The question is incomplete. The complete question is :
The population of a certain town was 10,000 in 1990. The rate of change of a population, measured in hundreds of people per year, is modeled by P prime of t equals two-hundred times e to the 0.02t power, where t is measured in years since 1990. Discuss the meaning of the integral from zero to twenty of P prime of t, d t. Calculate the change in population between 1995 and 2000. Do we have enough information to calculate the population in 2020? If so, what is the population in 2020?
Solution :
According to the question,
The rate of change of population is given as :
[tex]$\frac{dP(t)}{dt}=200e^{0.02t}$[/tex] in 1990.
Now integrating,
[tex]$\int_0^{20}\frac{dP(t)}{dt}dt=\int_0^{20}200e^{0.02t} \ dt$[/tex]
[tex]$=\frac{200}{0.02}\left[e^{0.02(20)}-1\right]$[/tex]
[tex]$=10,000[e^{0.4}-1]$[/tex]
[tex]$=10,000[0.49]$[/tex]
=4900
[tex]$\frac{dP(t)}{dt}=200e^{0.02t}$[/tex]
[tex]$\int1.dP(t)=200e^{0.02t}dt$[/tex]
[tex]$P=\frac{200}{0.02}e^{0.02t}$[/tex]
[tex]$P=10,000e^{0.02t}$[/tex]
[tex]$P=P_0e^{kt}$[/tex]
This is initial population.
k is change in population.
So in 1995,
[tex]$P=P_0e^{kt}$[/tex]
[tex]$=10,000e^{0.02(5)}$[/tex]
[tex]$=11051$[/tex]
In 2000,
[tex]$P=10,000e^{0.02(10)}$[/tex]
[tex]=12,214[/tex]
Therefore, the change in the population between 1995 and 2000 = 1,163.
Suppose the weights of apples are normally distributed with a mean of 85 grams and a standard deviation of 8 grams. The weights of oranges are also normally distributed with a mean of 131 grams and a standard deviation of 20 grams. Amy has an apple that weighs 90 grams and an orange that weighs 155 grams.
Required:
a. Find the probability a randomly chosen apple exceeds 100 g in weight.
b. What weight do 80% of the apples exceed?
Answer:
a) 0.0304 = 3.04% probability a randomly chosen apple exceeds 100 g in weight.
b) The weight that 80% of the apples exceed is of 78.28g.
Step-by-step explanation:
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.
Weights of apples are normally distributed with a mean of 85 grams and a standard deviation of 8 grams.
This means that [tex]\mu = 85, \sigma = 8[/tex]
a. Find the probability a randomly chosen apple exceeds 100 g in weight.
This is 1 subtracted by the p-value of Z when X = 100. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{100 - 85}{8}[/tex]
[tex]Z = 1.875[/tex]
[tex]Z = 1.875[/tex] has a p-value of 0.9697
1 - 0.9696 = 0.0304
0.0304 = 3.04% probability a randomly chosen apple exceeds 100 g in weight.
b. What weight do 80% of the apples exceed?
This is the 100 - 80 = 20th percentile, which is X when Z has a p-value of 0.2, so X when Z = -0.84.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-0.84 = \frac{X- 85}{8}[/tex]
[tex]X - 85 = -0.84*8[/tex]
[tex]X = 78.28[/tex]
The weight that 80% of the apples exceed is of 78.28g.
Find the value of x in the given figure using properties of parallel lines.
Answer:
x =42
Step-by-step explanation:
x and 138 are same side interior angles. Same side interior angles are supplementary when the lines are parallel
x+138 = 180
x = 180-138
x =42
Answer:
42°
Step-by-step explanation:
138° + x = 180°
180° - 138° = 42°
(2x - y + 3) (2x - y - 3)using identities
Step-by-step explanation:
(2x-y+3)(2x-y-3)=
4x²-2xy-6x-2xy+y²+3y+6x-3y-9=
4x²-4xy+y²-9=
(2x-y)²-9
The average age of the 12 people in a classroom is 10. After Ms. Xu walks into the room,
the average age of everyone in the classroom increases to 12. How old is Ms. Xu?
Answer:
24
Step-by-step explanation:
First: 12*10=120
Then: 12*12=144
=> Ms. Xu's old: 144-120=24
A researcher has obtained the number of hours worked per week during the summer for a sample of 15 students. 40 25 35 30 20 40 30 20 40 10 30 20 10 5 20 Using this data set, compute the following: a. Median b. Mean c. Mode d. 40th percentile e. Range f. Sample variance g. Standard deviation
Answer:
Mean = 25
Median = 25
Mode = 6
Step-by-step explanation:
Given the data :
Using calculator :
Mode = highest occurring data point
Range = max - min = 40 - 5 = 35
Sample variance = 128.57 (calculator)
Sample standard deviation = sqrt(variance) = 11.34
Are these triangles congruent?
Answer:
yes...
Step-by-step explanation:
its a congrate triangle
Complete the expressions.
Write each answer as a number, a variable, or the product of a number and a variable.
=7r6
=
7r
Commutative property of multiplication
=
Multiply
Complete question :
Complete the expressions Write each answer as a number, a variable, or the product of a number and a variable 7(9r + 2) = 7 . 9r + 7 . ___ = ___ +
Answer:
2 ; 63r ; 14
Step-by-step explanation:
Given :
7(9r + 2)
Opening the bracket :
7*9r + 7*2 - - - - (1)
Taking the product
63r + 14 - - - - (2)
Now filling the blanks :
First blank corresponds to 2 (from (1))
Second blank corresponds to 63r (from (2))
Third blank should be 14
A payday loan company charges a $90 fee for a $500 payday loan that will be repaid in 16 days.
Treating the fee as interest paid, what is the equivalent annual interest rate?
Answer:
Kindly check explanation
Step-by-step explanation:
Given :
Interest amount paid on loan = $90
Principal value, amount borrowed = $500
Period, t = 16 days
The equivalent annual interest :
Using the simple interest formula :
simple interest = principal * rate * time
Using, days of year = 365
Plugging in the values into the formula :
90 = 500 * rate * (16/365)
90 = 500 * rate * 0.0438356
90 = 21.917808 * rate
Rate = 90 / 21.917808
Rate = 4.10 = 4.10 * 100% = 410%
If days of year = 360 is used :
90 = 500 * rate * (16/360)
Rate = 90 / 22.222
Rate = 4.05 = 4.105 * 100% = 405%:
17.
What is the value of the expression
2a + 5b + 3c for a = 12, b = 6, and
C=3?
A 10
B 21
C49
D 63
D. 63
2a+5b+3c
2(12)+5(6)+3(3)
24+30+9=63
Hope this helps! :)
HELP MATH ANSWER QUESTION
Answer:
x = 84 , y = 168
Step-by-step explanation:
[tex]Sin 60 = \frac{opposite side}{hypotenuse}\\\\ \frac{\sqrt{3}}{2}= \frac{AB}{BC}\\\\ \frac{\sqrt{3}}{2} = \frac{84\sqrt{3}}{y}\\\\Cross\ multiply ,\\\\y*\sqrt{3} =2*84 \sqrt{3}\\\\y= \frac{2*84*\sqrt{3}}{\sqrt{3}}\\\\y=168[/tex]
[tex]Cos\60 = \frac{adjacent}{hypotenuse}\\\\ \frac{1}{2}= \frac{AC}{BC}\\\\ \frac{1}{2}= \frac{x}{168}\\\\ \frac{1}{2}*168=x\\\\x= 84[/tex]
At Dubai English School, 549 students use buses to go to school. If this number is 75% of the total school enrollment, then how many students are enrolled in total?
Which statements are true of the given function?
Check all that apply.
9514 1404 393
Answer:
B, E
Step-by-step explanation:
The table tells you that f(0) = 3/2. (0 is found in the x-column; 3/2 is found in the f(x) column.)
__
You can find f(4) by evaluating the formula.
f(4) = 1/2·4 +3/2 = 4/2 +3/2
f(4) = 7/2 . . . . agrees with last answer choice
Answer:
A ,B and E ;)
Step-by-step explanation:
Find Length of x line OR
Both figures r similar (given )
so :-[tex] \frac{5}{2.5} = \frac{3}{1.5} = \frac{2}{1} = \frac{4}{x} \\ \frac{2}{1} = \frac{4}{x} \\ \frac{ \cancel{2}}{1} = \frac{ \cancel{4}^ { \tiny{2}}}{x} \\ x = 2 \: \: ans[/tex]
A box with a square base and open top must have a volume of 256000 c m 3 . We wish to find the dimensions of the box that minimize the amount of material used. First, find a formula for the surface area of the box in terms of only x , the length of one side of the square base.
Answer:
Follows are the response to the given question:
Step-by-step explanation:
The volume of the box:
[tex]V = x\times x \times h = 256000 \ cm^3\\\\\to x^2 \times h = 256000\\\\\to h = \frac{256000}{x^2}[/tex]
The surface area of the open box is:
[tex]A(x) = x \times x + 2 \times (x \times h +x \times h)\\\\A(x) = x^2 + 4 \times x \times h\\\\A(x) = x^2 + \frac{1024000}{x}\\\\\frac{d(x^n)}{dx} = n \times x^{(n - 1)}\\\\[/tex]
Use above formula
[tex]A'(x) = 2 \times x - \frac{1024000}{x^2}\\\\[/tex]
[tex]A'(x) = 0\\\\2\times x - \frac{1024000}{x^2} = 0\\\\2x = \frac{1024000}{x^2}\\\\x^3 = 512000\\\\x = (512000)^{(\frac{1}{3})} = 80\ cm\\\\[/tex]
Now
[tex]A''(x) = 2\times 1 + 2\times \frac{1024000}{x^3}\\\\A''(x) = 2 + \frac{2048000}{x^3}\\\\x = 80 \ cm\\\\A''(80) = 2 + \frac{2048000}{80^3} = 6\\\\[/tex]
therefore [tex]A"(x) > 0,[/tex] x amount of material used in minimum.
[tex]h = \frac{256000}{80^2} = 40\ cm[/tex]
Which expression are greater than 1/2? Choose all the apply
Answer:
25/30
5/8
Step-by-step explanation:
Which fraction is it out of all of these 6/14,5/8,25/30,or 3/6?
to determine which fractions are greater than 1/2, convert the fractions to decimals
to convert to decimals, divide the numerator by the denominator
1/2 = 0.5 less than half
6/14 = 0.43 less than half
5/8 = 0.625 greater than half
25 / 30 = 0.83 greater than half
3 / 6 = 0.5 equal to half
Your manager is trying to determine what forecasting method to use. Based upon the following historical data, calculate the following forecast and specify what procedure you would utilize.MONTH DEMANDJanuary 59February 65March 65April 67May 71June 70July 77August 77September 77October 75November 83December 81Calculate the simple three-month moving average forecast for April through December. What is the forecast for December? (Round your answer to 2 decimal places)a) 78.33b) 74.67c) 76.33d) 77.00Calculate the weighted three-month moving average using weights of 0.50 (t-1), 0.30 (t-2), and 0.20 (t-3) for April through December. What is the forecast for December? (Round your answer to 2 decimal places)a) 79.40b) 77.00c) 76.00d) 73.70Calculate the single exponential smoothing forecast for February through December using an initial forecast (F1=F-January) of 63. (Use alpha of 0.2) What is the forecast for December? (Round your answer to 2 decimal places) a) 66.30b) 74.37c) 72.22d) 71.52Calculate the mean absolute deviation (MAD) for the forecasts made by each technique in April through December. Which forecasting method do you prefer? (Round your answer to 2 decimal places)a) 3-month moving average (4.15)b) 3-month weighted moving average (3.99)c) Exponential smoothing method (alpha=0.30) (3.58)d) 3-month weighted moving average (3.58)
Answer:
Following are the solution to the given question:
Step-by-step explanation:
Please find the attached file.
For question 1:
Forecast for December:
[tex]\to \frac{(77+75+83)}{3} \\\\ \to 78.33[/tex]
For question 2:
Forecast for December:
[tex]\to (77 \times .5+75 \times 3+83 \times .2) \\\\\to 79.40[/tex]
For question 3:
Forecast for December:
[tex]\to 72.22+(83-72.22)\times 0.2 \\\\\to 74.37[/tex]
For question 4:
So, the 3-month weighted moving average (3.58)
Part A: Factor x2b2 − xb2 − 6b2. Show your work.
Part B: Factor x2 + 4x + 4. Show your work.
Part C: Factor x2 − 4. Show your work
Answer:
A.2b2(x2-x-3)
B.x2+2x+2x+4
=x(x+2)+2(x+2)
=(x+2)(x+2)
C.x2-2^2
=(x+2)(x+2)
can anyone pls answer this! it's really urgent!
Answer:
The answer is C
Step-by-step explanation:
You need to find a common denominator and in this case its 20. SO you change 3/4ths to 15/20 and 4/5ths to 16/20ths and 19/20 stays the same. Then you cancel out the 20 because its all the same number (I think) and you have your answer.
What is the slope of the line represented by this equation?
-3x + 8y = 12
A -8/3
B -3/8
C 3/8
D 8/3
Answer:
C. 3/8
Step-by-step explanation:
[tex] - 3x + 8y = 12 \\ \therefore 8y =3x + 12 \\ \therefore \: y = \frac{3}{8} x + 12 \\ equating \: it \: with \\ y = mx + b \: we \: find: \\ m = \frac{3}{8} \\ \therefore \: slope = \frac{3}{8} [/tex]
The answer above is wrong I took the test. It's in the picture below!
I don’t really understand how to do this
Answer:
<A = 63degrees
Step-by-step explanation:
From triangle DEF;
<D + <E + <F = 180
87 + 30 + <F = 180
117 + <F = 180
<F = 180 - 117
<F = 63degrees
Since <A = <F based on similarities, then <A = 63degrees
In a regression analysis involving 30 observations, the following estimated regressionequation was obtained.y^ =17.6+3.8x 1 −2.3x 2 +7.6x 3 +2.7x 4For this estimated regression equation SST = 1805 and SSR = 1760. a. At \alpha =α= .05, test the significance of the relationship among the variables.Suppose variables x 1 and x 4 are dropped from the model and the following estimatedregression equation is obtained.y^ =11.1−3.6x 2 +8.1x 3For this model SST = 1805 and SSR = 1705.b. Compute SSE(x 1 ,x 2 ,x 3 ,x 4 )c. Compute SSE (x2 ,x3 ) d. Use an F test and a .05 level of significance to determine whether x1 and x4 contribute significantly to the model.
Answer:
(a) There is a significant relationship between y and [tex]x_1, x_2, x_3, x_4[/tex]
(b) [tex]SSE_{(x_1 ,x_2 ,x_3 ,x_4) }= 45[/tex]
(c) [tex]SSE_{(x_2,x_3)} = 100[/tex]
(d) [tex]x_1[/tex] and [tex]x_4[/tex] are significant
Step-by-step explanation:
Given
[tex]y = 17.6+3.8x_1 - 2.3x_2 +7.6x_3 +2.7x_4[/tex] --- estimated regression equation
[tex]n = 30[/tex]
[tex]p = 4[/tex] --- independent variables i.e. x1 to x4
[tex]SSR = 1760[/tex]
[tex]SST = 1805[/tex]
[tex]\alpha = 0.05[/tex]
Solving (a): Test of significance
We have:
[tex]H_o :[/tex] There is no significant relationship between y and [tex]x_1, x_2, x_3, x_4[/tex]
[tex]H_a :[/tex] There is a significant relationship between y and [tex]x_1, x_2, x_3, x_4[/tex]
First, we calculate the t-score using:
[tex]t = \frac{SSR}{p} \div \frac{SST - SSR}{n - p - 1}[/tex]
[tex]t = \frac{1760}{4} \div \frac{1805- 1760}{30 - 4 - 1}[/tex]
[tex]t = 440 \div \frac{45}{25}[/tex]
[tex]t = 440 \div 1.8[/tex]
[tex]t = 244.44[/tex]
Next, we calculate the p value from the t score
Where:
[tex]df = n - p - 1[/tex]
[tex]df = 30 -4 - 1=25[/tex]
The p value when [tex]t = 244.44[/tex] and [tex]df = 25[/tex] is:
[tex]p =0[/tex]
So:
[tex]p < \alpha[/tex] i.e. [tex]0 < 0.05[/tex]
Solving (b): [tex]SSE(x_1 ,x_2 ,x_3 ,x_4)[/tex]
To calculate SSE, we use:
[tex]SSE = SST - SSR[/tex]
Given that:
[tex]SSR = 1760[/tex] ----------- [tex](x_1 ,x_2 ,x_3 ,x_4)[/tex]
[tex]SST = 1805[/tex]
So:
[tex]SSE_{(x_1 ,x_2 ,x_3 ,x_4)} = 1805 - 1760[/tex]
[tex]SSE_{(x_1 ,x_2 ,x_3 ,x_4) }= 45[/tex]
Solving (c): [tex]SSE(x_2 ,x_3)[/tex]
To calculate SSE, we use:
[tex]SSE = SST - SSR[/tex]
Given that:
[tex]SSR = 1705[/tex] ----------- [tex](x_2 ,x_3)[/tex]
[tex]SST = 1805[/tex]
So:
[tex]SSE_{(x_2,x_3)} = 1805 - 1705[/tex]
[tex]SSE_{(x_2,x_3)} = 100[/tex]
Solving (d): F test of significance
The null and alternate hypothesis are:
We have:
[tex]H_o :[/tex] [tex]x_1[/tex] and [tex]x_4[/tex] are not significant
[tex]H_a :[/tex] [tex]x_1[/tex] and [tex]x_4[/tex] are significant
For this model:
[tex]y =11.1 -3.6x_2+8.1x_3[/tex]
[tex]SSE_{(x_2,x_3)} = 100[/tex]
[tex]SST = 1805[/tex]
[tex]SSR_{(x_2 ,x_3)} = 1705[/tex]
[tex]SSE_{(x_1 ,x_2 ,x_3 ,x_4) }= 45[/tex]
[tex]p_{(x_2,x_3)} = 2[/tex]
[tex]\alpha = 0.05[/tex]
Calculate the t-score
[tex]t = \frac{SSE_{(x_2,x_3)}-SSE_{(x_1,x_2,x_3,x_4)}}{p_{(x_2,x_3)}} \div \frac{SSE_{(x_1,x_2,x_3,x_4)}}{n - p - 1}[/tex]
[tex]t = \frac{100-45}{2} \div \frac{45}{30 - 4 - 1}[/tex]
[tex]t = \frac{55}{2} \div \frac{45}{25}[/tex]
[tex]t = 27.5 \div 1.8[/tex]
[tex]t = 15.28[/tex]
Next, we calculate the p value from the t score
Where:
[tex]df = n - p - 1[/tex]
[tex]df = 30 -4 - 1=25[/tex]
The p value when [tex]t = 15.28[/tex] and [tex]df = 25[/tex] is:
[tex]p =0[/tex]
So:
[tex]p < \alpha[/tex] i.e. [tex]0 < 0.05[/tex]
Hence, we reject the null hypothesis
PLEASE HELP WILL MARK YOU!
It says:state whay additional information is required in order to know that the triangles are congruent for the reason given
This is pt.1
Step-by-step explanation:
12) ASA - we need the second angle.
13) We need the side and second angle.
14) We need second side. First side we know is equal since both triangles share it.
If the first and last terms of a trinomial are perfect squares, the trinomial is a perfect square
trinomial.
True
O False
Answer:
A trinomial is a perfect trinomial if the first and last terms are positive, perfect squares and the middle term is twice the product of their square roots.
Therefore, if you mean perfect as in positive, the answer is True.
A fair charges an admission fee of 4 dollars for eacg person. Let C be the cost of admission in dollars for P people. Write an equation relating C to P. Then graph your equation using the axes
Answer:
Equation is C = 4P
Graph is shown below
============================================================
Explanation:
The equation is C = 4P since it costs $4 per person. We just multiply 4 with the number of people (P) to get the cost (C).
Let's say 0 people show up, so that means C = 4*P = 4*0 = 0
The input P = 0 leads to the output C = 0. This is basically the same as saying x = 0 leads to y = 0. The point (0,0) is on the graph.
Repeat for P = 1 and you'll find that C = 4. This is the same as x = 1 leading to y = 4. The point (1,4) is on the graph.
If you keep going for various values of P, you'll get corresponding values of C. It turns out that all you need are 2 points to graph this line. Plot (0,0) and (1,4) on the same xy grid. Draw a line through them to complete the graph.
The graph is shown below.
TASKI
END OF THE YEAR - ESCAPE ROOM
Movie Theme
Fnd the area and circumference of each figure below. Use 31 for it. If needed,
round your answers to the nearest hundredths place
CODE Type the numeral answer. NO LABELS Part a crea, circumference, part b
area, circumference For example 765, 326, 2004, 3563
6
10 mm
MOVIE
TICKET
Your answer
Error Error Error Error Error Error Error Error Error Error Error Error Error Error Error Error Error Error Error Error Error Error Error Error Error Error Error Error Error Error Error Error Error Error Error Error Error Error Error Error Error Error Error Error ErrorError Error Error Error Error Error Error Error Error Error Error Error Error Error Error Error Error Error Error Error
Instructions: Find the value of x
I’ll mark brainliest please help
The little lines theu each section are telling you all those sections are identical, which mean they are the same length.
You are told one section is 10, which means x is also 10
X = 10
CAN SOMEONE PLEASE HELP ME GOOD, I need this to graduate ): 5. Given that AABC - ADEC, find the
value of x.
Answer:
ans: 4
Step-by-step explanation:
corresponding sides are proportional since given triangle are similar triangle, I.e
(4/5.5) = { (2x+8)/(6x-2)}
8/11 = ( x+ 4 ) / ( 3x - 1 )
8( 3x - 1 )= 11( x + 4 )
24x - 8 = 11x + 44
13x = 52
x = 4
PLEASE HELP ME WILL GIVE BRAINLIEST
Answer:
Reason 5
Step-by-step explanation:
Reason 1 and 2 are Given
Reason 3 is Reflexive
Reason 4 is Side-Side-Side congruency
Answer:
Reason 5
Step-by-step explanation:
It helps to know what CPCTC means and how it's used.
CPCTC means "corresponding parts of congruent triangles are congruent."
To use it, you must first either prove two triangles to be congruent or be given that two triangles are congruent.
Once you have the congruent triangles, then you state that two corresponding parts of those triangles are congruent, and you use CPCTC as the reason.
In step 4, the triangles are proven congruent by SSS.
Then CPCTC can be used as reason 5 for stating that the corresponding angles A and C are congruent.
Kimberly loves science and just subscribed to KiwiCo.
a company that delivers STEAM kits to students to
build and create things at home. KiwiCo charges a
subscription fee of $16.99 for each of its members.
KiwiCo had 300 subscribers in March. In April, 50 new
people subscribed to KiwiCo, and 23 people canceled
their subscriptions. How much more money did KiwiCo
earn from subscriptions in April?
Answer:
$5555.73
Step-by-step explanation:
$16.99 per 1 person
300+50=350-23=. 327
327×$16.99= 5555.73
Try this and if it doesn't work then let me know
Which relationship is always true for the angles x,y and z of triangle ABC
Answer:
B. y + z = x
Step-by-step explanation:
x is an exterior angle of the triangle.
y and z are the opposite angles opposite the exterior angle.
The exterior angle theorem of a triangle states that the measure of an exterior angle equals the measure of the sum of the two angles opposite the exterior angle.
Thus:
y + z = x
