Analyze the diagram below and complete the instructions that follow.
A. 3/22
B. 3/7
C. 8/15
D.8/11
Answers
1. This question refers to conditional probability and is asking us to find the probability of Q occurring, given that R occurs. What this means is that we must divide the probability of Q and R occurring by the probability of R occurring (this is because we have the condition that R occurs). This may be written as such:
Pr(Q|R) = Pr(Q ∩ R) / Pr(R)
2. Now, the first step is to find Pr(Q ∩ R). This is given by the value in the centre of the Venn Diagram (ie. in the cross-over between the two circles) divided by the total of all the values:
Pr(Q ∩ R) = 3/(8 + 3 + 4 + 22)
= 3/37
3. The next step is to find Pr(R). This is given by the value in the circle denoted R (including the cross-over with Q) divided by the total of all the values.
Pr(R) = (4 + 3)/(8 + 3 + 4 + 22)
= 7/37
4. Thus, we can now subtitute the probabilities we defined in 2. and 3. into the formula for conditional probability we defined in 1.:
Pr(Q|R) = (3/37) / (7/37)
= 3/7
Thus, the answer is B.
Note that technically there is no need to write out the full probabilities before coming to this answer. The same exact answer could be found by using Pr(Q ∩ R) = 3 and Pr(R) = 7. This works because they are part of the same universal set - in other words, since the total of all the values in the Venn Diagram remains constant, the denominators of the two probabilities would be the same (given that no cancelling is done) and these denominators would be cancelled out when dividing Pr(Q ∩ R) by Pr(R). This can be particularly useful for a multiple choice question such as this one.
Related Questions
The point-slope form of a lone has a slope of -w and passes through point (-5,2) is shown below.
y+2=-2(x-5)
What is the equation in slope intercept form?
Answers
Answer:
y = -2x + 8Step-by-step explanation:
The point-slope form of an equationo f a line:
[tex]y-y_1=m(x-x_1)[/tex]
m - slope
We have
[tex]y+2=-2(x-5)\\\\y-(-2)=-2(x-5)[/tex]
Therefore we have
the slope: m = -2
the point: (5, -2) not (-5, 2)!!!
The slope-intercept form of an equation of a line:
[tex]y=mx+b[/tex]
m - slope
b - y-intercept
Convert:
[tex]y+2=-2(x-5)[/tex] use the distributive property a(b + c) = ab + ac
[tex]y+2=-2x+10[/tex] subtract 2 from both sides
[tex]y=-2x+8[/tex]
Which equation represents the line that passes through ( -8, 11) and ( 4, 7/2)?
A y= -5/8x+ 6
B y= -5/8x+ 16
C y= -15/2x- 49
D y= -15/2x+ 71
Answers
Answer:
A
Step-by-step explanation:
Recall the general equation for a straight line is
y = mx + b
where m is the gradient and b is the y-intercept
given 2 points whose coordinates are (x1, y1) and (x2, y2), m can be found with the following formula:
m = [tex]\frac{y1-y2}{x1-x2}[/tex]
in this case, x1 = -8, y1 = 11, x2 = 4, y2=7/2
applying these values to the formula for m will give
m = -(5/8)
We can see immediately that the only 2 possible answers are A or B.
If we substitute this back into the general equation, we get:
y = -(5/8)x + b
In order to find the value for b, we substitute any one of the 2 given points back into this equation. Lets choose (-8,11)
11 = -(5/8) (-8) + b
11 = -(5/8) (-8) + b
11 = 5 + b
b = 6
hence A is the answer.
I don’t really understand can y’all pls help me
Answers
[tex]\bf ~\hspace{7em}\textit{negative exponents} \\\\ a^{-n} \implies \cfrac{1}{a^n} ~\hspace{4.5em} a^n\implies \cfrac{1}{a^{-n}} ~\hspace{4.5em} \cfrac{a^n}{a^m}\implies a^na^{-m}\implies a^{n-m} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \left( 5^{\frac{3}{2}} \right)^{-\frac{2}{3}}\implies 5^{-\frac{3}{2}\cdot \frac{2}{3}}\implies 5^{-1}\implies \cfrac{1}{5}\implies 0.2 \\\\[-0.35em] ~\dotfill[/tex]
[tex]\bf (256^{0.5})^{1.25}\implies [(2^8)^{0.5}]^{1.25}\implies [2^{8\cdot 0.5}]^{1.25}\implies [2^4]^{1.25}\implies 2^{4\cdot 1.25} \\\\\\ 2^5\implies 32 \\\\[-0.35em] ~\dotfill\\\\ ( 81^{-\frac{1}{6}} )^{\frac{3}{2}}\implies [(3^4)^{-\frac{1}{6}} ]^{\frac{3}{2}}\implies 3^{4\cdot -\frac{1}{6}\cdot \frac{3}{2}}\implies 3^{-\frac{12}{12}}\implies 3^{-1} \\\\\\ \cfrac{1}{3}\implies 0.33...[/tex]
Can someone help me?
Answers
s = number of students books
we know there are many student's books, so since there are "s", and each one weights 2.3 kgs, then all together must weight 2.3s, now the teacher's edition is just 1 alone so that's just 4.3 kgs.
[tex]\bf \stackrel{\stackrel{total}{weight}}{30}~~=~~\stackrel{students'}{2.3s}+\stackrel{teacher's}{4.3}+\stackrel{box's}{0.4}\implies 30=2.3s+4.7 \\\\\\ 30-4.7=2.3s\implies 25.3=2.3\implies \cfrac{25.3}{2.3}=s\implies 11=s[/tex]
A sphere has a volume of 36 π square inches. What is the exact radius?
Answers
36π=4/3πr^3
Divide by 4/3π
27=r^3
Cube root
3=r
The exact radius is 3 inches
If a (z) =2z - 7, than a ( ) = 2(x+1) - 7
Answers
The function a(z) = 2z - 7 transforms into a(x + 1) = 2x - 5 when z is replaced with the quantity (x + 1)
Explanation:The question given has a mathematical function defined as a(z) = 2z - 7. The problem is asking what the function would look like if instead z is replaced by quantity (x+1).
To solve this, replace z in the function with (x+1). As such, instead of multiplying z by 2, we are now multiplying (x+1) by 2. The equation would stand as a(x + 1) = 2(x+1) - 7. Distribute the 2 in the parenthesis, the equation simplifies to a(x + 1) = 2x + 2 - 7.
Therefore, a(x + 1) = 2x - 5 is the function when z is replaced with quantity (x + 1).
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To find a(x) when a(z) = 2z - 7, we replace z with (x+1) in the expression for a(z). Simplifying, we get a(x+1) = 2x - 5.
Explanation:To find a(x) when a(z) = 2z - 7, we replace z with (x+1) in the expression for a(z). This gives us:
a(x+1) = 2(x+1) - 7
Simplifying, we get the values as -
a(x+1) = 2x + 2 - 7
a(x+1) = 2x - 5
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The measure of ∠d is 150°. What is the value of m∠b + m∠c +m∠e
A30°
B90°
C120°
D210°
Answers
Answer:
C. 120°
Step-by-step explanation:
m∠d = 150°
m∠ a = 90°
The sum of angles at a point add up to 360°
m∠b + m∠c +m∠e = 360° - (90° + 150°) = 120°
Answer:
c 120
Step-by-step explanation:
m∠d = 150°
m∠ a = 90°
The sum of angles at a point add up to 360°
m∠b + m∠c +m∠e = 360° - (90° + 150°) = 120°
how to us the foil method for x2 + 16x + 48
Answers
F irst
O uters
I nners
L ast
We first need to expand the equation By finding what adds up to 16 and multiples to 48
X^2 + 16x + 48 = x^2 + 12x + 4x + 48.
According to the foil method
(a + b)(c + d) = ac + ad + bc + bd
ac = x^2
ad = 12x
bc = 4x
bd = 48.
Which expression gives you the distance between the points (5,1)and(9,-6)
Answers
Answer:
[tex]D=\sqrt{(x_{2}-x_{1})^{2} +(y_{2}-y_{1})^{2} }[/tex]
Step-by-step explanation:
Here we are supposed to find the distance between the two coordinates in a plane. The coordinates given to us are
(5,1) and (9,-6)
We can find the distance using distance formula. The distance formula is given as
[tex]D=\sqrt{(x_{2}-x_{1})^{2} +(y_{2}-y_{1})^{2} }[/tex]
Where
[tex](x_{2},y_{2}) ; (x_{1},y_{1})[/tex]
are the two coordinates
Hence
[tex]x_{2} = 9 ; y_{2}= -6\\x_{1}=5; y_{1}=1[/tex]
Substituting these values in the distance formula we get
[tex]D=\sqrt{(9-5)^{2} +(-6-1)^{2}}\\D=\sqrt{(4)^{2} +(-7)^{2}}\\D=\sqrt{16+49}\\D=\sqrt{65}\\[/tex]
Hence the Distance is [tex]D=\sqrt{65}\\[/tex]
If C is the midpoint of segment AB and AB = 20, what is AC?
5
10
20
40
Answers
Answer:
AC= 10
Step-by-step explanation:
If AB is equal to 20 and C is the midpoint (meaning half of the segment), then you simply divide 20 by 2 which equals to 10.
Look at the image below for a drawing of the segment.
We know that the midpoint divides the segment in half. Which means that the length of the whole segment divided by 2 is equal to the length of one part of the segment
AC = AB / 2
AC = 20 / 2
AC = 10
Hope this helped!
~Just a girl in love with Shawn Mendes
write the standard equation of a circle that is tangent to the x-axis with the center located at (2,4)
Answers
Answer:
Step-by-step explanation:
radius=4 as it is tangent to x-axis.
y co-ordinate of center is 4 so radius=4
eq. of circle is (x-2)²+(y-4)²=4²
or x²-4x+4+y²-8y+16=16
or x²+y²-4x-8y+4=0
Final answer:
The standard equation of a circle tangent to the x-axis with center (2,4) is (x - 2)² + (y - 4)² = 16.
Explanation:
To write the standard equation of a circle that is tangent to the x-axis with the center located at (2,4), we must recognize that the distance from the center of the circle to the x-axis is equal to the radius of the circle. Since the center is at (2,4), the distance to the x-axis (which is y=0) is 4 units; thus, the radius of the circle is 4.
The standard form of the equation of a circle with center (h,k) and radius r is (x - h)² + (y - k)² = r². Substituting the given center (2,4) and the radius 4 into this formula, we get:
(x - 2)² + (y - 4)² = 4²
Simplifying the radius squared term, we obtain the final equation:
(x - 2)² + (y - 4)² = 16
Find the area and the circumference of a circle with diameter 7 ft
Answers
Answer:
A≈38.48ft²
C≈21.99ft
Step-by-step explanation:
Please mark brainliest and have a great day!
Answer:
The area is 38.5 ft² and the circumference is 21.99 or 22 ft
Step-by-step explanation:
Find the area and the circumference of a circle with diameter 7 ft,
first, Area of a circle is πr² or πd
D = 2r
7 = 7/2 = 3.5
π = 22/7
Area = πr²
A = 22/7 × (3.5)²
A = 22/7 × 12.25
A = 269.5/7
A = 38.5 ft²
Circumference of a circle is 2πd
C = 22/7 × 7
C = 154/7
C = 21.99
approximately 22.
Hope this helps!
What is the difference of the polynomials (12x2-11y2-13x - (5x2
Answers
The difference of polynomials (12x²-11y²-13x)-(5x²-14y²-9x) is 7x² +3y²-4x
What are Polynomials ?Polynomials are sum of terms of the form kxⁿ , where k is a constant and n is any positive integer.
it is given in the question
To find the difference of the polynomials
(12x²-11y²-13x)-(5x²-14y²-9x)
to add or subtract a polynomial we subtract the like terms with same variable .
12x²-11y²-13x -5x²+14y²+9x
7x² +3y²-4x
Therefore the difference of polynomials (12x²-11y²-13x)-(5x²-14y²-9x) is 7x² +3y²-4x .
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Big Bob’s Pizza is having a special on pizza and is offering two different choices:
Choice #1: One slice of pizza from a pizza with a 22 inch diameter and is cut into 8 slices. The cost is $4.95.
Choice #2: An entire personal-size pizza that has a diameter of 6 inches. The cost is $3.75.
Which choice will give you more pizza for your money? Justify your answer using numbers and words.
Answers
Answer:
The Choice N#1 will give more pizza for your money
Step-by-step explanation:
step 1
Find the area of one slice Choice #1
The area of the circle is equal to
[tex]A=\pi r^{2}[/tex]
we have
[tex]r=22/2=11\ in[/tex] ----> the radius is half the diameter
assume
[tex]\pi =3.14[/tex]
The area of one slice is equal to
[tex]A=(1/8)\pi r^{2}[/tex]
substitute
[tex]A=(1/8)(3.14)(11)^{2}[/tex]
[tex]A=47.4925\ in^{2}[/tex]
Divide the cost by the area
[tex]4.95/47.4925=0.10\frac{\$}{in^{2}}[/tex]
step 2
Find the area of the entire personal pizza Choice # 2
The area of the circle is equal to
[tex]A=\pi r^{2}[/tex]
we have
[tex]r=6/2=3\ in[/tex] ----> the radius is half the diameter
assume
[tex]\pi =3.14[/tex]
substitute
[tex]A=(3.14)(3)^{2}[/tex]
[tex]A=28.26\ in^{2}[/tex]
Divide the cost by the area
[tex]3.75/28.26=0.13\frac{\$}{in^{2}}[/tex]
therefore
The Choice N#1 will give more pizza for your money
Which equation(s) have x = –3 as the solution? log3(2x + 15) = 2 log5(8x + 9) = 2 log4(–20x + 4) = 3 logx81 = 4
Answers
Answer:
log_3(2x+15)=2 and log_4(-20x+4)=3
Step-by-step explanation:
Plug it in and see!
[tex]log_3(2x+15)=2\\log_3(2(-3)+15)=2\\log_3(-6+15)=2\\log_3(9)=2\\\text{ This is a true equation because } 3^2=9\\\\\\log_5(8(-3)+9)=2\\log_5(-24+9)=2\\log_5(-15)=2\\\\\text{ Not true because you cannot do log of a negative number }\\\\log_4(-20(-3)+4)=3\\log_4(64)=3\\\text{ this is true because } 4^3=64\\\\\\log_x (81)=4\\log_{-3}(81)=4\\\text{ the base cannot be negative }\\\\\\\\\text{ There is only two options here} \\\\log_3(2x+15)=2 \text{ and } log_4(-20x+4)=3[/tex]
Answer:
A and C
Step-by-step explanation:
Simplify the expression. Write the answer using scientific notation. (9x10^2)(2x10^10)
Answers
Answer:
1.8 x [tex]10^{13}[/tex]
Step-by-step explanation:
( 9 x 10²) (2 x [tex]10^{10}[/tex] )
= (9)(2) x [tex]10^{10+2}[/tex]
=18 x [tex]10^{12}[/tex]
= 1.8 x [tex]10^{13}[/tex]
Answer:
(9x10^2)(2x10^10)
= 1.9 x 10^13 (In scientific notation)
Step-by-step explanation:
Expression to be simplified is given as:
(9x10^2)(2x10^10)
= 9x10^2x2x10^10
= 9x2x10^2x10^10
The base here in the expression is same so the power will add up:
= 18 x 10^(2+10)
= 1.8 x 10^12
Using Scientific notation on the expression, we know that the decimal point must after the first digit so that the number let us say x is such that x > 0 and x < 10. To move decimal one place back, we will multiply it with 10^1:
18 x 10^12
= 1.8 x 10 x 10^12
= 1.8 x 10^(1+12)
= 1.8 x 10^13
Challenge 1:
The sum of two numbers is 20, and the difference between their squares is 40. Find the numbers.
Challenge 2:
What is the number?
It is greater than 15 squared. It is not a multiple of 3 or 5, but a multiple of 4. It is less than 20
squared. It is not a multiple of 17. It is a square number.
Answers
11+9=20
(11)^2-(9)^2=40
121-81=40
40=40
Find the slope of the line through (–3, 2) and (6, 2)
Answers
Step-by-step Answer:
Given points: P1(-3,2), P2(6,2)
Slope given two points = (y2-y1)/(x2-x1)
= (2-2)/(6-(-3))
=0/9
= 0
Answer:
Slope = 0
Step-by-step explanation:
We are given the following points and we are to find the slope of the line which passes through these points:
[tex] ( – 3 , 2 ) [/tex] and [tex] ( 6 , 2 ) [/tex]
We know that the formula of the slope is given by:
Slope = [tex] \frac { y _ 2 - y _ 1 } { x _ 2 - x _ 1 } [/tex]
Slope = [tex] \frac { 2 - 2 } { 6 - (- 3 )} = \frac { 0 } { 9 } [/tex] = 0
Help me with this question thanks:)
Answers
Answer:
see below
Step-by-step explanation:
3 > w/2
Multiply each side by 2
2*3 > w/2 *2
6 > w
w < 6
There is an open circle at 6 since there is no equal sign
The line goes to the left since w is less then 6
What is the number of ways to arrange 8 objects from a set of 12 different
objects?
A. 19,958,400
B. 495
C. 24,861,300
D. 2,026
Answers
Answer:
A. 19,958,400
Step-by-step explanation:
A portion of a hiking trail slopes downward at about an 84° angle. To the
nearest tenth of a flot, what is the value of x, the distance the hiker traveled
along the path, if he has traveled a horizontal distance of 120 feet?
A. 143.3
B. 12.5
C. 120.7
D. 130.2
Answers
C because if you divide the angle minus the feet you get 120
The distance the hiker traveled along the path if he has traveled a horizontal distance of 120 feet is 120.7 feet.
What are the trigonometric ratios?Trigonometric ratios for a right-angled triangle are from the perspective of a particular non-right angle.
In a right-angled triangle, two such angles are there which are not right angled(not of 90 degrees).
The slanted side is called the hypotenuse.
From the considered angle, the side opposite to it is called perpendicular, and the remaining side will be called the base.
A portion of a hiking trail slopes downward at about an 84° angle.
The distance the hiker traveled along the path if he has traveled a horizontal distance of 120 feet
cos θ=adjacent/hypotenuse
Let h be the hypotenuse, adjacent =120 ft, θ = 84°,
cos 84 = 120/h
h = 120/cos 84
h = 120 / 0.10 ft
h = 120.7 ft
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Evaluate the expression |2x – 5| for x = –3 and for x = 3.
A. 3, 13
B. 13, 3
C. 11, 1
D. 1, 11
Answers
Answer:
C. 11, 1
Step-by-step explanation:
I could have sworn I already answered this. Oh well. I guess I can answer it again. Simply plug in -3 and 3 for x, then find the absolute value [ALWAYS POSITIVE].
What is the area of the triangle
Answers
Answer:
The first choice, 8.64 sq. ft.
Step-by-step explanation:
Formula for area of triangle:
(Length x Height) / 2
4.8 * 3.6 = 17.28
17.28 / 2 = 8.64
A = 8.64 sq. ft. so, the first choice
Answer:
8.42ft square
Step-by-step explanation:
Base × height/2
base=4.8ft
height =3.6ft
4.8 × 3.6= 17.28
17.28/2=8.64ft
at an amusement park, Robin bought a t-shirt for $8 and 5 ticket for ride. she spent a total of $23. How much did each ticket cost?
Answers
Each ticket cost $3
8+5x=23
5x=15
x=3
Answer: 26 dollars
Step-by-step explanation:
8-5=3
23+3=26
Normal throttle position voltage on most vehicles is about 0.5 volt at idle (closed throttle) and about _______ volts at wide-open throttle (WOT).
A. 1.5 to 2.8
B. 13.5 to 15.0
C. 4.5
D. 2.5
Answers
Answer:
C. 4.5
Step-by-step explanation:
Normal throttle position voltage on most vehicles is about 0.5 volt at idle (closed throttle) and about 4.5 volts at wide-open throttle (WOT).
Answer:C. 4.5
Step-by-step explanation:
Normal throttle position voltage on most vehicles is about 0.5 volt at idle (closed throttle) and about _______ volts at wide-open throttle (WOT).
C. 4.5
which of these characteristics do a rhombus and a rectangle always have in common?
A. all angles are right angles
B. opposite sides with equal length
C. all sides with equal lenght
Answers
The characteristics a rhombus and a rectangle always have in common is opposite sides with equal length.
The right option is B. opposite sides with equal length
From the question,
We are to determine which of the given characteristics do a rhombus and a rectangle always have in common.
To determine which of the characteristics, we will list some of the characteristics of the two shapes
Characteristics of a Rhombus
All sides are of equal length Opposite sides are parallelOpposite angles are congruent Diagonals intersect perpendicularly Consecutive angles are supplementaryCharacteristics of a Rectangle
Opposite sides are congruent and parallel Diagonals bisect each other Each of the interior angles is a right angleDiagonals are congruentNow, from above,
We have that all the sides of rhombus are equal in length, which makes the opposite sides to be equal as well.
Also, among the characteristics of a rectangle is that, opposite sides are equal in length
Hence, the characteristics a rhombus and a rectangle always have in common is opposite sides with equal length. The right option is B. opposite sides with equal length
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The option B is correct. A rhombus and a rectangle always have opposite sides with equal length in common. This is a defining property of all parallelograms.
In geometry, both a rhombus and a rectangle are types of parallelograms. To determine what characteristics they have in common, we must identify their properties. A rhombus has all sides of equal length, but its angles are not necessarily right angles. In contrast, a rectangle has all angles as right angles, but its sides are not necessarily of equal length. Therefore, the characteristic that both a rhombus and a rectangle always have in common is:
Opposite sides with equal length (Option B)This means that in both a rhombus and a rectangle, the opposite sides are parallel and equal in length, which is a defining property of all parallelograms.
in a solution the substance dissolved in the liquid is called the
Answers
Hope this helps!
Complete the following sentence: Two events that are mutually exclusive... ...cannot be calculated ...sometimes occur at the same time ...always occur at the same time ...never occur at the same time
Answers
Answer:
never occur at the same time
Step-by-step explanation:
In Statistics, two events that are mutually exclusive never occur at the same time. For instance, in tossing a coin we can either land heads or tails but not both. The two events are said to be mutually exclusive.
Which geometic construction is shown below?
Answers
Answer:
AStep-by-step explanation:
Answer:
the answer is doubling the square on anywhere brainiest pls
Step-by-step explanation:
Find the measure indicated angle to the nearest degree.
Find the missing side. Round to the nearest tenth
Answers
Answer:
1. 34.4°
2. 18.8°
3. 37.7°
4. 36.6°
5. 40.6°
6. 7.5
7. 12.3
8. 14.7
9. 22.0
10. 6.3
Step-by-step explanation:
1. The missing angle is found by the use of the sine.
Sine ∅= opposite/ hypotenuse
=13/23
sin⁻¹(13/23)=34.4°
2. The missing angle is calculated by the use of the tan.
Tan∅=opposite/adjacent
=17/50
Tan⁻¹(17/50)=18.8°
3. The missing angle is calculated by the use of the tan.
Tan∅=opposite/adjacent
=17/22
Tan⁻¹ (17/22) = 37.7°
4. The missing angle is calculated by the use of the tan.
Tan∅=opposite/adjacent
=21/28
Tan⁻¹ (21/28)=36.9°
5. The missing angle is calculated by the use of the tan.
Tan∅=opposite/adjacent
=24/28
Tan⁻¹ (24/28) = 40.6°
6. Missing side is calculated by considering the tan of 58°
Tan 58°=12/x
x=12/Tan 58°
=7.5
7. Missing side is calculated by considering the sine of 43°
Sin 43°= opposite / hypotenuse
Sin 43 =x/18
x= 18 Sin 43
=12.3
8. Missing side is calculated by considering the sine of 62°
Sin 62° = 13/x
x=13/Sin 62°
=14.7
9. Missing side is calculated by considering the tan of 36°
Tan 36°= 16/x
x=16/Tan 36°
=22.0
10. Missing side is calculated by considering the sine of 23°
Sin 23° = x/16
x=16 Sin 23
=6.3