In a lab experiment, the decay of a radioactive isotope is being observed. At the
beginning of the first day of the experiment the mass of the substance was
and mass was decreasing by
500 grams
8% per day. Determine the mass of the radioactive
sample at the beginning of the 13th day of the experiment. Round to the nearest tenth
(if necessary).

Answer:

[tex]\textsf{Gradient\;$=-\dfrac{1}{3}$}[/tex]

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{6.3 cm}\underline{Slope-intercept form of a linear equation}\\\\$y=mx+b$\\\\where:\\ \phantom{ww}$\bullet$ $m$ is the slope (gradient). \\ \phantom{ww}$\bullet$ $b$ is the $y$-intercept.\\\end{minipage}}[/tex]

Given equation:

[tex]x+3y=13[/tex]

Rearrange the equation to make y the subject.

Subtract x from both sides of the equation:

[tex]\implies x+3y-x=13-x[/tex]

[tex]\implies 3y=-x+13[/tex]

Divide both sides of the equation by 3:

[tex]\implies \dfrac{3y}{3}=\dfrac{-x}{3}+\dfrac{13}{3}[/tex]

[tex]\implies y=-\dfrac{1}{3}x+\dfrac{13}{3}[/tex]

Compare the rearranged equation with the slope-intercept form.

Therefore, the gradient (slope) of the given equation is -¹/₃.

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Answer:

Step-by-step explanation:

y = mx + b

The gradient is slope "m" (coefficient by "x")

~~~~~~~~~~~~~~~~~

x + 3y = 13

Solve for "y" :

3y = - x + 13

[tex]\frac{3y}{3}[/tex] = - [tex]\frac{x}{3}[/tex] + [tex]\frac{13}{3}[/tex]

y = - [tex]\frac{1}{3}[/tex] x + [tex]\frac{13}{3}[/tex]

The gradient is ( - [tex]\frac{1}{3}[/tex] )

The weight of the plane with 20 gallons of fuel in its tank 2218 pounds. using a linear function.

what is linear function?
A straight line makes up the graph of a linear function. The following expression describes a linear function. Y equals f(x) = a + bx. Both the independent and dependent variables of a linear function are one.

Let y be the weight of the airplane and x be the amount of fuel

And we know that the general form of a linear

function is

(1) And given that the slope of the line is

y = mx + c

m = 5.9

Then (1) becomes

y = 5.9x + c

And given that for x = 53 , y = 2212.7

Then from (2), we have

2212.7 = 5.9 (53) + c

⇒ 2212.7 = 312.7 + c

c = 2212.7 - 312.7

c = 1900

Thus, (2) becomes

y = 5.9x + 1900

Then for x=22, from (3) y = 118 + 2100

= w = 2218

The weight of the plane with 20 gallons in its fuel tank is 2218 pounds

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The equation for the purchase of n number of notebooks by Caitlin is

4n = c , where c is representing the cost that Caitlin paid.

The unitary approach is a strategy for problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value.

Finding the value of a single unit using the unitary technique allows us to determine the value of the necessary number of units based on this value.

the price for one notebook was = $4 each

n number of notebooks were purchased by caitlin

therefore the cost price of 4 notebooks will be = 4 * n

as per given in the question cost price = c

therefore the equation formed will be

4n = c

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The area of a circle is changing at a rate of 576π cm²/sec when the radius of the circle is 32 cm.

For the given question;

Express the circle's area as a function of the its radius.

A = πr²

Determine the area's derivative with respect towards its radius.

dA/dr = 2πr

Using the chain rule, calculate the derivative of a area with respect to time.

dA/dt =  dA/dr . dr/dt

dA/dt = 2πr(9)

dA/dt = 18πr

When the radius is 32 cm, find the derivative of a area with respect to time.

dA/dt = 18π(32)

dA/dt = 576π

As a result, the area of a circle is changing at a rate of 576π cm²/sec when the radius of the circle is 32 cm.

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(a) We have 13 possibilities that a five-card hand will contain four of a kind.

(b) We have 12 possibilities that a five-card hand will contain a full house.

What do you mean by probability?

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true.

The probability of an occurrence is a number between 0 and 1, with 1 representing certainty and 0 representing impossibility.

Since there are no other conceivable outcomes and the coin is fair, the odds of both the possibilities, "heads" and "tails," are equally likely to occur. As a result, the probability of either occurrence is half (which could also be written as 0.5)

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Answer: (-5, 8)

Step-by-step explanation:

       The x-coordinate is responsible for left and right, and the y-coordinate is responsible for up and down translations. Coordinate points are written as (x, y).

(-8, 9) ➜ (-8 + 3, 9 - 1) ➜ (-5, 8)

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In the graph, which compares the snowfall for the same three months last year and this year, you can see that the total snowfall for last year was 36.4 inches. how much more snow fell over the course of three months this year than did so last year: 5.45

what is the explanation?

The first step is to calculate the amount of snowfall from the previous year, which are:

12.6+6+9.2

=27.8

The next stage is to calculate how much snow has fallen this year, which includes:

10+15.75+7.5

=33.25

Now let's compare the snowfall over the first three months of current year to that of last year.

33.25-27.8

=5.45

In conclusion Graph showing snowfall during the same three months last year and this year, if the total snowfall for last year was 36.4

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The single inequality:

y > |x + 2|

Can be rewritten into:

y > x + 2

y > -x - 2

So the second option is the correct one.

Remember that an absolute value equation like:

|x + a| = b

Can be rewritten as:

x + a = b

x + a = -b

So the inequality:

y > |x + 2|

Also can be rewritten into two equations, which are:

y > x + 2

-y < x + 2

The direction of the sign changes in the second one because the sign of the variable in the left changes.

