The half-life of radium-226 is 1600 years. Suppose we have a 27-mg sample.
(a) Find a function
m(t) = m02−t/h
that models the mass remaining after t years.
m(t) =



(b) Find a function
m(t) = m0e−rt
that models the mass remaining after t years. (Round your r value to six decimal places.)
m(t) =



(c) How much of the sample will remain after 4000 years? (Round your answer to one decimal place.)
mg

(d) After how many years will only 17 mg of the sample remain? (Round your answer to one decimal place.)
yr

The pentagon has the following type of symmetry:

This refers to a type of symmetry where one-half part of an object shows the other half of the object. It is also be called mirror symmetry.

Point symmetry refers to the shape of a figure or graph after begin turned about 180° and it still looks the same as its initial shape. eg Star, heart -shape, etc.

Note that When something is identical on all sides, it is said to be symmetrical. If a center dividing line (also known as a mirror line) can be drawn on a shape to demonstrate that both of its sides are identical, then the shape is said to be symmetrical.

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The Amplitude of the Wheel is 22.5

The Midline of the wheel is 25.5;

The period of the wheel is 6;

what is amplitude?

A sound is a type of energy that is created when objects vibrate. For it to spread, a medium is needed. As a result, sound cannot travel in a vacuum because there is nothing for the sound waves to travel through. The object's back-and-forth movement creates the sound. Sound vibration is the name for this. Additionally called oscillatory motion. Oscillation describes the regular rhythmic back-and-forth movement.

We know that:

Amplitude = [tex]=\frac{\max -\min }{2}[/tex]

So, substituting the minimum and maximum values as:

Maximum = 48;

minimum = 3;

So, Amplitude = [tex]=\frac{48-3}{2}=22.5[/tex]

So, Amplitude = 22.5;

Now,

we know that midline is half of the sum of minimum and maximum;

So,

Midline = [tex]=\frac{\max +\min }{2}[/tex]

So,

Maximum = 48;

minimum = 3;

Midline = [tex]=\frac{48+3}{2}=25.5[/tex]

So, Midline = 25.5;

and Period is 6 minutes;

So, we can frame the function by the negative cosine function;

[tex]n=f(t)=-a \cos (b t)+c[/tex]

[tex]\begin{aligned}&b=\frac{2 \pi}{\text { period }}=\frac{2 \pi}{6}=\frac{\pi}{3} \\&\therefore \quad h=-22.5 \cos \left(\frac{\pi}{3} t\right)+25.5\end{aligned}[/tex]

Height after time t = 3 will be:

[tex]\begin{aligned}&h=-22.5 \cos \left(\frac{\kappa}{3} \times 3 .\right)+25.5 \\&h=-22.5(-1)+25.5 \\&h=48\end{aligned}[/tex]

So, The height is 48;

Hence, After 3 minutes It is 48 meters high from the ground; is 48

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The equation -27v - 54v²-36v³ cannot be solved as it doesn't have a factor

What is an equation?

An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used. In the equation 3x + 5 = 14, for instance, the two expressions 3x + 5 and 14 are separated by the symbol "equal."

There are 3 main types of equation

1. Slope-intercept : y = mx + c

                              where m is the slope and b is the y-intercept

2. Point-slope : [tex](y - y_{1} ) = m (x - x_{1} )[/tex]

                          Where m is the slope and [tex](x_{1},y_{1})[/tex] is a point on the line

3. Standard : Ax + By = C

                     where A, Band C are constants

Factorizing the equation we get

-3v(9 + 18v + 12v²)

= -9v(4v² +6v +3)

(4v² +6v +3) as this equation doesn't have a factor it is difficult to solve

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The equation x² - 6x = 72 has a solution between 4 and 5

Use a trial and improvement method to find this solution.

There are a number of "improvement" techniques that can be used to improve an estimate of a solution to a polynomial. Some of them use the polynomial itself to form the iterator function.

Iterator

There are a number of ways we can solve the given equation for x. Often, at least one of these will converge when used for improving the estimated value of x.

 x₁ = ([tex]x^{2}[/tex] -72)/6 . . . . . . . add 6x-72, divide by 6

 x₂ = 72/(x^2 -6) . . . . . . . factor out x and divide by its coefficient

 x₃ = ∛(72 +6x) . . . . . . . add 6x and take the cube root

The first two of these iterators tend to diverge. For x = 4.5, they give ...

 x₁ = (4.5³ -72)/6 = 3.1875

 x₂ = 72/(4.5² -6) = 5.0526

Both of these stray out of the given interval of [4, 5].

However, the third one tends to converge, so can give us a useful approximation in one iteration:

 x₃ = ∛(72 +6×4.5) ≈ ∛99 ≈ 4.6261

Second iteration

Applying this again, we get ...

 x ≈ ∛(72 +6·4.6261) ≈ 4.6378

The approximate root to 1 decimal place is 4.6.

Additional comment

One of the quickest converging iterators is that provided by Newton's method. For finding the solution to f(x) = 0, it uses ...

 x₁ = x -f(x)/f'(x) . . . . . . . where f'(x) is the first derivative

For this problem, we can define ...

 f(x) = [tex]x^{2}[/tex] -6x -72   ⇒   f'(x) = 3x^2 -6

 x₁ = x -([tex]x^{2}[/tex] -6x -72)/(3x^2 -6) = (3[tex]x^{2}[/tex] -6x -[tex]x^{2}[/tex] +6x +72)/(3x^2 -6)

 x₁ = (2[tex]x^{2}[/tex] +72)/(3x^2 -6)

Then for x = 4.5, the "improved" solution is ...

 x₁ = (2(4.5³) +72)/(3(4.5²) -6)) = 254.25/54.75 = 339/73 ≈ 4.6438

A second iteration gives ...

 x ≈ 4.639026 . . . . accurate to 5 decimal places

Hence with this iterator, the number of accurate decimal places tends to double with each iteration.

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The expression for the amount when Kendra earns $11.60 per hour working at the movie theater is 11.60h.

An expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both.

Based on the information illustrated, let the number of hours be h.

Since Kendra earns $11.60 per hour working at the movie theater. The expression will be:

= Amount earned per hour × Number of hours

= 11.60 × h

= 11.60h

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Kendra earns $11.60 per hour working at the movie theater. How much will she earn for h hours?

The person has to deposit $1948.05 per year.

what is compound interest?

Interest that is added to a loan or deposit sum is known as compound interest. In our daily lives, it is the notion that is employed the most frequently. Compound interest is calculated for a sum using the principal and interest accrued over time. Compound interest and simple interest differ primarily in this way.

In the given question, to find the value to be added per year we will use the formula.

[tex]P= \frac{A \times \frac{r}{n}} {(1 +\frac{r}{n})^{t} - 1}[/tex]

Here A = 50,000

r (rate of interest) = 6 % or 0.06.

n = 1

t = 16

P = value deposit per year

On substituting the values,

[tex]P= \frac{50000 \times 0.06} {(1 +0.06)^{16} - 1}[/tex]

P =   3000 / 2.54- 1

 = $1948.05 .

Therefore, person has to deposit $1948.05 per year.

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Answer:

Yes, All the three recipes use a proportional amount of flour.

Step-by-step explanation:

A ratio indicates how many times one number contain in another number. The ratio of two number is written as x : y, which is equivalent to x/y.

Where, x and y are individual amount of two quantities.

And, Total quantity gives after combine as x + y.

Given that;

There are three different recipes to make cookies for different amount of flour.

Recipe 1 =  3 dozen cookies and 4.5 cups of flour

Recipe 2 =  4 dozen cookies and 6 cups of flour

Recipe 3 = 5 dozen cookies and 7.5 cups of flour

Now,

To check that all the recipes in proportion, we check the amount of flour for 1 dozen cookies.

For recipes 1;

The amount of flour = 4.5 / 3

                              = 1.5

For recipe 2;

The amount of flour = 6 / 4

                              = 1.5

For recipe 3;

The amount of flour = 7.5 / 5

                              = 1.5

Clearly, All are the same amount to make 1 dozen of cookies.

So, The all recipes are in proportions.

Therefore, All the three recipes use a proportional amount of flour.

Answer: 66%

Step-by-step explanation: To convert a fraction to a percentage, divide the top number by the bottom number. For example, [tex]\frac{1}{4}[/tex] is 25% because if divide them, (1÷4=0.25) then we get 25%. So, for this problem, we solve 2÷3, which equals 0.66, or 66%.

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The expression when factored out is 8(4s + 5)

From the question, we have the following expression that can be used in our computation:

32s + 40

The terms of the above expression are:

32s and 40

And the factor of 32 and 40 is

Factor = 8

So, we divide 32s and 40 by 8

The results of these divisions are

32s/8 = 4s

40/8 = 5

So, we have the following results

32s + 40 = 8(4s + 5)

Hence, the factored expression is 8(4s + 5)

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The number of three-letter sequences that can be made from the word "COMBINATORICS" where no 2 letters can be the same is 720 ways

The question is asking of permutation

arranging the letters without repeating a word gives

COMBINATORICS ⇒ COMBINATRS

The newly arranged word gives 10 letters and arranging 10 letters by taking 3 at a time is 10P₃

The required permutation is 10P₃

10P₃

= 10! / (10 - 3)!

= 10! / 7!

= 720

= 720 ways

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Answer:

Step-by-step explanation:

The original rectangle has dimensions of 70 x 35.

Therefore, we can find its perimeter and area with the standard formulas.

A = 70 * 35

= 2450 square units

P = 2(70) + 2(35)

= 210 units

The new rectangle is dilated by a 1/5 factor, so both dimensions will be one fifth the size of the original. When you have a scale factor that is 1 over some number, you can find the new measurement by dividing by that denominator.

Therefore, new rectangle's dimensions are:

70 ÷ 5 = 14

35 ÷ 5 = 7

Now, find area and perimeter of the new rectangle.

A = 14 * 7

= 98 square units

P = 2(14) + 2(7)

= 42 units

Answer:  c.60   is correct

Step-by-step explanation:

The Graph of x ≥ 3 is attach below

The definition of a linear inequality

The inequality symbol is used to compare two mathematical expressions in what are referred to as linear inequalities. The expression could be both numerical and algebraic, or it could just be one.

What does a linear inequality in mathematics look like?

What Is an Example of Linear Inequality? An example is the linear inequality x - 5 > 3x - 10. The LHS is obviously greater than the RHS because the greater than symbol is being used in this inequality. After being resolved, the inequality appears as follows: 2x 5 x (5/2).

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For the polynomial function,

The leading terms of the polynomial is 4

The degree of f(x) is 23

And the leading coefficient is 4x²³

Polynomial function:

Polynomial function means a function that involves only non-negative integer powers or only positive integer exponents of a variable in an equation like the quadratic equation, cubic equation, etc.

Given,

Here we have the polynomial function

f(x) = -4(x-2)¹²(6-x)¹¹

Now, we need to find the leading term, degree and the leading coefficient of the polynomial function.

The degree of a polynomial is the highest of the degrees of the polynomial's individual terms. In our case, the degree is 23.

The leading term is the term with the highest degree. In our case, the leading term is 4x²³

The leading coefficient is the coefficient of the leading term. In our case, the leading coefficient is 4.

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Answer:

  (c)  8!/(6!·2!)

Step-by-step explanation:

You want to know how to compute the number of possible ways 2 different pizzas can be chosen from a menu of 8.

The formula for computing the number of combinations of n things taken k at a time is ...

  nCk = n!/(k!(n -k)!)

For 8 specialty pizzas chosen 2 at a time, this is ...

  8C2 = 8!/(2!·6!)

The appropriate answer choice is ...

  possibilities = 8!/(6!·2!)

__

Additional comment

That is (8·7)/(2·1) = 28 possibilities, assuming choice of different pizzas.

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The zeros of the given function are -2, and 1 in the represented graph.

A function's zeros are the values of x when f(x) equals 0. As a result, its name. This indicates that when f(x) = 0, x is a function zero. When the graph crosses through x = a and is considered to be the function's zero. As a result, (a, 0) is a function zero.

The graph is given in the question,

According to the shown graph, the function in the given graph has located at the x-axis of the plane, which is the location or coordinates from where the line crosses which are -2, and 1.

Therefore, the zeros of the given function are -2, and 1 in the represented graph.

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The pounds of tomatoes Kent have now is 1.78 pound.

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.

We have been given that Keny had 2.43 pounds of tomatoes he sold 0.4 pound to Maria and 0.25 pound to Lara for their lunches.

The total pounds of tomatoes = 2.43

The pounds of tomatoes Kent have now;

2.43 - 0.4 - 0.25

= 1.78

Therefore, the pounds of tomatoes Kent have now is 1.78 pound.

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Answer:

n = -45

Step-by-step explanation:

2/3n + 4 = -26

subtract 4 from both sides:

2/3n + 4 - 4 = -26 - 4

2/3n = -30

divide both sides by 2/3:

(2/3n)/(2/3) = (-30)/(2/3)

n = -45

Answer:

n=-45

Step-by-step explanation:

2/3n+4=-26

        -4.  -4

2/3n=-30

/2/3.    /2/3

n=-30/1 *3/2

n=-90/2

n=-45

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Equation: [tex]\boxed{\pi}(8^2)[/tex]

Area: [tex]64\pi \approx 201.06[/tex]

Answer:

2m + 3n + 11

Step-by-step explanation:

You cannot combine the m and the n terms, but you can combine 5 and 6

The probability that a randomly selected teacher earns more than $400,000 a year is 57.26.

Given that, normally distributed with a mean of $45,000 and a standard deviation of $6,200.

Normal distribution, also known as the Gaussian distribution, is a probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean.

Let X be the annual salary for all U.S. teachers with a mean salary45,000 and standard deviation of 6,200.

Hence, X∼N(45000,6200²)

The standardized value is obtained by:

Z= (X-μ)/σ

Where μ and σ are the mean and standard deviation of X, respectively.

The probability that a randomly selected teacher earns between 400,000 a year can be obtained by the following expression

P(X<400,000)= (400,000-45,000)/6200

= 355000/6200

= 57.26

Therefore, the probability that a randomly selected teacher earns more than $400,000 a year is 57.26.

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Answer:

this is very easy, just do:

45(0.62/1)

and you get 27.9 miles

tada!

45 kilometers is equivalent to 27.9 miles.

Given that we need to convert 45 kilometers to miles.

We have given that,

1 kilometer = 0.62 miles)

To convert 45 kilometers to miles, we can use the conversion factor of 1 kilometer = 0.62 miles.

We multiply the given distance in kilometers by this conversion factor to obtain the equivalent distance in miles.

Step 1: Multiply 45 kilometers by 0.62 miles/kilometer:

45 km x 0.62 miles/kilometer = 27.9 miles

Therefore, 45 kilometers is equivalent to 27.9 miles.

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The simplified form of the expression [tex]\frac{6}{7}c-\frac{5}{9}d-\frac{1}{2}c+\frac{1}{3}d[/tex] is [tex]\frac{5}{14}c-\frac{2}{9}d[/tex]

In maths, an expression is a combination of numbers, variables, functions (such as addition, subtraction, multiplication or division etc.)

Therefore, let's simplify the expression as follows:

To simplify an expression means to write an equivalent expression which contains no similar terms.

his means that we will rewrite the expression with the fewest terms possible.

Hence,

[tex]\frac{6}{7}c-\frac{5}{9}d-\frac{1}{2}c+\frac{1}{3}d[/tex]

combine like terms

[tex]\frac{6}{7}c-\frac{1}{2}c-\frac{5}{9}d+\frac{1}{3}d[/tex]

Do the arithmetic

[tex]\frac{12c-7c}{14}+\frac{-5d+3d}{9}[/tex]

[tex]\frac{5}{14}c-\frac{2}{9}d[/tex]

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Answer:

  30.1°

Step-by-step explanation:

You want the acute angle whose sine is 0.5015.

When you know the sine of an angle and want to find the angle, you use the inverse sine, or arcsine, function.

  sin(x) = 0.5015

  x = arcsin(0.5015) ≈ 30.1°

The value of x is about 30.1 degrees.

__

Additional comment

There are an infinite number of angles that have that sine value. Only one of them is a positive angle less than 90°. Be sure your calculator is in degrees mode, if you don't want units of radians or grads. (Spreadsheet functions will give an answer in radians.)

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The total cost for Zap Electric Company and Bolt Electric Company are y = 0.06r + 6.55 and y = 0.12r + 2.83

An equation is an expression that shows the relationship between two or more numbers and variables.

Let r represent the number of kilowatt hours you use in one month, and let y represent the total cost of your electric service.

The Zap Electric Company charges $0.06 per kilowatt hour plus a $6.55 monthly service fee. Hence:

y = 0.06r + 6.55

The Bolt Electric Company charges $0. 12 per kilowatt hour plus a $2.83 monthly service fee. Hence:

y = 0.12r + 2.83

The cost is y = 0.06r + 6.55 and y = 0.12r + 2.83

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Answer:

inequality form: u≥−5

Interval Notation: [−5,∞)

The amount of liter in 37 gallons is 140.23 liter.

What is gallons and liter?

A gallon and liter (or US spelling liter) are units of measuring volume. There are two official symbols for liter: the Latin letter L in lower and upper case (l and L).

Given,

that 1 gallon is given as 3.79 liter

And to find the amount of liter in 37 gallon

After multiplication,

the amount of liter in gallon,

= 3.79(37)

=140.23

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