The probability that four boys are given the first four seats on the first teacup is approximately equal to 0.004.
How to find the Probability?To determine the probability that four boys are given the first four seats on the first teacup.
The total number of ways to distribute 12 tickets among 12 seats is 12! (12 factorial), which is equal to 479,001,600.
We need to find the number of ways that four boys can be selected from the seven boys, multiplied by the number of ways that eight people (including the remaining three boys and five girls) can be selected from the ten remaining people,
multiplied by the number of ways that the selected people can be arranged on the teacup ride.
The number of ways to select four boys from seven boys is 7C4, which is equal to 35. The number of ways to select eight people from the remaining ten people is 10C8, which is equal to 45.
Finally, the number of ways to arrange the selected twelve people on the teacup ride is 4!, which is equal to 24.
Therefore, the probability that four boys are given the first four seats on the first teacup is (35 x 45 x 24) / 12!, which is approximately equal to 0.004.
Learn more about Probability
brainly.com/question/30034780
#SPJ11
The dotted line is the perpendicular bisector of side AB. The distance between points E and A is 7 units. What is the distance between points E and B? Explain or show your reasoning
The distance between points E and B is (2/3)*AB, or (2/3)*(7+x) units.
Since the dotted line is the perpendicular bisector of side AB, it means that it cuts the line AB into two equal halves. Thus, the distance between points E and the dotted line is equal to the distance between point A and the dotted line.
We know that the distance between points E and A is 7 units, and since the dotted line bisects AB, the distance between point A and the dotted line is equal to the distance between point B and the dotted line. Let's call this distance 'x'.
Therefore, we have two equal distances (7 units and 'x') that add up to the length of AB. This means that:
AB = 7 units + x
However, we also know that the dotted line is the perpendicular bisector of AB, meaning that it forms right angles with both A and B. This creates two right-angled triangles, AED and BED, where DE is the perpendicular line from point E to AB.
Using Pythagoras' theorem, we can find the length of DE in terms of 'x':
(DE)² + (AE)² = (AD)²
(DE)² + (7)² = (AB/2)²
(DE)² + 49 = (AB²)/4
(DE)² = (AB²)/4 - 49
(DE)² = (AB² - 196)/4
(DE)² = (x²)/4
DE = x/2
Therefore, the distance between points E and B is equal to the length of DE plus the distance between point B and the dotted line, which is also equal to 'x'. Therefore, the distance between points E and B is:
EB = (x/2) + x = 1.5x
We can substitute this into the equation we found earlier:
AB = 7 units + x
AB = 7 units + (2/3)*EB
Know more about distance here:
https://brainly.com/question/15172156
#SPJ11
geometry geometry geometry
We can solve this problem by using some properties of centroids of the triangle and the fact that the centroid divides each median in a 2:1 ratio.
What is a centroid of a triangle?The centroid of a triangle is the point intersection of the three medians of the triangle.
First find the value of MR. The centroid divides each median in a 2:1 ratio, so we have:
MR = 2/3 * R + 1/3 * M
R is the centroid, so R = (P + V + M)/3.
Substituting, we get: MR = 2/3 * [(P + V + M)/3] + 1/3 * M
= 2/9 * P + 2/9 * V + 5/9 * M
Now, substitute the given values of PV and M to find MR:
MR = 2/9 * (3w+7) + 2/9 * (12y-9) + 5/9 * (5x-9) = (2w/3 + 8y/9 + 25x/9) - 1
Simplifying the expression: MR = (2w + 24y + 25x - 27)/9
Next, let's find the value of RP using the centroid. Since R is the midpoint of PV:
RP = 2/3 * R + 1/3 * P
Substituting the values of R and P:
RP = 2/3 * [(3w+7)/3 + (12y-9)/3 + (5x-9)/3] + 1/3 * (3w+7)
= (2w/9 + 8y/9 + 5x/3 + 7/3) + (w+7)/3
= (5w/3 + 8y/9 + 5x/3 + 10)/3
Simplifying this:
RP = (5w + 8y + 5x + 30)/9
Next, find the value of RV using the centroid. R is the midpoint of PV:
So, RV = 2/3 * R + 1/3 * V
Substituting R and V values:
RV = 2/3 * [(3w+7)/3 + (12y-9)/3 + (5x-9)/3] + 1/3 * (12y-9) = (2w/9 + 8y/9 + 5x/3 + 7/3) + 4y/3 - 3
Simplifying: RV = (5w + 20y + 5x - 18)/9
Find the value of RW using the centroid. R is the midpoint of VW, so: RW = 2/3 * R + 1/3 * W
Substituting the values of R and W:
RW = 2/3 * [(3w+7)/3 + (12y-9)/3 + (5x-9)/3] + 1/3 * 1.75x = (2w/9 + 8y
Read more about centroid of a triangle at brainly.com/question/29633268
#SPJ1
100-3(4. 25)-13-4(2. 99) SOMEONE PLSS HELP MEE THIS IS DIE TMRW!!
The simplified expression of 100-3(4. 25)-13-4(2. 99) is 48.29.
What is PEMDAS?
PEMDAS stands for Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right). It is a mnemonic or acronym used to remember the order of operations when simplifying mathematical expressions.
To simplify the expression 100-3(4.25)-13-4(2.99), you can follow the order of operations (PEMDAS) which is:
Parentheses
Exponents
Multiplication and Division (from left to right)
Addition and Subtraction (from left to right)
Using this order, you can simplify the expression as follows:
100 - 3(4.25) - 13 - 4(2.99)
= 100 - 12.75 - 13 - 11.96 // multiply 3 and 4 with their respective numbers
= 62.29 - 13 - 11.96 // perform subtraction within parentheses
= 48.29 // perform final subtraction
Therefore, the simplified expression is 48.29.
To learn more about PEDMAS from the given link:
https://brainly.com/question/24086845
#SPJ4
Given l||m||n, find the value of x
Answer:
x = 13
Step-by-step explanation:
We Know
(5x - 6) + (8x + 17) must equal 180°
Find the value of x.
Let's solve
5x - 6 + 8x + 17 = 180
13x + 11 = 180
13x = 169
x = 13
So, the value of x is 13.
A math teacher gave her class two tests. The results were 42 percent of the class passed the first test and 50 percent of the class passed thesecond test. Also, 60 percent of the students in the class who passed the first test passed the second test. What percentage of the class passed both tests? Are the events the class passed the first test and the class passed the second test independent? (1 point)
A) A total of 30 percent passed both tests. The events are independent.
B) A total of 25. 2 percent passed both tests. The events are independent.
C) A total of 25. 2 percent passed both tests. The events are not independent.
D) A total of 30 percent passed both tests. The events are not independent.
The answer is option C) A total of 25.2 percent passed both tests. The events are not independent.
To solve this problem, we can use a Venn diagram. Let P(A) be the probability of passing the first test, P(B) be the probability of passing the second test, and P(A and B) be the probability of passing both tests.
From the problem, we know:
P(A) = 0.42
P(B) = 0.50
P(B | A) = 0.60 (the probability of passing the second test given that the student passed the first test)
We can use the formula P(B | A) = P(A and B) / P(A) to find P(A and B):
0.60 = P(A and B) / 0.42
P(A and B) = 0.60 x 0.42
P(A and B) = 0.252
Therefore, 25.2% of the class passed both tests.
To determine if the events are independent, we can compare P(B) to P(B | A). If they are equal, the events are independent. If they are not equal, the events are dependent.
P(B) = 0.50
P(B | A) = 0.60
Since P(B) is not equal to P(B | A), the events are dependent.
Therefore, the answer is option C) A total of 25.2 percent passed both tests. The events are not independent.
To know more about probability refer here:
https://brainly.com/question/11234923
#SPJ11
Please help and explain if possibile
The missing lengths of triangles are 5in, 5mi, 13.9km,13.3mi respectively.
What is triangle?
A triangle is a closed, two-dimensional geometric figure with three straight sides and three angles.
What is Pythagorean theorem?
The Pythagorean Theorem is a fundamental theorem in Euclidean geometry that relates to the three sides of a right-angled triangle.
According to given information:Using the Pythagorean theorem [tex](a^2 + b^2 = c^2)[/tex], we can solve for the missing side in each triangle.
Triangle 1:
[tex]a = 12 in\\\\c = 13 in\\\\a^2 + b^2 = c^2\\\\12^2 + b^2 = 13^2\\\\144 + b^2 = 169\\\\b^2 = 25\\\\b = \sqrt{(25)}\\\\b = 5 in[/tex]
Therefore, the length of the missing side in Triangle 1 is 5 in.
Triangle 2:
[tex]a = 4 mi\\\\b = 3 mi\\\\c = x\\\\a^2 + b^2 = c^2\\\\4^2 + 3^2 = x^2\\\\16 + 9 = x^2\\\\25 = x^2\\\\x = \sqrt{(25)}\\\\x = 5 mi[/tex]
Therefore, the length of the hypotenuse in Triangle 2 is 5 mi.
Triangle 3:
[tex]a = x\\\\b = 11.9 km\\\\c = 14.7 km\\\\a^2 + b^2 = c^2\\\\x^2 + 11.9^2 = 14.7^2\\\\x^2 = 14.7^2 - 11.9^2\\\\x^2 = 192.36\\\\x = \sqrt{(192.36)}\\\\x = 13.9 km[/tex]
Therefore, the length of the height in Triangle 3 is 13.9 km.
Triangle 4:
[tex]a = x\\\\b = 6.3 mi\\\\c = 15.4 mi\\\\a^2 + b^2 = c^2\\\\x^2 + 6.3^2 = 15.4^2\\\\x^2 = 15.4^2 - 6.3^2\\\\x^2 = 178.09\\\\x = \sqrt{(178.09)}\\\\x = 13.3 mi[/tex]
Therefore, the length of the height in Triangle 4 is 13.3 mi.
To learn more about triangle visit:
https://brainly.com/question/1058720
#SPJ1
A ring-shaped region is shown below.
Its inner radius is 9m, and its outer radius is 13m.
Find the area of the shaded region.
Use 3.14 for Pie. Do not round your answer.
The area of the ring-shaped region with radii of 9m and 13m is approximately 276.32 square meters.
What is Area?
The area is the region defined by an object's shape. The area of a shape is the space covered by a figure or any two-dimensional geometric shape in a plane.
What is Perimeter?
The perimeter of a shape is defined as the total distance surrounding the shape. It is the length of any two-dimensional geometric shape's outline or boundary.
According to the given information:
The given shape is a two concentric circles with radii of 9m and 13m, we can calculate the area of this region using the formula for the area of a circle:
Area of shaded region = Area of outer circle - Area of inner circle
The area of a circle is given by the formula A = πr^2, where r is the radius of the circle.
Area of inner circle = π(9)^2 = 81π
Area of outer circle = π(13)^2 = 169π
Area of shaded region = 169π - 81π = 88π
Using the value of π = 3.14, we get:
Area of shaded region = 88π = 88(3.14) = 276.32 square meters (rounded to two decimal places)
Therefore, the area of the ring shaped region with radii of 9m and 13m is approximately 276.32 square meters.
To know more about Area visit : https://brainly.com/question/1631786
#SPJ1
Please help with this
a) The table is completed as follows:
x = -5, y = -3.x = 0, y = 2.x = 3, y = 5.b) The graph is given by the image presented at the end of the answer.
How to calculate the numeric value of a function or of an expression?To calculate the numeric value of a function or of an expression, we substitute each instance of any variable or unknown on the function by the value at which we want to find the numeric value of the function or of the expression presented in the context of a problem.
The function for this problem is given as follows:
y= x + 2.
Hence the numeric values of the function are given as follows:
x = -5, y = -5 + 2 = -3.x = 0, y = 0 + 2 = 2.x = 3, y = 3 + 2 = 5.Then the graph is constructed connecting two of these points and tracing a line through them.
Learn more about the numeric values of a function at brainly.com/question/28367050
#SPJ1
Ms.smith and mr brown took attendance at the fire drill. the actual count of students and teaches was between 96 and 105. what is the absolute error
Ms. Smith and Mr. Brown's attendance count had an absolute error of 1.5 people. This means that the measured value was 1.5 people off from the actual value, which was between 96 and 105.
The absolute error is a measure of the difference between the actual value and the measured value. In this case, Ms. Smith and Mr. Brown took attendance at a fire drill and the actual count of students and teachers was between 96 and 105. Let's say they counted 100 people in total.
To find the absolute error, we need to subtract the measured value from the actual value. In this case, the absolute error would be |100 - 98.5| = 1.5, where 98.5 is the midpoint between 96 and 105.
This means that the attendance count was off by 1.5 people. It is important to note that absolute error is always positive and represents the magnitude of the difference between the actual and measured values.
You can learn more about the absolute error at: brainly.com/question/30759250
#SPJ11
The absolute error is 0.5.
How to calculate absolute error range?
The absolute error is a measure of how far away a given estimate is from the actual value. In this case, we know that the actual count of students and teachers was between 96 and 105, but we don't know the exact number. Let's assume that Ms. Smith and Mr. Brown recorded the number of students and teachers as 100.
The absolute error is then calculated by taking the absolute value of the difference between the estimate and the actual value. In this case, the estimate is 100 and the actual value is somewhere between 96 and 105. So, the absolute error would be the difference between 100 and the midpoint between 96 and 105.
The midpoint between 96 and 105 is (96 + 105)/2 = 100.5. Therefore, the absolute error would be |100 - 100.5| = 0.5. So the absolute error in this case is 0.5.
Learn more about absolute error
brainly.com/question/31129826
#SPJ11
Leo is going to use a random number generator
400
400400 times. Each time he uses it, he will get a
1
,
2
,
3
,
4
,
1,2,3,4,1, comma, 2, comma, 3, comma, 4, comma or
5
55.
It sounds like Leo will be using a specific type of random number generator that produces only five possible outcomes: 1, 2, 3, 4, or 555. It seems that the generator produces a repeating pattern of four numbers (1, 2, 3, 4) followed by a fifth number (555).
If Leo uses this generator 400400400 times, then he will get 100100100 repetitions of the pattern. This means that he will get 100100100 x 4 = 400400400 numbers 1, 2, 3, or 4, and 100100100 occurrences of the number 555.
It is important to note that this type of random number generator is not truly random, as it is not generating numbers with equal probability. Instead, it is producing a predetermined sequence of numbers. This means that if Leo knows the pattern, he could predict the next number that will be generated with certainty.
In general, it is important to use truly random number generators for many applications, such as cryptography or scientific simulations, where the results need to be unpredictable and unbiased.
To know more about random number generator, refer to the link below:
https://brainly.com/question/31603339#
#SPJ11
Find the amount of force it takes to push jeff’s race car if the mass of the race car is 750 kg and the acceleration is 2. 5 startfraction m over s squared endfraction
the amount of force needed to push jeff’s race car is
newto
The amount of force required to push Jeff's race car is 1,875 Newtons (N).
How much force is required to push Jeff's race?The amount of force needed to push Jeff's race car is 1,875 Newtons (N), This problem provides us with the mass of Jeff's race car, which is 750 kg, and the acceleration it experiences, which is 2.5 m/s². We need to find the amount of force required to push the race car.
The formula to calculate force is:
Force = Mass x Acceleration
In this case, the mass of the race car is 750 kg and the acceleration is 2.5 m/s². We simply plug in these values into the formula to get:
Force = 750 kg x 2.5 m/s²
Simplifying the expression, we get:
Force = 1,875 N
Therefore, the amount of force required to push Jeff's race car is 1,875 Newtons (N).
Learn more about force
brainly.com/question/27816270
#SPJ11
Name
Chapter
5
1.On a calendar, each day is represented by a rectangle. To keep track of the date, you cross off the
previous day by connecting one pair of opposite corners of the rectangle, as shown.
10
E 177
11
F18
12
b. List the five triangle congruence theorems.
G10
a. Classify AABE by its sides and by measuring its angles. Explain your reasoning.
D
Date
c.For each of the triangle congruence theorems you listed in part (b), prove that AFBC = ACGF
using that theorem. (You will need to write five different proofs.)
The triangle theorems will be:
Side-Side-Side (SSS) Congruence Theorem:Side-Angle-Side (SAS) Congruence Theorem:Angle-Side-Angle (ASA) Congruence Theorem:Hypotenuse-Leg (HL) Congruence Theorem:Angle-Angle-Side (AAS) Congruence TheoremHow to explain the theoremSide-Side-Side (SSS) Congruence Theorem: If the three sides of one triangle are congruent to the three sides of another triangle, then the two triangles are congruent.
Side-Angle-Side (SAS) Congruence Theorem: If two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent.
Angle-Side-Angle (ASA) Congruence Theorem: If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent.
Angle-Angle-Side (AAS) Congruence Theorem: If two angles and a non-included side of one triangle are congruent to two angles and the corresponding non-included side of another triangle, then the two triangles are congruent.
Hypotenuse-Leg (HL) Congruence Theorem: If the hypotenuse and a leg of one right triangle are congruent to the hypotenuse and a leg of another right triangle, then the two triangles are congruent.
Learn more about theorem on
https://brainly.com/question/17335144
#SPJ1
What is the domain of the function f(x)=2x^2+5x-12
The domain of the function f(x) = 2x² + 5x - 12 is all real numbers, or (-∞, ∞).
This is because there are no restrictions on the input values of x that would make the function undefined. In other words, we can input any real number into the function and get a valid output.
To determine the domain of a function, we need to consider any restrictions on the independent variable that would make the function undefined.
Common examples of such restrictions include division by zero, taking the square root of a negative number, or taking the logarithm of a non-positive number. However, in this case, there are no such restrictions, and therefore the domain is all real numbers.
To know more about domain of the function, refer here:
https://brainly.com/question/29109048#
#SPJ11
Explain how to find the measure of angles a and b has a measure of 36 degrees
The measure of angles a and b is 36 degrees if they are alternate interior angles formed by a transversal intersecting two parallel lines.
How to find the measure of angles a and b with a measure of 36 degrees?To find the measure of angles a and b when angle b has a measure of 36 degrees, we need additional information.
If we assume that angles a and b are adjacent angles formed by two intersecting lines, then we can use the fact that adjacent angles are supplementary, meaning their measures add up to 180 degrees. Since angle b has a measure of 36 degrees, we subtract it from 180 to find angle a.
Thus, angle a = 180 - 36 = 144 degrees. Therefore, angle a has a measure of 144 degrees when angle b has a measure of 36 degrees.
Learn more about measure
brainly.com/question/4725561
#SPJ11
a city department of transportation studied traffic congestion on a certain highway. to encourage carpooling, the department will recommend a carpool lane if the average number of people in passenger cars on the highway is less than 2 . the probability distribution of the number of people in passenger cars on the highway is shown in the table. number of people 1 2 3 4 5 probability 0.56 0.28 0.08 0.06 0.02 based on the probability distribution, what is the mean number of people in passenger cars on the highway?
The mean number of people in passenger cars on the highway is 1.7 (approximately 2).
The mean of a probability distribution function is also known as Expectation of the probability distribution function.
The mean number of people in passenger cars (or expectation of number of people in passenger cars ) on the highway can be denoted as E(x) where x is the number of people in passenger cars on the highway.
Thus E(x) can be calculated as,
E(x) = ∑ [tex]x_{i} p_{i}[/tex] ∀ i= 1,2,3,4,5
where, [tex]p_{i}[/tex] is the probability of number of people in passenger cars on the highway
⇒ E(x) = (1)(0.56) + (2)(0.28) + (3)(0.08) + (4)(0.06) + (5)(0.02)
⇒ E(x) = 1.7
Hence the mean number of people in passenger cars on the highway is 1.7, which is less than 2.
To know more about mean (or, expectation) of a probability distribution here
https://brainly.com/question/29068283
#SPJ4
Plss answer correctly and be sure to show work!
Answer:
m<V=100.5°
u=84.86u
v=154.86u
Step-by-step explanation:
m<V= 180-46.9-32.6=100.5°
sin46.9°/115=sin32.6°/u
sin46.9°u=115sin32.6°
u=115sin32.6°/sin46.9°
u=84.86u
sin46.9°/115=sin100.5°/v
sin46.9°v=115sin100.5°
v=115sin100/5°/sin46.9°
v=154.86
Determine the unique solution, y(x), to the differential equation that satisfies the given initial condition. dy/dx = 8x⁷/y⁴, y(0) = 4
y(x) = ...
The unique solution, y(x), to the given differential equation with initial condition y(0) = 4 is
:
y(x) = [-(6x⁸ - 64)]¹/³
Determine the unique solution?
To determine the unique solution, y(x), to the given differential equation with initial condition y(0) = 4, we first need to separate the variables and integrate both sides with respect to x and y, respectively.
dy/y⁴ = 8x⁷ dx
Integrating both sides, we get:
-1/3y³ = 2x⁸ + C
where C is the constant of integration.
Now we can use the initial condition y(0) = 4 to solve for C:
-1/3(4)³ = 2(0)⁸ + C
C = -64/3
Substituting C back into the previous equation, we get:
-1/3y³ = 2x⁸ - 64/3
Multiplying both sides by -3 and taking the cube root, we get:
y(x) = [-(6x⁸ - 64)]¹/³
Therefore, the unique solution, y(x), to the given differential equation with initial condition y(0) = 4 is:
y(x) = [-(6x⁸ - 64)]¹/³
Learn more about differential equation.
brainly.com/question/14620493
#SPJ11
work out minimum and maximum number of hikers who could have walked between 7 miles and 18 miles
(a) The minimum number of hikers who could have walked between 7 miles and 18 miles: at least 5 hikers and at most 13 hikers.
(b) The maximum number of hikers who could have walked between 7 miles and 18 miles: at most 15 hikers.
According to the question and given conditions, we need to find the cumulative frequency of the distance intervals that fall within the range of 7 miles and 18 miles, to find the minimum number of hikers and the maximum number of hikers who could have walked between 7 miles and 18 miles.
The sum of the frequencies up to a certain point in the data is the cumulative frequency. By adding the frequency of the current interval to the frequency of the previous interval, we can calculate the cumulative frequency.
a) To find the minimum number of hikers who could have walked between 7 miles and 18 miles, we will find the cumulative frequency of the intervals from 5 miles to 10 miles and then from 10 miles to 15 miles.
Cumulative frequency for 5 < x <= 10: 2 + 3 = 5
Cumulative frequency for 10 < x <= 15: 5 + 8 = 13
Therefore, we find that at least 5 hikers and at most 13 hikers could have walked between 7 miles and 18 miles.
b) To find the maximum number of hikers who could have walked between 7 miles and 18 miles, we will find the cumulative frequency of the intervals from 10 miles to 15 miles and from 15 miles to 20 miles.
Cumulative frequency for 10 < x <= 15: 8
Cumulative frequency for 15 < x <= 20: 8 + 7 = 15
Therefore, we can conclude that at most 15 hikers could have walked between 7 miles and 18 miles.
To know more about statistics;
brainly.com/question/15525560
#SPJ1
The complete question is "a) work out the minimum number of hikers who could have walked between 7 miles and 18 miles b) work out the maximum number of hikers who could have walked between 7 miles and 18 miles."
For the cost function C(x) = 6000 + 242 + 0.005.03 find: A) The production level that will minimize the average cost. B) The minimal average cost.
To find the production level that will minimize the average cost, we need to differentiate the cost function with respect to x and set it equal to zero. So:
C'(x) = 0.005x^2 + 242x + 6000
0 = 0.005x^2 + 242x + 6000
Using the quadratic formula, we get:
x = (-242 ± sqrt(242^2 - 4(0.005)(6000))) / (2(0.005))
x = (-242 ± sqrt(146416)) / 0.01
x = (-242 ± 382) / 0.01
x = -14,000 or 27,000
Since the production level cannot be negative, we can discard the negative solution and conclude that the production level that will minimize the average cost is 27,000 units.
To find the minimal average cost, we need to plug the production level back into the cost function and divide by the production level. So:
C(27,000) = 6000 + 242(27,000) + 0.005(27,000)^2
C(27,000) = 6,594,000
Average cost = C(27,000) / 27,000
Average cost = 6,594,000 / 27,000
Average cost ≈ 244.22
Therefore, the minimal average cost is approximately $244.22.
To answer your question, first, let's correct the cost function, which should be in the form of C(x) = Fixed cost + Variable cost. Assuming it is C(x) = 6000 + 242x + 0.005x^2.
A) To find the production level that will minimize the average cost, we need to first determine the average cost function, which is AC(x) = C(x)/x. So, AC(x) = (6000 + 242x + 0.005x^2)/x.
Now, find the first derivative of AC(x) concerning x, and set it equal to zero to find the minimum point:
d(AC(x))/dx = 0
The first derivative of AC(x) is:
d(AC(x))/dx = (242 + 0.010x - 6000/x^2)
Setting this to zero and solving for x will give us the production level that minimizes the average cost:
242 + 0.010x - 6000/x^2 = 0
Now, you can solve for x using numerical methods, such as Newton-Raphson or others. After solving for x, you will get the production level that minimizes the average cost.
