x/3 - y/2= 1

x/4 - y/3 = 1

solve the sets of equation.​

Answer:

a) y=5000e^{0.099t}

b) 11.097 hours

Step-by-step explanation:

a

Many systems exhibit exponential growth. These systems follow a model of the form \(y=ae^{kt}\), where a represents the initial state of the system and k is a positive constant, called the growth constant.

So we have our value of which represents the initial state of the system, which is 5000.

We need to calculate k.

Now,

It says he doubling time of a population of bacteria is 7 hours there are 5000 present initially, which means at 0 hours there were 5000 bacteria (initially means at t = 0, and then after 7 hours it doubled so it became 10,000 at 07:00 hours then at 14:00 it became 20,000 and then at 21:00 it became 40,000 this is the doubling time. So to calculate the value of k we can use this data, lets take 10,000 bacteria at 07:00 hours and put in our equation.

\(y=ae^{kt} \\y=5000e^{kt}\)

value of a is 5000 which was the initial value now we need the value of y which is the total amount of bacteria after t hours. So after 7 hours we have a total of 10,000 bacteria so our value of t becomes 7 and value of y becomes 10,000.

\(10000=5000e^{7k}\)

\(2=e^{7k} \\\)

Apply natural logarithm on both sides

\(ln2=lne^{7k}\)

Ln e becomes 1 as we all know so we write 7k as it is.

\(ln2=7k\)

\(k=\frac{ln2}{7} \\k=0.099\)

Now our equation is

\(y=5000e^{0.099t}\)

we can confirm this by inserting time t as 7 , 14 , 21 , 28 , 35  and we will get the exact bacteria we need which is y 10,000 , 20,000 , 40,000 , 80,000 , 160,000, respectively.

b)

It says how long will it take the population to triple which means the triple of 5000 is 15,000 and we set that to the value of y which is the amount of bacteria, and calculate t.

\(y=5000e^{0.099t} \\\\15000=5000e^{0.099t} \\\\3=e^{0.099t} \\ln3=lne^{0.099t} \\\\ln3=0.099t\\\\t=\frac{ln3}{0.099} \\\\t=11.097\)

Which means it would take 11.097 hours for bacteria of 5000 to triple in size.

I passes for (2,-5) and (1,-3)

then

its open up

because y=-3 is over y =- 5

Answer is then: open up

Write Vertex form

y =2(x -2) ^2 -5

because x=1, y = -3

Then answer is

y= 2(x-2)^2 - 5. Its option D, from left to right.

Answer:

10 weeks

Step-by-step explanation:

40 books= ? weeks

4 books.  = 1 week

so do 40/4 and get 10

Answer:

10 weeks

Step-by-step explanation:

Answer:

180

Step-by-step explanation:

Answer:

x = -13

Step-by-step explanation:

-2 (x + 4) = 18

distributive property  -2x + (-8) = 18

simplify   -2x - 8 = 18

cancel out 8 by addition  -2x = 26

cancel out -2 by division  x = -13

Answer:

13

Step-by-step explanation:

75 / 6 = 12.5, so they need 13 cars

Answer:

6 servings

Step-by-step explanation:

1,25x6=7.5

The number of servings can you make deep-fried chicken will be 6.

Inequality is defined as an equation that does not contain an equal sign.

You have 8 cups of milk.

You need 1.25 cups to make one serving of deep-fried chicken.

Let x be the number of the deep-fried chicken.

Then the inequality will be

1.25x ≤ 8

On solving, we have

x ≤ 6.4

Then the number of servings can you make deep-fried chicken will be 6.

More about the inequality link is given below.

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Step-by-step explanation:

\( = 47.000\)

\( = 4,7 \times 10.000 \)

\( = 4,7 \times {10}^{1+1+1+1} \)

\( = 4,7 \times 10^4 \)

Answer:

Cuatro fabricantes de automóviles japoneses anunciaron el retiro de casi 3,4 millones de automóviles del mercado debido a un posible defecto en los airbags.

Un funcionario japonés aseguró que el problema con los airbags, fabricado por la firma japonesa Takata, afecta 1,73 millones de autos de Toyota (fabricados entre 2000 y 2004), 1,13 millones de Honda, 480.000 de Nissan y 45.000 de Mazda.

Una portavoz de Toyota dijo que se registraron cinco incidentes de mal funcionamiento del airbag en sus vehículos pero que no se habían registrado accidentes ni lesiones.

Una pieza defectuosa, agregó esta compañía, "podría hacer que el inflador del airbag se rompa y desplegarlo de forma anormal en un accidente".

Answer:

x=1/8

Step-by-step explanation:

Answer:

x=1/8

Step-by-step explanation:

Answer:

$1431

Step-by-step explanation:

If Stan pays a 10% deposit, he pays $159. 10% of $1590 is simply 0.1 * 1590 = 159. Assuming this is the only amount he pays, he then simply needs to pay the full price minus $159. We can find this by simply subtracting 159 from 1590 to get 1431. Stan still needs to pay $1431.

Answer:

y ≥ 8

Explanation:

Note that if f(x) is transformed into f(x + a) - b

The original functions is shifted a units to the left and b units downward.

Horizontal shifting will not affect the range of the function, only vertical shifting will change its range.

From the given, g(x) is the transformation of f(x) with

f(x) is shifted 2 units to the left and 3 units downward, we will disregard the horizontal shifting.

Since f(x) has a range of y ≥ 11, and g(x) is 3 units downward, the range will also move 3 units downward.

y ≥ 11 - 3

The answer is y ≥ 8

Step-by-step explanation:

Let the ratio constant be 'x'

Sum of the ratios=3x+5x=8x

First person gets:-

3/8 x 560 = 210

Second person gets:-

5/8 x 560 = 350

Answer:

B, He is -40 due to it asking which number is his point. If he was positive 40 then he would be on an island or flying in the sky. Your answer is -40

9514 1404 393

Answer:

  a) $169,234.59

  b) $19,234.59

Step-by-step explanation:

The first question you must answer is whether Colleen will earn interest on her first deposit in the first year. That is, does she deposit the money at the first of the year or the end of the year?

The usual "annuity" formula assumes the deposit is at the end of the year, so no interest at all is earned on the last deposit made. If the deposit is at the first of the year, an "annuity due" formula is used, that multiplies the entire ending account value by the annual multiplier, 1.017 in this case.

__

a) Assuming an "annuity", the formula is ...

  A = P((1 +r)^t -1)/r . . . . . for annual compounding at rate r for t years

  A = $10,000(1.017^15 -1)/0.017 = $169,234.59 . . . . ending balance

__

b) Colleen has made 15 deposits of $10,000, for a total of $150,000, so the amount of interest earned is ...

  $169,234.59 -150,000 = $19,234.59 . . . . interest earned

Answer:

8

Step-by-step explanation:

(1) Complementary angles always add up to 90 deg, if one angle is 48 deg then another one will be 90-48 = 42 deg

(2) Supplementary angles on the other hand always add up to 180 deg or half a circle so if one angle is 65 deg then another angle is 180-65 =115 deg

This is the answer.

Answer:

2

Step-by-step explanation:

Answer:

2 more cups

Step-by-step explanation:

This is the answer because:

1) Convert each fraction to an improper fraction.

5 1/5 = 26/5

3 1/5 = 16/5

2) Now, just subtract 26/5 and 16/5

26/5 - 16/5 = 10/5

3) 10/5 equals 2, therefore, the answer is 2

10/5 = 2

Hope this helps!

equation:3.25x+1.2=40.2

ansrew:x=12

Rational numbers include all the integers plus all the fractions, terminating decimal and repeating decimal.

All rational numbers can be represented as a fraction

the answer is No

All rational numbers are not integers.

hii! i just wanted to say hope you're having a fantastic day and hope that things are going well (: stay strong and stay safe!

The solution to given linear inequality, 6(x1.5) + 30 < 48, is x < 2

From the question, we are to solve the given linear inequality

The given linear inequality is

6(x1.5) + 30 < 48

First, we will write this inequality properly.

The inequality can be properly written as

6(1.5x) + 30 < 48

Now, we will solve the linear inequality

6(1.5x) + 30 < 48

Subtract 30 from both sides of the equation

6(1.5x) + 30 - 30 < 48 - 30

6(1.5x) < 18

Divide both sides of the inequality by 6

6(1.5x)/6 < 18/6

(1.5x) < 3
1.5x < 3

Divide both sides of the inequality by 1.5

1.5x/1.5 < 3/1.5

x < 2

Hence, the solution is x < 2

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Answer:

Correct answer: 32.12 yards2

Step-by-step explanation:

Area of a Rectangle

Given a rectangle of width W and length L, the area can be calculated as follows:

A = W.L

We are given the following dimensions of the rectangle: Length = 7.3 yards, Width = 4.4 yards. Calculate the area substituting the values into the formula:

A = 4.4 yards * 7.3 yards

\(A=32.32\ yards^2\)

Correct answer: 32.12 yards2

Answer:

Skewed Left

Step-by-step explanation:

Because it's going to the left side, so it has to be skewed left.

There are 20 students have more than 2 pets.

We have to given that;

A line plot titled Number of Pets of Third Grade Students.

Here, By given information we get;

Number of students have more than 2 pets are,

⇒ 4 + 2 + 3 + 0 + 1 + 5 + 1 + 1 + 3

⇒ 20

Thus, There are 20 students have more than 2 pets.

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Answer:

10,800

Step-by-step explanation:

9,000+ 20%= 10,800

Answer:

6.71428571 or 6 remainder 5

Step-by-step explanation:

A total of 7 Cyclists traveled more than 45 miles. 4 cyclists traveled 50 miles or more, and 3 cyclists traveled more than 54 1/4 miles.

A line plot is drawn with the cyclists' names plotted on the x-axis and their corresponding distances covered plotted on the y-axis.

The dots are then joined to form a line, revealing the relationship between the cyclist's names and their corresponding distance traveled. The cyclist names and their corresponding distances are given in the table below.

Name Distance (in miles) Gina 40 1/2 Rey 50 Faye 35 3/4 Mark 60 John 45 1/2 James 40 1/2 Albert 40 1/4 William 54 1/4 Nathan 40 Kate 40 1/4 Mary 60 Risa 40 Abi 35 3/4 Joan 50 1/2 1. The number of cyclists is 14. 2. The longest distance covered by a cyclist is 60 miles.

Mary and Mark both covered this distance.3. A total of 7 cyclists traveled less than 50 miles. 4. The most common distance traveled by cyclists is 40 1/2 miles. Gina, James, and Albert covered this distance. 5. 2 more cyclists traveled 45 miles than 55 1/4 miles. Only William traveled 55 1/4 miles, while John and James both traveled 45 1/2 miles.6.

A total of 7 cyclists traveled more than 45 miles. 4 cyclists traveled 50 miles or more, and 3 cyclists traveled more than 54 1/4 miles.

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