Answers
The horizontal distance the plane has covered is 3940 feet
Explanation:
The plane makes an angle 10° with the ground when it took off from the field.
We need to find the horizontal distance the plane when it has flown 4000 feet.
The length of the hypotenuse is 4000 feet.
Let the horizontal distance be x.
We shall find the value of x using the cosine formula.
The formula is given by
[tex]cos \theta=\frac{adj}{hyp}[/tex]
Substituting the values, we have,
[tex]cos \ 10^{\circ}=\frac{x}{4000}[/tex]
Substituting the value for cos 10°, we get,
[tex]0.985=\frac{x}{4000}[/tex]
Multiplying both sides of the equation by 4000, we get,
[tex]0.985\times 4000=x[/tex]
Simplifying, we get,
[tex]3940=x[/tex]
Thus, the horizontal distance the plane has covered is 3940 feet
Related Questions
Please help me with this!
Answers
Answer:
-540
Step-by-step explanation:
The coefficient of the k-th term of (a+b)^n is nCk. (k = 0, 1, 2, ..., n)
Here, we want the coefficient of a^3b^3 for n=6, so k=3 and the coefficient is ...
6C3 = 6!/(3!(6-3)!) = 5·4 = 20
So for a=3x and b=-y, we want ...
20a^3b^3 = 20(3x)^3(-y)^3 = -540x^3y^2
The coefficient you're looking for is -540.
Demont made one fourth pound of rock candy.He will separate the candy into four stacks.If he puts an equal amount of candy in each sack,what fraction of a pound of candy will be in each sack.
Answers
To determine the amount of candy per sack, divide the total one fourth pound of rock candy by four, resulting in 1/16 pound of candy in each sack.
Explanation:Demont has made one fourth pound of rock candy and needs to divide this equally into four sacks. To find the amount of candy in each sack, we divide the total amount of rock candy by the number of sacks.
Here's the calculation:
Total rock candy = 1/4 pound
Number of sacks = 4
Amount of candy per sack = 1/4 pound ÷ 4 = 1/16 pound per sack
Therefore, each sack will contain 1/16 pound of rock candy.
In a standard normal distribution, the a. mean and the standard deviation are both 1 b. mean is 0 and the standard deviation is 1 c. mean is 1 and the standard deviation is 0 d. mean and the standard deviation can have any value
Answers
The mean and standard deviation for the Standard normal distribution is 0 and 1 respectively. Option b is correct.
What is a standard normal distribution?The standard normal distribution is a type of normal distribution that has a mean of 0 and a standard deviation of 1. The standard deviation shows how much a particular measurement deviates from the mean, and the standard normal distribution is centered at zero.
Since the standard normal distribution is a normal distribution curve in which the values of the mean is 0 and the value of The standard normal distribution is a normal distribution curve where the values of the mean and standard deviation is 1.
Thus, the correct option for the given question is Option B.
Learn more about Statistics here:
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In a standard normal distribution, the mean is 0 and the standard deviation is 1. This defines a distribution where data is symmetrically spread around the mean, and a z-score can be used to determine how many standard deviations a value is from the mean.
In a standard normal distribution, the correct answer to the student's question is that the mean is 0 and the standard deviation is 1. This is represented by option b. In a standard normal distribution, often denoted as Z ~ N(0, 1), the mean (μ) equals 0, which signifies that the distribution is centered on the zero point on a number line.
The standard deviation (σ) equals 1, indicating that the values within the distribution are spread out in such a way that one standard deviation away from the mean encompasses approximately 68% of the data in a symmetrical fashion on both sides of the mean.
The concept of z-scores in the context of the standard normal distribution allows for the comparison of different values within different populations. A z-score represents how many standard deviations away a value is from the population mean.
It is crucial to note that the standard deviation cannot be negative; it represents the dispersion of the dataset around the mean, and therefore can only be positive or zero.
