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The scalar multiplication [tex]k(\overrightarrow{a}+\overrightarrow{b})=k\overrightarrow{a}+k\overrightarrow{b}[/tex]has been proved.

Scalar Multiplication Property:

Basically a scalar means the real number.

The scalar multiplication property states that the product of a sum or difference of a number is equal to the sum or difference of the products.

The general form of scalar multiplication as follows:

k (A + B) = kA + k B

where

k is the scalar.

Given,

Let

[tex]\overrightarrow{a}= < x_1,y_1 >[/tex]

and

[tex]\overrightarrow{b}= < x_2,y_2 >[/tex]

Then we have to prove the following scalar multiplication property,

[tex]k(\overrightarrow{a}+\overrightarrow{b})=k\overrightarrow{a}+k\overrightarrow{b}[/tex]

We know that,

"The vector is an object that has both a magnitude and a direction. And  vector as a directed line segment, whose length is the magnitude of the vector and with an arrow indicating the direction."

Here we have two vectors like [tex]\overrightarrow{a},\overrightarrow{b}[/tex].

Now we need to use the definition of the scalar multiplication property,

Then, the LHS of the expression is written as,

[tex]\implies k(\overrightarrow{a}+\overrightarrow{b})[/tex]

Apply the values of the vectors then we get,

=> k(<x₁, y₁> + <x₂, y₂>)

When we expand the terms then we get,

=> k<x₁, y₁> +  k<x₂, y₂>

And it can be written as,

[tex]\implies k\overrightarrow{a}+k\overrightarrow{b}[/tex]

Therefore, the scalar multiplication property has been proved.

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ABCD ∽ EFGH, meaning both quadrilaterals are similar, therefore the proportionos of their corresponding sides are equal, thus

[tex]\cfrac{AB}{EF}~~ = ~~\cfrac{CD}{HG}\implies \cfrac{\stackrel{AB}{3}}{\underset{EF}{2}}~~ = ~~\cfrac{\stackrel{CD}{4.5}}{\underset{HG}{y}}\implies 3y=9\implies y=\cfrac{9}{3}\implies y=3[/tex]

Answer:

first remove the brackets

then find the like terms

and work out

Using the normal distribution, it is found that:

b)

The maximum 39.5% obese has a z-score of 2.11, hence it is 2.11 standard deviations above the mean.

The minimum 23% obese has a z-score of -2.21, hence it is 2.21 standard deviations below the mean.

c) The interval is 23.79% to 39.07%.

The z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

For this problem, the parameters are given as follows:

[tex]\mu = 31.43, \sigma = 3.82[/tex]

The maximum weight is of 39.5, hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

Z = (39.5 - 31.43)/3.82

Z = 2.11.

The maximum 39.5% obese has a z-score of 2.11, hence it is 2.11 standard deviations above the mean.

The maximum weight is of 23, hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

Z = (23 - 31.43)/3.82

Z = -2.21

The minimum 23% obese has a z-score of -2.21, hence it is 2.21 standard deviations below the mean.

For item c, we consider the Empirical Rule, which states that 95% of the measures are within 2 standard deviations of the mean.

Then:

The interval is 23.79% to 39.07%.

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Answer:

i think the answer may be possibly 86%

The total of Sam's liabilities are $5225.

A liability is an obligation of an individual towards his creditors arising out of some transactions. Bank loans, credit card bills, accounts payable , accrued expenses are examples of liabilities.

Given that Sam has a car that is worth $8,500. However, he still owes $4,750 on the car. He also has $1,500 in his savings account, a comic book collection worth $900 and owes $475 on his credit card.

Irrespective of his assets and savings Sam still owes $4750 on the car and $475 in his card card , therefore these are his liabilities.

Total liabilities of Sam = $4750+$475 = $5225

Therefore, total of Sam's liabilities are $5225

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Answer:

[tex]2\sqrt{x}[/tex]

Step-by-step explanation:

[tex]\mathrm{Apply\:exponent\:rule}:\quad \:a^b\cdot \:a^c=a^{b+c}[/tex]

[tex]2x \cdot x^{-\frac{1}{2}} = 2x^{1-\frac{1}{2}} = 2x^{\frac{1}{2}} = 2\sqrt{x}[/tex]

Another way of doing this is to see that
[tex]x^{-\frac{1}{2}} = \frac{1}{\sqrt{x} }[/tex]

So [tex]2x \cdot x^{-\frac{1}{2}} = \frac{2x}{\sqrt{x} } =2\sqrt{x}[/tex]

On combining the like terms of the expression y²/2 + y/3 + y²/3 - y/5 the simplified value is  5y²/6 +2y/15.

In an algebraic expression Like terms are  defined as those terms that have same variable and that variable has the same power .

For Example : 5a,9a are like terms .

In the given question

=y²/2 +y/3 +y²/3 -y/5

On combining the like terms , one with y² and other with y.

We get;

=y²/2 +y²/3 +y/3  -y/5

Taking LCM of like terms with y² as "6"

and LCM of like terms with y as "15".

We get ;

=(3y²+2y²)/6 +(5y-3y)/15

=5y²/6 +2y/15

Therefore , On combining the like terms of the expression y²/2 + y/3 + y²/3 - y/5, the simplified value is  5y²/6 +2y/15.

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1/3 is the  probability when You roll a die and get a 2. You roll another die and get a 3.

In statistics, what does a probability mean?

when a dice is thrown we get the following out comes

S = { 1,2,3,4,5,6}

n(S) = 6

probability of getting 3 is 1/6 [as there is only one 3]

probability of getting 4 is 1/6 [ there is only one 4]

Using addition theorem of of probability ,

probability of getting 3 or 4 is 1/6 + 1/6 = 2/6 = 1/3

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Answer:

8:30 a.m.

Step-by-step explanation:

The total time it takes for Lyle to reach his friend's house is 720/80 + 1 + 0.25 * 2, which is 9 + 1.5 = 10.5 hours

The latest possible time that Lyle would be able to leave his house to reach on time is 8:30 a.m.

The equation of line in slope intercept form which passes through (-1, -5) and (4, -2) will be y = [tex]\frac{3}{5}[/tex] x .

What is the slope intercept form of a line ?

The equation of a straight line in the form y = mx + c is known as the slope intercept form, where m denotes the slope and c denotes the y-intercept of a line.

It is given that line is passing through (x1 , y1) and (x2 , y2) that is ,  (-1, -5) and (4, -2).

Let's find out the value of slope first.

We know that , slope (m) = (y2-y1) / (x2-x1)

⇒ m = [(-2-(-5)] / [4 - (-1)]

⇒ m = 3 / 5

Now we will use the slope to find the y-intercept.

∵ y = mx + c

where , c is the y-intercept.

(-2 -(-5)) = (3/5) × (4-(-1)) + c

3 = [ (3/5) × 5 ] + c

3 = 3 + c

c = 0

Now ; we will write the equation in slope intercept form that is ;

y = mx + c

or

y = [tex]\frac{3}{5}[/tex] × x + 0

or

y = [tex]\frac{3}{5}[/tex] x

Therefore , the equation of line in slope intercept form which passes through (-1, -5) and (4, -2) will be y = [tex]\frac{3}{5}[/tex] x .

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   From the list of numbers presented we can determine that this is a finite sequence.

 A sequence is defined by an order of values and/or elements that have a relationship of variation as a ratio or proportion that makes them predictable.

  A sequence maintains an order, and this numerical order can be finite or infinite, in the given case we have the following list:

2.3 + 4.6 + 9.2 +18.4

   We can clearly notice that we have a larger limit number and it is 18.4, as we know the beginning of the sequence and the exact end we can know that we are in the presence of a finite sequence.

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The sampling technique Greg used is stratified sampling.

Stratified sampling is used when the population is more heterogeneous. Then we divide the population into subgroups or strata which will be more homogeneous and take samples from each strata. This will ensure the equal representation from each group in population. Stratified sampling helps to reduce the variability of the estimates also.

Here the population of current season ticket holders consist both for men's basketball games and women's basketball games. So Greg considered both as separate subgroups of the population and collected random samples of size 100 from each group. This technique for sampling is known as stratified sampling.

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Answer:

8,000,000,000,000,000,000,000,000,000,000,000,000,000,000

Step-by-step explanation:

8(10^42)

Parenthesis is the multipication sign  btw

The inverse function as g⁻¹ (h)  = [(h+6)/10]² which is the correct answer would be an option (E).

The inverse function is defined as a function obtained by reversing the given function.

To determine the inverse of a function, all you have to do is switch where h and g are and resolve for g.

So after switching h and g,

g = g(h) = 10√h - 6

becomes

h = 10√g - 6

Now, we solve for h regularly.

h + 6 = 10√g

(h + 6)/10 = √g

[(h+6)/10]² ⇒ g = [(h+6)/10]² = g(x)

Therefore the inverse of g(x) is g⁻¹ (h)  = [(h+6)/10]²

Hence, the inverse function as g⁻¹ (h)  = [(h+6)/10]²

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answer:

x=0 or x=4.732050807568877 or x=1.2679491924311228

Answer:

4/31

Step-by-step explanation:

reciprocal=same thing upside- down,

Based on the calculations below, the amount of tuition per year is $36,000 while the amount of the increase in tuition each year is $1,000.

Note: There are two questions in this question as follows:

1. How much is tuition per year?

2. By how much will tuition increase each year?

We can calculate the tuition per year and the increase in the tuition each year as below:

Number of semesters in a year = 2

Tuition in each semester = $18,000

Increase in the tuition per semester = $500

Using the above information, we can proceed as follows:

Tuition per year = Tuition in each semester * Number of semesters in a year = $18,000 = $36,000

Increase in the tuition each year =  Increase in the tuition per semester * Number of semesters in a year = $500 * 2 = $1,000

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We can see that there is no element which is common Hence, they are mutually exclusive events.

Let A be the event of getting a sum of 7 on dice.

Let B be the events of getting a sum of 6 on dice.

A={ (1,6), (2,5), (3,4), (4,3), (5,2) }

B = { (1,5) , (2,4), (3,3),  (4,2), (5,1), }

Mutaullty exclusive events are those when there is no common event between two events.

Where there is empty set of intersection.

But we can see that there is no element which is common

So, n(A∩B) = ∅

Hence, they are mutually exclusive events.

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Answer:

y = 3x + 1

y = -x + 5

Step-by-step explanation:

Take the system of equations and substitute (1 ,4) in any one of the equations. If both the sides are justified, then (4,1) is the solution to that pair of equations.

  1) y = -3x  - 1   ---------(I)

     y = -x + 5

Substitute (1,4) in equation (I)

        4 = -3*1 - 1

        4 = -3-1

        4 ≠ -4

So, (1, 4) is not a solution.

2) y = 3x + 1   ---------------(II)

   y = - x + 5

Substitute (1 ,4) in equation (II)

      4 = 3*1 + 1

       4 = 3 + 1

       4 =  4

(1 ,4) is the solution for this system of equation.

Answer:

10 tents

Step-by-step explanation:

I don't know if Chetis a person name or not but if it a person name then 76÷8=9.5 because 75+1=76 (including him)

if Chetis is not a person name then 75÷8=9.375

The answer would still be the same which is 10 tents needed.

Answer:

A right triangle

Step-by-step explanation:

The angle of 90 degrees is a right angle

The correct option regarding the linear regression equation is:

No, the equation is not a good fit because the sum of the residuals is a large number.

To find the equation, we need to insert the points (x,y) in the calculator.

In possession of the equation, the residuals are given by the difference of the predicted values(with the equation) and the actual values.

The model represents a good fit if the sum of the residuals is close to 0.

For this problem, the sum of the residuals is given by:

90 - 50  - 100 - 100 + 150 - 50 = -60.

The sum is a large number, hence the model is not a good fit.

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Solving the problem with the arithmetic progression, the 32nd term of the sequence is 558.

Arithmetic progression is a sequence of numbers in which the next term is depicted by adding a fixed number 'd' to the preceding term. The series is in arithmetic progression.

We all know the formula for arithmetic progression is,

aⁿ = a + ( n-1 ) d

where d = difference between two corresponding terms, n = no. of term, a = first term

We have to find the 2nd term, and it's, a³⁸ = 3 + ( 38 - 1)( 18 - 3 ) = 3 + 37× 15 = 3 + 555 = 558.

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Considering the definition of an equation and the way to solve it, the money earned by Adriano's online business this month is $1,150.

An equation is the equality existing between two algebraic expressions connected through the equals sign in which one or more unknown values, called unknowns, appear in addition to certain known data.

In this case, you know that every month, Adriano receives a subscription fee of $5 from each of the subscribers to his website. Then, the amount of money earned by Adriano's online business each month will be represented by the following equation:

Money earned by Adriano's online business each month= $5x

where x is the number of subscribers on the website.

On the other hand, you know:

Then, the number of subscribers this month can be calculated as:

Number of subscribers this month = 200 + 40 - 10

Number of subscribers this month = 230

So, the amount of money earned by Adriano's online business this month is calculated by substituting this value in the equation above:

Money earned by Adriano's online business this month= $5×230 subscribers

Money earned by Adriano's online business this month=$1,150

Finally, the money earned by Adriano's online business this month is $1,150.

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Answer:

Calm down, I gotcha!

Step-by-step explanation:

4 7/12+ 2 3/4+ 7 5/12=14.75

Answer:

121° and 59°

Step-by-step explanation:

We'll assign the two angles 'a' and 'b'. Since they are supplementary, this means they add to 180°. We can model this peoblem with the expressions:

a + b = 180° and a - b = 62°

Let's use the second equation to find a substitution for a:

a - b = 62°

a = 62° + b

Now substitute this in the first equation and solve:

(62° + b) + b = 180°

62° + 2b = 180°

2b = 118°

b = 59°

59° + 62° = 121° this is angle a

Ava's age = b

Ava's sister's age = 2b -9

Part a - C = 120 + 5x

Part b - A = [120 + (5 x (x)] / x

Part c - The number of hours you must play before the average cost per hour drops to $10 per hour is 15 hours.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

We have,

Membership fees = $120

Cost per hour = $5

x = number of hours

The equation that represents the total cost:

C = 120 + 5x

The equation that represents the average cost per hour:

A = [120 + (5 x (x)] / x

From the graph, we can assume that the y-axis indicates the average cost per hour and the x-axis indicates the number of hours.

We see that in 16 hours the average cost per hour is $10 so the number of hours to play before the average cost per hour drops to $10 per hour is 15 hours.

Thus,

Part a - C = 120 + 5x

Part b - A = [120 + (5 x (x)] / x

Part c - The number of hours you must play before the average cost per hour drops to $10 per hour is 15 hours.

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volume of the largest sample is 7 times the volume of the smallest sample.

A box and whisker plot—also called a box plot—displays the five-number summary of a set of data. The five-number summary is the minimum, first quartile, median, third quartile, and maximum.

given:

The volume of the largest sample is 7/8 gallon.

The volume of smallest sample is is 1/8 gallon.

So,

volume of the largest sample/volume of the smallest sample

=7/8 / 1/8

=7/8 * 8/1

=7

Hence, volume of the largest sample is 7 times the volume of the smallest sample.

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