A bacteria culture grows with constant relative growth rate. The bacteria count was 1,920 after 4 hours and 1,966,080 after 12 hours.

(a) What is the relative growth rate? Express your answer as a percentage. (Round your answer to two decimal places.)

(b) What was the initial size of the culture?

(c)Find an expression for the exact number of bacteria after t hours, y(t).

(d) Find the number of bacteria after 9.5 hours. (Round your answer to the nearest whole number.)

(e) Find the rate of growth (in bacteria per hour) after 9.5 hours. (Round your answer to the nearest whole number.)

(f) How many hours did it take for the population to reach 72,000? (Round your answer to two decimal places.)

Answer:

17/24

Step-by-step explanation:

With the understanding that the three given cars form three mutually exhaustive and disjoint sets i.e., they form the partition of sample space, the probability that the selected car would be white is \(\frac{17}{24}\).

A collection of sets B1, B2, . . . , Bn is said to partition the sample space if the sets (i) are mutually disjoint and (ii) have as union the entire sample space.

In this question, we take three sets - set of all red cars, white cars and green cars.

A car can be either red, white or green. Thus they are mutually exclusive.

Also, let the cars in parking lot be the sample space. Every car we pick has to be of one of the three colors. This imply that the three sets of the three cars are mutually exhaustive.

P(selecting a red car) + P (selecting a green car) + P(selecting a white car) = 1

\(\frac{1}{8} + \frac{1}{6} + P(selecting\ a\ white\ car) = 1\\\\ P(selecting\ a\ white\ car) = \frac{17}{24}\)

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Answer:

a) a + b

Step-by-step explanation:

The value of the exterior angle x will be (a+b).

The angle made by the two lines of the figure which lie on the outside of the closed figure is called the exterior angle.

The exterior angle is the sum of the two opposite internal angles of any figure.

The exterior angle in the given figure will be equal to x = a+b the sum of the two opposite interior angles.

Therefore the value of the exterior angle x will be (a+b).

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The correct match for each number with its description would be :

Natural numbers are the counting numbers that are used to represent quantities of things. They are positive integers that start from 1 and go up to infinity. Whole numbers are the natural numbers (positive integers) including zero. They start from 0 and go up to infinity.

Integers are the set of whole numbers and their negatives. They include positive and negative numbers, as well as zero. Rational Numbers are numbers that can be expressed as a ratio of two integers. They include fractions and terminating or repeating decimals.

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Answer:

The answer to 1 1/2 + 1/6 is 1 2/3.

We apply associative property to rearrange:

We solve the sum of similar terms:

We add 9x to both sides (to cancel -9x):

We subtract 25/6 both sides (to cancel 25/6):

We divide by 5 both sides (to cancel 5):

Finally we simplify the fraction:

The correct option is the second one:

We know that:

We have the operation:

x - y + (-z)

Notice that because y is negative, then -y is positive.

Because z is positive, -z is negative.

Then we have:

positive + positive + negative

Or, in the number line:

right, right, left.

Second question:

Can we conclude the sign of the outcome?

No, we can't, the sign will depend on the values of x, y, and z.

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Answer:The correct option is the second one:i) right, right, left.ii) Undefined.

Step-by-step explanation:

Please provide specific data sets, and I would be happy to help you calculate the mean absolute deviation and determine which one has a MAD of 0.64.

Hello! Based on your question, you'd like to know which data set has a mean absolute deviation (MAD) of 0.64. Unfortunately, without any specific data sets provided, I am unable to directly calculate the MAD for you. However, I can help explain the concept of mean absolute deviation and how to calculate it for a given data set.

Mean absolute deviation is a measure of dispersion or variability within a data set. It helps in understanding how spread out the data points are from the mean (average) of the data set. To calculate the MAD, follow these steps:

1. Compute the mean of the data set by adding all the data points and dividing the sum by the total number of data points.
2. Calculate the absolute deviation for each data point by subtracting the mean from each data point and taking the absolute value of the result.
3. Add all the absolute deviations obtained in step 2.
4. Divide the sum of absolute deviations by the total number of data points to get the mean absolute deviation.

When you find a data set with a MAD of 0.64, it indicates that, on average, the data points are 0.64 units away from the mean. Keep in mind that a smaller MAD value means the data points are closer to the mean, indicating less variability, whereas a larger MAD value indicates more variability within the data set.

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After answering the provided question, we can conclude that As a result, with continuous compounding at a fixed annual interest rate of 2.67%, Jacob's investment will reach $25,000 in approximately 30.6 years.

In mathematics, interest refers to the amount of revenue raised or owed on an original cost or loan. You can use either simple or compound interest. Simple interest is determined by a proportion of the original amount, whereas compound interest is calculated on the principal amount and as well as any previously earned interest. If you put money $100 at a 5% yearly simple interest rate, visitors will earn $5 in interest every year for three years, for a total of $15.

To solve this problem, we can use the continuous compounding formula:

\(A = Pe^(rt)\\25000 = 8634e^(0.0267t)\\e^{(0.0267t)}= 2.893\\0.0267t = ln(2.893)\\t = ln(2.893) / 0.0267 ≈ 30.6 years\\\)

As a result, with continuous compounding at a fixed annual interest rate of 2.67%, Jacob's investment will reach $25,000 in approximately 30.6 years.

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Answer:

250 - \(\frac{p}{24}\)

Step-by-step explanation:

Since we have given that

Amount that Liam has = $250

Amount that he and his classmates spent on  present for their teacher =$p

Number of students in which $p will split = 24

According to question,

Amount that left to Liam is given by

250 - \(\frac{p}{24}\)

Hence, the required expression will be

250 - \(\frac{p}{24}\)

(Hope this helps can I please have brainlist (crown)☺️)

Using the arithmetic operation of division, the value for 3.12 / 6.5 is obtained as 0.48.

What is arithmetic operation?

A subject of mathematics known as arithmetic operations deals with the study and use of numbers in all other branches of mathematics. Basic operations including addition, subtraction, multiplication, and division are included.

To divide 3.12 by 6.5, we need to use the following steps -

We can align the decimal point by multiplying both the numerator and denominator by a power of 10 to get rid of the decimal in the numerator.

So, we can multiply both 3.12 and 6.5 by 100 to get -

312 / 650

We can simplify the fraction by dividing both the numerator and denominator by their greatest common factor (GCF).

In this case, the GCF is 26.

So, we can divide both 312 and 650 by 26 to get -

12 / 25

Use the arithmetic operation of division -

12 / 25 = 0.48

Therefore, 3.12 divided by 6.5 is equal to 12/25 or 0.48 when rounded to two decimal places.

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Answer:

Its C: 12 units × 8 units are the dimensions of the rectangle

Step-by-step explanation:

The answer is t ≤ 11.

The solution (X = 8, Y = 16) represents a minimum because the second partial derivatives are both positive.

The quadratic equation's roots 32

+6x+8=0 utilises the quadratic formula to determine. x = is the quadratic formula.

where the quadratic equation's coefficients are a, b, and c. Here, an equals 1, b equals 6, and c equals 8. We obtain the quadratic formula's result by entering these values: x =

x = (-6 ± √(36 - 32)) 2 x = (-6 to 4) 2 x = (-6 to 2) 2 x = (-3 to 1) 1 x = (-2 to 4)

Generally, any quadratic equation of the form may be solved using the quadratic formula to get the roots.

Whereas a, b, and c are real numbers, + bx + c=0. One effective method for tackling a wide range of physics and maths issues is the quadratic formula.

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Answer:

Step-by-step explanation:

To find the new coordinate of a point after it has been scaled by a factor of 1/2, you can multiply the x- and y-coordinates of the point by 1/2.

For example, to find the new coordinate of point K', you can multiply the x-coordinate of K' (-8) by 1/2 to get the new x-coordinate, and multiply the y-coordinate of K' (8) by 1/2 to get the new y-coordinate. This gives you the new coordinate of K' as (-4,4).

You can use the same method to find the new coordinates of points L' and M'. The new coordinate of L' is (4,4) and the new coordinate of M' is (-2,4).

I hope this helps! Let me know if you have any questions.

Area of a Triangle = A = ½ (b × h) square units

where b and h are the base and height of the triangle, respectively. Now, let's see how to calculate the area of a triangle using the given formula.

Define right triangle?

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The correct ratio of right angled triangle is \(\frac{c}{b} = \frac{b}{s}\)

There are a few unique varieties of right triangles, including the 45°-45° and the 30°-60° varieties.

Theorem: In a triangle, the angle across from the first side is a right angle if the square of one side equals the sum of the squares of the other two sides. To demonstrate: B=90° Proof: ABC has the formula \(AC^2 = AB^2 + BC^2\)

The right triangle. A triangle with one right angle, or 90°, is referred to as a right triangle. The longest side, which is the side opposite the right angle, is referred to as the hypotenuse. The remaining two sides are referred to as the right triangle's legs because they intersect to form the right angle.

The hypotenuse, along with the two legs, make up a right triangle. The hypotenuse, the longest side of the right triangle and the side opposite the right angle, is where the two legs of a right triangle come together at a 90° angle. \(AC^2 = AB^2 + BC^2\)

Given,

b/s = ratio of hypotenuse to height

c / b = ratio of hypotenuse to height

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Answer:

1) 10:1:3

2)a. Soup-20 oz. Cheese-2 cups, Pasta-6 cups

2)b. Soup-5 oz. Cheese-1/2 cup, Pasta-1 1/2 cups

2)c. Soup-50 oz. Cheese-5 cups, Pasta-15 cups

2)d. Soup-2 oz. Cheese- 1/5 cup, Pasta-3/5 cup

3) 3:6 = 1:2

4)a. 3 batches

4)b. 6 batches

4)c. 1/2 batch

Elaboration

1) Yes, because it simplifies down to 5:3.

2) Yes, because it also simplifies down to 5:3.

3) 25:15 and 35:21

4) If they share a zoom factor then they are equivalent.

5) Equivalent ratios are ratios that make the same comparison of numbers.

Evaluation

1) 2:3

2) They are equivalent because they share a zoom factor of 2.

Last Page

4)a. 28 oz of cream cheese. (35*0.8)

4)b. 4.8 weeks (1.6*3)

4)c. $4,000 (4*1,000)

Evaluation

1) 2 lbs-$6, 0.33 lbs-$1, 1 lbs-$3

2) 0.33 is the amount in pounds that you can get at the price of $1, and 1 pound of grapes will cost $3

Answer:

p//q

Step-by-step explanation:

p and q are parallel since the exterior angles are congruent

Answer:

complementary angles, x=19

Step-by-step explanation:

since the two parts of the angle add up to 90, they are complementary angles.

you can find x by adding them and setting it equal to 90:

3x-2+2x-3 = 90

5x-5 = 90

5x = 95

x = 19

Answer:

C=2πr

Step-by-step explanation:

If you have the diameter measurement, multiply it by pi to find the circumference. For example, a wheel with a 10-inch diameter will have a circumference of 10 x 3.14, or 31.4 inches. To calculate using the radius, multiply the radius by 2 and then multiply that result by pi

Answer:

123 degrees

Step-by-step explanation:

Answer:

123°

Step-by-step explanation:

360 - 114 - 43 - 80 = 123

The placement results provided, the student should start with Math 100.

The placement results indicate that the student has placements for Math 111, Math 100, and Math 102+. Math 111 typically corresponds to a higher-level course than Math 100, and Math 102+ implies a placement beyond Math 102.

To progress towards Math 103E, it is essential to follow the recommended course sequence. Usually, Math courses are designed to build upon previously learned concepts and skills. Starting with Math 100 would provide the foundational knowledge necessary to succeed in subsequent courses.

Therefore, the student should first start with Math 100, and upon successful completion, they can proceed to Math 103E. It is important for the student to consult with their academic advisor or the mathematics department at their institution for specific course placement and sequencing information to ensure they are following the appropriate path.

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Answer:

yo i live in florida

Step-by-step explanation:

Answer Ben plays video games for 1 1/2 hours per day for the 3 days

Step-by-step explanation:

He has (10 - 5 1/2) hours or 4 1/2 hours left to split evenly over the next 3 days.

Let D = #hours per day Ben plays, then

3D = 4 1/2

3D = 4.5

D = 4.5/3

D = 1.5

The equation for hyperbola with given foci is \(\frac{(x+3)^{2}}{49}-\frac{(y-6)^{2}}{32}=1\)

What is hyperbola?

In analytical geometry, a hyperbola is a conic section that results from the intersection of a plane with a double right circular cone at an angle that touches both of the cone's halves. The two distinct unbounded curves that result from the intersection of the plane and cone are known as hyperbolas.

The standard equation of a horizontal hyperbola with center (h,k) is

\(\frac{(x-h)^{2}}{a^{2} } -\frac{(y-k)^{2}}{b^{2} }=1\)

The given hyperbola has vertices at (–10, 6) and (4, 6).

The length of its major axis is 2a= 4-(-10)

2a=14

a=7

The center is the midpoint of the vertices (–10, 6) and (4, 6).

The center is \((\frac{-10+4}{2} , \frac{6+6}{2} )= (-3,6)\)

Now, we need to use the relation a^2+b^2=c^2 in order to find b^2.

The c-value is the distance from the center (-3,6) to one of the foci (6,6)

c= 6-(-3)=9

So, 7^2+b^2=9^2

b^2= 9^2-7^2

b^2= 81-49

b^2= 32

Hence, on substituting the obtained values in the standard equation of hyperbola, we get

\(\frac{(x-(-3))^{2} }{7^{2}}-\frac{(y-6)^{2} }{32} =1\)

\(\frac{(x+3)^{2} }{49}-\frac{(y-6)^{2} }{32} =1\)

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Answer:

the missing side is 90 because is a right triangle

Answer:

The scale factor is 3/2.

Step-by-step explanation:

Let's use the side PQ.

The original length was 8 units.

And the new length is 12 units.

Let the scale factor be k. Therefore:

\(8k=12\)

By dividing both sides by 8, we can see that our scale factor from ΔPQR to ΔP'Q'R' is:

\(\displaystyle k=\frac{12}{8}=\frac{3}{2}\)

Answer:

Sorry, but your question doesn't make sense

Step-by-step explanation:

where is the rest of the question/problem