The probability that the jury will make a wrong decision when it reaches a decision by majority rule is 0.033
To solve this, the number of jury that makes the wrong decision can be modeled as a binomial random with parameters n=7 and p=0.2. This jury as a whole will make wrong decision if 4, 5, 6, or 7 make the wrong decision.
We denote these events with A, B, C, D for 4, 5, 6, 7 respectively. The probability of this union is the sum of probabilities, so
P(Jury Error) = P(A)+P(B)+P(C)+P(D)
= [tex]\left({{7} \atop {4}} \right.)(0.2)^{4} *0.8^{3} +(\left \({7} \atop {5}} \right)(0.2)^{5} *0.8^{2} +(\left{7} \atop {6}} \right.)(0.2)^{6} *0.8^{1} +(\left{7} \atop {7}} \right.)(0.2)^{7} *0.8^{0}[/tex]
=0.033
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f(x) = 3 x + 1 and g (x) = 2x - 3. find g (f(x))
Answer:
6x -- 1
Step-by-step explanation:
To Solve for g(f(x)), bear in mind
f(x) = 3x + 1
g(x) = 2x -- 3
g(f(x)) = 2x -- 3. (Calm down right?)
Let x = f(x).
if you recheck g(x) = 2x -- 3 so we got the (x) from it (do you get?)
g(f(x)) = 2(3x + 1) -- 3
g(f(x)) = 6x + 2 -- 3
g(f(x)) = 6x -- 1
#AllonGod
Answer:
Step-by-step explanation:
To find g(f(x)), first, understand that this means we are going to use the function of f(x) where the x would be in g(x).
1. First, identify the x in g(x) and replace it with the function of f(x)
g(x)=2x-3; so g(f(x))= 2(3x+1) -3
2. Simplify the equation by distributing the 2 and combining like terms.
2*3x=6x and 2*1=2, so we are left with 6x+2-3. After, just do 2-3 to end up with
g(f(x))=6x-1
an elevator can carry 15 adults or 20 children at one time. During the course of a day, the elevator carries a full passenger load 52 times. if all the passengers were children, how many more people would the elevator carry then if all the passengers were adults
Answer:
Step-by-step explanation:
20(kids per ride) x 52(number of rides) = 1040. 15(adults per ride) x 52(number of rides) = 780. 1040-780= 260 more kids than adults.
Last night, Luis read 75% more pages than Dayja, and Dayja read 75% more pages than Michael. If Dayja read 84 pages, how many pages did Luis, Dayja, and Michael read all together?
Answer:
252
Step-by-step explanation:
Altogether, Luis, Dayja, and Michael read 279 pages.
How do we get the total number of pages read by each person?We can get the total number of pages read by each person by building from the number of pages read by Dayja.
Dayja read 84 pages
Luis read 75% more pages than Dayja and this is equal to:
84 + 84 × 75/100
84 + 84 × 0.75
84 + 63
= 147 pages.
Dayja read 75% more pages than Michael.
Believing that Michael read x number of pages.
84 = 175 ÷ 100 × x
8400 = 175x
x = 8400/175
x = 48
So, Michael read 48 pages.
Altogether we will have, 84 + 48 + 147 pages.
= 279 pages.
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Each of my children has at least two
brothers and one sister. Find the least
number of children I might have.
Answer:
4 kids.
Step-by-step explanation:
There could be 2 boys and 2 girls. Each of the 2 boys has at least one sister, and each of the 2 girls has at least two brothers.
Hope this helps!
-12/x = 24/8 what does x equal
Simply 24/8 to 3.
-12/x = 3
Since x is the number being divided, we take the divisor and divide it by the quotient.
x = -12/3 = -4.
I need help with this
Answer:
convert 10 hours 30 minutes to hours= 10.5
683/10.5
=65.04km/h
Decimal equivalent to three and nine hundredths
Answer: this bc well it decimals and those are kinda easy
3.09
Graph the function identify the vertex and axis of symmetry f(x)=x^2+4x-2
A. axis of symmetry:x=2
(2,6)
B. axis of symmetry: x= -2
(-2,6)
C. axis of symmetry: x= 2
(2,-6)
D. axis of symmetry: x=-2
Vertex: (-2,-6)
The vertex and the axis of symmetry are (-2, -6) and x = -2, respectively
How to determine the vertex and the axis of symmetry?The equation of the function is given as
f(x) = x^2 + 4x - 2
The above equation is a quadratic equation
Next, we plot the equation on a graph (see attachment)
The vertex of the graph is the minimum or the maximum of the graph
In this case, we have
Minimum= (-2, -6)
This means that
Vertex = (-2, -6)
The axis of symmetry is the x-coordinates of the vertex
So, we have
x = -2
Hence, the vertex is (-2, -6) and the axis of symmetry is x = -2
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Use the number line below, where RS=9y+3, ST=5y+8, RT=67 a. What is the value of y? b. Find RS and ST.
The value of y on the number line is 4.
How to find the side of a number line?A number line is a series of numbers placed on a straight line in order from least to greatest.
The number line is RT.
The point S is in between RT.
Therefore,
RT = RS + ST
Hence,
RT = 67
RS = 9y + 3
ST = 5y + 8
Therefore,
RT = RS + ST
67 = 9y + 3 + 5y + 8
67 = 9y + 5y + 11
67 = 14y + 11
subtract 11 from both sides of the equation
67 = 14y + 11
67 - 11 = 14y + 11 - 11
56 = 14y
divide both sides by 14
y = 56 / 14
Therefore,
y = 4
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(x^2-9/x+4=3-(x-3)/x+4
Answer:
x = 2.579248
Step-by-step explanation:
x^2 - 9/x + 4 = 3 - (x - 3/x) + 4
a) Multiply both sides by x.
x^3 + 4x - 9/x = 6x + 3
b) Multiply both sides by x.
x^4 + 4x^2 - 9x = 6x^2 + 3x
x^4 + 4x^2 - 9x - (6x^2 + 3x) = 6x^2 + 3x - (6x^2 + 3x)
x^4 - 2x^2 - 12x = 0
x(x^3 - 2x - 12) = 0
x = 0 or x^3 - 2x - 12 = 0
x = 0 or 2.5792479999999998
3.
Find the area of sector AOB. Round to the nearest tenth.
2
1.
A
18 cm
0
70°
4 ft
쏭
What is the answer for all three of those help
40%
1 mm
A
B
Area
Area =
C
Area =
mm²
a car travels 3.5 miles in 5 minutes. work out the average speed in miles per hour
The average speed of the car which travels 3.5 miles in 5 minutes is 42 miles per hour.
What is the average speed of the car?Speed is simply referred to as distance traveled per unit time. It is expressed mathematically as;
Speed = Distance ÷ time.
Given the data in the question;
Distance travelled = 3.5 milesTime elapsed = 5 minutesAverage speed = ?First, we convert unit of the elapsed time from minutes to hours.
Time = 5 min = ( 5/60 )hr = 5/60hr
Now, plug the given values into the speed formula and solve for speed.
Speed = 3.5 ÷ 5/60
Speed = 3.5 × 60/5
Speed = 210/5
Average speed = 42 mph
Therefore, the average speed of the car 42 mph.
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PLS ANSWER PART (f) ASAP
There are a total of 54 men.
Let's take x new men who joined the club, then according to the question (22-x) new women who joined the club.
[(98 × (5 ÷ 5 + 9)) + x ÷ [(98 × (9 ÷ 5 + 9)) + (22 - x)] ÷ [(98 × (9 ÷ 5 + 9)]= 9 ÷ 11
[(98 × (5 ÷ 14)) + x ÷ [(98 × (9 ÷ 14)) + (22 - x)] ÷ [(98 × (9 ÷ 5 + 9)]= 9 ÷ 11
[35 + x] ÷ [63 + (22 - x)] = 9 ÷ 11
11 × (35 + x) = 9 × (85 - x)
385 + 11x = 765 - 9x
11x + 9x = 765 - 385
20x = 380
x = 19.
Therefore, 19 new members have joined the club.
So, Step 10: 10 + (98 × (5 ÷ 5 + 9)) = 19 + 35 = 54.
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Answer:
19
Step-by-step explanation:
Originally there are 98 members
Ratio of men to women = M:W = M/W = 5/9
The ratio of men to total number of members = M/(M + W) and this should be the same as 5/(5+9) = 5/14
Since 5/14 th of the total membership of 98 members is the number of men,
Actual number of men
= 98 x (5/14)
= 35
After 22 members join the club, the total club membership is 98 + 22 = 120
The new ration M/W = 9/11
Actual number of men members
= 120 x 9/(9+11)
= 120 x 9/20
= 6 x 9
= 54
Increase in the membership of men = 54 - 35 = 19
which fraction is equivalt to 2/10
Answer: 1/5
Step-by-step explanation:
Answer:
[tex]{ \sf{ \frac{1}{5} }} \\ [/tex]
Step-by-step explanation:
[tex]{ \sf{ \frac{2 \div 2}{10 \div 2} \equiv \frac{1}{5} }} \\ [/tex]
simplify the square root of 217
Answer: 14.73091
Step-by-step explanation:
The square root of 217, (or root 217), is the number which when multiplied by itself gives the product as 217. Therefore, the square root of 217 = √217 = 14.730919862656235.
7653x213, please help me....
Answer:
Step-by-step explanation:
1630089 is the answer
Find the volume of the triangular prism,
Answer:
280 cm^3
Step-by-step explanation:
formula
1/2 * b * h * l
1/2 * 5 * 8 * 14
1/2 * 560
wikipedia
a rectangular piece of metal is 10 in longer than it is wide. squares with sides 2 in long are cut from the four corners and the flaps are folded upward to form an open box. if the volume of the box is 671 in, what were the original dimensions of the piece of metal?
The length and width of the piece of metal are 28 and 18 inches respectively.
What is volume?
The term “volume” refers to the amount of three-dimensional space taken up by an item or a closed surface. It is denoted by V and its SI unit is in cubic cm.
Dimension of the rectangle;
Width(w)
Length,L= 10 + w
volume of the box = length * width * height
Dimension of the box;
length of box, (x + 10) - 4 = x + 6
width of box,(x - 4)
height of box = 2
The volume of the box is 672 in³;
⇒V=lwh
⇒V=2 (x -4)( x + 6)
⇒672 in³ = 2x² + 4x - 48
⇒2x² + 4x - 720 = 0
⇒x^2 + 2x - 360 = 0
⇒(x +20)(x - 18) = 0
⇒x = 18
⇒x=-20 (value of the dimension will not be negative.
The width of an original piece of metal is;
Width,w=18 inches
length,l= 28 inches
Hence. the length and width of the piece of metal are 28 and 18 inches respectively.
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Answer the following. If needed, round your answers to two decimal places.
Roza and Rina are in the same maths class. On their unit test, Roza scored 70 out of 75
marks and Rina got a 92%.
Express Roza's mark as a simplified fraction.
Express Rina's mark as a simplified fraction.
By what percentage is Roza's mark higher?
%
Answer:
1) 14/15
2)23/25
3) 1.33%
Step-by-step explanation:
Area of a triangle with a vertical height of 1/2 m and base of 1/4 m.
Answer:
1/16 squared meters
Step-by-step explanation:
The formula to find the area of a triangle is [tex]\frac{Base * Height}{2}[/tex]
We can form an equation if we substitute the values (base and height).
[tex]\frac{1/2*1/4}{2}[/tex]
1/2 * 1/4 = 1/8
and [tex]\frac{1/8}{2}[/tex] = 1/16
Therefore, the area of a triangle with a vertical height of 1/2 m and a base of 1/4 m is 1/16 meters squared.
it costs $45 to rent a car each day there is also a fee of $12. how much does it cost to rent a car for 5 days including fee
Answer:
it would cost $285
Step-by-step explanation:
Answer:
285 po answer
Step-by-step explanation:
Pa brainlest po plsss
What is the domain of this relation?
