A town has a population of 5000 and grows at 3.5% every year. To the nearest tenth of a year, how long will it be until the population will reach 7300?
Answer:
Step-by-step explanation:
This is an exponential function. In order to find the answer to the question, we need to first determine what the equation is that models this information. The standard form for an exponential function is
where a is the initial value and b is the growth/decay rate. If the starting population is 5000, then
a = 5000
If the population is growing, that means that it retains 100% of the initial population and is added to by another 3.5%. So in a sense the population grows 100% + 3.5% = 103.5% or, in decimal form, 1.035. So
b = 1.035
Our function is
where y is the ending population and x is the number of years it takes to get to that ending population. We want to know how long, x, it will be til the population reaches 7300, y.
and we need to solve for x. The only way to do that is by using logs. I'll use natural logs for this.
Begin by dividing both sides by 5000 to get
and take the natural log of both sides:
The power rule for natural logs is that we can now bring the exponent down in front of the ln to get:
To solve for x, we now divide both sides by ln(1.035):
Do that division on your calculator and get that
x = 11.0 years.
That means that 11 years after the population was 5000 it will be expected to reach 7300 (as long as the growth rate remains 3.5%)
giving brainliest!!!
Answer:
133 square centimeters
Step-by-step explanation:
Answer:
Surface A≈146.25 square centimeters
Step-by-step explanation:
Determine if the triangles are similar. If they are similar state why they are similar and
complete the similarity statement. If the triangles are not similar, select "N/A" for the last
two dropdowns.
R
Q
11
14
U
V
22
28
S
[ Select)
The triangles are
vby
[ Select]
.Δ
SUV-A [Select]
is 6.762 greater than 6.649
find the selling price if the cost price is rupees 600 and profit is 13%
Answer:
=2277 Ans.
Step-by-step explanation:
Find the selling price
(a) Cost =600
Profit=13%
Selling price =Cost + profit
=600+
100
600×13
=600+78
=678 Ans.
(b) Cost=2475, loss=8%
Selling price = Cost+ profit/loss
=2475+(−
100
2475×3
)
=2475−198
=2277 Ans.
According to the guideline from the Health Department, every over-weight child needs to take a fitness test.
Every ten over-weight children would be randomly grouped together to attend the fitness test. According to
the past experience, the probability for each child to pass the fitness test is 0.75 and whether a child can pass
the test is independent with the test result of other children.
(a) Many test sessions will be conducted regularly, each with 10 independent children. Find the expectation
and standard deviation of the number of children can pass the fitness test in a test session.
(b) Most likely, how many children can pass the fitness test in a test session? Justify your answer by
comparing the two outcomes with the relatively high probability.
(c) Find the probability that less than 8 children can pass the fitness test in one test session.
Answer:
According to the guideline from the Health Department, every over-weight child needs to take a fitness test.
Every ten over-weight children would be randomly grouped together to attend the fitness test. According to
the past experience
Step-by-step explanation:
2 questions plz Both will be in the comments
The price of a carton of eggs at Supermarket A is $2.10. The price of a carton of eggs at Supermarket Bis 40% less than the price at Supermarket A
What is the price of a carton of eggs at Supermarket B?
Aaron currently earns $1,400 per month working. Each year he will get a $150 per month raise. How much money will Aaron earn per month in 7 years?
the correct answer is 10290000
Answer:
130,200
Step-by-step explanation:
Earnings for 7yrs= $1,400 × 12 months × 7yrs
= $117,600
Raise for 7 yrs= $150 × 12 months × 7yrs
=$ 12,600
Earnings in 7yrs= $117,600 + $12,600
= 130,200
I will mark you branlist!!
Answer:
25
Step-by-step explanation:
1/5 x 125 = 25
Answer:
25 :)
Step-by-step explanation:
For f(x) = 5x+1 find f(-4)
0 1
0-21
21
0 -19
Answer:
21 you is smart 8th
Step-by-step explanation:
smart smart 99
2(34 + 12) > 5b This inequality contains a variable, b. Choose ALL numbers that make this inequality true. A) 16 B) 18 C) 19 D) 20 E) 22
Answer:
A and B
Step-by-step explanation:
does a/9=25 i dont know
Answer:
225
Step-by-step explanation:
225 ÷ 9 =25
Solve −2x−4=3x+1
by graphing.
The solution is x=
Answer: x=-1
Step-by-step explanation:
What's the name of angle C thanks for the help :)
Answer:
Reflex angle
Step-by-step explanation:
Properties of reflex angles:
1). Any angle measuring between 180° and 360°.
2). Other side of the reflex angle is either acute or obtuse angle.
