function?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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Three vehicles recorded the following information about their trips.
Van: 500 miles in 7.5 hours
Truck: 300 miles in 5 hours
Car: 400 miles in 5.5 hours
Find the unit rate of miles/hour for the Van.
Answer:
66.6 miles/hour
Step-by-step explanation
50/7.5 = 66.6
From a point x, the bearing of a hill is 200⁰ and from another point Y 170km due east of x ,the bearing of the hill is 255⁰. Calculate the distance between the hill and Y
Answer:
Step-by-step explanation:
Write the following number in expanded form: fifty-four and eight tenths
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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PLEASE HELP
The triangle above has the following measures.
q = 6 yd
m/Q=43°
Find the length of side r.
Round to the nearest tenth and include correct units.
Show all your work.
Answer:
r=5.9
Step-by-step explanation:
What is the height, in meters, of a cylinder with surface area 104π m2 and radius 4 m?
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
6th grade pls help Thank you
Based on the information, tere are 16224000 possible passwords.
How to calculate the valueThere 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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I 10. The sides of a square are increased by a scale factor of 3. The area of the larger square is what percent of tne area of the smaller square?
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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kylie is wrapping a book for her sister.The box is 20" x 12"x 2 1/2. the book she wants to put it in is 18" x 3 1/2 x 8.How much empty space will be in the box once kyile puts the book inside
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.
Which representation shows y as a function of x?
The only relation that is a function is the one in option C.
Which relation is also a function?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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what is 300 in word form
Answer:
Three Hundred.
evelyn has 80 pens
15 pens are black and the other pens are blue
what is the probability of a black pen
Answer:
3/16 or 18.75%------------------
There are 15 black pens out of total 80.
The probability of a black pen is:
P(black) = black / totalP(black) = 15/80P(black) = 3/16 or 18.75%4. Maria also wants to study the relationship between the weight of puppies at birth
and their adult weight (at two years old). She collected data from five randomly
selected small-breed dogs and displayed the data in the table.
Birth weightAdult weight
(pounds) (pounds)
1.5 10
317
18
2.5 14
Birth weight Adult weight
(pounds) (pounds)
0.75 5
Part A. Use the data in the table to create a scatterplot. (5 points)
Part A.
(5 points)
Dog Birth and Adult Weights
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
jureks brother is 6 years older than him .Together they are 22 years old ,how old are the brothers.Write down the correct equation?
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
1
4
(
8
−
6
x
+
12
)
?
1
4
(
8
−
6
x
+
12
)
?
A.
7
2
x
7
2
x
B.
−
13
2
x
−
13
2
x
C.
−
6
x
+
14
−
6
x
+
14
D.
−
3
2
x
+
5
The equivalent expression is 5 - 3x/2. Option D
What are algebraic expressions?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;
BracketParenthesesSubtractionMultiplicationDivisionAdditionFrom 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)
Find a • b. a = <5, 2>, b = <4, 5> (2 points) a <20, 10> b <9, 7> c -10 d 30
The dot product of vectors a and b is option D. 30.
How did we get the value?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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thanks so much for the help!! you don't have to put the showed work!
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 :)
What is the sum of the interior angles of the polygon shown below?
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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Need help in solving this problem I’m stuck on it. Pls help me?????? If you can see the numbers it’s 3ft, 7ft, 5ft, 4ft.
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
Simplify this expression. 26 ÷ 23 A. 16 B. 8 C. 4 D. 1
Using a rule for exponents, we can simplify the expression and see that the correct option is B, 8.
How to simplify the expression?
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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Simplify (2x + 3)(x − 4) = ? A. 2x² - 5x + 12 O B. 2x²5x - 12 O C. 2x² + 5x + 12 O D. 2x² + 5x - 12
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
Help me !!!! Please I’m offering points
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.
What is the Side-Side- Angle Postulate?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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What is the value of c?
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°
A rectangular prism with a square base has a height of 17.2 cm and a volume of 24.768 cm² What is the side length of its base?
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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Find all Solutions of the equation
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]