A subway ride is $2.25 per ride.
a. Write a model for the cost (in $) for x rides on the subway.

b. A commuter can purchase an unlimited- ride Metrocard for $89 per month. How many rides are required for a commuter to save money by buying the metrocard?​

Answer:

The derivative is [tex]\frac{dR}{dM} = CM - M^2[/tex]

Step-by-step explanation:

From the question we are told that

The equation representing the reaction is [tex]R = M^2 (\frac{C}{2} - \frac{M}{3} )[/tex]

Generally this equation can be represented as

[tex]R = \frac{C M^2}{2} - \frac{M^3}{3}[/tex]

Generally [tex]\frac{dR}{dM}[/tex] as a function of M is mathematically represented as

[tex]\frac{dR}{dM} = 2 * \frac{C M^{2 - 1 }}{2} + 3 * \frac{M^{3-1}}{3}[/tex]

=> [tex]\frac{dR}{dM} = CM - M^2[/tex]

Answer: (z + 2)(z - 3)

Step-by-step explanation:

First, we have 1 as a coefficient on z², so we multiply that by -6, which gives us -6. Now we must find out what two numbers when multiplied, give us -6, and when added together, give us -1 (z's coefficient). Going through -6's factors, I got -3 and 2 since we need a negative one when they are added together. Now we can input our values:

(z - 3)(z + 2).

Double checking, we get the starting equation, which means our factorization was correct, and so is the solution.

Note: it does not matter which binomial comes first because you will get the same answer regardless of its position.

Answer:

The width is 34.6

Step-by-step explanation:

You have to assume that the cut is a straight cut.

Givens

c = 41

a = 22

b = ?

Formula

a^2 + b^2 = c^2

Solution

22^2 + b^2 = 41^2

484 + b^2 = 1681                   Subtract 484 from both sides

484-484 + b^2 = 1681-484   Combine

b^2 = 1197                              Take the square root of both sides.

sqrt(b^2) = sqrt(1197)

b = 3*sqrt(133)

b = 34.598  

b = 34.6

Answer:

-189

Step-by-step explanation:

Remember to follow the rules of signs:

- If there are two positive signs next to each other, you add:

- If there is one negative sign and one positive sign next to each other, you subtract.

- If there is two negative signs next to each other, you add:

- 412 - (-223) = -412 + 223

Subtract:

223 - 412 = -189

-189 is your answer.

~

Answer:

80

Step-by-step explanation:

Answer:

8

Step-by-step explanation:

2/3*12=24/3=8

easy way:

2/3*12/1=24/3=8

that is a rational number.

The 1st term is 60.

Add 50 to this to get the 2nd term, 60 + 50 = 110.

Add 50 to that to get the 3rd term, 110 + 50 = 160.

Add 50 to that to get the 4th term, 160 + 50 = 210.

And so on...

Notice that in the 2nd term, we added 1 copy of 50 to the 1st term.

In the 3rd, we ultimately added 2 copies of 50 to the 1st term.

In the 4th, we added 3 50s.

And so on... If the pattern continues, then the n-th term can be obtained by adding (n - 1) copies of 50 to the first term.

So, the 100th term is

60 + (100 - 1) * 50 = 5010

Answer:

I'm pretty sure it's increasing

Step-by-step explanation:

because the linear parent function is x=y, no negative signs

Answer:

Increasing

Step-by-step explanation:

Answer:

true

Step-by-step explanation:

Answer:

[tex]\frac{61}{99}[/tex]

Step-by-step explanation:

let x = 0.616161 (etc.)

make a second equation because you multiply by 100:

100x = 61.616161 (etc.)

subtract from each other

100x = 61.616161

     x =  0.616161

you get

99x = 61

solve for x

[tex]\frac{61}{99}[/tex]

Answer:

there are 32 bottles needed

Step-by-step explanation:

Thanks

Answer:

at least 8 gallons

Step-by-step explanation:

Answer:

B. Add/subtract the same quantity from both sides.

in this case, it would be adding x to both sides to simplify the equation.

Answer: ADD/SUB THE SAME QUANTITY TO/FROM BOTH SIDES

YES: THEY ARE EQUIVALENT

Step-by-step explanation:

Answer:

1.60x=32.00

Step-by-step explanation:

Since you do not how much gallons of gas he bought you would use the variable x.

Answer:

1.60x=32

Step-by-step explanation:

Answer:

a) 0.2588

b) 0.044015

c) 0.12609

Step-by-step explanation:

Using the TI-84 PLUS calculator

The formula for calculating a z-score is is z = (x-μ)/σ,

where x is the raw score

μ is the population mean

σ is the population standard deviation.

From the question, we know that:

μ = 119 inches

standard deviation σ = 17 inches

(a) What proportion of trees are more than 130 inches tall?

x = 130 inches

z = (130-119)/17

= 0.64706

Probabilty value from Z-Table:

P(x<130) = 0.7412

P(x>130) = 1 - P(x<130) = 0.2588

(b) What proportion of trees are less than 90 inches tall?

x = 90 inches

z = (90-119)/17

=-1.70588

Probability value from Z-Table:

P(x<90) = 0.044015

(c) What is the probability that a randomly chosen tree is between 95 and 105 inches tall?

For x = 95

z = (95-119)/17

= -1.41176

Probability value from Z-Table:

P(x = 95) = 0.07901

For x = 105

z = (105 -119)/17

=-0.82353

Probability value from Z-Table:

P(x<105) = 0.2051

The probability that a randomly chosen tree is between 95 and 105 inches tall

P(x = 105) - P(x = 95)

0.2051 - 0.07901

= 0.12609

Answer:

[tex]n=5/2[/tex]

Step-by-step explanation:

We have the equation:

[tex]5^{2n-2}=125[/tex]

Notice that 125 is the same as 5³. So:

[tex]5^{2n-2}=5^3[/tex]

Since they have the same base, the exponents must be equal. Therefore:

[tex]2n-2=3[/tex]

Solve for n. Add 2 to both sides:

[tex]2n=5[/tex]

Divide both sides by 2:

[tex]n=5/2=2.5[/tex]

So, the value of n is 5/2.

And we're done!

Answer:

N = 2.5

Step-by-step explanation:

Ok, so try this.

125 is 5^3, right?

And in this equation, we have 5 to the power of 2n-2 is equal to 125.

You need to make sure that the exponent ends up as 3.

How would you do this?

Try substituting N for 3.

That's too big.

Try Substituting N for 2.

That's a bit too small.

What number is in between 2 and 3?

2.5 is.

N = 2.5

Check your work, and see if you came up with the same answer

Work:

2.5 x 2 = 5

5 - 3 = 2

5^3 = 125

Answer:

Maggie is 7 years old

Step-by-step explanation:

Attached is an image that explains the question. Hope this helps!

Answer:

[tex]\boxed{2^{\frac{802}{27}} \cdot 3^9}[/tex]

Step-by-step explanation:

I will try to give as many details as possible.

First of all, I just would like to say:

[tex]\text{Use } \LaTeX ![/tex]

Texting in Latex is much more clear and depending on the question, just writing down without it may be confusing or ambiguous. Be together with Latex! （＊＾Ｕ＾）人（≧Ｖ≦＊）/

[tex]$(3^{-2} \cdot 4^{-5} \cdot 5^0)^{-3} \cdot (4^{-\frac{4}{3^3} })\cdot 3^3$[/tex]

Note that

[tex]\boxed{a^{-b} = \dfrac{1}{a^b}, a\neq 0 }[/tex]

The denominator can't be 0 because it would be undefined.

So, we can solve the expression inside both parentheses.

[tex]\left(\dfrac{1}{3^2} \cdot \dfrac{1}{4^5} \cdot 5^0 \right)^{-3} \cdot \left(\dfrac{1}{4^{\frac{4}{3^3} } }\right)\cdot 3^3[/tex]

Also,

[tex]\boxed{a^{0} = 1, a\neq 0 }[/tex]

[tex]\left(\dfrac{1}{9} \cdot \dfrac{1}{1024} \cdot 1 \right)^{-3} \cdot \left(\dfrac{1}{4^{\frac{4}{27} } }\right)\cdot 27[/tex]

Note

[tex]\boxed{\dfrac{1}{a} \cdot \dfrac{1}{b}= \frac{1}{ab} , a, b \neq 0}[/tex]

[tex]\left(\dfrac{1}{9216} \right)^{-3} \cdot \left(\dfrac{1}{4^{\frac{4}{27} } }\right)\cdot 27[/tex]

[tex]\left(\dfrac{1}{9216} \right)^{-3} \cdot \left(\dfrac{27}{4^{\frac{4}{27} } }\right)[/tex]

[tex]\left( \dfrac{1}{\left(\dfrac{1}{9216}\right)^3} \right)\cdot \left(\dfrac{27}{4^{\frac{4}{9} } }\right)[/tex]

[tex]\left( \dfrac{1}{\left(\dfrac{1}{9216}\right)^3} \right)\cdot \left(\dfrac{27}{4^{\frac{4}{27} } }\right)[/tex]

Note

[tex]\boxed{\dfrac{1}{\dfrac{1}{a} } = a}[/tex]

[tex]9216^3\cdot \left(\dfrac{27}{4^{\frac{4}{9} } }\right)[/tex]

[tex]\left(\dfrac{ 9216^3\cdot 27}{4^{\frac{4}{27} } }\right)[/tex]

Once

[tex]9216=2^{10}\cdot 3^2 \implies 9216^3=2^{30}\cdot 3^6[/tex]

[tex]\boxed{(a \cdot b)^n=a^n \cdot b^n}[/tex]

And

[tex]$4^{\frac{4}{27}} = 2^{\frac{8}{27} $[/tex]

We have

[tex]\left(\dfrac{ 2^{30} \cdot 3^6\cdot 27}{2^{\frac{8}{27} } }\right)[/tex]

Also, once

[tex]\boxed{\dfrac{c^a}{c^b}=c^{a-b}}[/tex]

[tex]2^{30-\frac{8}{27}} \cdot 3^6\cdot 27[/tex]

As

[tex]30-\dfrac{8}{27} = \dfrac{30 \cdot 27}{27}-\dfrac{8}{27} =\dfrac{802}{27}[/tex]

[tex]2^{30-\frac{8}{27}} \cdot 3^6\cdot 27 = 2^{\frac{802}{27}} \cdot 3^6 \cdot 3^3[/tex]

[tex]2^{\frac{802}{27}} \cdot 3^9[/tex]

Answer: 30 cents

Step-by-step explanation:

1/20 of a dollar is 5 cents

Then we multiply by the numerator (6) to get our answer....

5x6= 30

Hoped this helps! :)

Answer:

The answer would be -12x^2-4x+6

Step-by-step explanation:

This is the simplest form it could get since you subtract the two x^2 together.

Answer:

60

Step-by-step explanation:

percentage=18

rate=30%

base=_____

p/r=b

18/0.30=60

Answer:

60

Step-by-step explanation:

18=30%

6=10%

6x10=60

10x10=100%

Answer: x=8

Step-by-step explanation:

Answer:

7

The difference between 9 a positive number and - 2 a negative number is 7 because the question States 9 - 2.