A bottle of iron supplement has 45g of iron in 330ml of solution. How many grams of iron are in
100ml of solution?

Answer:

[tex]\mathbf{g^{-1} (t) = log _2 \ 20 \ t}[/tex]

Step-by-step explanation:

Here is the full question

A standard piece of paper is 0.05 mm thick. Let's imagine taking a piece of paper and folding the paper in half multiple times. We'll assume we can make "perfect folds," where each fold makes the folded paper exactly twice as thick as before - and we can make as many folds as we want.

Write a function g that determines the thickness of the folded paper (in mm) in terms of the number folds made, n. (Notice that g(0) 0.05,)

[tex]g(n )= (05)2^n[/tex]

The function g has an inverse. The function g⁻¹ determines the number of folds needed to give the folded paper a thickness of t mm. Write a function formula for g⁻¹).

SOLUTION:

If we represent g(n) with  t;

Then

[tex]\mathbf{t = (0.05)2^n} \\ \\ \mathbf{\dfrac{t}{0.05} = 2^n} \\ \\ \mathbf{\dfrac {100 \ t }{ 5} = 2^n} \\ \\ \mathbf{20 t = 2^n}[/tex]

Taking logarithm of both sides; we have :

[tex]\mathbf{log (20 t) = n log 2} \ \ \ \mathbf{(since \ , log \ a^b = b \ log \ a) } \\ \\ \mathbf{n = \dfrac{log \ 20 t }{log \ 2 }} \\ \\ \mathbf{g^{-1} (t) = \dfrac{log \ 20 t }{log \ 2 }} \\ \\ \mathbf{g^{-1} (t) = log _2 \ 20 \ t}[/tex]

Answer: D. (I, II, and III)

Step-by-step explanation:

having a ticket doesn't necessarily mean you will win the lottery, but you must have a ticket to win

not all numbers divisible by 3 are divisible by 6, but all numbers divisible by 6 are also by 3 (since 3 goes into 6 twice)

if a quadrilateral is a square, it is also a rhombus

Answer:

It is D.

Step-by-step explanation:

If you win the lottery, then you will need a ticket. But, if you have a ticket, it doesn't mean that you'll win the lottery.

If a number is divisible by 3. it is not necessarily divisible by 6. For example, 9 ÷ 3 = 3, but 9 ÷ 6 will not equal a whole number.

All squares are rhombuses, but not all rhombuses are squares (they need to have all interior right angles).

Complete Question:

The perimeter of triangle XYZ is 24 units. Triangle X Y Z is shown. The length of X Y is 3 and the length of Y Z is 11. Angle Y X Z is 102 degrees What is the area of triangle XYZ? Round to the nearest tenth of a square unit. Trigonometric area formula: Area 14.7 square units 14.9 square units 15.0 square units 15.3 square units

Answer:

14.7 square units

Step-by-step Explanation:

Given the triangle shown in the figure attached below, having the following measures:

<YXZ = 102°

Length of XY = z = 3

Length of YZ = x = 11

Length of XZ = y = ?

Perimeter of ∆XYZ = x+y+z = 24 units

Length XZ = y, would be 11+y+3 = 24

14+y = 24

y = 24 - 14

Therefore, y = 10

==>Required:

Area of ∆XYZ to the nearest tenth of a square unit

==>Solution:

Using the Trigonometric area formula, area of ∆XYZ = ½(yz)sin X

Plug in values for x, y, and sin X:

Area of ∆ XYZ = ½×10×3×sin 102

= ½×30×0.9782

= 15 × 0.9782

= 14.673

Area of triangle XYZ approximated to the nearest tenth = 14.7 square units

Answer:

10% = 1/10

20% = 1/5

100% = 3/3

75% = 3/4

Step-by-step explanation:

Answer:

Awnser is down below

Step-by-step explanation:

75= 3/4

20= 1/5

10 = 1/10

100= 3/3

Hope this helps :)

Answer: b. (6,27)

Step-by-step explanation:

y=5x- 3     x=6<---- put in the equation

y=5(6)-3 <------- mulitply 5 and 6

y=30-3 <---- subtracted

y= 27. <---- y value.

Answer being (6,27)

Hope it helps :)

Answer:

The answer is "Option C".

Step-by-step explanation:

In the given question attachment of the table is missing which can be defined as follows:

[tex]\left\begin{array}{cc}\bold{x} &\bold{f(x)}\\0 & 6 \\2 & 7\\4 & 0\\7 & 5 \end{array}\right[/tex]

In given table a method f(x) values corresponding to different values of x.  

We needed to try f(0) value  that is in this method, we have to calculate the f(x) value if x=0  

As we've seen from the table the f(x) value at x=0 is 6  

That's why the correct choice is option C that is 6.

Answer:

The answer would be C

Step-by-step explanation:

I just took the test !!

Answer:

A

Step-by-step explanation:

Since there are 28 days in a regular February and 365 days in a total year, the probability that a random person is born in February is 28/365. This means that the probability that they were NOT born in February is 337/365, or answer choice A. Hope this helps!

Answer:

a.

Step-by-step explanation:

A non leap year has 365 days. February of a non leap year has 28 days.

365 - 28 = 337

There are 337 days in a non leap year that are not in February.

p(not February) = 337/365

Answer:

24 in

Step-by-step explanation:

The diameter of a circle is twice its radius which is 12 * 2 = 24.

Answer:

The diameter is 24 inches

Step-by-step explanation:

The radius of a circle is 1/2 of the circles diameter

r = d/2

d = 2r

d = 2*12

d = 24

The diameter is 24 inches

Answer:

Expenditure x (in hundreds of dollars) = $2,000

Step-by-step explanation:

Given:

Profit p (in hundreds of dollars)

Expenditure x (in hundreds of dollars)

p(x) = -0.5x² + 20x + 23

Find:

Expenditure for advertising .

Computation:

x = -(Cofficient of x) / 2(Cofficient of x²)

x = -(20) / 2(-0.5)

x =  20

Expenditure x (in hundreds of dollars) = 20 × $100

Expenditure x (in hundreds of dollars) = $2,000

Answer: A (4, -7) B (9, -7)

Step-by-step explanation:

When it’s reflected over the x-axis, the y coordinates become negative but the x coordinates don’t change

x coordinates: 4, 9

y coordinates: 7, 7

Reflected over x-axis: (4, -7), (9, -7)

Answer:

There is no solution to the problem

Step-by-step explanation:

In order to find the solutions to the problem you can write the situation in an algebraic form.

You have that a number is equal to twice a smaller number plus 3. This can be written as follow:

[tex]x=2y+3[/tex]      (1)

where x is the number and y is the smaller number

Furthermore, the same number x is equal to twice the sum of the smaller number and 1, which can be written as follow:

[tex]x=2(y+1)[/tex]     (2)

To find the solution you equal the equation (1) with (2), and you solve for y:

[tex]2y+3=2y+1[/tex]

[tex]3=1[/tex]

You obtain an inconsistency, hence, the situation of the problem does not have solution

Answer:

3

Step-by-step explanation:

(volume)  21 * pi = 65.9734457254

height =7

Cone = (1/3)πr²h, where r is the radius and h is the height.

V = Ah/3

Answer:

6a^5

Step-by-step explanation:

3a^2*2a^3

3×2+a^2×a^3

6a^5

Answer:

The answer is 6a⁵.

Step-by-step explanation:

You have to use Indices Law,

[tex] {a}^{m} \times {a}^{n} \: ⇒ \: {a}^{m + n} [/tex]

So for this question :

[tex]3 {a}^{2} \times 2 {a}^{3} [/tex]

[tex] = (3 \times 2) \times ( {a}^{2 + 3}) [/tex]

[tex] = 6 \times {a}^{5} [/tex]

[tex] = 6 {a}^{5} [/tex]

Answer:

It is a gain.

Step-by-step explanation:

CLEAR STATEMENT:

Given that the fruit seller buys 10 apples for 45Rs each from wholesale market.

This implies her buys them for 10 × 45Rs = 450Rs.

UNCLEAR STATEMENT:

He packs them in a fruit basket for 40 and sells them each for 20 baskets Rs. 600.

ASSUMING:

What you are trying to say is that he bought baskets for 40Rs, and sold the apples for 600Rs.

Subtracting his expenses from this value, we have

600Rs - 450Rs - 40Rs = 110Rs

Since this amount is positive, we conclude that it is a gain of 110Rs.

Answer:

45.45 batteries

Step-by-step explanation:

The probability of any random battery being defective is 1 in 11, the number of expected defects in a population of 500 batteries is given by:

[tex]E= \frac{1}{11}*500\\E=45.45\ batteries[/tex]

45.45 batteries are expected to be defective.

Answer:

45

Step-by-step explanation:

The right answer is of option C.

hope it helps..

good luck on your assignment

Answer:

c

Step-by-step explanation:

Answer: -4

Step-by-step explanation:reverse the steps

3(x-7)= -9

3(x-7)/3= -9/3

x-7= -3

x= -3+7

x= -4

Answer:

7

Step-by-step explanation:

10+7+1+6+7+9+8+10+2+5

-----------------------------------

10

65 ÷ 10

= 6.5, round up, = 7

Answer:

I took the quiz and the answer is 7

Step-by-step explanation:

Answer:

x = -2

Step-by-step explanation:

-5x - 7 = 3

-5x = 10

x = 10/-5

x = -2

Answer:

1372

Step-by-step explanation:

4x7x7x7=1372:v=4/3 pi r^3

Therefore, 1372 is the value that should be multiplied by Pi in the numerator to correctly show the volume of the sphere.

please mark me brainliest :)

Answer:

103.5 m²

Step-by-step explanation:

To find the area of a right trapezoid, you can decompose it into a rectangle and a triangle. The sum of the area of  the rectangle and the triangle gives the area of the trapezoid.

For the right trapezoid attached below, the area can be gotten by:

Area of rectangle = length × breadth = 9 × 8 = 72 m²

Area of triangle = 1/2(base × height) = 0.5 × 7 × 9 = 31.5 m²

Area of trapezoid = Area of rectangle + Area of triangle = 72 m² + 31.5 m² = 103.5 m²

Answer:

V of cylinder = V=πr^2h

V of rectangular prism = l*w*h

V of cylinder = 16 * 3.14 * 8

                      = 401.92

V of rectangular prism = 14 * 8 * 12

                                      = 1344

Add = 401.92 + 1344

       = 1,745.92

Answer:

B)

Step-by-step explanation:

If two square matrix, with same dimensions, are inverse of one another, their product will always be the identity matrix with the same dimensions.

The matrix A and B are 2x2, so the result of the product A * B is a 2x2 identity matrix, that is represented as follows:

I = [1 0 ; 0 1]

(First line: 1 0, second line: 0 1)

So the correct option is B)

Answer: 210 grams of margarine, 180 grams of sugar, 150 millilitres of syrup, 360 grams of oats, 75 grams of raisins

Step-by-step explanation: 30 flapjacks is 1.5 more than 20 flapjacks.

140 * 1.5 = 210 grams

120 * 1.5 =  180 grams

100 * 1.5 = 150 millilitres

240 * 1.5 = 360 grams

50 * 1.5 = 75 grams

Answer:

(6, 1)

Step-by-step explanation:

Answer:

centre = (6, 1 )

Step-by-step explanation:

The equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k) are the coordinates of the centre and r is the radius

Given

x² + y² - 12x - 2y + 12 = 0

Collect the x and y terms together and subtract 12 from both sides

x² - 12x + y² - 2y = - 12

To obtain the equation in standard form use completing the square

add ( half the coefficient of the x/ y term )² to both sides

x² + 2(- 6)x + 36 + y² + 2(- 1)y + 1 = - 12 + 36 + 1

(x - 6)² + (y - 1)² = 25 ← in standard form

with centre = (6, 1 ) and radius = [tex]\sqrt{25}[/tex] = 5

Answer:

Step-by-step explanation:

5.volume=8×7×6=336 mi³

6.r=16/2=8 yd

volume=4/3×π×8³=2048/3 π yd³

≈2144.7 yd³

7.r=2.5/2=1.25 in

v=πr²h=π×1.25²×5

volume of 150 cups=7.8125 π×150=1171.875 π in³≈3681.6 in³

8. statement not visible.