Answers
Answer:
picture not clear what is the length
Related Questions
A bacteria culture grows with a constant relative growth rate. After 2 hours there are 400 bacteria and after 8 hours the count is 50,000.
(a) Find the initial population. P(0) = 80 )ãbacteria
(b) Find an expression for the population after t hours. r(t) = 180( 125(6 Plt) =180(125(2))-
(c) Find the number of cells after 7 hours. (Round your answer to the nearest integer.) P(7)=72.358- bacteria
(d) Find the rate of growth after 7 hours. (Round your answer to the nearest integer.) P(7) 2x bacteria/hour
(e) When will the population reach 200,000? (Round your answer to one decimal place.) hours
Answers
Answer:
a) P(0) = 80
b) [tex]P(t) = 80(2.2361)^t[/tex]
c) 22,363 cells.
d) The rate of growth after 7 hours is of 18,000 bacteria per hour.
e) 9.7 hours.
Step-by-step explanation:
A bacteria culture grows with a constant relative growth rate.
This means that the population is given by:
[tex]P(t) = P(0)(1+r)^t[/tex]
In which P(0) is the initial population and r is the growth rate, as a decimal.
After 2 hours there are 400 bacteria and after 8 hours the count is 50,000.
This means that in 6 hours, the population went from 400 bacteria to 50,000 bacteria. We use this to find r. So
[tex]50000 = 400(1+r)^6[/tex]
[tex](1+r)^6 = \frac{50000}{400}[/tex]
[tex](1+r)^6 = 125[/tex]
[tex]\sqrt[6]{(1+r)^6} = \sqrt[6]{125}[/tex]
[tex]1 + r = 125^{\frac{1}{6}}[/tex]
[tex]1 + r = 2.2361[/tex]
So
[tex]P(t) = P(0)(2.2361)^t[/tex]
(a) Find the initial population. P(0)
We have that P(2) = 400. We use this to find P(0). So
[tex]P(t) = P(0)(2.2361)^t[/tex]
[tex]400 = P(0)(2.2361)^2[/tex]
[tex]P(0) = \frac{400}{(2.2361)^2}[/tex]
[tex]P(0) = 80[/tex]
So
[tex]P(t) = 80(2.2361)^t[/tex]
(b) Find an expression for the population after t hours.
[tex]P(t) = 80(2.2361)^t[/tex]
(c) Find the number of cells after 7 hours.
This is P(7). So
[tex]P(7) = 80(2.2361)^7 = 22363[/tex]
22,363 cells.
(d) Find the rate of growth after 7 hours.
We have to find the derivative when t = 7. So
[tex]P(t) = 80(2.2361)^t[/tex]
[tex]P^{\prime}(t) = 80\ln{2.2361}(2.2361)^t[/tex]
[tex]P^{\prime}(7) = 80\ln{2.2361}(2.2361)^7 = 18000[/tex]
The rate of growth after 7 hours is of 18,000 bacteria per hour.
(e) When will the population reach 200,000?
This is t for which [tex]P(t) = 200000[/tex]. So
[tex]P(t) = 80(2.2361)^t[/tex]
[tex]200000 = 80(2.2361)^t[/tex]
[tex](2.2361)^t = \frac{200000}{80}[/tex]
[tex](2.2361)^t = 2500[/tex]
[tex]\log{(2.2361)^t} = \log{2500}[/tex]
[tex]t\log{2.2361} = \log{2500}[/tex]
[tex]t = \frac{\log{2500}}{\log{2.2361}}[/tex]
[tex]t = 9.7[/tex]
So 9.7 hours.
F(x) = 3x+5 G(x)= 4x^2-2 H(x) = x^2-3x+1 Find f(x) +g(x) -h(x)
Answers
Answer:
Step-by-step explanation:
f(x) + g(x) = 3x + 5 + 4x^2 - 2
f(x) + g(x) = 4x^2 + 3x + 3
f(x) + g(x) - h(x) = 4x^2 + 3x + 3 - (x^2 - 3x + 1) Remove the brackets.
f(x) + g(x) - h(x) = 3x^2 +3x + 3 - x^2 + 3x - 1 Collect like terms
f(x)+g(x) - h(x) = 2x^2 + 6x + 2
Answer:
f(x)=3x^2+6x+2
Step-by-step explanation:
A well-known brokerage firm executive claimed that 60% of investors are currently confident of meeting their investment goals. An XYZ Investor Optimism Survey, conducted over a two week period, found that in a sample of 100 people, 69% of them said they are confident of meeting their goals. Test the claim that the proportion of people who are confident is larger than 60% at the 0.01 significance level.
The null and alternative hypothesis would be:________
a. H0:μ=0.6H0:μ=0.6
H1:μ≠0.6H1:μ≠0.6
b. H0:μ=0.6H0:μ=0.6
H1:μ<0.6H1:μ<0.6
c. H0:μ=0.6H0:μ=0.6
H1:μ>0.6H1:μ>0.6
d. H0:p=0.6H0:p=0.6
H1:p≠0.6H1:p≠0.6
e. H0:p=0.6H0:p=0.6
H1:p>0.6H1:p>0.6
f. H0:p=0.6H0:p=0.6
H1:p<0.6H1:p<0.6
The test is:________
a. two-tailed
b. left-tailed
c. right-tailed
The test statistic is:_______ (to 3 decimals)
The p-value is:_______ (to 4 decimals)
Based on this we:________
a. Fail to reject the null hypothesis
b. Reject the null hypothesis
Answers
We are testing a hypothesis. So, first we identify the null and the alternative hypothesis, then we find the test statistic, and with the test statistic, the p-value is found.
Null and alternative hypothesis:
Claim the the proportion is of 60%, thus, the null hypothesis is:
[tex]H_0: p = 0.6[/tex]
Test if the proportion is greater than 60%, thus, the alternative hypothesis is:
[tex]H_1: p > 0.6[/tex]
And the answer to the first question is given by option c.
Classification:
We are testing if the proportion is greater than a value, so it is a right-tailed test.
Test statistic:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.
0.6 is tested at the null hypothesis:
This means that [tex]\mu = 0.6, \sigma = \sqrt{0.4*0.6}[/tex]
Survey, conducted over a two week period, found that in a sample of 100 people, 69% of them said they are confident of meeting their goals.
This means that [tex]n = 100, X = 0.69[/tex]
Value of the test statistic:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex]z = \frac{0.69 - 0.6}{\frac{\sqrt{0.4*0.6}}{\sqrt{100}}}[/tex]
[tex]z = 1.837[/tex]
The test statistic is z = 1.837.
p-value:
The p-value of the test is the probability of finding a sample proportion above 0.69, which is 1 subtracted by the p-value of z = 1.837.
Looking at the z-table, z = 1.837 has a p-value of 0.9669.
1 - 0.9669 = 0.0331
The p-value is 0.0331.
Decision:
The p-value of the test is 0.0331 > 0.01, and thus:
a. Fail to reject the null hypothesis
For another example of a problem of a test of hypothesis, you can take a look at:
https://brainly.com/question/24166849
Identify the pair numbers
Answers
Answer:
D. 212 degrees Fahrenheit and 100 degrees Celsius.
Step-by-step explanation:
The boiling point of water in Celsius is 100.
The way to calculate Celsius to Fahrenheit:
F = (C × 9/5) + 32
So we plug in 100 for C.
F = (100 × 9/5) + 32
F = 180 + 32
F = 212
Therefore, the numbered pair is 212 degrees F and 100 degrees C.
complete the square to form a true equation;
x^2-3/4x+__ = (x-__)^2
Answers
172273-3-$=$==8399993939384888884-%"%/=%=%8%
Step-by-step explanation:
(x^2-3/4x+y^2)=(x-y)2
(x-3/4*1/2)2
(x-3/8)(x-3/8)
(x^2-3x/8-3x/8+9/64)
(x^2-6x/8+9/64)
(x-3/8)2
Consider the equation below.
-2(53 + 8) = 14 + 60
The equation was solved using the following steps.
-10.3 – 16 = 14 + 6.r
Step 1:
Step 2:
Step 3:
-165 - 16 = 14
-16.r = 30
Step 4:
30
=
-16
Step 5:
=
Complete the statements below with the process used to achieve steps 1-4.
-2 to 5x and 8.
6x
Step 1:
Step 2:
Step 3:
Step 4:
16.
-16.
Answers
Answer:
See explanation
Step-by-step explanation:
Given
[tex]-2(5x+8)=14+6x[/tex]
Required
Complete the steps
[tex]-2(5x+8)=14+6x[/tex]
Multiply 5x and 8 by -2
[tex]-10x - 16 = 14 + 6x[/tex]
Subtract by 6x
[tex]-10x - 6x- 16 = 14 + 6x - 6x[/tex]
[tex]-16x- 16 = 14[/tex]
Add 16
[tex]-16x- 16 + 16= 14 + 16[/tex]
[tex]-16x= 30[/tex]
Divide by -16
[tex]x= \frac{30}{-16}[/tex]
[tex]x= -\frac{15}{8}[/tex]
See attachment
Cho hai tập hợp A={1;2;3;4},B={2;4;6;8} . Tập hợp nào sau đây bằng tập hợp A ∩B ?
Answers
Answer:
A∩B ={2;4}
Step-by-step explanation:
Chúc bạn học tốt
Help? Thanks!!!!!!!! If possible show work please!
Answers
Answer:
[tex]B =102[/tex]
[tex]Y = 32[/tex]
Step-by-step explanation:
Solving (47):
To solve for B, we have:
[tex]B + 50 + 28 = 180[/tex] --- sum of angles in a triangle
This gives
[tex]B + 78 = 180[/tex]
Collect like terms
[tex]B =- 78 + 180[/tex]
[tex]B =102[/tex]
Solving (48):
To solve for Y, we have:
[tex]X + Y+ Z = 180[/tex] --- sum of angles in a triangle
This gives
[tex]Y = 180 - X - Z[/tex]
Where
[tex]W+ X=180[/tex] -- angle on a straight line
Solve for X
[tex]X=180 -W[/tex]
[tex]X=180 -100 = 80[/tex]
So, we have:
[tex]Y = 180 - X - Z[/tex]
[tex]Y = 180 - 80 - 68[/tex]
[tex]Y = 32[/tex]
Keith is trying to figure out the area of his pool section in his backyard he knows that his pool is 20 feet long and 9 feet wide he also knows the sidewalk is 3 feet wide all around the floor what is the total area of the pool section of Keith’s backyard?
Answers
Answer:
The total area of the pool section of Keith's backyard is 390 square feet.
Step-by-step explanation:
Since Keith is trying to figure out the area of his pool section in his backyard, and he knows that his pool is 20 feet long and 9 feet wide, and he also knows the sidewalk is 3 feet wide all around the floor, to determine what is the total area of the pool section of Keith's backyard, the following calculation must be performed:
(20 + 3 + 3) x (9 + 3 + 3) = X
26 x 15 = X
390 = X
Therefore, the total area of the pool section of Keith's backyard is 390 square feet.
please please help its timed -H.M
Answers
Answer:
1
General Formulas and Concepts:
Algebra I
Functions
Function NotationStep-by-step explanation:
Step 1: Define
f(-2)
Step 2: Evaluate
f(-2) is x = -2 for function f(x).
According to the table, when x = -2, f(x) = 1.
∴ f(-2) = 1
What is 3.24 ( 4 repeating) as a fraction?
Answers
Answer:
81/25
Step-by-step explanation:
change 3.24 into faction
324 over 100 because there are two decimal points .
simplfy into the smallest fraction
the answer is 81 over 25
HELPinjjgk go hhjkkggb jjj
Answers
Answer:
what i dont understand
Step-by-step explanation:
Sample information: 24 out of 1000 people who were surveyed had type 2 diabetes. Use the above sample information and construct two confidence intervals (one with confidence level of 90% and the other one with confidence level of 99%) to estimate the proportion of people who have type 2 diabetes. What is the relationship between the confidence level and the size of the confidence interval? Is this significant? Why is it important to understand this concept?
Answers
Answer:
it is important because the number of people who are infected by the disease is rising
What is the y-intercept of the line that has a slope of `-4` and passes through the point (4, -6)`?
Answers
Answer:
(0, 10)
Step-by-step explanation:
Answer:
y = -4x + 10
Step-by-step explanation:
y = -4x + b
-6 = -4(4) + b
-6 = -16 + b
10 = b
A tank filled with water begins draining. The number of minutes t since the water began draining from the tank is a function of the number of gallons of water in the tank, v. We will call this function f so that f(t) = v.
Required:
a. Using function notation, represent the of gallons of water in me tank 4 minutes after the water darning from the Ink.
b. Suppose that f(4) = 7, what does this mean in the context of the problem?
Answers
Answer:
[tex](a)\ f(4) = v[/tex]
(b) There are 7 gallons left in the tank after 4 minuted
Step-by-step explanation:
Given
[tex]f(t) = v[/tex]
[tex]t \to[/tex] time since water began draining
[tex]v \to[/tex] gallons in the tank
Solving (a): Notation for gallons remaining at 4 minutes
This means that [tex]t=4[/tex]
[tex]f(t) = v[/tex] becomes
[tex]f(4) = v[/tex]
Solving (b): Interpret f(4) = 7
We have:
[tex]f(t) = v[/tex]
[tex]t \to[/tex] time since water began draining
[tex]v \to[/tex] gallons in the tank
This means that:
[tex]t =4[/tex]
[tex]v =7[/tex]
It can be interpreted as:
There are 7 gallons left in the tank after 4 minuted
In remodeling a house an architect finds that by adding the same amount to each dimension of a 15ft by 19ft rectangular room, the area would be increased by 98 ft^2. How
much must be added to each dimension?
Let x be the amount that is added to each dimension. After writing an equation in standard form with a > 0, a= ? b= ? and c= ?
(Simplify your answers.)
Answers
Answer:
Step-by-step explanation:
new length=15+x
width=19+x
then area=(15+x)×(19+x)=285+15x+19x+x²=x²+34x+285 ft²
original area=15×19=285 ft²
then 285+98=x²+34x+285
or
x²+34x-98=0
x²+34x+17²=98+17²
(x+17)²=98+289=387
x+17=√387=3√43
x=3√43-17 ft
Find the value of z.
54°
X
2049
(32+1)°
A. 25.25
OB. 129
Answers
Answer:
Step-by-step explanation:
(z)° + (3z + 1)° = 360° - ( 54° + 204° )
z + 3z + 1 = 360 - 258
4z = 101
z = 25.25
Rose walks 2 2/3 km in three-fifths of an hour. If her speed remains unchanged, how many kilometres can she walk in one and three quarters of an hour? Express your answer as a mixed number in lowest terms
Answers
Answer:
Distance = 7 7/9 Km
Step-by-step explanation:
Given the following data;
Distance = 2⅔ = 8/3 Km
Time = ⅗ hour
First of all, we would find her speed;
Speed = distance/time
Speed = (8/3)/(3/5)
Speed = 8/3 * 5/3
Speed = 40/9 km/h
Next, we would find the distance covered when time = 1¾ hours
Distance = speed * time
Distance = 40/9 * 1¾
Distance = 40/9 * 7/4
Distance = 10/9 * 7
Distance = 70/9
Distance = 7 7/9 Km
What is the more formal name used for describing the corporate-finance decision concerning which projects to invest in?
Answers
Answer:
i hope it will help you
Step-by-step explanation:
Working capital management is how companies are able to manage finances and continue operations.
Matt invests £1800 for 2 years at a simple interest rate of 10%.
How much money will he get back in interest?
Answers
Answer:
Step-by-step explanation:
P = 1800
R = 10%
T = 2 years
I = PRT
= 1800 * 10/100 * 2
= 1800 * 0.1 * 2
I = £360
The amount that will be gotten back as interest will be £360
Principal = £1800
Rate = 10%
Time = 2 years
Simple Interest will be calculated as:
= (P × R × T) / 100
= (£1800 × 10 × 2)/100
= £36000/100
= £360
Therefore, the interest is £360.
Read related link on:
https://brainly.com/question/24355322
define ascending and descending order by your and give one example
Answers
Answer:
ascending order} an order of numbers from least to greatest like 1 2 3 4
descending order} an order of numbers from greatest to least like 4 3 2 1
You are playing a game by drawing a card from a standard deck and replacing it. If the card is a face card, you win $30. If it is not a face card, you pay $2. There are 12 face cards in a deck of 52 cards. What is the expected value of playing the game
Answers
92 cardsㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤ
ㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤ
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ㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤ
ㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤ
Translations _______ side lengths of the figure.
A. change
B. alter
C. preserve
D. all of these
Answers
Answer:
C. preserve
Step-by-step explanation:
When you translate something in geometry, you're simply moving it around. You don't distort it in any way. If you translate a segment, it remains a segment, and its length doesn't change. Similarly, if you translate an angle, the measure of the angle doesn't change.
Using the diagram, which of the following choices represent alternate exterior angles
Answers
Answer:
A
Step-by-step explanation:
The answer is choice A.
The two angles are alternate exterior angles of lines LG and KH cut by transversal JF.
Convert 2933 in base 10 to base 2
Answers
Answer:
1011011101012
Step-by-step explanation:
Converting 2933 to base 10.
2*103=2000
9*102=900
3*101=30
3*100=3
Adding all to get Ans=293310
Step2 converting 293310 to 2
The equation calculation formula for 293310 number to 2 is like this below.
2|2933
2|1466|1
2|733|0
2|366|1
2|183|0
2|91|1
2|45|1
2|22|1
2|11|0
2|5|1
2|2|1
2|1|0
2|1|1
Ans:1011011101012
What is the image of (-4, -12) after a dilation by a scale factor of centered at the 1/4 origin?
Answers
9514 1404 393
Answer:
(-1, -3)
Step-by-step explanation:
Each coordinate is multiplied by the dilation factor when dilation is centered at the origin.
(1/4)(-4, -12) = (-1, -3) . . . . the image of the given point
44y + 321x = 0 biết x=30000
Answers
Answer:
y= -240750/11
Step-by-step explanation:
44y + 321. 30000 = 0
44y = - 963000
y= -240750/11
Point C partitions AB into two parts so that the ratio of the length of AC to the length of CB is 1:5. What are the coordinates of point ?
Select and drag a number to each empty box to correctly complete the coordinates of point
The coordinates of point C are?
Answers
9514 1404 393
Answer:
C(-1, -4)
Step-by-step explanation:
We want ...
AC/CB = 1/5
5(C-A) = B-C . . . . multiply by 5CB
6C = B +5A . . . . . add 5A-C
C = (B +5A)/6 . . . divide by 6
C = ((4, 6) +5(-2,-6))/6 = (4-10,6-30)/6 = (-6, -24)/6
C = (-1, -4)
Bill's father is three times Bill's age. Three years ago, Bill's father was four times Bill's age.
By forming two equations, find Bill's age now.
Answers
Answer:
12 and 36
Step-by-step explanation:
Call the age of both Bill and his father is a and b, respectively
we have:
b=3a
b-3=4(a-3) ->b=4a-12 -> 3a=4a-12 ->a =12 -> b=36
please help me with geometry
Answers
Answer:
x = 5Step-by-step explanation:
triangol BCD = triangle BDA
so
3x - 1 = 34 - 2x
5x = 35
x = 35 : 5
x = 5Answer:
x = 7
Step-by-step explanation:
BD is an angle bisector , so
∠ ABD = ∠ DBC , that is
3x - 1 = 34 - 2x ( add 2x to both sides )
5x - 1 = 34 ( add 1 to both sides )
5x = 35 ( divide both sides by 5 )
x = 7
