102 x5 multiply with expanded form

Answer:

The amount of oil was decreasing at 69300 barrels, yearly

Step-by-step explanation:

Given

[tex]Initial =1\ million[/tex]

[tex]6\ years\ later = 500,000[/tex]

Required

At what rate did oil decrease when 600000 barrels remain

To do this, we make use of the following notations

t = Time

A = Amount left in the well

So:

[tex]\frac{dA}{dt} = kA[/tex]

Where k represents the constant of proportionality

[tex]\frac{dA}{dt} = kA[/tex]

Multiply both sides by dt/A

[tex]\frac{dA}{dt} * \frac{dt}{A} = kA * \frac{dt}{A}[/tex]

[tex]\frac{dA}{A} = k\ dt[/tex]

Integrate both sides

[tex]\int\ {\frac{dA}{A} = \int\ {k\ dt}[/tex]

[tex]ln\ A = kt + lnC[/tex]

Make A, the subject

[tex]A = Ce^{kt}[/tex]

[tex]t = 0\ when\ A =1\ million[/tex] i.e. At initial

So, we have:

[tex]A = Ce^{kt}[/tex]

[tex]1000000 = Ce^{k*0}[/tex]

[tex]1000000 = Ce^{0}[/tex]

[tex]1000000 = C*1[/tex]

[tex]1000000 = C[/tex]

[tex]C =1000000[/tex]

Substitute [tex]C =1000000[/tex] in [tex]A = Ce^{kt}[/tex]

[tex]A = 1000000e^{kt}[/tex]

To solve for k;

[tex]6\ years\ later = 500,000[/tex]

i.e.

[tex]t = 6\ A = 500000[/tex]

So:

[tex]500000= 1000000e^{k*6}[/tex]

Divide both sides by 1000000

[tex]0.5= e^{k*6}[/tex]

Take natural logarithm (ln) of both sides

[tex]ln(0.5) = ln(e^{k*6})[/tex]

[tex]ln(0.5) = k*6[/tex]

Solve for k

[tex]k = \frac{ln(0.5)}{6}[/tex]

[tex]k = \frac{-0.693}{6}[/tex]

[tex]k = -0.1155[/tex]

Recall that:

[tex]\frac{dA}{dt} = kA[/tex]

Where

[tex]\frac{dA}{dt}[/tex] = Rate

So, when

[tex]A = 600000[/tex]

The rate is:

[tex]\frac{dA}{dt} = -0.1155 * 600000[/tex]

[tex]\frac{dA}{dt} = -69300[/tex]

Hence, the amount of oil was decreasing at 69300 barrels, yearly

Answer:

6+ x 7=8

Step-by-step explanation:

6 more product of a number and it equals 8

Answer:

Just over 6 pounds each

Step-by-step explanation:

or exactly 6.25 pounds each

[tex]\huge{\textbf{\textsf{{\color{pink}{An}}{\red{sw}}{\orange{er}} {\color{yellow}{:}}}}}[/tex]

The estimate weight of each bundle is 6 pounds.

exactly it's 6.25 (bcoz 50 ÷ 8 is 6.25)

Answer:

-1

Step-by-step explanation:

[tex] \sqrt{9 - 4 \sqrt{2} } - 2 \sqrt{2} \\ \\ = \sqrt{8 + 1 - 4 \sqrt{2} } - 2 \sqrt{2} \\ \\ = \sqrt{8 - 4 \sqrt{2} + 1} - 2 \sqrt{2} \\ \\ = \sqrt{ {(2 \sqrt{2}) }^{2} - 2 \times 2 \sqrt{2} \times 1 + {1}^{2} } - 2 \sqrt{2} \\ \\ = \sqrt{( {2 \sqrt{2} - 1)}^{2} } - 2 \sqrt{2} \\ \\ (2 \sqrt{2} - 1) - 2 \sqrt{2} \\ \\ = 2 \sqrt{2} - 1 - 2 \sqrt{2} \\ \\ = - 1[/tex]

Answer: X = 2 so Y=25, hope this helped!!

Step-by-step explanation:

Answer:

Step-by-step explanation:

Bonjour,

2x*3x =6x²

2x* -5 = -10x

-3 * 3x = -9x

-3*-5 = 15

=>

6x² -10x  - 9x +15 = 6x ² -19x  +15

Answer:

6x^2 - 19x + 15.

Step-by-step explanation:

(2x - 3)(3x -5)​

= 2x(3x - 5) - 3(3x - 5)

= 6x^2 - 10x - 9x + 15

= 6x^2 - 19x + 15.

9514 1404 393

Answer:

Step-by-step explanation:

In this isosceles right triangle, the acute angles are equal and the side lengths have the ratios 1 : 1 : √2

  y° = 90° -45° = 45°

  9 : x : z = 1 : 1 : √2 = 9 : 9 : 9√2

  x = 9; z = 9√2

Answer:

48

Step-by-step explanation:

12*4=48

Answer:

dude this is easy

Step-by-step explanation:

all you have to do is multiply; 7x13

in this case it equals 91.

=91

Answer:

-3/8, -3/16, 7/4

Answer:

1⁸,2⁴,5²,3³

Step-by-step explanation:

so its 1,16,25,27

Answer:

A

Step-by-step explanation:

AP EX

The transformation of f(x)=sin(x) to g(x)=sin(x-π/4), means that the function f(x) is shifted to the right by (π/4) units.

A function assigns the value of each element of one set to the other specific element of another set.

The transformation of f(x)=sin(x) to g(x)=sin(x-π/4), means that the function f(x) is shifted to the right by (π/4) units.

Learn more about Function:

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Answer:

Hi, The.

The domain of a function is the set of all possible values for x. The range is all possible values for y.

You should be able to see these pretty easily from the graph. If I understand your function correctly:

f(x) = square root(x+2) - 3

then x cannot be less than -2. Your domain is x > -2. In interval notation [-2,∞)

The lowest value for y is -3 so the range is y > -3. In interval notation [-3,∞)

Hope this helps!

Answer:

D

Step-by-step explanation:

y is directly proportional with x with a constant value.

The constant value ＝y ÷ x ＝35÷2.5 ＝14

y＝14x

y＝14×3.25＝45.5

Answer:

B. 1/3

Step-by-step explanation:

If we take the fist two boxes on top of the grid, we can divide 7 1/2 by 2 1/2 to find the ratio. In this case, the ratio is 3, meaning that for every cup of sugar their is 3 cups of flour. This means that 1 cup of flour would equal 1/3 cups of sugar.

Answer:

4

Step-by-step explanation:

0 is a significant figure and since there are no 0 in the number after the decimal point its 4 significant figures

37.5

Hope this helps :T

Answer:

There's only one answer, and that's x=0.

Step-by-step explanation:

Step 1: Simplify both sides of the equation.

3(3x−1)=6x−3

(3)(3x)+(3)(−1)=6x+−3(Distribute)

9x+−3=6x+−3

9x−3=6x−3

Step 2: Subtract 6x from both sides.

9x−3−6x=6x−3−6x

3x−3=−3

Step 3: Add 3 to both sides.

3x−3+3=−3+3

3x=0

Step 4: Divide both sides by 3.  

[tex]\frac{3x}{3}[/tex]=[tex]\frac{0}{3}[/tex]

x=0

hope this helps

Answer:

x=2

Step-by-step explanation:

x+19=21

subtract 19 so x can be by itself, move it to the 21 side

and subtract21-19=2

Answer:

You solve. for X. The photo is the work and answer

Answer:

x=15

Step-by-step explanation:

Answer:

Explanation:

2/3 (x-6) = 6

2x/3 - 12/3 = 6

(2x-12)/3 = 6

2x-12 = 18

2x = 18+12

2x = 30

x = 15

Answer:

D

Step-by-step explanation:

value of each:

A)  100/1000 + 20/1000 + 8/1000 = 128/1000 = 0.128

B)  3/10 = 0.30

C)  7/100 = 0.07

D)  24/1000 = 0.024

Answer:

a ko ans

= 2×2+9

=4+9

= 13ans

Answer: [tex]\sqrt{96}[/tex] or [tex]4\sqrt{6}[/tex], if you want the decimal form then its 9.79.

Step-by-step explanation:

14²-10²=96

[tex]\sqrt{96}[/tex] or [tex]4\sqrt{6}[/tex], if you want the decimal form then its 9.79.

The expressions equivalent to the given expressions are; (2y+12), 4(y/2+3) and 4(y/2-4+7)

An algebraic expression consists of unknown variables, numbers and arithmetic operators. It does not contain any equality or inequality symbols.

Given an expression, 4(7/8y-4-3/8y+7)

4(7/8y-4-3/8y+7) = 7/2y-16-3/2y+28

= 1/2(7y-32-3y+56)

= 1/2(4y+24)

= 2y+12

or, 4(1/2y+3) or 4(1/2y-4+7)

Hence, The expressions equivalent to the given expressions are; (2y+12), 4(y/2+3) and 4(y/2-4+7)

For more references on expression, click;

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Answer:I cannot see photo

Answer:

The average yearly replacement cost is approximately $32,211,500

Step-by-step explanation:

 Exponential Distribution

P(X < x) = 1 - e -x/

[tex]P(X < x) = 1 - e^{\dfrac{-x}{\mu}}[/tex]

For the CPU, μ = 3 years

The probability that a CPU fails in less than 1 year is therefore;

P(C) = [tex]P(X < 1) = 1 - e^{\dfrac{-1}{3}} \approx 0.2835[/tex]

For the RAM, μ = 2 years

The probability that a RAM fails in less than 1 year is therefore;

P(R) = [tex]P(X < 1) = 1 - e^{\dfrac{-1}{2}} \approx 0.3935[/tex]

For the hard drive, μ = 5 years

The probability that a hard drive fails in less than 1 year is therefore;

P(H) = [tex]P(X < 1) = 1 - e^{\dfrac{-1}{5}} \approx 0.1813[/tex]

The probability that either a CPU, or a RAM or a hard drive fails in 1 year so that a replacement is required, P(C ∪ R ∪ H), is given as follows;

P(C ∪ R ∪ H) = P(C) + P(R) + P(H) - P(C∩R) - P(C∩H) - P(R∩H) + P(C∩R∩H)

∴ P(C ∪ R ∪ H) = 0.2835 + 0.3935 + 0.1813 - (0.2835 × 0.3935) - (0.2835 × 0.1813) -(0.3935 × 0.1813) + (0.2835 × 0.3935 × 0.1813) ≈ 0.64423

∴ P(C ∪ R ∪ H) ≈ 0.64423

There is a 0.64423 chance that a laptop will require replacement

For 100,000 laptops sold a year and a replacement cost of $500 per laptop, we have;

The average yearly replacement cost, 'Cost' is given as follows;

Cost = 500 × 100,000 × 0.64423 = 32,211,500

The average yearly replacement cost, Cost ≈ $32,211,500

Answer:

On the 10th day, the suit should cost around $11.38.

Step-by-step explanation:

It was a long process. Not sure if it is right because that price drop is very drastic, but these math problems are always extreme. LOL

Good Luck!!

Answer:

The answer is 25 plants because all the frequencies add up to 25. While this graph could represent plants when they’re growing, all bars would be the same length though as all plants would hit a certain height.

B) Interval 150-155 has the highest frequency as 8 plants are 150-155cm.

Step-by-step explanation:

Answer:

B) The cost of milk by the gallon.

C) The price of pears by the pound.

Step-by-step explanation:

A linear function is one that both the dependent and independent variables increases or decreases proportionally.

Thus from the given options:

i. If the gallons of milk increase, then the cost of milk also would increase proportionally. A decrease in the gallons of milk would also reduce the cost of milk.

ii. An increase in the pounds of the pearls would cause an increase in the price of the pearls. Also, a decrease in the pounds of pearls would reduce the price of the pearls.

Thus, the answers to the question are options B and C.

Answer:

The other guy is correct however he missed one

The Answer is actually A, B, C

Step-by-step explanation:

I took the test on Usa test prep.