You are teaching your friend how to drive a boat. You drive 4 miles to an open location and
then let your friend drive for 15 minutes at a rate of 1.25 miles per 15 seconds. What total
distance do you and your friend cover?

Answer:

c) 4

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Equality Properties

Trigonometry

Step-by-step explanation:

Step 1: Identify Variables

Angle θ = 34°

Adjacent Leg = x

Hypotenuse = 4.8

Step 2: Solve for x

To show that the total charge contained in the charge distribution is Q, we integrate the charge density over the entire volume. The charge density is given by:

ρ(r) = ρ₀(1 - r/R) for r ≤ R,

ρ(r) = 0 for r > R,

where ρ₀ = 3Q/πR³.

To find the total charge, we integrate ρ(r) over the volume:

Q = ∫ρ(r) dV,

where dV represents the volume element.

Since the charge density is spherically symmetric, we can express dV as dV = 4πr² dr, where r is the radial distance.

The integral becomes:

Q = ∫₀ᴿ ρ₀(1 - r/R) * 4πr² dr.

Evaluating this integral gives:

Q = ρ₀ * 4π * [r³/3 - r⁴/(4R)] from 0 to R.

Simplifying further, we get:

Q = ρ₀ * 4π * [(R³/3) - (R⁴/4R)].

Simplifying the expression inside the parentheses:

Q = ρ₀ * 4π * [(4R³/12) - (R³/4)].

Simplifying once more:

Q = ρ₀ * π * (R³ - R³/3),

Q = ρ₀ * π * (2R³/3),

Q = (3Q/πR³) * π * (2R³/3),

Q = 2Q.

Therefore, the total charge contained in the charge distribution is Q.

To show that the electric field in the region r > R is identical to that created by a point charge Q at r = 0, we can use Gauss's law. Since the charge distribution is spherically symmetric, the electric field outside the distribution can be obtained by considering a Gaussian surface of radius r > R.

By Gauss's law, the electric field through a closed surface is given by:

∮E · dA = (1/ε₀) * Qenc,

where ε₀ is the permittivity of free space, Qenc is the enclosed charge, and the integral is taken over the closed surface.

Since the charge distribution is spherically symmetric, the enclosed charge within the Gaussian surface of radius r is Qenc = Q.

For the Gaussian surface outside the distribution, the electric field is radially directed, and its magnitude is constant on the surface. Hence, E · dA = E * 4πr².

Plugging these values into Gauss's law:

E * 4πr² = (1/ε₀) * Q,

Simplifying:

E = Q / (4πε₀r²).

This is the same expression as the electric field created by a point charge Q at the origin (r = 0).

To derive an expression for the electric field in the region r ≤ R, we can again use Gauss's law. This time we consider a Gaussian surface inside the charge distribution, such that the entire charge Q is enclosed.

The enclosed charge within the Gaussian surface of radius r ≤ R is Qenc = Q.

By Gauss's law, we have:

∮E · dA = (1/ε₀) * Qenc.

Since the charge distribution is spherically symmetric, the electric field is radially directed, and its magnitude is constant on the Gaussian surface. Hence, E · dA = E * 4πr².

Plugging these values into Gauss's law:

E * 4πr² = (1/ε₀) * Q.

Simplifying:

E = Q / (4πε₀r²).

This expression represents the electric field inside the charge distribution for r ≤ R.

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See the file attached (photo) above - That is the graph for (-(8*x))+15

Graph the line using the slope and y-intercept, or two points.

Slope: −8

y-intercept: (0,15)

x y

0 15

1 7

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The perimeter of triangle XYZ is equal to √192 or 8√3units.

In triangle XYZ, the base and the height are neither vertical nor horizontal and as such the calculations will be different.

In Mathematics and Geometry, the perimeter of a triangle can be calculated by using this mathematical equation:

P = a + b + c

Where:

P represents the perimeter of a triangle.

a, b, and c represents the side lengths of a triangle.

Next, we would determine the distance between each of the coordinates of triangle XYZ;

Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]

Distance XY = √[(10 - 2)² + (9 - 5)²]

Distance XY = √(64 + 16)

Distance XY = √80 units.

Distance XZ = √[(6 - 2)² + (1 - 5)²]

Distance XZ = √(16 + 16)

Distance XZ = √32 units.

Distance YZ = √[(6 - 10)² + (1 - 9)²]

Distance YZ = √(16 + 64)

Distance YZ = √80 units.

Perimeter of triangle XYZ = XY + XZ + YZ

Perimeter of triangle XYZ = √80 units + √32 units + √80 units

Perimeter of triangle XYZ = √192 or 8√3units.

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Answer:

\(8^{-5}\)

Step-by-step explanation:

When you multiply exponents together, you simply add them.

-8 + 3 = -5.

Answer:

x= -3

Step-by-step explanation:

the absolute value of -3, which would be shown as |-3|, is 3, so it's not equal to -3 itself.

The image point of (4,-7) after a translation right 4 units and up 5 units is; (8, -2)

When we translate an image a units to the right, it means that we add a units to the x-coordinate from which it was translated. However, when we translate an image b units upwards, it means that we add b units to the y-coordinate from which it was translated

Now, we are told that the image point of (4,-7) after a translation right 4 units and up 5 units. Thus, applying the translation rule above, we have;

(4 + 4),  (-7 + 5)

⇒(8, -2)

Thus, we conclude that the image point of (4,-7) after a translation right 4 units and up 5 units is; (8, -2)

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The function described by the points in this table is nonlinear.

Based on the given points in the table, we can determine whether the function is linear or nonlinear by examining the relationship between the x and y values.

Let's look at the x and y values:

x y

-3 9

-1 1

0 0

1 1

3 9

If we observe that for every change in x, the corresponding change in y remains constant, then the function is linear. In other words, if the ratio of the change in y to the change in x is constant, the function is linear.

Let's calculate the ratios:

For x = -3 to x = -1:

Change in y = 1 - 9 = -8

Change in x = -1 - (-3) = 2

Ratio = -8/2 = -4

For x = -1 to x = 0:

Change in y = 0 - 1 = -1

Change in x = 0 - (-1) = 1

Ratio = -1/1 = -1

For x = 0 to x = 1:

Change in y = 1 - 0 = 1

Change in x = 1 - 0 = 1

Ratio = 1/1 = 1

For x = 1 to x = 3:

Change in y = 9 - 1 = 8

Change in x = 3 - 1 = 2

Ratio = 8/2 = 4

As we can see, the ratios are not constant. The ratio changes from -4 to -1, then to 1, and finally to 4. Therefore, the function described by the points in this table is nonlinear.

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Answer:

3 stunts per movie

Step-by-step explanation:

Answer:

3:1

Step-by-step explanation:

12 sunts in 4 movies
simply this.
12:4 is the ratio
3:1 is the final ratio
Therefore, there is 3 stunts per movie.

The dimension of the box will be (40 inch × 40 inch × 10 inch).

How to determine the maximum and minimum values of an expression using differentiation?
Any given expression can have both minimum and maximum outcomes for any number in a real world scenario, which can be determined using differentiation; first order differentiation when equated to zero reveals the value that will solute to produce the maximum or minimum and then the upon differentiating the obtained expression again and then substituting the variable in acceptable positions, if the outcome is a positive number then the obtained number in first differentiation suggests a minimum value of the given expression.

Given, the volume of the box described = 4000 inch³
Let the dimension of the base of the box be = 'a' inch × 'a' inch = a² inch²
Therefore, height of the box = (4000 inch³)/(a² inch²) = (4000/a²) inch
Total surface area of the described box = S = a² + [4a×(4000/a²)]
= [a² + 16000/a] inch
For the limiting values of S, dS/da = 0 ⇒ d[a² + 16000/a]/da = 0
⇒ 2a - [16000/a²] = 0 ⇒ 2a = 16000/a² ⇒ a³ = 8000 ⇒ a = ∛8000 = 20
Therefore, the value of a is 20 inch.
Thus, height of the box = 4000/a² = 4000/400 = 10 inch
For S to have the minimum limited value, d²S/da² > 0 for a = 20 inch, which is satisfied by the available value of S.
∴ The minimal surface area = a² + 16000/a = 400 + (16000/400)
= 440 inch²
We are aware that the least amount of material will be needed to build the box when its overall surface area is the smallest.
Thus, to minimize the amount of material in consideration, the dimension of the box will be (40 inch × 40 inch × 10 inch).

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Answer:

B. 81

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Equality Properties

Step-by-step explanation:

Step 1: Define

Identify

√x + 3 = 12

Step 2: Solve for x

Answer:

B

Step-by-step explanation:

Given

\(\sqrt{x}\) + 3 = 12 ( subtract 3 from both sides )

\(\sqrt{x}\) = 9 ( square both sides )

x = 9² = 81 → B

Answer:0

Step-by-step explanation:2≠8,10 so we use the bottom formula. We get 4 - 6 + 2=0

Answer:

These kind of questions are called simply.

According to simply, there's a rule of solving which is BODMAS.

BODMAS stand for bracket of Divide, Multiple, Add, Subtraction.

> (9)2-4

> 18-4

> 16

• (6+3)2-4 = 16

2. 23+(14-4)÷2

> 23+10÷2

> 23+5

> 28

• 23+(14-4)÷2 = 28

Step-by-step explanation:

Hope it helps you

Answer:

9

13

23

59

116

238

Step-by-step explanation:

1) 14

1 × 5^1 + 4 × 5^0 = 9

2) 23

2 × 5^1 + 3 × 5^0 = 13

3) 43

4 × 5^1 + 3 × 5^0 = 23

4) 214

2 × 5² + 1 × 5^1 + 4 × 5^0 = 59

5) 431

4 × 5² + 3 × 5^1 + 1 × 5^0 = 116

6) 1423

1 × 5³ + 4 × 5² + 2 × 5^1 + 3 × 5^0 = 238

Answer:

The millimeter.

Step-by-step explanation:

The best choice here is the millimeter (mm).

Answer:22.96 u just divide 28/82

Step-by-step explanation:

Answer:

Step-by-step explanation:

Joule per meter second is the unit of measurement for momentum flux or power per unit area. It is commonly used in physics and engineering to quantify the rate of energy transfer or momentum flow per unit area.

Joule per meter second (J/m^2s) is not the correct unit for momentum flux or power per unit area. The correct unit for momentum flux is Newton per square meter (N/m^2), also known as Pascal (Pa), while the correct unit for power per unit area is watt per square meter (W/m^2). The joule per meter second (J/m^2s) is actually the unit for volumetric energy dissipation rate, which measures the rate at which energy is being dissipated within a fluid volume per unit volume. It is used in the study of fluid dynamics and turbulence.

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To solve this problem, we can use the formula for the number of subsets of a set with n elements, which is 2^n. So, for the set of 12 months, there are 2^12 = 4096 subsets in total.

Now, we need to find the number of subsets that have less than 11 elements. We can start by finding the number of subsets that have 11 elements. There are 12 ways to choose the first element, 11 ways to choose the second element, and so on until there is only one way to choose the twelfth element. So, there are 12 x 11 x 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 12! / (12-11)! = 12! = 479001600 subsets with 11 elements.
To find the number of subsets with less than 11 elements, we can subtract this from the total number of subsets: 4096 - 479001600 = -479001184. However, this answer doesn't make sense because we can't have a negative number of subsets.
So, we need to consider the subsets with fewer elements. There are 12 ways to choose a subset with 1 element, 12C2 = 66 ways to choose a subset with 2 elements, 12C3 = 220 ways to choose a subset with 3 elements, and so on until 12C10 = 66 ways to choose a subset with 10 elements.
Adding all of these up, we get 12 + 66 + 220 + 495 + 792 + 924 + 792 + 495 + 220 + 66 = 4095 subsets with less than 11 elements.
Therefore, the answer is (A) 212-13.

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Answer:

I think the answer is 2 because the top of black is 3 units but then the top of blue is 6 units. and 3×2=6. im mot completely sure tho

Answer:

When x takes the value of 4, the expression takes the value of 9.

Step-by-step explanation:

We are given that the expression:

\(\displaystyle ax^2 + bx + c\)

Evaluates to 0, 1, and 4 when x = 1, 2, and 3, respectively.

And we want to determine the value of the expression when x = 4.

The expression evaluates to 0 when x = 1. In other words:

\(\displaystyle a(1)^2 + b(1) +c = a + b + c = 0\)

We can complete the same for the other two:

\(\displaystyle a(2)^2 + b(2) + c = 4a + 2b + c = 1\text{ and } \\ \\ a(3)^2 + b(3) + c = 9a + 3b + c = 4\)

This yields a triple system of equations:

\(\displaystyle \left\{ \begin{array}{l} a + b + c = 0 \\ 4a + 2b + c = 1 \\ 9a + 3b + c = 4 \end{array}\)

Solve. We can cancel out the c by multiplying the first equation by negative one and adding it to both the second and the third:

\(\displaystyle \begin{aligned} (4a + 2b + c) + (-a - b -c ) &= (-0) + (1) \\ \\ 3a +b &= 1\end{aligned}\)

And:

\(\displaystyle \begin{aligned} (9a + 3b + c) + (-a - b -c) &= (-0) + (4) \\ \\ 8a + 2b &= 4\end{aligned}\)

Solve for the two resulting equations. We can multiply the first by negative two and add it to the second:

\(\displaystyle \begin{aligned}(8a + 2b) + (-6a -2b) &= (4) + (-2) \\ \\ 2a &= 2 \end{aligned}\)

Hence:

\(a = 1\)

Solve for b:

\(\displaystyle \begin{aligned} 3a + b &= 1 \\ b&= 1 - 3a \\ b&= 1 - 3(1) \\ b &= -2\end{aligned}\)

And finally, solve for c:

\(\displaystyle \begin{aligned} a + b + c &= 0 \\ (1) + (-2) + c &= 0 \\ c &= 1\end{aligned}\)

Hence, our expression is:

\(\displaystyle x^2 -2x + 1\)

Then when x = 4:

\(\displaystyle (4)^2 - 2(4) + 1= 9\)

In conclusion, when x = 4, the resulting value is 9.

Answer:

perp. just switch from -2/5 to positive 5/2

Step-by-step explanation:

Answer:

m2 =5/2

Step-by-step explanation:

m1=-1/m2

m2=-1/m1

y=-2/5x-10

m1=-2/5

m2= -1/-2/5

m2=5/2

y=5/2x-10 ⊥ y=-2/5x-10

Answer:

9

Step-by-step explanation:

-3*-3=9

- times a - = +

Answer:

-9

Step-by-step explanation:

An exponent is multiplying the number by itself. I understand why you might be confused though, with the negative number.

Have a great day!

Answer:

y = -2/3 x + 25/3

Step-by-step explanation:

The slope = (y_2 - y_1) / (x_2 - x_1) = (9 - 7) / (-1 - 2) = -2/3.

Our equation needs to be in y = mx + b form.

We can plug in (2, 7) as our (x, y) and find b:

7 = -2/3 (2) + b

b = 7 + 4/3 = 25 / 3.

Therefore, our equation is y = -2/3 x + 25/3

Use the Equation(in the picture) and plug in your variables to find m(slope)

\(\frac{9-7}{-1-2} = \frac{-2}{3} = -0.67\)

There are 10 different ways to choose 3 elements from a set of 5 elements. These 10 ways are: {A,B,C}, {A,B,D}, {A,B,E}, {A,C,D}, {A,C,E}, {A,D,E}, {B,C,D}, {B,C,E}, {B,D,E}, and {C,D,E}.

The number of subsets of size r that can be chosen from a set of n elements is denoted by nCr, and can be calculated using the formula nCr. This formula is typically referred to as the "combination formula" or the "binomial coefficient formula."

To clarify, the symbol nCr represents the number of ways to choose r elements from a set of n elements without regard to order (i.e., choosing {1,2,3} is the same as choosing {2,3,1}). The formula nCr calculates this number by dividing the total number of possible combinations by the number of redundancies (i.e., arrangements that are considered equivalent due to the lack of order).

The formula for nCr is given by:

nCr = n! / (r! * (n-r)!)

where n! represents the factorial of n (i.e., n! = n * (n-1) * (n-2) * ... * 2 * 1), and r! and (n-r)! represent the factorials of r and n-r, respectively.

For example, suppose we have a set of 5 elements (A, B, C, D, and E) and we want to know how many ways there are to choose 3 elements from this set. Using the formula above, we can calculate nCr as follows:

nCr = 5! / (3! * (5-3)!) = 5! / (3! * 2!) = (5 * 4 * 3 * 2 * 1) / ((3 * 2 * 1) * (2 * 1)) = 10

Therefore, there are 10 different ways to choose 3 elements from a set of 5 elements. These 10 ways are: {A,B,C}, {A,B,D}, {A,B,E}, {A,C,D}, {A,C,E}, {A,D,E}, {B,C,D}, {B,C,E}, {B,D,E}, and {C,D,E}.

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Correct question is "consider the following theorem. theorem 9.5.1: the number of subsets of size r that can be chosen from a set of n elements is denoted nCr and is given by the formula nCr"

The situation provided is exponential growth and the equation is

p = 225 * 1.133ˣ

This scenario represents a significant improvement as the number of students increases each year.

The basic approach to incremental growth is:

\(P = P_{0} * (1 + r)^t\)

where:

P. = initial population

r = increase in decimal form

t = time in years

Here

P₀ = 225 (initial population in 2021).

r = 13.3% = 0.133 (growth rate as decimal) .

t = x (time in years from the opening of the school in 2021)

Substituting these values ​​in the formula we get:

\(p = 225 * (1 + 0.133)^x\)

Simplifying further, we get:

p = 225 * 1.133ˣ

This is the equation that predicts school population x years after the school opens in 2021

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Answer:

vwhich principle prevents a brach from abusing  its power

Step-by-step explanation: