Suppose that the demand function for a product is given by ​D(p)equals=StartFraction 50 comma 000 Over p EndFraction 50,000 p and that the price p is a function of time given by pequals=1.91.9tplus+99​, where t is in days. ​a) Find the demand as a function of time t. ​b) Find the rate of change of the quantity demanded when tequals=115115 days. ​a)​ D(t)equals=nothing ​(Simplify your​ answer.)

Answer:

The answer is A.

Step-by-step explanation:

it isn't possible to just give extra points in a simple and reliableway. anyways, let's starts.

a. is simple, just put the terms in order

r² +6r -5

because:

\( {r}^{2} + {6r}^{1} + {5r}^{0} \)

anything to the power of 0 equals 1,

because it's the same as r/r, and 5 * r/r = 5*1

b. same logic as above

a²b² -5ab +33

c.

-c³ +ab +d +9

d.

-9y^5 - 2x³y²z +4x² +10x +1

^5 = to the power of five, it's the fastest way to type it without the special math input tool.

hope it helps you

Answer:

I agree with the above one.

Answer:

21.77

Step-by-step explanation:

Applying,

V = (4/3)π(R²-r²)³/²................. Equation 1

Where  V = Volume of the resultant shape, R = radius of the sphere, r = radius of the hole bored, π = pie

From the question,

Given: R = 2, r = 1

Constant: π = 3.14

Substitute these values into equation 1

V = 4/3(3.14)(2²-1²)³/²

V = (12.56/3)(3)³/²

V = 4.19(5.196)

V = 21.77

Answer:

the answer for y=4 and x=4✔3

Answer:

Starting with the equation:

(x + 1)^2 = 13/4

We can use the square root property, which states that if a^2 = b, then a is equal to the positive or negative square root of b.

Taking the square root of both sides, we get:

x + 1 = ±√(13/4)

Simplifying under the radical:

x + 1 = ±(√13)/2

Now we can solve for x by subtracting 1 from both sides:

x = -1 ± (√13)/2

Therefore, the solutions to the equation are:

x = -1 + (√13)/2 or x = -1 - (√13)/2

Step-by-step explanation:

Answer:

(12+2)(15+3)(9+4)(2+5)-48

=4

Answer:

4.4 ounces/ 4 ounce (if rounded)

Step-by-step explanation:

There are 16 ounces in a pound, therefore the equation 12/16 will be useful since 16 ounces in a pound can be divided by 12, in conclusion 12/16=0.75 which is how much an ounce costs.

Then you will take $3.30 and divide it by 0.75 to get your answer for how many ounces you can buy for $3.30 which will equal 4.4 ounces but if you were to round it would be 4 ounces

Hope this helps!

1. The x - intercepts of the parabola are

2. The meaning of the x-intercepts are the plane takes of at x = 2.5 s and lands at x = 7.5 s

3. The vertex of the parabola is at (5, 80).

A parabola is a curved shape

1. Given the parabola above, to find the x - intercepts, we proceed as follows.

The x-intercepts are the points at which the graph cuts the x-axis.

They are

2. The meaning of the x-intercepts in this problem are the points where the plane takes off and lands on the ground.

The plane takes of at x = 2.5 s and lands at x = 7.5 s

3. The vertex is the maximum point on the graph.

So, we see that the vertex is at x = 5 s and y = 80 ft

So, the vertex is at (5, 80).

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Answer:

Hope this helps! <3

( Pic Below )

Answer:

800+90+4

Step-by-step explanation:

800+90=890 and 890+4=894

HOPE THIS HELPS

Answer: 42 in all, 14 of each.

Step-by-step explanation

The color with the least amount of balloons is orange with 14. this means to have an equal amount of balloons for each color, you would need 14 of each color.

Answer:

42

Step-by-step explanation:

Answer:

(a) The average baggage-related revenue per passenger is $15.70.

(b) The standard deviation of baggage-related revenue is $19.95.

(c) The expected revenue for 120 passengers is $1,884.

Step-by-step explanation:

Let the random variable X represent the baggage-related revenue per passenger.

