What is the slope of the line that passes through the points (−9,8) (-9, 8) (−9,8) and (−21,10)? (-21, 10) ?(−21,10)? Write your answer in simplest form.

Frank's error is that his function suggests a linear growth model instead of an exponential one. The correct function should be B(h) = 150 * (1.2)^h to represent an exponential growth where the population increases by 20 percent every hour.

Frank's error in his prediction function lies in the incorrect representation of the exponential growth of bacteria. His function reads B(h) = 150(.2)h, which implies a linear growth model, adding only 20% of the original amount, rather than a certain percentage of the current population. In reality, as the context describes the bacteria population growing by 20 percent every hour, the function should represent an exponential growth model accurate to the situation. Hence, the correct function should be B(h) = 150 * (1.2)^h, where 1.2, which signifies 120 percent (the original 100% plus the additional 20%), raised to the power h, accounts for the continuous multiplication or compounding of the bacteria every hour.

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Frank's error lies in the formulation of his prediction function. It should reflect exponential growth rather than linear growth. The population is 1.20 times what it was the previous hour, not 0.20 times.

The function he created, [tex]\( B(h) = 150(0.2)^h \),[/tex] incorrectly implies that the population increases by a factor of 0.2 each hour, which would represent a decrease since 0.2 is less than 1. Additionally, the initial population is multiplied by 0.2 instead of being increased by 20% each hour.

The correct way to model the population growth, assuming it grows by 20% each hour, is to use an exponential growth formula where the population is multiplied by [tex]\( 1 + \text{growth rate} \)[/tex] each hour that passes. Since the growth rate is 20%, or 0.20 in decimal form, the correct prediction function should be: [tex]\[ B(h) = 150(1 + 0.20)^h \][/tex]

This can be simplified to: [tex]\[ B(h) = 150(1.20)^h \][/tex]

This function correctly represents a 20% increase in the population each hour, starting with an initial population of 150 cells.

Frank's error was in the growth factor used in his function. It should have been [tex]\( 1 + \text{growth rate} \)[/tex] (which is 1.20 for a 20% increase) instead of just the growth rate (0.20). The correct function reflects that each hour, the population is 1.20 times what it was the previous hour, not 0.20 times.

Step-by-step explanation:

Total profit = Revenue - expenses

= $1200 - ($600 + $105 + $115 + $130)

= $1200 - $950

= $ 250

Answer:

2/6<2/4

Step-by-step explanation:

We can start by simplifying the two fractions. 2/6=1/3 and 2/4=1/2. 1/3<1/2 so 2/6 is smaller than 2/4.

Answer:5 1/3

Step-by-step explanation:

number = n

second number = s

6n + 3s = 27

2n + 1 = s

6n + 3(2n + 1) = 27

6n + 6n + 1 = 27

12n = 26

n = 26/12

n = 2 1/6

2(2 1/6) + 1 = s

4 1/3 + 1 = s

5 1/3 = s

Final answer:

To find the second number, we create a system of linear equations using the given information and solve for the variables. The solution shows that the second number is 5.

Explanation:

The student's question involves setting up a system of two linear equations and solving them to find the values of two unknown numbers.

Let the first number be x and the second number be y. We are given the following equations based on the problem:

6x + 3y = 27

y = 2x + 1

First, we can substitute the second equation into the first to solve for x:

6x + 3(2x + 1) = 27

6x + 6x + 3 = 27

12x + 3 = 27

12x = 24

x = 2

Now, substitute x = 2 into the second equation to find y:

y = 2(2) + 1

y = 4 + 1

y = 5

Therefore, the second number, y, is 5.

Answer:

It would be C=(6, -9); D= (-5,-9)

Step-by-step explanation:

If you plot -6,9 and 5,9 on a four quadrant graph you can see the answer. (sorry I'm not good at explaining, I'm on the same question as you currently and this is the answer I got, I'm pretty sure the one above isn't correct.)

The locations of points C and D are (16, 9) and (5, 9) or (-17, 9) and (-6, 9), respectively depending on the orientation of the rectangle.

To calculate the locations of points C and D in the rectangle ABCD, consider that opposite sides of a rectangle are parallel and have equal lengths.

Given points A=(-6,9) and B=(5,9), know that points A and B lie on a horizontal line at y=9. Since opposite sides of a rectangle are parallel, points C and D should also lie on a horizontal line parallel to AB.

So, the y-coordinate of points C and D should be 9 as well.

The x-coordinate for points C and D, consider that opposite sides of a rectangle are of equal length. The length of AB represents the width of the rectangle.

The length of AB =  x-coordinate of B -  x-coordinate of A

AB = 5 - (-6)

AB = 11 units.

Since, opposite sides are parallel, points C and D should also have the same y-coordinate as A and B. Their x-coordinates must differ by 11 units to maintain equal side lengths.

Possible coordinates for C and D:

C = (5+11, 9) = (16, 9)

D = (-6+11, 9) = (5, 9)

Alternatively:

C = (-6-11, 9) = (-17, 9)

D = (5-11, 9) = (-6, 9)

Therefore, the possible locations for points C and D are (16, 9) and (5, 9) or (-17, 9) and (-6, 9) .

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Answer:

326.56

youre welcome

Step-by-step explanation:

Answer:

Option B

Step-by-step explanation:

Using the law of logarithms

[tex]n log x= log x^{n}[/tex]

Therefore, since all the logs are to the same base, I will assume the base.

Also, when the bases are the same

log y+ log x= log (x+y)

[tex]\frac {1}{2}(log 4+ log 16)=log 4^{0.5}+log 16^{0.5}=log 2+log 4=log 6[/tex]

Now log 6-log 2= log (6-2)= log 4

Therefore, option B is correct

Good morning ☕️

Answer:

Step-by-step explanation:

-7x + 5 = 8x - 25

then

25 + 5 = 8x + 7x

then

15x = 30

then

x = 2

___________________

:)

Answer:

    [tex]x=2[/tex]

Step-by-step explanation:

Given equation:

[tex]-7x + 5 = 8x - 25[/tex]

To find the value of 'x', take the terms of 'x' to one side and the constants to the other side:

Subtracting '[tex]5[/tex]' to both side:

   [tex]-7x+5-5=8x-25-5\\\\-7x=8x-30[/tex]

Subtracting '[tex]8x[/tex]' both side:

   [tex]-7x-8x=8x-8x-30\\\\-15x=-30[/tex]

          [tex]x=\frac{-30}{-15}[/tex]

          [tex]x=2[/tex]

Answer:

The total income from wages, bank interest, dividends, and the prize = $ 94577

Step-by-step explanation:

Total wages of Mike and Lisa in last year = $ 91301

Total bank interest of Mike and Lisa = $ 792 + $ 667 = $ 1459

Total income from dividends = $ 287 + $ 530 = $ 817

Prize of Lisa won = $ 1000

Thus the total income from wages, bank interest, dividends, and the prize =

$ 91301 + $ 1459 + $ 817 + $ 1000 = $ 94577

Final answer:

The total income from wages, bank interest, dividends, and the prize is $94,577.

Explanation:

To find the total income from wages, bank interest, dividends, and the prize, we need to add up all the amounts mentioned.

First, we add Mike and Lisa's wages: $91,301. Then we add their bank interests: $792 + $667 = $1,459. Next, we add their stock dividends: $287 + $530 = $817.

Finally, we add Lisa's prize: $1,000. Adding all these amounts together, the total income from wages, bank interest, dividends, and the prize is $91,301 + $1,459 + $817 + $1,000 = $94,577.

Step-by-step explanation:

[tex]5y + 1 = 1 \\ subtracting \: 1 \: from \: both \: sides \\ \red{ \boxed{ \bold{ 5y + 1 - 1 = 1 - 1}}} \\ 5y = 0 \\ y = 0[/tex]

Answer:

Option B, 1/4 (x - 5) = 13

Step-by-step explanation:

An inequality has a less than, greater than, less than or equal to, and greater than or equal to.  But, there are no equal signs allowed in a inequality.  That makes it an expression.

Answer:  Option B, 1/4 (x - 5) = 13

Answer:

B

Step-by-step explanation:

Answer: Slope: -1/4

Y-intercept: -8

Answer:Dante’s soccer team sells T-shirts to raise money for new equipment. For each T-shirt sold, the team raises $8. Parents also make a donation of $100 toward the equipment.

What is the equation that represents the total amount raised, y, if x T-shirts are sold?

Step-by-step explanation:

Answer:

n = 5

n = 8

Step-by-step explanation:

n^2 - 13n = -40

Equate everything to zero

n^2 - 13n + 40 = 0

Factorise

(n - 5)(n - 8) = 0

Either

n - 5 = 0

Add 5 to both sides

n - 5 + 5 = 0 + 5

n = 5

Or

n - 8 = 0

Add 8 to both sides

n - 8 + 8 = 0 + 8

n = 8

n = 5 or

n = 8

It has two real solutions

Answer:

attatch a picture

line AB im assuming

Step-by-step explanation:

Answer: -(x+8)(x-8)

Step-by-step explanation:

-(x^2-64)

x^2-8^2x^2

x^2-8^2=(x+8)(x-8)

-(x+8)(x-8)

Answer:

36

Step-by-step explanation:

30% as a decimal is 0.30, take that and multiply it by 120 to find 30% of 120

120 × 0.30 = 36

Answer:

X²+6X=112

Step-by-step explanation:

area=1/2 base x height

56=x(x=6)/2

Multiply each side by two to eliminate the denominator

112=x(x=6)

112=x²+6x

Answer: 42 square feet.

Step-by-step explanation:

1/2 times 12 times 7 is 42.

Answer:

42

Step-by-step explanation:

Answer:

x=  0.5

or x=  -1.5

Step-by-step explanation:

Let's solve your equation step-by-step.

4x2+4x−3=0

Step 1: Factor left side of equation.

(2x−1)(2x+3)=0

Step 2: Set factors equal to 0.

2x−1=0 or 2x+3=0

x= 1/2 or x= −3/2

Answer:

A. x = –1.5, 0.5

Answer:

3/4

Step-by-step explanation:

Parallel lines will always have the same slope, but their y-intercepts can be any real number.

Answer:100cm

Step-by-step explanation:

Answer:

put the ^ when you do exponents!

Step-by-step explanation:

There are three parts to graphing an inequality.

1. determine if the line will be dashed or solid

2. determine where you will shade in

3 graph with the appropriate line and shade

1. it is just > and not ≥ so the line will be dashed, which means the line itself is not part of the answer.

2. it is y> so you shade in the area inside the parabola.  if y was an actal number it might be more complicated

3. graph x^2 - 6x + 11.  If that seems a bit hard, put it into vertex form by completing the square.

y = x^2 - 6x + 11

y = (x - 3)^2 +2

Since x^2 is positive it opens upward and then plug in 0 for x and y in y = (x - 3)^2 +2 to get the x and y intercepts and the -3 and +2 tells you the vertex (in this case the minimum) is at (3,2),  then remember the points are mirrored on either side of the vertex.  so if the y intercept is 2 to the left and one higher than the vertex, there will also be a point 2 to the RIGHT and 1 up.  then just connect the dots.  Keep in mind there may not be any x intercepts if it never goes below the x axis *hinthintwinkwink*

if all else fails just graph a handful of points to get the idea of the shape.  Just remember you are shading inside of the parabola and using dashed lines.  

Answer:

2a² + a   (   or a(2a+1)   )

Step-by-step explanation:

(6a²+3a) - (4a² + 2a)  (expand parentheses)

= 6a²+3a - 4a² - 2a   (group like terms)

= 6a²- 4a²+3a- 2a

= 2a² + a

= a(2a+1)

Answer:

2a^2+a

Step-by-step explanation:

This is an algebra. An algebra is an expression with no equality sign, and it will be expressed till the simplest form.

(6a^2+3a) - (4a^2 + 2a)

Remove the brackets

6a^2+3a-4a^2-2a

6a^2-4a^2+3a-2a

2a^2+a

Answer:

-1 case D)

Step-by-step explanation:

5-x=-(x-5) so the unknown factor is -1

b-k=-(k-b), again, -1

Similar for third case.

Answer:

-0.625

Step-by-step explanation:

The stock's value decreased by -0.625 each day over a period of four days, calculated by dividing the total decrease of -2.5 by the number of days.

The student's question pertains to finding the amount by which a stock's value decreased each day over four days, given that the total decrease was -2.5. To solve this problem, we use the concept of an arithmetic series, where each term changes by a constant difference. Since we know the total change in the stock's value was -2.5 over four days, we divide the total change by the number of days to find the daily change.

To calculate the change in stock value each day, we can use the formula:

Daily Change = Total Change / Number of Days

Plugging the values into the formula, we get:

Daily Change = -2.5 / 4 = -0.625

Therefore, the stock value decreased by -0.625 each day for the 4-day period.

Answer:

6

Step-by-step explanation:

18/3=6 You have to divide 18 by 3 in order to know how many times older Jill is than her sister.

Answer:

8% is 0.08

275 + 0.08s > 560

0.08s > 285

s > 3562.5

Answer:

1/243 for edge

Step-by-step explanation:

The simplified form of the quotient 3⁻¹ divided by 3⁴ is 1/243.

A quotient is defined as when dividing one number by another, the result is called the quotient.

To simplify the quotient 3⁻¹ divided by 3⁴, we can use the rule that says when we divide two exponential expressions with the same base, we can subtract their exponents.

So, we have:

3⁻¹ ÷ 3⁴

3⁻¹ divided by 3⁴ = 3⁻¹⁻⁴

Now, we can simplify the expression by subtracting the exponents:

3⁻¹⁻⁴ = 3⁻⁵ = 1/3⁵ = 1/243

So, the simplified form of the quotient 3⁻¹ divided by 3⁴ is 1/243.

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Answer:

100 : 175

Step-by-step explanation:

Divide 275 into two parts which are in the ratio 4:7?

To divide 275 into 4 :7, we will follow the steps below

First, We will add the ratio numbers together, that is; 4 + 7 = 11  

4 : 7 of 275 will be;

4/11  × 275

=4 × 275    /   11

=1100/11

=100

Then we will now proceed to the second part;

7/11  × 275

=  7 × 275  / 11

=1925/11

=175

Therefore dividing 275 into 4 : 7 yields    100 : 175