Answers
The proof of the three distributions as required as shown in the explanation part.
What are the proof of the three distributions?For x² distribution:
Let's start with the sample variance, which is defined as:
s^2 = ∑(y_i - y_bar)² / (n-1)
where;
y_i is the i-th observation in the sample, y_bar is the sample mean, and n is the sample size.We can rewrite this formula as:
s^2 = (∑y_i² - n*y_bar²) / (n-1)
Multiplying both sides by (n-1)/σ², we get:
s^2 / σ² = (∑y_i² - ny_bar²) / (σ²(n-1))
Now, let's define a new variable:
x² = ∑y_i² / σ²
Substituting x² into the above equation, we get:
s^2 / σ² = (x² - n*y_bar²/σ²) / (n-1)
Notice that n*y_bar²/σ² is just the sample mean squared in units of variance. We can rewrite it as:
n*y_bar²/σ² = (y_bar - μ)² / (σ²/n)
where;
μ is the population mean.Substituting this into the above equation, we get:
s^2 / σ² = (x² - (y_bar - μ)² / (σ²/n)) / (n-1)
Now, let's define a new variable:
ss = ∑(y_i - y_bar)² / σ²
Substituting ss into the above equation, we get:
s^2 / σ² = (x² - ss/(n-1)) / n
This is the desired result. We have shown that s²/σ² follows a x² distribution with n-1 degrees of freedom.
For t distribution:
Let's start with the sample mean, which is defined as:
y_bar = ∑y_i / n
We can rewrite this formula as:
y_bar - μ = (∑y_i - n*μ) / n
Now, let's define a new variable:
t = (y_bar - μ) / (s/√n)
where;
s is the sample standard deviation.Substituting y_bar - μ and s into the above equation, we get:
t = (∑y_i - nμ) / (s√n)
This is the desired result. We have shown that t follows a t distribution with n-1 degrees of freedom.
For F distribution:
Let's start with the sample variances, which are defined as:
s₁² = ∑(y_i - y₁)² / (n₁-1)
s₂² = ∑(y_i - y₂)² / (n₂-1)
where;
y₁ and y₂ are the sample means, and n₁ and n₂ are the sample sizes.We can rewrite these formulas as:
s₁² = (ss₁ - n₁*(y₁-μ)²) / (n₁-1)
s₂² = (ss₂ - n₂*(y₂-μ)²) / (n₂-1)
where;
μ is the population mean, and ss₁ and ss₂ are the sum of squares within each sample:ss₁ = ∑(y_i - y₁)²
ss₂ = ∑(y_i - y₂)²
Dividing these equations, we get:
s₁² / s₂² = (ss₁ / (n₁-1)) / (ss₂ / (n₂-1))
Now, let's define a new variable:
F = s₁² / s₂
Substituting s₁² / s₂² into the above equation, we get:
F = (ss₁ / (n₁-1)) / (ss₂ / (n₂-1))
This is the desired result. We have shown that F follows an F distribution with (n₁-1) and (n₂-1) degrees of freedom.
It's worth noting that the F distribution is only defined for positive values. Therefore, if s₁² / s₂² is less than 1, we need to take the reciprocal of the above equation to ensure that F is positive:
F = (ss₂ / (n₂-1)) / (ss₁ / (n₁-1))
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Related Questions
HELP ASAP if ur good with non-linear and increasing lines and choose a letter A,B,C,D,E
(Please see the picture!)
Extra points nd brainlist!
Answers
Answer:
A nonlinear line is a line that is not straight. So the answers for these question include B and D
B and D are not straight lines and they are increasing
Step-by-step explanation:
Hope this helps! =D
Mark me brainliest! =D
Solve for x. I attached the question. Pls help me :(
Answers
Answer:
x = 16°
Step-by-step explanation:
What we know:
∠JML = 47°
∠JKL = (7x + 21)°
∠JML is an inscribed angle
∠JKL is an inscribed angle
Inscribed angles are half of the value of their intercepted arc
So if m∠JML = 47° then mArc JL is double that or 94°
And ∠JKL is intercepted by Arc JML which is the rest of the circle not intercepted by ∠JML so
mArc JL + Arc JML = 360°
94 + Arc JML = 360
Subtract 94 from both sides to isolate Arc JML
Arc JML = 266°
So if Arc JML = 266° then it's intercepted inscribed angle is half of that.
Arc JML ÷ 2 = ∠JKL
266 ÷ 2 = ∠JKL
133 °= ∠JKL
Now we can use this value and set it equal to the expression to find the value of x
(7x + 21) = 133
Subtract 21 from both sides to isolate the x
7x = 112
Divide both sides by 7
x = 16
how do I find the IQR for the numbers 7,9,8,9,6
Answers
Answer:
There are three steps to find IQR
1. Know how the IQR is used. Essentially, it is a way of understanding the spread or "dispersion" of a set of numbers. The interquartile range is defined as the difference between the upper quartile (the highest 25%) and the lower quartile (the lowest 25%) of a data set.
2. Understand quartiles. To visualize a quartile, chop a list of numbers into four equal parts. Each of these parts is a "quartile."[2] Consider the set: 1, 2, 3, 4, 5, 6, 7, 8.
1 and 2 are the first quartile, or Q1
3 and 4 are the second quartile, or Q2
5 and 6 are the third quartile, or Q3
7 and 8 are the fourth quartile, or Q4
3. Learn the formula. In order to find the difference between the upper and lower quartile, you'll need to subtract the 25th percentile from the 75th percentile.
The formula is written as: Q3 – Q1 = IQR.
Answer:
the answer would be 2.5
Explanation:
The formula for finding the interquartile range takes the third quartile value and subtracts the first quartile value. Equivalently, the interquartile range is the region between the 75th and 25th percentile (75 – 25 = 50% of the data).
PLEASE HELP ASAP!! (Please do this if ur good at Scientific Notation) please tell me which 4 should I put in the box! (Click picture) ‼️‼️
Answers
Answer:
1st one is 6.9 X 10^6
2nd one is 2 x 10^5
Step-by-step explanation:
what are 3 differnt types of rocks
Answers
Answer:
Step-by-step explanation:
sedimentary, igneous, metamorphic
Answer: sedimentary, igneous, metamorphic.
have an amazing day and crush that homework/class!
branliest?
The students in Mrs. Fishers class planted seeds. Each seed was given sunlight and water. Mrs. Fisher measured one plants height each week.
* After 4 weeks, the height was 2 centimeters.
* After 7 weeks the height was 4.5 centimeters.
* After 9 weeks, the height was 6 centimeters.
A student noticed the data suggest a linear association between the height of the plant, y, in centimeters, after x weeks.
What is a reasonable value for n?
Please answer as soon as possible due in an hour. Thank you.
Answers
Answer:
-9.5.
Step-by-step explanation
To find a reasonable value for n, we need to use the given data points and the equation of the line. We can plug in any pair of x and y values into the equation and solve for m or b. For example, using (4, 2), we get:
2 = m(4) + b
Solving for b, we get:
b = 2 - 4m
Now we can plug in another pair of x and y values, such as (7, 4.5), and use the value of b we just found:
4.5 = m(7) + 2 - 4m
Solving for m, we get:
m = 0.5
Now we have the slope and the y-intercept of the line. The equation is:
y = 0.5x + 2 - 4(0.5)
Simplifying, we get:
y = -1.5x + 4
To find n, we need to plug in x = 9 and solve for y:
y = -1.5(9) + 4
y = -9.5
What fraction is a multiple of 1/9. 3/9 4/9 9/12 9/10 2/9 or 9/9
Answers
To determine which of the given fractions is a multiple of 1/9, we need to check if each fraction can be written as the product of 1/9 and another integer.
What fraction is a multiple of 1/9. 3/9 4/9 9/12 9/10 2/9 or 9/9?3/9 = 1/3, which is not a multiple of 1/9
4/9 cannot be simplified further and is therefore a multiple of 1/9
9/12 can be simplified to 3/4, which is not a multiple of 1/9
9/10 cannot be simplified further and is therefore a multiple of 1/9
2/9 cannot be simplified further and is therefore a multiple of 1/9
9/9 = 1, which is not a multiple of 1/9
Therefore, the fractions that are multiples of 1/9 are 4/9, 9/10, and 2/9.
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What is the vertical displacement of the basic graph to produce a graph of
y =pi-3 cos(x-2)?
Answers
The value of D represents the vertical displacement or shift of the basic cosine graph. Therefore, the vertical displacement of the given graph is pi - 3.
What is Displacement?
In physics, displacement refers to the distance and direction of an object's change in position from its starting point. It is a vector quantity that measures the overall change in position of an object, regardless of the path it took to get there. Displacement can be positive, negative, or zero depending on the direction and distance of the movement.
To find the vertical displacement of the basic graph to produce a graph of y = pi - 3 cos(x - 2), we need to compare the given equation with the general cosine function y = A cos(Bx - C) + D.
Here, A = 3, B = 1, C = 2, and D = pi - 3.
The value of D represents the vertical displacement or shift of the basic cosine graph. Therefore, the vertical displacement of the given graph is pi - 3.
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Consider the two-loop circuit shown below:
Ignore the red and pencil markings, just worry about the printed questions
Answers
Answer:
(I₁, I₂) = (1, 1)
Step-by-step explanation:
You want the matrix version of the given circuit equations, and the solution by matrix methods and by Cramer's rule.
15I₁ +5I₂ = 2025I₁ +5I₂ = 30(a) Matrix equationThe coefficients of the variables fill matrix A; the constants fill matrix (column vector) B:
AI = B
[tex]\left[\begin{array}{cc}15&5\\25&5\end{array}\right]\left[\begin{array}{c}I_1\\I_2\end{array}\right]=\left[\begin{array}{c}20\\30\end{array}\right][/tex]
(b) Matrix algebraThe solution to this matrix equation can be found by left-multiplying both sides by the inverse of matrix A. The inverse of a 2×2 matrix is the transpose of the cofactor matrix, divided by its determinant. It can be written down, as the form is simple: diagonal elements are swapped; off-diagonal elements are negated.
[tex]A^{-1}=\dfrac{1}{15(5)-25(5)}\left[\begin{array}{cc}5&-5\\-25&15\end{array}\right]=\left[\begin{array}{cc}-0.1&0.1\\0.5&-0.3\end{array}\right]\\\\\textsf{Multiplying by $A^{-1}$, we have ...}\\\\\left[\begin{array}{cc}-0.1&0.1\\0.5&-0.3\end{array}\right]\left[\begin{array}{cc}15&5\\25&5\end{array}\right]\left[\begin{array}{c}I_1\\I_2\end{array}\right]=\left[\begin{array}{cc}-0.1&0.1\\0.5&-0.3\end{array}\right]\left[\begin{array}{c}20\\30\end{array}\right][/tex]
[tex]\left[\begin{array}{cc}1&0\\0&1\end{array}\right]\left[\begin{array}{c}I_1\\I_2\end{array}\right]=\left[\begin{array}{c}(-0.1)(20+(0.1)(30)\\(0.5)(20)+(-0.3)(30)\end{array}\right]\\\\\\\left[\begin{array}{c}I_1\\I_2\end{array}\right]=\left[\begin{array}{c}1\\1\end{array}\right][/tex]
(c) Cramer's ruleCramer's rule requires we find three determinants. We already found the determinant of the coefficient matrix, above. It is D = -50. The other two are ...
[tex]D_1=\left|\begin{array}{cc}20&5\\30&5\end{array}\right|=(20)(5)-(30)(5)=-50\\\\\\D_2=\left|\begin{array}{cc}15&20\\25&30\end{array}\right|=(15)(30)-(25)(20)=-50\\\\\\I_1=\dfrac{D_1}{D}=\dfrac{-50}{-50}=1\qquad I_2=\dfrac{D_2}{D}=\dfrac{-50}{-50}=1\\\\\\\left[\begin{array}{c}I_1\\I_2\end{array}\right]=\left[\begin{array}{c}1\\1\end{array}\right][/tex]
if n = 4 then σ(4)=1+2+4=7 and H4 = 1+1/2+1/3+1/4. Solve this equation to either prove or disprove the following inequality n≥1? Does it hold for all n≥1?
Answers
Using the method of mathematical induction, we show that the inequality σ(n) > H(n) holds for all n≥1. Thus, the inequality n≥1 is true for all n≥1.
What is mathematical induction?It is a a technique used in mathematics to prove that a statement is true for every positive integer or natural number. It consists of two steps:
Base case: Prove that the statement is true for the first positive integer (usually 1).Inductive step: Assume that the statement is true for some arbitrary positive integer k, and then prove that it must also be true for the next positive integer (k+1).We can calculate like this:
Base case: Show that the inequality holds for n=1.
When n=1, we have σ(1) = 1 and H1 = 1, so the inequality 1 ≤ 2^(σ(1)/H1) becomes 1 ≤ 2^(1/1), which is true.Inductive hypothesis: Assume that the inequality holds for some arbitrary positive integer k, i.e., k ≤ 2^(σ(k)/Hk).
Inductive step: Show that the inequality also holds for k+1. Consider σ(k+1) and H(k+1). We can express them as σ(k+1) = σ(k) + k+1 and H(k+1) = H(k) + 1/(k+1).
Using the inductive hypothesis, we have:
k ≤ 2^(σ(k)/Hk),So, we can raise both sides to the power of (k+1)/(kH(k+1)) to get:
k^(1/(kH(k+1))) ≤ 2^((k+1)/(kH(k+1)) * σ(k)/Hk).By the AM-GM inequality, we know that σ(k+1)/k+1 ≥ H(k+1), so we can replace the denominator (kH(k+1)) with H(k+1) and simplify to get
k^(1/H(k+1)) ≤ 2^(σ(k+1)/H(k+1)).Therefore, we have shown that k+1 ≤ 2^(σ(k+1)/H(k+1)), which means the inequality holds for all positive integers n by mathematical induction.
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Can someone please help me?
Answers
Answer:i think it is c
Step-by-step explanation:
I need help with questions 1,2, and 3. This class is microeconomics
Answers
Graph cookies and coffee, slope -2. Ben buys 2 cookies and 2 coffees. To optimize, allocate budget where MU per dollar is equal.
What is budget?A budget is a financial plan that outlines expected income and expenses over a certain period. It helps individuals or organizations manage their money and make informed decisions about spending and saving.
What is consumption?Consumption refers to the use of goods and services by individuals, households, or organizations. It is an essential part of the economy and can be influenced by factors such as income, preferences, and prices.
According to the given information:
To draw Ben's indifference curves, we need to plot different combinations of cookies and coffee that give Ben the same level of satisfaction. Since the slope of all his indifference curves is constant at -2, they will be downward-sloping straight lines. We can plot several indifference curves by varying the level of satisfaction they represent. The budget constraint is a straight line that represents all possible combinations of cookies and coffee that Ben can purchase with his $12 budget. The slope of the budget constraint is the ratio of the prices of coffee and cookies, which is 2:1. Ben optimally purchases the point where his budget constraint is tangent to his highest attainable indifference curve. In other words, he maximizes his satisfaction subject to his budget constraint. In the graph above, this point is labeled as "Optimal Consumption." At this point, Ben purchases 2 cookies and 2 coffees, spending $8 on coffee and $4 on cookies, which exhausts his $12 budget.To optimize his consumption, Ben should allocate his budget between cookies and coffee such that the ratio of their marginal utilities equals their prices. In other words, Ben should choose the combination of cookies and coffee where the marginal utility per dollar spent is the same for both goods. At his current consumption level of 3 coffees and 0 cookies, Ben's marginal utility per dollar spent on cookies is 2/2 = 1, and his marginal utility per dollar spent on coffee is 1/4 = 0.25. Since the marginal utility per dollar spent on cookies is higher than that of coffee, Ben should decrease his consumption of coffee and increase his consumption of cookies to achieve the optimal consumption level. He should continue adjusting his consumption until the marginal utility per dollar spent on each good is equal.To know more about budget and consumption visit:
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the table shows the favirote film of 20 people complete the pie chart
Answers
The complete table for the pie chart is;
Type of Film Frequency Angle in °
Action 4 72°
Horror 11 198
Comedy 5 90
How to interpret Pie chart?From the given table used to form the pie chart, we see that;
Type of Film Frequency Angle in °
Action 4 72°
Horror 11
Comedy 5
We know that the angles in a circle is equal to 360 degrees. Thus;
Angle composed of horror and comedy = 360 - 72 = 288°
Thus;
Angle for horror film = (11/(4 + 11 + 5)) * 360°
= (11/20) * 360°
= 198°
Thus;
Angle for comedy = 288° - 198° = 90°
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a) Use your calculator to solve sin x = 0.79 for 0° ≤ x ≤ 90°
b) Use the graph below to solve sin x = 0.79 for 90° ≤ x ≤ 180°
Give your answer to the nearest degree
Answers
Answer:
(a) 52°
(b) 128°
Step-by-step explanation:
You want the angle whose sine is 0.79 (a) in the interval [0, 90°], and (b) in the interval [90°, 180°].
a) Inverse sineThe inverse sine function is used to find the angle when its sine is known.
sin(x) = 0.79
x = arcsin(0.79) ≈ 52°
x ≈ 52° in the domain 0 ≤ x ≤ 90°.
b) Other valuesThe sine function is symmetrical about x = 90°, so other angles for which sin(x) = 0.79 can be found as 180° -x.
180° -52° = 128°
x = 128° in the domain 90° ≤ x ≤ 180°.
__
Additional comment
The attachment shows the angles and that their sine is 0.79. Note that the calculator is set to Degrees mode.
<95141404393>
PLEASEE HELP ITS URGENT
Answers
The ratio of the areas is given as follows:
1:5.8.
How to obtain the ratio of the areas?The ratio of the areas is obtained applying the proportions in the context of the problem.
When a prism is dilated by a scale factor of k, we have that:
The ratio of the perimeters is k, as both the side lengths and the perimeter are measured in units.The ratio of the areas is k², as the side lengths are measured in units, while the areas are in units squared.The ratio of the volumes is k³, as the side lengths are measured in units, while the volumes are in units cubed.Hence the ratio of the areas is the cubic root of the ratio of the volumes squared, thus, as the ratio of the volumes is of 1:14, we have that:
(14²)^(1/3) = 5.8.
Hence:
1:5.8.
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In a large population of students, 60% feel like they can do better in their math class. In a random sample of 5 students, what is the probability that at least 2 students feel like they can do better in their math class?
0.0870
0.2304
0.3174
0.6826
0.9130
Answers
The probability that at least 2 students feel like they can do better in their math class is E. 0.9130.
How to calculate the probabilityTo find the probability that at least 2 students feel like they can do better, we need to calculate P(X >= 2). This can be done using the cumulative distribution function (CDF) of the binomial distribution:
P(X >= 2) = 1 - P(X < 2) = 1 - P(X = 0) - P(X = 1)
Using the binomial probability formula, we can calculate:
P(X = 0) = (5 choose 0) * 0.6^0 * 0.4^5 = 0.01024
P(X = 1) = (5 choose 1) * 0.6^1 * 0.4^4 = 0.07680
Therefore,
P(X >= 2) = 1 - 0.01024 - 0.07680 = 0.91296
Rounding this to four decimal places, we get: 0.9130
Therefore, the answer is option E: 0.9130.
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find the surface area of the figure
Answers
Answer:
The answer for Surface area is 332m²
Step-by-step explanation:
S.A=area of 2 triangle +Area of 2 rectangle +Area of rectangle
S.A=2×1/2×4×3 + 2(20×5) + 20×6
S.A=12+2(100)+120
S.A=12+200+120
S.A=212+120
S.A=332m²
Use the given information to find a formula for the exponential function N = N(t). (Round the values to three decimal places.)
The initial value of N is 14. If t is increased by 6, the effect is to multiply N by 59.
Answers
the formula for the exponential function N(t) is N(t) = 14 * 59in power (t/6), where N is the population at time t and t is the time in hours, days, or any other unit of time as long as it is consistent with the time unit used in the formula
How to solve the question?
Let N(t) be the exponential function we are trying to find, where N is the population at time t.
From the given information, we know that when t=0, N(0) = 14, which is the initial value of N.
We also know that when t is increased by 6, N is multiplied by 59. In other words,
N(t+6) = 59N(t)
We can use this relationship to express N(t+6) in terms of N(t) by substituting N(t+6) with 59N(t) in the above equation, giving us:
59N(t) = N(t+6)
Now, we can use this equation to solve for N(t) in terms of N(0) by repeatedly substituting N(t) with 59N(t-6), 59²N(t-12), 59³N(t-18), and so on.
N(t) = 59 in power (t/6) * N(0)
Using the initial value of N(0) = 14, we get:
N(t) = 14 * 59 in power (t/6)
Therefore, the formula for the exponential function N(t) is N(t) = 14 * 59^(t/6), where N is the population at time t and t is the time in hours, days, or any other unit of time as long as it is consistent with the time unit used in the formula
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NO LINKS!!! URGENT HELP PLEASE!!!!
Express the statement as an inequality. Part (2a^2)
d. c is between 1/7 and 1/5
1. 1/5 ≥ c ≥ 1/7
2. 1/7 < 1/5 < c
3. c < 1/7 < 1/5
4. 1/7 < c < 1/5
5. 1/7 ≤ c ≤ 1/5
e. p is not greater than -6
1. p ≤ -6
2. p < -6
3. p ≥ -6
4. p > -6
5. p = -6
f. The negative of m is not less than -2
1. m ≤ -2
2. m < 2
3. -m < -2
4. m < -2
5. -m ≥ -2
Answers
Answer:d. The inequality that represents "c is between 1/7 and 1/5" is:
1/7 ≤ c ≤ 1/5
e. The inequality that represents "p is not greater than -6" is:
p ≤ -6
f. The inequality that represents "the negative of m is not less than -2" is:
-m ≥ -2
Note that we need to flip the inequality when we multiply or divide both sides by a negative number, which is the case in part (f).
Step-by-step explanation:
the answer to e is 1
the answer to f is 5
Jake and his friends
are bowling. The area of
the rectangular lane is 14x2-x-3
square feet. If the width of the lane is
2x -1 feet, write an expression to
represent the length of the lane.
SOLUTION:
Answers
Answer:
L = (14x^2 - x - 3) / (2x - 1)
Step-by-step explanation:
The area of the rectangular lane is given as 14x^2 - x - 3 square feet.
Let's assume that the length of the lane is L feet. Then the formula for the area of a rectangle is:
Area = Length x Width
Substituting the values given in the question, we have:
14x^2 - x - 3 = L x (2x - 1)
To find an expression for the length of the lane, we can rearrange the equation to solve for L:
L = (14x^2 - x - 3) / (2x - 1)
Therefore, the expression that represents the length of the lane is:
L = (14x^2 - x - 3) / (2x - 1)
Un problema de derivadas de la vida cotidiana utilizando la siguiente función:
f(x)= 2x^3-3x^2-12x+1
Answers
Suppose you are driving a car with the velocity function represented by the following equation: f(x)= 2x^3-3x^2-12x+1. The derivative would be: f'(x) = 6x^2 - 6x - 12
How can we use the derivative of a function to analyze a car's motion?To find the acceleration of the car at a particular moment, we would need to calculate the derivative of the velocity function f(x). In this case, the derivative would be:
f'(x) = 6x^2 - 6x - 12
The result of this calculation would give us the instantaneous acceleration of the car at a given time x.
In terms of the car's motion, a positive value for f'(x) would indicate that the car is accelerating, while a negative value would indicate that the car is decelerating. The magnitude of the value would indicate the rate of change of the car's velocity, with larger values indicating a more rapid change.
Translated question "A derivative problem from everyday life using the following function: f(x)= 2x^3-3x^2-12x+1"
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A 3 scoops ice-cream cone cost 4.80. A single Scoop ice-cream cost $2. Which one cost less for each scoop of ice cream ? How much less?
Answers
A single scoop is $0.40 cheaper per scoop than a scoop in a 3-scoop cone.
To compare the cost of each scoop of ice cream in a 3-scoop cone and a single scoop, we need to calculate the cost per scoop for each option.
In a 3-scoop cone, the cost of each scoop can be found by dividing the total cost by the number of scoops. Therefore, the cost of each scoop in a 3-scoop cone is:
4.80 ÷ 3 = 1.60
On the other hand, a single scoop of ice cream costs $2. Therefore, the cost of each scoop in a single scoop is:
2 ÷ 1 = 2
Comparing the two options, we can see that a single scoop of ice cream costs less per scoop than a 3-scoop cone. Specifically, a single scoop is $0.40 cheaper per scoop than a scoop in a 3-scoop cone.
Therefore, choosing a single scoop of ice cream over a 3-scoop cone will result in a cost savings of $0.40 per scoop.
In conclusion, when comparing the cost per scoop of ice cream, a single scoop is cheaper than a scoop in a 3-scoop cone. The cost savings per scoop is $0.40.
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The equity sections for Atticus Group at the beginning of the year (January 1) and end of the year (December 31) follow.
Answers
2. The total dollar amount for each cash dividend is $23,700.
Outstanding common shares, dividend and capitalization1. Calculation of outstanding common shares on each cash dividend date:
January 5: No change in outstanding shares since the date of record is January 10, which is after December 31, 2017. Therefore, the outstanding shares are 47,400 (47,400 issued - 3,000 treasury shares = 44,400 outstanding).April 5: No change in outstanding shares since the date of record is April 10, which is after December 31, 2017. Therefore, the outstanding shares are 47,400.July 5: No change in outstanding shares since the date of record is July 10, which is after December 31, 2017. Therefore, the outstanding shares are 47,400.October 5: No change in outstanding shares since the date of record is October 10, which is after December 31, 2017. Therefore, the outstanding shares are 47,400.2.
Calculation of total dollar amount for each cash dividend:
January 5: $0.50 per share x 47,400 outstanding shares = $23,700April 5: $0.50 per share x 47,400 outstanding shares = $23,700July 5: $0.50 per share x 47,400 outstanding shares = $23,700October 5: $0.50 per share x 47,400 outstanding shares = $23,700Therefore, the total dollar amount for each cash dividend is $23,700.
3.
Calculation of the capitalization of retained earnings for the stock dividend:
Market value per share on July 31: $12Number of outstanding shares before stock dividend: 47,400Number of shares to be issued for the stock dividend: 20% x 47,400 = 9,480Total value of shares to be issued for the stock dividend: 9,480 shares x $12 per share = $113,760The capitalization of retained earnings for the stock dividend is equal to the total value of shares issued, which is $113,760.Learn more on dividends here https://brainly.com/question/2960815
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The equity sections from Atticus Group’s 2016 and 2017 year-end balance sheets follow Stockholders’ Equity (December 31, 2016)
Common stock—$4 par value, 100,000 shares
authorized, 40,000 shares issued and outstanding . .. . . . . . . . . . $160,000
Paid-in capital in excess of par value, common stock .. . . . . . . . . . . . . . . . 120,000
Retained earnings .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 320,000
Total stockholders’ equity .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . $600,000
Stockholders’ Equity (December 31, 2017)
Common stock—$4 par value, 100,000 shares
authorized, 47,400 shares issued, 3,000 shares in treasury . .. . . . . . . $189,600
Paid-in capital in excess of par value, common stock . . . . . .. . . . . . . . . . . . 179,200
Retained earnings ($30,000 restricted by treasury stock) .. . . . . . . . . . . . . 400,000
768,800
Less cost of treasury stock . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (30,000)
Total stockholders’ equity . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . $738,800
The following transactions and events affected its equity during year 2017.
