A culture of bacteria has an initial population of 230 bacteria and doubles every 9 hours. Using the formula
Pt=P0*2t/d where
P
t
​
is the population after t hours,

0
P
0
​
is the initial population,

​
is the initial population, t is the time in hours and d is the doubling time, what is the population of bacteria in the culture after 13 hours, to the nearest whole number?

Step-by-step explanation:

Mohammed used 3 1/2 ink cartridges = \(\dfrac{7}{2}\)

Luigi used 1 3/4 ink cartridges = \(\dfrac{7}{3}\)

It means that Mohammed used more ink cartridges than Luigi. The more amount is calculated as follows :

\(\dfrac{7}{2}-\dfrac{7}{3}=\dfrac{7\times3-7\times 2}{6}\\\\=\dfrac{21-14}{6}\\\\=\dfrac{7}{6}\)

So, \(\dfrac{7}{6}\) more ink cartridges Mohammed used than Luigi.

Answer: Switch steps 2 and 3.

explanation: Have a good day stay safe

Answer:

its 8^16

Step-by-step explanation:

let 8=8^1

when dividing exponents, you subtract the exponents

8^17/8=8^(17-1)=8^16

Hope this helps

Answer:

26.411

Step-by-step explanation:

In 3a+bc-c you have to substitute

a=8.6, b=2.3, c=0.47

3*8.6 + 2.3*0.47 - 0.47 first do the multiplication then addition and subtraction

25.8 + 1.081 - 0.47=

26.411

The medicine bottle has 120 doses of 100 miligram each.

As per the known fact, 1000 miligram is 1 gram. So, the amount of medicine in the bottle in milligrams = 12×1000

Performing multiplication on Right Hand Side of the equation

Amount of medicine in bottle = 12000 milligrams.

Now, number of dose of 100 miligram medicine = 1

Amount of dose of 12000 miligram medicine = (1/100)×12000

Performing division and multiplication on Right Hand Side of the equation

Amount of doses in 12000 miligram medicine = 120

Thus, there are 120 doses in a medicine.

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t ≈ (12 / (4π))^(1/3) - 10. Evaluating this expression will give us the approximate thickness of the bubble.

To calculate the thickness of the bubble, we can use the linear approximation method.

The volume of the bubble gum is given as 4 cubic centimeters, which corresponds to the volume of the inflated bubble. The inner radius of the bubble, denoted as r, is 10 centimeters.

The volume of a sphere is given by the formula V = (4/3)πr^3. By rearranging the formula, we can express the radius in terms of the volume:

r = [(3V) / (4π)]^(1/3)

Substituting the given volume of 4 cubic centimeters, we have:

r = [(3*4) / (4π)]^(1/3)

r = (12 / (4π))^(1/3)

Now, to find the thickness of the bubble, we need to subtract the inner radius from the outer radius. The outer radius is the sum of the inner radius and the thickness, denoted as R = r + t.

Using the linear approximation method, we can assume that the thickness of the bubble, t, is very small compared to the radius. Therefore, we can neglect the higher-order terms in the expansion.

Approximately, we have:

R ≈ r + t

Substituting the value of r from earlier, we have:

R ≈ (12 / (4π))^(1/3) + t

The thickness of the bubble, t, is approximately equal to the difference between the outer radius R and the inner radius r:

t ≈ R - r

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Answer:

c and d

Step-by-step explanation:

Answer:C and D

Step-by-step explanation:

Answer:

perpendicular

Step-by-step explanation:

both lines meet at a 90 degree angle

Answer:

R = 10 cm

Step-by-step explanation:

The area of a spherical shape is given by :

\(A=4\pi r^2\)

Where

r is the radius of the sphere

ATQ,

One large bubble separates into four small bubbles so that the total area of the small bubbles is equal to the area of the large bubble.

The radius of each small bubble is 5 cm

Using the given condition,

\(4\pi R^2=4\times (4\pi r^2)\\\\R^2=4r^2\\\\R=\sqrt{4r^2} \\\\R=2r\\\\R=2\times 5\\\\R=10\ cm\)

So, the radius of the large bubble is equal to 10 cm.

Answer:

20cm

Step-by-step explanation:

5cm+5cm+5cm+5cm=20cm

We can take advantage of the integrand's symmetry over the y-axis to employ symmetry to evaluate the integral [-8, 8] (3 + x + x2 + x3) d.

As a result, the integral across the range [-8, 8] can be divided into two equally sized pieces, [-8, 0] and [0, 8].

Taking into account the integral throughout the range [-8, 0]: [-8, 0] (3 + x + x² + x³) dx

The integral of an odd function over a symmetric interval is zero because the integrand is an odd function (contains only odd powers of x). The integral over [-8, 0] hence evaluates to zero.

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Answer:

30.84 cm

Step-by-step explanation:

Correct.

You need half the perimeter of half a circle plus the 12-cm diameter.

Remember to include the units, cm.

Answer: 30.84 cm

Using the dot product properties the required values in the given scenario are:

\(w = (w₁, w₂) \\= (2, 5).\)

To find w, we can set up two equations using the dot product properties. Given u = (-4, 3) and v = (1, -2), we have the following equations:
\(-4w₁ + 3w₂ = 7   ...(1)\\w₁ - 2w₂ = -8    ...(2)\)
To solve this system of equations, we can use any method, such as substitution or elimination. Let's solve it using the substitution method.

From equation (2), we can express w₁ in terms of w₂:
\(w₁ = -8 + 2w₂\)
Now substitute this value of w₁ into equation (1):
\(-4(-8 + 2w₂) + 3w₂ = 7\)

Simplify and solve for w₂:
\(32 - 8w₂ + 3w₂ = 7\\-5w₂ = -25\\w₂ = 5\)

Now substitute the value of w₂ back into equation (2) to find w₁:
\(w₁ - 2(5) = -8\\w₁ - 10 = -8\\w₁ = 2\)

Therefore, \(w = (w₁, w₂) = (2, 5).\)

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To find vector w, we need to solve the system of equations formed by the dot products u . w = 7 and v . w = -8. By substituting the given values for u and v, and denoting the components of w as (x, y), we can solve the system to find w = (-3, -2).

To find w, we can use the dot product formula: u . w = |u| |w| cos(theta), where u and w are vectors, |u| is the magnitude of u, |w| is the magnitude of w, and theta is the angle between u and w.

Given that u = (-4, 3) and u . w = 7, we can substitute the values into the dot product formula:

\(7 = sqrt((-4)^2 + 3^2) |w| cos(theta)\)

Simplifying, we get:

7 = sqrt(16 + 9) |w| cos(theta)
7 = sqrt(25) |w| cos(theta)
7 = 5 |w| cos(theta)

Similarly, using the vector v = (1, -2) and v . w = -8:

\(-8 = sqrt(1^2 + (-2)^2) |w| cos(theta)-8 = sqrt(1 + 4) |w| cos(theta)-8 = sqrt(5) |w| cos(theta)\)

Now, we have two equations:

\(7 = 5 |w| cos(theta)-8 = sqrt(5) |w| cos(theta)\)

From here, we can set the two equations equal to each other:

5 |w| cos(theta) = sqrt(5) |w| cos(theta)

Since the magnitudes |w| and cos(theta) cannot be zero, we can divide both sides by |w| cos(theta):

\(5 = sqrt(5)\)

However, 5 is not equal to the square root of 5. Therefore, there is no solution for w that satisfies both equations.

In summary, there is no vector w that satisfies u . w = 7 and v . w = -8.

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Answer:

6,4

Step-by-step explanation:

Create a system of equations

l-2=w

w*l=24

Substitute

l-2*1=24

l=6

6-2=4

w=4

Dimensions of the rectangle are 6inch and 4 inch.

"Rectangle is a quadrilateral whose all  angles are right angle and opposite sides are parallel and equal in measurement."

" Dimension is measurement of any object such as length, width and height of any object."

"Area is a space occupied by an object."

Let 'l' be the length of the rectangle.

According to the question,

Width = l - 2

Area= 24 square inches

Formula used

Area of a rectangle = length x width

\(24 = l\) × \((l-2)\)

⇒\(24\) = \(l^{2} -2l\)

⇒ \(l^{2} -2l -24=0\)

⇒\(l^{2} -6l+4l -24 =0\)

⇒\(l(l-6) +4(l-6) =0\)

⇒\((l-6)(l+4) =0\)

⇒\(l=6\) or \(l= -4\)

length cannot be negative.

Therefore, \(l=6\)inch

⇒width = \(6-2\)

⇒ width = 4 inch

Hence the dimensions of the rectangle are 6inch and 4 inch.

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Answer:

Pythagorean Theorem: a² + b² = c²

Step-by-step explanation:

7-24-25

7² + 24² = 25²

49 + 576 = 625

625 = 625

9-40-41

9² + 40² = 41²

81 + 1600 = 1681

1681 = 1681

Answer: See Explanation

Step-by-step explanation:

Pythagoras' theorem is \(a^{2}\) + \(b^{2}\) = \(c^{2}\).

So \(7^{2}\) (49) + \(24^{2}\) (576) = \(25^{2}\) (625)

Same goes for the other one. It is always the smallest number squared (smallest side of triangle) + the middle number squared (middle length side of triangle, = the biggest side/number squared.

Answer:

Step-by-step explanation:

X=2y+15

2(2y+15) + 4y= -18

4y +30 +4y = -18

8y +30 =-18

8y= -48

-6= y

X-(2(-6))=15

X- (-12)=15

X= 3

The solution to the system is x = 2 and y = 6, represented as the ordered pair (2, 6). This corresponds to option (B) in the answer choices.

To solve the system using substitution, we'll substitute the value of one variable from one equation into the other equation and solve for the remaining variable.

Given the system:

x + y = 8

y = 3x

Substituting the value of y from the second equation into the first equation, we have:

x + (3x) = 8

4x = 8

x = 2

Now, substitute the value of x into the second equation to solve for y:

y = 3(2)

y = 6

Therefore, the solution to the system is (2, 6). Option (B) is the correct answer.

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Answer:

Marty's with a slope of 1/3

Step-by-step explanation:

The functions Marty and Ethan wrote are analyzed the find the slope of each of the function

The equation Marty wrote is presented here as follows;

\(y + 3 = \dfrac{1}{3} \cdot\left (x + 9 \right)\)

Marty's equation can be written in slope and intercept form, y = m·x + c, as follows;

\(y = \dfrac{1}{3} \cdot\left (x + 9 \right) - 3\)

\(y = \dfrac{1}{3} \cdot x + \dfrac{9}{3} \right) - 3 = \dfrac{1}{3} \cdot x + 0\)

\(y = \dfrac{1}{3} \cdot x\)

By comparison, the slope of the function, m = 1/3

\(\therefore \ the \ slope \ of \ Marty's \ function, \ y + 3 = \dfrac{1}{3} \cdot\left (x + 9 \right), \ m =\dfrac{1}{3}\)

Marty's function has a slope of m = 1/3

Ethan has the following two column table;

\(\begin{array}{rl}x&y\\-4&9.2\\-2&9.6\\0&10\\2&10.4\end{array}\)

The slope, m, of the data in the above table is given as follows;

\(Slope, \, m =\dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}\)

Taking any two points, (x₁, y₁) = (-4, 9.2), and (x₂, y₂) = (2, 10.4), we get;

\(Slope, \, m =\dfrac{10.4-9.2}{2-(-4)} = \dfrac{1.2}{6} = \dfrac{1}{5}\)

Ethan's function has a slope of m = 1/5

Therefore;

Marty's slope of 1/3 is larger, given that 1/3 > 1/5.

Answer:

C. Marty’s with a slope of 1/3

Step-by-step explanation:

Did the test and got it correct

Step-by-step explanation:

23.60/8 = 2.95

therefore, one duck cost $2.95

hope this answer helps you dear!

Answer:

2.95$

Step-by-step explanation:

23.60 ÷8 =2.95$

can buy 8 ducks for $23.60,

how much does each duck cost?

By using the combination formula (a) 8 kids can be lined up in 40,320 ways. (b) Felicia next to Bob has 5,040 arrangements. (c) Felicia next to Bob and Hubert has 720 arrangements. (d) Felicia next to one of her three friends has 4,320 arrangements.

(a) There are 8 kids, so there are 8! (8 factorial) ways to line them up, which is equal to 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 40,320 ways.

(b) If Felicia is next to Bob, we can treat Felicia and Bob as a single entity. So, there are 7 entities to arrange, which gives us 7! = 5,040 ways.

(c) If Felicia is next to both Bob and Hubert, we can treat Felicia, Bob, and Hubert as a single entity. So, there are 6 entities to arrange, which gives us 6! = 720 ways.

(d) If Felicia is next to exactly one of her three best friends, there are 3 possible friends she can be next to. For each friend, we can treat Felicia and the friend as a single entity. So, there are 2 entities to arrange (Felicia & friend) and 6 other entities, giving us 3 x (2 x 6!) = 3 x 2 x 720 = 4,320 ways.

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If the building itself will be used as one of the sides of the enclosed area. The maximum area that can be enclosed by the fencing is: 31,250ft².

Let the area be x ft long

Let the width be (500 -x )/2

Hence,

x × (500 - x)/2 = -1/2x² + 250x

When,

x = 250

So,

Maximum area =-1/2 × 250² +250 ×250

Maximum area = -31,250ft + 62,500ft

Maximum area = 31,250ft²

Therefore 31,250ft² is the maximum area.

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The probability that a class of 50 has an average score that is less than 77 is approximately 11.90%.

To solve this problem, we need to use the central limit theorem, which states that the distribution of sample means will be approximately normal with a mean equal to the population mean and a standard deviation equal to the population standard deviation divided by the square root of the sample size.
In this case, we have a population of marks on a biology final test that is normally distributed with a mean of 78 and a standard deviation of 6. We want to know the probability that a class of 50 has an average score that is less than 77.
Using the central limit theorem, we can calculate the standard error of the mean as follows:
standard error of the mean = standard deviation / square root of sample size
standard error of the mean = 6 / √50
standard error of the mean = 0.8485
Next, we need to calculate the z-score for a sample mean of 77:
z-score = (sample mean - population mean) / standard error of the mean
z-score = (77 - 78) / 0.8485
z-score = -1.18
We can use a standard normal distribution table or calculator to find the probability associated with a z-score of -1.18. The probability of a sample mean less than 77 is approximately 0.1190 or 11.90%.
Therefore, the probability that a class of 50 has an average score that is less than 77 is approximately 11.90%.

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The radical expression when written as an exponential expression is;

\( {15}^{ \frac{1}{2} } \)

According to the law of indices, the square root of. a number is equal to the number raised to a power of 1/2.

On this note, The radical expression √15 given can be written as an exponential expression to give;

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Answer: 26

Step-by-step explanation:

Answer:

36

Step-by-step explanation:

The solution will be that the home-decorating company will require 42 yards of fabric for the customer's window treatments.

As per the information we have received from the question,

A single window requires 13 yards and a double window requires 16 yards of fabric. We are asked to find out the length of fabric that will be required by the home-decorating company, in case there were 2 single windows and 1 double window. The total amount of fabric that will be required by the home-decorating company is hence equal to

13×(no of single windows)+ 16×(no of double windows)

Here, no of single windows= 2

And, no of double window= 1

Hence, total fabric length=13×2 + 16×1=26 + 16=42 yards

Hence the solution is 42 yards of fabric.

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The point (5, 10) has not been translated in the given figure.Hence this statement is false.

The graph shows five points.

A point has been translated right and up.

Now, the statements that are true based on the graph are as follows:

The point (9, D) has been translated right and up.Answer: False

There is no information given about point (9, D).

So, we cannot say anything about the translation of point (9, D).

The point (1, 8) has been translated right and up.Answer: True

As explained above, the point (1, 8) has been translated 7 units to the right and 2 units up to get the new point (8, 10). So, this statement is true.

The point (2, 9) has been translated right and up.Answer: False

The point (2, 9) has not been translated in the given figure.

So, this statement is false.

Statement 4: The point (8, B) has been translated right and up.Answer: True

The point (8, B) has been translated 1 unit up in the given figure. So, this statement is true.

The point (5, 10) has been translated right and up.Answer: False

The point (5, 10) has not been translated in the given figure.

So, this statement is false.

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Answer:

It was not my intention to post that answer, as it does not solve the question, but hope it helps somehow.  

Step-by-step explanation:

\($\text{b)} \frac{\sin(a)}{\sin(a)-\cos(a)} - \frac{\cos(a)}{\cos(a)-\sin(a)} = \frac{1+\cot^2 (a)}{1-\cot^2 (a)} $\)

You want to verify this identity.

\($\frac{\sin(a)(\cos(a)-\sin(a))}{(\sin(a)-\cos(a))(\cos(a)-\sin(a))} - \frac{\cos(a)(\sin(a)-\cos(a))}{(\sin(a)-\cos(a))(\cos(a)-\sin(a))} = \frac{1+\cot^2 (a)}{1-\cot^2 (a)} $\)

The common denominator is

\((\sin(a)-\cos(a))(\cos(a)-\sin(a))= \boxed{2\cos (a)\sin(a)-\cos ^2(a)-\sin ^2(a)}\)

Solving the first and second numerator:

\(\sin(a)(\cos(a)-\sin(a))=\sin(a)\cos(a)-\sin^2(a)\)

\(\cos(a)(\sin(a)-\cos(a))= \cos(a)\sin(a)-\cos^2(a)\)

Now we have

\($\frac{ \sin(a)\cos(a)-\sin^2(a) -(\cos(a)\sin(a)-\cos^2(a))}{2\cos (a)\sin(a)-\cos ^2(a)-\sin ^2(a)}$\)

\($\frac{ -\sin^2(a) +\cos^2(a)}{2\cos (a)\sin(a)-\cos ^2(a)-\sin ^2(a)}$\)

Once

\(-\sin^2(a) +\cos^2(a) = \cos(2a)\)

\(2\cos (a)\sin(a) = \sin(2a)\)

Also, consider the identity:

\(\boxed{\sin^2(a)+\cos^2(a)=1}\)

\($\frac{ -\sin^2(a) +\cos^2(a)}{2\cos (a)\sin(a)-\cos ^2(a)-\sin ^2(a)}=\boxed{\frac{ \cos(2a)}{\sin(2a)-1}}$\)

That last claim is true.

The population proportion who participated in voting (63%) is higher than the sample proportion from this survey (58.91%).

To determine whether the population proportion who participated in voting or the sample proportion from the survey is higher, we need to compare the percentages.

The population proportion who participated in voting is given as 63% of all registered voters.

This means that out of every 100 registered voters, 63 participated in voting.

In the survey of retired voters, 162 out of 275 participants voted. To calculate the sample proportion, we divide the number of retired voters who participated (162) by the total number of retired voters in the sample (275) and multiply by 100 to get a percentage.

Sample proportion = (162 / 275) \(\times\) 100 ≈ 58.91%, .

Comparing the population proportion (63%) with the sample proportion (58.91%), we can see that the population proportion who participated in voting (63%) is higher than the sample proportion from this survey (58.91%).

Therefore, based on the given data, the population proportion who participated in voting is higher than the sample proportion from this survey.

It's important to note that the sample proportion is an estimate based on the surveyed retired voters and may not perfectly represent the entire population of registered voters.

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Answer:

x < 3

Step-by-step explanation:

4x + 3 < 3x +6

4x < 3x + 3

4x - 3x < 3

x < 3

The game with 8 minutes of time-outs is 98 minutes long.

What is an algebraic expression?

An algebraic expression is a mathematical phrase that can contain numbers, variables, and operations such as addition, subtraction, multiplication, and division.

In this case, the algebraic expression that represents the length of the soccer game would be:

m = 90 + x

where m represents the total length of the game in minutes, 90 represents the fixed length of the game, and x represents the variable length of time-outs in minutes.

To find the length of the game with 8 minutes of time-outs, we substitute x = 8 into the expression:

m = 90 + 8 = 98

Therefore, the game with 8 minutes of time-outs is 98 minutes long.

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If the gas tank is 20% full then At $3. 00 per gallon of gas, the cost to fill the tank is $36

In this question we have been given that the gas tank is 20% full.

At $3. 00 per gallon of gas, we need to find the cost to fill the tank.

We have been given the dimensions of the gas tank is 1.25 ft. by 1.75 ft. by 11 in.

First we convert 1.25 ft. and 1.75 ft. into inches.

1.75 ft = (1.75 x 12 )in    

and 1.25 ft. = (1.25 x 12) in  

From given dimensions we find the volume of  gas tank.

V =  (1.75 x 12 ) * (1.25 x 12)* 11

V = 3465 cu.in.

The gas tank is 20% full.

This means, we need to fill 80 % of tank.

The 80 perecnt of total volume of gas tank would be,

3465 * 80/100 =  2772 cu. in.

We convert this value in gallon.

1 gal = 231 in^3

By unitary method,

2772 in^3 =  12 gal

The rate of filling the tank is $3. 00 per gallon of gas.

So, by unitary method,

for 12 gal, the total cost would be,

12 x 3=  $36

Therefore,  the cost to fill the tank = 36 dollars

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