The vector
u
u has magnitude
2
2 and direction
5
5
∘. 55
∘. If vector
v
=
−
2
u
,
v=−2u, then what is the magnitude and direction of vector
v
?
v? Write your direction in degrees in the interval
0
∘
≤
θ
<
36
0
∘. 0
∘
≤θ<
Answers
The magnitude of vector v is 4 and the direction is 125 degrees.
Given that vector u has a magnitude of 2 and a direction of 55 degrees, we can determine the magnitude and direction of vector v.
To find the magnitude of vector v, we can use the equation:
|v| = |-2u|
Since u has a magnitude of 2, we can substitute it into the equation:
|v| = |-2 * 2|
|v| = |-4|
|v| = 4
The magnitude of vector v is 4.
To find the direction of vector v, we can note that multiplying a vector by -1 (in this case, multiplying u by -2) reverses its direction. So the direction of v is the exact opposite of the direction of u.
Since the direction of u is 55 degrees, the direction of v is 55 degrees in the opposite direction. In the interval of 0 degrees ≤ θ < 360 degrees, the direction of v can be expressed as:
θ = 180 - 55
θ = 125 degrees
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Related Questions
select the δh values associated with the dissolution of lithium chloride that are exothermic
Answers
The ΔH values associated with the dissolution of lithium chloride that are exothermic involve the release of heat energy. When a substance dissolves in a solvent, it can either release heat (exothermic) or absorb heat (endothermic).
Here are the steps to determine if the dissolution of lithium chloride is exothermic:
1. Look for the chemical equation that represents the dissolution of lithium chloride. In this case, it would be:
LiCl(s) → Li+(aq) + Cl-(aq)
2. Examine the enthalpy change (ΔH) associated with this chemical equation. If the ΔH value is negative, it indicates an exothermic process, meaning that heat is released during the dissolution. If the ΔH value is positive, it indicates an endothermic process, meaning that heat is absorbed during the dissolution.
So, to identify the exothermic ΔH values associated with the dissolution of lithium chloride, you need to find experiments or reliable sources that provide the enthalpy change values for this reaction.
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A number cube is rolled and a marble is selected at random from a bag containing 2 green marbles, 2 yellow marbles, 2 red marbles, 1 purple marble, and 1 blue marble. Find each probability. Show your work. 1. P(1 and red) 2. P(3 and purple) 3. P(even and yellow) 4. P(odd and not green)
Answers
Answer:
1)
1 /6 × 1/8
1/6×8
1/48
2)
3/6 ×1/8
2×1/8
1/4
3)
3/6 ×1/8
2×1/8
1/4
4)
3/6×4/8
2÷2
1
Please help me, please
Answers
Answer:
\(9\pi \: (x - {4})^{2} \)
9π ( x - 4
The curve with equation y^2 = 5x^4 - x^2 is called a kampyle of Eudoxus. Find an equation of the tangent line to this curve at the point (1, 2).
Answers
Therefore, the equation of the tangent line to the curve y^2 = 5x^4 - x^2 at the point (1, 2) is y = (9/2)x - 7/2.
To find the equation of the tangent line to the curve y^2 = 5x^4 - x^2 at the point (1, 2), we can use the concept of derivatives.
First, we differentiate both sides of the equation y^2 = 5x^4 - x^2 with respect to x:
2y * dy/dx = 20x^3 - 2x.
Next, substitute the coordinates of the given point (1, 2) into the derivative equation:
2(2) * dy/dx = 20(1)^3 - 2(1).
Simplifying:
4 * dy/dx = 20 - 2,
4 * dy/dx = 18,
dy/dx = 18/4,
dy/dx = 9/2.
The derivative dy/dx represents the slope of the tangent line at any given point on the curve.
Now, using the point-slope form of a line, we can write the equation of the tangent line:
y - y1 = m(x - x1),
where (x1, y1) is the point (1, 2) and m is the slope dy/dx.
Plugging in the values, we have:
y - 2 = (9/2)(x - 1).
Simplifying and rearranging:
y = (9/2)x - 7/2
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If the two figures are congruent, which statement is true?
A. BCDA ≅ FEHG
B. ABCD ≅ EFGH
C. BADC ≅ EFGH
D. ADCB ≅ HGFE
Answers
Answer:
A
Step-by-step explanation:
the order of letter should resemble the same shape
6 yellow balls and 8 red balls are placed in an urn. two balls are then drawn in succession without replacement. what is the probability that the first ball drawn is a red ball if the second ball drawn is yellow?
Answers
The probability that the first ball drawn is a red is 8/14
the probability that the first ball drawn is a yellow is 6/13
Let A = getting a red ball
B= getting a yellow ball given that first was red ball
P( A ) = 8/14
P( B ) = 6/ 13 (since 1 red ball is out)
A(A ∩ B)= 6/13 x 8/14 =
48/182
Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1.
Mathematics has incorporated probability to forecast the likelihood of various events. The degree to which something is likely to happen is basically what probability means. You will understand the potential outcomes for a random experiment using this fundamental theory of probability, which is also applied to the probability distribution.
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find the surface area
Answers
Answer:
aww you had my question opennnn
Step-by-step explanation:
Elijah played 98 consecutive games of soccer without being taken off the field. Then, after a single game on the sidelines, he played another string of consecutive games, although this string was 50% shorter. How many consecutive games was that?
Answers
Answer:
If the game will start at 11:00 A.M., but the players must arrive at the field three-quarters of an hour early to warm up, it refers to 8:45 a.m. Why? If we start to count in 11 backward and start to trace the three-quarters, it shows that 10:45, 9:45, and 8:45 are the three-quarters. So Hamid statement that he has to be at the field at 9:45 A.M is not correct.
Step-by-step explanation:
in most situations, would it be reasonable to use a level .01 test in conjunction with a sample size of 40,000? why or why not?
Answers
In most situations, it would be reasonable to use a level .01 test with a sample size of 40,000 as it provides a high level of statistical power to detect smaller effects and reduce the likelihood of Type I error.
In most situations, it would be reasonable to use a level .01 test in conjunction with a sample size of 40,000. This is because a larger sample size provides more statistical power, meaning the test is more likely to detect a significant difference if one exists.
Additionally, a level .01 test is more conservative than a level .05 test, which reduces the risk of a type I error (rejecting the null hypothesis when it is actually true).
However, it is important to consider the context and specific research question being addressed, as well as potential confounding variables, to determine the appropriate statistical test and significance level for a given study.
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The terminal side of O is in quadrant II and cos 0What is sin ?1313O A. - 12O B.O c. 5O D. 1 / 1
Answers
Solution
Using the trigonometric ratio, SOHCAHTOA
\(\begin{gathered} \text{SOH, CAH and TOA respectively represents} \\ \sin e\text{ }\theta=\frac{opposite}{\text{hypothenus}} \\ \cos \theta=\frac{adjacent}{\text{hypothenuse}} \\ \text{Tan}\theta\text{ = }\frac{opposite}{\text{adjacent}} \end{gathered}\)
From the question
\(\begin{gathered} \cos \theta=-\frac{5}{13} \\ \text{Therefore } \\ \text{adjacent = 5} \\ hypothenuse\text{ = 13} \end{gathered}\)Using pythagoras theorem, we can find the opposite
so that
\(\begin{gathered} \text{Hypothenuse}^2=opposite^2+adjacent^2 \\ 13^2=opposite^2+5^2 \\ opposite\text{ }^2=169-25 \\ \text{opposite =}\sqrt[]{144} \\ \text{opposite = 12} \end{gathered}\)Hence,
\(\begin{gathered} \sin e\theta=\frac{opposite}{\text{hypothenuse}} \\ \sin e\theta=\frac{12}{13} \\ \sin ce\text{ the terminal side is in the quadrant II and sine positive in the quadrant II, } \\ Sine\text{ }\theta=\frac{12}{13} \end{gathered}\)Therefore the right answer is option B
Suppose that there are no restrictions on how many pages a printer can print. How many ways are there for the 100 pages to be assigned to the four printers
Answers
There are 176,851 ways to assign the 100 pages to the four printers.
Since there are no restrictions on how many pages a printer can print, we can think of this problem as distributing 100 identical pages among 4 distinct printers. This is an example of a "balls and urns" problem, which can be solved using the stars and bars formula.
The stars and bars formula states that the number of ways to distribute k identical objects among n distinct containers is:
C(k+n-1, n-1)
where C represents the combination function. In this case, we have k = 100 identical pages and n = 4 distinct printers. Therefore, the number of ways to assign the pages to the printers is:
C(100+4-1, 4-1) = C(103, 3) = 176,851
So there are 176,851 ways to assign the 100 pages to the four printers.
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The U.S. Open Women's Singles Championship begins with 128 players. The players compete in this single-elimination tournament until there is 1 winner. How many rounds of matches must be scheduled in order to complete the tournament
Answers
Using a geometric sequence, it is found that 7 rounds must be scheduled in order to complete the tournament.
What is a geometric sequence?A geometric sequence is a sequence in which the result of the division of consecutive terms is always the same, called common ratio q.
The nth term of a geometric sequence is given by:
\(a_n = a_1q^{n-1}\)
In which \(a_1\) is the first term.
In this problem, the first round has 128 players, and each round, the players who lose a game go home, hence the common ratio is of q = 0.5.
Then, the geometric sequence for the number of players after n rounds is given by:
\(a_n = 128(0.5)^n\)
In the final round, there is one player, hence:
\(1 = 128(0.5)^n\)
\((0.5)^n = \frac{1}{128}\)
\((0.5)^n = \left(\frac{1}{2}\right)^7\)
n = 7
7 rounds must be scheduled in order to complete the tournament.
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Help
NSNDNDNDN DNDNDN
Answers
1) - 3x - 8y = 73
x-74= - 46
Answers
Answer:
x = 28
y = 157/8
Step-by-step explanation:
Zoe earned $482.50 at her job when she worked for 25 hours. What was her hourly wage, in dollars per hour?
Answers
Answer:
19.3
Step-by-step explanation:
482.5/25=
19.3
$482.50 for 25 hours
all you need to do is divide!
$19.30 is most likely the answer
Find the function y whose derivative x is 0 dy is 7.x² +8.x-2 and y has a value of 1 when dx
Answers
The function y whose derivative is dy/dx = 7x² + 8x - 2 and has a value of 1 when x = 0 is y = (7/3)x³ + 4x² - 2x + 1.
To find the function y given its derivative and an initial condition, we can integrate the derivative with respect to x.
Given that dy/dx = 7x² + 8x - 2 and y(0) = 1, we can integrate the derivative to find y(x).
Integrating both sides of the equation with respect to x, we have:
∫ dy/dx dx = ∫ (7x² + 8x - 2) dx.
Integrating each term separately:
∫ dy/dx dx = ∫ 7x² dx + ∫ 8x dx - ∫ 2 dx.
Integrating the terms, we get:
y = (7/3)x³ + 4x² - 2x + C,
where C is the constant of integration.
Using the initial condition y(0) = 1, we can substitute x = 0 and y = 1 into the equation to solve for C:
1 = (7/3)(0)³ + 4(0)² - 2(0) + C,
1 = C.
Therefore, the function y is:
y = (7/3)x³ + 4x² - 2x + 1.
Thus, the function y whose derivative is dy/dx = 7x² + 8x - 2 and has a value of 1 when x = 0 is y = (7/3)x³ + 4x² - 2x + 1.
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Amanda has 4 books about reptiles and 12 books about mammals. How many times more books does Amanda have about mammals than about reptiles?
Answers
Answer:
3
Number of books_reptile = 4
number of books_mammals = 12
Number of times more books about mammals than reptile = 12/4
= 3
Answer:
48 books does Amanda about mamals than the reptiles
a firm has two plants(x and y) producing the same product which sells for $12 each. fixed costs are $5,000/year at plant x and $7,000/year at plant y and variable costs are $3.00/unit and $2.00/unit for x and y, respectively. the total profit at x and y are equal when the volume of each plant(units) is: group of answer choices 1,500 2,000 500 none of the above 1,000
Answers
A firm has two plants (X and Y) producing the same product which sells for $12 each. The total profit at plant X and plant Y are equal if the volume of each plant is 2,000 units.
To solve the problem, first translate the given problem into equations.
The formula for profit is:
profit = revenue from sales - total cost
total cost = fixed cost + variable cost
revenue = selling price x number of units sold
Let:
x = the number of units sold in plant X
y = the number of units sold in plant Y
From the problem, we can conclude:
Profit X = profit Y
x = y
Profit X = 12x - (5000 + 3x) (equation 1)
Profit Y = 12 y - (7000 + 2y) (equation 2)
Substitute y = x into equation 2
Profit Y = 12 x - (7000 + 2x)
Hence,
12x - (5000 + 3x) = 12 x - (7000 + 2x)
3x - 2x = 7000 - 5000
x = 2,000
Therefore, total profit at plant X and plant Y are equal if the volume of each plant is 2,000 units.
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Of 32 cars at a show, 18 cars have four-wheel drive, 21 are sports cars and 27 have four-wheel drive or are sports cars. a find the probability that a randomly selected car at the show is both four-wheel drive and a sports car. b find the probability that a randomly selected car at the show is neither four-wheel drive nor a sports car.
Answers
The probability that a randomly selected car at the show is neither four-wheel drive nor a sports car is P((A U B)') = 1 - 27/32
To solve this problem,
we'll use the principles of probability and set theory.
Let's define the following events:
A = Event that a car is four-wheel drive
B = Event that a car is a sports car
Given information,
Number of cars with four-wheel drive (A) = 18
Number of sports cars (B) = 21
Number of cars with four-wheel drive or sports cars (A U B) = 27
Total number of cars at the show = 32
a) To find the probability that a randomly selected car is both four-wheel drive and a sports car (A ∩ B), we can use the formula:
P(A ∩ B) = (Number of cars in A ∩ B) / (Total number of cars)
From the given information, we don't have the exact number of cars that are both four-wheel drive and sports cars. However, we can use the principle of inclusion-exclusion to calculate this probability using the given information.
P(A ∩ B) = P(A) + P(B) - P(A U B)
P(A ∩ B) = (Number of cars in A) / (Total number of cars) + (Number of cars in B) / (Total number of cars) - (Number of cars in A U B) / (Total number of cars)
P(A ∩ B) = 18/32 + 21/32 - 27/32
b) To find the probability that a randomly selected car is neither four-wheel drive nor a sports car, we can use the complement rule. The complement of the event (A U B) is the event of a car not being in A or B, which can be denoted as (A U B)'.
P((A U B)') = 1 - P(A U B)
P((A U B)') = 1 - (Number of cars in A U B) / (Total number of cars)
P((A U B)') = 1 - 27/32
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The probability that a randomly selected car at the show is both four-wheel drive and a sports car is 12/32, or 3/8. The probability that a randomly selected car at the show is neither four-wheel drive nor a sports car is 1/32.
Out of the 32 cars at the show, 18 have four-wheel drive, 21 are sports cars, and 27 have either four-wheel drive or are sports cars. To find the probability that a car is both four-wheel drive and a sports car, we need to determine the number of cars that satisfy both conditions. Since 27 cars have either four-wheel drive or are sports cars, the remaining number of cars that have only four-wheel drive or are only sports cars is 27 - 21 = 6. Therefore, the number of cars that are both four-wheel drive and sports cars is 18 - 6 = 12. The probability is calculated by dividing the number of cars that satisfy both conditions by the total number of cars: \(\frac{12}{32}\), which simplifies to \(\frac{3}{8}\).
To find the probability that a car is neither four-wheel drive nor a sports car, we need to determine the number of cars that do not fall into either category. Since there are 32 cars in total and only 27 have either four-wheel drive or are sports cars, the remaining number of cars that are neither four-wheel drive nor sports cars is 32 - 27 = 5. Therefore, the probability is calculated by dividing the number of cars that do not fall into either category by the total number of cars: \(\frac{5}{32}\).
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determine if the numerical value describes a population parameter or a sample statistic. the average price of a house in the new subdivision is $257,000.
Answers
The numerical value in this sentence, "the average price of a house in the new subdivision is $257,000" describes a Population Parameter.
What is a Population Parameter?A population parameter is a figure that describes a fact about a whole population. In this sentence, we can see that the figure quoted is representative of an entire population. A sample statistic, on the other hand, describes something about a part of a population.
So, for the statement above, we can see that the average price is representative of all the houses in the new subdivision. Thus, the figure is a population parameter.
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Find the sum of the first 11 terms of the series 4 /5+ 1 + 5/4 + .
Answers
Answer:
34.05
Step-by-step explanation:
HELP ANSWER QUICKLY PLS!!!!!
Answers
Answer:
Either B or C, most likely B tho
Step-by-step explanation:
we notice that the units of the covariance make it awkward to interpret. it is clear that if the value is zero, there is no correlation, while a positive value shows some correlation, and a negative value is some anti-correlation. but exactly how much correlation or anti-correlation does the value you calculated entail? the number is not given in mega-parsecs, or kilometers per second, but something entirely different. the sample correlation coefficient addresses this problem by scaling the covariance by its maximum possible value: where we use the unbiased estimate for the covariance on the previous page. what is the maximum possible value of ?
Answers
The sample correlation coefficient (also known as Pearson's correlation coefficient) can have a maximum value of 1.
When the sample correlation coefficient is 1, it indicates that the two variables have a perfect positive linear relationship, which means that as one variable increases, the other variable increases proportionally.
Similarly, when the sample correlation coefficient is -1, it indicates that the two variables have a perfect negative linear relationship, which means that as one variable increases, the other decreases proportionally.
If the sample correlation coefficient is zero, there is no linear relationship between the two variables. The sample correlation coefficient's magnitude indicates the strength of the linear relationship between the two variables, with values closer to 1 or -1 indicating a stronger relationship.
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Derek wants to determine the height of the top of the backbpard on the basketball goal at the playground. He places a standard 12-
inch ruler next to the goal post and measures the shadow of the ruler and the backboard. If the ruler has a shadow of 11 inches and
the backboard has a shadow of 7.5 feet, then about how high is the top of the backboard?
Answers
the actual height of the backboard is 8.18 feet.
What is proportion?A proportion is an equation that sets two ratios at the same value. For instance, you could express the ratio as follows: 1: 3 if there is 1 boy and 3 girls (for every one boy there are 3 girls)
Given
We have been given that Derek places a standard 12-inch ruler next to the goal post and measures the shadow of the ruler and the backboard. If the ruler has a shadow of 10 inches. We are asked t find the height of the backboard, if the backboard has a shadow of 8.5 feet.
We will use proportions to solve our given problem as ratio between sides ruler will be equal to ratio of sides of background.
\(\frac{Actual height of ruler}{Shadow of ruler} = \frac{Actual height of black board}{Shadow of black board} \\\\\frac{12}{11} =\frac{Actual height of black board}{7.5} \\\\Actual height of black board = \frac{12}{11} * 7.5 = 8.18\\\)
Therefore, the actual height of the back-board is 8.18 feet.
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Someone pls help me!!!
Answers
Answer:
1. 32
2. 5
3. 9
4. 3
5. 4.2
6. 5.6
A and B are two events. The notation for conditional probability is P (BIA).
Which statement about the conditional probability is true?
Answers
Answer:
The correct answers was C not A.
Step-by-step explanation:
The true statement about the conditional probability is P(B/A) = \(\frac{P(AandB)}{B}\), when two events are not independent.
What is conditional probability?Conditional probability is a measure of the probability of an event occurring, given that another event has already occurred.
Given that, A and B are two events. The notation for conditional probability is P (B/A).
We know that, formula give for conditional probability is P(B/A) = \(\frac{P(AandB)}{B}\),
Where A and B are non-dependent events.
Since, the events are non-dependent, So it is P(B|A) = P(B) that represents that the occurrence of B does not depend on the occurrence of A.
Hence, The true statement about the conditional probability is P(B/A) = \(\frac{P(AandB)}{B}\), when two events are not independent.
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What is the opposite of -10 located on the number line
Answers
Answer:
uh 10
Step-by-step explanation:
Can anyone give me the answer for X? Plz
Answers
Answer:
x=12
Step-by-step explanation:
Since the triangles are congruent, you can set each equation equal to each other and solve to find x:
11x-70=5x+2
6x-70=2
6x=72
x=12
I hope this helped!
The cost to mail a letter in the United States in 2008 was $0.41 for the first ounce and $0.26 for each additional ounce. The following equation can be used to count the cost for mails based on the weight. C = 0.41 + 0.26 (z - 1). Solve the equation for z.
Answers
The equation for z is z = (C - 0.41) / 0.26 + 1 .
What is the value of z?
In order to determine the value of z, take following steps given this equation: C = 0.41 + 0.26 (z - 1).
Subtract 0.41 from both sides of the equation:
C - 0.41 = 0.26 (z - 1).
Divide both sides of the equation by 0.26
(C - 0.41) / 0.26 = z - 1
Add one to both sides
z = (C - 0.41) / 0.26 + 1
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Consider the plate dealt with in Example 8.1. Plot has a function of the angle of inclination of the plate as the hot side is tilted both upward and downward over the range +90°. Note that you must make do with discontinuous formulæ in different ranges of 0.
Answers
The question refers to the plot of the plate's function of the angle of inclination. When the hot side is tilted both upward and downward over the range of +90°, the discontinuous formulas must be used in different ranges of 0.
It refers to the plot of the function of the angle of inclination of a plate. It is a graph that shows the relationship between the angle of inclination and the plate's function. A plate is tilted on its hot side both upward and downward over a range of +90°. The graph shows that different discontinuous formulas are needed for different ranges of 0. A discontinuous formula refers to a formula that consists of two or more parts, each with a different equation. The two or more parts of a discontinuous formula have different ranges, such that each range requires a different equation. These formulas are used in cases where the same equation cannot be applied throughout the entire range.
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