Is half the sum of two and a number multiplied by itself three times linear? (and how would I write it as a mathematical expression)

Answer:

The piecewise function is given as follows;

[tex]\begin{cases}C(n) = \$ 3.45 \times n & \text{ if } x< 4 \\ C(n) = \$ 3.00 \times n & \text{ if } x\geq 4 \end{cases}[/tex]

Step-by-step explanation:

The given parameters are;

The cost of each bag of snickers = $3.45

The cost of each bag of sneakers when buying 4 or more bags = $3.00

Let "n" be the number of bags of snickers and "C(n)" be the cost of all the snickers purchased

The piecewise function is C(n) = {($3.45 × n) for n < 3

{($3.00 × n) for n ≥ 4

Answer and Step-by-step explanation:

All we have to do is solve for x.

Divide both sides by 6.

x = [tex]\frac{25}{6}[/tex]

This is your answer.

If you want to have the decimal version, then it would be 4.166 repeating.

#teamtrees #WAP (Water And Plant) #SPEW (Society for the Promotion of Elfish Welfare)

Step-by-step explanation:

Let x be the money made in sales. Let y be the money made in commissions.

First, convert 2.5% to a decimal.

2.5% = 0.025

Equation:

0.025x = y

Robert:

0.025(8850) = y

y = $221.25

Francisca:

0.025x = 279

x = 279/0.025

x = $11,160

Answer:

55 complete days

Step-by-step explanation:

It is given that Jo is diabetic and she uses three doses of insulin in one day. One dose of insulin is 0.06 ml and one bottle has 1 cl of insulin.

We know, 1 cl = 10 ml

So the insulin bottle contains 10 ml of insulin.

1 dose = 0.06 ml

3 doses = 0.06 x 3

              = 0.18 ml

So Jo takes 0.18 ml of insulin in one day.

Dividing 10 ml by 0.18 ml, we get

[tex]$=\frac{10}{0.18}$[/tex]

[tex]$=\frac{1000}{18}$[/tex]

= 55.55

So, the bottle will last for 55 complete days.

Answer:

yes

Step-by-step explanation:

Answer:

The lowest point is 9 ft below see level and the highest point is 108 ft above sea level

Step-by-step explanation:

Here, we want to select the correct option

From the question, we have the following;

The lowest point is -9 while the highest point is +108

-9 indicates that it is 9 units below zero

+108 indicates that it is 108 units above zero

So, the correct option here is that;

The lowest point is 9 ft below see level and the highest point is 108 ft above sea level

Answer:

A. The lowest point is 9 feet below sea level and the highest point is 108 above sea level

Step-by-step explanation:

have a nice day

Answer:

2, 5, 14, 41, 122

Step-by-step explanation:

Using the recursive rule with a₁ = 2

a₂ = 3a₁ - 1 = 3(2) - 1 = 6 - 1 = 5

a₃ = 3a₂ - 1 = 3(5) - 1 = 15 - 1 = 14

a₄ = 3a₃ - 1 = 3(14) - 1 = 42 - 1 = 41

a₅ = 3a₄ - 1 = 3(41) - 1 = 123 - 1 = 122

The first 5 terms are 2, 5, 14, 41, 122

Answer:

[tex]a_{1}\\\\[/tex] = 2

[tex]a_{2\\}\\\\[/tex] = 5

[tex]a_{3\\}\\\\[/tex] = 14

[tex]a_{4\\}\\\\[/tex] = 41

[tex]a_{5\\}\\\\[/tex] = 122

Step-by-step explanation:

If I've properly understood:

[tex]a_{1}\\\\[/tex] = 2

[tex]a_{n} = 3 a_{n-1}\\[/tex] - 1

so, the first 5 terms are:

[tex]a_{1}\\\\[/tex] = 2

[tex]a_{2\\}\\\\[/tex] = 3. 2 - 1 = 5

[tex]a_{3\\}\\\\[/tex] = 3. 5 - 1 = 14

[tex]a_{4\\}\\\\[/tex] = 3. 14 - 1 = 41

[tex]a_{5\\}\\\\[/tex] = 3. 41 - 1 = 122

First you write down the formula. How do you get 132.60 in the first place? I included a pic, please try to understand it. As it'd be v useful in daily life too.

Answer:

the answer is 2%

Step-by-step explanation:

I got 2.0 but you round it so it would be 2% the other girl worked it out just right

Answer:

66 is the answer to your question

Answer:

66

Step-by-step explanation:

11 % = 0.11

600 × 0.11 = 66

9514 1404 393

Answer:

  (4, -6)

Step-by-step explanation:

The minimum is the vertex of the parabolic section in the 4th quadrant. The coordinates appear to be (4, -6).

Answer:

$0.45a+$0.60p ≤$28

Step-by-step explanation:

Answer:

0.45a + 0.60p <= 28

Step-by-step explanation:

Answer:

16.27

Step-by-step explanation:

if 1000m rep 1km

therefore :

58.6km/h in ms = 58.6km×1000/3600

=16.277 ms

Answer:

2x-5y

Step-by-step explanation:

9x-7x= 2x

3y-8y= -5y

Answer:

....................

Step-by-step explanation:

Answer:

x=5.889

Step-by-step explanation:

2(9x6)=18x+2

108=18x+2

106=18x

x=106÷18

x=5.888888889

Answer:

Just right the numbers they put

Answer:

see explanation

Step-by-step explanation:

Under a reflection in the line y = - x

a point (x, y ) → (- y, - x ) , thus

M(- 7, 1 ) → M'(- 1, 7 )

N(- 4, 1 ) → N'(- 1, 4 )

O(- 4, - 4 ) → O'(4, 4 )

P(- 7, - 4 ) → P'(4, 7 )

Answer: (C) 42 cm

Work Shown:

(length on paper)/(real length) = (length on paper)/(real length)

(1 cm)/(7 cm) = (6 cm)/(x cm)

1/7 = 6/x

1*x = 7*6

x = 42

The actual length of the dog is 42 cm.

Answer:

4x + 8 = 7.2 + 5x

1. 4x - 4x + 8 = 7.2 + 5x - 4x

2. 8 = 7.2 + x

3. 8 - 7.2 = 7.2 - 7.2 + x

4. 0.8 = x

Step-by-step explanation:

Final Answer: [tex]x = 0.8[/tex]

Steps/Reasons/Explanation:

Question: Equation with variables on both sides: decimals & fractions [tex]4x + 8 = 7.2 + 5x[/tex].

Step 1: Subtract [tex]4x[/tex] from both sides.

[tex]8 = 7.2 + 5x - 4x[/tex]

Step 2: Simplify [tex]7.2 + 5x - 4x[/tex] to [tex]7.2 + x[/tex].

[tex]8 = 7.2 + x[/tex]

Step 3: Subtract [tex]7.2[/tex] from both sides.

[tex]8 - 7.2 = x[/tex]

Step 4: Simplify [tex]8 - 7.2[/tex] to [tex]0.8[/tex].

[tex]0.8 = x[/tex]

Step 5: Switch sides.

[tex]x = 0.8[/tex]

~I hope I helped you :)~

Answer:

the is a

Step-by-step explanation:

Answer:

a) [tex]\frac{dA}{dt} = 48 \pi\frac{in^{2}}{min}[/tex]

b) [tex] \frac{dh}{dt} = - \frac{13}{3} \frac{in}{min}[/tex]

c) [tex]\frac{dh}{dt} = - 2\frac{h}{r} \frac {dr}{dt}[/tex]

Step-by-step explanation:

In order to solve this problem, we must first picture a cylinder of height h and radius r (see attached picture).

a) So, in order to find the rate at which the area of the circular surface of the dough is increasing with respect to time, we need to start by using the are formula for a circle:

[tex]A=\pi r^{2}[/tex]

So, to find the rate of change of the area, we can now take the derivative of this formula with respect to the radius r:

[tex]dA = \pi(2) r dr[/tex]

and divide both sides into dt so we get:

[tex]\frac{dA}{dr} = 2\pi r \frac{dr}{dt}[/tex]

and now we can substitute:

[tex]\frac{dA}{dr} = 2\pi(12in)(2\frac{in}{min})[/tex]

[tex]\frac{dA}{dt} = 48\pi\frac{in^{2}}{min}[/tex]

b) In order to solve part b, we can start with the formula for the volume:

[tex]V=\pi r^{2} h[/tex]

and solve the equation for h, so we get:

[tex]h=\frac{V}{\pi r^{2}}[/tex]

So now we can rewrite the equation so we get:

[tex]h=\frac{V}{\pi}r^{-2}[/tex]

and now we can take its derivative so we get:

[tex]dh=\frac{V}{\pi} (-2) r^{-3} dr[/tex]

we can rewrite the derivative so we get:

[tex]\frac{dh}{dt}=-2\frac{V}{\pi r^{3}}\frac{dr}{dt}[/tex]

we can take the original volume formula and substitute it into our current derivative, so we get:

[tex]\frac{dh}{dt}= -2\frac{\pi r^{2} h}{\pi r^{3}} \frac{dr}{dt}[/tex]

and simplify:

[tex]\frac{dh}{dt} =-2\frac{h}{r} \frac{dr}{dt}[/tex]

so now we can go ahead and substitute the values  provided by the problem:

[tex]\frac{dh}{dt} =-2\frac{13in}{12in} (2\frac{in}{min})[/tex]

Which simplifies to:

[tex] \frac{dh}{dt} = - \frac{13}{3} \frac{in}{min}[/tex]

c)

Part c was explained as part of part b where we got the expression for the rate of change of the height of the dough with respect to the radius of the dough in terms of the height h and the radius r:

[tex]\frac{dh}{dt} =-2\frac{h}{r} \frac{dr}{dt}[/tex]

The rate of change of the height of the pizza with respect to (w.r.t.) time

can be found given that the volume of the pizza is constant.

Reasons:

The height of the dough when t = k is 13 inches

Radius of the dough = 12 inches

Rate at which the radius of the dough is increasing, [tex]\dfrac{dr}{dt}[/tex] = 2 in.²/min

(a) Required: The rate of increase of the surface area with time

Solution:

The circular surface area, A = π·r²

By chain rule of differentiation, we have;

[tex]\dfrac{dA}{dt} = \mathbf{\dfrac{dA}{dr} \times \dfrac{dr}{dt}}[/tex]

[tex]\dfrac{dA}{dt} = \dfrac{d ( \pi \cdot r^2)}{dr} \times \dfrac{dr}{dt} = 2 \cdot \pi \times 2 = 4 \cdot \pi[/tex]

The rate of increase of the surface area with time, [tex]\mathbf{\dfrac{dA}{dt}}[/tex] = 4·π in.²/min.

(b) Required: The rate of decrease of the height with respect to time

The volume of the pizza is constant, given by; V = π·r² ·h

Therefore;

[tex]h = \mathbf{ \dfrac{V}{\pi \cdot r^2}}[/tex]

[tex]\dfrac{dh}{dt} = \dfrac{d \left( \dfrac{V}{\pi \cdot r^2} \right)}{dr} \times \dfrac{dr}{dt} = \dfrac{-2 \cdot V}{\pi \cdot r^3} = \dfrac{-2 \cdot \pi \cdot r^2 \cdot h}{\pi \cdot r^3} \times \dfrac{dr}{dt} = \mathbf{-2 \cdot \dfrac{h}{r} \times \dfrac{dr}{dt}}[/tex]

[tex]\dfrac{dh}{dt} = -2 \cdot \dfrac{h}{r} \times \dfrac{dr}{dt} = -2 \times \dfrac{13}{12} \times 2 = \dfrac{13}{3} = 4. \overline 3[/tex]

The rate at which the height of the dough is decreasing, [tex]\mathbf{\dfrac{dh}{dt}}[/tex]= [tex]\underline{4.\overline 3 \ in./min}[/tex]

(c) Required:]The expression for the rate of change the height of the dough with respect to the radius of the cone.

Solution:

[tex]\dfrac{dh}{dr} = \dfrac{d \left( \dfrac{V}{\pi \cdot r^2} \right)}{dr} = \dfrac{-2 \cdot V}{\pi \cdot r^3} = \dfrac{-2 \cdot \pi \cdot r^2 \cdot h}{\pi \cdot r^3} = -2 \cdot \dfrac{h}{r}[/tex]

[tex]\dfrac{dh}{dr} = \mathbf{ -2 \cdot \dfrac{h}{r}}[/tex]

The rate of change the height of the dough w.r.t. the radius is [tex]\underline{\dfrac{dh}{dr} = -2 \cdot \dfrac{h}{r}}[/tex]

Learn more here:

https://brainly.com/question/20489729

Answer:

y=-1/2x+1

Step-by-step explanation:

Answer:

x = 10

Step-by-step explanation:

RST is an isosceles triangle.

[tex]m\angle T = m \angle R\\\\

8x\degree = (3x + 50)\degree \\\\

8x = 3x + 50\\\\

8x - 3x = 50\\\|

5x = 50\\\\

x = \frac{50}{5} \\ \\ x = 10[/tex]

Answer:

Half an orange

Step-by-step explanation:

It would be half an orange because it says 4 other people. Joe, Luis, Albert, and Lupe. And it says 3 oranges so that everyone would get an equal amount. So if you think about it, theirs no other way to let everyone have an equal piece. So you would have to split them in half and through the left overs away that cant be shared.

please mark as brainly

Answer:

46

Step-by-step explanation:

Answer:

46

Step-by-step explanation:

First get x

x= (20/10) * 100

x=200

23% of 200 = (23*200)/100 = 46

Answer:

-6

Step-by-step explanation:

-4+8=4

4-10= -6

Step-by-step explanation:

I don't know if it's correct

9514 1404 393

Answer:

  H  the range is all real numbers

Step-by-step explanation:

The arrows on the ends of the curve mean the curve extends to infinity. Then the domain (x-extent) is -3 to infinity.

The range (y-extent) is -infinity to infinity, all real numbers.

The appropriate description is ...

  H  The range is all real numbers

Answer:

Yes, the bathroom has enough water and shampoo for all of them.

Step-by-step explanation:

Answer:It takes 250 g of pasta and 240 ml of sauce to make one batch of spaghetti and it takes 600g of pasta and 700ml of sauce to make one batch of lasagna.

Case 1: Pasta

The chef wants to make spaghetti and lasagna using more than 4000 g of pasta.

S denote the number of batches of spaghetti he makes and L the number of batches of lasagna he makes.

So the equation becomes :

Case 2: Sauce

chef wants to make spaghetti and lasagna using more than 5000 ml of sauce.

S denote the number of batches of spaghetti he makes and L the number of batches of lasagna he makes.

So the equation becomes:

Answer :

The two equations are :

For pasta:

For sauce:

Step-by-step explanation:

Answer:

960

Step-by-step explanation:

I'm not sure exactly what's the question, but here's what I found. Lets first put it in our own words.

Consider the speed 4/5 miles in 12 minutes to travel 2/8.

8 + 4 = 12, so you can replace that with 12 minutes.

Now, you can absolutely guess your question.

Time = 12 minutes.

Distance = x (Let x be distance)

Speed = 4/5.

Now, you find distance.

Distance Formula: You can use the equivalent formula d = st which means distance equals rate times time.

So 4/5 × 12, is 9.6.

In fraction, if you have 1 numbers after the decimal point, multiply both numerator and denominator by 10. So 9.6 = (9.6 × 10) × 10 = 960.

Here is a pattern I found

2/5 divided by 4 is 1/10

4/5 divided by 8 is 1/10

If , we consider the given rates , we find that both rates are equivalent.

Two rates are given which are 4/5 miles in 8 minutes and 2/5 miles in 4 minutes.

We have to find out what they actually indicate.

What is the unitary method?

The unitary method is a method in which we find the value of a unit and then the value of the required number of units.

As per the question ;

Two rates are given which are ;  4/5 miles in 8 minutes and 2/5 miles in 4 minutes.

Let's find out what they are actually indicating.

So ;

If , distance travelled in 8 minutes = 4/5 miles

Then ;

In 1 minute , distance travelled will be ;

= [tex]\frac{4}{5*8}[/tex]

= [tex]\frac{4}{40}[/tex]

= 1 / 10 miles

and

If , distance travelled in 4 minutes = 2/5 miles

Then ;

In 1 minute , distance travelled will be ;

= [tex]\frac{2}{5*4}[/tex]

= [tex]\frac{2}{20}[/tex]

= 1 / 10 miles

So , we can conclude that both rates are equivalent.

Thus , if we , consider the given rates , we find that both rates are equivalent.

To learn more about unitary method click here ;

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the granola bar costs $1.50

the yogurt costs 50 cents = $0.50

Answer: x = -49

Step-by-step explanation:

hope this helped