A 6-pound container of detergent costs $4.38. what is the price per pound?

It looks like you are trying to compute the improper integral,

[tex]I = \displaystyle\int_1^\infty \dfrac{\mathrm dx}{x(9+\ln^2(x))}[/tex]

or some flavor of this. If this interpretation is correct, substitute u = ln(x) and du = dx/x. Then

[tex]I = \displaystyle\int_0^\infty \dfrac{\mathrm du}{9+u^2} \\\\ = \frac13\arctan\left(\frac u3\right)\bigg|_{u=0}^{u\to\infty} \\\\ = \frac13\lim_{u\to\infty}\arctan\left(\frac u3\right) \\\\ = \frac13\times\frac\pi2 = \boxed{\frac\pi6}[/tex]

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Answer:

  (x +3) -14

Step-by-step explanation:

The total of a number and 3 will be represented by (x +3). Fourteen less than that is ...

  (x +3) -14  or  -14 +(x +3)

Answer:

Step-by-step explanation:

You have not provided the answers to choose from.

The expression can be simplified to δ⁴/a, but I cannot tell if that is one of the choices.

Step-by-step explanation:

simple formula application :

a1 = 8 + 3×(1-1) = 8

a2 = 8 + 3×(2-1) = 11

a3 = 8 + 3×(3-1) = 14

a4 = 8 + 3×(4-1) = 17

...

Answer:

h²=p²+b²

(7√2)²=x²+x²

(49×2)=2x²

2x²=49ײ

x²=49×2/2

x²=49

x=√49=7

x=7

OAmalOHopeO

Step-by-step explanation:

Fraction =

[tex] \frac{10}{100} = \frac{1}{10} [/tex]

Ratio is 1 : 10

Answer:

probability of the product of the chosen integers being a multiple of 3 is P(E)= 1 - (91/285)

=194/285 or 0.6807.

Step-by-step explanation:

The sample space of all possible choices of three integers from the set {1,2,…..,20} has C(20,3) = (20×19×18)/3! elements.

The complement of the event space E consists of all possible choices of three integers from the complement of the set of all the multiples of 3 in the above set because the product of the chosen integers is a multiple of 3 if and only if at least one of them is a multiple of 3. Hence we have to choose three elements from the set {1,2,4,5,7,8,10,11,13,14,16,17,19,20} which has 14 elements.

Hence

|E'| = C(14,3)

= 14×13×12/3!.

Therefore probability P(E')

= |E'|/|S|

= (14×13×12)/(20×19×18)

= (14×13×2)/(20×19×3)

=(7×13)/(5×19×3)

= 91/285.

Therefore the required probability of the product of the chosen integers being a multiple of 3 is P(E)= 1 - (91/285)=194/285 or 0.6807.

Answer:

V = 34,13*π   cubic units

Step-by-step explanation: See Annex

We find the common points of the two curves, solving the system of equations:

y²  = 2*x                           x = 2*y  ⇒  y = x/2

(x/2)² = 2*x

x²/4 = 2*x

x  =  2*4         x  = 8      and   y = 8/2       y = 4

Then point  P ( 8 ;  4 )

The other point Q is  Q ( 0; 0)

From these  two points, we get the integration limits for dy ( 0 , 4 )are the integration limits.

Now with the help of geogebra we have: In the annex segment ABCD is dy then

V = π *∫₀⁴ (R² - r² ) *dy   =  π *∫₀⁴ (2*y)² - (y²/2)² dy =  π * ∫₀⁴ [(4y²) - y⁴/4 ] dy

V = π * [(4/3)y³ - (1/20)y⁵] |₀⁴

V =  π * [ (4/3)*4³ - 0 - 1/20)*1024 + 0 )

V = π * [256/3  - 51,20]

V = 34,13*π   cubic units

Answer:

Step-by-step explanation:

0.09x - 0.085x = 25

0.005x = 25

x = 5000

The loan is for Rs 5000

Answer:

The answer is A

Step-by-step explanation:

(-2,-3) (3,-4) (0,-1) (-7,3)

inverse means the opposite signs

(2,3) (-3,4) (0,1) (7,-3)

Answer:

28462.5

Step-by-step explanation:

During the first year it gained 10% and during his second year he gained 15% so you first add those and you get 25%.

Then you multiply 25% with 37,950.

25/100 * 37950 = 948,750/100

= 9487.5

To get the original amount you subtract 9487.5 from 37,950

37,950 - 9487.5 = 28462.5

So the original amount was 28462.5

Answer:

[tex]x = -7[/tex] and [tex]x = 2[/tex]

Step-by-step explanation:

Given

See attachment for graph

Required

Find x, for [tex]f(x)= 1[/tex]

From the graph, we have the following readings

[tex]f(x)= 1[/tex] when:

[tex]x = 2[/tex] and [tex]x = -7[/tex]

Hence, (d) is correct

Answer:

48 NO seña hfjxsmisns sisbxbd

Step-by-step explanation:

9514 1404 393

Answer:

Step-by-step explanation:

A) If we let x represent "a number", then "seven times a number" is 7x. When 5 is subtracted from that, we have ...

  7x -5 . . . . . 5 subtracted from 7 times a number

This is said to be 9, so ...

  7x -5 = 9 . . . . . . . 5 from 7 times a number is 9. Your equation.

__

B) To solve this, we can add 5 to both sides. This eliminates the constant term we don't want on the left.

  7x = 14

Now, we can divide by 7, the coefficient of x that we don't want.

  x = 14/7

  x = 2

Answer:

$21.9 per gram

Step-by-step explanation:

Take the total price and divide by the number of grams

$162.18/7.4 grams

$21.91621 per gram

Rounding to the nearest tenth

$21.9 per gram

Answer:

$21.90 per gram (to the nearest tenth)

Step-by-step explanation:

Given information:

To find how much the necklace was worth per gram, divide the total cost by the number of grams:

[tex]\sf Worth\:per\:gram = \dfrac{\$162.18}{7.4\:g}=\$21.91621622... \:per\:gram[/tex]

Therefore, the necklace is worth $21.90 per gram (to the nearest tenth).

Answer:

If there are points that are named you can name it that way

Step-by-step explanation:

If there is a point and it's called A, and there is another point and it is called B, and they form a line together, you can call it "Line AB"

Answer:

a) 0.55 = 55% probability that the person is traveling on business

b) 0.14 = 14% probability that the person is traveling for business on a privately owned plane.

c) 0.2545 = 25.45% probability that the person arrived on a privately owned plane, given that the person is traveling for business reasons.

d) 0.2 = 20% probability that the person is traveling on business, given that the person is flying on a commercially owned plane.

Step-by-step explanation:

Conditional Probability

We use the conditional probability formula to solve this question. It is

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]

In which

P(B|A) is the probability of event B happening, given that A happened.

[tex]P(A \cap B)[/tex] is the probability of both A and B happening.

P(A) is the probability of A happening.

Question a:

50% of 60%(major airlines)

70% of 20%(privately owned airplanes)

80% of 100 - (60+20) = 20%(comercially owned airplanes). So

[tex]p = 0.5*0.5 + 0.7*0.2 + 0.8*0.2 = 0.55[/tex]

0.55 = 55% probability that the person is traveling on business.

Question b:

70% of 20%, so:

[tex]p = 0.7*0.2 = 0.14[/tex]

0.14 = 14% probability that the person is traveling for business on a privately owned plane.

Question c:

Event A: Traveling for business reasons.

Event B: Privately owned plane.

0.55 = 55% probability that the person is traveling on business.

This means that [tex]P(A) = 0.55[/tex]

0.14 = 14% probability that the person is traveling for business on a privately owned plane.

This means that [tex]P(A \cap B) = 0.14[/tex]

Desired probability:

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.14}{0.55} = 0.2545[/tex]

0.2545 = 25.45% probability that the person arrived on a privately owned plane, given that the person is traveling for business reasons.

Question d:

Event A: Commercially owned plane.

Event B: Business

80% of those arriving on other commercially owned planes are traveling for business reasons.

This means that:

[tex]P(B|A) = 0.2[/tex]

0.2 = 20% probability that the person is traveling on business, given that the person is flying on a commercially owned plane.

Answer:

A

Step-by-step explanation:i did the test

The value of the floating point number is A = 0.00072

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

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

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

Substituting the values in the equation , we get

A = 7.2e⁻⁴

On simplifying the equation , we get

A = 7.2 x 10⁻⁴

The value of the decimal point is moved 4 units to the left , so

The number A is A = 0.00072

Hence , the floating point number is A = 0.00072

To learn more about equations click :

https://brainly.com/question/19297665

#SPJ2

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Answer:

  92°

Step-by-step explanation:

The "givens" tell you the E and F are midpoints of their respective segments. That means EF ║ AB and angles DBF and EFC are "corresponding" angles with respect to transversal BC and those parallel lines. Corresponding angles are congruent, so ...

  m∠DBF = m∠EFC = 92°

Answer:

part 1:

a) After 37.72 years, there will be $270,183.29421

b) After 11.9 years, there will be double the amount originally put in the account(60,015.17148)

part 2:

38 years

Step-by-step explanation:

a)

30000(1.06)^t

t=37.72

30000(1.06)^37.73 = 270,183.29421

b)

30000(1.06)^t

t=11.9

30000(1.06)^11.9 = 60,015.17148

part 2)

37.72 rounded to the nearest tenth is 38

... select this as the brainliest please!!...

Answer:

i) 154m

ii) 495m^2

Step-by-step explanation:

2 layers around the garden = 2*perimeter = 2(10+20+12+35) = 2(77) = 154

shape is a trapezium, area = h(a+b)/2 = 18(20+35)/2 = 495

Step-by-step explanation:

the answer is regular octagon

i think

Answer:

b the answer

Step-by-step explanation:

Answer:

3.75 hours

Step-by-step explanation:

d = rt

where d is the distance, r is the rate and t is the time

45 = 12 t

Divide each side by 12

45/12 = t

3.75 hours = t

Answer:

The missing side length is of 5.

Step-by-step explanation:

The sides are proportional, which means that the missing side can be found using a rule of three.

x - 10

3 - 6

Applying cross multiplication:

[tex]6x = 30[/tex]

[tex]x = \frac{30}{6} = 5[/tex]

The missing side length is of 5.

Answer:

7x is monomial according to question.

Answer:

1/52

Step-by-step explanation:

Step-by-step explanation:

We determined above that the greatest perfect square from the list of all factors of 96 is 16.

Answer:

B. 13 units

Step-by-step explanation:

let

(x1 , y1) = (-4 , -6)

(x2 , y2) = (1 , 6)

distance between CD = root (x2 - x1)^3 + (y2 - y1)

= root {1 - ( -4)}^2 + {6 - ( -6)}^2

= root {1 +4}^2 + {6+6}^2

= root 5^2 + 12^2

= root 25 + 144

= root 169

= 13 units ans