Answer:
linear expressions is the answer
Suppose that the number of bacteria in a certain population increases according to a continuous exponential growth model. A sample of 1500 bacteria selected
from this population reached the size of 1805 bacteria in four hours. Find the hourly growth rate parameter.
Note: This is a continuous exponential growth model.
Write your answer as a percentage. Do not round any intermediate computations, and round your percentage to the nearest hundredth.
00
E
Answer:
The hourly growth rate parameter is of 4.74%
Step-by-step explanation:
Continuous growth model:
The continuous growth model for a population after t hours is given by:
[tex]P(t) = P(0)(1+r)^t[/tex]
In which P(0) is the initial population and r is the hourly growth rate parameter, as a decimal.
A sample of 1500 bacteria selected from this population reached the size of 1805 bacteria in four hours.
This means that [tex]P(0) = 1500, P(t) = 1805, t = 4[/tex]
Find the hourly growth rate parameter.
[tex]P(t) = P(0)(1+r)^t[/tex]
[tex]1805 = 1500(1+r)^4[/tex]
[tex](1+r)^4 = \frac{1805}{1500}[/tex]
[tex]\sqrt[4]{(1+r)^4} = \sqrt[4]{\frac{1805}{1500}}[/tex]
[tex]1 + r = (\frac{1805}{1500})^{\frac{1}{4}}[/tex]
[tex]1 + r = 1.0474[/tex]
[tex]r = 0.0474[/tex]
0.0474*100% = 4.74%
The hourly growth rate parameter is of 4.74%
What are the coordinates of point A" if triangle
ABC is reflected over the y-axis and then
translated by the rule (22, y) + (x – 5, y – 5) ?
A. (-2,-2)
B. (2,-2)
C. (-2,2)
D. (2,2)
Answer:
Reflected OVER Y makes A
A (-7,3) -> (7,3)
Translated makes
A (7,3) -> (7-5, 3-5) = (2,-2)
B)
Step-by-step explanation:
Chris drinks 3 pints of milk a day. How much is this in cups?
Answer:
He drinks 6 cups a day.
Step-by-step explanation:
1 pint - 2 cups
3 x 2 = 6
Hey, so I really put a lot of time and effort in my answers, so if you can, could you please give me a "Brainliest" because I really want to rank up! Thank you so much for the points, and I hope the answer helped you!!! :)
Answer:
6 cups.
Step-by-step Explanation:
1 pint is equal to 2 cups.
Therefore, 3 pints of milk is equal to 2 cups of milk.
What single percentage change is equivalent to a 11% decrease followed by a 13% decrease?
Answer:
77.43% decrease
Step-by-step explanation:
A decrease of 11% = (100 - 11)% = 89% = [tex]\frac{89}{100}[/tex] = 0.89
A decrease of 13% = (100 - 13)% = 87% = [tex]\frac{87}{100}[/tex] = 0.87
A 11% decrease followed by a 13% decrease has an overall change of
0.89 × 0.87 = 0.7743 × 100% = 77.43%
If P = (3,2), find the image
of P under the following rotation.
270° counterclockwise about the origin
([?], [])
Given:
The point P = (3,2) is rotated 270° counterclockwise about the origin.
To find:
The image of the given point after rotation.
Solution:
If a point rotated 270° counterclockwise about the origin, then the rule of rotation is:
[tex](x,y)\to (y,-x)[/tex]
Using this rule, we get
[tex]P(3,2)\to P'(2,-3)[/tex]
Therefore, the image of given point P = (3,2) after the rotation of 270° counterclockwise about the origin, is P'(2,-3).
Please help me it would mean a lot !!!!!!!!!!!!!!
Answer:
Step-by-step explanation:
Given
f(x) = 4x + 7
so
f(a + h) = 4(a + h) + h
= 4a + 4h +h
= 4a + 5h
f(a) = 4a + 7
now by the question
[tex]\frac{f(a+h) - f(a)}{h}\\=\frac{4a + 5h - 4a + 7}{h}\\=\frac{ 5h + 7}{h} \\= \frac{5h}{h} + \frac{7}{h} \\= 5 +\frac{7}{h}[/tex]
hope it helps :)
In the triangle, ABC, the measure of ∠A is 30° and the measure of ∠C is 90°. What is the measure of ∠B?
Answer:
60°
Step-by-step explanation:
angle A +angle B +angle C = 180
30° +B+90°= 180
120°+B=180°
B=180°-120°
B=60°
A mirror has a parabolic surface defined by the equation y =StartFraction 1 Over 24 EndFraction x2 with the vertex (0, 0) at the center of the mirror. When the width of the mirror is 8 inches, what is the depth, y, of the mirror?
1/36 in.
1/6 in.
2/3 in.
2 2/3 in.
ITS C: 2/3 in.
Answer:
Step-by-step explanation:
Edge 2022
Answer:
c
Step-by-step explanation:
2/3 in
The prices (in dollars) for a particular model of digital camera with 6.0 megapixels and an optical 3X zoom lens are shown below for 10 online retailers. Estimate the true mean price for this particular model with 93% confidence. Assume the variable is normally distributed. Use a graphing calculator and round the answers to at least one decimal place.
225 236 217 202 231 185 193 185 245 217
Solution :
Let [tex]$x_i$[/tex] represents the prices for the digital camera.
[tex]$x_i$[/tex] [tex]$x_i^2$[/tex]
225 50625
236 55696
217 47089
202 40804
231 53361
185 35225
193 37249
185 34225
217 47089
[tex]$\sum x_i = 2136$[/tex] [tex]$\sum x_i^2 = 460388$[/tex]
Mean, [tex]$(\overline X) = \frac{\sum x_i}{n}$[/tex]
[tex]$=\frac{2136}{10}$[/tex]
= 213.6
Variance, [tex]$\sigma^2 = \frac{\sum x_i^2}{n}-(\overline X)^2$[/tex]
[tex]$ = \frac{460388}{10}-(213.6)^2$[/tex]
= 46038.8 - 45624.96
= 413.84
Therefore, standard deviation,
[tex]$\sigma = \sqrt{Var}$[/tex]
[tex]$=\sqrt{413.84}$[/tex]
= 20.343
Now to find the 93% confidence interval, the formula us
[tex]$(\overline X)\pm (z) \times \frac{\sigma}{\sqrt{n}}$[/tex]
For 93%, the value of z is 1.81
∴ Confidence interval = [tex]$(\overline X)\pm (z) \times \frac{\sigma}{\sqrt{n}}$[/tex]
C.I. = [tex]$213.6\pm 1.81 \times \frac{20.343}{\sqrt{10}}$[/tex]
[tex]$=213.6 \pm 11.6438$[/tex]
Therefore, lower bound = 213.6 - 11.6438
= 201.9562
Upper bound = 213.6 + 11.6438
= 225.2438
∴ [tex]$201.9562 < \mu < 225.2438$[/tex]
or [tex]$202< \mu < 225.2$[/tex]
Morty spent $54 on tulips and roses and bought a total of 14 flowers. If tulips cost $5 and roses $3
Let t = number of tulips bought
Let r = number of roses bought
a) Write the system.
b) How many of each flower did Morty buy? (Solve the system)
Answer:
a) Let's define the variables:
t = number of tulips bought
r = number of roses bought
We know that each tulip costs $5, and each rose costs $3.
Then the total cost will be:
$5*t + $3*r
We know that Morty spent a total of $54, then we have the equation:
$5*t + $3*r = $54
We also know that he bought a total of 14 flowers, then:
r + t = 14
Then the system of equations is:
$5*t + $3*r = $54
r + t = 14
b) To solve the system, first, we need to isolate one of the variables in one of the equations. I will isolate r in the second one:
r = 14 - t
Now we can replace this into the other equation:
$5*t + $3*r = $54
$5*t + $3*(14 - t) = $54
Now we can solve this for t.
$5*t + $3*14 - $3*t = $54
$2*t + $42 = $54
$2*t = $54 - $42 = $12
t = $12/$2 = 6
t = 6
He bought 6 tulips.
Now we can use the equation r = 14 - t
r = 14 - 6 = 8
r = 8
He bought 8 roses.
How could you design an experiment to support the claim that people who watch television for at least 2 hours every night have lower energy in the evening than people who do not watch as much television Include any factors or steps that should be considered .
Step-by-step explanation:
Several ways in which television can disrupt or alter sleep patterns:
The blue light emitted by screens can interfere with your brain’s production of melatonin at night, making it harder for you to fall asleep. Exciting or disturbing content can switch your mind into high gear, making it harder to wind down, and harder to sleep deeply. The timing of television viewing may push back bedtime and contribute to sleep disturbances -- including sleep-related anxieties and difficulty falling asleep. Having a television in the bedroom can undermine your ability to sleep well. Extended viewing may lead to sleep loss, poor quality sleep, and daytime tiredness.People who don't watch Television won't have these problems.
Carefree offers two type of care packages. The food packages sell for 20$ and the game packages sell for 32$. In one day Carefree sold 25 Care packeges. the receipt for those packages totaled 602$ How many of each type of package were sold
Answer:
Number of game package = 16.5
Number of food package = 8.5
Step-by-step explanation:
LET :
Food package = a
Game package = b
a + b = 25 - - - (1)
20a + 32b = 602 - - - (2)
a = 25 - b
Put a = 25 - b into (2)
20(25 - b) + 32b = 602
500 - 20b + 32b = 602
12b = 102
b = 102 / 12
b = 8.5
a = 25 - b
a = 25 - 8.5
a = 16.5
Number of game package = 16.5
Number of food package = 8.5
10 POINTS FOR CORRECT ANSWER PLEASE HELP ME
look at pic 10 pts will mark brainilest
Answer:
A- point A
Step-by-step explanation:
Absolute value doesnt care about the sign so a negative is a positive.
PLease Brainliest
I need help with this question it would be nice if you could help
Answer:
v=433.33
Step-by-step explanation:
Determine the solution to this equation y= 3X + 1. 3y- 5x =11
Answer: y = 3,x =7
Step-by-step explanation:
The volume of a sphere is 5000x m . What is the surface area of the sphere to the nearest
square meter?
Answer:
Step-by-step explanation:600
round 36 to the nearest hundredth. for the brainiest
36 to the nearest hundredth is just 36
To round 36 to the nearest hundredth consider the thousandths' value of 36, which is 0 and less than 5. Therefore, the hundredths' value of 36 remains 36
Answer:
Round 36 to the nearest tenth, Leaving only one number after the decimal point, Then you have come to the right post.
Step-by-step explanation:
Round off to nearest 10. Rounding every place-value of number. Round off a number to the nearest tens round off to the nearest multiple of ten.
A large number may be rounded off to the nearest 10.
Hope It Helps!
find the angle of elevation of a kite on a 50m
string flying 40m vertically above the ground.
The angle of elevation of a kite is 53.13°
What is angle of elevation?"It is the angle formed by the line of sight and the horizontal plane for an object above the horizontal surface."
What is sine angle?"For a right triangle, the sine of acute angle [tex]\theta[/tex] is,
[tex]sin(\theta)=\frac{opposite ~side}{hypotenuse}[/tex]"
For given question,
Consider the following diagram for given question.
The length of the string (AC) = 50m
The kite is flying 40m vertically above the ground.
⇒AB = 40m
We need to find the angle of elevation [tex]\theta[/tex]
Consider the sine of angle [tex]\theta[/tex]
[tex]\Rightarrow sin(\theta)=\frac{AB}{AC} \\\\\Rightarrow sin(\theta)=\frac{40}{50}\\\\\Rightarrow sin(\theta)=0.8\\\\\Rightarrow \theta=sin^{-1}(0.8)\\\\\Rightarrow \theta=53.13^{\circ}[/tex]
Therefore, the angle of elevation of a kite is 53.13°
Learn more about the angle of elevation here:
https://brainly.com/question/21137209
#SPJ3
how should you write the proportion 9:36=10:40 using words
Answer:
Nine to thirty-six equals ten to forty.
Step-by-step explanation:
The word ‘to’ can be substituted in for the colon (:). This is to denote the mathematical concept of ratios.
The word ‘equals’ can be used in place of the equal sign (=).
PLEASE HELP I WILL MARK
BRIANLIST Caitlin has $24 to spend. She spent $8.50, including tax, to buy a book. She needs to save $6.25, but she wants to buy some candy. If each piece of candy costs $0.25 including tax, what inequality would show the maximum number of pieces Caitlin can buy? Let x represent the cost of one piece of candy.
Solve your inequality by showing your work and steps.
Answer: 37 pieces of candy
Step-by-step explanation:
24-8.50 is 15.50 she wants to save 6.25, so, 15.50-6.25 is 9.25. 9.25 divided by the cost of each candy (0.25) is 37
Convert 38,338,856 seconds to days. Round to 1 decimal.
Answer:
443.736759 day
Step-by-step explanation:
To convert a seconds to days, divide the time by the conversion ratio.
So.....
One day is equal to 86,400 seconds, you can use this formula to convert:
days = seconds ÷ 86,400
The time in days is equal to the seconds divided by 86,400.
Example: Convert 50,000 seconds to days (use the formula above)
50,000 sec = (50,000 ÷ 86,400) = 0.578704 day
HELP MEEE
Colin asked some of his classmates how many minutes they spent working on their math homework last night. He created a dot plot to show his results.
25
5 10 5 20
Amount of Time
(minutes)
What is the range of the data Colin collected?
05
0 20
o 25
11
Answer:
pretty sure its twenty
Step-by-step explanation:
you have to subtract the maximum from the minimum values
so 25-5=20
have a nice day!!!!!!!!
Evaluate cos(60 degrees). Write your answer simplified, rationalized form.
Answer:
1 / 2
Step-by-step explanation:
Cos 60°
= 1 / 2
1 / 2 is the answe.
Add or Subtract to Simplify:
(4x - 2x3) + (5x3 - 4x + 5)
I need the answer ?
Answer: =3x^3+5
Step-by-step explanation: Hope this help :D
Solve the inequality: x^6 - 64 > 0
Please help ASAP!!! Thank you!!!
Step-by-step explanation:
Step-by-step explanation: Here's your solution
Step-by-step explanation: Here's your solution=> x^2 - 64 > 0
Step-by-step explanation: Here's your solution=> x^2 - 64 > 0 => x^2 > 64
Step-by-step explanation: Here's your solution=> x^2 - 64 > 0 => x^2 > 64 => x = 6√64
=. x = 2
hope it helps
6.) Anne takes out an $8,000 loan to buy a car. She chooses the 8 year loan and will pay $120.55 per month. What is the total repayment on the loan?
A.$11,572.80
B.$9.644.00
C.$6,272.00
D. $23,145.60
I NEED HELP FAST THANK YOU
Answer:
D
Step-by-step explanation:
Find the area of EFGH
Answer:
42
Step-by-step explanation:
(8+13)*4/2 = 42
Answer:
42 in
Step-by-step explanation:
What is 2x10-50=x and I’m just typing this to get to 20 words or whatever
Step-by-step explanation:
sorry I don't know the answer I want some points so because I do this I really really sorry. and thanks for point
BRAINLIST!!!
A construction crew built 7 1/2 miles of road in 3 1/8 days.
What is the unit rate in miles per day?
Write your answer as a fraction or a mixed number in simplest form.
Answer:
If you think numbers with fractions are annoying, consider transforming the number into fractions!
Step-by-step explanation:
7 1/2 is (14+1)/2, and 3 1/8 is (24+1)/3. Not you have 15/2 miles for 25/3 days and by dividing them you get 0.9 miles a day