An acidophilus culture containing 150 bacteria doubles in population every hour. (a) Write a function representing the bacteria population for every hour that passes. (b) Graph the function. (c) Use the graph to predict the number of bacteria after 12 hours.,
Answers
We have then:
y = A * (b) ^ t
Where,
A: Initial population
b: Population growth as time passes
t: time
y: population after t hours.
Part A:
The equation for this case is:
y = 150 * (2) ^ t
Part B
See attached image.
Part C:
For this case we should evaluate the function for t = 12
We have then:
y = 150 * (2) ^ (12)
y = 614400
y = 150 * (2) ^ t
t= 12
y = 150 * (2) ^ (12)
y = 614400
The answer to your questions is y is equals to 614400.
Related Questions
Jeanette purchased a concert ticket on a website.The original price of the ticket was $75.She used a coupon code to receive a 20% discount.The website applied a 10% service fee to the discounted price.Jeanettes ticket was less than the original price by what percent?
Answers
Find discounted price.
Discounted $= original $ - (original $ * % discount)
Discounted $= $75 - ($75 * 20%)
Discounted $= 75 - 15
Discounted $= $60
STEP 2:
Find discounted $ plus service fee.
Price plus fee= discounted $ + (discounted $ * service fee %)
Price plus fee= $60 + ($60 * 10%)
Price plus fee= 60 + 6
Price plus fee= $66
STEP 3:
Find % change.
% change formula= (new # - original #) ÷ original # x 100
% change= (66-75)÷ 75 x 100
% change= -9 ÷ 75 x 100
% change= -0.12 x 100
% change= -12%
***the negative indicates a decrease
ANSWER: Her ticket was less than the original by 12%.
Hope this helps! :)
PLEASE HELP ME!! IM STUCK!!
Answers
The middle row has 3 piles. The tallest one is 3 cubes high.
The right row has 2 piles, both 1 cube high.
The answer is Choice A.
helppppppppppppppppppppppppppppppppppppppppp
Answers
Number of shaded triangles in the second figure = 3
Number of shaded triangles in the third figure = 9
If we observe these values, we can conclude that a Geometric Series is being formed.First number is multiplied by 3 to get the second number and second number is multiplied by 3 to get the third number. So the summation can be expressed using the Geometric Series.
The summation uses the general term to express the sum over the interval. So first we find the general term of geometric series.
First term of the series = 1
Common ratio = 3
So, the general term of the series will be: [tex]1(3)^{n-1} [/tex]
This general term gives the terms of given geometric series for different values of n. For n = 1, we will have the first term which will is 1. Similarly for n=2, we will have the second term which is 3.
So the summation will start with first term and end on 15th term. Therefore, correct summation for this case is expressed by first option.
Raymond has 120 books on his bookshelf that he has not read. He plans on reading 3 books per week until there are only 24 books that he still needs to read. Which equation can be used to determine the number of weeks, w, it will take Raymond to have only 24 books left, and how many weeks will it take? 3w - 24 = 120; 48 weeks 24w = 120 - 3; 4 weeks 120 - 3w = 24; 32 weeks 24w - 3 = 120; 5 weeks
Answers
⓶ To test it out, let’s start by isolating the “W” :
120 - 3w = 24
-24 -24
↓
96 - 3w = 0
+3w +3w
↓
96 = 3w
÷3 ÷3
↓
32 = w
⓷ Now let’s see if everything works :
32 should be the number of weeks it will take Raymond to have only 24 books left!
If Raymond reads 3 books per week, how many did he read in 32 weeks?
32 × 3 = 96
If Raymond read 96 books in 32 weeks, how many books does he have left?
120 - 96 = 24
So the equation in #⓵ works!
I really hope this helped, if there’s anything just let me know! ☻
When Katie was born her mother invested $5000 in an account for her college savings. The interest rate is 3.5% compounded annually. To represent this, we can use the formula V = 5000(1 + r)t where r represents the interest rate and t represents the time in years. How much will Katie have in her account when she turns 18
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Remember to turn the rate into a decimal by moving the decimal place to the left twice. Also remember that t is an exponent.
Let g(x)=2x and h(x)=x2+4. Find the value. (hog) (1)
Answers
You get this by putting the 1 into the g function, then placing the result into the h function. This will give you 2 and then the final answer of 8.
An office supply store in san diego sells 7 writing tablets and 4 pens for $6.40 also two tablets and 19 pens cost $5.40 find the price of each
Answers
2t+ 19p = 5.40
Let’s substitute equation 1 in equation 2
T= (6.40 -4p)/7
2(6.4-4p)/7)) +19p=5.4
(12.8-8p)/7 +19p = 5.5
12.8-8p +133p = 38.5
125p= 25.7
P = 0.21
Tablets = 0.79
Scott is beginning racquetball at a club. his equipment will cost $67.95, the fees are $70 membership plus $5.50 per hour for 40 hours, and he will make 30 trips at $1.34 per trip. what are his total costs?
Answers
Total cost = $398.15
Answer: Total cost will be $398.15.
Step-by-step explanation:
Since we have given that
Cost of his equipment = $67.95
Cost of membership fees = $70
Cost of per hour =$5.50
For 40 hours,
Cost will be [tex]5.50\times 40=\$220[/tex]
Cost of per trip = $1.34
Cost for 30 trips will be
[tex]1.34\times 30=\$40.2[/tex]
According to question,
[tex]\$67.95+\$70+\$220+\$40.2=\$398.15[/tex]
Hence, total cost will be $398.15.
Which of the following best describes how to measure the spread of the data?
Answers
Final answer:
To measure the spread of data, you can use the range, variance, or standard deviation, which respectively measure the absolute difference between extremes, the average squared deviation from the mean, and the average deviation from the mean in the same units as the data.
Explanation:
The question refers to the methods used to measure the spread of data in a dataset. The spread, or variability, indicates how much the data points in a set differ from each other and from the central measures like the mean. There are several ways to quantify this spread, including:
The range, which is the difference between the largest and smallest values in the set.
The variance, which is the average of the squared differences from the mean.
The standard deviation, which is the square root of the variance and provides a measure of spread in the same units as the data.
Knowing the spread of data helps in understanding the distribution and consistency of the dataset, which is essential for statistical analysis.
20. Find the measure of each interior angle AND each exterior angles of the following regular polygons. Show your work. a. Pentagon b. 16-gon c. Dodecagon
Answers
Interior angle:
5 sides => form 5 triangles => central angle: 360 / 5 = 72°
interior angle = 2x
angles in every triangle: x => x + x + 72° = 180°
=> 2x = 180° - 72° = 108°
Answer 108°
Exterior angles = 360° / number of sides = 360° / 5 = 72°
Answer: 72°
b. 16 - gon
Interior angles: 2x
number of triangles = 16
central angle = 360 / 16 = 22.5°
interior angle 2x, where 180° - 22.5° + x + x => 2x = 180° - 22.5° = 157.5°
Answer: interior angle 157.5°
Exterior angles: 360 / 16 = 22.5°
Answer: exterior angles = 22.5°
c. Dodecagon
number of sides 12
central angle = 360° / 12 = 30°
interior angle, 2x => 30 + 2x = 180 => 2x = 180 - 30 = 150°.
Answer: interior angle = 150°
Exterior angle = 360° / number of sides = 360° / 12 = 30°
Answer: exterior angle = 30°
Will give brainliest if correct
The value of a stock share in a new technology company has been increasing at a rate of 8.6% quarterly. The initial price of one share was $102.15. An investor plans to sell once the value of one share reaches $233.10.
If t is the number of quarters since the initial price of one share was set, which equation could be used to determine how long it will take the share to reach $233.10, assuming it continues to grow at the same rate?
A. 102.15 = 233.10(0.086)t
B. 102.15 = 233.10(0.914)t
C. 233.10 = 102.15(1.86)t
D. 233.10 = 102.15(1.086)t
Answers
It should be written as 233.10 = 102.15(1.086)^t
The t has to be an exponent because you are multiplying the investment by 1.086 repeatedly each quarter. We used 1.086 because we added on 8.6% (or 0.086) to the investment.
The correct equation to use is D. 233.10 = 102.15(1.086)^t, which represents how the value of the share increases over time assuming consistent growth. The growth factor is represented by (1.086)^t as the share is increasing by 8.6% quarterly.
Explanation:The correct equation to determine how long it will take for the share to reach $233.10 is D. 233.10 = 102.15(1.086)^t.
This equation represents a classic compound interest formula that describes how an investment grows over time, where 102.15 is the initial share price, 1.086 is the quarterly growth rate (1+8.6%), and t is the number of quarters.
The equation shows that the future value, $233.10, is equal to the initial value, $102.15, multiplied by the growth factor, (1.086)^t, raised to the number of quarters.
Learn more about Compound Interest Formula here:https://brainly.com/question/35413403
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What is the value of k
Answers
in triangle sum of angles =180
so
4k+5+6k+10+65=180
10k+80=180
10k=180+80=260
k=260/10
k=26
9, 21, 7, 11, 13, 21, 5, 14, whats the range?
Answers
Your Question(s):
[tex]9, 21, 7, 11, 13, 21, 5, 14,[/tex]
Whats the range?
My Answer(s):
First, we need to figure out what range is. The range is The difference between the lowest and highest values. So, we need to order the numbers from least to greatest. So order the numbers as:
5, 7, 9, 11, 13, 14, 21, 21.
Then subtract the lowest number from the biggest number:
[tex]21 - 5 = 16[/tex]
So, 16 is your range!
Hope I helped,
♥ Sir Chub-Chubs.
2. Quadrilateral ABCD is inscribed in a circle. Find the measure of each of the angles of the quadrilateral. Show your work
Would the measure of angle B be x for this??
Answers
On this exercise it is asked to find the measure of angle B, First of all, you need to find the value of x. To so you have to select two opposite angles on this case angles A and C.
m<A+m<C=180 Substitute the given values for angles A and C
x+2+x-2=180 Combine like terms
2x=180 Divide by 2 in both sides to isolate x
x=90
Now, that the value of x is known you can substitute it in the expression representing angle D, and then subtract that number from 180 to find the measure of angle B.
m<D=x-10 Substitute the value of x
m<D=90-10 Combine like terms
m<D=80
m<B=180-m<D Substitute the value of angle D
m<B=180-80 Combine like terms
m<B=100
The measure of angle B is 100 degrees, and the value of x is 90.
Which of the following circles have their centers in the second quadrant? Check all that apply.
A. (x - 5)2 + (y - 6)2 = 25
B. (x + 1)2 + (y - 7)2 = 16
C. (x - 4)2 + (y + 3)2 = 32
D. (x + 2)2 + (y - 5)2 = 9
PLEASE HELP AND EXPLAIN!!!,
Answers
(x - xc)² + (y - yc)² = r²
The second quadrant is the one that has negative x coordinates and positive y coordinates.
This said, let's see all your options:
A) (x - 5)² + (y - 6)² = 25
xc = -(-5) = +5
yc = -(-6) = +6
C (5 , 6) is in the first quadrant.
B) (x + 1)² + (y - 7)² = 16
xc = -(+1) = -1
yc = -(-7) = +7
C (-1 , 7) is in the second quadrant.
C) (x - 4)² + (y + 3)² = 32
xc = -(-4) = +4
yc = -(+3) = -3
C (4, -3) is in the fourth quadrant.
D) (x + 2)² + (y - 5)²= 9
xc = -(+2) = -2
yc = -(-5) = +5
C (-2 , +5) is in the second quadrant.
Therefore, the correct answers are B and D.
Graph the quadratic functions y = -2x^2 and y = -2x^2 + 4 on a separate piece of paper. Using those graphs, compare and contrast the shape and position of the graphs.
I know that since both functions are quadratic functions, they will both have a parabola shape.
Answers
_____
The thrust of this question is to get you to recognize that adding a constant to a function shifts its graph in the amount and direction of the constant value (positive ⇒ upward).
33 POINTS!!
3. A savings account has a 3% interest rate.
(a) Complete the ratio table shown. Show your work. Deposit ($) 100 50 300 Interest ($) 3 12
(b) How much more interest would you have if you deposited $200 than if you deposited $150? Show your work
Answers
A) 100*.03= $3
400*.03= $12 12/.03 =400
50*.03=$1.50
300*.03=$9
B) multiply .03*200=$6 and .03*150=$4.50 then subtract 6.00-4.50=$1.50 difference.
Hope this helps
The answer is in the file attached.
Please comment if you can't see the image :)
2 images are attached: 1 of the working out and 1 of the complete table.
Have a nice day!
(also, I didn't do part b sorry!)
The perimeter of an equilateral triangle is 186 cm. what is the length of one side of the triangle?
Answers
So, the length of one side of the triangle is 62 cm
Hope this helps! :)
Which equation represents y = −x^2 − 10x − 20 in vertex form?
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.. y = -(x +5)^2 +5
-1/6 + 2/3 ( 9 + - 3/4) + - 1/2
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-1/6 + 2/3(8 1/4) + -1/2
Then multiply 2/3 by 8 1/4.
-1/6 + 5 1/2 + -1/2
Add -1/2 to 5 1/2.
-1/6 + 5
Add 5 to -1/6.
4 5/6 is the fully simplified answer.
Hope this helps!
which is less -12.05 or -12.5
Answers
A 12 sided die, numbered 1 to 12 is rolled. Find the probability that the roll results in an odd number or number less than 4
Answers
Answer:
6/12+3/12-2/12=.583
Step-by-step explanation:
6/12 amount of odd numbers
3/12 numbers less than 4
2/12 the amount of numbers that overlap
The probability that the roll results in an odd number or number less than 4 is 3/4.
Given that, a 12 sided die, numbered 1 to 12 is rolled.
What is the probability?Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event.
We know that, probability of an event = Number of favorable outcomes/Total number of outcomes
Total number of outcomes = 12
Odd numbered sides = {1, 3, 5, 7, 9, 11} = 6
Number less than 4 = {1, 2, 3} = 3
Probability of getting an odd number = 6/12
Probability of getting a number less than 4 = 3/12
So, probability = 6/12 + 3/12
= 9/12
= 3/4
Therefore, the probability that the roll results in an odd number or number less than 4 is 3/4.
To learn more about the probability visit:
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0.25 r – 0.125 + 0.5 r = 0.5 + r
solve for r please show steps so i can actually understand.,
Answers
Step 1: Move all similar terms (r) to the same side of the equation by
subtracting "r" from each side of the equation
0.25r - 0.125 + 0.5r - r = 0.5
Move terms without r to the other side of the equation, by adding +0.125 to each side of the equation
0.25r + 0.5r - r = 0.5 + 0.125
Add similar terms, note that r is equal to 1r
0.75r - 1r = 0.625
-0.25r = 0.625
Solve for r by dividing both sides of the equation by -0.25
r= 0.625/(-0.25)
r=-2.5
Jesse has has n dollars in his bank account he deposits 132 write an expression that represents the total amount Jesse now has in his bank account
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n= dollars he has
t= total
PLEASE HELP ME QUICKLY HURRRYYY!!!!!!!!!!!!!!!
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Therefore the answer is the second from the top: c + a =109. c = a +15.
Holly wants to save money for an emergency. Holly invests $1500 in an account that pays an interest rate of 6.75%. How many years will it take for the account to reach $7300?
Answers
which equals t=24.23
Simplify the expression where possible. (r^3) -2
Answers
Answer:
r^-6
Step-by-step explanation:
Dan is 30 years older than Jake. In 8 years Dan will be 4 times Jake's age. How old is Jake now?
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Anna has 1/2 pound of trail mix. She evenly divides the trail mix into 4 bags. How much is in each bag?
Answers
1/2 ÷ 4 = 1/2 x 1/4 = 1/8 pound
There is 1/8 pound of trail mix in each bag.
How can you tell when a quadratic equation has no real solutions?
A. when the radicand is negative
B. when b in the quadratic formula is greater than the radicand
C. when the radicand equals zero
D. when the radicand is not a perfect square
I believe the answer is A? is that right?