Answer:
The total amount of pollution discharged during the first 7 years of operation is 1.955 tons
Step-by-step explanation:
Given
[tex]r(t) = \frac{t}{t^2 + 1}[/tex]
Required
The total amount in the first 7 years
This implies that:
[tex]r(t) = \frac{t}{t^2 + 1}; [0,7][/tex]
The total amount is calculated by integrating r(t) i.e.
[tex]v = \int\limits^a_b {r(t)} \, dt[/tex]
So:
[tex]v = \int\limits^7_0 {\frac{t}{t^2 + 1}} \, dt[/tex]
--------------------------------------------------------------
We have:
[tex]t^2 + 1[/tex]
Differentiate
[tex]d(t^2 + 1) = 2t[/tex]
Rewrite as:
[tex]2t = d(t^2 + 1)[/tex]
Solve for t
[tex]t = \frac{1}{2}d(t^2 + 1)[/tex]
---------------------------------------------------------------------------
So:
Make t the subject
[tex]v = \int\limits^7_0 {\frac{t}{t^2 + 1}} \, dt[/tex]
[tex]v = \int\limits^7_0\frac{1}{2}* {\frac{d(t^2 + 1)}{t^2 + 1}} \, dt[/tex]
[tex]v = \frac{1}{2}\int\limits^7_0 {\frac{d(t^2 + 1)}{t^2 + 1}} \, dt[/tex]
Integrate
[tex]v = \frac{1}{2}\ln(t^2 +1)|\limits^7_0[/tex]
Expand
[tex]v = \frac{1}{2}[\ln(7^2 +1) - \ln(0^2 +1)][/tex]
[tex]v = \frac{1}{2}[\ln(50) - \ln(1)][/tex]
[tex]v = \frac{1}{2}[3.91 - 0][/tex]
[tex]v = \frac{1}{2}[3.91][/tex]
[tex]v = 1.955[/tex]
What is the perimeter of the triangle
Answer:
56 units
Step-by-step explanation:
add each side, you can get the hypotenuse using the formula a^2+b^2=c^2
Can someone help me please.....
Answer:
the third one
Step-by-step explanation:
2 1/2
Answer help on this !
If the triangles are similar, then the angles are all congruent.
Therefore, we can start by setting the two middle angles equal to each other.
4x + 7 = 5x - 10
7 = x - 10
x = 17
Middle angle = 75
Now that we know our x-value, we can simply plug in x for our other two expressions.
3 * 17 = 51
4(17) - 14 = 54
We can check to make sure that our angle measures are correct by adding them all up and making sure they equal 180.
54 + 51 + 75 = 180
180 = 180
Hope this helps!! :)
Answer:
54, 51, 75
Step-by-step explanation:
4x+7=5x-10 because they are vertical angles and are therefore equal to eachother. x=17.
After plugging the 17 into the equations you get 4(17)+7=75. 3(17)=51. All angles in a triangle add up to 180. We already have 75 and 51 in the first triangle, to get the third length you need to subtract that from 180. 180-75+51=54.
The second triangle will give you the same lengths. 5x-10=75. 4(17)-14=54. Again, 180-75-54=51.
Your final lengths are 75,51,54.
PLS HELP 50 POINTS
To find the amount of water that would fill the inside of an aluminum can, which of the following formulas would you use?
SA = 2 B + Ph
V = lwh
SA = 2 π r 2 + 2 π rh
V = π r 2h
Answer:
V = π r 2h
Step-by-step explanation:
The solution is, the volume of the cylinder in cubic centimeters
V = π(3.5)2h.
What is volume?In mathematics, volume is the space taken by an object. Volume is a measure of three-dimensional space. It is often quantified numerically using SI derived units or by various imperial or US customary units. The definition of length is interrelated with volume.
The volume of a cylinder is given by the equation:
V = π(R)^^2*h
where π = 3.14, R is the radius and h is the height.
If in the image we see that the radius is 7, then the correct option is D.
If in the image we shee that the DIAMETER is 7 (a linear that goes from end to end of the circle and goes trough the middle) then we know that the radius is half of the diameter, 7/2 = 3.5
in this case he correct option is C.
Hence, The solution is, the volume of the cylinder in cubic centimeters
V = π(3.5)2h.
To learn more on volume click :
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complete question:
A cylinder and its dimensions are shown. Which equation can be used to find V, the volume of the cylinder in cubic centimeters?
A) V = π(3.5h)2
B) V = π(7h)2
C) V = π(3.5)2h
D) V = π(7)2h
A birthday cake was cut into equal pieces, and five pieces were eaten. The fraction below shows how much cake was left over. According to the fraction, into how many pieces was the cake cut? 8 /13
A. 5
B. 13
C. 18
D. 8
Answer:
13
Step-by-step explanation:
Answer:
B. 13
Step-by-step explanation:
if 5 were eaten, that's 5/13, and there's 8/13 left. 5 out of thirteen total were eaten and 8 out of thirteen total were left.
If a survey is selected at random, what is the probability that the student is a girl who chose apple as her favorite fruit
Answer:
0.15
Step-by-step explanation:
Total number of students surveyed = 300
From the table,
(Girl n apple) = 46
P(girl n apple) = 46 / 300 = 0.153
4(q-5) = 16
help pleaseee
Answer:
q = 9
Step-by-step explanation:
the key thing to understand in this problem is the distributive property. which basically means we can muliply what's on the interior of the parenthestes ( in this case q-5) by what's on the outside (4).
so 4 will distrubute to both the q and the -5
4q - 20 = 16
add 20 to both sides
4q = 36
divide both sides by 4
q = 9
Goldilocks needs to find at least 12 lbs gold and 18 lbs silver to pay monthly rent. Each day in Mine 1 she finds 2 lbs gold and 2 lbs silver. Each day in Mine 2, she finds 1 lb gold and 3 lbs silver. Set up and solve using either LPsolve or on-line solver How many total days in the mines
Answer:
Total number of days in the mines = 4.5 days + 3 days ≥ 7.5 days
Step-by-step explanation:
Requirement : 12 Ibs gold and 18 Ibs silver to pay monthly rent
Mine 1 ; 2 Ibs of gold , 2Ibs of silver.
Mine 2; 1 Ib of gold , 3 Ibs of silver
using LP
Gold : aX1 + bX2 ≥ 12 ---------- ( 1 )
Silver: cX1 + dX2 ≥ 18 --------- ( 2 )
where; X1 = days spent in Mine 1
X2 = days spent in Mine 2
Total days spent in mines : X1 + X2 =
a = Gold found in mine 1 = 2
b = Gold found in mine 2 = 1
c = silver found in mine 1 = 2
d = silver found in mine 2 = 3
Back to equations 1 and 2
2X1 + X2 ≥ 12 ----------- ( 3 )
2X1 + 3X2 ≥ 18 ------------ ( 4 )
solving equations 3 and 4
= 0 + 2X2 ≥ 6 ∴ X2 ≥ 3 days ( days spent in mine 2 )
Input value into ( 3)
2X1 ≥ 12 - 3 = 9
∴ X1 ≥ 4.5 days ( days spent in mine 1 )
Total number of days in the mines = 4.5 days + 3 days ≥ 7.5 days
Find the volume of the trapezoidal prism.
7 in.
6 in.
12 in.
4 in.
Answer: 48
Step-by-step explanation: you will have to multiply
Which phrase is represented by the expression 6/r+5?
A.the sum of 6 and 5 divided by a number, r
B.five more than a number, r, divided by 6
C.six divided by the sum of a number, r, and 5
D.five more than the quotient of 6 and a number, r
Answer:
D.five more than the quotient of 6 and a number,
Step-by-step explanation:
To evaluate the the phrase written as :
6/r+5
Here, there is no bracket to make any distinction, hence using the BODMAS mode of evaluation, we deal with the division first before the sum. Hence we interpr te the equation as :
6 / r = quotient ; then, 5 is added to the quotient obtained from the divison of 6 by r.
round to the nearest thousand 83,243 answer
Answer:
83,000
Step-by-step explanation:
Thousand = 1,000s place
1,000s place of 83,243 is the 3 (3,000)
The number right before 3 is the 2 (200)
2 is closer to zero than 10 so it rounds down
83,243 then becomes 83,000 since the other numbers before the (2) round down with it.
2/7, 3/4, 2/3. Arrange it in ascending order
Answer:
2,7 2,3 3/4
Step-by-step explanation:
2,7 = 0.29 2,3 = 0.67 3/4 = 0.75
The white Christmas tree is 7.55m tall.the green Christmas tree is twice as tall as the white Christmas tree which is 0.454m taller the golden Christmas tree. What is the total height of the 3:Christmas tree? A 37.296m b .372.96m.c.3729.6m.d.37296
help me guys
The white Christmas tree is 7.55m
Green Christmas tree is twice as tall as white Christmas tree: 7.55 * 2 = 15.1m
High golden Christmas tree: 15.1m - 0.454m = 14.646m
The total height of 3 Christmas trees is: 7.55m + 15.1m + 14.646m = 37.296m
Choose: A 37.296m
PLEASEEEE HELP MEEEEEEE
Answer:
The answer is A.
Step-by-step explanation:
If you count how many blocks it takes on the y axis, you will get 7 but note that it is reflected so it is -7. If you count how many blocks it takes on the x axis you get -3. So the answer is (-3,-7).
This is urgent please help me out.The side lengths of different triangles are given. Which triangle is a right triangle?
Answer:
C. √18, √7, 5
Step-by-step explanation:
_____________
An air-conditioning fan makes 125 revolutions per second. How many revolutions will it make if it runs for 30 minutes?
Answer:
225,000 revolutions
Step-by-step explanation:
An air conditioning fan makes 125 revolutions per second
The number of revolution in 30 minutes can be calculated as follows
60 secs= 1 min
x= 30 min
= 30×60
= 1800 secs
1800×125
= 225,000
Hence the airconditioning makes 225,000 revolutions in 30 minutes
How many different squads of 5 players can be picked from 10 basketball players?
Answer:
2 squads of five can be picked from 10 basketball players
Step-by-step explanation:
To solve this problem you have to divide 10 ÷ 2 which equals to 5.
Freddy earned $7.95 an hour, and last week he worked for 20 hours. About how much money did he earn?
Answer:
He earned $159
Step-by-step explanation:
7.95 Times 20
Answer:
$159
Step-by-step explanation:
[tex]\frac{1}{20} :\frac{7.95}{y}[/tex]
Cross multiply.
y · 1 = 7.95 · 20
Simplify.
y = 159
I need help with this asap thank you
Answer:a
Step-by-step explanation:a
If u + t = 5 and u-t=2, what is the value of
(u – t)(u² - 12) ?
Answer:
(u – t)(u² - 12) is equal to 0.5.
Step-by-step explanation:
First let's find u and t:
Given u + t = 5, and u - t = 2
We'll substitute one of those into the other equation.
Let's solve the second one for u:
u - t = 2
u = 2 + t
Now we can substitute that definition into the first equation:
u + t = 5
(2 + t) + t = 5
2 + 2t = 5
2t = 3
t = 1.5
Now we can substitute that into either of the original equations to find u:
u = 2 + t
u = 2 + 1.5
u = 3.5
So t = 1.5 and u = 3.5. Now we can substitute them into the given expression to solve it:
(u – t)(u² - 12)
= (3.5 – 1.5)(3.5² - 12)
= (3.5 – 1.5)(12.25 - 12)
= 2 × 0.25
= 0.5
Answer:
0.5
Step-by-step explanation:
You know that u-t is 2, so it'll be 2([tex]u^{2}[/tex] -12)
Now, system of equations to solve for u. if u+t=5, this means t=5-u, you can plug it in into u-t=2, so u-(5-u)=2. Now you know that u is 3.5, so do the calculations.
3. Find the volume of the following figure. 62 units 58 units 60 units) 64 units3
Answer:
60 units
Step-by-step explanation:
Its a 5 × 3 × 4 cube
To find volume multiply the dimensions and you will get 60
Answer:
60 units
Step-by-step explanation:
I did the test.
Please help and I would really appreciate if the answer is correct
Answer:
The value for 6 is ones that's the answer
Answer:
14) 0.01 or 1/100
15) 0.06
16) 3.02
17) >
18)0.6
19) 100
20) 0.35
Mary’s bedroom rug is shown below. Find the perimeter and area of the rug.
PLEASE HELP!!
Write an equation for the
line on the graph below:
Answer:
x =-1 i think
Step-by-step explanation:
Answer:
x = -1
This is because all values of x is -1 no matter the y value
Feel free to mark this as brainliest :D
ILL GIVE BRAINLIEST
Given the diagram, which of the following must be true?
Answer:
Choice D
Step-by-step explanation:
QS ≈ TR
they have same direction, sense and magnitude
Answer:
B. QR ≅ TS
Step-by-step explanation:
Angle TR shows us that it is a right angle. Flip it to the other side as the inverse and we get the angle QR.
the polynomial x^+3x - 1 is a factor of x^3+2x^2-5x-6
Answer:
If its x^2 + 3x - 1 it is not a factor.
Step-by-step explanation:
x^2+3x - 1 is a factor of x^3+2x^2-5x-6?
Try dividing:
x^2+3x - 1 ) x^3 + 2x^2 - 5x - 6( x - 1
x^3 + 3x^2 - x
- x^2 -4x - 6
-x^2 - 3x + 1
- x - 7 <------- remainder.
Plz help me this is urgent!!
Answer:
This type of graph is B a stem graph
Answer:
B. Stem-and-leaf plot.
Step-by-step explanation:
A stem and leaf plot will typically have numbers on the left and right side, with a line separating the numbers. This graph is an example of a stem-and-leaf plot.
A line plot (example shown).
A bar graph (example shown).
A pictograph (example shown).
sidney writes two equations: I = 350n and E = 150n + 1000. The equations relate income I and operating expenses E to number of customers. Sidney writes the equation P = 350n − (150n + 1000) to show how tour profit P depends on the number of customers n. Use the rule to find profits P for 8, 12, 20, and 30 customers.
9514 1404 393
Answer:
600, 1400, 3000, and 5000
Step-by-step explanation:
The profit equation can be simplified.
P = 350n -(150n +1000)
P = 200n -1000 . . . . . . . . . collect terms
P = 200(n -5) . . . . . . . . . . . factor out 200
For the given numbers n, we have ...
P = 200({8, 12, 20, 30} -5) = 200{3, 7, 15, 25} = {600, 1400, 3000, 5000}
Profits for 8, 12, 20, and 30 customers are 600, 1400, 3000, and 5000, respectively.
Type the correct answer in the box. If cos x=sin(20 + x) and 0° <x<90°, the value of x is:
Answer:
the value of x is 90 Your answer
Step-by-step explanation:
A sample of 28 sales transactions at Costco shows a mean transaction time of 296 seconds with a standard deviation of 48 seconds. Costco is interested in finding out whether the mean transaction time is less than 310 seconds. Answer the following questions. a) Write down the null and alternative hypotheses. b) Find the test statistic and the critical value at 1% significance level. c) At 1% level of significance, what is your conclusion
Answer:
a) The null hypothesis is [tex]H_0: \mu = 310[/tex] and the alternative hypothesis is [tex]H_1: \mu < 310[/tex].
b) The test statistic is [tex]t = -1.54[/tex]. The critical value is [tex]t_c = -2.473[/tex].
c) The test statistic is [tex]t = -1.54 < t_c = -2.473[/tex], which means that there is not enough evidence to reject the null hypothesis that the mean transaction time is of 310 times, so no evidence to conclude that the mean transaction time is less than 310 seconds.
Step-by-step explanation:
Question a:
Costco is interested in finding out whether the mean transaction time is less than 310 seconds.
At the null hypothesis, we test if the mean is of 310 seconds, that is:
[tex]H_0: \mu = 310[/tex]
At the alternative hypothesis, we test if the mean is of less than 310 seconds, that is:
[tex]H_1: \mu < 310[/tex]
b) Find the test statistic and the critical value at 1% significance level.
Test if the mean is less than a value, sample of 28, and standard deviation for the sample. Thus, we have a left-tailed t-test with 28 - 1 = 27 degrees of freedom and a 0.01 significance level, and the critical value is [tex]t_c = -2.473[/tex].
The test statistic is:
[tex]t = \frac{X - \mu}{\frac{s}{\sqrt{n}}}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, s is the standard deviation pf the sample and n is the size of the sample.
310 is tested at the null hypothesis:
This means that [tex]\mu = 310[/tex].
A sample of 28 sales transactions at Costco shows a mean transaction time of 296 seconds with a standard deviation of 48 seconds.
This means that [tex]n = 28, X = 296, s = 48[/tex].
Value of the test statistic:
[tex]t = \frac{X - \mu}{\frac{s}{\sqrt{n}}}[/tex]
[tex]t = \frac{296 - 310}{\frac{48}{\sqrt{28}}}[/tex]
[tex]t = -1.54[/tex]
The test statistic is [tex]t = -1.54[/tex].
c) At 1% level of significance, what is your conclusion
The test statistic is [tex]t = -1.54 < t_c = -2.473[/tex], which means that there is not enough evidence to reject the null hypothesis that the mean transaction time is of 310 times, so no evidence to conclude that the mean transaction time is less than 310 seconds.