Write the series using summation notation. Then find the sum of the series.

1 + 2 + 3 + ++ + 12

And

1/2 + 1/4 + 1/6 + ++ + 1/14

Step-by-step explanation:

Let coordinates of B be ( x , y )

X coordinate of B = (-1 + x) / 2 = - 3

Y coordinate of B = (-1 + y) / 2 = -3

Therefore, coordinates of B are ( - 5, - 5 ).

===================================================

Explanation:

The slope of f(x) is 4, since the equation y = 4x+2 has slope m = 4. Compare this to y = mx+b.

The slope of g(x) is 5. Note how if we started at (0,-2) on the red line and moved up 5 and to the right 1, we arrive at (1,3) which is another point on the red line. You could use the slope formula

m = (y2-y1)/(x2-x1)

to get the same result.

Since the slope of f(x) is 4 and the slope of g(x) is 5, we see that g(x) has a larger slope. The g(x) line is steeper compared to f(x).

Answer:

D

Step-by-step explanation:

From law of indices,( X^3)^2= x^3×2=x^6

Then the other one, also from law of indices, square

root of 5 is the same as 5 raised to power 1/2, then we multiply the powers, that will give us 5 and we have our complete expression which is x^6-5

Answer:

2n+3=3.2

2n=3.2-3

2n=0.2

n=0.2/2

n=0.1

The solution of the given equation for n will be -3.1.

There are many different ways to define an equation. The definition of an equation in algebra is a mathematical statement that demonstrates the equality of 2 mathematical expressions.

The equation must be constrained with some constraints.

As per the given equation,

2n + 3 = -3.2

2n = -3.2 - 3

n = -6.2/2

n = -3.1

Hence "The solution of the given equation for n will be -3.1".

For more about the equation,

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Answer: D) relationship between y intercepts cannot be determined

The graph of f(x) is a vertical line. It is completely parallel to the y axis, so it never crosses the y axis. We need the graph to cross the y axis somewhere in order to form a y intercept. Therefore f(x) does not have a y intercept. So we cannot compare y intercepts if f(x) doesn't have one at all.

Answer:

2<∛13<3      1<∛6<2

Step-by-step explanation:

Lets find the integers a and b  ∛13 lies between.

a<∛13<b

a³<13<b³

=> a=2 so 2³=8   and b=3 so 3³=27    8<13<27

Similarly     a<∛6<b

a³<6<b³

a=1    and b=2

Answer:

4/13

Step-by-step explanation:

There are 4 jacks in the deck and 13 spades. However 1 jack is a spade so we have a total of 16 cards which are either a jack or a spade. Therefore there are (13 + 4 - 1)/52 cards which are not a jack or a spade. Divided 16/52, thus the probability is 4/13.

The probability of drawing a spade or a jack from a standard deck of 52 cards is;

P(drawing either a spade or jack) = 4/13

We are told that the standard deck of cards has 52 cards.

Thus;

N = 52

Now,in a pack of cards there are usually 4 Jacks and 13 spades.

However, among the 4 Jacks, 1 of them is a spade. This means that 1 card will be both a spade and a jack. Thus,

Possible number of Jack's and spades = 13 + 4 - 1 = 16

Thus;

P(drawing either a spade or jack) = 16/52 = 4/13

Read more at; https://brainly.com/question/20971273

Answer:

x=4

Step-by-step explanation:

In order to solve for x, we must isolate x on one side of the equation.

x+3x+5=21

First, combine like terms. x and 3x are both terms with variables, and can be combined.

(x+3x) + 5=21

4x + 5=21

5 is being added to 4x. The inverse of addition is subtraction. Subtract 5 from both sides of the equation.

4x+5-5= 21-5

4x= 16

x is being multiplied by 4. The inverse of multiplication is division. Divide both sides by 4.

4x/4=16/4

x= 16/4

x=4

Let's check our solution. Plug 4 in for x and solve.

x+3x+5=21

4+3(4)+5=21

4+12+5=21

16+5=21

21=21

This solution checks out, so we know our answer is correct.

x is equal to 4, x=4.

Answer:

x = 4

Step-by-step explanation:

x + 3x + 5 = 21

4x + 5 = 21

4x = 21 - 5

4x = 16

x = 16/4

x = 4

verify:

4 + 3*4 + 5 = 21

4 + 12 + 5 = 21

Answer:

24-8i

Step-by-step explanation:

(8-8i)(2+i)=8*2+8i-8i*2-8i^2=16+8i-16i-8*(-1)=16-8i+8=24-8i

Answer:

[tex]\huge \boxed{x=12}[/tex]

Step-by-step explanation:

Let the unknown number be x.