Jan. 5 Declared a $0.50 per share cash dividend, date of record January 10.
Mar. 20 Purchased treasury stock for cash.
Apr. 5 Declared a $0.50 per share cash dividend, date of record April 10.
July 5 Declared a $0.50 per share cash dividend, date of record July 10.
July 31 Declared a 20% stock dividend when the stock’s market value was $12 per share.
Aug. 14 Issued the stock dividend that was declared on July 31.
Oct. 5 Declared a $0.50 per share cash dividend, date of record October 10.
Required
1. How many common shares are outstanding on each cash dividend date?
2. What is the total dollar amount for each of the four cash dividends?
3. What is the amount of the capitalization of retained earnings for the stock dividend?
Martin made a stick pattern such that each successive stick is twice as long as the one before it. If the shortest stick in the pattern is long, and there are sticks in total, which is closest to the combined length of the sticks in Martin's pattern?
Answers
S_n = a(1 - r^n) / (1 - r)
In this case, we have n sticks in total, so we need to calculate S_n with n:
S_n = a(1 - 2^n) / (1 - 2)
S_n = a(2^n - 1)
Therefore, the combined length of the sticks in Martin's pattern is closest to (2^n - 1) multiplied by the length of the shortest stick.
. How much you have to deposit in an account earning 8 percent compound monthly to pay a retired officer $1000 monthly for 12 years.
Answers
FV = PMT * [(1 + r/n)^(n*t) - 1]/(r/n)
where FV is the future value of the annuity, PMT is the payment amount, r is the annual interest rate (as a decimal), n is the number of compounding periods per year, and t is the number of years.
In this case, we have:
PMT = $1000 per month
r = 0.08 (8% annual interest rate)
n = 12 (compounded monthly)
t = 12 years
We need to solve for the future value, which represents the total amount of money that needs to be deposited to generate the $1000 monthly payment for 12 years. Plugging in the numbers, we get:
FV = $1000 * [(1 + 0.08/12)^(12*12) - 1]/(0.08/12) ≈ $149,139.77
Therefore, the retired officer would need to deposit approximately $149,139.77 in an account earning 8 percent compound monthly to pay a $1000 monthly payment for 12 years.
find the truth set of *-1/2 《 5/2 + 2
Answers
The truth set of the inequality is all values of x greater than -9. In interval notation, this can be written as (-9, ∞)
How to Solve the Inequality?Multiply both sides by -2 (and reversing the direction of the inequality because we are multiplying by a negative number) gives:
x > -2*(5/2 + 2)
x > -5 - 4
x > -9
Therefore, the truth set of the inequality is all values of x greater than -9. In interval notation, this can be written as:
(-9, ∞)
Below is the complete question:
Find the truth set of x*(-1/2) < 5/2 + 2
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answer ASAP pls with as as much detail in how to complete it as possible :))
in general, if you have the ratio of the volume of two figures how do you find the ratio of their edge lengths? And does how to do this differ between shapes (if so could you explain for triangles pls?)
Answers
To find the ratio of edge lengths of two triangles given their area ratio, we need to take the square root of the area ratio.
Finding the volumeTo find the ratio of edge lengths of two figures given their volume ratio, you need to use the fact that volume is proportional to the cube of the edge length.
If we have two figures, Figure A and Figure B, with edge lengths a and b respectively, and their volumes are in the ratio of V(A) : V(B) = k, then we can set up the following equation:
(Volume of A) / (Volume of B) = (a^3) / (b^3) = k
We can then solve for the ratio of edge lengths:
a / b = (k)^(1/3)
Therefore, to find the ratio of edge lengths given the volume ratio, we need to take the cube root of the volume ratio.
This method works for any shape, as long as the volume formula for that shape involves the cube of the edge length. For example, this method works for cubes, rectangular prisms, cylinders, spheres, and so on.
For triangles, however, we cannot use this method directly because the volume of a triangle is not a function of its edge length. Instead, we can use similar triangles to find the ratio of their edge lengths.
If we have two similar triangles, with corresponding sides in the ratio of a : b, then their areas are in the ratio of (a^2) : (b^2). We can use this fact to find the ratio of their edge lengths:
a / b = sqrt(Area of first triangle / Area of second triangle)
So, to find the ratio of edge lengths of two triangles given their area ratio, we need to take the square root of the area ratio.
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Lighthouse B is 9 miles west of lighthouse A. A boat leaves A and sails 4 miles. At this time, it is sighted from B. If the bearing of the boat from B is N65degreesE, how far from B is the boat? Round to the nearest tenth
(Note: Needs 2 Answers)
PLEASE HELP I'M GOING INSANE
*please include work/formulas for every step when needed*
Answers
Boat is 4.195 miles or 6.749755 km far from the lighthouse B.
How to find the distance?The boat has moved 4 kilometers from point A to point x. The distance between B and x is what we're looking for.
Trigonometry can be used to overcome this issue. Let's abbreviate the distance "d" from A to x. Then, we can apply the following formula:
tan(65°) = (9 / d)
We can rearrange this formula to solve for d:
d = 9 / tan(65°)
We find that:
tan(65°) = 2.1445
So, d = 9 / 2.1445
= 4.195 miles (rounded to the nearest tenth)
or 6.749755 km.
Hence, Boat is 4.195 miles or 6.749755 km far from the lighthouse B.
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Operations with Fractions
Solve for x.
2/5+x=1
Answers
Answer:
Hello... im exhausted but ill solve it i guess
To solve for x in the equation 2/5 + x = 1, we can follow these steps:
Subtract 2/5 from both sides of the equation to isolate the x term:
2/5 + x - 2/5 = 1 - 2/5
This simplifies to:
x = 1 - 2/5
Find a common denominator for 1 and 2/5, which is 5:
x = 5/5 - 2/5
Subtract 2/5 from 5/5:
x = 3/5
So, the solution for x in the given equation is x = 3/5.
Use the power-reducing formulas to rewrite the expression in terms of first powers of the cosines of multiple angles.
sin^8(x)
Answers
The answer for the given expression is =1/128[35-56cos2x+28cos4x-8cos6x+cos8x]
What is trignomatric functions?
All trigonometric identities are built upon the foundation of the six trigonometric ratios. Some of their names are sine, cosine, tangent, cosecant, secant, and cotangent. The adjacent side, opposite side, and hypotenuse side of the right triangle are used to define each of these trigonometric ratios.
What is multiple angles?
If angle A is taken as a given, then many angles are 2A, 3A, 4A, etc. The many angle formulas employ the double and triple angles formulas. Sine, cosine, and tangent are the often utilised trigonometric functions for the multiple angle formula.
Answer is attached as a image must check:
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We can rewrite sin⁸x in terms of first powers of the cosines of multiple angles as:
sin⁸x = 1/128 (35 - 4cos²x + 40cos⁴x - 64cos⁶x + cos⁸x)
What is power reducing formula?Trigonometric functions raised to powers can be rewritten using double-angle, half-angle, and Pythagorean identities in power lowering formulas. Equations can be made simpler using them, and trigonometric expressions can be precisely determined.
We can use the power-reducing formulas to rewrite sin⁸x in terms of cosines of multiple angles as follows:
sin²x = 1 - cos²x (first power-reducing formula)
sin⁴x = (sin²x)² = (1 - cos²x)²
= 1 - 2cos²x + cos⁴x (second power-reducing formula)
sin⁶x = (sin⁴x)(sin²x)
= (1 - 2cos²x + cos⁴x)(1 - cos²x)
= 1 - 3cos²x + 3cos⁴x - cos⁶x (third power-reducing formula)
sin⁸x = (sin⁶x)(sin²x)
= (1 - 3cos²x + 3cos⁴x - cos⁶x)(1 - cos²x)
= 1 - 4cos²x + 6cos⁴x - 4cos⁶x + cos⁸x
Now we can substitute the expression for sin⁸x into the given expression and simplify it:
1/128 (35 - 56 cos2x + 28 cos4x - 8 cos6x + cos8x)
= 1/128 (35 - 56(2cos²x-1) + 28(4cos⁴x-3cos²x) - 8(8cos⁶x-8cos⁴x+cos²x) + cos⁸x)
= 1/128 (35 - 112cos²x + 56 + 112cos⁴x - 84cos²x - 64cos⁶x + 64cos⁴x - 8cos²x + cos⁸x)
= 1/128 (35 - 4cos²x + 40cos⁴x - 64cos⁶x + cos⁸x)
Therefore, we can rewrite sin⁸x in terms of first powers of the cosines of multiple angles as:
sin⁸x = 1 - 4cos²x + 6cos⁴x - 4cos⁶x + cos⁸x
= 1/128 (35 - 4cos²x + 40cos⁴x - 64cos⁶x + cos⁸x)
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