a) We can reject the null hypothesis and cthat theronclude is significant evidence that the probability of Kerrich's coin coming up heads is not 0.5. b) we get a confidence interval of 0.495 to 0.517.
a) To test the hypothesis that the probability of Kerrich's coin coming up heads is not 0.5, we can use a one-sample proportion test at the 5% level of significance. The null hypothesis is that the true proportion of heads is 0.5, and the alternative hypothesis is that it is not equal to 0.5.
The test statistic can be calculated as (5067-0.510000)/(sqrt(100000.5*0.5)) which simplifies to 5.401. The corresponding P-value can be found using a standard normal distribution table or a calculator to be approximately 3.3x10^-8, which is much smaller than 0.05. Therefore, we can reject the null hypothesis .
b) To construct a 95% confidence interval for the true proportion of heads, we can use the formula p ± z*sqrt((p(1-p))/n), where p is the sample proportion, z is the z-score corresponding to a 95% confidence level (which is 1.96), and n is the sample size. Substituting the values, we get a confidence interval of 0.495 to 0.517, which means that we can be 95% confident that the true proportion of heads falls within this range.
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\( \: \: \: \: \)
hi pls someone help me
\({ \tt{write \: \: the \: \: equation \: \: of \: \: variation \: \: and \: \: solve \: \: for \: \: the \: \: constant \: \: of \: \: variation \: \: }}\)
Answer:
q = 7p²q = 48/pq = 48/p . . . same table as 2q = 1/3pStep-by-step explanation:
When faced with identifying sequences or forms of variation, the usual ones we look for are ...
directly proportional (y = kx)inversely proportional (y = k/x)proportional to the square (y = kx²)related by some polynomial function (y = ax³ +bx² +cx +d)exponential (y = a·b^x)Proportional relations will have a constant ratio between y and x. That ratio is the value of k.
Inversely proportional relations will have a constant product of x and y. That product is the value of k.
Relations that are proportional to a square will have ratios of adjacent terms that are ratios of square numbers. (It is helpful to be familiar with the first few square numbers, at least.)
Exponential relations will have a constant ratio between terms, the value of b.
Polynomial relations will have constant n-th differences when the polynomial is of degree n. (First differences of a linear sequence are constant. Second differences of a "proportional to square" sequence are constant.)
In these tables, we assume q is the output and p is the input. The constant in each equation is the "constant of variation."
__
1.Ratios of q-values are 28/7 = 4, 63/28 = 9/4, 112/63 = 16/9. These are ratios of consecutive squares. The constant of variation is the multiplier of 1² that results in the first term: 7
q = 7p²
__
2, 3.The products of table values are pq = 48. The equation is ...
q = 48/p
__
4.Ratios q/p are all the same, 2/6 = 4/12 = ... = 1/3. This is the constant of proportionality:
q = 1/3p
\( \large \gray{ \boxed{ { \colorbox{black}{answer}}}}\)
1.)\( \tt \: q = 7 \times {p}^{2} \)
for the given values of p,q the equation of variation is q=7×p²for constant of variation is 72.variation
p = 48/q
constant
48
3.)variation
p= 48/q
constant
48
4.)variation
q=kp
constant
k=⅓
hope it helps
Find the midpoint of the segment with the following endpoints. (6, 4) and (9,9)
Answer:
15/2, 13/2.
Step-by-step explanation:
Here's a graph as well.
Answer in fraction form = (15/2, 13/2)
Answer in decimal form = (7.5, 6.5)
========================================================
Explanation:
To get the midpoint, we average the two endpoint values. We handle the x and y coordinates separately.
The x coordinates of each point are 6 and 9. They average to (6+9)/2 = 15/2 = 7.5; so you add up the x coordinates and divide by 2.
The y coordinates are handled the same way. Add them to get 4+9 = 13 and then divide by 2 to get 13/2 = 6.5
The midpoint is (15/2, 13/2) = (7.5, 6.5)
Show that δ(x^2-a^2)=1/2a[δ(x-a)+ δ(x+a)]
δ(c0sθ- cosθ)= δ(θ-θ’)/sin θ’= δ (θ- θ’)/ sin θ
By using Dirac delta function, δ(c0sθ- cosθ)= δ(θ-θ’)/sin θ’= δ (θ- θ’)/ sin θ.
Here's how to show that δ(x^2-a^2)=1/2a[δ(x-a)+ δ(x+a)]
To show that δ(x^2-a^2)=1/2a[δ(x-a)+ δ(x+a)],
we can use the definition of Dirac delta function.
Dirac delta function is defined as follows:∫δ(x)dx=1and 0 if x≠0
In order to solve the given expression, we have to take the integral of both sides from negative infinity to infinity, which is given below:∫δ(x^2-a^2)dx=∫1/2a[δ(x-a)+ δ(x+a)]dx
To compute the left-hand side, we use a substitution u=x^2-a^2 du=2xdxWhen x=-a, u=a^2-a^2=0 and when x=a, u=a^2-a^2=0.
Therefore,-∞∫∞δ(x^2-a^2)dx=-∞∫∞δ(u)1/2adx=1/2a
Similarly, the right-hand side becomes:∫1/2a[δ(x-a)+ δ(x+a)]dx=1/2a∫δ(x-a)dx +1/2a∫δ(x+a)dx=1/2a + 1/2a=1/2a
Therefore,∫δ(x^2-a^2)dx=∫1/2a[δ(x-a)+ δ(x+a)]dxHence, δ(x^2-a^2)=1/2a[δ(x-a)+ δ(x+a)].
Next, we can show that δ(c0sθ- cosθ)= δ(θ-θ’)/sin θ’= δ (θ- θ’)/ sin θ as follows:We know that cosθ = cosθ' which implies θ=θ'+2nπ or θ=-θ'-2nπ.
Therefore, c0sθ-cosθ'=c0s(θ'-2nπ)-cosθ'=c0sθ'-cosθ' = sinθ'c0sθ-sinθ'cosθ'.
We can use the following identity to simplify the above expression:c0sA-B= c0sAcosB-sinAsinB
Therefore,c0sθ-cosθ' =sinθ'c0sθ-sinθ'cosθ'=sinθ'[c0sθ-sinθ'cosθ']/sinθ' =δ(θ-θ')/sinθ'
Hence,δ(c0sθ- cosθ)= δ(θ-θ’)/sin θ’= δ (θ- θ’)/ sin θ.
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Express 18 as a product of its factors?
Answer:
18= 2 x 3 x 3
Step-by-step explanation:
Basically, we branch out 18 into its prime factors. So, the prime factorization of 18 is 18= 2 × 3 × 3. A factor tree is not unique for a given number. Instead of expressing 18 as 2 × 9, we can express 18 as 3 × 6.
Two less than three times a number is the same as six more than twice the number. Write an equation and solve to find the number.
Answer: 8
Step-by-step explanation:
Let the number be represented by x.
Two less than three times a number is the same as six more than twice the number. This will be:
(3 × x) - 2 = (2 × x) + 6
3x - 2 = 2x + 6
Collect like terms.
3x - 2x = 6 + 2
x = 8.
The number is 8
Steve earn $15 and spent 2/3 of it how much did he spend
Steve spent 2/3 of $15, to find how much this 2/3 of $15 is, we have to multiply $15 by 2/3, as follows:
\(15\times\text{ }\frac{2}{3}=\frac{15\times2}{3}=\frac{30}{3}=10\)Therefore, we have found that Steve already spent $10 .
you are standing 80sqaure root 3 feet away from a building that is 80 feet tall and looking at the top of the building. what is the angle of elevation from the ground
Therefore, the angle of elevation from the ground to the top of the building is approximately 30 degrees.
To find the angle of elevation from the ground to the top of the building, we can use the tangent function. The tangent of an angle is defined as the ratio of the opposite side to the adjacent side in a right triangle.
In this case, the opposite side is the height of the building (80 feet), and the adjacent side is the distance between you and the building (80√3 feet).
The formula to find the angle of elevation (θ) is:
θ \(= tan^{(-1)}(opposite/adjacent)\)
Substituting the values:
\(θ = tan^{(-1)}(80/80√3)\)
Simplifying the equation:
θ = \(tan^{(-1)}(1/√3)\)
Now, we can calculate the value of θ using a calculator or trigonometric table. Taking the inverse tangent \((tan^{(-1)})\) of 1/√3, we find:
θ ≈ 30 degrees
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6. B, D, and F are the midpoints of each side, and G is the centroid. Find the following lengths.
(1) Given CD=2x-1, and CE-6, find x.
(3) AAFC-12 cm², find the area of ABCE
(2) AG=9x, GD=5x-1, find x and AD.
(4) AAGC-8 cm², find the area of AEGD
7 (1) Find the coordinates of the endpoints of goch midceomant
ADG
Area(AEGD) = 3 * Area(AAGC)
Area(AEGD) = 3 * 8
Area(AEGD) = 24 cm²
(1) Given CD = 2x - 1 and CE = 6, we can set up an equation based on the fact that F is the midpoint of DE:
2(2x - 1) = 6
4x - 2 = 6
4x = 8
x = 2
Therefore, x = 2.
(2) Given AG = 9x and GD = 5x - 1, we can use the fact that G is the centroid to set up an equation:
AG = 2GD
9x = 2(5x - 1)
9x = 10x - 2
x = 2
Therefore, x = 2.
To find AD, we substitute x = 2 into AG:
AD = AG - GD
AD = 9(2) - (5(2) - 1)
AD = 18 - 9
AD = 9
(3) Given that AAFC = 12 cm², we can find the area of ABCE. Since B and D are midpoints, we know that AB = 2CD and AD = 2GD.
AB = 2(2x - 1) = 4x - 2
AD = 2(5x - 1) = 10x - 2
The area of ABCE is the sum of the areas of the triangles ACF and ABE:
Area(ABCE) = Area(ACF) + Area(ABE)
Area(ACF) = 1/2 * AB * CF = 1/2 * (4x - 2) * (6 - CF)
Area(ABE) = 1/2 * AB * BE = 1/2 * (4x - 2) * (CF - 2)
Given that AAFC = 12 cm², we can set up an equation:
12 = 1/2 * (4x - 2) * (6 - CF)
Solving this equation will yield the value of CF. Substituting that value back into the equation for Area(ACF) and Area(ABE) will give the area of ABCE.
(4) Given that AAGC = 8 cm², we can find the area of AEGD. Since G is the centroid, we know that the area of AEGD is three times the area of AAGC.
Area(AEGD) = 3 * Area(AAGC)
Area(AEGD) = 3 * 8
Area(AEGD) = 24 cm²
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Two trees cast shadows on the ground as shown. The smaller tree is 17m high and cast a 10m long shadow.
The faller tree casts a 10m long shadow. What is the height of the taller tree?
HELP ME WITH THIS PLEASE
Answer:
2.8
Step-by-step explanation:
this is my best guess
The table shows the approximate lengths, in miles, of some rivers in the United States.
Use the information to answer each part. Round your answers to the nearest tenth.
a.) About how many times as great as the length of the Colorado River is the Mississippi River?
times greater than the Colorado River
b.) About how many times as great as the length of Colorado River is the Rio Grande?
times greater than the Colorado River
c.) About how many times as great as the length of the Rio Grande River is the Mississippi River?
times greater than the Rio Grande River
The length of the Mississippi River is 4.26 times as great as the length of Colorado River
The length of Rio Grande is 2.87 times as large as the length of the Colorado River
The length of the Mississippi River is 1.48 times as large as the Rio Grande River
In order to determine how much greater the length of a river is greater than that of another river, divide the length of longer river by the shorter river
a. Length of the Mississippi River / length of Colorado River
3.93 x 10³ ÷ 9.23 × 10² = 4.26 times
b. Length of the Rio Grande / length of Colorado River
2.65 x 10³ ÷ 9.23 × 10² = 2.87 times
c. . Length of the Mississippi River / length of the Rio Grande
3.93 x 10³ ÷ 2.65 x 10³ = 1.48 times
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If an 80 confidence interval and a 90 confidence interval are constructed from the same sample data, the 80 confidence interval will be___________________ the 90 confidence interval.
The 80% confidence interval will be narrower than the 90% confidence interval when constructed from the same sample data.
If an 80% confidence interval and a 90% confidence interval are constructed from the same sample data, the 80% confidence interval will be narrower than the 90% confidence interval.
