Given:
Three coins are tossed.
Let the event H represents all Heads and the event K represents at least one Heads.
To find:
a. The probability that the outcome is all heads if at least one coin shows a heads.
b. P(K) = ?
c. P(H∩K) = ?
Solution:
If three coins are tossed, then the total possible outcomes are:
{HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}
Total outcomes = 8
Possible outcomes for all Heads = 1
Possible outcomes for at least one Heads = 7
Let the following events:
H = all Heads
K = at least one Heads.
Then,
[tex]H=\{HHH\}[/tex]
[tex]K=\{HHH, HHT, HTH, HTT, THH, THT, TTH\}[/tex]
[tex]H\cap K=\{HHH\}[/tex]
Now,
[tex]P(K)=\dfrac{7}{8}[/tex]
[tex]P(H\cap K)=\dfrac{1}{8}[/tex]
a. The probability that the outcome is all heads if at least one coin shows a heads is:
[tex]P(H|K)=\dfrac{P(H\cap K)}{P(K)}[/tex]
[tex]P(H|K)=\dfrac{\dfrac{1}{8}}{\dfrac{7}{8}}[/tex]
[tex]P(H|K)=\dfrac{1}{7}[/tex]
Therefore, the probability that the outcome is all heads if at least one coin shows a heads is [tex]\dfrac{1}{7}[/tex].
b. [tex]P(K)=\dfrac{7}{8}[/tex]
c. [tex]P(H\cap K)=\dfrac{1}{8}[/tex]
How do you solve a system of linear equations by graphing?
9514 1404 393
Explanation:
This is a self-answering question: you solve it by graphing the equations.
The solution is where the lines intersect. The point of intersection of the lines is the point that satisfies all the equations for the lines, hence is a solution to the system. If they do not intersect, there are no solutions. If the lines are coincident, there are an infinite number of solutions.
__
The equations can be graphed by any of a number of methods. (My favorite is to let a graphing calculator do it.) The method of choice depends on the coefficients and the form the equations are given in. Methods of graphing are a topic for a more lengthy discussion.
PLS HELP TYSMMMM <33333333333333333333333333
Answer:
dvide 54 by 6 then the answer you get subrtact it by 3 then the answer you get multiply iy by 2 then thats will be your answer
Step-by-step explanation:
remember always use PEMDAS always add or subract wich ever comes first and if theres none of that then do Multiply or devide wich ever comes first ( btw your answer is ( 3 )
An inverted pyramid is being filled with water at a constant rate of 70 cubic centimeters per second. The pyramid, at the top, has the shape of a square with sides of length 8 cm, and the height is 15 cm. Find the rate at which the water level is rising when the water level is 4 cm.
Answer:
[tex]\frac{dh}{dt}=1.45cmsec^{-1}[/tex]
Step-by-step explanation:
Rate of Water Fill [tex]R=\frac{dv}{dt}=70cm^3[/tex]
Length [tex]l=8cm[/tex]
Height [tex]H=15cm[/tex]
Water level [tex]L_w= 4cm[/tex]
Generally the equation for relationship b/w h and a is mathematically given by
Since by the properties of similar triangles
[tex]k=\frac{h}{1/2}[/tex]
Let
[tex]h=15cm \\\\a=8cm[/tex]
[tex]k=\frac{h}{1/2a}[/tex]
[tex]k=\frac{15}{4}[/tex]
Therefore
[tex]\frac{h}{1/2a}=\frac{15}{4}[/tex]
[tex]a=\frac{8h}{15}[/tex]
Generally the equation for volume of Pyramid is mathematically given by
[tex]V=\frac{1}{3}ah^2h[/tex]
Subsitute a
[tex]V=\frac{1}{3}(\frac{8h}{15})h^2h[/tex]
Therefore
[tex]\frac{dv}{dt}=\frac{(\frac{1}{3}(\frac{8h}{15})h^2h)}{dt}[/tex]
[tex]\frac{dv}{dt}=\frac{64}{255}(h^2\frac{dh}{dt})[/tex]
Since
[tex]\frac{dv}{dt}=70cm^3s^{-1}[/tex]
Therefore
[tex]70cm^3s^{-1}=\frac{64}{255}(h^2\frac{dh}{dt})[/tex]
[tex]\frac{dh}{dt}=\frac{70}{169}*\frac{225}{64}[/tex]
[tex]\frac{dh}{dt}=1.45cmsec^{-1}[/tex]
HELP TIMER Write the equation of a hyperbola centered at the origin with x-intercept +/- 4 and foci of +/-2(squareroot 5)
Given:
x-intercepts of the hyperbola are ±4.
The foci of hyperbola are [tex]\pm 2\sqrt{5}[/tex].
Center of the hyperbola is at origin.
To find:
The equation of the hyperbola.
Solution:
The general equation of a hyperbola:
[tex]\dfrac{(x-h)^2}{a^2}-\dfrac{(y-k)^2}{b^2}=1[/tex] ...(i)
Where, (h,k) is the center of the hyperbola, ±a are x-intercepts, [tex](\pm c,0)[/tex] are foci.
Center of the hyperbola is at origin. So, h=0 and k=0.
x-intercepts of the hyperbola are ±4. So,
[tex]\pm a=\pm 4[/tex]
[tex]a=4[/tex]
The foci of hyperbola are [tex]\pm 2\sqrt{5}[/tex].
[tex]\pm c=\pm 2\sqrt{5}[/tex]
[tex]c=2\sqrt{5}[/tex]
We know that,
[tex]a^2+b^2=c^2[/tex]
[tex](4)^2+b^2=(2\sqrt{5})^2[/tex]
[tex]16+b^2=20[/tex]
[tex]b^2=20-16[/tex]
[tex]b^2=4[/tex]
Taking square root on both sides, we get
[tex]b=\sqrt{4}[/tex] [b>0]
[tex]b=2[/tex]
Substituting [tex]h=0,k=0,a=4,b=2[/tex] in (i), we get
[tex]\dfrac{(x-0)^2}{4^2}-\dfrac{(y-0)^2}{2^2}=1[/tex]
[tex]\dfrac{x^2}{4^2}-\dfrac{y^2}{2^2}=1[/tex]
Therefore, the correct option is (d).
what is equivalent to 7w +7w
Answer:
14w
Step-by-step explanation:
Hope this helps
A local salesman has forty-five stacks of magazines. If the salesman plans to sell three-fifths of the stacks, how many stacks will he have left?
Answer:
2
Step-by-step explanation:
Answer:
2
Step-by-step explanation:
If function f has zeros at -3 and 4, which graph could represent function f?
Answer:
A
Step-by-step explanation:
f has zero means that f(x)=0
if f(x)=0 we have to look intersection point or points in the graph on the x-axis.
for A
y=0
x=-3, x=4
for B
y=0
x=-4, x=3
for C
y=0
x=-4, x=-3
for D
y=0
x=3, x=4
Element X is a radioactive isotope such that its mass decreases by 73% every
hour. If an experiment starts out with 680 grams of Element X, write a
function to represent the mass of the sample after t hours, where the rate of
change per minute can be found from a constant in the function. Round all
coefficients in the function to four decimal places. Also, determine the
percentage rate of change per minute, to the nearest hundredth of a percent.
Mi
Answer:
Step-by-step explanation:
The element decay percentage rate of change 2.22% per minute.
What is radioactive isotope?
Radioisotope, radionuclide, or radioactive nuclide, any of several species of the same chemical element with different masses whose nuclei are unstable and dissipate excess energy by spontaneously emitting radiation in the form of alpha, beta, and gamma rays.
Here, mass decreases by 73% every hour.
Weight of element X is 680 grams.
According to question,
f(t) = 680 (1 - 73%)ⁿ
f(t) = 680 (1 - 0.73)ⁿ
f(t) = 680 X 0.27ⁿ
f(t) = 680 X 0.9778ⁿ
f(t) = 680 X (1 - 0.02322)ⁿ
Thus, the element decay percentage rate of change 2.22% per minute.
Learn more about radioactive isotope from:
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Help ASAP please!!
For a proof by induction of the math statement below,
identify the correct step for proving the theorem is true
for n=k+1
2+4+6+...+2n=n(n+1)
Answer:
2+4+6+...+2k+2(k+1) = k(k+1) + (k+1)(k+1)
Step-by-step explanation:
Proved case for n
2+4+6+...+2n = n(n+1) ................(1)
for n = k + 1, we replace n by k and add n = k+1 on both sides (
2+4+6+...+2k+2(k+1) = k(k+1) + 2(k+1))
rearrange by factoring the right-hand-side
2+4+6+...+2k+2(k+1) = (k+1)(k+2)
which if we substitute n=k+1, we get back
2+4+6+...+2(n-1) + 2(n) = n(n+1) ...............(2)
This means that equation (1) is applicable to case n+1, and the proof by induction is completed.
Find the slope of the line that passes through the points (-5,-6) and (5,10)
3.4 0.8 0.6 find the volume of the rectangular prism in cubic feet
Given:
Consider the dimensions of the rectangular prism are 3.4 ft by 0.8 ft by 0.6 ft.
To find:
The volume of rectangular prism.
Solution:
The volume of a cuboid or rectangular prism is:
[tex]V=l\times b\times h[/tex]
Where, l is length, b is breadth and h is height of the prism.
The dimensions of the rectangular prism are 3.4 ft by 0.8 ft by 0.6 ft. So, the volume of the prism is:
[tex]V=3.4\times 0.8\times 0.6[/tex]
[tex]V=1.632[/tex]
Therefore, the volume of the rectangular prism is 1.632 cubic feet .
Juan's work for solving by completing the square is below. In which step (if any) does Juan make a mistake?
(SEE PICTURE FOR STEPS)
Step 4
Step 1
Juan does not make a mistake.
Step 3
The solution is : x = 19 is the extraneous solution Li Juan obtained.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Here, we have,
The given equation is 13 - 2w = w + 6.
We need to solve the equation by squaring both sides of the equation.
Now, 13 - 2w = w + 6 squaring both sides of the equation.
That is, (13-2w)²= 169 - 52w + 4w²
(w+6)²= w²+ 12w + 36
Setting them equal, we get
169 - 52w + 4w² = w² + 12w + 36
⇒3w²- 64w + 133 = 0
Now, using the quadratic formula, we get
x = (64±√(64² - 4×3×133))/6
⇒x = (64±√2500)/6.
⇒x = (64±√50)/6.
⇒x = 19 or 14/6 = 7/3.
Solving the original equation, we get
7 = 3w⇒w = 7/3
Therefore, x = 19 is the extraneous solution Li Juan obtained.
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complete question:
Li Juan solves the equation below by first squaring both sides of the equation.
13 - 2w = w + 6
What extraneous solution does Li Juan obtain?
A high school has 32 players on the football team. The summary of the players' weights is given in the box plot. Approximately, what is the percentage of players weighing greater than or equal to 233 pounds
Answer:
[tex]\% = 11.96\%[/tex]
Step-by-step explanation:
Given
See attachment for box plot
Required
Percentage greater than or equal to 233
From the box plot, the maximum is:
[tex]Max = 244[/tex]
The minimum is:
[tex]Min = 152[/tex]
Percentage greater than 233 is calculated as:
[tex]\% = \frac{Max - 233}{Max - Min}[/tex]
[tex]\% = \frac{244 - 233}{244-152}[/tex]
[tex]\% = \frac{11}{92}[/tex]
Express as percentage
[tex]\% = \frac{11}{92}*100\%[/tex]
[tex]\% = \frac{1100}{92}\%[/tex]
[tex]\% = 11.96\%[/tex]
A spinner with 8 equal-size sections labeled as shown is spun 200 times. What is the sample
space for this experiment?
Answer:
hiiooioudzzxuxojxoufxodyzufxufxyfxuoxudr tztdxhxfuoxir d and
the number 3.14063 written correct to 3 decimal places is
Answer:
3.141
Step-by-step explanation:
3 decimals is .xxx, and you round the last digit up, so it becomes 3.141
Answer:
3.141
Step-by-step explanation:
since the forth number behind the decimal place is bigger than 5 we round up the third number.
I hope this helps in anyway.
2x+5y=20 y=-0.4x-1 i really need help over here
Answer:
x=6.25 and y=1.5
Step-by-step explanation:
Given equation
2x+5y=20
y=0.4x-1
Putting the value of y in above equation
2x+5(0.4x-1)=20
2x+2x-5=20
4x-5=20
4x=20+5
4x=25
x=6.25
Now,
y=0.4x-1( Given)
Putting the value of x=6.25 in above equation y
y=0.4(6.25)-1
y=2.5-1
y=1.5
What is my answer if I Add
-9+84+(-2)
Answer:
73
Step-by-step explanation:
-9+84+(-2) =
-9+82 =
= 73
Hope this helps
Which graph represents the function f(x)=|x|-4?
See the graph in the attached image.
Find the volume in the shape
Answer:
1205.76 m^3
Step-by-step explanation:
given:
radius = 8m
height = 18 m
volume of a cone = πr2h/3
=3.14 * (8)^2 * 18/3
=3.14 *64 *18/3
=3617.28/3
=1205.76 m^3
An English teacher needs to pick 4 books to put on his reading list for the next school year. He has narrowed down his choices to 8 novels and 6 plays.
a. How many different ways can he choose the books to put on the list if he wants to include at least two plays?
b. Find the standard deviation.
Answer:
A) 3 ways
B) sorry don't know.
Step-by-step explanation:
2 P and 2 N
3P and 1 N
4P
So 3 ways.
Determine if each proportion on the left is True or False. Answer options on the right side may be used more than once.
True
False
28/16=14/8
3/5=9/15
4/32=10/78
3/4=12/16
Answer:
28/16=14/8 true
3/5=9/15 true
4/32=10/78 false
3/4=12/16 true
Step-by-step explanation:
DID IT ON BRIDGE
32,131 round this to two decimal places
Answer:
Is 32,13
Step-by-step explanation:
Because one is not bigger than five so it disappears.
please help. having trouble with this question.
Answer:
Step-by-step explanation:
The problem told you what all the variables represent, so all we have to do it fill them in accordingly and solve:
[tex]V=6440e^{(.068)(8)}[/tex] and
[tex]V=6440e^{.544}[/tex] and
V = 6440(1.7228846) so
V = $11,095.38
m) Factorise:
x2/9+1+9/x2
Answer:
Cannot be factored
Step-by-step explanation:
Given
[tex]\frac{x^2}{9} + 1 + \frac{9}{x^2}[/tex]
Required
Factorize
Take LCM
[tex]\frac{x^2}{9} + 1 + \frac{9}{x^2} = \frac{x^4+9x^2+81}{9x^2}[/tex]
The expression cannot be factored
Dan has an old lawn mower! It takes him 1 hour to mow the whole lawn. How many square yards does Dan cut in one minute? Hints: There are 60 minutes in 1 hour. To find the unit rate divide the area of the lawn by the amount of time it takes Dan to mow the whole lawn.
40 square yards per minute
400 square yards per minute
2400 square yards per minute
240 square yards per minute
Answer: You didnt mention how much Dan mows in 1 hour, but just do that divided by 60
Step-by-step explanation:
+
y.com/student/dashboard/home
D
Solving Systems of Linear Equations Algebraically - Qutz - Level H
Question 7
Solve.
3
b=0
a + b = 21
a = 20
a = 12
a = 20
a = 37
b = 11
0 = 371
%
b = 9
b = 15
b = -16
ET
6:26
13. Find the area of the parallelogram.
Answer:
Step-by-step explanation:
make it 1 triangle and trapezium
1) 1/2 x 7 x 8 = 28 in2
Answer:
56 in^2
Step-by-step explanation:
A = b* h
A = (8) * (7)
A = 56
A = 56 in ^2
Hope this helps!
High School Dropouts
Number of Dropouts
1990
2000
Male
Female
MAMD.M.D.3: Which of the
following is true about the graph?
Answer:
There are more females dropping than males each year and that there are more females than males
1
Calculate the height, A. and the width, B. of the spice
cabinet shown in the figure. Don't forget to include the
1
--inch thickness of the wood where needed. The symbol
hardwood for all framing parts.
" means inches,
This
3
The height, A, of the spice cabinet is inches
(Type an integer, proper fraction, or mixed number.)
on
Answer:
Height A = [tex]12\frac{3}{4}[/tex] inches
Step-by-step explanation:
Height A = Sum of widths of all sections of the cabinet + thickness of the wood
Height A = [tex]1\frac{1}{4}+\frac{1}{4}+4\frac{1}{2}+\frac{1}{4}+4\frac{1}{2}+2[/tex]
= [tex](1+4+4+2)+(\frac{1}{4}+\frac{1}{4}+\frac{1}{2}+\frac{1}{4}+\frac{1}{2})[/tex]
= [tex]11+(\frac{1+1+2+1+2}{4} )[/tex]
= [tex]11+\frac{7}{4}[/tex]
= [tex]11+1\frac{3}{4}[/tex]
= [tex]11+1+\frac{3}{4}[/tex]
= [tex]12\frac{3}{4}[/tex] inches
How many Egyptian numerals (total) are needed to represent the following problem?
