Answer:
(a) An expression for the number n of bacteria after t hours is n(t)=700*[tex]3^{t}[/tex]
(b) The rate of growth of the bacteria population after 1.5 hours is 3,996 number of bacteria per hour.
Step-by-step explanation:
An exponential function is one in which the independent variable x appears in the exponent and has a constant a as its base. Its expression is:
f(x)=aˣ
being a real positive.
When 0 <a <1, then the exponential function is a decreasing function and when a> 1, it is an increasing function.
An exponential function allows us to refer to phenomena that grow faster and faster, such as population growth.
In that case, the formula used to model the growth of a population is given by:
P(t)=P0*[tex]a^{t}[/tex]
where the function P (t) grows exponentially and represents the quantity of the population at time t; a represents the constant of growth or decrease and P0 represents the initial population at time zero.
In this case:
P0=700a=3Replacing, you get:
P(t)=700*[tex]3^{t}[/tex]
An expression for the number n of bacteria after t hours is n(t)=700*[tex]3^{t}[/tex]
The derivative of this function P (t) is:
n'(t)=700*ln(3)*[tex]3^{t}[/tex]
and reflects the growth rate of the bacteria population.
So, the rate of growth of the bacteria population after 1.5 hours is:
n(1.5)=700*ln(3)*[tex]3^{1.5}[/tex]
Solving, you get:
n(1.5)≅ 3,996
The rate of growth of the bacteria population after 1.5 hours is 3,996 number of bacteria per hour.
$75 jacket: 5% markup
Answer:
75*1.05 = $78.75
Step-by-step explanation:
You can just multiply by 1.05 or go the long route and divide by 100 and multiply by 105.
Applicants to a psychology department have normally distributed GRE scores with a mean, LaTeX: \muμ, of 544 and a standard deviation, LaTeX: \sigmaÏ, of 103. What percentage of applicants scored between 500 and 700? Round to the nearest percent.A. -24% B. 78% C. 2296 D. 24% E. 5%
Answer:
The probability is P(500 < X < 700 ) = 0.60044
Step-by-step explanation:
From the question we are told that
The mean is [tex]\mu = 544[/tex]
The standard deviation is [tex]\sigma = 103[/tex]
Generally the percentage of applicant that scored between 500 and 700 is mathematically represented as
[tex]P(500 < X < 700 ) = P(\frac{500 - 544}{103} < \frac{X - \mu }{\sigma } < \frac{700 - 544}{103} )[/tex]
[tex]\frac{X -\mu}{\sigma } = Z (The \ standardized \ value\ of \ X )[/tex]
[tex]P(500 < X < 700 ) = P(-0.4272 < Z < 1.5146 )[/tex]
=> [tex]P(500 < X < 700 ) = P( Z< 1.5146 ) - P ( Z < -0.4272 )[/tex]
Generally from the z-table, the area under the normal curve to the left corresponding to 1.5146 and -0.4272 is
P( Z< 1.5146 ) = 0.93506
P ( Z < -0.4272 ) = 0.33462
So
P(500 < X < 700 ) = 0.93506 - 0.33462
=> P(500 < X < 700 ) = 0.60044
What is the quotient of the division below? 96-3= O 13 O 23 O 31 o 32
Answer:
32
Step-by-step explanation:
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May y'all please help me
Answer:
2x^2 - 11x + 6
Step-by-step explanation:
2x^2 + 4x - 3 * (5x - 2)
Distribute -3 between the parentheses like so.
2x^2 + 4x - 15x + 6
And then add like terms 4x and 15x together.
2x^2 - 11x + 6
What is the probability of getting one or fewer people with a chronic heart condition in a sample of 22 if 25% of the population in this age bracket?
The question is incomplete. The complete question is :
The National Center for Health Statistics reports that 25% of all Americans between the ages of 65 and 74 have a chronic heart condition. Suppose you live in a state where the environment is conducive to good health and low stress and you believe the conditions in your state promote healthy hearts. To investigate this theory, you conduct a random telephone survey of 25 persons 65 to 74 years of age in your state.
Suppose only one person in your survey has a chronic heart condition. What is the probability of getting one or fewer people with a chronic heart condition in a sample of 25 if 25% of the population in this age bracket has this health problem?
Solution :
Chronic heart disease is a condition where a person's heart have trouble to pump blood to the body. It develops over a period of time.
In the context, we can see from the figures from National Center for Health Statistics that the expected number of persons of age 65 - 74 years having a chronic heart disease is about
25 % of 25 = 6.25
Now by Poisson's ratio, the probability of choosing the sample where only one person having heart disease is 1.4%
Which expression is equivalent to 6x2 – 19x – 55?
Answer:
(6x + 11)(x – 5)
Step-by-step explanation:
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I put D since I believe HL applies here but am not sure. Could anybody please help?
====================================================
Explanation:
Check out the diagram below.
On the left side shows ASA can be used to prove the triangles congruent. Note the color coding to see how the angles match up. Also note that the segment TR is between angles STR and SRT. The order is important because ASA is different from AAS.
Angle STR = Angle VTU because they are vertical angles
Angle SRT = Angle VUT since they are alternate interior angles. Note how SR is parallel to UV. If the lines weren't parallel, then the alternate interior angles would not be congruent.
We can use AAS because if we know two angles of a triangle, we can find the third angle. Despite the fact that something like RST looks like a right angle, we don't have enough info to say it is or not. The square angle marker is missing. So it could be 90 degrees, or it might be something like 89 degrees instead. We don't have enough info. So we cannot use HL.
AAA or AA is not a congruence theorem. It's a similarity theorem. So we cross this off the list.
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Answer:
y = 2x-2
Step-by-step explanation:
Answer:
C: y=2x-2
2x= slope
-2= y intercept
Step-by-step explanation:
it starts at -2 and the slope continues to go up 2 over right 1
3x^2+5x+2=0
Find what x is for both
Answer:
x = -2/3 and -1
Step-by-step explanation:
3x²+5x+2 = 0
3x²+3x+2x+2=0
3x(x+1) + 2(x+1) =0
(3x + 2) (x + 1) = 0
x = -2/3 and -1
Answer:
Exact form:
x = - 2/3, -1
Decimal Form:
x = -0.6repeated, -1
Step-by-step explanation:
Move all terms to the left side and set equal to zero. Then set each factor equal to zero.
Find the midpoint of the segment with the following endpoints.
(-4,-9) and (4, -1)
Answer:
[tex](0,-5)[/tex]
General Formulas and Concepts:
Pre-Alg
Order of Operations: BPEMDASAlg I
Midpoint Formula: [tex](\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex]Step-by-step explanation:
Step 1: Define
Point (-4, -9)
Point (4, -1)
Step 2: Find midpoint
Substitute: [tex](\frac{-4+4}{2},\frac{-9-1}{2})[/tex]Add/Subtract: [tex](\frac{0}{2},\frac{-10}{2})[/tex]Divide: [tex](0,-5)[/tex]In order to accumulate enough money for a down payment on a house, a couple deposits $589 per
month into an account paying 3% compounded monthly. If payments are made at the end of each period,
how much money will be in the account in 4 years?
Type the amount in the account: $
(Round to the nearest dollar.)
you have four years 1767 dollars in account
What is the equation of the line that passes through the points (-6,2) and (4,-3)
Answer:
The equation is: 9x-y = 56
Step-by-step explanation:
Given two point: (x,y) = (-6,2)
(x,y) = (4,-3)
Now, to find the slope of the line:
Slope = y1-y2/x1-x2 => 2-4/-6-(-3) = -1/9
Then, the equation of the line passing through a point:
=> y-y1 = m(x-x1)
=> y-2 = -1/9(x-6)
=> 1(y-2) = -9(x-6)
=> y-2 = -9x+54
=> 9x-y = 56
I need to know the explanation will mark Brainliest
Answer:
the value of x is 23
Step-by-step explanation:
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Solve the equation.
3/4x+3-2x=-1/4+1/2x+5
Answer:
x=-1
Isolate the variable by dividing each side by factors that dont
contain the variable
Simplify the expression.
6(x+4)+1 =
Answer:
6x+25
Step-by-step explanation:
6(x+4)+1 =
Distribute
6x+24+1
Combine like terms
6x+25
How are fractions, decimals, and percents related?
Answer:
yes bc they all have sum to do wit eachother
Step-by-step explanation:
3.4+(-7)-(-0.2)
PLZ HELP
Answer:
-3.8
Step-by-step explanation:
I used my calculator.
Answer:
-3.8
Step-by-step explanation:
Please help me solve this i need help
Answer:
21
Step-by-step explanation:
gets paid 15 per hour what is the minumim number of hours that joseph must work per week to make $450 per moth? (1moth=4weeks)
Answer:
Minimum of 7 1/2 hours ( 7 hours, and 30 minutes )
Step-by-step explanation:
Rate = money / time
time = money / rate
_____________
1 month = 4 weeks
1 week = 7 days
1 day = 24 hours
1 hour = 60 minutes
_____________
$15 / 1 hour = 1 day / 24 hours = 1 week / 7 days = 1 month / 4 weeks = $450 / 1 month.
$15 / 1 hour / 1 week = $450 / 1 month
$15 / 1 hour / 1 week = $450 / 4 weeks
$15 / 1 hour / 1 week = $112.5 / 1 week
$15 / 1 hour = $112.5
112.5 / 15 = 7.5 hours.
Determine if the following vectors are orthogonal, parallel, or neither.
<2,5> and <-4, 10 >
Answer:
the are parallel to eachother
Please help needs to be rounded to the nearest hundredth
Answer: 0
Step-by-step explanation:
11 + 11= 22
22 is rounded to the nearest hundredth, which is not 100, so its 0
Write a four digit whole number that is divisible by 2. Use a divisibility rule and explain how you know that your number is divisible by 2.
During the winter months, heating bills can be expensive. A contractor claims that installing a new brand of insulation will considerably lower your heating bill (which was $205 last month). After conducting the test (assuming the data were provided). you find that the results are significant at the 5% level. You may also conclude: __________.a. the test would also be significant at the 10% level. b. the test would also be significant at the 1% level. c. both of the above. d. none of the above.
Answer:
The correct option is a
Step-by-step explanation:
Generally the null hypothesis is rejected (that the result is significant ) when the p-value is less that the the level of significance
Now from the question when the the level of significance was 5% the p-value was less than the level of significance so also when the level of significance is 10% the p-value will be less than the level of significance hence null hypothesis will also be rejected at this level(that is the result will also be significant at the level of significance )
Simplify.
7 (x-1) -2 (x-1)
Answer: 5x-5
Step-by-step explanation:
7 (x-1) -2 (x-1)
7x-7-2x+2
Combine like terms:
7x-2x=5x
-7+2=-5
Answer simplified is 5x-5.
Richmond High School purchased 90 graphing calculators for $110
each. The school received a manufacturer's rebate of $10 per
calculator. After the rebate, what was the total cost of the
calculators?
Answer:
$9000
Step-by-step explanation:
110 x 90 = 9900
90 x 10 = 900
9900 - 900 = 9000
need help please full question in image
0.5 (x4 - 3) + 12
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0.5x^4+10.5 or 12.5 simplified is correct answer. Remove any grouping symbol such as brackets and parentheses by multiplying factors.
Use the exponent rule to remove grouping if the terms are containing exponents.
Combine the like terms by addition or subtraction.
Combine the constants.
Please help if you can. I will give you a brainliest !!
Answer:
its blurry I cant even see it
Step-by-step explanation:
1) Find a unit rate for the following ratio. 135 words: 3 minutes
2 points
45 words: 1 minute
50 words: 1 minute
40 words: 1 minute
100 words: 2 minutes
(34+ (9 x 2)) divide2 = _
Answer:
26
Step-by-step explanation:
9 x 2= 18
18+34= 52
52/2= 26