To understand why this is the case, we need to know that a confidence interval is a range of values within which we estimate the true population parameter lies. The level of confidence associated with the interval represents the probability that the true parameter falls within that range.
In this scenario, an 80% confidence interval means that there is an 80% probability that the true parameter lies within the interval. On the other hand, a 90% confidence interval means that there is a 90% probability that the true parameter falls within the interval.
To construct a narrower interval, we need to have a higher level of confidence. As the confidence level increases, the range of possible values also widens to accommodate the higher probability. Therefore, the 80% confidence interval will be narrower than the 90% confidence interval.
In conclusion, the 80% confidence interval will be narrower than the 90% confidence interval when constructed from the same sample data.
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5. From Mario's house to school, you can walk in a straight line. In the afternoon he has to stop twice on
his way home. His first stop is the gas station that is exactly halfway between the school and his
house. The second stop will be a fast-food restaurant to get something to eat. The fast-food
restaurant's location partitions the way from the school to Mario's house in the ratio 3.1. The
coordinate of his house are (-3, -4) and the school coordinates are (5,0).
a) Find the coordinate of the gas station.
b) What is the ratio where the gas station partitions the path school to home?
c) Find the coordinate of the fast-food restaurant.
Answer:
a) the coordinates of the gas station are (1, -2)
b) 1 : 2 ratio, since the gas station is exactly at the middle.
c) the coordinates of the fast food restaurant are (3, -1)
On the attached graph, you will find Mario's house and school, plus the gas station and fast food restaurant.
Exponent question. image attached
Step-by-step explanation:
Find a common power for them all, then divide and get your answer
-1/2 = 3/8y
y = ______________
Answer:
y=-4/3
Step-by-step explanation:
i hope this helps
oint c is the center of the circle above. what fraction of the area of the circle is the area of the shaded regio
Fraction of the area of the circle is the area of the shaded region is 5/18.
From the figure:
The shaded region has angle = 100
In the circle the total angle is 360.
Fraction = 100/360
= 50/180
= 25/90
= 5/18
Therefore fraction of the area of the circle is the area of the shaded region is 5/18.
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I JUST NEED A SENTENCE OR TWO OF EXPLAINATION.
Answer: No, your friend is not correct. If the problem was addition, then yes it would equal the same answer, but with subtraction, the answers will be different.
Step-by-step explanation:
to bake a cake , raffy needs 3 cups of sugar for 5 cups of flour. if he uses 35 cups of flour, how much sugar doe he need and how many cakes will he bake
Answer: 21 cups of sugar, 7 cakes
Solve the following proportion:
3/5=x/35
Cross multiply:
5x=35(3)
5x=105
x=21 cups of sugar
3 cups of sugar= 1 cake
21 cups of sugar= x cakes
Cross multiply:
3x=21
21/3
7 cakes
need help w this question thanksss!
Given:
A figure of a circle.
To find:
The value of x.
Solution:
Central angle theorem: According to this theorem, the central angle on an arc is twice of the subtended angle on that arc.
Using the central angle theorem, we get
\(x=2\times 35^\circ\)
\(x=70^\circ\)
Therefore, the value of x is 70 degrees.
Jin sells concert tickets at the theater box office. The ratio of student tickets to adult tickets sold is 4 : 5. Each student ticket costs $5, and each adult ticket costs $7. Jin sells 189 tickets altogether. Part A: How many student tickets does Jin sell? How many adult tickets? Explain your reasoning. Part B: How much more money does Jin receive from selling adult tickets than from selling student tickets? Explain your reasoning
Step-by-step explanation:
1) if total number of the saled tickets is 189, then it is possible to write s+a=189, where s - number of student tickets, a - adult tickets.
2) if the ratio is 4:5, then it is possible to write s:a=4:5;
3) using the two equations it is possible to make up the system:
\(\left \{ {{s+a=189} \atop {\frac{s}{a} =\frac{4}{5} }} \right.\)
4) Part A: after solution the system above the number of student tickets = 84; adult tickets = 105.
5) Part B: the revenue from selling the adult tickets is: 105*7=735, the student tickets is: 84*5=420. Then the required difference is: 735-420=$ 315.
Bob bought a thing for $350 and sold it for $450. What was his percentage gain?
Plz need answers ASAP!!
Answer:
The answer 128.57%
Step-by-step explanation:
The explanation is
Answer:
28.57%
Step-by-step explanation:
I need help on this question
Answer:
105 \(cm^{2}\)
Step-by-step explanation:
Rectangle 2 is 3 times rectangle 1. We know this because one side of rectangle 2 is 3 times the same side of rectangle 1. Area of rectangle 1 × 3 = area of rectangle 2: 35 × 3 = 105 \(cm^{2}\)I hope this helps!
Answer:
B- 105 cm
Step-by-step explanation:
Deon's gas tank is 3/10
full. After he buys 11 gallons of gas, it is 4/5
full. How many gallons can Deon's tank hold?
Plsss this is urgent
Three charges (-25 nC, 79.1nC, and −55.9nC) are placed at three of the four corners of a square with sides of length 22.2 cm. What must be the value of the electric potential (in V) at the empty comer if the positive charge is placed in the opposite comer?
Given that three charges (-25 nC, 79.1nC, and −55.9nC) are placed at three of the four corners of a square with sides of length 22.2 cm. We need to determine the value of the electric potential (in V) at the empty comer if the positive charge is placed in the opposite corner.
The formula for the electric potential at a point in space is given by;V = k [ (q1 / r1) + (q2 / r2) + (q3 / r3) + ….. ]where;k = Coulomb's constant (8.99 × 10^9 Nm²/C²)q1, q2, q3,…. are the charges at the cornersr1, r2, r3,…. are the distances from the corner to the point whose potential is being calculated Now we can calculate the electric potential at the empty corner as follows;The three charges can be represented as shown below:Charges at corners of a square
The distance from any corner to the opposite corner (where the positive charge is placed) is given by d = √[ (22.2 cm)² + (22.2 cm)² ] = 31.4 cmTherefore, the electric potential at the empty corner is given by;V = k [ (q1 / r1) + (q2 / r2) + (q3 / r3) ]Here, q1 = -25 nC, q2 = -55.9 nC, q3 = 79.1 nC, r1 = r2 = r3 = d = 31.4 cm = 0.314 mPlugging in the values we get;V = 8.99 × 10^9 [ (-25 × 10^-9 / 0.314) + (-55.9 × 10^-9 / 0.314) + (79.1 × 10^-9 / 0.314) ]= 8.99 × 10^9 [ -0.0795 - 0.1783 + 0.252 ]= 8.99 × 10^9 × 0.0052= 46.8 VTherefore, the value of the electric potential at the empty comer if the positive charge is placed in the opposite comer is 46.8 V.
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Select the most accurate statement regarding the risk tolerance parameter. 1 The risk tolerance parameter of a highly profitable firm is likely to be smaller than the risk tolerance parameter of a less profitable firm. 2 The smaller the risk tolerance parameter, the greater the tolerance for risk. 3 The risk tolerance parameter of a large firm is likely to be smaller than the risk tolerance parameter of a small firm. 4 The risk tolerance parameter influences the relationship between a payoff and the utility of the payoff. 5 The risk tolerance parameter is a value between 0 and 1.
The most accurate statement regarding the risk tolerance parameter is:
The risk tolerance parameter influences the relationship between a payoff and the utility of the payoff.
The risk tolerance parameter is a measure of an individual's or firm's willingness to accept risk in exchange for potential reward. It influences the utility function, which maps payoffs to the utility they provide.
A higher risk tolerance parameter implies a greater willingness to accept risk, and a lower risk tolerance parameter implies a lesser willingness to accept risk. The parameter can be any positive number, not just between 0 and 1. Statements 1, 2, and 3 are incorrect.
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Plot 213, −56, and −312 on the number line.
Answer:
Step-by-step explanation:
Plot 213, −56, and −312 on the number line.
the 5th term of a geometric sequence is -256 and the 8th is -32. Find the value of the 12th term.
Answer:
36
Step-by-step explanation:
Find a number such that the sum and three times its reciprocal is 91/20.
For this exercise you need to remember the following:
1. The sum is the result of an Addition.
2. By definition, given:
\(\frac{a}{b}\)Its reciprocal is:
\(=\frac{b}{a}\)3. The word "times" indicates a Multiplication.
