2. What is the experimental probability of rolling a 4
3. Getting at least one tail
Experimental and theoretical
Answers
Answer:
1. 40%
2. The theoretical probability is 3% greater than the experimental probability.
Step-by-step explanation:
We are informed that a number cube is rolled 20 times and the number 4 is rolled 8 times. The experimental probability of rolling a 4 is;
(the number of times a 4 was rolled)/(total number of rolls)
8/20 = 0.4
0.4*100 = 40%
The experimental probability of obtaining at least one tails, one or more tails, is represented in mathematical notation as;
P(HT or TH or TT)
The above events are mutually exclusive, thus;
P(HT or TH or TT) = P(HT) + P(TH) + P( TT)
= (22+34+16)/(28+22+34+16)
= 0.72 = 72%
On the other hand, the theoretical probability of obtaining at least one tails,
P(HT or TH or TT) = 3/4
= 75%
This is because there is at least one tail in 3 out of 4 possible outcomes.
Therefore, it is true to say that the theoretical probability is 3% greater than the experimental probability.
Answer:
1. 40%
2. The theoretical probability is 3% greater than the experimental probability.
Step-by-step explanation:
1. Lets define experimental probability first.
Experimental probability is the probability of an event's occurrence when the experiment was conducted.
The number cube is rolled 20 times, so our sample space is 20.
And the number 4 came in result 8 times, so the the event space is 8.
So,
Experimental Probability = 8/20
=> 0.4
Converting into percentage will give:
=> 40%
So the first option is correct.
2. First we have to find the theoretical probability of getting at least one tail when two coins are tossed
The sample space is {HH, HT, TH, TT}
3 out of these 4 outcomes contain at least one tail
So the theoretical probability of getting at least one tail is: 3/4
=> 0.75 or 75%
Now for the experimental probability,
The total sample space is 28+22+34+16 = 100
The number of favorable outcomes are(Which contain at least one tail):
22+34+16 = 72
So, experimental probability of getting at least one tail = 72/100
=> 0.72 or 72%
We can see that the theoretical probability is 3% greater than the experimental probability. So second option is correct..
Related Questions
Which statements are true of the function f(x) = 3(2.5)x? The function is exponential.
The initial value of the function is 2.5.
The function increases by a factor of 2.5 for each unit increase in x.
The domain of the function is all real numbers.
The range of the function is all real numbers greater than 3.
Answers
Answer:
The function is exponential.
The function increases by a factor of 2.5 for each unit increase in x
The domain of the function is all real numbers
Step-by-step explanation:
The function is exponential.
The function increases by a factor of 2.5 for each unit increase in x
The domain of the function is all real numbers
When given a function and the point at which it is discontinuous, how do you classify the discontinuity as jump, removable, or asymptotic?
Answers
Answer:
Jump discontinuities - No defined limit; the left-handed and right-handed limits will be different, converging at two different finite values
Removable - The limit at this point is defined; the left and right-hand limits both converge on the same value
Asymptotic - The left-and-right-handed limits at this point will either tend to ∞ or -∞
The variable y varies directly to the variable x. If y = 9, when x = 5, what is the value of y when x = 20? Show your work to find the constant of variation (k) Write the equation using the constant of variation (k).
Show your work to find the value of y when x = 20.
Answers
For this case we have that if "and" varies directly proportional to "x", it follows that:
[tex]y = kx[/tex]
Where:
k: It is the constant of proportionality.
Then, we look for the value of "k":
[tex]9 = k (5)\\k = \frac {9} {5}[/tex]
So, now we look for the value of "y" when x = 20.
[tex]y = \frac {9} {5} (20)\\y = \frac {180} {5}\\y = 36[/tex]
Thus, the value of y is 36
Answer:
[tex]y = 36[/tex]
Answer:
Final answer is y=36 and the constant of variation is k=9/5.
Step-by-step explanation:
Given that the variable y varies directly to the variable x.
Then we can write equation as y=kx
Were k is the constant of variation.
Given that If y = 9, then x = 5.
Plug these values into above equation, we get:
y=kx
9=5k
5k=9
k=9/5
Now we need to find the value of y when x = 20. So plug x = 20 and k=9/5 into above formula
y=kx
y=(9/5)(20)
y=180/5
y=36
Hence final answer is y=36 and the constant of variation is k=9/5.
Drag each label to the correct location on the expression. Each label can be used more than once, but not all labels will be used. Complete this equation. __________
Answers
[tex]\frac{sin(x+y)}{sin(x-y)} = \frac{tan(x)+tan(y)}{tan(x)-tan(y)}[/tex]
Answer with explanation:
→sin (x+y)=sin x cos y +cos x sin y
→sin (x-y)= sin x cos y - cos x sin y
[tex]\Rightarrow \frac{\sin (x+y)}{\sin (x-y)}\\\\\Rightarrow \frac{\sin x \cos y + \cos x \sin y}{\sin x \cos y - \cos x \sin y}\\\\\rightarrow \text{Dividing numerator and Denominator by} \cos x \cos y\\\\ \Rightarrow \frac{\frac{ \sin x \cos y}{\cos x \cos y} +\frac{ \sin y \cos x}{\cos x \cos y}}{\frac{ \sin x \cos y}{\cos x \cos y} -\frac{ \sin y \cos x}{\cos x \cos y}}\\\\\Rightarrow \frac{\tan x +\tan y}{\tan x -\tan y}[/tex]
Question 8 (2 points)
What is the circumference of the circle?
140 i ft
280 T ft
4900 ft
19600 ft
Answers
The circumference of a circle is found by multiplying the diameter by PI.
Since the answer are in the form of PI, the answer is 140π ft.
Probability and Statistics question
Testing positive for a disease when you don't really have the disease is which of these?
A.Neither a false negative nor a false positive
B.Both a false negative and a false positive
C.A false positive
D.A false negative
Answers
Answer:
C.
Step-by-step explanation:
A false negative is when you test negative when you should have tested positive
A false positive is when you test positive on a test you should have been negative on
Testing positive for a disease when you don't really have the disease is option C. False positive.
What is False Positive Error?False positive is defined as the error caused by the false positive of an actual negative condition.
There are mainly two kinds of errors in probability.
One is false positive and the other one is false negative.
False positive error as discussed above is the false positive statement for an actual negative condition.
For example, a test result showing that you are pregnant while you are actually not.
False negative errors are those formed by the false negative for an actual positive statement.
For example, a test result showing that you are not pregnant while you are actually pregnant.
Here, since the test result is positive but actually you don't have the disease is a false positive.
Hence the given statement is false positive.
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I need help with geometry
Answers
Answer:
128
Step-by-step explanation:
4*4*8=
Answer:
109.85641
Step-by-step explanation:
A=2AB+(a+b+c)h
A=ah+bh+ch+1/2 squared rooted﹣a4+2(ab)2+2(ac)2﹣b4+2(bc)2﹣c4
=4·8+4·8+4·8+1/2·squared rooted﹣44+2·(4·4)2+2·(4·4)2﹣44+2·(4·4)2﹣44
≈109.85641
What is the area of the trapezoid?
Answers
Answer:
The area of the trapezoid should be:
A = (a + b)/2 · h = (4 + 8)/2 · 4 = 24
So the area of the trapezoid is 24 square units.
The answer is B.) 24 square units
What is the discontinuity of the function f(x)= x^2-4x-12/x+2
Answers
The function f(x) = (x^2 - 4x - 12) / (x + 2) is a rational function, which is a ratio of two polynomials. To find its discontinuity, we identify values of x which makes the denominator zero, in this case x = -2, making this the function's discontinuity.
Explanation:The function given is f(x) = (x^2 - 4x - 12) / (x + 2). This is a rational function, which is a ratio of two polynomial functions - in this case, a quadratic function (x^2 - 4x - 12) and a linear function (x + 2).
To find the discontinuity of a rational function, we need to identify the values of x that make the denominator zero since division by zero is undefined. In this case, that's when x = -2. Thus, this function has a discontinuity at x = -2.
Note that this does not factor into the asymptote of the function as some might believe, but it's instead a point at which the function is undefined. "Graphing this function would show a hole at x = -2".
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Write the equation of the circle with center (−3, 2) and (6, 4) a point on the circle.
A) (x + 3)2 + (y − 2)2 = 13
B) (x + 3)2 + (y − 2)2 = 25
C) (x + 3)2 + (y − 2)2 = 85
D) (x + 3)2 + (y − 2)2 = 117
Answers
Answer:
C
Step-by-step explanation:
The equation of a circle in standard form is
(x - h)² + (y - k)² = r²
where (h, k) are the coordinates of the centre and r is the radius
here (h, k) = (- 3, 2), thus
(x + 3)² + (y - 2)² = r²
The radius is the distance from the centre of the circle to a point on the circle.
Calculate r using the distance formula
r = √ (x₂ - x₁ )² + (y₂ - y₁ )²
with (x₁, y₁ ) = (- 3, 2) and (x₂, y₂ ) = (6, 4)
r = [tex]\sqrt{(6+3)^2+(4-2)^2}[/tex]
= [tex]\sqrt{9^2+2^2}[/tex] = [tex]\sqrt{85}[/tex]
Hence
(x + 3)² + (y - 2)² = ([tex]\sqrt{85}[/tex] )², that is
(x + 3)² + (y - 2)² = 85 → C
The chart shows the number of points Corie earned out of the number of points possible on each of the first four units of his math course.
On which two units did Corie earn equivalent scores?
Choose exactly two answers that are correct.
A.Unit 4
B.Unit 1
C.Unit 3
D.Unit 2
Corie's Unit Test Scores
Unit 1 91/100
Unit 2 45/50
Unit 3 18/20
Unit 4 23/25
Answers
Answer:
C & D
Step-by-step explanation:
Change all the test scores so they have common denominators.
Unit 1 91/100
Unit 2 45/50 * 2/2 = 90/100
Unit 3 18/20 * 5/5 = 90/100
Unit 4 23/25* 4/4 = 92/100
As you can see, Unit 2 and 3 are equivalent.
I believe the answers are C and D. You have to change the test scores so they have common denominators. Correct me if I'm wrong. Hope this helps!
Find the slope of the line that passes through (10, 9) and (3, 18).
Simplify your answer and write it as a proper fraction, improper fraction, or integer.
Answers
Answer: Slope of the line is -9/7
Step-by-step explanation:
Given :
Points : (10,9) and (3,18)
Now slope of line when two points are given
m=[tex]\frac{y2-y1}{x2-x1}[/tex]
Slope = [tex]\frac{18-9}{3-10}[/tex]
m=[tex]\frac{9}{-7}[/tex]
m=[tex]\frac{-9}{7}[/tex]
This is an improper fraction since numerator is greater than the denominator
Hence slope of the line is -9/7
what is the surface area of the right rectangular prism ?
Answers
Answer:
434
Step-by-step explanation:
2(wl+hl+hw)
Answer: the surface is 434 square feet.
Step-by-step explanation:
you can use the formula of right rectangular is 2(wl+wh+lh). The rectangular prism has 6 faces. So the surface area is 434 square feet.
Using four different numerators, write an equation in which four fractions, when added, have a sum of 1.
Answers
Answer:
1/2 + 1/4 + 1/12 + 8333/10000
help~~~~~~~~~````````````````
Answers
Answer:
112.98
Step-by-step explanation:
37.68/2π = 5.9969
5.9969²π = 112.98
ANSWER
The area is 112.9 square units to the nearest tenth.
EXPLANATION
The circumference is given by:
[tex]C=2\pi \: r[/tex]
This implies that,
[tex]37.68 = 2 \: \pi \: r[/tex]
[tex] \frac{37.68}{2\pi} = r[/tex]
[tex]r = 5.997[/tex]
The area of a circle is
[tex]\pi \: {r}^{2} [/tex]
We substitute the radius to get;
[tex]3.14 \times 5.997 ^{2} = 112.93 \: sq. \: units[/tex]
To the nearest tenth, the area of the circle is 112.9 square units.
A group of men and women were given a maze puzzle
Answers
Sooo whats the question
what is 1.400 as a common fraction and write as %
Answers
Answer:
1.400 as a common fraction is 7/5
as a percentage 140%
Step-by-step explanation:
1.4 written as a fraction is;
[tex]\frac{14}{10}[/tex]
simplifying we have;
[tex]\frac{14}{10}=\frac{7}{5}[/tex]
Converting to percentage we simply multiply by 100.
[tex]\frac{7}{5}*100=140[/tex]
what is the y-intercept for the linear function y-4=2(x-6)
Answers
Answer:
-8Step-by-step explanation:
Method 1:
The slope-intercept of an equation of a line:
[tex]y=mx+b[/tex]
m - slope
b - y-intercept
We have the equation of a line in the point-slope form:
[tex]y-4=2(x-6)[/tex]
Convert it the the slope-intercept formula:
[tex]y-4=2(x-6)[/tex] use the distributive property
[tex]y-4=2x-12[/tex] add 4 to both sides
[tex]y=2x-8\to b=-8[/tex]
Method 2:
The y-intercept is for x = 0. Put x = 0 to the equation:
[tex]y-4=2(0-6)[/tex]
[tex]y-4=2(-6)[/tex]
[tex]y-4=-12[/tex] add 4 to both sides
[tex]y=-8[/tex]
Can someone please help with this one
Answers
Answer:
m∠8 = 123°
Step-by-step explanation:
∠1 and ∠8 are alternate exterior angles, and since lines A and B are parallel, then they must be congruent.
So, m∠1 = m∠8
Substitute: 123 = m∠8
state the degree 5r^2s^3t^4
Answers
Answer:
Degree 9.
Step-by-step explanation:
The degree is the sum of all the exponents.
So it is 2 + 3 + 4 = 9.
The degree is the sum of all the exponents 5r^2s^3t^4, So it is 2 + 3 + 4 = 9.
What is the degree of the sum?The degree sum formula says that if you add up the degree of all the vertices in a (finite) graph, the result is twice the number of the edges in the graph. There's a neat way of proving this result, which involves double counting: you count the same quantity in two different ways that give you two different formulae.
The degree is the sum of all the exponents 5r^2s^3t^4
So it is 2 + 3 + 4 = 9.
What is the sum of the exponents called?Degree of the Term is the sum of the exponents of the variables. Example. 2x 4y 3 4 + 3 = 7 7 is the degree of the term. 5x-2y 5 NOT A TERM because it has a negative exponent.
To learn more about the degree sum formula, refer
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Find the interest earned and the future value of an annuity with weekly payments of $400 for three years into an account that pays 7% interest per year compounded semiannually.
Answers
Answer:
the interest earned= 93.401
and the future value of an annuity= 493.401
Step-by-step explanation:
Given Data:
Interest rate= 7%
time,t = 3 years
weekly payment, P= 400
At the end of 3 years, final investment A= ?
n= 52 as it is weekly
As per the interest formula
A= P(1+r/n)^nt
Putting value in above equation
= [tex]400\left(1+\frac{0.07}{52}\right)^{156}[/tex]
= 493.401
Interest earned = A-P
= 493.401-400
= 93.401 !
Find the Slope of a line That contains the points (5, 6), (1,4).
Answers
Answer:
1/2
Step-by-step explanation:
Use the slope formula:
[tex] slope = m = \dfrac{y_2 - y_1}{x_2 - x_1} [/tex]
[tex] slope = m = \dfrac{6 - 4}{5 - 1} [/tex]
[tex] slope = m = \dfrac{2}{4} [/tex]
[tex] slope = m = \dfrac{1}{2} [/tex]
[tex] \frac{y2 - y1}{x2 - x1} = \frac{4 - 6}{1 - 5} = - 2 \div - 4 = 1/2
City planners anticipate an 8.2% population growth per year, including new residents and births. The population, in millions of people, based on this increase can be modeled by the function p(x) = 2.5(1.082), where x is the number of years of tracked growth. The planners also estimate a 3% population loss over the same time period that can be modeled by the function L(p) = p(0.97).
Answers
Answer:
D) L(p(x)) = 2.5(1.04954)x
Step-by-step explanation:
In theoretical probability, what does it mean when the question asks ‘at least’, for example what is the probability of getting at least a 2 when a six sided die is rolled?
Answers
Answer:
Step-by-step explanation:
It means that you will a 2 or a 3 or a 4 or a 5 or 6.
All of these are permitted.
So the probability of getting at least a 2 is 5/6.
i need help asap ! this is 6th grade math surface area .
Answers
Answer:
S.A. = 62Step-by-step explanation:
We have:
two rectangles 2 × 3
two rectangles 3 × 5
two rectangles 2 × 5
Calculate the areas:
A₁ = (2)(3) = 6
A₂ = (3)(5) = 15
A₃ = (2)(5) = 10
The Surface Area:
S.A. = 2A₁ + 2A₂ + 2A₃
S.A. = (2)(6) + (2)(15) + (2)(10) = 12 + 30 + 20 = 62
The seventh-grade class is building target areas for a PE activity. The bases for the game will be in a circular shape. The diameter of each circle is 6 feet. Approximately how many square feet of the turf need to be painted for a base circle? Use 3.14 for π and round your answer to the nearest tenth.
Answers
Answer:
28.3 Square Feet
Step-by-step explanation:
Diameter of circle=6 feet
then
radius=diameter/2
=6/2
=3 feet
The area of circle is given by
A = πr^2
where r is the radius of the circle
Putting the values of pi and r
A =(3.14)(3)^2
=3.14*9
=28.26 sq. feet
Rounding off to the nearest tenth
A=28.3 sq. feet
So, 28.3 sq. feet need to be painted for the base circle ..
What is the solution to the inequality |x-4|<3?
Answers
|x-4| <3
=>. x-4<3 or -(x-4)<3
=>. x-4<3 or x+4>3
=>. x<7 or x>1
So solution is x>1 & x<7. =x€(1,7)
Hope it helps...
Regards,
Leukonov/Olegion.
The solution to the given inequality is:
[tex]1<x<7[/tex] i.e. in the interval form it is given by: (1,7)
Step-by-step explanation:We are given a inequality in term of variable x as follows:
[tex]|x-4|<3[/tex]
Now, we know that any inequality with modulus function is opened as follows:
If
[tex]|x-a|<b[/tex]
Then we have:
[tex]-b<x-a<b[/tex]
i.e. we may write it as:
[tex]a-b<x<a+b[/tex]
Here in the given expression we have:
a=4 and b=3
Hence, the solution is given by:
[tex]4-3<x<4+3\\\\i.e.\\\\1<x<7[/tex]
A group of 5 men and 5 women are applying for a job at a local company. Each of the 10 job candidates has the same chance of receiving a job offer. Using the diagram, what is the probability that the company will hire two women for two positions?
A:3/4
B:1/4
C:1
D:1/2
Answers
Answer: 1/4
Explanation: Because there is a 1/2 chance that a female will get the first job, and a half chance that a lady will get a second job. So (1/2)*(1/2)=(1/4)
When the function f(x) is divided by x + 2, the quotient is x2 – 7x – 9 and the
remainder is 6. Find the function f(x) and write the result in standard form.
Answers
Answer:
f(x)= x^3-5x^2-23x-12
Step-by-step explanation:
Given:
function f(x) divided by x + 2, the quotient is x2 – 7x – 9 and the
remainder is 6
When a polynomial f(x) is divided by any another polynomial d(x) and there is q(x) and r then it can be written as:
f(x)= d(x)q(x) + r
Now putting values of d(x)= x+2, q(x)= x2 – 7x – 9 and r=6, we get
f(x)= (x+2)(x^2-7x-9)+6
f(x)= x^3 -7x^2-9x+2x^2-14x-18+6
= x^3-5x^2-23x-12 !
Final answer:
To find the function given a quotient and remainder when divided by x + 2, combine the terms to get f(x) = x² - 7x - 3. The resulting function f(x) is in standard form.
Explanation:
The function f(x) is a polynomial that can be expressed as f(x) = x² - 7x - 9 + 6/(x + 2). Finding the function in standard form involves combining the quotient and remainder terms.
To write it in standard form, simplify the expression to f(x) = x² - 7x - 3.
Therefore, the function f(x) = x² - 7x - 3.
which of the following is an example of a combination
Answers
B and D are clearly permutation. A and B are selections but arrangement should be done for A where as C only requires selection so C is the combination.
The example which describes combination is:
Selecting 5 CD's to take with you on a trip from a collection of 30 CD's.Step-by-step explanation:Combination--
It is a method of choosing or selecting some items from a group of items.
The formula for choosing r items out of a total of n items is given by the formula:
[tex]n_C_r=\dfrac{n!}{r!\times (n-r)!}[/tex]
Also, if we are selecting as well as arranging some items from a group of items then that method is known as a method of permutation.
A)
Selecting the best cake and runner up best cake from a cake decorating competition.
In this case we are choosing as well as arranging the best and runner up cake according to their ranks.
Hence, it will be a process of permutation and not combination.
B)
The number of ways 6 people can arrive at a party if no one arrive at the same time.
Again it is a problem of permutation because we have to find the number of ways the people can arrive i.e. arranging people in different orders they may arrive.
C)
Selecting 5 CD's to take with you on a trip from a collection of 30 CD's.
This is a method of combination.
Since we have to select some items from a set of items.
D)
The number of ways triplets can be born.
This is again a process of permutation.
Since there are different order they may come.