Use the binomial distribution to determine the probability that 10 rolls of a fair die will show exactly seven fours. Express your answer as a decimal rounded to 4 decimal places.
Answers
The probability of getting exactly seven fours in ten rolls of a fair die is approximately 0.0574.
To determine the probability of exactly seven fours in 10 rolls of a fair die, we can use the binomial distribution formula:
P(X = k) = (nCk) * p^k * (1-p)^(n-k)
Where:
P(X = k) is the probability of getting exactly k successes (in this case, rolling a four) in n trials (in this case, rolling a die 10 times),
nCk is the number of combinations of n items taken k at a time,
p is the probability of success on a single trial (rolling a four), and
(1-p) is the probability of failure on a single trial (not rolling a four).
In this case, n = 10, k = 7, p = 1/6 (since there is a 1/6 chance of rolling a four on a fair die), and (1-p) = 5/6.
Plugging these values into the formula:
P(X = 7) = (10C7) * (1/6)^7 * (5/6)^(10-7)
Calculating the combinations:
(10C7) = 10! / (7! * (10-7)!) = 10! / (7! * 3!) = (10 * 9 * 8) / (3 * 2 * 1) = 120
Substituting the values:
P(X = 7) = 120 * (1/6)^7 * (5/6)^(10-7)
Calculating the probability:
P(X = 7) = 120 * (1/6)^7 * (5/6)^3 ≈ 0.0595
Therefore, the probability that exactly seven fours will appear in 10 rolls of a fair die is approximately 0.0595 (rounded to 4 decimal places).
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Related Questions
Can anyone help? The project is to make a 3D figure out of household items, that’s easy, but what does the other part mean, how should I calculate it and solve it? Please help.
Answers
Answer + Step-by-step explanation:
Example: =================
3D figure = rectangular prism
………………………………………………………………………………
Formula : =================
Volume of Rectangular Prism: V = lwh.
Surface Area of Rectangular Prism: S = 2(lw + lh + wh)
Graph the line given the point (4, 3) and the slope m = − 1/3
Answers
The line passes through the point (4, 3)
The line has a slope of m=-1/3
The equation of the line can be written in the form
\(y=mx+c\)Since the slope is -1/3
Then the equation becomes
\(y=-\frac{1}{3}x+c\)Since the line passes through the point (4, 3)
Substitute x = 4, y= 3 into the equation
\(3=-\frac{1}{3}(4)+c\)Simplify the equation and solve for c
\(\begin{gathered} 9=-4+3c \\ 9+4=3c \\ 13=3c \\ c=\frac{13}{3} \end{gathered}\)Hence, the equation becomes
\(y=-\frac{1}{3}x+\frac{13}{3}\)Using an online graphing calculator.
The graph of the line is shown
Which Input has more than 1 output?
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what is the exprssion -2 (3x+5) +1+4x written in simplest form
Answers
two linear functions are combined with addition, and then the same two linear functions are combined by multiplication.which functions could be the result of the combinations? select two options.16x – 1217x – 1272x2 – 96x72x2
Answers
The two options that could result from combining two linear functions with addition are "16x – 12" and "17x – 12". The r to your question is:
To combine two linear functions with addition, you simply add the coefficients of the same variables. For example, if you have the functions 3x + 4 and 2x - 5, when you combine them with addition, you add the coefficients of x and the constant terms. So, 3x + 4 + 2x - 5 becomes (3 + 2)x + (4 - 5) = 5x - 1.
To combine two linear functions with multiplication, you multiply the coefficients of the same variables. For example, if you have the functions 3x + 4 and 2x - 5, when you combine them with multiplication, you multiply the coefficients of x and the constant terms. So, (3x + 4)(2x - 5) becomes
(3 * 2)x^2 + (3 * -5)x + (4 * 2x) + (4 * -5)
= 6x^2 - 15x + 8x - 20
= 6x^2 - 7x - 20.
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find the surface area of 4, 6.5, 3.2
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The surface area of the rectangular prism is S = 174.4 cm²
Given data ,
The area of the triangular prism is A = ph + ( 1/2 ) bh
The side lengths of the prism are
a = 8 cm
b = 5.5 cm
c = 3.2 cm
Now , the surface area of the rectangular prism is
S = 2 ( ab + bc + ac )
On simplifying the equation , we get
S = 2 ( 8 ) ( 5.5 ) + 2 ( 5.5 ) ( 3.2 ) + 2 ( 8 ) ( 3.2 )
S = 88 + 35.2 + 51.2
S = 174.4 cm²
Hence , the surface area is 174.4 cm²
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You have a new 10-day workout routine. You want to do 10 sets of 10 sit-ups each day.
Which expression shows the total number of sit-ups you do in 10 days?
1.)10^3
2.)10+10+10
3.)10^2
4.)3x10
Answers
Answer:
4.
Step-by-step explanation:
Im sorry if im wrong but i think 4
If the original quantity is 10 and the new quantity is 12 , what is the percent increase?
Answers
Answer:
20 percent.
Step-by-step explanation:
This is because 2 is twenty percent of 10.
A 15 year variable rate mortgage offers a first year teaser rate of 3.11%. After that the rate starts at 5% adjusted based on actual interest rates. If the mortgage is $325,000 compute the monthly payment during the second year, if the interest rate increases to 5%
Answers
The monthly payment during the second year of the mortgage, when the interest rate increases to 5%, is approximately $1,654.58. To compute the monthly payment during the second year of a variable rate mortgage, we need to consider the loan amount, the interest rate, and the loan term.
Loan amount: $325,000
First-year teaser rate: 3.11%
Rate for the second year: 5%
To calculate the monthly payment during the second year, we can use the formula for calculating the fixed monthly payment on a mortgage:
Monthly payment = (Loan amount * Monthly interest rate) / (1 - (1 + Monthly interest rate)^(-n))
Where:
Loan amount = $325,000
Monthly interest rate = Annual interest rate / 12
Annual interest rate for the second year = 5%
n = Total number of monthly payments (12 payments in a year)
First, we calculate the monthly interest rate for the second year:
Monthly interest rate = 5% / 12 = 0.4167%
Next, we substitute the values into the formula:
Monthly payment = ($325,000 * 0.4167%) / (1 - (1 + 0.4167%)^(-12))
Using a calculator, we can evaluate this expression:
Monthly payment ≈ ($325,000 * 0.4167%) / (1 - (1 + 0.4167%)^(-12)) ≈ $1,654.58
Therefore, the monthly payment during the second year of the mortgage, when the interest rate increases to 5%, is approximately $1,654.58.
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what digit is in the
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We must solve for x using the addition principle, the equation is as follows
\(\begin{gathered} x-3=-12 \\ x=-12+3 \\ x=-9 \end{gathered}\)In conclusion, the answer is x = -9
7. Write the inverse of y = 1x + 10 given x < -10
Answers
Answer:
• (a) x-10
,• (b) (1-10x)/x
Explanation:
Part A
Given the function:
\(y=1x+10\)First, swap x and y:
\(x=1y+10\)Next, make y the subject of the equation:
\(y=x-10\)Therefore:
\(f^{-1}(x)=x-10\)Part B
Given the function:
\(y=\frac{1}{x+10}\)First, swap x and y:
\(x=\frac{1}{y+10}\)Next, make y the subject of the equation:
\(\begin{gathered} x=\frac{1}{y+10} \\ x(y+10)=1 \\ y+10=\frac{1}{x} \\ y=\frac{1}{x}-10 \\ y=\frac{1-10x}{x} \end{gathered}\)Therefore:
\(f^{-1}(x)=\frac{1-10x}{x}\)Kim has a rope that is 1/2 meter long.she wants to cut it into 5 pieces.each piece must be the same size.how long will each piece be?
Answers
Each piece must be the same size, each piece will be 1/10 meter long.
To determine the length of each piece, we divide the total length of the rope (which is 1/2 meter) by the number of pieces (which is 5).
In this case, we are dividing the length of the rope into 5 equal parts. By dividing 1/2 meter by 5, we are essentially distributing the length evenly among the 5 pieces.
Dividing 1/2 meter by 5 gives us 1/10 meter. This means that each piece will have a length of 1/10 meter.
By ensuring that each piece is the same size, Kim can divide her 1/2 meter rope into 5 equal pieces, with each piece measuring 1/10 meter in length.
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Graph the equation
y-3=-3/2(x+4)
Answers
Answer: x = (-2,0) y = (0,-3) slope is -3/2
Step-by-step explanation: graph the line by using the slope and y intercept
The graph for the points (0, -3) and (2, -6) is plotted on the graph below.
The given equation is y-3= -3/2(x+4).
What is the graph?Graph is a mathematical representation of a network and it describes the relationship between lines and points. A graph consists of some points and lines between them. The length of the lines and position of the points do not matter.
Graph the line using the slope and y-intercept, or two points.
Slope: -3/2
y-intercept: (0, -3)
Plot the points (0, -3) and (2, -6) on the graph
To find the x-intercept, substitute in 0 for y and solve for x. To find the y-intercept, substitute in 0 for x and solve for y.
x-intercept(s): (−2,0)
y-intercept(s): (0,−3)
Therefore, the graph for the points (0, -3) and (2, -6) is plotted on the graph below.
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Need help with this what to do with minus symbol between parenthesis
Answers
Given the expression below
\((6x^5-2x^3+x^2+5x)-(8x^5+2x^3-11x^2+9)\)Expanding the expression and simplifying them by multiplying the second expression by the negative(-) sign.
\(\begin{gathered} 6x^5-2x^3+x^2+5x-8x^5-2x^3+11x^2-9 \\ 6x^5-8x^5-2x^3-2x^3+x^2+11x^2+5x-9 \\ -2x^5-4x^3+12x^2+5x-9 \end{gathered}\)Hence, the answer is
\(-2x^5-4x^3+12x^2+5x-9\)Brief illustrations of multiplication of symbols
\(\begin{gathered} -\times-=+ \\ -\times+=- \\ +\times-=- \\ +\times+=+ \end{gathered}\)If you answer both of these i will give
Brainliest ( if thats how you spell it )
Answers
Answer:
first one:4/10
second one: 8/24
Step-by-step explanation:
i think this works but a hundred 100% sure though.
here you go hope its correct.
Find the arc length of AB if the
circumference of this circle is 187.
Answers
Answer:
π
Step-by-step explanation:
a circle contains 360° in total, so given it's circumference (lets say C),
the length of an arc with angle α is (α/360)*C
for our exanple, the length of arc AB, will be (20/360)*C
as C is given to be 18π cm, we can calculate:
Length(AB) = (20/360)*18π = π
shelly paid a total of $15 for bags of candy she ordered on-line. the cost of each bag was $0.75 and shipping was a flat rate of $3.00. how many bags of candy did shelly order?
Answers
Shelly ordered the 16 candy bags.
What is subtraction in math?The operation or process of finding the difference between two numbers or quantities, denoted by a minus sign (−).
We have the information from the question:
Shelly paid a total of $15 for bags of candy she ordered on-line.
The cost of each bag was $0.75
Shipping charge was a flat rate $3.00
We have to find the how many bags of candy did shelly order.
Now, According to the question:
We have to subtract shipping charge from total paid charges, we get:
Total paid - shipping charge
=> 15 - 3
= 12
Number of bags = 12/ 0.75
Number of bags = 16
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WILL GIVE BRANLEST EXPLAIN
Solve for x:
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Answer:
Angle between two tangents or two secants is the half of the difference of intercepted arcs.
#1
x = 1/2(250° - (360° - 250°)) = 1/2(250° - 110°) = 1/2(140°) = 70°#2
50° = 1/2(170° - x)100° = 170° - xx = 170° - 100°x = 70°Please help me figure these out!
Answers
Step-by-step explanation:
just u have to put the values of sin and cos and you will get the answer
hope u get help
What is the solution to the system of equations below?
Y=2/5x-3 and x=10
Answers
Answer:
Y=2/47
Step-by-step explanation:
Y=2/5(10)-3
Y=2/47
Is it possible to calculate the cube root of a negative number?
Answers
Answer:
Yes, the cube root of a negative number can be calculated.
Step-by-step explanation:
Explanation:
By calculating the cubed root of a negative, you will eventually have the square root of -1 which is unknown in the real number system. In the imaginary number system, this would resolve to i.
Cheers.
The area of a rectangle is the product of its length and width. A rectangular has an area of 260 square inches. The width of the poster is greater than 10 and is a prime number. what is the width of the poster?
Answers
Answer: 13
Step-by-step explanation:
13 is a prime number and 13x20=260
HELP PLEASEEE ASAP WILL GIVE. BRAINLIST
Answers
Answer:
width = 2x + 1
Step-by-step explanation:
A = lw
A = 10x² + 5x = 5x(2x + 1) = lw ⇒ w = 2x + 1
please help with this problem?!
Answers
Answer:
umm 33 i think
Step-by-step explanation:
How do I write an equation of a line that is perpendicular?
Answers
An equation of a line can be written by using the standard form of the equation of line y = mx + b,
What is the equation of a line?
The general equation of a straight line is y = mx + c, where m is the gradient, and y = c is the value where the line cuts the y-axis.
An equation of a line can be written in the form y = mx + b, where m is the slope of the line and b is the y-intercept.
To find the equation of a line that is perpendicular to another line, you will need to find the negative reciprocal of the slope of the original line.
For example, suppose you have a line with the equation y = 3x + 2.
The slope of this line is 3, so the slope of a line that is perpendicular to it would be the negative reciprocal of 3, which is -1/3.
The equation of the perpendicular line would be y = -1/3x + b, where b is the y-intercept.
To find the y-intercept of the perpendicular line, you can plug in the coordinates of a point on the original line into the equation of the perpendicular line.
For example, if you know that the original line passes through the point (4, 14), you can substitute these values into the equation y = -1/3x + b to find the value of b.
This gives you the equation -1/3x + b = 14, so b = 14 + 1/3x.
Substituting x = 4 gives you b = 14 + 1/3(4) = 14 + 4/3 = 18/3, so the equation of the perpendicular line is y = -1/3x + 18/3.
Hence, An equation of a line can be written by using the standard form of the equation of line y = mx + b,
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A recycling box has a square base with sides measuring 18 inches. The box is 16 inches tall. How much recycling can the inside of the recycling box hold?
Answers
V = 18 x 18 x 16
V = 5184 cubic inches or in^3
which of the following may be an explanation for the shift in aggregate demand from a to b?
Answers
The shift in aggregate demand from point A to B can be explained by factors such as increased consumer confidence, increased government spending, expansionary monetary policy, or an increase in net exports.
the possible explanations for the shift in aggregate demand from point A to B.
A shift in aggregate demand from point A to B can be caused by several factors. These may include:
Increase in consumer confidence: When consumers are more optimistic about the future, they are more likely to spend money, leading to an increase in aggregate demand.
Increase in government spending: If the government increases its spending on infrastructure, public services, or other areas, this can lead to an increase in aggregate demand.
Expansionary monetary policy: If the central bank lowers interest rates or increases the money supply, borrowing becomes more attractive and accessible, leading to increased spending and investment, and ultimately an increase in aggregate demand.
Increase in net exports: If a country exports more goods and services than it imports, this can lead to an increase in aggregate demand.
To summarize, the shift in aggregate demand from point A to B can be explained by factors such as increased consumer confidence, increased government spending, expansionary monetary policy, or an increase in net exports.
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Help will mark brainlist.
1=
2=
3=
4=
Answers
2=45
3=45
4=45
4x45=180
Simplify:
3x2 – 2x + 1 = [?]
x=4
![Simplify:3x2 2x + 1 = [?]x=4](https://i5t5.c14.e2-1.dev/h-images-qa/contents/attachments/P3mcsGyGu8LfRtyhI268uuCB6OCXTdyp.png)
Answers
Answer:
look at the picture i sent........
![Simplify:3x2 2x + 1 = [?]x=4](https://i5t5.c14.e2-1.dev/h-images-qa/answers/attachments/AFAmnVzigDH8NyJlq0wKiFCgyaBYqRmN.jpeg)
What is the triple of 6 answer?.
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Answer:
Not sure what you are asking, but 6 to the third power = 216 and 6 times 3 = 18. Hopefully one of those is the answer you are looking for.