What is negative 2/3 * 1/6

Answer:

Step-by-step explanation:

42)1.50/6=0.25

43)3/2=1.5

44)1x2=2

Answer:

42.) $0.25 per banana.

43.) 1.5 cakes per hour.

44.) 2 pounds of food per hour.

Step-by-step explanation:

42.)

\(\frac{Cost}{Amount}=\frac{1.50}{6}=0.25\)

43.)

\(\frac{Amount}{Time}=\frac{3}{2}=1.5\)

44.)

\(\frac{Amount}{Time}=\frac{1}{0.5}=2\)

The absolute maximum and minimum value of f on [π/4, 7π/4] are 2.1523 and -2.2160 respectively.

Given function is f(t) = t cot(1/2t) on [π/4, 7π/4].

To find the absolute maximum and minimum value of the given function f(t), let's follow the following steps:

Step 1: Find the critical numbers of f(t) on the given interval. Critical number is a number in the interval where the derivative is zero or undefined.

Step 2: Find the values of f(t) at the critical numbers, end points of the interval.

Step 3: Compare all the values found in Steps 1 and 2 to determine the absolute maximum and minimum of the function f(t) on the given interval.

1) First find the critical numbers of f(t) on the given interval:

Using the chain rule and product rule,differentiate

f(t) = t cot(1/2t)  w.r.t t :

f′(t) = cot(1/2t) – (t/2) csc^2(1/2t)

Critical numbers occur where f′(t) = 0 or is undefined.

Therefore, we solve cot(1/2t) – (t/2) csc^2(1/2t) = 0 ...[1]

Note that the function cot(1/2t) is defined on the interval [π/4, 7π/4] if and only if 1/2t ≠ kπ for integer k.

So, we solve [1] only for those values of t which are not multiple of π.

For simplicity, let's write x instead of 1/2t.

Now, we have, cot x - (2x)^-1 = 0i.e. cot x = 1/2x

Now, graph of cot x and y = 1/2x are shown below:

The x-coordinate of the intersection points of the two graphs are the solutions of the equation cot x = 1/2x.

There are two solutions on the interval [π/4, 7π/4]: x = 1.20256 and x = 5.44148

Therefore, the corresponding critical numbers t are t = 1/(2x) and t = 1/(2x) = 1.65214 and t = 11.01182 (approximate to five decimal places).

2) Now, find the value of f(t) at the critical numbers and end points of the interval:

f(π/4) = (π/4) cot(π/8)

≈ 0.76537f(7π/4)

= (7π/4) cot(7π/8)

≈ -0.76537

f(1.65214) = 1.65214 cot 0.82607

≈ 2.1523

f(11.01182) = 11.01182 cot 5.50591

≈ -2.2160

Therefore, absolute maximum of f(t) on the interval [π/4, 7π/4] is 2.1523 and it occurs at t = 1.65214.

Absolute minimum of f(t) on the interval [π/4, 7π/4] is -2.2160 and it occurs at t = 11.01182.

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Answer: y=4x+7

Step-by-step explanation: Parrallel lines have the same slope so you would plug in 4 as your slope (m) and 7 as the y-intercept (b) into the y=mx+b formula and get your answer

Answer:

The SF is 3

Step-by-step explanation:

The sides are 3x the length of the sides of ∆ABC

Answer:

y = - \(\frac{2}{7}\)x - \(\frac{32}{7}\)

Step-by-step explanation:

Find the slope with rise over run (y2 - y1) / (x2 - x1)

Plug in the points:

(-6 + 4) / (5 + 2)

-2/7

Then, plug in the slope and a point into y = mx + b to find b:

y = mx + b

-4 = -2/7(-2) + b

-4 = 4/7 + b

-4 4/7 = b

Then, plug in the slope and y intercept into y = mx + b

y = - \(\frac{2}{7}\)x - \(\frac{32}{7}\) will be the equation

Answer:

f(g(x)) = 2(7 - x) + 1

Step-by-step explanation:

f(x) = 2x + 1

g(x) = 7 - x

The question in the picture itself says to find f(g(x)) so i'll find that instead

f(g(x)) = 2(7 - x) + 1

f(g(x)) = 14 - 2x + 1

f(g(x)) = -2x + 15

The quadratic equation 2a^2 = -6 + 8a has two solutions: a = 3 and a = 1.