Which polygons are congruent?Select each correct answer. Two trapezoids labeled V R A S and B U W D. Sides B U and V R contain one tick mark. Sides B D, U W, V S, and R A each contain two tick marks. Sides A S and W D each contain three tick marks. The angles represented by vertex letters U, B, R, and V each contain two tick marks. The angles represented by vertex letters D, W, S, and A each contain one tick mark. a rhombus with all sides marked 15 units long. a square with two sides marked 15 units and four right angles. Two rectangles labeled B M D J and K Z Y A. Sides B M and D J are each labeled twelve, and sides D M and J B are each labeled six. Side K Z and side Y A are each labeled four. Side Y Z and side K A are each labeled three. All angles in both rectangles are right angles.
Answers
Answer:
Two trapezoids labeled V R A S and B U W D. Sides B U and V R contain one tick mark. Sides B D, U W, V S, and R A each contain two tick marks. Sides A S and W D each contain three tick marks. The angles represented by vertex letters U, B, R, and V each contain two tick marks. The angles represented by vertex letters D, W, S, and A each contain one tick mark.
Answer:
b m d j and k z y a
Step-by-step explanation:
A fruit drink company tested a new flavor .In a test 46% of the people talking part liked the new flavor.If 69 people liked the new flavor, how many people took the test
Answers
Answer:
150 people took the test.
Step-by-step explanation:
Given:
Number of people liked the new flavor = 69
Percentage of people liked the new flavor = 46%
We need to find the number of people who took the test.
Solution:
Let the number of people who took the test be 'x'.
So we can say that;
Percentage of people liked the new flavor multiplied by the number of people who took the test is equal to Number of people liked the new flavor.
framing in equation form we get;
[tex]46\%\times x =69\\\\\frac{46}{100}x=69\\\\0.46x =69[/tex]
Dividing both side by 0.46 we get;
[tex]\frac{0.46x}{0.46}=\frac{69}{0.46}\\\\x= 150[/tex]
Hence 150 people took the test.
Electron is organizing the bookcase in the school library. He makes sure each shelf has 15 books on it. There are 9 shelves of math books and 6 shelves of science books.
Answers
Answer:
Total amount of books in the bookcase = 225 books
Step-by-step explanation:
Each shelf is to have 15 books
Therefore total amount of books in the bookcase = {9×15} + {6×15} = 225 books
What is the domain of the function graphed below?
Answers
The domain is the X value ( input).
The line starts at (0,2) so 0 is the first part of the domain. The horizontal line has an arrow on it pointing to the right which means the line can continue to infinity.
The answer is the second choice, 0 to infinity
Angle x is a third quadrant angle such that cos x= −2/5 .
What is the exact value of cos(x/2) ?
Enter your answer, in simplest radical form, in the box.
cos(x/2) =
Answers
Answer:
-√(3/10)
Step-by-step explanation:
cos(x) = 2[cos(x/2)]² - 1
-2/5 = 2[cos(x/2)]² - 1
3/5 = 2[cos(x/2)]²
3/10 = [cos(x/2)]²
cos(x/2) = +/- sqrt(3/10)
Since x is in the 3rd quadrant, x/2 would be in the second quadrant.. so cos(x/2) is negative
[tex]x[/tex] is in quadrant III, so [tex]\pi<x<\frac{3\pi}2[/tex].
This makes [tex]\frac\pi2<\frac x2<\frac{3\pi}4[/tex], which means [tex]\frac x2[/tex] lies in quadrant II, for which we expect [tex]\cos\frac x2<0[/tex].
Recall the double-angle identity:
[tex]\cos^2\dfrac x2=\dfrac{1+\cos x}2[/tex]
[tex]\implies\cos\dfrac x2=-\sqrt{\dfrac{1-\frac25}2}=-\sqrt{\dfrac3{10}}[/tex]
What is an equation of the line that passes through the points (−5,−7) and (5,1)?
Answers
Answer:
y = 4/5x -3
Step-by-step explanation:
in order to do this :
firstly , find the midpoint of the points.use the formula :
[tex]\frac{x1 + x2}{2} , \frac{y1 + y2}{2}[/tex]
= [tex]\frac{-5 + 5}{2} , \frac{-7 + 1}{2}[/tex]
midpoint =(0 , -3)
secondly , get the gradientuse the formula :
[tex]\frac{y2-y1}{x2-x1}[/tex]
= [tex]\frac{1-(-7)}{5-(-5)}[/tex]
=[tex]\frac{8}{10}[/tex]
simplified to 4/5
gradient = 4/5
Thirdly , create the equationformula for the equation of a line
(Y-y1) = m( X-x1)
now use the values of the midpoint and the gradient(m)
y +7 = 4/5 (x + 5)
y = 4/5x + 4-7
y = 4/5x -3Answer:
y = 0.8x - 3
Step-by-step explanation:
Slope = (-7-1)/(-5-5) = -8/-10 = 0.8
When x = 5, y = 1
1 = 0.8(5) + c
1 = 4 + c
c = -3
y = 0.8x - 3
If the measure of angle T is 95 degrees and the measure of angle S is 100 degrees, then the measure of angle R is ___ degrees and the measure of angle Q is ___ degrees.
Answers
The cost for printing pages at a print shop is a $5 processing fee and $1 for each page. The rule is c=5+p, where p is the number of pages and c is the total cost
Answers
Answer:
Step-by-step explanation:
I think the photo below is your full question and my answer is presented in that too.
We create a table of values:
p c
0 5
1 6
2 7
Then draw on the graph.
Hope it will find you well
Please help I dont know where to start
the standard deviation of a simple random sample of 40 calling times on a payphone is found to be 2.6 minutes. find the test statistic to test a claim that the standard deviation of all phone calls on a payphone is less than 2.9 minutes. use a 0.05 significance level
32.152
31.348
48.519
34.966
Answers
Answer:
Option B) 31.348
Step-by-step explanation:
We are given the following in the question:
Sample size, n = 49
Sample standard deviation, s = 2.6 minutes
Population standard deviation, [tex]\sigma[/tex] = 2.9 minutes
Significance level, [tex]\alpha[/tex] = 0.05
We have o find the test statistic.
Formula:
[tex]\chi^2 = \dfrac{(n-1)s^2}{\sigma^2}\\\\\chi^2 =\displaystyle\frac{(40-1)(2.6)^2}{(2.9)^2}\\\\\chi^2=31.348[/tex]
Thus, the test statistic is
Option B) 31.348
As part of their work in a research methods class, a group of psychology students devised a survey to assess the relation between stress and health. Each member of the class administered the survey to 10 friends, and the data were then pooled. What method of sampling was used?
Answers
Answer:
The sampling method used is Convenience sampling.
Step-by-step explanation:
Convenience sampling is a non-probability sampling method that involves the selection of sample from the easiest source available. In this sampling method the samples are selected from the most convenient possible way.
Foe instance, samples taken from social media, nearest shopping mall, and so on.
In this case the students selected 10 friends to answer the survey.
This is an example of convenience sampling method because sampling your friend is the easiest sample anyone could collect.
Thus, the sampling method used is Convenience sampling.
The internal telephone numbers in the phone system on a campus consists of 4 digits, with the 1st not equal to 0. How many different numbers can be assigned in this system?
Answers
Answer:
This system have 9000 different numbers.
Step-by-step explanation:
We know that the internal telephone numbers in the phone system on a campus consists of 4 digits, with the 1st not equal to 0.
We have total 10 digits.
In the first place we have 9 possibilities, because from the conditions of the task in the first place there cannot be 0.
In second, third and fourth place we have 10 possibilities.
Therefore, we get
[tex]N=9\cdot 10\cdot10 \cdot 10=9000[/tex]
This system have 9000 different numbers.
In this phone system, there are 9,000 different internal telephone numbers that can be assigned.
Explanation:The internal telephone numbers in the phone system on a campus consists of 4 digits, with the 1st not equal to 0. To find the number of different numbers that can be assigned in this system, we need to consider the possibilities for each digit position. Since the first digit cannot be 0, there are 9 choices (1 through 9) for the first digit. For the remaining three digits, each digit can be any number from 0 to 9, resulting in 10 choices for each of the three remaining digits. Therefore, the total number of different numbers that can be assigned in this system is
9 * 10 * 10 * 10 = 9,000.
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Triangles LMN and XYZ are congruent. Write congruence statements comparing the corresponding parts. Then determine which transformation(s) map LMN onto XYZ
Answers
Answer:
180 degrees rotation
Step-by-step explanation:
Solution:
- The congruency statements are as follows:
Angles: L ≅ X
M ≅ Y
N ≅ Z
Sides: LM ≅ XY
MN ≅ YZ
LN ≅ XZ
Transformation:
L ( -4 , 1 ) ------- > X ( 4 , - 1 )
( x , y ) -----------> ( -x , -y )
180 degrees rotation
The congruence can be expressed as ∆LMN ≅ ∆XYZ. To map LMN onto XYZ, a transformation like translation, rotation, reflection, or a combination thereof can be used.
If triangles LMN and XYZ are congruent to each other, the corresponding parts must be equal in both measure and shape. The congruence statement for these triangles would be ∆LMN ≅ ∆XYZ, which implies that angle L is congruent to angle X, angle M to angle Y, and angle N to angle Z. Additionally, side LM is congruent to side XY, side MN to side YZ, and side NL to side XZ.
Regarding the transformation that maps triangle LMN onto XYZ, if they are congruent, any of the following rigid motions (also known as isometries) could be used: a translation, a rotation, a reflection, or a combination of these. Since these transformations preserve distance and angle measures, the size and shape of triangle LMN will remain unchanged, and it will match exactly onto triangle XYZ.
Seed mixture X is 40 percent ryegrass and 60 percent bluegrass by weight; seed mixture Y is 25 percent ryegrass and 75.percent fescue. If a mixture of X and Y contains 30 percent ryegrass, what percent of the weight of the mixture is X ?
Answers
Answer:
33%
Step-by-step explanation:
Assuming the weight of the mixture to be 100g**, then the weight of ryegrass in the mixture would be 30g.
Also, assume the weight mixture X used in the mixture is Xg, then the weight of mixture Y used in the mixture would be (100-X)g.
So we can now equate the parts of the ryegrass in the mixture as:
0.4X + 0.25(100-X) = 30
<=> 0.4X + 25 - 0.25X = 30
<=> 0.15X = 5
<=> X = 5/0.15 = 500/15 = 100/3
So the weight of mixture X as a percentage of the weight of the mixture
= (weight of X/weight of mixture) * 100%
= (100/3)/100 * 100%
= 33%
To estimate the average annual expenses of students on books and class materials a sample of size 36 is taken. The sample mean is $850 and the sample standard deviation is $54. A 99% confidence interval for the population mean is:_______.A) $823.72 to $876.28.
B) $832.36 to $867.64.
C) $826.82 to $873.18.
D) $825.48 to $874.52.
Answers
Answer:
its C i think
Step-by-step explanation:
The random variables X and Y have the joint PMF pX,Y(x,y)={c⋅(x+y)2,0,if x∈{1,2,4} and y∈{1,3},otherwise. All answers in this problem should be numerical. Find the value of the constant c . c=
Answers
Answer:
c= 1/26
Step-by-step explanation:
The joint probability mass function for X and Y must comply that:
[tex]\[\sum\]\sum\] c(x +y) = 1[/tex] for x∈{1,2,4} and y∈{1,3}
thus, all the possible values for the pairs (x,y) are:
(1,1) (1,3) (2,1) (2,3) (4,1) (4,3)
and then
c [(1+1)+(1+3)+(2+1)+(2+3)+(4+1)+(4+3)] = 1
c[26] = 1
c= 1/26
Find AB. (Brainly says it is too short this is why this is here)
Answers
The length of AB is 31 yd.
Solution:
Given data:
The side opposite to angle A is "a" = 22 yd
The side opposite to angle B is "b" = 26 yd
The side opposite to angle C is "c" = AB
Angle C = 80°
To find the length of AB:
Using cosine formula,
[tex]c^2=a^2+b^2-2ab \cdot \cos C[/tex]
Substitute the given values in the formula, we get
[tex]c^2=22^2+26^2-2(22)(26)\cdot \cos 80^\circ[/tex]
[tex]c^2=484+676-1144\cdot \cos 80^\circ[/tex]
[tex]c^2=1160-1144\cdot (0.1736)[/tex]
[tex]c^2=1160-198.5984[/tex]
[tex]c^2=961.4016[/tex]
Taking square root on both sides, we get
c = 31
AB = 31 yd
The length of AB is 31 yd.
Twin brothers, Billy and Bobby, kid mother grandparents lawn together for 60 minutes. Billy could mow the lawn by himself in 20 minutes less time then it would take Bobby. How long will it take Bobby to mow the lawn by himself
Answers
Answer:
Bobby around 131 minutes and Billy around 111 minutes
Step-by-step explanation:
To solve the problem it is important to raise equations regarding what happens.
They tell us that Billy (Bi) and Bobby (Bo) can mow the lawn in 60 minutes. That is to say that what they prune in a minute is giving as follows:
1 / Bo + 1 / Bi = 1/60 (1)
They say Billy could mow the lawn only in 20 minutes less than it would take Bobby, therefore
1 / Bi = 1 / (Bo-20) (2)
Replacing (2) in (1) we have:
1 / Bo + 1 / (Bo-20) = 1/60
Resolving
(Bo - 20 + B0) / (Bo * (Bo-20) = 1/60
120 * Bo - 1200 = Bo ^ 2 - 20Bo
Rearranging:
Bo ^ 2 - 140Bo -1200 = 0
Now applying the general equation
Bo = 130.82 or Bo = 9.17, this last value cannot be because Billy took 20 minutes less and neither can he prune faster than the two together, therefore Bobby only takes around 131 minutes and Billy around 111 minutes
Checking with equation 1:
1/131 +1/111 = ~ 1/60
Final answer:
Bobby would take 120 minutes to mow the lawn by himself.
Explanation:
The question asks us to calculate how long it will take Bobby to mow the lawn by himself if it takes his twin brother Billy 20 minutes less to do the job on his own, and they can mow the lawn together in 60 minutes. To solve this, we can use the concept of work rate and the idea that the combined work rate of Billy and Bobby equals the reciprocal of the time they take to work together.
Let's assume Bobby takes x minutes to mow the lawn by himself. Thus, Billy would take x - 20 minutes. We can express their work rates as:
Bobby's work rate: 1/x lawn/minuteBilly's work rate: 1/(x - 20) lawn/minuteThe combined work rate when they mow together is the sum of their individual work rates, which is equal to 1/60 since they take 60 minutes together. So, we have:
1/x + 1/(x - 20) = 1/60
By solving this equation for x, we find the time it takes Bobby to mow the lawn by himself.
Multiply through by 60x(x - 20) to clear the denominators:60(x - 20) + 60x = x(x - 20)60x - 1200 + 60x = x^2 - 20xCombine like terms:x^2 - 140x + 1200 = 0Solve for x using the quadratic formula or by factoring:(x - 120)(x - 10) = 0Therefore, x = 120 or x = 10. Since x has to be greater than 20, x = 120 is the correct solution.Hence, Bobby will take 120 minutes to mow the lawn by himself.
The volume of a rectangular prism is 960 cubic inches. If the dimensions of the base are doubled and the height remains the same to create a new prism, what will be the volume of the new rectangular prism in cubic inches?
Answers
Answer:
3840 cubic inches
Step-by-step explanation:
The volume of a rectangular prism is 960 cubic inches
Let the dimensions be lXwXh,
l=length of the base
w=width of the base
h=height of the base
The volume, lwh=960 cubic inches
If the dimensions of the base are doubled and the height remains the same
Volume of the new rectangular prism=2l X 2w X h =4lwh
=4 X 960 =3840 cubic inches
Toby and Betty Combs pay $8,719.38 in annual property taxes. Their home has a market value of $361,800.00 with a tax rate of 48.2 mills. What is the rate of assessment in their tax district?
