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%)
Helppppppppppp AND NO LINKS
Suppose lightning strikes at an average of 1.4 strikes per minute during a particular storm. You play the following game: if the next strike occurs within the next minute, you win 3 dollars, if the next strike occurs between 1 minute and 2 minutes from now, you win 5 dollars, and if the next strike occurs more than 2 minutes from now, you win 1 dollar. How much should someone be charged to play this game, to make it a "fair game?"
Answer:
$3.25
Step-by-step explanation:
Given that:
Mean, λ = 1.4
Strike within next minute = $3 won
Strike between one and 2 minutes = $5
Strike more than 2 minutes = $1
Probability that next strike occurs within the next minute :
Using poisson :
P(x < 1) = 1 - e^-(λx) ;
P(x < 1) = 1 - e^-(1.4*1) = 1 - e^-1.4
P(x < 1) = 1 - 0.2465969
P(x < 1) = 0.7534030
Next strike occurs between 1 and 2 minutes :
(1 < x < 2) :
P(x < 2) - P(x < 1)
P(x < 2) = 1 - e^-(λx) ;
P(x < 2) = 1 - e^-(1.4*2) = 1 - e^-2.8
P(x < 2) = 1 - 0.0608100
P(x < 2) = 0.9391899
P(x < 2) - P(x < 1)
0.9391899 - 0.7534030 = 0.1857869
P(striking after 2 minutes)
P(x > 2) = e^-(λx) ;
P(x > 2) = e^-(1.4*2) = e^-2.8
P(x > 2) = 0.0608100
Amount charged :
(0.7534030 * 3) + (0.1857869 * 5) + (0.06081 * 1)
= 3.2499
= $3.25
I don’t know what to do
Answer:
okay so, everytime you see anything that says "a number", that will automatically mean that there is a number in the equation that u dont know, so instead of putting a random number in its place, you put an "exponent" aka a letter like "x" for example. so it says, 12 is the sum of a "number" and 3, that means 3 plus a number gives u 12, you would have to make an equation to find the "number" so the equation would be "3 + x = 12".
Step-by-step explanation:
Answer please 9 - (-4).
can someone help me understand this problem?
Hello!
a. 10
b. 1
c. -11
To evaluate f(x) at a certain x, you simply substitute that value of x into the equation for x.
For example:
a. f(x) = 2x, find f(5)
Plug in 5 for x into f(x):
f(5) = 2(5) = 10.
b. f(x) = 4x + 5, find f(-1)
f(-1) = 4(-1) + 5 = 1
c. f(x) = -3x - 5, find f(2)
f(2) = -3(2) - 5 = -11
Order the angles in each triangle from smallest to largest.
9514 1404 393
Answer:
B: L, M, N
Step-by-step explanation:
The sides are listed from shortest to longest. The angles opposite these sides will be in order smallest to largest. The name of the opposite angle is the vertex whose name is missing from the side's name.
MN is opposite angle L, the smallest
LN is opposite angle M, the middle-size
LM is opposite angle N, the largest.
Smallest to largest, the angles are ∠L, ∠M, ∠N.
A scale model of a rectangular building lot measures 7feet by 5 feet. If the actual house will be built using a scale factor of 12 what is the area of the actual building lot
The height of one cylinder is 8 cm, and the radius of its base is 5 cm. The height of a second cylinder is 24 cm, and the radius of its base is 5 cm. How many times the volume of the first cylinder is the volume of the second cylinder?
Answer:
Step-by-step explanation:
volume₁ = π5²·8 = 200π cm³
volume₂ = π5²·24 = 600π cm³
volume₂ = 3×volume₁
Answer:
It is 3, hopefully you got a good score! :D
Step-by-step explanation:
8. How much paint are you going to need to paint the entire figure to the right? (you do paint the bottom
of the rectangles)
Will mark brainlest for foist answer
Answer:
The surface area would be 560 in.²
It doesn’t say how much paint it takes to cover area.
Step-by-step explanation:
6x5x2=60
4x6x2=48
18x6x2=216
18x5x2=180
7x4x2=56
60+48+216+180+56=560
Need help ASAP question 12
Answer:
Parallelogram
Step-by-step explanation:
Opposite sides are parallel
Y’all can you help on this?
2. The ratio of the angle measures in a
triangle is 1:12:17. What is the measure of
smallest angle?
Answer:
6 degrees
Step-by-step explanation:
x + 12x + 17x = 180
x = 6
The angles are 6 : 72 : 102 so the smallest is 6 degrees.
Answer:
sum of all angles = 180
given angle 1 X., 12 X, 17 X
SO 1 X + 12 X + 17 X= 180
13 X+17 X =180
30 X = 180
X=180\30
X =6
ANS =6
HOW; PUT X = 6 APPLY TO 1 X., 12 X, 17 X
1 X=1×6= 6
12X = 12×6 =72
17 X = 17 ×6 =102
ANS = 6
Step-by-step explanation:
4/7 of 29= (estimate each product)
Answer:
16
Step-by-step explanation:
Answer:
16.5714286. 17 because the .5 rounds up.
Step-by-step explanation:
Find a seventh of 29 by dividing the number by 7 and you will get 4.14285714.
Then, multiply that number by 4 to get your four sevenths. You will then get your answer which is 17.
Find the product of 5/3 with quotient of 2/11 and 4/11
Answer:
5/6
Step-by-step explanation:
quotient of 2/11 and 4/11 is 22/44 or 1/2
5/3 · 1/2 = 5/6
The variable z varies jointly with x and y. Also, z = -75 when x = 3 and y = -5.
What equation describes this variation?
x = kyz
y = kxz
z = kxy
k = xyz
What equation describes this variation?
z = kxy
What is the constant of variation?
k = 5
When x = 1 and y = –2, z =
-10
Step by Step Explanation:
With the equation z = kxy and the values for z, x, and y, we can find k.
z = kxy
-75 = (k) (3) (-5)
-75 = (k) (-15)
5 = k
k = 5 (final answer).
To check our work, we just enter all of the values and make sure it adds up.
z = kxy
-75 = (5)(3)(-5)
-75 = 15(-5)
-75 = -75
correct!
Do the same to find the answer for the next part to get -10.
Further proof in the file attached.
Answer:
C.
5
-10
NEXT SLIDE:
3/8
3/40
NEXT SLIDE:
A.
7
42
NEXT SLIDE:
D.
6
NEXT SLIDE:
B.
10
LAST SLIDE:
A.
D.
Step-by-step explanation:
100% Edge 2021
I did the Assignment.
Good luck catching up in Edge before the end date fam!
Concerns about climate change and CO2 reduction have initiated the commercial production of blends of biodiesel (e.g., from renewable sources) and petrodiesel (from fossil fuel). Random samples of 32 blended fuels are tested in a lab to ascertain the bio/total carbon ratio. (a) If the true mean is .9370 with a standard deviation of 0.0090, within what interval will 99 percent of the sample means fall
Answer:
99% of the sample means will fall between 0.93288 and 0.94112.
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.
The true mean is .9370 with a standard deviation of 0.0090
This means that [tex]\mu = 0.9370, \sigma = 0.0090[/tex]
Sample of 32:
This means that [tex]n = 32, s = \frac{0.009}{32} = 0.0016[/tex]
Within what interval will 99 percent of the sample means fall?
Between the 50 - (99/2) = 0.5th percentile and the 50 + (99/2) = 99.5th percentile.
0.5th percentile:
X when Z has a pvalue of 0.005. So X when Z = -2.575.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]-2.575 = \frac{X - 0.9370}{0.0016}[/tex]
[tex]X - 0.9370 = -2.575*0.0016[/tex]
[tex]X = 0.93288[/tex]
99.5th percentile:
X when Z has a pvalue of 0.995. So X when Z = 2.575.
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]2.575 = \frac{X - 0.9370}{0.0016}[/tex]
[tex]X - 0.9370 = 2.575*0.0016[/tex]
[tex]X = 0.94112[/tex]
99% of the sample means will fall between 0.93288 and 0.94112.
The total cost to go horseback riding is x dollars per hour plus a $2 fee for renting a helmet. Which expressions represent the cost, in dollars, for 4 people to go horseback riding for 3 hours each? Select all that apply.
4(3x+2)
3(4x+2)
6x+3+6x+5
4(3x)+4(2)
12x+8
3x(4)+2
Answer:
4(3x+2), 4(3x)+4(2), 12x+8
Step-by-step explanation:
A class has 28 children in it.
Can it be split in the ratio 3:2?
Answer:
Yes the class can
Step-by-step explanation:
Answer:
yes
Step-by-step explanation:
A surgeon has found that she can model the number of surgeries done per week with a Poisson distribution
in which y = 24.5.
How many surgeries would be expected in a year? assume no vacation or time off.
Round to one decimal if needed.
Answer:
94.5
Step-by-step explanation:
Pls help I give brain
Answer:
$480
Step-by-step explanation:
8x6x10=480
4. (5 x 3) x 2 = 5 x (3 x 2) is an example of which property?
A) Commutative Property for Addition
B) Associative Property for Multiplication
O C) Distributive Property for Multiplication
D) Commutative Property for Multiplication
Answer:
B, Associative property for multiplication
Step-by-step explanation:
Commutative property means the numbers can be multiplied in any order, so the (5 x 3) x 2 could be written as 3 x 5 x 2 and would be the same.
Associative property deals more with groupings of terms/numbers. Since the order of the numbers stayed the same, and the parentheses are moved, this is an example of the associative property.
In this rectangular box, EF = 6, FD = 5, and DB = 8. Find A F . A. V61 B. V89 C. 10 D. 5V5
Answer:
Step-by-step explanation: Got it right on E D G E N U I T Y
Answer:
D
Step-by-step explanation:
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Answer: A 128
Step-by-step explanation:
Complete the following to describe how to draw to diagram to represent the answer 3÷3/5
Answer:
you can do a diagram representing this product by drawing a box with six squares and then putting three lines for each box and divide 3÷3 and you will get 5
what is the greatest decimal in hundredths that can be rounded to 14.5? What is the least
Answer:
14.45 and 14.54Step-by-step explanation:
Rule for rounding:
Round up if number is between 5 and 9Round down if number is between 0 and 4What numbers in hundredths can be rounded to 14.5?
14.45 to 14.49and
14.50 to 14.54From above we see that:
The greatest decimal is 14.54The least decimal is 14.45Xander had $24, he spent 3/4 of it how much money does he have left?
Answer:
6.25
Step-by-step explanation:
help ill give brainliest
Peter Company, a produce distributer, always tries to sell its oldest produce first.
Peter company
Answer:
what is this a maths problem
Write an equivalent expression to x-6y+5
x-6y+5= x-(-6y)+5
x-6y+5= 5 (x-6y+1)
x-6y+5= x+5+(-6y)
x-6y+5= x+5+6y
Answer:
x-6y+5= x-(-6y)+5
Step-by-step explanation:
don't know if right just trying to help sorry