To solve the quadratic equation 2a^2 = -6 + 8a, we need to rearrange it into standard quadratic form, which is ax^2 + bx + c = 0, where a, b, and c are coefficients.

Step 1: Move all the terms to one side of the equation to set it equal to zero:

2a^2 - 8a + 6 = 0

Step 2: The equation is now in standard quadratic form, so we can apply the quadratic formula to find the solutions for 'a':

a = (-b ± √(b^2 - 4ac))/(2a)

Comparing with our equation, we have:

a = (-(-8) ± √((-8)^2 - 4(2)(6)))/(2(2))

Simplifying further:

a = (8 ± √(64 - 48))/(4)

a = (8 ± √16)/(4)

a = (8 ± 4)/(4)

Now, we can calculate the two possible solutions:

a1 = (8 + 4)/(4) = 12/4 = 3

a2 = (8 - 4)/(4) = 4/4 = 1

Therefore, the quadratic equation 2a^2 = -6 + 8a has two solutions: a = 3 and a = 1.

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Answer:

The goods will belong to the owner until all legal terms are met

Step-by-step explanation:

The ownership belongs to the owner and not the hirer, until the terms of the agreements are met the owner reserves all right to the goods, when all terms of the agreements are met the hirer will be the legal owner of the goods

Answer:998

Step-by-step explanation:

Answer:

0 ≤ t ≤ 18

Step-by-step explanation:

The cost of renting the boat without any discount is $8 per hour. However, Leila has a discount coupon for $3 off, so the effective cost per hour would be $8 - $3 = $5.

Let's assume Leila rents the boat for t hours. The total cost of renting the boat for t hours would be $5 multiplied by t, which is 5t.

According to the problem, Leila wants to spend at most $93. Therefore, we can set up the following inequality:

5t ≤ 93

This inequality represents the condition that the total cost of renting the boat (5t) should be less than or equal to $93.

Simplifying the inequality:

5t ≤ 93

Dividing both sides by 5 (since the coefficient of t is 5):

t ≤ 93/5

t ≤ 18.6

Since we cannot rent the boat for a fraction of an hour, we can round down the decimal value to the nearest whole number:

t ≤ 18

0 ≤ t ≤ 18

Answer: 0≤t≤12

Step-by-step explanation:

(I’m not sure if it’s 5 dollars off per hour, or total, but here’s what I did!)

If Leila has a $3 coupon, than she can spend +$3 because when you get a coupon, you can spend more, so 93+3 is equal to 96, now we just divide by 8 (because a boat costs $8 per hour) and we get 96/8=12.

Then, in inequality form it’s t≤12, because she can rent the boat for at most 12 hours, you could also do 0≤t≤12, because you can’t rent it for a negative amount of time, but either works.

Answer: b

Step-by-step explanation:

The given equation, 16x² - y² + 16z² = 4, represents a quadric surface known as an elliptic paraboloid.

To determine the classification, we can examine the coefficients of the squared terms. In this case, the coefficients of x², y², and z² are positive, indicating that the surface is bowl-shaped. Additionally, the signs of the coefficients are the same for x² and z², indicating that the bowl opens upward along the x and z directions.

The negative coefficient of y², on the other hand, means that the surface opens downward along the y direction. This creates a cross-section in the shape of an elliptical parabola.

Considering these characteristics, the given equation represents an elliptic paraboloid.

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Answer:

3. alternative interior angle

4. consecutive exterior angle

5. corresponding angle

6. consecutive interior angle

7. corresponding angle

8. alternative exterior angle

Step-by-step explanation:

since the braindead jacka** above was no help

Answer:

B

Step-by-step explanation:

the area of the triangle is  18 square units

Answer:

the third graph

Step-by-step explanation:

its the only one that has a y intercept of 3 and if you plug in each of the values of x it is correct

Answer:

y = 6x + 9

Step-by-step explanation:

y - 6x - 9 = 0

You haven't uploaded a picture of the solutions, but the function rearranged to make x the variable is:  y = 6x + 9

Answer:

f of x = 6 x + 9

Step-by-step explanation:

Edge

We need μ - 0.5σ^2 = 0, or equivalently:

μ = 0.5σ^2

In Example 5.4, we have the following:

The stock price at time t, St, is modeled as a geometric Brownian motion with constant drift and volatility, such that dSt = μSt dt + σSt dWt, where μ is the drift rate, σ is the volatility, and dWt is a Wiener process increment.

Taking the natural logarithm of both sides, we get d ln(St) = (μ - 0.5σ^2)dt + σdWt.

Letting Xt = ln(St), we have dXt = (μ - 0.5σ^2)dt + σdWt.

From the problem statement, we have that Xi = ei, where ei ~ N(0,1) for i = 1, 2, ..., n, where n is the number of time steps.

We want to find values of μ and σ such that Mn = exp(1/n Σi=1^n Xi) = exp(1/n Σi=1^n ei) = exp(1/n En) is a martingale, where En is the average of the N(0,1) random variables.

Using the fact that exp(a+b) = exp(a)exp(b), we have:

Mn+1 = exp(1/(n+1) Σi=1^(n+1) Xi) = exp(1/(n+1) Σi=1^n Xi)exp(Xn+1)

For Mn+1 to be a martingale, we need:

E[Mn+1 | Fn] = Mn

where Fn is the filtration up to time n. Since Xi are independent and identically distributed, we have:

E[Mn+1 | Fn] = E[exp(1/(n+1) En+1 + 1/(n+1) Σi=1^n ei) | Fn] = Mn exp(1/(n+1) E[en+1])

where en+1 ~ N(0,1). Note that E[en+1] = 0 and Var[en+1] = 1.

Thus, we need:

Mn exp(1/(n+1) E[en+1]) = Mn

or equivalently:

exp(1/(n+1) E[en+1]) = 1

Taking the logarithm of both sides, we get:

1/(n+1) E[en+1] = 0

or:

E[en+1] = 0

Therefore, we need μ - 0.5σ^2 = 0, or equivalently:

μ = 0.5σ^2

This is the same condition as in Example 5.4, which ensures that the lognormal stock prices follow a martingale.

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the answer is in the picture

The size of the angle PRQ is approximately 26.565 degrees.

Since PQ and QR are two sides of a regular 12-sided polygon, they are congruent, and the polygon can be divided into 12 congruent isosceles triangles with base PQ and QR.

Let's call the center of the polygon O. Since the polygon is regular, the angle POQ is 360/12 = 30 degrees. Also, since PR is a diagonal of the polygon, it divides angle POQ into two congruent angles, each measuring 15 degrees.

Now, let's consider the triangle PQR. We know that angle PQR is 180 - (15 + 15) = 150 degrees (since the sum of angles in a triangle is 180 degrees).

Using the Law of Cosines, we can find the length of PR:

PR² = PQ² + QR² - 2(PQ)(QR)cos(angle PQR)

PR² = PQ² + QR² - 2(PQ)(QR)cos(150)

PR² = PQ² + QR² + (PQ)(QR)

Since PQ = QR, we can simplify this to:

PR² = 2(PQ²) + PQ²

PR² = 3(PQ²)

Therefore,

PQ² = (1/3)(PR²)

Now, let's consider the triangle PRQ. We know that PQ is a side of the polygon, so it has length 1 (we can choose any unit of length we like). Also, we know that QR is a side of a regular 12-sided polygon, so we can use the formula for the side length of a regular polygon:

QR = 2PQsin(180/12) = PQ√(6 + 2sqrt(3))

Substituting PQ = 1, we get:

QR = √(6 + 2√(3))

Finally, we can use the Law of Cosines again to find the angle PRQ:

cos(angle PRQ) = (PQ² + QR² - PR²) / (2PQQR)

cos(angle PRQ) = (1 + 6 + 2√3) - PR^2) / (2√(6 + 2√(3)))

Substituting PR² = 3(PQ²) = 3, we get:

cos(angle PRQ) = (7 + 2√(3)) / (2√(6 + 2√(3)))

Taking the inverse cosine, we get:

angle PRQ = 26.565 degrees (to 3 decimal places)

Therefore,  the size of the angle PRQ is approximately 26.565 degrees.

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If the speed of the ball after kicking is 48 feet per second then the ball will return on the ground after 3 seconds.

Given that the speed of the ball after kicking is 48 feet per second and the function that represents the height of the ball is \(-16t^{2} +48t\).

We are required to find the time that the ball took to travel before returning the ground.

We know that speed is the distance a thing covers in a particular time period.

The height of the ball after t seconds is as follows:

h(t)=\(-16t^{2} +48t\)

It is at ground at the instants of t.

Hence,

\(-16t^{2} +48t\)=0

-16t(t-3)=0

We want value of t different of 0, hence :

t-3=0

t=3.

Hence if the speed of the ball after kicking is 48 feet per second then the ball will return on the ground after 3 seconds.

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Answer:

B. t=3

Step-by-step explanation:

i took the test and got it right

the probability of that there will be 2 defective items among them is 0.476 or 47.6%.

What is probability?

By simply dividing the favorable number of possibilities by the entire number of possible outcomes, the probability of an occurrence can be determined using the probability formula. Because the favorable number of outcomes can never exceed the entire number of outcomes, the chance of an event occurring might range from 0 to 1. Calculating the possibility of an event occurring is the focus of the math discipline of probability. Probability gauges the likelihood of an event occurring.

there are 4 defective items in a lot consisting of 10 items.

from this lot we select 5 items at random.

The number of ways in which 55 items can be selected 10 C 5 = 252.

Number of ways in which 2 defective systems and 3 non-defective systems can be selected

4C2 * 6C3 = 6*20=120

The probability = 120 / 252 = 0.476

Hence the probability of that there will be 2 defective items among them is 0.476 or 47.6%.

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Answer:

\(I=\frac{E}{R}; R\neq 0\)

Step-by-step explanation:

\(E=IR\\\\IR=E\\\\\frac{IR=E}{R}\\\\ \boxed{I=\frac{E}{R}; R\neq 0}\)

Hope this helps.

This is a linear recurrence relation, which can be solved using various techniques like characteristic equation, generating function, or matrix method. The general formula for the nth term of the sequence is 4an-2 - 3an-3

The given sequence is defined by a recursive Formula where the first term is a1 = 3 and the nth term is given by the formula 2an+1 - an-1. To find the value of a2, we need to substitute n = 2 in the formula, which gives:

a2 = 2a2+1 - a0

As a0 is not given, we cannot find the exact value of a2. Similarly, to find the value of a3, we need to substitute n = 3 in the formula, which gives:

a3 = 2a4 - a2

Again, we cannot find the exact value of a3 without knowing a4. However, we can find the general formula for the nth term of the sequence using the recursive formula. By repeatedly substituting the formula for an+1 into the formula for an, we get:

an = 2an-1 - an-2
      = 2(2an-2 - an-3) - an-2
      = 4an-2 - 3an-3

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Answer:

i dont know

Step-by-step explanation:

But can you just like it cause im trying get enough points to be able have a hundred points so i could have help with a college essay

please

Answer:

D

Step-by-step explanation:

   (1/3) / 8

= (1/3) * (1/8)

=1/24

Answer:

D

Step-by-step explanation:

Two angles form a linear pair.

so, the sum of the angles are 180

the measure of the angles are z and (2.4 * z + 10)

so,

z + (2.4 * z + 10) = 180

solve for z

so,

z + 2.4 * z + 10 = 180

3.4 z = 180 - 10

3.4 * z = 170

divide both sides by 3.4

so, z = 170/3.4 = 50

so, the angles are 50 and 130

Answer:

(C) 1/4 of the pie.

Step-by-step explanation:

Given that Fernando had 3/8 of a pumpkin pie left.

So, the remaining pie= 3/8 of a pie.

As Fernando ate 2/3 of the remaining pie, so,

the portion of a pie that Fernando ate = 2/3 x 3/8 of a pie = 1/4 of a pie.

So, Fernando ate 1/4 of a pie.

Hence, option (C) is correct.