Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30
Factors of 45: 1, 3, 5, 9, 15, 45
The common factors between the two numbers are 1, 3, 5, 15.
Hope this helps!
Find the distance traveled by a particle with position (x, y) as t varies in the given time interval.
x = 3 sin^2(t), y = 3 cos^2(t), 0< t<3pi
What is the length of the curve?
The length of the curve (and thus the total distance traveled by the particle along the curve) is
[tex]\displaystyle\int_0^{3\pi}\sqrt{x'(t)^2+y'(t)^2}\,\mathrm dt[/tex]
We have
x(t) = 3 sin²(t ) ==> x'(t) = 6 sin(t ) cos(t ) = 3 sin(2t )
y(t) = 3 cos²(t ) ==> y'(t) = -6 cos(t ) sin(t ) = -3 sin(2t )
Then
√(x'(t) ² + y'(t) ²) = √(18 sin²(2t )) = 18 |sin(2t )|
and the arc length is
[tex]\displaystyle 18 \int_0^{3\pi} |\sin(2t)| \,\mathrm dt[/tex]
Recall the definition of absolute value: |x| = x if x ≥ 0, and |x| = -x if x < 0.
Now,
• sin(2t ) ≥ 0 for t ∈ (0, π/2) U (π, 3π/2) U (2π, 5π/2)
• sin(2t ) < 0 for t ∈ (π/2, π) U (3π/2, 2π) U (5π/2, 3π)
so we split up the integral as
[tex]\displaystyle 18 \left(\int_0^{\pi/2} \sin(2t) \,\mathrm dt - \int_{\pi/2}^\pi \sin(2t) \,\mathrm dt + \cdots - \int_{5\pi/2}^{3\pi} \sin(2t) \,\mathrm dt\right)[/tex]
which evaluates to 18 × (1 - (-1) + 1 - (-1) + 1 - (-1)) = 18 × 6 = 108.
The diagram shows a wooden prism of height 5cm.
The cross section of the prism is a sector of a circle with sector angle 25º.
The radius of the sector is 15 cm.
Calculate the total surface area of the prism.
Answer:
280.8997
Step-by-step explanation:
cross section = 2*15*5+2*(25/360)*15*15*pi+5*(25/360)*2*pi*15
= 280.8997
Total surface area of prism is 280.890cm²
What is surface area?A solid object's surface area is a measurement of the overall space that the object's surface takes up, and it is always expressed in square units.
The term "surface area" is sometimes used to refer to "total surface area".
Find the sector angle in radians
α = 25× (π/180)
α = (25π)/(180) rad
Find the area of the prism:
A = 2×15×5 + 15×15×α + 5×15×α
A = 150 + 15×15×(25π)/(180) + 5×15×(25π)/(180)
A = 280.890cm²
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There are five cities in a network. The cost of building a road directly between i and j is the entry ai,j in the matrix below. An infinite entry indicates that there is a mountain in the way and the road cannot be built. Determine the least cost of making all the cities reachable from each other.
0 3 5 11 9
3 0 3 9 8
5 3 0 [infinity] 10
11 9 [infinity] 0 7
9 9 10 7 0
Solution :
Given :
There are five cities in a network and the cost of [tex]\text{building}[/tex] a road directly between [tex]i[/tex] and [tex]j[/tex] is the entry [tex]a_{i,j}[/tex]
[tex]a_{i,j}[/tex] refers to the matrix.
Road cannot be built because there is a mountain.
The given matrix :
[tex]\begin{bmatrix}0 & 3 & 5 & 11 & 9\\ 3 & 0 & 3 & 9 & 8\\ 5 & 3 & 0 & \infty & 10\\ 11 & 9 & \infty & 0 & 7\\ 9 & 8 & 10 & 7 & 0\end{bmatrix}[/tex]
The matrix on the left above corresponds to the weighted graph on the right.
Using the [tex]\text{Kruskal's algorithm}[/tex] we can select the cheapest edge that is not creating a cycle.
Starting with 2 edges of weight 3 and the edge of weight 5 is forbidden but the edge is 7 is available.
The edge of the weight 8 completes a minimum spanning tree and total weight 21.
If the edge of weight 8 had weight 10 then either of the edges of weight 9 could be chosen the complete the tree and in this case there could be 2 spanning trees with minimum value.
