Find the modulus and the unit vector along the sum of the vectors. - r₁ +r₂ +r3 given that r₁ = 2i+j+4k - r₂ = 3i-2j+7k, r3 = 5i + 2j - 3k. 2​

Answer:

(c) y = 3x - 16 or y - 2 = 3(x - 6)

Step-by-step explanation:

To be perpendicular, the slope must be the negative inverse of the other line,

so we know the slope must be -(-3/1) = 3

then the general point-slope form is

y = mx + b (m = slope and b = y-intercept) so

y = 3x + b (then use the point given (6,2) to find m)

2 = 3(6) + b

2 = 18 + b

2 - 18 = b

-16 = b

then

y = mx + b

y = 3x - 16

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about 45%

Answer:

for me I think a numerical expression

The mathematical phrase 5 + 2 x 18 is an example of an arithmetic expression.

In arithmetic expressions, mathematical operations consisting of addition, subtraction, multiplication, and department are used to combine numbers or variables. In this example, the expression consists of operations, addition and multiplication.

The multiplication operation takes priority over addition, so we ought to carry out it first, following the order of operations, which is a set of rules that dictate the order wherein operations have to be carried out.

Using the order of operations, we first perform the multiplication of 2 and 18, which offers 36. Then we add 5 to the result, giving a final answer of 41.

So the value of the arithmetic expression 5 + 2 x 18 is 41.

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The equation which is useful to find "n" number of weeks to reach our goal is 35n + 100 = 800.

How to form an equation?

Determine the known quantities and designate the unknown quantity as a variable while trying to set up or construct a linear equation to fit a real-world application.

As per the given table,

Amount of money in 0 weeks = $100

Amount of money in 1st week = $135

In 2nd week = $170, in 3rd week = $205

So there is a $35 increment each week.

Let's say it takes "n" number of weeks to reach the goal.

So, 35n + 100 = 800

Hence the answer is The equation which is useful to find "n" number of weeks to reach our goal is 35n + 100 = 800".

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Answer:

Step-by-step explanation:

Given that:

Number of books, b α number of children enrolled

b α C

b = kC

Number of books, b = 3 for each child, c = 1 enrolled

Total number of books in class room :

Total number of books = Number of books per child * Number of child)

Total number of books = 3 * Numbe of child

The answer is c i believe

The Lewis dot structure for BF2 is:

 F     B     F

  \   /    

   B    

  /   \

 F     B     F

In this molecule, there are three atoms (one boron and two fluorine) and a total of 12 valence electrons. Boron is in group 3, so it has 3 valence electrons, while each fluorine atom has 7 valence electrons.

To form the Lewis dot structure, we first place the atoms in a linear arrangement. Each fluorine atom shares one electron with the boron atom, giving a total of two shared electrons (or one bond) between the boron and each fluorine atom. This gives us a total of four electrons (or two bonds) between the boron and the two fluorine atoms.

The remaining four electrons are placed as nonbonding electron pairs around each fluorine atom to satisfy the octet rule. Therefore, there are a total of two bonding domains and two nonbonding electron domains around the boron atom. The electron domain geometry is tetrahedral, and the molecular geometry is linear.

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Answer:

150 total students

Step-by-step explanation:

10%=15 students

so 15×9=135 students

then add the first 15

15+135=150 students in total participated in the survey

Answer:

150! The other answer is correct :)

Step-by-step explanation:

Answer:

x=3

Step-by-step explanation:

Divide both sides by 8.

Answer:

3

Step-by-step explanation:

8x3=24..............

The complete factorization of the polynomial x³ + 2x² -x - 2 is equal to (x + 2)(x + 1)(x - 1)

An equation is an expression that shows how numbers and variables are related to each other using mathematical operators.

A polynomial is an expression consisting of coefficients and variables forming an equation.

Given the polynomial:

x³ + 2x² -x - 2

Factorizing:

= (x + 2)(x² - 1)

= (x + 2)(x + 1)(x - 1)

The polynomial x³ + 2x² -x - 2 is equal to (x + 2)(x + 1)(x - 1)

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The value of k for which the given function f(x) = 9k on [−1, 1] is a probability density function is k = 1/18.

To determine the value of k for which the given function is a probability density function, we need to ensure that the integral of the function over its domain is equal to 1.

In other words, we need to satisfy the following condition:
∫ f(x) dx = ∫ 9k dx = 1

The integral of a constant function over its domain is simply the value of the constant times the length of the domain.

In this case, the length of the domain [−1, 1] is 2. Thus, we have:

∫ f(x) dx = 9k ∫ dx = 9k(2) = 18k

Now, we can set 18k equal to 1 and solve for k:
18k = 1
k = 1/18

Therefore, the value of k for which the given function f(x) = 9k on [−1, 1] is a probability density function is k = 1/18.

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It will take Daquin 63min to finish rest of his homework which is 70% of the total homework, if 30% is done in 27 minutes.

Daquin has completed 30% of his work.

Remaining work will be 100-30 = 70%

Means 70% of the total work is remaining to do by Daquin.

By applying unitary method:

Since, to do 30% of the homework it take 27 minutes.

Therefore, To do 1% of the homework it will take 27/30 minutes.

So, To do 70% of the homework it will take (27/30)×70 min

= 63 min

Hence, It will take him 63min to finish rest of his homework.

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Answer:

the set of all the real values which are strictly greater than zero which is all positive real numbers

Step-by-step explanation:

In interval notation: (0, ∞)

Any exponential function with a positive base and positive multiplier will have a horizontal asymptote at y=0 and will extend to +∞. That's what this one does.

Range of a function--

The range of a function is the set of all the values that are attained by a function.

We are asked to find the range of the function f(x)

the set of all the real values which are strictly greater than zero

x > 0

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A. The lateral area of the Louvre Pyramid is approximately 2,460 square meters.

B. The surface area of the Louvre Pyramid is approximately 3,330 square meters.

A. The lateral area of a pyramid is the sum of the areas of all its triangular faces. In this case, the Louvre Pyramid has four triangular faces, each with a base of 35 meters and a height of 27.84 meters. The formula for the area of a triangle is 1/2 * base * height. Thus, the lateral area of the pyramid is 4 * (1/2 * 35 * 27.84) = 2,460 square meters.

B. The surface area of a pyramid includes the lateral area as well as the area of its base. The base of the Louvre Pyramid is a square with sides of 35 meters, so its area is 35 * 35 = 1,225 square meters. Therefore, the total surface area of the pyramid is the sum of the lateral area and the base area, which is 2,460 + 1,225 = 3,330 square meters.

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Answer:

50,20

Step-by-step explanation:

let the two numbers be x and y respectively.

According to the question,

y=2/5 times of x

Or,

y= 2x/5 ..........(1)

Again,

or, x+y=70

or, x+2x/5=70

or, (5x+2x)/5=70

or, 7x=350

therefore x=50

putting the value of y in equation (1)

y=2x/5

y= (2×50)/5

therefore, y=20

Answer:

x = 175

Step-by-step explanation:

given:

A number is 2 /5 times another number. Their sum is 70.

find: the numbers (coefficient)

solution:

cross multiply

2 ( x ) = 70

5

2 (x) = 70 (5)

2 (x) = 350

x = 350

       2

x = 175

check:

2 ( x ) = 70

5

2 ( 175 ) = 70

5

350 = 70

 5

70 = 70

The joint probability of a and b upto 2 decimal places is 0.12

The conditional probability P(B/A)  arises only in the case of dependent events. It gives the conditional probability of B given that A has occurred.

p(a) = 0. 40 and p(b | a) = 0. 30.

P(B/A) = P(A∩B) / P(A)

0.30 = P(A∩B) / 0.40

P(A∩B) = 0.30 x 0.40

P(A∩B) = 0.12

Therefore, the joint probability of a and b upto 2 decimal places is 0.12

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Answer: 3 times per second

Step-by-step explanation:

Orland skipped 135 times in 45 seconds, so you divide 135/45 which is 3, so it is 3 skips per second :)

hope this helped <33

Answer:

-2.2

Step-by-step explanation:

Answer:

-19.04 + 38.08 = 19.04

The analysis of the matrices and vectors components indicates;

a) coa(A) = 1

b) <A, B> = 37

c) ||u|| ≈ 91.79

A vector is an mathematical object has magnitude and direction. Vector quantities can be represented by an ordered list of numbers, representing the components of the vector.

a) The cosine of the angle between the vectors, can be obtained from the dot product formula as follows;

cos(A) = (5)·(0) + (0)·(0) + (82)·(1) = 82

The magnitudes of the vectors are; ||u|| = √(5² + 0² + 82²) = 82

||v|| = √(0² + 0² + 1²) = 1

cos(A) = (u·v)/(||u||·||v||) = 82/82 = 1

cos(A) = 1

b) The inner product of the matrices;  \(A=\begin{bmatrix} 4&7 \\ 8& 4 \\\end{bmatrix}\) and \(B = \begin{bmatrix}5 &-1 \\ 3&0 \\\end{bmatrix}\) can be found from the sum of the product of the corresponding entries of the matrices as follows;

<A, B> = 4 × 5 + 7 × (-1) + 8 × 3 + 4 × 0 = 37

The inner <A, B> = 37

c) The norm of a vector is defined as the square root of the sum of the squares of the components of the vector, therefore;

||u|| = √(|2 + 26i|² + |1 + 88i|² + |0|²)

|2 + 26i| = √(2² + 26²) = √(680)

|1 + 88i| = √(1² + 88²) = √(7745)

||u|| = √((√(680))² + (√(7745))² + (0)²) = √(8425) ≈ 91.79

The norm of the vector is ||u|| ≈ 91.79

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Answer:

16 fluid ounces

Step-by-step explanation:

\( - 6x - 42 = - 10x + 62\)

Add sides 42

\( - 6x - 42 + 42 = - 10x + 62 + 42 \\ \)

\( - 6x = - 10x + 104\)

Add sides 10x

\( 10x - 6x =10x - 10x + 104 \)

\(4x = 104\)

Divided sides by 4

\( \frac{4}{4}x = \frac{104}{4} \\ \)

\(x = 26\)

_________________________________

Done ♥️♥️♥️♥️♥️

The value of angle S is 53°

Exterior angle theorem states that the measure of an exterior angle of a triangle is equal to the sum of two remote interior angles.

With this theorem we can say that

7x+2 = 4x+13+19

collecting like terms

7x -4x = 13+19-2

3x = 30

divide both sides by 3

x = 30/3

x = 10

Since x = 10

angle S = 4x+13

angle S = 4(10) +13

= 40+13

= 53°

Therefore the measure of angle S is 53°

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Answer:

A

Step-by-step explanation:

(x, y) -----> (x + 4, y - 1)

Adding 4 to the x means you move right 4.  Subtracting 1 from the y means you move down one.

The next transformation (-(x + 4), y - 1)

If you look at the x coordinate and the transformation that is being applied

(-(x+4) that negative means you are taking the opposite of the x coordinate.

When you take the opposite of the x coordinate, it means you reflect it over the y axis.

1/2

what is whole number?

All natural numbers and 0 are included in the category of whole numbers. They are a subset of real numbers, which exclude negative numbers, decimals, and fractions. Whole numbers include counting numerals as well.

According to question,

heaviest squash than the lightest squash are,

\(7/8-3/8=4/8\)

\(=1/2\)

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Answer: 0.10175

Step-by-step explanation:

First, bring the decimal points to the right for both numbers, to be a total of 5 decimal points to the right. Then, with the numbers 25 and 407, multiply them, and we get 10175. Then, we must bring the 5 decimal points back, and we end up with 0.10175.

Answer: 0.10

Step-by-step explanation:

on time4llearning

The probability that a woman was wearing a belt given that she was also carrying a purse is 0.333 or 33.3%.

To find the probability that a woman was wearing a belt given that she was also carrying a purse, we need to use conditional probability.

We know that out of the 30 women observed, 18 were carrying purses and 6 were both carrying purses and wearing belts.

This means that the number of women carrying purses who were also wearing belts is 6.
Therefore, the probability that a woman was wearing a belt given that she was also carrying a purse is:
P(wearing a belt | carrying a purse) = number of women wearing a belt and carrying a purse / number of women carrying a purse
P(wearing a belt | carrying a purse) = 6 / 18
P(wearing a belt | carrying a purse) = 0.333
Given the information provided, we can determine the probability of a woman wearing a belt, given that she is also carrying a purse.

First, we need to find the number of women carrying a purse and wearing a belt, which is 6. There are 18 women carrying purses in total.
So, to find the probability, we will use the formula:
P(Belt | Purse) = (Number of women wearing belts and carrying purses) / (Number of women carrying purses)
P(Belt | Purse) = 6 / 18
P(Belt | Purse) = 1/3 or approximately 0.33
Therefore, the probability that a woman was wearing a belt, given that she was also carrying a purse, is 1/3 or approximately 0.33.

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Answer:

Manny.

Step-by-step explanation:

Because they split cleaning on Thursday and Manny finished first, then on Friday Manny will clean more stalls because they are faster.

Answer:

Y=5X because the slope is 5 and the Y-intercept is 0