Write the sum without sigma notation. Then evaluate the sum.∑2k=1 40k/k+3Choose the correct answer belowA. (40⋅1/1+3)+(40⋅2/2+3) B. 40k/2+3 C. 40⋅2/2+3 D. (40⋅1.1+3)+(40⋅2/2+3)+(40⋅3/3+3)

Answers

Answer 1

Answer:

A. (40⋅1/1+3)+(40⋅2/2+3)

Step-by-step explanation:

Given that:

[tex]\sum \limits ^2 _{k=1} \dfrac{40 \ k }{k + 3}[/tex]

which can be expressed as:

=[tex]\dfrac{40\times 1 }{1 + 3} + \dfrac{40\times 2 }{2 + 3}[/tex]

=[tex]\dfrac{40 }{4} + \dfrac{80 }{5}[/tex]

= [tex]10+ 16[/tex]

= 26

[tex]\sum \limits ^2 _{k=1} \dfrac{40 \ k }{k + 3} = 26[/tex]


Related Questions

Angles Find the values of x and y

Answers

Answer:

15 23

Step-by-step explanation:

Answer:

Step-by-step explanation:

11x - 6 + 15x - 8 = 90

26x - 14 = 90

26x = 104

x = 4

11(4) - 6 = 44 - 6 = 38

13y - 14 + 38= 180

13y + 24 = 180

13y = 156

y = 12

13(12) - 14 = 156 - 14=142

A lorry driver charges $1800 to carry 60 tonnes of weight. How much will he charge for carrying 80 tonnes at the same rate

Answers

Answer:

$2400

Step-by-step explanation:

60 tonnes = $1800

80 tonnes = $?

= 1800 × 80/60

= $2400

Step-by-step explanation:

$2400 to Carry 80tonnes of weight

Homer and Bart plan to buy one computer for $499.00 strictly for gaming purposes. Games cost $49.99 each. Part A: Define each variable and write an algebraic expression to describe how much they will spend before sales tax, based on purchasing the computer and the number of games. Part B: If they purchase one computer and five games, how much do they spend before sales tax? Part C: Homer and Bart have friends. They want to purchase extra controllers. Each controller costs $24.99. Use an algebraic expression to describe how much they spend in total (before sales tax) when they purchase one computer, when they purchase any number of games, and when they purchase any number of extra controllers. Part D: What would be the total cost, before sales tax, if Homer and Bart purchase one computer, four games, and three extra controllers?

Answers

Answer:

use 499.00+the number of games times 49.99

Step-by-step explanation:

Please brailiest

Math Math Math Math Math

Answers

Answer:

see below

Step-by-step explanation:

sqrt(2)+ sqrt(98)

sqrt(2) + sqrt( 2*49)

sqrt(2) + 7sqrt(2)

8 sqrt(2)

Answer:

[tex]\sqrt{2}[/tex]+ [tex]\sqrt{98}[/tex]

 [tex]\sqrt{2}[/tex]+   [tex]\sqrt{2}[/tex] *49

[tex]\sqrt{2}[/tex] + 7[tex]\sqrt{2}[/tex]

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

After your yearly checkup, the doctor has some bad news and some good news. The bad news is that you tested positive for a serious disease, and the test is 99% accurate( i.e. that probability of testing positive given that you have the disease is .99, as is the probability of testing negative given that you don’t have the disease). The good news is that this is a rare disease, striking only one in 10,000 people. What are the changes that you actually have the disease?

Answers

Answer:

0.009804

Step-by-step explanation:

We are given;

probability of testing positive given that you have the disease is 0.99

Also, probability of not testing positive and not having the disease is 0.99

We are also told that it is a rare disease and so strikes only 1 in 1000 people = 0.0001

Let's denote positive test by T+, negative test by T¯, having the disease by D+, not having the disease by D¯.

So, we can now denote all the values in probability we have written earlier.

Thus:

P(T+ | D+) = 0.99

P(T¯ | D¯) = 0.99

P(D+) = 0.0001

Thus, P(D¯) = 1 - P(D+) = 1 - 0.0001 = 0.9999

Now, let's find probability of testing positive;

P(T+) = (P(T+ | D+) × P(D+)) + (P(T+ | D¯) × P(D¯))

Now, (P(T+ | D¯) is not given but by inspection, we can infer from the values given that it is 0.01

Thus;

P(T+) = (0.99 × 0.0001) + (0.01 × 0.9999)

P(T+) = 0.010098

Chances that one has the disease would be gotten from Baye's theorem;

P(D+ | T+) = (P(T+ | D+) × P(D+))/P(T+) = (0.99 × 0.0001)/0.010098 = 0.009804

How do you do this question?

Answers

Answer:

y' = -4eˣ sin⁵(eˣ)

Step-by-step explanation:

Part 1 of the Fundamental Theorem of Calculus simply says that the definite integral of a function is equal to the antiderivative evaluated between the limits.

∫ₐᵇ f(x) dx = F(b) − F(a), where F(x) = ∫ f(x) dx.

y = ∫ₑₓ⁰ 4 sin⁵(t) dt

To integrate, use Pythagorean identity.

y = 4 ∫ₑₓ⁰ (1 − cos²(t))² sin(t) dt

Ignoring the limits for the moment, let's say u = cos(t) and du = -sin(t) dt.

y = 4 ∫ (1 − u²)² (-du)

y = -4 ∫ (1 − 2u² + u⁴) du

y = -4 (u − ⅔u³ + ⅕u⁵) + C

y = -4 (cos(t) − ⅔ cos³(t) + ⅕ cos⁵(t)) + C

Evaluate between t = eˣ and t = 0.

y = -4 (cos(0) − ⅔ cos³(0) + ⅕ cos⁵(0)) + C − [-4 (cos(eˣ) − ⅔ cos³(eˣ) + ⅕ cos⁵(eˣ)) + C]

y = -4 (1 − ⅔ + ⅕) + 4 (cos(eˣ) − ⅔ cos³(eˣ) + ⅕ cos⁵(eˣ))

Now take derivative with respect to x.

y' = 0 + 4 (-sin(eˣ) eˣ − 2 cos²(eˣ) (-sin(eˣ) eˣ) + cos⁴(eˣ) (-sin(eˣ) eˣ))

y' = -4eˣ sin(eˣ) (1 − 2 cos²(eˣ) + cos⁴(eˣ))

y' = -4eˣ sin(eˣ) (1 − cos²(eˣ))²

y' = -4eˣ sin⁵(eˣ)

This can be more easily calculated using the Second Fundamental Theorem of Calculus.

Dimensional analysis: How many atoms are in a kilogram of silver, if there are 6.02 x 10^23 atoms per mole and silver weighs 107.9 grams/mole?

Answers

Answer:

5.58×10²⁴ atoms.

Step-by-step explanation:

From the question given above, the following data were obtained:

1 mole of silver = 107.9 g

Number of atoms in 1 mole of silver = 6.02×10²³ atoms.

Number of atoms in a kilogram of silver =.?

Next, we shall convert 1 kg of silver to grams (g). This can be obtained as follow:

1 kg = 1000g

Therefore, 1 kg of silver is equivalent to 1000g.

Finally, we shall determine the number of atoms in 1 kg (i.e 1000 g) of silver as follow:

107.9 g of silver contains 6.02×10²³ atoms.

Therefore, 1000 g of silver will contain = (1000 × 6.02×10²³) / 107.9 = 5.58×10²⁴ atoms.

Thus, a kilogram of silver contains 5.58×10²⁴ atoms.

How I do this?
3x+4y=11
X-2y=-3

Answers

Answer:

[tex]\huge\boxed{x=1,\ y=2\to(1,\ 2)}[/tex]

Step-by-step explanation:

[tex]\left\{\begin{array}{ccc}3x+4y=11\\x-2y=-3&\text{multiply both sides by (-3)}\end{array}\right\\\\\underline{+\left\{\begin{array}{ccc}3x+4y=11\\-3x+6y=9\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad\ \ \ \ 10y=20\qquad\text{divide both sides by 10}\\.\qquad\qquad\boxed{y=2}\\\\\text{subtitute it to the second equation:}\\x-2(2)=-3\\x-4=-3\qquad\text{add 4 to both sides}\\\boxed{x=1}[/tex]

please help o.o ¯\_(ツ)_/¯¯\_(ツ)_/¯¯\_(ツ)_/¯¯\_(ツ)_/¯¯\_(ツ)_/¯(┬┬﹏┬┬)(┬┬﹏┬┬)(┬┬﹏┬┬)Simplify 3x - 4 - 5x = 6 + 4x + 2

Answers

Bring all the X to the left side and all the numbers to the right side. ( remember to flip the signs )

3x - 4 - 5x = 6 + 4x + 2

3x - 5x - 4x = 6 + 2 + 4

-6x = 12

6x = -12

x = -2

Can someone help me pls!

Answers

This question is about how transformations can affect graphs.

First, we'll want to get rid of that -4 on the function of F.

So we can reflect the function over the y-axis and then compress it by a factor of 4 to make the graph [tex]x^2[/tex].

Then we can move the graph over to the left 3 because the c value is positive, meaning that we move the graph over to the left.

Finally, we can move the function of by [tex]\frac{2}{3}[/tex] because the d value is positive, meaning that we move the graph up.

Hope this helps.

頑張って!

What are the correct intermediate steps of the following data set when it is being sorted with the bubble sort? 15, 20, 10, 18
A. 15,10,20,18 -- 15,10,18,20 -- 10,15,18,20
B. 10, 20,15,18 -- 10,15,20,18 -- 10,15,18,20
C. 15,20,10,18 -- 15,10,20,18 -- 10,15,20,18 -- 10,15,18,20
D. 15,18,10,20 -- 10,18,15,20 -- 10,15,18,20 -- 10,15,18,20

Answers

Answer:

A. 15,10,20,18 -- 15,10,18,20 -- 10,15,18,20

Step-by-step explanation:

Bubble sorting can be defined as a technique or methodology whereby numbers that are not in their proper order are sorted into proper order that is from smallest to highest( increasing to decreasing order).

The method of bubble sorting involves the shuffling or swapping of adjacent numbers until the numbers are well sorted or arranged.

In the above question, we were given, a set of numbers:

15, 20, 10, 18

Step 1

20 is adjacent to 10

20 > 10

hence we swap

= 15,10,20,18

Step 2

From, 15,10, 20,18

20 is adjacent to 18

20 > 18

hence we swap

= 15,10,18,20

Step 3

From step 2, which gave us 15,10,18,20

15 us adjacent to 10

15 > 10

We swap

= 10,15,18,20

Hence,

15, 20, 10, 18 -- 15,10,20,18 -- 15,10,18,20 -- 10,15,18,20

Therefore, Option A is the correct option.

The correct intermediate steps of data 15, 20, 10, 18 set when it is being sorted with the bubble sort is; Choice A: 15,10,20,18 -- 15,10,18,20 -- 10,15,18,20.

Definition;

Bubble sort, otherwise termed the sinking sort, is a simple sorting algorithm that repeatedly steps through the list, compares adjacent elements and swaps them if they are in the wrong order.

With emphasis on the word adjacent, it is evident Choice A is the correct intermediate steps of the data set 15, 20, 10, 18 when it is being sorted with the bubble sort.

Read more:

https://brainly.com/question/15148294

What is the slope of the line?

Answers

La pendiente de una recta es la tangente del ángulo que forma la recta con la dirección positiva del eje de abscisas. En funciones no lineales, la razón de cambio varía a lo largo de la curva. La derivada de la función en un punto dado es la pendiente de la línea tangente en dicho punto.

F:V  7w7

13w-8w =20 ??????????

Answers

Answer:

w = 4

Step-by-step explanation:

13w-8w =20

Combine like terms

5w = 20

Divide each side by 5

5w/5 = 20/5

w = 4

Answer:

w=4

Step-by-step explanation:

13w-8w=20

5w=20

w=4

Find the sum. r/r^2-q^2 + 5/r+q​

Answers

Answer:

The answer is:  

[tex]\frac{6r-5q}{r^2-q^2}[/tex]

which agrees with the last answer option (D) in the list.

Step-by-step explanation:

In order to add rational expressions, we need to express them with the same denominator. Therefore we examine what factors there are in the first denominator, which happens to be a difference of squares which is readily factored out as:

[tex]r^2-q^2=(r+q)\,(r-q)[/tex]

the second denominator consists of only one of these factors: [tex](r+q)[/tex], then in order to express both rational expressions with the same common denominator, we multiply numerator and denominator of the second fraction by the factor: [tex](r-q)[/tex]

Then we get two expressions that can be easily added as shown below:

[tex]\frac{r}{(r+q)\,(r-q)} +\frac{5\,(r-q)}{(r+q)\,(r-q)} =\frac{r+5(r-q)}{(r+q)(r-q)} =\frac{r+5r-5q}{(r+q)\,(r-q)} =\frac{6r-5q}{r^2-q^2}[/tex]

if you run for 4 hours at 8miles an hour and walk 8 hours at 2 miles an hour, how far will you you have gone at the end of 12 hours?​

Answers

Answer:

48 miles

Step-by-step explanation:

run -- 4 hrs at 8 mph = 4 • 8 = 32 miles

walk -- 8 hrs at 2 mph = 8 • 2 = 16 miles

32 + 16 = 48 miles

4 hours, 8 miles per hour. 8 times 4 equals 32. 8 hours, two miles an hour. 2 times 8 equals 16. Add them up, and you get 48 miles, which is the final answer.

1 mile to yards, as a fraction..

Answers

Answer:

[tex]\frac{1}{3}[/tex]

Step-by-step explanation:

Since 3 feet is a yard, one foot is 1/3.

So that is the answer.

Answer:

1/3

1 mile to yards as a fraction would probably be 1/3. I'm not so sure...

Given the formula below, solve for x. y - y1 = m(x-x1)

Answers

Answer:

y-3 = 2/9 (x-8)

Step-by-step explanation:

Which of the following is a statistical question? A. What state were you born in? B. How tall is Ms. Lin? C. What are the ages of the students in your class? D. What is the formula for the circumference of a circle?

Answers

Answer:

C

Step-by-step explanation:

makes sense

Answer please quick

Answers

Answer:

1 metric ton is = to 1000 kilograms

BRAINLY I NEED HELP ASAPPPP!!
After game 6, her mean number of points scored per game is 9.
How many points did Maya score in game 6?

A. 4
B. 8
C. 9
D. 10

Answers

Answer:

b

Step-by-step explanation:

8

Twice the sum of six "x" and seventy eight.

Answers

Answer:

2(6x+78)

Unless it's the exact number. You hadn't specified what x is.

How do you do this question?

Answers

Step-by-step explanation:

F(x) = ∫ₐˣ t⁷ dt

F(x) is the area under f(t) between t=a and t=x.  When x=a, the width of the interval is 0, so the area is zero.

F(6) = 0, so a = 6.

F(x) = ∫₆ˣ t⁷ dt

F(6) = ∫₆⁶ t⁷ dt

F(6) = 0

evaluate the numerical expression. 8 X {[(7 + 4) X 2] - [(11 - 7) X 4]}

Answers

Answer:

48

Step-by-step explanation:

To solve this we need to do the operations in the brackets first. We should start with the innermost brackets. Then, we work our way outwards. To show my working out I will use an asterisk (*) for multiplication to not confuse X as a variable.

8*{[(7 + 4) * 2] - [(11 - 7) * 4]}  

= 8*{[(11) X 2] - [(4) X 4]}

= 8*{[22] - [16]}

= 8*{6}

= 48

Find the slope (-4,8) and (-3,-6)

Answers

Answer:

-14

Step-by-step explanation:

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

Using the above formula, slope

[tex] = \frac{8 - ( - 6)}{ - 4 - ( -3 )} \\ = \frac{8 + 6}{ - 4 + 3} \\ = \frac{14}{ - 1} \\ = - 14[/tex]

What is the value of x?
3
6
10
12

Answers

Answer:

value of x is 6.

please follow me.

Your answer would be B- 6. Hope this helps you!!

HELP ASAP PLEASE Question 1 Part A What inference can be made about the "Using Our Imaginations" section in the Newsela article "Health Benefits of Reading, Writing, Are Not Just for Patients"? Part B Which evidence best supports the answer in Part A? “Reading stories is a chance for children and adults to talk about the complicated parts of life.”

Answers

The answer to the first one is A and the second one is D

(I took the test)

Answer:

Fist one:

A

Second one:

D

Step-by-step explanation:

→!Hope this helps I toke the test!←

Given the set A=(2,5) and B=(5,7,9) find the following: AnB
a
5
b
2.9
n
2,5,7,9
7,9
d

Answers

Greetings from Brasil....

The intersection of two sets is given by the elements that are common - present in both - to the sets.

A = {2; 5}

B = {5; 7; 9}

Element in both sets = 5.... So

A ∩ B = {5}

Acellus
x = [?]°
1040
1170
X
124°
1000
Hint: Sum = (n-2)180

Answers

Since the sum of the interior angles of a polygon of n sides is (n-2)*180 degrees.

Here n=5 (polygon), so that sum is (5-2)*180 degrees, or 3*180 degrees, or 540 degrees.

Adding up the 5 interior angles shown, we get
Sum = (n-2)*180 =540
100 + 117 + 104 + 124 + x = 540 (degrees).
217 + 228 + x = 540 (degrees).
445 + x =540
Thus, x = 540 - 445 degrees, or x = -4 degrees.

Answer is x = -4

Answer:

x = 95°

Step-by-step explanation:

The sum of the interior angles of any polygon is

sum = 180° (n - 2)

Here n = 5, thus

sum = 180° × 3 = 540°

Sum the given angles in the polygon and equate to 540

104° + 117° + 100° + 124° + x = 540°, that is

445° + x = 540° ( subtract 445° from both sides )

x = 95°

Solve the linear equation. 3x = 24 x = ?

Answers

Answer:

3x =24

x = 24 -3

x = 21 (ans)

Answer:

X=8

Step-by-step explanation:

3x=24

divide each side by 3 to isolate x

x=8

Factorise P(2m+n)+(q-r)(2m-n)

Answers

Answer:

2Pm+Pn+2qm-qn-2rm+rn

Step-by-step explanation:

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