cesium 134 decays exponentially. the half life of cesium-134 is 2 years. suppose we have a 50mg sample. after how long after how long will only a 10 mg sample

There is no definite formula for calculation of circumcenter of a triangle but a process for calculation of circumcenter has been described here.

What is circumcenter of a triangle?

Circumcenter of a triangle is the point of intersection of the perpendicular bisectors of every sides of the triangle.

Let the coordinate of A, B, C [tex]\Delta[/tex] ABC be ([tex]x_1, y_1[/tex]), [tex](x_2, y_2)[/tex] and [tex](x_3, y_3)[/tex] respectively and let the coordinate of circumcenter of [tex]\Delta ABC[/tex] is (x, y)

We need to find the length of AB, BC and AC

The length will be obtained in terms of x and y

On solving the equations, we will obtain the value of x and y

The value of x and y is the required coordinate of the circumcenter.

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The equation in slope-intercept form of line k is y = - x + 5.

What is the equation of the line?

A straight line's general equation is y = mx + c, where m denotes the gradient and y = c denotes the point at which the line crosses the y-axis. On the y-axis, this value c is referred to as the intercept.

The equation of a line in slope- intercept form is

y = mx + c

where,

   m is the slope and c the y- intercept.

We have,

y = x - 3

∴  It is in the slope intercept form.

with slope m = 1

Given a line with slope m then the slope of a line perpendicular to it is

[tex]m_{perpendicular} = -\frac{1}{m} = -\frac{1}{1} = -1[/tex] ,

The partial equation of line j is,

y = - x + c

By substituting (2, 0) into the partial equation we get, c

0 = - 2 + c

c = 0 + 2 = 2

∴ c = 2

The equation of line j is y = - x + 2.

Similarly,

The slopes of parallel lines are the same.

The partial equation of line k is,

∴ y = - x + c

By substituting (- 1, 6) into the partial equation we get, c

6 = 1 + c

c = 6 - 1 = 5

∴ c = 5

The equation of line k is y = - x + 5.

Therefore, the equation in slope-intercept form of line k is y = - x + 5.

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The equation of the line that is parallel to the given line, through the given point is y = -5x - 7

Given equation,

y = -5x + 1

Slope = m

          = -5

For two lines to be parallel, slope is equal.

Therefore, m = -5 for another line.

Let the equation of the line be y = mx + c

This line passes through A(-2,3)

Therefore, 3 = -5(-2) + c

                  3 = 10 + c

                  c = 3 - 10

                     = -7

Hence, equation of line is y = -5x - 7.

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The true statement about the graph is

It is a function with the domain {-6 < x < 0} and the range {0 ≤ y ≤ 5}.

The range refers to all possible value in the out put of a graph.

The out put is the y coordinate and the possible values here is within the interval

0 ≤ y ≤ 5

The domain refers to all possible value in the input of a graph.

The input is the x coordinate and the possible values here is within the interval

-6 ≤ x ≤ 0

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Answer:

8

Step-by-step explanation:

Price : %

  [tex]x[/tex]    :  100

 6.4  :  80     (Got 80 by 100 - 20)

Cross multiply

100*6.4 = 80[tex]x[/tex]

640 = 80[tex]x[/tex]

640/80 = [tex]x[/tex]

[tex]x[/tex] = 8

Answer: My answer is 4. You may want another answer.

Step-by-step explanation:

visual studying

The height is either 10 cm,12 cm,14 cm.

Given:

The base of the parallelogram has a length of 10 cm.

Here area is not given so the height may be anything.

suppose h = 10

area = base * height

= 10 * 10

= 100 cm^2

if h = 12

area = 10 * 12

= 120 cm^2

if h = 14

area = 10 * 14

= 140 cm^2

Therefore the height is either 10 cm,12 cm,14 cm.

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Using the t test statistic, the value of the test statistic is 1.25.

In the given question we have to find the value of the test statistic.

A manufacturer of chocolate potato chips would like to know whether its bag filling machine works correctly at the 400 gram setting.

= 400

A 25 bag sample had a mean of 399 grams and the variance is 400.

There is sufficient evidence at the 0.025 level that the bags are underfilled.

Sample size(n) = 25

sample Mean = 399

Sample Variance = 400

Standard Deviation = √Sample Variance

Standard Deviation = √400

Standard Deviation = 20

Population Mean = 400

So , the null and alternative hypothesis are

H0 : μ = 400

Ha : μ < 400

Using the sample t test statistic

t = (Population Mean - Sample Mean)/(Standard Deviation/Sample size)

t = (400 - 399)/(20/25)

t = 1*25/20

t = 1.25

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Since triangle P'Q'R' is the result of a transformation of triangle PQR, an algebraic representation which best describes this transformation is: C. (x, y) → (5x/2, 5y/2).

In Mathematics, a transformation can be defined as the movement of a point from its original (initial) position to a final (new) location. This ultimately implies that, when an object is transformed, all of its points would be transformed as well.

From the information provided above, we can logically deduce the following coordinates:

Therefore, the transformation rule is given by:

P (x, y)                      →               P' (x, y)

Point P = (-1, 1)      →  Point P' = ((5/2 × -1), (5/2 × 1)) = Point P' = (-5/2, 5/2).

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The greatest amount of sap collected from any one tree is ?

times as great as the least amount of sap collected from

any one tree. = 2 times

The picture for the condition is attached below.

What is factors of number?

A number or algebraic expression that evenly divides another number or expression—i.e., leaves no remainder—is referred to as a factor in mathematics. As an illustration, 3 and 6 are factors of 12 because 12 3 = 4 and 12 6 = 2, respectively. 1, 2, 4, and 12 are the other components that make up 12.

Let, the factors of 72 are

72 = 1, 2, 3, 4, 6, 8, 9, 12, 18, 24 36, 72.

When we divide 72 by 6 we get 12.

⇒ [tex]\frac{72}{6} = 12[/tex]

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The values of the function when x = 3 are -10. -1 and -3, respectively

Function 1

The equation of the function is given as

y = -4x + 2

We have the value of x to be 3

So, we have

y = -4 x 3 + 2

Evaluate

y = -10

Function 2

The graph represents the notation of the function

On the graph, we have the value of y to be -1, when x = 3

This means that

y = -1

Function 3

The table represents the notation of the function

On the table, we have the value of y to be -3, when x = 3

This means that

y = -3

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Angles 1 and 5 constitutes one of the pairs

Step-by-step explanation:

Answer:

[tex]\left(m+2\right)\left(n^2+2n+m+1\right)[/tex]

Step-by-step explanation:

Hoooo boy.

This is a long one.

But let's do it!!!!

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

Answer:

Step-by-step explanation:

By writing both variables in the same side of the linear equation, we will get the standard form:

2y + (-1)*x = 4

A linear equation between two variables x and y written in standard form is:

a*x + b*y = c

Where the coefficients a, b, and c, are all real numbers.

In this case, we have the linear equation:

2 + (1/2)*x = y

If we multiply both sides by 2, we get:

2*(2 + (1/2)*x) = 2*y

4 + x = 2y

Now we subtract x in both sides to get:

4 + x - x = 2y - x

4 = 2y - x

This is the linear equation in standard form:

2y + (-1)*x = 4

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The sine function is  y = 5 sin ([tex]16\pi x[/tex] ) + 3.

The function y =[tex]sin x[/tex] defines a sine wave as a geometric waveform that oscillates (moves up, down, or side to side) frequently.

It is an s-shaped, smooth wave that oscillates above and below zero, to put it another way.

In its most general form, the sine wave can be described using the function y=[tex]a sin (bx)[/tex]

Given:

Amplitude = 3

midline= 5

As, we know

General sine function:  a sin b[tex](x- c)[/tex] + d

and, amplitude = absolute value of a

b = 2π / period

c = phase shift (horizontal shift)

d = vertical shift  (i/e., midline is  y = d)

So,

a = 5, d = 3, and b = 2π / (1/8) = 16π, c = 0

Substituting the above value in Sine function we get

Thus, y = 5 sin ([tex]16\pi x[/tex]) + 3

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The value of x is -6 or 0 which is obtained by solving the giving equation using factoring.

Given equation: 2x³ + 12x² = 0

Solving this equation by factoring as follows:

2x³ + 12x² = 0

= 2x²(x+6) = 0

So, x + 6 = 0 or 2x² = 0

x = -6 or x = 0

Therefore, the value of x is -6 or 0 which is obtained by solving the giving equation using factoring.

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Answer:

x = 2.875

Step-by-step explanation:

1 1/3 (9 - 6x) = -11

        12 - 8x = -11

            - 8x = -23

                x = 2.875

Answer:

9

Step-by-step explanation:

(2(-3)+3)^2

(-6+3)^2

(-3)^2

since the power of 2 is even it will be a positive result (if its a odd number like 3 it will be a negative result)

3^2

=9

It will take 1.5 minutes for printer to print 12 papers.

Given,

Time taken to print 40 papers=5 minutes

then,

Time taken to print 1 paper =[tex]\frac{5}{40}=\frac{1}{8}[/tex] minutes

then to find time taken to print 12 papers, multiply 12

Time taken to print 12 paper,

[tex]Time=\frac{1}{8}*12\\\\Time=1.5\ minutes[/tex]

Thus, it will take 1.5 minutes for printer to print 12 papers.

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5761.4 feet is the height of the mountain prior to construction

Given: 1.1h – 622.5 = 5,675

This is an algebraic equation, we need to solve for h

1.1h – 622.5 = 5675

collect like terms:

1.1h =  5675 + 622.5

Add like terms:

1.1h = 6337.5

Divide both sides by 1.1:

h = 6337.5/1.1

h = 5761.4 feet

Therefore,  the height of the mountain prior to construction is 5761.4 feet

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Answer:

-4

Step-by-step explanation:

m= y2-y1/x2-x1

m= 11-3/0-2

m= 8/-2

m= -4

Answer: The slope is -4

Step-by-step explanation: The general formula for calculating the slope is  [tex]\frac{y2-y1}{x2-x1}[/tex].

x1 = 2, y1 = 3, x2 = 0, y2 = 11

So we have [tex]\frac{11-3}{0-2}[/tex] = [tex]\frac{8}{-2}[/tex] = -4.

Answer:

22ft

Step-by-step explanation:

2+2+5+4+4+2+2= 22

Answer:

5h+35y=390$

20h+20y=360$

Step-by-step explanation:

there are many answers possible.

The following are just examples:

5h+35y=390$

20h+20y=360$

The values of ∠PQR = 45° and ∠POR = 90°.

The circumference of a circle is defined as its linear distance around it. In other words, if a circle is opened to form a straight line, the length of that line equals the circumference of the circle.

The radius of a circle is the distance between the circle's center and any point on its circumference. It is usually denoted by the letters 'R' or 'r'.

Given that

O is the center of the circle, if ∠OPQ = 25° &∠ORQ = 20°

We have to determine the values of ∠PQR and ∠POR

Sol. OP = OQ

⇒∠OQP = ∠OPQ = 25° [Radii of the same circle]

Similarly, ∠OQR = 20°

∠PQR = 25° + 20°

∠PQR = 45°

Furthermore ∠POR = 2 ∠PQR [the angle at the centre is twice the angle at the circumference].

⇒∠POR = 2 × 45°

∠POR = 90°.

Therefore the values of ∠PQR = 45° and ∠POR = 90°.

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The percent of times the machine will dispense less than 7.75 oz. is 69.15%.

In the given question we have to find the percent of time the machine will dispene less than 7.75 oz.

A vending machine we deigned to dipene a mean of 7.5 oz of coffee into an​ 8-oz cup.

If the standard deviation of the amount of coffee dipened is 0.5 oz and the amount is normally​ ditributed.

Mean = 7.5 ,

Standard Deviation = 0.5

P(z< 7.5) = P(z<(X-Mean)/Standard Deviation)

P(z< 7.5) = P(z<(7.75-7.5)/0.5)

P(z< 7.5) = P(z<0.25/0.5)

P(z< 7.5) = P(z< 0.5)

P(z< 7.5) = 0.6915

P(z< 7.5) = 69.15%

Hence, the percent of times the machine will dispense less than 7.75 oz. is 69.15%.

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The 65 represents the speed.

97.5 miles covered in 1.5 hours.

A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.

Variables are the name given to these symbols because they lack set values.

In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.

Given: d= 65t

We know the Formula of Speed- distance

speed= Distance / time

and, distance = speed x time

So, comparing it with given equation

distance =d , time= t and speed= 65

Now, t=1.5 hours

Distance = 1.5 x 65 = 97.5 miles

and, d= 26 miles

t= 26 / 65

t= 0.4

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