The diameter of a semicircle is 8.6 miles. What is the semicircle’s radius

Answer:

The answer would be 1/6

The probability that both jurors selected are female is 1/6.

For a criminal trial, 8 active and 4 alternate jurors are selected.

Two of the alternate jurors are male and two are female.

During the trial, two of the active jurors are dismissed.

The judge decides to randomly select two replacement jurors from the 4 available alternates.

Total numbers of selected candidates is;

8 + 4 = 12

The judge decides to randomly select two replacement jurors from the 4 available alternates.

Therefore,

The probability that both jurors selected are female is;

\(= \dfrac{2}{12}\\\\= \dfrac{1}{6}\)

Hence, the probability that both jurors selected are female is 1/6.

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Answer:

I think it's 33 I don't know

Explanation:

First we need to find the volume of the cube

volume = length*width*height = 4*4*4 = 64 cubic cm

Then we'll divide the mass over this volume to get the density

density = mass/volume

density = (12 grams)/(64 cm^3)

density = (12/64) grams per cm^3

density = 0.1875 grams per cm^3

The notation cm^3 is another way of saying "cubic centimeter" as shorthand.

It takes the seagull less time to travel a longer distance.

The owl has a speed of 11 1/9 miles per hour.

The seagull has a speed of 18 3/4 miles per hour.

18 3/4 miles per hour is greater than 11 1/9 miles per hour, so the seagull is faster.

In Mathematics and Science, speed is the distance covered by a physical object per unit of time. In Mathematics and Science, the speed of any a physical object can be calculated by using this formula;

Speed = distance/time

Next, we would determine the speed of the owl as follows;

Speed of owl = (8 1/3)/(3/4)

Speed of owl = (25/3)/(3/4)

Speed of owl = 25/3 × 4/3

Speed of owl = 100/9 or 11 1/9 miles per hour.

For the speed of the seagull, we have:

Speed of seagull = (12 1/2)/(2/3)

Speed of seagull = (25/2)/(2/3)

Speed of seagull = 25/2 × 3/2

Speed of seagull = 75/4 or 18 3/4 miles per hour.

In conclusion, we can reasonably infer and logically deduce that the seagull is faster because it took less time to travel a longer distance.

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

Answer:

It takes the seagull LESS time to travel a LONGER distance.

============================================================

Explanation:

V is the circumcenter of the triangle PQR, which means that it's the center of the circle that goes through points P, Q, and R.

Furthermore it means

PV = QV = RV

as they are all radii of circle V.

We only really need to focus on PV = RV.

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

We're given that RV = 78, which then points us to PV = 78 as well.

We're also given that UV = 30.

Segment PU is the missing piece of right triangle PUV.

As you can probably guess, we'll use the pythagorean theorem to find this missing side.

a^2+b^2 = c^2

(PU)^2 + (UV)^2 = (PV)^2

(PU)^2 + (30)^2 = (78)^2

(PU)^2 + 900 = 6084

(PU)^2 = 6084 - 900

(PU)^2 = 5184

PU = sqrt(5184)

PU = 72

Answer:

Step-by-step explanation:

yes

The area of the polygon is 80 units².

What is a Polygon?

A polygon is a plane figure made up of line segments connected to form a closed polygonal chain. The segments of a closed polygonal chain are called its edges or sides.

Dividing the polygon into parts marked in the attached figure so as to calculate the area easily.

For triangle, DEF

Area = \(\frac{1}{2} bh\)

        = \(\frac{1}{2}\) × 3 × 4

       = 6 units²

For triangle BCD

Area = \(\frac{1}{2}bh\)

        = \(\frac{1}{2}\) × 2 × 4

        = 4 units²

For trapezoid ABFG,

Area = \(\frac{1}{2} (a + b) h\)

        = \(\frac{1}{2}\) × (5.5 + 12) × 8

        = 70 units²

Hence, total area = 6 + 4 + 70

                             = 80 units².

Therefore, the total area of the polygon is 80 units².

