Answer:
The engineer must verify and verify through a statistical inference that estimates and possible parameters may emerge, as well as determine what hypothesis tests should be performed to draw the most accurate conclusion.
Step-by-step explanation:
The engineer must assume that there may be more than one reasonable estimator for a different event or experiment; Something that could help you would be to perform an estimation of parameters, in that estimation it is required to know the properties of the estimators; that is to say that the closer the value of an estimator is to the real value of the parameter, it could be said that it is the most efficient or exact extimator.
Consider the differential equation4y'' − 4y' + y = 0; ex/2, xex/2.Verify that the functions ex/2 and xex/2 form a fundamental set of solutions of the differential equation on the interval (−[infinity], [infinity]).The functions satisfy the differential equation and are linearly independent since W(ex/2, xex/2) =
Step-by-step explanation:
Let y1 and y2 be (e^x)/2, and (xe^x)/2 respectively.
The Wronskian of them functions be
W = (y1y2' - y1'y2)
y1 = (e^x)/2 = y1'
y2 = (xe^x)/2
y2' = (1/2)(x + 1)e^x
W = (1/4)(x + 1)e^(2x) - (1/4)xe^(2x)
= (1/4)(x + 1 - x)e^(2x)
W = (1/4)e^(2x)
Since the Wronskian ≠ 0, we conclude that functions are linearly independent, and hence, form a set of fundamental solutions.
Answer:
W = (1/4)(x + 1)e^(2x) - (1/4)xe^(2x)
= (1/4)(x + 1 - x)e^(2x)
W = (1/4)e^(2x)
Step-by-step explanation:
Suppose you start at the origin, move along the x-axis a distance of 7 units in the positive direction, and then move downward along the z-axis a distance of 9 units. What are the coordinates of your position
Answer:
The coordinates of the new position are
(x, y, z) = (7, 0, -9)
Step-by-step explanation:
So assuming a 3D plane x, y, z
The starting point is the origin that is
(x, y, z) = (0, 0, 0)
Move a distance of 7 units along the positive x-axis
(x, y, z) = (7, 0, 0)
Then move a distance of 9 units downwards along the z-axis
downward = negative and upward = positive
(x, y, z) = (7, 0, -9)
Therefore, the coordinates of the new position are
(x, y, z) = (7, 0, -9)
Refer to the attached plot where the above coordinates are plotted on a 3D surface using an online 3D plotter.
Each small box corresponds to 1 unit.
Tyler drew a figure that has two pairs of equal sides, four angles formed by perpendicular lines, and two pairs of parallel sides. What geometric term best describes the figure Tyler drew? What geometric term best describes the figure Tyler drew?
Answer:
A shape with two pairs of parallel lines, perpendicular lines, and two pairs of equal sides can be best described as a rectangle.
Which statements are true of the function f(x) = 3(2.5)x? Check all that apply
Answer:
The function is exponential.
The function increases by a factor of 2.5 for each unit increase in x.
The domain of the function is all real numbers
The true statements are:
[tex]\mathbf{y = 3(2.5)^x}[/tex] is an exponential functionThe function represents an exponential growthThe domain of the function is the set of all real numbersThe function is given as:
[tex]\mathbf{y = 3(2.5)^x}[/tex]
An exponential function is represented as:
[tex]\mathbf{y = ab^x}[/tex]
Where: a represents the initial value, and b represents the rate
This means that:
[tex]\mathbf{y = 3(2.5)^x}[/tex] is an exponential function
By comparison:
[tex]\mathbf{b = 2.5}[/tex]
When b > 0, then the function represents an exponential growth
2.5 is greater than 0.
So, the function represents an exponential growth
Lastly, there is no restriction to the values of x.
So, the domain of the function is the set of all real numbers
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Let U be the 3 2 matrix [0.45 0.42, 0.25 0.35, 0.15 0.15]. The first column of U lists the costs per dollar of output for manufacturing product B, and the second column lists the costs per dollar of output for manufacturing product C. The first row is the cost of materials, the second row is the cost of labor, and the third row is the cost of overhead. Let q1 be a vector in set of real numbers R2 that lists the output (measured in dollars) of products B and C manufactured during the first quarter of the year, and let q2, q3 , and q4 be the analogous vectors that list the amounts of products B and C manufactured in the second, third, and fourth quarters, respectively. Give an economic desciption of the data in the matrix UQ, where Upper Q = [q1 q2 q3 q4].A. The 4 columns of UQ list the profit made from selling products B and C during the 4 quarters of the year. B. The 3 rows of UQ list the costs for materials, labor, and overhead used to manufacture products B and C for the year. C. The 4 columns of UQ list the total costs for materials, labor, and overhead used to manufacture products B and C during the 4 quarters of the year. D. The 4 columns of UQ list the total number of each product manufactured during the 4 quarters of the year.
Answer:
C. The 4 columns of UQ list the total costs for materials, labor, and overhead used to manufacture products B and C during the 4 quarters of the year.
Step-by-step explanation:
[tex]U=\left\begin{array}{ccc}\\$Cost of Materials\\ $Cost of Labour\\ $Cost of Overhead\end{array}\right\left(\begin{array}{cc}$Product B&$Product C\\0.45&0.42\\ 0.25&0.35\\ 0.15&0.15\end{array}\right)[/tex]
[tex]q_1[/tex] is a vector in the set of real numbers [tex]R^2[/tex] that lists the output (measured in dollars) of products B and C manufactured during the first quarter of the year.
Therefore:
[tex]UQ=\left\begin{array}{ccc}\\$Cost of Materials\\ $Cost of Labour\\ $Cost of Overhead\end{array}\right\left(\begin{array}{cc}$Product B&$Product C\\0.45&0.42\\ 0.25&0.35\\ 0.15&0.15\end{array}\right)\left(\begin{array}{ccc}q_{1B}\\q_{1C}\end{array}\right)\left(\begin{array}{ccc}q_{2B}\\q_{2C}\end{array}\right)\left(\begin{array}{ccc}q_{3B}\\q_{3C}\end{array}\right)\left(\begin{array}{ccc}q_{4B}\\q_{4C}\end{array}\right)[/tex]
[tex]=\left(\begin{array}{c|c|c|c}q_1&q_2&q_3&q_4\\0.45q_{1B}+0.42q_{1C}&0.45q_{2B}+0.42q_{2C}&0.45q_{3B}+0.42q_{3C}&0.45q_{4B}+0.42q_{4C}\\0.25q_{1B}+0.35q_{1C}&0.25q_{2B}+0.35q_{2C}&0.25q_{3B}+0.35q_{3C}&0.25q_{4B}+0.35q_{4C}\\0.15q_{1B}+0.15q_{1C}&0.15q_{2B}+0.15q_{2C}&0.15q_{3B}+0.15q_{3C}&0.15q_{4B}+0.15q_{4C}\end{array}\right)[/tex]Therefore, UQ has 4 columns and 3 rows.
The 4 columns of UQ list the total costs for materials(Row 1), labor(Row 2), and overhead(Row 3) used to manufacture products B and C during the 4 quarters of the year.
The management of a chain of frozen yogurt stores believes that t days after the end of an advertising campaign, the rate at which the volume V (in dollars) of sales is changing is approximated by V ' ( t ) = − 26400 e − 0.49 t . On the day the advertising campaign ends ( t = 0 ), the sales volume is $ 170 , 000 . Find both V ' ( 6 ) and its integral V ( 6 ) . Round your answers to the nearest cent.
Answer:
Step-by-step explanation:
Given the rate at which the volume V (in dollars) of sales is changing is approximated by the equation
V ' ( t ) = − 26400 e^− 0.49 t .
t = time (in days)
.v'(6) can be derived by simply substituting t = 6 into the modelled equation as shown:
V'(6) = − 26400 e− 0.49 (6)
V'(6) = -26400e-2.94
V'(6) = -26400×-0.2217
V'(6) = $5852.88
V'(6) = $5,853 to nearest dollars
V'(6) = 585300cents to nearest cent
To get v(6), we need to get v(t) first by integrating the given function as shown:
V(t) = ∫−26400 e− 0.49 t dt
V(t) = -26,400e-0.49t/-0.49
V(t) = 53,877.55e-0.49t + C.
When t = 0, V(t) = $170,000
170,000 = 53,877.55e-0 +C
170000 = 53,877.55(2.7183)+C
170,000 = 146,454.37+C
C = 170,000-146,454.37
C = 23545.64
V(6) = 53,877.55e-0.49(6)+ 23545.64
V(6) = -11,945.63+23545.64
V(6) = $11,600 (to the nearest dollars)
Since $1 = 100cents
$11,600 = 1,160,000cents
Edwin has 3 1 2 gallons of green paint. He uses 2 3 of the paint to paint his bedroom. He uses the rest of the paint for a mural in his garage. How much paint does Edwin use for the mural?
Answer:
1 1/6
Step-by-step explanation:
Edwin used a quantity of 2.833 gallons of paint for the mural which is the difference between the quantity of paint at the beginning and the used for the bedroom.
We have been given that Edwin has 3 1/2 gallons of green paint. He uses 2/3 of the paint to paint his bedroom. He uses the rest of the paint for a mural in his garage.
What is the fraction?A fraction is defined as a numerical representation of a part of a whole that represents a rational number.
To determine the quantity of paint Edwin used for the mural.
The quantity of paint Edwin used for the mural is the difference between the quantity of paint at the beginning and the used for the bedroom.
The quantity of paint used for the mural = 3 1/2 gallons - 2/3 gallons
The quantity of paint used for the mural = 3.5 - 0.66
The quantity of paint used for the mural = 2.833
Thus, Edwin used a quantity of 2.833 gallons of paint for the mural.
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Solve the equation? Help Please !!!?!?! 3-x/2>12
Answer:x<-18
Step-by-step explanation:
Step 1: Simplify both sides of the inequality.
-1/2x+3>12
Step 2: Subtract 3 from both sides.
-1/2x+3-3>12-3
-1/2x>9
Step 3: Multiply both sides by 2/(-1).
(2/-1)*(-1/2x)>(2/-1x)*(-1/2x)
X<-18
:D
∠A and ∠B are supplementary, and ∠A and ∠C are supplementary. Which conclusion is valid? Select one: A. ∠B and ∠C are supplementary. B. ∠B and ∠C are acute. C. ∠B and ∠C are complementary. D. ∠B and ∠C are congruent.
Option D is the correct answer.
Answer:
D. ∠B and ∠C are congruent.
Step-by-step explanation:
Since, ∠A and ∠B are supplementary.
Therefore,
∠A + ∠B = 180°.....(1)
Since, ∠A and ∠C are supplementary.
Therefore,
∠A + ∠C = 180°.....(2)
From equations (1) & (2)
∠A + ∠B = ∠A + ∠C
=> ∠B = ∠C
Hence, ∠B and ∠C are congruent.
P(AB) can be read as "the probability that A occurs given that Bhas
occurred."
A. True
B. False
Answer:
False
Step-by-step explanation:
from *millermoldwarp*
"Events are called dependent when the probability of an event depends on the occurrence of another. When event A depends on event B, the probability that A occurs, given that B has occurred, is different from the probability that A occurs only ."
hopes this helps
Answer:false
Step-by-step explanation:
What type of error is present in the underlined
sentence?
Which is the best revision to fix the error?
Answer:
Type of error: Run-on(comma splice).
Best revision to fix it: Adding a semicolon after beginners .
Explanation:
A run-on sentence is described as a sentence in which two independent clauses are joined inappropriately. It could be either comma splice where the two independent clauses are incorrectly linked using a comma or fused sentence when the two clauses run-on without employing appropriate coordinating conjunction or punctuation marks to separate the two ideas.
In the given sentence, it exemplifies a comma splice type of run-on sentence error. To fix this error, a semicolon after 'beginners' can be employed instead of a comma. This will help in connecting the two ideas appropriately where the first idea leads the second. Thus, the final sentence reads as:
'The guitar is another excellent instrument for beginners; however, it takes more practice than a recorder.'
Answer:
Many people play a musical instrument music can be soothing. A lot of schools teach the recorder; it is inexpensive and easy to play. The guitar is another excellent instrument for beginners, it takes more practice than a recorder.
What type of error is present in the underlined sentence?
✔ run-on
Which is the best revision to fix the error?
✔ adding a semicolon after instrument
Step-by-step explanation:
how to solve the birth rate in a certain country in 1994 was 14.6 births per thousand population. in 2004 the birth rate was 14.32 births per thousand. let x represent years after 1994 and y represent the birth rate. assume the relationship is linear
Answer:
[tex]y(x)=-0.028x+14.6[/tex]
Step-by-step explanation:
We are to write a linear equation that relates y in terms of x
The Birth Rate in 1994 = 14.6 births per thousand population.
The Birth Rate in 2004 = 14.32 births per thousand population.
A linear equation is of the form y=mx+b, where:
x=Number of Years after 1994y=the birth ratem=Birth rate per yearStep 1: Determine the birth rate per year
In 1994, x=0, y=14.6 thousands
In 2004, x=10, y=14.32 thousands
[tex]m=\dfrac{14.32-14.6}{10-0}\\=\dfrac{-0.28}{10}\\m=-0.028[/tex]
Substituting m into our linear equation, we have:
[tex]y(x)=-0.028x+b[/tex]
When x=10, y=14.32
[tex]14.32=-0.028(10)+b\\b=14.32+0.28\\b=14.6[/tex]
Therefore, a linear equation that relates y in terms of x is:
[tex]y(x)=-0.028x+14.6[/tex]
For every 1% increase in
unemployment, there is a 2%
decrease in potential GDP. This
creates a GDP gap. What is the GDP
gap when there is 4.5%
unemployment?
Answer:
The GDP gap is 9 % when there is 4.5 % unemployment.
Step-by-step explanation:
The statement shows a reverse relationship, where an increase in unemployment is following by decrease in potential GDP and can be translated into the following rate:
[tex]r = \frac{2\,\% \,GDP}{1\,\% unemp.}[/tex]
The GDP gap at a given increase in unemployment can be estimated by the following expression:
[tex]\frac{g}{u} = r[/tex]
[tex]g = r\cdot u[/tex]
Where:
[tex]r[/tex] - GDP gap-unemployment increase rate, dimensionless.
[tex]u[/tex] - Increase in unemployment rate, measured in percentage.
[tex]g[/tex] - GDP gap, measured in percentage.
If [tex]r = \frac{2\,\% \,GDP}{1\,\% unemp.}[/tex] and [tex]u = 4.5\,\%\,unemp.[/tex], the GDP gap is:
[tex]g = \left(\frac{2\,\%\,GDP}{1\,\%\,unemp.} \right)\cdot (4.5\,\%\,unemp.)[/tex]
[tex]g = 9\,\%\,GDP[/tex]
The GDP gap is 9 % when there is 4.5 % unemployment.
Connecticut families were asked how much they spent weekly on groceries. Using the following data, construct and interpret a 95% confidence interval for the population mean amount spent on groceries (in dollars) by Connecticut families. Assume the data come from a normal distribution
210 23 350 112 27 175 275 50 95 450
Answer:
The 95% confidence interval for the population mean amount spent on groceries by Connecticut families is ($73.20, $280.21).
Step-by-step explanation:
The data for the amount of money spent weekly on groceries is as follows:
S = {210, 23, 350, 112, 27, 175, 275, 50, 95, 450}
n = 10
Compute the sample mean and sample standard deviation:
[tex]\bar x =\frac{1}{n}\cdot\sum X=\frac{ 1767 }{ 10 }= 176.7[/tex]
[tex]s= \sqrt{ \frac{ \sum{\left(x_i - \overline{x}\right)^2 }}{n-1} } = \sqrt{ \frac{ 188448.1 }{ 10 - 1} } \approx 144.702[/tex]
It is assumed that the data come from a normal distribution.
Since the population standard deviation is not known, use a t confidence interval.
The critical value of t for 95% confidence level and degrees of freedom = n - 1 = 10 - 1 = 9 is:
[tex]t_{\alpha/2, (n-1)}=t_{0.05/2, (10-1)}=t_{0.025, 9}=2.262[/tex]
*Use a t-table.
Compute the 95% confidence interval for the population mean amount spent on groceries by Connecticut families as follows:
[tex]CI=\bar x\pm t_{\alpha/2, (n-1)}\cdot\ \frac{s}{\sqrt{n}}[/tex]
[tex]=176.7\pm 2.262\cdot\ \frac{144.702}{\sqrt{10}}\\\\=176.7\pm 103.5064\\\\=(73.1936, 280.2064)\\\\\approx (73.20, 280.21)[/tex]
Thus, the 95% confidence interval for the population mean amount spent on groceries by Connecticut families is ($73.20, $280.21).
Please answer this correctly
Answer:
The range would decrease by 2
Step-by-step explanation:
The range is the difference between the highest number and the lowest number.
8 is the highest number and 1 is the lowest number here, so to find the range we would subtract 1 from 8. 8-1=7
But since 8 is being replaced by 6, we would subtract 1 from that instead.
6-1=5
The range decreased from 7 to 5, so it decreased by 2.
Hope that helps :)
How many pairs are shown ?????????
Answer:8 i ithink
Step-by-step explanation:
Answer:
12, go for 24.
Step-by-step explanation:
There are 6 sides of a cube.
There are 2 pairs of parallel line segments for each side.
6 x 2 = 12
Although that answer is not there, you should go for 24. Since there are 2 variables for each line segment, 12 x 2 = 24. Not sure, hope this helps.
:/
hey guys, can you help me please
=========================================================
Work Shown:
The green triangle in the back has height 2.6 and an unknown base x. Half of this is x/2, which I'll call y. So y = x/2.
The green triangle in the back is split along the vertical dotted line to get two right triangles. The base of each right triangle is y = x/2.
Use the Pythagorean theorem to find y. Use that to find x
a^2+b^2 = c^2
y^2+(2.6)^2 = (3.2)^2
y^2 + 6.76 = 10.24
y^2 = 10.24 - 6.76
y^2 = 3.48
y = sqrt(3.48) .... apply square root
y = 1.8654758 approximately
x/2 = 1.8654758
x = 2*1.8654758
x = 3.7309516 also approximate
The base of the triangle is roughly 3.7309516 meters
We can now find the area of one green triangle
area of triangle = base*height/2 = 3.7309516*2.6/2 = 4.85023708
two triangles have approximate area 2*(4.85023708) = 9.70047416
----------------------------------
So far we've only considered the triangular faces. There are 3 more faces which are the rectangular sides. These are known as the lateral sides.
One way to get the lateral surface area is to multiply the perimeter of the triangle by the depth of the prism
perimeter of triangle = (side1)+(side2)+(side3)
perimeter = 3.7309516 + 3.2 + 3.2
perimeter = 10.1309516
lateral surface area = (depth)*(perimeter)
lateral surface area = (8.26)*(10.1309516)
lateral surface area = 83.681660216
----------------------------------
The last step is to add this lateral surface area onto the area of the two triangles to get the full surface area
surface area = (triangular area) + (lateral surface area)
surface area = (9.70047416) + (83.681660216)
surface area = 93.382134376
surface area = 93.382 square cm
A bank is reviewing its risk management policies with regards to mortgages. To minimize the risk of lending, the bank wants to compare the typical mortgage owed by their clients against other homebuyers. The average mortgage owed by Americans is $306,500, with a standard deviation of $24,500. Suppose a random sample of 150 Americans is selected. Identify each of the following, rounding your answers to the nearest cent when appropriate:
1. $mu=?
2. $sigma=?
3. $=n=$
4. $mu_{overlinex}=$x=?
5. $sigma_{overlinex}=$x=?
Answer:
1. [tex]$ \mu = \$306,500 $[/tex]
2. [tex]\sigma = \$24,500[/tex]
3. [tex]n = 150[/tex]
4. [tex]$ \mu_{x}= \mu = \$306,500 $[/tex]
5. [tex]\sigma_x = \$ 2,000 \\\\[/tex]
Step-by-step explanation:
The average mortgage owed by Americans is $306,500, with a standard deviation of $24,500.
From the above information, we know that,
The population mean is
[tex]$ \mu = \$306,500 $[/tex]
The population standard deviation is
[tex]\sigma = \$24,500[/tex]
Suppose a random sample of 150 Americans is selected
[tex]n = 150[/tex]
Since the sample size is quite large then according to the central limit theorem, the sample mean is approximately normally distributed.
The sample mean would be the same as the population mean that is
[tex]$ \mu_{x}= \mu = \$306,500 $[/tex]
The sample standard deviation is given by
[tex]\sigma_x = \frac{\sigma}{\sqrt{n} }[/tex]
Where [tex]\sigma[/tex] is the population standard deviation and n is the sample size.
[tex]\sigma_x = \frac{24,500}{\sqrt{150} } \\\\\sigma_x = \$ 2,000 \\\\[/tex]
Therefore, the required parameters are:
1. [tex]$ \mu = \$306,500 $[/tex]
2. [tex]\sigma = \$24,500[/tex]
3. [tex]n = 150[/tex]
4. [tex]$ \mu_{x}= \mu = \$306,500 $[/tex]
5. [tex]\sigma_x = \$ 2,000 \\\\[/tex]
Approximately 10% of all people are left-handed. If 200 people are randomly selected, what is the expected number of left-handed people? Round to the whole number. Do not use decimals. Answer:
Answer:
N(L) = 20
The expected number of left handed people is 20.
Step-by-step explanation:
Given;
Percentage of left handed people P(L) = 10%
Total number of selected people N(T) = 200
The Expected number of left handed people N(L) is;
N(L) = Total number of selected people × Percentage of left handed people/100%
N(L) = N(T) × P(L)/100%
Substituting the given values;
N(L) = 200 × 10%/100%
N(L) = 200 × 0.1
N(L) = 20
The expected number of left handed people is 20.
What number should go in the space? Multiplying by 0.65 is the same as decreasing by _____%
Answer: 35%
Step-by-step explanation:
If no is 10, 10 x 0.65 = 6.5. OR
10 - 35% of 10 = 6.5
Multiplying by 0.65 is the same as decreasing by 35%
Conversion of statements into algebraic expression:To convert the statement into algebraic expression choose the variables first.Then form the expression or equation as per given statements.
Let the number is 'a' and percentage decrease is 'b',
Expression for the given statement will be,
a × 0.65 = a - (b% of a)
[tex]0.65a=a(1-\frac{b}{100})[/tex]
[tex]0.65=1-\frac{b}{100}[/tex]
[tex]\frac{b}{100}=1-0.65[/tex]
[tex]b=100(0.35)[/tex]
[tex]b=35[/tex]
Therefore, Multiplying by 0.65 is the same as decreasing by 35%.
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A large toiletry distributor claims that 35% of all individuals who purchase toilet paper from the stores that carry its product choose original toilet paper, 28% choose sensitive toilet paper, 20% choose ultra-strong toilet paper, and 17% choose ultra-soft toilet paper. To investigate this claim, researchers collected data from a random sample of customers in a large city. The results were 170 packages of original, 105 sensitive, 80 ultra-strong, and 45 ultra-soft toilet paper purchases. Are the data from the sample consistent with the distributor's claim
p-value < 0.05, reject null hypothesis and we can conclude that data is not consistent with distributor's claim.
Given, data of toiletry distributors.
Total number of observations
= 170 + 105 + 80 + 45
= 400
Expected count = [tex]p_i \times 400[/tex]
Calculation table is attached below.
Test statistic:
Chi square score
= 6.429 + 0.438 + 0.000 + 7.779
= 14.645
Degree of freedom:
df = 4-1
=3
p-value = CHIDIST(14.645,3)
= 0.00215
Therefore , p-value < 0.05
Reject null hypothesis and we can conclude that data is not consistent with distributor's claim.
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A circular swimming pool has a diameter of 20 ft, the sides are 6 ft high, and the depth of the water is 5 ft. How much work (in ft-lb) is required to pump all of the water out over the side
Answer:
19467649.76 lb-ft^2/s^2
Step-by-step explanation:
diameter of the pool d = 20 ft
radius = d/2 = 20/2 = 10 ft
height of pool side h = 6 ft
depth of water d = 5 ft
the force on the bottom of the pool due to the water in the pool is
F = pgdA
where p = density of water = 62.4 lb/ft^3
g = acceleration due to gravity = 32.17 ft/s^2
Area A = [tex]\pi r^{2}[/tex] = [tex]3.142 * 10^{2}[/tex] = 314.2 ft^2
Force on pool bottom = 64.2 x 32.17 x 5 x 314.2 = 3244608.29 lb-ft/s^2
work done = force times the height the water will be pumped
work = F x h = 3244608.29 x 6 = 19467649.76 lb-ft^2/s^2
The work (in ft-lb) is required to pump all of the water out over the side is :
Given :Diameter of the pool d = 20 ftRadius = d/2 = 20/2 = 10 ftHeight of pool side h = 6 ftDepth of water d = 5 ftFormula:
F = pgdA
p = density of water = 62.4 lb/ft^3
g = acceleration due to gravity = 32.17 ft/s^2
Area A = [tex]\pi r2\\[/tex] = 314.2 ft^2
Force on pool bottom = 64.2 x 32.17 x 5 x 314.2 = 3244608.29 lb-ft/s^2work done = force times the height the water will be pumpedwork = F x h = 3244608.29 x 6 = 19467649.76 lb-ft^2/s^2The work (in ft-lb) is required to pump all of the water out over the side is 19467649.76 lb-ft^2/s^2.
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) Let an denote number of n-digit ternary sequences (sequences of 0,1 and 2) which have no consecutive 0’s in them. Find a recurrence relation for an. (Do not solve the recurrence. However, depending on the order of the recurrence, provide a sufficient number of initial conditions. )
Answer:
The recurrence relation for aₙ is aₙ = 2aₙ - 1 + 2aₙ -2 ; is n≥ 3 with the initial conditions as a₁ =3; a₂ = 8
Step-by-step explanation:
Solution
Recurrence relation for n - digit ternary sequence with no occurrence of consecutive 0's in them.
Ternary sequence is sequence with each of digits either 0, 1 or 2.
Now
Let aₙ = denote the number of n - digit ternary sequence with no occurrence of consecutive 0's in them.
Let us first find few initial values of aₙ
For n = 1
a₁ represent the number of 1- digit ternary sequence with no occurrence of consecutive 0's in them.
This 1-digit sequence can be either 0 or 1 or 2.
Thus,
a₁ = 3
For n =2
a₂ represent the number of 2- digit ternary sequence with no occurrence of consecutive 0's in them.
This 2-digit sequence can have either 0 or 1 or 2 as each of its two digit, but making sure that there are no two consecutive 0 in the sequence.
here are " 9 " 2-digit ternary sequence ........... (three choices for 1st digit and three choices for 2nd digit)
But one of these 9 sequence there are consecutive 0's .... (00)
So we eliminate this one sequence.
So, a₂ = 8
Now
let us find the recurrence relation
Fir n ≥ 3
aₙ s the number of n - digit ternary sequence with no occurrence of the consecutive 0's in them.
For the first case: if 1st digit of this n - digit ternary sequence is 1 or 2
Let assume the 1st digit of this n - digit ternary sequence is 1.
Then for remaining n - 1 digits of this n - digit ternary sequence we have to make sure that there is no consecutive 0's in them.
For example, we have to form a n-1-digit ternary sequence with no occurrence of consecutive 0's in them which is by definition aₙ -1
So,
The number of n - digit ternary sequence with no occurrence of consecutive 0's in them if 1st digit of this sequence is 1 is aₙ -1.
Likewise, the number of n - digit ternary sequence with no occurrence of consecutive 0's in them if 1st digit of this sequence is 2 is aₙ -1.
So
If 1st digit of this n - digit ternary sequence is 1 or 2, then the number of n - digit ternary sequence with no occurrence of consecutive 0's in them is shown as:
aₙ-1 + aₙ -1 = 2aₙ -1
For the second case: if 1st digit of this n - digit ternary sequence is 0
If 1st digit of this n - digit ternary sequence is 0, then the next digit cannot be 0 as well because that would make two consecutive 0's in the sequence Thus,
If 1st digit of this n - digit ternary sequence is 0, the next term can be either 1 or 2.
So there are 2 choices for 2nd digit.
After this there are more n-2 digits.
Then
For remaining n - 2 digits of this n - digit ternary sequence we have to make sure that there is no consecutive 0's in them
For example, we have to form a n-2-digit ternary sequence with no occurrence of consecutive 0's in them. which is by definition aₙ - 2.
Now,
The total number of sequence in this case is given as:
2aₙ -2........... (2 choices for 2nd digit and aₙ - 2 choices for remaining n-2 digit)
Hence
The number of n - digit ternary sequence with no occurrence of consecutive 0's in them if 1st digit of this sequence is 0 is aₙ = 2aₙ - 1 + 2aₙ -2 which is n≥ 3
Now,
The recurrence relation for aₙ is shown below:
aₙ = 2aₙ - 1 + 2aₙ -2; is n≥ 3
With the initial conditions as a₁ =3; a₂ = 8
What is the area of the triangle below?
18
Answer:
D. 32 sq. unit s
Step-by-step explanation:
4×18/2=32
AC =
Round your answer to the nearest hundredth.
A
5
35
B
C
Answer:
2.87 = AC
Step-by-step explanation:
Since this is a right triangle we can use trig functions
sin theta = opp / hyp
sin 35 = AC /5
5 sin 35 = AC
2.867882182= AC
To the nearest hundredth
2.87 = AC
Suppose we take repeated random samples of 50 college students from the same population and determine a 95% confidence interval for the mean GPA from each sample. Which of the following statements is true regarding the confidence intervals?
A. The intervals are centered around the population mean GPA.
B. The intervals are centered around the sample mean GPA.
C. 95% of the intervals will contain the sample mean in the long run.
D. 95% of the intervals will contain the population mean in the long run.
Answer:
B. The intervals are centered around the sample mean GPA.
D. 95% of the intervals will contain the population mean in the long run.
Step-by-step explanation:
Confidence interval:
Depends on two things: The sample mean and the margin of error.
Lower end: Sample mean - margin of error
Upper end: Sample mean + margin of error
This means that the intervals are centered around the sample mean.
x% level:
x% of the intervals will contain the population mean in the long run.
So the true statements are:
B. The intervals are centered around the sample mean GPA.
D. 95% of the intervals will contain the population mean in the long run.
Un importante grupo de inversionistas, asociado a una línea de buses interurbanos, está considerando instalar un centro logístico de mantención, a usted le ha encargado la evaluación de este proyecto, considerando un horizonte de 5 años. el estudio técnico del proyecto indica que se requiere disponer de un galpón 1000 m2 dentro de las instalaciones que la empresa ya cuenta, además de un acceso pavimentado con cimientos especiales de 6000 m2. el costo de construcción del galpón es de $ 42 por m2, y el costo de construcción del acceso pavimentado es de $ 32 por cada m2. adicionalmente, se requiere adquirir servidores de punta para realizar el check de los buses antes de comenzar sus recorridos, su costo se estima en $ 630.000, además se necesitan equipos especiales para la revisión de los neumáticos, con un costo de $ 400.000. finalmente, se deberá conseguir un terreno al interior del terminal de buses, con una superficie de 1 m2, con un costo de $50 por m2.
Answer:
Monto total de inicio requerido, de acuerdo con los detalles proporcionados en la pregunta = $ 1,264,000
Total start-up amount required, according to the details provided in the question = $1,264,000
Step-by-step explanation:
- Hay 1000 m² de espacio de almacén para construir a $ 42 por m². Dinero total requerido = 1000 × 42 = $ 42,000.
- Hay 6000 m² de espacio de acceso pavimentado para construir a $ 32 por m². Dinero total requerido = 6000 × 32 = $ 192,000.
- Compra de servidores de última generación para revisar los autobuses antes de comenzar sus recorridos. Costo total = $ 630,000.
- Se necesita comprar equipo especial para revisar los neumáticos. Costo = $ 400,000.
Monto total de inicio requerido, de acuerdo con los detalles proporcionados en la pregunta = 42000 + 192000 + 630000 + 400000 = $ 1,264,000
¡¡¡Espero que esto ayude!!!
English Translation
- There is 1000 m² of warehouse space to construct at $42 per m². Total required money = 1000 × 42 = $42,000
- There is 6000 m² of paved access space to construct at $32 per m². Total money required = 6000 × 32 = $192,000
- Purchase of state-of-the-art servers to check the buses before starting their tours. Total Cost = $630,000
- Purchase of special equipment is needed to check the tires. Cost = $400,000
Total start-up amount required, according to the details provided in the question = 42000 + 192000 + 630000 + 400000 = $1,264,000
Hope this Helps!!!
Data on the number of work days missed and the annual salary increase for a company’s employees show that, in general, employees who missed more days of work during the year received smaller raises than those who missed fewer days. A detailed analysis shows that the number of days missed explains 60% of the variation in salary increases. What is the correlation between the number of days missed and salary increase?
Answer:
Step-by-step explanation:
Correlation describes how strongly pairs of given variablé are related. In this case, a detailed analysis that was carried out shows that the number of days missed by employees explains 60% of the variation in salary increases and also impressed upon this fact that employees who missed more days of work during the year received smaller raises than those who missed fewer days.
From the analysis, we can draw a conclusion that there is a correction between days missed and variation in salary increase and that this type of correction is a negative correlation where an increase in the number of days missed will lead to a decrease in the raises awarded to each employee.
Adult male heights are a normal random variable with mean 69 inches and a standard deviation of 3 inches. Find the height, to the nearest inch, for which only 8 percent of adult males are taller (i. find the 92nd percentile)
Answer:
The height (corresponding to the [tex] \\ 92^{nd}[/tex] percentile) is (to the nearest inch) 73 inches (and, approximately, only 8% of adult males are taller than this height.)
Step-by-step explanation:
Roughly speaking, the [tex] \\ 92^{nd}[/tex] percentile is the x value (in the distribution) for which 92% of the observations in the [normal] distribution are below this x value, and 8% of the observations are above this x value.
To answer this question, we already know that:
Heights are a normal random variable, i.e, it follows a normal distribution.The mean for this distribution is [tex] \\ \mu = 69[/tex] inches.The standard deviation is [tex] \\ \sigma = 3[/tex] inches.Strategy for solving the question
For solving this, we have to use here the following key concepts: z-scores, the cumulative standard normal distribution, and the cumulative standard normal table.
Z-scores
To find the [tex] \\ 92^{nd}[/tex] percentile, we can use z-scores or standardized values. A z-score is a value that tells us the distance in standard deviations units from the mean. When the z-score is positive, it means that the value is above the mean. A negative indicates that the z-score is below the mean. The formula to obtain a z-score is as follows:
[tex] \\ z = \frac{x - \mu}{\sigma}[/tex] [1]
Where
z is the z-score.x is the raw score.[tex] \\ \mu[/tex] is the mean.[tex] \\ \sigma[/tex] is the standard deviation.Cumulative standard normal distribution and corresponding table
We still need to know the corresponding z-score, z, for the cumulative probability of 92%. For this, we have to consult the standard normal table, available on the Internet or in any Statistics books.
In this case, we look in the different columns of the standard normal table a probability value (exact or approximate) to 0.92 and then find the value for z that corresponds to this probability. The value for z is between 1.40 (0.91924) and 1.41 (0.92073).
Using z = 1.40 in [1], we have:
[tex] \\ z = \frac{x - \mu}{\sigma}[/tex]
[tex] \\ 1.40 = \frac{x - 69}{3}[/tex]
Then, solving for x:
Multiplying by 3 at each side of the equation:
[tex] \\ 1.40 * 3 = x - 69[/tex]
Adding 69 at both sides of the equation:
[tex] \\ (1.40 * 3) + 69 = x[/tex]
[tex] \\ x = (1.40 * 3) + 69[/tex]
[tex] \\ x = 4.20 + 69[/tex]
[tex] \\ x = 73.20[/tex]
That is, the [tex] \\ 92^{nd}[/tex] percentile is 73.20 inches, and to the nearest inch, this percentile is 73 inches.
This result indicates that, approximately, 92% of the heights are below 73 inches, and only 8% of heights are taller than this height.
The shaded area in the graph below shows an area of 0.08076 (8.076%) for 73.20 inches.
Which leader was a member of the Kikuyu tribe?
A. Kwame Nkrumah
B. Marcus Garvey
C. Mohandas Gandhi
D. Jomo Kenyatta
Answer:
Jomo Kenyatta
Step-by-step explanation:
Jomo Kenyatta was a Kenyan politician, who was one of the first African anti-colonial figures. He became the prime minister of Kenya from 1963 to 1964, and after Kenyan independence in 1964, he became president of Kenya. Jomo Kenyatta was born into a family of Kikuyu farmers in Kiambu, present day Kenya which was then, British East Africa. He had his basic schooling in a missionary school before proceeding to study at Moscow's Communist University of the Toilers of the East, University College London, and the London School of Economics.
Answer:
Jomo Kenyatta
Step-by-step explanation:
took the test