Answer: Exponential function: [tex]y=12000(1.05)^x[/tex]
Step-by-step explanation:
Exponential function: [tex]y=ab^x[/tex] , a = initial value , x= time, b= growth factor , b= 1+r , where r=rate of growth.
Given: Initial population = a= 12,000,
rate of growth = r= 5% = 0.05
Then, b= 1+r= 1+ 0.05 = 1.05
Substitute value of a and b in (i), we get
[tex]y=12000(1.05)^x[/tex]
Hence, The required exponential function: [tex]y=12000(1.05)^x[/tex], where x= time.
A petri dish has 10, 000 bacteria in it. After 4 hours the bacteria’s population increased to 20,000. If the number of colonies grows exponentially, write a formula for the number of bacteria in the dish at any time t, where t is in hours
Answer:
[tex]P(t) = 10000e^{0.1733t}[/tex]
Step-by-step explanation:
The population of bacteria grows exponentially, which means that it can be represented by a function in the following format:
[tex]P(t) = P(0)e^{rt}[/tex]
In which P(0) is the initial population and r is the growth rate.
A petri dish has 10, 000 bacteria in it.
This means that [tex]P(0) = 10000[/tex]. So
[tex]P(t) = 10000e^{rt}[/tex]
After 4 hours the bacteria’s population increased to 20,000.
This means that [tex]P(4) = 20000[/tex], and we use this to find the growth rate. So
[tex]P(t) = 10000e^{rt}[/tex]
[tex]20000 = 10000e^{4r}[/tex]
[tex]e^{4r} = \frac{20000}{10000}[/tex]
[tex]e^{4r} = 2[/tex]
[tex]\ln{e^{4r}} = \ln{2}[/tex]
[tex]4r = \ln{2}[/tex]
[tex]r = \frac{\ln{2}}{4}[/tex]
[tex]r = 0.1733[/tex]
So, the formula is given by:
[tex]P(t) = 10000e^{0.1733t}[/tex]
need help asap please!!
Answer:
b = 39
Step-by-step explanation:
The two sides are equivalent so we can use this information to form an equation.
2b - 39 = b
-39 = -b
39 = b
The following statement is a good definition of...
Answer:
It is not converse since converse is if q, then p in a conditional statement. So I will say that is a truth table
Round 723,084 to the nearest thousand.
Answer:
723,000
Step-by-step explanation:
Answer:
723,000
Step-by-step explanation:
Nearest thousand → 1000
723,000
help pls due today thanks
Answer:
the second one -9/4 divided (-2/3)
Step-by-step explanation:
Mr. Toshiro manages a company that supplies a variety of domestic and imported nuts to supermarkets. He received as order for 120 bags of cashews , 310 bags of walnuts, and 60 bags of Brazil nuts. The price per bag for each type are $29, $18, and $21, respectively. Represent the number of bags ordered and the cost as vectors.
Answer: Total cost would be 10,320
Step-by-step explanation: Hope this helps
Express 38% as a decimal number
38
3.8
0.38
Answer:
i think 0.38
Step-by-step explanation:
12x+9y=162. Fully reduce your answer.
Answer:
y=-1 1/3+18
Step-by-step explanation:
isolate the y and divide both by 9
Pls help lol I’ve been stuck forever
Question 8
1 pts
A group of adult males has foot lengths with a mean of 29.79 cm and a
standard deviation of 1.76 cm Use the range rule of thumb to identify the
following
Significantly high values are
cm or higher
Answer:
33.31 cm or higher
Step-by-step explanation:
Given that:
Mean = 29.79 cm
Standard deviation, s = 1.76 cm
According to the range rule of thumb, values which are greater than or equal to 2 standard deviations from the mean are significantly high values :
Significantly high values are :
Mean + 2(standard deviation)
29.79 cm + 2(1.76)
29.79 + 3.52
= 33.31cm
A new car is purchased for 20000 dollars.The value of the cat depreciates at 12.5% per year.What will the value of the car be, to the nearest cent, after 11 years?
Answer:
$460.38
Step-by-step explanation:
Use the exponential decay formula, y = C(1 - r)^t
Plug in the original price, depreciation rate, and amount of time:
y = 20000(0.875)^11
y = 460.38
So, the car's value after 11 years will be $460.38
Match each decimal to its equivalent percent.
12.5%
1
0.8
8%
0.125
80%
0.25
1%
0.5%
50%
0.01
100%
0.5
0.08
25%
0.005
Answer:
12.5%=.125, 1= 100%, .8=80% 8%=.08 .25= 25% .5 = 50% .01= 1% .005= 0.5%
Step-by-step explanation:
On the Decimal numbers just move the decimal place over 2 to the right
and add a percent
Find the measure of an interior angle and exterior angle of a regular 24gon
Answer:
Interior Angle: 165°
Exterior Angle: 15°
Step-by-step explanation:
So first you have to find the sum of all interior angles of a polygon with 24 sides. This can be found using the formula:
sum = ( n - 2 ) * 180° where 'n' is the number of sides.
When 'n = 24' then the sum is:
sum = ( 24 - 2 ) * 180°
Simplify and solve.
sum = 22 * 180°
sum = 3960°
Since there are 24 sides to the polygon, there are 24 interior angles. Assuming that this polygon is equilateral, you can surmise that:
Interior Angle = sum° / n where n is the number of sides,
3960° / 24 = 165° = Interior Angle
Using that information, and combine it with the [Supplementary Angles Theorem] the exterior angle can be found by:
165° + x = 180°
Solve for x.
SOMEONE PLEASE HELP ME THIS IS ALMOST DUE AND I NEED THE RIGHT ANSWER PLZ!!!
can I get an answer please
Answer:
It should be C.
Step-by-step explanation:
Answer:
it is the first bubble the one you have already selected
Please explain
swimming at a rate of 40 yards per minute for 30 minutes will burn 150 calories. How many minutes must a person swim at this rate to burn 900 calories?
Answer:
180 minutes so 3 hours
Step-by-step explanation:
What is the area of the shaded region?
(25/1 - 48) cm
(2571 - 30) cm
(2572 - 24) cm
(2571 – 12) cm2
Answer:
Option (3)
Step-by-step explanation:
From the figure attached,
Area of the shaded region = Area of circle - (Area of the ΔOAB + Area of ΔOED)
Area of the circle = πr²
= π(5)²
= 25π cm²
Area of ΔOAB = 2(Area of ΔOCB)
AB = 6 cm
OC = 5 - 1 = 4 cm
By applying Pythagoras theorem in ΔOCB,
OB² = OC² + BC²
5² = 4² + BC²
BC² = 25 - 16
BC = √9 = 3 cm
Area of ΔOCB = [tex]\frac{1}{2}(OC)(BC)[/tex]
= [tex]\frac{1}{2}(4)(3)[/tex]
= 6 cm²
Area of ΔAOB = 2(6) = 12 cm²
Area of ΔAOB = Area of ΔDOE = 12 cm²
Area of shaded region = 25π - (12 + 12)
= (25π - 24) cm²
Therefore, Option (3) will be the answer.
Does the sum of angles of any triangle will always equal 180 degrees?
Answer:
yes the sum of any triangle is 180°
Step-by-step explanation:
I hope it's helps you
Someone Help please with work!! 15pts
Answer:
f(5) is equal to 5.
Step-by-step explanation:
You can see this by looking at 5 on the horizontal axis, and seeing where the graph crosses vertical line for that value. If you look closely, you'll see that the x value of 5 has a y value of 5 as well.
Question 3
<
B0/2 pts
A friend has a 81% average before the final exam for a course. That score includes everything but
the final, which counts for 20% of the course grade.
What is the best course grade your friend can earn?
What is the minimum score would your friend would need on the final to earn a 75% for the course?
Give answers accurate to at least one decimal place.
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Answer:
The best course grade your friend can earn is 0.848 = 84.8%.
The minimum score would your friend would need on the final to earn a 75% for the course is of 0.51 = 51%.
Step-by-step explanation:
This is a weighed average problem, in which we multiply each grade by its weight.
We have that:
In 80% of the course, the friend has a grade of 81%.
In the other 20%, he will have x.
What is the best course grade your friend can earn?
This will happen if he earns 100% = 1 on the final test. So
[tex]G = 0.8*0.81 + 0.2*1 = 0.848[/tex]
The best course grade your friend can earn is 0.848 = 84.8%.
What is the minimum score would your friend would need on the final to earn a 75% for the course?
This is x, when the grade is 0.75. So
[tex]0.75 = 0.8*0.81 + 0.2x[/tex]
[tex]0.2x = 0.75 - 0.8*0.81[/tex]
[tex]x = \frac{0.75 - 0.8*0.81}{0.2}[/tex]
[tex]x = 0.51[/tex]
The minimum score would your friend would need on the final to earn a 75% for the course is of 0.51 = 51%.
Please answer correctly i will give brainliest
Answer: It is C
Step-by-step explanation:
Good luck on your test or homework
You are creating a model of the Gareway arch. You decide to use a scale of 1/2 yd=1/4in. The Gateway Arch is 310 yards tall. How tall will your model need to be?
Answer:
77.5
Step-by-step explanation:
You spent 9.5 hours playing Among Us
this week. This is 2.75 hours more than the
number of hours h you played last week.
Which equation can be used to find h?
Answer:
9.5-2.75=h
Step-by-step explanation:
−2y−8+4yminus, 2, y, minus, 8, plus, 4, y
Answer:
a number 12
Step-by-step explanation:
duh bro
What is the answer pls help
Julio has started his very own floral business. Center pieces 19.50 fixed cost $500 per month cost 8.00 to produce. If he sells 25 center peices to break even
Answer:The total cost, C, is the sum of the cost to produce the centerpieces and the fixed cost. The equation for C is C = 8n + 500.
The total revenue, R, of Julio's floral business is the product of the cost per centerpiece and the number of centerpieces sold. The equation for R is R = 19.50n.
Step-by-step explanation:
solve and identify the solution. 10+1.5x=3.5x
Answer:
x=5
Step-by-step explanation:
hope this is correct have a wonderful day! <3
Answer:
x=5
Step-by-step explanation:
10+1.5x=3.5x
Subtract 3.5x from both sides.
10+1.5x−3.5x=0
Combine 1.5x and −3.5x to get −2x.
10−2x=0
Subtract 10 from both sides. Anything subtracted from zero gives its negation.
−2x=−10
Divide both sides by −2.
x= −2 /−10
Divide −10 by −2 to get 5.
x=5
in abc, ac=bc cd is perpendicular with ab, d belongs to ab ab=4and cd=sqar root 3 find ac
Answer:
The answer is root 7
Step-by-step explanation:
You can find out that ΔABC is isosceles, and CD bisects AB, so AD = 2 - and now you have 2 sides given in ΔADC
Use the Pythagoras Theorum to find the hypotenuse AC
The answer is the square root of 7
need help asap please
Answer:
[tex]\displaystyle no[/tex]
Step-by-step explanation:
SR is slightly longer than TS, so with that being stated, we cannot use this theorem for this triangle.
I am joyous to assist you at any time.
can someone plz help me with this , i cant find out who created this equation..
Answer:
Answering the part about who created the first equation:
There are a lot of different ways to solving cubic equations, but the first one is given by Gerolamo Cardano, who published it, and the equation was created by Scipione del Ferro, an Italian mathematician who was born in 1465. He did not make a lot of other contributions to mathematics, some of his other works were related to the rationalization of fractions with denominators containing sums of cube roots
This equation was called "Cardano's formula", and originally only worked for depressed cubic equations ( x^3 + p*x + q = 0)
But there are variations that can be used for more general cubic equations, of the form:
a*x^3 + b*x^2 + c*x + d = 0.