Answer:
{-4, 0, 2, 5}
Step-by-step explanation:
The domain of a relation in a graph is a list of all the x values from the points plotted on it.
Therefore, we can take the coordinates of each point, and list all the x values. (You can't use the same number more than once)
Once you list all the x values, you put them in order from least to greatest, and then you're done! (make sure to use swirly brackets)
Good luck on your math journey! ^-^
a heap of rubbish in the shape of a cube is being compacted into a smaller cube. given that the volume decreases at a rate of 3 cubic meters per minute, find the rate of change of an edge, in meters per minute, of the cube when the volume is exactly 64 cubic meters.
-1/16 meters per minute is the rate of change of an edge.
What is the rate of change?The rate at which one quantity changes in relation to another quantity is known as the rate of change function. Simply put, the rate of change is calculated by dividing the amount of change in one item by the corresponding amount of change in another.So, the Volume of the cube: V = r³
Where the edge of the cube is represented as r.Differentiate with respect to t (time) as follows:
[tex]\frac{d V}{d t}=3 r^2 \frac{d r}{d t}[/tex]dV/dt = -3 : Cubic meters per minute
Also, V = 64 ⇒ r = ∛64 = 4Now, substitute the values:
-3 = 3(4)² dr/dt-3 = 48 dr/dtdr/dt = -3/48 = -1/16Therefore, -1/16 meters per minute is the rate of change of an edge.
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50 POINTS__ Solve for z and graph the solution.
–7 ≥ z–10 ≥ –14
Plot the endpoints. Select an endpoint to change it from closed to open. Select the middle of a segment, ray, or line to delete it.
Answer:
Step-by-step explanation:
Find the sum of the first 888 terms in the following geometric series.
2+8+32+...2+8+32+...
Answer:
Step-by-step explanation:
Nice question!!! It should be ####. and that's the answer that you want
alex has a circular rug the radius of the rug is 5 1/4 feet which is closest to the area of the rug use 22/7
The area when Alex has a circular rug the radius of the rug is 5 1/4 feet is 86.625 feet².
How to calculate the area?It should be noted that the area of a circle is given the formula:
Area of a circle = πr²
where π = 22/7
r = radius = 5 1/4
Therefore, the area will be:
Area = πr²
Area = 22/7 × (5 1/4)²
Area = 22/7 × 25 1/16
Area = 86.625 feet²
The area is 86.625 feet².
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The simplest form for 2(x + 3) + 3(2x -3)
Answer: 8x-3
Step-by-step explanation
2x + 6 + 6x - 9
8x - 3
Answer:
8x - 3
Step-by-step explanation:
2(x+3) + 3(2x-3)
2x+6 + 6x-9
2x+6x + 6-9
= 8x - 3
what is it please :)
The surface area of the sphere to the nearest square foot is 2463 feet.
What is a sphere?A sphere is a geometrical object that resembles a two-dimensional circle in three dimensions. In three-dimensional space, a sphere is a collection of points that are all located at the same r-distance from a single point. The radius of the sphere is denoted by the letter r, and the given point is its center.So, the surface area of the sphere:
The formula of the surface area of the sphere: 4πr²Radius = diameter/2 ⇒ 28/2 ⇒ 14Now, substitute the radius in the formula as follows:
4πr²4π14²2463.00864Rounding off: 2463 feet
Therefore, the surface area of the sphere to the nearest square foot is 2463 feet.
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this is a little difficult for me
Answer:
Step-by-step explanation:
the answer and steps are down below to check it out have a wonderful wonderful day and apologize if the answer is wrong
i’m not sure what the answer is help pls
Answer:
x = 33
Step-by-step explanation:
( x + 20 ) + ( 4× - 5) = 180 {m||n}
5×+20 - 5 = 180
5×+15 = 180
5× = 165
× = 33