Is there a known infinite product for e? What I mean is, it’s similar to an infinite series.

Answer:

Step-by-step explanation:

Given the vectors u (3,5,-8) and v (2,-5,7), they can also be written as;

u = 3i+5j-8k

v = 2i-5j+7k

To express the vector 3u - v in vector form, first let us find the vector 3u;

3u = 3(3i+5j-8k)

3u = 3(3i)+3(5j)-3(8k)

3u = 9i+15j-24k

Subtract v from the resulting vector.

Since v =  2i-5j+7k

3u - v = 9i+15j-24k - (2i-5j+7k)

3u-v = 9i+15j-24k -2i+5j-7k

collect the like terms

3u-v = 9i-2i+15j+5j-24k-7k

3u-v = 7i+20j-31k

Hence the vector 3u-v in the form v =  vi+V2j+ v3k is 7i+20j-31k

Answer:

8N - 4 border tiles.

Step-by-step explanation:

There are 4 border tiles in each corner and between  the tiles there are N-2 tiles along the 4 sides.

So the number of border tiles

= 4+ 4(N - 2)

= 4 + 4N - 8

= 8N - 4.

Answer:

[tex] \boxed{ \bold{ \huge{ \boxed{ \sf{m = 140}}}}}[/tex]

Step-by-step explanation:

[tex] \sf{1.9m + 14 = 2m}[/tex]

Move 2m to right hand side and change it's sign

Similarly, move 14 to left hand side and change it's sign

[tex] \dashrightarrow{ \sf{1.9m - 2m = - 14}}[/tex]

Collect like terms

[tex] \dashrightarrow{ \sf{ - 0.1m = - 14}}[/tex]

Divide both sides by -0.1

[tex] \dashrightarrow{ \sf{ \frac{ - 0.1m} { - 0.1} = \frac{ - 14}{ - 0.1}}} [/tex]

Calculate

[tex] \dashrightarrow{ \sf{m = 140}}[/tex]

Hope I helped!

Best regards! :D

Answer:

306 min

Step-by-step explanation:

Answer:

All the numbers ranging from 14,500 to 15444 would be rounded to 15000

Step-by-step explanation:

All the numbers ranging from 14,500 to 15444 would be rounded to 15000.

How this is possible.

1) all the numbers from 0-4 are not counted as the next number when rounded off.

2) all the numbers from 5-9 are counted as the next number when rounded off.

Example Suppose we have numbers from 15- 19.

These numbers can be rounded off to 20

But numbers from 10-14 would never be rounded off to 20 instead they are rounded as 10.

Same happens in the hundreds case.

If we have numbers from 450 - 499 they can be rounded as 500

And numbers from 400 - 444 cannot be rounded as 500  but the number 445 may be rounded as 450 . When we carry  5 from units place and replace it as 450 then again 450 can be rounded to 500.

Same happens with 15000  but when are rounding nearest hundred not ten.

Thus all the numbers ranging from 14,500 to 15444 would be rounded to 15000.

Answer:

Step-by-step explanation:

3x - 8 + 5x + 10 = 90

8x + 2 = 90

8x = 88

x = 11

3(11) - 8 = 33 - 8 = 25 for <A

5(11) + 10 = 55 + 10 = 65 for<B

Answer:

-6

Step-by-step explanation:

When an exponent is outside and inside the parenthesis you need to add them to get rid of the the parenthesis.  The answer is -6 because -6*2 is -12.

Hope this helps. If you have questions put them in the comments.

Answer:-6

Step-by-step explanation:

When an exponent is outside and inside the parenthesis you need to add them to get rid of the the parenthesis. The answer is -6 because -6*2 is -12.

Answer:

26/36

Step-by-step explanation:

The probability of something = the amount of favourable outcomes/total possible outcomes.

The total number of dice combinations is 36 (6x6).

In this case there are more outcomes more than 5 than less than 5 so for the sake of simplicity we are going to find the number of outcomes less than 5 and then find the inverse.

There are only 10 possible dice combos which add to totals 5 or under:

1,1 1,2 2,1 1,3 3,1 1,4 4,1 2,2 2,3 and 3,2

That means there is a 10/36 probability of getting a total score less than 5 so to get the probability of getting more than 5, we just do 36/36 - 10/36 (because all probabilities add to 1)

Therefore there is a 26/36 probability that the toatals will add to greater than 5.

Alternatively you could also draw up a possibilities table and count the favourable outcomes.

Hope this helped!

Answer:

13/18.

Step-by-step explanation:

The favourable outcomes are (1,5) (1,6) (2,4) (2,5) (2,6) (3,3) (3,4) (3,5) (3,6) (4,2)(4,3) (4,4) 4,5) (4,6) 5,1) (5,2) 5,3) (5,4) (5,5) (5,6 )(6,1) to (6,6).

= total of 26.

As the total of all possible outcomes is 36 the answer is 26/36

= 13/18.

Answer:

$140

Step-by-step explanation:

If a package of gift cards has a total value of $1050, the total price for 2 gift cards will be 2×$1050 = $2100

If there are 15 in an average set of 2 gift cards, the average cost of the two gift cards will be expressed as;

Total price of 2gift cards/amount of card per group.

Average cost of of 2 gift cards = $2100/15

= $140

Hence the average cost of 2gift cards if there are 15 in a group is $134

Answer:

13/65 miles in 1/65 of an hour, I believe is the answer you're looking for. Hope this helped!

Step-by-step explanation:

Answer:

The Set of Natural Numbers: {1, 2, 3, 4, 5, . . .}

The Set of Whole Numbers: {0, 1, 2, 3, 4, 5, . . .}

The Set of Integers: {. . . , −5, −4, −3, −2, −1, 0, 1, 2, 3, 4, 5, . . .}

Step-by-step explanation:

Answer:

The graph is in the image

Step-by-step explanation:

[tex]y = \frac{3}{5} x -3\\\\2x -y =-4\\\\y=-6,\:x=-5\\[/tex]

Answer:

$4000

Step-by-step explanation:

Assuming a = money invested at 9%

Assuming b = money invested at 8%

then we can form am equation from the question given

1) a + b = $10000, also

0.09a + 0.08b = $860 -> multiply by 100

2) 9a + 8b = $86000

Next we try to solve both equations simultaneously. We multiply both the left hand side and the right hand side of the first equation by 8. We have

3) 8a + 8b = $80000, now we subtract 3 from 2

9a + 8b = $86000

-8a - 8b = -$80000

a = $6000.

Then, we plug this in any of the first 2 equations, to get b

9 * $6000 + 8b = $86000

$54000 + 8b = $86000

8b = $86000 - $54000

8b = $32000

b = $32000/8

b = $4000.

Therefore, he invested $4000 at 8%

Answer: 1 million

Step-by-step explanation:

Answer:

1,000,000

Step-by-step explanation:

Step 1:

400,000 + 600,000 = 1,000,000

Answer:

1,000,000

Hope This Helps :)

Answer:

$216

Step-by-step explanation:

We know that the cost of an outfit for one team member is 10 + 26 + 18 = $54, therefore, the cost of outfits for all 4 team members will be 54 * 4 = $216.

The matrices C, D, F, and G are symmetric while matrix H is skew-symmetric and matrix E is non-symmetric.

A matrix is an array of elements(numbers) in a peculiar order. A matrix with m rows and n columns is said to be of order m × n.

As it is known that [tex](A + B)^t = A^t + B^t[/tex] and [tex](AB)^t = B^t A^t[/tex] for any n × n matrices A and B.

Also, if matrices A and B are symmetric, then

[tex]A^t = A[/tex] and [tex]B^t = B[/tex].

a) Given that

C = A + B

Take the transpose of matrix C,

[tex]C^t = (A + B)^t[/tex]

    [tex]= A^t + B^t \\= A + B = C[/tex].

Hence, matrix C is symmetric.

b) Given that

D = A²

Take the transpose of matrix D,

[tex]D = (A^2)^t[/tex]

   [tex]= (AA)^t \\= A^t A^t \\= AA \\= A^2 = D[/tex].

Hence, matrix D is symmetric.

c) Given that

E = AB

Let's take an example,

A = [tex]\left[\begin{array}{cc}1&2&2&1\end{array}\right][/tex] and

B = [tex]\left[\begin{array}{cc}1 &-1 &-1&2\end{array}\right][/tex]

So,

E = AB

  [tex]=\left[\begin{array}{cc}1&2&2&1\end{array}\right] \times \left[\begin{array}{cc}1 &-1 &-1&2\end{array}\right]\\= \left[\begin{array}{cc}-1&3&1&0\end{array}\right][/tex]

Clearly, matrix E is non-symmetric.

d) Given that

F = ABA

Take the transpose of matrix F,

[tex]F^t = (ABA)^t[/tex]

    [tex]= A^t B^t A^t\\ = ABA = F[/tex].

Hence, matrix F is symmetric.

e) Given that

G = AB + BA

Take the transpose of matrix G,

[tex]G^t = (AB + BA)^t[/tex]

    [tex]= (AB)^t + (BA)^t \\= B^t A^t + A^t B^t \\= BA + AB = G[/tex].

Hence, matrix G is symmetric.

f) Given that

H = AB-BA

Take the transpose of matrix H,

[tex]H^t = (AB - BA)^t[/tex]

     [tex]= (AB)^t - (BA)^t \\= B^t A^t - A^t B^t \\= BA - AB = -H[/tex].

Hence, matrix H is skew-symmetric.

Thus, the matrices C, D, F, and G are symmetric while the rest are not.

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the 4th one is a relationship that is a fuction I think

Answer:

4th image

Step-by-step explanation:

the others cannot be functions since one domain cannot be in two ranges

Answer:

c

Step-by-step explanation:

Answer:

96

Step-by-step explanation:

The value of AZ will be 40.

A is a point between Y and Z and YA = 14x , AZ = 10x and YZ = 12x + 48.

We have to calculate the value of AZ.

What is the value of MP , if N is the midpoint of M and P ?

The value of MP will be equal to the summation of NM and NP i.e., MP = NP + NM .

As per the question ;

A is the midpoint of Y and Z.

⇒ AZ + YA = YZ

⇒ 10x + 14x = 12x + 48

⇒ 24x = 12 x + 48

⇒ 12x = 48

⇒ x = 4

So ,

The value of AZ will be ;

AZ = 10 × 4

AZ = 40

Thus , the value of AZ will be 40.

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Answer:

10

Step-by-step explanation:

Answer:

the answer is 3.5

Step-by-step explanation:

1. the total is 4

2.each mug = .5 of a litre

3.jane drinks 3 mugs which=1.5

4.she drinks 1.5 litres which is 3.5 of the whole bottle

5.so the remaining will be 3.5 which is what remains after she drank 1.5 litres of the whole bottle

Answer:

c.

Step-by-step explanation:

Answer: m+3

Step-by-step explanation:

Since the jump from each number increases by 3, you would write m+3, since m is indicated in the pattern.

Answer:

13:9

Step-by-step explanation:

The ratio of the number of apples to the number of fruits in the fruit salad is given by the equation A = 9 : 22

What is Proportion?

The proportion formula is used to depict if two ratios or fractions are equal. The proportion formula can be given as a: b::c : d = a/b = c/d where a and d are the extreme terms and b and c are the mean terms.

The proportional equation is given as y ∝ x

And , y = kx where k is the proportionality constant

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Given data ,

Let the ratio of number of apples to the number of fruits be A

Now , the proportion will be

The number of pears = 13 pears

The number of apples = 9 apples

Now , the number of fruits = number of pears + number of apples

Substituting the values in the equation , we get

The number of fruits = 13 + 9 = 22

Now , the proportion of apples to fruits A is

Ratio of the number of apples to the number of fruits in the fruit salad A = number of apples : number of fruits

Substituting the values in the equation , we get

Ratio of the number of apples to the number of fruits in the fruit salad

A = 9 / 22

A = 9 : 22

Therefore , the value of A is 9 : 22

Hence , the proportion is 9 : 22

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Answer:

$10,000

Step-by-step explanation:

-12,000+23,200-1,200= 10,000

The profit of the restaurant during it's first 3 years is 9800 dollars.

When the amount of money we get is more than what we have invested is more we have profit and when the amount of money we get is less than what we have invested we have loss.

Let us assume Alice start with a net profit or or of 0 dollars.

During its first year in business, Alice's restaurant shows a loss of 12,000 dollars.

∴ He is in loss of (0 - 12000) dollars which is

= - 12000 dollars.
During its second year, the restaurant makes a profit of 23200 dollars.

∴ His net profit is

= ( -12000 + 23000 ) dollars.

= 11000 dollars.

During its third year, the restaurant shows a loss of 1200 dollars so his ne profit is

= ( 11000 - 1200 ) dollars

= 9800 dollars.

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Answer:

C ON EDGE 2020

The function f(x) = [tex]\sqrt{1/x}[/tex] if, F[g(x)] = [tex]\sqrt{(1/x^2 - 3)}[/tex], g(x) = x² - 3, so option C is correct.

The function is a relationship between a set of potential outputs and a set of possible inputs, where each input has a single relationship with each output. This means that if an object x is present in the set of inputs (also known as the domain), then a function f will map that object to exactly one object f(x) in the set of potential outputs (called the co-domain).

Given:

F[g(x)] = [tex]\sqrt{(1/x^2 - 3)}[/tex]

g(x) = x² - 3

Put the value of g(x) in all the options and check whether it is equal to F[g(x)]  as shown below,

Put it in option 3,

f{g(x)} = [tex]\sqrt{(1/x^2-3)}[/tex]

Thus, f(x) = [tex]\sqrt{1/x}[/tex]

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Answer:

x + 6 = 3

-3 + 6 = 3

Step-by-step explanation:

x + 6 = 3

x + 6 - 6 = 3 - 6

x = -3