What is the definition of a relation?
An association between two sets of data
Ordered pairs where each x-value is paired with only one y-value
The rules applied to a number
A set of data with a defined rule

Answer:

$24.

Step-by-step explanation:

I multiplied 4 by 7 to get 28. Then I multiplied $28 by three weeks and got $84. Since $84 is more than I owe I subtracted $84 by $60 and got $24. I would give my friend $60 and keep $24. Hope this helps! Have a great day!

Answer:

Step-by-step explanation:

(28 : 7 + 6 : 3) × 1/2 =

(4 + 2) × 1/2 =

6 × 1/2 =

3

(multiplying by 1/2 means dividing by 2 in fact 1/2 = 0.5 and 6 x 0.5 = 3)

Answer:

The Fourier series of a periodic function f(x) with period 2L can be expressed as:

f(x) = a0/2 + Σ[n=1 to ∞] (ancos(nπx/L) + bnsin(nπx/L))

where

a0 = (1/L) ∫[-L,L] f(x) dx

an = (1/L) ∫[-L,L] f(x)*cos(nπx/L) dx

bn = (1/L) ∫[-L,L] f(x)*sin(nπx/L) dx

In this case, we have f(x) = 1 for 2k - 0.25 <= x <= 2k + 0.25, and f(x) = 0 otherwise. The period is 0.5, so L = 0.25.

First, we can find the value of a0:

a0 = (1/0.5) ∫[-0.25,0.25] 1 dx = 1

Next, we can find the values of an and bn:

an = (1/0.5) ∫[-0.25,0.25] 1*cos(nπx/0.25) dx = 0

bn = (1/0.5) ∫[-0.25,0.25] 1*sin(nπx/0.25) dx

Since the integrand is odd, we have:

bn = (2/0.5) ∫[0,0.25] 1*sin(nπx/0.25) dx

Using the substitution u = nπx/0.25, du/dx = nπ/0.25, dx = 0.25du/(nπ), we get:

bn = (4/nπ) ∫[0,nπ/4] sin(u) du = (4/nπ) (1 - cos(nπ/4))

Therefore, the Fourier series of f(x) can be written as:

f(x) = 1/2 + Σ[n=1 to ∞] [(4/nπ) (1 - cos(nπ/4))] * sin(nπx/0.25)

for 2k - 0.25 <= x <= 2k + 0.25, and f(x) = 0 otherwise.

Despite changing the vertices, the opposite sides and opposite interior angles of the parallelogram remain equal.

Parallelogram:

A parallelogram is a simple (non-self-intersecting) quadrilateral with two pairs of parallel sides. Opposite or opposite sides of a parallelogram have equal length, and opposite angles of a parallelogram are equal.The congruence of opposite and opposite angles is a direct consequence of the Euclidean parallel postulate, the Euclidean parallel The condition cannot be proved without resorting to the line postulate or one of its equivalent formulations.

By contrast, a quadrilateral with only one pair of parallel sides is a trapezoid in American English and a trapezoid in British English. The 3D version of a parallelogram is a cuboid.

Properties of Parallelogram:

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Answer:

false

Step-by-step explanation:

False.

Access supports a wide range of built-in functions and operators that can be used to create calculated fields. These functions and operators include mathematical functions (such as multiplication, division, exponentiation), string functions (such as concatenation, trimming, and formatting), date and time functions, aggregate functions (such as sum, average, count), and more.

In addition, Access also allows you to create user-defined functions using VBA (Visual Basic for Applications), which can be used to perform custom calculations on your data.

Therefore, the statement "the only calculated fields you can create in Access are those involving addition and subtraction" is false.

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Answer:

10 m.

Step-by-step explanation:

We have a triangle with hypotenuse h m (the rope's length) and one leg 16 -  8  = 8 m and the other 6 m.

So h^2 = 8*2 + 6^2 = 100

h = 10 m.

Answer:

−35.948187

Step-by-step explanation:

To solve the question we must know about the conservation of momentum.

According to the law of conservation of momentum, when two bodies collide with each other then their momentum is conserved if no external force acts on the system. therefore, the combined momentum of the two objects before collision will be equal to the combined momentum of the two objects after the collision.

the momentum of the two objects before the collision

                       = momentum of the two objects after the collision

The mass of the box is 0.30141 kg.

Given to us

Let the mass of the box be M.

Momentum before collision = Momentum after collision

\(mu_1 + Mu_2 = mv_1 + Mv_2\)

given, the box was stationary before the collision,

\(mu_1 + Mu_2 = mv_1 + Mv_2\\\\ mu_1 + 0 = mv_1 + Mv_2\\\\ mu_1 - mv_1 = Mv_2\\\\ M= \dfrac{mu_1 - mv_1}{v_2}\)

Substituting the values,

\(M= \dfrac{mu_1 - mv_1}{v_2}\\\\ M = \dfrac{(0.0427 \times 22.3) - (0.0427\times 11.5)}{1.53}\\\\ M = 0.30141\ kg\)

Hence, the mass of the box is 0.30141 kg.

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Approximately 9.5% of the racers did not complete the marathon.

The total of those who quit and those who were disqualified represents the number of runners who did not finish the marathon

Number who did not complete = 12 + 8 = 20

To find the percentage of racers who did not complete the marathon, we need to divide this number by the total number of racers who started the marathon (210) and multiply by 100

Percentage who did not complete is

= (20 / 210) x 100

= 9.523%

Rounding this to the nearest tenth of a percent gives us a final answer of 9.5%. Therefore, approximately 9.5% of the racers did not complete the marathon.

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The correct option is 'The domain of both functions is all real numbers'.

According to statement

Here, functions are f(x) = 5x and g(x) =5x

Since the domain of f(x) is, D= { x : x belongs to all real numbers.}

Therefore, Domain of f(x) is all real numbers.

Since f(x) and g(x) have the same value,

Therefore, Domain of g(x) is also the set of real numbers.

Now, range of f(x) is , R=  { 5x : x belongs to all real numbers.}

Therefore, Range of f(x) is all real numbers.

Range of g(x) is also all real numbers.

So, we can say by the above explanation, only option (1) is correct.

DISCLAIMER: The question was incomplete. Please find the full content below.

QUESTION

Keshawn is asked to compare and contrast the domain and range for the two functions.

f(x) = 5x

g(x) = 5x

Which statements could he include in his explanation? Check all that apply.

1. The domain of both functions is all real numbers.

2. The domain of f(x) is x > 5.

3. The domain of g(x) is x > 5.

4. The range of both functions is y > 5.

5. The range of f(x) is y > 0.

6. The range of g(x) is y > 0.

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the actual distance between Snake World and the International Space Center is 76 miles.

To find the actual distance in miles between Snake World and the International Space Center, we need to use the given scale of the map: 5 inches = 95 miles.

If 5 inches on the map represents 95 miles, we can set up a proportion to find the actual distance in miles for the measured length on the map.

Let's denote the actual distance in miles as "x".

According to the given scale, we have the proportion:

5 inches / 95 miles = 4 inches / x miles

We can cross-multiply to solve for x:

5 inches * x miles = 4 inches * 95 miles

Simplifying further:

5x = 380

Dividing both sides by 5:

x = 380 / 5

Calculating the value:

x = 76

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Answer:

575.71

Step-by-step explanation:

Year 1: 960 x .88 (100%-12%)=844.80

Year 2: 844.80 x .88 =743.424

Year 3: 743.424x.88=654.21

Year 4: 654.21 x .88=575.71

The magnitude of the resultant force is approximately 57.60 pounds, and the direction is approximately -85.24 degrees (measured counterclockwise from the positive x-axis).

To find the magnitude and direction of the resultant force when the three force vectors are added together, we can use vector addition.

Convert the angles to radians.

Angle of wolf 1 = 45 degrees = π/4 radians

Angle of wolf 2 = 90 degrees = π/2 radians

Angle of wolf 3 = 230 degrees = (230/180)π radians

Resolve the forces into horizontal and vertical components.

Horizontal component of wolf 1 = 150 * cos(π/4) ≈ 106.07 pounds

Vertical component of wolf 1 = 150 * sin(π/4) ≈ 106.07 pounds

Horizontal component of wolf 2 = 200 * cos(π/2) = 0 pounds

Vertical component of wolf 2 = 200 * sin(π/2) = 200 pounds

Horizontal component of wolf 3 = 300 * cos((230/180)π) ≈ -112.36 pounds

Vertical component of wolf 3 = 300 * sin((230/180)π) ≈ -248.69 pounds

Sum the horizontal and vertical components of the forces.

Horizontal component of resultant force = 106.07 + 0 - 112.36 ≈ -6.29 pounds

Vertical component of resultant force = 106.07 + 200 - 248.69 ≈ 57.38 pounds

Find the magnitude of the resultant force using the Pythagorean theorem.

Magnitude of resultant force = √((-6.29)^2 + (57.38)^2) ≈ 57.60 pounds

Find the direction of the resultant force using the inverse tangent function.

Direction of resultant force = atan(57.38 / -6.29) ≈ -85.24 degrees

Therefore, the magnitude of the resultant force is approximately 57.60 pounds, and the direction is approximately -85.24 degrees (measured counterclockwise from the positive x-axis).

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Answer:

Slope is -2

Step-by-step explanation:

rise/run

Hoep this helsp. Pls give brainliest.

The inverse of the function f(x) = 2x+1 is (x-1)/2.

The output of a function is returned by the inverse function, which also returns the initial value. Consider the inverse relationship between the functions f and g: f(g(x)) = g(f(x)) = x. The initial value is fetched via a function that is its inverse.

Given;

Function, f(x) = 2x + 1.

To find the inverse of the function:

First, let y = f(x)

That is,

y = 2x +1

Then, make x the subject of the equation

y = 2x + 1

To make x the subject of this equation:

First, subtract 1 from both sides

We get

y -1 = 2x

Now, divide both sides by 2.

x = (y-1)/2

Now, rewrite as f⁻¹(x) by replacing y by x.

That is,

f⁻¹(x)  =  (x-1)/2

Therefore, the inverse of the function f(x) is (x-1)/2.

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The area under the standard normal curve between z=â1.16 and z=â0.03 is 0.3663.

To find the area under the standard normal curve between z = -1.16 and z = -0.03, we will use the following steps:

1. Look up the z-values in the standard normal distribution table (or use a calculator or online tool that provides the corresponding probability values).
2. Subtract the probability value for z = -1.16 from the probability value for z = -0.03.
3. Round your answer to four decimal places.

Step 1: Look up the z-values in the standard normal distribution table.
- For z = -1.16, the corresponding probability value is 0.1230.
- For z = -0.03, the corresponding probability value is 0.4893.

Step 2: Subtract the probability values.
Area = P(-0.03) - P(-1.16) = 0.4893 - 0.1230

Step 3: Round the answer to four decimal places.
Area = 0.3663

So, the area under the standard normal curve between z = -1.16 and z = -0.03 is approximately 0.3663.

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Answer:

B 2x - 31 = -2x - 31 have exactly one solution

Step-by-step explanation:

Which of the following equations have exactly one solution?

Choose all answers that apply:

A 2x - 31 = 2x - 31

B 2x - 31 = -2x - 31

C 2x + 31 = 2x - 31

D 2x - 2 = 2x - 31

A. 2x - 31 = 2x - 31

2x-31=2x-31

Collect like terms

2x-2x= -31+31

0=0

Infinite number of solutions

B 2x - 31 = -2x - 31

2x - 31 = -2x - 31

Collect like terms

2x+2x=-31+31

4x=0

x=0

One solution

C 2x + 31 = 2x - 31

2x + 31 = 2x - 31

Collect like terms

2x-2x= -31-31

0= -62

No solution

D 2x - 2 = 2x - 31

2x - 2 = 2x - 31

Collect like terms

2x-2x= -31+2

0= -29

No solution

By applying the algebra concept, it can be concluded that p = 3x or p = 2 - 3x.

Algebra is a branch of mathematics that uses symbols and mathematical operations, such as addition, subtraction, multiplication, and division to solve problems.

We want to express p in terms of x of this equation:

9x² – 6x + 5 = p² – 2p + 5

First, we have to eliminate 5, so we have:

9x² – 6x = p² – 2p

Then we add 1 on each side, so we have:

9x² – 6x + 1 = p² – 2p + 1

       (3x - 1)² = (p - 1)²

            p - 1 = √(3x - 1)²

Thus the solutions are:

p - 1 = 3x - 1      ⇔     p = 3x

or

p - 1 = -(3x - 1)   ⇔     p = 2 - 3x

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Answer:

exactly 21 sets of 3/8 fit into 8

Step-by-step explanation:

Basically you just draw 8 boxes split them in 8ths and you end up with 21 sets of 3/8

The function f(x) = ( x + 7)³ - 8 will shift left 7 units along x axis and will shift down 8 units along y axis to its parent function g(x) = x³.

By translation, we can stretch, shrink and shift graphs along the x-y coordinate.

We know a parent function is a function that is in its simplest form without any translation.

Given f(x) = (x + 7)³ - 8 and its parent function is g(x) = x³.

Now let us break this function f(x),

f(x) = ( x+ 7)³ implies x + 7 = 0 ⇒ x = -7.

So, x will shift 7 units to the left along the x-axis.

f(x) = ( x + 7)³ - 8, This will shift the function down 8 units along y-axis.

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Answer:

The slope of line is

The point slope form is found when point (7, -4) is used is

The slope intercept form is

Solution:

We have to find the equation of the line that passes through the points 7, -4 and -1, 3

Point slope form:

The point slope form is given as:

Where "m" is the slope of line

Given two points are (7, -4) and (-1, 3)

Let us find the slope of line

Substituting

Thus slope of line is found

Substitute value of m and point (7, -4) in eqn 1

Thus the point slope form is found when point (7, -4) is used

Slope intercept form:

The slope intercept form is given as:

y = mx + c  ----- eqn 1

Where "m" is the slope of line and "c" is the y - intercept

Substitute m = -7/8 and (x, y) = (7, -4) in eqn 1

Substitute m = -7/8 and  in eqn 1

Thus the required equation of line is found

Step-by-step explanation:

Answer:

g(x) = [x/6]

Step-by-step explanation:

The given graph is f(x)=[x]

On stretching the function f(x) by a factor of 6, the new function g(x) is

g(x) = f(x/6)

So, g(x) = [x/6]

Hence, on stretching the f(x) by a factor of 6, the new function g(x)=[x/6].

Note that none of the given options matched.

The total surface area of the pyramid is: 208.88 m²

The surface area of the pyramid is simply the sum of the areas of all the given surfaces.

Formula for the area of a triangle is:

Area = ¹/₂bh

where:

b is base

h is height

Area of four side triangles = 4(¹/₂ * 8 * 12) = 192 m²

Using Pythagoras theorem, the height of the base triangle is:

x = 4.22

Area of base = ¹/₂ * 8 * 4.22 = 16.88 m²

Total surface area = 192 + 16.88

= 208.88 m²

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Answer:

$68.20

Step-by-step explanation:

Answer:

85$

Step-by-step explanation:

p = original price

68 = p - 20%p

68 = p - 0.20p

68 = 0.80p

85 = p

The original price was $85.

The original price is 100%. The sales price was 20% off - subtract. So the sale price was 100% - 20% = 80%.

Incase you wanna know how I came up with the 0.80p :)

The sequence contains the reciprocals of consecutive integers. Let's denote the nth term of the sequence as a_n, so a_n = 1/(n+3).

As n increases, the denominator of a_n increases, so a_n decreases. Therefore, the sequence is decreasing.

To determine whether the sequence converges or diverges, we need to find its limit.

We can use the squeeze theorem to determine the limit. Let b_n = 1/n, and c_n = 1/(n+2). Then b_n > a_n > c_n for all n.

We know that lim b_n = 0, and lim c_n = 0, since both b_n and c_n are reciprocals of terms that go to infinity.

Therefore, by the squeeze theorem, lim a_n = 0.

So the sequence converges to 0.

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Answer:

19.36

Step-by-step explanation:

First you figure out what 20% of 22 is, which is 4.4
Then you subtract 4.4 from 22, which gets you 17.6
Then you add 10% of 17.6, that 10% being 1.76
So you lastly add 1.76 to 17.6 which gets you 19.36.

Answer:

i'd say that it's -3 and since it is where it starts going up not sure if it's and option but if anything it's a pair it should be (1,-1)

Step-by-step explanation:

trust me I'm supposed to be a college student but i forgot most of the stuff :((( make me brainliest

Answer:

u =√6

v =√5

Step-by-step explanation:

u = √(1²+2²+1²) =√(1+4+1) = √6

v = √(1²+2²) =√(1+4) = √5

Answer:900

Step-by-step explanation:

8.1x10^9/9x10^6

step 1: make it turn into 81x10^8/9x10^6

step2: divide top and bottom by 10^6

81x10^2/9

step 3: divide top and bottom by 9

9x10^2 = 900