The conditional probability formula is P(X|Y) = P(X and Y)/P(Y)
How to determine the formula?The conditional formula is represented as:
P(A|B) = P(A and B)/P(B)
In this case:
A = X
B = Y
So, we have:
P(X|Y) = P(X and Y)/P(Y)
Hence, the conditional probability formula is P(X|Y) = P(X and Y)/P(Y)
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State whether each of the following is an
open or closed question.
a) Why do you enjoy cooking?
b) What is your favourite fruit?
c) How tall are you?
d) Do you enjoy cooking?
e) What did you do on your holiday?
the answer the answer
Answer:
the answer
Step-by-step explanation:
Answer:
K?
Step-by-step explanation:
The answer of the answer is the answer.
Hope this helped :D
Consider [tex]$\triangle ABC$ such that $BC = 3AC$ and $\angle A = \pi/6$[/tex]
What are [tex]\[12 \sin(\angle B), 12 \sin(\angle C)\][/tex] in that order?
The answer to the question is,
12 sin(∠B) = 2, 12 sin(∠C) = √3+√35
Sin rule is,
sin(A)/BC = sin(B)/AC = sin(C)/AB
sin(B) = (sin(A)×AC)/BC
sin(C) =(sin(B)×AB)/AC
To solve this question we apply sin rule,
Now we take
12 sin(∠B) =12 (sin(∠A)×AC)/BC
12 sin(∠B) =12 (sin(π/6)×(x/3x)) where ∠A =π/6 and AC=x, BC =3x
12 sin(∠B) =12 ((1/2)×(1/3))
12 sin(∠B) =12/6 = 2
12 sin(∠B) = 2
now we find the value of 12 sin(∠C)
12 sin(∠C) = 12(sin B)×(AB/BC)
now put the value of 12 sin(∠B) = 2
12 sin(∠C) = 2×(AB/BC)
12 sin(∠C) = (2/AC)×[AC×(cos(π/6))+BC×(cos B)]
12 sin(∠C) = 2×[cos(π/6)+(BC/AC)×(cos B)]
cos (π/6) = √3/2 and BC/AC =3
then
12 sin(∠C) = 2×[(√3/2)+3×(cos B)]
cos B= √1-sin²B
12 sin(∠C) = 2×[(√3/2)+3×√(1-sin²B)]
12 sin(∠B) = 2
sin B = 1/6
12 sin(∠C) = 2×[(√3/2)+3×√(1-(1/6)²]
12 sin(∠C) = 2×[(√3/2)+3×√1-(1/36)]
12 sin(∠C) = 2×[(√3/2)+3×√(36-1)/36]
12 sin(∠C) = 2×[(√3/2)+3×√(35/36)]
12 sin(∠C) = 2×[(√3/2)+(3/6)×√35]
12 sin(∠C) = 2×[(√3/2)+(1/2)×√35]
12 sin(∠C) = 2×[(1/2)(√3+√35)]
12 sin(∠C) = √3+√35
Hence the answer is,
12 sin(∠B) = 2, 12 sin(∠C) = √3+√35
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TRUE or FALSE: The square root of R2 (the coefficient of determination) is r, the correlation coefficient. (remember that square roots are always positive)
The The square root of R² (the coefficient of determination) is not r, the correlation coefficient. Therefore, it's false.
What is a correlation coefficient?It should be noted that the correlation coefficient is used to measure how string the relationship between two variables are.
The correlation formula tells us the linear relationship between the variables. R² is the square of the correlation coefficient.
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Given that is the angle bisector of A, determine the length of x. (SHOW YOUR WORK PLEASE!!!)
The length of x will be 4 cm if is the angle bisector of A.
What is an angle bisector?A straight line that splits an angle in a triangle into two congruent angles is known as the angle bisector.
Given sides;
AB=12
AE=8
BD=6
DE=x
From the triangle angle bisector theorem;
[tex]\rm \frac{BD}{DE} = \frac{AB}{AE} \\\\ \frac{6}{x} =\frac{12}{8} \\\\ x=4[/tex]
Hence the length of x will be 4 cm.
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The number of cars parked in a car park increases from 50 to 73. what is the percentage increase?
73 is a 46% increase of 50.
What is percentage ?
A percentage is a relative value that represents the hundredth part of any quantity. One percent (symbolized 1%) is a hundredth part; thus, 100 percent represents the entire amount and 200 percent specifies twice the given amount.
Percentage is defined as a specific part or amount out of a hundred. It is a fraction with the denominator 100 and is denoted by the symbol "percent."
The percent increase formula is as follows:
Percent increase = [(new value - original value)/original value] * 100.
Number of car parking (original value)=50
Number of car parking(new value)=73
The Percentage increase =[(73-50)/50]*100
= [(23)/50]*100
=.46*100
=46%
73 is a 46% increase of 50.
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Complete the sentence below. if (3x2 22x 7) ÷(x 7) = 3x 1, then (x 7)( ) = . the check of the polynomial division problem shows that the product of two polynomials is a polynomial. this supports the fact that the property is satisfied for polynomial multiplication.
The full set is;
(x + 7) (3x + 1) = 3x² + 22x + 7
This question introduces the concept of polynomial long division.
This is what we are
Given: (3x² + 22x + 7) ÷ (x + 7) = 3x + 1
Now, from the concept of polynomial long division, we can see that:
if, f (x) ÷ g (x) = h (x),
This means that we can write:
f (x) = g (x) × h (x)
Applying the same concept to the question, we can also say:
(3x² + 22x + 7) ÷ (x + 7) = 3x + 1,
Next; (x + 7) (3x + 1) = 3x² + 22x + 7
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What is the value of x
Could someone help me out here and show the work for this question? Thank and this is much appreciated
Answer:
[tex]\boxed{\boxed{\bf x = 7}}[/tex]
Step-by-step explanation:
[tex] \sf \cfrac{4x - 4}{20} = \cfrac{30}{25} [/tex]
[tex]\sf 4x - 4 = \cfrac{(20)(30)}{25} [/tex]
[tex]\sf 4x - 4 = \cfrac{600}{25} [/tex]
[tex]\sf 4x - 4 = 24[/tex]
[tex]\sf 4x = 24 + 4[/tex]
[tex]\sf \cfrac{4x}{4} = \cfrac{28}{4} [/tex]
[tex]\sf x = 7[/tex]
----------------------------------Hi! Please help me find the slope of the line.
Answer:
3/2
Step-by-step explanation:
We can use the slope formula to find the slope of the line
m = ( y2-y1)/(x2-x1)
Using the points (0,-4) and (2,-1)
m = ( -1 - -4)/( 2 - 0)
= (-1+4)/ (2 -0)
= 3/2
Thé nth term rule for a sequence is 4n + 7 what is the 3rd term of this sequence?
Answer:
a₃ = 19
Step-by-step explanation:
to find the third term substitute n = 3 into the nth term rule
a₃ = 4(3) + 7 = 12 + 7 = 19
Answer:
a₃ = 19
Step-by-step explanation:
the relationship between any two terms of an arithmetic sequence (in our case the relationship between the 3rd term and nth term) gives us this equality :
[tex]a_n - a_3 = 4(n-3)[/tex]
Then
4n + 7 - a₃ = 4n - 12
Then
7 - a₃ = - 12
Then
7 + 12 = a₃
Then
a₃ = 19
Guys I need help! You and your friend are rolling number cubes. Each cube has 6 sides with the numbers 1 to 6. If a sum of 7 is rolled, your friend gets 1 point.
If a 2, 3, or 4 is rolled, you get 1 point.
After 108 rolls each, what scores should you expect?
1. Friend: 54; You: 54
2. Friend: 54; You: 18
3. Friend: 18; You: 18
4. Friend: 18; You: 54
Determine the value of x.
घ
55°
yo
E
(11x + 4)º
Answer: 6
Step-by-step explanation:
Because [tex]\overline{DE} \cong \overline{EF}[/tex], [tex]y=55[/tex]. So, because angles in a triangle add to 180 degrees, [tex]11x+4=70 \longrightarrow x=6[/tex]
Hi I need help with the question in the image. Step by step, thank you!
The exponential function is [tex]f(x) = 18(12)^{-x-4} + 2[/tex]
How to determine the equation?An exponential function is represented as:
y = b^x
Where b represents the base.
The base is given as:
b = 12
So, we have:
y = (12)^x
It is vertically compressed by a factor of 1/8.
So, we have:
y = 18(12)^x
When reflected across the y-axis, we have:
[tex]y = 18(12)^{-x}[/tex]
The horizontal asymptote is y = 2.
So, we have:
[tex]y = 18(12)^{-x} + 2[/tex]
It passes through the point (-3, 4).
So, we shift the function to the right by 4 units
[tex]y = 18(12)^{-x-4} + 2[/tex]
Express as a function
[tex]f(x) = 18(12)^{-x-4} + 2[/tex]
Hence, the exponential function is [tex]f(x) = 18(12)^{-x-4} + 2[/tex]
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Complete the following chart (check picture below)
The following requires the submission of the details of the parabola related to the equations.
What is a Parabola?A parabola, simply defined, is a plane curve that is created by a point that is moving such that it's distance from a fixed locus is equal to it's distance from a line that is fixed.
What are the details for equation y = -2(x-5)² + 3?Vertex → (5,3)Axis of Symmetry → x = 5Direction of Opening → Opens downMax or Min → (5, 3)Y-intercept → 25/8What are the details for equation y = (x + 2)²Vertex → (-2, 0)Axis of Symmetry → x = -2Direction of Opening → Opens UpMax or Min - (-2, 0)Y-intercept → (0,-47)Learn more about Parabola at;
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If y is inversely proportional to z^4, when y = 16 and z = 3, then 16 = k/81
true or false
Answer: 65
Step-by-step explanation:
1 + 64 = 65
What are the zeros of g(x)= x³ + 6x² - 9x-54?
Answer:
3,-3
Step-by-step explanation:
g(3)= (3)³+6(3)²-9(3)-54
= 27+54-27-54
=81-81
= 0
g(-3) = (-3)³+6(-3)²-9(-3)-54
= -27+54+27-54
= 27-27
= 0
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What is the best first step in solving the equation 3+√6x=5?
O Subtract 3 from both sides.
O Find the cube of Vex.
O Cube both sides of the equation.
O Subtract 5 from both sides.
Which of the following demonstrates the correct first step in copying an angle?
Create a line that intersects the angle.
Draw a ray with one endpoint.
Create a point outside of the angle.
Swing an arc that intersects the angle's rays.
"Draw a ray with one endpoint" demonstrates the correct first step in copying an angle. This is further explained below.
What is the angle?In general, the distance (which is sometimes stated as a degree) that occurs between two crossing lines or surfaces at or near the point where they meet. This distance might be positive or negative.
The formation of an angle is caused by the conjunction of two rays at a single point in space. The split or 'opening' that can be seen between these two rays is referred to as a 'angle,' and the symbol denotes this particular angle. The degree is the standard unit of measurement for angles, and its values include things like 60 degrees and 90 degrees, amongst other possible combinations.
In conclusion, "Draw a ray with one terminal" illustrates the correct first step in duplicating an angle. This step shows how to replicate an angle.
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what is the midpoint of the line segment that joins -3/4 and 2 1/2
The mid point between the two points is at 13/8 .
What is a Line Segment ?A line segment is a line of fixed measure .
The line segment extends from (-3/4) to [tex]\rm 2 \dfrac{1}{2}[/tex]
i.e the line extends form -3/4 to 5/2
To find the mid point , the total distance needs to be determined
So the distance between the two point is
(5/2) + (3/4) = 13/8
The mid point is at half the distance of this
so it is at 13/8 from both the points
Any point at 13/8 distance from 5/2 towards (-3/4) will be
= (5/2) - (13/8)
= 7/8
So the mid point between the two points is at 13/8 .
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A correlation coefficient of 0.08 indicates strong positive correlation. Group startsTrue or False
Since the correlation coefficient has an absolute value that is less than 0.6, it is not a strong relationship, hence the statement is False.
What is a correlation coefficient?It is an index that measures correlation between two variables, assuming values between -1 and 1.If it is positive, the relation is positive, that is, they are direct proportional. If it is negative, they are inverse proportional.If the absolute value of the correlation coefficient is greater than 0.6, the relationship is strong.In this problem, the correlation coefficient is of 0.08, hence:
The coefficient is positive, hence the is a positive correlation.The coefficient is of 0.08, which is less than 0.6, hence the correlation is not strong.Thus, the given statement is False.
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Knowing that sin 30° = 1, what is a?
OA. 3.5
OB. 14
OC. 12.12
OD. 7
30⁰
7
a
60⁰
Answer:
B
Step-by-step explanation:
sin30° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{7}{a}[/tex] = [tex]\frac{1}{2}[/tex] ( cross- multiply )
a = 7 × 2 = 14
in the number pattern below, in which row is 2007
1
2. 3.
4. 5. 6.
....
The number 2007 is in the 63rd row
How to determine the number of row?The pattern is given as
1
2 3
4 5 6
The sum of n natural numbers is:
Sum = 0.5n(n + 1)
Assume n = 62
Sum = 0.5 * 62 * (62 + 1)
Sum = 1953
Assume = 63
Sum = 0.5 * 63 * (63 + 1)
Sum = 2016
2007 is between 1953 and 2016
Since 2016 is greater than 1953, we can conclude that 2007 is in row 63
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The coordinate grid shows points A through K. What point is a solution to the system of inequalities? y < −2x + 10 y < 1 over 2x − 2 coordinate grid with plotted ordered pairs, point A at negative 5, 4 point B at 4, 7 point C at negative 2, 7 point D at negative 7, 1 point E at 4, negative 2 point F at 1, negative 6 point G at negative 3, negative 10 point H at negative 4, negative 4 point I at 9, 3 point J at 7, negative 4 and point K at 2, 3 I B A F
The point that is a solution to the system of inequalities on the coordinates grid is A.
How to illustrate the information?It should be noted that form the information given, the expression is y < −2x + 10. In this case, draw the solid line y = -2x + 10.
Shade the region below the like for x = 5.
y = -2(5) + 10
= -10 + 10
= 0
For x= 0
y = -2(0) + 10
= 0 + 10
= (0, 10)
The diagram is attached.
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Calculate the angle of depression from the
top of the flag pole to point A.
Give your answer to 1 d.p.
A
31 feet
25 feet
The angle of depression from the top of the flag pole to point A is 36.2 degrees.
What is the angle of depression?From trigonometric ratio: cos(θ) = Adjacent / Hypotenuse
Given that;
Adjacent = 25ftHypotenuse = 31ftAngle of depression θ = ?cos(θ) = Adjacent / Hypotenuse
Cos(θ) = 25ft/31ft
Cos(θ) = 0.80645
θ = cos⁻¹( 0.80645 )
θ = 36.2°
Therefore, the angle of depression from the top of the flag pole to point A is 36.2 degrees.
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Geometry)
Given the circle with center O and with m angle ROQ=144^o , find the measure of minor arc PR.
Answer choices…
72^o
216^o
36^o
18^o
(Picture is below) Thank you!
AMSWER :
Just remove the given angle from 180°
since , a straight line makes a angle of 180°
hence,
ROQ + ROP = 180°
144° + ROP = 180°
ROP = 180° - 144° = 36°
.
.
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The following graph describes function 1, and the equation below it describes function 2. Determine which function has a greater maximum value, and provide the ordered pair. (1 point)
Function 1
graph of function f of x equals negative x squared plus 8 multiplied by x minus 15
Function 2
f(x) = −x2 + 2x − 3
Function 1 has the larger maximum at (1, 4).
Function 1 has the larger maximum at (4, 1).
Function 2 has the larger maximum at (1, −2).
Function 2 has the larger maximum at (−2, 1).
13.
Answer: Function 1 has the larger maximum at (4,1).
Step-by-step explanation:
The vertex of f(x) is at [tex]x=-\frac{2}{2(-1)}=1[/tex], and [tex]f(1)=-2[/tex].
For the graph, the maximum is obviously at (4,1).
So, Function 1 has the larger maximum at (4,1).
Rohan's salary 1200$ per month he spends 75% of it how does he spend in dollars?
Answer:900
Step-by-step explanation:
Elvira College has an enrollment of 1,000 students and is located in a small Midwestern town named Johnsonville. Johnsonville has a total population of 2,500 people. The nearest town is 20 miles away. Most of the residents shop locally, but they travel about once a month to the larger city and pick up the large-ticket items. Johnsonville has one fairly good-size supply store named Jameson's Grocery. The only other place in town where you might buy supplies is at the gas station/convenience store located on the edge of town. What competitive situation is Jameson's Grocery experiencing?
Since there are only two (2) sellers in the town with many buyers, the competitive situation which Jameson's Grocery is experiencing is an oligopoly.
What is an oligopoly?An oligopoly can be defined as a market structure which comprises a small number of business firms (sellers) that are offering identical (similar) products to many buyers, wherein none of the sellers can limit the significant influence of others.
In this scenario, we can infer and logically deduce that the competitive situation which Jameson's Grocery is experiencing is an oligopoly because there are only two (2) sellers in the town with many buyers (1,000 students).
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( this is my summer math homework, please help!)
Find the selling price of each item.
1. Original price of a bunny: $46.00
Text: 2%
2. Original price of a CD: $14.99
Tax: 2%
3. Original price of a CD: $16.50
Tax: 4%
4. Original price of a car: $19,500.00
Tax: 4%
Using proportions, the selling prices are given as follows:
1. $46.92.
2. $15.29.
3. $17.16.
4. $20,280.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
To find the selling prices, we have to multiply the original prices by either 1.02(2% sales tax) or 1.04(4% sales tax), hence they are given as follows:
1. 46 x 1.02 = $46.92.2. 14.99 x 1.02 = $15.29.3. 16.50 x 1.04 = $17.16.4. 19500 x 1.04 = $20,280.More can be learned about proportions at https://brainly.com/question/24372153
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Abigail poured 8 x 10 milliliters of water into a beaker to use for an experiment. How is 8 x 10 written as a whole number?
Answer:
80?
hshsshjsjsjjsjajjsjsnnsnsnnw
Step-by-step explanation:
hhddussisusuis