The number of problems assigned as homework by a savvy math professor is a function of the length of the class on a particular day, which is either 45 minutes, 90 minutes, or 135 minutes. He first multiplies the number of minutes by 4 and then divides that number by 9. Finally, he subtracts 12 from that amount. Which of the following functions best represents the number of math problems the professor assigns depending on the length of the class, t, in minutes?

Answer: You get 0.06 which is 6 cents in terms of money.

Step-by-step explanation:

6 millions could be written as 6,000,000 and 1  billion could also be written as  1,000,000,000   so using this set up a fraction to divide it.

[tex]\frac{6000000}{1,000,000,000}[/tex] = 0.006  

0.006 * 10 = 0.06  

Answer:

12+5

Step-by-step explanation:

negative times negative is postive

Answer:

60 degrees.

Step-by-step explanation:

In mathematics, a "range" is described as the difference between the lowest and highest numbers in a data set. To find the range, we must subtract. (This is what the word "difference" indicates in math)

56 - (-4) =

56 + 4 = 60 (the negative signs cancel out)

Thus, the range of temperature for March is 60 degrees :) Hope this helped!

God bless and stay safe.

Answer:

  7/3

Step-by-step explanation:

The distances have the ratio ...

  (Q -P) = (2/3)(R -P)

  Q = P +(2/3)R -(2/3)P = (2R +P)/3

  Qy = (2Ry +Py)/3 = (2·0 +7)/3 = 7/3

Answer:

6(x^2)

Step-by-step explanation:

The square of a number is x^2 and then you multiply that by six so it has to have parenthesis

When Lisa flips 2 fair coins, the probability of obtaining two tails is 1/4.

Probability shows possibility to happen an event, it defines that an event will occur or not. The probability varies from 0 to 1.

Given that,

Number of coins flips by Lisa = 2,

To find the probability of obtaining two tales,

The sample pace of flipping two coins = {(H, H), (H, T), (T, H), (T, T)}

The tale on both coins can come one time.

So the probability = number of favorable outcome / total observation

                              = 1 / 4

The required probability of obtaining two tails is 1 /4.

To know more about Probability on:

https://brainly.com/question/12478394

#SPJ3

Answer:

B. [tex] 5 \sqrt{3} + \sqrt{6} [/tex]

Step-by-step explanation:

[tex] \huge\sqrt{3} (5 + \sqrt{2} ) = 5 \sqrt{3} + \sqrt{6} [/tex]

Answer: Each hamburger cost $3.50

Step-by-step explanation:

He spent $13 in total and bought one hot dog for $2.50  and 3 hamburgers but we don't know the price of one hamburger so we could represent it by the equation,

2.50 + 3h = 13   Now solve for x

-2.50            2.50

  3h = 10.50

 h = 3.50  

Check:

2.50 + 3(3.50) = 13

2.50 + 10.50 = 13

13=  13

Answer:

20°

Step-by-step explanation:

i just did it. got it correct

Answer:

b and g

Step-by-step explanation:

a. is y = 0³ = 0

b. is y = ln(0), which is undefined because ln(x) is only defined for x > 0

c. is y = 1 / (1 + e^-0) = 1 / (1 + 1) = 1/2

d. is y = 0

e. is y = 0² = 0

f. is y = sin(0) = 0

g. is y = 1/0, which is undefined because division by 0 is undefined

h. is y = e^0 = 1

i. is y = |0| = 0

j. is y = √0 = 0

Answer:

6.08333....

Step-by-step explanation:

.25 +w = 19/3

19/3=6.3333

6.3333-.25=6.08333....

Check:

.25+6.08333....=6.3333...

Step-by-step explanation:

1. 6 factors of 2 means, 2 multiplied by itself 6 times.  It can be written in the form of exponents as 2⁶.

2. [tex]2^m{\cdot} 2^n[/tex]

The law of exponent is : [tex]x^a{\cdot} x^b=x^{a+b}[/tex]

So,

[tex]2^m{\cdot} 2^n=2^{m+n}[/tex]

The correct option is (A).

3. If the power of any number is 0, then the value of that number is equal to 1.

So,

[tex]23^0=1[/tex]

Hence, this is the required solution.

Hey mate!

Question:

5x – 1 = x+ 27

Answer:

x=7

Step-by-step explanation:

Step 1:

5x-x=27+1

Step 2:

4x=28

step 3:

x=28÷4

step 4:

x=7

hope it helped you:)

Answer: b/a = -8

Step-by-step explanation:

When we have a quadratic equation:

y = a*x^2 + b*x + c.

The vertex of this function (and the axis of symetry) is located at:

x = -b/2a

Now, we know that the axis of symmetry is at x = 4.

then we have:

4 = -b/2a

And we want to find b/a.

Then we start with:

-b/2a = 4.

first we multiply by 2 in each side:

2*(-b/2a) = -b/a = 2*4 = 8.

now we multiply by -1 in each side:

-1*(-b/a) = b/a = -1*8.

Then we have: b/a = -8

Answer:

Scientific notation for 15,000,000

[tex] = 1.5 \times {10}^{7} [/tex]

Answer:

Step-by-step explanation:

hello :

x-32>32+9x

means : x-9x>32+32

-8x >64

dvid by :8        -x >8  .......continu

Answer: D. [tex] f(1) = 4,\ \ f(n+1)=\dfrac{-1}{2}f(n) [/tex]

Step-by-step explanation:

The given sequence:  [tex]4, -2,1,\dfrac{-1}{2},\dfrac14,....[/tex]

Here, first term: [tex]f(1)=4[/tex]

Second term: [tex]f(2)=-2[/tex]

Third term : [tex]f(3)=\dfrac{-1}{2}[/tex]

It can be observed that it is neither increasing nor decreasing sequence but having the common ratio.

Common ratio: [tex]r=\dfrac{f(2)}{f(1)}=\dfrac{-2}{4}=\dfrac{-1}{2}[/tex]

So, [tex]f(n+1)=\dfrac{-1}{2}f(n)[/tex]  [as in G.P. nth term= [tex]a_{n+1}=ar^n[/tex]]

Hence, correct option is D. [tex] f(1) = 4,\ \ f(n+1)=\dfrac{-1}{2}f(n) [/tex]

Answer:

  8.2 million years

Step-by-step explanation:

The time can be found from ...

  time = distance/speed

  time = (47.0×10^4 m)/(5.7×10^-2 m/yr) = 8.2×10^6 yr

It will take about 8.2 million years for LA to have the same latitude as SF.

__

The given numbers each have 2 significant digits, so the answer is appropriately rounded to 2 significant digits.

Answer:

a=16400 feet

Step-by-step explanation:

t = -0.0035 a +g

-17.40 = -0.0035 a+40

-17.40-40=-0.0035a+40-40

-57.40=-0.0035a

a = -57.40/-0.0035

a=16400 feet

Answer:

B)

Step-by-step explanation:

6 + 4*5 = 6 + 20

             = 26

According to BODMAS, multiplication should be done and then addition

Answer:

B

Step-by-step explanation:

By pemdas - multiplication first

6+4x5

6+(20)

so, b - 6 + 20 is the answer

Step-by-step explanation:

To solve, we have to remember PEMDAS (Parenthesis, Exponent, Multiply / Divide, Add or Subtract).

Here, the curly brackets act as parenthesis, so we solve that first.

• 3 + 7 = 10

Then, we multiply by 4.

• 10 • 4 = 40

Finally, we add 6 to 40.

• 40 + 6 = 46.

Our final answer: 46

Answer:

46

Step-by-step explanation:

We are asked to evaluate the expression. Remember to solve according to PEMDAS: Parentheses, Exponents, Multiplication, Division, Addition and Subtraction.

[tex]6+4 * (3+7)[/tex]

Solve inside the parentheses. Add 3 and 7.

⇒3+7=10

[tex]6+4*(10)[/tex]

Multiply 4 and 10.

⇒4*10=40

[tex]6+40[/tex]

Add 6 and 40.

⇒6+40=46

[tex]46[/tex]

When the expression 6+4*(3+7) is evaluated, the result is 46.

Answer:

4260

Step-by-step explanation:

Answer:

4260

Step-by-step explanation:

Answer:

-22/3

Step-by-step explanation:

-22/3 is the answer as a improper fraction.

Step 1

Multiply the denominator by the whole number

3 × 7 = 21

Step 2

Add the answer from Step 1 to the numerator

21 + 1 = 22

Step 3.

Write answer from Step 2 over the denominator

22/3

Answer:

-22/3

Step-by-step explanation:

7x3= 21

Answer:

8

Step-by-step explanation:

Please write this as (3/2)x + 1 = 13.

Start the process of solving for x by subtracting 1 from both sides:

(3/2)x = 12

Eliminate the fractional coefficient by multiplying both sides by 2/3:

(2/3)(3/2)x = (2/3)(12), or

x = 8

Answer:

Rs. (x - y + 2)

Step-by-step explanation:

The marked price is the price that a product is to be sold. The product can be sold at a discount which is below the marked price of the product.

The marked price of the article is Rs. X. The discount is Rs. y, therefore the article price = marked price - discount = x - y.

But since the article is sold with a VAT of Rs. 2, the VAT is added to the price, therefore the selling price of the article including VAT is Rs. (x - y + 2)

Answer:

The quantity of acid in the solution is 47.1 ml.

Step-by-step explanation:

Answer:

Step-by-step explanation:

fraction are not integers

Your question has been heard loud and clear/

we know,

4cos³x = 3cosx + cos3x

put here, x = 20°

then, 4cos³20° = 3cos20° + cos3 × 20°

= 3cos20° + cos60°

cos³20° = (3cos20° + cos60°)/4 -------(1)

similarly ,

4sin³x = 3sinx - sin3x

put here, x = 10°

4sin³10° = 3sin10° - sin30°

sin³10° = (3sin10° - sin30°)/4 -----------(2)

now,

LHS = cos³20° + sin³10°

put equations (1) and (2)

= 1/4(3cos20° + cos60°) + 1/4 ( 3sin10° - sin30°)

= 1/4( 3cos20° + cos60° + 3sin10° - sin30°)

we know,

cos60° = sin30° = 1/2

= 1/4 ( 3cos20° + 3sin10°)

= 3/4(cos20° + sin10°) = RHS

hence proved

Thank you

Answer:  see proof below

Step-by-step explanation:

Use the following identities & Unit Circle calculations:

 4cos³x = 3cos x + cos 3x

--> cos³x = (1/4)[3cos x + cos 3x]

 4sin³x = 3sin x - sin 3x

--> sin³x = (1/4)[3sin x - sin 3x]

cos 60° = sin 30° = (1/2)

Proof: LHS → RHS

Given:                          cos³ 20° + sin³ 10°

Triple Angle Identity: (1/4)[3cos 20° + cos 3·20°] + (1/4)[3sin 10° - sin 3·10°]

Simplify:                      (1/4)[3cos 20° + cos 60° + 3sin 10° - sin 30°]

                                   (1/4)[3cos 20° + (1/2) + 3sin 10° - (1/2)]

                                   (1/4)[3cos 20° + 3sin 10°]

Factor:                         (3/4)[cos 20° + sin 10°]        

Proven:  (3/4)[cos 20° + sin 10°]  = (3/4)[cos 20° + sin 10°]    [tex]\checkmark[/tex]

Answer:

0.100100010000...

Step-by-step explanation:

becoz in irrational numbers decimal goes on forever