The given boundary value problem, y'' + 4y = 0, with boundary conditions y(0) = 0 and y(L) = 0, has a unique solution. Therefore, the solution to the given boundary value problem is y(x) = c2 sin(2x), where c2 is a constant and L = nπ/2.
To solve the given boundary value problem, we start by finding the general solution to the homogeneous differential equation y'' + 4y = 0. The characteristic equation associated with this differential equation is r^2 + 4 = 0, which has complex roots: r1 = 2i and r2 = -2i.
The general solution to the homogeneous equation is y(x) = c1 cos(2x) + c2 sin(2x), where c1 and c2 are constants. Now, we apply the boundary conditions to determine the specific solution.
Using the first boundary condition y(0) = 0, we have 0 = c1 cos(0) + c2 sin(0), which simplifies to c1 = 0. Therefore, the solution becomes y(x) = c2 sin(2x).
Now, we use the second boundary condition y(L) = 0. Substituting L for x in the solution, we get 0 = c2 sin(2L). For this equation to hold for all L, sin(2L) must be equal to zero, which means 2L = nπ, where n is an integer. Solving for L, we have L = nπ/2.
Therefore, the solution to the given boundary value problem is y(x) = c2 sin(2x), where c2 is a constant and L = nπ/2. Since both boundary conditions are satisfied for y(x) = 0, we conclude that the only solution to the problem is y(x) = 0.
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was 10 years and 6 months old when I moved to Mumbai. have been living in Mumbai for the past 13
years 11 months. What is my age now?
24 years and 5 months
add 13 years to ten get 23 add 6 to 11 to get 1 year and 5 months
23 plus 1 years and 5 months = 24 years an 5months
have a nice day please mark brainliest
Which of the following sets of points would create a rectangle when connected?
A.
(1,2) , (2,3) , (3,5) , (5,1)
B.
(2,1) , (3,2) , (5,3) , (1,5)
C.
(1,2) , (3,1) , (3,2) , (1,5)
D.
(1,2) , (3,2) , (3,5) , (1,5)
evaluating quadratic functions using equations evaluate the function g(x) = –2x2 3x – 5 for the input values –2, 0, and 3. g(–2) = –2(–2)2 3(–2) – 5 g(–2) = –2(4) – 6 – 5 g(–2) = g(0) = g(3) =
Evaluating the quadratic function we will get:
g(-2) = -3
g(0) = -5
g(3) = 31
How to evaluate the quadratic function?Here we need to evaluate the quadratic function:
g(x) = -2x² + 3x - 5
To do so, just replace the value of x by the correspondent number.
For example, if x = -2
g(-2) = 2*(-2)² + 3*(-2) - 5 = -3
if x = 0
g(0) = 2*(0)² + 3*(0) - 5 = -5
if x = 3
g(3) = 2*(3)² + 3*(3) - 5 = 31
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4) A spinner has 8 congruent sections as shown in the diagram. If the
spinner is spun twice, what is the probability that the first spin will land on
a whistle and the second spin will land on a yo-yo?"
a. 1/2
b. 1/8
c. 2/8
d. 1/32
Evaluate the algebraic expression5m + 4n – 3 whenm=3 and n=4. Show your work.
Answer:
Given, m = 3 and n = 4
5×3 + 4×4 – 3
15 + 16 - 3
31 - 3
28
don't forget to like and mark me
From a survey taken by Survey 'R Us, 243 respondents out of the 1523 cat owners surveyed claim that their cats speak to them.
A.) With an 85% confidence level, provide the confidence interval that could be used to estimate the proportion of the population that hears their cats talking to them: use all three notations Set notation, interval notation, +/- notation
B.) Do the same as you did for 1a, but use a 95% confidence level instead Set Notation, Interval Notation, +/- notation
C.) Describe the differences between the ranges given for 1a and 1b. Why are the ranges different D.) Provide an interpretation for the interval given in 1b.
The interpretation of the interval in 1b (95% confidence level) is that we can be 95% confident that the true proportion of the population that hears their cats talking to them falls within the range of 0.1241 to 0.2137.
A.) With an 85% confidence level, the confidence interval that could be used to estimate the proportion of the population that hears their cats talking to them is [0.1459, 0.1919] in set notation, (0.1459, 0.1919) in interval notation, and +/- 0.023 in +/- notation.
B.) With a 95% confidence level, the confidence interval that could be used to estimate the proportion of the population that hears their cats talking to them is [0.1241, 0.2137] in set notation, (0.1241, 0.2137) in interval notation, and +/- 0.045 in +/- notation.
C.) The ranges for 1a and 1b are different because the confidence level affects the width of the interval. A higher confidence level requires a wider interval to provide a more reliable estimate. In this case, the 95% confidence level has a wider range compared to the 85% confidence level.
This means that if we were to repeat the survey multiple times, approximately 95% of the intervals calculated would contain the true proportion.
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a) The 85% confidence interval is given as follows: (0.146, 0.174).
b) The 95% confidence interval is given as follows: (0.142, 0.178).
c) The interval for item a is narrower than the interval for item b, as the lower confidence level leads to a lower critical value and a lower margin of error.
d) We are 95% sure that the true population proportion is between the two bounds found in item b.
What is a confidence interval of proportions?A confidence interval of proportions has the bounds given by the rule presented as follows:
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which the variables used to calculated these bounds are listed as follows:
[tex]\pi[/tex] is the sample proportion, which is also the estimate of the parameter.z is the critical value.n is the sample size.For the confidence level of 85%, the critical value z is the value of Z that has a p-value of [tex]\frac{1+0.85}{2} = 0.925[/tex], so the critical value is z = 1.44.
For the confidence level of 95%, the critical value z is the value of Z that has a p-value of [tex]\frac{1+0.95}{2} = 0.975[/tex], so the critical value is z = 1.96.
The parameters for the confidence interval are given as follows:
[tex]n = 1523, \pi = \frac{243}{1523} = 0.16[/tex]
Hence the bounds of the 85% confidence interval are given as follows:
[tex]0.16 - 1.44\sqrt{\frac{0.16(0.84)}{1523}} = 0.146[/tex][tex]0.16 + 1.44\sqrt{\frac{0.16(0.84)}{1523}} = 0.174[/tex]The bounds of the 95% confidence interval are given as follows:
[tex]0.16 - 1.96\sqrt{\frac{0.16(0.84)}{1523}} = 0.142[/tex][tex]0.16 + 1.96\sqrt{\frac{0.16(0.84)}{1523}} = 0.178[/tex]More can be learned about the z-distribution at https://brainly.com/question/25890103
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Emily asked the players on her volleyball team their height in inches and listed the results below. What is the mean of the data set? Round to the nearest tenth when necessary
Answer:the range is 10 pls gimme brainless plsss I need it
Step-by-step explanation:
a spinner has three same-sized sectors numbered 1, 3, and 5. the spinner is spun once and a coin is tossed. h represents heads, and t represents tails. what is the sample space of outcomes?
A spinner has three same-sized sectors numbered 1, 3, and 5. The spinner is spun once and a coin is tossed. H represents heads, and T represents tails.
The sample space of outcomes is given below: Sample Space of Outcomes: {1H, 1T, 3H, 3T, 5H, 5T}Explanation: In this given problem, the spinner has three same-sized sectors numbered 1, 3, and 5. It indicates that the probability of each sector is equal. The spinner is spun once and a coin is tossed, where H represents heads, and T represents tails. It means that the spinner will land on one of three sectors, and the coin will land on either heads or tails.Therefore, the sample space of outcomes is {1H, 1T, 3H, 3T, 5H, 5T}.
To determine the sample space of outcomes for this situation, we need to consider the possible combinations of the spinner's numbers (1, 3, 5) and the outcomes of the coin toss (H for heads, T for tails).
The spinner has three sectors numbered 1, 3, and 5. Therefore, there are three possible outcomes for the spinner.
The coin toss can result in two outcomes: heads (H) or tails (T).
To find the sample space, we need to consider all possible combinations of the spinner outcomes and the coin toss outcomes.
The sample space of outcomes can be listed as follows:
{1H, 1T, 3H, 3T, 5H, 5T}
Therefore, the sample space of outcomes for this situation consists of the six possible combinations: 1H, 1T, 3H, 3T, 5H, and 5T.
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Given information is that, a spinner has three same-sized sectors numbered 1, 3, and 5. The spinner is spun once and a coin is tossed. h represents heads, and t represents tails. We need to find the sample space of outcomes.
The required sample space of outcomes is {1H, 1T, 3H, 3T, 5H, 5T}.
We can use the formula for the sample space,
Sample space = Set of all possible outcomes.
The possible outcomes of the spinner are 1, 3, and 5. The possible outcomes of the coin are H and T. Therefore,
Sample space of outcomes = {1H, 1T, 3H, 3T, 5H, 5T}.
Hence, the required sample space of outcomes is {1H, 1T, 3H, 3T, 5H, 5T}.
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You measure 40 textbooks' weights, and find they have a mean weight of 42 ounces. Assume the population standard deviation is 3.8 ounces. Based on this, construct a 90% confidence interval for the true population mean textbook weight.
Give your answers as decimals, to two places
__________<μ<__________
The 90% confidence interval for the true population mean textbook weight, based on the given data, is approximately 41.44 ounces to 42.56 ounces.
To construct a confidence interval for the population mean textbook weight, we can use the formula:
Confidence Interval = sample mean ± (critical value * standard error)
Given that the sample mean is 42 ounces and the population standard deviation is 3.8 ounces, we need to determine the critical value and the standard error.
For a 90% confidence interval, the critical value corresponds to a two-tailed z-score of 1.645 (from the standard normal distribution).
The standard error can be calculated as the population standard deviation divided by the square root of the sample size. Since the sample size is not provided, we cannot calculate the exact standard error. However, if we assume a large sample size (usually considered to be greater than 30), we can use the formula for the standard error.
Assuming a large sample size, the standard error would be 3.8 ounces divided by the square root of the sample size.
Using the formula for the confidence interval, we can now calculate the range:
Confidence Interval = 42 ± (1.645 * standard error)
Substituting the values, we get:
Confidence Interval = 42 ± (1.645 * 3.8 / sqrt(sample size))
Since we do not know the sample size, we cannot calculate the exact confidence interval. However, based on the given data, we can conclude that the true population mean textbook weight falls between approximately 41.44 ounces and 42.56 ounces with 90% confidence.
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If you get this question right you’ll get points 100+356-123=?????
Answer:
333 :)
Step-by-step explanation:
8. find h[n], the unit impulse response of the system described by the following equation y[ n+2] +2y[ n+1] + y[n] = 2x[n+ 2] − x[n+ 1]
The unit impulse response of the system described by the equation y[n+2] + 2y[n+1] + y[n] = 2x[n+2] − x[n+1] is h[n] = 2δ[n+2] − δ[n+1] + δ[n], where δ[n] represents the unit impulse function.
To find the unit impulse response, we need to determine the output of the system when an impulse is applied at the input, i.e., x[n] = δ[n].
Substituting x[n] = δ[n] into the given equation, we have:
y[n+2] + 2y[n+1] + y[n] = 2δ[n+2] − δ[n+1].
Since δ[n] = 0 for n ≠ 0 and δ[0] = 1, we can simplify the equation:
y[n+2] + 2y[n+1] + y[n] = 2δ[n+2] − δ[n+1] + δ[n] = 2δ[n+2] − δ[n+1] + δ[n]δ[n].
Now, comparing the equation with the standard form of the unit impulse response:
h[n] = 2δ[n+2] − δ[n+1] + δ[n],
we can conclude that h[n] is the unit impulse response of the given system.
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Please help I’ll give brainliest if you answer all :)
Step-by-step explanation:
a^2 +b^2 = c^2
b^2 = c^2 - a^2
3 - solving for h
A = bh
h = A ÷h
4 - solving for r
I = prt
r = I÷ pt
5- solving for b
A= 1/2 bh
can rewrite as
A = bh ÷2
b = 2A ÷ h
HELP ME PLS
how do you graph a function??????
Answer:
It depends on the type of function, but essentially the process is the same
Step-by-step explanation:
You gather up all of the y values and x values and plot them onto a coordinate grid. If you are using a calculator, go to the "y=" button and input the function and then hit "graph"
5. Calculate the area.
9ft
4
11 ft.
ООО
40
44
о
396
[tex]area = b \times h \\ = 11 \times 4 \\ = 44[/tex]
How far apart are - 7 and |-7| on a number
line?
Answer:
the answer is 7. :)
Step-by-step explanation:
The company ALTA Ltd issued a bank accepted bill to fund its working capital requirement. The bill is issued for 60 days, with a face value of $150,000 and a yield of 2.5% per annum to the original discounter. After 25 days, the bank bill is sold by the wwwwww original discounter into the secondary market for $138,222. The purchaser holds the bill to maturity. What is the yield received by the holder of the bill at the date of maturity?
the yield received by the holder of the bill at the date of maturity is approximately 10.15%.
To calculate the yield received by the holder of the bill at the date of maturity, we need to use the formula for yield to maturity. The formula is:
Yield to Maturity = (Face Value - Purchase Price) / Purchase Price * (365 / Days to Maturity)
In this case:
Face Value = $150,000
Purchase Price = $138,222
Days to Maturity = 60 - 25 = 35
these values in the formula, we can calculate the yield to maturity:
Yield to Maturity = ($150,000 - $138,222) / $138,222 * (365 / 35)
Yield to Maturity ≈ 0.1015 or 10.15%
Therefore, the yield received by the holder of the bill at the date of maturity is approximately 10.15%.
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A rotating lawn sprinkler sprays water in a circular area of grass, as shown in the
picture. The diameter of the circular area of grass is 16 ft. what is the closest measurement to the area in square feet ?
Answer:
Area of the lawn = 64π square feet
Step-by-step explanation:
Area of the circular lawn = πd²/4
d is the diameter of the lawn = 16ft
Substitute the given value into the formula
Area = π(16)²/4
Arrea of the lawn = 256π/4
Area of the lawn = 64π square feet
Evaluate the triple integral. 4xy dV, where E lies under the plane z = 1 + x + y and above the region in the xy-plane bounded by the curves y = , y = 0, and x = 1
The value of the triple integral ∭E 4xy dV is 2/5. The limits of integration for x are from 0 to 1, and for y, the limits are from 0 to 1 - x, as y is bounded by the line x + y = 1.
To evaluate the triple integral ∭E 4xy dV, where E lies under the plane z = 1 + x + y and above the region in the xy-plane bounded by the curves y = 0, y = 1, and x = 1, we need to set up the integral using appropriate limits of integration.
The region in the xy-plane is a triangle bounded by the lines y = 0, y = 1, and x = 1. Therefore, the limits of integration for x are from 0 to 1, and for y, the limits are from 0 to 1 - x, as y is bounded by the line x + y = 1.
Now, let's determine the limits for z. The plane z = 1 + x + y intersects the xy-plane at z = 1, and as we move up in the positive z-direction, the plane extends infinitely. Thus, the limits for z can be taken from 1 to infinity.
Now, we can set up the triple integral:
∭E 4xy dV = ∫[0 to 1] ∫[0 to 1-x] ∫[1 to ∞] 4xy dz dy dx
The innermost integral with respect to z evaluates to z times the integrand:
∭E 4xy dV = ∫[0 to 1] ∫[0 to 1-x] [4xy(1 + x + y)] evaluated from 1 to ∞ dy dx
Simplifying further:
∭E 4xy dV = ∫[0 to 1] ∫[0 to 1-x] (4xy(1 + x + y) - 4xy(1)) dy dx
∭E 4xy dV = ∫[0 to 1] ∫[0 to 1-x] 4xy(x + y) dy dx
Now, we can integrate with respect to y:
∭E 4xy dV = ∫[0 to 1] [2xy²(x + y)] evaluated from 0 to 1-x dx
Simplifying further:
∭E 4xy dV = ∫[0 to 1] 2x(1-x)²(x + (1-x)) dx
∭E 4xy dV = ∫[0 to 1] 2x(1-x)² dx
Evaluating the integral:
∭E 4xy dV = 2/5
Therefore, the value of the triple integral ∭E 4xy dV is 2/5.
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A rectangle has a perimeter of 150 cm. The length is 3 cm more than twice the width. Find the length and width of the rectangle.
Answer:
Length of rectangle = 51 cm
Width of rectangle = 24 cm
Step-by-step explanation:
Given:
Perimeter of rectangle = 150 cm
Find:
Length and width of the rectangle
Computation:
Assume;
Width of rectangle = a cm
Length of rectangle = 2a + 3 cm
Perimeter of rectangle = 2[l + b]
150 = 2[(2a + 3) + a]
2[3a + 3] = 150
6a + 6 = 150
6a = 144
a = 24
Width of rectangle = 24 cm
Length of rectangle = 2a + 3 cm
Length of rectangle = 2(24) + 3 cm
Length of rectangle = 51 cm
Use the CVP Formulas to solve the following. JBL Speakers has annual fixed costs of $2,450,000, and variable costs of $25 per unit. The selling price per unit is $90. A) What annual revenue is required to break even? BER B) What annual unit sales are required to make a $1,000,000 profit?
Using the CVP Formulas to solve the following. JBL Speakers has annual fixed costs of $2,450,000, and variable costs of $25 per unit. The selling price per unit is $90.
A) 37,692 units
B) 53,077 units
A) To calculate the annual revenue required to break even, we need to find the point where total revenue equals total costs.
Total cost (TC) = Fixed costs (FC) + Variable costs per unit (VC) * Quantity (Q)
Total revenue (TR) = Selling price per unit (SP) * Quantity (Q)
At the break-even point, total revenue equals total cost:
TR = TC
SP * Q = FC + VC * Q
Substituting the given values:
$90 * Q = $2,450,000 + $25 * Q
$90Q - $25Q = $2,450,000
$65Q = $2,450,000
Q = $2,450,000 / $65
Q ≈ 37,692.31
Therefore, approximately 37,692 units need to be sold to break even.
B) To calculate the annual unit sales required to make a $1,000,000 profit, we can use the following formula:
Profit (P) = (SP * Q) - (FC + VC * Q)
Substituting the given values and the desired profit:
$1,000,000 = ($90 * Q) - ($2,450,000 + $25 * Q)
$90Q - $25Q = $1,000,000 + $2,450,000
$65Q = $3,450,000
Q = $3,450,000 / $65
Q ≈ 53,076.92
Therefore, approximately 53,077 units need to be sold to make a $1,000,000 profit.
In conclusion, to break even, JBL Speakers needs to generate an annual revenue of approximately $2,450,000, and to make a $1,000,000 profit, they need to sell approximately 53,077 units annually.
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Alex is a faster runner than Carlos. The chart below relates how many laps around the track each runs in the same amount of time.
Number of Laps Run
Alex Carlos
4 3
8 6
12 9
How many laps will Alex have run in the time it take Carlos to run 12 laps?
Answer:
16
Step-by-step explanation:
Alex will run 16 laps in the time it take for Carlos to run 12 laps.
What is Multiplication?Multiplication of two numbers is defined as the addition of one of the number repeatedly until the times of the other number.
a × b means that a is added to itself b times or b is added to itself a times.
Given are the values related to the number of laps run by Alex and Carlos.
The number of laps run by Alex is forming the multiples of 4 or 4x.
Number of laps run by Carlos is forming the multiples of 3 or 3x.
When x = 1,
Alex : 4 × 1 = 4
Carlos : 3 × 1 = 3
When x = 2,
Alex : 4 × 2 = 8
Carlos : 3 × 2 = 6
When x = 3,
Alex : 4 × 3 = 12
Carlos : 3 × 3 = 9
When x = 4,
Alex : 4 × 4 = 16
Carlos : 3 × 4 = 12
Hence Alex ran 16 laps in the same time for which Carlos ran 12 laps.
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a strain of peas has 3 green and one yellow for every four peas. if 12 peas are rendomly selected, what is the probability that exactly 8 peas are green? provide your answer to three decimal places
The probability of exactly 8 green peas is 0.475, rounded to three decimal places, i.e., 0.475.
We can use the binomial probability formula to solve this problem.
The formula is given as; $$P(X=k)={n\choose k}p^k(1-p)^{n-k}$$
Where;
n= sample size=12
k= number of green peas=8
p= probability of getting a green pea=3/4
q= probability of getting a yellow pea=1/4
Since we want the probability of exactly 8 green peas out of 12 peas,
we will plug in the values in the formula to get;
$$P(X=8)={12\choose 8}(\frac{3}{4})^8 (1-\frac{3}{4})^{12-8}$$$$
P(X=8)={12\choose 8}(\frac{3}{4})^8(\frac{1}{4})^{4}$$$$P(X=8)=495
(0.3164)(0.0039)$$$$P(X=8)=0.4749$$
Therefore, the probability of exactly 8 green peas is 0.475, rounded to three decimal places, i.e., 0.475.
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In 2005, there are 705 cable users in the small town of Whoville. The number of users
increases by 56% each year after 2005. Find the number of users to the nearest whole in 2020.
Answer:2008
Step-by-step explanation:
a) give stating reasons five other angles each equal to x
b) prove that AECF is a parallelogram
Simple Proof:
a) In the image, we know that ABCD is a parallelogram and that means opposite angel measures should be the same. We know that angel DCB is made up by angel 1 and 2, and angel DAB and DCB are equal and angel DAB is made up by angel 1 and x. So now we can conclude that angel x is equal to angel 2.
b) According to the definitions of a parallelogram, opposite angel measures have to be the same, while AECF have angle 1 to angel 1 and angel 2 to angel 1. We can conclude that AECF is NOT a parallelogram. (Sorry, you didn't give me the full question so some information remains unclear. )
WHAT WOULD THiS BE! ♀️
no scammers pleaseee!
Answer:
First find the unit rate for julie
3 hours/45 dollars
0.066 hours/1 dollar
Now based off table, find Jacksons
y = 25x
if x = 1, y would be 25
25 - .066 = 24.934 dollars
Step-by-step explanation:
"Marty purchased a car. The car cost him $16,500 and it depreciates in value at a rate of 4.3% per year. How much will the car be worth in 12 years?"
Answer:
"Marty purchased a car. The car cost him $16,500 and it depreciates in value at a rate of 4.3% per year. How much will the car be worth in 12 years?"
Step-by-step explanation:
Perform a hypothesis test for the following sample, the significance level alpha is 5%. Sample: 3.4,2.5,4.8, 2.9,3.6,2.8, 3.3, 5.5, 3.7, 2.8,4.4,4,5.2,3,4.8 Standard deviation is sd-1.05. Test if mean is greater than 3.16 Assume normality of the data. 1 Formulate the hypothesis by entering the corresponding signs
Based on the given sample, there is sufficient evidence to conclude that the mean is greater than 3.16 at a significance level of 5%.
To perform a hypothesis test, we need to state the null hypothesis and alternative hypothesis.
We want to test if the mean is greater than 3.16.
Null hypothesis (H0): μ ≤ 3.16 (Mean is less than or equal to 3.16)
Alternative hypothesis (Ha): μ > 3.16 (Mean is greater than 3.16)
Now, we can proceed with the hypothesis test.
We'll use a one-sample t-test since we don't know the population standard deviation and our sample size is relatively small.
The sample mean (X) and sample size (n) from the given data.
X= (3.4 + 2.5 + 4.8 + 2.9 + 3.6 + 2.8 + 3.3 + 5.5 + 3.7 + 2.8 + 4.4 + 4 + 5.2 + 3 + 4.8) / 15 = 3.66
n = 15
Now calculate the test statistic (t-value).
t = (X - μ) / (sd / √n)
= (3.66 - 3.16) / (1.05 / √15)
≈ 2.26
Since our alternative hypothesis is one-tailed (μ > 3.16), we need to find the critical value for a significance level of 5% in the right tail of the t-distribution.
Using a t-table, the critical value for a one-tailed test with α = 0.05 and degrees of freedom (df) = n - 1 = 15 - 1 = 14 is 1.761.
If the test statistic is greater than the critical value, we reject the null hypothesis.
t-value (2.26) > critical value (1.761)
Since the test statistic is greater than the critical value, we reject the null hypothesis.
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plssssssss help solve
Answer:
cosine = adjacent/hypotenuse
cos A = 20/29 (choice: yellow)
Step-by-step explanation:
Answer:
yellow
Step-by-step explanation:
In a game of chance, a fair die is tossed. If the number is 1 or 2, you will win $3. If the number is 3, you win $5. If the number is 4 or 5, you win nothing, and if the number is 6 you lose S2. Should you play the game, based on the long run expected amount you would win? von $3= / 116 (A) Yes! In the long run, you are expected to win $2.16. (B) Yes! In the long run, you are expected to win $1.00. (C) Yes! You have more opportunities to win money than you have to lose money, (D) No. In the long run, you are expected to lose $0.33 (E) No. Even with the opportunities to win money, it is not worth the risk to lose $2 in the long run
In the long run, you are expected to win $1.50 when playing the game. Therefore, the correct answer is :
(B) Yes! In the long run, you are expected to win $1.00.
To determine whether you should play the game based on the long run expected amount you would win, we need to calculate the expected value.
The probability of winning $3 is 2/6 (numbers 1 and 2), the probability of winning $5 is 1/6 (number 3), the probability of winning nothing is 2/6 (numbers 4 and 5), and the probability of losing $2 is 1/6 (number 6).
Now let's calculate the expected value:
Expected Value = (Probability of winning $3 * $3) + (Probability of winning $5 * $5) + (Probability of winning nothing * $0) + (Probability of losing $2 * -$2)
Expected Value = (2/6 * $3) + (1/6 * $5) + (2/6 * $0) + (1/6 * -$2)
Expected Value = ($6/6) + ($5/6) + ($0) + (-$2/6)
Expected Value = $11/6 - $2/6
Expected Value = $9/6
Expected Value = $1.50
Therefore, in the long run, you are expected to win $1.50.
The correct answer is option (B) Yes! In the long run, you are expected to win $1.00.
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1.13 UNIT TEST GRAPH OF SINUSOIDAL FUNCTION PART 1
What is the equation of the midline for the function f(x)?
f(x) =1/2 sin(x)+6
Answer:
The equation of the midline for the function [tex]f(x)[/tex] is [tex]y = 6[/tex].
Step-by-step explanation:
The sinusoidal function of the form [tex]y = A_{o}+A\cdot \sin x[/tex] is a periodic function whose range is bounded between [tex]A_{o}-A[/tex] (minimum) and [tex]A_{o}+A[/tex] (maximum). The equation of the midline is a line paralel to the x-axis, that is:
[tex]y = c,\forall\, c\in \mathbb{R}[/tex] (1)
Where [tex]c[/tex] is mean of the upper and lower bounds of the sinusoidal function, that is:
[tex]c = \frac{(A_{o}+A+A_{o}-A)}{2}[/tex]
[tex]c = A_{o}[/tex] (2)
If we know that [tex]y = \frac{1}{2}\cdot \sin x + 6[/tex], then the equation of the midline for the function [tex]y[/tex] is:
[tex]c = A_{0} = 6[/tex]
[tex]y = 6[/tex]
The equation of the midline for the function [tex]f(x)[/tex] is [tex]y = 6[/tex].