B) To find the minimal average cost, plug the production level x you found in part A into the average cost function, AC(x):
Minimal Average Cost = AC(production level)
This will give you the minimal average cost for the given cost function.
To learn more about production visit;
brainly.com/question/30333196
#SPJ11
solve for b
18, b, 27, 22
(round your answer to the nearest tenth
b=[?]
The length of side b for the triangle is equal to 21.8 to the nearest tenth using the sine rule.
What is the sine ruleThe sine rule is a relationship between the size of an angle in a triangle and the opposing side.
Using the sine rule;
18/sin22° = b/sin27°
b = (18 × sin27°)/sin22° {cross multiplication}
b = 21.8144
Therefore, the length of side b for the triangle is equal to 21.8 to the nearest tenth using the sine rule.
Read more about sine rule here: https://brainly.com/question/4372174
#SPJ1
MARKING BRAINLEIST IF CORRECT ASAP
Answer:
24.1 feet
Step-by-step explanation:
We can represent these 3 points as a triangle:
- place in the water fountain line
- where her lab partner is
- where her friend is
We know that the distance from the water fountain to the lab partner is 6.6 ft, and the distance from the water fountain to the friend is 7.5 ft.
These are the legs (shorter sides) of the right triangle. Now, we need to find the hypotenuse, which is the distance from the lab partner to the friend. We can solve for this using the Pythagorean Theorem.
[tex]a^2 + b^2 = c^2[/tex]
[tex]6.6^2 + 7.5^2 = c^2[/tex]
[tex]43.56 + 56.25 = c^2[/tex]
[tex]99.81 = c^2[/tex]
[tex]c = \sqrt{99.81}[/tex]
[tex]c \approx 10.0 \text{ ft}[/tex]
To finally answer this question, we need to find the perimeter of the triangle (i.e., the distance that will be walked).
[tex]P = 6.6 + 7.5 + 10.0[/tex]
[tex]\boxed{P = 24.1 \text{ ft}}[/tex]
Question 1 < Σ Use integration by parts to evaluate the definite integral: 2t sin( – 9t)dt = 5.25л ба
The value of the definite integral 2t sin(-9t)dt from 0 to π is 5.25π.
To evaluate the definite integral 2t sin(-9t)dt using integration by parts, we first need to choose u and dv.
Let u = 2t and dv = sin(-9t)dt. Then du/dt = 2 and v = (-1/9)cos(-9t).
Using the integration by parts formula ∫udv = uv - ∫vdu, we can evaluate the definite integral as follows: ∫2t sin(-9t)dt = [-2t/9 cos(-9t)] - ∫(-2/9)cos(-9t)dt
Next, we need to evaluate the integral on the right-hand side.
Let u = -2/9 and dv = cos(-9t)dt. Then du/dt = 0 and v = (1/9)sin(-9t).
Using integration by parts again, we get: ∫cos(-9t)dt = (1/9)sin(-9t) + ∫(1/81)sin(-9t)dt = (1/9)sin(-9t) - (1/729)cos(-9t)
Substituting this result back into the original equation, we get: ∫2t sin(-9t)dt = [-2t/9 cos(-9t)] - [(-2/9)(1/9)sin(-9t) + (2/9)(1/729)cos(-9t)]
Now, we can evaluate the definite integral by plugging in the limits of integration (0 and π) and simplifying:
∫π0 2t sin(-9t)dt
= [-2π/9 cos(-9π)] - [(-2/9)(1/9)sin(-9π) + (2/9)(1/729)cos(-9π)] - [(-2/9)cos(0)]
= [-2π/9 cos(9π)] - [(-2/9)(1/9)sin(9π) + (2/9)(1/729)cos(9π)] - [(-2/9)cos(0)]
= [-2π/9 (-1)] - [(-2/9)(1/9)(0) + (2/9)(1/729)(-1)] - [(-2/9)(1)]
= (2π/9) + (2/6561) + (2/9) = 5.25π
Therefore, the value of the definite integral 2t sin(-9t)dt from 0 to π is 5.25π.
Know more about definite integral,
https://brainly.com/question/31344244
#SPJ11
Use the Chain Rule to find Oz/as and Oz/ot. sin(e) cos(6), = st*, Q = st дz as az at 1 x
the Chain Rule to find Oz/as and Oz/ot for the expression sin(e) cos(6), we first need to break it down into its component parts.
Let u = sin(e) and v = cos(6), so that our expression becomes u*v.
Now we can find the partial derivative of Oz/as by using the Chain Rule:
Oz/as = (dOz/du) * (du/as) + (dOz/dv) * (dv/as)
Since Oz = st*, we have dOz/du = st and dOz/dv = t*, so we can substitute those values in:
Oz/as = (st) * (dcos(e)/das) + (t*) * (-sin(6)/das)
To simplify this expression, we need to find the partial derivative of u and v with respect to as:
du/as = (dcos(e)/das)
dv/as = (-sin(6)/das)
Substituting those values back into our original expression for Oz/as, we get:
Oz/as = st * du/as + t* * dv/as
Oz/as = st * (dcos(e)/das) + t* * (-sin(6)/das)
Finally, we can simplify this expression by factoring out the common factor of das:
Oz/as = (st * dcos(e) - t* * sin(6)) / das
To find Oz/ot, we can follow the same steps but with respect to ot instead of as:
Oz/ot = (dOz/du) * (du/ot) + (dOz/dv) * (dv/ot)
Since Oz = st*, we have dOz/du = st and dOz/dv = t*, so we can substitute those values in:
Oz/ot = (st) * (-sin(e)/dot) + (t*) * (-6sin(6)/dot)
To simplify this expression, we need to find the partial derivative of u and v with respect to ot:
du/ot = (-sin(e)/dot)
dv/ot = (-6sin(6)/dot)
Substituting those values back into our original expression for Oz/ot, we get:
Oz/ot = st * du/ot + t* * dv/ot
Oz/ot = st * (-sin(e)/dot) + t* * (-6sin(6)/dot)
Finally, we can simplify this expression by factoring out the common factor of dot:
Oz/ot = (-sin(e)st - 6sin(6)t*) / dot
To find ∂z/∂s and ∂z/∂t using the Chain Rule, let's first define the given functions:
1. z = st (where s and t are variables)
2. s = sin(e) (where e is a variable)
3. t = cos(θ) (where θ is a variable)
Now, apply the Chain Rule to find ∂z/∂s and ∂z/∂t:
Chain Rule states: ∂z/∂x = (∂z/∂s) * (∂s/∂x) + (∂z/∂t) * (∂t/∂x)
1. Find ∂z/∂s:
Since z = st, ∂z/∂s = t
2. Find ∂z/∂t:
Since z = st, ∂z/∂t = s
Now we have ∂z/∂s and ∂z/∂t. You can use these expressions to find the desired derivatives by substituting the given functions for s and t.
∂z/∂s = t = cos(θ)
∂z/∂t = s = sin(e)
To know more about Chain Rule click here:
brainly.com/question/30416222
#SPJ11
Find the value(s) of k for which u(x.t) = e-³sin(kt) satisfies the equation Ut=4uxx
When k = 0, both sides of the equation equal 0:
3cos(0) = 4(0)sin(0)
3 = 0
There are no other values of k for which the equation holds true, the only value of k that satisfies the given equation is k = 0.
To find the value(s) of k for which u(x, t) = e^(-3)sin(kt) satisfies the equation Ut = 4Uxx, we first need to calculate the partial derivatives with respect to t and x.
[tex]Ut = ∂u/∂t = -3ke^(-3)cos(kt)Uxx = ∂²u/∂x² = -k^2e^(-3)sin(kt)[/tex]
Now, we will substitute Ut and Uxx into the given equation:
[tex]-3ke^(-3)cos(kt) = 4(-k^2e^(-3)sin(kt))[/tex]
Divide both sides by e^(-3):
[tex]-3kcos(kt) = -4k^2sin(kt)[/tex]
Since we want to find the value(s) of k, we can divide both sides by -k:
3cos(kt) = 4ksin(kt)
Now we need to find the k value that satisfies this equation. Notice that when k = 0, both sides of the equation equal 0:
3cos(0) = 4(0)sin(0)
3 = 0
Since there are no other values of k for which the equation holds true, the only value of k that satisfies the given equation is k = 0.
To learn more about partial derivatives, refer below:
https://brainly.com/question/29652032
#SPJ11
Emir earned some money doing odd jobs last summer and put it in a savings account that earns 10% interest compounded monthly. After 9 years, there is $400. 00 in the account. How much did Emir earn doing odd jobs?
Round your answer to the nearest cent
Emir earned approximately $207.05 doing odd jobs.
Let x be the amount that Emir earned doing odd jobs. We can use the formula for compound interest, A = P(1+r/n)^(nt), where A is the final amount, P is the principal amount, r is the interest rate, n is the number of times the interest is compounded per year, and t is the number of years.
In this case, we have P = x, r = 0.1, n = 12 (since interest is compounded monthly), t = 9, and A = 400. Solving for x, we get:
x = A/(1+r/n)^(nt) = 400/(1+0.1/12)^(12*9) ≈ $207.05
Therefore, Emir earned approximately $207.05 doing odd jobs.
For more questions like Interest click the link below:
https://brainly.com/question/13324776
#SPJ11
1. In Circle O shown below, with a radius of 12 inches, a sector has been defined by two radii oB and o4 with a central angle of 60° as shown. Determine the area of shaded sector.
B
Step 1: Determine the area of the entire circle in terms of pi.
Step 2: Determine the portion (fraction) of the shaded sect in the circle by using the central angle value.
Step 3: Multiply the area of the circle with the portion (fraction) from step 2.
The area of the shaded sector of the given circle would be = 42,593.5 in²
How to calculate the area of a given sector?To calculate the area of the given sector the formula that should be used is given as follows;
The area of a sector =( ∅/2π) × πr²
where;
π = 3.14
r = 12 in
∅ = 60°
Area of the sector = (60/2×3.14)b × 3.14× 12×12
= 94.2× 452.16
= 42,593.5 in²
Learn more about area here:
https://brainly.com/question/28470545
#SPJ1
In triangle ABC below, m
AC = 3x + 32
BC = 7x + 16
A. Find the range of values for x.
Make sure to show your work in finding this answer.
B. Explain what you did in step A to find your answer.
The range of values for x in the triangle is 0 < x < 8
Finding the range of values for x.From the question, we have the following parameters that can be used in our computation:
AC = 3x + 32
BC = 7x + 16
Also, we know that
ADC is greater than BDC
This means that
AC > BC
So, we have
3x + 32 > 7x + 16
Evaluate the like terms
-4x > -32
Divide both sides by -4
x < 8
Also, the smallest value of x is greater than 0
So, we have
0 < x < 8
Hence, the range of values for x is 0 < x < 8
The steps to calculate the range is gotten from the theorem that implies that
The greater the angle opposite the side length of a triangle, the greater the side length itself
Read more about triangles at
https://brainly.com/question/14285697
#SPJ1
Scientists estimate that the mass of the sun is 1. 9891 x 10 kg. How many zeros are in this
number when it is written in standard notation?
A 26
B 30
C 35
D 25
There are 30 zeros in the mass of the sun which is 1.9891 x 10³⁰ kg when it is written in standard notation. The correct answer is option B.
To determine how many zeros are in the mass of the sun (1.9891 x 10³⁰ kg) when it is written in standard notation, you first need to recognize that the provided mass is not written correctly. It should be written as 1.9891 x 10^n kg, where n is an integer representing the exponent.
The actual mass of the sun is 1.9891 x 10³⁰ kg. When written in standard notation, this number would be:
1,989,100,000,000,000,000,000,000,000,000 kg
There are 30 zeros in this number when written in standard notation.
So, the correct answer is B) 30.
Learn more about integers:
https://brainly.com/question/929808
#SPJ11
6. Torrence wants to remodel his studio apartment. The first thing he is going to do is replace the
floors in the living space and kitchen (not the closet or bathroom)
24
Living Space
101
200
31
71
38
closet
HD
kitchen
bathroom
61
a How many square feet of flooring will Torrence need to buy?
Torrence needs to buy 468 square feet of flooring for his remodeling project.
To calculate the total square feet of flooring needed, we first need to find the area of the living space and the kitchen. The dimensions given for the living space are 24x10, while the kitchen dimensions are 12x13.
1: Calculate the area of the living space.
Area = Length x Width
Area = 24 x 10
Area = 240 square feet
2: Calculate the area of the kitchen.
Area = Length x Width
Area = 12 x 13
Area = 156 square feet
3: Add the areas of the living space and kitchen to find the total square footage.
Total Area = Living Space Area + Kitchen Area
Total Area = 240 + 156
Total Area = 468 square feet
To know more about square footage click on below link:
https://brainly.com/question/1000510#
#SPJ11
The world's population can be projected using the following exponential growth
model. using this function, a= pert, at the start of the year 2022, the world's
population will be around 7. 95 billion. the current growth rate is 1. 8%. in what
year would you expect the world's population to exceed 10 billion?
We can expect the world's population to exceed 10 billion around the year 2038, based on the given growth rate and exponential growth model.
Using the exponential growth model, the world's population (P) can be projected with the formula P = P0 * e^(rt), where P0 represents the initial population, r is the growth rate, t is time in years, and e is the base of the natural logarithm (approximately 2.718).
In this case, the initial population (P0) at the start of 2022 is 7.95 billion, and the current growth rate (r) is 1.8%, or 0.018 in decimal form.
To estimate when the population will exceed 10 billion, we can rearrange the formula as follows: t = ln(P/P0) / r. We want to find the year (t) when the population (P) surpasses 10 billion.
By plugging in the values, we get: t = ln(10/7.95) / 0.018. Calculating this, t ≈ 15.96 years.
Since we're starting from 2022, we need to add this value to the initial year: 2022 + 15.96 ≈ 2038.
You can learn more about the population at: brainly.com/question/27991860
#SPJ11
We would expect the world's population to exceed 10 billion in the year 2036 (2022 + 14.6).
How to find the growth population?The exponential growth model is given by:
P(t) = P0 * [tex]e^(^r^t^)[/tex]
where P0 is the initial population, r is the annual growth rate as a decimal, and t is the time in years.
From the problem, we know that:
P0 = 7.95 billion
r = 0.018 (1.8% as a decimal)
P(t) = 10 billion
We want to solve for t in the equation P(t) = 10 billion. Substituting in the values we know, we get:
10 billion = 7.95 billion *[tex]e^(0^.^0^1^8^t^)[/tex]
Dividing both sides by 7.95 billion, we get:
1.26 = [tex]e^(0^.^0^1^8^t^)[/tex]
Taking the natural logarithm of both sides, we get:
ln(1.26) = 0.018t
Solving for t, we get:
t = ln(1.26)/0.018
Using a calculator, we get:
t ≈ 14.6 years
So, we would expect the world's population to exceed 10 billion in the year 2036 (2022 + 14.6).
Learn more about population growth
brainly.com/question/18415071
#SPJ11