Outside temperature over a day can be modeled as a sinusoidal function. Suppose you know the high temperature of 87 degrees occurs at 6 PM and the average temperature for the day is 70 degrees. Find the temperature, to the nearest degree, at 11 AM.

Answer:

The dimensions of the drawing are 10 units by 8 units

Step-by-step explanation:                        

we know that

The scale drawing is [tex]\frac{1}{15}\ \frac{unit}{feet}[/tex]

That means ---> 1 unit in the drawing represent 15 feet in the actual

To find out the dimensions of the drawing, multiply the actual dimensions by the scale drawing

so

[tex]150\ ft=150(\frac{1}{15})=10\ units[/tex]

[tex]120\ ft=120(\frac{1}{15})=8\ units[/tex]

therefore

The dimensions of the drawing are 10 units by 8 units

Answer:

log base 6 of the cube root of 6 matches with 1/3

-3 log 5 of 25 matches with -6

log base 2 of the 4th root of 8 matches with 3/4

log base 3 of 1/81 matches with -4

Answer:

Step-by-step explanation:

Let's simplify all the possible answers:

Hope it will find you well.

Answer:

160 basket of each fruit baskets we can make using all fruit.

Step-by-step explanation:

Given:

Oranges comes in bags = 16

Apples comes in bags = 20

bananas come in bags = 32

We need to find the greatest number of fruit baskets that you can make using all fruit.

Also Given:

You have one bag of each fruit basket must be identical.

So we will first find the least common multiple of all the numbers we get;

20 = 20,40,60,80,100,120,140,160

16 = 16,32,48,64,80,96,112,128,144,160

32 = 32,64,96,128,160

The least common multiple is 160.

Hence we can say that, 160 basket of each fruit baskets we can make using all fruit.

Answer:

Members of Singing group will buy minimum 135 number of balcony tickets.

Step-by-step explanation:

Given:

Minimum of tickets will be bought =250

Let number of lawn tickets be 'l'.

Also Let number of balcony tickets be 'b'

Now given

The group buys 20 fewer lawn tickets than balcony tickets.

Framing in equation form we get;

[tex]l=b-20[/tex]

Now The Sum of Number of balcony tickets and Number of lawn tickets should be greater than or equal to Minimum of tickets will be bought by the group.

Framing in equation form we get;

[tex]l+b\geq 250[/tex]

Now substituting the value of 'l' in above equation we get;

[tex](b-20)+b\geq 250\\\\b-20+b\geq 250\\\\2b-20\geq 250\\\\2b\geq 250+20\\\\2b\geq 270\\\\b\geq \frac{270}{2}\\\\b\geq 135[/tex]

Now we know the value of b which is 135 we will substitute in equation [tex]l=b-20[/tex] to find the value of l we get;

[tex]l=135-20 = 115[/tex]

Hence Members of singing group will buy minimum 135 number of balcony tickets.

Answer:

whole numbers can be written in fraction form. But fraction can or cannot be whole number.

Answer is fraction.

Step-by-step explanation:

As, the fraction number is in the form of [tex]\frac{p}{q}[/tex] and the first number is whole number [tex](a)[/tex].

when fraction multiply by whole number,

[tex]\frac{p}{q} \times a=\frac{a \times p}{q}[/tex] is fraction.

For example, [tex]p=2,q=3 \ and \ a=4[/tex]

[tex]\frac{p}{q} \times a=\frac{4 \times 2}{3}[/tex]

[tex]\frac{p}{q} \times a=\frac{8}{3} \Rightarrow \ fraction[/tex]

For example, [tex]p=3,q=5 \ and \ a=5[/tex]

[tex]\frac{p}{q} \times a=\frac{5 \times 3}{5}[/tex]

[tex]\frac{p}{q} \times a=\frac{3}{1} \Rightarrow \ whole \ number[/tex]

Answer:

The answer to your question is below

Step-by-step explanation:

See the picture below

G ∩ M = { Max, Anael}

G ∪ S = { Max, Acel, Carl, Anael, Acton, Dario, Kai, Barek, Carlin}

Answer:

Step-by-step explanation:

From the table, the number of copies can be plotted on the y axis and against the number of minutes on x axis. The slope of the straight line graph that would be formed would represent the become n, the number of copies the machine can print in one minute.

n = (y2-y1)/(x2-x1)

Picking points from the table,

y2 = 650

y1 = 325

x2 = 10

x1 = 5

Slope, n = (650 - 325)/(10 - 5)

n = 325/5 = 65 copies per minute

Working at the same rate, the time that it will take the machine to print 5,200 copies would be

65 copies = 1 minute

5200 copies would take

5200/65 = 80 minutes

Answer:

The solution is x=-2, y=4

Step-by-step explanation:

we have

[tex]6x-5y=-32[/tex] ----> equation A

[tex]-7x+8y=46[/tex] ----> equation B

Solve the system by graphing

Remember that

The solution of the system of equations is the intersection point both graphs

using a graphing tool

The intersection point is (-2,4)

see the attached figure

therefore

The solution is x=-2, y=4

Answer:

The solution is x=-2, y=4

Step-by-step explanation:

Answer:

Y = 66x - 1200 will be the equation.

Step-by-step explanation:

This question is incomplete; Here is the complete question.

A charity organization had a fundraiser where they sold each ticket for a fixed price. After selling 200 tickets, they had a net profit of $12,000. They had to sell a few tickets just to cover necessary production costs of $1200.

       Let Y represent the net profit (in dollars) when they have sold c tickets. Complete the equation for the relationship between the net profit and the number of tickets sold.

If the selling price of one ticket is $x, then selling price of 200 tickets

= $200x

Since production cost of the tickets = $1200 and profit earned is $12000

Therefore, Profit = Selling price of x tickets - production cost

12000 = 200x - 1200

200x = 13200

x = $66

Now we can rewrite the equation for c tickets sold and profit earned $Y

Y = 66c - 1200

Answer:

2% area reduction

Step-by-step explanation:

The original area is 18.2*28.5=518.7 sq km

1.2% reduction of 18.2 km is 17.9816 km (18.2-18.2*1.2/100)

0.8% reduction of 28.5 km is 28.272 km (28.5-28.5*0.8/100)

The new are is 17.9816*28.272=508.3757 sq km (98 % of the original area)

Another way is (100-1.2)*(100-0.8) LW/(100*100)=0.98LW (98 % of the original area)

Answer:

Here's the answer ;)

Answer:

The opportunity cost will be 3 cars

So option (d) will be correct answer

Step-by-step explanation:

The opportunity is cost is best characterized as the following best action done without, it is something we give up to gain another.

For instance the opportunity cost of going to class can be the pleasure from watching movie, or spending time with companions or something different. The opportunity  cost can be determined by isolating what you forgone by what you gain.

So opportunity cost [tex]=\frac{12}{4}=3cars[/tex]

So option (d) will be the correct answer

Final answer:

Pete's opportunity cost of producing one truck is 3 cars, which is found by dividing Pete's car production rate by his truck production rate (12 cars per hour / 4 trucks per hour).

Explanation:

Pete's opportunity cost of producing one truck can be determined by looking at the alternative production of cars he could have achieved in the same amount of time. Since Pete can produce 12 cars per hour or 4 trucks per hour, we can set up a ratio of cars to trucks based on his production abilities. To find the opportunity cost of one truck, we divide the number of cars Pete can make by the number of trucks, which is 12/4, giving us 3. Hence, Pete's opportunity cost of one truck is 3 cars. This calculation is similar to how opportunity cost is determined in examples such as the production possibility frontier, where the slope shows the trade-off between two different products.

Answer:

Answer: a. 1.203 m/s   b.0.35m

Step-by-step explanation:

Good evening ,

Answer:

(-3x^3+5x^2+4x-7)-(6x^3-2x+3)​ = -9x³+5x²+6x−10

Step-by-step explanation:

(-3x^3+5x^2+4x-7)-(6x^3-2x+3)​ = -3x³+5x²+4x-7-6x³+2x−3

                                                   = -9x³+5x²+6x−10.

:)

Answer:

a. A minimum of 300

Step-by-step explanation:

If her bill  is $142 then it is a sum of the flat rate plus the money she pays for all the smses she sent. As an equation, it can be expressed this way

106 + 0.12x = 142  where x  is the number of smses

0.12x = 36

x = 300 smses

So if we were told that she pays $142 per month, we'd know that she sends 300 smses. But we are told she pays AT LEAST $142 so there is a possibility that she sends even more than 300 smses

Answer:

  [tex]h_1(t)=-16t^2+154[/tex]

Step-by-step explanation:

Put the initial height of ball 1 into the given formula:

  [tex]h_1(t)=-16t^2+154[/tex]

Answer:The equation to determine how much Elise will pay for a student ticket is 2x = 33

Step-by-step explanation:

Let x represent the price of one student ticket.

Elise and her dad are planning to attend the state fair and the price of an adult ticket is $21.00

The price of an adult ticket is $10.00 more than two thirds the price of a student ticket. This means that

21 = 2/3 × x + 10

The equation to determine how much Elise will pay for a student ticket would be

2x/3 + 10 = 21

2x/3 = 21 - 10 = 11

2x = 11×3 = 33

x = 33/2 = $16.5

To determine how much Elise will pay for a student ticket, we can follow these steps:

1. Let's assign a variable to represent the price of the student ticket. We'll call it "x".

2. According to the information given, the adult ticket is $10 more than two-thirds of the price of a student ticket. So, the equation can be written as:

Adult ticket price = 2/3 * x + $10

3. The adult ticket price is given as $21. Substituting this value into the equation, we have:

$21 = 2/3 * x + $10

4. To isolate the variable, we can subtract $10 from both sides of the equation:

$21 - $10 = 2/3 * x

Simplifying, we get:

$11 = 2/3 * x

5. Finally, to solve for "x", we can multiply both sides of the equation by the reciprocal of 2/3, which is 3/2:

($11) * (3/2) = x

Multiplying, we get:

$33/2 = x

Therefore, Elise will pay $16.50 for a student ticket.

In summary, the equation to determine how much Elise will pay for a student ticket is 2/3 * x + $10 = $21, and solving for "x" gives us x = $16.50.

Final answer:

The student asked for the completion of a Java function to compute the nth Fibonacci number using recursion. The base case for the function is missing, which should return the index when it is either 0 or 1. Two alternatives to improve runtime are memoization and dynamic programming, with an example provided for the latter technique.

Explanation:

The student is asking for the missing code in a recursive Java function to compute the nth Fibonacci number. To complete the base case of the provided function, we should return the index itself because the 0th and 1st Fibonacci numbers are defined as 0 and 1, respectively.

The function should look as follows:

public static int fib(int index) {
   if (index == 0) return 0; // Base case for 0
   if (index == 1) return 1; // Base case for 1
   else // Reduction and recursive calls
       return fib(index - 1) + fib(index - 2);
}

Using this recursive algorithm is inefficient due to its exponential time complexity, represented by O(2^n). To illustrate the concept of reducing computation time, two alternative approaches can be used: memoization and dynamic programming. Memoization stores the results of expensive function calls and reuses them when the same inputs occur again, thus avoiding the need to recompute them. Dynamic programming approaches the problem from a bottom-up perspective, computing and storing the result of smaller subproblems first, which then are used to compute larger ones.

An example of a dynamic programming approach is to use a loop to calculate the sequence iteratively:

public static int fib_loop(int index) {
   if (index == 0) return 0;
   if (index == 1) return 1;
   int a = 0, b = 1, sum;
   for (int i = 2; i <= index; i++) {
       sum = a + b;
       a = b;
       b = sum;
   }
   return b;
}

The time complexity for the iterative solution is O(n), which is significantly faster than the recursive approach. Therefore, fib_loop() can compute Fibonacci numbers much quicker than the recursive fib(). For example, calculating fib(40) using the recursive method can take a significant amount of time, while fib_loop(40) will complete in a fraction of the time due to its linear time complexity.

Answer:

A) The value of a is 29.

B) The value of b is greater than 29.

C) In both part A and part B we have used a common property  which is addition property and that we have add 9 on both side of equation in both parts.

D) The value of a in part A is equal to 29 whereas in part B the value of b is greater than 29.

Step-by-step explanation:

Solving for Part A.

Given,

[tex]a-9=20[/tex]

We have to solve for a.

[tex]a-9=20[/tex]

By using addition property of equality, we will add both side by 9;

[tex]a-9+9=20+9\\a=29[/tex]

Hence the value of a is 29.

Solving for Part B.

Given,

[tex]b-9>20[/tex]

We have to solve for b.

[tex]b-9>20[/tex]

By using addition property of inequality, we will add both side by 9;

[tex]b-9+9>20+9\\b>29[/tex]

Hence the value of b is greater than 29.

Solving for Part C.

In both part A and part B we have used a common property  which is addition property and that we have add 9 on both side of equation in both parts.

Solving for Part D.

The value of a in part A is equal to 29 whereas in part B the value of b is greater than 29.

To solve a - 9 = 20, we add 9 to 20, which results in a = 29. For b - 9 > 20, it's similar; we add 9 to 20, resulting in b > 29. The process is similar for both, but an equation's solution (a) is a single number, while an inequality's solution (b) represents a range of numbers.

To solve part A, which is a - 9 = 20, we will need to isolate the variable 'a' on the left side of the equation. Doing so gives us a = 20 + 9 or a = 29.

For part B, which is to solve b - 9 > 20, the operation is similar, but the result is an inequality, not a specific number. Solving it gives us b > 20 + 9 or b > 29.

The process is similar for both because you are essentially isolating the variable on one side of the equation or inequality. The difference is that the solution for an equation (part A) is a specific number, while the solution for an inequality (part B) is a range of numbers.

https://brainly.com/question/29731212

#SPJ11

Answer:

She would have to work 11 hours to get enough money to buy the sneakers

But if you want the hours included for the time she needs to work to pay off the loan she would have to work 8 hours, so all together 19 hours.

Answer:

It would be x ≥ 18

Step-by-step explanation:

Answer:

[tex] 2b+f = 8[/tex]   (1)

[tex]3b+f=11[/tex]   (2)

[tex] b = 11-8=3[/tex]

[tex]f= 8-2(3) = 8-6 =2[/tex]

Step-by-step explanation:

For this case we can put some notation

Let b= dozen bagels and f=  delivery fee

And for this case we know that "On Monday, they delivered two dozen bagels, b, to an office at a total cost of $8", so then the total taling in count the delivery fee we have this:

[tex] 2b+f = 8[/tex]

And for the other part "On Tuesday, three dozen bagels were delivered at a total cost of $11", we can write the expression like this:

[tex]3b+f=11[/tex]

And our system of equations would be:

[tex] 2b+f = 8[/tex]   (1)

[tex]3b+f=11[/tex]   (2)

If we solve for f from equation (1) we got:

[tex]f= 8-2b[/tex]

And if w replace this into equation (2) we got:

[tex]3b+8-2b=11[/tex]  

[tex] b = 11-8=3[/tex]

And solving for f we got:

[tex]f= 8-2(3) = 8-6 =2[/tex]

Answer: False.

Step-by-step explanation:

For any random variable x,

Formula to calculate the z-score : [tex]z=\dfrac{x-\mu}{\sigma}[/tex]

, where [tex]\mu[/tex] = Mean

[tex]\sigma[/tex] = Standard deviation

Let x be the data point has a corresponding z-score of -1.5.

Then , we have

[tex]-1.5=\dfrac{x-\mu}{\sigma}[/tex]

[tex]-1.5\sigma=x-\mu[/tex]

[tex]\mu-1.5\sigma=x[/tex]

i.e. x is one and a half standard deviations below the mean value.

( one and a half =[tex]1+\dfrac{1}{2}=1.5[/tex] )

Therefore , the given statement is false.

Answer:

Part A) [tex]sin(\alpha)=\frac{4}{7},\ cos(\beta)=\frac{4}{7}[/tex]

Part B) [tex]tan(\alpha)=\frac{4}{\sqrt{33}},\ tan(\beta)=\frac{4}{\sqrt{33}}[/tex]

Part C) [tex]sec(\alpha)=\frac{7}{\sqrt{33}},\ csc(\beta)=\frac{7}{\sqrt{33}}[/tex]

Step-by-step explanation:

Part A) Find [tex]sin(\alpha)\ and\ cos(\beta)[/tex]

we know that

If two angles are complementary, then the value of sine of one angle is equal to the cosine of the other angle

In this problem

[tex]\alpha+\beta=90^o[/tex] ---> by complementary angles

so

[tex]sin(\alpha)=cos(\beta)[/tex]

Find the value of [tex]sin(\alpha)[/tex] in the right triangle of the figure

[tex]sin(\alpha)=\frac{8}{14}[/tex] ---> opposite side divided by the hypotenuse

simplify

[tex]sin(\alpha)=\frac{4}{7}[/tex]

therefore

[tex]sin(\alpha)=\frac{4}{7}[/tex]

[tex]cos(\beta)=\frac{4}{7}[/tex]

Part B) Find [tex]tan(\alpha)\ and\ cot(\beta)[/tex]

we know that

If two angles are complementary, then the value of tangent of one angle is equal to the cotangent of the other angle

In this problem

[tex]\alpha+\beta=90^o[/tex] ---> by complementary angles

so

[tex]tan(\alpha)=cot(\beta)[/tex]

Find the value of the length side adjacent to the angle alpha

Applying the Pythagorean Theorem

Let

x ----> length side adjacent to angle alpha

[tex]14^2=x^2+8^2\\x^2=14^2-8^2\\x^2=132[/tex]

[tex]x=\sqrt{132}\ units[/tex]

simplify

[tex]x=2\sqrt{33}\ units[/tex]

Find the value of [tex]tan(\alpha)[/tex] in the right triangle of the figure

[tex]tan(\alpha)=\frac{8}{2\sqrt{33}}[/tex] ---> opposite side divided by the adjacent side angle alpha

simplify

[tex]tan(\alpha)=\frac{4}{\sqrt{33}}[/tex]

therefore

[tex]tan(\alpha)=\frac{4}{\sqrt{33}}[/tex]

[tex]tan(\beta)=\frac{4}{\sqrt{33}}[/tex]

Part C) Find [tex]sec(\alpha)\ and\ csc(\beta)[/tex]

we know that

If two angles are complementary, then the value of secant of one angle is equal to the cosecant of the other angle

In this problem

[tex]\alpha+\beta=90^o[/tex] ---> by complementary angles

so

[tex]sec(\alpha)=csc(\beta)[/tex]

Find the value of [tex]sec(\alpha)[/tex] in the right triangle of the figure

[tex]sec(\alpha)=\frac{1}{cos(\alpha)}[/tex]

Find the value of [tex]cos(\alpha)[/tex]

[tex]cos(\alpha)=\frac{2\sqrt{33}}{14}[/tex] ---> adjacent side divided by the hypotenuse

simplify

[tex]cos(\alpha)=\frac{\sqrt{33}}{7}[/tex]

therefore

[tex]sec(\alpha)=\frac{7}{\sqrt{33}}[/tex]

[tex]csc(\beta)=\frac{7}{\sqrt{33}}[/tex]

To find the values of sin(a)&cos(B), tan(a)&cot(B), and sec(a)&csc(B), use trigonometric identities and the reciprocal identities of trigonometric functions.

The question is asking to find the values of sin(a)&cos(B), tan(a)&cot(B), and sec(a)&csc(B). To solve these trigonometric expressions, you need to recall the definitions and relationships between trigonometric functions. Here are the step-by-step calculations:

18 kg of 15% copper and 72 kg of 60% copper should be combined by the metalworker to create 90 kg of 51% copper alloy.

Step-by-step explanation:

Let x = kg of 15% copper alloy

Let y = kg of 60% copper alloy

Since we need to create 90 kg of alloy we know:

x + y = 90

51% of 90 kg = 45.9 kg of copper

So we're interested in creating 45.9 kg of copper

We need some amount of 15% copper and some amount of 60% copper to create 45.9 kg of copper:

0.15x + 0.60y = 45.9

but

x + y = 90

x= 90 - y

substituting that value in for x

0.15(90 - y) + 0.60y = 45.9

13.5 - 0.15y + 0.60y = 45.9

0.45y = 32.4

y = 72

Substituting this y value to solve for x gives:

x + y = 90

x= 90-72

x=18

Therefore, in order to create 90kg of 51% alloy, we'd need 18 kg of 15% copper and 72 kg of 60% copper.

Answer: the maximum number of visits would be 38

Step-by-step explanation:

A person can pay $7 for a membership to the history museum and then go to the museum for just $1 per visit.

Let x represent the number of visits that the person makes to the museum after paying for the membership. This means that if the person makes x visits to the history museum, the total cost would be

7 + x

If a member of the history museum pays a total of $45. It means that the number of visits that he can make to the history museum would be

7 + x = 45

x = 45 - 7 = 38

Answer:

  27

Step-by-step explanation:

Let x represent the number of $0.15 stamps Ivan bought. Then the value of his stamps is ...

  0.15x +0.40(35-x) = 7.25

  -0.25x +14.00 = 7.25 . . . . . eliminate parentheses, collect terms

  -0.25x = -6.75 . . . . . . . . . . . subtract 14.00

  x = 27 . . . . . . . . . . . . . . . . . . divide by -0.25

Ivan bought 27 $0.15 stamps.

Answer:

We can use distributive law for the multiplication

And after multiplication result will be 264

Step-by-step explanation:

Lydia has to multiply 32×8.25

She is using standard algorithm of multiplication

Now we have to find the other way of multiplication of  32×8.25

We can use distributive law for the multiplication of the above number

We can write 8.25 as 8+0.25

So multiplication will become 32 ( 8+0.25 ) = 256 + 8 = 264

So after multiplication result will be 264

To solve 32 x 8.25 without the standard algorithm, Lydia can use the distributive property to separately multiply 32 by 8 and then by 0.25 (1/4), resulting in two simple multiplications: 256 and 8. Adding these together gives the answer, 264.

To solve the multiplication problem 32 x 8.25 without the standard algorithm, Lydia can break down the number 8.25 into 8 and 0.25 (which is 1/4) and use the distributive property of multiplication over addition. This allows Lydia to multiply 32 by each part separately and then add the results together.

This strategy simplifies the calculation and can be done with simpler computations or even mental math.

Answer:

Person 3 needs to pay $900.

Step-by-step explanation:

Consider the provided information.

The marginal cost of providing 25 neighborhood street lamps is $2000.

Person 1 is willing to pay $800 for the 25 lamps.

person 2 is willing to pay $300 for the 25 street lamps.

We need to find the minimum amount person 3 is willing to pay for 25 street lamps?

Let person 3 need to pay x amount.

Therefore, the sum of the amount should be equal to $2000.

$2000=$800+$300+x

$2000=$1100+x

x=$2000-$1100

x=$900

Hence, person 3 needs to pay $900.

Person 3 must be willing to pay at least $900 for 25 street lamps to meet the marginal cost of $2000 for efficient provision, considering person 1 and person 2 are contributing a total of $1100.

To determine the minimum amount person 3 must be willing to pay for the 25 street lamps, we need to consider the total cost of providing the lamps and the amount the other two people are willing to pay. The marginal cost for providing the 25 lamps is $2000. Person 1 is willing to pay $800, and person 2 is willing to pay $300. The sum paid by person 1 and person 2 is $800 + $300 = $1100.

Since the total cost is $2000, for efficiency, the total amount paid by all three people should at least match this cost. Therefore, the minimum amount that person 3 must be willing to pay is the difference between the total cost and the sum paid by the first two persons:

Total cost - Sum paid by person 1 and person 2 = Minimum amount person 3 must pay
$2000 - $1100 = $900

Thus, person 3 must be willing to pay at least $900 for the efficient provision of the 25 street lamps.

Answer:

[tex]y+6=(x+1)^{2}[/tex]

Step-by-step explanation:

we have

[tex]y=x^{2}+2x-5[/tex]

This is the equation of a vertical parabola open upward (because the leading coefficient is positive)

The vertex is a minimum

The equation of a vertical parabola into vertex form is

[tex]y-k=a(x-h)^2[/tex]

where

(h,k) is the vertex of the parabola

Convert the equation into vertex form

Move the constant term to the left side

[tex]y+5=x^{2}+2x[/tex]

Complete the square

[tex]y+5+1=x^{2}+2x+1[/tex]

[tex]y+6=x^{2}+2x+1[/tex]

Rewrite as perfect squares

[tex]y+6=(x+1)^{2}[/tex]

therefore

[tex]a=1\\h=-1\\k=-6[/tex]

The vertex is the point (-1,-6)

Answer:surface area = 2x^2 + 18x - 34

Step-by-step explanation:

The formula for determining the surface area of a rectangular prism is expressed as

Surface area = 2lh + 2wh + 2wl

Where

l represents the length of the rectangular prism.

h represents the height of the rectangular prism.

w represents the width of the rectangular prism

From the information given,

l = x+3

h = 5

w = x - 4

Surface area = 2 × 5 × (x+3) + 2 × (x - 4) × 5 + 2 × (x - 4) × (x + 3)

= 2(5x + 15) + 10(x - 4) + 2[x^2 + 3x - 4x - 12]

= 10x + 30 + 10x - 40 + 2x^2 - 2x - 24

= 2x^2 + 18x - 34

Answer: 1/16,384 microbes

Step-by-step explanation:

Since the microbes divides every 30minutes, if the microbes divides by half every 30minutes, then after an hour it will divides by another half that is (1/2)of 1/2 to give 1/4.

Subsequently after another hour, the microbes will reduces to 1/4 of its remains (i.e 1/4) to give 1/16.

Since the denominator is increasing geometrically each hour.

Looking at the trend;

After 1hr = 1/4 of the original microbe = 1/4

After 2 hrs = 1/4 of the remaining microbe = 1/4 of 1/4 = 1/16

Generalizing, we will let the number of hours be n

According to the progression, 1, 1/4,1/16,...n

Since its a Geometric Progression, nth term = ar^n-1

Where a is the first term = 1

r is the common ratio = 1/4

n is the number of hours of decay

After 8hours, the microbes will have been divided by

(1)(1/4)^8-1

= (1/4)^7

= 1/16,384 microbes

Answer:

1/2^16 or 0.0000152588 microbes

Step-by-step explanation:

Assuming you start with just one microbe that divides every 30 minutes.

This means that the half life of the microbe is 30 minutes or 0.5hours

The interpretation of this half life is that after every half-life, which in this case is 30 minutes, half of the microbe will be gone, and half will remain.

It follows that after another half hour the amount remaining will be

1/2 of 1/2= 1/4 microbes

Thus after 8 hours, there would have been (8/0.5)=16 half lives.

Therefore the amount of microbes remaining will be 1/2^16 of 1 = 0.0625

Alternatively, we could solve the differential equation

dM/dt=kM, where dM/dt is the rate of decay, and M is the amount at any time t, k is the decay constant

Solution of this first order differential equation by separating the variables and integrating yields {dM/M={kt+c, lnM=kt+c, and ......

M=Moexp(-kt)

The initial value Mo=1, when t=0, and given value M=0.5, t=0.5h yields the value of k as follows

0.5=exp(-k*0.5)

ln(0.5)=-k*0.5

k=1.386

After any time time, thus the given expression holds

M=exp(-1.386t)

Thus after 8 hours, the microbes remaining will be

M=exp(-1.386t)=exp(-1.386*8)=0.000152588 microbes.