At the start, the tank contains
(0.25 lb/gal) * (100 gal) = 25 lb
of sugar. Let [tex]S(t)[/tex] be the amount of sugar in the tank at time [tex]t[/tex]. Then [tex]S(0)=25[/tex].
Sugar is added to the tank at a rate of P lb/min, and removed at a rate of
[tex]\left(1\frac{\rm gal}{\rm min}\right)\left(\dfrac{S(t)}{100}\dfrac{\rm lb}{\rm gal}\right)=\dfrac{S(t)}{100}\dfrac{\rm lb}{\rm min}[/tex]
and so the amount of sugar in the tank changes at a net rate according to the separable differential equation,
[tex]\dfrac{\mathrm dS}{\mathrm dt}=P-\dfrac S{100}[/tex]
Separate variables, integrate, and solve for S.
[tex]\dfrac{\mathrm dS}{P-\frac S{100}}=\mathrm dt[/tex]
[tex]\displaystyle\int\dfrac{\mathrm dS}{P-\frac S{100}}=\int\mathrm dt[/tex]
[tex]-100\ln\left|P-\dfrac S{100}\right|=t+C[/tex]
[tex]\ln\left|P-\dfrac S{100}\right|=-100t-100C=C-100t[/tex]
[tex]P-\dfrac S{100}=e^{C-100t}=e^Ce^{-100t}=Ce^{-100t}[/tex]
[tex]\dfrac S{100}=P-Ce^{-100t}[/tex]
[tex]S(t)=100P-100Ce^{-100t}=100P-Ce^{-100t}[/tex]
Use the initial value to solve for C :
[tex]S(0)=25\implies 25=100P-C\implies C=100P-25[/tex]
[tex]\implies S(t)=100P-(100P-25)e^{-100t}[/tex]
The solution is being drained at a constant rate of 1 gal/min; there will be 5 gal of solution remaining after time
[tex]1000\,\mathrm{gal}+\left(-1\dfrac{\rm gal}{\rm min}\right)t=5\,\mathrm{gal}\implies t=995\,\mathrm{min}[/tex]
has passed. At this time, we want the tank to contain
(0.5 lb/gal) * (5 gal) = 2.5 lb
of sugar, so we pick P such that
[tex]S(995)=100P-(100P-25)e^{-99,500}=2.5\implies\boxed{P\approx0.025}[/tex]
what is the product of 72 x 0.45
Answer:
32.4
Step-by-step explanation:
Answer:
32.4
Step-by-step explanation:
Product means the answer of a multiplication problem. So 75 x 0.45 = 32.4.
[tex]75 \times 0.45 = 32.4[/tex]
Hope this helped :)
What is the equation of the line that is perpendicular to f(x) and passes through the point (4, –6)? a.4x + 3y = –2 b. 3x + 4y = –12 c.4x – 3y = 34 d.3x – 4y = 36
Answer:
8
Step-by-step explanation: because its even
Please help with this
A circle has an area of 45 square meters. What is the area of a sector with an arc measure of 70°? I need this asap someone help please
Answer:[tex]8.75\ m^2[/tex]
Step-by-step explanation:
Given
Area of circle is [tex]A=45\ m^2[/tex]
Arc measure [tex]\theta =70^{\circ}[/tex]
and area of sector is given by
[tex]\Rightarrow \frac{\theta }{360^{\circ}}\times \text{Area of circle}[/tex]
[tex]\Rightarrow \frac{70}{360}\times 45[/tex]
[tex]\Rightarrow 0.194\times 45[/tex]
[tex]\Rightarrow 8.75\ m^2[/tex]
So, area of sector is [tex]8.75\ m^2[/tex]
LOIHal y LU LIC LOIVCI SC VILHC ISUSLCICS langic TCUICHT
2. What type of angle is ZDBC if it measures exactly 180° and its rays form a straight line?
roofs
onships
8
on to
angles
Properties
DESCRIPTION
Answer:
straight angle
Step-by-step explanation:
A straight angle is one whose measure is 180°. Its formative rays point in opposite directions from the vertex and make a straight line.
ali's tyre pressure gauge shows a reading witch is 8 % lower than the actual pressure when the gauge shows 33.58
The actual pressure when the gauge shows 33.58 would be 36.5.
Used the concept of the percentage that states,
A number or ratio that can be expressed as a fraction of 100 or a relative value indicating the hundredth part of any quantity is called a percentage.
Given that,
Ali's tire pressure gauge shows a reading which is [tex]8 \%[/tex]lower than the actual pressure.
And, the gauge shows [tex]33.58.[/tex]
Let us assume that,
The actual pressure of Ali's tires = x
Hence, we can formulate the equation,
[tex]x \times (1 - 8\%) = 33.58[/tex]
Solve the equation for x,
[tex]x \times (1 - \dfrac{8}{100} ) = 33.58[/tex]
[tex]x \times (1 - 0.08) = 33.58[/tex]
[tex]x \times 0.92 = 33.58[/tex]
Divide both sides by 0.92;
[tex]x= \dfrac{33.58}{0.92}[/tex]
[tex]x = 36.5[/tex]
Therefore, The actual pressure of Ali's tires = 36.5
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The complete question is,
Ali's tire pressure gauge shows a reading which is 8% lower than the actual pressure.
What is the actual pressure of Ali's tires when the gauge shows 33.58?
Factor 9x^2+6x+1 completely
Answer:
[tex](3x+1)^2[/tex]
Step-by-step explanation:
[tex]9x^2+6x+1=\\(3x+1)^2[/tex]
You can confirm this by working and expanding backwards:
[tex](3x+1)^2=\\(3x+1)(3x+1)=\\9x^2+3x+3x+1=\\9x^2+6x+1[/tex]
Hope this helps!
The factorized form of 9x² + 6x + 1 is indeed (3x + 1)².
To find the factorized form of the quadratic expression 9x² + 6x + 1 is (3x + 1)², we can expand the factorized form and compare it with the given expression to check if they are equal.
Expanding (3x + 1)² using the square of a binomial formula, we get:
9x² + 6x + 1
= 9x² + 3x + 3x + 1
= 3x (3x + 1) + 1 (3x + 1)
(3x + 1)² = (3x + 1)(3x + 1)
Comparing the expanded form of (3x + 1)² with the given expression 9x² + 6x + 1, we can see that they are equal.
Therefore, we have found that the factorized form of 9x² + 6x + 1 is indeed (3x + 1)².
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The graph of f(x) = x2 was transformed to create the graph of g(x) = (x − 7.5)2. Which of these describes this transformation?
A.
A horizontal shift to the right 7.5 units
B.
A horizontal shift to the left 7.5 units
C.
A vertical shift down 56.25 units
D.
A vertical shift up 56.25 units
Answer:
A. A horizontal shift to the right 7.5 units
Step-by-step explanation:
Replacing x with x-7.5 shifts the graph 7.5 units to the right.
__
In general, g(x) = f(x-h)+k will shift h units right and k units up. In this problem there is no vertical shift.
A standard fair dice is rolled twice.
What is the probability of getting an odd number on the first roll and any factor of 12 on the other?
Answer:
5/12
Step-by-step explanation:
The probability of rolling an odd number is 3/6, which is 1/2
The probability of rolling a factor of 12 is 5/6 (1,2,3,4,6)
1/2 x 5/6 = 5/12
Can you help me(×+5) (4x-3)=0
sry my mistake wrong quesrion
Find an equation for the line perpendicular to the line 3x+2y=−1 3x+2y=−1 having the same y-intercept as 2x+7y=2
The general form for the equation of a line is:
[tex]y = mx + c[/tex]
Where:
m is the gradient of the line
c is the y intercept of the line (y - intercept is where the graph crosses the y-axis)
So if you had the following equation:
[tex]y = 3x + 2[/tex]
Then:
m = 3
c = 2
So gradient = 3, and y intercept = 2
---------------------------------------------------
Rearranging
So first rearrange both of the equations in the form y = mx + c :
[tex]3x + 2y = -1[/tex] becomes [tex]y = -\frac{3}{2} x-\frac{1}{2}[/tex] [tex](where: \ m = -\frac{3}{2} \ and, \ c = -\frac{1}{2} )[/tex]
and:
[tex]2x+7y=2[/tex] becomes [tex]y=-\frac{2}{7}x +\frac{2}{7}[/tex] [tex](where: \ m = -\frac{2}{7} \ and, \ c = \frac{2}{7})[/tex]
---------------------------------------------
The question tells us that the equation of the line we are looking for has the same y-intercept as:
[tex]2x+7y=2[/tex]
So the line we are trying to work out will also have a y intercept of [tex]\frac{2}{7}[/tex]
(refer to rearranging)
----------------------------
The question also tells us that the line is perpendicular to [tex]3x + 2y = -1[/tex]
Perpendicular gradient = negative reciprocal of the gradient of the line it is perpendicular to.
So the gradient of the new line will be the negative reciprocal of the gradient of [tex]3x + 2y = -1[/tex]
Gradient of [tex]3x + 2y = -1[/tex] is: [tex]-\frac{3}{2}[/tex]
(refer to rearranging)
Gradient of new line: = negative reciprocal of [tex]-\frac{3}{2}[/tex] , which is [tex]\frac{2}{3}[/tex]
(just flip fraction and change the sign)
------------------------------------
So for the new line: [tex]m = \frac{2}{3} \ and, \ c = \frac{2}{7}[/tex]
So just substitute in the values for m and c into: y = mx + c
[tex]y = mx + c\\y = \frac{2}{3} x + \frac{2}{7}[/tex]
-----------------------------
Answer:
So equation of the new line is:
[tex]y = \frac{2}{3}x + \frac{2}{7}[/tex]
------------
Any questions, just ask.
1. Solve the equation using the zero-product property.
-x(5x – 4) = 0
Answer:
x = 0, 4/5
Step-by-step explanation:
The zero-product property states that if the product of a and b is zero, then either a = 0, b = 0, or both terms equal zero
Here our a term is -x and our b term is (5x - 4)Setting each term equal to zero and solving for x we get-x = 0 → x = 05x - 4 = 0 → 5x = 4 → x = 4/5Find the volume of a cone with a radius of 3 millimeters and a 7 height of millimeters. Use 22/7 for 3.14 .
Answer:
66
Step-by-step explanation:
So the volume of a cone is [tex]\pi r^2*\frac{h}{3}[/tex]
r = 3
h = 7
[tex]9\pi *\frac{7}{3} = 21\pi[/tex]
[tex]\frac{22}{7} *21=66[/tex]
__-112=225+125 need help
Answer:
I think it's 462. I'm sry if I'm wrong.
Use the method of completing the square to transform the quadratic equation into the equation form (x – p)2 = q. −9 + 12x - 6x2 = 0
Answer:
Step-by-step explanation:espinal hola defryet iSight x0 do hulp
Answer:
(x-1)^2= -0.5
Step-by-step explanation:
I DID THE USA TEST PREP AND THIS ANSWER WAS CORRECT
What is the best category for the system of equations shown:
2x + 6y = 14
- 2x+2y =- 10
1.Consistent / Independent
2.Consistent / Dependent
3.Inconsistent / Independent
4.None of the above.
Answer:
Option (1)
Step-by-step explanation:
System of equations has been given as
2x + 6y = 14
By dividing this equation by 2
x + 3y = 7 --------(1)
Second equation is,
-2x + 2y = -10
-x + y = -5 -------(2)
By adding equation (1) and equation (2)
(x + 3y) + (-x + y) = 7 - 5
2x = 2
x = 1
By putting x = 1 in the equation (1)
1 + 3y = 7
3y = 6
y = 2
So, we get exactly one solution pair (1, 2) where these lines are intersecting.
Therefore, the best category that defines the system of equations is Consistent/Independent
Option (1) will be the answer.
Please answer this correctly
Answer:
40 cm.
Step-by-step explanation:
So what I tried to do in this case is compare 96 to 64. I subtracted those two numbers which is 32. So since thats the difference between those two shapes, I did the same thing with 72 and I subtracted it but 32, which led me to 40.
Hope this helped :)
Answer:
u=48
Step-by-step explanation:
In similar triangles, corresponding sides have the same ratio.
64/96=u/72
Step 1: Cross-multiply
(64)*(72)=u*(96)
4608=96u
Step 2: Flip the equation.
96u=4608
Step 3: Divide both sides by 96.
96u /96=4608 /96
u=48
I need help with B ASAP because work is due tomorrow and Im seriously stuck. I have tried so many, please help.
Part A is correct; good job.
The universe is even numbers between 1 and 25, that's 2 thru 24. Count; there are twelve of them.
There's only one of them in the intersection of A and B, namely 8.
So the probability is one in twelve.
Answer: 1/12
Which values are solutions to the inequality –3x – 4 < 2?
Answer: x>-2
Step-by-step explanation:
To find the values of the inequality, you treat this like it would be any other equation.
[tex]-3x<6[/tex]
[tex]x>-2[/tex]
Is -1.27 a rational number
Answer:
Yes.
Step-by-step explanation:
Answer:
si
Step-by-step explanation:
what happened to www.brainy.com?
As far as I'm concerned, it still exists
What do you mean becauae nothing happened
How many ways can the letters be arranged in the word: GLASS
Answer:
120
Step-by-step explanation:
Help! I just don't understand
Answer:
$71
Step-by-step explanation:
Since x denotes the number of miles and we know that the car rode 100 miles, this means that x=100, and when we plug this in, we get C(x) = 0.5* 100 + 21 = 50 + 21 = $71. Hope this helps!
Answer:
C(100) = 71
Step-by-step explanation:
C(x) = .5x+21
Let x= 100
C(100) = .5(100)+21
= 50+21
= 71
In the past, the mean running time for a certain type of flashlight battery has been 8.6 hours. The manufacturer has introduced a change in the production method and wants to perform a hypothesis test to determine whether the mean running time has increased as a result.
The hypotheses are:
H0: μ = 8.6 hours
Ha: μ > 8.6 hours
where μ is the mean running time of the new batteries.
Explain the meaning of a Type II error.A. The manufacturer will decide the mean battery life is greater than 8.3 hours when in fact it is greater than 8.3 hours. B. The manufacturer will decide the mean battery life is less than 8.3 hours when in fact it is greater than 8.3 hours. C. The manufacturer will decide the mean battery life is 8.3 hours when in fact it is 8.3 hours. D. The manufacturer will decide the mean battery life is 8.3 hours when in fact it is greater than 8.3 hours. E. The manufacturer will decide the mean battery life is greater than 8.3 hours when in fact it is 8.3 hours.
Answer:
H0: μ = 8.3 hours
Ha: μ > 8.3 hours
We need to remember that a type of error II if the error associated when we NO reject the null hypothesis when actually the alternative hypothesis is true. And is also known as false negative. The best answer for this case would be:
D. The manufacturer will decide the mean battery life is 8.3 hours when in fact it is greater than 8.3 hours.
Since we are FAILING to reject the null hypothesis when the true mean is actually higher than the value specified
Step-by-step explanation:
For this case we want to determine if mean running time has increased as a result of the new change so then the system of hypothesis are given by:
Note: we assume that the value to check in order to be consistent with the options is 8.3
H0: μ = 8.3 hours
Ha: μ > 8.3 hours
We need to remember that a type of error II if the error associated when we NO reject the null hypothesis when actually the alternative hypothesis is true. And is also known as false negative. The best answer for this case would be:
D. The manufacturer will decide the mean battery life is 8.3 hours when in fact it is greater than 8.3 hours.
Since we are FAILING to reject the null hypothesis when the true mean is actually higher than the value specified
I need help with question C
Type the correct answer in each box.
A circle is centered at the point (-7, -1) and passes through the point (8, 7).
The radius of the circle is _ units. The point (-15,_) lies on this circle.
Answer:
17, 23
Step-by-step explanation:
First, to find the radius, we need to find the distance between the center of the circle, (-7, -1), and the point that the circle passes through, (8, 7). Plugging these coordinates into the distance formula we do [tex]\sqrt{(-7-8)^2+(-1-7)^2}[/tex] which gives us 17. Therefore, the radius of the circle is 17 units.
Next to find the y-coordinate of the point (-15, ), we need to write out the equation of the circle and then plug in the point. The equation of the circle would be [tex](x+7)^{2} +(y-8)^{2}=289[/tex]. Now we can plug in -15 for x and solve for y. So now we have [tex](-15+7)^{2} +(y-8)^{2}=289[/tex].
Simplifying the equation we have [tex](8)^{2} +(y-8)^{2}=289[/tex]. Subract [tex]8^{2}[/tex] from 289 and now the equation is [tex](y-8)^{2}=225[/tex]. Square root both sides to get [tex]y-8=15[/tex]. We solve for y to get 23. Therefore, the point is (-15, 23).
Answer:
Well, the answer would be 17,23 Also i had the same question as you so i already know the answer
Jamie says the value of 1.43 × (− 22 43 ) is close to −0.75. Student A says this estimate is reasonable because the product is negative and about half of 1.5. Student B says you could find the product using a calculator as follows: "Divide −22 by 43, multiply the quotient by 1.43, then round the product to the nearest hundredth." Does student B's approach to find the product justify the claim that Jamie's estimate is reasonable?
Answer:
Student A says this estimate is reasonable because… Get ... Student A says this estimate is reasonable because the product is negative and about half of 1.5. Student B says you could find the product using a calculator as follows: "Divide −18 by 35, multiply the quotient by 1.43, then round the product
Step-by-step explanation:
calculations with a calculator or computer we need a way of checking that the answers it ... introduce students to this way of thinking and give them practice at estimating simple ... Do they always get the right answer no matter what? Invent a story illustrating a calculator error that you may have made or use the following.
Sasha’s daily tips this work week were $43, $32, $65, $88, $50, and $72. Is Sasha correct in thinking that the mean accurately represents how much money she makes in daily tips? Yes, Sasha is correct. The mean amount she makes is $58.33 in a day. Yes, Sasha is correct. The mean amount she makes is $65.33 in a day. No, Sasha is not correct. The median amount she makes is $53.00 in a day. No, Sasha is not correct. The median amount she makes is $60.00 in a day.
Answer: $58.33
Step-by-step explanation:
Yes, Sasha is correct. The mean amount she makes is in a day.
Answer:
a: Yes, Sasha is correct. The mean amount she makes is $58.33 in a day
Step-by-step explanation:
edg2020
It’s about angles use an equation to solve and ABCD?
And what is the measure of RST?
Answer:
A. 40 degree+ 90 degree = x
The sum of the angles = 130 degree
Step-by-step explanation:
[tex]Given:\:\:\angle RSV = 40\degree,\:\:\angle VST = 90\degree\\\because \angle RSV + \angle VST = \angle RST\\\therefore 40\degree + 90\degree = x[/tex]
x = 130 degree
At a local baseball game, the concession stand has two different meal choices. You can get 5 hotdogs and 4 drinks for $15.50 or you can get 6 hotdogs and 3 drinks for $15.00. If the price of hotdogs and drinks is the same for each meal, find how much it costs for an individual hotdog and an individual drink.
per hordog =
per drink=
Answer: Hot Dog $1.50 Drinks $2.00
Step-by-step explanation: