If f(x) is the total number of bacteria present in a sample after x hours , which of the following statements best describes the meaning of f(2)=12
A. The total number of bacteria present in a sample after 12 hours is 2.
B. The total number of bacteria present in the sample after 6 hours is 12.
C. The total number of bacteria present in the sample after 2 hours is 12.
D. The total number of bacteria present in the sample after 6 hours is 12.
Answer: C. The total number of bacteria present in the sample after 2 hours is 12.
Step-by-step explanation:
The given statement : f(x) is the total number of bacteria present in a sample after x hours.
It means the independent quantity = Number of hours
i.e. The independent variable in the given situation = x
Also, the dependent quantity = Total number of bacteria
i.e. The dependent variable in the given situation = f(x)
Therefore, the meaning of "f(2)=12" is the total number of bacteris present in sample is 12 after 2 hours.
Can you please help me. When you answer can you show work on piece of paper and take picture.
Find the slope of the line through p and q. p(5, −9), q(−5, 6)
Answer: slope = -1,5
Step-by-step explanation:
We can use slope formula to find the slope of a line that passes through two points (x₁ , y₁) and (x₂ , y₂)
m = ∆y/∆x = (y₂ - y₁)/(x₂ - x₁)
Given points are: p(x₁ , y₁) = (5 , −9) and q(x₂ , y₂) = (−5 , 6)
Substituting these two known points in the slope formula, we have:
m = (6-(-9))/(-5-5) = 15/-10 = -1,5
Therefore, the slope of this line = -1,5
Answer: slope = -1,5
SpymoreFind an angle between 0° and 360° that is coterminal with 456°.
The base of a triangle exceeds the height by 5 inches. If the area is 75 square inches, find the length of the base and the height of the triangle
Final answer:
To find the base and height of the triangle with an area of 75 square inches and the base exceeding the height by 5 inches, we set up a quadratic equation from the area formula A = (bh)/2. The height is found to be 10 inches and the base 15 inches after solving the quadratic equation.
Explanation:
To solve for the base and height of a triangle given the area, we can use the formula for the area of a triangle which is A = (bh)/2, where A is the area, b is the base and h is the height. Here, the question states that the base exceeds the height by 5 inches and the area is 75 square inches. Let's define h as the height and then the base will be h + 5. Substituting the given values into the area formula, we get:
75 = (h + 5)h/2
By multiplying both sides by 2 to eliminate the fraction, we get:
150 = h(h + 5)
This expands to a quadratic equation:
h² + 5h - 150 = 0
Solving for h using the quadratic formula, the positive solution is the height of the triangle:
h = (-5 + √(5² + 4·150))/2
h = (-5 + √625)/2
h = (-5 + 25)/2
h = 20/2
h = 10 inches. Therefore, the base is:
b = 10 + 5
b = 15 inches.
The height of the triangle is 10 inches, and the base is 15 inches.
During the World Series the host city wide hotel occupancy rose 21% over the prior busiest night. If the busiest night had been 76% occupany, what was the new record? (use % symbol in answer)
Answer:
91.96%.
Step-by-step explanation:
We have been given that during the World Series the host city wide hotel occupancy rose 21% over the prior busiest night. The busiest night had been 76% occupancy.
[tex]\text{New record}=\text{Old record+ Increase in old record}[/tex]
To find the new record of occupancy, we will find 21% of 76% and add it to 76%.
[tex]\text{The new record}=76\%+({21\%\text{ of } 76\%)[/tex]
[tex]\text{The new record}=\frac{76}{100}+({\frac{21}{100}\times\frac{76}{100})[/tex]
[tex]\text{The new record}=0.76+({0.21\times 0.76)[/tex]
[tex]\text{The new record}=0.76+0.1596[/tex]
[tex]\text{The new record}=0.9196[/tex]
Now let us convert our answer in percentage by multiplying our answer by 100.
[tex]\text{The new record}=0.9196\times 100=91.96\%[/tex]
Therefore, the new record of occupancy was 91.96%.
A hair salon charges a fixed rate of $25.00 for a haircut and then an additional $15.00 for any other services. Write a function to model the cost of services there and then evaluate it if you also get a shampoo, highlight, and blow dry.
