the sum of independent normally distributed random variables is normally distributed with mean equal to the sum of the individual means and variance equal to the sum of the individual variances. if x is the sum of three independent normally distributed random variables with respective means 100, 150, and 200 and respective standard deviations 15, 20, and 25, the probability that x is between 420 and 460 is closest to which of the following?

An experiment usually has three kinds of variables: independent, dependent, and controlled. The independent variable is the one that is changed by the scientist.

In mathematical modeling, statistical modeling, and experimental sciences, there are dependent and independent variables. Dependent variables get their name because, during an experiment, their values are investigated under the presumption or requirement that they are dependent on the values of other variables due to some law or rule.

The variable you alter, regulate, or change in an experimental study to examine its effects is known as an independent variable. It is named "independent" because it is unaffected by any other study variables.

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Solution:

Give the sequence:

The common difference is the difference between two consecutive terms.

Thus, the common diffrence is evaluated as

Thus, from the explicit formula,

The explicit form is evaluated to be

The recursive form is evaluated as

Given, the function is f(x,y,z)=5+yxz+g(x,z)Here, we need to find the directional derivative of f at the point (3,0,3) along the direction of the vector (0,4,0) . The directional derivative of f at the point (3,0,3) along the direction of the vector (0,4,0) is 0.

Using the formula of the directional derivative, the directional derivative of f at the point (3,0,3) along the direction of the vector (0,4,0) is given by

(f(x,y,z)) = grad(f(x,y,z)).v

where grad(f(x,y,z)) is the gradient of the function f(x,y,z) and v is the direction vector.

∴ grad(f(x,y,z)) = (fx, fy, fz)

                       = (∂f/∂x, ∂f/∂y, ∂f/∂z)

Hence, fx = ∂f/∂x = 0 + yzg′(x,z)fy

                = ∂f/∂y

                = xz and

fz = ∂f/∂z = yx + g′(x,z)

We need to evaluate the gradient at the point (3,0,3), then

we have:fx(3,0,3) = yzg′(3,3)fy(3,0,3)

                             = 3(0) = 0fz(3,0,3)

                             = 0 + g′(3,3)

                             = g′(3,3)

Therefore, grad(f(x,y,z))(3,0,3) = (0, 0, g′(3,3))Dv(f(x,y,z))(3,0,3)

                                                 = grad(f(x,y,z))(3,0,3)⋅v

where, v = (0,4,0)Thus, Dv(f(x,y,z))(3,0,3) = (0, 0, g′(3,3))⋅(0,4,0)   = 0

The directional derivative of f at the point (3,0,3) along the direction of the vector (0,4,0) is 0.

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A temperature change of 20°C corresponds to a Fahrenheit temperature change of 36°F. The Fahrenheit scale has a different conversion formula than the Celsius scale, resulting in a larger change in degrees for the same temperature difference.

To convert from Celsius to Fahrenheit, we use the formula: F = (C * 9/5) + 32, where F represents the temperature in Fahrenheit and C represents the temperature in Celsius.

In this case, the temperature change is given as 20°C. To find the corresponding Fahrenheit temperature change, we apply the conversion formula: F = (20 * 9/5) + 32 = 36 + 32 = 68°F.

Therefore, a temperature change of 20°C corresponds to a Fahrenheit temperature change of 68°F. Among the given answer choices, the closest option is 36°F.

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Answer:

Step-by-step explanation:

To identify some of the key features of a graph, follow these steps:

1. Monotonicity: Determine if the function is monotonically increasing or decreasing. To do this, analyze the direction of the graph. If the graph goes from left to right and consistently rises, then the function is monotonically increasing. If the graph goes from left to right and consistently falls, then the function is monotonically decreasing.

2. End Behavior: State the end behavior of the graph. This refers to the behavior of the graph as it approaches infinity or negative infinity. Determine if the graph approaches a specific value, approaches infinity, or approaches negative infinity.

3. X-intercepts: Find the x-intercepts of the graph. These are the points where the graph intersects the x-axis. To find the x-intercepts, set the y-coordinate equal to zero and solve for x. The solutions will be the x-intercepts.

4. Y-intercept: Find the y-intercept of the graph. This is the point where the graph intersects the y-axis. To find the y-intercept, set the x-coordinate equal to zero and solve for y. The solution will be the y-intercept.

5. Maximum or Minimum: Determine if there is a maximum or minimum point on the graph. If the graph has a highest point, it is called a maximum. If the graph has a lowest point, it is called a minimum. Identify the coordinates of the maximum or minimum point.

6. Domain: State the domain of the graph. The domain refers to the set of all possible x-values that the function can take. Look for any restrictions on the x-values or any values that the function cannot take.

7. Range: State the range of the graph. The range refers to the set of all possible y-values that the function can take. Look for any restrictions on the y-values or any values that the function cannot take.

By following these steps, you can identify the key features of a graph, including monotonicity, end behavior, x- and y-intercepts, maximum or minimum points, domain, and range. Remember to consider the context of the problem if provided, as it may affect the interpretation of the graph.

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Answer:

0.0000614

Step-by-step explanation:

Since it’s a -5 it’s 5 places back

Hope this helps! ;-)

Answer:

6blankets

Step-by-step explanation:

First let us find the rate of work done by the sewing club;

  Rate  = \(\frac{number of blankets}{length of fabric}\)    

Number of blankets  = 8

Length of fabric used  = 48ft

  Rate  = \(\frac{8}{48}\)    = 0.17blanket/ft

Now to find the number of blankets:

  Number of blankets = Rate x length of fabric

 length of fabric  = 12yards;

   Convert yards to feet;

                 1 yard  = 3ft

                12yards  = 3 x 12 = 36ft

So;

  Number of blankets  = 0.17blanket/ft  x  36ft  = 6blankets

Answer:

32747w31663875141t3644q58t93de

With a $3000 budget, the skateboard club can purchase used equipment for approximately 75 students.

To calculate the number of students the skateboard club can purchase used equipment for, we need to determine the cost per student.

if every student needs to replace their skateboard helmet and pads, and the skateboard club has a budget of $3000, we can calculate the approximate number of students they can purchase used equipment for.

To determine this, we need to know the cost of a set of used skateboard helmet and pads.

However, we can provide an estimate by dividing the budget by the assumed cost per set.

Let's assume that the cost of one set of used equipment is $40. Dividing the total budget of $3000 by the assumed cost per set ($40), we get 3000 / 40 = 75 students.

Therefore, with a $3000 budget, the skateboard club can potentially purchase used equipment for approximately 75 students.

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Answer:

∠ AED = 116°

Step-by-step explanation:

the measure of the chord- chord angle AED is half the sum of the measures of the arcs intercepted by the angle and its vertical angle , that is

∠ AED = \(\frac{1}{2}\) (AD + BC) = \(\frac{1}{2}\) (92 + 140)° = \(\frac{1}{2}\) × 232° = 116°

Answer:

A = 88 units²

Step-by-step explanation:

the area (A) of a trapezoid is calculated as

A = \(\frac{1}{2}\) h (b₁ + b₂ )

h is the height between the bases and b₁, b₂ are the bases

here h = 4 , b₁ = 17 + 5 + 5 = 27 , b₂ = 17 , then

A = \(\frac{1}{2}\) × 4 × (27 + 17) = 2 × 44 = 88 units²

Answer:1.) I chose coin A and B

2.) Coin: B Value: $40 Annual rate: %5

Coin: A Value: $25 Annual rate: %7

3.) Coin: A P: 25 R: 1.07 Function: v = 25(1.07)^t

Coin: B P: 40 R: 1.05 Function: v = 40(1.05)^t

4.) Base: 1+r Initial: P Exponent: t

If R increased, then P would also increase because you must distribute, and you would be distributing R into P there for if R changes then so would P.

5.) Coin A: Initial value: $25 10 years: $25.70 20 Years: $26.40 30 years: $27.10 60 years: $29.20

Coin B: Initial value: $40 10 years: $40.50 20 years: $41 30 years: $41.50 60 years: $43

Coin C: Initial value: $60 10 years: $60.40 20 years: $60.80 30 years: $61.50 60 years: $62.40

6.) Coin A because the value goes up the most and I probably wouldn't be able to keep the coin for more than 60 years because I would lose it.

Step-by-step explanation:

i did it

I also chose coin A and coin B. You can choose any two coins you want, but the answers would turn out different so I recommend using A and B.

Answer:

2.      

Coin: A                     Current value: $25                     Appriciation rate: 7%

Coin: B                     Current value: $25                     Appriciation rate: 5%

3.

Coin: A               P: 25                  R: 0.07                 V(t) = 25(1+0.07)^t

Coin: B               P: 40                  R: 0.05                 V(t) = 40(1+0.05)^t

4.a

Base: 1+R

Constant or initial value: P

Exponent: T

4.b

No, the initial value would not increase, although, by changing the rate would increase the growth.

5.

Value:          25                            

10 years:      V(t) = 25(1.07)^10   -   $49.18

See explaination

Step-by-step explanation:

5.

So when the value is 25, we use the formula from question 3 ( V(t) = 25(1.07)^10 ) and solve

Continue to use the same formula to answer the other numbers of years, only change the exponent, ^10, to the number of years.

For example:  20 years = ^20                 30 years = ^30 and so on.

Also, this is the correct answer to number 5. I got an A on this assignment

Hope this helps <333

Answer:

Step-by-step explanation:

The arcs that are congruent are:

Two geometric figures can be described as congruent if on can be superpose on the other.

Conclusively, congruent' is said to be a word that connote 'exactly equal' when looking at the shape and size of the angles. The options chosen above are congruent because they have the sides to be equal.

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The algebraic statement that is true is (c) (x²y - xz)/x² = (xy - z)/x

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

The algebraic statements

Next, we test the options

A/B + A/C = 2A/(B + C)

Take the LCM and evaluate

(AC + AB)/(BC) = 2A/(B + C)

This means that

A/B + A/C = 2A/(B + C) --- false

Next, we have

(a²b - c)/a² = b - c

Cross multiply

a²b - c = a²b - a²c

This means that

(a²b - c)/a² = b - c --- false

Lastly, we have

(x²y - xz)/x² = (xy - z)/x

Factor out x

x(xy - z)/x² = (xy - z)/x

Divide

(xy - z)/x = (xy - z)/x

This means that

(x²y - xz)/x² = (xy - z)/x --- true

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When the objective function coefficient for the product increases by $8, the impact on the current values of the optimal solution is that the current solution will change.

An objective function simply means the function whose value is to be either maximized or minimized over the alternatives.

In this case, when the objective function coefficient for the product increases by $8, the impact on the current values of the optimal solution is that the current solution will change. The change is due to the varied objectives.

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They are used in navigation, astronomy, and surveying. Rays are also used in computer graphics, physics, and optics. In addition, rays are used in the study of optics to describe the behavior of light as it travels through different mediums.

According to the video above, the geometric object called a ray has the characteristics that it has one endpoint and extends in away from that endpoint without end.A ray is a line that starts at a single point and extends in one direction to infinity. Rays are commonly used in geometry to explain lines and line segments. A ray has one endpoint, called the endpoint of the ray, from which it starts. The other end of the ray continues in the direction in which it is pointed without any limit. A ray is named by using its endpoint and another point on the ray, with the endpoint first. For example, if ray A starts at point P and passes through point Q, we write the name of the ray as ray PAQ or ray QAP. Rays can be part of line segments and other geometric objects. They can also be used to explain angles and the direction of a light source. Rays are commonly used in mathematics, science, and engineering.

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Answer:

Step-by-step explanation:

The time required for an account earning compound interest to achieve a particular balance is given by the formula ...

  t = log(A/P)/(n·log(1 +r/n))

where principal P is compounded n times per year at annual rate r. A is the account balance after that time. For this problem, n=1.

__

Here, we have ...

  P = $2000, A = $2500, r = 0.05, n = 1

The number of years is ...

  t = log(2500/2000)/log(1.05) ≈ 4.57 . . . years

__

For A = $3000, this becomes ...

  t = log(3000/2000)/log(1.05) ≈ 8.31 . . . years

The Answer:

The answer to the equation that Clare gets is:

X1= -3/2 + 7/2i , X2= -3/2 - 7/2i.

The Explanation:

4x^2+12x+58=0

2x^2+6x+29=0

a=2, b=6, c=29

The probability that at most 22 heads occur when a fair coin is tossed 25 times is 0.9313 (approximately).

When a fair coin is tossed, there are two possible outcomes: heads or tails. Since it is a fair coin, the probability of getting heads is equal to the probability of getting tails, which is 0.5. Therefore, the probability of getting a certain number of heads when the coin is tossed a certain number of times can be calculated using the binomial distribution formula.

P(X ≤ 22) = Σ P(X = i) for i = 0 to 22, where X is the random variable representing the number of heads obtained and P(X = i) is the probability of getting i heads in 25 tosses of a fair coin.

Using a binomial distribution calculator or a probability table, we can find that P(X = i) = (25 choose i) × 0.5^25 for i = 0 to 25. We can then add up the probabilities for i = 0 to 22 to get the probability that at most 22 heads occur:

P(X ≤ 22) = P(X = 0) + P(X = 1) + P(X = 2) + ... + P(X = 22)P(X ≤ 22) = Σ P(X = i) for i = 0 to 22P(X ≤ 22) = Σ (25 choose i) × 0.5^25 for i = 0 to 22Using a calculator or software, we can find that Σ (25 choose i) × 0.5^25 for i = 0 to 22 is approximately 0.9313.

Therefore, the probability that at most 22 heads occur when a fair coin is tossed 25 times is 0.9313 (approximately).

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Answer:

v=20π ft/s

Step-by-step explanation:

Given:

Distance from the security car to the movie theater, D=25 ft

Distance of the reflection from the car, d=30 ft

Speed of rotation of the strobe lights, 2 rev/s

To find the speed at which the reflection of the security strobe lights is moving along the wall of the movie theater, we need to calculate the linear velocity of the reflection when it is 30 ft from the car.

We can start by finding the angular velocity in radians per second. Since the strobe lights rotate at 2 revolutions per second, we can convert this to radians per second.

ω=2πf

=> ω=2π(2)

=> ω=4π rad/s

The distance between the security car and the reflection on the wall of the theater is...

r=30-25= 5 ft

The speed of reflection is given as (this is the linear velocity)...

v=ωr

Plug our know values into the equation.

v=ωr

=> v=(4π)(5)

∴ v=20π ft/s

Thus, the problem is solved.

The speed of the reflection of the security strobe lights along the wall of the movie theater is 2π ft/s.

To solve this problem, we can use the concept of related rates. Let's consider the following variables:

x: Distance between the security car and the movie theater wall

y: Distance between the reflection of the security strobe lights and the security car

θ: Angle between the line connecting the security car and the movie theater wall and the line connecting the security car and the reflection of the strobe lights

We are given:

x = 25 ft (constant)

y = 30 ft (changing)

θ = 2 revolutions per second (constant)

We need to find the speed at which the reflection of the security strobe lights is moving along the wall (dy/dt) when the reflection is 30 ft from the car.

Since we have a right triangle formed by the security car, the movie theater wall, and the reflection of the strobe lights, we can use the Pythagorean theorem:

x^2 + y^2 = z^2

Differentiating both sides of the equation with respect to time (t), we get:

2x(dx/dt) + 2y(dy/dt) = 2z(dz/dt)

Since x is constant, dx/dt = 0. Also, dz/dt is the rate at which the angle θ is changing, which is given as 2 revolutions per second.

Plugging in the known values, we have:

2(25)(0) + 2(30)(dy/dt) = 2(30)(2π)

Simplifying the equation, we find:

60(dy/dt) = 120π

Dividing both sides by 60, we get:

dy/dt = 2π ft/s

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Answer:

See Below.

Step-by-step explanation:

We want to prove that:

\(\displaystyle \sin^2 A + \sin^2 B \cdot \cos 2A = \sin^2 B + \sin^2 A \cdot \cos 2B\)

Recall that double-angle identity for cosine:

\(\displaystyle \begin{aligned} \cos 2x &= \cos^2x - \sin^2 x \\ &= 2\cos^2x -1 \\ &= 1 - 2\sin^2 x\end{aligned}\)

Substitute cos(2A) for its third form:

\(\displaystyle \sin^2 A + \sin^2 B \cdot \left(1 - 2\sin^2 A\right) = \sin^2 B + \sin^2 A \cdot \cos 2B\)

Distribute:

\(\displaystyle \sin^2 A + \sin^2 B - 2\sin^2B \sin^2A = \sin^2 B + \sin^2 A \cdot \cos 2B\)

Rewrite:

\(\displaystyle \sin^2 B + \left(\sin^2 A - 2\sin^2 B\sin^2 A\right)\)

Factor:

\(\displaystyle \sin^2 B + \sin^2A\left(1 - 2\sin^2 B\right) = \sin^2 B + \sin^2A\cdot \cos 2B\)

Double-Angle Identity for cosine:

\(\displaystyle \sin^2 B + \sin^2 A \cdot \cos 2B \stackrel{\checkmark}{=} \sin ^2 B + \sin^2 A\cdot \cos 2B\)

Hence proven.

Answer:

UT=17 because both UT and RU are the same length, same with QU and US

Step-by-step explanation:

The derivative dy/dx of the equation ysin(x^2) = xsin(y^2) is given by (sin(y^2) - ycos(x^2)2x) / (sin(x^2) - 2yxcos(y^2)).

In the given equation, y and x are both variables, and y is implicitly defined as a function of x. To find dy/dx, we differentiate each term using the chain rule and product rule as necessary.

Differentiating the left-hand side of the equation, we apply the product rule to ysin(x^2). The derivative of ysin(x^2) with respect to x is dy/dxsin(x^2) + ycos(x^2)*2x.

Differentiating the right-hand side of the equation, we apply the product rule to xsin(y^2). The derivative of xsin(y^2) with respect to x is sin(y^2) + x*cos(y^2)2ydy/dx.

Now we have two expression for the derivative of the left and right sides of the equation. To isolate dy/dx, we can rearrange the terms and solve for it.

Taking the derivative of ysin(x^2) = xsin(y^2) with respect to x using implicit differentiation yields:
dy/dxsin(x^2) + ycos(x^2)2x = sin(y^2) + xcos(y^2)2ydy/dx.

By rearranging the terms, we can solve for dy/dx:
dy/dx * (sin(x^2) - 2yxcos(y^2)) = sin(y^2) - y*cos(x^2)*2x.

Finally, we can obtain the value of dy/dx by dividing both sides by (sin(x^2) - 2yxcos(y^2)):
dy/dx = (sin(y^2) - ycos(x^2)2x) / (sin(x^2) - 2yxcos(y^2)).

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Answer: A number is a minimum of 6

Step-by-step explanation:

The < and > mean greater or less than. I learned these with this trick when I was little imagine they were mouths or maybe Pac-Man or something, the mouth would ways point to the bigger number. So here it means n is bigger than 6. When there is a line under the < or > it means it can also be equal to the number. SO this means n is equal to or bigger than 6 meaning the number of n is a minimum of 6.

Answer: x = 6, Angle ABC = 45, Angle DBC = 34

Step-by-step explanation:

79 = (5x + 4) + (8x - 3)

79 = 13x + 1

78 = 13x

x = 6

8x - 3      plug in 6 for x

8(6) - 3

Angle ABC = 45

5x + 4     plug in 6 for x

5(6) + 4

Angle DBC = 34

Answer: $56.25

Step-by-step explanation:

First, I'm going to assume that she makes 25% profit on the selling price.

Set the cost of the shirt as x. Profit is calculated as selling price - cost. Profit is stated to be 25% or \(\frac{1}{4}\), so an equation can be set up as:

\(\frac{1}{4} *75=75-cost\\\\cost = 75-\frac{1}{4} *75=56.25\)

The variance of the sample mean x = 7 is 18(option c).

Given table:

X          7  5  11   1   11

(x₁ - x)² 0  4  16 36 16​

n = number of observations = 5

Variance σ² = 1/n-1 Σ\(\ \ n} \atop {i=1} \right.\) (\(X_{1}\) - X)²

= 1/5-1 (0 +4 + 16 + 36 + 16)

= 1/4(72)

= 18

Therefore variance σ² = 18

Hence the variance of the sample mean x = 7 is 18.

so option c is correct.

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​

Answer:

The answer will always equal a positive when it comes to the n

Step-by-step explanation:

Step-by-step explanation:

please mark me as brainlest

Answer:

No

Step-by-step explanation:

People arent on brainly to do others work, they are here to help, NOT DO YOUR WORK

Resepect us more please. We stay on here just to help people. We take time out of our days to help people. So please dont make them do your work. They are here to help not be your personal servant.

Have a wonderful day! :)

Answer:

No

Step-by-step explanation:

I agree with Crankywolf, we are only here to help, not do your whole assignment just because your too lazy and dum to do it yourself

Bye :)