The population 5 years from now would be 60482
The population growth rate is given as:
[tex]r(t) = 400(1 + \frac{2t}{24 + t^2})[/tex]
The value of t, 5 years from now is represented as:
t = 5
Substitute 5 for t in the function r(t).
So, we have:
[tex]r(5) = 400(1 + \frac{2 \times 5}{24 + 5^2})[/tex]
Evaluate the exponent
[tex]r(5) = 400(1 + \frac{2 \times 5}{24 + 25})[/tex]
Evaluate the products
[tex]r(5) = 400(1 + \frac{10}{24 + 25})[/tex]
So, we have:
[tex]r(5) = 400(1 + \frac{10}{49})[/tex]
Divide 10 by 49
[tex]r(5) = 400(1 + 0.204)[/tex]
This gives
[tex]r(5) = 400(1.204)[/tex]
Expand
[tex]r(5) = 481.6[/tex]
The current population is given as 60000.
So, the population (P) 5 years from now would be
[tex]P = 60000 + 481.6[/tex]
[tex]P = 60481.6[/tex]
Approximate
[tex]P = 60482[/tex]
Hence, the population (P) 5 years from now would be 60482
Read more about population functions at:
https://brainly.com/question/20115298
Find the period of the function y=3/2 tan(1/3^x)
A) π/3
B) π/6
C) 3 π
D) π
the price of an article is Marked 25% above the cost price .if it is solid the profit of Rs.500 after allowing 15% discount .what will be it's selling price
Answer:
Rs 8500
Step-by-step explanation:
For a cost price of c, the marked price is ...
marked = c +25%·c = 1.25c
After the 15% discount, the sale price will be ...
s = marked -15%·marked = 0.85·marked = (0.85)(1.25c) = 1.0625c
The profit will be the difference between the sale price s and the cost c:
p = s -c
500 = (1.0625c) -c = 0.0625c
Then the cost is ...
500/0.0625 = c = 8000
and the sale price is ...
s = c +p = 8000 +500 = 8500 . . . rupees
The selling price will be Rs 8500.
Find the median of the numbers in the following list. 26, 13, 39, 22, 42,39, 18, 21, 32,14
Answer:
24
Step-by-step explanation:
13,14,18,21,22,26,32,39,39,42
middle is 22 and 26
therefore you add and divide by 2
then you'll get 24
your friend claims that the average maximum amount of time people can hold their breath is less than 60 seconds. to check whether your friend's claim is true, you take a random sample of the maximum amount of time 10 people can hold their breath. 42 45 47 50 58 60 61 63 64 68 assume the population is approximately normal. perform a hypothesis test to determine whether the average maximum amount of time people can hold their breath is less than 60 seconds. use the alpha =0.05 level of significance.
a. state the null and alternate hypothesis
b. compute the value of the test statistic. round your intermediate calculations and final answer to at least three decimal places.
c. give the p-value
d. determine whether to reject the null hypothesis
e. state a conclusion in the context of the question (in the story of the problem)
Using the t-distribution, it is found that:
a)
The null hypothesis is: [tex]H_0: \mu \geq 60[/tex]
The alternative hypothesis is: [tex]H_1: \mu < 60[/tex]
b) t = -1.47
c) 0.0878.
d) Do not reject the null hypothesis.
e) Not enough evidence to conclude that the average maximum amount of time people can hold their breath is less than 60 seconds.
Item a:
At the null hypothesis, it is tested if the mean is not less than 60 seconds, that is:
[tex]H_0: \mu \geq 60[/tex]
At the alternative hypothesis, it is tested if the mean is less than 60 seconds, that is:
[tex]H_1: \mu < 60[/tex]
Item b:
We can find the standard deviation for the sample, hence, the t-distribution is used to solve this question.
The test statistic is given by:
[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]
The parameters are:
[tex]\overline{x}[/tex] is the sample mean. [tex]\mu[/tex] is the value tested at the null hypothesis. s is the standard deviation of the sample. n is the sample size.With the help of a calculator to find the sample mean and the standard deviation, the values of the parameters are:
[tex]\overline{x} = 55.8, \mu = 60, s = 9.04, n = 10[/tex]
Hence, the value of the test statistic is:
[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]
[tex]t = \frac{55.8 - 60}{\frac{9.04}{\sqrt{10}}}[/tex]
[tex]t = -1.47[/tex]
Item c:
The p-value is found using a left-tailed test, as we are testing if the mean is less than a value, with 10 - 1 = 9 df and t = -1.47.
Using a t-distribution calculator, this p-value is of 0.0878.Item d:
The p-value is of 0.0878 > 0.05, hence, we do not reject the null hypothesis.
Item e:
Since the null hypothesis is not rejected, there is not enough evidence to conclude that the average maximum amount of time people can hold their breath is less than 60 seconds.
A similar problem is given at brainly.com/question/24826023
Does anyone know the answer please help!!
Help me with this plzzzzzzzzz
Answer:
B : x € (-∞, 1)
Step-by-step explanation:
we have 4x +9 -2 +3x < 14
7x +7 < 14
7(x+1) < 14
x + 1 < 2
x < 1
=> x € (-∞, 1)
For the point P(-25,10) and Q,(-18,15) find the distance d(P,Q) and the coordinates of the midpoint M of the segment PQ.
Step-by-step explanation:
I really hope that that will be helpful to you
Lieutenant James made an average of 3 arrests per week for 4 weeks. How many arrests does she need to make in the fifth week to raise her average to 4 arrests per week?
Answer:
5
Step-by-step explanation:
We want the average arrests to be 4. It can be done by calculating the average between the average arrests and arrests during the 5th week, so we get:
Avg(1,2,3,4,5) = (Avg(1,2,3,4) + A(5)) / 2
Where Avg(x) is the average of arrests in given weeks, and A(x) is the number of arrests in a given week.
Solving for A(5) => A(5) = 2*Avg(1,2,3,4,5) - Avg(1,2,3,4) = 2 * 4 - 3 = 8-3 = 5
The jazz band has 14 members. To raise money for a tour, each member sold r raffle tickets. Write an expression that shows the number of raffle tickets sold.
Answer:
14r
Step-by-step explanation:
since there are 14 members and each sold r tickets r x 14 which is 14r
Estimate 4 1/3 x 2 3/4
Answer:
11 11/12
Step-by-step explanation:
Answer:
≈ 12
Step-by-step explanation:
To estimate, we'll round these mixed numbers to the nearest whole number, then multiply. Let's start with 4 1/3. 4 1/3 is closest to 4, since 1/3 is smaller than 1/2. Then, we can look at 2 3/4. This mixed number is closest to 3, since 3/4 is greater than 1/2.
Now, the two numbers we have are 4 and 3. What is 4 × 3? Well, that's pretty simple - the answer is 12. So, 4 1/3 × 2 3/4 ≈ 12. Hopefully that's helpful! :)
give a pair of alternate interior angles, a pair of corresponding angles and a pair of alternate exterior angles.
What is an equation of the line that passes through the points (−3,8) and (-7, 8)
Answer:
y = 8
Step-by-step explanation:
Since the y- coordinates of the points are equal, both 8 , then
This indicates the line is horizontal and parallel to the x- axis with equation
y = c
where c is the value of the y- coordinates the line passes through
The line passes through (- 3, 8 ) and (- 7, 8 ) with y- coordinates 8 , then
y = 8 ← equation of line
How do you find the slope of a line given any 2 points on the line
Answer:
rise over run
Step-by-step explanation:
you look at the distance between the 2 points by looking at how many points its goes up or down, and you look at how points it goes from the left to the right or vice versa. but if you don't have a graph to look at, you will want to use the slope formula. look up the slope formula and plug it in.
Answer:
Step-by-step explanation:
From the point one on the graph, you go up (rise) making loops each time you go up (shown in red) then, once you've reached the same hight of point two, you go over (run), making loops once again (shown in blue). Then, you take the rise and put it over the run, so in the image attached it would be 4/3.
There is a rack of 7 billiards balls, numbered from 1 to 7. If one ball is selected at random, determine the odds against it being an odd-numbered ball.
The odds are 0:0
(Type whole numbers. Simplify your answer.)
Answer:
Step-by-step explanation:
seven options 1, 2, 3, 4, 5, 6, 7
three successes for it being even. 2, 4, 6
odds are 3:7 of against randomly drawing an odd numbered ball.
Helppp it’s due today
Answer:
128
Step-by-step explanation:
please solve this quick
9 times 11 = 0.818181...
Explain?
1) f(4) = g(4)
2) f(4) = g(-2)
3) f(2) = g(-2)
4) f(-2) = g(-2)
Answer: 4)
Step-by-step explanation:
f(4) = -14
g(4) = 10
g(-2) = 4
f(2) = -8
f(-2) = 4
The correct statement is 4) f(-2) = g(-2)
Or by inspection, we can see that the graph f(x) intersects g(x) at x = -2 and y = 4. So, f(-2) = g(-2) = 4 is true
8 with an exponent of 2 +9(12 divided by 3 x 2)-7 simplify with steps please
[tex]\huge \bf༆ Answer ༄[/tex]
Let's solve ~
[tex] \sf {8}^{2} + 9(12 \div 3 \times 2) - 7[/tex][tex] \sf64 + 9(4 \times 2) - 7[/tex][tex] \sf64 + 9(8) - 7[/tex][tex] \sf64 + 72 - 7[/tex][tex] \sf136 - 7[/tex][tex] \sf129[/tex]I need help asap very struggle with math
Answer:
16feet
part B is 18 feed for a good at a better than the price but the one
if your leg get cut off, where would you feel the pain if you got no leg. hehehe
Answer:
lol in your head , literally
Step-by-step explanation:
After one of your limbs is amputated, you may feel as if the limb is still there. This is called phantom sensation. You may feel: Pain in your limb even though it is physically not there.
Answer:
The nerve in your leg.
Explanation:
It's not your leg that will hurt but the nerve in your leg that'll hurt. So wherever the leg is cut, the nerves must be cut as well, but another thing is when one of your limbs is amputated, you may feel like the limb is still there. That's called phantom sensation. You might feel pain in your "limb" even though it's not physically there.
Which of the following tables represents a function?
A) x 1 −1 4 −4
y 8 8 10 10
B) x 2 2 3 3
y 6 −6 7 7
C) x 5 −5 5 −5
y 10 11 12 13
D) x 2 2 7 7
y 2 3 4 5
The only table that represents a function is table A
For a relation or table to represent a function, the input values (domain) must have a corresponding codomain (output) that is unique.
This means that there must not be two similar values as the domain in the table, if there is, such table does not represent a function.We can see that tables B, C, and D do not represent a function since they all have repeating values in their x-values.Hence the only table that represents a function is table A
Learn more on tables and functions here: https://brainly.com/question/3632175
For what values of x and y are the triangles to
the right congruent by HL?
M
X=1
35
=
and y=
Answer:
y=48
Step-by-step explanation:
180-135=55-7=y=48
hi, have a good day!
Which is the best estimate for the average rate of change for the quadratic function graph on the interval 0
Answer:
Step-by-step explanation:
0 is not an interval, it is just the origin
hard to make an estimate without knowing the limits.
average rate of change will be Δy / Δx or (y - y₀) / (x - x₀)
as (0, 0) is the origin and appears to be on the plot line, the average rate of change will be y/x for any other point on the curve relative to the origin.
EDIT
for interval 0 ≤ x ≤ 8
at x = 8 y appears to be -24
average change is -24 / 8 = -3
PLEASE HELP ME RN PLEASE
Answer:
1.
[tex] \frac{n^{2} - 1 }{2} [/tex]
2.
[tex] \sqrt{29} [/tex]
Step-by-step explanation:
Area of triangle=1/2×b×h
=
[tex] \frac{1}{2} \times (n - 1)(n + 1)[/tex]
[tex] \frac{( {n}^{2} + n - n - 1) }{2 } [/tex]
[tex] \frac{ {n}^{2} - 1 }{2} [/tex]
2. Area of triangle=14
[tex] \frac{ {n}^{2} - 1 }{2} = 14[/tex]
[tex] {n}^{2} - 1 = 28[/tex]
[tex] {n}^{2} = 29[/tex]
[tex]n = \sqrt{29} [/tex]
please rate well and mark BRAINLIEST.
thanks
help I have no clue what I'm doING
Answer:
3.0
4.5
6.0
7.5
Step-by-step explanation:
it rains at the rate of 1.5cm per hour
In two hours, the amount will be; 1.5 × 2
= 3cm
in the three hours, the amount will be 1.5×3
=4.5cm
in four hours, the amount will be; 1.5×4
=6cm
in five hours, the amount will be; 1.5×5
=7.5cm
I NEED HELP ON QUESTION B AND C ASAP.
Answer:
See belowStep-by-step explanation:
Part BAssumed the dimensions of the top and bottom parts are identical.
Since the cylindrical part has total height of 1.8 cm and the hemisphere volume is transferred to bottom part and the cone part is still full, the value of h is the difference of the total height of cylinder and full part of the top section of cylinder:
h = 1.8 cm - 0.3 cm = 1.5 cmPart CFind the volume of sand in the bottom part. It consists of a hemisphere and a cylinder of 1.5 cm height.
V(cylinder) = πr²h = 3.14*(2.6/2)²*1.5 ≈ 7.96 cm³V(hemisphere) = 2/3πr³ = 2/3*3.14*(2.6/2)³ ≈ 4.6 cm³Total sand in the bottom part:
7.96 + 4.6 = 12.56 cm³Time taken:
12.56 / 0.05 = 251.2 seconds = 4 min 11.2 secondsAt what rate would $1,200 earn $96 in 8 years?
ratio of boys to girls is 2:3 what is the ratio of boys of there are 6 girls
Answer:
4:6
Step-by-step explanation:
2 x
- = ----
3 6
6/3 = 2
2 x 2 = 4
Find the volume of a cone with a diameter of 12.9 cm and a height of 16.6 cm.
Answer:
112cm^3
Step-by-step explanation:
Formula for volume of a cone is:
[tex] \frac{1}{3} \times \pi \times {r}^{2} \times h[/tex]
r = radius and h = height
To find the radius you divide the diameter by 2:
12.9 ÷ 2 = 6.45
Now substitute values into the formula:
[tex] \frac{1}{3} \times \pi \times {6.45}^{2} \times 16.6[/tex]
Which equals 112cm^3