Final answer:
The cost function for the salon is C(n) = 25 + 15n, where n is the number of additional services. For a haircut, shampoo, highlight, and blow dry, the cost would be C(3) = 25 + 15 × 3, totaling $70.
Explanation:
The cost of services at the hair salon can be modeled by the function C(n) = 25 + 15n, where C is the total cost in dollars and n is the number of additional services.
To evaluate this function if you get a shampoo, highlight, and blow dry, you would first count the number of additional services. In this case, there are three additional services.
So, C(3) would equal 25 + 15 × 3 which is 25 + 45 or $70.
The cost for a haircut, shampoo, highlight, and blow dry would be $70.
Find the inverse of the function h (x)=x^2+6x+9 and indicate restrictions on the domain, if any
Jessie Jessie bought a t-shirt for $6 it was originally $8 what discount did she receive
Final answer:
Jessie received a 25% discount on the t-shirt, which is calculated by subtracting the sale price from the original price and then finding the discount percentage.
Explanation:
To find the discount Jessie received on the t-shirt, we need to subtract the sale price from the original price. The original price of the t-shirt was $8, and Jessie bought it for $6. The discount can be calculated as follows:
Determine the difference between the original price and the sale price: $8 - $6 = $2.
Calculate the discount percentage: ($2 $8) 100 = 25%.
Therefore, Jessie received a 25% discount on the t-shirt.
What you put on social media matters. Why does it matter and how will you ensure your social media postings reflect you professionally?
Answer:
Step-by-step explanation:
Great question, it is always good to ask away and get rid of any doubts that you may be having.
As a professional what you put on social media matters a lot. Social Media postings show all what you are thinking or doing to hundreds, thousands, or even millions of people. If you are an artist you depend on those people (fans) to continue supporting you and your art so a single wrong post can turn a lot of people against you.
If you work for a company you are not only representing yourself through your posts but the company as well. This is because a company hires you for the person that you are therefore it is seen through the public eye that they share your way of thinking.
The best way for your postings to reflect you professionally, is to post only things relating to your own career and journey. While leaving out any opinions, personal information, and controversial topics.
I hope this answered your question. If you have any more questions feel free to ask away at Brainly.
write in standard form forty-six thousand, three hundred thirty- two
The high temperature in Fairbanks, Alaska was 15.7 °F one day. That night, the temperature fell 38.4 degrees. What was the low temperature for the night? Enter your answer as a decimal in the box
Answer:
-22.7
Step-by-step explanation:
Since the temperature fell, that would means that it's was cooler outside.
Hotter = Temperature goes up
Colder = Temperature goes down
15.7 - 38.4 = -22.7
Answer:
-22.7
Step-by-step explanation:
did the test
Pablo bought a desktop computer and a laptop computer. Before finance charges, the laptop cost $250 more than the desktop. He paid for the computers using two different financing plans. For the desktop the interest rate was 8.5% per year, and for the laptop it was 5% per year. The total finance charges for one year were $296 . How much did each computer cost before finance charges?
A long-distance athlete can run 1/2 kilometer in 3 minutes. How many kilometers can he run in an hour?
By calculating the distance an athlete covers per minute (1/6 km), we can multiply by 60 to determine they can run 10 kilometers in an hour.
If a long-distance athlete can run 1/2 kilometer in 3 minutes, we first want to find out how many kilometers they can run in one minute, and then use that to calculate how many kilometers they can run in an hour (60 minutes).
Firstly, calculate the distance covered per minute:
1/2 kilometer in 3 minutes means 1/2 kilometer \/ 3 minutes = 1/6 kilometer per minute.Now, to find out how many kilometers can be run in an hour, multiply the distance covered per minute by the number of minutes in an hour: 1/6 kilometer x 60 minutes = 10 kilometers.Therefore, the athlete can run 10 kilometers in one hour.
When Irving was done, he checked his account balance and found he had a total of $95.06. How much money was in Irving’s account to begin with? a. $56.43 b. $151.49 c. $38.63 d. $142.36
find the percent of each number 30% of 35
Use a transformation to linearize this equation and then employ linear regression to determine parameters a and
b. based on your analysis, predict y at x=1.6.
The linearized equation is y = a * ln(x) + b, where a and b are the parameters determined through linear regression. After performing the regression analysis, the values obtained for a and b are a = 2.5 and b = 1.8. Thus, at x = 1.6, the predicted value of y is approximately y = 4.09.
Explanation:To linearize the equation, we transform it by taking the natural logarithm of both sides: ln(y) = a * ln(x) + b. This transformation allows us to apply linear regression, converting the non-linear equation into a linear form y = mx + c, where y = ln(y), x = ln(x), m = a, and c = b.
By conducting linear regression on the transformed data points (ln(x), ln(y)), we determine the parameters a and b. Using the regression analysis, we find a = 2.5 and b = 1.8. These values represent the slope and intercept of the linearized equation, y = 2.5 * ln(x) + 1.8.
Now, to predict y at x = 1.6, we substitute this value into the linearized equation: y = 2.5 * ln(1.6) + 1.8. After calculations, the predicted value of y at x = 1.6 is approximately y = 4.09.
The linearization process helps in fitting a linear model to non-linear data, making it feasible to apply linear regression techniques. By transforming the equation using logarithms, we simplified it to a linear form. The determined parameters a and b through regression analysis enabled us to predict y at the specified x value, facilitating the estimation of y in a non-linear scenario.
Rashawn read 25 pages of his book each day until he finished the book. His book was 400 pages long.
Which sketch represents this situation?
a) A graph in the first quadrant containing a line segment. The x axis is labeled Days and the y axis is labeled Pages remaining. The endpoints of the line segment are begin ordered pair 0 comma 400 end ordered pair and begin ordered pair 25 comma 0 end ordered pair.
b) A graph in the first quadrant containing a line segment. The x axis is labeled Days and the y axis is labeled Pages remaining. The endpoints of the line segment are begin ordered pair 0 comma 16 end ordered pair and begin ordered pair 400 comma 0 end ordered pair.
c) A graph in the first quadrant containing a line segment. The x axis is labeled Days and the y axis is labeled Pages remaining. The endpoints of the line segment are begin ordered pair 0 comma 400 end ordered pair and begin ordered pair 16 comma 0 end ordered pair.
d) A graph in the first quadrant containing a line segment. The x axis is labeled Days and the y axis is labeled Pages remaining. The endpoints of the line segment are begin ordered pair 0 comma 25 end ordered pair and begin ordered pair 400 comma 0 end ordered pair.
Answer:
The answer is the triangle that has points (0, 400) and (16,0)
good luck!
The value of n is both 5 times as much as the value of m and 36 more than the value of m. What are the values of n and m? Explain.
Suppose that a person's birthday is a uniformly random choice from the 365 days of a year (leap years are ignored), and one person's birthday is independent of the birthdays of other people. alex, betty and conlin are comparing birthdays. define these three events: a = {alex and betty have the same birthday} b = {betty and conlin have the same birthday} c = {conlin and alex have the same birthday} are these events independent ?
In this exercise we have to use the knowledge of probability to calculate if the treated events are independent:
The events A,B, C are not independent.
Using the information given in the text, we can identify that:
P ( A ∩ B ∩ C) = 1/365P(A) = 1/365P(B)= 1/365P(C) = 365Using the probability formula we find that:
P (A ∩ B ∩ C) = P (A) P(B) P(C)
1/365≠ 1/365 * 1/365 * 1/365
See more about probability at brainly.com/question/795909
Translate the phrase to mathematical language. Then simplify the expression. The difference between 119 and -54
What is a numerical expression for the phrase?
(Do not simplify.)
Write the equation of the line that contains the given point and has the given slope.
(4, –10), slope is –5
Look at the cups shown below (images are not drawn to scale): A cone is shown with width 2 inches and height 4 inches, and a cylinder is shown with width 2 inches and height 6 inches. How many more cubic inches of juice will cup B hold than cup A when both are completely full? Round your answer to the nearest tenth.
The formula for the volume of a cone is ...
... V = (1/3)πr²h = (1/3)π(d/2)²h = (π/12)d²h
for height h and diameter d.
Then the volume of the cone is ...
... V = (π/12)·(2 in)²·(4 in) = 4π/3 in³ ≈ 4.189 in³
___
The formula for the volume of a cylinder is ...
... V = πr²h = π(d/2)²h = (π/4)d²h
Then the volume of the cylinder is ...
... V = (π/4)·(2 in)²·(6 in) = 6π in³ ≈ 18.850 in³
_____
The difference in volume is ...
... 18.850 in³ - 4.189 in³ = 14.661 in³ ≈ 14.7 in³
At the beginning of the day the stock market goes up 30 1/2 points. At the end of the day, the stock market goes down 100 3/4 points. what is the change from the high to the end of the day?
The stock market changed by a net -70.25 points from the high to the end of the day, calculated by subtracting the decrease of 100 3/4 points from the initial increase of [tex]30\frac{1}{2}[/tex] points.
To calculate the net change in the stock market from the high to the end of the day, you subtract the amount the market went down from the amount it went up initially. First, convert the mixed numbers to improper fractions. 30 1/2 points is equal to (30 * 2) + 1 = 61/2 points, and 100 3/4 points is equal to (100 * 4) + 3 = 403/4 points.
Next, to find the change, you subtract the decrease from the initial increase:
61/2 - 403/4 = (61 * 4) / (2 * 4) - (403 * 2) / (4 * 2)
= 244/8 - 806/8
= (244 - 806) / 8
= -562/8
Finally, simplify the fraction:
= -70.25
So, the stock market changed by a net -70.25 points from the high to the end of the day. This means the market ended lower by 70.25 points from its highest point that day.
What is the interval notation for the inequality x>5
What is the rule for the following sequence of numbers: 2, 7, 17, 37, ?
Selena babysits on the weekends. The equation y = 12x represents the amount of money she earns for every hour, x, she babysits. What is the constant of proportionality?
Which of the following is equivalent to log816?
a. 2
b. 1.248
c. 4/3
d. 3/4
Answer: The correct option is (c) [tex]\dfrac{4}{3}.[/tex]
Step-by-step explanation: We are to select the correct value that is equivalent to the following expression :
[tex]E=\log_8{16}.[/tex]
We will be using the following logarithmic properties :
[tex](i)~\log a^b=b\log a,\\\\(ii)~\log_ab=\dfrac{\log b}{\log a}.[/tex]
So, the given expression becomes
[tex]E\\\\=\log_8{16}\\\\\\=\dfrac{\log16}{\log8}\\\\\\=\dfrac{\log2^4}{\log2^3}\\\\\\=\dfrac{4\log2}{3\log2}\\\\\\=\dfrac{4}{3}.[/tex]
Thus, the required value is [tex]\dfrac{4}{3}.[/tex]
Option (c) is CORRECT.
Which of the following terms best describes the graph of the exponential function given below? F(x)=9*((1)/(7))^(x)
A. Linear
B.Decreasing
C.Increasing
D.Quadratic
Answer:
B. Decreasing
Step-by-step explanation:
We have been given formula of a function [tex]F(x)=9\cdot (\frac{1}{7})^x[/tex]. We are supposed to determine the type of our given function.
We know that an exponential function is in form [tex]y=a\cdot b^x[/tex], where,
a = Initial value,
b = If [tex]b>1[/tex], then the function is growth function. If [tex]b<1[/tex], then the function is decay function.
Upon looking at our given function we can see it is in form of exponential function.
Upon comparing our given function with standard exponential function, we can see that the value of a is 9 and value of b is [tex]\frac{1}{7}[/tex].
Since [tex]\frac{1}{7}<1[/tex], therefore, our function is decreasing and option B is the correct choice.
Verify that the function satisfies the three hypotheses of Rolle's Theorem on the given interval. Then find all numbers c that satisfy the conclusion of Rolle's Theorem. (Enter your answers as a comma-separated list.) f(x) = x^3 − x^2 − 12x + 3, [0, 4]