When one event's occurrence or non-occurrence doesn't affect the occurrence or non-occurrence of another event, then such events are called independent events. The correct options are A and B.
Which pair of events are called independent events?When one event's occurrence or non-occurrence doesn't affect the occurrence or non-occurrence of another event, then such events are called independent events.
Symbolically, we have:
Two events A and B are said to be independent iff we have:
[tex]P(A \cap B) = P(A)P(B)[/tex]
Comparing it with chain rule will give
[tex]P(A|B) = P(A)\\P(B|A) = P(B)[/tex]
Thus, showing that whether one occurred or not, the other one doesn't care about it (independence).
Two events are known to be independent even if the result of one event does not affect the result of the second event.
Rolling a dice in an independent event and choosing a blue marble is another independent event. The two events are independent and the result of one does not affect the other.
Thus, A is correct.
Rolling a dice in an independent event, and rolling it again won't affect the result of the second roll. Therefore, rolling a dice twice or for n number of times is an independent event.
Thus, B is correct.
Hence, the correct options are A and B.
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Geometry triangle question
Answer:
Step-by-step explanation:
Answer:
x = 44 1/3°4x = 177 1/3°2x = 88 2/3°Step-by-step explanation:
The angle sum theorem tells you the sum of angles of a triangle is 180°. Angles of a linear pair are supplementary, so total 180°. These facts can be used to write a relation that can be solved for x.
__
interior anglesThe interior angle at the right end of the line is the supplement of 4x:
180° -4x
The interior angle at the left end of the line is the supplement of 2x:
180° -2x
angle sum86° +(180° -4x) +(180° -2x) = 180°
Then the solution to the triangle is ...
266° = 6x . . . . . . . . . add 6x-180°
x = 266°/6 = 44 1/3° . . . . . divide by 6
exterior angle 4x = 177 1/3°exterior angle 2x = 88 2/3°interior left side angle 180° -88 2/3° = 91 1/3°interior right side angle: 180° -177 1/3° = 2 2/3°8- Determine the midpoint of a line segment with the endpoints (8, 0) and
(4,6)
A. (3,6)
B. (7,3)
C. (6,3)
D. (7.6)
Can someone help pls ?
Answer:
C. (6, 3)
Step-by-step explanation:
Use the midpoint formula!
Midpoint Formula
[tex]\text{midpoint} = (\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2})[/tex]
x₁, x₂ ... x-coordinates of the endpoints
y₁, y₂ ... y-coordinates of the endpoints
Given endpoints:
(8, 0)
(4, 6)
Points are in form (x, y).
Now let's substitute the variables in the formula with our values.
[tex](\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2})[/tex]
[tex](\frac{8 + 4}{2}, \frac{0+ 6}{2})[/tex]
[tex](\frac{12}{2}, \frac{6}{2})[/tex]
[tex](6, 3)[/tex]
(6, 3) is our midpoint!
Please solve the question in the picture
Answer:
A. 11"
B. 39"
25 - 15 < x < 25 + 15
10 < x < 40
*x = whole number
Answer:
shortest: 11 incheslongest: 39 inchesStep-by-step explanation:
Given two side lengths for a triangle, the triangle inequality tells you the third side must have a length between the difference and the sum of the given sides.
__
A. minimum lengthThe difference of the given sides 25 and 15 is ...
25 -15 = 10
The smallest integer greater than 10 is 11.
The third side must be at least 11 inches long.
__
B. maximum lengthThe sum of the given sides is ...
25 +15 = 40
The largest integer smaller than 40 is 39.
The third side must be at most 39 inches long.
_____
Additional comment
Formally, the triangle inequality tells you that sides a, b, c must satisfy ...
a +b > c and b +c > a and c +a > b
When we're considering the length of third side (c), there are 3 cases to consider. 1) c is shortest; 2) c is between the other lengths; 3) c is longest. Without loss of generality, we can assume a > b.
1) c is shortest:
a+b>c is always true. b+c>a ⇒ c>a-b (the positive difference)c+a>b ⇒ c>b-a (the negative difference)conclusion: c > a-b
2) a > c > b:
a+b>c is always true. b+c>a ⇒ c>a-b (the positive difference) c+a>b ⇒ c>b-a (the negative difference)conclusion: c > a-b
3) c is longest:
a+b>c (the sum)b+c>a ⇒ c>a-b (the difference will be less than the sum)c+a>b ⇒ c>b-a (the negative difference will be less than the sum)conclusion: a -b < c < a+b . . . . . . for a>b
Which graph can be used to find the solution(s) to x2 – 4x + 4 = 2x + 1 + x2?
The solution to the equation x² – 4x + 4 = 2x + 1 + x² is x = 2.5 and the graph is shown in the picture.
What is a function?It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
We have an equation:
x² – 4x + 4 = 2x + 1 + x²
After solving:
-4x + 4 = 2x + 1
6x = 3
x = 1/2 = 0.5
Thus, the solution to the equation x² – 4x + 4 = 2x + 1 + x² is x = 2.5 and the graph is shown in the picture.
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Katy invests a total of $13,000 in two accounts paying 2% and 7% annual interest, respectively. How much was invested in each account if, after one year, the total interest was $310.00.
Invested at 2%___?
Invested at 7%___?
Answer:
2 % amount = 12000 7% amount = 1000 dollars
Step-by-step explanation:
x = 2% amount
then 13 000 - x = 7% amount
.02x + .07 (13000-x) = 310
-.05x + 910 = 310
.05x = 600
x = 600/.05 = 12000 then the 7% amount is 1000
dependent or independent
The probability of coin landing with heads is an independent event.
The probability of winning 1st and 2nd prize is a dependent event.
What are independent and dependent events?
Independents events are events whose occurrence do not depend on each other. They are random events. The probability of a coin landing on heads is a random event.
Dependent events are events that are not random. The outcome of one event depends on the outcome of another event.
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) The gym teacher divided a class into four teams with 7 students per team. How many students are in the class?
Answer:
28 students
Step-by-step explanation:
7 times 4 = 28
there are are seven students in 4 teams, so that means there are 4 groups of seven, and you multiply them together to get how many students in the class
Answer:
28
Keyword(s):
divided, four, 7, per team, how many
Step-by-step explanation:
7 × 4 = 28
I NEED HELP ASAPPPPPP
Its height (in feet) as a function of time (in seconds after the timer was started) is given by the equation h(t)=−(t−12)2+81
. Which of the following statements is true?
The airplane reaches its minimum height of 12 feet in 81 seconds.
The airplane reaches its maximum height of 81 feet in 12 seconds.
The airplane reaches its minimum height of 81 feet in 12 seconds.
The airplane reaches its maximum height of 12 feet in 81 seconds.
Considering the given quadratic equation, the correct statement is given by:
The airplane reaches its maximum height of 81 feet in 12 seconds.
What is the equation of a parabola given it’s vertex?The equation of a quadratic function, of vertex (h,k), is given by:
y = a(x - h)² + k
In which a is the leading coefficient.
In this problem, the equation is given by:
h(t) = -(t - 12)² - 81.
The vertex is (12,81), with a negative leading coefficient, hence it is a maximum point and the correct statement is given by:
The airplane reaches its maximum height of 81 feet in 12 seconds.
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2/3 - 5/4 + 7/3 whats the4 answer pls
Answer:
7/4Step-by-step explanation:
2/3 - 5/4 + 7/3
=8/12 - 15/12 + 28/12 (LCM=12)
(8 - 15 + 28)/12
=21/12
=7/4
Using complete sentences, describe how the variable h and the variable k of the general formula for a cube root function effects the graph. The general formula is y=a^3√ x-h+k
Using translation concepts, it is found that the variables h and k affect the graph of the function as follows:
The function is shifted h units to the right.The function is shift k units up.What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.
In this problem, we consider the parent cube root function as follows:
[tex]y = \sqrt[3]{x}[/tex]
Then, these following changes happened:
x -> x - h, which means that the function was shifted h units to the right.y -> y + k, which means that the function was shifted k units up.More can be learned about translation concepts at https://brainly.com/question/4521517
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My sister needs help on this question and I am too lazy to figure this out please help ASAP
The question was: Which figure has exactly one line of symmetry?
Answer:
its the Pentagon, the other shaps have 2 lines if symmetry
f(x) = 5 + 4x2, then f(3) =
Step-by-step explanation:
To answer this, we need to plug in 3 as x in the equation f(x) = 5 + 4x².
That would look like this: f(3) = 5 + 4(3)²
f(3) = 5 + 4(3)²
f(3) = 5 + 36
f(5)=41
Therefore, the answer is 41.
I hope this helps!! :)
The starting line for a race in Cass is 2.4 miles from the finish line. On a map of the course,
the starting and finish lines are 6 inches apart. What scale does the map use?
Write your answer in simplest form using whole numbers.
__ inches = __ miles
Answer:
5 in. = 2 mi.
Step-by-step explanation:
2.4mi = 6in
1 mi = 2.5in
2.5 inches = 1mile
Convert to whole #'s as the question asks
5 in. = 2 mi
-- Gage Millar, Algebra 1/2 Tutor (Pending Pre-Calc Tutor)
Answer:
3 inches = 1 miles
Step-by-step explanation:
The first scale you get is with the information that is given:
6 inches = 2.4 miles
Then you simplify, dividing both sides by 2.4:
2.5 inches = 1 miles
Rounding up: 3 inches = 1 miles
Hope it helps!
Given that the expression x³_ ax² + bx+c leaves the same remainder when divided by x + 1 or x-2, find 'a' in terms of 'b'.
Answer:
Hi,
a=b+3
Step-by-step explanation:
[tex]\begin{array}{c||c|c|c|c}&x^3&x^2&x&1\\---&---&---&---&---\\&1&-a&b&c\\x=-1&&-1&a+1&-a-b-1\\---&---&---&---&---\\&1&-a-1&a+b+1&c-a-b-1\\\end{array}[/tex]
[tex]\begin{array}{c||c|c|c|c}&x^3&x^2&x&1\\---&---&---&---&---\\&1&-a&b&c\\x=2&&2&4-2a&2b+8-4a\\---&---&---&---&---\\&1&2-a&b+4-2a&c+2b+8-4a\\\end{array}[/tex]
Thus:
c+2b+8-4a=c-a-b-1
3b-3a=-9
a=b+3
A bottle contains 20 blue bags and 15 red bags. If two bags are picked at random one after the other with replacement, what is the probability that the first bag is blue and then red?
Answer:
12÷49Step-by-step explanation:
The total number of bags in the bottle = 20 + 15 = 35
Then
the probability that the first bag is blue = 20/35
If we replace the first bag :
the probability that the second (picked) bag is blue = 15/35
Conclusion:
If two bags are picked at random one after the other with replacement
Then
the probability that the first bag is blue and then red is :
(20÷35)×(15÷35)
= (4÷7)×(3÷7)
= 12÷49
= 0.244897959184
for each sequences, find the first 4 term and the 10th term the sequences are
(a) n^2+3
(b)2n^2
Answer:
see explanation
Step-by-step explanation:
to find the first 4 terms substitute n = 1, 2, 3, 4 into the sequence rule
to find the 10th term substitute n = 10 into the rule
(a)
a₁ = 1² + 3 = 1 + 3 = 4
a₂ = 2² + 3 = 4 + 3 = 7
a₃ = 3² + 3 = 9 + 3 = 12
a₄ = 4² + 3 = 16 + 3 = 19
a₁₀ = 10² + 3 = 100 + 3 = 103
(b)
a₁ = 2(1)² = 2(1) = 2
a₂ = 2(2)² = 2(4) = 8
a₃ = 2(3)² = 2(9) = 18
a₄ = 2(4)² = 2(16) = 32
a₁₀ = 2(10)² = 2(100) = 200
What is the discriminant of the quadratic equation 0 = -x² + 4x − 2?
Answer: 8
Step-by-step explanation:
The discriminant is [tex]b^2-4ac[/tex]
in the equation:
[tex]-x^2+4x-2[/tex]
A = -1, B = 4, C = -2
plug into equation
[tex]4^2-4(-1)(-2)[/tex]
[tex]16-8[/tex]
⇒ [tex]8[/tex]
Use Pemdas to evaluate: 5c - 19, c=10
A stack of 30 science flashcards includes a review card for each of the following: 10 insects, 8 trees, 8 flowers, and 4 birds.
What is the probability of randomly selecting an insect?
Express the probability as a reduced fraction
Answer:
1/3
Step-by-step explanation:
[tex]|\Omega|=30\\|A|=10\\\\P(A)=\dfrac{10}{30}=\dfrac{1}{3}[/tex]
help me pleaseeeeeeeeeeeeeee
Answer:
C
Step-by-step explanation:
Evaluating the options :
Option A
⇒ 5/2x + 7/2 = 3/4x + 14
⇒ 2.5x - 0.75x = 14 - 3.5
⇒ 1.75x = 10.5
⇒ x = 6
⇒ No ×
===========================================================
Option B
⇒ 5/4x - 9 = 3/2x - 12
⇒ 1.5x - 1.25x = -9 + 12
⇒ 0.25x = 3
⇒ x = 12
⇒ No ×
=========================================================
Option C
⇒ 5/4x - 2 = 3/2x - 4
⇒ 1.5x - 1.25x = -2 + 4
⇒ 0.25x = 2
⇒ x = 8
⇒ Yes √
C is the right answer.
Please help me thanks!
Problem 1
Any pair of equilateral triangles are always similar triangles. We can use the SSS (side side side) similarity theorem to prove this. One triangle is an enlarged copy of the other, or a shrunken reduced copy.
The rectangle is NOT similar to the square. They are different shapes. Similar figures are figures that are the same shape, but different sizes.
==========================================================
Problem 2
horizontal/vertical = horizontal/vertical
24/x = 6/5
24*5 = 6x
120 = 6x
x = 120/6
x = 20
Answer: The flagpole is 20 ft high (about 2 stories tall)
==========================================================
Problem 3
The formula to use is [tex]z = \sqrt{x*y}[/tex]
z = geometric mean of x and y
We multiply the numbers and take the square root. This only works for two values at a time. The geometric mean of three numbers will involve the cube root. Four numbers involves the 4th root, and so on.
Geometric mean of 6 and 10 is sqrt(60) = 7.74597 approximatelyGeometric mean of 2 and 32 is 8 exactlyGeometric mean of 2 and 8 is 4 exactlyGeometric mean of 7 and 9 is sqrt(63) = 7.93725 approximately==========================================================
Problem 4
For each figure, the y is the altitude and can be determined using the geometric mean formula.
Figure on the left: y = sqrt(2*6) = sqrt(12) = 3.4641Figure on the right: y = sqrt(6*14) = sqrt(84) = 9.1652The decimal values are approximate.
==========================================================
Problem 5
For 45-45-90 triangles, we divide the hypotenuse over sqrt(2) to find the leg length.
For the first triangle in the first row, we have y = 18/sqrt(2) = 9*sqrt(2) after rationalizing the denominator. Multiply top and bottom by sqrt(2).
Take this process in reverse to determine the hypotenuse if you know the leg length. This explains why the hypotenuse is 3.2*sqrt(2) for the second triangle in the first row.
-------------------
For 30-60-90 triangles, we go from the short leg x to the hypotenuse 2x.
Double the short leg to get the hypotenuse.
2x = 36
x = 36/2
x = 18
This is for the first triangle in the bottom row.
For the other triangle in this bottom row, we have a long leg of 4*sqrt(3). This must mean the short leg is exactly 4 units long. Therefore, the hypotenuse is 2*4 = 8 units long.
-------------------
Summary:Top row, first column: y = 9*sqrt(2)Top row, second column: y = 3.2*sqrt(2)Bottom row, first column: x = 18Bottom row, second column: y = 8What is the equivalent to a dash?
Answer:
a dash is 1/8 tsp.
Step-by-step explanation:
a dash is 1/8 tsp or called 0.13
expression equivlant (x+5)^2
Answer:
(x+5) (x+5)
Step-by-step explanation:
it's just (x+5)^2 twice
if 7544644555- x is 45000 whats the value of x
Answer:
Step-by-step explanation:
45000+7544644555=x
x=7544689555
Answer:
x = 7544599555
Step-by-step explanation:
First let's make an equation :
7544644555 - x = 45000
Now to make x the subject and positive :
We add x to both sides :
7544644555 = 45000 + x
Now we subtract 45000 from both sides :
7544644555 - 45000 = x
x = 7544599555
Hope this helped and brainliest please
Find the mean and median of the data. 31, 14, 18, 26, 17, 32
Answer:
The mean is 23
The median is 22
Step-by-step explanation:
To find the mean you have to do 2 steps:
Step 1: Add up all your numbers:
31 + 14 + 26 + 17 + 32 + 18
= 138
Step 2: Divide you answer by how many numbers there are(6):
138 ÷ 6
= 23
Now to find you median
First put the numbers in order:
14, 17, 18, 26, 31, 32
Now grab the middle number and since there are an even amount of numbers grab the 2 middle numbers:
14, 17, 18, 26, 31, 32
Now add the 2 numbers:
18 + 26
= 44
The last step is to divide your answer by 2:
44 ÷ 2
= 22
please help me thank you :)
The function on the table is decreasing on the interval [-2, 0).
Over what interval is the function shown in the table decreasing?
A function is decreasing if, as x increases, f(x) decreases.
We can see that at x = -2, f(-2) = 12.
Then at x = 0, f(0) = 0.
And for the value after that:
x = 1, f(1) = 3
So now the function increases. Then we conclude that the function is decreasing on the interval [-2, 0), and after that the function increases.
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pls help... Prove (1+tanx)/(1+cotx)=tanx by algebra
[tex]\text{L.H.S}\\\\=\dfrac{1+\tan x}{ 1+ \cot x}\\\\\\=\dfrac{1+ \tan x}{ 1+ \tfrac 1{\tan x}}\\\\\\=\dfrac{1+\tan x}{\tfrac{\tan x+1}{\tan x}}\\\\\\=(1+\tan x) \times \dfrac{\tan x}{1+ \tan x}\\\\=\tan x\\\\=\text{R.H.S}\\\\\text{Proved.}[/tex]
Please Help I Don't Understand!
Answer:
5.3
Step-by-step explanation:
Since they are similar triangles, we assume the ratio between AM/AN is equal to the ratio between MB/NC.
AM/AN = 6/8 = 3/4
If MB is 4
3/4 = MB/NC = 4/NC
3/4 = 4/NC
3NC = 16
NC = 16/3
16/3 = 5.333333
explanation/proof why the lines are parallel and insights
Answer:
The lines are parallel is the will never touch.
Step-by-step explanation:
temp change -4.2 and 9.1
Subtraction is a mathematical operation that reflects the removal of things from a collection. The temperature change from -4.2 to 9.1 is 13.3.
What is subtraction?Subtraction is a mathematical operation that reflects the removal of things from a collection. The negative symbol represents subtraction.
The temperature change from -4.2 to 9.1 is,
ΔT = 9.1 - (-4.2) = 9.1 + 4.2 = 13.3
Hence, the temperature change from -4.2 to 9.1 is 13.3.
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