A binomial probability experiment is conducted with the given parameters. Compute the probability of x successes in the n independent trials of the experiment.
n=8, p=0.45, x=5
P(5)= ______(round to four decimal places as needed.)
Answers
In a binomial probability experiment with parameters n = 8 and p = 0.45, we want to compute the probability of obtaining exactly 5 successes (x = 5) in the 8 independent trials.
The binomial probability formula is given by P(x) = C(n, x) * \(p^x\) * (1 - p)^(n - x), where C(n, x) represents the number of combinations of n items taken x at a time.
In this case, we have n = 8, p = 0.45, and x = 5. Plugging these values into the formula, we get:
P(5) = C(8, 5) * (0.45\()^5\) * (1 - 0.45)^(8 - 5)
To calculate the combination C(8, 5), we use the formula C(n, x) = n! / (x! * (n - x)!), where "!" denotes the factorial of a number.
C(8, 5) = 8! / (5! * (8 - 5)!) = 8! / (5! * 3!) = (8 * 7 * 6) / (3 * 2 * 1) = 56
Now, substituting the values into the formula, we have:
P(5) = 56 * (0.45\()^5\) * (1 - 0.45)^(8 - 5)
Calculating this expression gives us:
P(5) ≈ 0.2601
Therefore, the probability of obtaining exactly 5 successes in the 8 independent trials is approximately 0.2601 (rounded to four decimal places).
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Related Questions
A student sets up the following equation to convert a measurement. (The ? stands for a number the student is going to calculate.) Fill in the missing part of this equation. (−7.0×104 s2g⋅m2)⋅ΠΠ=? s2kg⋅m2
Answers
The missing part of the equation is \(-7.0\times10^4 s^2kg⋅m^2 / 1000000.\)
What is the value of the missing part in the equation?To fill in the missing part of the equation, let's analyze the given information and the desired conversion. The equation is:
\((-7.0\times 10^4 s^2g⋅m^2)\cdot \pi = ? s^2kg\cdot m^2\)
In this equation, we have a quantity expressed in\(s^2g\cdot m^2\) units on the left-hand side. To convert it to \(s^2kg\cdot m^2\) units, we need to multiply it by a conversion factor.
To perform the conversion, we can use the fact that 1 kg is equal to 1000 g. Therefore, the conversion factor we need is:
1 kg / 1000 g
To ensure that the units cancel out correctly, we need to square this conversion factor because we have \(s^2g\cdot m^2\) on the left-hand side. So the missing part of the equation is:
\((-7.0\times 10^4 s^2g\cdot m^2)\cdot \pi = (-7.0\times 10^4 s^2g\cdot m^2)\cdot (1 kg / 1000 g)^2\)
Simplifying this expression, we get:
\((-7.0\times10^4 s^2g\cdot m^2)\cdot \pi = -7.0 \times10^4 s^2kg\cdot m^2 / 1000000\)
Therefore, the missing part of the equation is \(-7.0 \times 10^4 s^2kg\cdot m^2 / 1000000.\)
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the product of 28 and g?
Answers
Answer:
28g
Step-by-step explanation:
If we were constructing a box with length 1 width w, and height = 8 cm, where the length of the box is twice the width, which could we use as a volume function? OV = 1622 OV – 8w? DV - 1612 DV = 162
Answers
The volume of the box can be calculated using the equation V = 16w.
The volume of the box can be calculated using the equation V = l x w x h.
In this case, the length is 1, the width is w, and the height is 8 cm. Thus, the volume of the box is V = 1 x w x 8 = 8w. As the length of the box is twice the width, the length can be written as 2w, and the volume becomes V = 2w x w x 8 = 16w. So, the volume of the box is 16w.
To calculate the volume of the box, the equation V = l x w x h is used, where l is the length, w is the width, and h is the height of the box. The given values of the length, width, and height of the box are 1, w, and 8 cm respectively.
So, the volume of the box is V = 1 x w x 8 = 8w. A
s the length of the box is twice the width, the length can be written as 2w. So, the volume of the box becomes V = 2w x w x 8 = 16w.
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Find the equation of a line which passes through (2,3)and is perpendicular to y-3x+1=0.give your answer in the form y=mx+c
Answers
Answer:
3x - 1 = 0
Step-by-step explanation:
3x + 1 = 0
The perpendicular of a line has a slope that is the negative reciprocal of that lines slope.
So the answer is 3x - 1 = 0
_____ suggests that the threat of a loss has a greater impact on a decision than the possibility of an equivalent gain.
a. The Carnegie model
b. Prospect theory
c. The bounded rationality perspective
d. McGregor's Theory X
Answers
The term that suggests that the threat of loss has a greater impact on a decision than the possibility of an equivalent gain is prospect theory.
Prospect theory is a theory that describes how individuals make decisions under uncertainty. The theory suggests that people think about gains and losses differently and that the value they assign to a particular change in their situation depends on their current situation. The theory is based on the observation that people often violate the principle of expected utility. They make decisions that do not maximize their expected utility. The theory suggests that people evaluate outcomes based on changes from a reference point, rather than in absolute terms. This means that people are more sensitive to changes in their situation than to the situation itself.
For example, a loss of $100 is more painful than the pleasure of gaining $100, and the pleasure of gaining $100 is less than the pain of losing $100.
In summary, Prospect theory suggests that the threat of a loss has a greater impact on a decision than the possibility of an equivalent gain.
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2. Araw surveyed people that were standing in a line to vote in an election. One of his questions was "How old are you?" The data set shows the results. {47, 61, 25, 19, 30, 33, 72, 65, 55, 29, 54, 49, 38, 81, 77, 33, 40} Create a stem-and-eaf plot to represent the data set. Include a key.
Answers
Solutiion
We are given
\(\mleft\{47,61,25,19,30,33,72,65,55,29,54,49,38,81,77,33,40\mright\}\)The stem and leaf plot will be
Key: Stem- Mutiplie by 10
Leaf - Multiplied by 1
Which is the better buy?
Frozen Peas
Cost (dollars)
Weight (ounces)
O Brand A
A B
2
16
3
28
O Brand B
O The unit cost is the same.
Answers
The better buy is given by the following brand:
Brand A.
How to obtain the better buy?The better buy is obtained applying the proportions in the context of the problem.
A proportion is applied as the cost per ounce is given dividing the total cost by the number of ounces.
Then the better buy is given by the option with the lowest cost per ounce.
The cost per ounce for each brand is given as follows:
Brand A: 16/2 = $8 per ounce.Brand B: 28/3 = $9.3 per ounce.$8 per ounce is a lesser cost than $9.3 per ounce, hence the better buy is given by Brand A.
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Find the area of the trapezoid.4 in4 in.5 inA=in 2
Answers
To determine the area of the trapezoid we need to use the following expression:
\(A=\frac{B+b}{2}\cdot h\)Applying the dimmensions given in the problem we can calculate the area as shown below:
\(A=\frac{5+4}{2}\cdot4=\frac{9}{2}\cdot4=\frac{36}{2}=18\text{ square inches}\)The area of the trapezoid is 18 square inches.
Each time the carousel runs, 11 children
can ride it. If 50 children want to ride
the carousel, what is the fewest number
of times that the carousel needs to
run?
Hellppppp quickkkk it’s due in a hour
Answers
Answer: 5 times
Step-by-step explanation: 11 goes into 50 four times. That means that the first four times the carousel runs, 11 kids will be on it. But since six ungrateful children were left out, the carousel will need to run one extra time so those brats can get a turn.
Jack bought a coin for $200, which he sold later for $175. Find the percent of change. Did Jack make a good investment?
Answers
When using the regression analysis tool in excel the input Y range are the values for _______ variables and the input X range are the ____________ variables dependent, independent independent, dependent
Answers
When using the regression analysis tool in Excel, the input Y range refers to the values for the dependent variables, while the input X range refers to the independent variables.
In other words, the Y variable is the outcome or response variable, which is affected or influenced by one or more X variables. The X variable is the predictor or explanatory variable, which helps to explain the variation in the Y variable. The regression analysis tool helps to establish a linear relationship between the dependent and independent variables by estimating the coefficients of the equation that best describes the relationship.
It is important to note that the regression analysis assumes that there is a causal relationship between the independent and dependent variables, which means that changes in the independent variable can cause changes in the dependent variable. Therefore, careful consideration should be given to selecting the appropriate independent variables to include in the analysis, to ensure that the results are accurate and meaningful.
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curve is defined by the parametric functions x(t)=e^3t and y(t)=e^4t et. what is d2y/dx2 in terms
Answers
The second derivative of y with respect to x, d²y/dx², is 0 for the curve defined by the parametric equations x(t) = \(e^{3t}\) and y(t) = \(e^{4t}\) × et.
To find d²y/dx², we need to differentiate the parametric equations x(t) and y(t) with respect to t and apply the chain rule.
Given x(t) = \(e^{3t}\) and y(t) = \(e^{4t}\) × et, we can express y as a function of x by eliminating t. Solving x = \(e^{3t}\) for t, we get t = ln(x)/3. Substituting this into the equation for y, we have y(x) = \(e^{(4ln(x)/3) }\) × \(e^{(ln(x)/3) }\) = \(x^{4/3}\) × \(x^{1/3}\) = x.
Now, differentiating y(x) with respect to x, we have dy/dx = 1.
To find the second derivative, we differentiate dy/dx = 1 with respect to x, yielding d²y/dx² = 0.
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Let \(f(x)=9-2^x\)
Calculate the area that approximates \(A(f,1\leq x\leq 3)\)
Answers
![Let [tex]f(x)=9-2^x[/tex]Calculate the area that approximates [tex]A(f,1\leq x\leq 3)[/tex]](https://i5t5.c14.e2-1.dev/h-images-qa/answers/attachments/KFIg3WdTy6uOsPiZgSe5taRU67HiBtiM.png)
I need answer Immediately pls!!!!!!
Answers
Answer:
14 players.
Step-by-step explanation:
The bus is a fixed cost, so the unknown “p” comes after the player meals, as that price isn’t fixed and is per player.
993.5 + 74.25p = 2033
74.25p = 1039.5
p = 14
PLS HELP WILL MARK BRAINIEST!!!!!!!!!!!!!!!!!!!!!!!!!
Answers
Answer:
\(\textsf{1)} \quad 10000(1.06)^t\)
2) €17,908.48
3) 0.5%
4) 120
\(\textsf{5)} \quad 10000(1.005)^{120}\)
6) €18,193.97
7) More money.
Step-by-step explanation:
\(\boxed{\begin{minipage}{7 cm}\underline{Annual Compound Interest Formula}\\\\$ A=P\left(1+r\right)^{t}$\\\\where:\\\\ \phantom{ww}$\bullet$ $A =$ final amount \\ \phantom{ww}$\bullet$ $P =$ principal amount \\ \phantom{ww}$\bullet$ $r =$ interest rate (in decimal form) \\ \phantom{ww}$\bullet$ $t =$ time (in years) \\ \end{minipage}}\)
Question 1Given:
P = €10,000r = 6% = 0.06Substitute the given values into the compound interest formula to write an expression that describes the given scenario over t years:
\(\implies A=10000(1+0.06)^t\)
\(\implies A=10000(1.06)^t\)
Question 2To calculate how much money will be in the fund after 10 years, substitute t = 10 into the equation from question 1:
\(\implies A=10000(1.06)^{10}\)
\(\implies A=10000(1.79084769...)\)
\(\implies A=17908.4769...\)
Therefore, there will be €17,908.48 in the emergency fund after 10 years.
Question 3If the annual rate is 6%, the monthly interest rate is the annual rate divided by 12 (since there are 12 months in a year):
\(\implies \dfrac{6\%}{12}=0.5\%\)
Question 4Given that are 10 years in the scenario, the exponent will be the number of months in 10 years:
\(\implies 10 \times 12 = 120\)
Question 50.5% = 0.005
Therefore, the complete expression that describes the scenario, given an annual interest rate of 6% that compounds monthly over 10 years is:
\(\implies 10000(1 + 0.005)^{120}\)
\(\implies 10000(1.005)^{120}\)
Question 6To calculate how much money will be in the emergency fund after 10 years if the interest compounds monthly, calculate the expression from question 5:
\(\implies 10000(1.005)^{120}\)
\(\implies 10000(1.81939673...)\)
\(\implies 18193.9673...\)
Therefore, there will be €18,193.97 in the emergency fund after 10 years.
Question 7Amount in fund when compounded annually = €17,908.48
Amount in fund when compounded monthly = €18,193.97
Therefore, there is more money in the emergency fund when it is compounded monthly as the compounding frequency is greater (interest is earned on both the principal and the interest, so the more frequent the compounding periods are, the more interest is earned).
The general rule about compounding in exponential functions is the higher the number of compounding periods, the greater the amount of compound interest.
In terms of compounding interest in investment:
The annual interest rate should be divided by the compounding frequency, and the exponent should be multiplied by the compounding frequency.Need math help please
Answers
Answer:
D
Step-by-step explanation:
the question is in the attachment...
Answers
Answer:
Rest of the part will be = x - 5x/10- x/10
solution will be 4x/10 i.e 4/10 part of the garden
Step-by-step explanation:
Let the sum total of parts of garden be x
If it is divided into 10 equal parts then
one part will be equal to x/10
Given carrots are planted on 5/10 of the garden
parts on which garden is planted = 5/10 * total part of garden = 5x/10
Given peas are planted on 1/10 of the garden
parts on which peas are is planted = 1/10 * total part of garden = x/10
On rest of the part corn is planted.
Rest of the part will be = total parts of garden - part on which carrots are planted - part on which carrots are planted
Rest of the part will be = x - 5x/10- x/10 = (10x-5x-x)/10 = 4x/10
Model will be
Rest of the part will be = x - 5x/10- x/10
solution will be 4x/10 i.e 4/10 part of the garden
Work out the size of angle : x
Answers
Answer:
129
Step-by-step explanation:
180-51= 129
129 is corresponding with x
and corresponding angles are equal
so 129 is the answer
Answer:129
Step-by-step explanation:
Because of the rule of alternate exterior angles the angle to the right of angle X would also be 51 and since we know a straight line is 180 degrees we will subtract the angle we know from 180 and you get 129 as your answer.
Need Help ASAP! Please
Answers
Explanation:A straight line is 180 degrees.
(Using the diagonal line): 180 - 140 = 40
(Using horizontal line): 40 + 112 = 152
180 - 152 = 28
Which of the following shows the graph of y= 2e*?
-5-4
?
7
4
3+
2+
1+
-11
-2
?TY
s
-
234
5 X
Answers
A diagram that shows the graph of \(y= 2e^{x}\) include the following: A. graph A.
What is an exponential function?In Mathematics and Geometry, an exponential function can be modeled by using this mathematical equation:
\(f(x) = a(b)^x\)
Where:
a represents the initial value or y-intercept.x represents x-variable.b represents the rate of change, common ratio, decay rate, or growth rate.Next, we would determine the y-intercept when x = 0 as follows;
\(y= 2e^{x}\\\\y= 2e^{0}\)
y = 2
By critically observing each of the graphs, we can reasonably infer and logically deduce that the only graph that has a y-intercept of (0, 2) is graph A.
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Missing information:
The question is incomplete and the complete question is shown in the attached picture.
the green triangle is set inside a rectangle. is the green triangle a right angle? explain.
Answers
Answer:
yes it has a right angle
Step-by-step explanation:
you can rent time on computers at the local copy center for a $10 setup charge and an additional $2 for every 5 minutes. how much time can you rent for $25?
Answers
You can rent time on computers at the local copy center for 35 minutes with $25.
To find out how much time you can rent for $25 at the local copy center, follow these steps:
1. Subtract the $10 setup charge from the total amount you have: $25 - $10 = $15.
2. Now you have $15 left for renting time on the computers. Since it costs $2 for every 5 minutes, you need to find out how many 5-minute increments can be covered by $15.
3. Divide the remaining amount by the cost per 5-minute increment: $15 / $2 = 7.5. Since you can't have half an increment, round down to 7.
4. Multiply the number of 5-minute increments by the time per increment: 7 * 5 = 35 minutes.
So, you can rent time on computers at the local copy center for 35 minutes with $25.
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can someone help please
Answers
When Tracey pours all the water from the smaller 5-inch cube container into the larger 7-inch cube container, the water will be approximately 7 inches deep in the larger container.
To find out how deep the water will be in the larger container, we need to consider the volume of water transferred from the smaller container. Since both containers are cube-shaped, the volume of each container is equal to the length of one side cubed.
The volume of the smaller container is 5 inches * 5 inches * 5 inches = 125 cubic inches.
When Tracey pours all the water from the smaller container into the larger container, the water completely fills the larger container. The volume of the larger container is 7 inches * 7 inches * 7 inches = 343 cubic inches.
Since the water fills the larger container completely, the depth of the water in the larger container will be equal to the height of the larger container. Since all sides of the larger container have the same length, the height of the larger container is 7 inches.
Therefore, the water will be approximately 7 inches deep in the larger container.
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Although, Lara Croft was successful at stopping the enemy in
Tomb Raider, it was discovered that one artifact is still missing.
Luckily, the whereabouts are known: A cruise ship leaving
Seattle. By the time Ms. Croft arrives in Seattle, she has missed
the boat by 5 hours. What should she do?
FACTS:
- The cruise ship can go 528 mi in one day.
- A speedboat travels 100 miles in 2.5 hours.
- A helicopter goes 90 mph, but takes 3.5 hours to get to the harbor.
what should Ms. Croft do? Prepare a poster answering this question
with multiple representations of your thinking.
Answers
Answer:
The time it takes Ms. Croft to reach the cruise ship by speedboat = 6.11 hours
The time it takes Ms. Croft to reach the cruise ship by helicopter = 6.25 hours
since it takes less time for Ms. Croft to reach the cruise ship by taking the speedboat, her best choice to retrieve the artifact is to take the speedboat.
Step-by-step explanation:
The given parameters are;
The elapsed time by which Ms. Croft missed the boat = 5 hours
The speed of the cruise ship = 528 mi/day
The speed of the speedboat = 100 miles in 2.5 hours
The speed of the helicopter = 90 mph
The time it would take Ms. Croft to arrive at the harbor = 3.5 hours
Therefore, we have;
The cruise ship's speed = 528 miles per 24 hours = 528/24 mph = 22 mph
The location of the cruise after the first 5 hours = 5 × 22 = 110 miles
The speed of the speedboat = 100 miles per 2.5 hours = 100/2.5 = 40 mph
By traveling with a speed boat
The time at which Ms. Croft will intercept the cruise ship is given by the following relation;
40 mph × t = 22 mph × t + 110 miles
Which gives;
40 mph × t - 22 mph × t = 110 miles
18 mph = 110 miles
t = 110 miles/(18 mph) = 55/9 hours ≈ 6.11 hours
By taking the helicopter, we have;
Upon arrival at the harbor, after 3.5 hours, we find
90 mph × t = 22 mph × t + 22 mph × 3.5 hours + 110 miles
90 mph × t - 22 mph × t = 22 mph × 3.5 hours + 110 miles
68 mph × t = 77 miles + 110 miles = 187 miles
t = 187 miles/(68 mph) = 11/4 hours = 2.75 hours
The total time it takes Ms. Croft to reach the cruise ship by taking the helicopter = 3.5 + 2.75 = 6.25 hours
Therefore, since it takes less time for Ms. Croft to reach the cruise ship by taking the speedboat, her best choice to retrieve the artifact is to take the speedboat.
Simplify the rational expression. 3x^3+4x+5/x+3
Answers
Answer:
hey its 8
Step-by-step explanation:
Hold on, our servers are swamped. Wait for your answer to fully load.
The cost y
(in dollars) to rent a kayak is proportional to the number x
of hours that the kayak is rented. It costs $60 to rent the kayak for 4 hours. Write an equation that represents the cost to rent a kayak for x
hours.
Answers
y=kx
60=4k
K=60/4
K=15
For x hours,
y=15x
This graph shows the populations of Baltimore and Cleveland in the 20th century. `B\left(t\right)` is the population of Baltimore in year `t`. `C\left(t\right)`is the population of Cleveland in year `t`.
How could we use function notation to express that the populations of Baltimore and Cleveland were equal in 1910?
Answers
in a recent poll, 410 people were asked if they liked dogs, and 12% said they did. find the margin of error for this poll, at the 95% confidence level. give your answer to four decimal places if possible.
Answers
The margin error for the given poll having 95% confidence level with sample size of 410 is equal to 3.15%.
Sample size n = 410
Confidence level = 95%
Margin of error for this poll, use the formula,
ME = Z× (√(p₁(1-p₁) / n))
where Z is the z-score corresponding to the desired level of confidence.
p₁ is the sample proportion = 0.12
Using attached z-score table,
For a 95% confidence level, the corresponding z-score is 1.96.
Substituting the given values, we get,
ME = 1.96 × (√(0.12× (1-0.12) / 410))
Simplifying the expression inside the parentheses, we get,
⇒ME = 1.96 × 0.0160
⇒ME = 0.0315
Margin of error for this poll at the 95% confidence level is approximately 0.0315.
Therefore, 95% confidence level represents that the true proportion of people who like dogs is within 3.15% of the observed proportion of 12%.
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hello, can someone help please!!
Answers
Answer:f(3)=3
Step-by-step explanat
n=3
f(3)=f(2)*(-1/5)
f(2)=f(1)/(-1/5)=25*(-1/5)=-5
f(3)=-5*(-1/5)=1
who can help asap!?
Answers
Answer:
49/3 or 16⅓
Step-by-step explanation:
gallons ordered = 62
gallons used = 45⅔
so we have to subtract gallons used from gallons ordered to get our answer.
so,. 62 - 45⅔
=16⅓
hope it helps .