Growth of Bacteria The growth rate of Escherichia coli, a common bacterium found in the human intestine, is proportional to its size. Under ideal laboratory conditions, when this bacterium is grown in a nutrient broth medium, the number of cells in a culture doubles approximately every 30 min. (a) If the initial population is 100, determine the function Q(t) that expresses the growth of the number of cells of this bacterium as a function of time t (in minutes).

The expression '-7/8 - (-5/6)' simplifies to '-1/24' by eliminating the double negative and adding the fractions with a common denominator.

By concept of addition of fraction

To reduce the expression -7/8 - (-5/6) to its simplest form, we need to eliminate the double negative and add the two fractions. First, -(-5/6) becomes +5/6. Now you need to add -7/8 and 5/6, but they have different denominators. To add fractions, they must have the same denominator. The least common denominator (LCD) of 8 and 6 is 24. So, -7/8 becomes -21/24 and 5/6 becomes 20/24. Then, we add -21/24 and 20/24, which gives us -1/24. So, the simplest form of -7/8 - (-5/6) is -1/24.

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To simplify the expression -7/8 - (-5/6), we first convert it to -7/8 + 5/6 by removing the double negative. Then, we find a common denominator (24) and add the fractions to get -1/24, which is the simplest form of the expression.

To reduce the expression -7/8 - (-5/6) to its simplest form, we need to add the two fractions. Since we have a double negative in the second term, it becomes addition:

-7/8 + 5/6

To add fractions, we need a common denominator. The least common multiple of 8 and 6 is 24, so we convert each fraction:

(-7 times 3)/(8 times 3) + (5 times 4)/(6 times 4)

-21/24 + 20/24

Now we can add the numerators while keeping the denominator the same:

(-21 + 20)/24 = -1/24

Therefore, the expression simplifies to -1/24.

Answer:

$136.78

Step-by-step explanation:

Step 1: add 54 + 95= 149

Step 2: Multiply 149 and 15% (You can convert to a decimal) = 22.35

Step 3: Minus 149- 22.35= 126.65

Step 4: Multiply 126.65 by 8% (or 0.08)= 10.1320

Step 5: Round 10.1320 to the nearest cent= 10.13

Step 6: Add 126.65 to 10.13= 136.78

Misty spent $136.78 total.

(make sure to include your units!)

Answer:

13

Step-by-step explanation:

square root y^2 = square root 169

so

y = 13

Answer:

y=13

Step-by-step explanation:

y=square root of 169

y=13

Answer:

50 questions x 10 points = 500 points

500 points x 2 years = 1000 points

365 days / 2 = 182 1/2 days

182 1/2 days x 2 years = 365 days

Answer:

2 years

Step-by-step explanation:

Answer:

y < 2,000 - 2x

Step-by-step explanation:

Solution:-

- The number of adult ticket sold = x

- The number of children ticket sold = y

- The profit from a adult ticket, L1 = $15

- The profit from a adult ticket, L2 = $7.5

- The amount of profit ( P )made by selling "x" adult tickets and "y" children tickets:

                           P = L1*x + L2*y

                           P = 15x + 7.5y

Where, We are to set up an equality for Profit P < $15000:

                           15x + 7.5y < 150,000

- Re-arrange to develop the slope-intercept form of an inequality:

                           7.5y < 150,000 - 15x

                           y < 2,000 - 2x

Where, the slope = -2 and intercept = $2,000

Answer: y<-2x+2,000

Step-by-step explanation:

Answer:

60%

Step-by-step explanation:

3

---

5

x 100% = 60%

The calculated percentage of 5 that is 3 is 60%

From the question, we have the following parameters that can be used in our computation:

Percent of 5 is 3

This means that

x% * 5 = 3

So, we have

x% = 3/5

Evaluate the quotient of 3 and 5

x% = 0.6

Multiply through by 100

x = 60

Hence, the percentage of 5 that is 3 is 60%

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Answer:

3/7+r = 13/15

r=46/105

Step-by-step explanation:

Given ribbon of her project= 13/15

Used 3/7

left=r

3/7+r = 13/15

r=13/15 - 3/7

r=46/105

Answer:

1.80m + 3 ≤ 25

Step-by-step explanation:

We have a flat rate of $3, which means that's the base value. Now, we see that Jennifer has to pay $1.80 per mile, which means that when she has ridden m miles, she has to pay 1.80m. However, remember to add 3 to this:

1.80m + 3

Jennifer only has $25 to spend, so she can't spend any more than 25. This means that the money she can spend must be less than or equal to $25:

1.80m + 3 ≤ 25

Hope this helps!

Answer:

3 + 1.80m《25

m《12 2/9

Step-by-step explanation:

Fixed cost: $3

Per mile: $1.80

Cost for m miles:

3 + 1.80m

She can afford at max $25

3 + 1.80m《25

1.80m《22

m《12 2/9

Answer:

The equation that represents this relation is y = 3x - 5

The relation is a function

If the domain of the relation is x > 2, the range of the relation is y > 1

Answer:

The equation that represents this relation is   y = 3x - 5 .

The relation is  a function.

If the domain of the relation is x > 2, the range of the relation is y >  1  .

Step-by-step explanation:

The output, y, of a relation, is the difference of three times the input, or 3x, and 5. So, y = 3x − 5.

Substituting any x-value from the domain into the equation will result in exactly one value of y, so the relation is a function.

To find the range of the relation, given the domain, substitute the boundary point of the domain into the function equation:

When x = 2, y = 3(2) − 5 = 6 − 5 = 1.

Because substituting values of x that are greater than 2 will result in values of y that are greater than 1, the range of the relation is y > 1.

Answer:

18:24 or simplest form is 3:4

Step-by-step explanation: If you don't need to simplify then it is 18:24, but if you simplify it by dividing 18 and 24 by 6, then the answer is 3:4 :)

Answer:

18:24 18 to 24 so 3:4

Step-by-step explanation:

Answer:

Total ten  students can feed on 6 slices of pizza with each student getting [tex]\frac{3}{5}[/tex] of a pizza slice

Step-by-step explanation:

Given-

Teacher wished to give [tex]\frac{3}{5}[/tex] of a pizza slice to each student

This means that each student will get only [tex]\frac{3}{5} *[/tex] one slice of pizza

Now the total number of slices of pizza [tex]= 6[/tex]

Thus,

[tex]\frac{3}{5}[/tex] of a pizza slice to each student  [tex]*[/tex] total number of students [tex]= 6[/tex]

Rearranging the above equation, we get -

[tex]\frac{3}{5} * 1 * X = 6[/tex]

Where X is the number of students

[tex]X = \frac{6}{\frac{3}{5} } \\X = \frac{5}{3} * 6\\X = 10[/tex]

Total ten  students can feed on 6 slices of pizza with each student getting [tex]\frac{3}{5}[/tex] of a pizza slice

They're trying to trick you with √2.  Remember in the 30/60/90 triangle the sides are in ratio 1:√3:2, with the "1" opposite the 30 degrees.

Here we have

1:√3:2  = 6√2:x:hypotenuse

or

x/(6√2) = √3/ 1

x = 6√2×√3 = 6√6

Answer: AC=6√6

Answer:

Step-by-step explanation:

[tex]u.v=|u||v| cos \theta\\(8)(9)+(7)(7)=\sqrt{8^2+7^2 } \sqrt{9^2+7^2} cos \theta\\72+49=\sqrt{64+49} \sqrt{81+49}~ cos ~\theta\\121=\sqrt{113} \sqrt{130} ~cos~\theta\\cos~\theta=\frac{121}{\sqrt{113} \sqrt{130} } \\\theta=cos^{-1} (\frac{121}{\sqrt{113}\sqrt{130} } )\approx 3.3^\circ[/tex]

Answer:

Hey briannah its haley lol. I thought I'd help you out with this for Mrs F's class! The answer is 333.

Step-by-step explanation: Basically you do 180-63-90 and that equals 27. Then from there you subtract 360 from 27, then there is your answer 333!!

Basically you do 180-63-90 and that equals 27. Then from there you subtract 360 from 27, then there is your answer 333!!

The given question is incomplete. The complete question is:

The test scores of 40 students are summarized in the frequency distribution below a summarized in the given frequency distribution. score Find the mean Score Students 50-59 (5) 60-69(15) 70-79(6) 80-89(5) 90-99(9)

A) 70.3 B) 74.0 ) 74.5 D) 66.6

The correct option is B.

Step-by-step explanation:

Given,

Data              Frequency      

50-59                   5                    

60-69                   15                    

70-79                   6                      

80-89                   5                    

90-99                   9                      

To find the mean of given data.

Formula

Mean = Sum of ( Freq× Mid point)÷ total frequency

Data              Frequency       Mid internal         Freq× Mid point

50-59                   5                      54.5                      272.5

60-69                   15                     64.5                      967.5

70-79                   6                       74.5                      447

80-89                   5                      84.5                       422.5

90-99                   9                      94.5                      850.5

Now,

Sum of ( Freq× Mid point) = 2960

Number of students = 40

So,

Mean = 2960÷40 = 74

The correct option is B.

To find the mean of the test scores, add up all the scores and divide by the total number of scores.

To find the mean of the test scores, we need to add up all the scores and divide by the total number of scores. In this case, we have 40 students, so we add up all the scores: 15.5 + 70.3 + 14.1 + 13.3 + ... (continue adding up all the scores). Once we have the sum of all the scores, we divide by 40 to find the mean.

Let's assume that the sum of all the scores is 1000 (this is just an example). We would then divide 1000 by 40 to get the mean: 1000 ÷ 40 = 25. Therefore, the mean of the test scores is 25.

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Answer:

The slope is -3 and the y-intercept is -4. So D.

Step-by-step explanation:

It should be c because the relationship between the frequency and the function matters.  

Answer:

251

Step-by-step explanation:

Answer:

251

Step-by-step explanation:

Hope tis helped brainliest is appreciated. :) stay safe

Answer:

4 units

Step-by-step explanation:

Answer:

C. [tex]\sqrt{98}[/tex]

Step-by-step explanation:

This is the answer

Answer:

The correct option is;

The line of best fit is not reasonable because it has more points below it than above it.

Step-by-step explanation:

Here we note that there are a total of seven points in the scatter plot and there are five of the points below the line of best fit and just two above the line.

Of the five points below the line of best fit, four are just about touching the underside of the line while one of the two points above the line is just about touching the line.

The proper positioning of the line can be reviewed, therefore, with a line drawn through the four points presently touching the underside of the line of best fit.

The feedback the other lab group should give is (d) the line of best fit is not reasonable because it has more points below it than above it.

From the scattered plot (see attachment), we can see that the scattered plot has a total of 7 dots,

There are more points below the scattered plot, than above it.

This means that the scattered plot is not reasonable because of (d)

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Answer:

(a) 5040°

(b) 168°

(c) 12°

Step-by-step explanation:

(a) The sum of angles in a polygon of N sides is given as:

S = (N - 2) * 180

For a 30-gon, N = 30.

Therefore, the sum of the angles in the 30-gon will be:

S = (30 - 2) * 180

S = 28 * 180

S = 5040°

(b) To find each interior angle, we simply divide S by 30:

Interior Angle = 5040/30

Interior Angle = 168°

(c) Each exterior angle of a polygon is gotten by subtracting the interior angle from 180°.

Hence, each exterior angle is:

180 - 168 = 12°

Answer:

step1

3520268-3433145

step 2

answer after subracting divide that answer by the total area of the texas

Answer:

(1,13) is a solution

Step-by-step explanation:

y> 2x + 5

Substitute the point in and see if the inequality is true

13> 2(1) + 5

13 > 2+5

13>7

This is true so the point is a solution

Answer:

Yes

Step-by-step explanation:

Substitute the point into the inequality to see if it is true.

(1,13) --> (x,y)

So, x is 1, and y is 13, and we can substitute them in to the inequality

y> 2x + 5

13 > 2(1) + 5

13> 2 + 5

13 > 7

Since 13 is greater than 7, it is true, and (1,13) is a solution

Answer:

The angle is in the second quadrant.

Step-by-step explanation:

The cosecant of an angle is the same as the reciprocal of the sine of that angle. In other words, as long as [tex]\sin (t) \ne 0[/tex],

[tex]\displaystyle \csc t = \frac{1}{\sin t}[/tex].

Therefore, [tex]\csc(t) > 0[/tex] is equivalent to [tex]\sin (t) > 0[/tex].

Consider a unit circle centered at the origin. If the terminal side of angle [tex]t[/tex] intersects the unit circle at point [tex](x,\, y)[/tex], then

For angle [tex]t[/tex],

In other words, this intersection is above and to the left of the origin. That corresponds to second quadrant of the cartesian plane.

Answer:

1. False 2. False 3. True 4. False 5. True

Step-by-step explanation:

Given:

Fred bought 4 liters of liquid laundry detergent,

3,260 millilitres of fabric softener, and

2.3 liters of bleach.

Select true or false for each statement.

1. Fred bought 96 millilitres more fabric softener than bleach.

Solution:

Fred bought fabric softener = 3,260 millilitres

Fred bought bleach = 2.3 liters = 2300 millilitres

1 liter = 1000 millilitres

2.3 liter = 1000 [tex]\times[/tex] 2.3 = 2300 millilitres

Fred bought more fabric softer than bleach = 3,260 - 2300 = 960

Hence, it is false and actually Fred bought 960 millilitres more fabric softer than bleach.

2. Fred bought 1.95 liters more laundry detergent than bleach.

Solution:

Fred bought laundry detergent = 4 liters

Fred bought bleach = 2.3 liters

Fred bought more laundry detergent than bleach = 4 - 2.3 = 1.7 liters

Hence, it is false and actually Fred bought 1.7 liters more laundry detergent than bleach.

3. Fred bought 960 millilitres more fabric softener than bleach.

It is true, as solved above:

4. Fred bought 170 millilitres more laundry detergent than bleach.

Solution:

Solved above:

Fred bought 1.7 liters more laundry detergent than bleach.

1.7 liters = 1.7 [tex]\times[/tex] 1000 = 1700 millilitres

1.7 liters = 1700 millilitres not 170 millilitres

Hence, it is false.

5. Fred bought 0.96 liters more fabric softener than bleach.

Solution:

Solved above:

Fred bought 960 millilitres more fabric softer than bleach.

1000 millilitres = 1 liters

1 millilitre = [tex]\frac{1}{1000}[/tex]

960 millilitre =  [tex]\frac{1}{1000}\times960=\frac{960}{1000} =0.96\ liter[/tex]

960 millilitres = 0.96 liter

Hence, it is true.

Upon converting all quantities to millilitres, Fred bought 960 millilitres more fabric softener than bleach, which is also 0.96 litres more. The other statements comparing millilitres and litres of purchased items are false.

Let's address each statement one by one and convert all measurements to the same unit (millilitres) for consistency:

Fred bought 4 litres of liquid laundry detergent: 1 litre = 1000 millilitres, so 4 litres = 4000 millilitres.

Fred bought 3,260 millilitres of fabric softener.

Fred bought 2.3 litres of bleach: 2.3 litres = 2300 millilitres.

Now, we can compare Fred's purchases:

Fred bought 96 millilitres more fabric softener than bleach: 3,260 millilitres (fabric softener) - 2,300 millilitres (bleach) = 960 millilitres more, not 96. False.

Fred bought 1.95 litres more laundry detergent than bleach: 4 litres (detergent) - 2.3 litres (bleach) = 1.7 litres more, not 1.95. False.

Fred bought 960 millilitres more fabric softener than bleach: As calculated earlier, this is True.

Fred bought 170 milliliters more laundry detergent than bleach is incorrect because the difference is actually 4 liters - 2.3 liters which is significantly more than 170 milliliters. False.

Fred bought 0.96 litres more fabric softener than bleach: Since we have established that he bought 960 millilitres (or 0.96 litres) more of fabric softener, this is True.

Answer:

On the 12th day after Lou starts they will be reading the same page

Step-by-step explanation:

Sabrina:

Write the equation for sabrina starting today

36+12d

Lou

Write the equation for lou

15d

Set them equal

36+12d = 15d

Subtract 12d from each side

36+12d-12d = 15d-12d

36 = 3d

Divide by 3

36/3 = 3d/3

12 =d

On the 12th day after Lou starts they will be reading the same page

Answer:

Yes,

12 days after Lou starts reading, they'll be on the same page

Step-by-step explanation:

36 is already read, 12 per day

36 + 12d

15 per day

15d

36 + 12d = 15d

3d = 36

d = 12

Answer:

12

Step-by-step explanation: Because 12 old dolls - 6 dolls = 6 dolls. Then you add 6 old dolls and 6 new dolls and you get 12 old and new dolls. Sorry  if this is confusing. I tried to make it less confusing.

Answer:

350 points.      

Step-by-step explanation:

Given:

Charlie , a frequent business traveler, is considering signing up for hotel reward program.

Hotel Elegance is currently offering 50 points for signing up, plus 15 points for every night charlie books at the hotel.

Alternatively , hotel Paradiso is offering a sign-up bonus of 250 points, plus 5 points per night.

If charlie books a certain number of nights, points he earns the hotel will be the same.

Question asked:

How many points will he have ?

Solution:

Let Charlie books for number of nights = [tex]x[/tex]

Hotel Elegance is offering = 50 points for signing up + 15 points for every night

Total points, Charlie can earn from this hotel [tex]=50+15x[/tex]

Similarly, Charlie can earn from hotel Paradiso = [tex]250+5x[/tex]

As given, that for certain number of nights, points he earns the hotel will be the same. Hence, the equation will be:-

[tex]50+15x=250+5x\\ \\ By\ subtracting \ both\ sides\ by\ 5x\ and\ 50\\ \\ 50-50+15x-5x=250-50+5x-5x\\ \\ 10x=200\\ \\ By \ dividing\ both\ sides\ by\ 10\\ \\ x=20[/tex]

By substituting the value:-

Charlie books for number of nights = [tex]x[/tex] = 20

You can take any one equation as both are equal.

Number of points, he will get  [tex]=50+15x[/tex]

                                                  [tex]=50+15\times20\\ \\= 50+300\\ \\ =350[/tex]

Thus, he will have 350 points.      

Final answer:

By setting up an equation to equate points from Hotel Elegance and Hotel Paradiso, solving for 'n' shows Charlie must book 20 nights at either hotel to earn a total of 350 points.

Explanation:

To determine the number of nights Charlie would need to book for the points he earns at Hotel Elegance and Hotel Paradiso to be the same, we need to set up an equation. Hotel Elegance offers 50 points for signing up and 15 points per night, and Hotel Paradiso offers 250 points for signing up and 5 points per night. Let n represent the number of nights Charlie books. For Hotel Elegance, the points earned will be 50 + 15n, and for Hotel Paradiso it will be 250 + 5n. We set up the equation 50 + 15n = 250 + 5n.

Solving the equation, we subtract 5n from both sides to get 50 + 10n = 250. Then, we subtract 50 from both sides which gives us 10n = 200. Dividing both sides by 10, we get n = 20. This means Charlie needs to book 20 nights for the points to be equal. Substituting n = 20 back into either equation, we get 50 + 15(20) or 250 + 5(20), both resulting in 350 points.