Step-by-step explanation:
Let the initial population of a community be P0 and the population after time t is P(t).
If the population of a community is known to increase at a rate proportional to the number of people present at time t, this is expressed as:
[tex]P(t) = P_0e^{kt}[/tex]
at t = 5 years, P(t) = 2P0
substitute:
[tex]2P_0 = P_0e^{5k}\\2 = e^{5k}\\ln2 = lne^{5k}\\ln2 = 5k\\k = \frac{ln2}{5}\\k = 0.1386[/tex]
If the population is 9,000 after 3 years
at t = 3, P(t) = 9000
a) Substitute into the formula to get P0
[tex]9000 = P_0e^{0.1386\times 3}\\9000 = P_0e^{0.4158}\\9000 = 1.5156P_0\\P_0 = \frac{9000}{1.5156}\\ P_0 = 5938.24[/tex]
Hence the initial population is approximately 5938.
b) In order to know how fast the population growing at t = 10, we will substitute t = 10 into the formula as shown:
[tex]P(10) = 5938.24e^{0.1386(10)}\\P(10) = 5938.24e^{1.386}\\P(10) = 5938.24(3.9988)\\P(10) = 23,745.97[/tex]
Hence the population of the community after 10 years is approximately 23,746
What is the slope of the line that passes through the points (8, 1) and (5, 7)?
Answer:
m= -2
Step-by-step explanation:
For future reference, you should try using Symbolab, it works really well and I use it ALL the time!
What is the measurement of G?
Answer:
59 Degrees!!
Step-by-step explanation:
Answer:
59°
Step-by-step explanation:
180 - (57 + 64) =
180 - 121 = 59
Romeo looks up at Juliet in her second-floor balcony at an angle of 57o. Of the balcony is 10 feet above the ground, how far is Romeo standing from the base of her house
Answer:
500
Step-by-step explanation:
50 points
explanation please
3f(-2)-4f(2)
Multiply a positive and a negative equals a negative: (+)×(-)=(-)
-3f×2-4f×2
Calculate the product
-6f-4f×2
-------------‐-------
-3f×2
Multiply a negative and a positive equals a negative: (-)×(+)=(-)
-(3×2)f
Multiply the numbers
-6f
-----------------------------------------------
-6f-8f
Collect like terms
-14f
ANSWER:-14f
PLEASE MARK ME AS BRAINLIEST
Answer:
14f is your answer
Step-by-step explanation:
A farmer has 107 acres on which to plant oats or corn. Each acre of oats requires $18 capital and 2 hours of labor. Each acre of corn requires $36 capital and 6 hours
of labor. Labor costs are $8 per hour. The farmer has $2100 available for capital and $2400 available for labor. If the revenue is $47 from each acre of oats and $111
from each acre of corn, what planting combination will produce the greatest total profit? (Profit here is revenue plus leftover capital and labor cash reserve.) What is
the maximum profit?
orn
Answer:
$6049.63Step-by-step explanation:
the objective is to maximize profit
let x be corn and y be oat
let us begging by formulating the linear program for the problem
The objective function is
111x+47y=P
The constraints are
1. capital
36x+18y=2100------------1
2. labor
6x(8)+2y(8)=2400
48x+16y=2400-------------2
solving 1 and 2 we apply substitution method
36x+18y=2100------1
36x=2100-18y
x=(2100-18y)/36
put x=(2100-18y)/36 in 2 we have
48(2100-18y)/36+16y=2400
(100800-864y)/36+16y=2400
2800-24y+16y=2400
-8y=2400-2800
-8y=-400
8y=400
y=400/8
y=50
to find x put y=50 in 36x+18y=2100------------1
36x+18(50)=2100------------1
36x+900=2100
36x=2100-900
36x=1200
x=1200/36
x=33.33
profit is
111x+47y=P
111(33.33)+47(50)=P
3699.63+2350=P
P=6049.63
$6049.63
the planning comnination is to work on
33.33 acre of corn and 50 acre of oat
Question 3 of 6 (1 point) Attempt 33 of Unlimited View question in a popup
2.4 Section Exercise 6
In a study of 550 meals served at 75 campus cafeterias, 77 had less than 10 grams of fat but not less than 350 calories; 81 had
less than 350 calories but not less than 10 grams of fat; 186 had over 350 calories and over 10 grams of fat.
Part: 0/2
E
Part 1 of 2
(a) What percentage of meals had less than 10 grams of fat? Round your answer to the nearest tenth of a percent.
of the meals studied, 1% of them had less than 10 grams of fat.
Answer:
10%
Step-by-step explanation:
(a) What percentage of meals had less than 10 grams of fat?
(b) Round your answer to the nearest tenth of a percent.
To find the percentage of meals with less than 10 grams of fat, count the number of meals with less than 10 grams of fat and divide by the total number of meals; multiply this figure by a hundred.
(A) Total number of meals = 550
Number of meals having less than 10 grams of fat = 77
Percentage of meals having less than 10 grams of fat = 77/550 × 100
= 0.14 × 100 = 14%
(B) Rounding the answer to the nearest tenth of a percent means approximating it to the nearest multiple of 10 that is not more than 100 (where 100 here represents a full cent or 'percent').
The multiples of 10 that are close to 14 are 10 and 20. The closest being 10, your answer becomes 10%
What is the value of X?
Answer:
80 degrees
Step-by-step explanation:
The total sum of all angles is 180 in every triangle, 70 + 30 = 100, 180 - 100 = 80
The Answer is 80 degrees
Pls help me on my mathhhh
I can’t do it cuzzzz I’m dummmmm bro
Answer:
C
Step-by-step explanation:
Slope equals rise over run, which means the change in y for every x value. On the table, we see that y increases by 10 and x increases by 2, so that would be 10/2. However, the slope must be shown in the simplest form so divide the fraction by 2 to get the final slope, 5/1=5.
To get the intercept you must find when x=0. Since the lowest x-value on the graph is 2 we need to subtract the slope twice to get to zero. So 10-5-5, which equals 0.
The equation would be y=5x.
x={(2,4),(3,4),(4,4),(5,4) The Range of x is
Answer:
2-5
Step-by-step explanation:
Each of 7 students reported the number of movies they saw in the past year. Here is what they reported.
13, 8, 18, 19, 13, 14, 12
Find the mean number of movies that the students saw.
If necessary, round your answer to the nearest tenth.
Answer:
13.9
Step-by-step explanation:
The mean of a set of numbers is the sum divided by the number of terms
What is the answer for 2
If the data below were represented with a stem-and-leaf plot, a stem of 2
would have how many leaves?
17, 22, 53, 74, 42, 26, 93, 15, 67, 29, 50
A. 2
B. 3
C. 4
D. 5
A stem of 2 would have 3 leaves.
The correct answer is option (B) 3.
What is stem-and-leaf plot?"It is a special table where each data value is split into a 'stem' (the first digit) and a 'leaf'( the last digit)."
For given data,
17, 22, 53, 74, 42, 26, 93, 15, 67, 29, 50
A stem-and-leaf representation would be:
Stem Leaf/leaves
1 7, 5
2 2, 6, 9
4 2
5 3, 0
6 7
7 4
9 3
From above plot, we can observe that a stem of 2 would have three leaves.
Therefore, option (B) is the correct answer.
Learn more about stem-and-leaf plot here:
https://brainly.com/question/12857419
#SPJ2
Simon & Iris earned money
by selling candy. They
earned $12 by recycling.
They split the total and
each got $100. How much
did they earn selling
candy?
Answer:
[tex]Candy = \$188[/tex]
Step-by-step explanation:
[tex]Recycling = \$12[/tex] ---- earnings
[tex]Each = \$100[/tex] --- individual earnings
[tex]Individuals = 2[/tex] ---- Simon & Iris
Required
Determine earnings of selling candy
First, we need to determine the total earnings.
[tex]Total\ Earnings = Individuals * Individual\ Earnings[/tex]
[tex]Total\ Earnings = 2 * \$100[/tex]
[tex]Total\ Earnings = \$200[/tex]
Since the total earnings is from recycling and candy, we have:
[tex]Candy + Recycling = Total\ Earnings[/tex]
[tex]Candy + \$12= \$200[/tex]
[tex]Candy = \$200 - \$12[/tex]
[tex]Candy = \$188[/tex]
Jon reads 23 pages per hour. In all. How many hours of reading will Jon have to do this
week in order to have read a total of 46 pages?
Answer:
he would have to read 3.307692308 hour
Step-by-step explanation:
Suppose the average yearly salary of an individual whose final degree is a master's is $40 thousand less than twice that of an individual whose final degree is a bachelor's. Combined, two people with each of these educational attainments earn $119 thousand. Find the average yearly salary of an individual with each of these final degrees. HELP ME!
Bachelor's degree salary = $53000
Master's degree salary = $66000
Step-by-step explanation:
Given that :
Let Salary of bachelor's degree holder = x
Salary of Master's degree holder = 2x - 40000
Master's salary + bachelor's salary = $119,000
Hence,
Master's salary + bachelor's salary = 119,000
2x - 40000 + x = 119,000
3x = 119000 + 40000
3x = 159000
x = 159000 / 3
x = $53,000
Bachelor's degree salary = $53,000
Master's degree salary ; 2x - 40000 ; 2(53000) - 40000 = $106,000 - $40,000 = $66000
the following shape is made by cutting an equilateral triangle from rectangle find its perimeter
Answer:
47.6 cm
Step-by-step explanation:
Since the triangle is equilateral then the 2 inclined sides = 7.2 cm
Perimeter is then the sum of the 5 sides
P = 13 + 7.2 + 13 + 7.2 + 7.2 = 47.6 cm
Find the sum of 15 and the difference between 9 and 5.
Answer:
9 and 5 is thesum of 15
5×3=15and in sum 15×3=45 and 5×9 =45 and 9 and 45 cut and remaining 5
thus the different between is solve
Find the slope and the y-intercept of the line.
y=2x-9
Answer: The Slope Is: m=2. The y -intercept Is: b=9 or (0,9) hope this helps :)
Step-by-step explanation:
list the first six nonzero multiples of 16? ANSWER IT!!!!
Answer:
2, 8
Step-by-step explanation:
What isthmus solution to the equation 2x+2=10
Answer:
addition
Step-by-step explanation:
Answer:
4
Step-by-step explanation:
10-2=8
8/2=4
Hope this helps!
What is the y-intercept of the line?
YA
2
-2
-2
0
Answer:
1 the line hits the y line at 1
12.5.17
Two dice are rolled.
a) Determine the number of points in the sample space.
b) Determine the probability that a double (a 1, 1 or 2, 2, etc.) is rolled.
c) Determine the probability that a sum of 6 is rolled.
d) Determine the probability that a sum of 11 is rolled.
e) Are you as likely to roll a sum of 6 as you are of rolling a sum of 11?
a) There are 36 points in the sample space.
b) The probability that a double is rolled is
(Simplify your answer.)
Answer:
(a) 36 points
(b) Pr(rolling a double number) ≅ 0.167
(c) Pr(a sum of 6 is rolled) ≅ 0.139
(d) Pr(a sum of 11 is rolled) ≅ 0.056
(e) No.
Step-by-step explanation:
Sample space = {1,1 1,2 1,3 1,4 1,5 1,6 2,1 2,2 2,3 2,4 2,5 2,6 3,1 3,2 3,3 3,4 3,5 3,6 4,1 4,2 4,3 4,4 4,5 4,6 5,1 5,2 5,3 5,4 5,5 5,6 6,1 6,2 6,3 6,4 6,5 6,6}
(a) The number of points in the sample space is 36.
(b) Pr(rolling a double number) = [tex]\frac{6}{36}[/tex]
= [tex]\frac{1}{6}[/tex] ≅ 0.167
(c) Pr(a sum of 6 is rolled) = [tex]\frac{5}{36}[/tex] ≅ 0.139
(d) Pr(a sum of 11 is rolled) = [tex]\frac{2}{36}[/tex]
= [tex]\frac{1}{18}[/tex] ≅ 0.056
(e) No. It is more likely to roll a sum of 6 than that a sum of 11.
Jade used 3/4
yard of fabric to make a scart. Can she make 2 of these scarves with 1 4/5 yards of fabric, and why?
Answer:
Yes she can
Step-by-step explanation:
3/4 = 0.75
1 4/5= 1.8
0.75 x 2 = 1.5 which is less that 1.8 so she can
Find the midpoint M of the line segment joining the points P = (3, - 7) and Q = (-7, 1).
Answer:
The answer is (-2 , - 3)Step-by-step explanation:
The midpoint M of two endpoints of a line segment can be found by using the formula
[tex]M = ( \frac{x1 + x2}{2} , \: \frac{y1 + y2}{2} ) \\ [/tex]
where
(x1 , y1) and (x2 , y2) are the points
So we have
[tex]m = ( \frac{3 - 7}{2} , \frac{ - 7 + 1}{2} ) \\ = ( - \frac{4}{2} , - \frac{6}{2} )[/tex]
We have the final answer as
( - 2 , - 3)Hope this helps you
Step-by-step explanation:
Hey there!
The given points are; P(3,-7) and Q(-7,1)
Note: Use midpoint formula.
[tex]midpoint(x,y) = (\frac{x1 + x2}{2} , \frac{y1 + y2}{2} )[/tex]
Put all values.
[tex](x,y) =( \frac{3 - 7}{2} , \frac{ - 7 + 1}{2} )[/tex]
Simplify it.
[tex](x,y) = (-2 , - 3[/tex])
Therefore, midpoint is (-2 ,-3).
Hope it helps...
A racing car consumes a mean of 106 gallons of gas per race with a standard deviation of 6 gallons. If 33 racing cars are randomly selected, what is the probability that the sample mean would be greater than 103.7 gallons? Round your answer to four decimal places.
Answer:
The probability is [tex]P(\= X > 103.7 ) = 0.9862 [/tex]
Step-by-step explanation:
From the question we are told that
The population mean is [tex]\mu = 106 \ gallons[/tex]
The population standard deviation is [tex]\sigma = 6 \ gallons[/tex]
The sample size is [tex]n = 33[/tex]
Generally the standard deviation of sample mean is mathematically represented as
[tex]\sigma_{x} = \frac{\sigma }{\sqrt{n} }[/tex]
=> [tex]\sigma_{x} = \frac{6}{\sqrt{33} }[/tex]
=> [tex]\sigma_{x} = 1.044[/tex]
Generally the probability that the sample mean would be greater than 103.7 gallons is mathematically represented as
[tex]P(\= X > 103.7 ) = P(\frac{X - \mu }{\sigma_{x}} > \frac{103.7 - 106}{1.044 } )[/tex]
Generally [tex]\frac{X - \mu }{\sigma_{x}} = Z (The \ standardized \ value \ of \= X )[/tex]
So
[tex]P(\= X > 103.7 ) = P(Z > -2.203 )[/tex]
From the z table the probability of (Z > -2.203 ) is
[tex]P(Z > -2.203 ) = 0.9862[/tex]
So
[tex]P(\= X > 103.7 ) = 0.9862 [/tex]
A polynomial function has roots -5 and 1. Which
of the following could represent this function?
f(x) = (x + 5)(x + 1)
f(x) = (x - 5)(x - 1)
f(x) = (x - 5)(x + 1)
f(x) = (x + 5Yx - 1)
Answer:
f(x) = (x + 5)(x - 1)
Step-by-step explanation:
f(x) = (x + 5)(x - 1) has the roots of -5 and 1, when you set each factor equal to zero.
x + 5 = 0
x = -5
So, -5 is a root of the function.
x - 1 = 0
x = 1
So, 1 is the other root of the function.
f(x) = (x + 5)(x - 1) is the polynomial function with the roots of -5 and 1
Are of a rectangle 4ft by 1/2ft
Answer:
2
Step-by-step explanation:
Answer:
2ft squared
Step-by-step explanation:
4ft ⋅ 0.5 = 2ft
(0.5 is the same as 1/2)
Hope I helped :)
Please consider Brainliest :)
20 Points.........................
A polynomial has a leading coefficient of 1 and the following roots. What is the factored form of the polynomial?
3, Sqrt 3
A. g(x)= (x- 3) (x- sqrt(3)) (x+ sqrt(3))
B. g(x) = (x + 3) (x- sqrt(3)) (x+ sqrt(3))
C. g(x) = (x- 3) (x- sqrt(3))
D. g(x) = (x + 3) (x+ sqrt(3))
The equation for line A is shown below: Y= -2/3x-4 Line A and Line B are perpendicular, and the point (-2 , 1) lies on Line B. Which equation Below represents line B?
Answer:
[tex]y = \frac{2}{3}x + \frac{7}{3}[/tex]
Step-by-step explanation:
Given
Line A:
[tex]y = -\frac{2}{3}x - 4[/tex]
Line B:
[tex](-2,1)[/tex]
Required
Determine the equation of Line B
First, we need to determine the slope of A using
[tex]y =mx + b[/tex]
Where:
[tex]m = slope[/tex]
By comparison:
[tex]y = -\frac{2}{3}x - 4[/tex]
[tex]m = -\frac{2}{3}[/tex]
Since A and B are perpendicular:
The slope of B (m2) is:
[tex]m_2 = \frac{-1}{m}[/tex]
[tex]m_2 = -1/\frac{-2}{3}[/tex]
[tex]m_2 = -1 * \frac{-3}{2}[/tex]
[tex]m_2 = \frac{3}{2}[/tex]
The equation of B is calculated as thus:
[tex]y - y_1 = m(x - x_1)[/tex]
Where
[tex](x_1,y_1) = (-2,1)[/tex]
[tex]m = \frac{2}{3}[/tex]
So, the equation becomes
[tex]y - 1 = \frac{2}{3}(x - (-2))[/tex]
[tex]y - 1 = \frac{2}{3}(x + 2)[/tex]
Open bracket
[tex]y - 1 = \frac{2}{3}x + \frac{4}{3}[/tex]
Make y the subject
[tex]y = \frac{2}{3}x + \frac{4}{3} + 1[/tex]
[tex]y = \frac{2}{3}x + \frac{4 + 3}{3}[/tex]
[tex]y = \frac{2}{3}x + \frac{7}{3}[/tex]
In 2016, Southwest Airlines boasted that 70% of its flights were on time. If we select 8 Southwest flights at random and assume independence, what is the probability that at least 3 flights are on time
Answer: 0.9887
Step-by-step explanation:
Let p be the probability that flights are on time.
As per given, p =70% = 0.7
Sample size : n = 8
Let x be a binomial variable that represents the number of fights are on time ( i.e. success).
Using binomial formula: [tex]P(X=x) = \ ^nC_xp^x(1-p)^{n-x}[/tex]
Now, the probability that at least 3 flights are on time = [tex]P(X\geq 3)=1-P(X<3)\\\\=1-[P(X=0)+P(X=1)+P(X=2)]\\\\=1-[^8C_0(0.7)^0(0.3)^8+^8C_1(0.7)^1(0.3)^7+^8C_2(0.7)^2(0.3)^6]\\\\=1-[(0.3)^8+8(0.7)(0.3)^7+\dfrac{8!}{2!6!}(0.7)^2(0.3)^6]\\\\=1-[0.00006561+0.00122472+0.01000188]\\\\=1-0.01129221\\\\=0.98870779\approx\ 0.9887[/tex]
The probability that at least 3 flights are on time = 0.9887