Then if we multiply both sides by -1 of the second inequality, we get:

y > -x - 2

Then the two inequalities are:

y > x + 2

y > -x - 2

So the correct option is the second one.

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Answer:

[tex]y = -\dfrac{1}{2}x + \dfrac{13}{2} \;\; \text{or}\\\\y = -0.5x + 6.5\\\\[/tex]

Step-by-step explanation:

The slope-intercept form of a straight line is

y = mx + b

where m = slope and b = y-intercept

A line perpendicular to the above line will have a slope = -1/m and an intercept b which has to be determined depending on a point the line passes through

Given
Line 1:  y = 2x - 6
Slope m = 2

Line 2 perpendicular to Line 1 will have slope = -1/2 = -0.5

So the equation would be y = (-1/2)x + b

We can solve for b given the info that the line passes through (5,4)

Substitute x = 5 and y = 4 in line 2 equation:
4 = (-1/2)5 + b

4 = -5/2 + b

4 + 5/2 = b

8/2 + 5/2 = b

13/2 = b

or b = 13/2

So equation of line perpendicular to 2x -6 is
y = (-1/2)x + 13/2

or
y = -0.5x + 6.5

Answer:

Assuming that this is referring to simple interest, your answer is C) 1,750.

Step-by-step explanation:

[tex]5000[/tex] x [tex]0.05[/tex] = [tex]250[/tex]

[tex]250[/tex] x [tex]7[/tex] = [tex]1750[/tex]

The measure of the angles x and z is 95 degrees and 30 degrees after applying the property of interior angles.

When two lines or rays converge at the same point, the measurement between them is called a "Angle."

The figure is given in the picture:

From the property of interior angles:

x + 85 = 180

x = 95 degrees

6z - 85 + 85  = 180

z = 180/6

z = 30 degrees

Thus, the measure of the angles x and z is 95 degrees and 30 degrees after applying the property of interior angles.

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Answer:

x = 130°

Step-by-step explanation:

the exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.

x is an exterior angle of the triangle , then

x = 50° + 80° = 130°

Answer: 130

Step-by-step explanation:

180 = y + 50 + 80

y = 50

180 - y = x

x = 130

The length of side AB after the dilation is 2 units.

Given that, ΔABC is dilated by a factor of 1/4.

To adjust the size of a figure without altering its shape, a scale factor is a number or conversion factor that is utilized.

The fundamental equation to determine a figure's scale factor is written as, Scale factor is equal to the difference between the dimensions of the new and old shapes.

From the given figure, AB=8 units, BC=6 units and AC=10 units.

Let the x be the length of side AB after the dilation.

Now, using scale factor formula 1/4 = x ÷ 8

⇒x=2 units

Therefore, the length of side AB after the dilation is 2 units.

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x = milliliters of 40% alcohol

y = milliliters of 20% alcohol

so just alcohol alone in each quantity will just be "x" * (40/100) = 0.4x and "y" * (20/100) = 0.2y, whilst trying to get 1000 mL of 36% alcohol only.

[tex]\begin{array}{lcccl} &\stackrel{solution}{quantity}&\stackrel{\textit{\% of }}{amount}&\stackrel{\textit{mL of }}{amount}\\ \cline{2-4}&\\ \textit{40\% solution}&x&0.4&0.4x\\ \textit{20\% solution}&y&0.2&0.2y\\ \cline{2-4}&\\ mixture&1000&0.36&360 \end{array}~\hfill \begin{cases} x+y=1000\\\\ 0.4x+0.2y=360 \end{cases} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\stackrel{\textit{using the 1st equation}}{x+y=1000\implies }x=1000-y ~\hfill \stackrel{\textit{substituting on the 2nd equation}}{0.4(1000-y)+0.2y=360} \\\\\\ 400-0.4y+0.2y=360\implies 40-0.4y+0.2y=0\implies 40-0.2y=0 \\\\\\ 40=0.2y\implies \cfrac{40}{0.2}=y\implies \boxed{\stackrel{mL}{200}=y} ~\hfill \boxed{\underset{mL}{\stackrel{1000~~ - ~~200}{x=800}}}[/tex]

Answer:

86

Step-by-step explanation:

I'll assume the expression is meant to be 10^2 - 5a +6

4a- 3 =13

4a = 16

a = 4

10^2 - 5a +6

10^2 - 5(4) +6

10^2 - 20 +6

100 - 14 = 86

Answer:

f(x) = ax^2 + bx + c

I) f(1) = a + b + c = -2

II) f(2) = 4a + 2b + c = -2

III) f(3) = 9a + 3b + c = -4

II - I

IV) 3a + b = 0

III - I

V) 8a + 2b = -2

V - 2IV

2a = -2 --> a = -1

3(-1) + b = 0 --> b = 3

(-1) + (3) + c = -2 --> c = -4

f(x) = -x^2 + 3x - 4

The graph of the quadratic equation:

y = x^2 -8x + 16

Can be seen in the image at the end.

First, we have a quadratic function:

y = x^2 -8x + 16

To graph this we need to find some points on the parabola, to do that, we will evaluate it in some values of x.

if x = 0

y = 0^2 - 8*0 + 16 = 16

So we have the point (0, 16)

if x = 1

y = 1^2 - 8*1 + 16 = 9

So we have the point (1, 9)

if x = -1 we have:

y = (-1)^2 - 8*-1 + 16 = 23

So we have the point (-1, 23)

And so on, once you have enough points, you can graph them in a coordinate axis and then draw a parabola that connects them, the graph of the quadratic equation can be seen in the image below.

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Answer: Width = 8/20 ÷ 7/8  = 8/20 x 8/7   = 16/35 Therefore, the width will be 16/35 miles. Hope you do great :) !

The final value of n is -7 for linear equation 3(n - 9) - 2(n + 4) = 6n.

3(n - 9) - 2(n + 4) = 6n

6n = 3n - 27 - 2n - 8

-6n + n - 35 = 0

-5n = 35

5n = -35

n = -7

Given equation is 3(n-9)-2(n+4)=6n.

Open the brackets for multiplication, 3n - 27 - 2n - 8 = 6n.

After shifting the variables to the left-hand side and constant to the right-hand side, 5n = -35.

As the value of the constant in the above step is negative the final constant value will be also negative, n = -7.

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Answer: 4x-9y=27 is this equation in standard form.

Reason:

We look for two values that

Using trial and error, you should find those two values are 2 and 6

This is how we arrive at (x+2)(x+6)

Use the FOIL rule to expand that out and you should get x^2+8x+12 to confirm the answer.

If a circle has a circumference of 320 cm, then its radius can be calculated as 50.92 cm according to the formula of circumference of a circle.

In geometry, the circumference can be defined as the perimeter of a circle or an ellipse. It can also be said as the linear distance present around it.

To better describe it, you can imagine that if a circle is opened out and placed as a straight line, then the total length of that straight line can be described as the circumference of the circle.

It is synonymous to perimeter, but the terminology can only be used with circled and ellipses. It is the curved length of the object. In this case, the object is mostly 2 dimensional but sometimes 3 dimensional objects can also be placed to take out their circumference with other methods.

In this particular question,

2[tex]\pi[/tex]r = 320

⇒ r = 320/2[tex]\pi[/tex]

⇒ r = 50.92

⇒ r ≈ 51 cm

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Hellow what grade of math is this?

The value of x and y in the angles are 15.6 and 10.5 respectively.

When parallel lines are cut by a transversal lines, angle relationships are formed such as corresponding angles, alternate angles, linear angles, vertically opposite angles etc.

Therefore, line XD, TZ, YF and LP are parallel to each other.

WC is the transversal line.

Hence,

m∠CNL = 6x - 17.6

m∠FBH = 12y - 22

m∠THR = 3x + 29.2

Hence,

180 - (12y - 22) = 6x - 17.6(corresponding angles)

Corresponding angles are congruent

180 - 12y + 22 = 6x - 17.6

6x + 12y = 180 + 22 + 17.6

6x + 12y = 219.6

Therefore,

180 - (3x + 29.2) = 12y - 22 (alternate angles)

Alternate angles are congruent .

180 - 3x - 29.2 = 12y - 22

180 + 22 - 29.2 = 12y + 3x

172.8 = 3x + 12y

combine the equation

6x + 12y = 219.6

3x + 12y = 172.8

subtract equation(ii) from equation(i)

3x = 46.8

x = 46.8 / 3

x = 15.6

12y = 219.6 - 6(15.6)

12y = 219.6 - 93.6

12y = 126

y = 126 / 12

y = 10.5

Therefore,

x = 15.6

y = 10.5

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The formula for getting the volume of a sphere is:

where r = radius of the sphere.

Let's plug into the formula the given radius of the sphere in the question.

Then solve.

Multiply 10 cm by itself three times.

Multiply 1000 by 4, then divide by 3.

Rounding the calculated volume to the nearest whole number, the volume of the sphere is 1,333π cm³ (Option D or 4)

Answer:

The volume of the sphere is 1,333π cm³ (Option D or 4)

By the concept of basic arithmetic solo acts are 5 minutes long and ensemble acts are 15 minutes long

Mathematics' fundamentals are arithmetic operations. Addition, subtraction, multiplication, and division are the main operations that make up this concept. The phrase "mathematical operations" also refers to these.

The math operation of subtracting two integers reveals the difference between them. The '-' sign is used to indicate it. In math, subtraction is the process of taking one number away from another to determine what is left over after something has been taken away. Rational number operations are equivalent to those performed on whole numbers. The main distinction is that rational numbers take the form p/q, where p and q are integers and q is not equal to 0. It is necessary to take the LCM of the numerators when adding or subtracting two rational integers.

Here we are discussing the four basic rules of arithmetic operations for all real numbers.

12 × x + 2 × y = 90

6 × x + 2 × y = 60

To write system of equation you just need to sum all solo and ensemble acts and make it equal to how much they will last for.

B.  Here we can multiply second equation with negative 1 and add it to first equation.

6x = 30

x = 5

Now we replace x in any of 2 equations to get y.

30 + 2y = 60

2y = 30

y=15

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