The mass of a radioactive substance follows a continuous exponential decay model, with the decay rate parameter 4% per day. A sample of this radioactive substance has an initial mass of 2.05 kg. Find the mass of the sample after four days. Round your answer to two decimal places.

Answer:

No, because 234 / 36 is 6.5 which is what Chad makes hourly. 288 / 40 is 7.2 which is what Geo makes hourly so it is not proportional.

Answer:

see  below

Step-by-step explanation:

Chad earns $234 for 36 hours of work.  so 234/36 = 6.5/hr

Geo earns $288 for 40 hours of work. so 7.2/hr

No they are not because their hourly rates are different.  

There are 4 kilograms of type B in one bag of the blend.

What is a linear equation in one variable?

A linear equation in one variable is an equation that can be written in the form ax + b = 0, where a and b are constants and x is the variable. This equation represents a straight line in a coordinate plane and the solution to the equation corresponds to the x-coordinate of the point where the line intersects the x-axis.

Let's call the amount of type B in one bag of the blend "x".

Since one bag of the blend is 4 kilograms of type A, we know that one bag is 4 + x kilograms of coffee.

And since 6 bags of the blend is a total of 48 kilograms, we can write an equation:

6 * (4 + x) = 48

Expanding the left-side of the equation:

24 + 6x = 48

Subtracting 24 from both sides:

6x = 24

Dividing both sides by 6:

x = 4

Hence, there are 4 kilograms of type B in one bag of the blend.

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The correct equation for the graph include the following: C. y = 2x/3 - 4.

Mathematically, the point-slope form of a straight line can be calculated by using this mathematical expression:

y - y₁ = m(x - x₁) or y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)

Where:

From the information provided above, we have the following slope and data points on the line:

At point (0, -4), a linear equation of this line can be calculated in slope-intercept form as follows:

y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)

y - (-4) = (0 + 4)/(6 - 0)(x - 0)

y + 4 = 2x/3

y = 2x/3 - 4

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Therefore , the solution of the given problem of speed comes out to be

speed of freight train is 10 mi/h.

We can determine how fast that anything is traveling by looking at it from a distance. The amount of distance an object can go in a given length of time depends on its speed. Velocity is calculated using the formula velocity = distance/time. The three most used units of speed are meters per second (m/s), kilometers per hour (km/h), and miles per hour (mph) (mph).

Here,

Given :

passenger train covers a distance of 175 mi.

freight train covers a distance of 125 mi.

Speed of passenger train is 14 mi /h

Using formula of time -distance,

=> 175/14 = 12.5 hour

So, speed of freight train is :

=> speed = 125/12.5 = 10 mi/h

Therefore , the solution of the given problem of speed comes out to be

speed of freight train is 10 mi/h.

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If Hiba needs 40g of sugar to make 15 biscuits. The amount of flour she needs is 480g and the number of packs of butter will she have to buy is 3 pack of butter.

a. Amount of flour she needs

Amount of flour she needs =(3×40) × 60/15

Amount of flour she needs = 120 × 60/15

Amount of flour she needs = 480g

b.  Packs of butter will she have to buy

Packs of butter needed = [(2×40) × 60/15] /125g

Packs of butter needed = [80 × 60/15] /125g

Packs of butter needed = 320 /125g

Packs of butter needed = 2.56

Packs of butter needed = 3 packs (Approximately)

Therefore the amount of flour she needs is 480g and the number of packs of butter will she have to buy is 3 pack of butter.

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The simplified form of the expression is 2/3x-1+2(x-6)​ is 8x/3 -13.

Bracket, Of, Division, Multiplication, Addition, and Subtraction is referred to as BODMAS. A mathematical expression's order of execution is explained using the BODMAS. The acronym PEDMAS, which stands for Parentheses, Exponents, Division, Multiplication, Addition, and Subtraction, is sometimes used to refer to the BODMAS.

The brackets must be solved first, then powers or roots (i.e. of), Division, Multiplication, Addition, and finally Subtraction, according to BODMAS rule. Any expression can only be solved correctly if the BODMAS rule or the PEDMAS rule are applied.

The given expression is: 2/3x-1+2(x-6)​

2/3x-1+2(x-6)​

2/3x - 1 + 2x - 12

2/3x - 1 + 6x/3 -12

8x/3 -13

Hence the simplified form of 2/3x-1+2(x-6)​ is 8x/3 -13.

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[tex]\displaystyle \lim_{x\to 16} ~~ \cfrac{4-\sqrt{x}}{16x-x^2} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{4-\sqrt{x}}{16x-x^2}\implies \cfrac{4-\sqrt{x}}{x(16-x)}\implies \cfrac{4-\sqrt{x}}{x( ~~ 4^2-(\sqrt{x})^2 ~~ )} \\\\\\ \cfrac{4-\sqrt{x}}{x( ~~ [4-(\sqrt{x})][4+(\sqrt{x})] ~~ )}\implies \cfrac{1}{x( ~~ 4+\sqrt{x} ~~ )} \\\\[-0.35em] ~\dotfill\\\\ \displaystyle \lim_{x\to 16} ~~ \cfrac{1}{x( ~~ 4+\sqrt{x} ~~ )}\implies \cfrac{1}{16( ~~ 4+\sqrt{16} ~~ )}\implies \cfrac{1}{16(4+4)}\implies \cfrac{1}{128}[/tex]

Answer: To find the limit as x approaches 16, we can substitute x = 16 into the expression:

lim (4-√X)/16X-X² = (4 - √16)/16 * 16 - 16^2 = (4 - 4)/16 * 16 - 256 = 0/256 - 256 = -256.

So the limit as x approaches 16 is -256.

Step-by-step explanation:

A wheelchair ramp is too steep, it may be difficult to use so we need to choose correct slope to design wheel chair.

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

Slope is also important to people who use wheelchairs. If a wheelchair ramp is too steep, it may be difficult to use. Constructing a ramp with the right slope is especially important for people who use manual wheelchairs instead of power wheelchairs. If a ramp is too steep, the user may not have the upper arm strength necessary to power a manual chair up the ramp.

Therefore, a wheelchair ramp is too steep, it may be difficult to use so we need to choose correct slope to design wheel chair.

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It took 3 hours to travel 150 miles with a speed of 50 miles per hour.

The speed of an object tells how fast or slow an object will cover a distance in the time period. The speed of an object is directly proportional to the distance covered by the object and will be inversely proportional to time.

Here we have

A drive of 50 miles per hour between Seattle and Portland
which are 150 miles apart  

Given speed = 50 miles per hour

Distance covered = 150 miles  

The time is taken to travel the distance, Time = Distance / Speed  

= (150/50) =  3 hrs

Therefore,

It took 3 hours to travel 150 miles with a speed of 50 miles per hour.  

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Answer:

The inequality to compare the number of pictures taken during school to the number of pictures taken after school is: 19 < 24.

Step-by-step explanation:

Here's a step-by-step explanation of the inequality comparison:

Start with the two values being compared: 19 pictures taken during school and 24 pictures taken after school.

Use the inequality symbol (<) to compare the two values: 19 < 24.

Read the inequality as "19 is less than 24". This means that there were fewer pictures taken during school (19) than after school (24).

So the inequality comparison between the number of pictures taken during school and after school is: 19 < 24.

Answer: We will do (A) then you will be able to do most of them

Step-by-step explanation: For (A) first write it down

18x - 2y=0

Now we can explore many different combinations but I will give you something simple

18(1) - 2(9)=0  (note that two numbers beside each other means multiplication)

Now we can see this is now = 18 - 18 = 0

The answers to each part is mentioned above.

Given is the term -

Accompanying percentiles

The kth percentile of a set of data is a value such that {k} percent of the observations are less than or equal to the value.

10% of​ 3- to​ 5-month-old males have a head circumference that is 41.0 cm or less.

90​% of​ 2-year-old females have a waist circumference that is 52.7 cm or less.

At each​ percentile, the heights generally decrease as the age increases. Assuming that an adult male does not grow after age​ 20, the percentiles imply that adults born in 1990 are generally taller than adults who were born in 1950.

Therefore, the answers to each part is mentioned above.

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Yes, we can fit four (2 in x 2 in x 2 in) cubes inside a sphere with a diameter of 4 inches.

Given are four 2 in x 2 in x 2 in cubes and a sphere with a diameter of 4 inches.

The cubes can fit if -

V{cubes} < V{sphere}

{4 x a³} < {4/3πr³}

{4 x 8} < {4/3 x 3.14 x 8}

32 < 33.49

which is true

Therefore, Yes, we can fit four (2 in x 2 in x 2 in) cubes inside a sphere with a diameter of 4 inches.

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The equation of the line passing through the point (-4, 1), and having a slope of m = -3/2 is 2y = -3x - 10.

The slope of the line and a point on the line can be used to create the equation of a line. To better comprehend how the equation for a line is formed, let's learn more about the line's slope and the necessary point on the line. The slope of the line, which can be stated as a numeric integer, fraction, or the tangent of the angle it forms with the positive x-axis, is the line's inclination with respect to the positive x-axis. The coordinate system's point with the x coordinate and the y coordinate is referred to as the point.

The equation of the line passing through the points (x1, y1), with a slope of m is given by the formula:

(y - y1) = m (x - x1)

Given that the point is (-4, 1) and the slope, m = -3/2.

Substituting the values we have:

(y - y1) = m (x - x1)

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

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

2y - 2 = -3x - 12

2y = -3x - 10

Hence, the equation of the line passing through the point (-4, 1), and having a slope of m = -3/2 is 2y = -3x - 10.

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On solving the provided question, we cans ay that by unitary method, for 875 miles = car will take 0.04*875 = 35 gallons

The unit technique is an approach to problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value. The unit method, to put it simply, is used to extract a single unit value from a supplied multiple. For instance, 40 pens would cost 400 rupees, or the price of one pen. The process for doing this may be standardized. a single country. anything that has an identity element. (mathematics, algebra) (Linear algebra, mathematical analysis, mathematics of matrices or operators) Its adjoint and reciprocal are equivalent.

by unitary method,

Sera drove 450 miles

car used 18 gallons of gas

for 1 mile, car take = 18/450 = 0.04gallons

for 875 miles = car will take 0.04*875 = 35 gallons

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The solution to the equation -1/5 = -2y + 8/5 is y = 9/10

Given the equation in the question;

-1/5 = -2y + 8/5

First, rewrite the equation as;

-2y + 8/5 = -1/5

Move all terms not containing y to the right side of the equation

-2y + 8/5 - 8/5 = -1/5 - 8/5

-2y = -1/5 - 8/5

Add  -1/5 and -8/5

-2y = ( -1 - 8) / 5

-2y = -9 / 5

Divide both sides by -2

-2y / -2 = -9/5 ÷ -2

y = -9/5 × -1/2

y = 9/10

Therefore, the value of y is 9/10.

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The current asset is $10,150, the total long term asset is $13108, the total current liabilities is $985, the long term liabilities is $9982 and the total equity is $12273

The company has $10,150 in current assets, which are made up of $8,250 in cash, $1,225 in inventory, and $675 in accounts receivable.

The company has $985 in current liabilities, which are made up of $485 payable to suppliers and a $500 loan that must be repaid in the following six months.

The owner's equity is equal to the $12,000 initial investment plus the $1,291 in earnings retained less the $2,018 in long-term loan repayment plus the $1,000 set aside for long-term investment, for a total of $12,273.

The value of the company's assets (land, buildings, and equipment) plus the owner's equity, or $12,273 + $8,878 + $4,230, equals the net worth of the business, or $25,381.

a) The current assets of the company are:

$8,250 in cash

$1,225 in inventory

$675 in accounts receivable

The current assets total $10,150.

b) The long-term assets of the company are:

Land and building worth $8,878

Equipment worth $4,230

The total long-term assets of the company are $8,878 + $4,230 = $13,108.

c)The current liabilities of the company are:

$485 owed to suppliers

$500 loan to be paid off in the next six months

The total current liabilities of the company are $485 + $500 = $985.

d)The long-term liability of the company is the five-year loan of $12,000, of which $2,018 has been paid back, leaving a remaining balance of

= $12,000 - $2,018 = $9,982.

e) The total equity of Company X

= $12,000 (initial investment) + $1,291 (retained earnings) - $2,018 (repaid long-term loan) + $1,000 (long-term investment)

= $12,273.

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Therefore , the solution of the given problem of mean comes out to be

23.679 the isotopic mass of the least abundant isotope.

The arithmetic mean, often known as the average, of a dataset is the total of all values divided by the number of values (as opposed to the geometric mean). It is the most used often index of central tendency, sometimes known as the "mean." This result can be obtained by simply dividing the number of variables values in the dataset by the sum of all the values.

Here,

The abundant isotope has an isotopic mass of 123.39 u, compared to the most prevalent isotope's mass of 121.560 u.

22.567 u is the average atomic mass.

84.236% is the most prevalent isotope.

22.653 u is the isotope's mass.

Least prevalent isotope: 100 - 84.236% = 15.764%

Take into account that x is the mass of both the least common isotope.

The same element's atoms called abundant isotopes have different quantities of neutrons than other isotopes. These species always have the same number of protons and electrons. Although there is a change in the number of neutrons, the atomic number is unaffected. The weighted value of all the isotopes that an element naturally presents is its atomic mass.

Average atomic mass is equal to the sum of the natural abundances of the isotopes A and x divided by 100.

=> 22.653 = ( 22.567 * 84.236) + (x * 15.764 ) / 100

=>22.653 * 100 = 1900.953 + 15.764 x

=> x = 22.653 * 100 - 1900.953/ 15.764

=> 23.679

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The proof is given as follows:

The transitive property argues that "if two quantities are equal to the third quantity, then we may claim that all the quantities are equal to one other".

The term transitive refers to a transfer. If there are three quantities a, b, and c, and if an is connected to b by some rule and b is related to c by the same method, then a and c are related to each other by the same rule; this property is known as the transitive property of equality.

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D -3/2 is the right answer. In other words, the sum of their slopes is -1. So, if the green line has a slope of 2/3, the red line has a slope of -3/2.

The slope of a line indicates its steepness. Slope is computed mathematically as "rise over run" (change in y divided by change in x). The slope of a line is its steepness as it goes from LEFT to RIGHT. Slope is the ratio of a line's rise, or vertical change, to its run, or horizontal change. The slope of a line is always constant (it never changes) regardless of whatever two locations on the line are chosen. The slope-intercept form of an equation occurs when the equation of a line is stated in the form y = mx + b. The slope of the line is given by m.

Here,

The correct answer is D -3/2 that is, the product of their slopes is -1. So, if the slope of the green line is 2/3, then the slope of the red line is -3/2.

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The solution to the equations are as follows:

1. X^2 + 6X + 3 = 0, the solution is (-3,-1).

2. 52726 - 6 = 52,720

3. 12 - 8 + (-5) = -1

4. X^2 + 8X + 20 = 0, the solution is (-5, -4).

5. x⁻¹+4x⁻²=0

X^2 + 6X + 3 = 0, can be solved by the quadratic formula: X = (-b ± √(b^2 - 4ac)) / 2a, where a = 1, b = 6, and c = 3.

X = (-6 ± √(6^2 - 4 * 1 * 3)) / 2 * 1

X = (-6 ± √(36 - 12)) / 2

X = (-6 ± √(24)) / 2

X = (-6 ± 2√6) / 2

X = (-3 ± √6), (-3 - √6)

52726 - 6 = 52720

12 - 8 + (-5) = -1

X^2 + 8X + 20 = 0, can be solved by the quadratic formula: X = (-b ± √(b^2 - 4ac)) / 2a, where a = 1, b = 8, and c = 20.

X = (-8 ± √(8^2 - 4 * 1 * 20)) / 2 * 1

X = (-8 ± √(64 - 80)) / 2

X = (-8 ± √(-16)) / 2

Since the square root of a negative number is not defined in real numbers, there are no real solutions to this equation.

x⁻¹ + 4x⁻² = 0

Dividing both sides by x⁻², we get x + 4 = 0

Subtracting 4 from both sides, we get x = -4.

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The complete question goes thus:

Solve:

1.X2 +6x +3=0

2.52726-6=0

3.12-8+-5:0

4.X(X+8)=-20

5.x⁻¹+4x⁻²=0

Answer:

-1

Step-by-step explanation:

Both approaches -1.

Answer:

(x - 1)² + (y - 1)² = 25

Step-by-step explanation:

the distance from the center of the circle to any point on the edge (or arc) of the circle is the radius of the circle.

per the distance formula (= Pythagoras for the right-angled triangle of the coordinate differences between the 2 points) we know

AB² = (xb - xa)² + (yb - ya)² = (5 - 1)² + (4 - 1)² =

= 4² + 3² = 16 + 9 = 25

AB = radius = 5

the standard form of a circle is

(x - h)² + (y - k)² = r²

(h, k) being the coordinates of the center of the circle, r being the radius.

(x - 1)² + (y - 1)² = 25

is the correct equation.

The table for the number of steps Anne walked in x hours is:

Hours    Steps

1             700

2            1400

3            2100

Anne walked more than Elyse for different numbers of hours.

A function is a relationship between inputs where each input is related to exactly one output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

Anne function:

y = 700x

Now,

The table for the number of steps Anne walked in x hours.

Hours    Steps

1             700

2            1400

3            2100

Now,

Anne has walked more than Elyse for different numbers of hours.

Thus,

The table comparison is given above.

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Answer:

11,209

Step-by-step explanation:

1 x 10,000 is 10,000, 1 x 1,000 is 1,000 100 x 200 is 200, 0 x 10 = 0, 9 x 1 = 9. 10,000 + 1,000 + 200 + 0 + 9 = 11209

The exact value of θ can not be expressed in terms of elementary functions and is difficult to find without numerical methods.

To find the angle of intersection between two curves, we need to find the dot product of the two vectors that represent their tangent lines at the intersection point.

Let's find the first derivative of both r1(t) and r2(t) with respect to t:

r1'(t) = -sint i + cost j + k

r2'(t) = i + 2tj + 3t^2 k

The tangent lines at (1,0,0) are given by:

r1'(1) = -sin(1) i + cos(1) j + k

r2'(1) = i + 2j + 3k

The angle of intersection between these two lines is given by the dot product of the two vectors divided by the product of their magnitudes:

cos(θ) = (r1'(1) * r2'(1)) / (||r1'(1)|| * ||r2'(1)||)

= (-sin(1)i + cos(1)j + k) * (i + 2j + 3k) / (||-sin(1)i + cos(1)j + k|| * ||i + 2j + 3k||)

To find the angle of intersection, we can use the arccosine function:

θ = arccos(cos(θ))

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Answer:

Step-by-step explanation:

yes

Answer:

yes

Step-by-step explanation:

each 'x-value' maps to a unique 'y-value'

Check the picture below.

so hmmm let's firstly convert the angles to degrees only.

so there are 60 minutes in 1 degree, so 10' is really 10/60 = 1/6 of a degree, so 112°10' is really just 112 and 1/6 degrees.

15°20' is just well, 20/60 = 1/3, so that converted to degrees only will be 15 and 1/3 degrees.

now, a triangle has a total of 180° interior angles, so let's get the angle A

[tex]\stackrel{mixed}{112\frac{1}{6}}\implies \cfrac{112\cdot 6+1}{6}\implies \stackrel{improper}{\cfrac{673}{6}} ~\hfill \stackrel{mixed}{15\frac{1}{3}} \implies \cfrac{15\cdot 3+1}{3} \implies \stackrel{improper}{\cfrac{46}{3}} \\\\[-0.35em] ~\dotfill\\\\ 180-\cfrac{673}{6}-\cfrac{46}{3}\implies \cfrac{105}{2}\implies 52.5^o\impliedby \measuredangle A \\\\[-0.35em] \rule{34em}{0.25pt}[/tex]

[tex]\textit{Law of sines} \\\\ \cfrac{sin(\measuredangle A)}{a}=\cfrac{sin(\measuredangle B)}{b}=\cfrac{sin(\measuredangle C)}{c} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{\sin(C)}{c}=\cfrac{\sin(A)}{a}\implies \cfrac{\sin(\frac{46}{3}^o)}{c}=\cfrac{\sin(52.5^o)}{354}\implies \cfrac{\sin(\frac{46}{3}^o)}{\sin(52.5^o)}=\cfrac{c}{354} \\\\\\ \cfrac{354\sin(\frac{46}{3}^o)}{\sin(52.5^o)}=c\implies 117.99^o\approx c=AB[/tex]

Make sure your calculator is in Degree mode.

Answer:

c(3a) = 2(3a)^2 - 4(3a) + 3 = 18a^2 - 12a + 3.

Step-by-step explanation:

c(3a) = 18a^2 - 12a + 3

Note: this is the simplified form of the expression.