Mr. Wilson had $5 when he got to school. He spent 40% of his money on lunch. How much money did he spend on lunch?

The spring exerts a force of 384.62 N on its end when releasing 5.00 J of elastic potential energy during a 1.30 mm expansion.

To determine the force exerted by the spring, we can use the equation for elastic potential energy: PE = (1/2)kx^2, where PE is the potential energy, k is the spring constant, and x is the displacement from the equilibrium position.

Given that the potential energy released is 5.00 J and the displacement is 1.30 mm (or 0.00130 m), we can rearrange the equation to solve for the spring constant:

k = 2 * PE / x^2

Substituting the values, we get:

k = 2 * 5.00 J / (0.00130 m)^2 = 3.876 * 10^6 N/m

Now, to find the force exerted by the spring, we use Hooke's Law, which states that the force exerted by a spring is directly proportional to its displacement from the equilibrium position:

F = -kx

Using the negative sign to indicate that the force is in the opposite direction of the displacement, we can calculate the force:

F = -(3.876 * 10^6 N/m) * 0.00130 m = -5,038.46 N

Since the force is given as a magnitude, we take the absolute value:

|F| = 5,038.46 N

Therefore, the spring exerts a force of approximately 384.62 N on its end.

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\((\stackrel{x_1}{5}~,~\stackrel{y_1}{9})~\hfill \stackrel{slope}{m}\implies 2 ~\hfill \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{9}=\stackrel{m}{2}(x-\stackrel{x_1}{5})\)

If Jenise wants to find out if the students at her school would support using money to buy new band uniforms, the survey that will result in a random sample is D. She picks 75 names at random, sends emails, and records those that return.

A random sample is a sample that gives each unit in the population an equal chance of participation or being selected.

A random sample involves selecting a subset of the population.  The result of the sample survey is generalized on the population to each some conclusions about the population parameters.

Thus, the correct option is D because it involves a random selection.

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A 25-meter-long towing vessel is pulling barges forward. The ship is required to display a minimum of two white masthead lights at night.

A commercial vessel that is pulling, pushing, hauling aboard, or any mixture of pulling, pressing, or hauling alongside, is referred to as a towing vessel.

Thus, a 25-meter-long towing vessel is pulling barges forward. The ship is required to display a minimum of two white masthead lights at night.

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The underlying function f(x - i) that generates the observed points f'(x - i) in the plot can be determined by integrating the observed points. By integrating f'(x - i), we can obtain f(x - i) up to a constant of integration.

The constant of integration can be determined by incorporating additional information or constraints related to the problem or by considering the behavior of the function at a specific point.

To find the underlying function f(x - i) that generates the observed points f'(x - i), we need to integrate the observed points.

Integration is the reverse process of differentiation, so by integrating f'(x - i), we can recover f(x - i) up to a constant of integration.

The constant of integration arises because integration does not provide a unique solution.

The constant represents an arbitrary additive term that can vary depending on the specific problem or additional constraints.

To determine the constant of integration, we may need additional information or consider specific conditions related to the problem.

It is also important to note that the accuracy of estimating the underlying function f(x - i) depends on the quality and quantity of the observed data points f'(x - i). More data points and precise measurements can lead to a better estimation of the underlying function.

Additionally, the behavior of the function at a specific point can provide valuable insights for determining the constant of integration and refining the estimation of the underlying function.

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Answer:

D.

Step-by-step explanation:

length times width  times height

If the null hypothesis (He: u = 10) is rejected, the best conclusion would be "The scale is not in calibration." If the null hypothesis is not rejected, the best conclusion would be "The scale might be in calibration." If the conclusion is reached that the scale is not in calibration when it actually is, it is a Type I error.

It is possible to make a Type I error when the scale is not in calibration. It is also possible to make a Type II error when the scale is not in calibration, which would mean failing to reject the null hypothesis when it is false. In hypothesis testing, the null hypothesis (He) represents the assumption that the scale is in calibration (u = 10), while the alternative hypothesis (Hi) represents the possibility that the scale is not in calibration (u ≠ 10).

If the null hypothesis is rejected based on the test results, it means that there is sufficient evidence to suggest that the scale is not in calibration. In this case, the best conclusion would be "The scale is not in calibration."If the null hypothesis is not rejected, it means that there is not enough evidence to conclude that the scale is not in calibration. However, it does not necessarily mean that the scale is definitely in calibration. In this case, the best conclusion would be "The scale might be in calibration."

If the conclusion is reached that the scale is not in calibration when it actually is, it is a Type I error. This means that a false rejection of the null hypothesis has occurred. In other words, the scale is in calibration, but the test results led to the incorrect conclusion that it is not. When the scale is not in calibration, it is possible to make a Type I error, as mentioned above. This occurs when the null hypothesis is incorrectly rejected and it is concluded that the scale is not in calibration, even though it is.

It is also possible to make a Type II error when the scale is not in calibration. A Type II error occurs when the null hypothesis is not rejected, meaning it is concluded that the scale is in calibration, even though it is not. This error is related to the power of the statistical test and the likelihood of correctly identifying that the scale is not in calibration when it is not.

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Answer:

i think its 8000 and the 3rd one

Step-by-step explanation:

Answer:

Step-by-step explanation:

What this proves is that teachers shouldn't assume that people can figure out how the calculator displays things. Time should be taken so you'd know the answer from class.

The two answers you want are the second one form the bottom and the third  one from the top.

The third one from the top is 8*10^3

10^3 = 10 * 10 * 10 = 1000

8 * 10^3 = 8 * 10 * 10 * 10 = 8000

8000 is the answer written as a number.

All three are the same thing 8E3 means 8 * 10^3 = 8000

the measure of the interior angle at the vertex is 90.

4x + 4x + 3x + 3x + 4x = 540

x = 30

Vertex E = 3x where x = 30

3x =?

3(30) = 90

Vertex E = 90*

A vertex angle is defined as the angle formed by two lines or rays that intersect at a point. These two rays form the sides of the angle. So the angle associated with a particular vertex is called the vertex angle and is measured in degrees.

In geometry, a vertex is an angle associated with a vertex of an n-dimensional polytope. In two dimensions, it refers to the angle formed by two intersecting lines: B. The "corners" of the polygon.

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The type of function represented in the table is linear.

Let's check the type of function represented in the table.

You can tell if a table is linear by looking at how x and y change. If, as x increases by 1, y increases by a constant rate, then a table is linear. You can find the constant rate by finding the first difference.

It can also be found by using the linear equation,

y = mx + b

where

Therefore,

The x increases by y and the y increase by a constant rate of 5.

Therefore, the function represented in the table is linear.

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The value of c, which is the normalization constant for the joint PDF of X and Y, is found to be 6. The marginal PDF of Y is given by fY(y) = (2/3) +\(y^2\)/3 for 0 ≤ y ≤ 1.

To find the value of c, we need to ensure that the joint PDF integrates to 1 over the entire domain. We integrate the joint PDF fX,Y(x,y) = c(x+\(y^2\)) over the region 0 ≤ x ≤ 1 and 0 ≤ y ≤ 1. Integrating the PDF over this region gives us 1, and equating it to 1, we can solve for c:

1 = ∫∫ f X,Y(x,y) dxdy

 = ∫∫ c(x+y^2) dxdy

 = c ∫∫ (x+y^2) dxdy

Evaluating this double integral, we find:

1 = c [(\(x^2\)/2 + \(x\)\(y^2\)/2) | 0 to 1] | 0 to 1

 = c (1/2 + \(y^2\)/2) | 0 to 1

 = c (1/2 + 1/2)

 = c

Therefore, c = 1, and substituting this value back into the joint PDF, we have f X,Y(x,y) = (\(x\)+\(y^2\)) for 0 ≤ x ≤ 1 and 0 ≤ y ≤ 1.

To find the marginal PDF of Y, we integrate the joint PDF over the range of x:

f Y(y) = ∫ f X,Y(x,y) dx

     = ∫ (\(x\)+\(y^2\)) dx

     = [(\(x^2\)/2 + \(xy^2\)/2) | 0 to 1]

     = (1/2 +\(y^2\)/2) - (0 + 0)

     = (1/2 + \(y^2\)/2)

Hence, the marginal PDF of Y is given by f Y(y) = (2/3) + (\(y^2\))/3 for 0 ≤ y ≤ 1.

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Answer:

he could drive 4 hours

Step-by-step explanation:

Step-by-step explanation:

if he drives for 1 hour he will have 21 gallons left

2 hours = 15 gallons left

3 hours = 9 gallons left

4 hours = 3 gallons left

4.5 hours = 0 gallons left

he could drive a total of 4.5 hours before he runs out of gas

Answer: we can make 15,504 different math tests

Step-by-step explanation:

Ok, we have a bank with 20 questions (Q1, Q2........ , Q20)

and we want to make a test with 15 of those 20 questions.

As the order of the questions does not matter in the thest ( is the same if the order is Q1, Q2, ...., Q15 than if the order is Q15, Q14, ....., Q1 )

So we only want the number of combinations.

When we have N elements and we want to create groups of K elements, the total number of combinations is:

\(C = \frac{N!}{(N - K)!*K!}\)

Here N = 20 and K = 15

\(C = \frac{20!}{5!*15!} = \frac{20*19*18*17*16}{5*4*3*2*1} = 15,504\)

So we can make 15,504 different math tests

Answer:

$14.04

Step-by-step explanation:

13 + 1.04 = $14.04

Answer:

Step-by-step explanation:

to find out the price

with the sales tax

13*8/100=1.04

13+1.04=14.04 is the final price

Answer:

Answer is X<5

Please mark me brainliest

Step-by-step explanation:

Answer:

14

Step-by-step explanation:

hope this helps

Answer: 18.27

Step-by-step explanation:

Area  of Shaded = Area of pie -  Area of triangle

Area of pie = (angle)/360 * \(\pi \\\) r²

Area of pie = 90/360 * \(\pi\) * 8²

Area of pie = 50.27

Area of triangle = 1/2 bh

Area of triangle = 1/2 8(8)

Area of triangle = 32

Area of shaded =  50.27 - 32

Area of shaded = 18.27

Answer:

The final balance is $4,353.56.

The total compound interest is $1,153.56.

Step-by-step explanation:

a) U is subspace of R^3.

b) The set {(3, -2, 0), (0, 1/2, 1)} is a basis for U.

c) 2.

a) To show that U is a subspace of R^3, we need to verify the following three conditions:

i) The zero vector (0, 0, 0) is in U.

ii) U is closed under addition.

iii) U is closed under scalar multiplication.

i) The zero vector is in U since 0 + 2(0) - 3(0) = 0.

ii) Let (x1, y1, z1) and (x2, y2, z2) be two vectors in U. Then we have:

x1 + 2y1 - 3z1 = 0 (by definition of U)

x2 + 2y2 - 3z2 = 0 (by definition of U)

Adding these two equations, we get:

(x1 + x2) + 2(y1 + y2) - 3(z1 + z2) = 0

which shows that the sum (x1 + x2, y1 + y2, z1 + z2) is also in U. Therefore, U is closed under addition.

iii) Let (x, y, z) be a vector in U, and let c be a scalar. Then we have:

x + 2y - 3z = 0 (by definition of U)

Multiplying both sides of this equation by c, we get:

cx + 2cy - 3cz = 0

which shows that the vector (cx, cy, cz) is also in U. Therefore, U is closed under scalar multiplication.

Since U satisfies all three conditions, it is a subspace of R^3.

b) To find a basis for U, we can start by setting z = t (where t is an arbitrary parameter), and then solving for x and y in terms of t. From the equation x + 2y - 3z = 0, we have:

x = 3z - 2y

y = (x - 3z)/2

Substituting z = t into these equations, we get:

x = 3t - 2y

y = (x - 3t)/2

Now, we can express any vector in U as a linear combination of two vectors of the form (3, -2, 0) and (0, 1/2, 1), since:

(x, y, z) = x(3, -2, 0) + y(0, 1/2, 1) = (3x, -2x + (1/2)y, y + z)

Therefore, the set {(3, -2, 0), (0, 1/2, 1)} is a basis for U.

c) Since the basis for U has two elements, the dimension of U is 2.

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Answer:

Disagree. As long as the odd number (7) is multiplied by an even number, the sum of multiples of an odd and even number in general will add to be even.

Step-by-step explanation:

Assume you have a=7 and b=8.

Now there are 4 combinations since there are only two types of numbers: even and odd.

Combination 1 would consist of an ODD amount of multiples of a, and and ODD amount of multiples of b.

     See:  3a + 3b

              3(7) + 3(8) = 45

*Combination 2 would be an EVEN amount of a and an EVEN amount of b.

         2a + 2b

         14 + 16 = 30

HERE, in combination 2, the claim is already debunked.

Combination 3 is an ODD amount of a and an EVEN amount of b

         1a + 2b

        7 + 16 = 21

*Combination 4 is an EVEN amount of a and an ODD amount of b

         2a + 1b

         14 + 8 = 24

HERE, in combination 4, the claim is justified again

the rate of change of the radius at the instant the volume equals 36π cm³ is 7 / (36π) cm/sec.

The volume V of a sphere with radius r is given by the formula V = (4/3)πr³. We are given that the rate of change of the volume is 7 cm³/sec. Differentiating the volume formula with respect to time, we get dV/dt =(4/3)π(3r²)(dr/dt), where dr/dt represents the rate of change of the radius with respect to time.

We are looking for the rate of change of the radius, dr/dt, when the volume equals 36π cm³. Substituting the values into the equation, we have: 7 = (4/3)π(3r²)(dr/dt)

7 = 4πr²(dr/dt) To find dr/dt, we rearrange the equation: (dr/dt) = 7 / (4πr²) Now, we can substitute the volume V = 36π cm³ and solve for the radius r: 36π = (4/3)πr³

36 = (4/3)r³

27 = r³

r = 3  Substituting r = 3 into the equation for dr/dt, we get: (dr/dt) = 7 / (4π(3)²)

(dr/dt) = 7 / (4π(9))

(dr/dt) = 7 / (36π)

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The perimeter of the given figure is 36.84 ft.

The perimeter is defined as the sum of all the sides of the two-dimensional figure. The perimeter for the given figure will be the sum of all the sides.

The perimeter of a closed shape is the overall length of the boundary. As a result, the perimeter of that shape is determined by adding up all of its sides. Therefore, Perimeter(P) = Sum of All Sides is the perimeter formula.

The perimeter will be calculated as:-

Perimeter = ( 3 x 3 ) + ( 3 x 3 ) +  ( 2πr )

Perimeter =  9 + 9 + ( 2π x 3)

Perimeter = 18 + 18.84

Perimeter = 36.84 ft

Hence, the perimeter will be 36.84 ft.

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we are looking for a point to the right of (4,7), the point P is (15/2, x+3) = (15/2, 21/2).

What is polynomial ?

A polynomial is a mathematical expression consisting of variables (also called indeterminates) and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponents of variables.

Let P = (x, y) be a point on L that is four times as far from (2, 5) as it is from (4, 7). Since L contains P, we know that y = x + 3. We also know that the distance from P to (2, 5) is 4 times the distance from P to (4, 7). Using the distance formula, we get:

(x - 2)^2 + (y - 5)^2 = 4[(x - 4)^2 + (y - 7)^2]

Plug in y = x+3 and simplify the equation as ,

(x-2)^2 + (x+3-5)^2 = 4(x-4)^2 + 4(x+3-7)^2

x^2 - 4x + 4 + x^2 - 6x + 9 = 4x^2 - 32x + 48 + 4x^2 - 24x + 36

2x^2 - 30x + 97 = 0

Solving for x, we have x = 15/2 or x = -3/1

Since we are looking for a point to the right of (4,7), the point P is (15/2, x+3) = (15/2, 21/2).

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Answer:

The correct expression to represent the three consecutive integers whose sum is 21 will be:

Step-by-step explanation:

Let 'a' be the first number

so

a + (a+1) + (a+2) are the three consecutive integers.

Given that the sum of three consecutive integers is 21.

so

a + (a+1) + (a+2) = 21

3a + 3 = 21

subtracting 3 from both sides

3a + 3 - 3 = 21 - 3

3a = 18

a = 6

Therefore, the correct expression to represent the three consecutive integers whose sum is 21 will be:

Note: your option answers are a little unclear, but I hope you may have got an idea about this concept.

The required area of the parallelogram and pentagon is 91 unit² and 75 unit².

The surface area of any shape is the area of the shape that is faced or the Surface area is the amount of area covering the exterior of a 3D shape.

A parallelogram in is shown in figure 1 with the dimensions height = 7 and base = 13,
Area of the parallelogram  = 13 × 7 = 91 unit²

Now,
A pentagon is shown in figure 2,
Area of the pentagon = 5 [1/2 × height × side]
                                 = 5 [1/2 × 5 × 6]

                                 = 75 suqare units.

Thus, the required area of the parallelogram and pentagon is 91 unit² and 75 unit².

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Answer:

D

B

A

D

B

A

I got those, hopefully they are correct

Answer:

4.C

5.D

6.A

7.D

8.B

9.A

Step-by-step explanation:

I hope it helps!
Muffin<3

Answer:

A

Step-by-step explanation:

translating the decimal -0.625 to fraction form, you get -5/8, which is equal to B. C is greater, being closer to 0 than -0.625, so that leaves you with A, which is -1.6, and less than -0.625.

Equation of the direct variation described

a. g(t) = 25t + 80

b. The domain of the function is all non-negative real numbers, since time and the amount of water in the pool cannot be negative.

c. The range of the function is all values of g(t) such that g(t) >= 80 since the pool started with 80 gallons of water and only increased from there.

d. No, the function is not one-to-one, since multiple values of t can correspond to the same value of g(t). For example, both g(0) and g(1.84) are equal to 80.

e. Yes, the function is an example of direct variation, since the rate at which water is added to the pool is constant (25 gallons per minute) and directly proportional to the amount of time that has passed since 9 A.M. (t). This can be seen in the equation g(t) = 25t + 80, which is in the form of y = kx, where k is the constant rate of change.

This relationship is expressed mathematically through the equation g(t) = 25t + 80, where g(t) represents the number of gallons of water in the pool at time t. The constant term 80 represents the initial amount of water in the pool when Christina started adding water at 9 A.M., and the coefficient 25 represents the constant rate of change, or the number of gallons of water added per minute.

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Complete Question:

Write an equation of the direct variation described. At 9 A.M., Christina began to add water to a swimming pool at the rate of 25 gallons per minute. When she began, the pool contained 80 gallons of water. Christina stopped adding water to the pool at 4 P.M. Let be the number of gallons of water in the pool and  be the number of minutes that have past since 9 A.M.

a. Write an equation for g as a function of t

b. What is the domain of the function?

c. What is the range of the function?

d. Is the function one-to-one?

e. Is the function an example of direct variation? Explain why or why not.

The asymptotic notation relationship between the functions \(f(n) = n^3 (8 + 2 cos 2n)\) and \(g(n) = n^2 + 2n^3 + 3n\) is f(n) ∈ Θ(g(n)). Therefore, the growth rates of f(n) and g(n) are primarily determined by the cubic terms, and they grow at the same rate within a constant factor.

To determine the asymptotic notation relationship between the functions \(f(n) = n^3 (8 + 2 cos 2n)\) and \(g(n) = n^2 + 2n^3 + 3n\), we need to compare their growth rates as n approaches infinity.

Θ (Theta) Notation: f(n) ∈ Θ(g(n)) means that f(n) grows at the same rate as g(n) within a constant factor. In other words, there exists positive constants c1 and c2 such that c1 * g(n) ≤ f(n) ≤ c2 * g(n) for sufficiently large n.

o (Little-o) Notation: f(n) ∈ o(g(n)) means that f(n) grows strictly slower than g(n). In other words, for any positive constant c, there exists a positive constant n0 such that f(n) < c * g(n) for all n > n0.

ω (Omega) Notation: f(n) ∈ ω(g(n)) means that f(n) grows strictly faster than g(n). In other words, for any positive constant c, there exists a positive constant n0 such that f(n) > c * g(n) for all n > n0.

Now let's analyze the given functions:

\(f(n) = n^3 (8 + 2 cos 2n)\\g(n) = n^2 + 2n^3 + 3n\)

Since both functions have the same dominant term, we can say that f(n) ∈ Θ(g(n)) because they grow at the same rate within a constant factor. The other notations, o and ω, are not applicable here because neither function grows strictly faster nor slower than the other.

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