The value of a stock in 1940 is $1.25. Its value grows by 7% each year after 1940.
Write an equation representing the value of the stock V(t), in dollars, t years after 1940.
Answers
toStep-by-step explanation:
1.25 each year plus 7% for each year
V(t) = t(m) + (c)
m is the gradient
c is the y-intercept
first m
m is what it changes by each year
it is 7% as it changes by 7% each year
we need 7% as a decimal though so
what is 7% as a decimal
write in comments if you don't know tell me
then i will do c
The representation of the value of stock in dollars after 1940 is given as
V(t) = $1.25(1 + 0.07)^t.
How to write the expression for a growing exponential?The growing exponential can be written generally as f(x) = N(1 + r)ˣ, where N is the initial value and r is the rate of growth.
To find the expression different values of x and f(x) should be known.
Given that,
The value of the stock in 1940 is $1.25.
And, its rate of growth per year is 7%.
The general expression for the growing exponential can be written as,
f(x) = N(1 + r)ˣ
The given data shows N = 1.25 and r = 7/100 = 0.07.
Thus, the required expression can be written as,
V(t) = 1.25(1 + 0.07)^t
Hence, the required expression for representing the value of the stock V(t), in dollars, t years after 1940 is V(t) = $1.25(1 + 0.07)^t.
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Related Questions
Evaluate 32 + (5 − 2) ⋅ 4 − 6 over 3
Answers
Answer:
12.66666 infinity or 38/3
Step-by-step explanation:
Parentheses first so 5-2 is 3... then multiply so then 12... 12+32-6 is 38. 38 over 3 is 12.6666 infinity or 38/3, cannot be simplified...
our environment is very sensitive to the amount of ozone in the upper atmosphere. the level of ozone normally found is 4.7 parts/million (ppm). a researcher believes that the current ozone level is not at a normal level. the mean of 21 samples is 5.1 ppm with a standard deviation of 1.1 . assume the population is normally distributed. a level of significance of 0.01 will be used. find the value of the test statistic. round your answer to two decimal places.
Answers
A researcher believes that the current ozone level is not at a normal level. the mean of 21 samples is 5.1 ppm with a standard deviation of 1.1 . The value of the test statistic is 1.72 (rounded to two decimal places).
To answer this question, we need to conduct a one-sample t-test.
Null hypothesis: The population mean of ozone level is 4.7 ppm.
Alternative hypothesis: The population mean of ozone level is not 4.7 ppm.
The level of significance is 0.01, which means that we will reject the null hypothesis if the p-value is less than 0.01.
The formula for the t-test statistic is:
t = (sample mean - hypothesized population mean) / (standard deviation / square root of sample size)
Plugging in the values:
t = (5.1 - 4.7) / (1.1 / sqrt(21))
t = 1.72
Using a t-distribution table with 20 degrees of freedom (sample size - 1), the two-tailed p-value for t = 1.72 is approximately 0.099.
Since the p-value is greater than the level of significance (0.099 > 0.01), we fail to reject the null hypothesis. Therefore, we do not have enough evidence to conclude that the current ozone level is significantly different from the normal level of 4.7 ppm.
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Write the equation of a line that passes through (4, 6) and is parallel to y = 4x + 4.
Answers
Answer:
y = 4x - 10
Step-by-step explanation:
6 = 4 (4) + b
-10 = b
solve the given initial-value problem. dy/dt 2(t+1)y2 = 0, y(0) = − 1/15 y(t) = 1/t^2 + 2t + 15Give the largest interval i on which the solution is defined. (enter your answer using interval notation.)
Answers
The largest interval on which the solution is defined is (-∞, -1) ∪ (-1, ∞). The interval notation for the largest interval is (-∞, -1) U (-1, ∞).
What is the initial-value problem?An initial-value problem is a type of boundary-value problem in mathematics, particularly in the field of differential equations.
The given initial-value problem is a separable differential equation, which can be written as:
dy/dt = -2(t + 1)y²
Integrating both sides, we get:
(1/y) = t² + 2t + C
where C is the constant of integration.
Since we have an initial condition, we can use it to find the value of C:
y(0) = -1/15
C = -1/15
Solving for C, we get:
C = -1/15
So, the solution to the differential equation is:
(1/y) = t² + 2t -1/15
y = 1 / (t² + 2t -1/15)
The solution is defined for all t ≠ -1, since y = 0 is not defined. So, the largest interval on which the solution is defined is (-∞, -1) ∪ (-1, ∞). The interval notation for the largest interval is (-∞, -1) U (-1, ∞).
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Solve the equation.
pls help
Answers
Answer:
y=-3
Hope this helps!
a water balloon was thrown from the window. The height of the water balloon over time can be modeled by the function y=-16square2+160x+50
Answers
The maximum height of the water balloon : 450 m
Further explanationQuadratic function is a function that has the term x²
The quadratic function forms a parabolic curve
The general formula is
f (x) = ax² + bx + c
where a, b, and c are real numbers and a ≠ 0.
The parabolic curve can be opened up or down determined from the value of a. If a is positive, the parabolic curve opens up and has a minimum value. If a is negative, the parabolic curve opens down and has a maximum value
So the maximum is if a <0 and the minimum if a> 0.
The formula for finding the coordinates of the maximum and minimum points of the quadratic function is the same.
The maximum / minimum point of the quadratic function is
\(\rm -\dfrac{b}{2a},-\dfrac{D}{4a}\)
Where
D = b²-4ac
The function h (t) = -16x²+160x+50
so the value of a <0, then it has a maximum value
Because we are looking for maximum height, then we find the value of the y coordinate, with the formula
\(\rm -\dfrac{D}{4a}\)
Questions we might add :
What was the maximum height of the water balloon after it was thrown?
We can also use the first derivative of the above function to find the maximum value
\(\tt h'=0=-32x+160\\\\-32x=-160\\\\x=5\)
input to function :
\(\tt h=-16x^2+160x+50\\\\h=-16(5^2)+160(5)+50\\\\h=-400+800+50=\boxed{\bold{450~m}}\)
he gypsy moth is a serious threat to oak and aspen trees. A state agriculture department places traps throughout the state to detect the moths. When traps are checked periodically, the mean number of moths trapped is only 0.5, but some traps have several moths. The distribution of moth counts is discrete and strongly skewed, with standard deviation 0.7. (a) What are the mean and standard deviation of the average number of moths ž in 60 traps? (b) Use the central limit theorem to find the probability that the average number of moths in 60 traps is greater than 0.4.
Answers
The probability that the average number of moths in 60 traps is greater than 0.4 is approximately 0.9738 or 97.38%.
(a) To find the mean and standard deviation of the average number of moths in 60 traps, we can use the properties of the normal distribution and the central limit theorem.
The mean of the average number of moths in 60 traps is equal to the mean of the individual moth counts, which is 0.5.
The standard deviation of the average number of moths in 60 traps is equal to the standard deviation of the individual moth counts, divided by the square root of the sample size.
standard deviation = 0.7 / sqrt(60) = 0.0905
the mean and standard deviation of the average number of moths in 60 traps are 0.5 and 0.0905, respectively.
(b) To use the central limit theorem to find the probability that the average number of moths in 60 traps is greater than 0.4, we need to standardize the distribution of sample means using the Z-score formula:
Z = (sample mean - population mean) / (standard deviation / sqrt(sample size))
Substituting the given values, we have:
Z = (0.4 - 0.5) / (0.7 / sqrt(60)) = -1.94
Using a standard normal table or a calculator with a normal distribution function, we can find that the probability of getting a Z-score greater than -1.94 is approximately 0.9738.
The probability that the average number of moths in 60 traps is greater than 0.4 is approximately 0.9738 or 97.38%.
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Evaluate 5y+x2÷2 when x=4 and y=−3. When x=4 and y=−3, 5y+x2÷2=
Answers
Reasoning true or false: if an augmented square matrix in row-echelon form has a row of zeros as its last row, then the corresponding system of equations has no solution. explain your reasoning.
Answers
False, if an augmented square matrix in row-echelon form has a row of zeros as its last row, then the corresponding system of equations has no solution.
A square matrix with a row of zeroes means that one variable can be written as a linear combination of the other variables.What does the term "echelon form" mean?
If a matrix in linear algebra has the shape that comes from a Gaussian elimination, it is said to be in echelon form. When a matrix is in row echelon form, Gaussian elimination has been applied to the rows, and when it is in column echelon form, Gaussian elimination has been applied to the columns.What purpose does echelon matrix serve?
By reducing a complex matrix to a simple matrix, the Echelon Form of a matrix can be utilized to solve a linear equation. If a matrix meets certain criteria, which we'll go over in this post, it is said to be in an echelon form.Learn more about echelon form
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What is the difference between a checking and savings account quizlet?
Answers
A checking account is used for daily basis transaction and a debt and is usually associated with it.Saving accounts is just used for saving money.It has a time limit then you can withdraw your money.It is not on daily basis.
What is check account quizlet?A bank account that allow the user to withdraw the money ,pay bill,transfer money to other person or make a purchase anything by writing checks.Check accounts typically don't earn interest.By checking accounts we can easily deposit and withdraw money for daily transaction.
What is saving account quizlet?Saving accounts are intended for storing your money which you don't plan to use daily.saving accounts earns interest at your money.saving account is designed for the accumulation of money in a safe place for future use.saving accounts offer easy access to your money in any emergency.so keeping your money in a saving account means that your money is safe for your future use.
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given a set of data and a corresponding regression line, describe all values of x that provide meaningful predictions for y. a. prediction value are meaningful for all x-values that are realistic in the context of the original data setb. prediction value are meaningful only for x-values that are not included in the original data setc. prediction value are meaningful only for x-values in (or close to) the range of the original data
Answers
Once the regression line has been constructed, it can be used to make predictions about the value of y for a given value of x. However, these predictions are only meaningful if the value of x is in or close to the range of the original data. This is because the regression line is constructed based on the data points, and therefore it only accurately models the relationship between x and y within the range of the data.
For example, if the original data points have x-values between 0 and 100, then the regression line will provide meaningful predictions for y only for x-values between 0 and 100, or close to this range. Predictions for x-values outside of this range may not be accurate, because the regression line may not accurately represent the relationship between x and y outside of the range of the data.
Therefore, in order for the prediction value to be meaningful, the value of x must be in or close to the range of the original data.
Convert the following double integral to polar coordinates and evaluate. √4y-y² 1 55 dx dy √x² + y²
Answers
The given double integral ∫∫√(4y-y²) dA over the region bounded by 1 ≤ x ≤ 5 and 5 ≤ y ≤ 9 can be converted to polar coordinates. For θ, since the region is bounded by 5 ≤ y ≤ 9, we have arcsin(5/r) ≤ θ ≤ arcsin(9/r).
To convert the double integral to polar coordinates, we substitute x = r cos(θ) and y = r sin(θ), where r represents the radius and θ represents the angle.
The limits of integration in the x-y plane, 1 ≤ x ≤ 5 and 5 ≤ y ≤ 9, correspond to the region in polar coordinates where 1 ≤ r cos(θ) ≤ 5 and 5 ≤ r sin(θ) ≤ 9. We can determine the limits for r and θ accordingly.
For r, we find the limits by considering the values of r that satisfy the inequalities. From the first inequality, 1 ≤ r cos(θ), we obtain r ≥ 1/cos(θ). From the second inequality, 5 ≤ r sin(θ), we have r ≥ 5/sin(θ). Therefore, the lower limit for r is max(1/cos(θ), 5/sin(θ)), and the upper limit is 5.
For θ, since the region is bounded by 5 ≤ y ≤ 9, we have arcsin(5/r) ≤ θ ≤ arcsin(9/r).
By substituting these limits and the conversion factor r into the original integral and evaluating it, we can find the exact value of the double integral in polar coordinates.
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You have been collecting data on a nonlinear amplifier. Ideally, the output voltage [mV] should equal the input voltage [mV] squared. Thus an input of 5 mV should yield an output of 25 mV. You have measured the output at each integer value from 1 mV to N mV and recorded the outputs (in mV) in the vector SqOut. Note that the INDEX of each output value equals the input value in mV.
SqOut contains [0.9985 4.052 8.973 15.81 25.15]
Create a vector OutOfSpec that contains a list of all inputs that generated an output differing from the ideal value by more than 1%. Note that the difference can be above or below the ideal value.
(Matlab)
Answers
To create the vector OutOfSpec, we need to compare the values in SqOut with the ideal output values, which can be calculated using the formula (input voltage)^2. We can then use the following steps in Matlab:
1. Create a vector of input voltages from 1 mV to N mV:
inputVoltage = 1:N;
2. Calculate the ideal output values using the formula (input voltage)^2:
idealOutput = inputVoltage.^2;
3. Calculate the percentage difference between the actual and ideal output values:
percentDiff = abs(SqOut - idealOutput) ./ idealOutput * 100;
4. Find the indices of the values in percentDiff that exceed 1%:
outOfSpecIdx = find(percentDiff > 1);
5. Use the outOfSpecIdx vector to extract the input voltages that generated out-of-spec output values:
OutOfSpec = inputVoltage(outOfSpecIdx);
The resulting vector OutOfSpec will contain a list of all inputs that generated an output differing from the ideal value by more than 1%.
To create a vector OutOfSpec in Matlab that contains a list of all inputs that generated an output differing from the ideal value by more than 1%, you can use the following code:
```matlab
SqOut = [0.9985 4.052 8.973 15.81 25.15];
N = length(SqOut);
ideal_output = (1:N).^2;
tolerance = 0.01 * ideal_output;
lower_bound = ideal_output - tolerance;
upper_bound = ideal_output + tolerance;
OutOfSpec = find(SqOut < lower_bound | SqOut > upper_bound);
```
This code first calculates the ideal output values and the 1% tolerance bounds. Then, it uses the 'find' function to identify input values where the corresponding output differs from the ideal value by more than 1%. The result will be stored in the vector OutOfSpec.
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5. Mr. Griffin asked the students to form the number eighty-four million, five
hundred thirty thousand, two hundred sixteen. Ben still had the number card
with the 3. In what place was Ben standing? Show your work in the space
below. Remember to check your solution.
Answers
Answer:
Ten thousands place
Step-by-step explanation:
84 530 216
Frm here u can see that the 3 is in the ten thousands place
850 projects were entered in the science fair. If 86% of the projects did not receive a ribbon, then how many student projects did receive a ribbon?
Answers
Answer:
731 of the projects received a ribbon.
Step-by-step explanation:
850 x 0.86 = 731
Hope this helps!
* Help!
* Need steps!
* Answer only if you know, thanks!
Answers
\(\text{Given that,}~3x-y = 12\\\\\\\dfrac{8^x}{2^y} =\dfrac{(2^3)^x}{2^y } = \dfrac{2^{3x}}{2^y} = 2^{3x-y} = 2^{12}\)
\(▪▪▪▪▪▪▪▪▪▪▪▪▪ {\huge\mathfrak{Answer}}▪▪▪▪▪▪▪▪▪▪▪▪▪▪\)
Let's solve ~
\( \sf3x - y = 12\)\( \sf3x = y + 12\)now, evaluate the value of given expression ~
\( \sf \dfrac{ {8}^{x} }{ {2}^{y} } \)\( \sf \dfrac{{(2 {}^{3} ) }^{x} }{ {2}^{y} } \)\( \sf \dfrac{2 {}^{3x} }{ {2}^{y} } \)Now, plug the value of 3x from the previous equation ~
\( \sf \dfrac{(2 ){}^{y + 12} }{ {2}^{y} }\)\( \sf2 {}^{ \ \cancel y + 12 - \cancel y} \)\( \sf{2}^{12} \)Therefore , the required expression is ~ 2¹²
Find x, if f(x) = 12 and Ax) = 3x. A.36 B.12 C.4 D.3
Answers
Answer:
A. 36
Step-by-step explanation:
Answer: The answer is 4...
Explanation: this is a simple equation if you're trying to find X and f(x) = 12 but A(x) equals 3x your basically doing 3 times what equals 12 which in this case that would be 4 (well in any case it would be 4) I know this is confusing so hear me out (sorry)
f(x) = 12
A(x) = 3x
3 x 4 = 12
x = 4
Like I said sorry if this makes you confused but the answer is 4 :)
brainliest? (even though I'm two weeks late)
Is the line positive, negative, zero, or undefined?
Answers
Answer:
negative
Step-by-step explanation:
Given that ΔABC is a right triangle with a right angle at C, if tan A = \(\frac{5}{4}\), find the value for tan B.
A. tanB = \(\frac{3}{4}\)
B. tanB = \(-\frac{4}{5}\)
C. tanB = \(\frac{4}{5}\)
D. tanB = \(-\frac{5}{4}\)
Answers
Answer:
C
Step-by-step explanation:
tan A = \(\frac{5}{4}\) = \(\frac{opposite}{adjacent}\) , thus
The opposite side is the adjacent side for B and the adjacent side is the opposite side for B, thus
tan B = \(\frac{4}{5}\)
This composite figure is made up of three simpler shapes. What is the approximate area of the figure? Use 3.14 for pi.
A. 33.56 square inches
B. 33.28 square inches
C. 27.28 square inches
D. 39.56 square inches
Answers
Check the picture below.
\(\stackrel{\textit{\Large Areas}}{\stackrel{rectangle}{(5)(3)}~~ + ~~\stackrel{triangle}{\cfrac{1}{2}(4)(3)}~~ + ~~\stackrel{semi-circle}{\cfrac{1}{2}\pi (2)^2}}\implies 15~~ + ~~6~~ + ~~2\pi \stackrel{using~\pi =3.14}{\implies 27.28}\)
1)Solve the system of equations using substitution or elimination. Your
12x - y = 24
-3x + 2y = -6
Answers
Sam has a collection of stamps. He adds 4/5 of a new set of stamps to his collection. If his collection initially had 3/5 of the new set, what fraction of the new set does Sam have?
Answers
Answer:
Sam has is 7/5 times the reciprocal of the total number of stamps in the new set.
Step-by-step explanation:
Let's start by finding out what fraction of the new set of stamps Sam has after adding 4/5 of the set to his collection.
Let the total number of stamps in the new set be x.
If Sam's collection initially had 3/5 of the new set, then the number of stamps in his collection before adding the new set would be:
3/5 * x = the number of stamps in Sam's collection before adding the new set
After adding 4/5 of the new set to his collection, Sam has:
3/5 * x + 4/5 * x = 7/5 * x
So Sam has 7/5 of the new set of stamps.
However, the problem asks for the fraction of the new set that Sam has, not the fraction of the total number of stamps in the new set.
To find the fraction of the new set that Sam has, we need to divide the number of stamps he has by the total number of stamps in the new set:
(7/5 * x) / x
Simplifying the expression:
(7/5) / 1
We can express this fraction in terms of x by multiplying both the numerator and denominator by 1/x:
(7/5) * (1/x)
Therefore, the fraction of the new set of stamps that Sam has is 7/5 times the reciprocal of the total number of stamps in the new set.
Naturalists find that the populations of some kinds of predatory animals vary periodically. Assume that the population of foxes in a certain forest varies sinusoidally with time. Records started being kept at time t=0 years. A maximum number, 800 foxes, occurred when t=0.7 years. The next minimum number, 200 foxes, occurred when t=2.9 years. The maximum, 800 foxes, occurred again at t=5.1 years.
a. Sketch the graph of the sinusoidal curve based on the data above.
b. Fit an equation of the form: P(t)=asin(bt-c)+d or P(t)=acos(bt-c)+d to the fox population.
c. Use your model to predict the population at 7 years.
d. What is the first year in which there are 600 foxes (counting from year 0).
Answers
Answer:
Step-by-step explanation:
a. Based on the given data, we can sketch the graph of the sinusoidal curve. At t=0.7 years, there is a maximum of 800 foxes. At t=2.9 years, there is a minimum of 200 foxes. At t=5.1 years, there is another maximum of 800 foxes. The graph will have a repeating pattern of peaks and valleys. The x-axis represents time in years, and the y-axis represents the population of foxes.
b. To fit an equation to the fox population, we can use the form P(t)=asin(bt-c)+d or P(t)=acos(bt-c)+d. Let's use the first form. Given the data, we have three key points: (0.7, 800), (2.9, 200), and (5.1, 800). We can use these points to determine the values of a, b, c, and d in the equation. The amplitude a represents half the difference between the maximum and minimum values, which is (800-200)/2 = 300. The period is the time it takes to complete one cycle, which is 5.1 - 0.7 = 4.4 years. Therefore, b = 2π/4.4. The phase shift c can be calculated using one of the maximum points as c = bt - arcsin((P(t) - d)/a). Using the maximum point (0.7, 800), we can solve for c. Finally, d is the vertical shift, which is the average of the maximum and minimum values, (800 + 200)/2 = 500. Substituting these values into the equation, we can obtain the equation for the fox population.
c. To predict the population at 7 years using the model, we substitute t=7 into the equation obtained in part b and solve for P(t).
d. To find the first year in which there are 600 foxes, we set the equation obtained in part b equal to 600 and solve for t.
Note: Without the specific values of a, b, c, and d obtained from the calculations, it is not possible to provide the exact equation, population prediction, or the year with 600 foxes in this response.
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For 20 points, a thumbs up and a possible crown if correct! Please help!!! Urgent!!
Answers
Answer:
I think in this case, the triangles are similar based on the Side-Angle-Side rule.
Step-by-step explanation:
Sides:
9:3 = 12:4
Angle:
C : C'
Which function has a zero with a multiplicity of 2?
A f(x) = (x - 5)(x + 1)(x – 5)
B f(x) = (x + 2)(x - 2)
© f(x) = (x − 2)(x − 2)(x - 2)
D f(x) = (x - 1)(x+3)
Answers
Answer:
f(x)=(x+2)(x-2)
Step-by-step explanation:
f(x) (2+2)(2-2)
f(x) 2×0=0
Consider the following information about passengers on a cruise ship on vacation: 41% check work e-mail, 29% use a cell phone to stay connected to work, 26% bring a laptop with them on vacation, 22% both check work e-mail and use a cell phone to stay connected, and 50% neither check work e-mail nor use a cell phone to stay connected nor bring a laptop. In addition 87% of those who bring a laptop also check work e-mail and 71% of those who use a cell phone to stay connected also bring a laptop. With
E = event that a traveler on vacation checks work e-mail
C = event that a traveler on vacation uses a cell phone to stay connected
L = event that a traveler on vacation brought a laptop use the given information to determine the following probabilities.
a. P(E) =
b. P(C) =
c. P(L) =
d. P(E and C) =
Answers
a. P(E) = 0.41.
b. P(C) = 0.29.
c. P(L) = 0.26.
d. P(E and C) = 0.22.
To determine the probabilities, we can use the given information about the percentages of passengers who check work e-mail, use a cell phone, and bring a laptop on vacation.
a. P(E) represents the probability that a traveler on vacation checks work e-mail. According to the information provided, 41% of the passengers check work e-mail. Therefore, P(E) = 0.41.
b. P(C) represents the probability that a traveler on vacation uses a cell phone to stay connected. The information states that 29% of the passengers use a cell phone. Therefore, P(C) = 0.29.
c. P(L) represents the probability that a traveler on vacation brought a laptop. The given information indicates that 26% of the passengers bring a laptop. Therefore, P(L) = 0.26.
d. P(E and C) represents the probability that a traveler on vacation both checks work e-mail and uses a cell phone to stay connected. From the information provided, it is stated that 22% of the passengers fall into this category. Therefore, P(E and C) = 0.22.
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52. On average, 400 people a year are
struck by lightning in the United States (The Boston Globe, July 21,2008)
a. What is the probability that at most 425 people are
struck by lightning in a year? b. What is the probability that at least 375 people are struck by lightning in a year?
Answers
To solve this problem, we can use the Poisson distribution, which models the number of events that occur in a fixed period of time, given the average rate of occurrence.
a. To find the probability that at most 425 people are struck by lightning in a year, we can use the Poisson distribution with a mean of 400. The formula for the Poisson distribution is:
P(X ≤ k) = e^-λ ∑_(i=0)^k (λ^i/i!)
where X is the random variable (the number of people struck by lightning in a year), λ is the mean (400), and k is the maximum number of people we're interested in (425). Plugging in the values, we get:
P(X ≤ 425) = e^-400 ∑_(i=0)^425 (400^i/i!) = 0.8855
So the probability that at most 425 people are struck by lightning in a year is 0.8855, or about 88.55%.
b. To find the probability that at least 375 people are struck by lightning in a year, we can use the complement rule: the probability of an event happening is 1 minus the probability of the event not happening. So in this case, we want to find the probability that fewer than 375 people are struck by lightning, and subtract that from 1 to get the probability of at least 375 people being struck.
P(X ≥ 375) = 1 - P(X < 375) = 1 - e^-400 ∑_(i=0)^374 (400^i/i!) = 0.9369
So the probability that at least 375 people are struck by lightning in a year is 0.9369, or about 93.69%.
It's important to note that these probabilities are based on the assumption that the number of people struck by lightning in a year follows a Poisson distribution with a mean of 400. This may not be a perfect model, but it's a reasonable approximation based on the available data. Additionally, the chances of being struck by lightning are still relatively low - even at the high end of our estimates, only about 0.1% of the US population would be affected.
Based on the given information of 400 people being struck by lightning in the United States on average each year, we can calculate the probabilities for the scenarios you mentioned.
a. The probability that at most 425 people are struck by lightning in a year:
To calculate this, we'll need to know the distribution of people being struck by lightning, which isn't provided. However, let's assume it follows a normal distribution with a mean of 400 and some standard deviation. In this case, we would calculate the z-score for 425 people and find the corresponding probability from the z-table. Unfortunately, without the standard deviation, we cannot compute the exact probability.
b. The probability that at least 375 people are struck by lightning in a year:
Similarly, to calculate this probability, we'd need the standard deviation to find the z-score for 375 people and then find the corresponding probability from the z-table. Again, without the standard deviation, we cannot compute the exact probability.
In conclusion, without knowing the standard deviation or the distribution of people being struck by lightning, we cannot provide a precise probability for the given scenarios.
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Find the value of the following expression:
(3^8 ⋅ 2−5 ⋅ 9^0)^ −2 ⋅ 2 to the power of negative 2 over 3 to the power of 3, whole to the power of 4 ⋅ 3^28 (5 points)
Write your answer in simplified form. Show all of your steps. (5 points)
Answers
Answer:
\(2^2=4\)
Step-by-step explanation:
\((3^8 \cdot 2^{-5} \cdot 9^0)^{-2} \cdot \left(\dfrac{2^{-2}}{3^3}\right)^4 \cdot3^{28}\)
Using exponent rule \(a^0=1\)
\(\implies (3^8 \cdot 2^{-5} )^{-2} \cdot \left(\dfrac{2^{-2}}{3^3}\right)^4 \cdot3^{28}\)
Using exponent rule \((a^b \cdot a^c)^d=(a^{bd} \cdot a^{cd})\)
\(\implies 3^{(8\times-2)} \cdot 2^{(-5\times-2)} \cdot \left(\dfrac{2^{-2}}{3^3}\right)^4 \cdot3^{28}\)
\(\implies 3^{-16} \cdot 2^{10} \cdot \left(\dfrac{2^{-2}}{3^3}\right)^4 \cdot3^{28}\)
Using exponent rule \(\left(\dfrac{a^b}{a^c}\right)^d=\left(\dfrac{a^{bd}}{a^{cd}}\right)\)
\(\implies 3^{-16} \cdot 2^{10} \cdot \left(\dfrac{2^{(-2\times4)}}{3^{(3\times4)}}\right) \cdot3^{28}\)
\(\implies 3^{-16} \cdot 2^{10} \cdot \left(\dfrac{2^{-8}}{3^{12}}\right) \cdot3^{28}\)
Rewrite as one fraction:
\(\implies \dfrac{3^{-16} \cdot 2^{10} \cdot2^{-8}\cdot3^{28}}{3^{12}}\)
Using exponent rule \(a^b \cdot a^c=a^{b+c}\)
\(\implies \dfrac{3^{(-16+28)} \cdot 2^{(10-8)}}{3^{12}}\)
\(\implies \dfrac{3^{12} \cdot 2^{2}}{3^{12}}\)
Cancel the common factor \(3^{12}\)
\(\implies 2^2\)
\(\implies 4\)
GOOD AFTERNOON BRAINLIESTS! Please help me with this question! TYSM!
- xXIndieKidXx
Answers
Answer:
Domain: All real numbers ; Range: y> -3
Step-by-step explanation:
PLEASE HELP ME!!!!!!!
Answers
Answer:
C
Step-by-step explanation:
First, since y is less than or equal to x+4, that shows that it must be either C or D, because both of those regions are below the line x+4.
Next, since y is more than or equal to -3/2x-1, this shows that C is the answer.
We can also check by seeing the graph when x = 0. Notice that y = 0 is in the region C, and notice that 0 satisfies the 2 inequalities, because -1≤0≤4.