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%)
Charles invested $15,000 in stocks and bonds. He made a 12% profit on his stock investments and a 5% profit on his bond investments. If Charles's combined profits on both types of investments were $1,450, how much did he invest in stocks?
Answer:When you leave the interest in your
account or reinvest the money you earn on your
investments, the money you earn starts to earn
money too. Over time, the magic of
compounding works, allowing your money to
grow with dramatic results. The more time you
have to save, the less money you need to save
because of compounding. And the longer you
wait to start saving, the more you have to spend
to reach your goal. For example, let’s assume
that Maria’s savings grow by 5% a year. If she
starts to save $243 a month now, it will cost her
$58,320 to have $100,000 in twenty years. If
she waits 10 years to start saving, she will have to
save $644 a month for 10 years, and it will cost
her $77,280 to reach $100,000 in twenty years.
Step-by-step explanation:Hope this helps!!!!
Answer:
$10,000 invested into stocks
Step-by-step explanation:
pls answer any that you can!!!
Answer:
12, 45, 1.8, -9, 18
Step-by-step explanation:
up up down down left right left right b a start
HELP ASAP
The radius of a quarter circle is 1.4 millimeters. What is the quarter circle's area?
Answer:
A = 1.5386
Step-by-step explanation:
Quarter circle area formula:
A = (πr²)/4
A= (π1.4²)/4
A = (3.14*1.96)/4
A = (6.1544)/4
A = 1.5386
1. Find the slope of the line in the graph
Mr. Kramer bought his daughter a kitten for her birthday, so now he needs to buy cat food. First, he gets a 20-pound bag of dry cat food. Then, he finds a good deal on 3-ounce cans of wet cat food, so he buys 48 of them. How many pounds of cat food does Mr. Kramer get in all?
Answer: 29 lbs
Step-by-step explanation: If you do 48 times 3 you will get 144 and if you do 144 divided by 16 you will get 9 and if you do 9 plus 20 you will get 29 lbs in total.
The required pounds of cat food Mr. Kramer get in all is 9.
given that,
First, he gets a 20-pound bag of dry cat food.
Then, he finds a good deal on 3-ounce cans of wet cat food,
so he buys 48 of them.
It is to determine how many pounds of cat food Mr. Kramer get in all.
In mathematics, it deals with numbers of operations according to the statements.
In a can, there are 3 ounces of wet cat food.
1 can = 3 ounce
multiplying both sides by 48
48 can = 3 * 48 ounce
48 can = 144 ounce
1 pound = 16 ounce
1/16 pound = 1 ounce
multiplying both sides by 144 on both sides
144 / 16 pound = 144 ounce
9 pound = 144 ounce
Thus, the required pounds of cat food Mr. Kramer gets in all is 9.
Learn more about arithmetic here:
brainly.com/question/14753192
#SPJ2
A roller coaster is being designed that starts at (0,22) and ends at (19,2),
Along the ride there is a relative minimum at (5,6) and a relative
maximum at (10,18). The roller coaster is almost finished but one
section is missing. Find the correct function that completes the roller
coaster so that the ride is smooth and continuous.
Answer:
The function is, f(x) = 6·sin((π/5)(x + 3π/2)) + 12
Step-by-step explanation:
The general form of equation of a roller coaster is given as follows;
y = A·sin(B(x - C)) + D
Where;
A = The amplitude = (18 - 6)/2 = 6
D = The vertical shift = 12
One revolution = 10 unit
∴2·π = 10 unit
Therefore, 10 = 2·π/B
B = 2·π/10
The phase shift = 3·π/2
Therefore, we have the function as follows;
f(x) = 6·sin(2·π/10(x + 3π/2)) + 12 = 6·sin((π/5)(x + 3π/2)) + 12
A family is trying to pick from different shades of paint for their living room. They have narrowed it down to 3 different blues and 6 different greens.
The family decides to just randomly select a color from these.
What is the probability they will pick a shade of blue?
Enter your answer to the nearest percent in the box.
For ratios, the numerator usually indicates how much of a specific option you have, and the denomenator is often times the total of the set.
In this case, you have a total of 9 shades, if you add the greens and blues together. Three of them, are blue.
Hopefully this helps!
Answer: yes
Step-by-step explanation:
i had this quesion too and i got it correct
What is the ratio as a fraction 9 and 6
Answer:
9/15 will become 3/5 and 6/15 will become 2/5.
Nathan inherited $100,000 from a wealthy uncle and invested the money in an account that earns 4% interest compounded annually.
How much interest will this money earn if Nathan leaves it in the account for 10 years?
whats the answer a b c and d?
Answer:
VC & WC
Step-by-step explanation:
It's going to be the sides opposite the equal angles.
A fair cube has 2 blue sides, 2 red sides, and 2 green sides.
What is the probability of rolling a blue or red side?
Testing:
H0:μ=54.5
H1:μ<54.5
Your sample consists of 48 subjects, with a mean of 54.1 and standard deviation of 1.8.
Calculate the test statistic, rounded to 2 decimal places.
t=
Answer:
t = -1.54.
Step-by-step explanation:
The test statistic is:
[tex]t = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.
H0:μ=54.5
This means that [tex]\mu = 54.5[/tex]
Your sample consists of 48 subjects, with a mean of 54.1 and standard deviation of 1.8.
This means, respectively, that [tex]n = 48, \mu = 54.1, \sigma = 1.8[/tex]
Test statistic
[tex]t = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex]t = \frac{54.1 - 54.5}{\frac{1.8}{\sqrt{48}}}[/tex]
[tex]t = -1.54[/tex]
The test statistic is t = -1.54.
Mr. Moretti is making welcome bags to give to the 18 students in his homeroom on the first day of school. He puts m mechanical pencils in each bag. He puts twice as many regular pencils in each bag. What is the total number of pencils that Mr. Moretti gives to his students if he puts 3 mechanical pencils in each bag?M
Answer:
The total number of pencils that Mr. Moretti gives to his is 162.
Step-by-step explanation:
He puts 3 mechanincal pencils in each bag.
In each bag, there is also twice as many regular pencils, that is, 3*2 = 6 regular pencils.
So in each bag, 3 + 6 = 9 pencils.
What is the total number of pencils that Mr. Moretti gives to his students if he puts 3 mechanical pencils in each bag?
18 students, and each gets 9 pencils.
18*9 = 162
The total number of pencils that Mr. Moretti gives to his is 162.
Answer:
162 pencils
Step-by-step explanation:
i did the i ready lesson!
The first term of an arithmetic sequence is -5, and the tenth term is 13.
Find the common difference.
2
1.8
8/9
Answer:
Step-by-step explanation:
Let d be the common difference.
a₁₀ = a₁ + (10-1)d
13 = -5 + 9d
d = 2
It’s worth 13 points thank you!
:)
Answer: the answer is the 3rd bubble:)
Step-by-step explanation:
According to Newton's Second Law, if force equals 17 N and acceleration equals 8 m/s2, what is the mass in kilograms?
Answer as a number, rounded to the nearest thousandth?
Answer:
2.13kg
Step-by-step explanation:
fnet=ma
17=m(8)
17÷8 =m
2.13=m
Answer:
The mass is 2¹/₈, or 2.125, kg
Step-by-step explanation:
We know that force is equal to mass times acceleration, so given a force of 17 newtons and an acceleration of 8m/s², we can say:
[tex]f = ma\\m = f/a\\m = \frac{17\ N}{8\ m/s^2}\\m = \frac{17\ kg\times m/s^2}{8\ m/s^2}\\m = 17/8\ kg\\m = 2.125 kg[/tex]
giving us a mass of 2¹/₈, or 2.125 kg.
A bank loaned out $19,000, part of it at the rate of 7% per year and the rest at 15% per year. If the interest received i. 1 year totaled $2000, how much was loaned at 7%
Answer:
$28571.43 was loaned out.
Step-by-step explanation:
2000 x 100 / 7=28571.43
Answer:
$28571.43 was loaned.
this is because
2000 x 100 / 7
=28571.43
In ΔDEF, the measure of ∠F=90°, the measure of ∠D=69°, and FD = 64 feet. Find the length of DE to the nearest tenth of a foot.
Answer:
Step-by-step explanation:
Christina built a small hot air balloon and recorded the distance it traveler (v) during the first 4 seconds after starting (s)
Which of the following equations representd the relationship between the distance traveled and the elpsed time?
A: v=1.2s
B: s=1.2v
C:v=1.2+s
D:s=1.2+v
Table is attatched
Answer "v = 1.2s"
Step-by-step explanation: because 1.2 is 1*1.2, 2.4 is 2*1.2 and so on..
Find the area of the rectangle 2 1/4 1 1/2
Answer:
3 3/8
I converted the fractions in to decimals, multiplied them and then converted the decimal into a fraction.
A bouncy ball is dropped such that the height of its first bounce is 6.75
feet and each successive bounce is 68% of the previous bounce's
height. What would be the height of the 6th bounce of the ball? Round
to the nearest tenth (if necessary).
Step-by-step explanation:
0,4 ft
It can be convinient to let a spreedsheet compute the values for you
Here we have written an expiliclit formula for the height of the 9th bounce
H= 5.5 x 0.64'(n-1)
We have written the formuka this way beacause we are given the height of the firrrst bounce not the satrting height so as you see each bounce multiples the height by a factor of 0,64 then the 7th bounce will be
H= 5.5 x 0.64'6 = 0.378 = 0,4 feet
Hope it helpsAnswer: 1
Step-by-step explanation:
A package delivery company experiences high variability in daily customer demand, which in turn results in high variability in the daily workload at the central sorting facility. The company relies on its sorting facility employees working overtime to provide on-time delivery when the workload demand is very high. A sorting facility employee receives a salary of $12/hour for a 40 hour week, and the employee receives $18/hour for every hour worked overtime, that is, for every hour worked over 40 hours in a given week. The number of overtime hours that an employee works in any given week is a random variable, with a mean of 15 hours and a standard deviation of 4 hours.
Required:
What are the mean, the standard deviation, and the variance of an employee's total weekly salary?
Solution :
Let :
X = number of overtime hours
S = total weekly salary
S = [tex]$12 \times 40 + 18 \times X$[/tex]
S = 480 + 18X
E(S) = [tex]$480 + 18 \times E(X)$[/tex]
[tex]$E(S) = 480 + 18 \times 15$[/tex]
= 750
Mean of S = 750
Var (S) = [tex]$18^2 \times Var(X)$[/tex]
Var(S) = [tex]$18^2 \times 4^2$[/tex]
= 5184
Variance of S = 5184
The standard deviation equals square root of 5184 = 72
Please help me I will get you a thanks :-)
Answer:
A=32.5
Step-by-step explanation:
A=(4+9)*5/2
A=13*5/2
A=65/2
A=32.5
"Death Valley Hike"
A hiker in Death Valley begins the climb out of the valley from 150 feet below sea level. 5
minutes later, the hiker is 87.5 feet below sea level.
a) Write an equation that models this situation.
b) What is the y-intercept and what does it represent?
c) What is the x-intercept and what does it represent?
d) What is the slope and what does it represent?
e) What is the hiker's distance below sea level after 10 minutes?
Answer:
I'm pretty sure E
Step-by-step explanation:
think about it he traveled 70 feet in 5 minutes so he would still be below sea level
At a school, 40% of the sixth-grade students said that hip-hop is their favorite kind of music. If 68 sixth-grade students prefer hip hop music, how many sixth-grade students are at the school?
Answer:
170
Step-by-step explanation:
11 dived by 2=
Long divination pls help
Answer:
11/2 is 5 1/2 this is which is 5 remainer 1 if you are a lower grade. If not then the complete form is 5.5
Step-by-step explanation:
z^m-n (z^m+ z^m+n + z^n)
Answer:Your left hand side evaluates to:
m+(−1)mn+(−1)m+(−1)mnp
and your right hand side evaluates to:
m+(−1)mn+(−1)m+np
After eliminating the common terms:
m+(−1)mn from both sides, we are left with showing:
(−1)m+(−1)mnp=(−1)m+np
If p=0, both sides are clearly equal, so assume p≠0, and we can (by cancellation) simply prove:
(−1)(−1)mn=(−1)n.
It should be clear that if m is even, we have equality (both sides are (−1)n), so we are down to the case where m is odd. In this case:
(−1)(−1)mn=(−1)−n=1(−1)n
Multiplying both sides by (−1)n then yields:
1=(−1)2n=[(−1)n]2 which is always true, no matter what n is
What is the area of the base of the prism?
Answer:
your answer will be 6cm^2
Step-by-step explanation:
hope it helps you
have a great day
PLEASE HELP
A family originally bought a home for $712,980. Now, a few years later, the home is
worth $1,180,627.70. What was the percent of increase in its value? (Round your answer to
the nearest whole number.)
Answer:
86
Step-by-step explanation:
find the mad: 250, 249, 251, 253, and 253
Its 250 for sure i have not done mads for a while now.
So maybe double check me with someone else
Answer:
It's 1.44
Step-by-step explanation: