Captain Ishaan has a ship, the H.M.S Crimson Lynx. The ship is four furlongs from the dread pirate Michael and his merciless band of thieves. If his ship hasn't already been hit, Captain Ishaan has probability 2/5 of hitting the pirate ship. If his ship has been hit, Captain Ishaan will always miss. If his ship hasn't already been hit, dread pirate Michael has probability 3/8 of hitting the Captain's ship. If his ship has been hit, dread pirate Michael will always miss. If the Captain and the pirate each shoot once, and the Captain shoots first, what is the probability that both the Captain and the pirate hit each other's ships?

An absolute value is the numerical value of a number without consideration of its sign. It can be represented graphically by a straight line known as a number line. Absolute value equations are equations that include absolute values of variables or unknown quantities. The following are examples of how to write an absolute value equation in the form |x-c|=d to fit the provided solution sets:

Example 1:

Solution set: {x|x≤-3 or x≥1}
Absolute value equation: |x-(-1)|=4
Explanation: -1 is the midpoint of the two ranges (-3 and 1) in the solution set. |x-(-1)|=|x+1| is the absolute value expression for the midpoint -1. The distance d from -1 to the solutions' furthest endpoints, 1 and -3, is four, hence the value of d in the absolute value equation is 4.
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according to the given information we can say that the fraction of the area of the circle that is shaded is 1/4 or 0.25.

Every point in a horizontal surface that is a certain distance above another point forms a circle (centre). It is a circle made out of point that are separated from each other in a horizontal direction as a result. At all angles, it is rotating symmetric about the centre. In the closed, two-dimensional plane of a circle, each pair of points is evenly separated from the "centre." A line that pierces the circle creates a specular symmetrical line. At all angles, it rotates symmetrically about the centre.

given,

If the circle is divided into two equal parts and one of them is shaded, then the shaded area is half of the total area of the circle. So the fraction of the area of the circle that is shaded is 1/2 or 0.5.

If the circle is divided into four equal parts and one of them is shaded, then the shaded area is one-fourth of the total area of the circle. So the fraction of the area of the circle that is shaded is 1/4 or 0.25.

Therefore, the answer depends on how many equal parts the circle is divided into and the number of shaded parts.

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Answer:

A keeper is someone who is responsible for something, especially a property or a lot of animals. A keeper might take care of a big summer house during the winter months. You can use keeper to mean "caretaker", someone whose job involves maintaining a house, farm, estate, or grounds.

Hope it helps :)

Answer:

The first 4 terms of the sequence are: 3, 9, 81, 6561

Step-by-step explanation:

We are given the following recursive function:

\(f(n) = [f(n-1)]^{2}\)

And the following initial condition:

\(f(1) = 3\)

The second term of the sequence is:

\(f(2) = [f(2-1)]^{2} = f(1)^2 = 3^2 = 9\)

The third term of the sequence is:

\(f(3) = [f(3-1)]^{2} = f(2)^2 = 9^2 = 81\)

The fourth term of the sequence is:

\(f(4) = [f(4-1)]^{2} = f(3)^2 = 81^2 = 6561\)

The first 4 terms of the sequence are: 3, 9, 81, 6561

i removed my answer because it was wrong look at the other peoples answers

Answer: 213/40 or 5.325

Step-by-step explanation:

We can find common denominators for 8 1/5 and 2 7/8.

The Lowest Common Denominator for 8 1/5 and 2 7/8 is 40.

8 1/5 = 41/5 = 328/40.

2 7/8 = 23/8 = 115/40.

Now we can subtract.

328/40 - 115/40 = 213/40.

Therefore, the answer is 213/40 or 5 13/40.

Answer:

Interest I = $10.67

Step-by-step explanation:

Simple interest I = principal × rate × time

I = Prt

Given;

Principal P = $200

rate r = 4% = 0.04

time t = 16 months = 16/12 years

Substituting the given values;

I = $200 × 0.04 × 16/12

I = $10.66666666666

I = $10.67

She will pay $10.67 interest.

Answer:

Co-ordinates of the focus is; (0, -4)

Step-by-step explanation:

We are given;

Vertex at origin; (0, 0)

Equation of parabola; y = x²/4p

4p = -16

Now,in parabola with vertex at origin, the coordinates of the focus is usually at (0, p)

Now, from 4p = -16 we can find p

p = -16/4

p = -4

Thus coordinates of the focus is; (0, -4)

The ratio of chocolate bars More Preferred: (9 chocolate bars, 3 glasses of milk); Equally Preferred: (6 chocolate bars, 3 glasses of milk); Less Preferred: (3 chocolate bars, 2 glasses of milk) and (9 chocolate bars, 2 glasses of milk).

The ratio of chocolate bars to glasses of milk that Isabel consumes is 3-to-1. This means that whenever she has 3 chocolate bars, she also has 1 glass of milk. Currently, Isabel has 6 chocolate bars and 2 glasses of milk. The bundles listed above are compared to Isabel's current consumption. Out of the five bundles, the one with 9 chocolate bars and 3 glasses of milk is more preferred than what Isabel currently has because it has more of the ratio than Isabel's current consumption. The bundle with 6 chocolate bars and 3 glasses of milk is equally preferred because it holds the same ratio as Isabel's current consumption. The bundles with 3 chocolate bars and 2 glasses of milk and 9 chocolate bars and 2 glasses of milk are less preferred because they both have less of the ratio than Isabel's current consumption.

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Answer:

\(60\)

Step-by-step explanation:

Evaluate 7p + 6(p ÷ q)^2 - 2q (if p = 6 and q = 3)

\(7p + 6(p \div q)^2 - 2q\\\\7(6) + 6(6 \div 3)^2 - 2(3)\\\\7(6) + 6(2)^2 - 2(3)\\\\7(6) + 6(4) - 2(3)\\\\42 + 24 - 6\\\\66-6\\\\60\)

Hope this helps!

1. The x - intercepts of the parabola are

2. The meaning of the x-intercepts are the plane takes of at x = 2.5 s and lands at x = 7.5 s

3. The vertex of the parabola is at (5, 80).

A parabola is a curved shape

1. Given the parabola above, to find the x - intercepts, we proceed as follows.

The x-intercepts are the points at which the graph cuts the x-axis.

They are

2. The meaning of the x-intercepts in this problem are the points where the plane takes off and lands on the ground.

The plane takes of at x = 2.5 s and lands at x = 7.5 s

3. The vertex is the maximum point on the graph.

So, we see that the vertex is at x = 5 s and y = 80 ft

So, the vertex is at (5, 80).

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The algebraic rule for translating the figure 3 units left and 2 units up is (x-3, y+2).  Option B.

To translate a figure 3 units to the left and 2 units up, we need to adjust the coordinates of the figure accordingly. The algebraic rule that represents this translation can be determined by examining the changes in the x and y coordinates.

When we move a figure to the left, we subtract a certain value from the x coordinates. In this case, we want to move the figure 3 units to the left, so we subtract 3 from the x coordinates.

Similarly, when we move a figure up, we add a certain value to the y coordinates. In this case, we want to move the figure 2 units up, so we add 2 to the y coordinates.

Taking these changes into account, we can conclude that the algebraic rule for translating the figure 3 units left and 2 units up is (x-3, y+2). The x coordinates are shifted by subtracting 3, and the y coordinates are shifted by adding 2. SO Option B is correct.

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Answer:

\(8 {x}^{2} - 6x - 5 = x\)

\(8 {x}^{2} - 7x - 5 = 0\)

x = (7 + √((-7)^2 - 4(8)(-5)))/(2×8)

= (7 + √(49 + 160))/16

= (7 + √209)/16

= -.4661, 1.3411 (to 4 decimal places)

Hello,

\(f(x)=2x^4-x^3-18x+9x\\\\=x(2x^3-x^2-18x+9)\\\\=x(x^2(2x-1)-9(2x-1))\\\\=x(2x-1)(x^2-9)\\=x(2x-1)(x-3)(x+3)\\\)

Zeros are : 0;  1/2; -3; 3.

The zeros of the function are -3, 0, 1/2 and 3.

The given function is \(f(x)=2x^{4} -x^{3} -18x^{2} +9x\).

Zeros of a function are the points where the graph of the function meets the X-axis i.e., at the solutions of f(x) = 0.

Now, factorise the given function, that is f(x)=x(2x³-x²-18x+9).

=x[x²(2x-1)-9x(2x-1)]

=x(2x-1)(x²-9)

=x(2x-1)(x+3)(x-3)

= -3, 0, 1/2, 3

Therefore, the zeros of the function are -3, 0, 1/2 and 3.

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\(\huge\text{Hey there!}\)

\(\rm{f(x) = \dfrac{1}{2}x + 4}\\\\\\\rm{f(x)= \dfrac{1}{2}(8) + 4}\\\\\\\rm{y = \dfrac{1}{2}(8) + 4}\\\\\\\rm{\dfrac{1}{2}(8)\rightarrow \dfrac{1}{2}\times8=\boxed{\bf 4}}\\\\\\\rm{y = \bold{4} + 4}\\\\\\\rm{y = \boxed{\bf 8}}\\\\\\\\\huge\boxed{\rm{Therefore, your\ answer\ is: y = \bf 8}}\huge\checkmark\)

\(\huge\text{Good luck on your assignment \& enjoy your day!}\)

~\(\frak{Amphitrite1040:)}\)

The value of is -26

First, to determine the value of x, we need to know that index forms are described as mathematical forms that are used to represent numbers of values that are too small or large in more convenient forms

From the information given, we have that;

5⁷ˣ⁺⁵ = 125²ˣ⁻⁷

Now,  make that the bases are like terms, we have that;

125 = 5³

Substitute the value and we have;

5⁷ˣ⁺⁵ = 5³⁽²ˣ⁻⁷⁾

Take the exponents, we get;

7x + 5 = 6x - 21

collect the like terms, we have;

7x - 6x = -21 - 5

x = - 26

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Abby should write her equation as k = 1.61m.

The correct option is B.

A pair of algebraic equations with the equal symbol (=) in the center and the same value are referred to as an equation.

Given:

Abby knows that 1 mile is about 1.61 kilometers.

To write an equation, which she can use to convert any given distance in miles (m) to kilometers (k):

Let m be the total number of miles and k be the kilometers.

So, the equation is,

k = 1.61m

Where 1.61 is multiplied by m.

Therefore, the equation is k = 1.61m.

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Answer:

you can make 12 cans of them

Answer:

\( \frac{1}{x {}^{2} y {}^{4} }\)

Step-by-step explanation:

\( \frac{x {}^{ - 2} }{y {}^{4} } = x {}^{ - 2} \times \frac{1}{y {}^{4} } \)

\(x {}^{ - 2} = \frac{1}{x {}^{2} } \)

\(therefore \: \frac{x {}^{ - 2} }{y {}^{4} } = \frac{1}{x {}^{2} } \times \frac{1}{y {}^{4} } \\ = \frac{1}{x {}^{2}y {}^{4} }\)

Answer:

12

Step-by-step explanation:

\(y = - x {}^{2} + bx + 10 \\ y = - (x {}^{2} - bx - 10) \\ y = -( (x - \frac{b}{2} ) {}^{2} - \frac{b {}^{2} }{4} - 10) \\ y = - (x - \frac{b}{2} ) {}^{2} + 10 + \frac{b {}^{2} }{4} \\ \\ therefore \: \frac{b}{2} = 6 \\ b = 12\)

The inverse function:  \(f^{-1} (x) =\) \((\frac{x -5}{5} )^{2} -13\)

The inverse is defined on the domain x < 5 and x ≥ -13 for the original function, which means that the range of the original function is y ≥ 5.

A function is a relationship that exists between two sets of numbers, with each input from the first set, known as the domain, corresponding to only one output from the second set, known as the range.

Given function is;   \(f(x) = 5\sqrt{(x + 13)} + 5\)

To find the inverse of the given function, we first replace f(x) with y:

⇒  \(y = 5\sqrt{(x + 13)} + 5\)

Subtract 5 from both sides:

⇒ \(y -5 = 5\sqrt{(x + 13)}\)

⇒ \(\frac{(y -5)}{5} = \sqrt{(x + 13)}\)

⇒ \((\frac{y -5}{5} )^{2} = x + 13\)

⇒ \((\frac{y -5}{5} )^{2} -13 = x\)

Now we have x in terms of y, so we can replace x with f⁻¹(x) and y with x to get the inverse function:

f⁻¹(x) = \((\frac{x -5}{5} )^{2} -13\)

The domain of the inverse function is x ≥ 5, because this is the range of the original function, and we were given that the inverse is defined on the domain x < 5. However, we must also exclude the value x = 5, because the denominator of the fraction \((\frac{x -5}{5} )^{2}\) becomes zero at this value. Therefore, the domain of f⁻¹(x) is x > 5.

We were given that x ≥ -13 for the original function, which means that the range of the original function is y ≥ 5. Therefore, the domain of the inverse function becomes the range of the original function, and the range of the inverse function becomes the domain of the original function.

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Answer:

\(x=8, y=3\)

Step-by-step explanation:

Recall that if a matrix multiplication of two matrices is defined, then the number of columns of the first matrix is equivalent to the number of rows of the second matrix.

Since matrix M has (11-x) columns and matrix N has y rows, and MN is defined, so it follows:

\(y=11-x----(1)\)

Since matrix N has (y+5) columns and matrix M has x rows, and NM is defined, so it follows:

\(y+5=x----(2)\)

Substitute (1) into (2):

\(11-x+5=x\\2x=16\\\therefore x=8--(3)\)

Substitute (3) into (1):

\(y=11-8=3\)

Answer:

actual length of the second wall is 43.2 ft

Step-by-step explanation:

Let x be the actual length of the second wall

Write measurements in ratios with feet to inches:

First wall:      12 : 2.5 = 12/2.5

Second wall:      x : 9 = x/9

Equate the two fractions and solve for x:

12/2.5 = x/9

Multiply both sides by 9:  43.2 = x

Therefore, the actual length of the second wall is 43.2 ft

The range of function for the given domain are {25, 8, -7, 11}

Given that, a function f(x) = 2x²-7, we need to find the range of the function, for the given domain, x = {-4, -2, 0, 3},

So,

Domain = All the input values.

Range = All the output values.

So, to find the range we will put the value of x which is the domain and the value obtained of f(x) will be the range,

f(x) = 2x²-7

For, x = -4,

f(-4) = 16×2 - 7 = 25

f(-4) = 25

f(-2) = 4 × 2 - 7 = 8

f(-2) = 8

f(0) = -7

f(3) = 9 × 2 - 7

f(3) = 11

Hence the range of function for the given domain are {25, 8, -7, 11}

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Answer:

1 or 3

Step-by-step explanation:

factors of 3 r 1 and 3

that's why 3 is a prime number

Answer:

the cost of filling the pool is $386.3

Step-by-step explanation:

Given;

dimension of the rectangular pool, = 25 yd by 30 yd by 5.1 ft

covert the given dimensions to feet;

1 yd = 3 ft

25 yd = 25 x 3 ft = 75 ft

30 yd = 30 x 3 ft = 90 ft

The volume of the rectangular pool in cubic feet (ft³);

Volume = 75 ft  x 90 ft  x 5.1 ft

Volume = 34,425 ft³

Convert the volume to gallons;

1 ft³ = 7.481 gallons

10,125 ft³ = 34,425 x 7.481 gallons

               = 257,533.425 gallons

The cost per a 1000 gallons is $1.50, then cost of the 257,533.425 gallons is calculated as;

\(cost = \frac{\$ 1.50}{1000 \ gallons} \times 257,533.425 \ gallons = \$ 386.3\)

Therefore, the cost of filling the pool is $386.3

Option (D).

Given:

The objective is to select the correct plot correctly.

The frequency of number of toppings 1 is 2.

The frequency of number of toppings 2 is 5.

The frequency of number of toppings 3 is 4.

The frequency of number of toppings 4 is 1.

By comparing the given choices, the dot plots in options (D) matches with the given frequency values.

Hence, option (D) is the correct answer.