The vector u has length 10 and points at an angle of 5°
The vector has length 16 and points at an angle of 25°
Answers
The dot product between u and v is 150.35 units²
What is dot productIn the problem given;
u = 10cos5
v = 16cos25
To find the dot product of two vectors, we need to find the product of the magnitude of the vectors and the cosine of the angle between them. Let's call the angle between the vectors θ.
The dot product of u and v is given by:
u•v = |u| * |v| * cos(θ)
where |u| and |v| are the magnitudes of vectors u and v. We are given the magnitudes of the vectors, which are |u| = 10 and |v| = 16.
To find cos(θ), we need to use the dot product formula with the given angle values:
cos(θ) = (u•v) / (|u| * |v|) = (|u| * |v| * cos(θ)) / (|u| * |v|)
Since u and v are both vectors in 2-dimensional space, we can use the law of cosines to find the angle between them:
cos(θ) = (u•v) / (|u| * |v|) = (u1 * v1 + u2 * v2) / (|u| * |v|)
where u1 and u2 are the components of vector u and v1 and v2 are the components of vector v.
To find the components of the vectors, we need to use the given angle values and the magnitudes of the vectors:
u1 = |u| * cos(5°) = 10 * cos(5°)
u2 = |u| * sin(5°) = 10 * sin(5°)
v1 = |v| * cos(25°) = 16 * cos(25°)
v2 = |v| * sin(25°) = 16 * sin(25°)
Substituting these values into the formula for cos(θ), we get:
cos(θ) = (u1 * v1 + u2 * v2) / (|u| * |v|) = (10 * cos(5°) * 16 * cos(25°) + 10 * sin(5°) * 16 * sin(25°)) / (10 * 16)
θ = 20°
u.v = 10 * 16 * cos 20
u.v = 150.35
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Related Questions
if m+1 is an even integer, which one of the flollowing must be add integer?
Answers
If m + 1 is an even integer, then 2m + 1 is an odd integer.
What do you understand by even and odd numbers?Even number: An even number is a number that is a multiple of 2. It can be said that any number that is completely divisible by 2 is an even number.
Odd number: Odd numbers are those numbers that are not completely divisible by 2.
let us understand by addition on different combinations of odd numbers and even numbers.
Odd number + Odd number = Even number
Even number + Even number = Even number
Even number + Odd number = Odd number
Odd number + Even number = Odd number
In subtraction
Even number - Even number = Even number
Even number - Odd number = Odd number
Odd number - Even number = Odd number
Odd number - Odd number = Even number
In multiplication
Even number × Even number = Even number
Even number × Odd number = Even number
Odd number × Odd number = Odd number
Given:
m + 1 is an even integer.
since alternate numbers are even.
Therefore, m must be an odd number.
If m is odd, then m - 1 is even.
2m is divisible by 2, so it is always an even number.
So,
2m - 2 is even.
2m + 1 is odd.
2m + 2 is even.
Since 2m + 1 is an odd number.
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1. what is the last name of whom we honor for discovering ways to express and minimize logic though a new but similar form of algebra? 2. what does the k in k-map stand for? 3,4,5,
Answers
Boole. K-map stands for Karnaugh Map and is used to simplify and minimize the expression of logic in a similar form to algebra.
George Boole is the mathematician we honor for discovering ways to express and minimize logic through a new but similar form of algebra. The technique used to simplify and minimize these expressions is known as a Karnaugh Map, or K-map for short. A K-map is a visual representation of a Boolean expression using squares and circles to represent true or false variables in a table. By arranging the variables in the table, the same logic can be expressed in a simpler form with fewer variables. This allows for a simpler and more efficient form of logic expression. K-maps are used in many fields, such as digital logic design, where the efficiency of expression is important.
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Find the indicated IQ score. The graph to the right depicts IQ scores of adults, and those scores are normally distributed with a mean of 100 and a standard deviation of 15.
The indicated IQ score, x, is enter your response here. (Round to one decimal place as needed.)
Answers
The indicated IQ score is given as 117.
How to solve for the IQ scoreThe area under the curve is given as 0.1431
the area to the left of x = 1 - 0.1431
= 0.8569
for 0.8569 the z stat is 1.07
u = 100
sd = 15
x = u + z * sd
= 100 + 0.8569 * 15
= 116.05
approximately 117
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Find the indicated IQ score. The graph to the right depicts IQ scores of adults, and those scores are normally distributed with a mean of 100 and a standard deviation of 15.
xx
0.1431
A symmetric bell-shaped curve is plotted over a horizontal scale. A vertical line runs from the scale to the curve at labeled coordinate x, which is to the right of the curve’s center and peak. The area under the curve to the right of the vertical line is shaded and labeled 0.1431.
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An observer in watertown, new york, would see the star polaris at an altitude of approximately. ?
44°
45°
75°
76°
Answers
Answer:
44
Step-by-step explanation:
If a²=b+c,b² = c+a and c² = a +b, prove that: (1/a+1)+(1/b+1)+(1/c+1)=1
Answers
The proof is as shown below
How to prove that 1/(a+1) + 1/(b+1) + 1/(c+1) = 1?Trigonometry is a branch of mathematics dealing with the relationship between the ratios of the sides of a right-angled triangle with its angles.
If a² = b + c , b² = c + a and c² = a + b
We want to prove that 1/(a+1) + 1/(b+1) + 1/(c+1) = 1
Since a² = b + c
a²+a = a + b + c
a (a+1) = a + b + c
a+1 = (a + b + c)/a
Repeat the same process for b² = c + a and c² = a +b, we have:
1 + b= (a + b + c)/b
1 + c =(a + b + c)/c
Substitute the values 1+a, 1+b and 1+c into 1/(a+1) + 1/(b+1) + 1/(c+1):
1/(a+1) + 1/(b+1) + 1/(c+1) = a/(a+b+c) + b/(a+b+c) + c/(a+b+c) (Taking LCM)
= (a+b+c )/ (a+b+c ) = 1
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question 2
help me plsssss
Answers
Answer:
∠ CAB = 144°
Step-by-step explanation:
the central angle CAB is twice the measure of ∠ BDC , that is
∠ CAB = 2 × 72° = 144°
You and your friend could go to Theater X and each buy an adult ticket, drink, and popcorn, or you and your friend
could rent a video for $3.50, buy a 2 liter of cola for $1.60, and a bag of microwave popcorn for $1.98.
Which situation costs less and by how much?
Answers
The second situation costs less by
$16.92How to know the situation that cost lessThe cost of the first situation is
Adult = 8 * 2 = 16
drink = 2 * 2 = 4
popcorn = 2 * 2 = 4
Total = $24
Second situation
rent a video = $3.50
buy a 2 liter of cola = $1.60
a bag of microwave popcorn = $1.98.
Total = $7.03
The second situation costs less by
$24 - $7.03
= $16.92
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do the data provide convincing statistical evidence, at the level of , that the preferences are different between the two regions of the country? complete the appropriate inference procedure to support your answer.
Answers
The corresponding p-value for this test statistic is 0.005, which is smaller than our significance level of α=0.05.
To begin, we define the population proportion of people who shop for groceries online in region A as p₁ and the population proportion of people who shop for groceries online in region B as p₂.
Our null hypothesis is that there is no difference in these proportions, which we can write as H0=> p₁ = p₂. Our alternative hypothesis is that there is a difference, which we can write as H1=> p₁ ≠ p₂.
Next, we need to calculate the sample proportions and standard errors for each region. We can do this using the formulas:
p₁ = x₁/n₁, p₂ = x₂/n₂
where x₁ and x₂ are the number of people in each sample who shop for groceries online, and n₁ and n₂ are the sample sizes. The standard errors are given by:
=> SE₁ = √(p₁(1-p₁)/n₁),
=> SE₂ = √(p₂(1-p₂)/n₂)
Using the given data, we find that p₁ = 0.16, p₂ = 0.24, SE₁ = 0.037 and SE₂ = 0.042.
We can now calculate the test statistic, which measures the difference between the sample proportions under the assumption that the null hypothesis is true. We use the formula:
z = (p₁ - p₂) / √(SE₁² + SE₂²)
Substituting the values we calculated, we get:
z = (0.16 - 0.24) / √(0.037² + 0.042²) = -2.83
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Complete Question:
A random sample of 100 people from region A and a random sample of 100 people from region B were surveyed about their grocery-shopping habits. From the region A sample, 16 percent of the people indicated that they shop for groceries online. From the region B sample, 24 percent of the people indicated that they shop for groceries online. At the significance level of α=0.05, do the data provide convincing statistical evidence that there is a difference between the two regions for the population proportions of people who shop online for groceries? Complete the appropriate inference procedure to support your answer.
Write the number for three million twenty thousand
Answers
Answer: 3,020,000
Step-by-step explanation:
three million twenty thousand
Answer: 3,020,000
Step-by-step explanation: 3,000,000 + 20,000 = 3020000
La fábrica tiene 300 obreros de los cuales 2/3 son hombres. 3/3 trabajadores por la mañana, 1/2 son sindicalizado y 1/6 son personal de confiancia. ¿Cuántos hombres trabajan en la fábrica?_________ ¿Y cuántas mujeres?_______ ¿Cuántos hobreros trabajan por la mañana?__________ ¿Cuántos son sindicalizados?______________ ¿Cuántos son de confianza? AYUDA ES PARA MAÑANA SINO MIS PADRES ME MATAS AYUDA
Answers
From the total of 300 workers in the factory :
a. Number of men = 200 and Women = 100
b. Number of workers works in the morning = 225
c. Number of workers unionized are 150.
d. Number of workers trustworthy are 50.
Total number of workers in the factory are 300.
a. Fraction of men in the factory are ( 2/3)
= 2/3 of 300
= 200
Women
= 300 -200
= 100
b. Number of workers in the morning shift are
= 3/4 of 300
= 225
c. Total number of workers unionized
= 1/ 2 of 300
= 150
d. Number of trustworthy workers
= 1/6 of 300
= 50
Therefore, out of 300 workers in the factory answer of the following questions are:
a. Number of men and women work in the factory are 200 and 100 respectively.
b. Number of workers works in the morning is 225.
c. Unionized workers = 150
d. Trustworthy workers = 50.
The above question is incomplete , the complete question is :
The Factory has 300 workers of which 2/3 are men, 3/4 work in the morning, 1/2 are unionized and 1/6 are trusted personnel.
a. How many men work in the factory and how many women?
b. How many workers work in the morning?
c. How many are unionized?
d. How many are trustworthy?
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calculate the area of a rectangle in cm2 with a width of 7.6 cm and height of 3.3 cm. be sure to include the proper number of significant figures.
Answers
The width and height are given to one decimal place, and we have multiplied them together, the answer should be rounded to one decimal place. Therefore, the area of the rectangle is 25.1 cm²
To calculate the area of a rectangle, we need to multiply its width by its height.
The size of a patch on a surface is determined by its area. Surface area refers to the area of an open surface or the boundary of a three-dimensional object, whereas the area of a plane region or plane area refers to the area of a form or planar lamina. Area can be interpreted as the quantity of material with a specific thickness required to create a model of the shape or as the quantity of paint required to completely cover the surface in a single coat.
Area = width x height
Substituting the given values, we get:
Area = 7.6 cm x 3.3 cm
Area = 25.08 cm²
Since the width and height are given to one decimal place, and we have multiplied them together, the answer should be rounded to one decimal place. Therefore, the area of the rectangle is 25.1 cm² (rounded to one decimal place).
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Helppppppppppp meeeeee guyssssssss
Answers
Answer:
2. $9.99
3. 45 tickets for $27
4. 20 cents
Step-by-step explanation:
2. 79.92/8 = 9.99
3. 27/45 0.6 and 15/20 = 0.75 and 60 cents is less than 75 cents
4. 6/30 = 20
Answer:
Step-by-step explanation:
79.92/8= 9.12 per cd
15/20= .75
27/45=.6 better deal because it is .60 cents per ticket
6/30= .20 per can
The price of a Loungy Chair was $400. The price of this chair has just gone up by 20%. Make a percent table to find the new price of the Loungy Chair
Answers
The percent table is:
100 % ⇒ $400
120 % ⇒ $480
The initial price of the Loungy chair was $400.
So, the initial price(P₀) = $400
The price of the chair has gone up by 20%
So, increase in price(r) = 20%
The final price will be calculated by using the formula:
P = P₀(1 + r/100) (where P is the final price)
P = 400(1 + 20/100)
P = 400(1 + 0.2)
P = 400 × 1.2
P = $480
Hence, the final price of the Loungy chair is $480
Percent table:
100 % ⇒ $400
120 % ⇒ $480
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70% of ____ is 14.
O 10
O 20
O 30
O 50
Answers
Answer:
20
Step-by-step explanation:
snajakskdmcjwiwjcjf
Answer:
20
Step-by-step explanation:
70% is 70/100 = 0.70
20 x 0.70 = 14
how do you do it please help
Answers
Answer:
5.1
Step-by-step explanation:
11.5 + 5.6 + 8.8 = 29.5
31 - 29.5 = 5.1
5. A Set of Speakers costs $35 and Songs cost $195 each. The sales tax
rate is 8.25%. The expression 0.0825(35+ 195s) can be used to determine
the amount of sales tax due on the entire purchase of a set of Speakers
and S.Songs. Expand the expression and round to the nearest hundredth.
Answers
The amount of sales tax due on the entire purchase of a set of speakers and s songs is $2.89 plus $16.09 for each song purchased, rounded to the nearest hundredth.
What is an expression?
In mathematics, an expression is a combination of numbers, variables, and/or operators that represents a mathematical quantity or relationship. It can be a single number or variable, or a combination of multiple numbers, variables, and operators.
The given expression 0.0825(35+195s) represents the amount of sales tax due on the entire purchase of a set of speakers and s songs, where s is the number of songs purchased.
Expanding the expression, we get:
0.0825(35+195s) = 0.0825(35) + 0.0825(195s)
= 2.8875 + 16.0875s
Rounding this expression to the nearest hundredth, we get:
2.89 + 16.09s
Therefore, the amount of sales tax due on the entire purchase of a set of speakers and s songs is $2.89 plus $16.09 for each song purchased, rounded to the nearest hundredth.
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how do i do these types of problems?
Answers
Answer:
1/24.
Step-by-step explanation:
There are 2 events here and they are independent, so the single probabilities are multiplied.
P(4 when die is rolled) = 1/6
P(A on the spinner) = 1/4
So, P(4 and A)
= 1/6 * 1/4
= 1/24.
what ratios are equivalent to 6 : 3?
Answers
Answer: 12: 6 and 24: 12 and 3: 1.5
Step-by-step explanation: A ratio can be equivalent through multiplication such as 6: 3 to 12: 6
Answer:
2 : 1,
12/
Step-by-step explanation:
all you have to do is cross out the numbers, basically simplify the
the answer is 2:1 because in 3's multiplication table,
3×2=
and
3×1=
similarly , for 12/6, divide instead of multiplication, there area few other ratios equivalent to 6/
200$ marked down 20% now increased by 20% is it equal to 200 again?
Answers
Answer: nope
Step-by-step explanation:
No, the 200$ marked down 20% would be 200 - 0.2 * 200 = 160$. Then, if it is increased by 20%, it would be 160 + 0.2 * 160 = 192$. So, 200$ is not equal to 192$.
help
(5th-grade math)
Answers
Answer: equation: 3/5 * 5/8 = 38 = 0.375
Spelled result in numbers/words is three eighths/ 3/8.
Step-by-step explanation:
the basketball field takes up 3/8 of the playground
3/5 * 5/8 = 38 = 0.375 = 3/8
then (simplify) 0.375 into a fraction.
3/5 * 5/8 = 38 = 3/8
Answer:
Equation: 3/8 * 5/8
Answer:3/8
Step-by-step explanation:
Equation: 3/5 * 5/8. Since it is 5/8 of 3/5, you can do 3/5 * 5/8.
Answer: 3/8. Since 3/5 * 5/8 = 3/8, the answer will be 3/8
Please help, I’ll give brainliest
Answers
Answer: Distributive property and Commutative property (of multiplication)
Step-by-step explanation:
From 1 to 2, the parentheses coefficient is multiplied out to the parentheses. This is called distribution.
From 2 to 3, the numbers in each multiplication are rearranged. This would be the commutative property of multiplication.
HOPE THIS HELPS _- MM
I NEED HELP PLEASEEEE!!!!
Answers
Answer:
Step-by-step explanation:
the answer is 420 cuase the manufatcure of math is hard i wont give an explanation.
mr hall is doggie-paddling in the school pool at a speed of 1 m/sec when he spots his favorite rubber ducky. He increases his speed to 3m/sec over a period of 3 seconds. What is Mr. Halls acceleration?
Answers
Answer:
1m/sec
Step-by-step explanation:
Mr. Hall spent 3 seconds to increase his speed to 3m/sec increasing 1m/sec, don't over think it.
Select the correct answer.
Which graph is the graph of f(x) = 3 log2 (x +1)?
Answers
The graph of the equation of function f (x) = 3 log₂ (x + 1) is shown in figure.
What is mean by Function?A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
Given that;
The equation of function is,
⇒ f (x) = 3 log₂ (x + 1)
Now, By using tool we can draw the graph of the equation of function
f (x) = 3 log₂ (x + 1) as shown in figure.
Thus, The graph of the equation of function f (x) = 3 log₂ (x + 1) is shown in figure.
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The mean height of the students in Juan's math class is equal to the mean height of the students in his English class. However, while the standard deviation of the heights of students in his math class is 3.2 inches, the standard deviation of the heights of students in his English class is 6.1 inches. Which of the following statements must be true?
A) The mean height of the students in Juan's English class is 2.9 inches greater than the mean height of the students in his math class.
B) The median height of the students in Juan's English class is 2.9 inches greater than the median height of the students in his math class.
C) The median height of the students in Juan's math class is 2.9 inches greater than the median height of the students in his English class.
D) The heights of the students in Juan's math class are less variable than the heights of the students in his English class.
Answers
Answer: The statement "The mean height of the students in Juan's math class is equal to the mean height of the students in his English class" means that the center or average of both groups is the same. However, the statement "the standard deviation of the heights of students in his math class is 3.2 inches, the standard deviation of the heights of students in his English class is 6.1 inches" implies that the heights of the students in the English class are more spread out than the heights of the students in the math class.
Therefore, the answer is:
D) The heights of the students in Juan's math class are less variable than the heights of the students in his English class.
Step-by-step explanation:
1) Write the equation of the line passing through point P with slope m, if
a) P(1,4) and m = 3
c) P (3,0) and m = −1
b) P(-1,-2) and m = 4
d) P(0,0) and m = -5
Answers
Answer:
a) y - 4 =3(x - 1)
b) y + 2 = 4(x+ 1)
c) y = -(x - 3)
d) y = -5x
Step-by-step explanation:
You did not say which form, so I put them in the point-slope form of a line that follows the pattern:
y - [tex]y_{1}[/tex] = m( x - [tex]x_{1}[/tex])
Answer:
see explanation
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
(a)
given m = 3 , then
y = 3x + c ← is the partial equation
to find c substitute (1, 4 ) into the partial equation
4 = 3(1) + c = 3 + c ( subtract 3 from both sides )
1 = c
y = 3x + 1 ← equation of line
(b)
given m = 4 , then
y = 4x + c ← is the partial equation
to find c substitute (- 1, - 2 ) into the partial equation
- 2 = 4(- 1) + c = - 4 + c ( add 4 to both sides )
2 = c
y = 4x + 2 ← equation of line
(c)
given m = - 1 , then
y = - x + c ← is the partial equation
to find c substitute (3, 0 ) into the partial equation
0 = - 3 + c ( add 3 to both sides )
3 = c
y = - x + 3 ← equation of line
(d)
given m = - 5 , then
y = - 5x + c ← is the partial equation
to find c substitute (0, 0 ) into the partial equation
0 = - 5(0) + c = 0 + c ⇒ c = 0
y = - 5x ← equation of line
Sara can read 19 pages an hour. How many pages can Sara read in 95 min? Round to the nearest whole number.
Answers
Sara can read about 30 pages in 95 minutes.
What does per hour mean?To start, multiply the weekly hours by the number of weeks in a year to get the overall number of hours worked (52). Then subtract this amount from the annual pay. For instance, if a worker earns $50,000 annually and puts in 40 hours per week, their hourly rate would be $50,000/2,080 (40 x 52) = $24.04.
Accordion to question:First, we need to convert 95 minutes to hours by dividing by 60:
95 min ÷ 60 min/hour = 1.5833 hours (rounded to 4 decimal places)
Next, we can use the conversion factor to find the number of pages Sara can read in 1.5833 hours:
19 pages/hour x 1.5833 hours = 30.1391 pages
Rounding to the nearest whole number, Sara can read about 30 pages in 95 minutes.
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when running Chao has a stride length of 70cm,correct to the nearet 5cm.
Chao runs a distance of 11.2 km, correct to the nearest 0.1km
work out the minumum number of stride that Chao could take to complete this distance
Answers
The minimum number of strides that Chao could take to complete a distance of 11.2 km is approximately 16,000.
What is simplification?The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
To calculate the minimum number of strides that Chao could take to complete a distance of 11.2 km, we need to first convert the distance to meters since the stride length is given in centimeters.
11.2 km = 11,200 meters (1 km = 1000 meters)
Stride length in meters = 70 cm / 100 cm/m = 0.7 m
Now, we can calculate the minimum number of strides as follows,
Minimum number of strides = (Distance covered in meters) / (Stride length in meters)
Minimum number of strides = 11,200 m / 0.7 m ≈ 16,000
Therefore, the minimum number of strides that Chao could take to complete a distance of 11.2 km is approximately 16,000.
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the foreign language club is showing a four-movie marathon of subtitled movies. how many ways can they choose from the available?
Answers
The number of ways the foreign language club can choose 4 movies from the available is [tex]nC4 = n! / 4!(n-4)![/tex].
To calculate the number of ways the foreign language club can choose four movies from the available subtitled movies, we need to use the combination formula, which is:
[tex]nCr = n! / r!(n-r)![/tex]
Where n is the total number of available subtitled movies and r is the number of movies to choose (in this case, r=4).
Assuming there are at least four subtitled movies available, the number of ways to choose four movies would be:
[tex]nC4 = n! / 4!(n-4)![/tex]
Simplifying the equation further, we have:
[tex]nC4 = (n * (n-1) * (n-2) * (n-3)) / 4 * 3 * 2 *1[/tex]
Therefore, the number of ways the foreign language club can choose four movies from the available subtitled movies is given by the formula nC4.
The formula calculates the number of possible combinations of four movies that can be selected from the total number of available subtitled movies, without regard to the order in which they are shown.
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Which situation most accurately matches the graph?
Answers
A
im going to guess that the top of the graph has a flat line.
its easy to visualize since the graph looks like a hill, and the story describes the graph the most accurately
