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Elena L [17]
3 years ago
8

A group of friends was working on a student film. They spent $330 on costumes, which was 55% of their total budget. What was the

total budget for their student film?
Mathematics
1 answer:
wariber [46]3 years ago
7 0

Answer:

$600

Step-by-step explanation:

Let "x" represent their total budget for the film.

Amount spent on costumes = $330

Percent spent on costumes = 55%

Therefore:

55% of x = $330

55/100 × x = 330

55x/100 = 330

Cross multiply

55x = 100 × 330

55x = 33,000

Divide both sides by 55

x = 33,000/55

x = 600

Total budget = x = $600

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Am i blind or does this just not make any sense? Pls help!
allsm [11]

Answer:

0.4

Step-by-step explanation:

2/5 converted into hundredths is 40/100.

40/100 as a decimal is 0.40, or 0.4

-hope it helps

5 0
2 years ago
Read 2 more answers
Please help! Its for my big test tomorrow!
Travka [436]

Answer:

# The solution x = -5

# The solution is x = 1

# The solution is x = 6.4

# The solution is x = 4

# The solution is 1.7427

# The solution is 0.190757

Step-by-step explanation:

* Lets revise some rules of the exponents and the logarithmic equation

# Exponent rules:

1- b^m  ×  b^n  =  b^(m + n) ⇒ in multiplication if they have same base

  we add  the power

2- b^m  ÷  b^n =  b^(m – n) ⇒  in division if they have same base we

   subtract  the power

3- (b^m)^n = b^(mn) ⇒ if we have power over power we multiply

   them

4- a^m × b^m = (ab)^m ⇒ if we multiply different bases with same  

   power then we multiply them ad put over the answer the power

5- b^(-m) = 1/(b^m)  (for all nonzero real numbers b) ⇒ If we have

   negative power we reciprocal the base to get positive power

6- If  a^m  =  a^n  ,  then  m  =  n ⇒ equal bases get equal powers

7- If  a^m  =  b^m  ,  then  a  =  b    or    m  =  0

# Logarithmic rules:

1- log_{a}b=n-----a^{n}=b

2- loga_{1}=0---log_{a}a=1---ln(e)=1

3- log_{a}q+log_{a}p=log_{a}qp

4- log_{a}q-log_{a}p=log_{a}\frac{q}{p}

5- log_{a}q^{n}=nlog_{a}q

* Now lets solve the problems

# 3^{x+1}=9^{x+3}

- Change the base 9 to 3²

∴ 9^{x+3}=3^{2(x+3)}=3^{2x+6}

∴ 3^{x+1}=3^{2x+6}

- Same bases have equal powers

∴ x + 1 = 2x + 6 ⇒ subtract x and 6 from both sides

∴ 1 - 6 = 2x - x

∴ -5 = x

* The solution x = -5

# ㏒(9x - 2) = ㏒(4x + 3)

- If ㏒(a) = ㏒(b), then a = b

∴ 9x - 2 = 4x + 3 ⇒ subtract 4x from both sides and add 2 to both sides

∴ 5x = 5 ⇒ divide both sides by 5

∴ x = 1

* The solution is x = 1

# log_{6}(5x+4)=2

- Use the 1st rule in the logarithmic equation

∴ 6² = 5x + 4

∴ 36 = 5x + 4 ⇒ subtract 4 from both sides

∴ 32 = 5x ⇒ divide both sides by 5

∴ 6.4 = x

* The solution is x = 6.4

# log_{2}x+log_{2}(x-3)=2

- Use the rule 3 in the logarithmic equation

∴ log_{2}x(x-3)=2

- Use the 1st rule in the logarithmic equation

∴ 2² = x(x - 3) ⇒ simplify

∴ 4 = x² - 3x ⇒ subtract 4 from both sides

∴ x² - 3x - 4 = 0 ⇒ factorize it into two brackets

∴ (x - 4)(x + 1) = 0 ⇒ equate each bract by 0

∴ x - 4 = 0 ⇒ add 4 to both sides

∴ x = 4

OR

∵ x + 1 = 0 ⇒ subtract 1 from both sides

∴ x = -1

- We will reject this answer because when we substitute the value

 of x in the given equation we will find log_{2}(-1) and this

 value is undefined, there is no logarithm for negative number

* The solution is x = 4

# log_{4}11.2=x

- You can use the calculator directly to find x

∴ x = 1.7427

* The solution is 1.7427

# 2e^{8x}=9.2 ⇒ divide the both sides by 2

∴ e^{8x}=4.6

- Insert ln for both sides

∴ lne^{8x}=ln(4.6)

- Use the rule ln(e^{n})=nln(e) ⇒ ln(e) = 1

∴ 8x = ln(4.6) ⇒ divide both sides by 8

∴ x = ln(4.6)/8 = 0.190757

* The solution is 0.190757

7 0
4 years ago
Read 2 more answers
14. Mashud and Iqbal are security guards at a top secret federal vault. They each work 8 hour shifts, consecutively. If Mashud b
Vlada [557]

At the time 4 PM will it be after they each have worked 4 shifts. Option E is correct.

<h3>What exactly is simplification?</h3>

Simplifying means making something easier to do or comprehend, as well as making something less difficult.

Mashud and Iqbal are security guards at a top-secret federal vault. They each work 8-hour shifts, If Mashud begins his shift at 8 PM,

The time will it be after they each have worked 4 shifts;

8 PM + 8 hour =4 AM

4 AM + 8 hour = 12 PM

12 PM+ 8 hour =8 PM

8 PM + 8 hour = 4 PM

Hence,  option E  is correct.

They will each have worked four shifts by the time it is 8 PM.

To learn more about the simplification, refer to:

brainly.com/question/23509407

#SPJ1

3 0
2 years ago
Jamal claims that the graph of f(x)+2 is equivalent to the graph of f(x+k). For the case where Jamal claim is correct, what must
rusak2 [61]

Answer:

K=2

Hope this helps

6 0
3 years ago
Read 2 more answers
The profit per acre from a grove of orange trees is given by x(190 − x) dollars, where x is the number of orange trees per acre.
nasty-shy [4]

Answer:

P(x) = 190 x -x^2

In order to maximize the last equation we can derivate the function in term of x and we got:

\frac{dP}{dx} = 190 -2x

And setting this derivate equal to 0 we got:

\frac{dP}{dx} = 190 -2x=0

And solving for x we got:

x = 95

And for this case the value that maximize the profit would be x =95 and the corresponding profit would be:

P(x=95)= 95(190-95)= 95*95 = 9025

Step-by-step explanation:

For this case we have the following function for the profit:

P(x) = x(190-x)

And we can rewrite this expression like this:

P(x) = 190 x -x^2

In order to maximize the last equation we can derivate the function in term of x and we got:

\frac{dP}{dx} = 190 -2x

And setting this derivate equal to 0 we got:

\frac{dP}{dx} = 190 -2x=0

And solving for x we got:

x = 95

And for this case the value that maximize the profit would be x =95 and the corresponding profit would be:

P(x=95)= 95(190-95)= 95*95 = 9025

7 0
3 years ago
Read 2 more answers
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