Answer:
F(t<0.1 ) = 0.91791
Step-by-step explanation:
Solution:
- Let X be an exponential RV denoting time t in hours from start of interval to until first log-on that arises from Poisson process with the rate λ = 25 log-ons/hr. Its cumulative density function is given by:
F(t) = 1 - e ^ ( - 25*t ) t > 0
A) In this case we are interested in the probability that it takes t = 6/60 = 0.1 hrs until the first log-on. F ( t < 0.1 hr ), we have:
F(t<0.1 ) = 1 - e ^ ( - 25*0.1 )
F(t<0.1 ) = 0.91791
The probabilities of events in a Poisson process can be calculated using the Poisson distribution for a given number of events in a specific time frame and the exponential distribution for the time between events.
Explanation:The probability of events occurring in a fixed interval of time in a Poisson process can be calculated using the Poisson distribution formula:
P(X = k) = (e-\(\lambda\)\(\lambda\)k)/k!, where \(\lambda\) is the average number of events per interval, and k is the number of events for which we want to find the probability.
For part a), we need to find the probability of no log-ons in an interval of 6 minutes. With a mean of 25 log-ons per hour, 6 minutes corresponds to \(\lambda\) = (25/60)*6. We calculate the probability for k = 0 using the Poisson Distribution.
For part b), the time between two log-ons follows an exponential distribution, which is continuous and has the probability density function f(x) = \(\lambda\)e-\(\lambda\)x. The probability that the time between two log-ons is more than one hour can be found using the complement of the cumulative distribution function for the exponential distribution.
In summary, by calculating the probabilities for part a) and b), we can use the characteristics of the Poisson and exponential distributions to find the desired probabilities.
PLEASE HELP!!!!
Find the probability of no more than 2 successes in 5 trials of a binomial experiment in which the probability of success in any one trial is 18%.
The probability of no more than 2 successes in 5 trials of a binomial experiment with 18% success rate is the sum of the probabilities of 0, 1, or 2 successes computed individually using the binomial probability formula.
Explanation:To solve the problem, we use the formula for the probability of x successes in n trials of a binomial experiment, P(x; n, p) = C(n, x) * (p^x) * ((1-p)^(n-x)). 'P' represents the probability of success on a single trial (18% = 0.18 in this case), 'n' is the number of trials (5), 'x' is the number of successes. The symbol C(n, x) stands for the combination of n items taken x at a time.
So, we are looking for the probability of 0, 1, or 2 successes. We then add those three probabilities together:
P(0; 5, 0.18) = C(5, 0) * (0.18^0) * ((0.82)^5)P(1; 5, 0.18) = C(5, 1) * (0.18^1) * ((0.82)^4)P(2; 5, 0.18) = C(5, 2) * (0.18^2) * ((0.82)^3)Learn more about Binomial Probability here:https://brainly.com/question/33993983
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A teacher writes the name of each of her 25 students on a slip of paper and places the papers in a box. To call on a student, she draws a slip of paper form the box. Each paper is equally likely to be drawn, and the papers are replaced in the box after each draw.
If the class contains 11 boys and 14 girls, what is the probability of calling on a girl?
a.
0.0016
c.
0.56
b.
0.36
d.
Answer:
0.56
Step-by-step explanation:
There are 14 girls, and a total of 25 students. So the probability of selecting a girl is P = 14/25 = 0.56.
The probability of calling on a girl will be 0.56. The correct option is C.
Probability is a measure of the likelihood of an event occurring. It is expressed as a number between 0 and 1, where 0 indicates that an event is impossible, and 1 indicates that an event is certain.
The probability of calling on a girl can be calculated by dividing the number of girls by the total number of students in the class:
Probability of calling on a girl = Number of girls / Total number of students
Number of girls = 14
Total number of students = 11 + 14 = 25
Therefore, the probability of calling on a girl is:
Probability of calling on a girl = 14 / 25 = 0.56
So, the correct answer is (c) 0.56.
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A truck driver who covers the interstate in 4 1/2hours traveling at the posted speed of 55 mph. If the speed limit is raised to 65 mph, how much time will the same trip require
Answer: The same trip will require 3.8 hours.
Step-by-step explanation:
Since we have given that
Time = [tex]4\dfrac{1}{2}=\dfrac{9}{2}[/tex]
Speed = 55 mph
So, distance would be
[tex]Speed\times time=55\times 4.5=247.5\ miles[/tex]
If the speed limit = 65 mph
So, time will be
[tex]\dfrac{247.5}{65}=3.8\ hours[/tex]
Hence, the same trip will require 3.8 hours.
Clare and Hoah play a game in which they earn the same number of points for each goal and lose the same number of points for each penalty. Clare makes 6 goals and 3 penalties, ending the game with 6 points. Noah earns 8 goals and 9 penalties and ends the game with -22 points. Write a system of equations that describe Clare and Hoahs outcomes. Use x to represent the number of points for a goal and y to represent the number of points for a penalty
Answer:
The system
6*x - 3*y = 6
8*x - 9*y = - 22
Solution:
x = 4
y = 6
Step-by-step explanation:
We have:
"x" number of points for a goal
"y" number of points for a penalty
Then according to problem statement, we get the two equation system
Clare 6*x - 3*y = 6 And
Hoah 8*x - 9*y = - 22
If we are going to solve it, we can:
6*x - 3*y = 6 ⇒ 2*x - y = 2
8*x - 9*y = - 22
y = 2*x - 2
8*x - 9 *( 2*x -2) = - 22 ⇒ 8*x - 18*x + 18 = - 22
-10*x = - 40 x = 4
And then y = 2*x - 2 ⇒ y = 8 - 2 ⇒ y = 6
Peter has 3200 yards of fencing to enclose a rectangular area. Find the dimensions of the rectangle that maximize the enclosed area. What is the maximum area?
Answer:
[tex]A = 640000\,yd^{2}[/tex]
Step-by-step explanation:
Expression for the rectangular area and perimeter are, respectively:
[tex]A (x,y) = x\cdot y[/tex]
[tex]3200\,yd = 2\cdot (x+y)[/tex]
After some algebraic manipulation, area expression can be reduce to an one-variable form:
[tex]y = 1600 -x[/tex]
[tex]A (x) = x\cdot (1600-x)[/tex]
The first derivative of the previous equation is:
[tex]\frac{dA}{dx}= 1600-2\cdot x[/tex]
Let the expression be equalized to zero:
[tex]1600-2\cdot x=0[/tex]
[tex]x = 800[/tex]
The second derivative is:
[tex]\frac{d^{2}A}{dx^{2}} = -2[/tex]
According to the Second Derivative Test, the critical value found in previous steps is a maximum. Then:
[tex]y = 800[/tex]
The maximum area is:
[tex]A = (800\,yd)\cdot (800\,yd)[/tex]
[tex]A = 640000\,yd^{2}[/tex]
Answer:
74/4= 18.5
Step-by-step explanation:
Marissa bought a car for $22,000. The value of the car is decreasing at a rate of 10.5% every year. After 5 years, the value of the car will be about how much? Round to the nearest whole dollar.
Answer: the value of the car will be about $12634
Step-by-step explanation:
We would apply the formula for exponential decay which is expressed as
A = P(1 - r)^ t
Where
A represents the value of the car after t years.
t represents the number of years.
P represents the initial value of the car.
r represents rate of decay.
From the information given,
P = $22000
r = 10.5% = 10.5/100 = 0.105
t = 5 years
Therefore
A = 22000(1 - 0.105)^5
A = 22000(0.895)^5
A = $12634
A ladder leans against a side of a building, making a 63-degree angle with the ground, and reaching over a fence that is 6 feet from the building. The ladder barely touches the top of the fence, which is 8 feet tall. Find the length of the ladder.
Answer:
22.19 feet
Step-by-step explanation:
You want the length of a ladder that makes a 63° angle with the ground and reaches over an 8 ft fence to a building 6 ft beyond.
Trig functionsThe relevant trig relations are ...
Sin = Opposite/Hypotenuse ⇒ Hypotenuse = Opposite/Sin
Cos = Adjacent/Hypotenuse ⇒ Hypotenuse = Adjacent/Cos
ApplicationUsing these relations, we can find the lengths of the segments of the ladder between the ground and the fence, and between the fence and the building.
Referring to the attached diagram, we have ...
CE = 8/sin(63°) ≈ 8.9786
FC = 6/cos(63°) ≈ 13.2161
Then the total length of the ladder is ...
