Answers
because if u solve it
2(x+y+1)
=2x+2y+2
which is the same as the expression. u just gotta combine like terms
Related Questions
Determine the amount of an
investment if $1000 is invested at an
interest rate of 8% for 6 years
Answers
Answer
480
Step-by-step explanation:
Congrats on your first question!
The investment is 480 because
(80 / 100) x 1000 = 80 x 6 = 480
The total is 1480.
7. Evaluate the expression ab for a = 8 and b=5.
Answers
Answer:
40
Step-by-step explanation:
First, we must know that ab is the same as:
a × b
Now, since a is given as 8, we can substitute a with 8. This is shown below:
ab = 8 × b
Similarly, b is given as 5. So, we can substitute b with 5:
ab = 8 × 5
With this, we can now evaluate ab as shown below:
ab = 8 × 5
= 40
jenny reads a book with 92 pages. jenny's book has 13 more pages than the book macy reads. which equation could you solve to find how many pages, m, macy's book has?
Answers
Given parallelogram L M N O below, LP = 81 If PN = -7x-3 solve for x
Answers
-7x=81+3
-7x/7=84/-7
Solution
X=-12
Answer:-12x
Step-by-step explanation:
just trust me on this
Use the below information for questions 2a - 2b:
State Probability Return on A Return on B Return on C
Boom 0.30 0.35 0.25 0.10
Average 0.50 0.20 0.15 0.25
Bust 0.20 0.05 0.10 0.35
2a. Find the Mean and Variance of Asset A
2b. Find the Correlation coefficient of A and C
Answers
Answer to 2a: The mean of Asset A is 0.235 and the variance is 0.0123
Answer to 2b: The correlation coefficient between Asset A and C is approximately\(\(-0.670\) (Boom), \(-0.187\) (Average), \(-0.670\)\)(Bust).
2a. Mean of Asset A (Expected Value):
The mean of Asset A (E(A)) can be calculated as:
\(\[E(A) = \sum_{i} (x_i \cdot P_i)\]\)
where \(\(x_i\)\) represents the return on Asset A in each state and\(v \(P_i\)\) represents the probability of that state.
Using the given information, we have:
Boom:
\(\(E(A) = (0.35 \cdot 0.30) + (0.20 \cdot 0.50) + (0.05 \cdot 0.20) = 0.235\)\)
Average:
\(\(E(A) = (0.35 \cdot 0.30) + (0.20 \cdot 0.50) + (0.05 \cdot 0.20) = 0.235\)\)
Bust:
\(\(E(A) = (0.35 \cdot 0.30) + (0.20 \cdot 0.50) + (0.05 \cdot 0.20) = 0.235\)\)
Therefore, the mean of Asset A is\(\(E(A) = 0.235\).\)
2b. Correlation Coefficient of A and C:
The correlation coefficient\((\(\rho\))\)between Asset A and C can be calculated using the formula:
\(\[\rho = \frac{{\text{{Cov}}(A, C)}}{{\sigma_A \cdot \sigma_C}}\]\)
where\(\(\text{{Cov}}(A, C)\)\) represents the covariance between Asset A and C, and \((\sigma_A\)\) and\(\(\sigma_C\)\)represent the standard deviations of Asset A and C, respectively.
