Answer:
dI/dt = 0.0001(2000 - I)I
I(0) = 20
[tex]I(t)=\frac{2000}{1+99e^{-0.2t}}[/tex]
Step-by-step explanation:
It is given in the question that the rate of spread of the disease is proportional to the product of the non infected and the infected population.
Also given I(t) is the number of the infected individual at a time t.
[tex]\frac{dI}{dt}\propto \textup{ the product of the infected and the non infected populations}[/tex]
Given total population is 2000. So the non infected population = 2000 - I.
[tex]\frac{dI}{dt}\propto (2000-I)I\\\frac{dI}{dt}=k (2000-I)I, \ \textup{ k is proportionality constant.}\\\textup{Since}\ k = 0.0001\\ \therefore \frac{dI}{dt}=0.0001 (2000-I)I[/tex]
Now, I(0) is the number of infected persons at time t = 0.
So, I(0) = 1% of 2000
= 20
Now, we have dI/dt = 0.0001(2000 - I)I and I(0) = 20
[tex]\frac{dI}{dt}=0.0001(2000-I)I\\\frac{dI}{(2000-I)I}=0.0001 dt\\\left ( \frac{1}{2000I}-\frac{1}{2000(I-2000)} \right )dI=0.0001dt\\\frac{dI}{2000I}-\frac{dI}{2000(I-2000)}=0.0001dt\\\textup{Integrating we get},\\\frac{lnI}{2000}-\frac{ln(I-2000)}{2000}=0.0001t+k \ \ \ (k \text{ is constant})\\ln\left ( \frac{I}{I-222} \right )=0.2t+2000k[/tex]
[tex]\frac{I}{I-2000}=Ae^{0.2t}\\\frac{I-2000}{I}=Be^{-0.2t}\\\frac{2000}{I}=1-Be^{-0.2t}\\I(t)=\frac{2000}{1-Be^{-0.2t}}\textup{Now we have}, I(0)=20\\\frac{2000}{1-B}=20\\\frac{100}{1-B}=1\\B=-99\\ \therefore I(t)=\frac{2000}{1+99e^{-0.2t}}[/tex]
The required expressions are presented below:
Differential equation[tex]\frac{dI}{dt} = 0.0001\cdot I\cdot (2000-I)[/tex] [tex]\blacksquare[/tex]
Initial value[tex]I(0) = \frac{1}{100}[/tex] [tex]\blacksquare[/tex]
Solution of the differential equation[tex]I(t) = \frac{20\cdot e^{\frac{t}{5} }}{1+20\cdot e^{\frac{t}{5} }}[/tex] [tex]\blacksquare[/tex]
Analysis of an ordinary differential equation for the spread of a disease in an isolated population
After reading the statement, we obtain the following differential equation:
[tex]\frac{dI}{dt} = k\cdot I\cdot (n-I)[/tex] (1)
Where:
[tex]k[/tex] - Proportionality constant[tex]I[/tex] - Number of infected individuals[tex]n[/tex] - Total population[tex]\frac{dI}{dt}[/tex] - Rate of change of the infected population.Then, we solve the expression by variable separation and partial fraction integration:
[tex]\frac{1}{k} \int {\frac{dI}{I\cdot (n-I)} } = \int {dt}[/tex]
[tex]\frac{1}{k\cdot n} \int {\frac{dl}{l} } + \frac{1}{kn}\int {\frac{dI}{n-I} } = \int {dt}[/tex]
[tex]\frac{1}{k\cdot n} \cdot \ln |I| -\frac{1}{k\cdot n}\cdot \ln|n-I| = t + C[/tex]
[tex]\frac{1}{k\cdot n}\cdot \ln \left|\frac{I}{n-I} \right| = C\cdot e^{k\cdot n \cdot t}[/tex]
[tex]I(t) = \frac{n\cdot C\cdot e^{k\cdot n\cdot t}}{1+C\cdot e^{k\cdot n \cdot t}}[/tex], where [tex]C = \frac{I_{o}}{n}[/tex] (2, 3)
Note - Please notice that [tex]I_{o}[/tex] is the initial infected population.
If we know that [tex]n = 2000[/tex], [tex]k = 0.0001[/tex] and [tex]I_{o} = 20[/tex], then we have the following set of expressions:
Differential equation[tex]\frac{dI}{dt} = 0.0001\cdot I\cdot (2000-I)[/tex] [tex]\blacksquare[/tex]
Initial value[tex]I(0) = \frac{1}{100}[/tex] [tex]\blacksquare[/tex]
Solution of the differential equation[tex]I(t) = \frac{20\cdot e^{\frac{t}{5} }}{1+20\cdot e^{\frac{t}{5} }}[/tex] [tex]\blacksquare[/tex]
To learn more on differential equations, we kindly invite to check this verified question: https://brainly.com/question/1164377
2. Look at the figure below.
Which angle is congruent to 26?
Answer:
<4 is congruent to angle <6
Step-by-step explanation:
Assuming the lines are parallel
<2 , <4 , <6 , <8 are all equal
Congruent means they are equal.
There are 3 angles that are the same as angle 6, they are 2, 4, 8
The answer would be B. angle 4
Determine which type of correlation is shown in the graphed relationship
Answer:
No correlation
Step-by-step explanation:
Hey there! :)
This has no correlation because all the points are spread out throughout the graph making no correlation.
Answer:
D no correlation
Step-by-step explanation:
too many scattered dot all over the place if its some going up down its NO CORRELATION!!!
A 75 lb boy and a 65 lb girl play on a seesaw. The seesaw is 14 ft long and is pivoted exactly in the middle. If the girl sits on the end of her side, where must the boy sit to make the seesaw balance?
Answer: 6 feet from the pivot point
Step-by-step explanation:
Girl's weight x distance from center = Boy's weight x distance from center
65 (7) = 75x
[tex]\dfrac{65(7)}{75}=x[/tex]
6.066 = x
The boy needs to be placed 6 feet from the center (aka pivot point) which is the same as saying 1 foot from the end of the seesaw.
what is improper sampling in statistical analysis and how can i use it in day-to-day life
Answer:
Statistical concepts are used in quality testing. Companies make many products on a daily basis and every company should make sure that they sold the best quality items.
Step-by-step explanation:
pls keep brainly questions only school related thank you!
Two ballpoint pens are selected at random from a box that contains3 blue pens, 2 red pensand 3 green pens. If X is the number of blue pens
Answer: 3/(28) ≈ 10.7%
Step-by-step explanation:
3 blue + 2 red + 3 green = 8 total pens
First pick and Second pick
[tex]\dfrac{3\ blue\ pens}{8\ total\ pens}\quad \times \quad \dfrac{2\ remaining\ blue\ pens}{7\ remaining\ total\ pens}\quad =\large\boxed{\dfrac{3}{28}}[/tex]
If four times the brother's age is subtracted from three times the sister's age, the difference is 17. Give an equation that represents this statement using bbb as the age of the brother and s as the age of the sister.
Answer:
3s-4bbb=17
Step-by-step explanation:
brother=4bbb
sister=3s
3s-4bbb=17
WHat is the answer to this?
Answer:
0.9
Step-by-step explanation:
First, convert them all into fractions:
[tex]2\frac{1}{3}=\frac{7}{3}[/tex]
[tex].5=\frac{1}{2}[/tex]
Now, we have:
[tex]\frac{4x+9}{\frac{7}{3} } =\frac{3x}{\frac{1}{2} }[/tex]
Cross multiply:
[tex]\frac{1}{2} (4x+9)=\frac{7}{3} (3x)[/tex]
On the left, distribute. On the right, notice that the 3 in the denominator and the coefficient 3 cancel:
[tex]2x+4.5=7x[/tex]
[tex]4.5=5x[/tex]
[tex]x=0.9=9/10[/tex]
Answer and step-by-step explanation:
Photo
Solve for x : 2^x+4^x+8^x=−14
●✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎❀✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎●
Hi my lil bunny!
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Let's solve this step by step.
[tex]2^x + 4^x + 8^x = -14[/tex]
↓
In order to factor an integer, we need to repeatedly divide it by the ascending sequence of primes (2, 3, 5...).
The number of times that each prime divides the original integer becomes its exponent in the final result.
Prime number 2 to the power of 2 = 4
[tex]2^x + (2^2)^x + (2^3) ^x = -14[/tex]
↓
Prime number 2 to the power of 3 = 8
[tex]2^x + 2^2x + 2^3x = -14[/tex]
↓
We need to exponentiate the power.
The following rule is applied:
[tex](A^B) ^C = A^BC[/tex]
In our example,
A is equal to 2,
B is equal to 2 and
C is equal to x.
[tex]( 2^x + 2^2x + 2^3x ) + 14 = -14 + 14[/tex]
↑
In order to solve this non-linear equation, we need to move all the terms to the left side.
In our example,
- term −14, will be moved to the left side.
Notice that a term changes sign when it 'moves' from one side of the equation to the other.
___________________
We need to get rid of expression parentheses.
If there is a negative sign in front of it, each term within the expression changes sign.
Otherwise, the expression remains unchanged.
In our example, there are no negative expressions.
↓
[tex]2^x + 2^2x + 2^3x + 14 = 0[/tex]
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Hope this helped you.
Could you maybe give brainliest..?
❀*May*❀
Blue ribbon taxis offers shuttle service to the nearest airport. You loop up online reviews for blue ribbon taxis and find that there are 17 reviews, six of which report that the taxi never showed up.
Is this a biased sampling method for obtaining customer opinion on the taxi service?
If so, what is the likely direction of bias?
explain your reasoning carefully.
Answer:
In order for a sample to be considered biased, some members of the total population must have either a larger or lower chance of being included in the sample. In this case, your sample contained 17 reviews. It is biased because it was completely voluntary and customers who have a bad experience with a product or service generally tend to express more their dissatisfaction than satisfied customers show their satisfaction.
In marketing, there is a saying that unsatisfied clients talk bad about our product or service 4 times more than satisfied clients. I'm not sure if this saying is exact or not, but all marketing research point in the same direction.
This means that clients that did not get a good service or got no service at all, are more likely to post a review about the company than clients who got a good service. This is what makes the sample biased.
Which of the following
examples have a constant rate of change?
A : You drive from Colorado to Texas. In the first 4 hours, you cover 240 miles, and in the second 5 hours, you cover another 240 miles.
B : The money you put in the bank earns 5% Interest. This means that the bank pays you 5% of the amount of the money kept in the bank each year.
C : A salesperson earns $50 plus $10 for every $100 of merchandise he sells.
D : The amount bacteria double every hour.
Answer:
C : A salesperson earns $50 plus $10 for every $100 of merchandise he sells.
Step-by-step explanation:
If a salesperson earns $50 plus $10 for every $100 of merchandise he sells, the rate of change is 100. The linear equation is T = 50 + 100h, where T is the total amount he earns and h is the number of $100 in merchandise he sells.
The example that represents the constant rate will be a salesperson who earns $50 plus $10 for every $100 of merchandise he sells. Then the correct option is C.
What is the average rate change?It is the average amount by which the function varied per unit throughout that time period. It is calculated using the gradient of the line linking the interval's ends on the graph depicting the function.
Let's check all the options, then we have
A: You drive from Colorado to Texas. In the first 4 hours, you cover 240 miles, and in the second 5 hours, you cover another 240 miles. It is an example of a linear function but the slope gets changed after 2 hours.
B: The money you put in the bank earns 5% Interest. This means that the bank pays you 5% of the amount of the money kept in the bank each year. It is an example of the exponential function.
C: A salesperson earns $50 plus $10 for every $100 of merchandise he sells. It is an example of a linear function.
D: The number of bacteria doubles every hour. It is an example of the exponential function.
The example that represents the constant rate will be a salesperson who earns $50 plus $10 for every $100 of merchandise he sells. Then the correct option is C.
More about the average rate change link is given below.
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HELP ASAP I NEED THIS RIGHTNOW 30 points
Answer:
Pretty sure it is c
Step-by-step explanation:
Answer:
C.
Step-by-step explanation:
She will be painting the outsides of the table, so we need to find the surface area of the table.
There is the flat part of the table, which is a rectangular prism. There are also four legs, which are rectangular prism.
So, she will paint C. the surface area of 6 rectangular prisms.
Hope this helps!
Quick!!! Urgent!!!!!!!!!
Answer:
my best answer for this is B. False.
I calculated as fast as i can.
Need Help finding the process for both of these ( due today)
Similar triangles have side lengths that are proportional to each other. To find each of the missing lengths, we need to set up proportions.
The proportions will look as follows:
(length or unknown of triangle 1) / (length or unknown of triangle 2) = (length of triangle 1) / (length of triangle 2)
-On both sides, remember to be consistent with which length/unknown you put on top! If a triangle 1 length is the numerator on the left, then it also needs to be the numerator on the right! And this also works vice versa with triangle 2.
In each proportion equation, we can only have one unknown. On the left side of the equation, we choose one length or unknown of triangle 1, and the corresponding side length of unknown of triangle 2 (whichever you did not choose from triangle 1). On the right side of the equation, we use a completed proportion. This is because all of the sides of one triangle are proportional to the other triangle, but we need to know that proportion/ratio in order to find other side lengths.
Let's start with problem a, to show how this works:
Triangle 1 side lengths - 16, a, 11
Triangle 2 side lengths - 8, 3, b
As you can tell, the side lengths match up (corresponding!) on each triangle, as in they are in the same position on each triangle. Now, we will set up a proportion to find the length of side a on triangle 1.
a / 3 = 16 / 8
48 = 8a
a = 6
Next, let's find the length of side b on triangle 2.
11 / b = 16 / 8
16b = 88
b = 5.5
Moving on to problem b, we'll apply the same concept and steps from problem a in order to find the missing side lengths.
Triangle 1 side lengths: 5, 5.5, d
Triangle 2 side lengths: 15, c, 18
5 / 15 = 5.5 / c
5c = 82.5
c = 16.5
5 / 15 = d / 18
15d = 90
d = 6
Hope this helps!! :)
Answer:
On a) you can see the shapes are simular. The blue line signatures that they are equal just reduced. You can see that 8 goes into 16 two times so for the orange line 3 must times 2. Which would mean a is 6. Now on the red line all you see is 11. So divide 11 by 2 and your answer should be 5.5 for b.
On b) it is the same thing but you have to find how the blue line is divisible. 5 divided by 15 is 3. So 3 is the number you will be using to divide or multiply. For the orange line you divide 18 by 3. The answer is 6 for d. For the red line 5.5 times 3 and you should get 11 for c.
Step-by-step explanation:
Hope this helped
Let x represent the number of times a student visits a gym in a one month period. Assume that the probability distribution of X is as follows: x 0 1 2 3 p(x) 0.17 0.33 0.32 0.18 Determine the probability the student visits the gym at most twice in a month. Report your answer to two decimal places.
Answer: Probability of visiting at most twice = 0.82
Step-by-step explanation: The probability distribution is of the form:
X 0 1 2 3
P(X) 0.17 0.33 0.32 0.18
It wants the probability of visiting the gym at most twice in a month, which means the probability of never going to the gym, P(X=0), or going once, P(X=1), or going twice, P(X=2).
Using the "OR" probability:
P(visiting at most twice) = P(X=0) + P(X=1) + P(X=2)
P(visiting at most twice) = 0.17 + 0.33 + 0.32
P(visiting at most twice) = 0.82
Therefore, the probability of visiting the gym at most twice in a month is 0.82 or 82%
The snowfall from this snowstorm above covered most of IA, northern IL, northern IN, and southern MI. While some locations in that swath saw over a foot of snow, let’s assume the average depth of the snow over this area was 8 inches. If the total area covered by the 8 inch average depth was 72,150 square miles, what percentage of the volume of the Grand Canyon would this amount of snow fill?
Answer:
Percentage volume of the Grand Canyon filled by the snow = 0.911 %
Step-by-step explanation:
This question is incomplete; please find the complete question in the attachment.
Given :
Area of the snow cover = 72150 square miles
Depth of the snow = 8 inches
Volume of the Grand Canyon = 4.166 × 101² m³
Solution:
Area of the snow cover = 72150 square miles
≈ 72150 × 2589988 square meter
≈ 1.868 × 10¹¹ square meter
Depth of the snow = 8 inches ≈ 0.2032 m
Volume of the snow on this area = Area × depth of the snow
= 1.868 × 10¹¹ × 0.2032
= 3.796 × 10¹⁰ m³
Volume of the Grand Canyon = 4.166 × 10¹² m³
Percentage volume of the Grand Canyon filled by the snow
= [tex]\frac{\text{Volume of the snow}}{\text{Volume of the Grand Canyon}}\times 100[/tex]
= [tex]\frac{3.796\times 10^{10} }{4.166\times 10^{12} }\times 100[/tex]
= 0.911%
There were females and males present at the high school pep rally. Find the ratio of males to the total number of people present. Express as a simplified ratio.
Answer: 4:9
Step-by-step explanation:
The complete question is provide in the attachment below.
Given, Number of females = 125
Number of males = 100
Total people = 120+100=225
Now, the ratio of males to the total number of people present = [tex]\dfrac{\text{Total number of males}}{\text{Total people}}[/tex]
[tex]=\dfrac{100}{225}[/tex]
Divide numerator and denominator by 25 , we get
Ratio of males to the total number of people present =[tex]\dfrac{4}{9}[/tex]
Hence, the ratio of males to the total number of people present = 4:9
j/2 +7=-12 solve for j
Answer:
j/2+7= -12
(j+14)/2= -12
cross-multiply
j+14= -24
j= -38
Answer:
[tex]\boxed{j=-38}[/tex]
Step-by-step explanation:
[tex]\frac{j}{2} +7=-12[/tex]
Subtract 7 on both sides.
[tex]\frac{j}{2} +7-7=-12-7[/tex]
[tex]\frac{j}{2}=-19[/tex]
Multiply both sides by 2.
[tex]\frac{j}{2}(2)=-19(2)[/tex]
[tex]j=-38[/tex]
Which is the graph of linear inequality x - 2y 2-12?
10
10
10
1034
Help asappp!!!pls
It would have to have a positive slope and the bottom needs to be shaded, since -2y is negative it means we will be dividing by a negative. The inequality sign will switch.
also if it is < then the line is dotted, if it’s the “greater or equal to sign” then the line is not dotted.
dunno if I explained it very well
The shaded region common to both the inequalities represents the solution set of the inequality → x - 2y² < 12.
What is inequality?An inequality is used to compare two or more expressions or numbers.
For example -
2x > 4y + 3
x + y > 3
x - y < 6
Given is the inequality as -
x - 2y² < 12
The given inequality is -
x - 2y² < 12
2y² - x < - 12
2y² < x - 12
y² < (x/2) - 6
[tex]$y < \pm\sqrt{\frac{x}{2}-6 }[/tex]
[tex]$y < \sqrt{\frac{x}{2}-6 }[/tex]
and
[tex]$y < -\sqrt{\frac{x}{2}-6 }[/tex]
Refer to the graph of the equation attached. The shaded region common to both the inequalities represents the solution set of the inequality.
Therefore, the shaded region common to both the inequalities represents the solution set of the inequality → x - 2y² < 12.
To solve more questions on inequality, visit the link-
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given that H0: μ=40 against H1: μ < 40 if mice have an average life of 38 months with a standard deviation of 5.8 months. If the distribution of life spans is approximately normal, how large a sample is required in order that the probability of committing a type II error be 0.1 when the true mean is 35.9 months? Assume that level of significance 0.05.
Answer: sample required n = 18
Step-by-step explanation:
Given that the value under under null hypothesis is 40 while the value under the alternative is less than 40, specifically 35.9
∴ H₀ : u = 40
H₁ : u = 35.9
therefore β = ( 35.9 - 40 ) = -4.1
The level of significance ∝ = 0.05
Probability of committing type 11 error P = 0.1
standard deviation α = 5.8
Therefore our z-vales (z table)
Z₀.₅ = 1.645
Z₀.₁ = 1.282
NOW let n be sample size
n = {( Z₀.₅ + Z₀.₁ )² × α²} / β²
n = {( 1.645 + 1.282 )² × 5.8²} / (- 4.1)²
n = 17.14485
Since we are talking about sample size; it has to be a whole number
therefore
sample required n = 18
limit xtens to 0 x^2logx^2 what is the ans of interminate forms?
Rewrite the limit as
[tex]\displaystyle\lim_{x\to0}x^2\log x^2=\lim_{x\to0}\frac{\log x^2}{\frac1{x^2}}[/tex]
Then both numerator and denominator approach infinity (with different signs, but that's not important). Applying L'Hopital's rule, we get
[tex]\displaystyle\lim_{x\to0}\frac{\log x^2}{\frac1{x^2}}=\lim_{x\to0}\frac{\frac2x}{-\frac2{x^3}}=\lim_{x\to0}-x^2=\boxed{0}[/tex]
Investment: Suppose you receive a gift of $1,000 and decide to open a CD (certificate of
deposit) as a low risk investment. The best CD rate you could find is 2.25%, which means that
your original investment will grow at a rate of 2.25% each year.
Assuming the rate of increase does not change, which of the following statements is TRUE
about your CD account balance?
It will no longer grow after several years.
It will triple in approximately 3 years.
O 4 years after the original investment, it is approximately $1,093.
O It will double in approximately 10 years.
Answer: 4 years after the original investment, it is approximately $1,093.
Step-by-step explanation:
Hi, to answer this question we have to apply the simple interest formula:
I = p x r x t
Where:
I = interest
P = Principal Amount
r = Interest Rate (decimal form)
t= years
Replacing with the values given
I = 1000x (2.25/100) x t
It will triple in approximately 3 years. FALSEI = 1000x (2.25/100) x 3 =67.5
1000+67.5 = 1067.5
It will no longer grow after several years: False, it will grow because it has a growth rate.4 years after the original investment, it is approximately $1,093. TRUEI = 1000x (2.25/100) x 4 =90
1000+90 = $1090
It will double in approximately 10 years.I = 1000x (2.25/100) x 10 =225
1000+90 = $1225
Feel free to ask for more if needed or if you did not understand something.
hey guys can you please help me with this. i’m really desperate please help anything helps. thank u :(
Answer:
- 29 / 20
Step-by-step explanation
The cosec (x) = 1 / sin(x)
There are 2 ways to do this:
Either using a calculator:
sin^-1(20 / 29) = 43.60281897
so inputting into 1/sin(-x) where x = 43.6.....
This gives: -29 / 20
OR
1 / sin(x) = cosec ( x)
so cosec (x) = 1/(20/29)
= 29/20
By observing the cosec(x) graph, we see that to get cosec (-x), all we need to do is to minus our answer seeing as the graph is symmetrical across the axes. Therefore x = -29/20
Write an equation perpendicular to 5x+6y=18 that passes through the point (10,7)
Answer:
Step-by-step explanation:
6y = -5x + 18
y = -5/6x + 3
perp slope: 6/5
y - 7 = 6/5(x - 10)
y - 7 = 6/5x - 12
y = 6/5x - 5
Here, we are required to write an equation perpendicular to 5x + 6y = 18.
The equation perpendicular to 5x+6y=18 that passes through the point (10,7) is;6x - 5y = 25.
By rearranging 5x+6y=18 to resemble the end of a straight line; y = Mx + c; we have;y = (-5/6)x +3Therefore, slope of equation 5x + 6y = 18 is -5/6.
However, the product of the slopes of 2 perpendicular lines is -1.Therefore, m1m2 = -1
Therefore, the slope of the required line, m2 is;
m2 = -1/(-5/6)m2 = 6/5
Therefore, the equation of a line perpendicular to the equation 5x+6y=18 and passes through the point (10,7) is given as;
6/5 = (y - 7)/(x - 10).
By cross product; we have;
6x - 60 = 5y - 35
6x - 5y = 25.
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water drips from a faucet at a rate of 41 drops/ minute. Assuming there are 15,000 drops in gallon, how many minutes would it take for the dripping faucet to fill a 1 gallon bucket? Round your answer to the nearest whole number
Answer:
366 Minutes
Step-by-step explanation:
Fine the value of x in the triangle. Then classify the triangle as acute, right,
or obtuse.
47* 45* x
Answer:
x = 88
Step-by-step explanation:
The sum of the angles in a triangle add to 180
47+45 +x = 180
Combine like terms
92+x = 180
Subtract 92 from each side
92+x-92= 180-92
x =88
which point is a solution tot eh linear inequality y < -1/2x + 2?
(2,3)
(2,1)
(3,-2)
(-1,3)
Answer:
Step-by-step explanation:
(3,-2)
plug in 3 for x and -2 for y
-2< -1/2x3+2
-2<-1.5+2
-2<0.5
WHY CAN'T ANYONE HELP ME PLEASE? THANKS! A student at a university makes money by buying and selling used cars. Charles bought a used car and later sold it for a 15% profit. If he sold it for $4669, how much did Charles pay for the car?
Step-by-step explanation:
Given,
a student (Charles) bought a car and sold it in 15 % profit for $4669.
we have the formula,
[tex]cp = \frac{sp \times 100}{100 + p\%} [/tex]
so,
[tex]cp = \frac{4669 \times 100}{100 + 15} [/tex]
by simplifying it we get,
CP is $4060.
Therefore, the cp was $4060.
Hope it helps...
Students in management science class have just received their grades on the first test. The instructor has provided information about the first test grades in some previous classes as well as the final average for the same students. Some of these grades have been sampled and are as follow:
1st test Grade 98 77 88 80 96 61 64 95 79
Final average 93 78 84 75 84 64 66 95 86
Develop a regression model that could be used to predict the final average in the course based on the first test grade.
Predict the final average of a students who made an 83 on the first test.
Give the value of r and r2 for this model.
Interpret the value of r2 in the context of this problem.
Answer:
The regression model is:
y = 20.29 + 0.73·x
Step-by-step explanation:
In this case a regression model is to be formed to predict the final average in the course based on the first test grade.
Use Excel to form the regression model.
The output is attached below.
The regression model is:
y = 20.29 + 0.73·x
Predict the final average of a students who made an 83 on the first test as follows:
y = 20.29 + 0.73·x
= 20.29 + 0.73 × 83
= 80.88
The final average of a students who made an 83 on the first test would be 80.88.
From the output:
R² = 0.839
Then the correlation coefficient will be:
[tex]r=\sqrt{R^{2}}=\sqrt{0.839}=0.91597\approx 0.92[/tex]
The value of r is 0.92.
The coefficient of determination R² specifies the percentage of the variance in the dependent-variable (Y) that is forecasted or explained by linear regression and the forecaster variable (X, also recognized as the independent-variable).
In this case, the R² value of 0.839 implies that 83.9% of the variation in the final average can be explained by the grades in the first test.
In a Gallup poll of randomly selected adults, 66% said that they worry about identity theft. For a group of 1013 adults, the mean of those who do not worry about identify theft is closest to:
Answer:
[tex]Mean = 344[/tex]
Step-by-step explanation:
Given
[tex]Population = 1013[/tex]
Let p represents the proportion of those who worry about identity theft;
[tex]p = 66\%[/tex]
Required
Mean of those who do not worry about identity theft
First, the proportion of those who do not worry, has to be calculated;
Represent this with q
In probability;
[tex]p + q = 1[/tex]
Make q the subject of formula
[tex]q = 1 - p[/tex]
Substitute [tex]p = 66\%[/tex]
[tex]q = 1 - 66\%[/tex]
Convert percentage to fraction
[tex]q = 1 - 0.66[/tex]
[tex]q = 0.34[/tex]
Now, the mean can be calculated using:
[tex]Mean = nq[/tex]
Where n represents the population
[tex]Mean = 1013 * 0.34[/tex]
[tex]Mean = 344.42[/tex]
[tex]Mean = 344[/tex] (Approximated)
I need help! I don’t understand and need helping
Answer:
125
Step-by-step explanation:
30+25+x=180
55+x=180
x=180-55
x=125
Answer:
x = 64.3Step-by-step explanation:
To find x we use tan
tan ∅ = opposite / adjacent
From the question
x is the adjacent
30 is the hypotenuse
So we have
tan 25 = 30/x
x = 30/tan 25
x = 64.33
x = 64.3 to the nearest tenth
Hope this helps you