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Answer:

The magnitude of the velocity of the cars after they stick is approximately 3.7 m/s

Step-by-step explanation:

The given parameters are;

The mass of the cart traveling East, m₁ = 10.0 kg

The speed of the cart traveling East v₁=  5.00 m/s

The mass of the cart traveling at an angle of 55° m₂= 7.50 kg

The speed of the cart traveling at an angle of 55°, v₂ = 3.00 m/s

The component of the velocities of the cart raveling at an angle are given as follows;

v = 3.00 × cos(55°)·i + 3.00 × sin(55°)·j

The total momentum before collision = m₁ × v₁ + m₂ × v₂  by substitution is therefore;

m₁ × v₁ + m₂ × v₂ = 10 × 5.00·i + 7.5 × (3.00 × cos(55°)·i + 3.00 × sin(55°)·j)

The total momentum after collision = (m₁ + m₂) × v₃

By the principle of the conservation of linear momentum, whereby the momentum is conserved, we have;

m₁ × v₁ + m₂ × v₂ = (m₁ + m₂) × v₃

10 × 5.00·i + 7.5 × (3.00 × cos(55°)·i + 3.00 × sin(55°)·j) = (10 + 7.5) × v₃

50.00·i + 12.91·i + 18.43·j = 17.5·v₃

62.91·i + 18.43·j = 17.5·v₃

∴ v₃ = (62.91·i + 18.43·j)/17.5 ≈ 3.59·i + 1.05·j

Therefore, the magnitude of the velocity of the cars after they stick = √(3.59² + 1.053²) ≈ 3.7

The magnitude of the velocity of the cars after they stick ≈ 3.7 m/s.

The left-hand side is approximately equal to the right-hand side, the solution x ≈ 8.965 checks out.

To solve the equation x^((5)/(2)) = 32, we need to isolate x. Here's how we can do it:

Take the square root of both sides to get rid of the exponent:

√(x^((5)/(2))) = √(32)

Simplify the square root of x^((5)/(2)):

x^((5)/(4)) = √(32)

Simplify the square root of 32:

x^((5)/(4)) = √(2^5)

Since the square root of a number raised to a power is equal to the number raised to half of that power, we have:

x^((5)/(4)) = 2^((5)/(2))

Now, we can equate the exponents:

x^((5)/(4)) = (2^((1)/(2)))^5

Simplify 2^((1)/(2)):

x^((5)/(4)) = (√2)^5

Take the fifth power of (√2):

x^((5)/(4)) = 2^(5/2)

The equation becomes:

x^((5)/(4)) = 32

To get rid of the exponent (5/4), we can raise both sides of the equation to the reciprocal power (4/5):

(x^((5)/(4)))^((4)/(5)) = 32^((4)/(5))

Simplify the exponents:

x^1 = 32^((4)/(5))

We are left with:

x = 32^((4)/(5))

Now, we can evaluate x by calculating the right-hand side of the equation:

x = 32^((4)/(5))

x ≈ 8.965

Therefore, the solution to the equation x^((5)/(2)) = 32 is approximately x ≈ 8.965.

To check the solution, substitute x = 8.965 back into the original equation:

(8.965)^((5)/(2)) ≈ 32

Calculating the left-hand side:

(8.965)^((5)/(2)) ≈ 32.000 (rounded to three decimal places)

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The two solutions of the quadratic equation are f(x) = x² - 5x - 7 are (-1.14) and (6.14).

The general equation of a quadratic equation is -

y = ax² + bx + c

It has two possible roots. It has a degree of 2.

Given is the graph of the function, f(x) = x² - 5x - 7.

We have the following -

f(x) = x² - 5x - 7.

We will draw the graph of this function.

Now, the graph cuts the [x] axis at (-1.14) and (6.14).

Therefore, the two solutions of the quadratic equation are f(x) = x² - 5x - 7 are (-1.14) and (6.14). The graph opens upwards.

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Answer:

If 5 + 6i is a root of the polynomial function f(x), then its complex conjugate 5 - 6i must also be a root of f(x). This is because complex roots of polynomial functions always come in conjugate pairs.

To see why this is true, consider a polynomial function with real coefficients. If a complex number z = a + bi is a root of the polynomial, then we have:

f(z) = 0

Substituting z = a + bi into the polynomial function, we get:

f(a + bi) = 0

Now we can take the complex conjugate of both sides:

f(a - bi) = (f(a + bi))^*

Since the coefficients of the polynomial are real, we have:

(f(a + bi))^* = f(a - bi)

Therefore, if a + bi is a root of the polynomial, then so is its conjugate a - bi.

In this case, since 5 + 6i is a root of f(x), we know that 5 - 6i must also be a root of f(x). Therefore, the answer is the complex number 5 - 6i.

The area of the regular polygons with 12 sides(dodecagon) and 5 sides (pentagon) are 389.06 in² and 19.87 in² respectively.

Area of regular polygon = 1/2 × apothem × perimeter

perimeter = (s)side length of octagon × (n)number of side.

apothem = s/[2tan(180/n)].

11 = s/[2tan(180/12)]

s = 11 × 2tan15

s = 5.8949

perimeter = 5.8949 × 12 = 70.7388

Area of dodecagon = 1/2 × 11 × 70.7388

Area of dodecagon = 389.0634 in²

Area of pentagon = 1/2 × 5.23 × 7.6

Area of pentagon = 19.874 in²

Therefore, the area of the regular polygons with 12 sides(dodecagon) and 5 sides (pentagon) are 389.06 in² and 19.87 in² respectively.

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Answer:

-2y-1

Step-by-step explanation:

whats the 24% for?

2. The ratio of the percent increase is not the same as the percent decrease.

3. The ratio for the percent increase has a smaller denominator than the percent decrease.

5. The original amount for the percent increase is different from the original amount for the percent decrease.

B,C,E

The mean of the scores if 6 students in a competitive exam is 25 marks.

Given scores of 6 students are: 10,30,50,40,20 in a competitive exam.

We have to find out the mean of the mark of 6 students in a competitive exam.

Mean is the sum of all the values in a set of data, such as numbers, measurements, divided by the number of values. It is also known as average.

Mean=∑X/n

∑X=10+30+50+40+20

=150

N=6

Now to calculate the mean we have to divide 150 by number of students which is 6.

Mean=150/6

=25 marks.

Hence the mean of the scores of 6  students is 25 marks.

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Question is incomplete as it should include :

Marks of students =10,30,50,40,20.

Answer:

Step-by-step explanation:

5x - 9 <= 21

5x <=30

x <= 6

The bat is already marked down to $50.00, and there is an additional 30% discount on the sales price.

To calculate the final price, we need to find 30% of $50.00:

30% of $50.00 = 0.30 x $50.00 = $15.00

So the additional discount is $15.00, and we can subtract that from the sale price:

$50.00 - $15.00 = $35.00

Therefore, the bat will cost Finley $35.00 on clearance.

The discounted price at which products or services are being sold is known as a sale price. Often, this price is provided for a brief period of time in an effort to boost sales during a slow period or get rid of extra inventory. The discount is represented in the advertisement as a percentage off the list price.

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The rate at which the top of the ladder is slipping down at the instant when the bottom of the ladder is 15 feet from the base of the building is -75/8 feet per second

The length of the ladder = 17

Consider the length of the base as x and the height is h

The rate at which the ladder is sliding = 5 feet per second

dx/dt = 5

Apply the Pythagorean theorem

x^2 + h^2 = 17^2

h^2 = 289 - x^2

h = \(\sqrt{289-x^2}\)

The rate of change of height with respect to x is

dh/dx = - x / (289 - x^2)^(1/2)

dh/dt = dh/dx × dx/dt

Substitute the values in the equation

= - 15 / (289 - 15^2)^(1/2) × 5

= -15/8 × 5

= -75/8 feet per second

Therefore, the rate of change of height when x = 15 is -75/8 feet per second

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Answer:

70 cubic feel. 3. Abox of oat cereal measures 24 centimeters long by 5 centimeters wide by 25 centimeters high.

Step-by-step explanation:

70 cubic feel. 3. Abox of oat cereal measures 24 centimeters long by 5 centimeters wide by 25 centimeters high.

Answer:

18 units

Step-by-step explanation:

since the y- coordinates are equal then the 2 points lie on a horizontal line and the distance (d) between them is the absolute value of the x- coordinates, that is

d = | - 4 - 14 | = | - 18 | = 18

or

d = |  14 - (- 4) | = | 14 + 4 | =   18  = 18

In this triangle, the product of tan A and tan C is `(BC)^2/(AB)^2`.

The given triangle ABC has angle A measuring 45 degrees, angle B measuring 90 degrees, and angle C measuring 45 degrees , Answer: `(BC)^2/(AB)^2`.

We have to find the product of tan A and tan C.

In triangle ABC, tan A and tan C are equal as the opposite and adjacent sides of angles A and C are the same.

So, we have, tan A = tan C

Therefore, the product of tan A and tan C will be equal to (tan A)^2 or (tan C)^2.

Using the formula of tan: tan A = opposite/adjacent=BC/A Band, tan C = opposite/adjacent=AB/BC.

Thus, tan A = BC/AB tan C = AB/BC Taking the ratio of these two equations, we have: tan A/tan C = BC/AB ÷ AB/BC Tan A * tan C = BC^2/AB^2So, the product of tan A and tan C is equal to `(BC)^2/(AB)^2`.

Answer: `(BC)^2/(AB)^2`.

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Answer:

D.

Step-by-step explanation:

Answer:

sin

Step-by-step explanation:

The value of general solutions are X = c1[3,1]\(e^{-3t}\) + c2[1,3]\(e^{6t}\), X = c1[1,1]\(e^{-t}\) + c2[1,2]\(e^{-2t}\), X = c1[5,-3]\(e^{-2t}\) + c2[1,1]\(e^{-2t}\) , X = c1[5,3]\(e^{t}\) + c2[5,-3]\(e^{-5t/5}\),X = c1[1,2]\(e^{-t}\) + c2[1,-1]\(e^{5t}\), X = c1[1,-1]\(e^{-t}\) + c2[1,-1/5]\(e^{3t}\).

To solve the system of equations {x = -18x + 6y, y = -45x + 15y} using matrix method, we can represent the system in matrix form as AX = λX, where

A = [[-18, 6], [-45, 15]]

X = [x, y]

λ = eigenvalue

The eigenvalues of A can be found by solving the characteristic equation

det(A - λI) = 0

|-18-λ 6 |

|-45 15-λ| = (λ+3)(λ-6) = 0

Thus, λ = -3, 6.

To find the eigenvectors, we solve for AX = λX for each eigenvalue

For λ = -3, we have

A - λI = [[-15, 6], [-45, 18]]

[[3], [1]] is an eigenvector for λ = -3.

For λ = 6, we have

A - λI = [[-24, 6], [-45, 9]]

[[1], [3]] is an eigenvector for λ = 6.

Thus, the general solution is

X = c1[3,1]\(e^{-3t}\) + c2[1,3]\(e^{6t}\)

To solve the system of equations {x = (0 -1) (-2 -3)x} using matrix method, we can represent the system in matrix form as AX = λX, where

A = [[0, -1], [-2, -3]]

X = [x1, x2]

λ = eigenvalue

The eigenvalues of A can be found by solving the characteristic equation

det(A - λI) = 0

|-λ -1|

|-2 -3-λ| = (λ+1)(λ+2) = 0

Thus, λ = -1, -2.

To find the eigenvectors, we solve for AX = λX for each eigenvalue:

For λ = -1, we have

A - λI = [[1, -1], [-2, -2]]

[[1], [1]] is an eigenvector for λ = -1.

For λ = -2, we have:

A - λI = [[2, -1], [-2, -1]]

[[1], [2]] is an eigenvector for λ = -2.

Thus, the general solution is

X = c1[1,1]\(e^{-t}\) + c2[1,2]\(e^{-2t}\)

To solve the system of equations {x1 = x1 + 5x2, x2 = x1 - 3x2} using matrix method, we can represent the system in matrix form as AX = λX, where

A = [[1, 5], [1, -3]]

X = [x1, x2]

λ = eigenvalue

The eigenvalues of A can be found by solving the characteristic equation

det(A - λI) = 0

|(1-λ) 5 |

| 1 (-3-λ)| = (λ+2)(λ-4) = 0

Thus, λ = -2, 4.

To find the eigenvectors, we solve for AX = λX for each eigenvalue

For λ = -2, we have:

A - λI = [[3, 5], [1, -1]]

[[5], [-3]] is an eigenvector for λ = -2.

For λ = 4, we have

A - λI = [[-3, 5], [1, -7]]

[[1], [1]] is an eigenvector for λ = 4.

Thus, the general solution is

X = c1[5,-3]\(e^{-2t}\) + c2[1,1]\(e^{-2t}\)

To solve the system of equations {x = 4x + 5y, y = -x + 2y} using matrix method, we can represent the system in matrix form as AX = λX, where

A = [[4, 5], [-1, 2]]

X = [x, y]

λ = eigenvalue

The eigenvalues of A can be found by solving the characteristic equation

det(A - λI) = 0

|(4-λ) 5 |

| -1 (2-λ)| = (λ-1)(λ+5) = 0

Thus, λ = 1, -5.

To find the eigenvectors, we solve for AX = λX for each eigenvalue:

For λ = 1, we have:

A - λI = [[3, 5], [-1, 1]]

[[5], [3]] is an eigenvector for λ = 1.

For λ = -5, we have:

A - λI = [[9, 5], [-1, -3]]

[[1], [-3/5]] is an eigenvector for λ = -5.

Thus, the general solution is

X = c1[5,3]\(e^{t}\) + c2[5,-3]\(e^{-5t/5}\)

To solve the system of equations {x = (3 2) (-8 -3)x} using matrix method, we can represent the system in matrix form as AX = λX, where

A = [[3, 2], [-8, -3]]

X = [x1, x2]

λ = eigenvalue

The eigenvalues of A can be found by solving the characteristic equation

det(A - λI) = 0

|(3-λ) 2 |

|-8 (-3-λ)| = (λ+1)(λ-5) = 0

Thus, λ = -1, 5.

To find the eigenvectors, we solve for AX = λX for each eigenvalue:

For λ = -1, we have

A - λI = [[4, 2], [-8, -2]]

[[1], [2]] is an eigenvector for λ = -1.

For λ = 5, we have

A - λI = [[-2, 2], [-8, -8]]

[[1], [-1]] is an eigenvector for λ = 5.

Thus, the general solution is

X = c1[1,2]\(e^{-t}\) + c2[1,-1]\(e^{5t}\)

To solve the system of equations {x1 = -2x1 - x2, x2 = x1 - 4x2} using matrix method, we can represent the system in matrix form as AX = λX, where

A = [[-2, -1], [1, -4]]

X = [x1, x2]

λ = eigenvalue

The eigenvalues of A can be found by solving the characteristic equation

det(A - λI) = 0

|(-2-λ) -1 |

| 1 (-4-λ)| = (λ+1)(λ-3)

Thus, λ = -1, 3.

To find the eigenvectors, we solve for AX = λX for each eigenvalue:

For λ = -1, we have

A - λI = [[-1, -1], [1, -3]]

[[1], [-1]] is an eigenvector for λ = -1.

For λ = 3, we have:

A - λI = [[-5, -1], [1, -7]]

[[1], [-1/5]] is an eigenvector for λ = 3.

Thus, the general solution is

X = c1[1,-1]\(e^{-t}\) + c2[1,-1/5]\(e^{3t}\)

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-- The complete question is given below

" Solve the following systems of equations by matrix method (i.e., by solving the eigenvalue problem). (a) { x=−18x+6y

y=−45x+15y}

​(b) x =(0−1)

(-2 −3)x

(c) {x1 =x1 + 5x2

​ x2 =x1 − 3x2} (d) {x =4x+5y

y =−x+2y}

(e) x = (3 2

−8 −3)x

(f) {x1 =−2x1 - x2 x2 = x1 − 4x2}"--

The value of the expression (x + a) (x + b) (x + c) will be x^3 + (b + c + a)x^2 + (ab + ac + bc)x + abc.

The value of the second expression will be x^3 + 22x^2 + 147x + 270

It should be noted that to expand the expression (x + a) (x + b) (x + c), we can use the distributive property of multiplication as follows:

(x + a) (x + b) (x + c)

= x³ + (b + c + a)x² + (ab + ac + bc)x + abc

Similarly, we can expand (x + 9) (x+3)(x + 10) as follows:

(x + 9) (x+3)(x + 10)

= (x + 9) ((x+3) (x + 10))

= x³ + 22x² + 147x + 270

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If lines A, B and C shows proportional relationships, then the line A has a constant of proportionality between y and x is 5

Given the line A, B and C

The constant of proportionality is the ratio of the y coordinates to the x coordinate

k = y /x

Where k is the constant of proportionality

Consider the line A

One point on the line = (1, 5)

Constant of proportionality K = 5/1

= 5

Consider the line B

One point on the line = (3, 5)

Constant of proportionality k = 5/3

Consider the line C

One point on the line = (7, 5)

Constant of proportionality = 5/7

Therefore, the line A has the constant of proportionality of 5

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The given question is incomplete, the complete question is

Lines A, B, and C show proportional relationships. Which line has a constant of proportionality between y and x of 5?

The given function f, with the provided set of ordered pairs, has a domain of {10, 17, 45, 51} and a range of {-6, 1, 5}.

The domain of a function refers to the set of all possible input values or x-values for which the function is defined. In this case, the given set of ordered pairs determines the domain. Looking at the x-values in the set {10, 17, 45, 51}, these are the unique inputs for which the function f is defined. Hence, the domain of f is {10, 17, 45, 51}.
On the other hand, the range of a function refers to the set of all possible output values or y-values that the function can take. By examining the y-values in the set {-6, 1, 5}, we can observe the distinct outputs generated by the function f. Thus, the range of f is {-6, 1, 5}.
In summary, the domain of the function f is {10, 17, 45, 51}, and the range of f is {-6, 1, 5}.

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Step-by-step explanation:

They will not intersect because they do not have a pair of solutions

Answer:

D) 8x - 1

Step-by-step explanation:

Let's say that x = 5.  That would mean Amelia put 15(5) - 4 gallons of gas in her car, which equals 71 gallons.  She used 7(5) - 3 gallons driving to work, which is 32 gallons used.  71 - 32 = 39 gallons left.  

What else equals 39, you might ask?

8(5) - 1

40 - 1

39.

Answer:

D is the answer

Step-by-step explanation: