Approximate probability that at least 30 have used a discount broker: 0.918
In this scenario, we are given that 28% of all individual investors have used a discount broker. We want to approximate the probability of at least 30 out of 105 investors having used a discount broker. To solve this, we can use the normal approximation to the binomial distribution, which is valid when the sample size is large enough.
To apply the normal approximation, we need to calculate the mean (μ) and standard deviation (σ) of the binomial distribution. The mean can be found by multiplying the sample size (n) by the probability of success (p). In this case, μ = n * p = 105 * 0.28 = 29.4. The standard deviation is the square root of (n * p * q), where q is the probability of failure (1 - p). So, σ = sqrt(n * p * q) = sqrt(105 * 0.28 * 0.72) = 4.319.
Since we are interested in the probability of at least 30 individuals using a discount broker, we can use the normal distribution to approximate this probability. However, since the binomial distribution is discrete and the normal distribution is continuous, we need to apply a correction for continuity.
To calculate the probability, we convert the discrete distribution into a continuous one by considering the range from 29.5 (30 - 0.5, applying the continuity correction) to infinity. We then standardize this range using the z-score formula: z = (x - μ) / σ, where x is the value we are interested in (29.5) and μ and σ are the mean and standard deviation, respectively.
After standardizing, we consult the standard normal distribution table or use a calculator to find the cumulative probability associated with the z-score. In this case, the probability corresponds to the area under the curve to the right of the z-score. We find that the z-score is approximately 0.0348. Thus, the probability of having at least 30 individuals who have used a discount broker is approximately 1 - 0.0348 = 0.9652.
However, we need to subtract the probability of exactly 29 individuals using a discount broker from this result. To find this probability, we calculate the cumulative probability up to 29 using the z-score formula and subtract it from 0.9652. By doing this, we find that the probability of at least 30 individuals using a discount broker is approximately 0.918.
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A plane is flying at an altitude of 7000 feet. The angle of elevation to the plane from a truck travelling on a highway is about 68.5 degrees. How far apart are the plane and the truck?
Answer: About 2477.16 feet
Step-by-step explanation:
What is the greatest common factor of
12x3 + 6xy + 18x?
Answer:
6x
Step-by-step explanation:
12x^3, 6xy, and 18x can all be evenly divided by 6x
If you are given a 16 sided dice. What is the
probability that you get a number less than or
equal to 5?
Answer:
numbers less than 5 are 1,2,3,4 and equal to 5 is 5.
probability of less than 5 is 4/16
while equal to 5 is 1/16
or means additions; so its 4/16 +1/16=5/16
Sketch the graph for each function. Choose either A, B, C, or D.
HELP!!!!!! will give brainlist
Answer:
1. 112 cm
2 135 ft
3 53.67
Step-by-step explanation:
Answer:i
Step-by-step explanation:
A spinner has the numbers 11-20 on it. What is the probability that it will land on a multiple of 3?
Answer:
[tex]P(A) = \frac{3}{10}[/tex]
Step-by-step explanation:
Given
[tex]S = \{11,12,13,14,15,16,17,18,19,20\}[/tex]
Required
The probability of having a multiple of 3
Let the event of having a multiple of 3 be represented as: A
So:
[tex]A = \{12,15,18\}[/tex]
[tex]n(A) = 3[/tex]
So, the probability is:
[tex]P(A) = \frac{n(A)}{n(S)}[/tex]
Where
[tex]n(S) = 10[/tex] i.e. the sample size
So:
[tex]P(A) = \frac{n(A)}{n(S)}[/tex]
[tex]P(A) = \frac{3}{10}[/tex]
Need Help ASAP!!! I don’t get it
Answer:
Step-by-step explanation:
134-(-80)=134+80=214
HELP PLEASE VERY MUCH AND THANK YOU!!! look at screenshot
Answer:
They are both correcte
Step-by-step explanation:
Imagine a pizza with 6 slices
Half of 6 slices is 3 slices, or 3/6
If you simplify 3/6, you will get 1/2
So, both fractions are equal, but in different forms.
For better context see images below!
do this and thanks for help
Cereal box Design Project Connexus
30 points
The most cost-efficient container is the Rectangular Prism.
1. Rectangular Prism:
Volume: V = lwh = 10 x 5 x 15 = 750 cubic units
Cost: C = $0.01 x 750 = $7.50
Cost per unit volume: C/V = $7.50 / 750 = $0.01 per cubic unit
2. Rectangular Pyramid:
Volume: V = (1/3) x lwh = (1/3) x 10 x 5 x 15 = 250 cubic units
Cost: C = $0.02 x 250 = $5.00
Cost per unit volume: C/V = $5.00 / 250 = $0.02 per cubic unit
3. Cylinder:
Volume: V = πr²h = π x 5² x 15 ≈ 1178.1 cubic units
Cost: C = $0.015 x 1178.1 = $17.67
Cost per unit volume: C/V = $17.67 / 1178.1 ≈ $0.015 per cubic unit
Now, comparing the cost per unit volume for each container:
a. Rectangular Prism: $0.01 per cubic unit
b. Rectangular Pyramid: $0.02 per cubic unit
c. Cylinder: $0.015 per cubic unit
The container with the lowest cost per unit volume is the Rectangular Prism, with a cost of $0.01 per cubic unit.
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Which of the following identify all the names that apply to the given quadrilateral?
A Square
B Rectangle, Square
C Parallelogram, Rectangle, Square
D Parallelogram, Rhombus, Rectangle, Square
3
If f(x) = 3x^0 - 2x^-1 +4 then f(2)=
Answer:
try this link
Step-by-step explanation:
https://www3.nd.edu › WorkPDF
Web results
MATH 10550, EXAM 1 SOLUTIONS 1. If f(2) = 5, f(3) = 2, f(4) = 5, g(2 ...
The formula to convert Celcius to Fahrenheit is F=\frac{9}{5}C+32F=
5
9
C+32. If the temperature is -22°F−22°F what is the temperature in Celcius.
Answer:
-30C - -5.56C
Solve the following system of equations 7x - 3y = 11
Answer:
x= 11/7 + 3y/7
Step-by-step explanation:
Answer:
y=11 -7/3x
Step-by-step explanation:
subtract the 7
bring the seven to the other side
then divide by 3
Evaluate the work done between point 1 and point 2 for the conservative field F.
F = (y + z) i + x j + x k; P 1(0, 0, 0), P 2(9, 10, 8)
a) W = 0
b) W = 90
c)W = 18
d)W = 162
Option (d) W = 162 is the correct answer.
The question asks us to evaluate the work done between point 1 and point 2 for the conservative field F, where F = (y + z) i + x j + x k, P 1(0, 0, 0), P 2(9, 10, 8).
Step-by-step solution: Let us find the work done (W) between point 1 and point 2 using line integral of vector field F. The formula for line integral of vector field F along the curve C is as follows:$$W=\int_C{F\cdot dr}$$Since we know the points, let us find the curve C, which is the line joining the two points P1 and P2. Let P1 be the initial point and P2 be the final point. The equation of the line in vector form is given by:$$r=t{(x_2 - x_1 )\over ||\overrightarrow{P_1P_2}||} + P_1$$Where t varies from 0 to 1.Now, let's substitute the given values:$${\overrightarrow{P_1P_2}} = \left\langle {9 - 0,10 - 0,8 - 0} \right\rangle = \left\langle {9,10,8} \right\rangle $$Hence,$${\overrightarrow{P_1P_2}} = ||\overrightarrow{P_1P_2}|| = \sqrt {9^2 + 10^2 + 8^2} = \sqrt {245} $$Let the position vector be r(t) = xi + yj + zk. Then, the vector dr = dx i + dy j + dz k.Substitute r(t) and dr in the formula of line integral. Then,$$W = \int_C {F\cdot dr} = \int_0^1 {\left\langle {y + z,x,x} \right\rangle \cdot \left\langle {\frac{{dx}}{{dt}},\frac{{dy}}{{dt}},\frac{{dz}}{{dt}}} \right\rangle dt} $$On integrating with respect to t, we get,$$W = \int_0^1 {((y + z)\frac{{dx}}{{dt}} + x\frac{{dy}}{{dt}} + x\frac{{dz}}{{dt}})dt} $$We know that x = 0, y = 0, z = 0 at P1 and x = 9, y = 10, z = 8 at P2.Substituting these values in the above integral, we get,$$W = \int_0^1 {((y + z)\frac{{dx}}{{dt}} + x\frac{{dy}}{{dt}} + x\frac{{dz}}{{dt}})dt} $$On integrating, we get the value of W as:$$W = \int_0^1 {(8t + 10t)(\frac{{9}}{{\sqrt {245} }})dt} + \int_0^1 {(9t)(\frac{{10}}{{\sqrt {245} }})dt} + \int_0^1 {(9t)(\frac{8}{{\sqrt {245} }})dt} $$Simplifying further, we get,$$W = \frac{{18}}{{\sqrt {245} }}\int_0^1 {t(8 + 10)dt} + \frac{{72}}{{245}}\int_0^1 {t^2 dt} = \frac{{18}}{{\sqrt {245} }}\int_0^1 {18tdt} + \frac{{72}}{{245}}[\frac{{{t^3}}}{3}]_0^1 $$On evaluating the integral and simplifying, we get the final answer.$$W = \frac{{81}}{{\sqrt {245} }}$$
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def simulate(xk, yk, models): model = linearregression() (x, y) predictions = [model.predict(xk) for model in models]
The code simulates predictions using linear regression models on input data (xk, yk) and stores the predictions in the list "predictions".
The code snippet provided performs a simulation using linear regression models on input data (xk, yk) to generate predictions. Here is a step-by-step explanation:
Initialize a list called "predictions" to store the predicted values.
Iterate over the list of models. For each model:
Use the model to predict the values of y for the given input data xk. Append the predicted values to the "predictions" list.
By using the linear regression models, the code generates predictions based on the provided input data (xk). Each model in the "models" list is applied to the input data, and the predicted values for y are stored in the "predictions" list.
It's worth noting that the code assumes the existence of a linear regression model called "linear regression()" which is used to make predictions. The input data (xk, yk) is expected to be in a format compatible with the linear regression models for accurate prediction generation.
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Find the limit by substitution.
lim (e^x sin x)
x→5x
The overall limit of the expression (e^x sin x) as x approaches 5x is undefined.
To find the limit of (e^x sin x) as x approaches 5x, we can substitute 5x into the expression and evaluate the result.
lim (e^x sin x) (substituting 5x for x)
x→5x
= lim (e^(5x) sin (5x))
x→5x
Now, let's analyze the behavior of the function as x approaches 5x. As x approaches 5x, the value of x becomes much larger, approaching infinity. In this case, we can examine the limits of the individual components.
1. Limit of e^(5x) as x approaches infinity:
lim e^(5x) = ∞
x→∞
Exponential functions grow exponentially as their input approaches infinity, so the limit of e^(5x) as x approaches infinity is infinity (∞).
2. Limit of sin (5x) as x approaches infinity:
lim sin (5x) = DNE
x→∞
The sine function oscillates between -1 and 1 as its input increases indefinitely. Therefore, it does not approach a specific limit as x approaches infinity.
Combining these results, we have:
lim (e^(5x) sin (5x))
x→∞
Since the limit of e^(5x) is ∞ and the limit of sin (5x) does not exist, the overall limit of the expression (e^x sin x) as x approaches 5x is undefined.
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Explain, using complete sentences, how you would reconcile your check register with your monthly bank statement
How do you reconcile a bank statement?
Step 1: Adjust the bank statement balance. All your transactions for the month may not be on your bank statement. ...
Step 2: Adjust the check register balance. Your bank statement may include items that you didn't record in the check register. ...
Step 3: Compare the adjusted balances.
Can someone please help me with this??
The diameter of a circle is 19 meters. Complete the description for how you would find the circumference.
Answer:
The circumference of a circle is 2*pi*r or pi*diameter. The circumference is 19pi
Please help me! I need help solving this!
Answer:
18Step-by-step explanation:
if An = n+4
then A14 = 14+4 = 18
that's all .....have fun
HELP I WILL MARK BRAINLIEST
Answer:
the answer is A.
Step-by-step explanation:
Explain why this is wrong:
(Student's Solution): "Factor the polynomial"
y^2-6y+9=y^2-2(y)(3)+3^2 = (y-3)(y+3)
Note: Please help, I have been working on this for like 4 days im so tired.
Answer:
See below.
Step-by-step explanation:
y^2 - 6y + 9 can be changed correctly into y^2 - 2(y)(3) + 3^2.
Up to here, it's correct.
The right side above shows a polynomial that is the square of a binomial.
It factors into (y - 3)^2.
The correct factorization is (y - 3)^2.
The incorrect factorization of the student's solution is the product of a sum and difference.
The product of a sum and a difference is the correct factorization for a difference of squares.
For example, y^2 - 9 is the same as y^2 - 3^2 and is a difference of squares.
It factors into (y + 3)(y - 3), a product of a sum and a difference.
A heptagon has angles x, 105 degrees, 105 degrees, 160 degrees, 124 degrees, 97 degrees, 137 degrees. Find the missing angle measure in the heptagon. The sum of the interior angles of a heptagon is °. The measure of the missing angle is °.
Answer:
900 and 172 for edg 2020-2021
Step-by-step explanation:
Someone plsss helppp
Answer:
wtfrick- that's so confusing
Step-by-step explanation:
sorry I don't have an answer wish this was a comment
Solve the given initial-value problem for yo > 0. dy = Vy, y(x) = Yo dx y(x) = (1 xo 2. х 2 + Yo ) Find the largest interval I on which the solution is defined.
The given differential equation is given by `dy/dx = V*y` and the initial condition is `y(x) = Yo`.
The solution of the differential equation is given by `y(x) = Yo*e^(V*x)`.
Using this formula and the initial condition `y(x) = Yo`,
we get `Yo = Yo*e^(V*x)`.
This implies that `e^(V*x) = 1` or `V*x = 0`.
Thus `x = 0` is the only value of x on which `y(x) = Yo` for any value of `V`.
Now, we are given `y(x) = (1 + x^2)/(x^2 + Yo)` which is valid only if `Yo > 0` (as given). We need to find the largest interval on which the solution is defined. This means that we need to find the largest interval of x-values for which the given expression for `y(x)` makes sense. Since the denominator of the expression `y(x) = (1 + x^2)/(x^2 + Yo)` is `x^2 + Yo`, the expression is defined only if `x^2 + Yo > 0`. As `Yo > 0`, this inequality holds for all values of `x`. Thus, the solution is defined for all `x` in the real line. Therefore, the largest interval on which the solution is defined is `(-∞, ∞)`.
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Find the potential function f for the field F.
F = (y - z) i + (x + 2y - z) j - (x + y) k
f(x, y, z) = xy + y2 - x - y + C
f(x, y, z) = xy + y2 - xz - yz + C
f(x, y, z) = x(y + y2) - xz - yz + C
f(x, y, z) = x + y2 - xz - yz + C
Answer is f(x, y, z) = xy + y² - xz - yz + C
Given field, F is F = (y - z) i + (x + 2y - z) j - (x + y) k
To find potential function f,
we need to find the antiderivative of each component of F, with respect to its respective variable.
The antiderivative of the x-component is
∫ (y - z) dx= xy - xz + C1
The antiderivative of the y-component is
∫ (x + 2y - z) dy= xy + y² - yz + C2
The antiderivative of the z-component is:
∫ -(x + y) dz= -xz - yz + C3
Therefore, potential function f is
f(x, y, z) = xy + y² - xz - yz + C.
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What is the solution to the equation
Answer:
n=1
Step-by-step explanation:
4/5n-3/5=1/5n
4n/5-3/5=1/5n
4n/5-3/5=n/5
4n-3/5=n/5
4n-3=n
-3=n-4n
-3=-3n
1=n
n=1
Answer:
n=1
isolate the n's on one side and isolate the 3/5 to the other
4/5n-1/5n = 3/5
3/5n = 3/5
n=1
Ben wants to join a fitness club. The fitness club charges an initial membership fee of $49.50 and a monthly fee of 17.50. Part B ben's company will pay $300.00 each year toward his fitness club membership. Ben thinks he will have to pay $40.50 for his membership his first year. Is he correct?
Answer:
no he is not correct
Step-by-step explanation:
Let's say, LM30 has entered the Barcelona camp for the last time with a backpack of W Kg before moving to PSG. After a while he needs to carry his memorable products without breaking anything by using that backpack. Now your task is to apply a suitable algorithm to help LM30 to choose his best items. In mathematical form, LM30 has a set of N items each with weight wi and value vi, for i=1 to N, choose a subset of items so that the total value carried is maximized, and the total weight carried is less than or equal to the backpack capacity, W. In that purpose, write down the last 9 digits of your mobile number, sort it in descending order. Then pick the highest value as W (digitl), consider N=4 items as follows: (Wi, vi) = (3, digit2), (1, digit3), (2, digit4), (4, digit5). Example: if the last 9 digits of your mobile number is: 684049627, then the descending order will be: 98766440. That means, the backpack capacity is W =9, and the 4 items are: (4, 8), (1, 7), (3, 6), (2,6).
The subset of items that should be carried is (2, 4) and (4, 2).
The last 9 digits of my mobile number are 904202527.
So, when I sort them in descending order, I get 975422000.
Therefore, W (backpack capacity) = 9. N = 4 items as follows: (Wi, vi) = (3, 7), (1, 5), (2, 4), (4, 2).
To find the subset of items that LM30 should choose so that the total value carried is maximized, and the total weight carried is less than or equal to the backpack capacity, we can use the 0/1 Knapsack algorithm.
Here are the steps:
Step 1: Create a table with (N+1) rows and (W+1) columns.
Step 2: Initialize the first row and first column with 0.
Step 3: For each item (i), fill the values in the table as follows:- If the weight of the item (wi) is greater than the current backpack capacity (j), copy the value from the cell above (same column).- If the weight of the item (wi) is less than or equal to the current backpack capacity (j), find the maximum value between:- The value in the cell above (same column)- The value in the cell (i-1, j-wi) + vi
Step 4: The maximum value that can be carried in the backpack is the value in the last cell (N, W).
Step 5: To find the subset of items that should be carried, start from the last cell (N, W) and trace back through the table by checking which cells contributed to this value.
For our case, the table would look like this:
Table 1The last cell (N, W) is 11, so the maximum value that can be carried in the backpack is 11.
To find the subset of items that should be carried, we can start from the last cell (N, W) and trace back through the table by checking which cells contributed to this value.
We can see that the cells (2, 6) and (4, 2) contributed to this value.
Therefore, the subset of items that should be carried is: (2, 4) and (4, 2).
Thus, LM30 should choose the items with weight 2 and 4, and values 4 and 2, respectively, to carry in his backpack so that the total value carried is maximized, and the total weight carried is less than or equal to the backpack capacity of 9.
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