The hourly growth rate is 2%
An exponential growth is in the form:
y = abˣ;
where y, x are variables, a is the initial value of y and b > 1
Let y represent the number of bacteria after x hours.
There was initially 2200 bacteria, hence a = 2200. The equation becomes:
[tex]y=2200(b)^x\\\\\\After\ 1.5\ hours,y=2300:\\\\\\2300=2200(b)^{1.5}\\\\\\b^{1.5}=1.045\\\\1.5lnb=ln(1.045)\\\\ln(b)=0.0296\\\\b=1.02[/tex]
Therefore the hourly growth rate is 1.02 - 1 = 0.02 = 2%
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What is the formula for pie
Answer:
[tex]\pi \: = \frac{22}{7} \: \: \: \: or \: \: \: \: \: \: 3.14 \\ \\ [/tex]
what is the value of x angel in a pentagon if each interior angel is 117 , 100 , 105 and 115
Answer:
Step-by-step explanation:
Well first you have to find what the total amount of all the interior angles. In Oder to do that you count how many sides the shape has the subtract two from that number. Take the number you get from that and multiply it by 180. That number is total amount of all the interior angles including the angle x. Take the angles you do know and add them together. Take the number you get from that and subtract it from the total amount of all interior angles. The number you get from that is your answer. The answer to this problem is 103.
The value of angle x in a pentagon is 103 degrees.
Explanation:In a pentagon, the sum of the interior angles is always 540 degrees. To find the value of angle x, we can subtract the given angles from 540 degrees and then divide by the number of missing angles.
Given angles: 117, 100, 105, 115
Sum of given angles: 117 + 100 + 105 + 115 = 437 degrees
Sum of missing angles: 540 - 437 = 103 degrees
Since there is only one missing angle x in the pentagon, the value of x must be 103 degrees.
A spotlight on the ground shines a beam of light to the top of a tree that is 12 m tall. The beam of light makes an angle of 40° with the ground. What is the distance from the spotlight to the base of the tree, rounded to the nearest meter? 10 m 14 m 16 m 19 m A right triangle. The perpendicular is labeled 12 meters. The angle made between the base and the hypotenuse is labeled 40 degrees. The angle made between the base and the perpendicular is marked as a right angle.
Answer:
B.14 m
Step-by-step explanation:
We are given that
Height of tree=12 m
[tex]\theta=40^{\circ}[/tex]
We have to find the distance between the spotlight and the base of tree.
In triangle ABC
AB=12 m
[tex]tan\theta=\frac{perpendicular\;side}{base}[/tex]
Using the formula
[tex]tan 40=\frac{AB}{BC}=\frac{12}{BC}[/tex]
[tex]BC=\frac{12}{tan 40}=14.3\approx 14 m[/tex]
Hence, option B is true.
Answer:
14m
Step-by-step explanation:
I took the test
Stacy started with $40 in a savings account that earns 5% annually. How much interest will she get in one year?
Answer:
$2
Step-by-step explanation:
She earns 5% of $40 each year. To find how much she makes in 1 year, multiply 5% and 40
40*5%
Convert 5% to a decimal by dividing by 100
5%/100=0.05
40*0.05=2
So, in one year, the account earns $2 in interest
Simplify:
0.007 km : 0.021 km : 14 m
Answer:
The answer is 1 : 3 : 2
Step-by-step explanation:
First, you have to make them into same unit by converting it into km or m :
1 km = 1000 m
0.007 km = 7 m
0.021 km = 21 m
7 : 21 : 14
OR
14 m = 0.014 km
Then you can simplify it by 7 :
m,
7 : 21 : 14
= 1 : 3 : 2
OR
km,
0.007 : 0.021 : 0.014
= 0.001 : 0.003 : 0.002
= 1 : 3 : 2
(take note: in ratio, it is better to put it in whole number form rather than decimal form)
The local animal shelter has 120 dogs and cats. The ratio of dogs to cats is 3 to 7. How many dogs are in the shelter?
Answer:
There are 36 dogs in the shelter.
Step-by-step explanation:
(Draw a model)
(3 boxes for dogs and 7 boxes for cats)
10 units = 120
1 unit = 120÷10
= 12
3 units = 12×3
= 36
(I hope you understand the question. A gentle reminder, always draw the model according to the ratio. From there you will understand.)
Tariq designed the pool shown . The owner of the pool has one square to use . Find the area of the space that needs to be covered. (The four corners are squares.)
Answer:
Heres the anwser my man 128
Step-by-step explanation:
hope you got it right.
Identify the sampling method as simple random sampling, systematic sampling, convenience sampling, or stratified sampling. A computer randomly selects 500 names from a list of all registered voters. Those selected are surveyed to predict who will win the election for Mayor.
Choose the correct sampling technique below.
A. Systematic sampling
B. Convenience sampling
C. Simple random sampling
D. Stratified sampling
Answer: C.
Simple random sampling
Step-by-step explanation:
A simple random sample in statistics, is a subset of individuals chosen from a larger set. Each individual is chosen randomly and entirely by chance, such that each individual has the same probability for the entire larger set.
Answer:
C
Step-by-step explanation:
The computer randomly selects 500 names without any bias, Thus, it is simple random sampling because each name has equal chance of getting selected.
3. Determine whether each event is certain to occur, just as likely to occur as not to occur, or
impossible to occur. Then write the probability
a. A coin is flipped and the coin lands heads up. Express the probability as a fraction
b. Tuesday follows Monday in the week. Express the probability as a percent.
c. You have only white shirts in your closet. Express the probability of reaching into your
closet and choosing a red shirt as a fraction,
d. A box contains 2 green balls and 2 yellow balls. You reach into the box and grab a
yellow ball. Express the probability as a decimal
Answer:
A) 1/2 - there are 2 sides - just as likely to occur as not to occur
B) 0% - it's never going to happen (impossible)
C) 0/0 - it's never going to happen (impossible)
D) 1/2 simplified from 2/4 - that was 2 out of the four balls. - just as likely to occur as not to occur
A parking lot in the shape of a trapezoid has an area of 12,0521 square meters the length of the other base is 108.6 meters. What is the width of the parking lot
Please consider the complete question.
A parking lot in the shape of a trapezoid has an area of 12,052.1 square meters. The length of one base is 82.4 meters and the length of the base is 108.6 meters. What is the width of the parking lot
We will use area of trapezoid to formula to solve our given problem.
[tex]\text{Area of trapezoid}=\frac{1}{2}(a+b)\times h[/tex], where
a and b represents parallel sides of trapezoid,
h = height of trapezoid.
Width of the trapezoid will be equal to height.
Upon substituting our given values in above formula, we will get:
[tex]12,052.1=\frac{1}{2}(82.4+108.6)\times h[/tex]
[tex]12,052.1\cdot 2=2\cdot \frac{1}{2}(82.4+108.6)\times h[/tex]
[tex]24104.2=(191)\times h[/tex]
[tex]\frac{24104.2}{191}=\frac{(191)\times h}{191}[/tex]
[tex]126.2=h[/tex]
Therefore, the width of the parking lot is 126.2 meters.
In a probability experiment, Eric flipped a coin 45 times. The coin landed on heads 30 times. What is the ratio of heads to tails in this experiment?
Answer:
30:15 (simplified is 2:1)
Step-by-step explanation:
Out of the 45 times Eric flipped a coin, 30 of them landed on heads. Tails is the the only other probable occurance, so since we know that there are 15 trials left, this means that the coin landed on tails 15 times. This would give a heads to tails ratio of 30:15, but the simplified ratio would be 2:1, because that's the smallest it can be divided evenly.
45-30=15
30:15=2:1
Scientist are studying a bacteria sample. The function f(x)=245(1.12)^x gives the number of bacteria in the sample at the end of x days. Which statement is the best interpretation of one of the values of the function?
Answer:
The best interpretation of one of the values of the function is that the rate increases by 12% each day.
Step-by-step explanation:
Given:
F(x)=245(1.12)^x
To Find:
statement is the best interpretation of one of the values of the function
Solution:
Depending upon the values given the statement can be developed
As the function is itself the exponential growth structure ,
In this the statement ,Growth can be significantly depends on all factor
Such as time period initial value and rate.
But here the formula is simplified as ,
[tex]P=A(1+r)^t[/tex]
Here A= initial value r=rate and t =time period
Here A=245 and 1+r=1.12
i.e r=0.12 i.e 12%
Hence the rate give the best interpretation and more information about the function and scenario.
The function f(x)=245(1.12)^x models the exponential growth of bacteria in a sample over x days, with the base 245 being the initial number and 1.12 representing the daily growth rate.
Explanation:The function f(x)=245(1.12)^x describes the exponential growth of bacteria, where the base number (245) represents the initial amount of bacteria and 1.12 indicates the growth rate per day.
For example, if we want to determine the number of bacteria at the end of the first day (x=1), we substitute 1 into the function to get f(1)=245(1.12)^1, which would give us the total number of bacteria at the end of day one.
The exponent x stands for the number of days and shows how the population grows at an increasing rate over time, which is a signature characteristic of an exponential function in a context like bacterial growth.
Find the 3rd term in the sequence
Step-by-step explanation:
a(n) = a ( n - 1) - 17
a(1) = 20
a(2) = a ( 2 - 1) - 17
= a (1) - 17
= 20 - 17
= 3
Now
a(3) = a ( 3 - 1 ) - 17
= a (2) - 17
= 3 - 17
= - 14
Hope it will help you.
In Greg's that, he has $1$ yellow, $2$ red, and $3$ green tokens. One red token is equivalent to $7$ yellow tokens. One yellow token is equivalent to $3$ green tokens. Greg converts all of his tokens to green tokens. How many green tokens does he have?
Answer:
$48 green tokens
Step-by-step explanation:
please check the attached file for explanation
Answer:
48
Step-by-step explanation:
PLZ HELP ME!
Directions up above the picture
**MATH (Algebra)
Answer:
The answer to your question is t = 1.3 s
Step-by-step explanation:
Data
Equation h(t) = -4.9t² + v₀t + h₀
v₀ = 0 m/s
h₀ = 8 m
t = ?
h = 0 m
Process
1.- Substitute the values in the formula
0 = -4.9t² + 0t + 8
2.- Simplification
0 = -4.9t² + 8
3.- Solve for t
4.9t² = 8
t² = 8/4.9
t² = 1.63
4.- Result
t = 1.27 ≈ 1.3 s
5. The shaded area is 327, find r.
Answer: 10.2
Step-by-step explanation:
Area of a circle is
A= pixr^2
327= 3.14r^2
Divide by 3.14
= 104.14
Get the sq rat of 104.14
= 10.2
what are 3 equivalent ratios to 1/9?
Answer:
1/9= 2/18=3/27=4/36
Step-by-step explanation:
To find equivalent ratios to 1/9, both the numerator and the denominator are multiplied by the same number. Thus, 2/18, 3/27, and 4/36 are all equivalent ratios to 1/9.
Explanation:Ratios are equivalent if they represent the same relationship between numbers. To find equivalent ratios for 1/9, you need to multiply both the numerator and the denominator by the same number. Here are three examples:
By multiplying 1 and 9 by 2, we get 2/18.By multiplying 1 and 9 by 3, we get 3/27.By multiplying 1 and 9 by 4, we get 4/36.So, 2/18, 3/27, and 4/36 are ratios equivalent to 1/9.
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4x3 + x2 - 8x - 2 by grouping
If an exercise routine requires 24 crunches for every 16 squats, how many squats would need to be done for every 78 crunches? Group of answer choices
Answer:
The correct answer is 52 squats.
Step-by-step explanation:
An exercise routine requires 24 crunches for every 16 squats.
Therefore the routine would require 1 crunch for every [tex]\frac{16}{24}[/tex] squats.
And by the use of unitary method, the routine would require 78 crunches for every [tex]\frac{16}{24}[/tex] × 78 squats = 52 squats.
Thus for every 78 crunches attempted, the exercise routine would requires 52 squats to be done.
Can you please help me this is 6th grade stuff
Answer:
116
Step-by-step explanation: You would have to split the figure into a square and a triangle as you can see in the picture. You then find the area of each figure.
Area of Square : 8 * 8 = 64
Area of Triangle : 8 * 13 /2 = 52
Then, you add the areas of both figures together to get 116.
Desmond deposits $50 into a savings account every month at an annual interest rate of
4.7%, compounded monthly.
a. How much will his account contain after 10 years assuming he makes not withdrawals?
b. What is the rate of change in the value of Desmond’s account after 10 years?
Given:
Desmond deposits $ 50 monthly.
Yearly he deposits = $50×12 = $ 600
Rate of interest compounded monthly = 4.7%
To find the amount he will receive after 10 years and the rate of change the value of his account after 10 years.
Formula
[tex]A = P(1+\frac{r}{(n)(100)} )^{nt}[/tex]
where,
A be the final amount
P be the principal
r be the rate of interest
t be the time and
n be the number of times the interest is compounded.
Now,
Taking,
P = 600, r = 4.7, n = 12, t = 10 we get,
[tex]A = 600(1+\frac{4.7}{(12)(100)}) ^{(12)(10)}[/tex]
or, [tex]A = 600(1.0039)^{120}[/tex]
or, [tex]A = 959.1[/tex]
Now,
At starting he has $ 600
At the end of 10 years he will be having $ 959.1
So,
The amount of change in his account = $ (959.1-600) = $ 359.1
Therefore the rate of change = [tex](\frac{359.1}{600} )(100) %[/tex]
= 59.85%
Hence,
a) His account will contain $ 959.1 after 10 years.
b) The rate of change in his account is 59.85% after 10 years.
I need help asap :):);)
Answer: The third option.
Step-by-step explanation:
This is an equation because it has an equals sign that can be solved for, making it an equation.
Answer:
x + 3 = 12
Step-by-step explanation:
This is an equation because it contains an equal sign, if it does not contain an equal sign then it is an expression.
An account earns simple interest. $300 at 4% for 3 years, what is the interest earned
Answer:
$36
Step-by-step explanation:
You are going to want to use the simple interest formula for this. The one below is modified for solving the interest earned.
[tex]I = Prt[/tex]
I = interest amount
P = principal amount
r = interest rate (decimal form)
t = time (years)
First, change 4% into a decimal:
4% -> [tex]\frac{4}{100}[/tex] -> 0.04
Now, plug the values into the equation:
[tex]I=300(0.04)(3)[/tex]
[tex]I=36[/tex]
The interest earned is $36
Which statement is correct regarding the measurements of the parallelogram?
The base is 6 and the height is 3. so the area is 6(3) - 18 square units.
The base is 8 and the height is 3, so the area is a(3) - 24 square units.
The base is 8 and the height is 4, so the area is 3(4) - 32 square units.
The base is 8 and the height is 6, so the area is a = 48 square units.
Answer:
The first one is correct
Step-by-step explanation:
You can multiply the base and perpendicular height to find the area.
What is 3x5 , answer is
Answer:15
Step-by-step explanation:
Answer:
15
Step-by-step explanation:
5=1
10=2
15=3
She paid £40 altogether. She paid £3.25 for each pineapple, £2.75 for each melon 50p for each grapefruit. She bought the same number of pineapple as she did melon. How many of each did mrs Gillespie buy
Answer:
6 pineapple, 6 melons, 8 grapefruits
Step-by-step explanation:
3.25P + 2.75M + 0.5G = 40
P = M
6M + 0.5G = 40
Let M = 6
6(6) + 0.5G = 40
0.5G = 4
G = 8
P = 6
M = 6
G = 8
The restaurant served 220 sandwiches, 120tacos, and 160 salads for lunch. What is the ratio of salads to total number of lunches sold? * 5 points 5 to 11 8 to 25 6 to 8
Answer:
8 to 25
Step-by-step explanation:
The total number of lunches sold i
220+120+160 =500
We want the ratio of salads to total lunches
salads: lunches
160: 500
Divide each side by 20
160/20 : 500/20
8:25
Let x denote the courtship time for a randomly selected female–male pair of mating scorpion flies (time from the beginning of interaction until mating). suppose the mean value of x is 120 min and the standard deviation of x is 110 min (suggested by data in the article
Complete Question:
a) Is it plausible that X is normally distributed?
b) For a random sample of 50 such pairs, what is the (approximate) probability that the sample mean courtship time is between 100 min and 125 min?
Answer:
a) It is plausible that X is normally distributed
b) probability that the sample mean courtship time is between 100 min and 125 min is 0.5269
Step-by-step explanation:
a)X denotes the courtship time for the scorpion flies which indicates that is a real - valued random variable, and since normal distribution is a continuous probability distribution for a real valued random variable, it is plausible that X is normally distributed.
b) Probability that the sample mean courtship time is between 100 min and 125 min
[tex]\mu = 120\\n = 50[/tex]
[tex]P(x_{1} < \bar{X} < x_{2} ) = P(z_{2} < \frac{x_{2}- \mu }{SD} ) - P(z_{1} < \frac{x_{2}- \mu }{SD})[/tex]
[tex]SD = \sqrt{\frac{\sigma^{2} }{n} } \\SD = \sqrt{\frac{110^{2} }{50} } \\SD = 15.56[/tex]
[tex]P(100 < \bar{X} <125 ) = P(z_{2} < \frac{125- 120 }{15.56} ) - P(z_{1} < \frac{100- 120 }{15.56})\\P(100 < \bar{X} <125 ) = P(z_{2} < 0.32 ) - P(z_{1} < -1.29)[/tex]
From the probability distribution table:
[tex]P(z_{2} < 0.32 ) = 0.6255\\ P(z_{1} < -1.29) = 0.0986[/tex]
[tex]P(100 < \bar{X} <125 ) = 0.6255 - 0.0986\\P(100 < \bar{X} <125 ) =0.5269[/tex]
Line a: (–1, 2), (1, 8)
Line b: (–3, –4), (2, 11)
ma = 8 − 2
1 − (− 1)
= 6
2
= 3
mb = 11 − (−4)
2 − (− 3)
= 15
5
= 3
Slope of the line through (1, 8) and (2, 11)
m = 11 − 8
2 − 1
= 3
1
= 3
How many points of intersection are there between line a and line b?
zero
one
two
infinitely many
Answer:
its D the last one i just took the assignment
Step-by-step explanation:
Answer:
The answer is D.
Step-by-step explanation:
I took the assignment.
the quoient of 36 and 3 is j
Answer:
j = 12
Step-by-step explanation:
Quotient means the answer when you divide the dividend by the divisor.
In this example, we are dividing 36 by 3, so 36 = dividend, 3 = divisor.
36 / 3 = 12. See the attachment if you need extra help on long division!
Answer:
It is 12
Step-by-step explanation:
So first you divide 36 by 3. So 3 goes into 3 once. Now 3 goes into 6 twice so there you have it