Find the area of the figure. (Sides meet at right angles.)
Answer:
[tex]9 \times 2 = 18 \: \: \\ 4 \times 5 = 20 \\ 20 + 18 = 38 \\ 38 {in}^{2} [/tex]
hi please give brainly
Which of the following is an advantage of using systematic random sampling?
Systematic random sampling reduces sampling variability.
Systematic random sampling does not require a finite population size.
Systematic random sampling could inadvertently miss patterns in the population.
Systematic random sampling uses clusters, which are close in proximity, making data collection easier.
This is a question that asks about the advantages of a systematic random sampling. Thus, we first take a look at the types of sampling, and then we see the advantage of systematic random sampling.
Samples may be classified as:
Convenient: Sample drawn from a conveniently available pool.
Random: Basically, put all the options into a hat and drawn some of them.
Systematic: Every kth element is taken. For example, you want to survey something on the street, you interview every 5th person, for example.
Cluster: Divides population into groups, called clusters, and each element in the cluster is surveyed.
Stratified: Also divides the population into groups. However, then only some elements of the group are surveyed.
Systematic:
One of the bigger advantages is that the systematic sampling eliminate clusters, which means that the last option is wrong.
Inadvertently missing patterns is a problem in systematic sampling, and not an advantage, thus the third option is also wrong.
It also does not reduce sampling variability, thus the first option is wrong.
From this, it can be concluded that the correct option is:
Systematic random sampling does not require a finite population size.
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Needddd annnsssweeerrr
Answer:
90in2
Step-by-step explanation:
3x5x6=90
Answer:
C.90
Step-by-step explanation:
first multiply 3 and 5 which is 15 then times it with 6 which equals 90
What is the equation of a parabola that has a vertical axis, passes through the point (–1, 3), and has its vertex at (3, 2)? x= –y216+6y16–4116 y= –x216+6x16–4116 y=x216–6x16+4116 x=y216–6y16+4116
Answer:
y=x216–6x16+4116
Step-by-step explanation:
plato :)
The equation of the parabola is in option (C) if the parabola that has a vertical axis, passes through the point (–1, 3), and has its vertex at (3, 2) option (C) is correct.
What is a parabola?It is defined as the graph of a quadratic function that has something bowl-shaped.
(x - h)² = 4a(y - k)
(h, k) is the vertex of the parabola:
a = √[(c-h)² + (d-k²]
(c, d) is the focus of the parabola:
The question is incomplete.
The complete question is in the picture, please refer to the attached picture.
It is given that:
The equation of a parabola that has a vertical axis, passes through the point (–1, 3)
The vertex of the parabola is at (3, 2)
As we know, in the standard form of the parabola (h, k) represents the vertex of the parabola.
h = 3
k = 2
Plug the above point in the equation:
[tex]\rm y\ =\ \dfrac{x^{2}}{16}-\dfrac{6x}{16}+\dfrac{41}{16}[/tex]
x = 3
y = 2
[tex]\rm 2\ =\ \dfrac{3^{2}}{16}-\dfrac{6(3)}{16}+\dfrac{41}{16}[/tex]
= 9/16 - 18/16 + 41/16
= (9-18+41)/16
= 32/16
2 = 2 ( true)
The equation of the parabola is:
[tex]\rm y\ =\ \dfrac{x^{2}}{16}-\dfrac{6x}{16}+\dfrac{41}{16}[/tex]
Thus, the equation of the parabola is in option (C) if the parabola that has a vertical axis, passes through the point (–1, 3), and has its vertex at (3, 2) option (C) is correct.
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Parallel Lines:
If the two lines are parallel and cut by a transversal line, what is the value of x?
Step-by-step explanation:
The corresponding angles theorem tells us that angles that correspond with each other are equal. In this case, B and C are corresponding angles.
(2x+8) = 60
2x = 60 - 8
2x = 52
x = 26
A diameter perpendicular to a chord
that chord
Select one:
a. is parallel to
b. bisects
c. is equal to
solve 3 1/5 = y - 12/25
3 1/5 = y - 12/25
31/5+y = -12/25
31+y = -12/25×5
31+y = -12/5
y = -12/5-31
y = -143/5
y = -28.6
HOPE IT HELPS
100.331 divide 99.355
Answer:
1.009823361
Step-by-step explanation:
Just divide like this:
[tex] \frac{100.331}{99.355} = 1.009853361[/tex]
if x¹=xcosA+ysinA and y¹=xsinA-ycosA, show that (x¹)²+(y¹)²=x²+y²
Expanding each square on the left side, you have
(x cos(A) + y sin(A))² = x² cos²(A) + 2xy cos(A) sin(A) + y² sin²(A)
(x sin(A) - y cos(A))² = x² sin²(A) - 2xy sin(A) cos(A) + y² cos²(A)
so that adding them together eliminates the identical middle terms and reduces to the sum to
x² cos²(A) + y² sin²(A) + x² sin²(A) + y² cos²(A)
Collecting terms to factorize gives us
(y² + x²) sin²(A) + (x² + y²) cos²(A)
(x² + y²) (sin²(A) + cos²(A))
and sin²(A) + cos²(A) = 1 for any A, so we end up with
x² + y²
as required.
Factorise: x^3 + x^2 + x^2y + xy + y
Plz also show me the process.
Seven and one-half foot-pounds of work is required to compress a spring 2 inches from its natural length. Find the work required to compress the spring an additional 3 inch.
Answer:
Apply Hooke's Law to the integral application for work: W = int_a^b F dx , we get:
W = int_a^b kx dx
W = k * int_a^b x dx
Apply Power rule for integration: int x^n(dx) = x^(n+1)/(n+1)
W = k * x^(1+1)/(1+1)|_a^b
W = k * x^2/2|_a^b
From the given work: seven and one-half foot-pounds (7.5 ft-lbs) , note that the units has "ft" instead of inches. To be consistent, apply the conversion factor: 12 inches = 1 foot then:
2 inches = 1/6 ft
1/2 or 0.5 inches =1/24 ft
To solve for k, we consider the initial condition of applying 7.5 ft-lbs to compress a spring 2 inches or 1/6 ft from its natural length. Compressing 1/6 ft of it natural length implies the boundary values: a=0 to b=1/6 ft.
Applying W = k * x^2/2|_a^b , we get:
7.5= k * x^2/2|_0^(1/6)
Apply definite integral formula: F(x)|_a^b = F(b)-F(a) .
7.5 =k [(1/6)^2/2-(0)^2/2]
7.5 = k * [(1/36)/2 -0]
7.5= k *[1/72]
k =7.5*72
k =540
To solve for the work needed to compress the spring with additional 1/24 ft, we plug-in: k =540 , a=1/6 , and b = 5/24 on W = k * x^2/2|_a^b .
Note that compressing "additional one-half inches" from its 2 inches compression is the same as to compress a spring 2.5 inches or 5/24 ft from its natural length.
W= 540 * x^2/2|_((1/6))^((5/24))
W = 540 [ (5/24)^2/2-(1/6)^2/2 ]
W =540 [25/1152- 1/72 ]
W =540[1/128]
W=135/32 or 4.21875 ft-lbs
Step-by-step explanation:
If an angle of a right angle triangle is 81 find the remaining angle in grades
Answer:
9
Step-by-step explanation:
90+81+mising angle=180, missing angle is 9
Help please:)) 2. When shipping ice cream, melting is understandably a big concern. You will notice that ice cream is not generally packaged in a cube-shaped container. A standard container of ice cream contains 1 L, or 1000 cm3 of ice cream,
a. What would be the optimal dimensions (radius and height) to minimize surface area?
b. What would the surface area be?
C. Suggest at least two reasons why this is different from the ice cream packaging that you see in the stores.
Answer:
a. The radius r = 5.42 cm and the height h = 10.84 cm
b. 553.73 cm²
c. i. Beauty ii. Design
Step-by-step explanation:
a. What would be the optimal dimensions (radius and height) to minimize surface area?
The volume of the standard container is a cylinder and its volume is V = πr²h where r = radius of container and h = height of container.
Since V = 1000 cm³,
1000 cm³ = πr²h (1)
Now, the surface area of a cylinder is A = 2πr² + 2πrh where r and h are the radius and height of the cylinder.
From (1), h = 1000/πr².
Substituting h into A, we have
A = 2πr² + 2πrh
A = 2πr² + 2πr(1000/πr²)
A = 2πr² + 2000/r
To maximize A, we differentiate A with respect to r and equate to zero to find the value of r at which A is maximum.
So, dA/dr = d[2πr² + 2000/r]/dr
dA/dr = d[2πr²]/dr + d[2000/r]/dr
dA/dr = 4πr - 2000/r²
Equating the equation to zero, we have
4πr - 2000/r² = 0
4πr = 2000/r²
r³ = 2000/4π
r = ∛(1000/2π)
r = 10(1/∛(2π))
r = 10(1/∛(6.283))
r = 10/1.8453
r = 5.42 cm
To determine if this value of r gives a minimum for A, we differentiate dA/dr with respect to r.
So, d(dA/dr)/dr = d²A/dr²
= d[4πr - 2000/r²]/dr
= d[4πr]/dr - d[2000/r²]/dr
= 4π + 4000/r³
Substituting r³ = 2000/4π into the equation, we have
d²A/dr² = 4π + 4000/r³ = 4π + 4000/(2000/4π) = 4π + 2 × 4π = 4π + 8π = 12π > 0
Since d²A/dr² = 12π > 0, then r = 5.42 cm gives a minimum for A.
Since h = 1000/πr²
h = 1000/π(5.42)²
h = 1000/92.288
h = 10.84 cm
So, the radius r = 5.42 cm and the height h = 10.84 cm
b. What would the surface area be?
Since the surface area, A = 2πr² + 2πrh
Substituting the values of r and h into A, we have
A = 2πr² + 2πrh
A = 2πr(r + h)
A = 2π5.42(5.42 + 10.84)
A = 10.84π(16.26)
A = 176.2584π
A = 553.73 cm²
c. Suggest at least two reasons why this is different from the ice cream packaging that you see in the stores.
i. Beauty
ii. Design
The point of a square pyramid is cut off, making each lateral face of the pyramid a trapezoid with the dimensions shown. A trapezoid has a base of 3 inches, height of 1 inches, and top side length of 1 inch:
What is the area of one trapezoidal face of the figure?
Find the missing side length in the image below
Answer:
? = 5
Step-by-step explanation:
Recall: when 2 transversal lines cuts across 3 parallel lines, the parallel lines are divided proportionally by the transversals.
Therefore:
?/10 = 3/6
Cross multiply
?*6 = 3*10
?*6 = 30
Divide both sides by 6
? = 30/6
? = 5
please help find the solution to the system of equations
Answer:
x = 2 y = 3
Step-by-step explanation:
-2x + 7 = 5x - 7
-7x + 7 = -7
-7x = -14
x = 2
y = -2(2) + 7
y = -4 + 7
y = 3
A rectangle auditorium seats 1260 people. The number of seats in each row exceeds the number of rows by 12. Find the number of seats in each row
Answer:
Easy, all you ha
Step-by-step explanation:
Cars arrive at an automatic car wash system every 10 minutes on average. The cars inter-arrival times are exponentially distributed. Washing time for each is 6 minutes per car and is purely deterministic (i.e., the waiting line system is M/D/c). Assuming that the car wash has a single bay to serve the cars, what is the average number of cars waiting in line (L.)?
Answer:
the average number of cars waiting in line L[tex]q[/tex] is 0.45
Step-by-step explanation:
Given the data in the question;
Cars arrive at an automatic car wash system every 10 minutes on average.
Car arrival rate λ = 1 per 10 min = [ 1/10 × 60 ]per hrs = 6 cars per hour
Washing time for each is 6 minutes per car
Car service rate μ = 6min per car = [ 1/6 × 60 ] per hrs = 10 cars per hour
so
P = λ/μ = 6 / 10 = 0.6
Using the length of queue in M/D/1 system since there is only one service bay;
L[tex]q[/tex] = [tex]\frac{1}{2}[/tex][ P² / ( 1 - P ) ]
so we substitute
L[tex]q[/tex] = [tex]\frac{1}{2}[/tex][ (0.6)² / ( 1 - 0.6 ) ]
L[tex]q[/tex] = [tex]\frac{1}{2}[/tex][ 0.36 / 0.4 ]
L[tex]q[/tex] = [tex]\frac{1}{2}[/tex][ 0.9 ]
L[tex]q[/tex] = 0.45
Therefore, the average number of cars waiting in line L[tex]q[/tex] is 0.45
In one year, a government collected $6770 per person in taxes. If the population was 220,000,000, how much did the government collect in taxes that year?
Answer:
$1,489,400,000,000
Step-by-step explanation:
Multiply to get the solution.
220,000,000 × 6770 = 1,489,400,000
The graph shows the distribution of lengths of songs (in seconds). The distribution is approximately Normal, with a mean of 227 seconds and a standard deviation of 31 seconds.
A graph titled Song length has length (seconds) on the x-axis, going from 103 to 351 in increments of 31. The highest point of the curve is at 227.
What percentage of songs have lengths that are within 31 seconds of the mean?
34%
68%
95%
99.7%
its everything between 196 and 258 seconds (at max 31secs away from the mean). imagine straight upward lines separating this area from the rest.
34% would be way too low, 95 and above way too much.
only 68% is remotely plausible.
What is the order of rotational symmetry for the figure?
A. 4 or more
B. 2
C. 1
D. 3
9514 1404 393
Answer:
C. 1
Step-by-step explanation:
The only rotation that maps the figure to itself is rotation by 360°. The rotational order is 1.
Factor this polynomial expression.
3x^2 - 12x+ 12
A. (3x - 2)(x-6)
B. 3(x-2)(x + 2)
C. 3(x-2)(x-2)
D. 3(x + 2)(x + 2)
Find the average rate of change from x=1 to x=2 f(x) = -18/x^2
Answer:
13.5
Step-by-step explanation:
Average rate of change=(f(2)-f(1))/1=-18/2^2-(-18))=13.5
What is the probability that z equals 1.5
Answer:
0.1
Step-by-step explanation:
The probability value corresponding to z = 1.5 is 0.9332.
What is probability?Probability is a number that expresses the likelihood or chance that a specific event will take place. Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to describe probabilities.
The standard normal curve is a special case of a normal curve with a mean of 0 and a standard deviation of 1. Since it is symmetric around the mean, 50% of the observations lie under the mean while the other 50% of the observations lie above the mean.
Thus the probability value corresponding to z = 1.5 is 0.9332.
Since the total probability value under the curve is 1, we subtract 0.9332 from 1 to calculate the area to the right.
P(Z>1.5)
=P(Z≤1.5)
=1−0.9332
=0.0668
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A triangle. A ABC, has angle measures of 82*, 75, and 23' and no sides equal (congruent) in length. How would this triangle be
classified?
Equilateral right
Isosceles obtuse
O Scalene acute
Isosceles acute
The triangle given is a scalene acute triangle
Classification of TriangleA triangle can be classified based on the measures of its angles and the lengths of its sides.
In this case, the angle measures of the triangle are 82, 75, and 23 degrees. Since the sum of the angles in a triangle is always 180 degrees, we can verify that these angles satisfy this condition: 82 + 75 + 23 = 180.
The triangle is not an equilateral triangle because all the sides are not of equal length.
The triangle also doesn't have one right angle so it can't be right triangle.
Now, as per the angle measures, none of the angles are right angles, but one angle is greater than 90 degree, so this triangle is not acute triangle.
So, this triangle is not an Obtuse triangle since it has no angle greater than 90 degrees.
As the triangle has no sides of equal length, it is also a Scalene triangle.
Therefore, the triangle would be classified as a Scalene acute triangle (c).
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HURRY! HELP PLS
Janelle is conducting an experiment to determine whether a new medication is effective in reducing sneezing she finds 1000 volunteers with sneezing issues and divides them into two groups the control group does not receive any medication the treatment group received the medication the patients in the treatment group show reduced signs of sneezing what can genetic include from this experiment?
Janelle can conclude that the medication used in this experiment was effective and it decreases sneezing.
What is a control experiment?A control experiment can be defined as a type of experiment in which a condition assumed to be a probable cause of an effect is compared with the same situation without involving or using the suspected condition.
What is a treatment group?A treatment group refers to a group of participants in an experiment that are exposed to some manipulation in the independent variable such as an administration of medication to a particular group.
Thus, Janelle can conclude that the medication used in this experiment was effective and it decreases sneezing because the treatment group show reduced signs of sneezing.
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6 times the sum of 5 and K
Answer:
6(5+k)
Step-by-step explanation:
The sum of 5 and k
5+k
6 times the sum
6(5+k)