In this case, let be "n" the number mentioned in the exercise. Its reciprocal is:
\(\frac{1}{n}\)Based on the information given in the exercise, you can set up the following equation:
\(n+3(\frac{1}{n})=\frac{91}{20}\)Now you must solve for "n":
1. Simplify:
\(\begin{gathered} n+\frac{3}{n}=\frac{91}{20} \\ \\ \frac{(n)(n)+3}{n}=\frac{91}{20} \\ \\ \frac{n^2+3}{n}=\frac{91}{20} \\ \\ n^2+3=\frac{91}{20}n \end{gathered}\)2. Make the equation equal to zero:
\(n^2-\frac{91}{20}n+3=0\)3. Apply the Quadratic formula. This is:
\(n=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}\)In this case:
\(\begin{gathered} a=1 \\ b=-\frac{91}{20}_{} \\ \\ c=3 \end{gathered}\)Substituting values and evaluating, you get:
\(\begin{gathered} n=\frac{-(-\frac{91}{20})\pm\sqrt[]{(-\frac{91}{20})^2-2(1)(3)}}{2\cdot1} \\ \\ n_1=\frac{15}{4} \\ \\ n_2=\frac{4}{5} \end{gathered}\)The answer
There are two numbers:
\(\begin{gathered} n_1=\frac{15}{4} \\ \\ n_2=\frac{4}{5} \end{gathered}\)
Answer:
0.8 and 3.75.
Step-by-step explanation:
If the number is x, then:-
x + 3 * 1/x = 91/20
x^2 + 3 = 91x/20
x^2 - (91/20)x + 3 = 0
x^2 - 4.55x + 3 = 0
x = [-(-4.55) +/- sqrt((-4.55)^2 - 4*1*3)] / 2
x = 0.8, 3.75.
the cricketplayer class was created so that we can track different stats. it was designed to create a player, then add a match’s statistics, and report the stats.
The cricket Player class has been designed to keep track of the different stats.
This class was created with the aim of creating a player, incorporating a match's statistics, and finally displaying the stats.
Creating an object of the cricketPlayer class is the first step.The object can then be used to call the various member functions of the class.
The stats can be added by calling the appropriate member functions and providing the required data as parameters. Finally, the stats can be displayed by calling the member function that displays the stats.
The cricket Player class has the following member functions:
• setData() - This function is used to set the data members of the cricket Player class. It takes four parameters that represent the player's name, team name, the total number of runs scored, and the number of wickets taken by the player. The function then sets these values to the appropriate data members.
• displayData() - This function is used to display the data members of the cricket Player class. It displays the player's name, team name, the total number of runs scored, and the number of wickets taken by the player.
• addRuns() - This function is used to add runs to the total runs scored by the player. It takes a single parameter that represents the number of runs scored in a particular match. The function then adds this value to the total runs scored by the player.
• addWickets() - This function is used to add wickets to the total number of wickets taken by the player. It takes a single parameter that represents the number of wickets taken in a particular match. The function then adds this value to the total number of wickets taken by the player.
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in a certain town, in 90 minutes 1/2 inch of rain falls. It continues at the same rate for a total of 24 hours. Which of the following statements are true about the amount of rain in the 24- hour period? show your work
The statement that is true is that the amount of rain in the 24- hour period is 8 inches
Which statement is true about the amount of rain in the 24- hour period?From the question, we have the following parameters that can be used in our computation:
In 90 minutes 1/2 inch of rain falls
This means that
Rate = (1/2 inch)/90 minutes
So, we have
Rate = (1/2 inch)/(1.5 hour)
The amount of rain in the 24- hour period is
Amount = Rate * Time
So, we have
Amount = (1/2 inch)/(1.5 hour) * 24 hours
Evaluate
Amount = 8 inches
Hence, the amount of rain in the 24- hour period is 8 inches
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Sabas Company has 20,000 shares of $100 par, 2% cumulative preferred stock and 100,000 shares of $50 par common stock. The following amounts were distributed as dividends: Year 1: $10,000 Year 2: 45,000 Year 3: 90,000 Determine the dividends in arrears for preferred stock for the second year.
Answer:
b
Step-by-step explanation: