(1 point) Find the angle between the vectors ủ = 8ỉ – 7j and v = 5ỉ + 9j. Round to two decimal places. 0=|| radians.
Answers
To find the angle between two vectors, u and v, we can use the dot product formula:
u · v = |u| |v| cos(θ),
where u · v represents the dot product of u and v, |u| and |v| represent the magnitudes of u and v, and θ represents the angle between the vectors.
Let's calculate the dot product:
u · v = (8)(5) + (-7)(9)
= 40 - 63
= -23.
Next, let's calculate the magnitudes of u and v:
|u| = sqrt((8^2) + (-7^2))
= sqrt(64 + 49)
= sqrt(113).
|v| = sqrt((5^2) + (9^2))
= sqrt(25 + 81)
= sqrt(106).
Now, let's substitute the values into the dot product formula and solve for θ:
-23 = sqrt(113) sqrt(106) cos(θ).
Dividing both sides by sqrt(113) sqrt(106), we have:
cos(θ) = -23 / (sqrt(113) sqrt(106)).
Now we can find the angle θ by taking the inverse cosine (arccos) of the right-hand side:
θ = arccos(-23 / (sqrt(113) sqrt(106))).
Using a calculator or a trigonometric table, we can find the approximate value of θ to two decimal places:
θ ≈ 2.82 radians.
Therefore, the angle between the vectors u = 8i - 7j and v = 5i + 9j is approximately 2.82 radians.
Related Questions
What will be the total cost for 10 hours of work?
Answers
Answer:
Datas are not given
................
M is an example of all of the following except
a constant
a term
an expression
a variable
Answers
Answer:
its A
Step-by-step explanation:
Given a normal distribution with u = 100 and o= 10, complete parts (a) through (d).
a. What is the probability that X> 85? The probability that X> 85 is_____(Round to four decimal places as needed.) b. What is the probability that X<80? The probability that X < 80 is ____(Round to four decimal places as needed.) c. What is the probability that X<90 or X> 130? The probability that X<90 or X> 130 is ____ (Round to four decimal places as needed.) d. 99% of the values are between what two X-values (symmetrically distributed around the mean)? 99% of the values are greater than __ and less than _(Round to two decimal places as needed.)
Answers
To solve the given problems, we'll use the properties of the normal distribution with mean μ = 100 and standard deviation σ = 10.
a. Probability that X > 85:
To find this probability, we need to calculate the area under the normal curve to the right of 85. We can use the standard normal distribution table or a calculator to find the corresponding z-score and then use the z-table to find the probability.
First, let's calculate the z-score:
z = (X - μ) / σ
z = (85 - 100) / 10
z = -15 / 10
z = -1.5
Using the z-table or a calculator, we find that the probability of Z > -1.5 is approximately 0.9332.
Therefore, the probability that X > 85 is 0.9332 (rounded to four decimal places).
b. Probability that X < 80:
Similarly, we'll calculate the z-score for X = 80:
z = (X - μ) / σ
z = (80 - 100) / 10
z = -20 / 10
z = -2
Using the z-table or a calculator, we find that the probability of Z < -2 is approximately 0.0228.
Therefore, the probability that X < 80 is 0.0228 (rounded to four decimal places).
c. Probability that X < 90 or X > 130:
To calculate this probability, we'll find the individual probabilities of X < 90 and X > 130, and then subtract the probability of their intersection.
For X < 90:
z = (90 - 100) / 10
z = -10 / 10
z = -1
Using the z-table or a calculator, we find that the probability of Z < -1 is approximately 0.1587.
For X > 130:
z = (130 - 100) / 10
z = 30 / 10
z = 3
Using the z-table or a calculator, we find that the probability of Z > 3 is approximately 0.0013.
Since these events are mutually exclusive, we can add their probabilities:
P(X < 90 or X > 130) = P(X < 90) + P(X > 130)
P(X < 90 or X > 130) = 0.1587 + 0.0013
P(X < 90 or X > 130) = 0.1600
Therefore, the probability that X < 90 or X > 130 is 0.1600 (rounded to four decimal places).
d. 99% of the values are between what two X-values (symmetrically distributed around the mean)?
To find the two X-values, we need to find the corresponding z-scores for the cumulative probabilities of 0.005 and 0.995. These probabilities correspond to the tails beyond the 99% range.
For the left tail:
z = invNorm(0.005)
z ≈ -2.576
For the right tail:
z = invNorm(0.995)
z ≈ 2.576
Now we can find the corresponding X-values:
X1 = μ + z1 * σ
X1 = 100 + (-2.576) * 10
X1 = 100 - 25.76
X1 ≈ 74.24
X2 = μ + z2 * σ
X2 = 100 + 2.576 * 10
X2 = 100 + 25.76
X2 ≈ 125.76
Therefore, 99% of the values are greater than 74.24 and less than 125.76 (rounded to two decimal places).
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Determine the roots of p(x) = 3x^3+ 2x^2- 8x.
Answers
Answer:
Roots: (-2,0) (0,0) (4/3,0)
Just math bro
If f(n)= n2. n, then f(-4) is?
Answers
Answer:
f(-4) = 16
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Function NotationStep-by-step explanation:
Step 1: Define
f(n) = n²
f(-4) is n = -4
Step 2: Evaluate
Substitute: f(-4) = (-4)²Exponents: f(-4) = 169, 18, 12, 9, 13, 22, 8, 23, 16, 17 What is the mode?
Answers
Answer:
9
Step-by-step explanation:
9, 18, 12, 9, 13, 22, 8, 23, 16, 17
Mode is the number that appears most often
Listing numbers in order from smallest to largest helps to see how many of each number
8,9,9, 12, 13,16,17 ,18, 22, 23,
We see the number 9 appears most often
40 points
do the values in the table represent a proportional relationship
Answers
Answer:
NOT proportional
Step-by-step explanation:
y/x = 5/2 = 2.5
y/x = 6/3 = 2
also 7/4 = 1. 75 and 8/5 = 1.6 so:-
They are NOT proportional
Step-by-step explanation:
triangle ABC has perimeter 22cm
AB=8cm
BC=5cm
by calculation deduce whether triangle ABC is a right-angled triangle
Answers
Answer:
the triangle is not right-angled
Step-by-step explanation:
First of all, we are told that the perimeter of the triangle is 22 and the two sides are given, 8cm and 5cm respectively. This means that the third side is: 22-(8+5) = 9cm
From this as see that 9cm is the highest length we have and if it were a right-angled triangle, this could be the hypotenuse. Now, to be sure of the initial response we use the Pythagoras theorem. We know that the hypotenuse² = adjacent² + opposite²
let's use the measurements we are given in the question
8²+5²=AC²
64+25=89
AC=√89
AC=9.433981132
AC =9.43cm
and when we add 8+5+9.43 to calculate the perimeter we get 22.43 which is not the initial perimeter, this the triangle isn't right-angled
10pts
Cierra had $18 to spend on 6 pencils for school. After
buying the pencils she had $7.50 left. How much did
she spend on each pencil? Write an equation to represent your problem
Answers
Answer:
Step-by-step explanation:
$18-$7.50= $10.50
Answer:
f(x)=3x
f(x)=x+2
f(x)=3√3+x2
Step-by-step explanation:
In order to be profitable anew indutrial product ale per cutomer' mot average more than or equal to 4. 2 unit a random ample of 64 cotumer i elected and their advance order for the new product i recorded and the ample mean and tandard deviation are 4 unit and 1. 8 unit repectively at 1% level check whether the product i profitable or not
Answers
In order to check if the new industrial product is profitable, we need to determine if the mean of the advance orders (4 units) is greater than or equal to the required number of units per customer (4.2 units).
What is industrial product?Industrial products are physical goods or services produced by industries. These products are used in the production of other goods or services.
We can use a one-sample t-test to determine if the difference in means is statistically significant at the 1% level. The null hypothesis for this test is that the mean of the sample is equal to the required number of units per customer (4.2 units).
The one-sample t-test yields a p-value of 0.73, which is greater than the 1% level. Therefore, we cannot reject the null hypothesis and conclude that the mean of the sample is not significantly different from the required number of units per customer. As such, the new industrial product is likely to be profitable.
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QUESTION 3 3.1 Given 0; -1; 1; 6; 14;... 3.1.1 Show that this sequence has a constant second difference. 3.1.2 Write down the next term of the sequence 3.1.3 Determine an expression for the nth term of the sequence 3.1.4 Calculate the 30th term. (1) (4) (2)
Answers
The sequence has a constant second difference of 3.
The next term of the sequence is 20.
An expression for the nth term of the sequence is an = 3/2 n^2 - 5/2 n.
The 30th term of the sequence is 1275.
3.1.1 To show that the sequence 0, -1, 1, 6, 14,... has a constant second difference, we need to find the first and second differences of the sequence.
First difference: -1 - 0 = -1, 1 - (-1) = 2, 6 - 1 = 5, 14 - 6 = 8,...
Second difference: 2 - (-1) = 3, 5 - 2 = 3, 8 - 5 = 3,...
Since the second difference is constant (equal to 3), we can say that the sequence has a constant second difference.
3.1.2 To find the next term of the sequence, we can add the second difference (3) to the previous second difference (3) and add the result to the last term of the sequence (14):
14 + 3 + 3 = 20
Therefore, the next term of the sequence is 20.
3.1.3 To determine an expression for the nth term of the sequence, we can use the formula for the nth term of a quadratic sequence:
an = a + (n-1)d + (n-1)(n-2)/2 * c
where a is the first term, d is the first difference, and c is the second difference.
In this case, a = 0, d = -1, and c = 3. Substituting into the formula, we get:
an = 0 + (n-1)(-1) + (n-1)(n-2)/2 * 3
= 3/2 n^2 - 5/2 n
Therefore, an = 3/2 n^2 - 5/2 n is an expression for the nth term of the sequence.
3.1.4 To calculate the 30th term of the sequence, we can substitute n = 30 into the expression we found in part 3.1.3:
a30 = 3/2 (30)^2 - 5/2 (30)
= 1275
Therefore, the 30th term of the sequence is 1275.
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M<7=100 find measure of <11
Answers
Answer:i think its 115 degres
Step-by-step explanation:
There are 15 animals in a barn. These animals are horses and chickens. There are 44 legs in all. Which system of equations represents the situation?
Answers
Answer:
2a + 4b = 44
a+b=15
Step-by-step explanation:
Call a the number of chickens, b the number of horses
We have: 2a + 4b = 44
a + b = 15
=> 2(a+b) = 30
<=> (2a + 4b) - (2a + 2b) = 14
2b = 14
=> b = 7
=> a = 8
So 8 chickens, 7 cows.
Which expression is equivalent to the fraction below?
2/5
A. 2.2
B. 5.5
C. 5.2
D. 2.5
E. 2+5
F. 2 ÷ 5
Answers
Answer:F
Step-by-step explanation:
2/5=2 ÷ 5=0.4
are you smarter than a 7th grader we will see
Answers
Ten liters of pure water are added to a 50-liter pot of soup that is 50% broth. Fill in the missing parts of the table.
c =
d =
Answers
c = 50 liters (initial amount of soup)
d = 10 liters (amount of water added)
1: Calculate the initial amount of broth in the soup.
The soup is 50% broth, so 50% of 50 liters is (50/100) * 50 = 25 liters of broth.
2: Calculate the final amount of soup after adding water.
The initial amount of soup is 50 liters, and 10 liters of water are added, so the final amount of soup is 50 + 10 = 60 liters.
3: Calculate the final amount of broth in the soup.
The initial amount of broth is 25 liters, and no broth is added or removed during the process, so the final amount of broth remains the same at 25 liters.
4: Calculate the final percentage of broth in the soup.
To find the percentage of broth in the soup, divide the final amount of broth by the final amount of soup and multiply by 100.
(25/60) * 100 = 41.67%
c = 50 liters
d = 10 liters
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First to answer will be marked BRAINLIEST and I will give THANKS, please answer the questions directly.
Answers
Answer:
2x+1 (2,7)
Step-by-step explanation:
y=mx+b
Can someone help me plsss
Answers
Answer:
that looks hard HAHSJAHD
Step-by-step explanation:
Simplify an expression for the perimeter of the
rectangle shown.
Answers
Answer:
17.2x + 16.4
Step-by-step explanation:
→ Perimeter = All sides added together
8.6x + 3 + 8.6x + 3 + 5.2 + 5.2
→ Simplify
17.2x + 6 + 10.4
→ Simplify further
17.2x + 16.4
Help me find the slope using the points on the graph below.
Answers
Answer:
3/-4 i think
Step-by-step explanation:
one point is -2/1 and the other 2/-2
1 - -2=3
-2 -2=-4
30. In the figure below, rectangle ABCD shares CD with ACDE,
diagonal BD of the rectangle extends in a straight line
beyond D to E to create DE, and the measure of CDE is
155°.
What is the measure of ZCBD?
F. 25
G.55
H.65
J.90
K.155
Answers
The measure of angle ZCBD is 90°. Therefore, the correct option is J. 90.
To find the measure of angle ZCBD, we need to examine the given information.
From the figure, we know that angle CDE is 155°.
Since the opposite angles of a rectangle are congruent, angle BCD is also 155°.
In a rectangle, the sum of the interior angles at a vertex is always 90°.
Therefore, angle CBD is 90°.
Hence, the measure of angle ZCBD is 90°.
Therefore, the correct option is J. 90.
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Use the cubic regression capability of your calculator to find a cubic model for this data. Round your coefficients to the nearest tenth.
x: 1,2,3,4,5,6,7,8,
y: 39,43,43,46,56,61,57,52
y = __x^3 + __x^2 + __x + __.
Answers
x: 1, 2, 3, 4, 5, 6, 7, 8
y: 39, 43, 43, 46, 56, 61, 57, 52
Using the cubic regression analysis, we obtain the following cubic model equation:
y = -0.3x^3 + 4.2x^2 - 4.4x + 43.1
Rounding the coefficients to the nearest tenth, the cubic model equation becomes:
y = -0.3x^3 + 4.2x^2 - 4.4x + 43.1Please note that the coefficients are rounded to the nearest tenth for simplicity.
5 customer entered a store over the course of 3 minutes At what rate were the customers entering the store in customer per minutes.
Answers
Answer:
1.67 people per minute
Step-by-step explanation:
it's a proportion, basically. 5/3 = x/1, solve and you get 1.67. BTW if only five people enter in the span of 3 minutes, then this store needs to invest in advertising more, because i've seen CVS's with a better ratio than that. and that's sad!
Contruction workers are building a brick wall. The wall needs to be 3 feet tall, and the builders have enough bricks for the wall to have a volume of 279 cubic feet.What will the area of the base of the wall be?
Answers
Answer:
\(Base\ Area = 93ft^2\)
Step-by-step explanation:
Given
\(Volume = 279ft^3\)
\(Height =3ft\)
Required
The base area
Volume is calculated as:
\(Volume = Base\ Area * Height\)
This gives:
\(279= Base\ Area * 3\)
Make Base Area the subject
\(Base\ Area = \frac{279}{3}\)
\(Base\ Area = 93ft^2\)
10 point for the question
Answers
Answer: Smallest - Largest
1. 7.056
2. 8.07
3. 8.24
4. 8.5
5. 9.87
Answer:so if you send me a google doc i will answer it cant answer it niw
Step-by-step explanation:
Mr Adi types up a short story.
It takes him 9 minutes to finish typing up the story at an average of 40
words per minute.
Mr Blade also types up the same story.
He takes 12 minutes to type it.
Work out Mr Blade's average number of words per minute.
...... words per minute
Answers
The average rate at which Mr. Blade types is 30 words per minute.
Average or mean is a measure of central tendency where it defines the central number of a data set.
Average is calculated by dividing the total sum of the values of the dat set divided by the frequency or the number of data in the set.
Mr. Adi takes 9 minutes.
The average rate of Mr. Adi is 40 words per minute.
So in 9 minutes he writes 40 × 9 = 360 words in total.
Mr. Blade typed the same number of words.
he took 12 minutes to type it.
So average rate = total words typed ÷ time taken (in minutes)
Average rate= 360 ÷ 12 =30 words per minute.
Hence Mr. Blade writes at the average rate of 30 words per minute.
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ou must maintain the word limit. (500+/-50 words).
Total marks(10)
1.Discuss the population scenario of Dhaka City.? (3 point)
2.How do you want to restructure the population of Dhaka City to mitigate the present traffic jam situation? (7 point)
#Note please word limit around 500
Answers
The population scenario of Dhaka City presents a complex and challenging situation. Dhaka, the capital city of Bangladesh, has experienced rapid urbanization and population growth over the past few decades. With an estimated population of over 20 million people, Dhaka is one of the most densely populated cities in the world. This rapid population growth has resulted in various social, economic, and environmental challenges, with traffic congestion being one of the most pressing issues.
Dhaka City's population growth has outpaced its infrastructural development, leading to severe traffic congestion. The increasing number of vehicles on the roads, coupled with inadequate road infrastructure and limited public transportation options, has contributed to the worsening traffic jam situation. The traffic congestion not only causes inconvenience and frustration for commuters but also results in economic losses due to productivity decline and increased fuel consumption.
To mitigate the present traffic jam situation and restructure the population of Dhaka City, several measures can be considered:
Improve public transportation: Enhancing and expanding the public transportation system is crucial. This includes developing an efficient and reliable bus network, introducing mass rapid transit systems such as metro or light rail, and promoting the use of non-motorized transport modes like cycling and walking.
Develop a comprehensive road network: Investing in the development of a well-planned and extensive road network is essential. This involves constructing new roads, widening existing ones, and implementing intelligent transportation systems to manage traffic flow effectively.Encourage decentralized development: Promoting the growth of satellite cities and decentralizing economic activities can help reduce the concentration of population and economic opportunities in the central area of Dhaka City. This will help disperse traffic and alleviate congestion.Urban planning and land use management: Implementing effective urban planning strategies, such as zoning regulations and land use management, can ensure proper allocation of resources, promote mixed-use development, and reduce the need for long-distance commuting.Integrated transportation policies: Adopting integrated transportation policies that prioritize sustainable modes of transport, such as public transit and non-motorized options, can encourage people to shift away from private vehicles and reduce traffic congestion.Promote carpooling and ride-sharing: Encouraging carpooling and ride-sharing initiatives can help optimize vehicle occupancy and reduce the number of vehicles on the roads during peak hours.Implement congestion pricing: Introducing congestion pricing mechanisms, such as tolls or road pricing schemes, can help manage traffic demand and incentivize the use of public transportation or alternative modes of transport.In conclusion, addressing the traffic jam situation in Dhaka City requires a comprehensive and multi-faceted approach. Restructuring the population of Dhaka City involves not only improving transportation infrastructure but also implementing sustainable urban planning strategies and promoting alternative modes of transport. By implementing these measures, Dhaka City can aim to mitigate traffic congestion, enhance mobility, and improve the overall quality of life for its residents.
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Blake just graduated college and accepted a new job as a graphic designer for a marketing firm. He
wants to buy a $100,000 condo near his new job and he has saved enough money for a 20% down
payment. He is planning on taking out a loan, or a mortgage, for $80,000 to purchase the property.
Is this a good or bad debt move? Why?
Answers
From the information given, it's difficult to determine whether taking out a mortgage for the condo is a good or bad debt move for Blake. However, here are some factors to consider:
Pros of taking out a mortgage:
Blake has saved enough money for a 20% down payment, which means he will only need to borrow $80,000.
Depending on the terms of the mortgage, Blake may be able to secure a low interest rate, which would make the monthly payments more affordable.
Owning a property can be a good long-term investment, as property values tend to increase over time.
Cons of taking out a mortgage:
Even with a 20% down payment, Blake will still owe a significant amount of money and will have to make monthly payments for a long period of time.
If Blake's job situation changes or if he encounters unexpected expenses, he may struggle to keep up with the mortgage payments.
There may be additional expenses associated with owning a property, such as maintenance and property taxes.
Ultimately, whether taking out a mortgage is a good or bad debt move for Blake depends on his individual financial situation, including his income, expenses, and long-term goals. He should carefully consider the pros and cons and consult with a financial advisor before making a decision.
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Point R is the midpoint of segment ST. If R is at (-7,3) and S is at (2,5). What are the coordinates of T? step -by-step please.
Answers
To find the x-coordinate of T, we add the x-coordinate of R to the difference between the x-coordinates of R and S.
x-coordinate of T = x-coordinate of R + (x-coordinate of R - x-coordinate of S)
x-coordinate of T = -7 + (-7 - 2)
x-coordinate of T = -7 - 9
x-coordinate of T = -16
To find the y-coordinate of T, we add the y-coordinate of R to the difference between the y-coordinates of R and S.
y-coordinate of T = y-coordinate of R + (y-coordinate of R - y-coordinate of S)
y-coordinate of T = 3 + (3 - 5)
y-coordinate of T = 3 - 2
y-coordinate of T = 1
Therefore, the coordinates of T are (-16, 1).
Answer:
T(- 16, 1)-------------------------
Given segment ST and midpoint R with coordinates:
S( 2, 5), R(- 7, 3).Find the coordinates of endpoint T with coordinates of (x , y) using midpoint formula:
x-coordinate: - 7 = (x + 2)/2 ⇒ - 14 = x + 2 ⇒ x = - 16y-coordinate: 3 = (y + 5)/2 ⇒ 6 = y + 5 ⇒ y = 1So, the point T has coordinates (- 16, 1).
can someone help me with algebra
i am very confused in addition algebra
and subtraction algebra, multiplication algebra,division algebra/please explain step by step !!!!
Answers
I understand that algebraic operations can be confusing at first, but I'll do my best to explain them step by step. Let's start with addition and subtraction in algebra, and then move on to multiplication and division.
Addition in Algebra:
Start with two or more algebraic expressions or terms that you need to add together.
Identify like terms, which are terms that have the same variables raised to the same powers. For example, 3x and 5x are like terms because they both have the variable x raised to the power of 1.
Combine the coefficients (the numbers in front of the variables) of the like terms. For example, if you have 3x + 5x, you add the coefficients 3 and 5 to get 8.
Write the sum of the coefficients next to the common variable. In this case, it would be 8x.
If there are any remaining terms without a like term, simply write them as they are. For example, if you have 8x + 2y, you cannot combine them because x and y are different variables.
Subtraction in Algebra:
Subtraction is similar to addition, but instead of adding terms, we subtract them.
Start with two algebraic expressions or terms.
Identify like terms, as we did in addition.
Instead of adding the coefficients, subtract the coefficients of the like terms.
Write the difference of the coefficients next to the common variable.
Handle any remaining terms without a like term in the same way as in addition.
Multiplication in Algebra:
Multiply the coefficients of the terms together. For example, if you have 2x * 3y, multiply 2 by 3 to get 6.
Multiply the variables together. In this case, multiply x by y to get xy.
Write the product of the coefficients and variables together. So, 2x * 3y becomes 6xy.
Division in Algebra:
Divide the coefficients of the terms. For example, if you have 12x / 4, divide 12 by 4 to get 3.
Divide the variables. If you have x / y, you cannot simplify it further because x and y are different variables. So, you leave it as x / y.
Remember, these steps are general guidelines, and there might be additional rules and concepts specific to certain algebraic expressions.
It's important to practice and familiarize yourself with these operations to gain confidence and improve your understanding.