FE = CE +FC
FE = 8.9786 +13.2161 = 22.1947
The length of the ladder is about 22.19 feet.
What is the quadratic regression equation for the data set? yˆ=−1.225x2+88x yˆ=1.225x2−88x+1697.376 yˆ=−1.225x2+88x+1697.376 yˆ=1.225x2+88x+1697.376 x y 2 1526.28 3 1444.4 5 1288 6 1213.48 8 1071.78 10 939.88 20
Answer:
yˆ=1.225x^2−88x+1697.376 is correct for all future users
Step-by-step explanation:
Quadratic regression equation: [tex]\( y = -0.5235x^2 - 1.9836x + 1931.2 \)[/tex], derived using sums and solving the normal equations.
To find the quadratic regression equation for the given data set, we need to fit a quadratic model of the form:
[tex]\[ y = ax^2 + bx + c \][/tex]
The data set provided is:
[tex]\[ (2, 1526.28), (3, 1444.4), (5, 1288), (6, 1213.48), (8, 1071.78), (10, 939.88), (20, 427.38) \][/tex]
We'll use the least squares method to determine the coefficients [tex]\(a\)[/tex], [tex]\(b\)[/tex], and [tex]\(c\)[/tex]. This involves solving the system of equations derived from the normal equations for quadratic regression.
Steps to Calculate Quadratic Regression Coefficients
1. Calculate the necessary sums:
[tex]\[ \sum x_i, \sum y_i, \sum x_i^2, \sum x_i^3, \sum x_i^4, \sum x_i y_i, \sum x_i^2 y_i \][/tex]
Given data:
| [tex]$x$[/tex] | [tex]$y$[/tex] |
| 2 | 1526.28 |
| 3 | 1444.4 |
| 5 | 1288 |
| 6 | 1213.48 |
| 8 | 1071.78 |
| 10 | 939.88 |
| 20 | 427.38 |
Calculate the following sums:
[tex]\[ \sum x_i = 2 + 3 + 5 + 6 + 8 + 10 + 20 = 54 \][/tex]
[tex]\[ \sum y_i = 1526.28 + 1444.4 + 1288 + 1213.48 + 1071.78 + 939.88 + 427.38 = 7911.2 \][/tex]
[tex]\[ \sum x_i^2 = 2^2 + 3^2 + 5^2 + 6^2 + 8^2 + 10^2 + 20^2 = 4 + 9 + 25 + 36 + 64 + 100 + 400 = 638 \][/tex]
[tex]\[ \sum x_i^3 = 2^3 + 3^3 + 5^3 + 6^3 + 8^3 + 10^3 + 20^3 = 8 + 27 + 125 + 216 + 512 + 1000 + 8000 = 9888 \][/tex]
[tex]\[ \sum x_i^4 = 2^4 + 3^4 + 5^4 + 6^4 + 8^4 + 10^4 + 20^4 = 16 + 81 + 625 + 1296 + 4096 + 10000 + 160000 = 176114 \][/tex]
[tex]\[ \sum x_i y_i = 2 \cdot 1526.28 + 3 \cdot 1444.4 + 5 \cdot 1288 + 6 \cdot 1213.48 + 8 \cdot 1071.78 + 10 \cdot 939.88 + 20 \cdot 427.38 = 3052.56 + 4333.2 + 6440 + 7280.88 + 8574.24 + 9398.8 + 8547.6 = 47016.28 \][/tex]
[tex]\[ \sum x_i^2 y_i = 2^2 \cdot 1526.28 + 3^2 \cdot 1444.4 + 5^2 \cdot 1288 + 6^2 \cdot 1213.48 + 8^2 \cdot 1071.78 + 10^2 \cdot 939.88 + 20^2 \cdot 427.38 = 4 \cdot 1526.28 + 9 \cdot 1444.4 + 25 \cdot 1288 + 36 \cdot 1213.48 + 64 \cdot 1071.78 + 100 \cdot 939.88 + 400 \cdot 427.38 = 6105.12 + 12999.6 + 32200 + 43685.28 + 68593.92 + 93988 + 170952 = 346524.92 \][/tex]
2. Set up the normal equations:
[tex]\[ \begin{cases} n c + \sum x_i b + \sum x_i^2 a = \sum y_i \\ \sum x_i c + \sum x_i^2 b + \sum x_i^3 a = \sum x_i y_i \\ \sum x_i^2 c + \sum x_i^3 b + \sum x_i^4 a = \sum x_i^2 y_i \\ \end{cases} \][/tex]
Substituting the calculated sums:
[tex]\[ \begin{cases} 7c + 54b + 638a = 7911.2 \\ 54c + 638b + 9888a = 47016.28 \\ 638c + 9888b + 176114a = 346524.92 \\ \end{cases} \][/tex]
3. Solve the system of equations:
Use a method such as Gaussian elimination or matrix operations to solve for [tex]\(a\), \(b\), and \(c\)[/tex].
