Find the value of and round to the nearest hundredth.
8 cm
13 cm
8°

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 required graph shows the x-intercepts and the minimum value.

To find the x-intercepts of the function y = 3x² - 12x + 9, we set y = 0 and solve for x:

3x² - 12x + 9 = 0

Dividing both sides by 3 gives:

x² - 4x + 3 = 0

(x - 1)(x - 3) = 0

So, the x-intercepts are x = 1 and x = 3.

To find the minimum value of the function, we can use the formula:

x = -b / 2a

Here a = 3 and b = -12.

Substitute these values gives:

x = -(-12) / 2(3) = 2

So the minimum value occurs at x = 2.

To find the corresponding y-value, we can plug in x = 2 into the original function:

y = 3(2)² - 12(2) + 9 = -3

So the minimum value is y = -3.

Here is a graph showing the x-intercepts and the minimum value.

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Note that the graph of the function f(x) = a(b)^x is attached accordingly. Here a = 8 and b = 5

f(x) = a(b^x)......1

from the graph we can see that

When x = 0, y = 8

f(0) = 8

8 = a(b^0)
8 = a x 1

a = 8


f(1) = 4

4 = a(b^1)
4 = ab
8b = 4
b = 0.5

Thus a = 8 and b = 5

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Full Question:

Another copy machine also has the ability to reduce image dimensions, but by a different percentage. This graph shows the results found when copying a design x times. Use the graph to write the equation modeling this relationship

Enter the correct answer in the box by replacing the values of a and b.

f(x) = a(b)^x

Answer: 380

Step-by-step explanation:

95% = 95/100

95/100 x 400

= 380

Answer: 380 students

Step-by-step explanation:

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 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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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 ;)

Answer:

Step-by-step explanation:

The point estimate of the population mean is 25 and the margin of error for the confidence interval is 2.04.

To determine the point estimate of the population mean, we take the midpoint of the interval.

Point estimate of population mean = (Lower bound + Upper bound) / 2 = (20 + 30) / 2 = 25

To calculate the margin of error, we need to know the level of confidence for the interval. Assuming a 95% confidence level, we can use the formula:

The margin of error = (Upper bound - Lower bound) / (2 * z-score)

Where the z-score for a 95% confidence level is 1.96.

Margin of error = (30 - 20) / (2 x 1.96) = 2.04

Hence, the population means point estimate is 25, and the confidence interval's margin of error is 2.04 percent.

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Answer:

Value-Added Tax

Step-by-step explanation:

Value-added tax (VAT) is a consumption tax on goods and services that is levied at each stage of the supply chain where value is added, from initial production to the point of sale.

The equation of line perpendicular to "y = (1/2)x - 1" and passing through point (5,6) is y = -2x + 16,

The equation of the line is y = (1/2)x - 1, is in slope-intercept form "y = mx + b", where m is slope,

To find the slope of the given line, we see that it is in the form y = mx + b, where m = 1/2.

We know that, slope of a line perpendicular to this line will be the "negative-reciprocal" of this slope.

So, the slope of the perpendicular line will be -2.

Now we use the point-slope form of the equation of a line to find the equation of the perpendicular line passing through the point (5, 6). The point-slope form is : y - y₁ = m(x - x₁),

where (x₁, y₁) is given point and "m" is slope of the line;

Substituting the values, we get:

⇒ y - 6 = -2(x - 5),

⇒ y = -2x + 16,

Therefore, the equation of perpendicular line is y = -2x + 16.

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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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The value of the given algebraic expression is -2.

To find the value of the expression 2x³ - 2x² + 2x - 8 / 2x² - 5x when x = -2, we simply substitute -2 for every instance of x in the expression:

2(-2)³ - 2(-2)² + 2(-2) - 8 / 2(-2)² - 5(-2)

= 2(-8) - 2(4) - 4 - 8 / 8 + 10

= -16 - 8 - 4 - 8 / 18

= -36 / 18

= -2

Therefore, the value of the expression 2x³ - 2x² + 2x - 8 / 2x² - 5x when x = -2 is -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

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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Answer:

To calculate the monthly deposit required, we can use the formula for future value of an annuity, which is:

FV = Pmt x (((1 + r)^n - 1) / r)

where FV is the future value, Pmt is the monthly payment, r is the monthly interest rate, and n is the number of months.

In this case, we want to find the monthly payment required to achieve a future value of $12,000 in 6 years, or 72 months. The monthly interest rate is the annual percentage rate (APR) divided by 12, so:

r = 6.5% / 12 = 0.00541666667

Substituting these values into the formula, we get:

12,000 = Pmt x (((1 + 0.00541666667)^72 - 1) / 0.00541666667)

Solving for Pmt, we get:

Pmt = 12,000 / (((1 + 0.00541666667)^72 - 1) / 0.00541666667)

≈ $164.41

Therefore, you should deposit $164.41 each month to end up with $12,000 in 6 years

Answer:x = midpoint_x - (midpoint_x - (-3)) * (sqrt(5)/6) = 19.5 - (22.5 * sqrt(5))/6 = 19.5 - 3.75sqrt(5)

Step-by-step explanation:To find the x-coordinate of the point that is 2/3 of the distance from (-3, 2) to (42, 32), we first need to find the coordinates of that point.