It is provided that the baggage fees is $25 for the first bag and $35 for the second.

The probability model is:

    X :   0         25      60

P (X) : 0.54    0.34    0.12

(a)

Compute the average baggage-related revenue per passenger as follows:

\(E(X)=\sum {X\times P (X)}\)

         \(=(0\times 0.54)+(25\times 0.34)+(60\times 0.12)\\\\=0+8.50+7.20\\\\=15.70\)

Thus, the average baggage-related revenue per passenger is $15.70.

(b)

Compute the standard deviation of baggage-related revenue as follows:

\(E (X^{2})=\sum X^{2}\times P(X)}\\\\=(0^{2}\times 0.54)+(25^{2}\times 0.34)+(60^{2}\times 0.12)\\\\=0+212.50+432\\\\=644.5\\\)

\(SD(X)=\sqrt{E(X^{2})-(E(X))^{2}}\)

           \(=\sqrt{644.5-(15.7)^{2}}\\\\=19.950188\\\\\approx 19.95\)

Thus, the standard deviation of baggage-related revenue is $19.95.

(c)

Compute the expected revenue for 120 passengers as follows:

\(E(R)=n\times E(X)\)

        \(=120\times 15.7\\\\=1884\)

Thus, the expected revenue for 120 passengers is $1,884.

Answer:

Answer is (A.)

Step-by-step explanation:

Answer:

(A)

Step-by-step explanation:

Answer:

(x,y) = (25,15)

Step-by-step explanation:

In a parallelogram, alternate angles are equal, so

\(\left \{ {{3x-8=4y+7} \atop {4x+13=5x-12}} \right.\)

From the latter equation we obtain \(x= 13 + 12 = 25\). So substituting in the former equation gives

\(75-8 = 4y + 7\\4y = 60\\y = 15\)

Answer:

The graph will shift 3 units down

Answer: J = 33

Step-by-step explanation:

the corner of the triangle is 90 degrees so

90 + 57 = 147

Now the rest is 33 degrees.

Since it'll equal to 180 degrees.

Answer:

It's 33 degree

explanation:

Two triangles are similar so

angle K is equal angleQ=90DEGREE

ANGLE J=AngleP=33

Answer:

x=-3; x=4

Step-by-step explanation:

first, you should bring 12 to the other side, so subtract both sides by 12.

it would look like this:

x^2 - x - 12 = 0

next, you want to factor it out.

it would become

(x+3)(x-4) = 0

then, you can remove the parenthesis and create two separate equations:

x+3 = 0 ; x-4 = 0

then solve for x for both equations.

x=-3; x=4

hope this helped!! lmk if you have any questions about my work.

Answer:

Option 4

Step-by-step explanation:

                h = x units

   diameter = x units

                 r = (x/2) units

    \(\sf \boxed{\text{ \bf Volume of cone = $\dfrac{1}{3} \pi r^2h$}}\)

                                   \(\sf =\dfrac{1}{3}*\pi * (\dfrac{x}{2})^2*x\\\\=\dfrac{1}{3}*\pi*\dfrac{x^2}{4}*x\\\\=\dfrac{1}{12}\pi x^3\)

Answer:

9cm

Step-by-step explanation:if im wrong sorry

Answer:

4 nights

Step-by-step explanation:

use the equation

y = 100x + 35

substitute y for 500

500 = 100x + 35

solve for x

465 = 100x

x = 4.65

so based on the situation he could only stay 4 nights

Answer:

Step-by-step explanation:

C

The lines are have one solution and are consistent and Independent.

Gaining values for x and y allows us to determine whether the pair of linear equations is consistent or inconsistent. The system is consistent if x and y both have the same value. When there are no x and y values that fulfil both equations, the system becomes inconsistent.

Given:

y = 0.5x

2y = x + 4

Now solving the Above Equation

2(0.5x) = x+ 4

x = x+ 4

0 = 4

and, \(a_1= 0.5, b_1= -1, c_1= 0\\a_2= 1, b_2 = -2, c_ 2 = 4\)

Now, \(a_1/ a_2 = b_1/ b_2\neq c_1/ c_2\)

Then, the lines are have one solution and are consistent and Independent.

