Answer:
[tex]C(t) =\dfrac{ r}{k} - \left (\dfrac{r-kC_{0}}{k} \right )e^{ -kt}[/tex]
[tex]C(t) =\dfrac{ r}{k}- e^{ -kt}[/tex] ,thus, the function is said to be an increasing function.
Step-by-step explanation:
Given that:
[tex]\dfrac{dC}{dt}= r-kC[/tex]
[tex]\dfrac{dC}{r-kC}= dt[/tex]
Taking integration on both sides ;
[tex]\int\limits\dfrac{dC}{r-kC}= \int\limits \ dt[/tex]
[tex]- \dfrac{1}{k}In (r-kC)= t +D[/tex]
[tex]In(r-kC) = -kt - kD \\ \\ r- kC = e^{-kt - kD} \\ \\ r- kC = e^{-kt} e^{ - kD} \\ \\r- kC = Ae^{-kt} \\ \\ kC = r - Ae^{-kt} \\ \\ C = \dfrac{r}{k} - \dfrac{A}{k}e ^{-kt} \\ \\[/tex]
[tex]C(t) =\frac{ r}{k} - \frac{A}{k}e^{ -kt}[/tex]
here;
A is an integration constant
In order to determine A, we have [tex]C(0) = C0[/tex]
[tex]C(0) =\frac{ r}{k} - \frac{A}{k}e^{0}[/tex]
[tex]C_0 =\frac{r}{k}- \frac{A}{k}[/tex]
[tex]C_{0} =\frac{ r-A}{k}[/tex]
[tex]kC_{0} =r-A[/tex]
[tex]A =r-kC_{0}[/tex]
Thus:
[tex]C(t) =\dfrac{ r}{k} - \left (\dfrac{r-kC_{0}}{k} \right )e^{ -kt}[/tex]
2. Assuming that C0 < r/k, find lim t→[infinity] C(t) and interpret your answer
[tex]C_{0} < \lim_{t \to \infty }C(t) \\ \\C_0 < \dfrac{r}{k} \\ \\kC_0 <r[/tex]
The equation for C(t) can be rewritten as :
[tex]C(t) =\dfrac{ r}{k} - \left (\dfrac{r-kC_{0}}{k} \right )e^{ -kt}C(t) =\dfrac{ r}{k} - \left (+ve \right )e^{ -kt} \\ \\C(t) =\dfrac{ r}{k}- e^{ -kt}[/tex]
Thus; the function is said to be an increasing function.
URGENT!! MY LAST 2 QUESTION WILL FOREVER BE GRATEFUL PLS HELP WILL GIVE BRANLIEST!! AT LEAST TAKE A LOOK!!!! PLS I AM BEGGING!!!
13. Assume that you have a square. What can you conclude from applying the law of detachment to this conditional?
If you have a square, then you have a rectangle.
A) You have a quadrilateral.
B) All sides are the same length.
C) Squares and rectangles are the same.
D) You have a rectangle.
14. Which two theorems would justify that m∠4 = m∠6, given that m∠5 = m∠6 in the diagram below?
IMAGE BELOW
A) vertical angles theorem, consecutive interior angles theorem
B) vertical angles theorem, alternate interior angles theorem
C) right angles theorem, exterior angles theorem
D) corresponding angles theorem, angle addition theorem
Answer:
d: please note I am not sure about this but look at my reasoning and maybe you can find your own answer that you are sure about.
D: i am sure about this.
Step-by-step explanation:
From what I looked up, i believe what you are talking about is deductive reasoning, which is based off of facts. It can't be a or b because that wasn't defined in the statement. Squares and rectangles are not the same thing since you can have a square that is a rectangle, but a rectangle that is not a square, so D is correct.
corresponding angles i believe since they are matching
I know that the 2 lines are parallel because 5 and 6 are alternate interior angles since they are on opposite sides.
4 and 6 are not vertical or right angles, so it must be d, also they follow what a corresponding angle is, which is them being matching.
Answer:
13. B
14. D
Step-by-step explanation:
13. Law of Detachment says that if two statements are true then we can derive a third true statement. So, for example, say the first statement is that you are a human. Say the second statement is that you breathe. You can write this as: if you are a human, you breathe. In this case, if you have a square, then you have a rectangle. You have a quadrilateral.
14. 4 and 6 are corresponding angles, since you can tell that there are two parallel lines from angle 5 = angle 6. You can also use angle addition theorem.
I want the answer of this question
[tex]the \: answer \: is \: 10 \\ please \: see \: the \: attached \: picture \: for \\ full \: solution \\ hope \: it \: helps[/tex]
Answer:
10 is the answer for this question.
Please help me with this math problem, urgent please
Answer:
see below
Step-by-step explanation:
To find the x intercept set y =0 and solve for x
6x+5y = -30
6x = -30
Divide by 6
x = -30/6 = -5
The x intercept is (-5,0)
To find the y intercept set x =0 and solve for y
6x+5y = -30
5y = -30
Divide by 5
y = -30/5 = -6
The y intercept is (0,-6)
To find the x-intercept set y =0. Solve for x.
6x+5y=-30
6x+5(0)=-30
6x+0=-30
6x=-30
x=-30/6
x=-5
The x-intercept is at (-5, 0)
To find the y-intercept set x =0. Solve for y.
6x+5y=-30
6(0)+5y=-30
0+5y=-30
5y=-30
y=-30/5
y=-6
The y-intercept is at (0, -6)
A population of protozoa develops with a constant relative growth rate of 0.7781 per member per day. On day zero the population consists of six members. Find the population size after four days. (Round your answer to the nearest whole number.) P(4)
Answer:
[tex] P(t) = A (1+r)^t [/tex]
Where P represent the population after t days. a the initial amount on this case 6 and r the growth factor rate of 0.7781. so then our model would be given by:
[tex] P(t)= 6(1.7781)^t [/tex]
And replacing t=4 we got:
[tex] P(4) = 6(1.7781)^4 =59.975 \approx 60[/tex]
So then after 4 days we would expect about 60 protzoa
Step-by-step explanation:
For this case we can use the following function to model the population of protzoa:
[tex] P(t) = A (1+r)^t [/tex]
Where P represent the population after t days. a the initial amount on this case 6 and r the growth factor rate of 0.7781. so then our model would be given by:
[tex] P(t)= 6(1.7781)^t [/tex]
And replacing t=4 we got:
[tex] P(4) = 6(1.7781)^4 =59.975 \approx 60[/tex]
So then after 4 days we would expect about 60 protzoa
CAN SOMEONE HELP ME IN THIS INTEGRAL QUESTION PLS
''Find the surface area between the z = 1 and z = 4 planes of z = x ^ 2 + y ^ 2 paraboloid.''
Due to the symmetry of the paraboloid about the z-axis, you can treat this is a surface of revolution. Consider the curve [tex]y=x^2[/tex], with [tex]1\le x\le2[/tex], and revolve it about the y-axis. The area of the resulting surface is then
[tex]\displaystyle2\pi\int_1^2x\sqrt{1+(y')^2}\,\mathrm dx=2\pi\int_1^2x\sqrt{1+4x^2}\,\mathrm dx=\frac{(17^{3/2}-5^{3/2})\pi}6[/tex]
But perhaps you'd like the surface integral treatment. Parameterize the surface by
[tex]\vec s(u,v)=u\cos v\,\vec\imath+u\sin v\,\vec\jmath+u^2\,\vec k[/tex]
with [tex]1\le u\le2[/tex] and [tex]0\le v\le2\pi[/tex], where the third component follows from
[tex]z=x^2+y^2=(u\cos v)^2+(u\sin v)^2=u^2[/tex]
Take the normal vector to the surface to be
[tex]\dfrac{\partial\vec s}{\partial u}\times\dfrac{\partial\vec s}{\partial u}=-2u^2\cos v\,\vec\imath-2u^2\sin v\,\vec\jmath+u\,\vec k[/tex]
The precise order of the partial derivatives doesn't matter, because we're ultimately interested in the magnitude of the cross product:
[tex]\left\|\dfrac{\partial\vec s}{\partial u}\times\dfrac{\partial\vec s}{\partial v}\right\|=u\sqrt{1+4u^2}[/tex]
Then the area of the surface is
[tex]\displaystyle\int_0^{2\pi}\int_1^2\left\|\dfrac{\partial\vec s}{\partial u}\times\dfrac{\partial\vec s}{\partial v}\right\|\,\mathrm du\,\mathrm dv=\int_0^{2\pi}\int_1^2u\sqrt{1+4u^2}\,\mathrm du\,\mathrm dv[/tex]
which reduces to the integral used in the surface-of-revolution setup.
A market research firm supplies manufacturers with estimates of the retail sales of their products from samples of retail stores. Marketing managers are prone to look at the estimate and ignore sampling error. A random sample of 36 stores this year shows mean sales of 53 units of a small appliance with a standard deviation of 12 units. During the same point in time last year, a random sample of 49 stores had mean sales of 41 units with standard deviation 6 units.
It is of interest to construct a 95 percent confidence interval for the difference in population means ?1??2, where ?1 is the mean of this year's sales and ?2 is the mean of last year's sales.
Enter values below rounded to three decimal places.
(a) The estimate is: _________ .
(b) The standard error is: ____________________ .
Answer:
The 95% confidence interval for the difference of means is (7.67, 16.33).
The estimate is Md = 12.
The standard error is sM_d = 2.176.
Step-by-step explanation:
We have to calculate a 95% confidence interval for the difference between means.
The sample 1 (this year's sales), of size n1=36 has a mean of 53 and a standard deviation of 12.
The sample 2 (last year's sales), of size n2=49 has a mean of 41 and a standard deviation of 6.
The difference between sample means is Md=12.
[tex]M_d=M_1-M_2=53-41=12[/tex]
The estimated standard error of the difference between means is computed using the formula:
[tex]s_{M_d}=\sqrt{\dfrac{\sigma_1^2}{n_1}+\dfrac{\sigma_2^2}{n_2}}=\sqrt{\dfrac{12^2}{36}+\dfrac{6^2}{49}}\\\\\\s_{M_d}=\sqrt{4+0.735}=\sqrt{4.735}=2.176[/tex]
The degrees of freedom are:
[tex]df=n_1+n_2-1=36+49-2=83[/tex]
The critical t-value for a 95% confidence interval and 83 degrees of fredom is t=1.989.
The margin of error (MOE) can be calculated as:
[tex]MOE=t \cdot s_{M_d}=1.989 \cdot 2.176=4.328[/tex]
Then, the lower and upper bounds of the confidence interval are:
[tex]LL=M_d-t \cdot s_{M_d} = 12-4.328=7.67\\\\UL=M_d+t \cdot s_{M_d} = 12+4.328=16.33[/tex]
The 95% confidence interval for the difference of means is (7.67, 16.33).
A large car insurance company selected samples of single and married male policyholders and recorded the number who made an insurance claim over the preceding three-year period. Single Policyholders Married Policyholders n1 = 450 n2 = 925 # making claim = 67 # making claim = 93 Using alpha = 0.05, determine whether the claim rates are higher for single male policyholders verses married male policyholders. Solve using the p-value approach only.
Answer:
The null hypothesis is rejected.
There is enough evidence to support the claim that rates are higher for single male policyholders verses married male policyholders (P-value = 0.004).
Step-by-step explanation:
This is a hypothesis test for the difference between proportions.
The claim is that rates are higher for single male policyholders verses married male policyholders.
Then, the null and alternative hypothesis are:
[tex]H_0: \pi_1-\pi_2=0\\\\H_a:\pi_1-\pi_2> 0[/tex]
The significance level is 0.05.
The sample 1 (single group), of size n1=450 has a proportion of p1=0.1489.
[tex]p_1=X_1/n_1=67/450=0.1489[/tex]
The sample 2 (married group), of size n2=925 has a proportion of p2=0.1005.
[tex]p_2=X_2/n_2=93/925=0.1005[/tex]
The difference between proportions is (p1-p2)=0.0483.
[tex]p_d=p_1-p_2=0.1489-0.1005=0.0483[/tex]
The pooled proportion, needed to calculate the standard error, is:
[tex]p=\dfrac{X_1+X_2}{n_1+n_2}=\dfrac{67.005+93}{450+925}=\dfrac{160}{1375}=0.1164[/tex]
The estimated standard error of the difference between means is computed using the formula:
[tex]s_{p1-p2}=\sqrt{\dfrac{p(1-p)}{n_1}+\dfrac{p(1-p)}{n_2}}=\sqrt{\dfrac{0.1164*0.8836}{450}+\dfrac{0.1164*0.8836}{925}}\\\\\\s_{p1-p2}=\sqrt{0.0002+0.0001}=\sqrt{0.0003}=0.0184[/tex]
Then, we can calculate the z-statistic as:
[tex]z=\dfrac{p_d-(\pi_1-\pi_2)}{s_{p1-p2}}=\dfrac{0.0483-0}{0.0184}=\dfrac{0.0483}{0.0184}=2.62[/tex]
This test is a right-tailed test, so the P-value for this test is calculated as (using a z-table):
[tex]P-value=P(z>2.62)=0.004[/tex]
As the P-value (0.004) is smaller than the significance level (0.05), the effect is significant.
The null hypothesis is rejected.
There is enough evidence to support the claim that rates are higher for single male policyholders verses married male policyholders.
g Brian Vanecek, VP of Operations at Portland Trust Bank, is evaluating the service level provided to walk-in customers. Accordingly, his staff recorded the waiting times for 64 randomly selected walk-in customers, and determined that their mean waiting time was 15 minutes and that the standard deviation was 4 minutes. The 88% confidence interval for the population mean of waiting times is __________.
Answer:
The 88% confidence interval for the population mean of waiting times is between 7.34 minutes and 22.66 minutes.
Step-by-step explanation:
We have the standard deviation for the sample, so we use the t-distribution to solve this question.
The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So
df = 64 - 1 = 63
88% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 63 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.88}{2} = 0.94[/tex]. So we have T = 1.9153
The margin of error is:
M = T*s = 1.9153*4 = 7.66.
In which s is the standard deviation of the sample.
The lower end of the interval is the sample mean subtracted by M. So it is 15 - 7.66 = 7.34 minutes
The upper end of the interval is the sample mean added to M. So it is 15 + 7.66 = 22.66 minutes.
The 88% confidence interval for the population mean of waiting times is between 7.34 minutes and 22.66 minutes.
which shows the equation below written in the form ax^2 + BX + C=0
x+10=3(x - 1)^2
Answer:
C
Step-by-step explanation:
Given
x + 10 = 3(x - 1)² ← expand (x - 1)² using FOIL
x + 10 = 3(x² - 2x + 1) ← distribute
x + 10 = 3x² - 6x + 3 ← subtract x + 10 from both sides
0 = 3x² - 7x - 7 → C
Answer:
Step-by-step explanation:
what is an example of a literal question
Answer:
an example of a literal question is "what size do you wear", "what time does the show start", "who was the protagonist in your story" etc
Step-by-step explanation:
BP Under 30 30-49 Over 50 Total Low 27 38 31 96 Normal 48 90 92 230 High 23 59 72 154 Total 98 187 195 480 What is the percentage of employees who are 30 and over and have normal or low blood pressure? Group of answer choices 67.9% 52.3% 41.7% 75.4%
Answer:
The correct answer to the following question will be Option A (67.9%).
Step-by-step explanation:
As we know,
The number of total employees will be:
= 480
The number of employees having normal or low BP will be:
= 96 + 230
= 326
Hence, the percentage of low or normal BP workers will be:
= [tex](\frac{326}{480} )\times 100 \ percent[/tex]
= [tex]67.9 \ percent[/tex]
Note:- % (percent)
Find the m∠YAX in the figure below
Answer:
76
Step-by-step explanation:
The two angles are vertical angles so they are equal
3x+7 = 4x-16
Subtract 3x from each side
3x-3x+7 = 4x-3x-16
7 = x-16
Add 16 to each side
7+16 = x-16+16
23 =x
We want YAX
YAX = 3x+7
3*23+7
69+7
76
I need help with this one
Answer:
I think 4^0 is the answer
B
ABC is a right-angled triangle.
AC = 16 cm
Angle C = 90°
А.
size of angle B : size of angle A = 3:2
С
16 cm
Work out the length of AB.
Give your answer correct to 3 significant figures.
Answer:
19.8 cm
Step-by-step explanation:
Angle B is the complement of angle A, so we have this relation for the angles:
B/A = 3/2 = (90°-A)/A
2(90° -A) = 3A . . . . . cross multiply
180° = 5A . . . . . . . . . eliminate parentheses, add 2A
36° = A . . . . . . . . . . . divide by 5
The relations expressed by the mnemonic SOH CAH TOA remind you that ...
Cos = Adjacent/Hypotenuse
cos(A) = AC/AB
AB = AC/cos(A) = (16 cm)/cos(36°)
AB ≈ 19.8 cm
ملی
A man left one-fifth of his property to his
Son , one third to his daughter
and remaining
to his wife. If his wife got 35ooo RS what was the
worth of his total property?
Answer:
Rs 75,000
Step-by-step explanation:
Let the total value of property be x
If one-fifth of that is given to son
property with son = 1/5 of total value of property = 1/5 of x = x/5
If one-third of that is given to daughter
property with daughter = 1/3 of total value of property = 1/3 of x = x/3
remaining property after giving the portions to son and daughter
= total value of property - property with son -property with daughter
= x - x/5 - x/3
taking LCM of 5 and 3 (15)
= (15x - 3x - 5x)/15
= 7x/15
Given that remaining property was given to wife
property with wife = 7x/15
it is given that wife got 35000 Rs
thus,
7x/15 = 35,000
7x = 35,000*15 = 525,000
x = 525,000/7 = 75,000
Thus, total worth of property =Rs 75,000 Answer
Answer:
Rs 75,000
Step-by-step explanation:
Let the total value of property be x
If one-fifth of that is given to son
property with son = 1/5 of total value of property = 1/5 of x = x/5
If one-third of that is given to daughter
property with daughter = 1/3 of total value of property = 1/3 of x = x/3
remaining property after giving the portions to son and daughter
= total value of property - property with son -property with daughter
= x - x/5 - x/3
taking LCM of 5 and 3 (15)
= (15x - 3x - 5x)/15
= 7x/15
Given that remaining property was given to wife
property with wife = 7x/15
it is given that wife got 35000 Rs
thus,
7x/15 = 35,000
7x = 35,000*15 = 525,000
x = 525,000/7 = 75,000
Thus, total worth of property =Rs 75,000 Answer
Patrick’s luck had changed over night – but not his skill at mathematical reasoning. The day after graduating from college he used the $20 that his grandmother had given him as a graduation gift to buy a lottery ticket. He knew his chances of winning the lottery were extremely low and it probably was not a good way to spend this money. But he also remembered from the class he took in business analytics that bad decisions some-times result in good outcomes. So he said to himself, "What the heck? Maybe this bad decision will be the one with a good outcome." And with that thought, he bought his lottery ticket.The next day Patrick pulled the crumpled lottery ticket out of the back pocket of his bluejeans and tried to compare his numbers to the winning numbers printed in the paper. When his eyes finally came into focus on the numbers they also just about popped out of his head. He had a winning ticket! In the ensuing days he learned that his share of the jackpot would give him a lump sum payout of about $500,000 after taxes. He knew what he was going to do with part of the money, buy a new car, pay off his college loans, and send his grandmother on an all expenses paid trip to Hawaii. But he also knew that he couldn’t continue to hope for good outcomes to arise from more bad decisions. So he decided to take half of his winnings and invest it for his retirement. So what do you think? Who is right, Josh or Peyton? And more important, why?
Answer:
I assume Josh and Peyton are his friends and both gave him advice on what to do with half of the money from the big lottery win.
Let's say Josh said "save it or invest it for your retirement" and Peyton said "use it to keep playing the lottery.
We will now look at the sense in each piece of advice!
Step-by-step explanation:
JOSH
By investing the $250,000 (half of the money won), Patrick will be sure that the money is available for him anytime and would even have gotten interest, by the time he's ready to use it.
PEYTON
By playing the lottery continuously, Patrick could get lucky once in a while and win big again. How big though?
Analyzing with the figures given,
$20 gets Patrick a lottery ticket.
$250,000 will get him 12,500 lottery tickets!
Whether he's buying the tickets at once or he'll play the lottery once in a while, I'll say he has good chances of winning big again.
So if the probability of winning big after purchasing up to 12,500 tickets is close to 1, Patrick should play the lottery with the $250,000
If the probability of winning big after purchasing 12,500 lottery tickets is close to 0 (closer to 0 than it is to 1) then Patrick should invest the $250,000 in retirement.
Tara is graphing the equation 4x + 2y = 10. Which of these shows the correct equation in slope-intercept form, slope, and y-intercept?
Answer:
y = -2x + 5
slope = -2
y intercept = 5
Step-by-step explanation:
Slope intercept form of equation of line is given by y = mx + c
where m is the slope of line
c is the y intercept i.e point where given line intersect y axis.
________________________________________________
given equation 4x + 2y = 10
we have to re-write this equation in form y = mx + c
4x + 2y = 10
subtraction 4x from LHS and RHS
4x + 2y - 4x= 10 - 4x
2y = 10- 4x
we have to eliminate 2 from y for that we
divide LHS and RHS by 2 we
2y /2 = 10/2- 4x/2
y = 5 - 2x
rearranging it in y = mx+c form
y = -2x + 5
thus, m = -2 , c = 5
Which system of linear inequalities is represented by the
graph?
O y2x - 2 and y = x + 1
O y< x-2 and y> x + 1
O y < x-2 and y? x + 1
O y> x-2 and y < x + 1
Answer:
answer c.
y <= x - 2 and y >= x + 1
Step-by-step explanation:
You wrote the given answers wrong. Here are the right choices that are given as possible solutions:
O y >= x - 2 and y <= x + 1
O y < x - 2 and y > x + 1
O y <= x - 2 and y >= x + 1
O y > x - 2 and y < x + 1
The graph clearly shows two lines and the intended area is shaded and it is clearly including the lines.
Because the lines are included in the solution, by that alone, you can exclude two answers b and d.
Now you still need to decide between the in equalities in answer a and c. Both lines have a gradient of 1, so that does not help to distinguish...
The y intercept of the top line is at y= +1 and the shaded area is bigger then that....
So y >= x + 1 is the right inequality.By now it is absolutely clear that answer c must be the right answer and you are done!
EXTRA
Although you have deduced beyond any doubt, that answer c must be the right answer, you still can check your findings 'to be sure' by looking and checking for the bottom line...
BE CAREFUL, ONLY DO THIS IF YOU HAVE ENOUGH TIME. Again, you already know the right answer, and this is "just to confirm", so what is the harm in that?
By double checking yourself, it will sort of "undermine" your appproach. Basically you are doing something which is strictly spoken not nessasary any more. So I urge you to basically step over the urge to check yourself, and stick to your answer.
However, if you can not resit the temptation of checking to see if you actually found the right answer, you could test the y intercept of the bottom line, which is at y= -2 and the shaded area is smalller then that....
So y <= x - 2 is the right inequality.So again, it is now confirmed that answer c is indeed the right answer.
The correct system of linear inequalities is represented by the graph are,
⇒ y > x - 2
⇒ y < x + 1
What is mean by Inequality?A relation by which we can compare two or more mathematical expression is called an inequality.
Given that;
The system of linear inequalities is shown in graph.
Hence, By graph;
The value of y - intercepts are,
⇒ - 2 and - 1
Hence, The correct system of linear inequalities is represented by the graph are,
⇒ y > x - 2
⇒ y < x + 1
Thus, The correct system of linear inequalities is represented by the graph are,
⇒ y > x - 2
⇒ y < x + 1
Learn more about the inequality visit:
https://brainly.com/question/25944814
#SPJ7
Your company made $120,000 in revenue and $50,000 in costs for 2017. What was your profit?
Answer:
$70,000
Step-by-step explanation:
Profit = Revenue - Costs
x = 120,000 - 50,000
x = 70,000
A cylindrical metal pipe has a diameter of 8.4 millimeters and a height of 10 millimeters. A hole cut out of the center has a diameter of 6 millimeters.
A smaller cylinder is cut out of a larger cylinder. The smaller cylinder has a diameter of 6 millimeters. The larger cylinder has a diameter of 8.4 millimeters. Both cylinders have a height of 10 millimeters.
What is the volume of metal in the pipe? Use 3.14 for and round the answer to the nearest tenth of a cubic millimeter.
Answer:
[tex]271.3 mm^3\\[/tex]
Step-by-step explanation:
We have to find the volume of the hole and subtract it from the volume of the cylinder.
The volume of a cylinder is given as:
[tex]V = \pi r^2h[/tex]
where r = radius
h = height
A cylindrical metal pipe has a diameter of 8.4 mm and a height of 10 mm.
Its radius is 4.2 mm. Therefore, its volume is:
[tex]V = 3.14 * 4.2^2 * 10 = 553.9 mm^3[/tex]
A hole cut out of the center has a diameter of 6 mm. Its height is also 10 mm.
Its radius is 3 mm. Therefore, its volume is:
[tex]V = 3.14 * 3^2 * 10 = 282.6 mm^3[/tex]
Therefore, the volume of metal in the pipe is:
[tex]553.9 - 282.6 = 271.3 mm^3[/tex]
Answer:
B
Step-by-step explanation:
nu
a. Write the equation of a line through the points (-4,- 10) and (8,5) in slope-intercept form.
b. Write the equation in standard form Ax+By = C, where A, B, and C are integers and A>0.
ents
Thoquution
Answer:
5x - 4y = 20
Step-by-step explanation:
First find slope
(5- -10)/(8- -4) = 15/12 = 5/4
(y - 5) = 5/4 (x - 8), multiply everything by 4 so you don't have fractions
4y - 20 = 5x - 40
5x - 4y = 20
What’s the correct answer for this question?
Answer:
A and B
Step-by-step explanation:
1) Distance to the focus
From (x,y) to the focus(2,-4) {using distance formula}
=√(x-2)²+(y+4)²
2) Distance to the directrix
Is, y+p where P here is (-6)
So
d2 = y+p
= y+(-6)
= y-6
A: What are the solutions to the quadratic equation x2+9=0? B: What is the factored form of the quadratic expression x2+9? Select one answer for question A, and select one answer for question B. B: (x+3)(x−3) B: (x+3i)(x−3i) B: (x−3i)(x−3i) B: (x+3)(x+3) A: x=3 or x=−3 A: x=3i or x=−3i A: x=3 A: x=−3i
Answer:
A. The solutions are [tex]x=3i,\:x=-3i[/tex].
B. The factored form of the quadratic expression [tex]x^2+9=(x-3i)(x+3i)[/tex]
Step-by-step explanation:
A. To find the solutions to the quadratic equation [tex]x^2+9=0[/tex] you must:
[tex]\mathrm{Subtract\:}9\mathrm{\:from\:both\:sides}\\\\x^2+9-9=0-9\\\\\mathrm{Simplify}\\\\x^2=-9\\\\\mathrm{For\:}x^2=f\left(a\right)\mathrm{\:the\:solutions\:are\:}x=\sqrt{f\left(a\right)},\:\:-\sqrt{f\left(a\right)}\\\\x=\sqrt{-9},\:x=-\sqrt{-9}[/tex]
[tex]x=\sqrt{-9} = \sqrt{-1}\sqrt{9}=\sqrt{9}i=3i\\\\x=-\sqrt{-9}=-\sqrt{-1}\sqrt{9}=-\sqrt{9}i=-3i[/tex]
The solutions are:
[tex]x=3i,\:x=-3i[/tex]
B. Two expressions are equivalent to each other if they represent the same value no matter which values we choose for the variables.
To factor [tex]x^2+9[/tex]:
First, multiply the constant in the polynomial by [tex]i^2[/tex] where [tex]i^2[/tex] is equal to -1.
[tex]x^2+9i^2[/tex]
Since both terms are perfect squares, factor using the difference of squares formula
[tex]a^2-i^2=(a+i)(a-i)[/tex]
[tex]x^2+9=x^2+9i^2=\left(-3i+x\right)\left(3i+x\right)[/tex]
A survey found that women's heights are normally distributed with mean 63.3 in. and standard deviation 2.7 in. The survey also found that men's heights are normally distributed with a mean 67.3 in. and standard deviation 2.8. Complete parts a through c below.
a) most of the live characters at an amusement park have height requirements with a minimum of 4ft 9in and a maximum of 6ft 4in find the percentage of women meeting the height requirement
the percentage of woment who meet the height requirement?
(round to two decimal places as needed)
b) find the percentage of men meeting the height requirement
the percentage of men meeting the height requirement
(round to two decimal places as needed )
c) If the height requirements are changed to exclude only the tallest 5% of men and the shortest 5% of women what are the new height requirements
the new height requirements are at least ___ in. and at most ___ in.
(round to one decimal place as needed)
a) The percentage of women meeting the height requirement is approximately 99.99%.
b) The percentage of men meeting the height requirement is approximately 99.95%.
c) The new height requirements are at least 58.5 inches and at most 71.8 inches.
a) To find the percentage of women meeting the height requirement of being between 4ft 9in (57 inches) and 6ft 4in (76 inches), we need to calculate the proportion of women within this range using the normal distribution.
First, we standardize the height requirement using the formula:
Z = (X - μ) / σ
where X is the value (height), μ is the mean, and σ is the standard deviation.
For the lower limit (57 inches):
Z_lower = (57 - 63.3) / 2.7 ≈ -2.33
For the upper limit (76 inches):
Z_upper = (76 - 63.3) / 2.7 ≈ 4.70
Using a standard normal distribution table or calculator, we can find the area between -2.33 and 4.70. This represents the percentage of women meeting the height requirement.
The percentage of women meeting the height requirement is approximately 99.99%.
b) Similarly, for men meeting the height requirement of being between 4ft 9in (57 inches) and 6ft 4in (76 inches), we standardize the values:
For the lower limit (57 inches):
Z_lower = (57 - 67.3) / 2.8 ≈ -3.68
For the upper limit (76 inches):
Z_upper = (76 - 67.3) / 2.8 ≈ 3.11
Using the standard normal distribution table or calculator, we find the area between -3.68 and 3.11.
The percentage of men meeting the height requirement is approximately 99.95%.
c) To find the new height requirements that exclude the tallest 5% of men and the shortest 5% of women, we need to determine the corresponding Z-scores.
For men:
Z_upper_men = Z(0.95) ≈ 1.645
For women:
Z_lower_women = Z(0.05) ≈ -1.645
Using these Z-scores, we can calculate the new height requirements:
For the new lower limit:
X_lower = Z_lower_women * σ + μ
For the new upper limit:
X_upper = Z_upper_men * σ + μ
Substituting the values:
X_lower = -1.645 * 2.7 + 63.3 ≈ 58.53 inches
X_upper = 1.645 * 2.8 + 67.3 ≈ 71.78 inches
Therefore, the new height requirements are at least 58.5 inches and at most 71.8 inches.
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a) The percentage of women meeting the height requirement is 99.99%.
b) The percentage of men meeting the height requirement is 99.95%.
c) The new height requirements are at least 58.5 inches and at most 71.8 inches.
a) For women meeting the height requirement:
Given: Mean (μ) = 63.3 in.
Standard Deviation (σ) = 2.7 in.
So, Minimum height requirement:
= 4 ft 9 in
= 4 * 12 + 9
= 57 inches
and, Maximum height requirement:
= 6 ft 4 in
= 6 * 12 + 4
= 76 inches
We will calculate the Z-scores for these heights using the formula:
Z = (x - μ) / σ
For the minimum height requirement:
[tex]Z_{min[/tex] = (57 - 63.3) / 2.7 ≈ -2.33
For the maximum height requirement:
[tex]Z_{max[/tex] = (76 - 63.3) / 2.7 ≈ 4.70
So, the the area between -2.33 and 4.70.
Thus, the percentage is 99.99%.
b) For men meeting the height requirement:
Given: Mean (μ) = 67.3 in., Standard Deviation (σ) = 2.8 in.
Minimum height requirement: 4 ft 9 in = 57 inches
Maximum height requirement: 6 ft 4 in = 76 inches
For the minimum height requirement:
[tex]Z_{min[/tex]= (57 - 67.3) / 2.8 ≈ -3.68
For the maximum height requirement:
[tex]Z_{max[/tex] = (76 - 67.3) / 2.8 ≈ 3.11
So, the area between -3.68 and 3.11.
Thus, the percentage is 99.95%.
c) For the new height requirements:
For men:
[tex]Z_{upper_{men[/tex] = Z(0.95) ≈ 1.645
For women:
[tex]Z_{lower_{women[/tex] = Z(0.05) ≈ -1.645
For the new lower limit:
[tex]X_{lower} = Z_{lower}_{women} \sigma+ \mu[/tex]
For the new upper limit:
[tex]X_{upper} = Z_{upper}_{men} \sigma+ \mu[/tex]
Substituting the values:
[tex]X_{lower} = -1.645 * 2.7 + 63.3[/tex]
= 58.53 inches
and, [tex]X_{upper} = 1.645 * 2.8 + 67.3[/tex]
= 71.78 inches
Therefore, the new height at least 58.5 inches and at most 71.8 inches.
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What’s the correct answer for this?
Answer:
s = 4.43
Step-by-step explanation:
Using formula for bigger circle
s =r∅
Where s is the Arc length, r is rdius and ∅ is theta(angle)
8.84=5∅
∅= 8.84/5
Angle = 1.77 radians
So both angles equal to 1.77 radians
Now again
Using formula
s = r∅
Where s is the Arc length, r is rdius and ∅ is theta(angle)
s = (2.5)(1.77)
s ≈ 4.43
Lola bought x pencils that cost $0.25 each and y erasers that cost $0.50. She spent less than $3. Which graph represents Lola’s purchase?
Answer:
Graph C is the answer.
Step-by-step explanation:
Lola bought X pencils that cost $0.25 and Y erasers that cost $0.50.
Total expenditure is less than $3.
If we represent expense in the equation form then it will be
Expense on pencils + expense on erasers = Total expense which is < 3
0.25X + 0.50Y < 3
Now we divide the inequality by 0.25
X + 2Y < 12
This inequality when graphed, line will be plotted in dots and area below the line will be in the shaded form.
Slope of this line is = (-1/2) {from the standard equation of line y = mx + c)
Now we come to the graphs. Here dotted line graphs are A or C.
We will calculate the slopes of the lines from the graphs A and C to get tha answer.
For Graph A
The end points are (12, 0) and (0, 3)
So slope = (y-y')/(x-x') = (3-0)/(0-12) = -3/12 = -1/4
For Graph C.
End points the line are (0, 6) and (12, 0)
Slope of the line = (0-6)/(12-0) = -6/12 = -1/2
Therefore Graph C is the answer.
Answer:
Graph C is the answer.
Step-by-step explanation:
Lola bought X pencils that cost $0.25 and Y erasers that cost $0.50.
Total expenditure is less than $3.
If we represent expense in the equation form then it will be
Expense on pencils + expense on erasers = Total expense which is < 3
0.25X + 0.50Y < 3
Now we divide the inequality by 0.25
X + 2Y < 12
This inequality when graphed, line will be plotted in dots and area below the line will be in the shaded form.
Slope of this line is = (-1/2) {from the standard equation of line y = mx + c)
Now we come to the graphs. Here dotted line graphs are A or C.
We will calculate the slopes of the lines from the graphs A and C to get tha answer.
For Graph A
The end points are (12, 0) and (0, 3)
So slope = (y-y')/(x-x') = (3-0)/(0-12) = -3/12 = -1/4
For Graph C.
End points the line are (0, 6) and (12, 0)
Slope of the line = (0-6)/(12-0) = -6/12 = -1/2
Therefore Graph C is the answer.
Step-by-step explanation:
make brainiest please
2. The width of a rectangle is 12 inches less than its length. The perimeter of the rect-
angle is 56 inches. Find the length and width of the rectangle.
Answer:
[tex] P= 2*Lenght + 2*Width[/tex]
Since the perimeter is 56 inches we can solve for the lenght with this equation:
[tex] 56 in = 2*12in + 2*Length[/tex]
And solving for the length we got:
[tex] Length = \frac{56in -24 in}{2} 16 in[/tex]
So then the lenght = 16 inhes and the width of 12 inches
Step-by-step explanation:
For a rectangle of width 12 inches and lenght y inches we know that the perimeter is given by:
[tex] P= 2*Lenght + 2*Width[/tex]
Since the perimeter is 56 inches we can solve for the lenght with this equation:
[tex] 56 in = 2*12in + 2*Length[/tex]
And solving for the length we got:
[tex] Length = \frac{56in -24 in}{2} 16 in[/tex]
So then the lenght = 16 inhes and the width of 12 inches
3
Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar.
The product of (3 + 2) and a complex number is (17 + 71).
The complex number is
Answer:
5-i
Step-by-step explanation:
Product=multiplication
Let the complex number=x
(3+2i)*x=17+7i
x=17+7i / 3+2i
x=(17-7i)*(3-2i)/(3+2i)*(3+2i)
=51-34i+21i+14i^2 / 9+6i+6i+4i^2
=51+13i+14i^2 / 9+12i+4i^2
= (51+14 - 13i) / 13
= (65 -13i) / 13
= 65 / 13 - 13 i / 13
= 5 - i.
11. List and describe three factors that may affect body temperature.
it is age heart rate and weather
Please answer this correctly without making mistakes
Answer:
508
Step-by-step explanation:
use l x w
40x7
10x18
8x6
508
