The distribution of the number of fair coin tosses before one observed three heads in a row is 14.
We have a coin. We have to find the number of fair coin tosses before one observes three heads in a row. We need to use the Markov chain. The probability of getting a head when a coin is flipped is 1/2. Let the probability be represented by the variable "p". Let the number of heads we want in a row be "n".
p = 1/2
n = 3
Using the Markov chain, the formula for getting "n" numbers of the same event in a row with the probability "p" is given below.
A(n) = [1 - p^(n)]/[(1 - p)*p^(n)]
We need to find the value of A(3).
A(3) = [1 - (0.5)^(3)]/[(1 - 0.5)*(0.5)^(3)]
A(3) = [1 - 0.125]/[(0.5)*(0.125)]
A(3) = 0.875/0.0625
A(3) = 14
Hence, the number of fair coin tosses before one observes three heads in a row is 14.
To learn more about numbers, visit :
https://brainly.com/question/17429689
#SPJ4
The table shows the amount of dietary fiber in bananas. Use the table to find the constant of proportionality. Express your answer in decimal form.
Dietary fiber (g) 9.3 18.6 27.9 37.2
Servings 3 6 9 12
The Constant Of Proportionality Is 3.1
A per the table,
Amount of dietary fiber in 3 servings of banana = 9.3 grams
Amount of dietary fiber in 6 servings of banana = 9.3 grams
Amount of dietary fiber in 9 servings of banana = 9.3 grams
Amount of dietary fiber in 12 servings of banana = 9.3 grams
We need to find
The constant of proportionality.
We know that the constant of proportionality is a constant number that represents the rate at which ratios of a quantity decrease or increase.
Let the constant of proportionality be, k.
So, k = x/y
Where,
x = Quantity
y = Total Number of the quantity.
Ratio 1 = 9.3/3 = 3.1
Similarly,
Ratio 2 = 18.6/6 = 3.1
Ratio 3 = 27.9/9 = 3.1
Ratio 4 = 37.2/12 = 3.1
since all the ratios are equal;
Hence, The Constant Of Proportionality Is 3.1
To learn more about proportinality refer here
https://brainly.com/question/12242745
#SPJ1
Find the length of, side x in simplest radical form with a rational denominator.
The side x is √2 cm when the right angle triangle is given with hypothesis 2 cm.
Given that,
In the picture we have a right angle triangle.
We have to find the side x.
The angles are 90°, 45° and 45°.
The hypothesis is 2cm.
By the trigonometric ratio.
The study of angles and the angular relationships between two-dimensional and three-dimensional shapes is known as trigonometry.
Sin45°= opposite side/ hypothesis
1/√2= x/2
x=2/√2
x=√2
Therefore, The side x is √2 cm when the right angle triangle is given with hypothesis 2 cm.
To learn more about triangle visit: https://brainly.com/question/2773823
#SPJ1
Please help ASAP!!! I need help! More points coming!
Answer:
x=2
y=-4
Step-by-step explanation:
a) we isolate y
18=7x-y
+y. +y
y+18=7x
-18. -18
y=7x-18
b) now fill this in
3x+(7x-18)=2
10x-18=2
+18. +18
10x=20
/10. /10
x=2
Now fill in X to find y
3(2)+y=2
6+y=2
-6. -6
y=-4
Hopes this helps
A chef's specialty calls for one-twentieth of an ounce of a spice per serving. The chef has a digital scale that shows the weight as a decimal. What scale reading
does the chef need to see for this spice when preparing the specialty for 19 people?
The scale of reading that the chef needs to see for this spice when preparing the specialty for 19 people would be = 4.5 ounce.
Who is a chef?A chef is a trained individual in various aspects of preparation of dishes, who has the knowledge of combination of food products to achieve an adequate meal.
The quantity of spice per serving= 1/20 ounce.( For an individual)
The quantity of people to prepare specialty for = 90 people
The quantity of spice that would be used to prepare specialty for 90 people would be;
= 1/20 × 90
= 90/20
= 4.5 ounce.
Therefore, the scale reading the chef needs to see for preparing of specialty for 90 people would be = 4.5 ounce.
Learn more about scale factor here:
https://brainly.com/question/28367894
#SPJ1
Select all of the following equation(s) that are quadratic in form. x4 – 6x2 – 27 = 0 3x4 = 2x 2(x + 5)4 + 2x2 + 5 = 0 6(2x + 4)2 = (2x + 4) + 2 6x4 = -x2 + 5 8x4 + 2x2 – 4x = 0
The equations in quadratic will be:
a) x⁴ – 6x² – 27 = 0
d) 6(2x + 4)² = (2x + 4) + 2
e) 6x⁴ = -x² + 5.
What is a quadratic equation?The quadratic equation au² +bu + c=0 can be written as a formula. where u is an algebraic expression. In each of these examples, doubling the exponent of the middle term equals doubling the exponent of the leading term.
The quadratic function f(x) = a(x - h)² + k is said to be in standard form if an is not equal to zero. If an is positive, the graph will open upward; if an is negative, it will open downward. The vertical line x = h is the line of symmetry, and the point is the vertex (h,k)
Learn more about equations on:
https://brainly.com/question/16923993
#SPJ1
Carmen has a rope that is 18 meters long. She cuts away a piece that is 8.16 meters long. How long is the remaining piece of rope?
In a case whereby Carmen has a rope that is 18 meters long. She cuts away a piece that is 8.16 meters long the lenght of the remaining piece of rope is 9.84 metres.
What is distance?Distance can be described as the space that exist between two or more point, the concept that willbe used in the question is the concept of distance.
The total distance of the rope is 18 meters long , and she cut 8.16 meters long awya which implies that the remaining lenght of the rope will be ( 18 - 8.16)= 9.84 metres
Learn more about distance here: https://brainly.com/question/4931057
#SPJ1
A salami is 2 3/5 inches long. The salami is cut into 1/8 inch thick slices.
How many slices of salami were cut?
Answer:
20 slices
Step-by-step explanation:
2 3/5 = 13/5
13/5 / 1/8
(13/5)(8/1) = 20.8
about 20 slices
Calculate P(3, 2)
12
8
7
6
Answer: the answer is number 6
if you are conducting an experiment where the probability of a success is .02 and you are interested in the probability of two successes in 15 trials, the correct probability function to use is the . a. normal probability density function b. binomial probability function c. poisson probability function d. standard normal probability density function
When conducting an experiment with the probability of a success of 0.02 and you are interested in the probability of 2 successes in 15 trials, the correct probability function to use is the binomial probability function. (Option B)
Binomial probability function, in probability theory and statistics, refers to the discrete probability distribution of the number of successes in a sequence of repeated independent experiments. Generally, the binomial distribution represents data generated from a yes–no question, and each with its own Boolean-valued outcome: success or failure. As the experiment where probability of success is given and you are interested in the probability of 2 successes in 15 trials, the appropriate probability function is binomial probability function.
Learn more about Binomial probability function:
https://brainly.com/question/9325204
#SPJ4
The monthly property tax for a home, in dollars, in a certain city y years after 1990 is $333 + $35y
Which of the following is correct?
OA. The property tax increased by $333 each year after 1990.
OB. The property tax decreased by $333 each year after 1990.
OC. The property tax increased by $35 each year after 1990.
OD. The property tax decreased by $35 each year after 1990.
Answer:
The property tax increases by 35
Step-by-step explanation:
The number 333 in the equation is a constant. It is added to the total no matter how many years after 1990. The 35 is what is increasing every year after 1990.
a plumber charges $12.00 per hour for her work, plus a $32.00 materials fee. If you pay her $74.00, how many hours did the plumber work?
Answer:
3.5 hours
Step-by-step explanation:
74-32=42
42/12=3.5
The dimensions of a room are 4.2 m by 6 m. On a plan, the longer side is equal to 4cm. What is the length of the shorter side on this plan?
The length of the shorter side on this plan is 2.8cm.
How to calculate the length?Based on the information illustrated, let the length of the shorter side on this plan be represented by x.
In this case, the dimensions of a room are 4.2 m by 6 m and on a plan, the longer side is equal to 4cm.
This will be illustrated as:
x/4 = 4.2 / 6
Cross multiply
6x = 4 × 4.2
x = (4 × 4.2) / 6
x = 2.8cm
The length is 2.8 cm.
Learn more about length on:
brainly.com/question/2217700
#SPJ1
In a certain Algebra 2 class of 24 students, 6 of them play basketball and 7 of them play baseball. There are 13 students who play neither sport. What is the probability that a student chosen randomly from the class plays basketball or baseball?
Answer:
P(basketball or baseball) = 11/24
Step-by-step explanation:
You want the probability that a randomly chosen student plays either sport, given the probability that 13 of the 24 students plays neither sport.
ComplementThe probability that a student plays at least one (of the two) sports is the complement of the probability they play neither sport. If 13 of 24 students play neither sport, then (24-13)/24 = 11/24 must play at least one of the two sports.
P(basketball or baseball) = 11/24
__
Additional comment
6+7-11 = 2 students play both sports.
<95141404393>
Solve: (1+i)^14. And show workings
Step-by-step explanation:
(1 + i)¹⁴ = (1 + i)²×(1 + i)¹² = ((1 + i)²)⁷
(1 + i)² = 1 + 2i - 1 = 2i
((1 + i)²)⁷ = (2i)⁷ = 2⁷×i⁷ = 128×i²×i²×i²×i =
= 128×-1×-1×-1×i = -128i
Please help! Four transformed absolute value functions are shown in the graph. Write the name of the function that matches each equation on the blank.
The name of the function that matches each equation on the blank is,
-|x-7|= h(x)
0.5|x-3|= g(x)
|x-3|-2= f(x)
-5|x-7|=j(x)
What is meant by a function?A function from a set X to a set Y in mathematics assigns to each element of X exactly one element of Y. The domain of the function is the set X, and the codomain of the function is the set Y.
The first known approximation to the concept of function is attributed to the Persian mathematicians Al-Biruni and Sharaf al-Din al-Tusi. Functions were originally idealistic representations of how one variable quantity depended on another. The location of a planet, for example, changes throughout time. Historically, the concept was formed with infinitesimal calculus near the end of the 17th century, and the functions that were analyzed were differentiable until the 19th century.
The name of the function that matches each equation on the blank is,
-|x-7|= h(x)
0.5|x-3|= g(x)
|x-3|-2= f(x)
-5|x-7|=j(x)
To know more about function, visit:
https://brainly.com/question/12976942
#SPJ1
2x+y=1 and y=2x+1 how many solutions
The expression 2x + 1 = y and y = 2x + 1 has no solution.
Expression:
The expression means a mathematical statements that have two terms at least that contain variables, numbers, or both connected by the arithmetic operators.
Given,
Here we have the expressions 2x + 1 = y and y = 2x + 1.
Now, we have to find the number of solution for this expression.
When we try to find the solution(s) graphically, you would plot both of the equations as straight lines. The solution(s) lies where the lines intersect.
But here we looking into the given equation both are equal.
And if we plot these on the graph then it will simply present the straight line. And there is no intersection in it.
Which also states that there is no solution for this expression.
To know more about Expression here.
https://brainly.com/question/14083225
#SPJ9
The directions on a swimming pattern says to cut an extra 15 percent of fabric to account for error chloe needs 0.75 yard of fabric to make a skirt and she cuts 0.8625 yards did chloe cut the correct amount of fabric white or why not
The directions on a swimming pattern says to cut an extra 15 percent of fabric to account for error, Chloe needs 0.75 yard of fabric to make a skirt and she cuts 0.8625 yards,
Given that the directions on a sewing pattern say to cut an extra 15% of fabric to account for an error, and Chloe needs a 0.75 yard of fabric to make a skirt, so she cuts 0.1125 yard, to determine if Chloe cut the correct amount of fabric the following calculation must be made:
0.75 x 1.15 = X
0.8625 = X
0.8625 - 0.1125 = 0.75
Therefore, the amount of fabric that Chloe cut is correct.
To learn more about proportions, click here https://brainly.com/question/870035
#SPJ4
Solve each problem by writing and solving an equation. use "x" for the variable and type with no spaces. during the spring car wash, asb washed 14 fewer cars than during the summer car wash. they washed a total of 96 cars during both car washes. how many cars did they wash during the spring car wash?
Answer:
55 cars
Step-by-step explanation:
x + (x-14) = 96
Using the figure below, which table correctly lists the steps and reasons used to find the measure of angle d?
The correct option is (c).
(A) We know that sum of the interior angles of a triangle is equal to 180°.
m∠a + m∠b + m∠c = 180° (all three are interior angles)
(B) If the sum of two angles is 180°, that angle is called a supplementary angle. In other words, when two angles add to form a straight line, they are called supplementary angles.
m∠d + m∠c = 180° (both are in a straight line making an angle)
(C) Transitive properties help establish a connection by stating that if a = b and b = c, then a = c.
m∠a + m∠b + m∠c = 180°
m∠d + m∠c = 180°
Therefore, this property
We can say,
m∠a + m∠b + m∠c = m∠d + m∠c
(D) Subtraction equality properties: Subtraction equality properties indicate that subtracting or removing an equal value from two equal elements results in a new equal quantity.
The formula for this is if a = b, then a-c = b-c
In the question,
m∠a + m∠b = m∠d
Both ∠a and ∠b are two interior angles and the exterior angle is ∠d.
According to the exterior angle property of a triangle theorem, the sum of two opposite interior angles is equal to exterior angles.
Hence, this is also correct.
Therefore, the correct option is (c) which has the correct steps and reasons for the given question.
To learn more about the exterior angle visit: https://brainly.com/question/10638383
#SPJ1
is y=1/3x+5 proportional or non proportional
The following equation is not proportional.
What is equation?
An equation is a formula that uses the equals sign to connect two expressions to show that they are equal.
Main Body:
we now that
A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form k=y/x or y= kx.
In a proportional relationship the constant of proportionality k is equal to the slope m of the line and the line passes through the origin
In this problem we have
y= 1/(3x+5)
This is the equation of the line in slope intercept form
where
m= 3
b= 5
The given equation not represent a proportional relationship, because the line not pass through the origin
In a proportional relationship the value of b (y-intercept) is equal to zero
Hence , equation is not proportional.
To learn more about equation click on the link below
https://brainly.com/question/25896797
#SPJ9
A tank ha 120 gallon of water and i being drained at a rate of 1/2 gallon each econd. Another tank ha 100 gallon of water and i being drained at a rate of 1/4 gallon each econd. Which equation could be ued to determine x, the number of econd, when the two tank have the ame amount of water?
The equation that could be used to determine x, the number of seconds, when the two tanks have the same amount of water is 120 - 1/2(x) = 100 - 1/4(x) or x = 80.
An algebraic expression is the combination of numbers and variables in expressing and solving a particular mathematical question. An equation is the equality of expressions.
Let x be the number of seconds at the moment that the two tanks have the same amount of water.
If a tank has 120 gallons of water and is being drained at a rate of 1/2 gallon each second, the the amount of water left after time = x is "120 - 1/2(x)".
If another tank has 100 gallons of water and is being drained at a rate of 1/4 gallon each second, the the amount of water left after time = x is "100 - 1/4(x)".
Equate the two expressions to determine the time, x , at which the two tanks have the same amount of water left.
120 - 1/2(x) = 100 - 1/4(x)
20 = 1/4 x
x = 80
Learn more about algebraic expression and equation here: brainly.com/question/3927786
#SPJ4
what is 5.37 divided by 3 equal put 5.37 at the top and 3 at the bottom PLEASE EXPLAIN YOUR ANSWER. my lil sister need help
Answer:
5.37/3 = 1.79
Step-by-step explanation:
Given statement,
→ 5.37 divided by 3 equals?
Forming the problem,
→ 5.37/3
Let's solve the problem,
→ 5.37/3
→ (5.37 ÷ 3)
→ 1.79
Hence, the answer is 1.79.
The area of a rectangle is 44 square inches . The length of one side is 11 inches.what is the length of the other side
Answer:
Step-by-step explanation:
A = 44
a = 11
______
b - ?
A = a·b
b = A / a = 44 / 11 = 4 ( inches)
(Real-World Proportional Problems MC)
The time it takes to read 5 pages of a book can be represented with the equation y equals 4.5 divided by 5 times x, where y represents the total time in minutes and x represents the number of pages read.
Determine how long it will take to read a book that has 218 pages.
242.22 minutes
218.63 minutes
196.2 minutes
54.5 minutes
Answer:
C. 196.2 minutes===========================
Equationy = (4.5 / 5) xGivenx = 218Find yy = (4.5/5)*218 y = 0.9*218y = 196.2Correct choice is C
Answer:
c) 196.2 minutes
Step-by-step explanation:
Forming the equation,
→ y = (4.5/5) × 218
Now required value of y will be,
→ y = (4.5/5) × 218
→ y = 981/5
→ [ y = 196.2 min ]
Hence, the value of y is 196.2.
Find the equation for the line of best fit for the scatter plot shown below.
Answer Choices:
y=1.5x+0.5
y=1.5x+4.5
y=1.5x+5
The equation for the line of best fit of the scatter plot according to the attached image is; y = 1.5x + 0.5.
What is the equation of the line of best fit of the scatter plot given?It follows from the task content that the equation of the line of best fit of the scatter plot is to be determined.
By observation, it can be inferred that the y-intercept of the line of best fit is at the point; (0, 0.5).
Also, the slope of the equation can be determined by considering the points; ( 2 , 1 ) and ( 9 , 12 ).
Therefore, since the slope is given by; m = (y2 - y1) / (x2 - x1).
In this scenario, slope, m = (12 - 1) / (9 - 2)
m = 11/7.
Hence, the slope is approximately; 1.5.
Ultimately, the equation of the line of best fit is; y = 1.5x + 0.5.
Read more on line of best fit;
https://brainly.com/question/17013321
#SPJ1
PLEASE HELP ASAP
Given 2 and 1 over 10 times negative seven times 5 over 12, determine the product.
negative fourteen and 5 over 120
negative six and 1 over 8
fourteen and 5 over 60
six and 1 over 8
Answer:A
Step-by-step explanation:negative fourteen and 5 over 120
Because you multiple
2 x -7 = -14
10 x 12 = 120
1 x 5 = 5
At a local high school, gpa's are normally distributed with a mean of 2. 9 and standard deviation of 0. 6. What is the gpa of the highest 2. 5% of the students?.
At a local high school, GPA's are normally distributed with a mean of 2.9 and standard deviation of 0.6.
x=4.25 is the GPA highest 2.5% of the students.
We have to find the GPA of the highest 2.5% of the students.
Mean = μ = 2.9
Standard deviation = σ = 0.6
Finding the z value for corresponding area 0.9750
For 95% confidence interval ,
z = 1.96
For 97.5% confidence interval,
We get z = 2.25
From
Z = ( x - μ ) / σ
For 2.5% of the students
To solve for x
x = Z*σ + μ
x = 2.25*0.6 + 2.9
x = 1.35 + 2.9
x = 4.25 GPA of highest 2.5% of students
Hence the answer is, x=4.25 is the GPA highest 2.5% of the students.
To learn more about distribution click here https://brainly.com/question/4079902
#SPJ4
Jason decided to begin a workout program. He wants to start running three times a week. At the beginning of the workout program, his weekly average per run is 1 mi. He increases his weekly average per run by 17% each week, according to an exponential growth model. Jason makes a sketch of the graph for this situation. He plots the point containing the y-intercept, (0,1) . He then plots the point representing the weekly average per run for Week 7 and rounds the coordinates of the point to the nearest tenth. What are the coordinates of the point that represents the weekly average per run for Week 7?
The coordinates of the point that represents the weekly average per run for Week 7 is (7, 3.00).
What is an exponential function?It is defined as a function that rapidly increases and the value of the exponential function is always positive. It denotes with exponent y = aˣ
where a is a constant and a>1
It is given that:
Jason decided to begin a workout program. He wants to start running three times a week.
As we know, the exponential function can be represented as:
f(x) = abˣ
The weekly average per run is 1 mi.
He increases his weekly average per run by 17% each week,
The exponential function:
f(x) = 1(1.17)ˣ
Plug x = 7
f(7) = 1(3.0012)
f(7) = 3.00
Thus, the coordinates of the point that represents the weekly average per run for Week 7 is (7, 3.00).
The complete question is:
Jason decided to begin a workout program. He wants to start running three times a week. At the beginning of the workout program, his weekly average per run is 1 mi. He increases his weekly average per run by 17% each week, according to an exponential growth model. Jason makes a sketch of the graph for this situation. He plots the point containing the y-intercept, (0,1) . He then plots the point representing the weekly average per run for Week 7 and rounds the coordinates of the point to the nearest tenth. What are the coordinates of the point that represents the weekly average per run for Week 7?
options:
A. (7, 3.2)
B. (7, 2.7)
C. (7, 3.0)
D. (7, 4.6)
E. (7, 4.1)
Learn more about the exponential function here:
brainly.com/question/11487261
#SPJ2
Answer:
7,3,0
Step-by-step explanation:
Yesterday, Grace drove 41 1/2 miles. She used 1 1/4 gallons of gasoline. What is the unit rate for miles per gallon?
33.2 miles per gallon is the unit rate for miles per gallon.
Given, Grace drove 41 1/2 miles.
She used 1 1/4 gallons of gasoline.
So, Grace drove 41 1/2 miles = Grace used 1 1/4 gallons of gasoline
41(1/2) miles = 1(1/4) gallons of gasoline
83/2 miles = 5/4 gallons of gasoline
as, 5/4 gallons of gasoline = 83/2 miles
1 gallon of gasoline = (4/5)×(83/2)
1 gallon of gasoline = (2/5)×83
1 gallon of gasoline = 166/5
1 gallon of gasoline = 33.2 miles
33.2 miles/gallon is the unit rate.
Hence, 33.2 miles per gallon is the unit rate for miles per gallon.
Learn more about Unitary Method here https://brainly.com/question/28731562
#SPJ1
Need help pls
I HAVE A BAD GRADE IN MATH HELP PLS
The rounded value of x² = 521/73 is ± 2.67 and already rounded to the nearest hundred.
What is a perfect square number?A perfect square number when taken the square root of it results in an integer.
Numbers that are not perfect squares when taken the square root of it are irrational numbers.
One method of obtaining square roots for perfect squares is prime factorization.
Given, x² = 521/73.
∴ x² = 7.13.
x = ± √7.13.
x = ± 2.67.
learn more about perfect squares here :
https://brainly.com/question/385286
#SPJ1