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Answer:

1.9 gallons of 80% and 5.7 gallons of 20%

Step-by-step explanation:

x gallons of 80% alcohol solution is mixed with y gallons of 20% alcohol to make 7.6 gallons of 35% alcohol solution.

Based on the given, we get two equations:

Let's substitute y with y = 7.6 - x:

Then we find the value of y:

So the answer is:

Answer:

1.9 gallons of the 80% solution.

5.7 gallons of the 20% solution,

Step-by-step explanation:

Let the volumes of the 80% and 20 % solutions be x  and y gallons.

Then:

x  +  y = 7.6.

Also, using amounts of pure alcohol:

0.8x + 0.2y = 7.6 * 0.35

0.8x + 0.2y = 2.66           Multiplying this equation by -5:

-4x - y = - 13.3                   Adding this to the first equation:

-3x = -5.7

= 1.9 gallons.

y = 7.6 - 1.9

=  5.7  gallons.

The equation to find Shanti's age is y = x - 3 where y is Shanti's age.

Given,

Shanti's sister Uri is Shanti's age plus 3 years.

Uri is 7 years old.

We need to write an equation to find Shanti's age.

We have,

Uri age = Shanti age + 3______(1)

Uri = 7 years old

Putting in (1)

We get,

Uri age = Shanti age + 3

7 = Shanti age + 3

Subtracting 3 on both sides.

7 - 3 = Shanti age + 3 - 3

4 = Shanti age

We see that Shanti's age is 4 years old.

If we have to write an equation then,

Consider Uri's age to be x and Shanti's age to be y.

Now,

Uri age = Shanti age + 3

x = y + 3

Subtracting 3 on both sides

x -3 = y

y = x - 3 is our equation.

Thus the equation to find Shanti's age is y = x - 3.

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Answer:

The answer is "Cannot determine from the information given".

Step-by-step explanation:

Please find the image file in the attachment.

Its positive correlation is nothing but the dependent share changes whenever we increase its different variables, and then we can say the situation is non-linear, though decrease or increase can occur. Likewise, the dependent variable as well decreases because once we decrease the independent variable.

Answer:

  7. P(q) = 60 -0.03(x -80)²

  8. P(q) = -0.03x² +4.8x -132

  9. q = 35 balloons

  10. see attached

Step-by-step explanation:

You want the profit equation, break-even sales, and a graph for a party supply company that makes a maximum profit of $60 when they sell 80 balloons, and a profit of $33 when they sell 50 balloons.

If the profit is described by a quadratic equation with a maximum at (quantity, dollars) = (80, 60), and a point on the curve of (50, 33), we can write the equation in two steps.

The vertex-form equation will look like ...

  P(q) = 60 -a(q -80)² . . . . . for some scale factor 'a'

We want P(50) = 33, so we have ...

  P(50) = 33 = 60 -a(50 -80)²

  33 = 60 -900a

  a = (60 -33)/900 = 3/100 = 0.03

The profit equation is ...

  P(q) = 60 -0.03(q -80)²

Expanding the equation gives ...

  P(q) = 60 -0.03(q² -160q +6400)

  P(q) = -0.03q² +4.8q -132

The profit is zero at ...

  P(q) = 0 = 60 -0.03(q -80)²

  0.03(q -80)² = 60

  (q -80)² = 2000 . . . . . . . . divide by 0.03

  q = 80 ±20√5 = 35.3 or 124.7 . . . . . take the square root, add 80

The store will no longer make a profit when sales drops to 35 balloons.

The attachment shows a graph of the profit function.

__

Additional comment

You can find where the profit goes to zero using the graph, the quadratic formula, or by solving it using vertex form, as above. The graph is quick and easy; using the vertex form equation works nicely.

Selling 36 balloons will result in a profit of $1.92.

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The amount invested at 3% is $400, the amount invested at 4% is $700, and the amount invested at 5% is $1000.

Let's assume the amount invested at 4% is x dollars.

According to the given information, the amount invested at 5% is $1000 more than the amount invested at 4%.

So, the amount invested at 5% is (x + $1000).

The total amount invested is the sum of the amounts invested at each rate, which is $2100.

Therefore, we can write the equation:

x + (x + $1000) + (amount invested at 3%) = $2100

Now, we can calculate the amount invested at 3%.

We subtract the sum of the amounts invested at 4% and 5% from the total investment:

(amount invested at 3%) = $2100 - (x + x + $1000) = $2100 - (2x + $1000)

Given that Elena receives $95 per year in simple interest from the investments, we can use the formula for simple interest:

Simple Interest = Principal × Interest Rate

The interest earned from the investment at 3% is (amount invested at 3%) × 0.03, the interest earned from the investment at 4% is (amount invested at 4%) × 0.04, and the interest earned from the investment at 5% is (amount invested at 5%) × 0.05.

According to the problem, the total interest earned is $95.

So we can write the equation:

(amount invested at 3%) × 0.03 + (amount invested at 4%) × 0.04 + (amount invested at 5%) × 0.05 = $95

Now we can substitute the expression for (amount invested at 3%) and solve for x.

Once we have the value of x, we can calculate the amounts invested at 3%, 4%, and 5% using the given information.

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Answer:

a. x = 7; b. 75

Step-by-step explanation:

Equilateral means all sides equal the same measurement

4x - 3 = 2x + 11

4x - 2x = 11 + 3

2x = 14

x = 7

Plug in x = 7 to any equation

4(7) - 3

28 - 3

25

Perimeter means add up all 3 sides

25 + 25 + 25

75

Easy way to do this, divide 24 with 3, you will get 8. That means 8 is 1/3 of 24. To get 2/3 you just add 8+8 which equals to 16

Answer:

21.1 minutes

Step-by-step explanation:

Time for first mile + second + third

6.75+ 7.1+ 7.25

21.1 minutes or (21.1 * 60) seconds = 1266 seconds

For the given triangles:

(1) x = 5.4

(2)  x  =  √23

(3) θ = 25.84 degree

(4)   x = 9.5

(5) n = 41

(1) In the given triangle,

One angle = 16 degree

Perpendicular = x

Hypotenuse    = 20

Since we know that

Sinθ = opposite side of θ/hypotenuse

Therefore,

⇒ sin 16 = x/20

⇒   0.27 = x/20

⇒         x = 5.4

(2)  In the given triangle,

Hypotenuse = 12 km

Base = 11 km

perpendicular = x

We know that the Pythagoras theorem for a right angled triangle:

⇒  (Hypotenuse)²= (Perpendicular)² + (Base)²

⇒ (12)²= (x)² + (11)²

⇒ 144 = (x)² + 121

⇒   x² =  23

Taking square root both sides we get,

Hence,

⇒   x  =  √23

(3) In the given,

Base = 20

Perpendicular = 42

We know that the Pythagoras theorem for a right angled triangle:

⇒  (Hypotenuse)²= (Perpendicular)² + (Base)²

⇒ (Hypotenuse)² =  (42)² + (20)²

⇒ (Hypotenuse)² =  2164

Taking square root both sides,

⇒ (Hypotenuse)  = 46.51

⇒ cosθ = Adjacent/hypotenuse

             = 42/46.51

             = 0.90

Taking inverse of cosθ,

⇒ θ = 25.84 degree

(4) In the given triangle,

One angle = 30 degree

Base = x

Hypotenuse    = 11

Since we know that

cosθ = Adjacent/hypotenuse

Therefore,

⇒ cos 30  = x/11

⇒   √3/2 = x/11

⇒         x = 9.5

(4) In the given triangle,

Base = 40

Perpendicular = 9

Hypotenuse = n

We know that the Pythagoras theorem for a right angled triangle:

⇒  (Hypotenuse)²= (Perpendicular)² + (Base)²

⇒  n² = 9² + 40²

⇒  n² = 81 + 1600

⇒  n² = 1681

⇒  n = 41

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