Element X is a radioactive isotope such that every 28 years, its mass decreases by half. Given that the initial mass of a sample of Element X is 40 grams, how much of the element would remain after 11 years, to the nearest whole number?

Therefore, the perimeter of the square is increasing at a rate of 3 * sqrt(2) inches per minute.

Let's denote the side length of the square as "s" (in inches) and the diagonal as "d" (in inches).

We know that the diagonal of a square is related to the side length by the Pythagorean theorem:

d^2 = s^2 + s^2

d^2 = 2s^2

s^2 = (1/2) * d^2

Differentiating both sides with respect to time (t), we get:

2s * ds/dt = (1/2) * 2d * dd/dt

Since we are given that dd/dt (the rate of change of the diagonal) is 3 inches per minute, we can substitute these values:

2s * ds/dt = (1/2) * 2d * 3

2s * ds/dt = 3d

Now, we need to find the relationship between the side length (s) and the area (A) of the square. Since the area of a square is given by A = s^2, we can express the side length in terms of the area:

s^2 = A

s = sqrt(A)

We are given that the area of the square is 18 square inches, so the side length is:

s = sqrt(18) = 3 * sqrt(2) inches

Substituting this value into the previous equation, we can solve for ds/dt:

2 * (3 * sqrt(2)) * ds/dt = 3 * d

Simplifying the equation:

6 * sqrt(2) * ds/dt = 3d

ds/dt = (3d) / (6 * sqrt(2))

ds/dt = d / (2 * sqrt(2))

To find the rate at which the perimeter (P) of the square is increasing, we multiply ds/dt by 4 (since the perimeter is equal to 4 times the side length):

dP/dt = 4 * ds/dt

dP/dt = 4 * (d / (2 * sqrt(2)))

dP/dt = (2d) / sqrt(2)

dP/dt = d * sqrt(2)

Since we know that the diagonal is increasing at a rate of 3 inches per minute (dd/dt = 3), we can substitute this value into the equation to find dP/dt:

dP/dt = 3 * sqrt(2)

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The total distance the courier biked can be determined by calculating the sum of the distances between consecutive buildings.

Given that each unit on the coordinate grid equals 100 feet, we can find the total distance in feet.

Starting from building 1 and proceeding to buildings 2, 3, and 4, and then returning to building 1 forms a closed path.

Since the path consists of straight lines, we can calculate the distances between the buildings using the distance formula, which is the straight-line distance between two points in a coordinate system.

Let's assume the coordinates of the buildings are (x1, y1) = (0, 0) for building 1, (x2, y2) for building 2, (x3, y3) for building 3, and (x4, y4) for building 4. We can calculate the distance using the formula:

Distance = √((x2 - x1)^2 + (y2 - y1)^2) + √((x3 - x2)^2 + (y3 - y2)^2) + √((x4 - x3)^2 + (y4 - y3)^2) + √((x1 - x4)^2 + (y1 - y4)^2)

By substituting the appropriate coordinates and evaluating the equation, we can find the total distance the courier biked in feet.

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Answer: 41.85 or 41 17/20.

Step-by-step explanation:

Formulate : 2511 / 12 / 5

calculate the product/quotient : 2511/60

Cross out the common factor:  837/20

Getting the result of 41.85 or 41 17/20.

Answer - 41.85 or 41 17/20.

A triangle is a plane figure that consists of three sides and three internal angles. Thus m<FHG is \(122^{o}\).

A triangle is a family of polygon which is bounded by three straight sides, thus forming three internal angles. The sum of the internal angles of a trigon is \(180^{o}\). While exterior angles are angles which are outside the edges of a triangle.

