The tree diagram represents the sample space for the repeated experiment of a coin being tossed 4 times.
Determine P(at least 2 heads).
0.8125
0.6875
0.4375
0.0625
Answers
The probability of obtaining at least 2 heads is 0.6875.
option B.
What is the probability of getting at least 2 heads?
The probability of obtaining at least 2 heads in 4 coin tosses can be calculated by adding the probabilities of getting exactly 2 heads, exactly 3 heads, and exactly 4 heads. This can be done using the binomial distribution formula:
P(X >= 2) = P(X = 2) + P(X = 3) + P(X = 4)
Where;
X is the number of heads in 4 coin tossesEach coin toss has a probability of 0.5 of landing heads.
P(X = 2) = 4C2 x (0.5)^2 x (0.5)^2 = 6 x 0.25 x 0.25 = 0.375
P(X = 3) = 4C3 x (0.5)^3 x (0.5)^1 = 4 x 0.125 x 0.5 = 0.25
P(X = 4) = 4C4 x (0.5)^4 = 1 x 0.0625 = 0.0625
The total probability is calculated as follows;
P(X >= 2) = 0.375 + 0.25 + 0.0625 = 0.6875
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Answer:
The probability of obtaining at least 2 heads is 0.6875.
option B.
Step-by-step explanation:
Related Questions
John is measuring a piece of glass to fit in a triangular frame. He can only remerber to sides of the frame, which are 6 centimeters and 11 centimeters. Between what wwo numbers must the tried side of the frame fall?
Answers
The length of the third side should be between 5 and 17.
What are triangles?A triangle is a three-sided polygon because it has three edges and three vertices. The most important attribute of a triangle is the sum of its internal angles to 180 degrees.
Given John is measuring a piece of glass to fit in a triangular frame,
the two sides of the frame are 6 cm and 11 cm,
let the third side be x,
Any two sides of a triangle can be added together to have a length larger than the third side. Similar to this, any two triangle sides have length differences between them that are smaller than the length of the third side.
i.e. 11 - 6 < x < 11 + 6
5 < x < 17
Hence the third side should vary from 5 cm to 17 cm.
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One more question before I leave my aunt house!
Grade 8th
Answers
Answer:
2. y = 3x + 6
3. y = 2x
4. y = 5x + 60
Step-by-step explanation:
Slope-intercept form: y = mx + b
2.
Pick 2 points (0,6) (1,9)
The y increase by 3, and the x increase by 1, so the slope is
m = 3
the y-intercept is located at (0,6)
Our equation is y = 3x + 6
3.
Pick 2 points (0,0) (1,2)
The y increase by 2, and the x increase by 1, so the slope is
m = 2
the y-intercept is located at (0,0)
Our equation is y = 2x
4.
Pick 2 points (0,60) (2,70)
The y increase by 10, and the x increase by 2, so the slope is
m = 10/2 = 5
the y-intercept is located at (0,60)
Our equation is y = 5x + 60
mr. Smith started 8 yards away from the motion detector, and two seconds later, he was 4 yards away from the detector. The graph below shows Mr. Smith’s motion. What is the difference between the rate of change of the intervals: 1,2 and 2,4?
Answers
The difference between the rate of change of the intervals: 1,2 and 2,4 is; 2
How to find the rate of change over an interval?The average rate of change over the intervals (x₁, y₁) and (x₂, y₂) is given by the formula;
Average rate of change = (y₂ - y₁)/(x₂ - x₁)
Thus, the average rate of change between the intervals (1, 2) and (2, 4) is;
Average rate of change = (4 - 2)/(2 - 1)
Average rate of change = 2/1
Average rate of change = 2
That is the difference between the rate of change over the two given intervals.
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if you are tossing a six-sided die, what is the probability of getting either a 1 or a 2 on your first toss and your second toss?
Answers
It is based on the likelihood of something occurring. The reasoning behind probability is the foundation of theoretical probability. The probability of getting one or two in first and second toss is [tex]\frac{1}{9}[/tex].
Probability is a number that represents the likelihood or chance that an event will occur. Probabilities can be expressed as proportions ranging from 0 to 1, as well as percentages ranging from 0% to 100%.
The probability of getting one or two in first toss will be:-
[tex]\frac{1}{6} + \frac{1}{6} = \frac{1+1}{6} = \frac{2}{6} = \frac{1}{3}[/tex] ( as the probability of getting one in first toss is [tex]\frac{1}{6}[/tex] and getting two is also [tex]\frac{1}{6}[/tex]).
Similarly the probability of getting one or two in second toss will be:-
[tex]\frac{1}{6} +\frac{1}{6} = \frac{1+1}{6} = \frac{2}{6} = \frac{1}{3}[/tex]
The total probability of getting one or two in first and second toss will be:-
[tex]\frac{1}{3} *\frac{1}{3} = \frac{1}{9}[/tex]
Hence, Henceprobability is [tex]\frac{1}{9}[/tex].
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assuming that this population successfully colonizes the island and persists until the present, add a histogram of the 21st century island population to your figure (make sure that they can be easily compared to each other). describe the population in terms of light, medium, and dark individuals. write a brief statement justifying your graph and answer.
Answers
a) A histogram representing coat color for the initial colony your graph is given below.
b) Due to the fact that beach mice, which often have light coast colors, outnumber Oldfield colonizers by a factor of several, making dark coat colors less prevalent as time passes.
a) It's critical to understand the geographic distribution of Oldfield mice prior to the histogram presentation. Santa Rosa Island is classified into two primary geographic locations: inland and coastal, although having various different geographical settings.
Oldfield mice come in a variety of colors; fawn-colored (medium or dark) individuals are typically found in inland regions, whilst lighter or white individuals are found in coastal regions. As a result, Santa Rosa Island should have more colored mice and the beach should have more light-hued mice.
b) Oldfield colonists have predominantly dark coat colors, according to the image. The second histogram shows the coast color of the population following 6000 years of Oldfield and beach mouse hybridization. This is due to the fact that beach mice, which often have light coast colors, outnumber Oldfield colonizers by a factor of several, making dark coat colors less prevalent as time passes.
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The complete question is:
Imagine you have a time machine and are able to go back in same so 6,000 years ago. You are standing on newly formed Santa Rosa Island, a barrier island off the coast of Florida that consists entirely of beach habitate. You see that a large and genetically diverse mainland population of oldfield mice have just colonized the island Using all of the information in this case study, answer the following questions and justify your answers with reasoning Questions ists on the island. Write a brief statement justifying.
1. Draw a histogram representing coat color for the initial colony your graph. Describe the population in terms of the proportion of light, medium, and dark individuals.
2. Assuming that this population successfully colonizes the island and persists until the present, add a histogram of the 21" century island population to your figure (make sure that they can be easily compared to each other) Describe the population in terms of light, medium, and dark individuals. Write a brief statement justifying your graph and answer
question 11 pts suppose is an -matrix such that has only the trivial solution. how many pivot columns does have?
Answers
A matrix A is said to have only the trivial solution if the only solution to the system of equations, A x = 0, is the zero vector, x = 0.
The number of pivot columns in a matrix is equal to the rank of the matrix. Therefore, if A has only the trivial solution, it has rank 0, and so it has 0 pivot columns. To calculate the rank of a matrix, we can use the following formula: rank(A) = min(m, n) - dim(null A), where m and n are the number of rows and columns of A, respectively, and dim(null A) is the dimension of the null space of A.
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complete question:
Given an m x n matrix A, what is the number of pivot columns for A if it has only the trivial solution?
a number n is rounded to 2 decimal place
the result is 3.87
using inequalities write down the error interval for n
Answers
Answer:
3.90
hope its help
Step-by-step explanation:
y=3.87
n=d/3.90
Excute. by down interval 34.0
based on the residual plot shown, is a linear model appropriate for comparing tree age to basal area? because the residuals are centered about zero, a linear model is appropriate. because the residual plot does not show a clear pattern, a linear model is appropriate. because the residual plot shows a random a scatter of points, a linear model is not appropriate. because the residual plot does not appear linear, it is likely that tree age and basal area do not have a linear relationship.
Answers
Answer:
Because the residual plot does not show a clear pattern, a linear model is appropriate.
Step-by-step explanation:
Short answer need please.
Answers
The surface area of the right prism is equal 142 square inches.
How to calculate the surface area of a right prism
Surface area is the sum of the areas of all faces in a solid, herein we find the case of a right prism with six rectangular faces. The area formula for a rectangle is shown below:
A = w · l
Where:
A - Area, in square inches. w - Width, in inches.l - Length, in inches.Now we calculate the surface area of the rectangular prism:
A = 2 · (7 in) · (3 in) + 2 · (5 in) · (7 in) + 2 · (3 in) · (5 in)
A = 42 in² + 70 in² + 30 in²
A = 142 in²
The right prism has a surface area of 142 square inches.
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what is the soulution 8x + 4x = 0
Answers
Answer:
0
Step-by-step explanation:
8x + 4x = 0
12x = 0
x = 0/12
x = 0
Step-by-step explanation:
combine like terms[tex]8x + 4x = 0[/tex]
[tex]12x = 0[/tex]
divide both sides by the same factor[tex] \frac{12x}{12} = \frac{0}{12} [/tex]
cancel terms that are in both the numerator and denominator[tex] \frac{12x}{12} = \frac{0}{12} [/tex]
[tex]x = \frac{0}{12} [/tex]
which is basically 0
Question located in picture below:
Answers
Answer:
5a^2 + 1
Step-by-step explanation:
7a^2 - 4 - 2a^2 + 5
5a^2 + 1
Answer:
5a^2+1
Step-by-step explanation:
Combining like terms in polynomials can go based on the degree it has.
Since 7a^2 and -2a^2 have the same degree as one another, we can just add them, which gives us 5a^2
Now since -4 and 5 dont have any degree, they are liked terms.
Add: -4+5=1
Now when simplified, we get:
5a^2+1
what is the slope and y intercept of the graph of y=3x-5
Answers
Y intercept is -5
I solved this because in the equation y=mx+b
M is the slope which is 3
And b is the y intercept which is -5
what was the ending balance? a sample bank statement. responses $597.35 $597.35 $715.26 $715.26 $751.58 $751.58 $880.88 $880.88
Answers
The final balance of the bank statement was $880.88. This amount reflects deposits, withdrawals, fees, and interest accrued during the statement period.
The final balance of a bank statement is the amount of money that is in the account after all deposits, withdrawals, fees, and interest have been accounted for during the statement period. To calculate the ending balance, start with the beginning balance and then add any deposits that were made during the statement period. Then, subtract any withdrawals, fees, and interest that were charged during the statement period. The final balance will be the amount that remains after all transactions have been accounted for. In this example, the ending balance was $880.88.
The complete question:
what was the ending balance? a sample bank statement.
A) $597.35
B) $715.26
C) $751.58
D)$880.88.
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if you laid a billion dollars worth of 10-dollar 10 -dollar bills side by side, how many dollar bills would you use? how many miles long would the trail be? (the width of a 10-dollar 10 -dollar bill is 2.61 inches.) is 2.61 inches.) (give your answers to the nearest whole number.)
Answers
The correct answer is it will stretch far 59.3 lakh miles .
Given that,
If a billion 10-dollar bills were placed side by side, the total value would be $1.
To find :What amount of dollars would you use? How far would the trail stretch?
A dollar bill is 2.61 inches wide.
The dimensions of a billion dollar bill are 2.61 x 1,000,000,000 inches.
Divide this by 12 to convert to feet: 2.61 x 1,000,000,000 / 12.
Divide that by 5280 to convert it to miles: 2.61 x 1,000,000,000 x 12 /5280.
(Instead of 2.61 inches, use 6.14 inches if you meant to say it from end to end, the long way.)
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i need help whatsb the answer
Answers
Answer:Simplify the expression.
Exact Form:
35
8
Decimal Form:
4.375
Mixed Number Form:
4 3/8
Step-by-step explanation:
this is the answer
50 apples cost $25. How much would 75 apples cost?
Answers
To find out how much 75 apples would cost, we need to find out the cost per apple and then multiply that amount by 75. If 50 apples cost $25, then the cost per apple is $25/50 = $0.50. So, 75 apples would cost $0.50 x 75 = $37.50.
Answer:
$37.50
Step-by-step explanation:
$25/50=$0.50 per apple
0.50 x 75 = $37.50
the college board reports that in the recent year, the mean mathematics sat score was 514 and standard deviation of 118. a sample of 50 scores is chosen. a) the probability that the sample mean score is less than 500 is [ select ] b) [ select ] c) the 80th percentile of the sample scores is [ select ]
Answers
The College Board reported that in a recent year, the mean mathematics SAT score was 514 and the standard deviation was 118. A sample of 65 scores was chosen.
a) The probability that the sample mean score is less than 500 can be found by using the mean and standard deviation of the SAT scores population. The formula to calculate this probability can be found in 3.
c) The 80th percentile of the sample scores is also not mentioned in the search results. To find the 80th percentile, a probability distribution of the sample mean scores must be created and then solved for the desired percentile.
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Identify the initial amount a and the rate of decay r (as a percent) of the exponential function f(t)=475(0.5)t. Evaluate the function when t=3. Round your answer to the nearest tenth.
Answers
The function when t=3 to the nearest tenth is 59.4.
How did we get the value?The initial amount is a = 475, and the rate of decay r is 50%.
To evaluate the function when t=3, we plug in t=3:
f(3) = 475(0.5)^3 = 475 * (0.125) = 59.375
Rounding to the nearest tenth, f(3) = 59.4.
Therefore, the correct answer is as given above. It could be concluded that the rounded answer to the nearest tenth is 59.4
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if the average service rate is 6 customers per hour, and assuming the negative exponential distribution is used to describe the randomness of the service time distribution, what is the probability that the service time will be less than or equal to 6 minutes? a. 0.451 b. 0.549 c. 0.017 d. 0.632
Answers
If the average service rate is 6 customers per hour, and assuming the negative exponential distribution is used to describe the randomness of the service time distribution. The probability that the service time will be less than or equal to 6 minutes is 0.549 [B]
The average service rate of 6 customers per hour corresponds to a mean service time of 1/6 = 0.1 hour = 6 minutes. To find the probability that the service time will be less than or equal to 6 minutes, we need to find the cumulative distribution function (CDF) of the exponential distribution evaluated at 6 minutes. The CDF of the exponential distribution is given by:
F(x) = 1 - exp(-λx)
where,
λ = 1/mean = 1/0.1 = 10. Plugging in x = 6, we get:
F(6) = 1 - exp(-10 * 6) = 1 - exp(-60) ≈ 0.549
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How do you solve
-6y+2=4x
y-2=x
In elimination for linear equations
Answers
The solution to the given system of linear equations is (x, y) = (-1, 1).
What is the Linear equation?A linear equation is defined as an equation in which the highest power of the variable is always one.
The system of equations is given in the question, as follows:
-6y + 2 = 4x
y - 2 = x
Here's how to solve this system of equations using the elimination method:
Multiply the first equation by 2:
-12y + 4 = 8x
Add the two equations:
-12y + 4 + y - 2 = 8x + x
-11y + 2 = 9x
Solve for x:
x = (2 - 11y)/9
Substitute the value of x back into one of the original equations to find y:
-6y + 2 = 4x
-6y + 2 = 4((2 - 11y)/9)
-6y + 2 = (8 - 44y)/9
-54y + 18 = 8 - 44y
26y = 26
y = 1
Use the value of y to find x:
x = (2 - 11y)/9
x = (2 - 11 * 1)/9
x = (2 - 11)/9
x = -9/9
x = -1
Thus, the solution is (x, y) = (-1, 1).
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HELP PLEASEEEEEEEEEEE i will give brainliest<33
Answers
Answer:
The unit rate of pages per hour is 39 pages and the unit rate of hour per pages is 1/39 hours
Step-by-step explanation:
We can solve this problem using proportion.
From the question; Leo reads 13 pages in 1/3 hours.
The first part of the question is to find the unit rate for pages per hour.
To find this;
Let x = the number of pages read in 1 hour
13 pages = 1/3 hours
x = 1 hour
Cross-multiply
1/3 × x = 13 × 1
= 13
Multiply both-side of the equation by 3
× 3 = 13× 3
x = 39 pages
Therefore, the number of pages read in 1 hour is 39 which implies the unit rate for pages per hour is 39
For the second part of the question, we are to find the unit rate for hours per page, that is; how many hours can he use to read a page.
Let x = the number of hour use to read a page
13 pages = 1/3 hour
1 pages = x
Cross-multiply
13x = 1/3
To get the value of x, we will divide both-side of the equation by 1/13
13x × = ×
x = hour
Therefore, the number of hour taken to read 1 page is , which implies the unit rate of hours per page is
Distributive property 42÷3
Answers
Answer: 14
Step-by-step explanation: 42 divided by 3 is 14.
As a fraction: 42/3
Answer:
42÷3= 14?
Step-by-step explanation:
The price of an item has been reduced by 80%. The original price was $95. What is the price of the item now?
Answers
Answer: $19
Step-by-step explanation:
100% - 80% = 20%
20% ÷100 = 0.2
$95 x0.2 = $19
0r
10% of $95 = $9.50
9.50 x 2 = 19
elzny I NEED HELP PLS
Answers
Answer:
105
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Neil rents a canopy for $21.75 per
hour with a $25 delivery and
set-up fee. The rental costs a
total of $155.50. For how many
hours does Neil rent the canopy?
Create and solve the equation.
Answers
Answer:
21.75x + 25 = 155.50
-25 = -25
21.75x = 130.50
divide your slope from your variable
x = 6
What is 10x9+2
Anyways can someone help me with my other question on english.
Answers
Answer: 92
Step-by-step explanation: multiply first. 9x10=90. now add the two to the answer we just got. 90+2? 92.
Chelsea left the WHite House and traveled toward the capital at an average speed of 34km/h. Jasmine left at the same time and traveled in the opposite direction with an average speed of 65km/h. Find Jasmine's and Chelsea's time, rate, and distance.
Answers
The distance traveled by Jasmine and Chelsea is given by the equations of speed and J = 20.4 km and C = 39 km , where T is the time taken and T = 0.6 hours
What is Speed?Speed is defined as the rate of change of position of an object in any direction. Speed is measured as the ratio of distance to the time in which the distance was covered. Speed is a scalar quantity as it has only direction and no magnitude
Speed = Distance / Time
Given data ,
Let the speed of Jasmine be represented as S₁ = 34 km/h
Let the speed of Chelsea be represented as S₂ = 65 km/h
Now , the distance traveled by Jasmine = J
And , the distance traveled by Chelsea = C
The measure of J = measure of C
So , the distances are the same
Let the time taken by both Jasmine and Chelsea be T
Now , Speed = Distance / Time
Substituting the values in the equation , we get
Distance D = 34T
And , distance D = 65T
Now , the total distance D = 59.4 km
So , 34T + 65T = 59.4
On simplifying the equation , we get
99T = 59.4
T = 0.6 hours
Hence ,
The distance traveled by Jasmine and Chelsea are 20.4 km and 39 km respectively
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defin the domen and range fanction
Answers
Answer:
The domain is the set of all the input values of a function and the range is the possible output given by the function.
What is the image point (70,0) after a rotation of 270° counterclockwise about the origin?
Answers
Answer: ( 0, -70)
Step-by-step explanation: make a sketch on the x-y plane to see why
At the nut farm, the cost price of a bag of almonds is R290. It is sold with a profit of 45%. What is the selling price?
Answers
The selling price of the bags of almonds that yields a profit of 45% is $420.5
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables using mathematical operations. An equation can be linear, quadratic, cubic and so on, depending on the degree of the variable.
The formula for profit is given by:
Profit = [(selling price - cost price) / cost price] * 100%
At the nut farm, the cost price of a bag of almonds is R290. It is sold with a profit of 45%. Hence, substituting:
45% = [(selling price - 290)/290] * 100%
0.45 = (selling price - 290)/290
selling price - 290 = 130.5
selling price = 420.5
The selling price is $420.5
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