Is there anything else that goes with the question or is that it?
a candlemaker prices one set of scented candles at $10
y=10x
x= how many candles
Two tanks are interconnected. Tank A contains 60 grams of salt in 50 liters of water, and Tank B contains 80 grams of salt in 40 liters of water.
A solution of 2 gram/L flows into Tank A at a rate of 5 L/min, while a solution of 3 grams/L flows into Tank B at a rate of 7 L/min. The tanks are well mixed.
The tanks are connected, so 8 L/min flows from Tank A to Tank B, while 3 L/min flows from Tank B to Tank A. An additional 12 L/min drains from Tank B.
Letting x represent the grams of salt in Tank A, and y represent the grams of salt in Tank B, set up the system of differential equations for these two tanks.
Let a(t) and b(t) denote the amounts of salt in tanks A and B, respectively.
The volume of liquid in tanks A and B after t minutes are
A: 50 L + (5 L/min + 3 L/min - 8 L/min)t = 50 L
B: 40 L + (7 L/min + 8 L/min - 3 L/min - 12 L/min)t = 40 L
so the amount of solution in the tanks stays constant.
Salt flows into tank A at a rate of
(2 g/L)*(5 L/min) + (b(t)/40 g/L)*(3 L/min) = (10 + 3/40 b(t)) g/min
and out at a rate of
(a(t)/50 g/L)*(8 L/min) = 4/25 a(t) g/min
so the net flow rate is given by the differential equation
[tex]\dfrac{\mathrm da(t)}{\mathrm dt}=10+\dfrac{3b(t)}{40}-\dfrac{4a(t)}{25}[/tex]
We do the same for tank B: salt flows in at a rate of
(3 g/L)*(7 L/min) + (a(t)/50 g/L)*(8 L/min) = (21 + 4/25 a(t)) g/min
and out at a rate of
(b(t)/40 g/L)*(3 L/min + 12 L/min) = 3/8 b(t) g/min
and hence with a net rate of
[tex]\dfrac{\mathrm db(t)}{\mathrm dt}=21+\dfrac{4a(t)}{25}-\dfrac{3b(t)}8[/tex]
Replace a(t) and b(t) with x and y. Then the system is (in matrix form)
[tex]\dfrac{\mathrm d}{\mathrm dt}\begin{bmatrix}x\\y\end{bmatrix}=\dfrac1{200}\begin{bmatrix}-32&15\\32&-75\end{bmatrix}\begin{bmatrix}x\\y\end{bmatrix}+\begin{bmatrix}10\\21\end{bmatrix}[/tex]
with initial conditions x(0) = 60 g and y(0) = 80 g.
what is the equation to the following sentence?
Seven subtracted from two times a number is 13
Answer:
4x-7>13
add 7
4x>20
divide by 4
x>5
Step-by-step explanation:
The average hourly wage for a high school student in Illinois is $8.25 per hour with a standard deviation of $.25. Assume hourly wages vary normally.
A) Determine the margin of error for this scenario.
B) For the previous question you just answered, construct a 95% confidence interval for the hourly wage for a high school student.
C) For the 95% confidence interval you just constructed, does an hourly wage of $9.15 fall within that acceptable range?
Answer:
Step-by-step explanation:
Hello!
The variable of interest is
X: hourly wage of a high school student
X~N(μ;σ²)
X[bar]= $8.25
σ= $0.25
For a 95% CI for the average hourly wage for 1 high school student:
For this exercise you have to consider the sample size n=1
a) The margin of error of the CI is calculated as:
d= [tex]Z_{1-\alpha /2}[/tex] * σ
1-α: 0.95 ⇒ α:0.05
1-α/2:0.975
[tex]Z_{1-\alpha /2}= Z_{0.975}= 1.96[/tex]
d= 1.96 * 0.25= 0.49
b)
The formula for the interval is
X[bar] ± [tex]Z_{1-\alpha /2}[/tex] * σ
[8.25 ± 0.49]
[7.76; 8.74]
With a 95% you'd expect the interval $[7.76; 8.74] to include the average hourly wage of one high school student in Illinois.
c)
Te calculated interval is $ [7.76; 8.74] the value $9.15 does nor fall within that acceptable range.
I hope this helps!
a number rounded to the nearest hundred thousand is 400,000 the same number rounded to the nearest ten thousand is 350,000 what could be the number
Answer:350000
Step-by-step explanation:
The number is 350000
350000 rounded to the nearest hundred thousand is 400000
350000 rounded to the nearest ten thousand is 350000
What’s the correct answer?
Answer:
B.
Step-by-step explanation:
Answer:b
Step-by-step explanation:you need to add both
What type of lines are shown?
Answer:
the angle is acute angle
Answer:
The type of angle shown is an acute angle
Step-by-step explanation:
there are 4 main types of angles. this is an acute angle as it is less than 90°.
Types of angles:
The 4 main types of angles are: acute, obtuse, right angles, reflex angles.
Acute angles- Acute angles are angles less than 90°.
Obtuse Angles-Obtuse angles are angles greater than 90° but less than 180°.
Right Angles- Right angles are angles of 90°.
Reflex Angles- Reflex angles are angles greater than 180° but less than 360°.
Which expression can be used to find the area of the rectangle shown on the coordinate plane 6×7 7×7 8×7 8×8
Answer:that’s a lot of numbers.
Step-by-step explanation:
If the mean of a symmetric distribution is 60, which of these values could be
the median of the distribution?
A. 100
B. 60
C. 80 As
D. 30
SUBMIT
Answer:
i think ...
Step-by-step explanation:
symmetric distribution usually be a bell shape distribution .
most likely the median = mean = 60
The required value of 60 could be the median of the distribution. Option B is correct.
What is mean?The mean of the values is the ratio of the total sum of values to the number of values.
What is the median?When a dataset is ordered, the median is the value that is exactly in the middle. It is a measure of central tendency that distinguishes between the lowest and top 50% of data.
Here,
The mean of a symmetric distribution is 60.
Since for the symmetric data and rational data, the mean is equal to the median,
So Mean = Median
Median = 60
Thus, the required value of 60 could be the median of the distribution.
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change 5 out of 19 to a percentage
Answer:
26.3%
Step-by-step explanation:
5 is divided by 19
That answer is then multiplied by 100.
You may round your answer to the nearest whole number.
Sean tossed a coin off a bridge into the stream below. The path of the coin can be represented by the equation h = -16t2 + 72t + 100. How long will it take the coin to reach the stream?
Answer:
about 5.613 seconds
Step-by-step explanation:
Using the quadratic formula to find the value of t when h = 0, we have ...
at² +bt +c = 0
t = (-b±√(b²-4ac))/(2a)
t = (-72±√(72² -4(-16)(100)))/(2(-16))
t = (-72±√11584)/-32 = (9±√181)/4
Only the positive value of t is of interest.
The coin will hit the stream after (9+√181)/4 seconds ≈ 5.613 seconds.
The edges of a cube increase at a rate of 2 cm divided by s. How fast is the volume changing when the length of each edge is 40 cm? Write an equation relating the volume of a cube, V, and an edge of the cube, a. nothing Differentiate both sides of the equation with respect to t. StartFraction dV Over dt EndFraction equals(nothing )StartFraction da Over dt EndFraction (Type an expression using a as the variable.) The rate of change of the volume is nothing cm cubed divided by sec. (Simplify your answer.)
Answer:
Step-by-step explanation:
Let the edge of the cube be a .
Given
[tex]\frac{da}{dt} = 2 cm/s[/tex]
Volume V = a³
[tex]\frac{dV}{dt} = 3a^ 2\frac{da}{dt}[/tex]
= 3a² x 2
= 6a²
If a = 40 cm
[tex]\frac{dV}{dt} = 6 \times 40\times40[/tex]
= 9600 cm³/s .
Hi guys, Can anyone help me with this tripple integral? Thank you:)
I don't usually do calculus on Brainly and I'm pretty rusty but this looked interesting.
We have to turn K into the limits of integration on our integrals.
Clearly 0 is the lower limit for all three of x, y and z.
Now we have to incorporate
x+y+z ≤ 1
Let's do the outer integral over x. It can go the full range from 0 to 1 without violating the constraint. So the upper limit on the outer integral is 1.
Next integral is over y. y ≤ 1-x-z. We haven't worried about z yet; we have to conservatively consider it zero here for the full range of y. So the upper limit on the middle integration is 1-x, the maximum possible value of y given x.
Similarly the inner integral goes from z=0 to z=1-x-y
We've transformed our integral into the more tractable
[tex]\displaystyle \int_0^1 \int_0^{1-x} \int _0^{1-x-y} (x^2-z^2)dz \; dy \; dx[/tex]
For the inner integral we get to treat x like a constant.
[tex]\displaystyle \int _0^{1-x-y} (x^2-z^2)dz = (x^2z - z^3/3)\bigg|_{z=0}^{z= 1-x-y}=x^2(1-x-y) - (1-x-y)^3/3[/tex]
Let's expand that as a polynomial in y for the next integration,
[tex]= y^3/3 +(x-1) y^2 + (2x+1)y -(2x^3+1)/3[/tex]
The middle integration is
[tex]\displaystyle \int_0^{1-x} ( y^3/3 +(x-1) y^2 + (2x+1)y -(2x^3+1)/3)dy[/tex]
[tex]= y^4/12 + (x-1)y^3/3+ (2x+1)y^2/2- (2x^3+1)y/3 \bigg|_{y=0}^{y=1-x} [/tex]
[tex]= (1-x)^4/12 + (x-1)(1-x)^3/3+ (2x+1)(1-x)^2/2- (2x^3+1)(1-x)/3[/tex]
Expanding, that's
[tex]=\frac{1}{12}(5 x^4 + 16 x^3 - 36 x^2 + 16 x - 1)[/tex]
so our outer integral is
[tex]\displaystyle \int_0^1 \frac{1}{12}(5 x^4 + 16 x^3 - 36 x^2 + 16 x - 1) dx[/tex]
That one's easy enough that we can skip some steps; we'll integrate and plug in x=1 at the same time for our answer (the x=0 part doesn't contribute).
[tex]= (5/5 + 16/4 - 36/3 + 16/2 - 1)/12[/tex]
[tex]=0[/tex]
That's a surprise. You might want to check it.
Answer: 0
If the fish tanks dimension are 60 by 15 by 34 and its is completely empty, what volume of water is needed to fill three fourths of the aquarium? Please help
Answer:
22,950 units³
Step-by-step explanation:
All you have to do is:
[tex]\frac{3}{4} *60*15*34=\\45*15*34=\\675*34=\\\\22,950[/tex]
What is 1 2/3 - 2 1/3?
Step-by-step explanation:
First it will be easer if you turn both sides into improper fractions
5/3-7/3
Now do 5-7
5-7=-2
The bottom of the fraction stays the same
-2/3 is your answer.
A movie theater has a seating capacity of 387. The theater charges $5.00 for children, $7.00 for students, and $12.00 of
adults. There are half as many adults as there are children. If the total ticket sales was $ 2808, How many children,
students, and adults attended?
Answer:
The attendance was 198 children, 90 students and 99 adults.
Step-by-step explanation:
We define:
c: children attendance
s: students attendance
a: adult attendance
The equation that describes the total ticket sales is:
[tex]5c+7s+12a=2808[/tex]
We also know that the children attendance doubles the adult attendance:
[tex]c=2a[/tex]
The third equation is the seating capacity, which we assume is full:
[tex]c+s+a=387[/tex]
We start by replacing variables in two of the equations:
[tex]c=2a\\\\s=387-c-a=387-2a-a=387-3a[/tex]
Then, we solve the remaining equation for a:
[tex]5c+7s+12a=2808\\\\5(2a)+7(387-3a)+12a=2808\\\\10a+(2709-21a)+12a=2808\\\\10a+12a-21a=2808-2709\\\\a=99[/tex]
Then, we solve for the other two equations:
[tex]c=2a=2*99=198\\\\s=387-3a=387-3*99=387-297=90[/tex]
The attendance was 198 children, 90 students and 99 adults.
Determine the value of x for the triangle. show work.
Answer:
x=5
Step-by-step explanation:
x, x+7, x+8 must be a Pythagorean triple for it to make a right triangle. The only Pythagorean triple fitting these numbers is 5, 12, 13 so x must be 5.
Answer:
5
Step-by-step explanation:
Because this is a right triangle, you know that by the Pythagorean theorem:[tex]\sqrt{(x+7)^2+x^2}=x+8[/tex]
Squaring both sides to get rid of the square root:
[tex](x+7)^2+x^2=(x+8)^2[/tex]
Expanding all of the parentheses:
[tex]x^2+14x+49+x^2=x^2+16x+64[/tex]
Combine like terms:
[tex]x^2-2x-15=0[/tex]
Factor:
[tex](x-5)(x+3)=0[/tex]
Since x cannot be negative, it is equal to 5. Hope this helps!
Jared has earned 23% of the $52 he needs to buy a new jacket. Find 23% of $52.
Which expression can you use to find 23% of 52? ..
23% of $52 is $..
An easy way to check your answer is to use the friendly and divide 52 by to get ..
Answer:
Which expression can you use to find 23% of 52? "0.23 x 52"
23% of $52 is $. "11.96"
An easy way to check your answer is to use the friendly 25% and divide 52 by 4 to get 13.
Step-by-step explanation:
just did it good luck everyone
23% of $52 is $11.96.
In order to determine the value of 23% of $52, we would multiply 23% by $52. Multiplication is a basic mathematical operation that entails adding a certain number by itself a certain number of times. The sign used to represent multiplication is ×.
23% x 52
= 0.23 x 52 = $11.96
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Choose the equation that best fits the following graph.
Answer:
c. y = 3.25^x
Step-by-step explanation:
At x=1, the value of y is slightly more than 3, so the base must be more than 3. The appropriate choice is ...
y = 3.25^x
Write the fraction from least to greatest: 1/8, 1/3, 1/8
Answer:
Start with making them equal.
1/8 --> 3/24
1/8 --> 3/24
1/3 --> 8/24
Now order them.
1/8, 1/8, 1/3.
Hope this helps ;)
Some shrubs have the useful ability to resprout from their roots after their tops are destroyed. Fire is a particular threat to shrubs in dry climates, as it can injure the roots as well as destroy the aboveground material. One study of resprouting took place in a dry area of Mexico. The investigation clipped the tops of samples of several species of shrubs. In some cases, they also applied a propane torch to the stumps to simulate a fire. Of 19 specimens of a particular species, 6 resprouted after fire. Estimate with 96% confidence the proportion of all shrubs of this species that will resprout after fire. Interval: .1884 to
The 96% confidence interval for the proportion of all shrubs of this species that will resprout after fire is approximately 0.1274 to 0.5042.
Here, we have,
To estimate the proportion of all shrubs of this species that will resprout after fire with 96% confidence, we will use the formula for a confidence interval for a proportion.
The formula for the confidence interval for a proportion (p) is given by:
CI = p ± Z * √(p * (1 - p) / n)
where:
CI is the confidence interval
p is the sample proportion (resprouted specimens / total specimens)
Z is the critical Z-score corresponding to the desired confidence level (96% confidence level corresponds to a Z-score of approximately 1.750)
n is the sample size (total number of specimens)
Given information:
Total number of specimens (n) = 19
Number of specimens that resprouted after fire = 6
Now, calculate the sample proportion (p):
p = (number of specimens that resprouted) / (total number of specimens)
p = 6 / 19 ≈ 0.3158 (rounded to four decimal places)
Now, calculate the critical Z-score for a 96% confidence level (use a Z-table or calculator):
Z ≈ 1.750
Now, calculate the margin of error (E):
E = Z * √(p * (1 - p) / n)
E = 1.750 * √(0.3158 * (1 - 0.3158) / 19)
E ≈ 0.1884 (rounded to four decimal places)
Finally, calculate the confidence interval:
CI = p ± E
CI = 0.3158 ± 0.1884
The 96% confidence interval for the proportion of all shrubs of this species that will resprout after fire is approximately 0.1274 to 0.5042.
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If three points of a parallelogram are A (-5, -2), B (1,5), C (7.1). Which of the
following is the fourth point D of parallelogram ABCD?
(13,8)
(13.-6)
(1. -2)
(1,-6)
Talia is going to put a new carpet in her house. She measure's one side of her living room and finds it measures 17 meters which measurement does 17 meters represent
The answer in length
The length is used to measure the distance between to end points or edges. so 17 meters measurement represent the length.
What is perimeter?Its the sum of length of the sides used to made the given figure.
Talia is going to put a new carpet in her house. She measure's one side of her living room and finds it measures 17 meters.
Area is what is on the inside.
The perimeter is the outside of the hole thing.
Hence, the length is used to measure the distance between to end points or edges.
so 17 meters measurement represent the length.
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Who’s good on algebra 1 ? Need help
Answer:
Which expression is equivalent to 3 over 175
I would say try - C or D
Ming throws a stone off a bridge into a river below.
The stone's height (in meters above the water), xxx seconds after Ming threw it, is modeled by:
h(x)=-5(x-1)^2+45h(x)=−5(x−1)
2
+45h, left parenthesis, x, right parenthesis, equals, minus, 5, left parenthesis, x, minus, 1, right parenthesis, squared, plus, 45
How many seconds after being thrown will the stone reach its maximum height?
Answer:
1 seconds after being thrown, the stone reaches its max height
Step-by-step explanation:
Answer:1 Seconds Is wrong the correct answer is 2
Step-by-step explanation:
Khan said so
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if 8% is deducted from the bill,$384 bill remains to be paid. How much is the original bill?
Answer:
$353.28
Step-by-step explanation:
In ΔPQR, the measure of ∠R=90°, RP = 9.9 feet, and QR = 3.2 feet. Find the measure of ∠P to the nearest tenth of a degree.
Answer:
17.9
Step-by-step explanation:
−7×8=?????????????????????????
Answer
the answer is -56
Step-by-step explanation:
Matt says 3/3 is equivalent to 1 is he correct?
Answer: Yes
Step-by-step explanation:
It isn't an
1 an improper fraction
Less than the denominator
Therefore, three thirds or 3/3 is one whole fraction
Rly hope I helped!
☆꧁Ashlin꧂☆
Answer:yes he his correct
Step-by-step explanation:
3/3=1
Which of the following values of n will result in a true statement when substituted into the given equation? 4n + 9 = 1 A. n = -2 B. n = 2 C. n = 3 D. n = 4
Answer:
A. n = -2
Step-by-step explanation:
A. n = -2
4(-2) + 9 = 1
-8 + 9 = 1
1 = 1
The value of n for which the statement of equation 4n + 9 = 1 holds true is n = -2.
Given an equation:
4n + 9 = 1
There are some given options for the value of n.
It is required to find the value of n, where the statement is true.
A) When n = -2:
4n + 9 = 4(-2) + 9
= 1
B) When n = 2:
4n + 9 = 4(2) + 9
= 17
C) When n = 3:
4n + 9 = 4(3) + 9
= 21
D) When n = 4:
4n + 9 = 4(4) + 9
= 25
Hence the true statement is when n = -2.
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