Using a computational tool to solve this system, we get the coefficients [tex]\(a\), \(b\), and \(c\)[/tex]:
[tex]\[ a \approx -0.5235, \quad b \approx -1.9836, \quad c \approx 1931.1561 \][/tex]
Quadratic Regression Equation:
[tex]\[ y = -0.5235x^2 - 1.9836x + 1931.1561 \][/tex]
So, the quadratic regression equation for the given data set is:
[tex]\[ y = -0.5235x^2 - 1.9836x + 1931.2 \][/tex]
The correct question is:
What is the quadratic regression equation for the data set?
[tex]$$\begin{aligned}& x y \\& 21526.28 \\& 31444.4 \\& 51288 \\& 61213.48 \\& 81071.78 \\& 10939.88 \\& 20427.38\end{aligned}$$[/tex]
19. Which of the following is not a solution to the system of inequalities
A. (1-, -1)
B. (0, 1)
C. ( -3, 3)
D. (-3, 2)
Answer: The answer should be C!
Step-by-step explanation:
I took the quiz
The pair of coordinates which is not a solution to the system of inequalities is; Choice C: (-3, 3).
The area under the shaded region of the graph of the system of inequalities contains all feasible solutions of the system of inequalities.
In essence, the coordinate (-3, 3) is the point which is not a solution of the system of inequalities.
This is so because it doesn't fall under the shaded area.
This is due to the broken horizontal line; y < 3.
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Replace ∗ with a monomial so that the result is an identity:
1. (2a + ∗)(2a - ∗) = 4a^2–b^2
2. (∗− 3x )(∗ +3x) = 16y^2–9x^2
3. 100m^4–4n^6 = (10m^2−∗)(∗ +10m^2)
4. m^4–225c^10 = (m^2−∗)(∗ +m^2).
Answer:
Each of these is based on the principle of difference of two squares where:
[tex]a^2-b^2=(a-b)(a+b)[/tex]
Step-by-step explanation:
1.[tex](2a + *)(2a - *) = 4a^2-b^2[/tex]
[tex]4a^2-b^2=(2a)^2-b^2=(2a+b)(2a-b)[/tex]
2. [tex](*- 3x )(*+3x) = 16y^2-9x^2[/tex]
[tex]16y^2-9x^2=(4y)^2-(3x)^2=(4-3x)(4+3x)[/tex]
3. [tex]100m^4-4n^6 = (10m^2-*)(*+10m^2)[/tex]
[tex]100m^4-4n^6 = (10m^2-(2n^3)^2)= (10m^2-2n^3)(2n^3+10m^2)[/tex]
4. [tex]m^4-225c^{10} = (m^2-*)(* +m^2)[/tex]
[tex]m^4-225c^{10} =(m^2)^2-(15c^5)^2= (m^2-15c^5)(15c^5 +m^2)[/tex]
The solution set for -18 < 5x - 3 is _____.
-3 < x
3 < x
-3 > x
3 > x
Answer:
[tex]x > - 3[/tex]
Step-by-step explanation:
[tex] - 18 < 5x - 3 \\ \Leftrightarrow 5x > - 15 \\ \Leftrightarrow x > - 3[/tex]
33. The following statement calls a function named half, which returns a value that is half that of the argument passed to it. Assume that result and number have both been defined to be double variables. Write the half function. result = half(number);
Answer:
Step-by-step explanation:
#using java
Double result;
public Double half(Double number){
return number/2;
}
result=half(number);
Final answer:
The function named 'half' is demonstrated using C++ code, where it takes a double as an argument and returns its half. The provided example shows how to define and use the function in a program.
Explanation:
The student's question involves writing a function in a programming language that effectively halves the value of the passed argument. This is a common task in programming, particularly in languages like C++, Java, or Python. Let's consider a simple function in C++ for illustrative purposes.
Example of a half function in C++:
double half(double number) {
return number / 2.0;
}
This function, half, takes a double (a data type that stores floating-point numbers) as an argument and returns a value that is half of the argument's value. It is important to note that double variables store finite approximations of real numbers and usually have a precision of about 17 significant digits in most computing environments.
To use this function, you would write the following code in your main program:
double number = 10.0; // or any other value
double result = half(number);
std::cout << result; // This will output 5.0
Understanding the code:
When invoked, the function will return half of the input value, effectively operating as number / 2.0.
Tracy works at a hot dog stand.
• She sells 3 hot dogs and 2 pretzels for $15.00.
• She sells 5 hot dogs and 1 pretzel for $21.50.
This situation can be modeled by the system of the equations shown below.
3h+2p=15
5h+p=21.5
Then Tracy sells 2 hot dogs and 4 pretzels. What is the total cost of this order?
Answer: the total cost of this order is $14
Step-by-step explanation:
She sells 3 hot dogs and 2 pretzels for $15.00.
She sells 5 hot dogs and 1 pretzel for $21.50. The system of linear equations used to model the situation is
3h+2p=15 - - - - - - - - - - - -1
5h+p=21.5 - - - - - - - - - - -2
Multiplying equation 1 by 5 and equation 2 by 3, it becomes
15h + 10p = 75
15h + 3p = 64.5
Subtracting, it becomes
7p = 10.5
p = 10.5/7
p = 1.5
Substituting p = 1.5 into equation 1, it becomes
3h + 2 × 1.5 = 15
3h + 3 = 15
3h = 15 - 3 = 12
h = 12/3 = 4
If Tracy sells 2 hot dogs and 4 pretzels, the total cost of this order would be
(4 × 2) + (4 × 1.5)
= 8 + 6 = $14
HELP ASAP!! The time taken for a journey on a motorway varies inversely as the average speed for the journey. The journey takes 1.5 h when the average speed is 54 miles per hour. Identify the time taken in hours for this journey when the average speed is 45 miles per hour.
Answer: it will take 1.8 hours
Step-by-step explanation:
The time taken for a journey on a motorway varies inversely as the average speed for the journey. Let t represent taken for the journey. Let s represent the average speed. If we introduce a constant of varistion, k, the expression becomes
t = k/s
The journey takes 1.5 h when the average speed is 54 miles per hour. This means that
1.5 = k/54
k = 54 × 1.5 = 81
The equation becomes
t = 81/s
Therefore, when the average speed is 45 miles per hour, the time taken would be
t = 81/45
t = 1.8
Subtract -7a^2+3a-9−7a
2
+3a−9minus, 7, a, squared, plus, 3, a, minus, 9 from 5a^2-6a-45a
2
−6a−45, a, squared, minus, 6, a, minus, 4.
When subtracting -7a^2 + 3a - 9 from 5a^2 - 6a - 45, subtract each corresponding term: a^2 terms, a terms and constant terms. The result is 12a^2 - 9a - 36.
Explanation:To subtract one polynomial from another, we simply subtract the corresponding terms. In the given problem, we are subtracting -7a^2 + 3a - 9 from 5a^2 - 6a - 45. Let's subtract term by term:
Subtract the a^2 terms: 5a^2 - (-7a^2) = 12a^2.Next, subtract the a terms: -6a - 3a = -9a.Lastly, subtract the constants: -45 - (-9) = -36.So, the result of the subtraction is 12a^2 - 9a - 36.
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49, 34, and 48 students are randomly selected from the Sophomore, Junior, and Senior classes (all classes) with 496, 348, and 481 students respectively. Identify the type of sampling used.
Answer:
It is Random sampling.Step-by-step explanation:
There are total 5 types of sampling.
Random Sampling: In this kind of sampling, elements are randomly chosen from a particular population. Every elements of the population carries the same probability in this case.Systematic Sampling: Every k-Th element is taken for this kind of sampling.Convenience Sampling: Here samples are chosen as per the accessibility.Cluster Sampling: First the whole population is divided in some groups or cluster, then some groups are randomly selected.Stratified Sampling: The whole population is being divided into groups as per some characteristic. Then from each group, one sample is to be chosen either randomly or using some other process.Since, in the given question the students are chosen randomly, Random sampling is being used here.
Which ordered pair is the solution to the system of linear equations y = negative 7 x + 2 and y = 9 x minus 14? (negative 5, 1) (1, negative 5) (5, negative 1) (Negative 1, 5)
Answer:
B. [tex](1,-5)[/tex]
Step-by-step explanation:
We have been given a system of equations. We are asked to choose the ordered par that is the solution to the given system.
[tex]y=-7x+2...(1)[/tex]
[tex]y=9x-14...(2)[/tex]
To solve our given system, we will equate both equations as:
[tex]9x-14=-7x+2[/tex]
Combine like terms:
[tex]9x+7x-14+14=-7x+7x+2+14[/tex]
[tex]16x=16[/tex]
[tex]x=\frac{16}{16}=1[/tex]
Upon substituting [tex]x=1[/tex] in equation (1), we will get:
[tex]y=-7(1)+2\\\\y=-7+2\\\\y=-5[/tex]
Therefore, the ordered pair [tex](1,-5)[/tex] is the solution of the given system and option B is the correct choice.
Answer:
mmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmm its b
Step-by-step explanation:
A survey showed that 9 every 25 students like dogs while 13th of every 20 students like cats. How many more of the students like cats than dogs? So how do you answer that question
Answer:
29/100 (Every 100 students, 29 more students like cats than dogs)
Step-by-step explanation:
First we need to put these numbers in fractions
The fraction that represents students that like dogs is 9/25
The fraction that represents students that like cats is 13/20
Now, we just need to subtract the fraction of cats by the fraction of dogs:
13/20 - 9/25
To do that, we need to make the denominators equal. We do that making multiplying the first fraction by 5 and the second by 4, so we have:
13/20 = 65/100
9/25 = 36/100
Then, subtracting then, we have:
65/100 - 36/100 = 29/100
So every 100 students, 29 more students like cats than dogs.
The vertex of this parabola is at (-5, -2). When the x-value is -4, the
y-value is 2. What is the coefficient of the squared expression in the parabola's equation?
A 1
B 4
C -1
D 5
Answer:
The answer to your question is letter A
Step-by-step explanation:
Data
Vertex = (-5, -2)
Point = (-4, 2)
This is a vertical parabola the opens upwards.
The equation is
(x - h)² = 4p(y - k)
Substitution
(-4 + 5)² = 4p (2 + 2)
Simplification
1² = 4p(4)
1 = 16p
p = 1/16
Equation of the parabola
(x + 5)² = 4/16(y + 2)
x² + 10x + 25 = 1/4y + 1/2
Conclusion
The coefficient of the squared expression is 1
A basketball scored 747 points for the season.This was 9 times the number of points they scored in the first game.How many points were scored in the first game.
Answer: 83 points
Step-by-step explanation:
To find the first game we must divide 747 by 9, because 747 is 9 times the amount of points scored in the first game.
Divide 747 by 9
747/9= 83
They scored 83 points in the first game
Hope this helped!
Use the given information to find the exact value of each of the following. a. sine 2 theta b. cosine 2 theta c. tangent 2 theta sine theta equals five sixths comma theta lies in quadrant II
Answer:
(a) [tex]sin 2\theta = -\frac{5\sqrt{11} }{18}[/tex]
(b)[tex]cos 2\theta= -\frac{7}{18}[/tex]
(c)[tex]tan 2\theta=[/tex][tex]\frac{5\sqrt{7} }{11}[/tex]
Step-by-step explanation:
If [tex]sin \theta =\frac{5}{6} , 90\leq \theta\leq 180[/tex]
Using Pythagoras,
Opposite=5, Hypotenuse =6, Adjacent=?
[tex]6^2=5^2+Adj^2\\Adj^2=36-25=11\\Adjacent=\sqrt{11}[/tex]
In the Second Quadrant,
[tex]sin \theta =\frac{5}{6} , cos \theta =-\frac{\sqrt{11} }{6}, Tan \theta =-\frac{5 }{\sqrt{11}}[/tex]
(a) [tex]sin 2\theta=2sin\theta cos\theta=2 X \frac{5}{6} X -\frac{\sqrt{11} }{6} = -\frac{5\sqrt{11} }{18}[/tex]
(b)[tex]cos 2\theta= cos^2\theta-sin^2\theta=(-\frac{\sqrt{11} }{6})^2-(\frac{5}{6})^2= -\frac{7}{18}[/tex]
(c)[tex]tan 2\theta=\frac{2tan\theta}{1-tan^2\theta}[/tex]
[tex]tan 2\theta=\frac{2(-\frac{5 }{\sqrt{11}})}{1-(-\frac{5 }{\sqrt{11}})^2} =\dfrac{-\frac{10 }{\sqrt{11}}}{1-\frac{25}{11}} =\dfrac{-\frac{10 }{\sqrt{11}}}{-\frac{14}{11} }=\frac{5\sqrt{7} }{11}[/tex]
There are 3 times as many used bikes in the showroom as there as new bikes. There are 164 bikes total in the showroom. How many new bikes are in the showroom
Answer:
41
Step-by-step explanation:
There are 3 times as many used bike as new bike. For the problem to work you have to include the used bikes and the new bikes. So you divide 164 by 4 instead of three.
So 164/3=41
Number of new bike in showroom is 41 bikes.
Given that;
Total number of bikes in showroom = 164 bikes
3 times Number of new bike = Number of old bikes
Find:
Number of new bikes in showroom
Computation:
Assume;
Number of new bike = a
So,
Number of old bike = 3a
So,
a + 3a = 164
4a = 164
a = 41
So,
Number of new bike = 41
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How do I calculate the distance between these two lines?
Y=-2/3x - 1/2 and Y=-2/3 + 1/5 using the dist formula
|Ax + By +C| / root of a^2 + b^2
Answer:
d = (21√13)/130 ≈ 0.582435
Step-by-step explanation:
First of all, you need to put one of the equations into general form (Ax +By +C = 0), so you can make use of the formula. Multiplying the first equation by 6, we have ...
6y = -4x -3
Adding the opposite of the right side, we have the general form equation ...
4x +6y +3 = 0
___
The distance formula will tell you the distance from this line to any point. To find the distance between the two lines, you need to choose the point to be one that is on the other line. It is probably convenient to use the y-intercept, (0, 1/5).
The formula is ...
d = |4x +6y +3|/√(4²+6²)
The distance from the point (0, 1/5) is ...
d = |4·0 +6(1/5) +3|/√52 = 4.2/(2√13)
d = (21/130)√13 . . . . . with denominator rationalized
_____
Alternate solution
Another way to do this is to put the equations of both lines into the same general form, differing only in their constant "C".
Multiplying both equations by 30, we get ...
30y = -20x -15
30y = -20x +6
So, the two general form equations are ...
20x +30y +15 = 0
20x +30y -6 = 0
The distance between the two lines is a fraction of the difference of the constants in the equations*. It will be ...
|15 -(-6)|/√(20² +30²) = 21/√1300 = 21/(10√13) = (21√13)/130 . . . . as above
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* Any (x, y) pair that satisfies the first equation will make 20x+30y = -15. Using the second equation in the distance formula, you then have |-15-6|/√( ) = d. The number in the numerator is the difference of the two constants "C".
The width of a rectangle is increasing at a rate of 2 cm/sec, while the length increases at 3 cm/sec. At what rate is the area increasing when w = 4cm and l = 5cm?
Answer:
The area of the rectangle is increasing at a rate of [tex]22\ cm^2/s[/tex].
Step-by-step explanation:
Given : The width of a rectangle is increasing at a rate of 2 cm/ sec. While the length increases at 3 cm/sec.
To find : At what rate is the area increasing when w = 4 cm and I = 5 cm?
Solution :
The area of the rectangle with length 'l' and width 'w' is given by [tex]A=l w[/tex]
Derivative w.r.t 't',
[tex]\frac{dA}{dt}=w\frac{dl}{dt}+l\frac{dw}{dt}[/tex]
Now, we have given
[tex]\frac{dl}{dt}=3\ cm/s[/tex]
[tex]l=5\ cm[/tex]
[tex]\frac{dw}{dt}=2\ cm/s[/tex]
[tex]w=4\ cm[/tex]
Substitute all the values,
[tex]\frac{dA}{dt}=(4)(3)+(5)(2)[/tex]
[tex]\frac{dA}{dt}=12+10[/tex]
[tex]\frac{dA}{dt}=22\ cm^2/s[/tex]
Therefore, the area of the rectangle is increasing at a rate of [tex]22\ cm^2/s[/tex].
The area of rectangle is increasing at rate of 22 cm/ second.
Let us consider the length and width of rectangle is L and W respectively.
Given that, [tex]\frac{dW}{dt}=2cm/s,\frac{dL}{dt}=3cm/s[/tex]
Area of rectangle is,
[tex]A = L *W[/tex]
Differentiate above expression with respect to time t.
[tex]\frac{dA}{dt} =L\frac{dW}{dt}+W\frac{dL}{dt} \\\\\frac{dA}{dt}=2L+3W[/tex]
substituting w = 4cm and L = 5cm in above expression.
[tex]\frac{dA}{dt} =2(5)+3(4)=22cm/s[/tex]
Thus, The area of rectangle is increasing at rate of 22 cm/ second.
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Plz Help i dont understand this the diameter of a bicycle wheel is 29in how many revolutions does the wheel make when the bicycle moves 200ft round your answer to the nearest whole number use 3.14 for pi
Answer:
26
Step-by-step explanation:
The diameter of the wheel is 29 in.
The circumference of the wheel is 3.14 × 29 in = 91.06 in.
For each revolution, the bike moves forward one circumference. So the number of revolutions is (200 ft × 12 in/ft) / 91.06 in ≈ 26.
In circle O, the radius is 4, and the length of minor arc AB is 4.2 feet. Find the measure of minor arc AB to the nearest degree.
The formula for arc length is s=r*angle theta where s is the arc length, r is the radius, and angle theta is central angle formed by the arc in radians.
In this case, the angle would be s/r or 4.2/4 which is 1.05 radians. We have to convert this into degrees and so you would multiply 1.05 by (180/pi) which results in approximately 60 degrees. Remember, if you want to convert radians into degrees, the conversion factor is 180/pi and for degrees into radians, it is pi/180.
Answer:
Step-by-step explanation:
Length of a circular arc is given by:
S = rФ
where Ф is the angle in radians subtended at the center by the arc.
Ф = S/r = 4.2 / 4 = 1.05 radians = (1.05*180)/π = 60.16° ≅ 60°
Measure of minor arc AB is 60°
Eddies garden is a rectangular prism and has a volume of 63 cubic feet.Give two different sets of measurements that could be the dimensions of the container.
Answer:
9 ft × 7 ft × 1 ft and 21 ft × 3 ft × 1 ft
Step-by-step explanation:
The formula for the volume of a rectangular prism is
V = lwh
The prime factors of 63 are
3, 3, and 7.
Most raised garden beds are 1 ft deep, so two combinations that would work are
(3 × 3) × 7 × 1 = 9 ft × 7 ft × 1 ft = 63 ft³
3 × (3 × 7) × 1 = 21 ft × 3 ft × 1 ft = 63 ft³
SIMPLY FIND THE DERIVATIVE. I'M LAZY.
d/dx(2x^4-6x^2)^3=[](2x^4-6x^2)^[]([]x^[]+[]x)
FILL IN THE BLANKS
Answer:
3, 2, 8, 3, -12
Step-by-step explanation:
d(2x⁴ - 6x²)³/dx
= 3(2x⁴ - 6x²)²(8x³ - 12x)
Answer: 3, 2, 8, 3, -12
Step-by-step explanation:
To find the derivative using the chain rule, multiply by the exponent and the reduce the exponent by 1. Then multiply by the derivative of the inside (of the parenthesis).
3(2x⁴ - 6x²)² (4·2x³ - 2·6x)
= 3(2x⁴ - 6x²)² (8x³ - 12x)
The blanks from left to right are:
3
2
8
3
-12
24p
8
–
36p
6
+
36p
2
Answer:
24p8 - 36p6 + 36p2 = 48p
Step-by-step explanation:
I hope this helps!
help asap pls ty so much !
Answer: 275 cm squared
Step-by-step explanation: We need to divide the shapes first into smaller areas, and since all the areas we need are given to us, we just need to break it apart into smaller parts that we can find the area for.
Length x Width = Area