Mist ate 2 slices of cake. Flout ate 1 slice. If Mist ate 2/4 of the cake and all the slices were the same size, what fraction of the cake remained after Mist and Flout had eaten?

Answers

Answer 1
Answer: 1/4 remained
2/4 - mist + 1/4 -flout = 3/4
4/4 - 3/4 = 1/4
Answer 2
Answer: one fourths would be left

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Solve the equation for x 2x+y=5x-6

Answers

Answer:

x = 2+(y)/(3)

Step-by-step explanation:

An owner of a key rings manufacturing company found that the profit earned (in thousands of dollars) per day by selling n number of key rings is given by , where n is the number of key rings in thousands. Find the number of key rings sold on a particular day when the total profit is $5,000.

Answers

Answer:

The number of key rings sold on a particular day when the total profit is $5,000 is 4,000 rings.

Step-by-step explanation:

The question is incomplete.

An owner of a key rings manufacturing company found that the profit earned (in thousands of dollars) per day by selling n number of key rings is given by

P=n^2-2n-3

where n is the number of key rings in thousands.

Find the number of key rings sold on a particular day when the total profit is $5,000.

We have the profit defined by a quadratic function.

We have to calculate n, for which the profit is $5,000.

P=n^2-2n-3=5\n\nn^2-2n-8=0

We have to calculate the roots of the polynomial we use the quadratic equation:

n=(-b\pm√(b^2-4ac))/(2a)\n\nn= (-2\pm√(4-4*1*(-8)))/(2)= (-2\pm√(4-32))/(2) = (-2\pm√(36))/(2) =(-2\pm6)/(2) \n\nn_1=(-2-6)/2=-8/2=-4\n\nn_2=(-2+6)/2=4/2=2

n1 is not valid, as the amount of rings sold can not be negative.

Then, the solution is n=4 or 4,000 rings sold.

A total of 707
tickets were sold for the school play. They were either adult tickets or student tickets. There were
57
more student tickets sold than adult tickets. How many adult tickets were sold?

Answers

325 adult tickets, 382 student

On 1st September 2014 there were 5400 trees planted in a wood.On 1st September 2015, only 5184 of these trees were still alive.
It is assumed that the number of trees still alive is given by N = art
where / is the number of trees still alive t years after 1st September 2014.
a) Write down the value

c) Show that on 1st September 2040
the number of trees still alive is predicted
o have decreased by over 65% compared
with September 2014.

b) Show that r = 0.96​

Answers

Answer:

1. a = 5400

2. r = 0.96

3. Percentage decrement = 65.4%

Step-by-step explanation:

Given

N = ar^t

Solving (a): Write down the value of a

a implies the first term

And from the question, we understand that the initial number of trees is 5400.

Hence,

a = 5400

Solving (b): Show that r = 0.96

Using

N = ar^t

When a = 5400, t = 1 i.e. the first year and N = 5184

Substitute these values in the above expression

5184 = 5400 * r¹

5184 = 5400 * r

5184 = 5400r

Solve for r

r = 5184/5400

r = 0.96

Solving (c): Show that the trees has decreased by over 65% in 2040

First, we need to calculate number of years (t) in 2040

t = 2040 - 2014

t = 26

Substitute 26 for t, 5400 for a and 0.96 for r in N = ar^t to get the number of trees left

N = 5400 * 0.96^26

N = 1868.29658019

N = 1868 (approximated)

Next, we calculate the percentage change as thus:

%Change = (Final - Initial)/Initial * 100%

Where the initial number of trees =5400 and final = 1868

%Change = (1868 - 5400)/5400 * 100%

%Change = -3532/5400 * 100%

%Change = -3532%/54

%Change = -65.4%

The negative sign indicates a decrements or reduction.

Hence, percentage decrement = 65.4% and this is over 65%

Find the slope and y- of the table​

Answers

Answer:

y = (3/2) x +6

Step-by-step explanation:

The y-intercept is clearly at y = 6 point (0, 6) of the table.

The slope can be calculated using any two pairs, for example (-4,0) and (-2, 3)

slope = (y2 - y1)/(x2 - x1) = (3 - 0) / (-2 + 4 ) = 3/2

Then the equations of the line in slope y-intercept form is:

y = (3/2) x +6

the answer is y=(3/2)x+6

Solbe for x : x-1/x+3x+3=0​

Answers

Answer:

x=1/4 or x=-1

Step-by-step explanation:

x−

1

x

+3x+3=0

4x2+3x−1

x

=0

Step 1: Multiply both sides by x.

4x2+3x−1=0

(4x−1)(x+1)=0(Factor left side of equation)

4x−1=0 or x+1=0(Set factors equal to 0)

x=

1

4

or x=−1

Check answers. (Plug them in to make sure they work.)

x=

1

4

(Works in original equation)

x=−1(Works in original equation)

Answer:

x=

1

4

or x=−1