How much pure acid is in 780 milliliters of a 18​% ​solution?

After one hour, there would be 337,500 bacteria in the hamburger.

This problem involves exponential growth relation, which is as below:

[tex]P(t)=P_{o}*e^{rt}[/tex]

where, [tex]P_{o}[/tex] is the initial value (i.e. at t=0), P(t) is the value at time 't' and r is the growth rate.

Usually, one perceives growth as linear, which might seem logical in unspecified cases. But, when specified exponential growth, the scenario changes. The difference between linear and exponential growth is like the difference between velocity and acceleration.

In case of above stated problem; [tex]P_{o}[/tex]=100,000 and P(20)=150,000

For calculating r, we substitute values:

[tex]150,000=100,000*e^{r*20}\\e^{20r}=1.5\\20r=ln(1.5)\\r=0.0202733[/tex]

Now we have our growth rate. Using the same formula for t=60, we have:

[tex]P(60)=100,000*e^{0.0202733*60}\\P(60)=100,000*3.375\\P(60)=337,500[/tex]

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Answer: For fiction Gabriel needs about 3 shelves with an extra 4 more books. For nonfiction books it's the same with 3 shelves with 1 more to put.

By taking some simple quotients, we will see that a gold star gives 3 points more than a silver star.

First, we know that 80 silver stars are equivalent to 160 points, to get the number of points that each star gives, we need to take the quotient between the number of points and the number of stars.

160/80 = 2

Each silver star gives 2 points.

We also know that 30 gold starts give 150 points, then:

150/30 = 5

Each gold star gives 5 points.

The difference is:

5 - 2 = 3

A gold star gives 3 points more than a silver star.

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Factor:

A factor is a number that divides another number, leaving no remainder. In other words, if multiplying two whole numbers gives us a product, then the numbers we are multiplying are factors of the product because they are divisible by the product. There are two methods of finding factors: multiplication and division.

Multiple:

multiple in math are the numbers you get when you multiply a certain number by an integer. For example, multiples of 5 are: 10, 15, 20, 25, 30…etc. Multiples of 7 are: 14, 21, 28, 35, 42, 49…etc.

How to find hcf of two or more numbers :

Steps 1:

Find all the factors of each given number.

Step 2:

Find common factors of the given number.

Step 3:

The greatest of all the factors obtained in Step 2, is the required highest common factor (H.C.F).

I'm only writing the answers below as I already told how to find it.

Highest common factor:

1. The factors of 18 are: 1, 2, 3, 6, 9, 18

The factors of 20 are: 1, 2, 4, 5, 10, 20

Then the greatest common factor is 2.

2. The factors of 15 are: 1, 3, 5, 15

The factors of 15 are: 1, 3, 5, 15The factors of 20 are: 1, 2, 4, 5, 10, 20

The factors of 15 are: 1, 3, 5, 15The factors of 20 are: 1, 2, 4, 5, 10, 20Then the greatest common factor is 5.

3. 8

4. 12

5. 10

6. 14

How to find lcm. of numbers :

Step 1: Find the prime factors of the given numbers by repeated division method.

Step 2: Write the numbers in their exponent form. Find the product of only those prime factors that have the highest power.

Step 3: The product of these factors with the highest powers is the LCM of the given numbers.

I'm only writing the answers below as I already told how to find it.

Lowest common multiple :

1. 42

2. 12

3. 40

4. 20

5. 80

6. 42

hope it helps you..

The inverse of the function is, [tex]f^-^1(x)=x^2+4x+4[/tex].

What is inverse of the function?

The inverse function of a function f in mathematics is a function that reverses the operation of f. If the inverse of f exists, it is denoted by f-1 and exists only if f is a bijective function.

Given that f(x) = √x - 2

We have to find the value of f-¹(x).

Let, y = √x - 2

Replace x with y.

⇒ x = √y - 2

Adding 2 on both sides,

x + 2 = √y - 2 + 2

x + 2 = √y

Taking square on both sides,

(x + 2)^2 = (√y)^2

x^2 + 4x + 4 = y

y = x^2 + 4x + 4

Rewrite y as .[tex]f^-^1(x)[/tex]

So, we get [tex]f^-^1(x)[/tex] = x^2 + 4x + 4

Hence, the inverse of the function is, [tex]f^-^1(x)=x^2+4x+4[/tex].

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Answer:

b) 6

Step-by-step explanation:

Given information,

→ P = (5x + 30)°

→ S = 80°

Forming the equation,

→ P + S = 140°

→ (5x + 30)° + 80° = 140°

Now the value of x will be,

→ (5x + 30)° + 80° = 140°

→ 5x + 110° = 140°

→ 5x = 140° - 110°

→ x = 30°/5

→ [ x = 6° ]

Hence, the value of x is 6.

The answer of the given multiplication is, 30.935.

What is multiplication?

A mathematical formula that specifies the objects to be multiplied, known as a factor, produces a product. For instance, the product of x and is cdot, while the product of x and is 30.

Consider, the product

          1  1.  5

   x     2.  6  9

__________________

           1  0  3  5

+         6  9  0  0

+      2  3  0  0  0

____________________

       3  0  9  3  5

There is one after after decimal point in 11.5, and there are two digits after decimal point in 2.69

So, there are total three digits after decimal point.

Therefore, we place the decimal after 0.

Hence, the multiplication of given numbers is, 30.935

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Answer:

$4.21

Step-by-step explanation:

6*70+1=421

The number of miles it takes the snail to move for an hour is 25/4 miles

how far, in miles, does it move in one hour?

Equate the ratio of number of miles to number of hours

7/50 : 7/8 = x : 1

7/50 ÷ 7/8 = x / 1

7/50 × 8/7 = x / 1

50/8 = x / 1

50 × 1 = 8 × x

50 = 8x

divide both sides by 8

x = 50/8

x = 25/4 miles

In conclusion, the snail moves 25/4 miles when traveling for an hour.

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Answer:

i need help please by german

The value of x is 36 feet and the length of the rectangle is 36 feet and the width is 78 feet.

According to the question,

We have the following information:

The perimeter (adding up all the sides) of a rectangular piece of land is 228 feet. The length of the land can be shown by x and its width can be shown by (2x + 6).

We know that the perimeter of rectangle is given by the following formula:

2(length+width)

2(x+2x+6) = 228

2(3x+6) = 228

Dividing by 2 on both the sides:

3x+6 = 228/2

3x+6 = 114

Subtracting 6 from both the sides:

3x = 114-6

3x = 108

x = 108/3

x = 36 feet

Now, the length of the rectangle = 36 feet

Width = 2x+6

Width = 2*36+6

Width = 72+6

Width = 78 feet

Hence, the value of x is 36 feet and the length of the rectangle is 36 feet and the width is 78 feet.

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The graph of the polynomial f(x) is added as an attachment

From the question, the equation of the polynomial is given as

f(x) = x^3 + 3x^2 – 4x – 12

To start with, we need to represent the function of the polynomial properly

So, we have the following representation

f(x) = x³ + 3x² – 4x – 12

Solving further, we need to factorize the function

This gives

f(x) = x²(x + 3) - 4(x + 3)

Factor out x + 3

f(x) = (x² - 4)(x + 3)

Express as difference of two squares

f(x) = (x - 2)(x + 2)(x + 3)

When the above equation is solved, we have

x = 2, x = -2 or  = -3

This means that the intercepts of the function are -3, -2 and 2

Next, we plot the polynomial function using the above intercepts and the end behavior

See attachment for the graph of the function

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Answer:

s = 16

Step-by-step explanation:

4s+s+36+4s =180  The sum of the interior angles of a triangle is 180  Combine like terms.

9s + 36 =180  Subtract 36 from both sides

9s = 144  Divide both sides by 9+

s = 16

Answer:

s = 16

Step-by-step explanation:

the three angles of a triangle should add up to 180 degrees.

30 boxes of popcorn and 20 free DVD rentals were given away.

What is the solution to an equation?

In order to make the equation's equality true, the unknown variables must be given values as a solution. In other words, the definition of a solution is a value or set of values (one for each unknown) that, when used as a replacement for the unknowns, transforms the equation into equality.

let a variable represent the number of the highest-cost item (boxes of popcorn). If that is p, then the number of DVD rentals is (53-p) and the total cost is ...

 2p +(50 -p) = 80

 p = 80 -50 = 30 . . . . . . . boxes of popcorn

50-p= (50 -30) = 20 . . . DVD rentals

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The graph of the proportional relationship is

(c) A line from (0, 0) going through (38, 34.20) where the x-axis is labeled Weight (in pounds) and the y-axis is labeled Cost (in dollars)

The graph is simply a structured representation of the data. It aids in our comprehension of the data. The numerical information gathered through observation is referred to as data.

In a line graph, the information or data is represented as a series of markers, or dots, and is then connected to one another by a straight line.

Given:

It costs $20.70 for 23 pounds of laundry and $34.20 for 38 pounds of laundry.

which shows that

(x, y) = (20.70, 23) and (34.20, 38)

Where

x = Weight and y = Cost

So, The graph is a proportional graph which means that line passes through the origin

So, we have

(x, y) = (0, 0), (20.70, 23) and (34.20, 38)

Hence, the graph of the proportional relationship is (c)

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The distribution of the number of fair coin tosses before one observed three heads in a row is 14.

We have a coin. We have to find the number of fair coin tosses before one observes three heads in a row. We need to use the Markov chain. The probability of getting a head when a coin is flipped is 1/2. Let the probability be represented by the variable "p". Let the number of heads we want in a row be "n".

p = 1/2

n = 3

Using the Markov chain, the formula for getting "n" numbers of the same event in a row with the probability "p" is given below.

A(n) = [1 - p^(n)]/[(1 - p)*p^(n)]

We need to find the value of A(3).

A(3) = [1 - (0.5)^(3)]/[(1 - 0.5)*(0.5)^(3)]

A(3) = [1 - 0.125]/[(0.5)*(0.125)]

A(3) = 0.875/0.0625

A(3) = 14

Hence, the number of fair coin tosses before one observes three heads in a row is 14.

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Based on Mark's and Gigi's expenditure, a pound of ham costs $3.67.

Let us represent 1 pound of ham by x and 1 pound of turkey by y. Forming equation based on Mark's ham and turkey

2x + 4y = 40 : Equation 1

Forming equation based on Gigi's ham and turkey

5x + 4y = 51 : Equation 2

Subtracting Equation 1 from equation 2

5x + 4y = 51

(-) 2x (-) + 4y = (-) 40

The result we get on subtraction -

3x = 11

x = 11/3

Performing division on Right Hand Side of the equation

x = 3.67

Thus, one pound of ham cost $3.67.

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The diameter of this circle has length of 65 when it is inscribed in a circle is a quadrilateral.

The straight line that runs through the center of a round shape or object from one point on one edge to another: The diameter is twice as large as the radius. The pond is six feet across. Both definitions hold true for the diameter of a sphere.

We note that 25²+60²=65² and 39²+52²=65²

Let [tex]\bar{AB}[/tex]=25, [tex]\bar{BC}[/tex]=39, [tex]\bar{CD}[/tex]=52, [tex]\bar{DA}[/tex]=60

Let [tex]\bar{BD}[/tex]=x and ∠DAB=y

x²=25²+60²-3000cos(y)

x²=39²+52²-4056cos(180-y)

We obtain by performing some computation x²=4225-3000cos(y) and x²=4225-4056cos(y).

4056cos(y)=3000cos(180-y)

cos(180-y)=-cos(y)

So, by substituting we get 4056cos(y)= -3000cos(y)

cos(y)=0 or y=90.

∠BAD=90 and ∠BCD=90.

The diameter of a right triangle inscribed in a circle is the hypotenuse.

This means that the diameter is √4225=65

Therefore, the diameter of this circle has length of 65.

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The first four terms are -4 , -1 , 4, 11 respectively

Sequence is the arrangement of set of number in a particular order.

A se.q.u.e.n.c.e. can be defined based on the number of terms.

The function f (n) =n^2-5, where n is the number of term

therefore, when n= 1, (first term)

f (n) = 1^2-5= -4

when n= 2 (second term)

f (n) = 2^2-5=4-5= -1

when n= 3 (Third term)

f (n)= 3^2-5=9-5= 4

when n = 4 (fourth term)

f (n)= 4^2-5=16-5= 11

therefore the first four term of the sequence are -4 , -1 , 4, 11 respectively

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The amount that the customer be charged before tax and tip is $25.55

Given,

The markup on a restaurant = 250%

The cost of a meal to produce = $7.30

We have to find the amount will the customer be charged before tax and tip;

The markup price = 250/100 × 7.30 = 5/2 × 7.30 = 2.5 × 7.30 = 18.25

The Markup price on a restaurant is $18.25

Now,

The amount that the customer be charged before tax and tip = The cost of a meal to produce + The markup price

= 7.30 + 18.25

= 25.55

That is,

The amount that the customer be charged before tax and tip is $25.55

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A teacher buys pencils= 100

the equation is y=8x/100.

total number of pencils = 100

average number of pencil lost in months = 8

number of pencil lost in one month = 8/100

pencil left = y

months = x

so the equation would be:

y = 8x/100.

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a) The number of students studying abroad in the year 2001 is; 150.38 thousand

b) The number of students studying abroad in the year 2018 is; 467.53 thousand

An exponential growth or decay function is defined as a function that grows or shrinks at a constant percent growth rate.

We are given the equation as;

y = 123.1(1.069)ˣ

This equation models the number of students who studied abroad each year from 1998 to 2013

where;

y is the number of students from a certain country studying abroad

x is the number of years after 1998

a) In the year 2001, this is 3 years after 1998 and so we have;

y = 123.1(1.069)³

y = 150.38 thousand

b) In the year 2018, it will have been 20 years after 1998. Thus, we have;

y = 123.1(1.069)²⁰

y = 467.53 thousand

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There are total 246 ways to select a committee of 3 from a gorup of 13.

What is Combination?

A combination is a mathematical approach for determining the number of potential arrangements in a set of objects when the order of the selection is irrelevant. You can choose the components in any order in combinations.

Solution:

Given that,

Total Number of Applicants = 13

Total Seats Available for the Committee = 3

Since, the order of selection is not relevant in the given question we will use combination.

13C3 = 13! / (10! * 3!)

13C3 = 13*12*11*10!/(10! * 6)

13C3 = 286

This means there are total 246 ways to select a committee from a gorup of 13.

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Answer:

Below

Step-by-step explanation:

= 2000 (.9)^2 (.9)^t

    = 2000(.81)(.9)^t

         = 1620 (.9)^t

Answer:

[tex]K(t)=1620(0.9)^{t}[/tex]

Step-by-step explanation:

Given function:

[tex]K(t)=2000(0.9)^{t+2}[/tex]

[tex]\textsf{Apply exponent rule} \quad a^{b+c}=a^b \cdot a^c:[/tex]

[tex]\implies K(t)=2000(0.9)^{t}\cdot(0.9)^2[/tex]

Simplify:

[tex]\implies K(t)=2000(0.9)^{t}\cdot0.81[/tex]

[tex]\implies K(t)=0.81 \cdot 2000(0.9)^{t}[/tex]

[tex]\implies K(t)=1620(0.9)^{t}[/tex]

Rounded to the whole number: 6

A line segment that connects a circle, sphere, or other shape's center to its perimeter or border. Radius: 12 units

According to the Pythagorean Theorem, a right triangle's hypotenuse (the side opposite the right angle) or, using conventional algebraic notation,[tex]a^{2} + b^{2} = c^{2}[/tex]

The Greeks established the existence of numbers that could not be expressed as rational numbers thanks to Pythagoras' theorem. For instance, if we assume that the two shorter sides of a right triangle are 1 and 1, we are left with a length hypotenuse that is not a rational number.

By Pythagoras theorem-

[tex]adjacent side^{2} + opposite side^{2} = hypotenuse^{2}[/tex]

35= opposite side

r= adjacent side

25+r= hypotenuse

[tex](25+r)^{2} = 35^{2} + r^{2}\\ 665 + r^{2} + 50r = 1225 + r^{2} \\50r = 600\\r=12 units[/tex]

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When an English-language survey questionnaire is converted into a Korean version for usage in south Korea and then translated back into English to ensure accuracy.

Given statement;

When a survey questionnaire in English is translated into Korean for use in south Korea and then translated back into English to check its accuracy.

It can be described as back translation,

Back Translation:

Back translation, also known as reverse translation, is the process of literally translating text back into the source language from the target language. Translations from English to Swedish not affect would also include a reverse translation into English so that the meaning of the translated option could be clearly understood. Back translations have no effect on the translator's translation memory or other tools, such as glossaries.

It is described as a back translation.

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Answer:

a. -13

b. 14

c. -6

Step-by-step explanation:

a.

Substitute x = -3 into the equation.

f(-3) = 2(-3) - 7

= - 6 - 7

= -13

b.

Substitute f(x) = 21 into the equation.

2x - 7 = 21

2x = 28

x = 14

c.

Substitute x = 1/2 into the equation.

f(1/2) = 2(1/2) - 7

= 1 - 7

= -6

The perimeter of the parallelogram is 35 cm.

The length of the continuous line that a parallelogram's boundary forms are considered to be its perimeter. The same unit applies to it as it does to its sides. A closed shape made up of four line segments is referred to as a quadrilateral. If the opposing sides of a quadrilateral are parallel and the same length, the shape is referred to as a parallelogram.

Given, the area of the parallelogram = 62 cm²

We know the area of the parallelogram = base × height

62 = b × 6.2 cm

b = 62/6.2

b = 10 cm

So, the perimeter of the parallelogram is given by

P = 7.5 + 10 + 7.5 + 10 cm

P =  35 cm

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