True, Because in a transformation, the preimage is the original figure and the image is the figure in the new location.
What is Translation?A transformation that occurs when a figure is moved from one location to another location without changing its size or shape is called translation.
Given that;
The statement is,
''In a transformation, the preimage is the original figure and the image is the figure in the new location.''
Now,
Since, We know that;
The preimage is the original figure and the image is the figure in the new location.
Hence, In a transformation, the preimage is the original figure and the image is the figure in the new location.
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Use inductive reasoning to predict the most probable next number in the list.
8, 15, 1, 8, −6, 1, −13, −6, −20, ?
Answer:
-13
Step-by-step explanation:
the pattern goes +7 - 14, so -20 + 7 = 13
find the least positive integer $n$ such that the set of $1000$ consecutive integers beginning with $1000\cdot n$ contains no square of an integer.
The difference between consecutive integral squares must be greater than 1000. (x+1)^2-x^2>=1000, so x>=999/2 implies x>=500. x=500 does not work, so x>500. Let n=x-500. The sum of the square of n and a number a little over 1000 must result in a new perfect square. By inspection, n^2 should end in a number close to but less than 1000 such that there exists 1000N within the difference of the two squares. Examine when n^2=1000. Then, n=10sqrt(10). One example way to estimate sqrt(10) follows.
3^2=9, so 10=(x+3)^2=x^2+6x+9. x^2 is small, so 10=6x+9. x=1/6 implies sqrt(10)\approx 19/6. This is 3.16.
Then, n approx 31.6. n^2<1000, so n could be 31. Add 500 to get the first square and 501 to get the second. Then, the two integral squares are 531^2 and 532^2. Checking, 531^2=281961 and 532^2=283024. 282,000 straddles the two squares, which have a difference of 1063. The difference has been minimized, so N is minimized N=282000 implies 282
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A farmer needs to construct twO adjoining rectangular pens of identical areas (15 points) showa in the figure below . If each pen is to have an area of 1200 square feet, what dimeosions will minimize the length of fencing? 1200 sq: ft. 1200 sq. ft,
A farmer needs to construct two adjoining rectangular pens with each pen is to have an area of 1200 square feet. So dimeosions will minimize the length of fencing is length = 40 ft and width = 30 ft.
Determine dimeosions will minimize the length of fencingFor pictures of two rectangular pens, see the attachment.
Area of rectangle = length × width
A = x × y
1200 = xy
y = 1200/x
The entire length of the fence
P = 3x + 4y
P = 3x + 4 (1200/x)
P = 3x + 4800/x
P = 3x + 4800x⁻¹
Find dimentions will minimize the length of fencing, if P' = 0.
P = 3x + 4800x⁻¹
P' = 3 - 1 × 4800x⁻¹⁻¹
0 = 3 - 4800x⁻²
4800x⁻² = 3
4800/x² = 3
4800 = 3x²
x² = 4800/3
x² = 1600
x = 40
y = 1200/x
y = 1200/40
y = 30
So dimeosions will minimize the length of fencing is length = 40 ft and width = 30 ft.
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a norman window has the shape of a rectangle surmounted by a semicircle. (thus the diameter of the semicircle is equal to the width of the rectangle, labeled x.) a window with the shape of a rectangle surmounted by a semicircle. the diameter of the semicircle is equal to the width of the rectangle. the rectangle has width x. if the perimeter of the window is 32 feet, find the exact value of x (in ft) so that the greatest possible amount of light is admitted.
The exact value of x (in ft) so that the greatest possible amount of light is admitted is 8.96 ft
According to the question,
A norman window has the shape of a rectangle surmounted by a semicircle.
Let The width of rectangle be x and height be y
It is given that the diameter of the semicircle is equal to the width of the rectangle
Therefore , Diameter of circle = x
Radius = x/2
Perimeter of window = 32 = Perimeter of rectangle + Perimeter of semi-circle
=> 32 = Width + 2height + πr
=> x + 2y + πx/2 = 32
=> 2x + 4y + πx = 64
Solving for y,
=> 4y = 64 - 2x - πx
=> y = 64 - 2x - πx/ 4 ----------(1)
Area of the window = Area of rectangle + area of semi-circle
=> A = Width × hiegth + πx²/8
=> A = xy + πx²/8
Substituting the value of y from equation (1)
=> A = x ( 64 - 2x - πx/ 4 ) + πx²/8
[tex]A = x ( \frac{64 - 2x -\pi x}{ 4} ) + \frac{\pi x^2}{8}\\A = ( \frac{ 64x - x^2 ( 2 + \pi)}{4 } ) + \frac{\pi x^2}{8}[/tex]
Differentiating A w.r.t x
=> [tex]\frac{dA}{dx} = (\frac{64 - 2x(2 + \pi)}{4} ) + \frac{\pi x}{4}[/tex]
Now , To find a maximum area
dA/dx = 0
=> [tex]\frac{dA}{dx} = (\frac{64 - 2x(2 + \pi)}{4} ) + \frac{\pi x}{4} = 0[/tex]
Solving for x ,
64 - 4x - 2π + πx = 0
=> x = 64 / 4 + π ------(2)
Differentiating A again w.r.t x
=> d²A / dx² = -2(2 + π)/4 + π/4
=> -π+4 / 4 which is less than zero
Therefore,
Area is maximum when x = 64 / 4 + π
The exact value of x (in ft) so that the greatest possible amount of light is admitted is 8.96 ft
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explain how to use the multiplication table to solve 5 x 4
Answer:
Go and look up your tables and read below
Step-by-step explanation:
To solve the problem 5 x 4 using the multiplication table, you would look up the corresponding entries in the table for the numbers 5 and 4. In the row labeled 5 and the column labeled 4, you would find the product 20, which is the answer to the problem 5 x 4.
answer
Step-by-step explanation:
the diagrqam shows an object with a mass of 1.0 kiolgram attached to a string 0.50 merer long. the object is moving at a constant speed of 5.0 meters per second in hporizontal circular path with center at point o
The object is undergoing uniform circular motion. The radius of the circular path is equal to 0.50 meters. The centripetal force, F, acting on the object can be calculated using the equation F= mv^2/r in hporizontal circular path
m is the mass of the object, v is the velocity of the object and r is the radius of the circular path.
F = (1.0 kg) (5.0 m/s)^2 / 0.50 m
F = 50.0 kg m/s^2
The object is undergoing uniform circular motion, which means it is moving at a constant speed in a circular path with its center at point O. The radius of the circular path is equal to 0.50 meters. The force acting on the object is known as the centripetal force, and can be calculated by using the equation F= mv^2/r. This equation requires the mass of the object (m), its velocity (v), and the radius of the circular path (r). In this case, the mass is 1.0 kg, the velocity is 5.0 m/s, and the radius is 0.50 m. Plugging these values into the equation gives the centripetal force acting on the object as 50.0 kg m/s^2.
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find a polynomial f(x) 3 of degree that has the following zeros. 0,-5,4
The polynomial f(x) of degree 3 is
f(x) = x³ + x² - 20x
What is a polynomial?Polynomial is an equation written as the sum of terms of the form kx^n.
where k and n are positive integers.
We have,
The zeroes of the polynomial are 0, -5, and 4.
This can be written as,
x = 0, x
x = -5, (x + 5)
x = 4, (x - 4)
x(x + 5)(x - 4)
(x² + 5x)(x - 4)
x³ - 4x² + 5x² - 20x
x³ + x² - 20x
Thus,
The polynomial is f(x) = x³ + x² - 20x
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Can someone help please? Picture is already attached. If its wrong please correct it. This isn’t mine by the way, I’m posting it for someone else to double check if it’s right
The value of the other points in each of the number line is;
a) M = -2¹/₂; N = -1; R = 4
b) M = -1; P = 1; R = 1.6
c) M = -125; P = 125; N = -50
d) N = -6; P = 15; R = 24
How to interpret Number Lines?a) The point P = 2¹/₂
The distance from point 0 of the number line to point P is 5 units and therefore;
Each unit = 2¹/₂/5 = ¹/₂
Thus;
M = -2¹/₂
N = -1
R = 4
b) The point N = -0.4
The distance from point 0 of the number line to point N is 2 units and therefore;
Each unit = 0.4/2 = 0.2
Thus;
M = -1
P = 1
R = 1.6
C) The point R = 200
The distance from point 0 of the number line to point R is 8 units and therefore;
Each unit = 200/8 = 25
Thus;
M = -125
P = 125
N = -50
D) The point M = -15
The distance from point 0 of the number line to point N is 5 units and therefore;
Each unit = 15/5 = 3
Thus;
N = -6
P = 15
R = 24
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The table below shows the linear relationship between the distance in feet below sea level and the time in seconds traveled by a submarine.
What is the rate of change (slope) of the distance in feet below sea level with respect to time that the submarine traveled? Place your answer in the box:
The rate of change (slope) of the distance in feet below sea level with respect to time that the submarine traveled is 11 feet .
Given :
The table below shows the linear relationship between the distance in feet below sea level and the time in seconds traveled by a submarine .
From the table:
Take any two points ( 0 , 380 ) and ( 15 , 545 )
slope m = 545 - 380 / 15 - 0
= 165 / 15
= 33 / 3
= 11 / 1
= 11 feet
Hence the slope m is 11 feet .
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Solve the system of equations using elimination. 2x + 3y = −15 3x + y = 2 (0, 5) (1, −1) (3, −7) (4, −10)
The solution to the system of equations is x = 3 and y = -7. The correct option is C. (3, -7).
The system of equations is given as follows:
2x + 3y = −15 ....(1)
3x + y = 2 ....(2)
Multiply Equation 2 by 3:
9x + 3y = 6 ....(3)
Now, we can subtract Equation 1 from Equation 3 to eliminate y:
(9x + 3y) - (2x + 3y) = 6 - (-15)
9x + 3y - 2x - 3y = 6 + 15
7x = 21
x = 21/7
x = 3
Substituting the value of x into Equation 2 to solve for y:
3(3) + y = 2
9 + y = 2
y = 2 - 9
y = -7
Therefore, the solution to the system of equations is x = 3 and y = -7.
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Complete question:
Solve the system of equations using elimination.
2x + 3y = −15
3x + y = 2
A. (0, 5)
B. (1, −1)
C. (3, −7)
D. (4, −10)
Help me with these pairs thank u
Answer: R(7, 9), S(6, 7), T(2, 3), U(8, 5), V(5, 5)
consider the sample space given below. a die is a cube with six sides on which each side contains one to six dots. suppose a blue die and a gray die are rolled together, and the numbers of dots that occur face up on each are recorded. the possible outcomes of the sample space s are listed as follows, where in each case the die on the left is blue and the one on the right is gray. s = {11, 12, 13, 14, 15, 16, 21, 22, 23, 24, 25, 26, 31, 32, 33, 34, 35, 36, 41, 42, 43, 44, 45, 46, 51, 52, 53, 54, 55, 56, 61, 62, 63, 64, 65, 66} Write the following event as a set. (Enter your answer in roster notation. Enter EMPTY or o for the empty set.) The event that the sum of the numbers showing face up is at least 9. E Compute its probability.
consider the sample space given below. a die is a cube with six sides on which each side contains one to six dots. Suppose probability a blue die and a gray die are rolled together, and the numbers of dots that occur face up on each are recorded.a fraction in lowest terms. 21/36
The sample space given in the question is the set S = {11, 12, 13, 14, 15, 16, 21, 22, 23, 24, 25, 26, 31, 32, 33, 34, 35, 36, 41, 42, 43, 44, 45, 46, 51, 52, 53, 54, 55, 56, 61, 62, 63, 64, 65, 66} The event that the sum of the numbers showing face up is at least 9 is represented by the set E = {9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26}.
To compute the probability of this event, we need to count how many elements are in the set E and divide this number by the total number of elements in the set S. There are 18 elements in the set E and 36 elements in the set S. Therefore, the probability of the event is 18/36, which can be simplified to 21/36.
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Complete the proof of the identity by choosing the Rule that justifies each step. Sin^2x + 4cos^2x = 4 -3sin^2x To see a detailed description of a Rule in the Rule menu, select the corresponding question mark. Statement Rule sin^2 x + 4cos^2 x sin^2 x + 4 (1 -sin^2 x) Rule? sin^2 x + 4 -4sin^2 x Rule? 4 -3sin^2 x Rule? Reciprocal identities: sin u = 1/csc u cos u = 1/sec u tan u = 1/cot u csc u = 1/sin u sec u = 1/cos u cot u = 1/tan u Quotient identities: tan u = sin u/cos u cot u = cos u/sin u Pythagorean identities: sin^2u + cos^2u = 1 tan^2u + 1 = sec^2 u cot^2 u + 1 = csc^2 u Odd/Even function identities: sin(-u) = -sin(u) cos(-u) = cos(u) tan(-u) = -tan(u) csc(-u) = -csc(u) sec(-u) = sec(u) cot(-u) = -cot(u)
Previous question
Find a function f whose graph is a parabola with the given vertex and that passes through the given point.
vertex (−1, 8) point (−2, −1)
f(x) =?
Answer:
y=-7(x+1)^2 +8
Step-by-step explanation:
Vertex as shown in vertex form, and solve for the coefficient by plugging in the point.
y=-9(x+1)^2+8
start with the vertex form of a parabola:
y=a(x-h)^2+k , "h" and "k" are the vertex coordinates, and "a" is the leading coefficient.
1. plug in the vertex coordinates
y=a(x+1)^2+8
2. to find "a", plug in the point coordinates in the function from step 1 for x and y
-1=a(-2+1)^2+8
when you solve this equation, you will find that a=-9
3. substitute "a" value in the equation from step 1
Done
Calculate the difference and enter below. -4 + (-4)
[tex]-4-4[/tex]
[tex]-4+(-4)[/tex]
[tex]=\fbox{-8}[/tex]
[tex]-4+(-4)[/tex] on a number line:
Consider independent simple random samples that are taken to test the difference between the means of two populations. The variances of the populations are unknown, but are assumed to be equal. The sample sizes of each population are n1 = 37 and n2 = 45. The appropriate distribution to use is the:
rev: 12_26_2015_QC_CS-36924
t distribution with df = 81.
t distribution with df = 82.
t distribution with df = 41.
t distribution with df = 80.
The appropriate distribution to use is t distribution with df = 80.
Variance
The variance of a random variable is the expected squared deviation from its population mean or sample mean. Variance is a measure of dispersion, which means it measures how far apart a set of numbers is from their average value.Distribution
A probability distribution is a mathematical function that calculates the chances of various possible outcomes for an experiment. It is a mathematical description of a random phenomenon in terms of its sample space and event probabilities (subsets of the sample space).Given that:
n1 = 37
n2 = 45
The variances of the populations are not know so we can use t distribution
Degree of freedom = n1 + n2 - 2
= 37 + 45 - 2
= 80
Therefore, t distribution with df = 80
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The price of desktop computer decrease from 3160 to 1020 find the percentage
Answer:
67.7215189873%
Step-by-step explanation:
The price of a desktop computer decreases from $3160 to $1020
Initial price of desktop =$3160
New Price= $1020
Change in price = 3160 - 1020 = 2140
Percentage decrease = [tex]\frac{2140}{3160}[/tex][tex]X[/tex][tex]100[/tex]=67.7215189873%
Hence , the answer is 67.7215189873%
Hope it helps u
many partitional clustering algorithms that automatically determine the number of clusters claim that this is an advantage. list two situations in which this is not the case. g'
When the data set is extremely small, the algorithm might fail to detect the inherent clusters in the data set. When the data set has a high degree of overlap between clusters, the algorithm might generate too many clusters and fail to capture the underlying structure of the data.
Partitional clustering algorithms can automatically determine the number of clusters, which is often perceived as an advantage. However, this is not always the case. For example, when the data set is small the algorithm might be unable to detect the true clusters in the data set. Additionally, when the data set has high levels of overlap between clusters, the algorithm might generate too many clusters and fail to recognize the underlying structure of the data. In these cases, the automatic determination of the number of clusters can be disadvantageous as it fails to capture the true structure of the data.
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4(2x-1)+3(2x+15) what is the answer to this question
Answer:
14x+41
Step-by-step explanation:
Answer:
14x + 41
Step-by-step explanation:
4(2X - 1) + 3(2X + 15) distribute the 4 and 3.
8x - 4 + 6x + 45 Combine like terms
14x + 41 This is your answer simplified.
Round 23.492 the nearest hundredth
Answer: 23.49
Step-by-step explanation:
Look at the thousandths place and the hundredths place.
92
Now we round 92.
1-4 it stays the same
5 or more you raise it
92 is about 90.
So you would get 23.490
You can eliminate the excess zero.
Your answer is 23.49
One of the methods forensic investigators use for estimating the age at death of a human, or the age of a living individual (for example for legal reasons or to verify identity) is based on measurement of the biochemical changes in amino acids within the teeth or bones. As bones and teeth age the ratio (R/L) of two amino acids, denoted simply as R and L, increases. The biochemical changes that occur over time in these amino acids follow an exponential law. The age t, in years, can be estimated from (R/L) using the equation t = b0 + b1*LN((1+R/L)/(1-R/L))^(), where LN denotes the natural logarithm (logarithm base e). This Excel file has data on the ratio (R/L) from the teeth of human subjects of known age. Question 1. Use the data to find the least squares intercept b0 and slope b1 in the equation t = b0 + b1*LN((1+R/L)/(1-R/L))^(). intercept b0 slope b1 Question 2. While tending to his flower garden, Sherlock Holmes discovers a body buried in his backyard. Forensic analysis yields the value 0.045 for the ratio (R/L). Use the least squares equation to estimate the age of Sherlock Holmes' surprise garden visitor. years Question 3. Calculate a 95% prediction interval for the age at death of Sherlock Holmes' surprise garden visitor. lower bound upper bound Question 4. Several years ago a man in Sherlock Holmes's neighborhood mysteriously disappeared. At the time of the disappearance the man was 35 years old. Do you think that this is the body of that man? No Yes
Age as a Function of R/L
R/L
LN[(1+(R/L))/(1-(R/L))]
Age(yrs)
0.0253
14
0.026
18
0.0314
21
0.0302
21
0.0343
25
0.0327
25
0.0317
26
0.0312
26
0.0342
26
0.0338
27
0.0325
28
0.0334
28
0.0334
29
0.0333
30
0.0362
33
0.0359
33
0.0401
36
0.0375
36
0.0398
37
0.0424
38
0.0424
38
0.0404
41
0.0489
49
0.0498
53
0.0518
57
0.0526
63
0.0588
69
0.0579
69
1)The regression equation is Age--26.7+809 LN [(1+(R/1))/(1-(R/L))]. Hence, the value of the regression coefficients by is-26.7 and by is 809
2)The forecasted value for 0.0901 LN [(1+(RL)) (1- (RL))) is 46.103.
3)The 95% prediction interval for the age at death of Sherlock Holmes' surprise garden visitor is 41.013,51.193.
4)Yes, a man in Sherlock Holmes's neighborhood thought that the body because; the man's age comes under the age in years that is, the smaller age is 14 and the larger age is 69. Thus, this is the body of that man.
Exponential law=The first law states that to multiply two exponential functions with the same base, we simply add the exponents. The second law states that to divide two exponential functions with the same base, we subtract the exponents.
MINITAB procedure:
Choose Stat > Regression Regression
Step 2: In Responses, enter the column of Age (yrs)
Step 3: In Predictors, enter the column of LN [(1+(R/L))/ (1-(R/1))] Step 4: In Options, enter the value of Prediction interval for new observation as 0.0901
The regression equation Age (year 26,7 809 28(13+1/233/4-1-26.7252.025 -13.20 0.00025.61 31.37 0.000)
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A 6.05 percent coupon bond with 20 years left to maturity is offered for sale at $1,075.25. What yield to maturity is the bond offering? (Assume interest payments are semiannual.) (Round your answer to 2 decimal places.)
Answer:
TVM calculator: N = 40, PV = -1,075.25, PMT = 30.25, FV = 1,000; CPT I = 2.714% YTM = 2.714% × 2 = 5.43%
Step-by-step explanation:
08
En completes an exercise program at a fitness center The graph shown below represents
the percentage of her exerclee program 09 Erin has completed when she has exerched for
*minutes
Erin's Exercise Program
felpaydung
2882882822
100
0 8 10 15 20 25 30 35 40 45 50 558 00 08
Time (minutes)
Based on the graph what does the value of the y-coordinate represent when x = 15
A Bin has completed ON of her exercise program
8
Bin has completed 25% of her exercise program
0
Bin has completed 0 minutes of her exercise program
D. Ein has completed 28 minutes of her exercise program
The meaning of the y-coordinate of the graph when x = 15 is given as follows:
B. Erin has completed 25% of her exercise program.
What is shown by the graph?The graph is a relation that represents a function between two variables.
The variables for this problem are given as follows:
Variable x: time that Erin spent exercising.Variable y: percentage of the exercise program that Erin has completed, considering that she has been exercising for x minutes.One ordered pair for the graph in this problem is given as follows:
(15, 25).
This means that when Erin spends 15 minutes exercising, she has completed a percentage of 25% of her exercise program, and thus option B is correct.
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Write the following inequality in slope-intercept form.
5x - y > -14
Answer:
y > 5x + 14
Step-by-step explanation:
5x – y > –14
–y > –5x–14
divide both sides by (–)
–(–y) > –(–5x–14)
y > 5x + 14
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Read the following prompt and type your response in the space provided.
The perimeter of Dawna's new flat screen television is 70 inches. The ratio of its length to width is 4:3. Write and solve an algebraic equation to determine the dimensions of the television.
Answer:4*3+70=840
Step-by-step explanation:
Perimeter = 2(Length + Width)
length = 4x ; width = 3x ; perimeter = 70
SOLUTION:Perimeter = 2(Length + Width)
70 = 2(4x + 3x)
70 = 2(7x)
70 = 14x
x = 5
Length = 4x = 4(5) = 20 inchesWidth = 3x = 3(5) = 15 inchesCHECKING:Perimeter = 2(Length + Width)
70 = 2(20 + 15)
70 = 2(35)
70 = 70
We proved and checked the answer.Therefore, the length of the screen television is 20 inches while the width is 15 inches.CREDITS:heart and star pls <3 brainliest will be appreciated <3(っ◔◡◔)っ -{ elyna s }-
convert the following equation into slope intercept form. 2x - 4y = 8
Answer:
hey
4y = 2x – 8
Step-by-step explanation:
2x – 4y = 8
–4y = –2x + 8
multiply both sides by (–)
–(–4y) = –(–2x + 8)
4y = 2x – 8
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To find the length of the diagonal from point A (front/bottom/left) to point G(back/top/right):
You would first use on the bottom of the box rectangle to find the diagonal AC=
Then use CG as of the triangle ACG, with AG being the
AG is approximately =
Word Bank:
square root 73 cm the Pythagorean Theorem the area formula for a rectangle 11 cm the hypotenuse
the perimeter formula for a rectangle 9.4cm a leg 3cm square root 11cm 73 cm 89 cm
Blank 1:
Blank 2:
Blank 3 :
Blank 4:
Blank 5:
The length of the diagonal from point A to point G is √89.
Blank 1: Using the Pythagorean Theorem
Blank 2: Finding the AC.
Blank 3: Now use CG as a adjacent side.
Blank 4: Now AG is being Hypotenuse.
Blank 5: Now find AG.
In the given question, we have to find the length of the diagonal from point A to point G.
We would first use on the bottom of the box rectangle to find the diagonal AC.
Then we use CG as of the triangle ACG.
Blank 1: Using the Pythagorean Theorem
In this theorem; a^2+b^2=c^2
Where a=adjacent side, b=base, c=hypotenuse
Blank 2: Finding the AC.
Now in the triangle ABC, use Pythagorean Theorem
So AC = √(AB)^2+(BC)^2
AC = √(8)^2+(3)^2
AC = √64+9
AC = √73
Blank 3: Now use CG as a adjacent side.
Blank 4: Now AG is being Hypotenuse.
Blank 5: Now find AG.
Now in the triangle ACG, use Pythagorean Theorem
So AG = √(AC)^2+(CG)^2
AG = √(√73)^2+(4)^2
AG = √73+16
AG = √89
Hence, the length of the diagonal from point A to point G is √89.
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a manufacturer of detergent claims that the contents of boxes sold weigh on average at least 16 ounces. the distribution of weight is known to be normal, with a standard deviation of 0.4 ounce. a random sample of 16 boxes yielded a sample mean weight of 15.84 ounces. test at the 10% significance level the null hypothesis that the population mean weight is at least 16 ounces.
As there is sufficient evidence to conclude that the population mean weight is at least 16 ounces.
What is standard deviation ?
The term "standard deviation" (or "") refers to a measurement of the data's dispersion from the mean. A low standard deviation implies that the data are grouped around the mean, whereas a large standard deviation shows that the data are more dispersed.
Think about the following data: 2, 1, 3, 2, 4. The average and the total square of the observations' departures from the mean will be 2.4 and 5.2, respectively. This means that (5.2/5) = 1.01 will be the standard deviation.
The following null and alternative hypotheses need to be tested
H0 : µ = 16
Hα : µ < 16
This corresponds to a left-tailed test , for which a z-test for one mean, with known population standard deviation will be used.
Based on the information provided, the significance level is α = 0.1, and the critical value for the left-tailed test is [tex]Z_{c}[/tex] = -1.28
The rejection region for this left-tailed test is R = {z : z < -1.282}
The z-statistics is computed as follow
[tex]z = \frac{X - µ _{0} }{sigma / \sqrt{n} }[/tex]
= (15.84 - 16) / (0.4 / √16)
= -1.6
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Matteo bought a car that cost $12500. He put $4000 down and financed the rest at 3.8%/a compounded monthly. He wants to pay off his car in 19 months. a. How money does he need to pay each month? how much will he end up paying for his car
Answer:
a. $461.67
b. $12771.73
Step-by-step explanation:
You want to know the monthly payment and total amount paid for a car that costs $12500 when $4000 is the down payment and the interest is 3.8% for 19 months.
AmortizationThe formula for the monthly payment is ...
A = P(r/12)/(1 -(1 +r/12)^-n)
where P is the amount borrowed at interest rate r compounded monthly for n months.
Here, the down payment of $4000 reduces the loan amount to ...
$12500 -4000 = 8500
a. Monthly paymentSo, the monthly payment is ...
A = 8500(0.038/12)/(1 -(1 +0.038/12)^-19) ≈ 461.67
Matteo needs to pay $461.67 each month.
b. Total paidThe total Matteo pays for the car will be the sum of the down payment and the 19 monthly payments:
total = $4000 +19×461.67 = $12771.73
Matteo will end up paying $12771.73 for his car.
problem 9-6 determine the distance yc to the center of gravity of the homogeneous rod bent into the parabolic shape. given: a
Step 1
We are given a homogenous rod in a cubic curve shape having two free ends, upper end B
and lower end x
The distance of the upper end from x
axis is 1m
and from y axis is 2m.
The rod is bent in a cubic curve shape between two ends and the equation for the rod is given by
[tex]y=2 x^3[/tex]
Here, [tex]$\bar{x}_1$[/tex]and [tex]$\bar{y}_1$[/tex]are the centroidal distances of the strip element from [tex]x$and $y$[/tex] axes respectively.
Step 3
The given equation of the homogenous rod is,
[tex]\begin{gathered}y=2 x^3 \\\frac{d y}{d x}=6 x^2\end{gathered}[/tex]
The given equation of the homogenous rod is,
\begin{aligned}
[tex]& d L=\sqrt{d x^2+d y^2} \\& d L=d x \times \sqrt{1+\left(\frac{d y}{d x}\right)^2} \\& d L=\sqrt{1+\left(6 x^2\right)^2} \cdot d x \\& d L=\sqrt{1+36 x^4} \cdot d x\end{aligned}[/tex]
[tex]& d L=\sqrt{d x^2+d y^2} \\& d L=d x \times \sqrt{1+\left(\frac{d y}{d x}\right)^2} \\& d L=\sqrt{1+\left(6 x^2\right)^2} \cdot d x \\& d L=\sqrt{1+36 x^4} \cdot d x\end{aligned}[/tex]
[tex]& L=\int_{x=0}^{x=1 \mathrm{~m}} d L \\& L=\int_{x=0}^{x=1 \mathrm{~m}} \sqrt{1+36 x^4} \cdot d x \\[/tex]
[tex]& L=6 \times \int_{x=0}^{x=1 \mathrm{~m}} \sqrt{\left(x^2\right)^2+\frac{1}{36}} \cdot d x \\[/tex]
[tex]& L=6 \times\left[x^2 \sqrt{x^4+\frac{1}{36}}+\frac{1}{36} \ln \left|\left(x^2+\sqrt{x^4+\frac{1}{36}}\right)\right|\right]_0^{1 \mathrm{~m}}\end{aligned}[/tex]
Substituting the values in the above expression and solving,
[tex]& \int_L y \cdot d L=\left[\frac{\left(36 \times(1 \mathrm{~m})^4+1\right)^{\frac{3}{2}}}{108}\right]-\left[\frac{\left(0+1 \mathrm{~m}^4\right)^{\frac{3}{2}}}{108}\right] \\& \int_L y \cdot d L=\frac{224.062}{108} \mathrm{~m}^2 \\& \int_L y \cdot d L=2.075 \mathrm{~m}^2[/tex]
Now according to the formula for the center of gravity of a curve, the expression for the center of gravity of the homogenous rod is given by,
[tex]& \bar{y}=\frac{\int_L \bar{y}_1 \cdot d L}{\int_L d L} \\& \bar{y}=\frac{2.075 \mathrm{~m}^2}{2.42 \mathrm{~m}} \\& \bar{y}=0.857 \mathrm{~m}[/tex]
Therefore, the center of gravity of the given homogeneous rod is
0.857 m above the horizontal axis
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