From the given question;<IGH = <BGD = 42°   (vertically opposite angles)<HIG = 180 - <CIH         = 180 - 100<GIH = \(80^{o}\)

Thus, we can conclude that;<IGH + <GIH + <GHI =   \(180^{o}\)42 + 80 + <GHI =  \(180^{o}\)<GHI =  \(180^{o}\) - 122         = 58<GHI = \(58^{o}\)So that;m<FHG

=  \(180^{o}\) - M<GHI             =  \(180^{o}\) - 58            

= \(122^{o}\)m<FHG

= \(122^{o}\)

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Answer:

What are the distinct features of:

1. Rational Function

2. Rational Equation

3. Rational Inequality​

This is your question anwer below

Step-by-step explanation:

f(x) = 2/(x-3) is a rational function

4 = (3x^2 - 5x +2) / (x + 2) is a rational equation

2x - 7 < x + 1/(x - 2) is a rational inequality

An expression is rational in simplest form if it can be written as N/D where N and D have no common factors.

So 2/3 and (x-2)/x^2 and (3x^2 + 3x)/ (2x + 7) are all rational expressions

Pls mark be Brilliant and rate 5 and pls pls pls give 5 heart

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a) The average selling price in Bloomington is $301,596.27.

b) The average and standard deviation of the square footage of houses in Bloomington are 2,164.57 sqft and 954.61 sqft, respectively.

c) There are 98 houses made primarily of brick and 102 not.

d) There is a positive moderate relationship between selling price and square footage of houses in Bloomington.

e) On average, houses in newer neighborhoods have a higher selling price than more traditional ones.

The descriptive analysis in Bloomington has given the following insights: The average selling price in Bloomington is $301,596.27. The average and standard deviation of the square footage of houses in Bloomington are 2,164.57 sqft and 954.61 sqft, respectively. There are 98 houses made primarily of brick and 102 not. There is a positive moderate relationship between selling price and square footage of houses in Bloomington. On average, houses in newer neighborhoods have a higher selling price than more traditional ones.

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Answer:

D, 36/8

Step-by-step explanation:

12*3/8

Since all the answers are in a fraction, we can leave our answer in one.

12x3 = 36

36/8

Answer:

35 as a fraction is 7/20

Step-by-step explanation:

Answer:

11/35

Step-by-step explanation:

Answer:

∠ABD = 45°

Step-by-step explanation:

Since ABCD is a square, its diagonals (Line BD) bisect the angles of the corners of the square (∠ABC) into two equal angles (∠ABD and ∠CBD). The angle of each corner is 90° so you can find ∠ABD.

2(∠ABD) = 90°

∠ABD = 90° ÷ 2

∠ABD = 45°

Answer:

2(6+1)

Step-by-step explanation:

its so easy because in sec..134 there is a • like this and look

2(6+1)

2 of 7

2×7

14,,,

and

24-5×2=14,,, is the answer,,,

Answer:

C. 72

Hope it helps :)

The expected value of a roll of this weighted die is; 13/3 or 4.33

We are given that;

A $6 sided die is weighted.

Probability of any number being rolled is proportional to the value of the roll.

Probability of a $2 being rolled is twice that of a $1 being rolled.

Thus, the expected Value is;

E(x) =  (1*1 + 2*2 + 3*3 + 4*4 + 5*5 + 6*6)/(1 + 2 + 3 + 4 + 5 + 6)

E(x) = 13/3 = 4.33

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If a blood stain has a length of 3.0cm and a width of 1.5cm, the angle of impact is 30 degrees

The length of the blood stain = 3 cm

The width of the blood stain = 1.5 cm

The equation for measuring the angle of impact is

sin (angle of impact) = The width of the blood stain / The length of the blood stain

Angle of impact = sin^-1 (The width of the blood stain / The length of the blood stain)

Substitute the values in the equation

Angle of impact = sin^-1(1.5 / 3)

= sin^-1(0.5)

= 30 degrees

Therefore, the angle of impact is 30 degrees

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Answer:

Step-by-step explanation:

Use SOH CAH TOA.

Using TOA or tangent = tan0 = opp/adj.

tan0 = 1500m/800m  ->  tan0 = 1.875

Use inverse tan or tan^-1.

0 = tan^-1(1.875)

0 = 61.93 degrees.

Thus he can cut it into six pieces

Answer:

the set of all the real values which are strictly greater than zero which is all positive real numbers

Step-by-step explanation:

In interval notation: (0, ∞)

Any exponential function with a positive base and positive multiplier will have a horizontal asymptote at y=0 and will extend to +∞. That's what this one does.

Range of a function--

The range of a function is the set of all the values that are attained by a function.

We are asked to find the range of the function f(x)

the set of all the real values which are strictly greater than zero

x > 0

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Answer:

so you wold do I=t×r×A ok so I=6,500 t=5 r=4.3 and u have to find A so you wolf multiple 5×4.3=21.5 and than you wold divide 6500÷21.5=302.3255813953488×21.5= 6500 so A=302.3255813953488

The given statement is true. If f '(x) < 0 for 7 < x < 10, then f is decreasing on (7, 10).

If f '(x) < 0 for 7 < x < 10, then f is decreasing on (7, 10).

Declining Function: A function f is said to be decreasing on an interval I if for any two values x₁ and x₂ in I, with x₁ < x₂, then f (x₁) > f (x₂).

Since f '(x) < 0 for 7 < x < 10, it implies that the slope of the tangent line to the curve at every point in the interval (7,10) is negative. That means the graph of f is declining in that interval.

Therefore, the given statement is true. If f '(x) < 0 for 7 < x < 10, then f is decreasing on (7, 10).
This is because a negative first derivative, f'(x), indicates that the function is decreasing. The fact that f'(x) < 0 for all values of x in the given interval (7, 10) implies that the function is continuously decreasing throughout that interval.

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Answer:

30/13

Step-by-step explanation:

15/13x2

15/13x2/1

30/13

The statement is false. The assumptions of discharge and friction head loss in series and parallel pipes are the same, not different. In pipes in series, the total discharge is equal to the individual discharge in each pipe. This means that the flow rate remains the same as it passes through each pipe in series. For example, if Pipe A has a discharge of 10 liters per second and Pipe B has a discharge of 5 liters per second, the total discharge in the series will be 10 liters per second.

In pipes in parallel, the total friction head loss is equal to the individual friction head loss in each pipe. This means that the pressure drop across each pipe is independent of the others. For example, if Pipe A has a friction head loss of 20 meters and Pipe B has a friction head loss of 30 meters, the total friction head loss in the parallel pipes will be 50 meters. Therefore, the correct statement would be: For pipes in series, the total discharge equals the individual discharge in each pipe, and for pipes in parallel, the total friction head loss equals the individual friction head loss in each pipe.

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Answer: Most customers who rate their service as high quality return for additional services.

Step-by-step explanation: just took the test :)

Answer:

f(x)

Step-by-step explanation:

f(x) changes at a constant rate   when x changes from 1 to 2 the change in y = 7      when x changes from 2 to 3 the change in y = 7   etc

the others do not change at a constant rate when x changes by one

The data represented by table number one is showing the linear relation.

A linear relationship (or linear association) is a statistical term that describes a two-variable relationship that follows a straight line.

The momentum of a variable is represented by the rate of change, which is used to mathematically describe the percentage change in value over a defined period of time. If the rate of change is constant then the relationship will be linear.

For table number one the data is,

x    F(x)

1     12

2    19

3    26

4    33

The rate of change will be,

R₁ = ( 19 - 12 ) / ( 2 - 1 )  = 7

R₂ = ( 26 - 19 ) / ( 3 - 1 ) = 7

R₃ = ( 33 - 26 ) / ( 4 - 3 )= 7

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Answer:

100000000000000000

Step-by-step explanation:

Evaluating expressions with decimals:

\(10^{10} \times 10^7\)

10^10 is essentially the same as saying:

\(10\times 10\times10\times\ 10\times 10 \times 10 \times 10 \times 10 \times 10 \times 10\)

Evaluating this, we get

\(10000000000\)

Now, for 10^7, that is the same as

\(10\times 10\times10\times\ 10\times 10 \times 10 \times 10\)

Evaluating this, we get

\(10000000\)

Now we have to multiply both of the numbers together

\(10000000000 \times 10000000\)

Multiply

\(100000000000000000\)

Answer:g(x)=-x2-3

Step-by-step explanation: we have the a and the c we have a negative a so the graph goes down as we have a negative c so the vertex moves down that much