The rate of growth dP / dt of a population of bacteria is proportional to the square root of t, where P is the population size and t is the time in days (0 ? t ? 10) as shown below.
dP/dt=k \sqrt{t}
The initial size of the population is 300. After 1 day the population has grown to 600. Estimate the population after 8 days. (Round your answer to the nearest whole number.)

Answer:

x = 2 2/5

Step-by-step explanation:

I will insert an image of my work below

The value of x is 12/5 from the equation 2x+[tex]4\frac{1}{5}[/tex]=9

Two or more expressions with an Equal sign is called as Equation.

The given equation is 2x+[tex]4\frac{1}{5}[/tex]=9

Two times of x plus four and one fifth equal to nine.

Convert the mixed fraction to improper

[tex]4\frac{1}{5}[/tex]=21/5

Now the equation will be 2x+21/5=9

Now subtract 21/5 from both sides by substitution property

2x=9-21/5

2x=45-21/5

2x=24/5

Divide both sides by two by division property.

x=24/10

x=12/5

Hence, the value of x is 12/5 from the equation 2x+[tex]4\frac{1}{5}[/tex]=9

To learn more on Equation:

https://brainly.com/question/10413253

#SPJ2

Answer:

48 cents

Step-by-step explanation:

Answer:

48 cents

Step-by-step explanation:

Answer:

If x-3 is directly proportional to the square of y, then we can say that:

(x-3) = ky^2

Where k is a constant of proportionality.

If x=5 when y=2, we can substitute these values into the equation to find the value of k:

(5-3) = k(2)^2

2 = 4k

k = 0.5

Now that we have the value of k, we can use it to find the value of x when y=6:

(x-3) = (0.5)(6)^2

x-3 = 18

x = 21

So, if x is directly proportional to the square of y and x=5 when y=2, then x=21 when y=6.

Answer:

Orinal number of cats=  171

Step-by-step explanation:

Giving the following information:

Decrease in population= 30%

Current population= 120

To calculate the original number of cats, we need to use the following formula:

Orinal number of cats= current population / (1 - decrease)

Orinal number of cats= 120 / (1 - 0.3)

Orinal number of cats=  171

On solving the provided question, we can say that by unitary method With ten power crystals, 35 zombie troops can be raised.

What is unitary method ?

The unit technique is an approach to problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value.

Liliana raised 14 zombie troops with the help of four dark power stones.

Zombie troops can be increased to a total of 14 with 4 Dark power crystals. Zombies can be raised with 1 Dark power crystal, or 14/4.

Zombie soldiers can be raised using 1 Dark power crystal, or 7/2.

Zombie troops can be generated with 1 Dark power crystal by adding 10 to 7/2. You can produce 5 * 7 zombie troops with 1 Dark power crystal.

35 zombie troops can be generated with 1 dark power crystal.

With ten power crystals, 35 zombie troops can be raised.

To know more about unitary method  visit:

https://brainly.com/question/28276953

#SPJ4

Step-by-step explanation:

[tex] \frac{7}{2x + 1} + \frac{4}{4x + 2}[/tex]

[tex] =\frac{7(4x + 2) + 4(2x + 1)}{(2x + 1)(4x + 2)}[/tex]

[tex]= \frac{28x + 14 + 8x + 4}{(2x + 1)(4x + 2)}[/tex]

[tex]=\frac{36x + 18}{(2x + 1)(4x + 2)} [/tex]

[tex]=\frac{9(4x + 2)}{(2x + 1)(4x + 2)}[/tex]

[tex]=\frac{9}{2x + 1}[/tex]

Answer:

12

Step-by-step explanation:

Just count the dots

Answer: horse = 61.6

donkey = 38.4

Step-by-step explanation:

Let number of donkey be d

Let number of horse be h

Based on the question given, we can form an equation which will be:

d + h = 100 ........ i

230d + 730h = 53800 ........ ii

Multiply equation i by 230

230d + 230h = 23000 ...... iii

230d + 730h = 53800 ....... iv

Subtract iii from iv

500h = 30800

h = 30800/500

h = 61.6

Since d + h = 100

d = 100 - 61.6 = 38.4

Based on the data, the statement that is most likely correct is D. In Grade 9, 18% of students liked running.

The ratio (fraction or proportion) of the number of times a data value appears in the set of all outcomes to the total number of outcomes is known as the relative frequency.

From the information, the Dean collected data on the favorite sports of the students of two grades.

Here, the table shows the relative frequencies of rows for the data collected:

Swimming      Running Volleyball Row     totals

Grade 8          0.17       0.24              0.05     0.46

Grade 9           0.14       0.18             0.22      0.54

Column totals 0.31      0.42              0.27        1

In the table, Grade 9, 18% of students liked running. This is Illustrated above. The correct option is D.

Learn more about data on:

https://brainly.com/question/27951780

#SPJ1

Answer:

Step-by-step explanation:

if your doisjw0= and yes it would be 35%

Answer:

standard form

= x⁶ + 53x⁵ + 2x⁴ -2

Step-by-step explanation:

the degree is 6.

leading coefficient is 1

this is called a polynomial.

it has 4 terms

Answer:

c

Step-by-step explanation:

i think

Answer:

[tex]CB = 7.5[/tex]

Step-by-step explanation:

Well, if the question gave you a right triangle, an angle, and the side length of the side opposite to that angle, this question should scream (TRIGONOMETRY). So tap into your brain and think about how you can use sin, cosine, and/or tangent to solve the problem.

So notice that the question is asking for the side length of CB, the side adjacent to the angle C (53 degrees). Since we already have the length of the side opposite to C (10), we can use tangent, because we know the value of tan58 if we put it in a calculator, and we know the length opposite to C.

[tex]tan(53) = 10/CB[/tex]

[tex]CB * tan(53) = 10[/tex]

[tex]CB = \frac{10}{tan(53)}[/tex]

[tex]CB = \frac{10}{1.327} = 7.5359...[/tex]

Given equation 3 = 3 is an identity, so it has infinite solutions.

Consider the given mathematical equation 3 = 3

We need to check whether the given mathematical equation has solution or not.

We know that a statement 3 = 3 's true no matter what.

We can observe that for given statement 3 = 3, there's no variable in sight.

This means, 3 = 3 must has infinite solutions.

We know that an equation which is always true, no matter what values we substituted is called as an identity.

This equation is an identity, all real numbers are solutions.

Therefore, the equation 3 = 3 have infinitely many solutions.

Learn more about an equation here:

https://brainly.com/question/649785

#SPJ4

Answer:

40

Step-by-step explanation:

Answer: A

Step-by-step explanation: The other answer choices have 2 negatives which cancel and make a positive number.

Answer:

Lauren will finish the race faster 7 seconds faster, and 14 meters ahead.

Step-by-step explanation:

To answer this question, I will use the strategy of finding the slope of each of the proportional relationships (y = 8x for Lauren's run and y = ?x for Amani's run). The slope represents the rate at which the distance changes for each unit of time, so the person with the greater slope will finish the race faster.

To find the slope of Amani's run, I will use the tool of point-slope form, which is y - y1 = m(x - x1). I will plug in the coordinates for the second point listed in the table for Amani's run (5 seconds and 30 meters) to get y - 30 = m(5 - x1). Since I don't know the value of x1, I will solve for it in terms of m. I get x1 = 5 - (30/m).

Next, I will plug in the coordinates for the first point listed in the table for Amani's run (3 seconds and 18 meters) into the equation y - 30 = m(5 - (30/m)). I get 18 - 30 = m(5 - (30/m)). Solving for m, I find that Amani's run has a slope of m = -6.

Since Lauren's run has a slope of 8 and Amani's run has a slope of -6, Lauren will finish the race faster. To find out by how much, I will use the tool of proportional reasoning. Since the slope represents the rate at which the distance changes for each unit of time, the difference in the slopes (8 - (-6)) represents the difference in the rate at which the distance changes for each unit of time between the two runs. The difference is 14, so Lauren will finish the race 14 meters ahead of Amani for each second that they run. Since the race is 100 meters long, Lauren will finish the race approximately 7 seconds faster than Amani.

The right angled triangle is missing, so i have attached it.

Answer:

Proved below

Step-by-step explanation:

From the attached image, we can see that QP is parallel to BC.

Now, looking at triangles AQP and ABC, we can see that;

∠ AQP = ∠ ABC

Also;

∠ APQ = ∠ ACB

This means that triangles ABC and AQP are similar.

We are told that P is the mid-point of AC.

Thus; AP = PC

We can now say that;

AP:AC = 1:2 and AQ:AB = 1:2

Since AQ:AB = 1:2, it means Q is the midpoint of AB.

Now, ∠ AQP = ∠ BQP

However, according to SAS congruence test, AQP is congruent to BQP.

Thus; AP = BP = CP

Since AP:AC = 1:2 as we saw earlier, then;

BP:AC = 1:2

Thus:

BP/AC = ½

BP = ½AC

A watch increased in price by 4/5 is priced at £126, then the original price of the watch was £100.

We know that the price of the watch increased by 4/5. To find the original price of the watch, we can use the following formula:

original price = new price / (1 + increase percentage)

In this case, the new price of the watch is £126 and the increase rate is 4/5. So we have:

original price(1 + 4/5) = 126

original price = 126 / (1 + 4/5)

original price = 126 / (1+ 0.8)

original price = 126/1.8

original price = 70

So, the original price of the watch was £70.

To know more on increase

https://brainly.com/question/24497438

#SPJ4

Answer:

cant answer sorry i didnt realize it was an equation

Step-by-step explanation:

Answer:

don't know that sorry can you help me though

Answer:

D. 19

Step-by-step explanation:

veritically opposite angles are congruent so:

8x+2=154

8x=154-2

8x=152

x=152/8

x=19

hope this helps!! :D

Answer: 718

Step-by-step explanation:

The formula for determining the cost of the cell phone bill (when more than the base number of minutes is used) is

c=p+(m−b)r

Where:

c is the total cost of the bill: $48.10 for this problem.

p is the base price of the plan: $40 for this problem.

m is the number of minutes used: what we are solving for this problem.

b is the base number of minutes allowed: 700 for this problem

r is the rate for additional minutes: 0.45 for this problem

Substituting and solving for m gives:

$48.10 = $40.00 + (m − 700)$0.45

$48.10 − -$40- = $40.00 − -$40- + (m − 700)$0.45 $8.10= 0 + (m−700)$0.45

$8.10 = (m - 700)$0.45

$8.10 = ($0.45 × m) − ($0.45 × 700)

$8.10 = $0.45m − $315.00

$8.10 + -$315.00- = $0.45m − $315.00 + -$315.00-

$323.10 = $0.45m − 0

$323.10 = $0.45m

[tex]\frac{323.10}{-0.45-}=\frac{0.45m}{-0.45-}[/tex] (Money)

[tex]\frac{323.10}{0.45}=\frac{0.45m}{0.45}[/tex] (Money): cross out the dollar sign for 323.10 and 0.45 under it... then cross out 0.45m but leave the m, and then cross out 0.45 under it.

[tex]\frac{323.10}{-0.45-}=m[/tex]

718 = m

m = 718

John used 718 total minutes during the month.

Answer:

Hi! Not sure if this is the answer you're looking for, but 12÷90 is 0.13333333333 repeating :)

Answer:

12/90 as a decimal is 0.13333333333 recurring

Step-by-step explanation:

simplified it should be 2/15

Answer:

2,30

the difference between 3,45 and 4,60 is 1,15. So if you add 1,15 and 1,15 it will be 2,30. you can't do 1,10 because the rate is 1,15 neither can you do 6,85 because 5,75 plus 1,15 is 6,90 not 6,85 so 2,30 is the final choice.

9 hours will it take to clean the 15 pools.

The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.

For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.

12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.

As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.

This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.

Given:

Dave can clean pools at a constant rate of 3/5 pools per hour.

This also means that he cleans 3 pools in 5 hours

So, the time taken to clean 15 pools is

= 15×3/5

= 9 hours.

Hence, the time taken is 9 hours.

Learn more about unitary Method here:

https://brainly.com/question/22056199

#SPJ1

The fractions is simplified to 8ac²/ 5

A fraction can be described as the part of a whole element, number or variable.

There are different types of fractions, which includes;

Examples of improper fractions; 5/3, 7/5

Examples of proper fractions; 3/4, 5/6

Examples of mixed fractions; 3 1/2, 4 5/6

Examples of simple fractions; 1/2 , 1/ 4

From the information given, we have that;

[tex]\frac{32a^2bc^3}{20abc}[/tex]

This is simplified to;

32 × a × a × b × c × c × c/ 20 × a × b × c

Divide the common terms

8ac²/ 5

Hence, the fractions is 8ac²/ 5

Lean more about fractions here:

https://brainly.com/question/11562149

#SPJ1

Answer:

0.0108 kg

Step-by-step explanation:

Jiri is on a special diet

Over 5 days he eats 0.054

Therefore the food consumed in a day can be calculated as follows

5 days= 0.054

1 day= 0.054/5

= 0.0108kg

X²-3There are a number of ways to factor equations like x2 -3x+2=3x+2=0. If all the terms are positive: (x + ) (x + )=0,  If the center term is negative: ( (-)( x -)=0 • If the last or if both terms are negative: ( x +)(x-)=0

The following are the rulesIf, ll trinomial terms are positive, then all binomial terms will be positive.If the trinomial’s last term is negative but the middle and first terms are positive, one term of the binomial will be negative and the other will be positive.

If we can find two numbers whose product is A * C and whose sum is B, we may factor a trinomial of the type Ax2 + Bx + C. Exemplification 1. Determine if 4x2 + 8x + 3 can be factored. Solution. We want for two numbers whose product is (4)(3) = 12 and whose total is 8. (the coefficient of x).

To learn more about trinomial rules to refer:

https://brainly.com/question/16863737

#SPJ1

Answer:

Step-by-step explanation:

4.6 x 10^6

Answer:

4.6 x 10^6

Step-by-step explanation: