The total number of cookies needed for the bake sale is 812 dozen. Two of your friends will each bake 14 of the cookies. Your sister will bake 18 of the cookies. What fraction of the cookies do you need to bake?

Answers

Answer 1
Answer:

Answer: (28)/(51)

Step-by-step explanation:

1 dozen = 12

Given, Total cookies needed = 8\frac12\ dozen = (17)/(2)\ dozen

=(17)/(2)* 12\n\n=102

2 friends bake 14 cookies each, and your sister will bake 18.

So total cookies already assigned = 2 (14)+18

= 28 + 18 = 46

Remaining cookies you need to bake = 102 - 46 =56

Required Fraction = \frac{\text{Number of cookies you bake}}{\text{Total}}=(56)/(102)=(28)/(51)

Hence,  fraction of the cookies you need to bake =(28)/(51) .


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What is the solution to the system of equations y= -5x +3 y=1

Answers

To find the solution to this, we need to use the substitution method.

y = -5x + 3

Substitute the value for y.

y =1

1 = -5x + 3

Now, solve for x.

1-3 = -5x + 3           Apply the inverse operation to both sides of the equation.
            -3

1-3 is -2

-2 = -5x

-5x/-5 = -2/-5 
x = 0.4

Final answer:-   x = 0.4     y = 1

Answer:

(0.4, 1)

Step-by-step explanation:

A study is done on the population of a certain fish species in a lake. Suppose that the population size P(t) after t years is given by the following exponential function. P(t)=280(1.29)^t Find the initial population size?
does the function represent growth or decay?
By what percentage does the population change each year?

Answers

Answer:

  1. 280
  2. function represent growth.
  3. 29 %

Step-by-step explanation:

Equation to calculate population size after time, t

P(t) = 280(1.29)^t

To find initial population size we will take t = 0

P(0) = 280(1.29)^0

       = 280(1)

       = 280

To find that function represent growth or decay

P(1) = 280(1.29)^1

      = 280(1.29)

      = 361.2

Its means that after a year population increases. Hence, function represent growth.

By what percentage does the population change each year?

(361.2 - 280 / 280) * 100%

 = 29 %

Answer:

280

function represent growth.

29 %

Log8(2-5x)=log8(-4x+3)

Answers

2 - 5x > 0 and -4x + 3> 0

log8(2-5x)=log8(-4x+3) <=> 2 - 5x = - 4x + 3 <=> -5x + 4x = 3 - 2 <=> -x = 1 <=> x = -1;

2 - 5(-1) = 7 > 0 and -4(-1) + 3 = 7 > 0 ;

the solution is -1;

If w = 7, what is the value of 21 - 2w?

Answers

do order off operations first
so 7 time 2 which is 14
then 21-14
which is 7
21-2(7)=
=21-14
=7
The answer is 7

Martha Owens is paid $14.50per hour for a regular forty-hour work
week. Her overtime pay is one-and-one-
half times her regular hourly rate. This
past week Martha earned S754.00 in total
рау. .
How many hours of overtime did
Martha work this pas week?

Answers

Martha worked approximately 8 hours of overtime during the past week.

Martha's regular hourly rate is $14.50, and she works a regular forty-hour work week. Her overtime pay is one-and-one-half times her regular hourly rate.

Let's break down Martha's earnings for the week:

Regular Earnings (for 40 hours): Regular Hourly Rate × Hours Worked

Regular Earnings = $14.50 × 40 = $580

Total Earnings (including overtime): $754

Overtime Earnings = Total Earnings - Regular Earnings

Overtime Earnings = $754 - $580 = $174

Since Martha's overtime pay is one-and-one-half times her regular hourly rate, we can set up an equation:

Overtime Earnings = Overtime Hourly Rate × Hours of Overtime Worked

Solving for Hours of Overtime Worked:

Hours of Overtime Worked = Overtime Earnings / Overtime Hourly Rate

Overtime Hourly Rate = 1.5 × Regular Hourly Rate

Overtime Hourly Rate = 1.5 × $14.50 = $21.75

Now, plug in the values:

Hours of Overtime Worked = $174 / $21.75 ≈ 8

Martha worked approximately 8 hours of overtime during the past week.

Learn more about work here

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Answer:

Step-by-step explanation:

14.50*40=580 for reg pay

754-580=174 over time

14.50*1.5=21.75 an hour for ot

174/21.75=8 hours of overtime

Use implicit differentiation to find dy/dx. xy+5tan⁻¹(y)=7

Answers

i wrote the answer you can check