In a hockey Skills competition, Olga scored on 3 of 5 breakaways. Tara scored on 5 of 7 breakaways. Whose performance was better?

By evaluating f(6) and confirming that it equals zero, we can determine that x - 6 is a factor of the polynomial f(x) = x^4 - 32x^2 - 144.

To determine if x - 6 is a factor of f(x) = x^4 - 32x^2 - 144 using the Factor Theorem, we need to check if f(6) equals zero. If f(6) is zero, then x - 6 is a factor of f(x); otherwise, it is not a factor.

Let's calculate f(6):

f(6) = (6)^4 - 32(6)^2 - 144

= 1296 - 32(36) - 144

= 1296 - 1152 - 144

= 0

Since f(6) equals zero, we can conclude that x - 6 is indeed a factor of f(x).

The Factor Theorem states that if f(c) equals zero, where c is a constant, then x - c is a factor of f(x). In this case, since f(6) is zero, x - 6 is a factor of f(x).

Therefore, the answer is: Yes, x - 6 is a factor of f(x).

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Answer:

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

Use coordinates of endpoints, taken from the diagram, B(6, 2) and C(2, - 1) and the distance formula:

Substitute BC for d and given coordinates to find the radius:

Hence the segment BC is 5 units long.

Answer:

3 units to the left of the y-axis

Step-by-step explanation:

Since all answers involve 3, I believe we are looking at the x-axis. To answer your question, a negative x value means that it is to the left of the origin. Therefore the answer would be 3 units to the left of the y-axis.

Answer:

Step-by-step explanation:

To determine the share of Winta in the profit, we need to calculate the ratio of her initial investment to the total initial investment and then apply that ratio to the total profit.

Winta's initial investment: Birr 21,000

Lensa's initial investment: Birr 17,500

Total initial investment: Birr 21,000 + Birr 17,500 = Birr 38,500

To find the share of Winta in the profit, we calculate:

Winta's share = (Winta's initial investment / Total initial investment) * Total profit

Winta's share = (Birr 21,000 / Birr 38,500) * Birr 24,600

Simplifying the calculation:

Winta's share = (0.5455) * Birr 24,600

Winta's share ≈ Birr 13,414.55

Therefore, Winta's share in the profit is approximately Birr 13,414.55.

The area of the shaded portion in the equilateral triangle with sides 6 is 9√3 - 36π.

To find the area of the shaded portion in the equilateral triangle, we need to determine the area of the three arcs and subtract it from the area of the equilateral triangle.

First, let's find the area of one arc. Each arc has a radius equal to the length of the side of the equilateral triangle, which is 6. The formula for the area of a sector is A = (θ/360)πr², where θ is the central angle in degrees.

In an equilateral triangle, each interior angle measures 60 degrees, so the central angle of the arc is 120 degrees (360 degrees divided by 3). Plugging these values into the formula, we get A_arc = (120/360)π(6)² = (1/3)π(6)² = 12π.

Since there are three identical arcs, the total area of the arcs is 3 times the area of one arc, which is 3(12π) = 36π.

Now, let's find the area of the equilateral triangle. The formula for the area of an equilateral triangle is A_triangle = (√3/4)s², where s is the length of a side.

Plugging in the value of the side length, we have A_triangle = (√3/4)(6)² = (√3/4)(36) = 9√3.

Finally, we subtract the area of the arcs from the area of the equilateral triangle to find the shaded portion's area: A_shaded = A_triangle - A_arc = 9√3 - 36π.

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After 3 days, the two friends will earn the same profit.

To find the number of days after which the two friends will earn the same profit, we need to set the profit functions P(x) and Q(x) equal to each other and solve for x.

P(x) = Q(x)

−x^2 + 5x + 12 = 6x

Rearranging the equation:

−x^2 + 5x + 12 - 6x = 0

Combining like terms:

−x^2 - x + 12 = 0

To solve this quadratic equation, we can factor it or use the quadratic formula. In this case, let's factor the equation:

-(x - 3)(x + 4) = 0

Setting each factor equal to zero:

x - 3 = 0 or x + 4 = 0

Solving for x:

x = 3 or x = -4

Both x = 3 and x = -4 are solutions to the equation. However, we need to determine which one is a viable answer and which one is a nonviable answer.

The question asks for the number of days, which cannot be negative. Therefore, x = -4 is a nonviable answer since it represents a negative number of days. The viable answer is x = 3.

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3/5 or 60% of the grass died because the sprinkler could only water 1/5 of the yard.

Let's start by breaking down the information given:

- Three-fourths of the yard is covered with grass.

- One-fourth of the yard is used as a garden.

- The sprinkler could only water 1/5 of the yard.

To find out how much of the grass died, we need to determine the portion of the grass that was not watered by the sprinkler.

Let's assume the total area of the yard is represented by the value 1. Therefore, we can calculate the area of the grass as 3/4 of the total yard, which is (3/4) * 1 = 3/4.

The sprinkler can only water 1/5 of the yard, so the portion of the grass that was watered is (1/5) * (3/4) = 3/20.

To find the portion of the grass that died, we subtract the watered portion from the total grass area:

Portion of grass that died = (3/4) - (3/20) = 15/20 - 3/20 = 12/20.

Simplifying, we get:

Portion of grass that died = 3/5.

Therefore, 3/5 or 60% of the grass died because the sprinkler could only water 1/5 of the yard.

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The graph that correctly represents Marie's situation is the graph B or the second graph.

For the graph to correctly represent Marie's situation the followin elements are needed:

Note: This question is incomplete; below are the missing graphs:

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Answer

a=93

b=74

Step-by-step explanation:

a=180-87=93 b=180-106=74

The value of the improper integral ∫[0 to 1] arctan(√(x/(1-x))) dx is π/4.

To evaluate the improper integral

∫[0 to 1] arctan(√(x/(1-x))) dx,

we can use a trigonometric substitution. Let's substitute x = sin²θ, which gives dx = 2sinθcosθ dθ and modifies the limits of integration as well.

When x = 0, sin²θ = 0, and when x = 1, sin²θ = 1. Therefore, the new limits of integration are θ = 0 to θ = π/2.

Now, let's substitute these expressions into the integral:

∫[0 to 1] arctan(√(x/(1-x))) dx

= ∫[0 to π/2] arctan(√(sin²θ/(1-sin²θ))) * 2sinθcosθ dθ

= 2∫[0 to π/2] arctan(√(sin²θ/cos²θ)) * sinθcosθ dθ.

Simplifying inside the arctan, we have:

√(sin²θ/cos²θ) = √tan²θ = tanθ.

Substituting this back into the integral, we get:

2∫[0 to π/2] arctan(tanθ) * sinθcosθ dθ.

Since arctan(tanθ) is equivalent to θ for 0 ≤ θ < π/2, the integral becomes:

2∫[0 to π/2] θ * sinθcosθ dθ.

We can rewrite sinθcosθ as (1/2)sin(2θ):

2∫[0 to π/2] θ * (1/2)sin(2θ) dθ

= ∫[0 to π/2] θ * sin(2θ) dθ.

Now, we can integrate by parts with u = θ and dv = sin(2θ) dθ:

∫ u dv = uv - ∫ v du.

Differentiating u = θ gives du = dθ, and integrating dv = sin(2θ) dθ gives v = -(1/2)cos(2θ).

Applying the formula for integration by parts:

∫[0 to π/2] θ * sin(2θ) dθ = [-(1/2)θ * cos(2θ)] from 0 to π/2 - ∫[0 to π/2] (-(1/2)cos(2θ)) dθ

= [-(1/2)(π/2) * cos(π)] - [-(1/2)(0) * cos(0)] - [-(1/2) ∫[0 to π/2] cos(2θ) dθ]

= [-(π/4)(-1)] - [0] - [-(1/2) ∫[0 to π/2] cos(2θ) dθ]

= π/4 + (1/4) ∫[0 to π/2] cos(2θ) dθ.

Now, let's integrate ∫[0 to π/2] cos(2θ) dθ:

∫ cos(2θ) dθ = (1/2)sin(2θ).

Evaluating this integral from 0 to π/2:

∫[0 to π/2] cos(2θ) dθ = (1/2)sin(π) - (1/2)sin(0)

= (1/2)(0) - (1/2)(0)

= 0.

Substituting this result back into the previous expression:

π/4 + (1/4) ∫[0 to π/2] cos(2θ) dθ = π/4 + (1/4)(0)

= π/4.

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The calculated value of the improper integral [tex]\int\limits^{1}_0 \arctan\sqrt{\frac{x}{1 - x}} \, dx[/tex] is 0.7853

From the question, we have the following parameters that can be used in our computation:

[tex]\int\limits^{1}_0 \arctan\sqrt{\frac{x}{1 - x}} \, dx[/tex]

The above expression can be integrated using integration by parts method

When integrated, we have

[tex]\int\limits^{1}_0 \arctan\sqrt{\frac{x}{1 - x}} \, dx = \arctan\left(\frac{\sqrt{x}}{\sqrt{1-x}}\right)\,x+\frac{\sqrt{1-x}\sqrt{x}+\arctan\left(\frac{\sqrt{1-x}}{\sqrt{x}}\right)}{2}[/tex]

When simplified, we have

[tex]\int\limits^{1}_0 \arctan\sqrt{\frac{x}{1 - x}} \, dx = \frac{\left(2x-1\right)\arctan\left(\sqrt{\frac{x}{1-x}}\right)+\left(1-x\right)\sqrt{\frac{x}{1-x}}}{2}[/tex]

Recall that the x values are from 0 to 1

This means that

[tex]\int\limits^{1}_0 \arctan\sqrt{\frac{x}{1 - x}} \, dx = \frac{\left(2(1)-1\right)\arctan\left(\sqrt{\frac{1}{1-1}}\right)+\left(1-1\right)\sqrt{\frac{1}{1-1}}}{2}- \frac{\left(2(0)-1\right)\arctan\left(\sqrt{\frac{0}{1-0}}\right)+\left(1-0\right)\sqrt{\frac{0}{1-0}}}{2}[/tex]

When evaluated, we have

[tex]\int\limits^{1}_0 \arctan\sqrt{\frac{x}{1 - x}} \, dx = 0.7853[/tex]

Hence, the value of the integral is 0.7853

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Answer:

1. The solution to the differential equation is y = (4*t/3 + 2/3*t + C)/(t**2 + 4), where C is the constant of integration.

2. The general solution to the differential equation is y = (3/4)*exp(t/6) + C*exp(-t/2), where C is the constant of integration.

3. The solution to the initial value problem is y = t^2 + 4/3.

Probabilities are:
Even number = 0.5
Odd Number = 0.5
Number 1 face up = 1/6

Number 2 face up = 1/6

Number 3 face up = 1/6

Number 4 face up = 1/6

Number 5 face up = 1/6

Number 6 face up = 1/6

Answer:

1428

Step-by-step explanation:

Area=L×B/W

34×42

=1428

The correct options are:

Esmerelda converted the mixed number to the wrong improper fraction.

Esmerelda added the numerators.

Esmerelda did not divide –24 by 6 correctly.

The errors made by Esmerelda are as follows:

1. Esmerelda converted the mixed number to the wrong improper fraction.

2. Esmerelda added the numerators.

3. Esmerelda did not divide –24 by 6 correctly.

Let's go through each error:

1. Esmerelda converted the mixed number to the wrong improper fraction:

Esmerelda incorrectly converted "Negative 5 and one-fourth" to "Negative StartFraction 21 over 4 EndFraction." The correct conversion would be "Negative StartFraction 5 over 4 EndFraction" since the mixed number -5 1/4 can be expressed as -5 + 1/4 = -5  (1/4) = -5 (4/4) + (1/4) = -5 (4 + 1)/4 = -5 (5/4) = -5 (5 over 4).

2. Esmerelda added the numerators:

Esmerelda incorrectly added the numerators of the fractions, resulting in "Negative StartFraction 21 over 4 EndFraction" instead of the correct numerator of -5 * 4 = -20.

3. Esmerelda did not divide –24 by 6 correctly:

Esmerelda made an error in dividing -24 by 6, resulting in "StartFraction 24 over 6 EndFraction" instead of the correct value of -24 divided by 6, which is -4.

Therefore, the correct options are:

- Esmerelda converted the mixed number to the wrong improper fraction.

- Esmerelda added the numerators.

- Esmerelda did not divide –24 by 6 correctly.

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The angle BAM is 40°. as the correct angle based on the given values is not 160°, but rather 40°.

To solve this problem within the topic of inscribed and circumscribed circles, we can utilize the property of angles subtended by the same arc on a circle.

Let's consider triangle ABC and point M within angle ABC. Since triangle ABC is isosceles with AB = AC, we can draw the circumcircle passing through points A, B, and C. Let O be the center of this circumcircle.

Based on the property mentioned earlier, angle BAM will be equal to half the measure of arc BC on the circumcircle, subtended by chord BM.

Given that ∠ABC = 50° and ∠BMC = 40°, we can deduce that arc BC on the circumcircle will have a measure of 2 * ∠BMC = 2 * 40° = 80°.

Since angle BAM is half the measure of arc BC, we have:

∠BAM = 0.5 * 80° = 40°

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Shan performed better in his science test than in his math test based on the respective scores of 15 out of 20 and 7 out of 10.

To determine which test Shan achieved better results in, we need to compare the scores he obtained in both the math and science tests.

Shan scored 7 out of 10 in his math test, which can be written as a fraction 7/10. This fraction can also be converted to a decimal by dividing 7 by 10, resulting in 0.7.

Similarly, Shan scored 15 out of 20 in his science test, which can be written as a fraction 15/20. This fraction can also be simplified by dividing both the numerator and denominator by 5, resulting in 3/4. Converting this fraction to a decimal by dividing 3 by 4 yields 0.75.

Comparing the decimal values, we can see that 0.75 (science test) is greater than 0.7 (math test). Therefore, Shan achieved better results in his science test compared to his math test.

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The graph can represent a normal curve because it represent a normal density function. The Option C.

The answer is yes. While these characteristics may deviate from the ideal properties of a normal distribution, they do not necessarily invalidate the possibility of the graph representing a normal density function.

A normal curve can have tails that extend indefinitely allowing for the graph to increase as x becomes very large or very small. Negative values can occur if the graph represents a standard normal distribution which is centered at zero.

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Answer:

324 cm³

Step-by-step explanation:

Square based pyramid volume formula:
[tex]V=a^2\frac{h}{3}[/tex]

with a being the base length and h being the height

We can substitute in our values:

[tex]V=a^2\frac{h}{3} \\V=9^2\frac{12}{3}\\V=81(4)\\V=324[/tex]

So, the volume is 324 cm³.

Hope this helps! :)

Answer:

The volume of the buoy can be calculated by finding the volumes of the cone and hemisphere separately and then adding them together.

The volume of the cone is given by:

Vcone = (1/3)πr^2h

where r is the radius of the base of the cone and h is the height of the cone.

Substituting the given values, we get:

Vcone = (1/3)π(0.95)^2(1.2) = 1.08 m^3 (rounded to two decimal places)

The volume of the hemisphere is given by:

Vhemisphere = (2/3)πr^3

where r is the radius of the hemisphere.

Substituting the given value, we get:

Vhemisphere = (2/3)π(0.95)^3 = 1.05 × 10^-3 m^3 (rounded to two decimal places)

Therefore, the total volume of the buoy is:

Vbuoy = Vcone + Vhemisphere = 1.08 + 1.05 × 10^-3 = 1.08 m^3 (rounded to two decimal places)

Answer:

19.0285

Step-by-step explanation:

For this, we have to work backwards.

First, the equation for the circumference of a circle is:
[tex]2\pi r[/tex]

We already know the circumference, so we can solve for r:
[tex]119.56=2\pi r[/tex]

divide both sides by 2

[tex]59.78=\pi r[/tex]

divide both sides by pi

[tex]19.0285...=r[/tex]

So, depending on the answer choices, the answer is 19.0285 rounded to the according decimal place.

Hope this helps! :)

Answer:

First you draw the lines zjkl and then you make an archs to bisect the line using a compass and a pencil first you go to each point and it's corresponding letter you arch then draw a straight line which passes through the arch

Answer:

18

Step-by-step explanation:

[tex]\sqrt{x-2} =4\\x-2=16\\x=18[/tex]

Given equation :

[tex] \sqrt{x - 2} = 4[/tex]

Squaring both sides

[tex]( { \sqrt{x - 2} })^{2} = {(4)}^{2} [/tex]

[tex]x - 2 = 16[/tex]

Move all terms containing x to the left, all other terms to the right.

[tex]x = 16 + 2[/tex]

[tex]x = 18[/tex]

Verification:

Put value the x in the given equation.

[tex] \sqrt{x - 2} = 4[/tex]

[tex] \sqrt{18 - 2} = 4[/tex]

[tex] \sqrt {16} = 4[/tex]

[tex] \sqrt {4 \times 4 } = 4[/tex]

[tex]4 = 4[/tex]

Hence, The answer is 18.

Answer:

What is the equation?

Step-by-step explanation:

Can't solve it without knowing where c is in the equation

Answer:

Step-by-step explanation:  -3.655 hopefully that works

The correct equation for the parabola is [tex]x^2 = 16(y - 4)[/tex].

The standard equation of the parabola in the graph can be determined based on its characteristics.

Given:

Vertex: (0, 4)

Focus: (4, 4)

P (the distance from the vertex to the focus or directrix): 4

We can conclude that the parabola opens to the right because the axis is horizontal.

The standard equation of a parabola with a horizontal axis and vertex (h, k) is given by:

[tex](x - h)^2 = 4p(y - k)[/tex]

In this case, the vertex is (0, 4), so the equation becomes:

[tex](x - 0)^2 = 4p(y - 4)[/tex]

Now, we need to determine the value of p. The distance from the vertex to the focus is p, which is 4 in this case.

Therefore, the standard equation of the parabola in the graph is:

[tex]x^2 = 4(4)(y - 4)\\x^2 = 16(y - 4)[/tex]

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Answer:

37.5

Step-by-step explanation:

the therom of a parallelogram is width*height

so 7.5*5

=37.5

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Answer:

A = 37.5

Step-by-step explanation:

The area of a parallelogram is:

Area = base × height

In your picture the base is 7.5 and the height is 5.

So multiply 7.5×5 and you get 37.5.

The area is 37.5cm^2

The farmer should use 660 pounds of the 75% protein supplement and 440 pounds of the 25% protein ration to make 1100 pounds of a high-grade 55% protein ration.

Let 75% protein supplement be x and 25% protein ration be y

The total weight of the mixture is x + y = 1100

The second equation related  to the protein in the mixture is 0.75x + 0.25y = 0.55 × 1100

= 0.75x + 0.25y = 605

By using the elimination method multiply the first equation by 0.25 to match the coefficients of y:

0.25x + 0.25y = 0.25 × 1100

0.25x + 0.25y = 275

by subtracting this equation from the second equation:

0.75 x + 0.25 y - {0.25 x + 0.25y} = 605 - 275

0.75 x - 0.25 x = 330

0.5x = 330

x = 660

by substituting this in the first equation:

660 + y = 1100

y = 440

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The fourth table of values represents an exponential function (Correct choice: D).

Herein we find four tables of values, three representing a linear function and one representing an exponential function. Each function is introduced below:

Linear equation:

n = m + r · n

Exponential function

n = m · rⁿ

Where:

Common rate is the most appropriate criterion to distinguish linear equations of exponential equations. Now we proceed to summarize the results of each table of values:

Case A: Linear equation, r = 8.

Case B: Linear equation, r = 1.

Case C: Linear equation, r = 5.

Case D: Exponential equation: r = 2.

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