Write the series 1-0.5-2+ ... for 12 terms using summation notation

Answer:

Step-by-step explanation:

Given the sequence 1.4,5.5,9.6,13.7,...

The nth term of am arithmetic sequence is expressed as;

Tn = a+(n-1)d

a is the first term

n is the number of terms

d is the common difference

From the given data;

a = 1.4

d = 5.5-1.4 = 9.6-5.5 = 4.1

n = 72 (since we are looking for the 72nd term)

Substitute;

T₇₂ = 1.4+(72-1)(4.1)

T₇₂ = 1.4+71(4.1)

T₇₂ = 1.4+291.1

T₇₂ = 292.5

Hence the 72nd term of the sequence is 292.5

Answer:78.75

Step-by-step explanation:21 percent of 4500 945 divided my 12 which is 78.75

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

Work Shown:

(6x-2)-(-x+5)

6x-2+x-5

(6x+x)+(-2-5)

7x-7

When distributing the negative, don't forget to apply the negative to every term inside the parenthesis. So that means -x flips to x, while +5 flips to -5.

Answer:

There are 3,628,800 different ways for the runners to finish.

Step-by-step explanation:

Arrangments of x elements:

The number of possible arrangments of x elements is given by the following formula:

[tex]A_{x} = x![/tex]

In this question:

10 different runners, which means that the number of different ways that there are for the runners to finish is an arrangment of 10 elements. So

[tex]A_{10} = 10! = 3628800[/tex]

There are 3,628,800 different ways for the runners to finish.

Answer:

22

Step-by-step explanation:

Sum of two integers is 15. One integer is -7 and suppose other integer is x. Then  

x+(-7)=15

x=22

Answer:

(A) ∫₁⁵[Xₙ + k] where n ranges from 1 to 5

(B) 73.6

Step-by-step explanation:

The question is clear enough. Kudos!

So there are many players but we're focusing on Ricky.

Ricky has already recorded his score for each of the 5 rounds in the tournament.

The number of strokes in Ricky's record are to be added to or subtracted from a given number 72

ROUND 1:    [72 - 5] strokes = 67

ROUND 2:   [72 + 6] strokes = 78

ROUND 3:   [72 - 2] strokes = 70

ROUND 4:   [72 + 4] strokes = 76

ROUND 5:   [72 + 5] strokes = 77

(A) Write an expression to represent Ricky's total number of strokes for the five rounds.

Do not panic at this first exercise. You are to write an expression which when evaluated, will give the total number of strokes for all five rounds!

You are already given an abstract number '72' to work with in this question.

It is a fixed quantity which influences the value of strokes for each round.

We will represent this by an algebra, if we have to create the above required expression.

The expression will then be:

∫₁⁵[Xₙ + k] where n ranges from 1 to 5

You already know that the sigma sign '∫' represents summation and that's summation from the subscript '1' to the superscript '5'.

X₁ would be -5,   X₂ would be +6,   X₃ would be -2,   X₄ would be +4,   X₅ would be +5

K is the constant 72

(B) What was Ricky's average number of strokes per round?

Out of the 5 rounds, the average number of strokes per round would be

[67 + 78 + 70 + 76 +77] ÷ 5

= 368/5  = 73.6

Answer:

its 12 :)

Step-by-step explanation:

Answer:

12

Step-by-step explanation:

THE ANSWER IS 12

Answer:

x=(3-y)/2  

y=3-2x)

Step-by-step explanation:

2x+y = 3

x=(3-y)/2

y=3-2x)

Answer:  [tex]X =\frac{3-y}{2}[/tex]  OR  [tex]y = 3 - 2x[/tex]

Step-by-step explanation:

Answer:

The volume of cone changing at rate [tex]\frac{400}{3}\pi in^3/s[/tex]

Step-by-step explanation:

Let r be the radius of cone and h be the height of cone

[tex]\frac{dr}{dt}=2 in/s[/tex]

[tex]\frac{dh}{dt}=-4 in/s[/tex]

We have to find the rate at which the volume of cone changing when r=10 in and h=20 in

Volume of cone

[tex]V=\frac{1}{3}\pi r^2 h[/tex]

Differentiate w.r.t t

[tex]\frac{dV}{dt}=\frac{1}{3}\pi (2rh\frac{dr}{dt}+r^2\frac{dh}{dt})[/tex]

Substitute the values

[tex]\frac{dV}{dt}=\frac{1}{3}\pi(2\times 10\times 20\times 2+(10)^2\times (-4))[/tex]

[tex]\frac{dV}{dt}=\frac{1}{3}\pi(400)=\frac{400}{3}\pi in^3/s[/tex]

Hence, the volume of cone changing at rate [tex]\frac{400}{3}\pi in^3/s[/tex]

Answer:

Nope

Step-by-step explanation:

It's a exponent, x^2 means x*x so it's actually a function

Answer:

-2

Step-by-step explanation:

Answer:

Step-by-step explanation:

Its 0.42

Answer:

[tex]y= -\frac{7}{3}x -7[/tex]

Step-by-step explanation:

Answer:

y

=

−

7

3

x

−

7

Step-by-step explanation:

Brainliest?

Answer:

She can play a total of 7 games.

Step-by-step explanation:

First, S must be 4, as if S was 5 the sum would be a 4 digit number.

T+N should be greater than 10 as we want to find the maximum.

Similarly, A+U must be greater than 10, making O equal to 9

We know that A+U-10 = T+N if T+N is less than 10 -- if T+N is greater than 10, A+U-10 = T+N - 10

Writing a quick python script that's not the cleanest nor most concise, I have

import pandas as pd

sols = []

sols_combos = []

num_sols = 0

for a in range(0, 10):

   for u in range (0,10):

       for t in range(0,10):

           for n in range(0,10):

               if (len({a,u,t,n}) == 4) & (4 not in {a,u,t,n}) & (9 not in {a,u,t,n}):

                   if (a+u >= 10):

                       if (t+n >= 10):

                           if ((a+u-10) == (t+n-10)):

                               sols.append(a+u-10)

                               sols_combos.append([a,u,t,n])

                               num_sols += 1

                       else:

                           if ((a+u-10) == (t+n)):

                               sols.append(a+u-10)

                               sols_combos.append([a,u,t,n])

                               num_sols += 1

list_max = [i for i, x in enumerate(sols) if x == max(sols)]

pd.Series(sols_combos).loc[list_max]

as my script.

the maximum I get for F is 5, and the solutions, in terms of A, U, T, and N are as follows:

[7, 8, 0, 5]

[7, 8, 2, 3]

[7, 8, 3, 2]

[7, 8, 5, 0]

[8, 7, 0, 5]

[8, 7, 2, 3]

[8, 7, 3, 2]

[8, 7, 5, 0]

This means that F is 5

Answer:

6570

Step-by-step explanation:

18x365=^

Answer:

9%=15,000

7%=12,000

thats what i think.

Answer:

The amount of 12% note is $90,000

The amount of 9% note is $80,000

Step-by-step explanation:

Missing word "The amount of the 12% note is $ and the amount of the 9% note is $"

Selling price = $170,000

Let x be the amount of money paid short term, therefore the amount of money paid long term is (170000 - x)

Given total annual interest = $18,000

Total annual interest = Interest due to short term (x) + interest due to long term (170000 - x)

18,000 = 0.12x + 0.09*(170000 - x)

18,000 = 0.12x + 15,300 - 0.09x

18,000 = 0.03x + 15,300

0.03x = 18,000 - 15,300

0.03x = 2,700

x = 2,700/0.03

x = 90,000

So, the amount of 12% note is $90,000

So long term paid money = $170,000 - $90,000 = $80,000

So, the amount of 9% note is $80,000

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

2x + 1 =5

2x=4

x=2

First isolate the term containing x which is 2x.

Subtract 1 from both sides to get 2x = 4.

Since x is being multiplied by 2, divide both sides by 2 and we have x = 2.

Answer:

x=-2

Step-by-step explanation:

Step 1: Subtract 6 from both sides.

−2x+6−6=10−6

−2x=4

Step 2: Divide both sides by -2.

−2x=4

Answer: 41-7=m

Mike is 34 yrs

Step-by-step explanation:

Answer:

the point C(x,0) = C(3,0) is the point where AC + BC is minimum.

Step-by-step explanation:

Solution:

This question is very simple to solve.

We need to find the x and y elements of point C, which is on the x-axis such that AC + BC = minimum.

So,

As, we have said that, point C is on the x-axis then, it means its y co ordinate will be equals to zero.

Now, we just need to find x co ordinate of the point C.

C (x, 0) as it is on the y -axis.

So, for that, we need to take the mirror image of point B. It means, its x co-ordinate will remain same but y co-ordinate will be negative.

So, our mirror image of B(6,9) = B'(6,-9)

Now, we have to join the points A and B'. Point C, which we are trying to find is the point where this line AB' intersects with x - axis.

So,

Slope of the line AB'

m = [tex]\frac{y1-y2}{x1-x2}[/tex]

m = [tex]\frac{3- - 9}{2 - 6}[/tex] =  [tex]\frac{3+9}{2-6}[/tex]

m = [tex]\frac{12}{-4}[/tex] = -3

m = slope = -3

We also know that the equation of line:

y = mx + b

where b = y-intercept.

Now, we need to find the y - intercept of this line.

y = (-3) x + b

where y = -9 and x = 6

so,

-9 = (-3) (6) + b

b = -9 + 18

b = 9 = y - intercept.

SO,

y = mx + b

and For point C(x, 0) y = 0

0 = -3x + 9

Solve for x:

3x = 9

x = 3

Hence, the point C(x,0) = C(3,0) is the point where AC + BC is minimum.

Answer:

0.63

Step-by-step explanation:

Answer:

The mean of the sampling distribution of p is of 0.7 and the standard deviation 0.029

Step-by-step explanation:

We use the Central Limit Theorem to solve this question. So

Central Limit Theorem

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]

Percentage of 70%, sample of 250.

This means that [tex]p = 0.7, n = 250[/tex]

Mean:

[tex]\mu = p = 0.7[/tex]

Standard deviation:

[tex]s = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.7*0.3}{250}} = 0.0290[/tex]

The mean of the sampling distribution of p is of 0.7 and the standard deviation 0.029

Answer:

μp^ ​​​​= 0.7

σp^ = √0.7(0.3)/250​​​

Step-by-step explanation:

I had this question on khans

5789 he has that much holp this helps

Answer:

77.5

Step-by-step explanation:

105-27.5

Answer: 9

Step-by-step explanation:

2x+3

2(3)+3

6+3

9

We know the value of x. We just have to substitute 3 in x in the equation.

2(3) + 3

6 + 3

9

9 is your answer. I hope this helps! Let me know if you need more help!

Answer:

no solutions or infinite solutions

Step-by-step explanation:

Step-by-step explanation:

True

When an equation has one solution,The variable terms on both sides are the same

Answer:

true

hope it helps

thank you.....

Answer:

[tex]1.\ x = 5\ in[/tex]

[tex]2.\ x = 5\ mi[/tex]

[tex]3.\ x = 8.6\ km[/tex]

[tex]4.\ x= 14.1\ mi[/tex]

Step-by-step explanation:

Given

See attachment for triangles

Required

Determine the missing sides

All 4 triangles are right-angled. So, to calculate the missing sides, we apply Pythagoras theorem which states that:

[tex]Hyp^2 = Adj^2 + Opp^2[/tex]

Solving (1):

[tex]Hypotenuse = 13[/tex]

So, we have:

[tex]13^2 = 12^2 + x^2[/tex]

[tex]169 = 144 + x^2[/tex]

Make [tex]x^2[/tex] the subject

[tex]x^2 = 169 - 144[/tex]

[tex]x^2 = 25[/tex]

Take positive square root of both sides

[tex]x = \sqrt{25[/tex]

[tex]x = 5\ in[/tex]

Solving (2):

[tex]Hypotenuse = x[/tex]

So, we have:

[tex]x^2 = 4^2 + 3^2[/tex]

[tex]x^2 = 16 + 9[/tex]

[tex]x^2 = 25[/tex]

Take positive square root of both sides

[tex]x = \sqrt{25[/tex]

[tex]x = 5\ mi[/tex]

Solving (3):

[tex]Hypotenuse = 14.7[/tex]

So, we have:

[tex]14.7^2 = x^2 + 11.9^2[/tex]

[tex]216.09 = x^2 + 141.61[/tex]

Make [tex]x^2[/tex] the subject

[tex]x^2 = 216.09 - 141.61[/tex]

[tex]x^2 = 74.48[/tex]

Take positive square root of both sides

[tex]x = \sqrt{74.48[/tex]

[tex]x = 8.6\ km[/tex]

Solving (4):

[tex]Hypotenuse = 15.4[/tex]

So, we have:

[tex]15.4^2 = x^2 + 6.3^2[/tex]

[tex]237.16 = x^2 + 39.69[/tex]

Make [tex]x^2[/tex] the subject

[tex]x^2= 237.16 - 39.69[/tex]

[tex]x^2= 197.47[/tex]

Take positive square root of both sides

[tex]x= \sqrt{197.47[/tex]

[tex]x= 14.1\ mi[/tex]