Alf a passenger rides counter-clockwise from point m to point j, approximately how many feet has the passenger traveled?
Answers
We have to calculate how many feet the passenger traveled from M to J.
This distance is the arc length between M to J.
To calculate the arc length between two points on the circle, we need the central angle measure of the arc and the radius length.
As each seat is equidistant, we assme that each pair of seat has a constant central angle.
There are 18 sectors, so each sector will represent an angle of 360° / 18 = 20° per sector.
Now, we count how many sectors have between M to J, following the trajectory of the seat (counterclockwise):
We have 14 sectors that will represent a central angle of 14*20° = 280°.
Then, we can calculate the arc length as:
\(\begin{gathered} L=f\cdot C \\ L=\frac{280}{360}\cdot2\pi r \\ L=\frac{14}{18}\cdot2\pi\cdot200 \\ L\approx977.38 \end{gathered}\)To calculate it we use the fraction of the arc measure relative to the full circle measure.
We then multiply this fraction by the circumference of the wheel and obtain the arc length.
Answer: 977.38 feet.
Related Questions
What is the smallest positive integer $n$ such that $\sqrt[4]{56 \cdot n}$ is an integer?
Answers
The smallest positive integer n such that t \($\sqrt[4]{56 \cdot n}$\) is an integer is 686.
We have to find the smallest positive integer n such that \($\sqrt[4]{56 \cdot n}$\) is an integer
To find the smallest positive integer n such that \($\sqrt[4]{56 \cdot n}$\) is an integer, we need to determine the factors of 56 and find the smallest value of n that, when multiplied by 56, results in a perfect fourth power.
The prime factorization of 56 is:
56 = 2³ × 7
The prime factors of 56 need to be raised to multiples of 4.
Therefore, we need to determine the smallest value of n that includes additional factors of 2 and 7.
To make the expression a perfect fourth power, we need to raise 2 and 7 to the power of 4, which is 2⁴ × 7⁴
The smallest value of n that satisfies this condition is:
n = 2 × 7³ = 2× 343 = 686
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how many are 5 x 5 ?
Answers
Can you help me please asap
Answers
The general solution to the given differential equation is:
y = (x/12) - (1/288)
How to solve the Differential Equation?
We want to solve the differential equation given as: y' - 24xy = -2x
The integrating factor is given by the exponential of the integral of the coefficient of y, which in this case is -24x. Therefore, the integrating factor is e^(-24x).
Multiplying the entire equation by the integrating factor, we get:
e^(-24x)y' - 24xe^(-24x)y = -2xe^(-24x)
The left side of the equation is the derivative of (e^(-24x)y) with respect to x:
(d/dx)(e^(-24x)y) = -2xe^(-24x)
Integrating both sides with respect to x, we have:
e^(-24x)y = ∫(-2xe^(-24x))dx
Integrating the right side, we get:
e^(-24x)y = -∫(2xe^(-24x))dx
To evaluate the integral on the right side, we can use integration by parts. Let's differentiate -2x and integrate e^(-24x):
u = -2x (differential of u = -2dx)
dv = e^(-24x) (integral of dv = -1/24e^(-24x)dx)
Using the integration by parts formula:
∫uv dx = uv - ∫v du
We can compute the integral as follows:
-∫(2xe^(-24x))dx = -[(-2x)(-1/24e^(-24x)) - ∫(-1/24e^(-24x))(-2dx)]
= -[x/12e^(-24x) + 1/12∫e^(-24x)dx]
= -[x/12e^(-24x) + 1/12(-1/24)e^(-24x)]
= -[x/12e^(-24x) - 1/(12*24)e^(-24x)]
= -[x/12e^(-24x) - 1/(288e^(-24x))]
= -[x/12 - 1/288]e^(-24x)
Substituting this back into the previous equation, we have:
e^(-24x)y = -[-(x/12 - 1/288)e^(-24x)]
Simplifying further:
e^(-24x)y = (x/12 - 1/288)e^(-24x)
Canceling out e^(-24x) on both sides:
y = x/12 - 1/288
Therefore, the general solution to the given differential equation is:
y = x/12 - 1/288
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(3)/(2x+3)=(2)/(10x+4)
Answers
Answer:
x = -3/13
Step-by-step explanation:
cross multiply
4x + 6 = 30x + 12
combine like terms
-6 = 26x
x = -6/26 = -3/13
Which of the following is an example of perpendicular lines
Answers
Answer:
B...........................................................
Answer:
second option
Step-by-step explanation:
11. What is the unknown number in
Sequence 2 in the chart?
Sequence Number
Sequence 1
Sequence 2
A 126
B 127
c 147
D 154
2 3 5
7
14 21 35 49
?
1
7
21 42 63 105
Answers
The missing number in Sequence 2 is 780.
To find the missing number in Sequence 2, let's analyze the pattern:
In Sequence 1, the numbers increase by 1 each time: 126, 127, 128, 129, ...
In Sequence 2, the numbers seem to follow a pattern where each number is obtained by multiplying the corresponding number in Sequence 1 by a certain factor:
2 x 126 = 252
3 x 127 = 381
4 x 128 = 512
5 x 129 = 645
...
Looking at this pattern, we can see that the missing number in Sequence 2 should be:
6 x 130 = 780
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3/x=2
How do you solve this without get a loop
Answers
Answer:
x= 3/2
Step-by-step explanation:
3/x=2
Multiply x both sides so,
3 =2x
Divide 2 to get the value of x so,
x= 3/2
A regression was run to determine if there is a relationship between hours of TV watched per day (x) and number of situps a person can do (y).
The results of the regression were:
y=ax+b
a=-1.284
b=39.108
r2=0.819025
r=-0.905
Use this to predict the number of situps a person who watches 14 hours of TV can do (to one decimal place)
Answers
A person who watches 14 hours of TV can do 21.1 sit-ups.
What is the regression equation?The regression equation is used to predict or estimate the value of the response (or dependant) variables based on an understanding of the explanatory (or predictor) variables.
A regression equation has the following general form:
y = ax + b
Here,
y = dependent variable
x = independent variable
a = intercept
b = slope
The regression equation showing the relationship between the number of sit-ups a person can accomplish (y) and the number of hours of TV viewed each day (x) is:
y = -1.284x + 39.108
Compute the number of sit-ups a person who watches 14 hours of TV can do as follows:
y = -1.284(14) + 39.108
y = -17.976 + 39.108
y = 21.132 ≈ 21.1
Thus, a person who watches 14 hours of TV can do 21.1 sit-ups.
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center =
3. A diameter of a circle has endpoints P(-7,-4) and Q (3,2).
a. Find the center of the circle (hint use midpoint formula)
b. Find the radius. If your answer is not and integer, express in radical form. (hint use
distance formula)
c. Write an equation for the circle.
17
radius=
equation of the circle:
work:
< 2/3
I
>
Answers
a. The center of the circle is (-2, -1).
b. The radius of the circle is √136.
c. The equation of the circle is (x + 2)^2 + (y + 1)^2 = 136.
a. To find the center of the circle, we can use the midpoint formula, which states that the midpoint of a line segment with endpoints (x1, y1) and (x2, y2) is given by:
Midpoint = ((x1 + x2)/2, (y1 + y2)/2)
In this case, the endpoints of the diameter are P(-7, -4) and Q(3, 2).Applying the midpoint formula:
Midpoint = ((-7 + 3)/2, (-4 + 2)/2)
= (-4/2, -2/2)
= (-2, -1)
Therefore, the center of the circle is at the coordinates (-2, -1).
b. To find the radius of the circle, we can use the distance formula, which calculates the distance between two points (x1, y1) and (x2, y2). The radius of the circle is half the length of the diameter, which is the distance between points P and Q.
Distance = √\([(x2 - x1)^2 + (y2 - y1)^2]\)
Using the distance formula:
Distance = √[(3 - (-7))^2 + (2 - (-4))^2]
= √\([(3 + 7)^2 + (2 + 4)^2]\)
= √\([10^2 + 6^2\)]
= √[100 + 36]
= √136
Therefore, the radius of the circle is √136.
c. The equation for a circle with center (h, k) and radius r is given by:
\((x - h)^2 + (y - k)^2 = r^2\)
In this case, the center of the circle is (-2, -1), and the radius is √136. Substituting these values into the equation:
\((x - (-2))^2 + (y - (-1))^2\) = (√\(136)^2\)
\((x + 2)^2 + (y + 1)^2 = 136\)
Therefore, the equation of the circle is (x + 2)^2 + (y + 1)^2 = 136.
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Verónica Ana y Luis pintan una barda y les pagan 300 cuánto dinero debería recibir cada quien
Answers
Si Verónica, Ana y Luis están pintando una barda y se les paga un total de 300 unidades monetarias (por ejemplo, dólares, pesos, etc.), para determinar cuánto dinero debería recibir cada uno, necesitamos más información sobre cómo se distribuye el trabajo entre ellos.
Si los tres contribuyen de manera equitativa y realizan la misma cantidad de trabajo, podrían dividir el pago de manera igualitaria. En ese caso, cada uno recibiría 100 unidades monetarias (300 dividido entre 3).
Sin embargo, si uno de ellos realiza más trabajo o tiene una mayor responsabilidad en la tarea, podría ser justo que reciba una porción mayor del pago. En ese caso, la distribución de los 300 unidades monetarias dependerá de un acuerdo previo entre ellos sobre cómo se divide el pago en función de la cantidad o calidad del trabajo realizado.
Es importante tener en cuenta que la asignación exacta de dinero puede variar dependiendo de las circunstancias y el acuerdo al que lleguen Verónica, Ana y Luis.
Which is a whole number?
0.86
2/5
98
35%
Answers
Answer:
98 is a whole number
Step-by-step explanation:
0.86 is a decimal
2/5 is a fraction
35% is a percentage
Use the inequality 24 ≥ 58 + 5(x - 3.8)
Solve for the inequality X.
Pls help I need to hand it in by 4:00..
Answers
Answer:
Work shown below!
Step-by-step explanation:
24 ≥ 58 + 5(x - 3.8)
Distribute;
24 ≥ 58 + 5x - 19
Collect like terms;
24 ≥ 39 + 5x
Subtract 39 from both sides;
-15 ≥ 5x
Divide both sides by 5;
x ≥ -3
Write the standard form of the line that passes through the given points. Include your work in your final answer. Type your answer in the box provided to submit your solution.
(3,1) and (-2,3)
Answers
The equation of the line is 2x + 5y = 11 hat passes through the points (3,1) and (-2,3)
What is a straight line?A straight line is a combination of endless points joined on both sides of the point.
The slope 'm' of any straight line is given by:
\(\rm m =\dfrac{y_2-y_1}{x_2-x_1}\)
We have two points:
(3,1) and (-2,3)
The equation of the line passing through the points (3,1) and (-2,3)
\(\rm (y - 3) = \dfrac{3-1}{-2-3}(x+2)\)
\(\rm (y - 3) = -\dfrac{2}{5}(x+2)\)
5y - 15 = -2x - 4
2x + 5y = 11
Thus, the equation of the line is 2x + 5y = 11 hat passes through the points (3,1) and (-2,3)
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A store in Hampton bought a leather chair for $494.47 and marked it up 100% from the original cost. Later on, Sally purchased the leather chair and paid Hampton sales tax of 5.5%. How much, including tax, did she pay for the leather chair?
$
Answers
Answer: The markup percentage of 100% means the store added an amount equal to the original cost of the chair to its price, so the selling price of the chair before tax was 494.47 * 2 = $989.94.
The sales tax is calculated as 5.5% of the selling price before tax, which is 5.5/100 * 989.94 = $54.45.
The total amount paid by Sally for the leather chair, including tax, is 989.94 + 54.45 = $1044.39.
Step-by-step explanation:
Can you find X? Show how did u find
Answers
Answer:
x=90°
Step-by-step explanation:
As in the angle, there is a box giving us info that x has to be 90°.
But to be sure that there is no mistake we have to do the following:
Look at all the other angles (see what kind of angles they are).Add all the angles up to 360°( in this case as the angle we are looking for is on a straight line which gives straight line=180°).Checking and comparing the two answers.So we are looking at the surroundings of angle x (which is on a straight line) we see that it is a right angle and look at the angle on the same line is a right angle too.
The equation right angle=90° helps us see that because there are two right angles on a 180° line (90°+90°+180°).
Therefore the answer is:
x=90°
What is the Volume of the prism below
Answers
Answer:
140
Step-by-step explanation:
(5*7*8)/2= 280/2 =140
Write a exponential growth word problem and a exponential decay word problem
Answers
Answer:
Step-by-step explanation:
Growth:
You put 100 dollars into a fund which accumulates at a rate of 5% per annum. How much will be in the fund at the end of 10 years (to the nearest cent)?
answer: 100(1.05)¹⁰=162.89
Decay:
You buy a car for 10,000, and each year its value decreases by 5%. What is the car worth 10 years from now (to the nearest cent)?
answer: 10000(.95)¹⁰=5987.37
what is: a + 1/10=5/10 ? pls dont delete this its school work.
Answers
Answer:
a = 2/5
Step-by-step explanation:
a + 1/10 = 5/10
Subtract 1/10 from both sides of the equation.
a + 1/10 = 5/10
-1/10 -1/10
a = 4/10
This answer is not incorrect but we usually need to simplify it if possible.
4/10 can be reduced to 2/5.
a = 2/5
Answer:
a=2/5
Step-by-step explanation:
To solve this, we first need to isolate the a so we can solve from there
First, we subtract 1/10. But whatever we do to one side we have to do to the other side. So when we subtract 1/10 from the left side we cancel it out and we subtract 1/10 from the right side so 5/10-1/10
So our equation becomes…
a=5/10-1/10
We can simplify this to…
a=4/10
4/10 is equal to 2/5
So that is our final answer
Now since we have nothing else to do that is our final answer
PLEASE AWARD BRAINLIEST I REALLY NEED TO LEVEL UP!
Marissa bought 60 horns for her New years eve party for $83.40. She needs to purchase an additional 18 horns for the party at the same unit price. Complete the sentences below.
Answer A: Marissa will spend $____ for each horn.
Answer B: She will spend $_____ on the additional.
Answer C: she will have a total of _______ horns.
Answer D: She will spend a total of $_____ on horns for the party.
Answers
A: Marissa will spend $1.39 for each horn.
B: She will spend $25.02 on the additional.
C: She will have a total of 78 horns.
D: She will spend a total of $108.42 on horns for the party.
Answer: A IS 1.39. B Is 25.O2. C IS 78.D IS 108.42
Step-by-step explanation:
A We know that 60 horn cost 83.40. 83.40/60 is 1.39 (for each horn). B 1.39 time 18 is 25.02. C 60 PLUS 18 = 78. D . 83.40 PLUS 25.02 =108.42
Mr. Hooper has a tree in his front yard that grows every year. If the tree was 3 feet tall when he planted it 6 years ago , what is the current height of the tree in terms of f?
A. 3f + 6 feet
B. 6f + 3 feet
C. 3f + 18 feet
D. 6f + 18 feet
Answers
Therefore, the current height of the tree in terms of "f" would be 3f + 6 feet. So the correct answer is A. 3f + 6 feet.
Given: sin 18° = p Without using a calculator,
Answers
Answer:
P = 0.309
Step-by-step explanation:
Please please please help me
I really need to pass this I will give brainliest and a lot of points please just help me solve this correctly
Answers
The length of side AB is about 5.87 units.
How to find the side of a right triangle?The triangle ABC is a right angle triangle. A right angle triangle is a triangle that has one of its angles as 90 degrees.
Therefore, let's find the length AB in the right triangle.
Using trigonometric ratios,
cos 33 = adjacent / hypotenuse
Therefore,
Adjacent side = AB
hypotenuse side = 7 units
cos 33° = AB / 7
cross multiply
AB = 7 cos 33
AB = 7 × 0.83867056794
AB = 5.87069397562
AB = 5.87 units
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What are the length and width of a rectangle if the length is
3 inches longer than twice the width and the area of the
rectangle is 5 in2?
Answers
The length and width of the rectangle are 5 inches and 1 inches respectively.
How to find the length and width of a rectangle?The length and width of the rectangle can be found as follows;
l = 3 + 2w
area of a rectangle = lw
where
l = lengthw = widthTherefore,
5 = lw
5 = (3 + 2w)w
5 = 3w + 2w²
2w² + 3w - 5 = 0
Hence,
2w² + 3w - 5 = 0
Therefore,
w = 1 and w = - 5 / 2
width = 1 inches
length = 3 + 2(1) = 5 inches
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if it cost $5980 to have a picket fence installed around a rectangular lot that is 110 ft by 150 ft how much will it cost to have a picket fence installed around a rectangular light that is 125 ft by 170 ft
Answers
Answer:
6785 dollars
Step-by-step explanation:
It cost 5980 dollars for a rectangular lot that is 110 ft by 150 ft. 110 + 150 = 260. 5980/260=23. 125 + 170= 295. 295 x 23= 6785.
to 2 6/12 simplified
Answers
Answer:
2 1/2 or 2.5
Step-by-step explanation:
I believe it's 1 1/2
Step-by-step explanation:
I think it's either 1/6 or 1/2
solve for X 3(X+2) = 7 (x-6)
Answers
Answer: X = 54
Step-by-step explanation: Hope this help
Find each length below.
Answers
a) The length of the secant segment \(HC = 31.5\).
b) The length of the secant segment \(XY = 4.8\)
What is the secant segment?In geometry, a secant is a line that intersects a circle at two distinct points. A secant segment is part of a secant that lies between its two points of intersection with the circle.
In geometry, a segment is part of a line that is bounded by two distinct endpoints. A segment can be straight or curved. Straight segments are also called line segments, and curved segments are also called arcs.
According to the given information
a) In the figure, HG is a tangent and HD is a secant to the circle, and HC is the length of the secant segment.
We know that the product of the lengths of the two segments of a secant from an exterior point to a circle is equal to the product of the lengths of the entire secant and its external segment. That is,
\(HD*HE =HG^{2}\)
where \(HE\) is the length of the external segment of the secant.
Substituting the given values, we get:
\(31.5*HE =21^{2}\)
\(HE = 21^{2} /31.5 = 14\)
Now, we can use the same property to find \(HC\). That is,
\(HC *HE =HG^{2}\)
Substituting the values we have found, we get:
\(HC*14 = 21^{2} \\HC = 21^{2} /14 = 31.5\)
Therefore, the length of the secant segment \(HC = 31.5\).
b) \(VX*VZ= VY*VW\)
Substituting the given values, we get:
\(14.4*12= VY *36\\VY = (14.4*12)/36 = 4.8\)
Therefore, the length of \(VY, XY = 4.8\)
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Drag the tiles to the boxes to form correct pairs. Not all tiles will be used.
Match the function with its inverse.
Answers
The correct pairs of the functions and their inverses are given by the image at the end of the answer.
How to find the inverse function?To find the inverse function, we exchange x and y in the original function, then isolate y.
The first function that we want to find the inverse is:
f(x) = (2x - 1)/(x + 2).
Hence:
x = (2y - 1)/(y + 2)
(y + 2)x = 2y - 1
xy + 2x = 2y - 1
xy - 2y = -1 - 2x
y(x - 2) = -1 - 2x
y = (-1 - 2x)/(x - 2) (which is the inverse function).
The second function which we want to find the inverse is:
y = (x + 2)/(-2x + 1)
Then:
x = (y + 2)/(-2y + 1)
x(-2y + 1) = y + 2
-2yx + x = y + 2
-2yx - y = 2 - x
-y(2x + 1) = 2 - x
y = (x - 2)/(2x + 1) (which is the inverse function).
The third function which we want to find the inverse is:
y = (x - 1)/(2x + 1)
Then:
x = (y - 1)/(2y + 1)
2yx + x = y - 1
2yx - y = -1 - x
y(2x - 1) = -1 - x
y = (-x - 1)/(2x - 1) (which is the inverse function).
The fourth function which we want to find the inverse is:
y = (2x + 1)/(2x - 1)
Then:
x = (2y + 1)(2y - 1)
2yx - x = 2y + 1
2yx - 2y = 1 + x
2y(x - 1) = (1 + x)
y = (x + 1)/(2(x - 1)) (which is the inverse function).
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Robert spun the fair spinner shown below 1,060 times,
About how many times would Robert expect to spin a 1, 3, or 8?
Answers
Answer:
About 400 times
Step-by-step explanation:
Given
\(n = 1060\)
See attachment for spinner
Required
Determine the number of times an outcome of 1, 3 or 8 is expected
First, calculate the theoretical probability of 1, 3, or 8
This is calculated as:
\(Pr = P(1) + P(3) + P(8)\)
The spinner is divided into 8 equal segments and each outcome appears once.
So, we have:
\(Pr = \frac{1}{8}+\frac{1}{8}+\frac{1}{8}\)
Take LCM and add
\(Pr = \frac{1+1+1}{8}\)
\(Pr = \frac{3}{8}\)
So, the expected number of times (E) is:
\(E = Pr * n\)
\(E = \frac{3}{8} * 1060\)
\(E = \frac{3* 1060}{8}\)
\(E = \frac{3180}{8}\)
\(E = 397.5\)
Approximate
\(E = 398\)
This means about 400 times
Find the area, in square units, of the shaded region without counting every square. (please help)
Answers
so the area of each individual triangle is 4
4x4=
16 units^2