12+24=2(6+x)

Switch sides.

2(6+x)=12+24

Expand brackets.

12+2x=12+24

Subtract 12 from both sides of the equation.

12+2x-12=12+24-12

2x=24

Divide both sides of the equation by 2.

(2x)/2=24/2

x=12

12+24=2(6+x )

36=2(6+ )

36\2=(6+x)

18=(6+x)

18-6=x

12=x

the answer is 12

Answer:

x = ((30 sqrt(1462809) + 36253)^(2/3) - 131)/(60 (30 sqrt(1462809) + 36253)^(1/3)) + 7/60 or x = 7/60 - 1/60 ((-1)/(30 sqrt(1462809) + 36253))^(1/3) (131 (-1)^(1/3) + (30 sqrt(1462809) + 36253)^(2/3)) or x = 1/60 (131 (-1/(36253 + 30 sqrt(1462809)))^(1/3) + (-1)^(2/3) (36253 + 30 sqrt(1462809))^(1/3)) + 7/60

see atachement it's more legible.

Step-by-step explanation:

Solve for x:

(20 x^3 - 7 x^2 + 3 x - 7)/(-13 x^2 - 5) = 0

Hint: | Multiply both sides by a polynomial to clear fractions.

Multiply both sides by -13 x^2 - 5:

20 x^3 - 7 x^2 + 3 x - 7 = 0

Hint: | Look for a simple substitution that eliminates the quadratic term of 20 x^3 - 7 x^2 + 3 x - 7.

Eliminate the quadratic term by substituting y = x - 7/60:

-7 + 3 (y + 7/60) - 7 (y + 7/60)^2 + 20 (y + 7/60)^3 = 0

Hint: | Write the cubic polynomial on the left hand side in standard form.

Expand out terms of the left hand side:

20 y^3 + (131 y)/60 - 36253/5400 = 0

Hint: | Write the cubic equation in standard form.

Divide both sides by 20:

y^3 + (131 y)/1200 - 36253/108000 = 0

Hint: | Perform the substitution y = z + λ/z.

Change coordinates by substituting y = z + λ/z, where λ is a constant value that will be determined later:

-36253/108000 + (131 (z + λ/z))/1200 + (z + λ/z)^3 = 0

Hint: | Transform the rational equation into a polynomial equation.

Multiply both sides by z^3 and collect in terms of z:

z^6 + z^4 (3 λ + 131/1200) - (36253 z^3)/108000 + z^2 (3 λ^2 + (131 λ)/1200) + λ^3 = 0

Hint: | Find an appropriate value for λ in order to make the coefficients of z^2 and z^4 both zero.

Substitute λ = -131/3600 and then u = z^3, yielding a quadratic equation in the variable u:

u^2 - (36253 u)/108000 - 2248091/46656000000 = 0

Hint: | Solve for u.

Find the positive solution to the quadratic equation:

u = (36253 + 30 sqrt(1462809))/216000

Hint: | Perform back substitution on u = (36253 + 30 sqrt(1462809))/216000.

Substitute back for u = z^3:

z^3 = (36253 + 30 sqrt(1462809))/216000

Hint: | Take the cube root of both sides.

Taking cube roots gives 1/60 (36253 + 30 sqrt(1462809))^(1/3) times the third roots of unity:

z = 1/60 (36253 + 30 sqrt(1462809))^(1/3) or z = -1/60 (-36253 - 30 sqrt(1462809))^(1/3) or z = 1/60 (-1)^(2/3) (36253 + 30 sqrt(1462809))^(1/3)

Hint: | Perform back substitution with y = z - 131/(3600 z).

Substitute each value of z into y = z - 131/(3600 z):

y = 1/60 (30 sqrt(1462809) + 36253)^(1/3) - 131/(60 (30 sqrt(1462809) + 36253)^(1/3)) or y = -1/60 (-30 sqrt(1462809) - 36253)^(1/3) - (131 (-1)^(2/3))/(60 (30 sqrt(1462809) + 36253)^(1/3)) or y = 131/60 ((-1)/(30 sqrt(1462809) + 36253))^(1/3) + 1/60 (-1)^(2/3) (30 sqrt(1462809) + 36253)^(1/3)

Hint: | Simplify each solution.

Bring each solution to a common denominator and simplify:

y = ((30 sqrt(1462809) + 36253)^(2/3) - 131)/(60 (36253 + 30 sqrt(1462809))^(1/3)) or y = -1/60 (-1/(36253 + 30 sqrt(1462809)))^(1/3) ((30 sqrt(1462809) + 36253)^(2/3) + 131 (-1)^(1/3)) or y = 1/60 (131 ((-1)/(30 sqrt(1462809) + 36253))^(1/3) + (-1)^(2/3) (30 sqrt(1462809) + 36253)^(1/3))

Hint: | Perform back substitution on the three roots.

Substitute back for x = y + 7/60:

Answer: x = ((30 sqrt(1462809) + 36253)^(2/3) - 131)/(60 (30 sqrt(1462809) + 36253)^(1/3)) + 7/60 or x = 7/60 - 1/60 ((-1)/(30 sqrt(1462809) + 36253))^(1/3) (131 (-1)^(1/3) + (30 sqrt(1462809) + 36253)^(2/3)) or x = 1/60 (131 (-1/(36253 + 30 sqrt(1462809)))^(1/3) + (-1)^(2/3) (36253 + 30 sqrt(1462809))^(1/3)) + 7/60

Answer:

B' is (3,2)

Step-by-step explanation:

In the original B coordinate pair, 6 is the y-coordinate.  When we talk about shifting images or points up or down, we will normally see a change in the y-coordinate.  In this case, the image is being translated 4 units down, so subtract 4 from 6 to get 2 as your y-ccoordinate for B'.  Since no horizontal shift is being made, the x-coordinate from the original B point stays the same and B' becomes (3,2).

Answer:

b is (3,2)

Step-by-step explanation:

ggchvvbggggghhh

Answer:

2(15 - 5) + 3(9 - 8)

Step-by-step explanation:

Profit for each $5 bracelet: 15 - 5

Profit for 2 $5 bracelets: 2(15 - 5)

Profit for each $8 bracelet: 9 - 8

Profit for 3 $8 bracelets: 3(9 - 8)

Total profit: 2(15 - 5) + 3(9 - 8)

Answer:

2(-5)+3(-8)+2(15)+3(9)=23

Step-by-step explanation:

For this expression, every time she payed for something we will use a negative number, and whenever she sold it we will use a positive number.

Lets start off with what she payed for, she bought two 5 dollar bracelets, and three 8 dollar bracelets.

2(-5)+3(-8)

Now we will see what she sold. She sold two bracelets for 15 dollars, and then sold three bracelets for 9 dollars.

2(15)+3(9)

Now we combine these to find out her profit.

2(-5)+3(-8)+2(15)+3(9)=23

Answer:

x=26

y=9

Step-by-step explanation:

5x-17+3x-11=180

8x=180+17+11

8x=208

x=26

3(26)-11=78-11=67

2y+5=90-67

2y=90-67-5

2y=18

y=9

Answer:

The average value of the function [tex]f(x) = 6 - x^{2}[/tex] over the interval [tex][-1,4][/tex] is [tex]\frac{5}{3}[/tex].

Step-by-step explanation:

The average value of a function over an interval is represented by this integral:

[tex]\bar y = \frac{1}{b-a}\cdot \int\limits^{b}_{a} {f(x)} \, dx[/tex]

Where:

[tex]a[/tex], [tex]b[/tex] - Lower and upper bounds of the interval, dimensionless.

[tex]f(x)[/tex] - Function, dimensionless.

If [tex]a = -1[/tex], [tex]b = 4[/tex] and [tex]f(x) = 6 - x^{2}[/tex], the average value of the function is:

[tex]\bar y = \frac{1}{4-(-1)}\int\limits^{4}_{-1} {6-x^{2}} \, dx[/tex]

[tex]\bar y = \frac{6}{5}\int\limits^{4}_{-1} \, dx - \frac{1}{5}\int\limits^{4}_{-1} {x^{2}} \, dx[/tex]

[tex]\bar y = \frac{6}{5}\cdot x |_{-1}^{4} - \frac{1}{15}\cdot x^{3}|_{-1}^{4}[/tex]

[tex]\bar y = \frac{6}{5}\cdot [4-(-1)]- \frac{1}{15}\cdot [4^{3}-(-1)^{3}][/tex]

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

The average value of the function [tex]f(x) = 6 - x^{2}[/tex] over the interval [tex][-1,4][/tex] is [tex]\frac{5}{3}[/tex].

This question above is incomplete

Complete Question

Jim had 103 red and blue marbles. After giving 2/5 of his blue marbles and 15 of his red marbles to Samantha, Jim had 3/7 as many red marbles as blue marbles. How many blue marbles did he have originally?

Answer:

70 Blue marbles

Step-by-step explanation:

Let red marbles = R

Blue marbles = B

Step 1

Jim had 103 red and blue marbles.

R + B = 103.......Equation 1

R = 103 - B

Step 2

After giving 2/5 of his blue marbles and 15 of his red marbles to Samantha, Jim had 3/7 as many red marbles as blue marbles

2/5 of B to Samantha

Jim has = B - 2/5B = 3/5B left

He also gave 15 red marbles to Samantha

= R - 15

The ratio of what Jim has left

= Red: Blue

= 3:7

= 3/7

Hence,

R - 15/(3/5)B = 3/7

Cross Multiply

7(R - 15) = 3(3/5B)

7R - 105 = 3(3B/5)

7R - 105 = 9B/5

Cross Multiply

5(7R - 105) = 9B

35R - 525 = 9B............ Equation 2

From Equation 1, we substitute 103 - B for R in Equation 2

35(103 - B) - 525 = 9B

3605 - 35B - 525 = 9B

Collect like terms

3605 - 525 = 9B + 35B

3080 = 44B

B = 3080/44

B = 70

Therefore, Jim originally had 70 Blue marbles.

Answer:

please mark my answer brainliest

Step-by-step explanation:

these types of input variables are called integer...

Answer:

answer below

Step-by-step explanation:

from the question the

mean = ∑x/n

∑x = 317

n = 16

mean = 19.8125

x           x-Ц           x-Ц²

19       -0.8125      0.66015625

20       0.1875      0.03515625

19          -0.8125      0.66015625

20         0.1875      0.03515625

18         -1.8125       3.28515625

21          1.1875        1.41015625

17           -2.8125      7.91015625

19           -0.8125      0.66015625

24           4.1875       17.53515625

23            3.1875      10.16015625

21           1.1875        1.41015625

21            1.1875        1.41015625

17             -2.8125      7.91015625

20          -0.8125      0.66015625

20           -0.8125      0.66015625

18            -1.8125       3.28515625

∑(x-Ц)² = 56.44

s.d = 1.9

b.

19.81 + 2*1.9= 23.61

19.81-2*1.9 = 16.01

=

Answer:

28.60×.35=10.01

10.01+28.60=$38.61

56.347..........

just simply put the value 3175 under division root and make pairs of 31 and 75.Now think of a number whose square will be nearest to 31 and that ll be 5.Now write 5 in the quotient and 5 also 5 under the divider.Now by multiplying 5 with the 5 in the quotient you ll get 25 write this under 31.And by adding 5 in the divider 5 youll get 10.write this under the divider.no by subtracting 25 from 31 you ll get 6 and by bringing 75 down it ll be 675.Now think of a number again and write it with 10.Like 6 into 6 is 36 and when you multiply 6 with 106 you ll get nearest number to 675 that ll be 636.Now because its giving a remainder just add a .0 in the question and continue to solve it the same way.And as it ll be a continuous answer so just add continuty dots........ or just round it off to nearest whole number

Answer:

56.347138347923

Step-by-step explanation:

Answer:

The value of [tex]v[/tex] is ± 22.729.

Step-by-step explanation:

Let be [tex]a=m\cdot g -\frac{k\cdot v^{2}}{m}[/tex], the variable [tex]v[/tex] is now cleared:

[tex]\frac{k\cdot v^{2}}{m}=m\cdot g -a[/tex]

[tex]k\cdot v^{2} = m^{2}\cdot g- m\cdot a[/tex]

[tex]v^{2} = \frac{m^{2}\cdot g - m\cdot a}{k}[/tex]

[tex]v =\pm \sqrt{\frac{m^{2}\cdot g-m\cdot a}{k} }[/tex]

If [tex]a = 2.8[/tex], [tex]m=12[/tex], [tex]g = 9.8[/tex] and [tex]k = \frac{8}{3}[/tex], the value of [tex]v[/tex] is:

[tex]v=\pm \sqrt{\frac{(12)^{2}\cdot (9.8)-(12)\cdot (2.8)}{\frac{8}{3} } }[/tex]

[tex]v \approx \pm 22.729[/tex]

The value of [tex]v[/tex] is ± 22.729.

Answer:

Step-by-step explanation:

Probability is the likelihood or chance that an event will occur.

Probabiity = expected outcome/total outcome

Let the total outcome be 100% = 1.0

Given three different colored balls: orange, green and purple. If the probability of randomly choosing orange ball from a bag is 45%. The probability of randomly choosing a green ball from bag is 0.10

The probability of choosing both orange ball and green ball is 0.45+0.10 = 0.55.

Since the total outcome of probability is 1, then the probability for Jared to randomly choose a purple ball from the bag will be expressed as;

Pr(purple) = 1 - [Pr(green)+Pr(orange)]

Pr(purple) = 1 - [0.45+0.10]

Pr(purple) = 1 - 0.55

Pr(purple) = 0.45

Hence it is 45% likely for Jared to randomly choose a purple ball from the bag.

Answer:

The answer is below

Step-by-step explanation:

The graph used to estimate the consumption (in billions) in the United States for the years 1900 to  2007 is attached.

The year is plotted on the x axis and the number of cigarettes is on the y axis. To estimate the number of cigarattes smoked in year 2000, we have to find the y coordinate that corresponds to an x coordinate of 2000. This is done by drawing a line vertically to touch the graph from the point 2000 on the x axis. The point it touches the graph is then traced to the y axis to get the consumption as shown in the graph attached.

From the graph  the number of cigarettes smoked in 2000 is about 420 billion cigarettes

Answer:

5

Step-by-step explanation:

15/3=5 when the y are 3 it division

Answer:

What the other guy said

Step-by-step explanation:

Answer:

Σ( xi ) / n ; $29

Step-by-step explanation:

Given the following data:

X= $27, $31, $30, $26, $25, $27, $37, $33, $32, $28, $26, $26

Number of observations (n) = 12

Mean formula (m) = ( Σ xi ) / n

Where i = each individual value in X

Mean water bill for the years is thus :

m = Σ [(27 + 31 + 30 + 26 + 25 + 27 + 37 + 33 + 32 + 28 + 26 + 26)] / 12

m = 348 / 12

m = 29

Hence, the mean water bill for the year is $29

Answer:

Your answer is -32

Step-by-step explanation:

First you add $220 and $12 together giving you $232

Then you subtract $76 from the $232 giving you $156

Then subtract $188 from $156 giving you a total of -$-32

Answer:

Yes

Step-by-step explanation:

Because a - - - - - - - - - - b

Same as b-----------------a

For example, let's say we had the equation x+10 = 30

We are adding 10 onto some unknown number x to get 30. To find x, we undo what is happening to x, so we subtract 10 from both sides. Subtraction is the inverse operation of addition.

Answer:

d, i took the test i can confirm its correct lol

Step-by-step explanation:

Answer/Step-by-step explanation:

Length of rectangle = [tex] l [/tex]

Width of rectangle = [tex] \frac{1}{3} of l - 1 = \frac{1}{3}l - 1 = \frac{l}{3} - 1 [/tex]

A. Expression for finding area of the rectangle:

Area of rectangle is given as [tex] length*width [/tex]

[tex] Area = l(\frac{l}{3} - 1) [/tex]

Or

[tex] Area = l*\frac{l}{3} - l*1 [/tex]

[tex] Area = \frac{l^2}{3} - l [/tex]

b. Expression for finding perimeter:

Perimeter of rectangle is given as [tex] 2(Length + Width) [/tex]

[tex] Perimeter = 2(l + (\frac{l}{3} - 1)) [/tex]

Or

[tex] Perimeter = 2(l) + 2(\frac{l}{3} - 1) [/tex]

[tex] Perimeter = 2l + \frac{2l}{3} - 2) [/tex]

c. Quotient of Perimeter divided by area:

[tex] 2(l + (\frac{l}{3} - 1)) [/tex] ÷ [tex] l(\frac{l}{3} - 1) [/tex]

[tex]2(l + (\frac{l}{3} - 1))[/tex] ÷ [tex]\frac{l^2 - 3l}{3}[/tex]

Change the ÷ to × and flip the fraction on your right upside down.

[tex]2(l + (\frac{l}{3} - 1)) * \frac{3}{l^2 - 3l}[/tex]

[tex]2l + 2(\frac{l}{3} - 1) * \frac{3}{l^2 - 3l}[/tex]