Engineers must consider the breadths of male heads when designing helmets. The company researchers have determined that the population of potential clientele have head breadths that are normally distributed with a mean of 6.5-in and a standard deviation of 1-in. Due to financial constraints, the helmets will be designed to fit all men except those with head breadths that are in the smallest 1.9% or largest 1.9%. a) What is the minimum head breadth that will fit the clientele? b) What is the maximum head breadth that will fit the clientele?

The value of r'(1) and s'(4) is 0 that can be interpreted with the help of the graph that is given in the question.

Derivative in mathematics, the rate of change of a characteristic with recognize to a variable. Derivatives are essential to the answer of troubles in calculus and differential equations. The essence of calculus is the by-product. The by-product is the immediately price of extrade of a characteristic with recognize to certainly considered one among its variables. This is equal to locating the slope of the tangent line to the characteristic at a point

\(r(x) = f(g(x))\)therefore the derivative of r is given by \(r'(x) = f'g(x)\times g'(x)\)

\(r'(1) = f'(g(1))\times g'(1)\) from the graphs

r'(1) = f'4 \times g'1 = (5/4) \times(0) = 0

Similarly s'(1) = g'(f(1))\times f'(1) from the graphs

 f(1)=1.5, f'(1)

=\dfrac{ (3-0)}{(0-2)}

= -3/2 , g'(3/2) = 0

s'(4) = g'(3/2) \times f'(4) = 0(-1.5) = 0

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Complete question:

let r(x) = f(g(x)) and s(x) = g(f(x)), where f and g are shown in the figure. find r'(1) and s'(4).

If r = 2 then substitute it for where r is in your given equation

New equation:

\(\dfrac{7(2)}{2}\)

\(\bf{7(2) = 14}\)

\(\dfrac{14}{2} = 7\)

\(\bf{Answer: 7}\) ☑️

Good luck on your assignment and enjoy your day!

\(\frak{LoveYourselfFirst:)}\)

The area of a regular octagon with sides 1/3 the length of sides of the larger octagon is 173.82 ft sq.

The area of a polygon = n side^2 / (4 tan(180/n))

where "n" is the number of sides

To calculate area for side = 2

area = 8 x 2^2 / (4  tan(180/8))

area = 32 / (4  tan(22.5))

area = 32 / 4 x 0.41421

area = 19.3138746047

To calculate area for side = 6

area = 8*6^2 / (4 * tan(180/8))

area = 288 / 1.65684

area = 173.824871442

173.824871442 / 19.3138746047 =  9

So, the area would be 9 times larger.

Therefore, if we increase the side length is increased by 1/3, then the area increases by 1/9.

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Answer:

y=-3x+6

Step-by-step explanation:

(y-y1)=m(x-x1)

m=(y2-y1)/(x2-x1)

m=(-3-6)/(3-0)

m=(-9)/(3)

m=-3

(choose whichever point for the first formula, i will be using(0,6))

(y-6)=-3(x-0)

y-6=-3x

y=-3x+6

ANSWER

EXPLANATION

To find the scale factor of the model to the sculpture, we have to divide one set of measurements of the model and sculpture.

Let us divide the length of the model by that of the sculpture:

That is the scale factor of the model to the real sculpture.

a. The flow is physically possible, b. The flow is rotational, c. The velocity potential function is φ(x,y) = x^2y - xt^2 + yt^2, d. The stream function is ψ(x,y) = x^2 - y^2 + 10xyt, e. The flow is not permanent.

a. The flow is physically possible because the velocity field is defined everywhere and is continuous.

b. The flow is rotational because the curl of the velocity field is not zero. The curl of the velocity field is given by:

curl(u,v) = (-2y + 20t, 2x - 20t, 0)

The curl is not zero because the z-component is not zero. This means that the flow has vorticity, which is a measure of how much the fluid is rotating.

c. The velocity potential function is given by:

φ(x,y) = x^2y - xt^2 + yt^2

The velocity potential function is a scalar field that can be used to calculate the velocity field. The velocity field can be calculated using the following formula:

u = -grad(φ)

v = -grad(ψ)

where φ and ψ are the velocity potential functions.

d. The stream function is given by:

ψ(x,y) = x^2 - y^2 + 10xyt

The stream function is a scalar field that can be used to calculate the streamlines of the flow. The streamlines are the curves that are tangent to the velocity field.

e. The flow is not permanent because the velocity field is not time-independent. The velocity field depends on the time variable t. This means that the flow will change over time.

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Answer:

x = 60.5

Step-by-step explanation:

ok this simple you already have the variable and the number on different sides

x2 = 121

divide each side by 2

x2 / 2 = x

121 / 2 = 60.5

x = 60.5

Answer:

60.5  

Step-by-step explanation:

    Divide 121 by 2, or just add 600.5 or multiply it by 2 and you get 121

The number of students that leave by bus or car is given as follows:

5801 students.

The union and intersection sets of multiple sets are defined as follows:

The or operation is equivalent to the union operation, meaning that we add the number of students that leave by bus to the number of students that leave by car.

Hence the number of students that leave by bus or car is given as follows:

3232 + 2549 = 5801 students.

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In an observational study, the statement that a cause and effect can be determined is false.

Observational studies simply establish associations between predictor and outcome variables. Observational studies cannot confirm that an association contemplates cause and effect.

In observational studies, confounding variables may explain an observed relationship between predictor and outcome variables.

In an observational study, a cause and effect cannot be determined. Observational studies are used to gather data about a particular population or phenomenon, but they do not allow for the determination of cause-and-effect relationships.

This is because observational studies do not control the variables that are being studied and, therefore, cannot determine the relationship between two variables.

In order to determine cause and effect, a controlled experiment is needed in which the variables are manipulated, and their effects are observed.

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We will prove the statement  \(n^n / 3^n < n!\)for n ≥ 6 by induction. The base case is n = 6, and we will assume the inequality holds for some k ≥ 6. Using the induction hypothesis, we will show that it also holds for k + 1. Thus, proving the statement for n ≥ 6.

Base case: For n = 6, we have 6⁶ / 3⁶ = 46656 / 729 ≈ 64. As 6! = 720, we can see that the statement holds for n = 6.

Inductive step: Assume that the inequality holds for some k ≥ 6, i.e.,

\(k^k / 3^k < k!.\) We need to show that it holds for k + 1 as well.

Starting with the left side of the inequality:

\((k + 1)^{k + 1} / 3^{k + 1} = (k + 1) * (k + 1)^k / 3 * 3^k\)

\(= (k + 1) * (k^k / 3^k) * (k + 1) / 3\)

Since k ≥ 6, we know that (k + 1) / 3 < 1. Therefore, we can write:

\((k + 1) * (k^k / 3^k) * (k + 1) / 3 < (k + 1) * (k^k / 3^k) * 1\)

\(= (k + 1) * (k^k / 3^k)\)

< (k + 1) * k!

= (k + 1)!

Thus, we have shown that if the inequality holds for k, then it also holds for k + 1. By the principle of mathematical induction, the statement

\(n^n / 3^n < n!\) is proven for all n ≥ 6.

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Mesh technology has been introduced at two levels: the device level, enabling devices to form local mesh networks, and more recently at the network level, where mesh networking spans larger areas and provides decentralized and robust connectivity options

Mesh technology has revolutionized the way devices communicate and form networks. Initially, mesh technology was introduced at the device level, enabling devices to create a local mesh network where each device acts as a node and can communicate with other devices in the network directly. This device-level mesh networking provides several advantages, such as increased range, improved reliability, and self-healing capabilities. It allows for seamless communication between devices, even if one or more nodes fail or are out of range, by automatically rerouting data through alternate paths in the network.

More recently, mesh technology has been extended to operate at the network level, introducing mesh networks on a larger scale. In this context, mesh networks refer to a decentralized network architecture where multiple interconnected devices create a network that spans a broader area. These networks typically consist of various access points, routers, and other devices that work together to form a mesh topology. By employing mesh networking at the network level, organizations and communities can create expansive wireless networks that cover large areas, such as campuses, cities, or even entire regions. This approach offers increased scalability, flexibility, and robustness compared to traditional centralized network architectures.

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Therefore, the volume of the paper cone to the nearest tenth is 418.7 inches cubed.

The volume of the paper cone that Gretchen made to hold a gift for a friend is given by;V= (1/3)πr²hWhere;r = radius of the paper coneh = height of the paper coneπ = 3.14

Given that;Height of the paper cone (h) = 16 inches Radius of the paper cone (r) = 5 inchesWe are to find the volume (V) of the paper cone to the nearest tenth of an inch.

To obtain the volume of the paper cone, we can substitute the values of r and h in the formula above to obtain;

\(V= (1/3)\pir^2hV\)= \((\frac{1}{3} ) \times 3.14\times5^2 \times16V = (\frac{1}{3} ) \times 3.14\times25\times16V = (\frac{1}{3}) \times 1256V=418.7\)

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Answer: 23

Step-by-step explanation:

Answer:

23

Step-by-step explanation:

=>2(3)^2+5(root(3-2))

=>2(9)+5(root(1))

=>18+5

=>23

Answer:

7/15

Step-by-step explanation:

For me, it is easier to take the 3/5 and put it in decimal form which is .6 and add the 5 to it, making 5.6, and then in a calculator put in 5.6 divided by 12 and you should get a big decimal that's pretty big but if you have a graphing calculator and convert that to a fraction and you should get 7/15, This is a pretty lazy way of me doing it but that's how I did it.

To find dy/dt, we can use implicit differentiation. Let's differentiate both sides of the given equation with respect to t:

For the equation xy² = 4,

Differentiation implicitly:

d/dt (xy²) = d/dt (4)

Using the product rule on the left side:

y² * dx/dt + 2xy * dy/dt = 0

Now we can substitute the given values: dx/dt = -5, x = 4, and y = 1.

Plugging in the values, we have:

(1²)(-5) + 2(4)(dy/dt) = 0

-5 + 8(dy/dt) = 0

8(dy/dt) = 5

dy/dt = 5/8

Therefore, when x = 4 and y = 1, dy/dt = 5/8.

The correct option is C) 5/8.  

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Answer:

8 and 4 = 8

8 and 10 = 40

Step-by-step explanation:

The least common multiple is the smallest value that both numbers equal when you look at their multiples.

The multiples of 8 are 8, 16, 24, 32, 40...

The multiples of 4 are 4, 8, 12, 16, 20, 24, 28, 32...

The multiples of 10 are 10, 20, 30, 40...

The first multiple 8 and 4 have in common is 8.

The first multiple 8 and 10 have in common is 40.

Answer:

Step-by-step explanation:

Angles 1 and 3 are same as vertical pair, they are also same with angles 5 and 7 for same reason.

Angle 8 is supplementary with angle 5, so:

m∠1 = m∠3 = m∠5 = 180° - 64° = 116°

Answer:

5=c

Step-by-step explanation:

c= number of camels

6-1=c

5=c

The seventh term of the given binomial expansion is; 15625

The binomial theorem states the expansion of (a + b)ⁿ as the sum of

n + 1 terms given by the binomial expansion formula that has the binomial coefficient as (n, k) = n!/((n - k)!(k!))

We are looking at the expression;

(x - 5)⁶

The objective is to evaluate the 7th term of the expansion.

Using the formula;

t_r + 1 = (n, r) * a^(n - r) * b^(r)

we can calculate the 7th term for n = 6, r = 6, a = x , b = −5.

t₇ = (6, 6) * x⁶⁻⁶ * (-5)⁶

t₇ = 15625

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Answer:

It is a reduction because it is smaller than the original one.

The scale factor is 1/3 because the dimensions of the dilated figure is 3 by 3 units, which is 1/3 of the dimensions of the original figure; 9 by 9 units.

Answer:

Reduction

Step-by-step explanation:

As size is decreased it's reduction

Take two sides

scale factor :-

Answer:

  -6, 1

Step-by-step explanation:

You want the real roots of the quadratic x^2 + 5x = 6.

The roots are easily identified from the factored form of the equation. The factors will involve the constants that have a sum of +5 and a product of -6.

  -6 = 6·(-1) = 3·(-2)

Sums of the factor pairs are 5 and 1. We will use the constants that have a sum of 5.

  x^2 +5x = 6 . . . . . . given

  x^2 +5x -6 = 0 . . . . . standard form

  (x +6)(x -1) = 0 . . . . . . . factored form

The zero product rule tells us that a product will be zero if and only if at least one of the factors is zero. To find the values of x, we set the factors equal to zero and solve for x.

  (x +6) = 0   ⇒   x = -6

  (x -1) = 0   ⇒   x = 1

  x = -6, or x = 1 . . . . . . . . roots of the quadratic

Answer:

5/1

Step-by-step explanation:

Answer:

5/1

Step-by-step explanation:

Answer:

A.

Step-by-step explanation:

Answer: No problem

Step-by-step explanation:

The area of a triangle is 1/2bh. We know the area, a, the base, b, and we are attempting to find the height, h. So, we simplify the area formula with the value of b and solve for h, given a.

1/2(6)h = 30
3h = 30

Isolate h.

3h/3 = 30/3
h = 10

Answer: 340.2

Step-by-step explanation:

The nine principles of inference are logical guidelines that let us draw reasonable conclusions from a set of assertions or propositions

So the nine principles of inference are logical guidelines that let us draw reasonable conclusions from a set of assertions or propositions. These guidelines are frequently used in mathematics, philosophy, and computer science to establish the veracity of claims or create new assertions from preexisting ones. These are the nine inference rules:

Modus Ponens (MP) states that if p implies q and p is true, q must also be true.

Modus Tollens (MT) states that if p implies q but q is untrue, then p is untrue.

Hypothetical Syllogism (HS): P implies R if and only if P implies Q and Q implies R.

Disjunctive Syllogism (DS): If p or q and p are both true, then q is true.

When adding (ADD), if p is true, p or q and these guidelines are frequently used in mathematics, philosophy, and computer science to establish the veracity of claims or create new assertions from pre existing ones. These are the nine inference rules.

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Answer:

answer would be A. The median is 3, is greater than the mean 2.

Step-by-step explanation:

the medial is 3 because it is in the middle while the mean is 2 because you add all them up and divide how many people there are. So 10 divided by 5 is 2.

The schedule is as follows:

T1 -> T2 -> T1 -> T3 -> T1 -> T2 -> T1.

To construct a schedule using the Earliest Deadline First (EDF) scheduling algorithm, we need to consider the execution time, period, and deadline of each task and assign them priorities based on their deadlines. The task with the earliest deadline will be scheduled first. Let's create a schedule for the given task set:

Task T1: Execution time (e) = 2 ns, Period (P) = 5 ns, Deadline (D) = 5 ns

Task T2: Execution time (e) = 4 ns, Period (P) = 7 ns, Deadline (D) = 7 ns

Task T3: Execution time (e) = 7 ns, Period (P) = 7 ns, Deadline (D) = 7 ns

We have a period of 22 ns, and we need to schedule these tasks within that period. Let's start with the task with the earliest deadline:

At time 0 ns: Execute T1 (2 ns)

At time 2 ns: Execute T2 (4 ns)

At time 6 ns: Execute T1 (2 ns)

At time 8 ns: Execute T3 (7 ns)

At time 15 ns: Execute T1 (2 ns)

At time 17 ns: Execute T2 (4 ns)

At time 21 ns: Execute T1 (2 ns)

This completes the execution of all tasks within the given period of 22 ns. The schedule is as follows:

T1 -> T2 -> T1 -> T3 -> T1 -> T2 -> T1

In this schedule, we have followed the EDF algorithm by selecting tasks based on their deadlines. The task with the earliest deadline is always scheduled first to meet the timing requirements of the system.

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Simplify (-2)² + 15 ÷ 3

Answer: 9

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