A group is planning its annual fund-raiser in which it raises money by selling pasta dinners. The group will charge $2.21 per serving of pasta. The expenses the group will incur are the cost of the pasta, $0.44 per serving, and the $318 cost of renting the facility for the evening. Find the associated cost, revenue, and profit function. What will be the resulting profit if they sell 99 servings of pasta? (Round to the nearest cent which is two decimal places. Do not include units or symbols.)

Answer:

y=-2x+5

Step-by-step explanation:

y=-2x+5

Answer:

It had two acute angles, two sides are the same so also an isosceles, and it also has a right angle, so right.

Step-by-step explanation:

Answer:

D and F are the right options.

Answer:

sin(100°) = 0.985

sin(-100°) = -0.985

Step-by-step explanation:

In a unit circle, each point (x, y) on the circumference corresponds to the coordinates (cos θ, sin θ), where θ represents the angle formed between the positive x-axis and the line segment connecting the origin to the point (x, y).

Therefore, sin(100°) equals the y-coordinate of the point (-0.174, 0.985), so:

\(\boxed{\sin(100^{\circ}) = 0.985}\)

Similarly, sin(-100°) equals the y-coordinate of the point (-0.174, -0.985), so:

\(\boxed{\sin(-100^{\circ}) = -0.985}\)

In the unit circle the value of sin (100) = 0.985 and the value of sin (-100) = -0.985, in three decimal places.

The value of the sine of the angles is calculated by applying the following formula as follows;

The value of sin (100) is calculated as follows;

sin(100°) corresponds to the y-coordinate of the point (-0.174, 0.985) as given on the coordinates of the unit circle.

sin (100) = 0.985

The value of sin (-100) is calculated as follows;

sin(100°) corresponds to the y-coordinate of the point (-0.174, -0.985), as given on the coordinates of the circle.

sin (-100) = -0.985

Thus, in the unit circle the value of sin (100) = 0.985 and the value of sin (-100) = -0.985, in three decimal places.

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Answer:

x=3

Step-by-step explanation:

The integral value of  ∫1/√(100-8x²) dx is 1/√8 sin⁻¹(√8x/10)+C

The given integral is ∫1/√(100-8x²) dx

We have to solve this integral by substitution method

Apply trigonometric substitution

\(=\int \frac{1}{2\sqrt{2}}du\)

\(=\frac{1}{2\sqrt{2}}\cdot \int \:1du\)

\(=\frac{1}{2\sqrt{2}}\cdot \:1\cdot \:u\)

Substitute \(u=\arcsin \left(\frac{2\sqrt{2}}{10}x\right)\) in the above integrand

\(=\frac{1}{2\sqrt{2}}\cdot \:1\cdot \arcsin \left(\frac{2\sqrt{2}}{10}x\right)\)

\(=\frac{1}{2\sqrt{2}}\cdot \:1\cdot \arcsin \left(\frac{2\sqrt{2}}{10}x\right)\)

Add the constant term C in the above answer

\(=\frac{1}{2\sqrt{2}}\arcsin \left(\frac{\sqrt{2}x}{5}\right)+C\)

When we simplify the above integral value we get

One by root eight sin inverse of root eight x by ten plus c

=1/√8 sin⁻¹(√8x/10)+C

Hence, the integral value of  ∫1/√(100-8x²) dx is 1/√8 sin⁻¹(√8x/10)+C

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Answer:

\(\textsf{A.} \quad \dfrac{1}{\sqrt{8}}\sin^{-1}\left(\dfrac{\sqrt{8}x}{10}\right)+\text{C}\)

Step-by-step explanation:

\(\boxed{\displaystyle \int \text{f}(x)\:\text{d}x=\text{F}(x)+\text{C} \iff \text{f}(x)=\dfrac{\text{d}}{\text{d}x}(\text{F}(x))}\)

If differentiating takes you from one function to another, then integrating the second function will take you back to the first with a constant of integration.

Given indefinite integral:

\(\displaystyle \int \dfrac{1}{\sqrt{100-8x^2}}\; \text{d}x\)

The derivative of the inverse sine function is:

\(\boxed{\dfrac{\text{d}}{\text{d}x}\left(\sin^{-1}(f(x))\right)=\dfrac{f'(x)}{\sqrt{1-(f(x))^2}}}\)

Therefore, to solve the given indefinite integral, we need to rewrite the function so that its denominator is in the form 1 - (f(x))²:

\(\begin{aligned}\dfrac{1}{\sqrt{100-8x^2}}&=\dfrac{1}{\sqrt{100\left(1-\frac{8x^2}{100}}\right)}\\\\&=\dfrac{1}{\sqrt{100}\sqrt{\left(1-\frac{8x^2}{100}}\right)}\\\\&=\dfrac{1}{10\sqrt{1-\frac{8x^2}{100}}}\\\\&=\dfrac{1}{10\sqrt{1-\left(\frac{\sqrt{8}x}{10}\right)^2}}\\\\ \end{aligned}\)

\(\textsf{Therefore,}\;\; f(x)=\dfrac{\sqrt{8}x}{10} \implies f'(x)=\dfrac{\sqrt{8}}{10}\)

Multiply the numerator and the denominator by f'(x):

                   \(\begin{aligned}&=\dfrac{1}{10\sqrt{1-\left(\frac{\sqrt{8}x}{10}\right)^2}} \cdot \dfrac{\dfrac{\sqrt{8}}{10}}{\dfrac{\sqrt{8}}{10}}\\\\&=\dfrac{\frac{\sqrt{8}}{10}}{\sqrt{8}\sqrt{1-\left(\frac{\sqrt{8}x}{10}\right)^2}}\end{aligned}\)

Therefore:

\(\displaystyle \int \dfrac{1}{\sqrt{100-8x^2}}\; \text{d}x=\int \dfrac{\frac{\sqrt{8}}{10}}{\sqrt{8}\sqrt{1-\left(\frac{\sqrt{8}x}{10}\right)^2}}\; \text{d}x\)

Take out the constant 1/√8:

                           \(=\dfrac{1}{\sqrt{8}}\displaystyle \int \dfrac{\frac{\sqrt{8}}{10}}{\sqrt{1-\left(\frac{\sqrt{8}x}{10}\right)^2}}\; \text{d}x\)

We have now rewritten the integral in the correct form to be able to integrate using:

\(\boxed{\displaystyle \int \dfrac{f'(x)}{\sqrt{1-(f(x))^2}}\;\text{d}x=\sin^{-1}(f(x))+\text{C}}\)

Therefore:

\(\displaystyle \dfrac{1}{\sqrt{8}}\int \dfrac{\frac{\sqrt{8}}{10}}{\sqrt{1-\left(\frac{\sqrt{8}x}{10}\right)^2}}\; \text{d}x=\dfrac{1}{\sqrt{8}}\arcsin\left(\dfrac{\sqrt{8}x}{10}\right)+\text{C}\)

Answer:

B is the correct answer

Step-by-step explanation:

You can use a graphing calculator to help with these kind of questions, Desmos is a good graphing calculator

The common ratio of a geometric sequence will be;

⇒ r = 5 / 10

What is Geometric sequence?

An sequence has the ratio of every two successive terms is a constant, is called a Geometric sequence.

Given that;

In a geometric sequence,

The third term is 100 and the eighth term is 3.125.

Now,

We know that;

The nth term of geometric sequence is,

⇒ \(T_{n} = a r^{n - 1}\)

Hence, The third term is;

⇒ \(T_{3} = a r^{3 - 1} = 100\)

⇒ \(a r^{2} = 100\)   ..(i)

And, The eighth term is,

⇒ \(T_{8} = a r^{8 - 1} = 3.125\)

⇒ \(a r^{7} = 3.125\)   ..(ii)

Divide equation (ii) by (i), we get;

⇒ ar⁷ / ar² = 3.125/100

⇒ r⁷ / r² = 3125 / 100000

⇒ r⁷⁻² = 3125 / 100000

⇒ r⁵ = 3125 / 100000

⇒ r = 5/10

Thus, The common ratio of a geometric sequence will be;

⇒ r = 5 / 10

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Answer:

3·6 - 21

Step-by-step explanation:

just replace x with 6

Inverse relationships between operations are used to solve two-step inequalities because they allow us to isolate the variable on one side of the inequality.

A two-step inequality involves two operations that need to be undone in reverse order to solve for the variable. Inverse relationships between operations are used to "undo" these operations, leading to an isolated variable.

For example, consider the inequality 2x + 5 > 11. The first operation being performed on x is multiplication by 2, and the second operation is adding 5. To solve for x, we need to undo these operations in reverse order.

The inverse relationship of multiplication by 2 is division by 2, and the inverse relationship of adding 5 is subtracting 5. Therefore, we can solve the inequality as follows:

2x + 5 > 11

2x > 6 (subtract 5 from both sides)

x > 3 (divide both sides by 2)

Here, we first subtracted 5 from both sides to undo the addition of 5, and then divided both sides by 2 to undo the multiplication by 2.

Inverse relationships between operations are used in two-step inequalities because they help to simplify the equation by undoing the operations one by one, leading to an isolated variable.

By using inverse relationships between operations, we can efficiently and systematically solve two-step inequalities and isolate the variable to find the solution set.

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They can buy 120 vans, 60 small trucks, and 80 large trucks.

The truck company plans to spend 10 million on 260 vehicles. Each commercial van cost 25,000 dollars. Each small truck 50,000 dollars and each large truck 50,000 dollars. They needed twice as many van as small truck

Therefore,

let

s = number of small truck

number of van = v

let

l = number of large truck

v + s + l = 260

25,000(v) + 50,000(s) + 50,000(l) = 10,000, 000

v + 2s + 2l = 400

Hence,

v = 2s

So,

2s + 2s + 2l = 400

4s + 2l = 400

2s + s + l = 260

3s + l = 260

2s + l = 200

s = 60

l = 200 - 2(60)

l = 200 - 120

l = 80

v = 2(600 = 120

Therefore, they can buy the following:

number of small truck = 60

number of van = 120

number of large truck = 80

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a)The value of acceleration will be 4.8 m/s²

b)The total distance travelled is 505 m.

a) As all the movement happens along a straight line, we need to define an axis only, which we call x-axis, being the positive direction the one followed by the car.

We can choose to place our origin at the location where the motorcycle was stopped at the side of the road (assuming that it is the same point  for the car when it passes him), so our initial position is 0.

We can also choose our time origin to be the same as the instant that the motorcycle starts from rest, so t₀ = 0.

With these assumptions, and assuming also that the acceleration is constant, we can write two equations, one for the car (at constant speed) and the another one for the motorcycle, as follows:

xc = vx*t

xm= 1/2*a*t²

When the motorcycle passes the car, both distances traveled from the origin will be equal each other, i.e., xc = xm :

⇒ vx*t = 1/2*a*t²

We have as givens vx=35 m/s and t = 14.5 sec when both equations are equal each other.

⇒ 35 m/s* 14.5 s = 1/2*a*(14.5)²(s)²

Solving for a:

a = (2* 35 m/s) / 14.5 s = 4.8 m/s²

b) Replacing the value of a in the equation for xm, we have:

xm = 1/2*4.8 m/s²* (14.5)²s² = 505 m.

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Answer:

I forget about these theorems and such, but pretty sure this is the Hypotenuse - Leg congruence theorem.

Step-by-step explanation:

As the name infers, you need the length hypotenuse and the length of one leg of each triangle. This is because you can use Pythagorean to find the last side, turning it into SSS congruence theorem. You also need them both to be right triangles for pythag to work.

Answer:what 2 triangles

Step-by-step explanation:Happy new year btw

Answer:

The answer is increased by 9

Step-by-step explanation:

Nope, it sure isn't, because both pairs of its opposite sides are not parallel.

Trapezoid IS NOT a parallelogram. A parallelogram is a given shape with BOTH pairs of its opposite sides are parallel.

Complete Question

Let x be a continuous random variable that follows a normal distribution with a mean of 550 and a standard deviation of 75.

a

Find the value of x so that the area under the normal curve to the left of x is .0250.

b

Find the value of x so that the area under the normal curve to the right ot x is .9345.

Answer:

a

  \(x = 403\)

b

 \(x = 436.75\)

Step-by-step explanation:

From the question we are told that

   The  mean is  \(\mu = 550\)

   The standard deviation is  \(\sigma = 75\)

Generally the value of x so that the area under the normal curve to the left of x is 0.0250 is mathematically represented as

     \(P( X < x) = P( \frac{x - \mu }{ \sigma} < \frac{x - 550 }{75 } ) = 0.0250\)

\(\frac{X -\mu}{\sigma }  =  Z (The  \ standardized \  value\  of  \ X )\)

     \(P( X < x) = P( Z < z ) = 0.0250\)

Generally the critical value of  0.0250 to the left  is  

       \(z = -1.96\)

=>    \(\frac{x- 550 }{75} = -1.96\)

=>    \(x = [-1.96 * 75 ]+ 550\)      

=>    \(x = 403\)

Generally  the value of x so that the area under the normal curve to the right of x is 0.9345 is mathematically represented as

        \(P( X < x) = P( \frac{x - \mu }{ \sigma} < \frac{x - 550 }{75 } ) = 0.9345\)

\(\frac{X -\mu}{\sigma }  =  Z (The  \ standardized \  value\  of  \ X )\)

     \(P( X < x) = P( Z < z ) = 0.9345\)

Generally the critical value of  0.9345 to the right  is  

       \(z = -1.51\)

=>    \(\frac{x- 550 }{75} = -1.51\)

=>    \(x = [-1.51 * 75 ]+ 550\)      

=>    \(x = 436.75\)

Answer:

h(x) = (x+8)^3

Step-by-step explanation:

1. Graph all of these options and h(x) = x^3

(Second one does not make sense: h(x) = 23-8 = 15

2. Answer is found

Answer:

h(x)= (x+8)3 answer C

Step-by-step explanation:

Answer:

8

Step-by-step explanation:

let x be the number , then

\(\frac{3}{4}\) x = 27 ( multiply both sides by 4 to clear the fraction )

3x = 108 ( divide both sides by 3 )

x = 36

the number is 36, so

\(\frac{2}{9}\) × 36 = 2 × 4 = 8

The two ninths of the number is 8

We know that Three quarters of a number is  \(\frac{3}{4}\)  times of a number

Hence we will assume the number x ,

                     \(\frac{3}{4} of x = 27\)

                     \(x = 27 X \frac{4}{3}\)

                       \(x = 36\)

Now as we know the number is 36

Therefore , the two ninths of the number assumed as y

We will multiply the number 36 by 2 and then divide by 9

Hence,

                           \(y = 36 X \frac{2}{9}\)

                               \(y = 8\)

Thus, the two ninths of the number 36  is 8                            

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If the length of the rectangle be (3x+2) units and width (4x+10)units then the area of the rectangle be \($x=-\frac{2}{3}, x=-\frac{5}{2}$$\).

The region enclosed by an object's shape is referred to as the area. The area of the shape is the area that the figure or any other two-dimensional geometric shape occupies in a plane.

A rectangle's sides determine its area. In essence, the length and breadth of the rectangle multiplied together gives the area of the rectangle.

Let the length of the rectangle be (3x + 2) units and width of the rectangle be (4x + 10)units.

Area of rectangle = length × breadth

= (3x +2) × (4x +10)

simplifying the above equation, we get

= (3x) × (4x +10) + 2(4x +10)

= 12x² + 30x +8x +20

12x² + 38x + 20 = 0

simplifying the above equation, we get

By using quadratic equation, then

\($x_{1,2}=\frac{-38 \pm \sqrt{38^2-4 \cdot 12 \cdot 20}}{2 \cdot 12}$$\)

simplifying the above equation, we get

\($$\begin{gathered}x_{1,2}=\frac{-38 \pm 22}{2 \cdot 12}\end{gathered}$$\)

Separate the solutions, we get

\($$\begin{aligned}& x_1=\frac{-38+22}{2 \cdot 12}, x_2=\frac{-38-22}{2 \cdot 12} \\& x=\frac{-38+22}{2 \cdot 12}:-\frac{2}{3} \\& x=\frac{-38-22}{2 \cdot 12}:-\frac{5}{2}\end{aligned}$$\)

The solutions to the quadratic equation are:

\($x=-\frac{2}{3}, x=-\frac{5}{2}$$\)

The complete question is:

Find the area of rectangle with length (3x+2) units and width (4x+10)units.

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The ordered triple representing \(3u - 2v\) is \((13, -8, 5)\).

To find an ordered triple representing \(3u - 2v\),

where \(u = (5, -2, 3)\) and \(v = (1, 1, 2)\),

we can perform the following operations:

\(3u = 3(5, -2, 3)\)

\(3u = (15, -6, 9)\)

\(2v = 2(1, 1, 2)\)

\(2v = (2, 2, 4)\)

Now, subtracting 2v from 3u gives:

\(3u - 2v = (15, -6, 9) - (2, 2, 4)\)

\(3u - 2v = (15-2, -6-2, 9-4)\)

\(3u - 2v = (13, -8, 5)\)

Therefore, the ordered triple representing 3u - 2v is (13, -8, 5).

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The value of x for each item is given as follows:

28. x = 5.

29. x = 3.44.

For item 28, we apply the crossing chord theorem, which states that the products of the parts of the chords are equal, hence the value of x is obtained as follows:

16x = 10 x 8

16x = 80

x = 5.

For item 29, we apply the two secant theorem, hence the value of x is obtained as follows:

10(x + 10) = 12(12 + 25)

10x + 100 = 444

10x = 344

x = 3.44.

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Answer:

b = (-4/5)a - (3/10)c

--------------

-2(8a + 10b) = 6c

8a + 10b = -3c

10b = -8a - 3c

b = (-8/10)a - (3/10)c

b = (-4/5)a - (3/10)c

Certainly! The problem can be solved using the Pythagorean theorem,

which states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

In this case, the ladder acts as the hypotenuse, and we need to find the length of the vertical side (height) it reaches up the wall.

The ladder forms the hypotenuse, and its length is given as 12 meters. The distance from the foot of the ladder to the base of the wall represents one side of the triangle, which is 4.5 meters.

By substituting the given values into the Pythagorean theorem equation: (12m)^2 = h^2 + (4.5m)^2, we can solve for the unknown height 'h'.

Squaring 12m gives us 144m^2, and squaring 4.5m yields 20.25m^2. By subtracting 20.25m^2 from both sides of the equation, we isolate 'h^2'.

We then take the square root of both sides to find 'h'. The square root of 123.75m^2 is approximately 11.12m.

Therefore, the ladder reaches a height of approximately 11.12 meters up the wall.

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Answer:

3x

Step-by-step explanation:

39*x / 13

39/13 * x

3*x

3x

Answer:

3x

Step-by-step explanation:

We are given the expression:

39*x /13

We want to simplify this expression. It can be simplified because both the numerator (top number) and denominator (bottom number) can be evenly divided by 13.

(39*x /13) / (13/13)

(39x/13) / 1

3x / 1

When the denominator is 1, we can simply eliminate the denominator and leave the numerator as our answer.

3x

The expression 39*x/13 can be simplified to 3x

The measures of the angles are JKN = 27 degrees and JNK = 126

The complete question is added as an attachment

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

The rectangle

On the rectangle, we have

JKN = NJK

Using the above as a guide, we have the following:

JKN = 27 degrees

Next, we use the sum of angles in a triangle theorem

The sum of angles in a triangle is 180

Mathematically, this is represented as

J + N + K = 180

So, we have the following representation

JNK = 180 - 27 * 2

Evaluate

JNK = 126

Hence, the measure of the angle JNK is 126 degrees

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Answer:

1 cubic meter equals 1000 liters

Step-by-step explanation:

i think this is right

The distance from the floor when t = 6.5 seconds is about 13.7 cm.

We are given that;

H(t)=A cos (Bt) +D

Now,

b. To write an equation of the form H(t) = A cos (Bt) + D for the graph, we need to find the values of A, B, and D.

A is the amplitude of the cosine function, which is half the difference between the maximum and minimum values of H(t). In this case, the maximum value is 36 and the minimum value is 12, so:

A = (36 - 12) / 2 A = 12

D is the vertical shift of the cosine function, which is the average of the maximum and minimum values of H(t). In this case:

D = (36 + 12) / 2 D = 24

B is related to the period of the cosine function, which is the time it takes for one complete cycle. In this case, the period is 8 seconds, because H(t) repeats its values every 8 seconds. The formula for B is:

B = 2π / period

So:

B = 2π / 8 B = π / 4

Therefore, the equation is:

H(t) = 12 cos (π/4 t) + 24

c. To find the distance from the floor when t = 6.5 seconds, we need to plug in t = 6.5 into the equation and evaluate H(t). Using a calculator, we get:

H(6.5) = 12 cos (π/4 × 6.5) + 24 H(6.5) ≈ 13.7

Therefore, by the equation answer will be 13.7 cm.

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Answer:

C: Lines r and s and lines t and u must be parallel.

Step-by-step explanation:

The true statement is (c) Only lines r and s must be parallel.

From the figure, we can see that:

Lines r and s point in the same direction, while lines t and u point in the same direction

If angle 8 = angle 10 and angle 1 = angle 7, then it means that:

Lines r and s must be parallel.

Line t and u may or may not be parallel.

Hence, the true statement is (c) Only lines r and s must be parallel.

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Answer:    50%

Step-by-step explanation:

Answer:

50

Step-by-step explanation:

50/100 = .5

.5*18 = 9

HOPE THIS HELPS

PLZZ MARK BRAINLIEST