Using the given information, we have:
Boom:
\(\(\text{{Cov}}(A, C) = (0.35 - 0.235) \cdot (0.10 - 0.25) = -0.017\)\)
Average:
\(\(\text{{Cov}}(A, C) = (0.20 - 0.235) \cdot (0.15 - 0.25) = -0.005\)\)
Bust:
\(\(\text{{Cov}}(A, C) = (0.05 - 0.235) \cdot (0.35 - 0.25) = -0.017\)\)
Now, we calculate the standard deviations of Assets A and C:
\(\(\sigma_A = \sqrt{{\text{{Var}}(A)}} = \sqrt{0.0123} \approx 0.1108\)\)
\(\(\sigma_C = \sqrt{{\text{{Var}}(C)}} = \sqrt{0.0517} \approx 0.2274\)\)
Finally, we can calculate the correlation coefficient:
Boom:
\(\(\rho = \frac{{-0.017}}{{0.1108 \cdot 0.2274}} \approx -0.670\)\)
Average:
\(\(\rho = \frac{{-0.005}}{{0.1108 \cdot 0.2274}} \approx -0.187\)\)
Bust:
\(\(\rho = \frac{{-0.017}}{{0.1108 \cdot 0.2274}} \approx -0.670\)\)
Therefore, the correlation coefficient between Asset A and C is approximately\(\(\rho \approx -0.670\) (Boom), \(\rho \approx -0.187\) (Average), and \(\rho \approx -0.670\) (Bust).\)
Answer to 2a: \(The mean of Asset A is \(0.235\) and the variance is \(0.0123\.\)
Answer to 2b: The correlation coefficient between Asset A and C is approximately\(\(-0.670\) (Boom), \(-0.187\) (Average), \(-0.670\)\)(Bust).
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PLEASE HELP!!
The diagram shows the cross-section ABCD of a sculpture in the shape of
a prism
with perpendicular height 9 cm.
AB = 14 cm, CD = 8cm, AD = 12cm and BC = 10cm
The height of the prism is also 9 cm.
What is the total surface area of the sculpture in cm2?
Type each step of your working on a separate line.
Answers
Answer:
99 (cm^2)
Step-by-step explanation:
Perpendicular to the AB segment at points D and C, the graph is divided into two triangles and a rectangle.
The area of the middle rectangle is equal to 8*9=72. The hypotenuse of the right triangle is 10cm, and one of the right sides is 9cm, so the other side is SQRT (10^2-9^2) = SQRT (19).
One side of the left triangle is 9cm long and the other side is 14-8-sqRT (19) = 6-sqRT (19) cm.
Then, add the area of the three parts.
72+9*sqrt（19）/2+9*（6-sqrt（19））/2=99 (cm^2)
imagine you compare the effectiveness of four different types of stimulants to keep you awake while revising statistics using a one-way anova. the null hypothesis would be that all four treatments have the same effect on the mean time kept awake. how would you interpret the alternative hypothesis?
Answers
The alternative hypothesis in this case would be that at least one of the four treatments has a different effect on the mean time kept awake compared to the others.
If the one-way ANOVA test rejects the null hypothesis, it means that there is a significant difference in the mean time kept awake among the four treatments. This means that at least one of the treatments is more effective in keeping you awake than the others. It is important to note that the alternative hypothesis does not specify which of the treatments is more effective, only that at least one is different from the others. To determine which treatment is more effective, you would need to conduct additional tests, such as post-hoc tests.
The alternative hypothesis in this case would be that at least one of the four treatments has a different effect on the mean time kept awake compared to the others.
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Solve x^2 -24 = -80 by completing the square.
What is the solution set of the equation?
A.(2,40)
B.(4,20)
C.(5,16)
D.(8,10)
Answers
Answer:
B.(4,20)
Step-by-step explanation:
Given: \(x^2 -24x = -80\)
To solve the quadratic equation by completing the square, we follow these steps.
Step 1: Divide the coefficient of x by 2
\(-\dfrac{24}{2}=-12\)
Step 2: Square your result fro Step 1
\((-12)^2\)
Step 3: Add the result form step 2 to both sides of the equation
\(x^2 -24x+(-12)^2 = -80+(-12)^2\)
Step 4: Rewrite the Left hand side in the form \((x+k)^2\)
\((x-12)^2=-80+144\\(x-12)^2=64\)
Step 5: Take square roots of both sides
\(x-12=\pm \sqrt{64}\)
Step 6: Solve for x
\(x=12\pm \sqrt{64}\\=12\pm8\\x=12+8$ or x=12-8\\x=20 or x=4.\)
Therefore, the solution set of the equation is (4,20).
a roller coaster train with 6 passenger cars and the front decoration has a mass of 3,500kg. when the train has the front decoration and only 4 passenger cars, it has a mass of 2,400kg.
what is the mass of the decoration and of each passenger car?
Answers
The mass of the decoration and of each passenger car are 200 kg and 550 kg, respectively
How to determine the masses?The given parameters in the question are
6 passenger cars and the front decoration = 3,500kg4 passenger cars and the front decoration = 2,400kgThese can be represented as
(6, 3500) and (4, 2400)
The slope of the above points represent the mass of each passenger car
This is calculated as
Slope = Difference in mass/Difference in number of cars
So, we have
Slope = (3500 - 2400)/(6 - 4)
Evaluate
Slope = 550
When there are no passenger cars in the train, we have
(0, Mass of decoration)
Using the slope formula, we have
Slope = (Mass of decoration - 3500)/(0 - 6)
So, we have
Slope = (Mass of decoration - 3500)/(-6)
This gives
(Mass of decoration - 3500)/(-6) = 550
Cross multiply
Mass of decoration - 3500 = -3300
Add 3500 to both sides
Mass of decoration = 200
Hence, the mass of each car is 550 kg
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Draw the NFA for the following regular expressions: [6 Marks - 3
Marks each]
i) a*(a+b)* + abc*
ii) a+(c*+d).(bc)*
Answers
The NFAs for a+ and (c*+d).(bc)* by adding appropriate transitions. (q21) becomes the accepting state, representing the completion of the regular expression.
To draw the NFA for the given regular expressions, let's break them down step by step.
i) a*(a+b)* + abc*
NFA for a*
First, let's create the NFA for the subexpression "a*":
┌───┐ a ε
--> │ q0 │─────►(q1)
└───┘
q0 is the initial state, and (q1) is the accepting state. The transition from q0 to (q1) is labeled with "a", and there is also an ε-transition from q0 to (q1). This allows for zero or more occurrences of "a".
NFA for (a+b)*
Next, let's create the NFA for the subexpression "(a+b)*":
a b ε
┌───────┐ ┌─────┐ ┌─────┐
│ │ │ │ │ │
│ q2 ├──► q3 ├──► q4 │
│(start)│ │ │ │ │
└───────┘ └─────┘ └─────┘
│ │ │
│ a │ b │ε
▼ ▼ ▼
┌─────┐ ┌─────┐ ┌─────┐
│ q5 │ │ q6 │ │ q7 │
│(a+b)│ │(a+b)│ │(a+b)│
└─────┘ └─────┘ └─────┘
│ │ │
└─────►(q8) (q9)
accepting
state
q2 is the initial state, q5 and q6 represent the subexpression (a+b). q3 and q4 are intermediary states to allow for looping within the subexpression. The transitions labeled with "a" and "b" connect q2 to q5 and q6, respectively. There are also ε-transitions from q2 to q3 and q6 to q4 to allow for zero or more occurrences of (a+b). Finally, q8 is an accepting state, as it represents the completion of the subexpression (a+b).
NFA for abc*
Now, let's create the NFA for the subexpression "abc*":
┌─────┐ a ε
--> │ q10 │─────►(q11)
└─────┘
│ │
c │ε
│ │
▼ ▼
┌─────┐
│ q12 │
│ c │
└─────┘
q10 is the initial state, and (q11) is the accepting state. There is a transition labeled with "a" from q10 to (q11), and an ε-transition from q10 to q12. From q12, there is a transition labeled with "c", forming a loop back to q12. This allows for zero or more occurrences of "c".
Combining subexpressions
Finally, let's combine the NFAs for the subexpressions a*(a+b)* and abc*:
a ε
┌────
───┐ ┌─────┐ ε
│ │ │ │
│ q0 ├──►(q1) ├──► (q2)
│(start)│ │ │
└───────┘ └─────┘
│ │
│ ε │ε
▼ ▼
┌───────┐ ┌─────┐
│ │ │ │
│ q3 ├──► q4 │
│ │ │ │
└───────┘ └─────┘
│ │
│ ε │ε
▼ ▼
┌─────┐ ┌─────┐
│ q5 │ │ q6 │
│(a+b)│ │(a+b)│
└─────┘ └─────┘
│ │
└─────►(q7)
accepting
state
Here, we have connected the NFAs for a*(a+b)* and abc* by adding ε-transitions. q2 becomes the accepting state, representing the completion of the regular expression.
ii) a+(c*+d).(bc)*
Step 1: NFA for a+
First, let's create the NFA for the subexpression "a+":
┌───┐ a
--> │ q13 │────►(q14)
└───┘
q13 is the initial state, and (q14) is the accepting state. The transition from q13 to (q14) is labeled with "a", allowing for one or more occurrences of "a".
NFA for (c*+d)
Next, let's create the NFA for the subexpression "(c*+d)":
c d
┌───────┐ ┌─────┐
│ │ │ │
│ q15 ├──► q16 │
│(start)│ │ │
└───────┘ └─────┘
│ │
│ c │ d
▼ ▼
┌─────┐ ┌─────┐
│ q17 │ │ q18 │
│ c* │ │ d │
└─────┘ └─────┘
│ │
└─────►(q19)
accepting
state
q15 is the initial state, q17 represents the subexpression c*, and q18 represents the subexpression d. The transitions labeled with "c" and "d" connect q15 to q17 and q15 to q18, respectively. Finally, q19 is an accepting state, representing the completion of the subexpression (c*+d).
NFA for (bc)*
Now, let's create the NFA for the subexpression "(bc)*":
┌─────┐ b ε
--> │ q20 │─────►(q21)
└─────┘ │ │
│ c │ │ε
│ │ ▼ ▼
▼ │
┌─────┐
┌─────┐ │ q22 │
│ q23 │ │ c │
│ b │ └─────┘
└─────┘
q20 is the initial state, and (q21) is the accepting state. There is a transition labeled with "b" from q20 to (q21), and an ε-transition from q20 to q23. From q23, there is a transition labeled with "c" back to q23, forming a loop. This allows for zero or more occurrences of "bc".
Combining subexpressions
Finally, let's combine the NFAs for the subexpressions a+ and (c*+d).(bc)*:
a
┌───────┐
│ │
│ q13 │
│ │
└───────┘
│
│
▼
┌───────┐
│ │
│ q14 │
│ │
└───────┘
│ │
c │ d
│ │
▼ ▼
┌───────┐ b ε
│ │─────►(q21)
│ q15 │ │ │
│(start)│ │ │ε
└───────┘ ▼ ▼
│ ┌─────┐
│ │ q22 │
│ │ c │
│ └─────┘
│
└────►(q19)
accepting
state
Here, we have connected the NFAs for a+ and (c*+d).(bc)* by adding appropriate transitions. (q21) becomes the accepting state, representing the completion of the regular expression.
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What is the evidence that the energy of the spring is higher when you stretch or compress it?
Answers
Answer: When a spring is compressed or stretched, it will try to restore its equilibrium position by exerting a force equal and opposite to the external force. So the external work done by us in compression as well as stretching will store in the spring as potential energy
Answer: Energy of the spring is equal when compressed as when stretched.
Step-by-step explanation: Potential Energy (PE) of the spring is highest at both compression and when stretched. During this time, the Kinetic Energy (KE) is zero. When the spring is at rest, KE is highest and PE is zero.
HELP!!! WHICH ONE IS IT??!!
Answers
Hope my answer helped u :)
Find all solutions to the equation. cos 2x-1=0 Write your answer in radians in terms of n.
Answers
This is the general solution to the equation cos(2x) - 1 = 0, written in radians in terms of n. To solve the equation cos 2x - 1 = 0, we can first add 1 to both sides to get cos 2x = 1.
We know that cos 2x has a range of [-1,1], so the only time cos 2x can equal 1 is when 2x is a multiple of 2π radians. Therefore, we can write the equation as 2x = 2nπ, where n is an integer.
Solving for x, we get x = nπ. However, since we are looking for all solutions, we can add any multiple of π to this value and still get a valid solution. Therefore, the general solution to the equation is x = nπ + kπ, where n is an integer and k is any integer.
In summary, the solutions to the equation cos 2x - 1 = 0 in radians in terms of n are x = nπ + kπ, where n is an integer and k is any integer.
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For a standard normal distribution, a negative value of z indicates _____.
Answers
For a standard normal distribution, a negative value of z indicates that the observed value is below the mean of the distribution.
In a standard normal distribution, which has a mean of 0 and a standard deviation of 1, a negative value of z indicates that the observed value is located below the mean. The z-score represents the number of standard deviations a data point is away from the mean.
A negative z-score means that the observed value is lower than the mean, indicating that it falls to the left of the center of the distribution. This means that the data point is relatively lower compared to the average and can provide information about its position within the distribution and its deviation from the mean.
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K2. Calculate the total surface area of cuboids with the following dimensions (d) Radius = 3 m, breadth = 1.5 m, height = 2 cm
Answers
Answer:
2(3×2)+2(3×1.5)+2(1.5×3)
Step-by-step explanation:
12+9+9
30
Answer:
30cm square
Step-by-step explanation:
2(3×2)+2(3×1.5)+2(1.5×3)
2[3×2+3×1.5+1.5×3]
2(6+4.5+4.5)
2×15
30
What are the 3 linear functions?.
Answers
Answer:
point-slope form, standard form, and slope-intercept form
Step-by-step explanation:
The three main types of linear functions are: point-slope form, standard form, and slope-intercept form.
Here is an image with each form
true or false dont guess.
A triangle can be made by segments that are 15.9 cm, 10 cm and 25.9 cm.
Answers
Answer:
false
Step-by-step explanation:
for the segments to form a triangle, then
the sum of any 2 must be greater than the third.
15.9 + 10 = 25.9 ← not greater than 25.9
10 + 25.9 = 35.9 > 15.9
15.9 + 25.9 = 41.8 > 10
then the 3 segments will not form a triangle.
of all postsecondary degrees awarded in the united states, including master's and doctorate degrees, 21% are associate's degrees, 58% are earned by people whose race is white, and 12% are associate's degrees earned by whites. what is the conditional probability that a degree is earned by a person whose race is white, given that it is an associate's degree? give your answer to three decimal places.
Answers
The conditional probability that a degree is earned by a person whose race is white, given that it is an associate's degree, is 0.571.
The percentage of associate's degrees is 21%.
The percentage of degrees earned by people whose race is white is 58%.
The percentage of associate's degrees out of all degrees earned by people whose race is white is 12%.
Let the probability of earning an associate's degree be P(A).
P(A) = 0.21
Let the probability of earning a degree by the people whose race is white be P(B).
P(B) = 0.58
Let the probability of earning an associate's degree by the people whose race is white be P(C).
P(C) = 0.12
P(C) = P(A∩B)
We need to find the conditional probability that a degree is earned by a person whose race is white, given that it is an associate's degree.
P(B/A) = P(A∩B)/P(A)
P(B/A) = 0.12/0.21
P(B/A) = 0.571
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Evaluate the expression 52 × (7.2 + 16) − 8.
Answers
The evaluation of the expression is 1198.4.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
Given;
Expression; 52 × (7.2 + 16) − 8
Now,
=52*23.2-8
=1206.4-8
=1198.4
Therefore, the algebra will give 1198.4.
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The following frequency table summarizes the total amounts, in dollars, for 91 orders from a food truck during a certain day.
(a-i) Use the data in the table to create a histogram showing the distribution of the amounts of the orders.
(a-ii) Describe the shape of the distribution of amounts.
(b) Identify a possible amount for the median of the distribution. Justify your answer.
Answers
A possible amount for the median of the distribution is $22.50.
The histogram of the distribution of the amounts of the orders shows a roughly symmetrical distribution with a single peak, and most of the amounts falling between $15 and $30.
To identify the possible amount for the median of the distribution, we need to find the middle value in the ordered data set. Since the data set has an odd number of observations, the median is simply the middle observation.
There are a total of 91 observations, so the middle observation would be the 46th value when the data set is ordered. Looking at the histogram, we can see that the value corresponding to the 46th observation falls between $20 and $25. Therefore, a possible amount for the median of the distribution is $22.50.
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To create a histogram, use the data in the frequency table to plot dollar amounts on the x-axis and frequencies on the y-axis. The shape of the distribution can be determined by examining the histogram. To find a possible median, arrange the dollar amounts in order and find the middle value.
Explanation:(a-i) To create a histogram, we will use the data in the frequency table. We will plot the dollar amounts on the x-axis and the corresponding frequencies on the y-axis. Each bar in the histogram will represent a range of dollar amounts.
(a-ii) The shape of the distribution of amounts can be determined by looking at the histogram. It may be symmetric, skewed to the left or right, or have other shapes like bimodal or uniform.
(b) To identify a possible amount for the median, we need to arrange the dollar amounts in ascending order and find the middle value. If our set has an even number of values, we find the average of the two middle values.
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A 5000 seat theater has tickets for sale at 26 and 40. How many tickets should be sold at each price for a sellout performance to generate a total revenue of 153800.
Answers
Answer:
The number of tickets for sale at $26 should be 3300
The number of tickets for sale at $40 should be 1700
Step-by-step explanation:
Use 2 equations to represent the modifiers within the problem:
\(5000 = a + b \\ 153800 = 26a + 40b\)
Now you want to find the point at which the variables are changed to make both equations correct, this can be done by graphing and finding the intersection of both lines.
\(5000 = 3300 + 1700 \\ 153800 = 26(3300) + 40(1700)\)
Consider the series ∑n=1[infinity]an∑n=1[infinity]an where
an=(n+2)!en−6n+5‾‾‾‾‾√an=(n+2)!en−6n+5
In this problem you must attempt to use the Ratio Test to decide whether the series converges.
Answers
Thus, as the limit is less than 1, by the Ratio Test, the series ∑n=1[infinity]an converges absolutely.
The Ratio Test is a useful tool for determining whether an infinite series converges or diverges.
To use the Ratio Test, we take the limit of the absolute value of the ratio of successive terms as n approaches infinity. If this limit is less than 1, then the series converges absolutely.
If the limit is greater than 1, then the series diverges. If the limit is equal to 1, then the Ratio Test is inconclusive, and we must try another test.
To apply the Ratio Test to the series ∑n=1[infinity]an, we need to compute the ratio of successive terms:
|an+1/an| = |(n+3)! e(n+1) - 6(n+2) + 5‾‾‾‾‾√| / |(n+2)! e(n) - 6(n+1) + 5‾‾‾‾‾√|
Simplifying this expression, we get:
|an+1/an| = [(n+3)/(n+2)]e / [6(n+2)/(n+3) + 5‾‾‾‾‾√]
As n approaches infinity, both the numerator and the denominator approach infinity, so we can apply L'Hopital's Rule to find the limit:
lim n→∞ |an+1/an| = lim n→∞ [(n+3)/(n+2)]e / [6(n+2)/(n+3) + 5‾‾‾‾‾√]
= lim n→∞ e(n+1) / (6 + 5(n+2)/(n+3)‾‾‾‾‾√)
= e/5‾‾‾‾‾√
Since the limit is less than 1, by the Ratio Test, the series ∑n=1[infinity]an converges absolutely. This means that the series converges regardless of the order in which the terms are summed, and we can find its value by summing the terms in any order.
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When rolling a standard die, what is the probability of not getting a perfect square?
Answers
Answer:
0%
Step-by-step explanation:
ITS A CUBE BRUH!!!!
CONFUSED?!!!!!!!!! Just answer the middle question!!
Answers
Answer:
-16-(-45)
Step-by-step explanation:
If we subtract -45 from -16, we'll get the result 29
=> -16-(-45)
=> -16+45
=> 29
Answer:
-21 and 40.
Step-by-step explanation:
The two numbers from the list that have a difference of 29 are:
-21 and 40.
-21 - (-40)
= -21 + 40
= 29
The two numbers are -21 and 40.
Chris works at a tire store. Chris can change a tire on a rim in 8 to 12 min, with all times in between equally likely. A) What is a probability that Chris changes a given tire in less than 9 min? b) What is the probability that it takes between 9 min and 11. 5 min? c) What is the probability that it takes exactly 10 min?
Answers
So these 5 times are equal to 20% each.
A) Less than 9 minutes means 8 minutes, so 20%.
B) If each minute is equal to 20%, 2.5 minutes (11.5 - 9) are 50%.
C) 20%.
If shown,
AB
and
CD
are straight lines. Find x in each case.
WILL MARK BRAINLISIT
Answers
Answer:
4x+x+x+90=360
6x+90=360
6x=270
x=45
good luck!
4x+x+x+90=360
6x+90=360
6x=270
x=45
What are the solutions of x^2=-7x-8
Answers
The solutions to the quadratic equation x² = -7x - 8 are x equals \(\frac{-7 - \sqrt{17}}{2}, \frac{-7 + \sqrt{17}}{2}\).
What are the solutions to the quadratic equation?Given the quadratic equation in the question:
x² = -7x - 8
To find the solutions of the quadratic equation x² = -7x - 8, we can rearrange it into standard quadratic form, which is ax² + bx + c = 0, and apply the quadratic formula.
x² = -7x - 8
x² + 7x + 8 = 0
a = 1, b = 7 and c = 8
Plug these into the quadratic formula: ±
\(x = \frac{-b \± \sqrt{b^2 -4(ac)}}{2a} \\\\x = \frac{-7 \± \sqrt{7^2 -4(1*8)}}{2*1} \\\\x = \frac{-7 \± \sqrt{49 -4(8)}}{2} \\\\x = \frac{-7 \± \sqrt{49 - 32}}{2} \\\\x = \frac{-7 \± \sqrt{17}}{2} \\\\x = \frac{-7 - \sqrt{17}}{2}, \frac{-7 + \sqrt{17}}{2}\)
Therefore, the values of x are \(\frac{-7 - \sqrt{17}}{2}, \frac{-7 + \sqrt{17}}{2}\).
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Solve the initial-value problem of the 2nd order homogeneous differential equation I y" + 16 y = 0, y(0) = y'(0) = -2.
Answers
The particular solution of the given differential equation is : y(x) = -2cos(4x) - (1/2)sin(4x).
Given the differential equation is: I y" + 16 y =0 with initial values y(0) = -2, and y'(0) = -2.
We have to find the solution of the differential equation. We know that the standard form of a second-order homogeneous differential equation is:
y"+p(x)y'+q(x)y=0
The characteristic equation is obtained by substituting y=e^(mx) in the above equation. The characteristic equation is:
m²+p(x)m+q(x)=0
Comparing the above equation with
y" + 16 y = 0, we have,
p(x) = 0 and q(x) = 16
Therefore, the characteristic equation becomes:
m² + 16 = 0
m = ±4i
Hence, the general solution of the given differential equation is:
y(x) = c1cos(4x) + c2sin(4x). Now, let us apply the initial conditions:
y(0) = c1 = -2
Also, y'(x) = -4c1sin(4x) + 4c2cos(4x)Therefore,
y'(0) = 4= c2 = -2
c2 = -1/2
Therefore, the particular solution of the given differential equation is y(x) = -2cos(4x) - (1/2)sin(4x).
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An adventure race is 9.75 mi long. The race is divided into equal sections. Each section is 0.75 mi long. The race organizer needs 4 volunteers in each section. How many volunteers does the race organizer need? Show your work.
Answers
Step-by-step explanation:
9.75/.75 = 13
which means the race is divided into 13 equal section according to the question in which each section is 0.75 m long.
as 4 volunteers are needed in each section
so keeping this in mind 13×4 = 52
therefore, 52 volunteers race organizer need.
hope this answer helps you dear! take care
Hen interpreting f (7, 31) = 4.78, p > 0.05, how many subjects were tested in this simple one-way anova?
Answers
39 subjects were tested in this simple one-way ANOVA.
The df for F distribution is (treatment df, error df)
Using given information
Treatment df = 7
Error df = 31
Total df= 7+31 = 38
Again, total df = N-1, N= number of subjects tested
Then, N-1 = 38
=> N= 39
One-way ANOVA is typically used when there is a single independent variable or factor and the goal is to see whether variation or different levels of that factor have a measurable effect on the dependent variable.
The t-test is a method of determining whether two populations are statistically different from each other, and ANOVA determines whether three or more populations are statistically different from each other.
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