The radioactive substance cesium-137 has a half-life of 30 years. The amount A(t) (in grams) of a sample of cesium-137 remaining after t years is given by the following exponential function.
A(t)=647(1/2)^1/30
Find the amount of the sample remaining after 10 years and after 80 years.
Round your answers to the nearest gram as necessary.
Amount after 10 years: ? grams
Amount after 80 years: ? grams

x = -5±-55i/5 is the solution and the best method to solve is by using the general formula.

Given the quadratic equation below;

2x^2+5x+10=0

The best method to solve the equation is by using the completing the square method as shown below:
[tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]

From the equation;

a = 2

b = 5

c = 10

Substitute into the formula to have:
x = -5±√5²-4(2)(10)/2(2)
x = -5±√25-80/4

x = -5±√-55/5

x = -5±-55i/5

Hence the solution to the given system of equation is x = -5±-55i/5

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The money Brooke initially invest is  $1.21.

Using the formula for compound interest formula:

A = P(1 + r/n)^(nt)

where:

A = final amount after t years

P = initial investment

r = annual interest rate

n = number of times interest is compounded per year

t = number of years

Substituting the given values:

1.47 = P(1 + 0.10/1)^(1*2)

1.47 = P(1.10)^2

1.47 = P(1.21)

P = 1.47/1.21

P = 1.2148...

Rounding to the nearest cent, Brooke initially invested $1.21.

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The graph of the table is attached accordingly. It examines the relationship betwen Hours and Height of the tides.

The graph shows that there is very wide variations between the height of the tides.

The relationship cannot said to be inverse or positive

Note, the following are three advantages of graphs: It makes data more attractive and understandable. It aids in the concise summarization of facts. It allows for more accurate data comparison.

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Answer:

48

Step-by-step explanation:

total cost will be the answer

Answer:

z=199.68

Step-by-step explanation:

For safety purposes, the maximum lift-off weight of each rocket is 10 pounds. but Cole’s rocket doesn't meet the requirement for launch.

The volume of the cylinder is the product of the height, pie, and square of the radius.

The volume of the cylinder = [tex]\pi* r^2 *h[/tex]

Part A

The total length of the assembled rocket will be the length of the cone and the cylinder.

The total length of the assembled rocket  = 25 + 3 = 28cm

Part B

The volume of the rocket is the combined volume of the cone and cylinder.

=  4/3 × 3.14 × 16 × 28

= 1875.62 cubic cm

To convert cm into pounds

1875.62 cubic cm = 4.135 pound

Part C

If Cole’s rocket parts are made of aluminum weighing 0.006 pounds per cubic centimeter.

Then 1875.62 cubic cm × 0.006

= 11.253

For safety purposes, the maximum lift-off weight of each rocket is 10 pounds. but Cole’s rocket doesn't meet the requirement for launch.

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The number of times on the hour in 3 days at least two owls will not hoot obtained using number theory are 69 times.

Number theory is the study of integers and functions of arithmetic.

The number of hours in 3 days = 72 hours

Number theory indicates that the multiples of the periods of hooting are;

The multiples of 8 are; 8, 16, 24, 32, 40, 48, 56, 64, 72

The multiples of 3 are; 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45, 48, 51, 54, 57, 60, 63, 66, 69, 72

The multiples of 12 are; 12, 24, 36, 48, 60, 72

The common multiples of 3 and 8 are 24, 48, 72

The common multiples of 8 and 12 are 24, 48, 72

The number of times in 72 hours when at least 2 owls are hooting are therefore;

The times when only one owl is hooting are

8, 16, 32, 40, 56, 64, = 6 times only the second owl is hooting

3, 6, 9, 12, 15, 18, 21, 27, 30, 33, 36, 39, 42, 45, 51, 54, 57, 60, 63, 66, 69   = 21 times when only the first owl hoots

The times when non of the owls hoot  are;

72 - 24 - 6 = 42 times

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Answer: 380

Step-by-step explanation:

95% = 95/100

95/100 x 400

= 380

Answer: 380 students

Step-by-step explanation:

Samuel runs 5 meters per second  best describes the slope of the linear equation

Given that Samuel runs around a 100 meter track.

He uses the linear equation y=200+5x to describe how far he runs after he has already jogged two laps.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

y=200+5x

y=5x+200

Slope is 5

Hence, Samuel runs 5 meters per second  best describes the slope of the linear equation

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a) To calculate SSTr, we need to first find the overall mean of the samples and then use it to calculate the sum of squares due to treatments (SSTr).

The overall mean of the samples can be found by adding up all the sample means and dividing by the number of samples:

Overall mean = (650 + 750 + 700 + 650) / 4 = 687.5

Next, we can calculate SSTr using the formula:

SSTr = n * (sample mean - overall mean)^2

where n is the number of observations in each sample. In this case, n = 5 for each sample.

So for the first sample, SSTr = 5 * (650 - 687.5)^2 = 5362.5

For the second sample, SSTr = 5 * (750 - 687.5)^2 = 14062.5

For the third sample, SSTr = 5 * (700 - 687.5)^2 = 3062.5

For the fourth sample, SSTr = 5 * (650 - 687.5)^2 = 5362.5

Therefore, the total SSTr is:

SSTr = 5362.5 + 14062.5 + 3062.5 + 5362.5 = 27750

b) The degrees of freedom (df) for SSTr is k-1 where k is the number of groups/populations, and df for SSE is N-k where N is the total number of observations.

df(SSTr) = k - 1 = 5 - 1 = 4

df(SSE) = N - k = 20 - 5 = 15

The mean square for treatments (MSTr) is calculated as:

MSTr = SSTr / df(SSTr) = 12 / 4 = 3

The mean square for error (MSE) is calculated as:

MSE = SSE / df(SSE) = (20 - 5) / 15 = 1

Finally, we can calculate the F-test statistic as:

F = MSTr / MSE = 3 / 1 = 3

Therefore, the MSTr is 3, the MSE is 1, and the F-test statistic is 3.

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Alan paid  an amount $850 to the bank each month to repay his debt.

The total amount that Alan paid back to the bank is equal to the initial amount that he owed minus the remaining amount after 0.5 year(s):

Total amount paid = Initial amount - Remaining amount

= $11750 - $6650

= $5100

We know that Alan paid this amount back over a period of 0.5 year(s), which is equivalent to 6 months.

Let x be the fixed amount that Alan paid back to the bank each month. Therefore, we can set up the following equation:

Total amount paid = Monthly payment × Number of months

$5100 = x × 6

x = $5100 / 6

= $850

Therefore, Alan paid  an amount $850 to the bank each month to repay his debt.

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this is a answer, thanks

Answer:

Step-by-step explanation:

Answer:45.06

Step-by-step explanation:

no explanation

The height of the low tide at 7 AM was 45.06 feet.

Given that, the high tide at midnight was 15.42 feet.

A nearing hurricane tripled the tide height. At low tide it went down by 1.2 feet at 7 AM.

We need to find the height of the low tide at 7 AM,

So,

When the hurricane is near the height of the tide is triples so the height is 15.42 × 3 = 46.26 feet

Now, at low tide it went down by 1.2 feet at 7 AM.

so, the height will be = 45.26 feet - 1.2 feet = 45.06 feet

Hence, the height of the low tide at 7 AM was 45.06 feet.

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There are 60 seconds in 1 minute, so 4 minutes would be:

4 minutes * 60 seconds/minute = 240 seconds

Therefore, it takes 240 seconds to complete the administrative task.

Johnson's pizza had a 120-degree angle when he ate it. The solution is choice C.

When a pizza is cut into 12 equal pieces, each piece has a central angle of:

360 degrees / 12 pieces = 30 degrees/piece

If Johnson ate 4 adjacent pieces, then he ate a total central angle of:

4 pieces * 30 degrees/piece = 120 degrees

Therefore, the measure of the angle of the pizza that Johnson ate is 120 degrees. The answer is option C).

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Answer:

The probability of getting a sum of 5 or 8 when 2 dice are rolled once is 1/4.

Step-by-step explanation:

Your welcome ;)

The correct equation is 45(x+3)=60x. Option A

We are told in the word problem that the contractor got 45 expensive wood and 60 cheap wood for the same total price and that  the 45 expensive wood cost $3.00 more than the 60 cheap wood.

If x =price of the 60 cheap wood then we have that 45(x + 3) + 60x = total cost of the wood.

45x + 135 + 60x = total cost of the wood

105x + 135 = total cost of the wood

45(x + 3) + 60x = 105x + 135

Simplifying;

45(x + 3) = 60x

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Answer:
y=2x3 - 3

Step-by-step explanation:

Here's the photo for the solution if needed.

The linear model for the given equation would be the model that has the points (1, - 1 ) ( 0, - 3 ) ( 1, - 5 ) ( 2, - 7 ) and ( 3, - 9 ).

To find the linear model that has the given equation, come up with values of x and then use the equation to solve for y. The linear model that has the points that you solve for, would be the right one.

Assuming values of x of -1, 0, 1, 2, 3

The y values would be:

x = - 1 :

y = - 2 x ( - 1 ) - 3

y = - 1

x = 0

y = - 3

x = 1

y = - 5

x = 2

y = - 7

x = 3
y = - 9

The linear model has points (1, - 1 ) ( 0, - 3 ) ( 1, - 5 ) ( 2, - 7 ) and ( 3, - 9 ).

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Answer:

your answer

Step-by-step explanation:

analogous colors

The missing height of the triangle is h = 66 inches

Given data ,

Let's denote the missing height of the triangle as "h" inches.

The formula for the area of a triangle is given by:

Area = (1/2) * base * height

Given that the area of the triangle is 6,460 inches squared and the base is either 136 inches or 196 inches, we can set up two equations to solve for "h".

For the base of 136 inches:

Area = (1/2) * 136 * h

6460 = 68h

h = 6460 / 68

h ≈ 95 inches

For the base of 196 inches:

Area = (1/2) * 196 * h

6460 = 98h

h = 6460 / 98

h ≈ 66 inches

Hence , the height of the triangle is h = 66 inches or 95 inches

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The statement and reason that completes the proof that ∠UYV ≅ ∠WYX is:


Statement         -        Reason

∠UYV ≅ ∠WYX -       Equivalent Substitution Postulate.

Incorporating various postulates into math problems  has been an essential aspect of mathematics education for decades.

One such idea is the Equivalent Substitution Postulate, which relates specifically to geometry. This postulate indicates that if two geometric figures have identical size and shape, they can effectively substitute each other in any mathematical equation or statement without changing its accuracy.

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The equation is solved to give 16z² - z - 4 = 0

Note that algebraic expressions  are defined as expressions that are composed of terms, variables, coefficients, constants and also factors.

The expressions are also identified with mathematical operations, such as;

From the information given, we have that;

√z= -4z - 2

Find the square of both sides, we get;

z = 16z² - 4

collect the like terms

16z² - z - 4

Equate to zero

16z² - z - 4 = 0

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The box plot that represents the data is the second box plot.

To find the box plot, look for the measure that is different in both box plots and you will find it to be the value of Q1.

Therefore find the value of Q1 in the data by Ellen by first arranging the riders in order :

0, 0, 2, 2, 3, 4, 6, 8, 8, 9, 11, 14, 16

Q1 would be at the 25 th percentile :

= 25 / 100 x 13

= 3.25 position

Q1 is therefore 2 which makes the correct box plot the second one which shows the Q1 value as 2.

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Step-by-step explanation:

x - y = 0.77

5x - y = 77

let's subtract the first from the second equation :

5x - y = 77

- x - y = 0.77

---------------------

4x 0 = 76.23

x = 76.23/4 = 19.0575

x - y = 0.77

y = x - 0.77 = 19.0575 - 0.77 = 18.2875

Answer:

Here's an interesting project idea for mathematics that can relate three different topics:

Topic 1: Fractals

Topic 2: Chaos Theory

Topic 3: Differential Equations

Research Question: Can fractals be used to model chaotic systems described by differential equations?

In this project, you can explore the concept of fractals and their applications in modeling complex systems. You can also delve into chaos theory and differential equations to understand how they are used to describe chaotic systems. By combining these three topics, you can investigate whether fractals can provide a better understanding of chaotic systems by modeling them more accurately.

Your research paper can cover the following areas:

Introduction: Provide an overview of fractals, chaos theory, and differential equations, and explain their relevance to the research question.

Fractals: Discuss the properties of fractals and how they can be used to model complex systems. Provide examples of fractals in nature and technology.

Chaos Theory: Explain the concept of chaos and how it is described by differential equations. Discuss the importance of chaos theory in understanding complex systems.

Differential Equations: Provide an overview of differential equations and their applications in physics, engineering, and other fields. Explain how differential equations are used to model chaotic systems.

Combining the three topics: Explain how fractals can be used to model chaotic systems described by differential equations. Provide examples of fractals used in modeling chaotic systems and compare the results to traditional methods.

Conclusion: Summarize the findings of your research and discuss the implications of using fractals to model chaotic systems.

Overall, this project can be a challenging and rewarding exploration of the interplay between three different mathematical topics.

Step-by-step explanation:

The required, there were 644 premium seats and 646 regular seats sold.

Let x be the number of premium seats sold and y be the number of regular seats sold. Then we have two equations:

x + y = 1290 (total seats sold)

30x + 20y = 32240 (total revenue)

We can use the first equation to solve for y in terms of x:

y = 1290 - x

Substituting this into the second equation, we get:

30x + 20(1290 - x) = 32240

Simplifying and solving for x, we get:

x=644

So 644 premium seats were sold. Substituting this into the first equation, we get:

644+ y = 1290

y = 646

So 646 regular seats were sold.

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Answer:  Oki should make 0 bags of her recipe, and Stephen should make 30 bags of his recipe.

For vertex (15,15):

3x + 4y = 120 --> 3(15) + 4(15) = 120 --> x = 15

3x + 2y = 90 --> 3(15) + 2y = 90 -->

Step-by-step explanation: A. To find the maximum number of bags of trail mix that Oki and Stephen can make together, we can use a system of inequalities to represent the constraints:

Let "x" be the number of bags of trail mix that Oki makes and "y" be the number of bags that Stephen makes. Then we have:

3x + 4y ≤ 120 (constraint on the number of cups of nuts)

3x + 2y ≤ 90 (constraint on the number of cups of dried fruit)

x ≥ 0 (non-negative constraint for Oki's bags)

y ≥ 0 (non-negative constraint for Stephen's bags)

B. To graph the feasible region, we can start by graphing the two constraint equations as lines:

3x + 4y = 120 (line A)

3x + 2y = 90 (line B)

We can find the x and y intercepts for each line:

For line A:

When x = 0, 4y = 120, y = 30 (y-intercept)

When y = 0, 3x = 120, x = 40 (x-intercept)

For line B:

When x = 0, 2y = 90, y = 45 (y-intercept)

When y = 0, 3x = 90, x = 30 (x-intercept)

Next, we can shade the region that satisfies all of the constraints. This region is below line A and to the left of line B, and is bounded by the x and y axes.

We can find the vertices of the feasible region by finding the intersection points of the two lines and the axes. These vertices are (0,0), (0,30), (15,15), and (30,0).

C. To find the maximum number of bags of trail mix that Oki and Stephen can make together, we need to evaluate the objective function at each vertex of the feasible region, and choose the vertex that maximizes the objective function.

The objective function is the total number of bags of trail mix:

z = x + y

Evaluating at the vertices:

Vertex (0,0): z = 0 + 0 = 0

Vertex (0,30): z = 0 + 30 = 30

Vertex (15,15): z = 15 + 15 = 30

Vertex (30,0): z = 30 + 0 = 30

The maximum value of the objective function occurs at vertices (0,30) and (15,15), where z = 30 bags of trail mix.

To determine how many of each type of recipe to make, we can substitute each vertex into the two constraint equations to find the corresponding values of x and y.

For vertex (0,30):

3x + 4y = 120 --> 3x + 4(30) = 120 --> 3x = -90 --> x = -30

3x + 2y = 90 --> 3(-30) + 2(30) = 90 --> y = 15

Therefore, Oki should make 0 bags of her recipe, and Stephen should make 30 bags of his recipe.

For vertex (15,15):

3x + 4y = 120 --> 3(15) + 4(15) = 120 --> x = 15

3x + 2y = 90 --> 3(15) + 2y = 90 -->

The rectangular coordinate from the given polar coordinate is (2.73, -0.73)

To find the rectangular coordinate from the polar coordinates, we can rewrite this as;

x = r cosθ

y = r sinθ

x = r cosθ

Let's substitute the values into it;

x = (2√2)* cos(-π/12)

x =(2√2)cos(-15)

x = √3 + 1

x = 2.73

y = r sin θ

y = (2√2)sin(-π/12)

y = (2√2) * sin (-15)

y = -√3 + 1

y = -0.73

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Answer:

∠ GJK = 102°

Step-by-step explanation:

(2x + 92) and (3x + 63) are same- side interior angles and sum to 180° , so

2x + 92 + 3x + 63 = 180

5x + 155 = 180 ( subtract 155 from both sides )

5x = 25 ( divide both sides by 5 )

x = 5

Then

∠ GJK = 2x + 92 = 2(5) + 92 = 10 + 92 = 102°