Answer:
3800 tickets
Step-by-step explanation:
we are given that,
total people seated:266
yet to come:93%
so the percentage of people who have arrived is 100%-93%=7%
and one ticket for each people
therefore,
[tex] \displaystyle \begin{array}{ccc} \displaystyle \rm7\% \quad \text{People} \implies266 \: \text{tickets} \\ \displaystyle100 \%\: \quad \imath \imath \implies \frac{266}{7\%} \: \: \: \: \imath \imath \\ \\ \qquad \displaystyle \qquad\rm as \: \% = \frac{1}{100} \longleftarrow \frac{266}{ \dfrac{7}{100} } \\ \\ \displaystyle \rm \: by \: simplifying \: complex \: fraction\longleftarrow 266 \times \frac{100}{7} \\ \rm reduce \: fraction \longleftarrow 38 \times 100 \\ \rm simplify \:multiplication \longleftarrow3800\end{array}[/tex]
hence,
3800 tickets were sold for the movie
Answer:
Solutions given:
[100%-97%]=266people
7% =266people
Each people is 1 ticket.
266 people =266tickets
so
7% of people=266ticket
100% of people =266/7×100=3800tickets
3800tickets were sold for the movie
Consider the initial value problem my''+cy'+ky=F(t), y(0)=0, y'(0)=0, modeling the motion of a spring mass dashpot system initially at rest and subjected to an applied force F(t), where the unit of force is the Newton (N). Assume that m=2 kilograms, c=8 kilograms per second, k=80 Newtons per meter, and F(t)=20 sin(6t) Newtons.
1. Solve the initial value problem. y(t)=?
2. Determine the long term behavior of the system. Is lim as t goes to infinity of y(t)=0? If it is, enter zero. If not, enter a function that approximates y(t) for very large positive values of t. For very large positive values of t, y(t) is approximately.. ?
Answer:
Hence, the [tex]y(t)=e^{-2 t}\left(\frac{75}{74} \cos 6 t+\frac{75}{148} \sin 6 t\right)-\frac{25}{148}(6 \cos (6 t)-\sin (6 t))\end{array}[/tex] and approximately value of [tex]y(t)[/tex] is [tex]-0.844[/tex].
Given :
[tex]my''+cy'+ky=F(t), y(0)=0, y'(0)=0,[/tex]
Where [tex]m=2[/tex] kilograms
[tex]c=8[/tex] kilograms per second
[tex]k=80[/tex] Newtons per meter
[tex]F(t)=20\sin (6t)[/tex] Newtons
Explanation :
(1)
Solve the initial value problem. [tex]y(t)[/tex]
[tex]my''+cy'+ky=F(t), y(0)=0, y'(0)=0,[/tex]
[tex]\Rightarrow 2y''+8y'+80y=20\sin (6t)[/tex]
[tex]\Rightarrow y''+4y'+40y=10\sin (6t)[/tex]
Auxilary equations :[tex]F(t)=0[/tex]
[tex]\Rightarrow r^2+4r+40=0[/tex]
[tex]\Rightarrow r=\frac{-4\pm\sqrt{4^2-4\times 1\times 40}}{2\times 1}[/tex]
[tex]\Rightarrow r=\frac{-4\pm\sqrt{16-160}}{2}[/tex]
[tex]\Rightarrow r=\frac{-4\pm\sqrt{-144}}{2}[/tex]
[tex]\Rightarrow r=\frac{-4\pm12i}{2}[/tex]
[tex]\Rightarrow r=-2\pm6i[/tex]
The complementary solution is [tex]y_c=e^{-2t}\left(c_1\cos 6t+c_2\sin 6t\right)[/tex]
The particular Integral, [tex]y_p=\frac{1}{f(D)}F(t)[/tex]
[tex]y_{y} &=\frac{1}{D^{2}+4 D+40} 25 \sin (6 t) \\\\ y_{y} &=\frac{25}{-6^{2}+4 D+40} \sin (6 t) \quad\left(D^{2} \text { is replaced with }-6^{2}=-36\right) \\\\y_{y} &=\frac{25}{4 D+4} \sin (6 t) \\\\y_{y} &=\frac{25}{4(D+1)} \sin (6 t) \\\\y_{y} &=\frac{25(D-1)}{4(D+1)(D-1)} \sin (6 t) \\\\y_{y} &=\frac{25(D-1)}{4\left(D^{2}-1\right)} \sin (6 t) \\\\y_{y} &=\frac{25(D-1)}{4(-36-1)} \sin (6 t) \\\\y_{y} &=-\frac{25}{148}(D-1) \sin (6 t) \\y_{y} &=-\frac{25}{148}\left(\frac{d}{d t} \sin (6 t)-\sin (6[/tex]
Hence the general solution is :[tex]y=y_c+y_p=e^{-2t}(c_1\cos 6t+c_2\sin 6t)-\frac{25}{148}(6\cos 6t-\sin 6t)[/tex]
Now we use given initial condition.
[tex]y(t) &=e^{-2 t}\left(c_{1} \cos 6 t+c_{2} \sin 6 t\right)-\frac{25}{148}(6 \cos (6 t)-\sin (6 t)) \\\\\y(0) &=e^{-\alpha 0)}\left(c_{1} \cos (0)+c_{2} \sin (0)\right)-\frac{25}{148}(6 \cos (0)-\sin (0)) \\\\0 &=\left(c_{1}\right)-\frac{25}{148}(6) \\\\c_{1} &=\frac{75}{74} \\\\y(t) &=e^{-2 t}\left(c_{1} \cos 6 t+c_{2} \sin 6 t\right)-\frac{25}{148}(6 \cos (6 t)-\sin (6 t)) \\\\[/tex]
[tex]y^{\prime}(t)=-2 e^{-2 t}\left(c_{1} \cos 6 t+c_{2} \sin 6 t\right)+e^{-2 t}\left(-6 c_{1} \sin 6 t+6 c_{2} \cos 6 t\right)-\frac{25}{148}(-36 \sin (6 t)-6 \cos (6 t)) \\\\y^{\prime}(0)=-2 e^{0}\left(c_{1} \cos 0+c_{2} \sin 0\right)+e^{0}\left(-6 c_{1} \sin 0+6 c_{2} \cos 0\right)-\frac{25}{148}(-36 \sin 0-6 \cos 0) \\\\0=-2\left(c_{1}\right)+\left(6 c_{2}\right)-\frac{25}{148}(-6) \\\\0=-2 c_{1}+6 c_{2}+\frac{75}{74} \\\\0=-2\left(\frac{75}{74}\right)+6 c_{2}+\frac{75}{74} \\\\[/tex][tex]\begin{array}{l}0=-\frac{150}{74}+6 c_{2}+\frac{75}{74} \\\\\frac{150}{74}-\frac{75}{74}=6 c_{2}\end{array}[/tex]
[tex]\begin{array}{l}c_{2}=\frac{25}{148}\\\\\text { Substitute } c_{1} \text { and } c_{2} \text { in } y(t) \text { . Then }\\\\y(t)=e^{-2 t}\left(\frac{75}{74} \cos 6 t+\frac{75}{148} \sin 6 t\right)-\frac{25}{148}(6 \cos (6 t)-\sin (6 t))\end{array}[/tex]
(2)
[tex]y(t)=e^{-2 t}\left(\frac{75}{74} \cos 6 t+\frac{75}{148} \sin 6 t\right)-\frac{25}{148}(6 \cos (6 t)-\sin (6 t)) \\\\y(t)=\left(\frac{75}{74} e^{-2 t} \cos 6 t+\frac{75}{148} e^{-2 t} \sin 6 t\right)-\frac{25}{148}(6 \cos (6 t)-\sin (6 t)) \\\\y(t)=\frac{75}{74}\left(e^{-2 t}-1\right) \cos 6 t+\frac{25}{148}\left(3 e^{-2 t}+1\right) \sin 6 t \\\\|y(t)| \leq \frac{75}{74} e^{-2 t}-1|\cos 6 t|+\frac{25}{148}\left|3 e^{-2 t}+1\right||\sin 6 t| \\\\[/tex]
[tex]|y(t)| \leq \frac{75}{74}\left|e^{-2 t}-1\right|+\frac{25}{148}\left|3 e^{-2 t}+1\right| \\\\\lim _{t \rightarrow \infty} y(t) \leq \lim _{t \rightarrow \infty}\left\{\frac{75}{74}\left|e^{-2 t}-1\right|+\frac{25}{148}\left|3 e^{-2 t}+1\right|\right\} \\\\\lim _{t \rightarrow \infty} y(t)=\left\{\frac{75}{74}\left|\lim _{t \rightarrow \infty}\left(e^{-2 t}-1\right)\right|+\frac{25}{148}\left|\lim _{t \rightarrow \infty}\left(3 e^{-2 t}+1\right)\right|\right\} \\[/tex]
[tex]\lim _{t \rightarrow \infty} y(t)=\left\{\frac{75}{74}(-1)+\frac{25}{148}(1)\right\}=-\frac{75}{74}+\frac{25}{148}=-\frac{-150+25}{148}=-\frac{125}{148} \approx-0.844[/tex]
The scale on a map is 55 cm : 88 km.
If the distance between two cities is 5656 km, how far apart in cm are the two cities on the map?
Answer:
look at the picture i have sent
Answer:
The cities are 35 cm apart in map.
The scale on a map is 5 cm : 8 km.
Step-by-step explanation:
mrk me brainliest please
Find the exact value of sin A in simplest radical form.
Using the sine rule,
[tex] \frac{a}{sin(a)} = \frac{b}{sin(b)} = \frac{c}{sin(c)} [/tex]
Here we are going to use the values of A and C,
[tex] \frac{12}{sin(a)} = \frac{14}{sin(90)} \\ \frac{12}{sin(a)} = \frac{14}{1} \\ sin(a) = 12 \div 14 \\ sin(a) = 0.8571[/tex]
So sin(A) = 12/14 = 6/7 = 0.8571, but since the question says in its simplest radical form, I think the closest answer to it should be
[tex] \frac{ \sqrt{3} }{2} [/tex]
Which statement describes whether the function is continuous at x = 2?
O The function is continuous at x = 2 because f(2) exists.
O The function is continuous at x = 2 because lim f(x) exists.
X-2
The function is not continuous at x = 2 because f(2) does not exist.
The function is not continuous at x = 2 because lim f(x) does not equal f(2).
X-2
Answer: (b)
Step-by-step explanation:
Given
The function is given as
[tex]f(x)=\dfrac{x^2-12x+20}{x-2}[/tex]
Solving the function
[tex]f(x)=\dfrac{x^2-2x-10x+20}{x-2}\\\\f(x)=\dfrac{(x-2)(x-10)}{(x-2)}\\\\f(x)=x-10[/tex]
for [tex]x=2[/tex]
[tex]f(2)=2-10\\f(2)=-8[/tex]
The function is continuous at [tex]x=2[/tex] because [tex]\lim_{x \to 2} f(x)[/tex] exists.
If the limit exists at a point, then the function is continuous.
Answer:
on edge its fs not b or c
Step-by-step explanation:
A babysitter earns the same amount per hour. She earned $36 for 3 hours of babysitting. Which equation describes the relationship between x, the number of hours spent babysitting, and y, the total amount
in dollars earned?
Answer:
y= 12x
Step-by-step explanation:
36/3=12
12× x =y
________________________
5% equals what fraction, in lowest terms?
Answer:
1/20
Step-by-step explanation:
According to G0ogle 5 percent equals 1/20 in lowest terms.
Answer:
5% equals 5/100 which is 1/20 in lowest terms.
Step-by-step explanation:
5% is basically equivalent to 5/100. 5/100 in lowest terms is 1/20 since you divide the numerator and denominator by 5.
I hope this helps, have a nice day.
PLEASE HELP FAST WILL MARK BRAINLIEST PLEASEEE
Answer:
[tex]\frac{8x^{18} }{y^{2} }[/tex]
Step-by-step explanation:
I need some help please
9514 1404 393
Answer:
(d) {-7, -2, 11, 20}
Step-by-step explanation:
You can put the domain values into the function and evaluate to find the corresponding range values. Here, we'll do them "all at once."
y = 3{-4, -1, 2, 5} +5
= {-12, -3, 6, 15} +5
= {-7, 2, 11, 20} . . . . . matches choice d
_____
To save yourself some arithmetic, you can observe that the answer choices differ in the 2nd and 4th values, so you only need to evaluate the function for x=-1 or x=5 to determine the correct answer choice.
Can someone help me please?
Slope : -2
y - intercept : 3
Equation : y = -2x+3
Answer:
Step-by-step explanation:
Slope: -0.5
Y-Intercept: 3
y = -0.5x+3
Which number line best models the expression 3 divided by 1/3?
Answer:
3 (divided by sign) 1/3
Step-by-step explanation:
The times that a cashier spends processing individual customers' orders are independent random variables with mean 3.5 minutes and standard deviation 3 minutes. Find the number of customers n such that the probability that the orders of all n customers can be processed in less than 2 hours, is approximately 0.1. (Round your answer to the nearest integer.)
Answer:
26 customers
Step-by-step explanation:
First: determine the z score from standard normal probability table with an indicative area of 0.1
Z-score from probability table = - 1.28
mean = 3.5 minutes
std = 3 minutes
next determine the Z-score based on the information given in the question
Z = ( std - mean ) / processing time
= ( 3 - 3.5 ) / 2 = -0.25
Finally determine the number of customers
N = [tex](\frac{-1.28}{-0.25} )^2[/tex] = 1.6384 / 0.0625 = 26.21 ≈ 26 customers
Simran has a bag containing white and yellow marbles. Simran randomly selects one marble from the bag,
records the result, and returns the marble to the bag. The results of the first 65 selections are shown below.
A white marble was selected 41 times.
A yellow marble was selected 24 times.
Based on these results, what is the probability that the next marble Simran selects, rounded to the nearest
Answer:
d. 63%
Step-by-step explanation:
percent, will be white?
A41% b50% c59% d63%
The probability of white = P (w) = 41/65= 0.63
The probability of yellow = P (y)= 24/65= 0.369=0.37
The probability of choosing white is 0.63 . When rounded to nearest percent gives
0.63*100/100
=0.63*100 percent
= 63 percent
= 63%
the probability of getting the next marble white is the same as the probability of getting a white.
Find the quotient: 28 ÷ 4 2/3
Answer:
6
Step-by-step explanation:
Answer:
6
Step-by-step explanation:
Find the area of the triangle
Answer:
About 292.72
Step-by-step explanation:
We can imagine a circle circumscribed around the triangle, then solve it as we normally do using the apothem. By dividing 360 by the number of sides (3) we know that the central angle constructed by the apothem and radiuses would be 120. Divided by 2 (because we are using a right triangle to solve it) is 60. Now with this you can either use trig ratios (sin, cos, or tan) or use special right triangles (30-60-90 or 45-45-90). I used special rights. With this I know my apothem is [tex]\frac{13\sqrt{3} }{3}[/tex]. Perimeter is 26 times 3 which is 78. The formula for area of regular polygons is 1/2(perimeter times apothem). When we plug our values in the answer is about 292.72. You are lucky that I just had my test on this, I hope it helps.
Here is my work since this is very visual for me:
a cylinder has a diameter of 12 and height of 12. the volume of the cylinder is:
A. 1728π cubic units
B. 288π cubic units
C. 144π cubic units
D. 432π cubic units
The first question
(Worth 10 points) please help
9514 1404 393
Answer:
C. 7
Step-by-step explanation:
To find the value of 2Ω3 using the definition of AΩB, we are replacing A with 2, and B with 3. This seems to give us ...
2Ω3 = 2² +3² -2·3 = 4 + 9 - 6 = 7
The value of 2Ω3 is 7.
Find the perimeter of a rectangle with a base of 12 ft and a height of 5 ft.
Answer:
P=34ft
Step-by-step explanation:
Solution
P=2(l+w)=2·(12+5)=34ft
Which of the following names the figure in the diagram below?
A. pentagon
B. prism
C. triangle
D. polygon
E.pyramid
F. square
Answer: Prism
Step-by-step explanation:
What is the value of x?
How much is three times two
Answer:
the answer is 6.
Step-by-step explanation:
Answer:
6.
Step-by-step explanation:
3+3=6 = 2×3=6
you can do draw 3 circles 2 times and add it all together.
I need help please.
Is the line a good fit for the data points plotted in the scatter plot below?
Is a triangle with side lengths of 33 inches, 56 inches, and65 inches a right triangle? Explain your reasoning.
Answer:
Yes
Step-by-step explanation:
Pythagorean's Theorum is that a^2 + b^2 = c^2
a and b are the sides of the triangle and c is the hypotenuse. 33x33+56x56=4225 sqrt4225 is 65. Everything checks out.
The scatter chart below displays the residuals verses the dependent variable, x. Which of the following conclusions can be drawn based upon this scatter chart? a. The residuals are normally distributed. b. The model over predicts the value of the dependent variable for small values and large values of the independent variable. c. The model fails to capture the relationship between the variables accurately, and there may exist nonlinear relationship. d. The residuals have a constant variance.
Answer: Hello the scatter plot related to your question is missing attached below is the scatter plot
answer : The model fails to capture the relationship between the variables accurately, and there may exist nonlinear relationship ( C )
Step-by-step explanation:
The conclusion that can be drawn based upon the scatter chart is that The model fails to capture the relationship between the variables accurately, and there may exist nonlinear relationship
A scatter plot helps in observing the relationship within different numeric variables but the scatter plot attached fails in the showing the actual relationship
Find the component form of the resultant vector.
u=-12i + 35j
Find: -8u
A) 10V 47 - 1 + 10j
B) -40i + 35j
C) 961 – 280j
D) 151 – 5V3.j
Answer:
C) 96i – 280j
Step-by-step explanation:
Multiplying vector by constant:
When a vector is multiplied by a constant, each component of the vector is multiplied by this constant.
In this question:
u = -12i + 35j
-8u = -8(-12i + 35j) = (8*12i - 8*35j) = 96i - 280j.
The answer is C) 96i – 280j
There are 50 pennies in a roll. If you have 150 rolls of pennies, how many pennies do you have?
Answer: 7500
Step-by-step explanation:
multiply 150 by 50
Find the length of arc AB.
Answer:
11.17
Step-by-step explanation:
arc length = 2πr(θ/360)
= 2π(8)(80/360)
= 11.1701072...
= 11.17 to nearest hundredth
which best describes a rectangle with diagonals that are perpendicular
Answer: If a parallelogram has diagonals that are perpendicular, it is a rhombus. … This definition can also be stated as: A square is a quadrilateral that is also a rectangle and a rhombus.
Step-by-step explanation:
Hi, i need to calculate roots x1 and x2 using the vieta theorem, can anyone help me? I have found the answer for x1 and x2, its 1,5 and 2, all i need is a solution on how to get this answer, the equation is in the picture, will give you brainliest if you type down the correct solution for me, thanks.
I have left a similar equation that i did. The only thing why i cant do the equation, because in front of x2 there’s an number, so i don’t understand.
Answer:
Solution given:
x²-12x+11=0
Comparing above equation with ax²+bx+c
we get
a=1
b=-12
c=11
By using Vieta's theorem
X1+X2=[tex] \frac{-b}{a} [/tex]=[tex] \frac{- -12}{1} [/tex]=12
again
X1X2=[tex] \frac{c}{a} [/tex]=[tex] \frac{11}{1} [/tex]=11
x1.x2=11
x1+x2=12
Pls help math lol. Yeah
Answer:
X = 65 degrees
Step-by-step explanation:
180 = 70 + 45 + X
180 = 115 + X
X = 65 degrees