Complete the following problem "by hand", using pencil and paper. Start with a general equation, and simplify one step at a time. Or, use the shortcut method shown in class (circling the appropriate values). You must show more than just the answer. Use correct math notation and complete math sentences. The goal is not merely to get the right answer, but to show me that you understand the correct process to arrive at the right answer.

9514 1404 393

Answer:

  r ≈ 19.6% per day

Step-by-step explanation:

The growth of the population can be modeled by ...

  P = P0 × (1 +r)^t

where P0 is the initial population, r is the growth rate (per day), and t is the number of days. Using the given numbers, we can find r to be ...

  600,000 = 100,000 × (1 +r)^10

  6^(1/10) = 1 +r

  r = 6^0.1 -1 ≈ 0.196231

The growth rate per day is about 19.6%.

9514 1404 393

Answer:

  (a) the diagram is incorrect

Step-by-step explanation:

There is no overlap between the sets of rational and irrational numbers. The diagram is incorrect.

v=t^2-8t+15

[tex]\boxed{\sf {\displaystyle{\int}^b_a}x^ndx=\left[\dfrac{x^{n+1}}{n+1}\right]^b_a}[/tex]

[tex]\\ \sf\longmapsto s={\displaystyle{\int}}vdt[/tex]

[tex]\\ \sf\longmapsto s={\displaystyle{\int^4_2}}t^2-8t+15[/tex]

[tex]\\ \sf\longmapsto s=\left[\dfrac{t^3}{3}-8\dfrac{t^2}{2}+15t\right]^4_2[/tex]

[tex]\\ \sf\longmapsto s=\left[\dfrac{t^3}{3}-4t^2+15t\right]^4_2[/tex]

[tex]\\ \sf\longmapsto s=\left(\dfrac{4^3}{3}-4(4)^2+15(4)\right)-\left(\dfrac{2^3}{3}-4(2)^2+15(2)\right)[/tex]

[tex]\\ \sf\longmapsto s=\left(\dfrac{64}{3}-64+60\right)-\left(\dfrac{8}{3}-16+30\right)[/tex]

[tex]\\ \sf\longmapsto s=\left(\dfrac{64}{3}-4\right)-\left(\dfrac{8}{3}+14\right)[/tex]

[tex]\\ \sf\longmapsto s=\dfrac{64}{3}-4-\dfrac{8}{3}-14[/tex]

[tex]\\ \sf\longmapsto s=\dfrac{64}{3}-\dfrac{8}{3}-4-14[/tex]

[tex]\\ \sf\longmapsto s=\dfrac{46}{3}-18[/tex]

[tex]\\ \sf\longmapsto s=15.3-18[/tex]

[tex]\\ \sf\longmapsto s=|-2.7|[/tex]

[tex]\\ \sf\longmapsto s=2.7km[/tex]

Answer:

A positive number.

Step-by-step explanation:

Absolute value means that no matter if the number is positive or negative, it will always be positive, e.g. | -4 | would be 4 or | 4 | would also be 4.

Answer:

28

Step-by-step explanation:

x=blue

y=white

x+y=40

30x+20y=920

30(x+y=40) ; 30x+30y=1200___[1]

30x+20y=920 ; 30x+20y=920___[2]

[1]-[2] : 30x+30y-30x-20y=1200-920

       10y=280

       y=28

painter buys 28 white gallons

Answer:

1.309

Step-by-step explanation:

75° =the radian of 1.309

hope it's right have a great day!

Answer:

[tex] \frac{5 {\pi}^{c} }{12} [/tex]

Step-by-step explanation:

Radian measure of 75°

[tex] = 75 \times \frac{ {\pi}^{c} }{180 \degree} \\ \\ = \frac{5 {\pi}^{c} }{12} [/tex]

This is because the fraction 1/10 turns into 0.1

Note that in 0.1, the "1" is in the tenths place to represent "one tenth".

Answer:

15.

(P.S: Messi is the greatest footballer of all time) :)

To get the number of people who like both Messi and Ronaldo, you will add the two figures and the remain 20 that is not in the box minus x =120

The decimal for the first one is 0.4, and the fraction is 2/5.

The second one is also 0.4 and 2/5.

Yes, this means that both of these models are equal to each other. This is because Model 1 is equal to 4/10, while Model 2 is equivalent to 40/100. 4/10 is the same thing as 40/100, though. It's just a little bit more simplified, but the fully simplified answer would be 2/5.

So, therefore, the final answer is that both of these models are equal.

Anyways, I hope that this has helped you.

C. ....................

Regarding aggregate supply in long and short run (C) is the correct option.

The whole supply of goods and services produced within an economy at a certain overall price in a given period is known as aggregate supply, also known as total output.

What is the TRUE statement below regarding aggregate supply in the long and short run ?

During short run there is no relationship between price level and RGDP.

The intersection of the aggregate demand and short-run aggregate supply curves determines real GDP and price level in the short run. However, keep in mind that in the near run, sticky pricing may impede the economy from attaining its natural level of employment and output.

Hence we can say that In the short run, there is no relationship between price level and RGDP , (c) option is the correct answer.

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Answer:

10800

Step-by-step explanation:

Answer:

-6 + 4 = -2

Step-by-step explanation:

Just start from -6 then go to the right four places and you'll get -2

9514 1404 393

Answer:

  (a)  103°

Step-by-step explanation:

The trapezoid is isosceles, so left-side angles are congruent to right-side angles. That is, ∠2≅∠3.

Each side of the trapezoid is a transversal between two parallel lines. The interior angles of the trapezoid are "consecutive interior angles", so are supplementary.

  ∠2 = ∠3 = 180° -77° = 103°

Formula-

If a set has “n” elements, then the number of subset of the given set is 2n and the number of proper subsets of the given subset is given by 2n-1. Consider an example, If set A has the elements, A = {a, b}, then the proper subset of the given subset are { }, {a}, and {b}

Symbol that can be used-

The symbol "⊆" means "is a subset of". The symbol "⊂" means "is a proper subset of".

Hope it helps you... pls mark brainliest if it helped you.

9514 1404 393

Answer:

  (a) 1. Distributive property 2. Combine like terms 3. Addition property of equality 4. Division property of equality

Step-by-step explanation:

Replacement of -1/2(8x +2) by -4x -1 is use of the distributive property, eliminating choices B and D.

In step 3, addition of 1 to both sides of the equation is use of the addition property of equality, eliminating choice C. This leaves only choice A.

_____

Additional comment

This problem makes a distinction between the addition property of equality and the subtraction property of equality. They are essentially the same property, since addition of +1 is the same as subtraction of -1. The result shown in Step 3 could be from addition of +1 to both sides of the equation, or it could be from subtraction of -1 from both sides of the equation.

In general, you want to add the opposite of the number you don't want. Here, that number is -1, so we add +1. Of course, adding an opposite is the same as subtracting.

In short, you can argue both choices A and C have correct justifications. The only reason to prefer choice A is that we usually think of adding positive numbers as addition, and adding negative numbers as subtraction.

Answer:1. Distributive property 2. Combine like terms 3. Addition property of equality 4. Division property of equality

Step-by-step explanation:

x - 2 < 5   ⇒   x < 7

x + 7 > 6   ⇒   x > -1

Together, we have -1 < x < 7, which in set notation is

[tex]\left\{x \mid -1 < x < 7\right\}[/tex]

(third choice)

Answer:

you go this! i ant expain but its mostly false and rue but sorry

Step-by-step explanation:

[tex]750[/tex] grams is [tex]25%[/tex][tex]%[/tex] percentage of [tex]3[/tex] kilograms.

A percentage is a number or ratio that represents a fraction of [tex]100[/tex].

[tex]\text{Percentage}=\dfrac{\text{actual value}}{\text{total value}}\times 100[/tex]

[tex]3[/tex] kilograms = [tex]3000[/tex] grams

So, the required percent = [tex]\frac{750}{3000}[/tex] × [tex]100[/tex] = 25

Thus, [tex]750[/tex] grams is [tex]25%[/tex][tex]%[/tex] percent of [tex]3[/tex] kilograms.

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Area of rectangle = Length * Width

Area = 11.3 cm * 14.8 cm

Area = 167.24

Perimeter of rectangle = 2 (L + W)

Perimeter = 2 (11.3 cm + 14.8 cm)

Perimeter = 2 (26.1 cm)

Perimeter = 52.2 cm²

Area of rectangle is 167.24 cm²

Perimeter of rectangle is 52.2 cm²

Answer:

Pretty sure it would be 525/1500

Step-by-step explanation:

Read the problem outloud and you would hear that 525 is divided BY 1500, so 525 goes on top of the line since it is being divided by 1500. hope this helps!

Answer:

525 ÷ 1500

1500/525

525

-------

1500

are the correct answers.

Step-by-step explanation:

9514 1404 393

Answer:

  (x, y) = (1/2, 1)

Step-by-step explanation:

Subtract twice the second equation from the first to eliminate the x-variable.

  (2/x +3/y) -2(1/x -4/y) = (7) -2(-2)

  11/y = 11 . . . . . . . simplify

  y = 1 . . . . . . . . multiply by y/11

__

Substituting into the second equation gives ...

  1/x -4/1 = -2

  1/x = 2 . . . . . . add 4

  1/2 = x . . . . . . multiply by x/2

The solution is (x, y) = (1/2, 1).

_____

Additional comment

The attached graph seems to show that the graphs of the two equations also intersect at (x, y) = (0, 0). However, careful consideration of these equations leads to the conclusion that x=0 and y=0 are not in the domain of either equation. (Division by 0 is undefined.) So, the only solution is (x, y) = (1/2, 1).

If you were to multiply both equations by xy to eliminate fractions, you would, indeed, arrive at the conclusion that (x, y) = (0, 0) is a solution. As we noted, that "solution" is extraneous. Whenever you multiply an equation by an expression that can have the value 0, you need to be careful to exclude any "solution" that makes that expression 0.

Answer:

[tex]4( \sqrt[5]{ {x}^{2} y} ) + 3( \sqrt[5]{ {x}^{2}y } ) \\ [/tex]

factorise out the 5th root of x²y :

[tex] = \sqrt[5]{ {x}^{2}y } (4 + 3) \\ = 7( \sqrt[5]{ {x}^{2} y} )[/tex]

Answer:

[tex]\$\ 6400[/tex]

Step-by-step explanation:

1. Approach

The easiest way to solve this problem is to find the area of the first room with the dimensions of (12ft) by (14ft). Then one will divide the cost of carpeting the room by the area of the room, this will yield the price of carpeting per square foot. After finding the price of carpeting per square foot, one will find the area of the second room, with the dimensions of (48ft) by (56ft). Finally, one will multiply the price per square foot of carpeting by the area of the second room to find the price for carpeting the second room.

2. Find the area of the first room

Assume that the first room is a rectangle. the following formula can be used to find the area of a rectangle,

[tex](length)(width)=Area[/tex]

The following are the dimensions of the given room,

[tex]length = 14\\width = 12[/tex]

Substitute into the formula to find the area and simplify to solve,

[tex](length)(width)=Area[/tex]

[tex](14)(12)=Area_1[/tex]

[tex]168=Area_1[/tex]

3. Find the price of carpeting per square foot

To find the price of carpeting per square foot, divide the total price for carpeting the first room by the area of the first room.

[tex]\frac{carpeting\ price_1}{area_1}[/tex]

[tex]=\frac{400}{168}[/tex]

Simplify,

[tex]=\frac{400}{168}[/tex]

[tex]=\frac{50}{21}[/tex]

4. FInd the area of the second room

Assume that the second room is also a rectangle. Use a similar strategy to find the area of this room as used for the area of the first room.

[tex](length)(width)=Area[/tex]

[tex]length = 48\\width = 56[/tex]

Substitute and simplify to sovle,

[tex](length)(width)=Area[/tex]

[tex](48)(56)=Area_2[/tex]

[tex]2688=Area_2[/tex]

5. Find the price for carpeting the room

Multiply the area of the room by the price for carpeting per square foot to find the price for carpeting the second room.

[tex](Area_2)*(carpeting\ price)[/tex]

[tex]2688=Area_2[/tex]

[tex]\frac{50}{21}=carpeting\ price[/tex]

[tex](Area_2)*(carpeting\ price)[/tex]

[tex]=(2688)*(\frac{50}{21})[/tex]

Simplify to solve,

[tex]=(2688)*(\frac{50}{21})[/tex]

[tex]=(2688)*(\frac{50}{21})[/tex]

[tex]=6400[/tex]

Answer:

Given [tex]f(x)=2x^3+4[/tex], the average rate of change of [tex]f[/tex] on the interval [tex][4,6][/tex] is [tex]152[/tex]

Step-by-step explanation:

Applying the average rate of change formula, we find[tex]\frac{f(6)-f(4)}{6-4}=\frac{2\cdot6^3+4-2\cdot4^3-4}2=\frac{432-128}2=\frac{304}2=152[/tex]

Answer:

D ig?

Step-by-step explanation:

Because opposite angles are equal in parallelogram

Answer: y = 8, x =5

Step-by-step explanation:

x+y = 13

or, x = 13-y

so

2x - y = 2

substituting x's value

2(13-y)-y = 2

or, 26-2y-y = 2

or, 26-3y=2

or, 26-2 = 3y

or, 24  = 3y

so, y = 8

now

x = 13-y

so, x = 13-8 = 5

Step-by-step explanation:

Number of Elements in Power Set - For a given set S with n elements, number of elements in P(S) is 2^n. As each element has two possibilities (present or absent), possible subsets are 2x2x2.. n times = 2^n. Therefore, power set contains 2^n elements.

Answer:

UW = 67

Step-by-step explanation:

UW = 6x - 35

VW = 4x - 20

UV = 19

So that means

4x - 20 + 19 = 6x - 35

4x - 1 = 6x - 35

-1 = 2x - 35

34 = 2x

x = 17

6(17) - 35

102 - 35 = 67

If my answer is incorrect, pls correct me!

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-Chetan K

Answer:

Step-by-step explanation:

19 + ( 4x - 20 ) = 6x - 35

4x - 1 = 6x - 35

2x = 34

x = 17

UW = 6(17) - 35 = 67

Answer:

Step-by-step explanation:

L = w + 10

w = w

P = 2w + 2L

P = 80 m

2L + 2w = 80                      Substitute for L

2(w + 10) + 2w = 80           Remove the brackets

2w + 20 + 2w = 80           Combine on the left

4w + 20 = 80                     Subtract 20 from both sides

4w = 80 - 20

4w = 60                              Divide by 4

w = 60/4

w = 15

L = 15 + 10 = 25

Check

2*25 + 2*15

50 + 30

80

So this checks