Answer:
4
Step-by-step explanation:
it's just another way of saying find the slope
Answer:
the answer is 4:10
Step-by-step explanation:
Please help!! I’ll give you brainlist
The area of the parallelogram is 45 square units.
The area of the right trapezoid is 42.5 square units.
What is the area of a parallelogram?A parallelogram is a convex quadrilateral in which each pair of opposite edges are parallel and of equal length.
Area of parallelogram = base × height
= 9 × 5
= 45 square units
Area of a right trapezoid = 1/2 (a + b)h
= 1/2(10 + 7)5
= 1/2(17)5
= 1/2(85)
= 42.5 square units
Therefore, the area of the parallelogram and right trapezoid is 45 square units and 42.5 square units respectively.
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Tuesday, May 4, 2021 6 Grade Question of the Day Methods of Division Ashleigh's band won $854 in a talent contest. The band has five members. How much money will each member get if they split the winnings equally? 1. Identify (write) the key word in the passage that requires you to add, subtract, multiply or divide 2. Perform the operation(s) 3. Show all work 4. Upload the assignment
The total prize is $854. and in order to split the amount of money equally we divide the total price in 5 equal parts(You should identigy the word "split" to let you know you need to divide):
\(\frac{854}{5}=\text{ }170.8\)So, every member will get $170.8
Multi step equation help
3 - 4z = -5 + 8z
Answer:
\(z = \frac23\)
Step-by-step explanation:
Hello!
We can solve the equation by isolating the variable z.
Solve for z3 - 4z = -5 + 8z3 + 5 - 4z = 8z8 = 12z2/3 = zThe value of z is 2/3.
∑ Hey, microhiezv ⊃
Answer:
z = 2/3 - Fraction Form
z = 0.67 - Decimal Form
Step-by-step explanation:
Given:
\(3 - 4z = -5 + 8z\)
Solution:
Subtracting 3 from both sides:
\(3-4z-3=-5+8z-3\)
\(-4z=8z-8\)
Subtracting 8z from both sides:
\(-4z-8z=8z-8-8z\)
\(-12z=-8\)
Divide both sides by -12
\(\frac{-12z}{-12}=\frac{-8}{-12}\)
\(z=\frac{2}{3}\)
\(z=0.67\)
xcookiex12
8/22/2022
Ji-yoon has a savings account with $690 in it that earns 7% simple interest per year. How much money, to the nearest penny, will Ji-yoon have in 8 years? Give your answer in dollars.
Let's begin by identifying key information given to us:
Principal (p) = $690
Interest rate (r) = 7% = 0.07 per year
Time (t) = 8 years
The amount of money that Ji-yoon has in 8 years is calculated as shown below:
\(\begin{gathered} I=p\times r\times t \\ I=690\times0.07\times8=386.4 \\ I=\text{ \$}386.40 \\ \\ \text{The total amount Ji-yoon has after 8 years is:} \\ Total=\text{\$(}386.40+$690$) \\ Total=\text{\$}1,076.40 \end{gathered}\)a ______ is a descriptiion of the approach that is used to obtain samples from a population prior to an data collection activity.
A.
population frame
B.
sampling weight
C.
sampling plan
D.
probability interval
The correct answer is option C. A sampling plan refers to a detailed strategy for obtaining a sample from a population for the purpose of data collection.
It describes the precise procedures needed to choose the sample, determine the members of the sample, and gather the data.
The sampling strategy should take into account the type of sampling design, sample size, sampling process, and the methods to be employed for data collecting.
The strategy for implementing sampling should be outlined in the plan, along with instructions on how to make sure the sample is representative of the population, how to prevent bias in the sampling process, and how to make sure the data gathered is of high quality.
A good sampling plan should provide a clear and consistent method for gathering data and be founded on basic statistical concepts.
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A water tank at Camp Newton holds 1200 gallons of water at time t = 0. During the time interval Osts 18 hours, water is pumped into the tank at the rate
W(t) = 95Vt sin^2 (t/6) gallons per hour During the same time interval water is removed from the tank at the rate R(t) = 275 sin^2 (1/3) gallons per hour a. Is the amount of water in the tank increasing at time t = 15? Why or why not?
b. To the nearest whole number, how many gallons of water are in the tank at time t = 18? c. At what time t, for 0 st 18, is the amount of water in the tank at an absolute minimum? Show the work that leads to your conclusion d. For t > 18, no water is pumped into the tank, but water continues to be removed at the rate R(C) until the tank becomes empty. Write, but do not solve, an equation involving an integral expression that can be used to find the value of k.
(a)The amount of water in the tank is increasing.
(b)Evaluate \(\int\limits^{18}_0(W(t) - R(t)) dt\) to get the number of gallons of water in the tank at t = 18.
(c)Solve part (b) to get the absolute minimum from the critical points.
(d)The equation can be set up as \(\int\limits^k_{18}-R(t) dt = 1200\) and solve this equation to find the value of k.
What is the absolute value of a number?
The absolute value of a number is its distance from zero on the number line. It represents the magnitude or size of a real number without considering its sign.
To solve the given problems, we need to integrate the given rates of water flow to determine the amount of water in the tank at various times. Let's go through each part step by step:
a)To determine if the amount of water in the tank is increasing at time t = 15, we need to compare the rate of water being pumped in with the rate of water being removed.
At t = 15, the rate of water being pumped in is given by \(W(t) = 95Vt sin^2(\frac{t}{6})\) gallons per hour. The rate of water being removed is \(R(t) = 275 sin^2(\frac{1}{3})\) gallons per hour.
Evaluate both rates at t = 15 and compare them. If the rate of water being pumped in is greater than the rate of water being removed, then the amount of water in the tank is increasing. Otherwise, it is decreasing.
b) To find the number of gallons of water in the tank at time t = 18, we need to integrate the net rate of water flow from t = 0 to t = 18. The net rate of water flow is given by the difference between the rate of water being pumped in and the rate of water being removed. So the integral to find the total amount of water in the tank at t = 18 is:
\(\int\limits^{18}_0(W(t) - R(t)) dt\)
Evaluate this integral to get the number of gallons of water in the tank at t = 18.
c)To find the time t when the amount of water in the tank is at an absolute minimum, we need to find the minimum of the function that represents the total amount of water in the tank. The total amount of water in the tank is obtained by integrating the net rate of water flow over the interval [0, 18] as mentioned in part b. Find the critical points and determine the absolute minimum from those points.
d. For t > 18, no water is pumped into the tank, but water continues to be removed at the rate R(t) until the tank becomes empty. To find the value of k, we need to set up an equation involving an integral expression that represents the remaining water in the tank after time t = 18. This equation will represent the condition for the tank to become empty.
The equation can be set up as:
\(\int\limits^k_{18}-R(t) dt = 1200\)
Here, k represents the time at which the tank becomes empty, and the integral represents the cumulative removal of water from t = 18 to t = k. Solve this equation to find the value of k.
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given list: ( 6, 13, 14, 30, 38, 50, 60, 72, 76, 87, 90, 92 ) ex: 42, 32, 12 which list elements will be compared to key 60 using binary search? enter elements in the order checked.
Using binary search to find the key 60 in the given list, the elements compared in order are: 38, 76, 60.
1. We start by comparing the key (60) to the middle element of the list, which is 38. Since 60 is greater than 38, we know that the key must be in the second half of the list.
2. Next, we compare the key to the middle element of the second half of the list, which is 76. Since 60 is less than 76, we know that the key must be in the first half of the second half of the list.
3. We then compare the key to the middle element of the first half of the second half of the list, which is 50. Since 60 is greater than 50, we know that the key must be in the second half of the first half of the second half of the list.
4. Next, we compare the key to the middle element of the second half of the first half of the second half of the list, which is 72. Since 60 is less than 72, we know that the key must be in the first half of the second half of the first half of the second half of the list.
5. Finally, we compare the key to the middle element of the first half of the second half of the first half of the second half of the list, which is 60. Since 60 is equal to 60, we have found the position of the key in the list.
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calculate the volume of water in the ocean in liters
The volume of water in the ocean is estimated to be approximately 1,332,000,000,000,000,000 liters.
The Earth's oceans cover about 71% of the planet's surface and contain a vast amount of water. To calculate the volume of water in the ocean, we need to consider the average depth and the total surface area of the oceans.
The average depth of the ocean is estimated to be around 3,800 meters. The total surface area of the oceans is approximately 361,900,000 square kilometers. By multiplying the average depth by the surface area, we can find the volume of water.
Volume = Average Depth × Surface Area
Using the given values, we have:
Volume = 3,800 meters × 361,900,000 square kilometers
To convert this volume to liters, we need to consider that 1 cubic meter is equal to 1,000 liters. Therefore, we can multiply the volume in cubic meters by 1,000 to obtain the volume in liters.
Calculating the above expression, we find that the volume of water in the ocean is approximately 1,332,000,000,000,000,000 liters. This is an estimation and may vary slightly depending on the sources and assumptions used for average depth and surface area calculations.
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What is the equation of the line?
Answer:
UNDEFINED!
Step-by-step explanation:
The x-coordinate never changes no matter what the y-coordinate is!
Suppose the following equations describe a scenario involving an externality: MSB=MPB=12−0.5Q
MSC=2+1.5Q
MPC=2+0.5Q
1. What kind of externality (positive or negative) is this? How do you know? 2. Sketch a graph of the marginal cost and benefit curves for this scenario. 3. Compute the quantity that will result from private decision-making. Show your work. 4. Compute the quantity that would be best from society's viewpoint. Show your work. 5. How do the social and private optima compare? Why is this the expected result in the presence of this type of externality?
The presence of a negative externality causes the MSC to be higher than the MSB, which leads to the market over-producing the good. This is because producers are only taking their private costs and benefits into account, not the costs and benefits to society as a whole. The difference between the private and social optima is known as the deadweight loss. In this case, the deadweight loss is equal to the shaded triangle in the attached image.
1. This is a negative externality. We can see this by the MSC being higher than the MSB. This means that the cost to society of producing the good is higher than the benefit to society, resulting in the market over-producing the good.2. See the attached image. 3. At private decision making, we set the MSB equal to the MPC: 12-0.5Q = 2+0.5Q. Solving for Q gives Q = 8. 4. To find the socially optimal quantity, we need to set MSB equal to MSC: 12-0.5Q = 2+1.5Q. Solving for Q gives Q = 4. 5. The private and social optima are different because of the negative externality.
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give an example of a solid from which a triangular, hexagonal, and trapezoidal cross-section can be formed.
Triangular prism is an example of a solid from which a triangular, hexagonal, and trapezoidal cross-section can be formed.
What is a triangular prism?A triangular prism is a polyhedron that is made up of triangular bases and three rectangular sides. It is a three-dimensional shape that has three side faces and two base faces, connected to each other through the edges to the vertex.
Some properties of a triangular prism:
It has five faces in total - looks a trapezoidHas nine edgesHas six vertices; hexagonaltwo triangular bases that are equalThus, triangular prism is an example of a solid from which a triangular, hexagonal, and trapezoidal cross-section can be formed.
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What is the value of x?
Enter your answer in the box.
X =??
Answer:
x = 9
Step-by-step explanation:
Triangles are similar due to AAA (all angles are congruent due to shared angle and corresponding angles). Thus, the sides are proportional, and we can set up a proportion with corresponding sides:
9/(72 + 9) = (3x - 20)/(3x - 20 + 56)
9/81 = (3x - 20)/(3x + 36)
(1/9) * (3x + 36) = 3x - 20
(3x + 36)/9 = 3x - 20
3x + 36 = (3x - 20)*9
3x + 36 = 27x - 180
36 + 180 = 27x - 3x
216 = 24x
x = 9
-6/5 k -3/4 = -2 + 1/7 k solve for k
hello
to solve for k, we'll do it in a stepwise manner
step 1
collect like terms
\(\begin{gathered} -\frac{6}{5}k-\frac{3}{4}=-2+\frac{1}{7}k \\ -\frac{3}{4}+2=\frac{1}{7}k+\frac{6}{5}k \end{gathered}\)\(\begin{gathered} -\frac{3}{4}+2=\frac{1}{7}k+\frac{6}{5}k \\ \text{take LCM} \\ -\frac{3+8}{4}=\frac{5+42}{35}k \\ \frac{5}{4}=\frac{47}{35}k \end{gathered}\)step 2 above was to take LCM
step 3
cross multiply both sides and solve for k
\(\begin{gathered} \frac{5}{4}=\frac{47}{35}k \\ 4\times47=(5\times35)k \\ 188=175k \\ k=\frac{188}{175} \\ k=1.074 \end{gathered}\)Abraham Lincoln was the tallest president. His height was 76 inches. How tall was Abe in feet?
Select the correct answer. What is the y-intercept of f(x) = 3x+2? A. (9, 0) B. (0, 9) C. (0, -9) D. (9, -9)
The correct answer is not provided among the given choices.
The y-intercept of the function f(x) = 3x + 2 is (0, 2).
To find the y-intercept of the function f(x) = 3x + 2, we need to determine the value of y when x is equal to 0.
The y-intercept represents the point where the graph of the function intersects the y-axis.
Substituting x = 0 into the equation, we get:
f(0) = 3(0) + 2
f(0) = 0 + 2
f(0) = 2
So, when x = 0, the corresponding value of y is 2.
Therefore, the y-intercept of the function f(x) = 3x + 2 is (0, 2).
Among the given answer choices:
A. (9, 0) does not represent the y-intercept.
B. (0, 9) does not represent the y-intercept.
C. (0, -9) does not represent the y-intercept.
D. (9, -9) does not represent the y-intercept.
None of the given answer choices correctly represent the y-intercept of the function f(x) = 3x + 2, which is (0, 2).
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Micah is 6 years younger than Raul.
Write an expression to show how to find Micah’s age when Raul is 14. Help plz
Answer:
14-6
Step-by-step explanation:
I’ll give brainliest
Answer:
B
Step-by-step explanation:
We know that it costs 37 cents to mail a letter that weighs 1 oz or less. This would mean that for x ≤ 1, P(x) should equal 37. Already, we can eliminate A and D.
We also know that it costs an additional 26 cents for at most another ounce added to the original 1 ounce. This means that for 1 < x ≤ 2, P(x) = 26 + 37 = 63. This is shown by B.
Thus, the answer is B.
~ an aesthetics lover
describe an efficient algorithm that will determine an optimal s to t path given your preference for stopping at u along the way if not too inconve- nient. it should either return the shortest path from s to t or the shortest path from s to t containing u. name your algorithm appropriately and provide pseudocode for it
Dijkstra's algorithm should be executed twice, once from s and once from u.
Given,
We have to determine an effective algorithm that, provided it's not too inconvenient, will choose the best route from s to t based on your choice for stopping at u along the way. Either the shortest path from s to t or the shortest path from s to t that includes u should be returned.
Algorithm;-
An algorithm is a process used to carry out a computation or solve a problem. In either hardware-based or software-based routines, algorithms function as a detailed sequence of instructions that carry out predetermined operations sequentially. All aspects of information technology employ algorithms extensively.
Here,
Run Dijkstra's algorithm two times, from s and u, respectively.
The shortest path from s to u and the shortest path from u to t make up the shortest path from s to t containing u.
Choose the path to return to based on their lengths by comparing this path's length to the path's length from s to t.
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3cos²∅ (1+tan²∅) = 3
Answer:
Reflection Paper on "Freedom Riders"
Ankit Mishra
title movie
freedom riders
instructions create a reflection paper that summarize the documentary and how brougth about social changes and lead to the Civil rigths act of 1964
please help me
2,3 pages
Please read the instructions please I need your help watch the movie and the instructions
Reflection Paper on "Freedom Riders" Documentary
The "Freedom Riders" is a powerful documentary that recounts the story of a group of civil rights activists who rode buses across the American South in 1961 to challenge the segregated public transportation system. The film provides a vivid and moving account of their journey and the challenges they faced along the way, from beatings and arrests to bombings and arson attacks. Through interviews with surviving freedom riders and archival footage, the film sheds light on the bravery and determination of these activists and the impact they had on the civil rights movement.
The freedom riders were inspired by the nonviolent protest movement led by Dr. Martin Luther King Jr. and other civil rights leaders. They believed that segregation was a moral wrong and that they had a duty to resist it through nonviolent means. Despite the danger they faced, the freedom riders refused to back down, putting their lives on the line for the cause of justice and equality.
The bravery of the freedom riders had a profound impact on the civil rights movement. Their actions galvanized support for the cause and drew national attention to the issue of segregation. The freedom rides sparked a wave of protests and civil disobedience across the South, and helped to build momentum for the passage of the Civil Rights Act of 1964. This landmark legislation banned segregation in public places and made it illegal to discriminate against someone on the basis of race, color, religion, sex, or national origin.
The "Freedom Riders" documentary serves as a powerful reminder of the sacrifices made by those who fought for civil rights in the United States. It highlights the courage and determination of the freedom riders and the impact they had on the country. It is an important film that teaches us about the past and the struggles of those who fought for justice and equality.
In conclusion, the "Freedom Riders" documentary is a powerful reminder of the sacrifices made by those who fought for civil rights in the United States. It highlights the bravery and determination of the freedom riders and the impact they had on the civil rights movement. The film serves as a testament to the power of nonviolent protest and the importance of standing up for what is right, even in the face of opposition. The lessons of the freedom riders should inspire us all to continue working towards a more just and equal society.
Ankit Mishra
3cos²∅ (1+tan²∅) = 3
This equation involves trigonometric functions and can be simplified using trigonometric identities.
Starting with the right-hand side of the equation, we have 3. On the left-hand side, we have the expression 3cos^2(θ)(1 + tan^2(θ)).
We can simplify the expression as follows:
cos^2(θ) = 1 - sin^2(θ)
and
tan^2(θ) = sin^2(θ) / cos^2(θ)
Substituting these identities into the expression on the left-hand side, we get:
3(1 - sin^2(θ))(1 + sin^2(θ) / (1 - sin^2(θ))
Expanding the product and simplifying, we get:
3
Thus, the equation is true and holds true for all values of θ.
Ben's monthly housing costs for his new home will be $2100 per month. What
must his monthly net income be to keep housing as 30% of his budget?
The percentage is calculated by dividing the required value by the total value and multiplying it by 100.
The monthly net income to keep housing a 30% of his budget is $7000.
What is a percentage?The percentage is calculated by dividing the required value by the total value and multiplying it by 100.
Example:
Required percentage value = a
total value = b
Percentage = a/b x 100
We have,
Cost of monthly housing per month = $2100
$2100 = 30%
Monthly income = 100%
30% = 2100
Multiply 100/30 on both sides.
100/30 x 30% = 100/30 x 2100
100% = 7000
Thus,
The monthly net income to keep housing a 30% of his budget is $7000.
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find the number degree of freedom, Critical value X², X² Given 95% confidence; n = 25, s = 0.24 Degree of freedom, df = 24 Critical value: X= [Select] X²= [Select] [Select] 39.364 32.852 12.401
The number of degrees of freedom is 24, and the critical value X² for a 95% confidence level and 24 degrees of freedom is approximately 36.415.
To find the number of degrees of freedom and the critical value X² for a 95% confidence level with n = 25 and s = 0.24, we need to determine the appropriate values based on the chi-square distribution.
The number of degrees of freedom (df) is equal to n - 1, where n is the sample size. In this case, df = 25 - 1 = 24.
To find the critical value X² for a 95% confidence level and 24 degrees of freedom, we need to consult a chi-square distribution table or use statistical software. The critical value corresponds to the chi-square value that leaves 5% (0.05) in the right tail.
Looking up the chi-square distribution table or using software, we find that the critical value for a 95% confidence level and 24 degrees of freedom is approximately 36.415.
Therefore, the number of degrees of freedom is 24, and the critical value X² for a 95% confidence level and 24 degrees of freedom is approximately 36.415.
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In which of the expressions below will ? x=6 Select all that apply. in freckle
The expressions that have x = 6 as their solutions are
8x/12 = 4, 4(2 + 3x) = 80, 15 - (x - 3) = 12 and 24 - (x + 12) = 6
How to determine the expressionsThe complete question is added as an attachment
Next, we solve each of the options
From the question, we have the following expressions that can be used in our computation:
8x/12 = 4
This gives
8x = 48
So, we have
x = 6
4(2 + 3x) = 80
This gives
2 + 3x = 20
So, we have
x = 6
x^2 + 8 = 57
This gives
x = +/- 7
15 - (x - 3) = 12
This gvies
x - 3 = 3
So, we have
x = 6
Lastly, we have
24 - (x + 12) = 6
This gvies
x + 12 = 18
So, we have
x = 6
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Challenge A store is giving out cards labeled 1 through 10 when customers enter the store. If the
card is an even number, you get a 10% discount on your purchase that day. If the card is an odd
number greater than 6, you get a 30% discount. Otherwise, you get a 20% discount. The table
shows the results of 400 customers. What is the relative frequency for each discount? Use pencil
and paper. If the manager of the store wants approximately half of the customers to receive the
20% discount, does this seem like an appropriate method? Explain.
The relative frequency for a 10% discount is?
The relative frequency for a 30% discount is?
The relative frequency for as 20% discount is?
The relative frequency for a 10% discount is 0.25, the relative frequency for a 30% discount is 0.1375, and the relative frequency for a 20% discount is 0.6125.
To calculate the relative frequency for each discount, we need to divide the number of customers who received that discount by the total number of customers. Using the table, we can see that 100 customers received a 10% discount, 55 received a 30% discount, and 245 received a 20% discount. Dividing each of these numbers by 400, we get:
Relative frequency for a 10% discount = 100/400 = 0.25
Relative frequency for a 30% discount = 55/400 = 0.1375
Relative frequency for a 20% discount = 245/400 = 0.6125
Based on these calculations, it seems like the majority of customers are receiving the 20% discount. If the manager wants approximately half of the customers to receive the 20% discount, then this method does not seem appropriate. They may need to adjust the criteria for the discounts or find a different promotional strategy to achieve their desired outcome.
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Karen has $20 in an account that earns 10% interest compounded annually.
To the nearest cent, how much will she have in 2 years?
$24.20
Step-by-step explanation:Compound interest is the amount of interest paid on the principal and accumulated interest.
Interest Formula
The compound interest formula is \(A = P(1+\frac{r}{n} )^{nt}\). The variables for this formula are as follows:
A is the total amount in the accountP is the principal or the original balance of the account.r is the interest rate expressed as a decimaln is the number of times compounded per yeart is time in yearsTo find the total amount in Karen's account after 2 years, we need to define our variables and plug them into the formula.
Solving Compound Interest
Firstly, let's identify the value of each of the variables. The original amount in the account is $20. So, P = 20. Additionally, the interest rate is 10%, which is equal to 0.1. So, r = 0.1. Since interest is compounded annually, it is compounded once a year. Thus, n = 1. Finally, we want to know the amount after 2 years, so t = 2.
Now, let's plug these values into the formula above.
\(A=20(1+\frac{0.1}{1})^{1*2}\)This can be simplified to make the equation easier to solve.
A = 20(1.1)²Using this equation, we can say A = 24.20. Therefore, after 2 years, Karen will have $24.20 in her account.
algebra 2-2
solve \(\sqrt{x}+3=-6\)
√x+3=-6
The solution of equation is x=-3
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
The equation;√x+3=-6
Now,
√x=-6-3
√x=-9
x=-3
Therefore the answer of the given equation will be -3
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(-5/7-11/7 x=-y, 2y=7+5x)
Answer:
Solve the system of equations:
x= -3
y= -4
Step-by-step explanation:
This is right if x went with 11/17:
11/17x
I didn't know if they were separated or not
Find the equation for the plane through P0(8,1,−4) perpendicular to the following line.
x=8−t, y=1−2t, z=3t, −[infinity]
Using a coefficient of −1 for x, the equation of the plane is.
The equation for the plane through P0(8,1,−4) perpendicular to the following line is x + 4y + 5z - 8 = 0
How to determine the equation?The slope of the perpendicular line should be a/b, and if one line is perpendicular to this line, the product of slopes should be -1. The equation of a line perpendicular to a given line ax + by + c = 0 is bx - ay + = 0, where is a constant.
The given parameters are
x=8−t, y=1−2t, z=3t,
P0(- 9, 6, - 5).
Direction vector of line is < -1, 4, 5>,
This vector is normal vector for unknown plane.
So, equation of plane: -1(x - (-9)) + 4(y - 6) + 5(z - (-5)) = 0; - x - 9 + 4y - 24 + 5z + 25 = 0;
In conclusion the equation is given as -x + 4y + 5z - 8 = 0
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Help me with my math hw about angles
The measures of the numbered angles are:
m∠1 = 65°
m∠2 = 55°
m∠3 = 60°
m∠4 = 65°
m∠5 = 55°
m∠6 = 60°
m∠7 = 120°
m∠8 = 60°
m∠9 = 120°
m∠10 = 115°
m∠11 = 85°
m∠12 = 115°
How to find the measures of the numbered angles?Angle geometry is a branch of mathematics that deals with the study of angles and their properties. Angles are formed when two lines or rays intersect or when a line intersects a plane.
m∠1 = 65° (corresponding angles)
m∠2 = 180 - 60 - m∠1 (angles on a straight line)
m∠2 = 180 - 60 - 65 = 55°
m∠3 = 60° (vertically opposite angles)
m∠4 = m∠1 (vertically opposite angles)
m∠4 = 65°
m∠5 = m∠2 (vertically opposite angles)
m∠5 = 55°
m∠6 = m∠3 (alternate angles)
m∠6 = 60°
m∠7 = 180 - m∠6 (angles on a straight line)
m∠7 = 180 - 60 = 120°
m∠8 = m∠6 (vertically opposite angles)
m∠8 = 60°
m∠9 = m∠7 (vertically opposite angles)
m∠9 = 120°
m∠10 = 180 - 65 (angles on a straight line)
m∠10 = 180 - 65 = 115°
m∠11 = 85° (vertically opposite angles)
m∠12 = m∠10 (vertically opposite angles)
m∠12 = 115°
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Force f acts between a pair of charges, q1 and q2, separated by a distance d. for each of the statements, use the drop-down menus to express the new force in terms of f. q1 is halved, q2 is doubled, but the distance between the charges remains d. q1 and q2 are unchanged. the distance between the charges is doubled to 2d. q1 is doubled and q2 is tripled. the distance between the charges remains d.
The initial force between the two charges is given by:
\(F=k\frac{q_{1} q_{2} }{d^2}\)
where k is Coulomb's constant, q1 and q2 are the two charges, and d is their separation. Let's analyze now the other situations:
1. F
In this case, q1 is halved, q2 is doubled, but the distance between the charges remains d.
So, we have:
q'₁=q₁/2
q'₂=2q₂
d'=d
So, the new force is:
\(F'=k\frac{q'_{1}q'_{2} }{d^2} \\\\F'=k\frac{(\frac{q_{1} }{2})(\frac{q_{2} }{2}) }{d^2} \\\\F'=k\frac{q_{1}q_{2} }{d^2} =F\)
So the force has not changed.
2. F/4
In this case, q1 and q2 are unchanged. The distance between the charges is doubled to 2d.
So, we have:
q'₁=q₁
q'₂=q₂
d'=2d
So, the new force is:
\(\\F'=k\frac{q'_{1} q'_{2} }{d^2} \\\\F'=k\frac{q_{1}q_{2} }{2d^2} \\\\F'=\frac{1}{4} k\frac{q_{1}q_{2} }{d^2} \\\\F'=\frac{F}{4}\)
So the force has decreased by a factor of 4.
3. 6F
In this case, q1 is doubled and q2 is tripled. The distance between the charges remains d.
So, we have:
q'₁=2q₁
q'₂=3q₂
d'=d
So, the new force is:
\(F'=k\frac{q'_{1} q'_{2} }{d^2} \\\\F'=k\frac{2q_{1}3q_{2} }{d^2}\\ \\F'=6k\frac{q_{1}q_{2} }{d^2} =6F\)
So the force has increased by a factor of 6.
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Answer:
1. F
2. F/4
3. 6F
Dean has worn a white shirt on 6 of the last 18 days. what is the experimental probability
that dean will wear a white shirt tomorrow?
The probability of wearing a white shirt tomorrow is 1/3 according to the stated data.
It must be noted that probability of wearing the white shirt will remain same for each day based on the stated data. Now, calculating probability for wearing white shirt on any random day.
Probability = likelihood of events/total number of events
Likelihood of events = 6
Total number of events is the number of days considered
Keep the values in formula
Probability = 6/18
Simplifying the formed fraction
Probability = 1/3
Hence, the probability of wearing a white shirt tomorrow is 1/3.
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