Answers
Answer:
50% of market value
Step-by-step explanation:
The actual tax rate on the Combs home is ...
$8719.38/$361800 = 0.0241 = 24.1 mils
The rate of assessment is ...
(24.1 mils)/(48.2 mils) = 0.50 = 50%
The Combs pay tax on 50% of their home's market value.
PLEASE HELP ASAP!!!! WILL MARK BRAINLIEST
Answers
Answer:
Boi
Step-by-step ex:
Answer:
Option 4
Step-by-step explanation:
x - 4 is negative for x < 4
Mod makes it positive,
-(x - 4) = 4 - x
4 - x for x < 4,
x - 4 for other x values (which are greater than/equal to 4)
The sum of the differences must be zero for any distribution consisting of n observations.
A. True
B. False
Answers
Answer:
false
Step-by-step explanation:
Use the following information to complete parts I, II, and III. 1 hour=3600 seconds
1 year = 31556952 secondsI. Use scientific notation to estimate the number of hours in one year. II. Use scientific notation to calculate the exact number of hours in one year. III. In two or more complete sentences, compare your answers to parts I and II. In your comparison, discuss similarities and differences.
Answers
Answer:
I) There are [tex]8.760\times 10^3[/tex] hours in 1 year.
II) The exact number of hours in one year is [tex]8.76582\times 10^3[/tex] hours.
Step-by-step explanation:
Given : 1 hour=3600 seconds
1 year = 31556952 seconds.
To find :
I) Use scientific notation to estimate the number of hours in one year.
1 day = 24 hours
1 year = 365 days
So, number of hours in one year is given by,
[tex]n=24\times 365[/tex]
[tex]n=8760[/tex]
In scientific notation,
[tex]8760=8.760\times 10^3[/tex]
So, there are [tex]8.760\times 10^3[/tex] hours in 1 year.
II) 1 year = 31556952 seconds.
1 hour = 3600 seconds
In one year the number of hour is given by,
[tex]n=\frac{31556952}{3600}[/tex]
[tex]n=8765.82[/tex]
In scientific notation,
[tex]8765.82=8.76582\times 10^3[/tex]
So, the exact number of hours in one year is [tex]8.76582\times 10^3[/tex] hours.
III) In two or more complete sentences, compare your answers to parts I and II. In your comparison, discuss similarities and differences.
The exact numbers of hours using 365 days is 8760 which is written as [tex]8.760\times 10^3[/tex] in scientific notation but using the given data we get [tex]8.76582\times 10^3[/tex] hours.Comparing these answers the first one has only 3 significant figures and the second answer has six significant figures.If we round these we get [tex]8.8\times 10^3[/tex] hours which has two significant numbers.need help fast, please help
Answers
Yo sup??
by Pythagoras theorem we can say
38²=34²+b²
b²=1444-1156
=288
b=17
Hope this helps
Answer:
D = 17
Step-by-step explanation:
Hope this helps
Please show your work. Thank you for taking the time of day to help me!
At Best Burgers, Jack collected sales data on the type of side order served with each type of burger purchased for a week.
Jack serves a half pound of onion rings or french fries with every kind of burger.
If Jack sells 120 bacon cheeseburgers total, about how many pounds of onion rings will he serve with them? (round to nearest whole number)
A) 15 pounds
B) 18 pounds
C) 30 pounds
D) 54 pounds
Answers
Answer:
30
Step-by-step explanation:
Look at the bottom line of the chart.
He sold 41 sides of French fries and 40 sides of onion rings.
41 + 40 = 81
Since he sold a total of 81 sides with bacon cheeseburgers, that means he sold a total of 81 bacon cheeseburgers.
We have a ratio:
81 bacon cheeseburgers to 40 sides of onion rings
Now he sold 120 bacon cheeseburgers, so we set up a proportion to find the number of sides of onion rings. Let the unknown number be x.
81 burgers is to 40 sides as 120 burgers is to x sides
81/40 = 120/x
We solve for x by cross multiplying.
81x = 40 * 120
81x = 4800
x = 4800/81 = 59.3
That means he serves 59 sides of onion rings.
Each serving of onion rings is half pound.
59 * 0.5 = 29.5
For 120 bacon cheeseburgers, he serves approximately 29.5 lb of onion rings.
Answer: 30
Answer:
30 pounds
Bacon cheeseburger with onion rings:
40
(41 + 40)
=
40
81
= 0.4938
then,
120 x 0.4938 = 59.256
then,
59.256 x .50 = 29.628
Faculty members at Lowell Place High School want to determine whether there are enough students to have a Valentine's Day Formal. Eighty-eight of the 200 students said they would attend the Valentine's Day Formal. Construct and interpret a 90% confidence interval for p.
Answers
Answer:
The 90% confidence interval is (0.383,0.497)
Step-by-step explanation:
We are given the following in the question:
Sample size, n = 200
Number of children that would attend Valentine's Day Forma, x = 88
[tex]\hat{p} = \dfrac{x}{n} = \dfrac{88}{200} = 0.44[/tex]
90% Confidence interval:
[tex]\hat{p}\pm z_{stat}\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}[/tex]
[tex]z_{critical}\text{ at}~\alpha_{0.10} = \pm 1.64[/tex]
Putting the values, we get:
[tex]0.44\pm 1.64(\sqrt{\dfrac{0.44(1-0.44)}{200}}) = 0.44\pm 0.057\\\\=(0.383,0.497)[/tex]
Interpretation:
The 90% confidence interval is (0.383,0.497). We are 90% confident that the proportion of children attending Valentine's Day Formal is between 38.3% and 49.7%
The height of a rectangular prism is 20cm. It has a surface area of 2400 square centimeters. What are two possible sets of lengths and widths? Find one set of dimensions with l and w equal in length as well as a set dimensions that are not equal
Answers
Step-by-step explanation:
Below is an attachment containing the solution.
Final answer:
The dimensions are 24cm x 15cm x 20cm.
Explanation:
To find two possible sets of lengths and widths for the rectangular prism with a height of 20cm and a surface area of 2400cm2, we need to understand the formula for the surface area of a rectangular prism: SA = 2(lw + lh + wh). Here, l = length, w = width, and h = height.
Since we know the height (h = 20cm) and the surface area (SA = 2400cm2), we can set up the equation:
2(lw + 20l + 20w) = 2400
We will consider two cases: one where the length and width are equal (since that is a specific request), and another where they are not.
Case 1: Length and width are equal (l = w). We simplify the equation to:
2(l2 + 40l) = 2400
Solving for l gives us l = w = 20cm. Therefore, the dimensions are 20cm x 20cm x 20cm.
Case 2: Length and width are not equal. To find a possible set, we can assume a width and solve for the length:
Let's assume w = 15cm. Plugging this into the equation gives us:
2(l15 + 20l + 20 x 15) = 2400
Solving for l gives us l = 24cm.
Therefore, the dimensions are 24cm x 15cm x 20cm.
Hometown Grocery, Inc. has 50 comma 000 shares of common stock outstanding and 4 comma 000 shares of preferred stock outstanding. The common stock is $ 4.00 par value; the preferred stock is 9% noncumulative with a $ 100.00 par value. On October 15, 2018, the company declares a total dividend payment of $ 54 comma 000. What is the amount of dividend that will be paid for each share of common stock? (Round your answer to the nearest cent.)
Answers
Answer:
$0.36 per share
Step-by-step explanation:
The data provided in the question are as follows
Common stock outstanding = 50,000 shares
Preferred stock outstanding = 4,000 shares
Par value of common stock = $4
Interest rate and par value of preferred stock = 9% and $100
Total dividend payment declared = $54,000
So, the amount of dividend for each share of common stock is
= (Total dividend payment declared - Preferred stock outstanding × interest rate × par value) ÷ (common stock outstanding)
= ($54,000 - 4,000 × $100 × 9%) ÷ (50,000 shares)
= ($54,000 - $36,000) ÷ (50,000 shares)
= $18,000 ÷ 50,000 shares
= $0.36 per share