By these properties,
Since, angle C measures more than 180° but less than 360° and opposite angle is an acute angle.
By these properties angle C and angle D are the reflex angles.
At a new exhibit in the Museum of Science, people are asked to choose between 94 or 220 random draws from a machine. The machine is known to have 99 green balls and 78 red balls. After each draw, the color of the ball is noted and the ball is put back for the next draw. You win a prize if more than 61% of the draws result in a green ball. a. Calculate the probability of getting more than 61% green balls.
Answer:
0.0869 = 8.69% probability of getting more than 61% green balls.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
The machine is known to have 99 green balls and 78 red balls.
This means that [tex]p = \frac{99}{99+78} = 0.5593[/tex]
Mean and standard deviation:
[tex]\mu = p = 0.5593[/tex]
[tex]s = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.5593*0.4407}{99+78}} = 0.0373[/tex]
a. Calculate the probability of getting more than 61% green balls.
This is 1 subtracted by the pvalue of Z when X = 0.61. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{0.61 - 0.5593}{0.0373}[/tex]
[tex]Z = 1.36[/tex]
[tex]Z = 1.36[/tex] has a pvalue of 0.9131
1 - 0.9131 = 0.0869
0.0869 = 8.69% probability of getting more than 61% green balls.
2 2/5 x 3/4
plz help me! and plz show your work.
Answer:1.8
Step-by-step explanation:
Two trains on opposite tracks leave the same station at the same time. One train travels at an average speed of 80 kilometres per hour and the other travels at an average speed of 70 kilometres per hour. How long after they leave the station will they be 50 km apart?
9514 1404 393
Answer:
20 minutes
Step-by-step explanation:
The trains are separating at the rate of 80 +70 = 150 km/hour. The time required to be 50 km apart is then ...
time = distance/speed = (50 km)/(150 km/h) = 1/3 h = 20 minutes
ONLY answer if you know! Which of the following will have a negative result? (1 point)
O-8-(-10)
O 12-14
07-(-3)
2√63
Simplify
Bsbahajjssjjxjsjsjj
please help me if you know the answer
The figure is a kite. The m < 4 = 72 and m < 3 = 18. Find m < 2.
The sum of the angles for a 4 sides figure must add up to 360.
Angle 1 and angle 2 are between similar sides so the 2 angles are identical.
Subtract the known angles from 360:
360 - 72 - 18 = 270
Divide that by 2:
270*2 = 135
Angle 2 = 135 degrees.
what is -4 * 7/10. please hlp!
Answer:
-4 * 7/10 = -2.8
Pls help!! I’ve been trining to get the answer but I can’t pls help!!
Answer:
$5740
Step-by-step explanation:
get 2.5% of 5600
5600/x=100/2.5
(5600/x)*x=(100/2.5)*x
5600=40*x
5600/40=x
140=x
x=140 <----- 2.5% of 5600
5600 + 140 = $5740
An amoeba divides to form two amoebas after one hour. One hour later, each of the two
amoebas divides to form two more. Every hour, each amoeba divides to form two more.
1. How many amoebas are there after 1 hour?
2. How many amoebas are there after 2 hours?
3. Write an expression for the number of amoebas after 6 hours.
Answer: 2 1 4
Step-by-step explanation: cant say.
Find the area of the shape below.
Give your answer in terms of pi
6cm
8cm
32cm
The diagram is not drawn to scale.
9514 1404 393
Answer:
164π cm²
Step-by-step explanation:
The area of a circle is given by the formula ...
A = πr²
The radius (r) is half the diameter (d), so the area of a semicircle in terms of its diameter is ...
1/2A = (1/2)(π)(d/2)² = (π/8)d²
The given shape is the combination of three (3) semicircles. The smallest has a diameter of 6 cm; the middle-sized one has a diameter of (32 cm -6 cm -8 cm) = 18 cm. The largest has a diameter of 32 cm.
The total area will be ...
area of largest + area of middle-size - area of smallest
= (π/8)(32² +18² -6²) = (π/8)(1312) . . . . cm²
The area of the shape is 164π cm².
Find the difference 7/9 - 5/13 in lowest term
Answer:
46/117
Step-by-step explanation:
Answer:
46/117
Step-by-step explanation:
this is a type of fraction which can not be simplified
What is the value of x
15x + 1=46
Help plz
I will give brainliest
Answer:
3
Step-by-step explanation:
Answer:
The answer to this question is X=3
Step-by-step explanation:
15x3=45
45+1=46
Hope my answer helps you!!!
What is the inverse function
Answer:
it's simple just divide
What is 0.9 divide by 2.647
Answer:
0.340007556
Step-by-step explanation:
its correct