The town of Tola has a population of 45,000 and produces 6 tons of garbage each week. Express this information in terms of the function f

Answer:

  g(x) = (1/6)(x +7)^2 -8

Step-by-step explanation:

The transformation ...

  g(x) = a·f(x -h) +k

represents vertical scaling by a factor of 'a', right shift by h units, and up shift by k units. You want the function g(x) for f(x) = x^2, a = 1/6, h = -7, and k = -8. Those transformations give you ...

  g(x) = (1/6)(x +7)^2 -8

Answer:

$

180

Step-by-step explanation:

The original price is the quotient between $120 and 2/3, we get:

P = $180

We know that 2/3 of the original price is $120, then to get the original price, we need to take the quotient between $120 and 2/3.

[tex]P = \frac{\$120}{2/3} = (3/2)*\$ 120[/tex]

By taking that quotient we will see that the original price of the coat is:

[tex]P = (3/2)*\$120 = $180[/tex]

We conclude that the original price of the coat is $120.

If you want to learn more about quotients:

https://brainly.com/question/8952483

#SPJ2

Answer:

A. 8.3

B.18.7

C. 10.4

D. 1.04

Step-by-step explanation:

p(x) = 0.03x² + 0.56x + 6.35

A. Determination of p(3)

p(x) = 0.03x² + 0.56x + 6.35

x = 3

p(3) = 0.03(3)² + 0.56(3) + 6.35

p(3) = 0.03(9) + 1.68 + 6.35

p(3) = 0.27 + 1.68 + 6.35

p(3) = 8.3

B. Determination of p(13)

p(x) = 0.03x² + 0.56x + 6.35

x = 13

p(13) = 0.03(13)² + 0.56(13) + 6.35

p(13) = 0.03(169) + 7.28 + 6.35

p(13) = 5.07 + 7.28 + 6.35

p(13) = 18.7

C. Determination of p(13) – p(3)

From A and B above,

p(13) = 18.7

p(3) = 8.3

p(13) – p(3) = 18.7 – 8.3

p(13) – p(3) = 10.4

D. Determination of p(13) – p(3) / 13 – 3

From C above,

p(13) – p(3) = 10.4

p(13) – p(3) / 13 – 3 = 10.4/ 13 – 3

= 10.4 / 10

= 1.04

Answer:

x^2 -9

Step-by-step explanation:

(x + 3)(x − 3)

FOIL

first x*x =x^2

outer -3x

inner 3x

last -3*-3 =-9

Add together

x^2 -3x+3x -9

Combine like terms

x^2 -9

Answer:

2L - the third picture

2W - the fifth picture

4 - the first picture

L+2 - the 6th picture

W - the 7th picture

Step-by-step explanation:

2L - the third picture

2W - the fifth picture

4 - the first picture

L+2 - the 6th picture

W - the 7th picture

Answer:

b. $7,482.

Step-by-step explanation:

20,403 nets $5,996,106 after 35 years.

7,482 nets $2,198,837 after 35 years.

$7,482 is over 2 million and the smallest amount, so you don't have to solve for the other ones.

The real amount that must deposit each year to achieve your goal is $16,017 option (c) is correct.

An investment is a payment made to acquire the securities of other firms with the intention of making a profit.

First, we will calculate the real rate of interest:

r = [(1+nominal rate)/(1+inflation rate)] - 1

Nominal rate = 9.94% = 0.094

Inflation rate = 3.2% = 0.032

r = [(1+0.094)/(1+0.032)] - 1

After calculating,

r = 0.0653 or 6.53%

Deposit amount each year:

Future value = PV[(1+r)ⁿ - 1]/(r)

2000000 = PV[(1+0.0653)³⁵ - 1]/(0.0653)

After calculating,

PV = $16020.544

The value $16020.544 is near the $16,017.

Thus, the real amount that must deposit each year to achieve your goal is $16,017 option (c) is correct.

Learn more about the invested amount here:

brainly.com/question/16995381

#SPJ2

━━━━━━━☆☆━━━━━━━

▹ Answer

(w = 7, w = 8/5)

▹ Step-by-Step Explanation

(7 - w)(5w - 8) = 0

Separate:

7 - w = 0

5w - 8 = 0

Solve:

w = 7

5w - 8 = 0

(w = 7, w = 8/5)

Hope this helps!

CloutAnswers ❁

━━━━━━━☆☆━━━━━━━

Answer:

w = 7, 8/5

Step-by-step explanation:

(7 - w) (5w - 8) = 0

(7 - w) × (5w - 8) = 0

7 × 5w - 7 × 8 - w × 5w + w × 8 = 0

35w - 56 - 5w² + 8w = 0

- 5w² + 43w - 56 = 0

5w² - 43w + 56 = 0

5w² - 35w - 8w + 56 = 0

5w(w - 7) - 8(w - 7) = 0

(w - 7) (5w - 8) = 0

w - 7 = 0 OR 5w - 8 = 0

w = 7 OR w = 8/5

Thus, the value of w is 7, 8/5

Solve the "f" function with substitute 4 and solve the "g" function with what we get for the "f" function.

f(4) = 2(8) + 3

f(4) = 16 + 3

f(4) = 19

g(19) = 4(19) - 1

g(19) = 76 - 1

g(19) = 75

Best of Luck!

Answer: ps = 1012.5

Therefore the producers' surplus for the supply equation at the indicated unit price p is 1012.5

Step-by-step explanation:

Given that;

p = 120 + q ; p = 165

Now to find the producer's surplus for supply equation p=f(q) at the indicated unit price; we find p

so from p = 120 + q ; p = 165, if we substitute for q

120 + q = 165

q = 165 - 120 = 45

so

ps = ⁴⁵∫₀ ( 165 - (120+q) dq

ps = ⁴⁵∫₀ ( 45 - q) dq

USING THE EXPRESSION [ xⁿdx = xⁿ⁺¹ / n+1]

ps =  [45q - q²/2]₀⁴⁵

ps = [45(45) - 45²/2] [45(0) - (0)²/2]  

ps =  [2025 - 1012.5] - [0]

ps = 1012.5

Therefore the producers' surplus for the supply equation at the indicated unit price p is 1012.5

Answer: (a) 5   (b)1      (c)5    (d)120

Step-by-step explanation:

Formula for combinations: [tex]C(n,r)=\dfrac{n!}{r!(n-r)!}[/tex]

Formula for permutations: [tex]C(n,r)=\dfrac{n!}{(n-r)!}[/tex]

(a) C(5, 4)  = [tex]\dfrac{5!}{4!(5-4)!}=\dfrac{5\times4!}{4! (1)}=5[/tex]

(b) C(5, 0) = [tex]\dfrac{5!}{0!(5-0)!}=\dfrac{5!}{5! }=1[/tex]

(c) P(5, 1)  = [tex]\dfrac{5!}{(5-1)!}=\dfrac{5\times4!}{4! }=5[/tex]

(d) P(5, 5)  = [tex]\dfrac{5!}{(5-5)!}=\dfrac{5!}{1}=5!= 5\times4\times3\times2\times1=120[/tex]   [as 0!=1]

Hence, the required answer is

(a) 5   (b)1      (c)5    (d)120

Answer:

Step-by-step explanation:

The correct answer is 15.15.

The solution is 15.2625

The value of the equation 5% of 55% of 555 is A = 15.2625

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 number be represented as n = 555

Now , let the equation be represented as A

The value of A = 5% of 55% of 555

On simplifying the equation , we get

55 % of 555 = 555 x ( 55/100 )

55 % of 555 = 555 x 0.55

55 % of 555 = 305.25

Now , 5% of 55% of 555 = A

A = 5 % of 305.25

The value of A = 305.25 x ( 5/100 )

The value of A = 305.25 x ( 0.05 )

The value of A = 15.2625

Hence , the value of the equation is A = 15.2625

To learn more about equations click :

https://brainly.com/question/19297665

#SPJ2

Answer:

the flux of the flow field F across σ = 135

Step-by-step explanation:

Given that :

F = 2xi + 3yj

and σ is the cube with opposite corners at (0,0,0) and (3,3,3) oriented outwards.

Using divergence theorem,

[tex]\iint \ F.ds = \iiint \ div. f \ dV[/tex]

[tex]div \ f = \dfrac{\partial }{\partial x}2x + \dfrac{\partial}{\partial y }(3y)[/tex]

f = 2 +3 = 5

where ;

F = 2xi + 3yj

Thus , the triple integral can now be ;

[tex]= \iiint 5.dV[/tex]

[tex]=5 \iiint \ dV[/tex]

[tex]= 5 \ \int^{3}_{0}\int^{3}_{0}\int^{3}_{0} \ dV[/tex]

= 5(3)(3)(3)

= 135

Answer:

1200

Step-by-step explanation:

First we need to figure out how many bricks can be set in an hour, so you do 2.5*60, since there are 60 min. in an hour. That's 150.

Now we do 8 hours. You do 150*8, which is 1200.

Hope this helps.

Answer:

1200

Step-by-step explanation:

The reason behind this answer is because you first multiply 2.5 by 60 for the 60 minutes in an hour and ultimately get 150 then you multiply that answer by 8 to get 1200.

Answer:

[tex]n = 241[/tex]

Step-by-step explanation:

Given

[tex]5x^2 + nx + 48[/tex]

Required

Determine the highest value of n

From the given equation, 5 is a prime number;

So, the factors of x² is 5x and x or -5x and -x

Since [tex]5x^2 + nx + 48[/tex] has all shades of positive terms, we'll make use of 5x and x

The factorized expression can then be:

[tex](5x + a)(x + b)[/tex]

Open the brackets

[tex]5x^2 + ax + 5bx + ab[/tex]

Equate this to the given expression

[tex]5x^2 + ax + 5bx + ab = 5x^2 + nx + 48[/tex]

[tex]5x^2 + (a + 5b)x + ab = 5x^2 + nx + 48[/tex]

By direct comparison;

[tex]5x^2 = 5x^2[/tex]

[tex](a + 5b)x = nx[/tex]

[tex]a + 5b = n[/tex]  ---- (1)

[tex]ab = 48[/tex] --- (2)

From (2) above, the possible values of a and b are:

[tex]a = 1, b = 48[/tex]

[tex]a = 2, b = 24[/tex]

[tex]a = 3, b = 16[/tex]

[tex]a = 4, c = 12[/tex]

[tex]a = 6, b = 8[/tex]

[tex]a = 8, b = 6[/tex]

[tex]a = 12, b = 4[/tex]

[tex]a = 16, b = 3[/tex]

[tex]a = 24, b = 2[/tex]

[tex]a = 48, b = 1[/tex]

Of all these values; the value of a and b that gives the highest value of n is;

[tex]a = 1, b = 48[/tex]

So;

Substitute 1 for a and 48 for b in (2) [tex]a + 5b = n[/tex]

[tex]1 + 5 * 48 = n[/tex]

[tex]1 + 240 = n[/tex]

[tex]241 = n[/tex]

[tex]n = 241[/tex]

Hence, the largest value of n is 241

Answer:

Step-by-step explanation:

The two factors of $5x^2+nx+48$ must be in the form $(5x+A)(x+B)$. $A$ and $B$ must be positive integers to form the largest value of $n$. Therefore, $AB=48$ and $5B+A=n$. To form the largest value of $n$, $B$ must equal $48$. Therefore, $A=1$. \[5B+A=5(48)+1=\boxed{241}\]

Answer: Find the answer in the attachment

Step-by-step explanation:

The volume constrained both by the cone and the sphere is [tex]21.905\pi[/tex] cubic units.

The volume of a solid in cylindrical coordinates ([tex]V[/tex]) can be determined by the following triple integral:

[tex]V = \iiint dz\,r\,dr\,d\theta[/tex] (1)

The solid is constrained by the following equations in cylindrical coordinates:

Sphere

[tex]r^{2}+z^{2} = 32[/tex] (2)

Cone

[tex]z = r[/tex] (3)

The integration limits can be identified by using the following intervals:

[tex]z \in [0, +\sqrt{32-4^{2}}][/tex], [tex]r \in [0,4][/tex], [tex]\theta \in [0,2\pi][/tex]

And the triple integral has the following form:

[tex]V = \int\limits_{0}^{2\pi}\int\limits_{0}^{4}\int\limits_{0}^{+\sqrt{32-r^{2}}} dz\,r\,dr\,d\theta[/tex] (4)

Now we proceed to integrate the expression thrice:

[tex]V = \int\limits_{0}^{2\pi}\int\limits_{0}^{4}\sqrt{32-r^{2}}\,r\,dr\,d\theta = 10.952\int\limits_{0}^{2\pi}\,d\theta = 21.905\pi[/tex]

The volume constrained both by the cone and the sphere is [tex]21.905\pi[/tex] cubic units.

We kindly invite to check this question on triple integrals: https://brainly.com/question/6821707

A point in geometry is a location.

It has no size, width, length or depth. A point is shown by a dot. A line is defined as a line of points that extends infinitely in two directions.

Answer:

y^2+8y+16

Step-by-step explanation:

6y^2 +2y +5 - ( 5y^2 -6y-11)

Distribute the minus sign

6y^2 +2y +5 -  5y^2 +6y+11

Combine like terms

y^2+8y+16

Answer:

A rational number is a number that can be written as a fraction.

A. 7.11

=> 711/100

So, the 1st option is a rational number.

B. 4.333....

=> 4  1/3

=> 13/3

So, the 2nd option is a rational number.

C. 8/11

=> This is in its fractional form.

=> So, the 3rd option is a rational number.

D. -2852664798743

=> This can't be written in a fractional form.

=> So, the 4th option is NOT a rational number.

Answer:

The rate of change for A is 4. For B, it is 2

Step-by-step explanation:

the slope of A is 4 and for B it is 2. Slope is the same as rate of change.

Answer:

(9,3)

Step-by-step explanation:

(8+10)/2. (5+1)/2

18/2. 6/2

9,3

Answer:

[tex](y+4)(x-4)[/tex]

Step-by-step explanation:

Given the expression:

[tex]xy-4y+4x-16[/tex]

[tex](xy-4y)+(4x-16)[/tex]

Take the common factor

[tex]y(x-4)+4(x-4)[/tex]

[tex](y+4)(x-4)[/tex]

The factored expression is (x - 4)(y + 4).

To factor the expression xy - 4y + 4x - 16 by grouping, we first group the terms in pairs and look for common factors:

xy - 4y + 4x - 16

Now, let's factor by grouping:

Step 1: Group the terms in pairs.

(xy - 4y) + (4x - 16)

Step 2: Factor out the common factor from each group.

In the first group, we can factor out "y" from the two terms:

y(x - 4)

In the second group, we can factor out "4" from the two terms:

4(x - 4)

Step 3: Notice that both groups have a common factor of (x - 4). Factor it out.

(x - 4)(y + 4)

So, the factored expression is (x - 4)(y + 4).

To know more about factored:

https://brainly.com/question/34290719

#SPJ2

Answer:

0.898

Step-by-step explanation:

The formula for the Coefficient of determination = ratio of explained variation to Total variation

From the above question, we have the following values

Explained variation = 18.592

Total variation = 20.711

The coefficient of determination = 18.592 : 20.711

= 18.592/20.711

= 0.8976872194

Approximately ≈ 0.898

Therefore, the coefficient of determination is 0.898

Answer:

[tex] \boxed{ \bold{{ \boxed{ \sf8 {x}^{7} + 3 {x}^{6} + {x}^{5} + 5 {x}^{4} - 2 {x}^{3} }}}}[/tex]

Step-by-step explanation:

Here, we have to arrange the polynomial from higher power to lower power.

So, Option C is the correct option

Hope I helped!

Best regards! :D

Answer:

The answer is

Step-by-step explanation:

The distance between two points can be found by using the formula

where

(x1 , y1) and (x2 , y2) are the points

From the question the points are

(-7,-2) and (11,3)

The distance between the points is

We have the final answer as

Hope this helps you

Answer:

29,937,952 mark me as brainliest

Step-by-step explanation:

Answer:

That would be false

Step-by-step explanation:

if you look at where the decimal is, 40.7 would be bigger

Answer:

 100,000 + 10,000+ 2,000+ 700+ 80+ 3    

We can use the FOIL method to solve.

(5x + 3)(7x - 7)

(5x * 7x) + (5x * -7) + (3 * 7x) + (3 * -7)

35x - 35x + 21x - 21

0 + 0

0

Best of Luck!

Answer:

There are 10 $1 bills and 7 $5 bills

Step-by-step explanation:

7($5 bills) x 5

=35

7+3 (3 more $1 bills)

=10

10+35

=45

Answer:

$1: 10

$5: 7

Step-by-step explanation:

To find out how many of each bill is in the cash box, create an expression

x = the dollar bills

This makes the $5 bills 5x and the $1 bills x (this can also be 1x)

When it says "The number of $1 bills is 3 more than the number of $5 bills" This means that the number of $1 is x + 3 and the number of $5 is 5x

When you put it together the expression will be x + 3 + 5x = 45

First add x and 5x, making it 6x

Next subtract 3 from each side, which makes the equation 6x = 42

Lastly, divide 6 from each side, this means that x = 7

To find out how many bills there are substitute 7 wherever there is an x

This mean that the number of $1 is 7 + 3 (10), and the number of $5 bills are 5x7 (35), but its just 7 because they are $5 each