The distance between the two endpoints of the line segment is:

d = sqrt((42 - (-3))^2 + (32 - 2)^2) = sqrt(45^2 + 30^2) = 15sqrt(45)

The distance from (-3, 2) to the desired point is:

(2/3)d = (2/3)sqrt(45^2 + 30^2)

Let's call the desired point (x, y). We can use the midpoint formula to find the coordinates of the midpoint of the line segment:

midpoint = ((-3 + 42)/2, (2 + 32)/2) = (19.5, 17)

The midpoint is halfway between the two endpoints, so the distance from (-3, 2) to the midpoint is:

sqrt((19.5 - (-3))^2 + (17 - 2)^2) = sqrt(22.5^2 + 15^2) = 15sqrt(5)

To find the coordinates of the desired point, we can use similar triangles. The ratio of the distance from (-3, 2) to the midpoint to the distance from (-3, 2) to the desired point is:

15sqrt(5) / (2/3)sqrt(45^2 + 30^2) = 15sqrt(5) / 30sqrt(45) = sqrt(5)/6

The ratio of the distance from (42, 32) to the midpoint to the distance from (42, 32) to the desired point is the same:

15sqrt(5) / (2/3)sqrt(45^2 + 30^2) = sqrt(5)/6

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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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:

z=199.68

Step-by-step explanation:

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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The end behavior of the given function is Both ends of the graph goes down(In the same direction),

The degree and the leading coefficient (The coefficient of the highest degree monomial) of a function shows the end behavior of its graph.

if Degree  is even and leading coefficient is negative then the end behavior of the function f(x) is,

f(x)---> -∞, as x---> -∞

f(x)---> -∞, as x---> + ∞

That is, Both ends of the graph goes down(In the same direction)

Here, the given function is f(x)=-4x⁶+6x²-52

Degree = 6(even), leading coefficient = -4 (negative)

Thus, the end behavior of the given function is Both ends of the graph goes down(In the same direction),

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this is a answer, thanks

Answer:

Step-by-step explanation:

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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Answer:

48

Step-by-step explanation:

total cost will be the answer

The Venn diagram is attached in the solution.

Given that, a Venn Diagram with sets B, D, and the universal set U, we need to Shade (BUD)’ on the Venn diagram,

We know that, the complement of a set is the set that includes all the elements of the universal set that are not present in the given set.

Therefore, (BUD)’ = U - (BUD)

therefore, we will shade all the portion except (BUD),

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For points A and B in the economy:

x₁ = 2p₂/p₁ and x₂ = p₂/p₁.

x₁ = 2p₁ / p₂ and x₂ = p₁ / p₂.

2 - p₂ / p₁

1 - p₁ / p₂

2 - p₂ / p₁ + 1 - p₁ / p₂

The market clears for both items at the Walrasian equilibrium, and the aggregate excess demands are zero.

1. To derive agent A's demands for goods 1 and 2, maximize her utility subject to her budget constraint:

max ln x₁ + 2ln x₂

s.t. p₁x₁ + p₂x₂ ≤ p₁(1) + p₂(2)

Using Lagrange multiplier method:

1/x₁ = p₁/(2p₂)

1/x₂ = p₁/p₂

Solving for x₁ and x₂:

x₁ = 2p₂/p₁

x₂ = p₂/p₁

So, agent A's demands for goods 1 and 2 are x₁ = 2p₂/p₁ and x₂ = p₂/p₁.

2. To derive agent B's demands for goods 1 and 2, maximize her utility subject to her budget constraint:

max 2ln x₁ + ln x₂

s.t. p₁x₁ + p₂x₂ ≤ p₁(2) + p₂(1)

Using Lagrange multiplier method:

2/x₁ = p₁/p₂

1/x₂ = p₂/p₁

Solving for x₁ and x₂:

x₁ = 2p₁/p₂

x₂ = p₁/p₂

So, agent B's demands for goods 1 and 2 are x₁ = 2p₁ / p₂ and x₂ = p₁ / p₂.

3. Agent A's excess demands for goods 1 and 2 are:

z₁ = 1 - x₁ = 1 - 2p₂ / p₁

z₂ = 2 - x₂ = 2 - p₂ / p₁

4. Agent B's excess demands for goods 1 and 2 are:

z₁ = 2 - x₁ = 2 - 2p₁ / p₂

z₂ = 1 - x₂ = 1 - p₁ / p₂

5. The aggregate excess demands for goods 1 and 2 are:

Z₁ = z₁ᵃ + z₁ᵇ = 1 - 2p₂ / p₁ + 2 - 2p₁ / p₂

Z₂ = z₂ᵃ + z₂ᵇ = 2 - p₂ / p₁ + 1 - p₁ / p₂

6. At Walrasian equilibrium, Z₁ and Z₂ are both equal to zero. So, solve the system of equations:

1 - 2p₂ / p₁ + 2 - 2p₁ / p₂ = 0

2 - p₂ / p₁ + 1 - p₁ / p₂ = 0

Solving for p₁ and p₂:

p₁ = 2

p₂ = 1

So, the Walrasian equilibrium prices for goods 1 and 2 are p₁ = 2 and p₂ = 1.

7. At the Walrasian equilibrium, the market clears for both goods and the aggregate excess demands are zero. This means that the prices are set such that both agents are willing to buy exactly what is being sold in the market.

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Four seconds after the boulder is hurled, it will hit the ground.

When the boulder hits the ground, its height will be 0. So, we need to solve the equation:

[tex]h(t) = -16t^2 + 64t = 0[/tex]

We can factor out -16t from the expression:

h(t) = -16t(t - 4)

Setting each factor to zero, we get:

-16t = 0 or t - 4 = 0

Solving for t, we get:

t = 0 or t = 4

Since t = 0 represents the time when the boulder is launched, we can ignore it. Therefore, the boulder will hit the ground 4 seconds after it is launched.

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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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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: