suppose a sample of a certain substance decayed to 77.8% of its original amount after 300 days. (round your answers to two decimal places.) (a) what is the half-life (in days) of this substance? days (b) how long would it take the sample to decay to one-third of its original amount?

Alexander made $742 last week in commission. He made $40068 in commission in 2011.

Sold = $5300

Commission percent = 14%

Commission = 14% of 5300

                     = (14/100)*5300

                     = 14*53

                     = 742

No. of weeks in 2011 = 54

Commission = 54 * 742

                     = 40068

Hence, he makes $742 in weeks and $40068 in year 2011.

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Answer:

slope: (6+10)/(15-0)

M: 16/15

B = -10

y = 16/15x -10

Answer:

y(y+27)

Step-by-step explanation:

as per it is y2 it is two times counted so

y(y+27)

Answer:

True

Step-by-step explanation:

True.

1 and 2/5 can be rewritten as 1 and 4/10, and thus is equal to 1.4.

Answer: 0.83

Step-by-step explanation:

14.5/17.5 = 0.828571429

We stop at the 2nd decimal placement after 0.82 but because the following number 8 > 0 we round up the hundredths place which gives us 0.83

30 L of 26% and 15L of 20% of each mixture should be added to make 45 l of a solution that is 24% alcohol.

The quantity of a substance, like salt, that is present in a specific volume of tissue or liquid, like blood, according to science. When there is less water present, the substance becomes more concentrated. You can determine how much solute has been dissolved in the solvent by looking at the concentration of the solution.

Here,

26x + 20(45-x) = 45(24) 

26x -20x = 45(24) -(20(45) 

6x = 4(45) = 180 x = 180/6 = 30 L of 26%

45-x = 45-30 = 15L of 20%

To make 45 l of a 24% alcohol solution, combine 30 l of 26% and 15 l of each mixture.

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Answer:

  x = 42

Step-by-step explanation:

You want to know the value of x that makes alternate interior angles 105° and (3x-21)° congruent.

When alternate interior angles are congruent, the lines forming them are parallel. Congruent angles have the same measure, so we want ...

  3x -21 = 105

  3x = 126 . . . . . . add 21

  x = 42 . . . . . . . divide by 3

The value of x is 42 when the lines are parallel.

The measure of angles ∠1 = 60 degrees, ∠2=120 degrees, ∠3 = 60 degrees, ∠4=60 degrees, ∠5 = 120 degrees, ∠6= 120degreesa and ∠7 = 60 degrees

The measure of angle 3 = 180 - 120

= 60 degrees

Because the sum of angles on a straight line will be 180 degrees

The measure of angle 6 = 120 degrees

The measure of angle 3 = The measure of angle 7  = 60 degrees

Because the corresponding angle will be equal

The measure of angle 1 = 180-120

= 60 degrees

The measure of angle 2 = 180 - 60

= 120 degrees

Because the sum of angles on a straight line will be 180 degrees

The measure of angle 2 = The measure of angle 5 = 120 degrees

The measure of angle 1 = The measure of angle 4 = 60 degrees

Because the corresponding angles will be equal

Hence, the measure of angles ∠1 = 60 degrees, ∠2=120 degrees, ∠3 = 60 degrees, ∠4=60 degrees, ∠5 = 120 degrees, ∠6= 120degrees and ∠7 = 60 degrees

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The 3 geometric means between 5 and 3125 is 5, 25, 125, 625, 3125 using Geometric progression.

The geometric mean is a mean or average used in mathematics that uses the product of the values of a collection of numbers to show the central tendency of that set of numbers. The Geometric Mean (GM) in mathematics is the average value or mean that, by calculating the product of the values of the set of numbers, denotes the central tendency of the numbers. In essence, we multiply the numbers together and calculate their nth root, where n is the total number of data values. An average that multiplies all values and determines the number's root is known as the geometric mean. You locate the nth root of their product for a collection of n integers. This descriptive statistic can be used to sum up your data.

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The solution of the quadratic equation [tex]x^2 - 6x = 72[/tex] is

x = 12 or x = -6

What is a quadratic equation?

At first it is important to know about equation

Equation shows the equality between two algebraic expressions by connecting the two algebraic expressions by an equal to sign.

A one degree equation is known as linear equation.

The given quadratic equation is

[tex]x^2 - 6x = 72[/tex]

Now,

[tex]x^2 - 6x = 72\\x^2 - 6x - 72 = 0\\x^2 - 12x + 6x -72 = 0\\x(x -12)+6(x -12)=0\\(x-12)(x+6)=0\\x-12=0 \ or \ x+6 = 0\\x = 12 \ or \ x = -6[/tex]

The solution of the quadratic equation [tex]x^2 - 6x = 72[/tex] is

x = 12 or x = -6

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Answer:

0.75

Step-by-step explanation:

because 9/12 is 0.75

Let's establish what this rate indicates through an equation:

inches burned

       hour

Now, plug in the information you have:

inches burned      =          9

       hour                          12

9/12 = 0.75

0.75 inches of the candle is burned per hour

Answer:

Step-by-step explanation:

3x + 4y when x = 6 and y = -3

Put in values of x and y:

3(6) + 4(-3) = 18 + (-12) = 6

Answer:

x = - 1/2

Step-by-step explanation:

3x - 6 = -7.5

3x = -7.5 + 6

3x = - 1.5

3/3 x = -1.5 / 3

x =  - 0.5

x = - 1/2

Answer:

x = -1/2

Step-by-step explanation:

Given equation,

→ 3(x - 2) = -7 1/2

Now the value of x will be,

→ 3(x - 2) = -7 1/2

→ 3x - 6 = -15/2

→ 3x = -7.5 + 6

→ x = -1.5/3

→ [ x = -1/2 ]

Hence, value of x is -1/2.

The decimal division of 18.92 by 11 gives us; 1.72

When dividing decimals  we first of all have to convert the divisor to a whole number by moving the decimal point to the right. Thereafter, we now carry the dividend's decimal point up to the exact same number of places to the right and then divide the resultant numbers in the normal way like in regular long division.

We want to divide 18.92 by 11. Thus, let us apply that rule described above to get;

18.92/11 = 1892/1100

= 1 + (1892 - 1100)/1100

= 1 + (792/1100)

= 1 + 0.72

= 1.72

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Given that the directrix is -2 and the vertex is  (-4,-3), the graph will be the parabola plotted in the negative quadrant.

Any point on a parabola is at an equal distance from both the focus, a fixed point, and the directrix, a fixed straight line. A parabola is a U-shaped plane curve. Three crucial components make up a parabola: a focus, a directrix, and a vertex. This upward-opening parabola illustrates how all points along its curve will be equally distant from the directrix and the focus.

Here,

The equation of the parabola is,

f(x)=-2(x+4)²-3

a=-2

(h,k)=(-4,-3)

The graph will be the parabola plotted in the negative quadrant as the directrix is -2. and the vertex is (-4,-3).

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Answer:

$90

Step-by-step explanation:

The amount Oliver borrowed = 1,500

The interest rate applied to the loan = 12%

Required: To calculate the simple interest using the formula, I = P•R•T

Where;

I = The simple interest

P = The principal borrowed = $1,500

T = The time or loan duration = 6 months = 1/2 year

R = The rate at which the loan is applied = 12% = 0.12

Therefore;

I = $1,500 × 0.12/year × 6/12 year = $90

The correct option for the interest paid on the loan is therefore;

$90

Answer:

A: 7

Since the slope is 3 and passes down (1, 10), the answer will be 7

The answer will be:

The equation has one real root. And the root is -1/2.

The equation y= 2[tex](x+1)^2[/tex] has one real root and that is x=-1.

What is real roots of the equation?

    We are aware that when we resolve a linear or quadratic equation, we always arrive at the value variable of the equation, or, to put it another way, we always locate the equation's solution. This "solution" is what we refer to as the real roots. For instance, when the equation [tex]X^2[/tex]-7x+12=0 is solved, the actual roots are 3 and 4.

Here given,

=> y = 2[tex](x+1)^2[/tex]

Take y=0 then,

=> 2[tex](x+1)^2[/tex]=0

=> [tex](x+1)^2[/tex]=0

=>(x+1)=0

=> x=-1

Hence the given equation has one real root and that is x=-1.

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Answer:

2³⁰ > 30²

Step-by-step explanation:

Now the values of,

→ 2³⁰ = 1073741824

→ 30² = 900

Then the expression will be,

→ 2³⁰ ? 30²

→ 1073741824 > 900

→ 2³⁰ > 30²

Hence, answer is 2³⁰ > 30².

Answer:

x=20

x= -20

Step-by-step explanation:

Answer:250

Step-by-step explanation:5((6(8))+2)=250 using pemdas start with parenthesis so 6*8=48 this puts the equation at 5(48+2) then do the parenthesis again so 48+2=50 this puts the equation at 5*50 then do your last step which will give you your answer of 250

60 positive integers of 3 digits may be made from the digit 1,2,3,4 and 5 if the digits are not repeated.

According to the question,

We have the following information:

3 digits integers are to be made from 1,2,3,4 and 5

So, we will use permutation to find the possible number of digits that can be made if we apply all the given conditions.

Now, we have:

Total number of digits = 5

Number of digits to be made = 3

So, we have:

[tex]^{5} P_{3}[/tex]

Solving this expression:

5*4*3

60

Hence, 60 positive integers of 3 digits may be made from the digit 1,2,3,4 and 5 if the digits are not repeated.

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A new company wants to offer a line queuing service where customers book someone to wait in line on their behalf through a smart phone app.

The possibility that no one wants to pay someone else to wait in line can be represented by the concept of probability.

The probability of an event occurring is defined by probability.

The outcome of an event may be known to us or unknown to us. When this happens we say that there is a chance that the event will happen or not.

We can identify probability by simply dividing the favorable number of possibilities by the entire number of possible outcomes.

Hence, probability is a numerical representation of the chance that a specific event will take place.

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In the video about the construction of the insect phylogeny, the researchers faced the problem that there was not enough computational power in all of the world to construct every possible tree.

The use of computing algorithms, tools, and programmes to phylogenetic analysis is known as computational phylogenetics. The purpose is to create a phylogenetic tree that represents a hypothesis about a set of genes, species, or other taxa's evolutionary ancestry.

There was not enough computational power to construct every possible tree in all of the world. So the probable solution for this problem will be:

Use math to avoid constructing improbable trees

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The sequence of transformations is described as follows:

B. Reflection over the y-axis, translation 6 units right and 4 units up, dilation with center (0,0) and scale factor 2.

The two polygons have vertical symmetry, hence the reflection was over the y-axis.

Two equivalent vertices are given as follows:

R(4,-4) and V(2,-4).

After the reflection over the y-axis, the coordinates would be of:

R'(-2,-4).

The polygon increases after the transformation, hence the dilation has a scale factor greater than 1, which is of 2, as VZ = 8, RU = 4.

With a dilation with scale factor of 2, the coordinates of R'' would be given as follows:

R''(-4,-8).

The coordinates of V are:

(2,-4).

Hence the translation is:

Hence option B is correct.

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A system of equations to describe this situation is:

c(n) = 25n + 30

c(n) = 15n + 50

The total cost is equal to $80.

The solution to this system of equations is 2.

In order to write a system of equations to describe this situation, we would assign variables to the number of portrait sheets and cost of a photography session respectively, and then translate the word problem into algebraic equation as follows:

The cost for Murray Photography is given by:

c(n) = 25n + 30

The cost for Lasting Memories Company is given by:

c(n) = 15n + 50

Next, we would solve the system of equations as follows:

25n + 30 = 15n + 50

25n - 15n = 50 - 30

10n = 20

n = 20/10

n = 2.

Now, we can calculate the total cost:

c(n) = 25n + 30

c(2) = 25(2) + 30

c(2) = $80.

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There are 2730 ways in which 15 race cars can finish in first, second, and third place.

Let's examine this logically now. Any one of the 15 runners can cross the finish line in first place. You can still have any one of the 14 race cars who are still running finish in second place. Any one of the 13 race cars who haven't crossed the finish line yet can take third place.

As a result, multiplying all the possibilities will give us the number of ways ;

Number of ways =15*14*13

                            =2730

So, the total number of ways in which the race cars finish in first, second, and third place is 2730.

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Answer:log base 2 of the quantity x cubed z squared all divided by y to the fourth end log

Step-by-step explanation: