Six bags of trail mix are divided among 17 people, how much trail mix does each person recive?

None of the given options (A, B, C, or D) is a solution to sin x − cos 2x = 0 on the interval [0, 2π).

The solution of any trigonometric equation represents the value of the parameter which satisfies the given equation. The solution should lie within a given range and it should have the same value as ±π .

To find the solutions to sin x − cos 2x = 0 on the interval [0, 2π), we can start by using the identity cos 2x = 1 - 2sin² x, which gives:

sin x - (1 - 2sin² x) = 0

Simplifying this equation, we get:

2sin² x - sin x + 1 = 0

We can solve this quadratic equation using the quadratic formula:

sin x = [1 ± √(1 - 8)] / 4

sin x = [1 ± √(-7)] / 4

Since the square root of a negative number is not a real number, this equation has no real solutions. Therefore, none of the given options (A, B, C, or D) is a solution to sin x − cos 2x = 0 on the interval [0, 2π).

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10/9 is the number of regular polygons, each with interior angles measured in Pretti.

A regular polygon is described as  a polygon that is direct equiangular and equilateral. Regular polygons may be either convex, star or skew

9 degrees is equal to 10 Prettis (9° = 10P),  we then  set up a proportion to convert between degrees and Prettis:

9° / 10P = 1° / xP

9° * xP = 10P * 1°

9x = 10

x = 10 / 9

In conclusion, we considered the relationship between degrees and Pretti  in order to determine the number of regular polygons each of whose interior angles.

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\(revenue = selling \: price \times quantity \: sold\)

\(m(t) = 3t\)

#1

Because

revenue=sold price×no of items

#2

The restriction is of 75tickets and the tickets can't be negative

so

Domain

The coefficient for the interval -T ≤ x ≤ 0 in the function g(x) is 1. However, the coefficient for the interval 0 ≤ x ≤ 2π depends on the specific form of the function f(x). Without additional information about f(x), we cannot determine its coefficient for that interval.

To solve for the coefficients in the function g(x), we need to consider the conditions given:

g(x) = { 1, -1, -T ≤ x ≤ 0

{ 1, f(x + 2π) = g(x)

We have two pieces to the function g(x), one for the interval -T ≤ x ≤ 0 and another for the interval 0 ≤ x ≤ 2π.

For the interval -T ≤ x ≤ 0, we are given that g(x) = 1, so the coefficient for this interval is 1.

For the interval 0 ≤ x ≤ 2π, we are given that f(x + 2π) = g(x). This means that the function g(x) is equal to the function f(x) shifted by 2π. Since f(x) is not specified, we cannot determine the coefficient for this interval without additional information about f(x).

The coefficient for the interval -T ≤ x ≤ 0 is 1, but the coefficient for the interval 0 ≤ x ≤ 2π depends on the specific form of the function f(x).

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Answer:

$15.12

Step-by-step explanation:

got it on khan academy

Note that the coordinates of V after it has been reflected over the x-axis will be: V' (3, -5)

The coordinates given are

V (3, 5)

W(5,8)

X (9, 6)

y (3, 3)

When point is reflected over the x- ais, it's y - coordinate takes on a polarized sign that is it goes from positive to negative of vice versa while the x-cordinte remains the same

So after the image on point v hs been reflected, the new coordinates for V = V' = (3, -5)

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"Basketball players are generally taller.

Basketball player heights vary slightly more.

Step-by-step explanation:

I hope this helps!

Basketball players are taller because the average (mean) of basketball players is greater than soccer players.

Basketball player heights vary more because the MAD is greater or more than the soccer players."

We can see that the statement is not always true for any vectors u and v in V3.

The statement is not always true.

The cross product of vectors u and v in V3 is a vector that is orthogonal to both u and v. That is,

u x v ⊥ u and u x v ⊥ v

However, this does not necessarily mean that (u x v) * u = 0 for all u and v in V3.

For example, let u = <1, 0, 0> and v = <0, 1, 0>. Then,

u x v = <0, 0, 1>

(u x v) * u = <0, 0, 1> * <1, 0, 0> = 0

So in this case, the statement is true. However, consider the vectors u = <1, 1, 0> and v = <0, 1, 1>. Then,

u x v = <1, -1, 1>

(u x v) * u = <1, -1, 1> * <1, 1, 0> = 0

So in this case, the statement is also true. However, if we take the vector u = <1, 0, 0> and v = <0, 0, 1>, then

u x v = <0, 1, 0>

(u x v) * u = <0, 1, 0> * <1, 0, 0> = 0

So in this case, the statement is true as well.

However, if we take the vector u = <1, 1, 1> and v = <0, 1, 0>, then

u x v = <1, 0, 1>

(u x v) * u = <1, 0, 1> * <1, 1, 1> = 2

So in this case, the statement is not true.

Therefore, we can see that the statement is not always true for any vectors u and v in V3.

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Answer:

Step-by-step explanation:

For a point to be a solution to a system of inequalities, the points must make the signs of the inequalities true.

For example, the points must give results like 2<3 or 0>-2, these are true solutions. If the points gives 1>2, then that point is not a solution.

Answer:

yes

Step-by-step explanation:

every value of the domain only has one corresponding value

The information is not enough to prove that triangles DEF and OPQ are congruent through SAS, as we need two equal side lengths and one angle measure.

The Side-Angle-Side (SAS) congruence theorem states that if two sides of two similar triangles form a proportional relationship, and the angle measure between these two triangles is the same, then the two triangles are congruent.

The parameters given for this problem are given as follows:

As we are given only one side, instead of the two sides needed, we have that the information given is not enough to prove that the two triangles are congruent by the SAS congruence theorem.

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We are given the following picture

We are given the following statements

- Line BA is congruent to line OC

- Line ON is congruent to line DA

- Angle A is congruent to angle O

If we highlight the congruencies we get

where the matching colors indicate congruency. As we can see, we have a pair of sides that are congruent and the included angle are also congruent. This is the condition for the SAS theorem to apply. Hence both triangles are congruent by the SAS theorem

Answer:

Step-by-step explanation:

5ˣ⁺² = 5⁹

log₅(5ˣ⁺²) = log₅(5⁹)

x+2 = 9

x = 7

The unit rate of miles/hour taken by the van is 66.67 miles/hr.

Here given that,

The records of the trip of three vehicles are:

Van:500 miles in 7.5 hours

Truck:300 miles in 5 hours

Car:400 miles in 5.5 hours

We have to find unit rate miles/hour of the van.

So ,

Van covers 500 miles in 7.5hrs.

To find the unit rate,

Unit rate = total distance covered / total time taken

By substituting the values,

unit rate = 500/7.5

              = 66.67 miles/hr

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Answer:

            \(a_1=1\\a_n=a_{n-1}-5\)

Step-by-step explanation:

a₁ = 1 - 5(1 - 1) = 1 - 5·0 = 1

a₂ = 1 - 5(2 - 1) = 1 - 5·1 = 1 - 5 = a₁ - 5

a₃ = 1 - 5(3 - 1) = 1 - 5·2 = 1 - 5 - 5 = a₂ - 5

a₄ = 1 - 5(4 - 1)  = 1 - 5·3 = 1 - 5 - 5 - 5 = a₃ - 5

and so on, therefore:

Thus, Coordinates of image of points A', B' and C' are- A'(-6, 10), B'(-2, -8), C'(4 , -7)

A figure is transformed into a reflection by a transformational process. In a point, a line, or a plane, figures can be reflected. The image and preimage coincide when reflecting any symbol in a line or a point.

Given coordinates of points A, B and C

A(6, 10), B(2, -8), C(-4 , -7)

After reflection  (x, y) ---> (-x, y).

Thus,  Coordinates of image of points A', B' and C' are-

A'(-6, 10), B'(-2, -8), C'(4 , -7)

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Answer:

1) 48

2)44

Step-by-step explanation:

Answer:  48 44 Are The Correct Answers

Step-by-step explanation:Hope This Helps

Answer:

0.3904

Step-by-step explanation:

0.8^-3 = 0.8^1 - 0.8^4 = 0.8 - 0.4096 = 0.3904

Answer:

x=number1 and y=number2

product of the two numbers is 14 which translates to

xy=14

either x or y are 3.5 times big as the other one

so 3.5x=y

substituting in xy=14

x(3.5x)=14

\(3.5x^2=14\\x^2 =\frac{14}{3.5}=4\)

then x must be equal to 2 or -2

x+y=

by substituting

x+3.5x=

if x =2 then 2+7=9 or if x=-2 then -2-7=-9

The velocity of the cylinder when it reaches the bottom of the incline is v = sqrt(4gh/3).

The velocity of the cylinder when it reaches the bottom of the incline can be calculated using the principle of conservation of energy. The velocity of the cylinder is given by the formula v = sqrt(2gh/(1+I/(mr^2))), where g is the acceleration due to gravity, h is the height of the incline, and I is the moment of inertia of the cylinder.

In this case, the cylinder is released from rest at a height h on an incline without slipping, which means that all the potential energy at the top of the incline is converted to kinetic energy at the bottom of the incline. Therefore, we can write:

1/2 mv^2 = mgh

where v is the velocity of the cylinder at the bottom of the incline.

The moment of inertia of the cylinder is given as 1/2mr^2. Substituting this into the formula for v and simplifying, we get:

v = sqrt(2gh/(1+1/2)) = sqrt(4gh/3)

Therefore, the velocity of the cylinder when it reaches the bottom of the incline is v = sqrt(4gh/3).

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Therefore, Alvin's average paddling rate for a canoe trip to a campsite was 6 km/hr

Let's find out Alvin's average paddling rate for a canoe trip to a campsite.The distance Alvin paddled on the way to the campsite is the same as on the way back since he travelled to the same place and back to his initial location.

The rate at which Alvin paddled to the campsite is given by the relation;

r - 3 = (total distance)/(time taken to get to the campsite).

Where r is Alvin's average paddling rate, 3 is the speed of the river current, the total distance is D, and the time taken to get to the campsite is 9 hours.

On the way back, Alvin's rate of paddling is given by;

r + 3 = (total distance)/(time taken to get back from the campsite).

Where r is Alvin's average paddling rate, 3 is the speed of the river current, the total distance is D, and the time taken to get back from the campsite is 4 hours.Since the distance Alvin paddled to and from the campsite is the same, we can use D = rt.

Therefore, we can get an equation in r only:

r - 3 = D/9(r) + 3

r= D/4

Now, we need to solve for D. We can do this by setting both expressions equal to each other. That is:

r - 3 = r + 3D/9

r-3 = D/4(4)D/9

r-3= D/4

Multiplying both sides by 36 gives:

4D = 9D/4 * 36D

D= 81 km

Therefore, the distance of the campsite is 81 km.

Using D = rt,

we can find the average paddling rate r:

r = D/t

r = 81/(9 + 4) r

r = 6 km/hr.

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Answer:

Step-by-step explanation:

Write in slope-intercept form,

y=mx + b. − mowing, week, 20, 450

In the given scenario, an optical inspection system is used to classify different part types. The probability of a correct classification for any part is 0.98.

We are interested in determining the probability mass function (PMF) of the random variable x, which represents the number of parts correctly classified. Since the classifications are independent, we can use the binomial distribution to model this situation. The PMF of x is given by the binomial distribution formula: P(x) = C(n, x) * p^x * (1-p)^(n-x), where n is the number of parts inspected, p is the probability of correct classification (0.98), and C(n, x) represents the binomial coefficient.

To determine the probability mass function (PMF) of the random variable x, we use the binomial distribution formula. The binomial distribution is applicable in this case because the classifications of the parts are independent events and have a fixed probability of success (correct classification) for each trial.

The PMF of x, denoted as P(x), represents the probability of obtaining exactly x parts correctly classified out of the total number of inspected parts. It is calculated using the binomial distribution formula:

P(x) = C(n, x) * p^x * (1-p)^(n-x),

where n is the number of parts inspected, p is the probability of correct classification (0.98), C(n, x) is the binomial coefficient, and x takes on values from 0 to n.

The binomial coefficient C(n, x) represents the number of ways to choose x successes from n trials and is calculated as C(n, x) = n! / (x! * (n-x)!), where "!" denotes the factorial function.

By plugging in the given values, we can calculate the PMF for each possible value of x. For example, if three parts are inspected (n = 3), the PMF of x can be calculated for x = 0, 1, 2, and 3 using the formula above.

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The original amount Sara has left is 172/209

The calculation can be done as follows

Let y represent the amount left

9/11 × 836

= 7524/11

= 110

Y  can be calculated as follows

Y + 38 +110= 836

148 + Y= 836

Y= 836 - 148

Y= 688

Therefore the fraction is

688/836

= 172/209

Hence the fraction of the original amount left is 172/209


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is this a different language-

James will fully clear the loan after approximately 12 years when the remaining balance reaches zero.

To determine the number of years it will take for James to fully clear the loan, we need to calculate the remaining balance after each payment and divide the initial loan amount by the annual payment until the remaining balance reaches zero.

The loan amount is 9000 euros, and James pays off 770 euros each year. Since the interest is charged at a rate of 3% of the original amount per annum, the interest for each year will be \(0.03 \times 9000 = 270\) euros.

In the first year, James pays off 770 euros, and the interest on the remaining balance of 9000 - 770 = 8230 euros is \(8230 \times 0.03 = 246.9\)euros. Therefore, the remaining balance after the first year is 8230 + 246.9 = 8476.9 euros.

In the second year, James again pays off 770 euros, and the interest on the remaining balance of 8476.9 - 770 = 7706.9 euros is \(7706.9 \times 0.03 = 231.21\) euros. The remaining balance after the second year is 7706.9 + 231.21 = 7938.11 euros.

This process continues until the remaining balance reaches zero. We can set up the equation \((9000 - x) + 0.03 \times (9000 - x) = x\), where x represents the remaining balance.

Simplifying the equation, we get 9000 - x + 270 - 0.03x = x.

Combining like terms, we have 9000 + 270 = 1.04x.

Solving for x, we find x = 9270 / 1.04 = 8913.46 euros.

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The set s is linearly dependent.

Let us discuss the concept of linearly independent and dependent setsLinearly independent sets.

A set S = {v_1, v_2, ..., vn} of vectors in a vector space V is said to be linearly independent if the only solution of the equation a_1v_1+a_2v_2+⋯+a_nv_n=0 is a_1=a_2=⋯=a_n=0.

Linearly dependent set- A set S = {v_1, v_2, ..., v_n} of vectors in a vector space V is said to be linearly dependent if there exists a non-trivial solution of the equation a_1v_1+a_2v_2+⋯+a_nv_n=0 that is not all the scalars are 0. This equation is called a linear dependence relation among the vectors v_1,v_2,…,v_n.

Now let us come to the solution for the given problem;

Given set s = {(−2, 1, 3), (2, 9, −2), (2, 3, −3)}We have to check whether this set is linearly independent or dependent.For this we will assume that a_1(−2, 1, 3)+a_2(2, 9, −2)+a_3(2, 3, −3)=(0, 0, 0)or

(-2a_1+2a_2+2a_3, a_1+9a_2+3a_3, 3a_1-2a_2-3a_3)=(0, 0, 0)

On solving these equations we get,

a_1 = a_3,a_2 = -a_3

so, the set has infinitely many solutions other than a_1 = a_2 = a_3 = 0.

Therefore the given set s is linearly dependent.

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The expression for the inverse function f^-1(x) is:

\(`f^-1(x) = (x + 4)^(1/3)`\)

An inverse function or an anti function is defined as a function, which can reverse into another function. In simple words, if any function “f” takes x to y then, the inverse of “f” will take y to x. If the function is denoted by 'f' or 'F', then the inverse function is denoted by f-1 or F-1.

Given function is

\(f(x) = x³ - 4.\)

To find the inverse function, let y = f(x) and swap x and y.

Then, the equation becomes:

\(x = y³ - 4\)

Next, we will solve for y in terms of x:

\(x + 4 = y³ y = (x + 4)^(1/3)\)

Thus, the inverse function is:

\(f⁻¹(x) = (x + 4)^(1/3)\)

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