A tank contains 3,000 L of brine with 16 kg of dissolved salt. Pure water enters the tank at a rate of 30 L/min. The solution is kept thoroughly mixed and drains from the tank at the same rate. (a) How much salt is in the tank after t minutes
Answer:
The amount of salt in the tank after t minutes is
y= 16e^(t/100)kg
Step- by-step Explanation
The tank contain 3000L of the brine
The rate is 30L/ min
The solution is mixed thoroughly, therefore, the rate in= rate out
dy/dt= rate in to the tank= rate out of the tank
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A charity is raising money by selling two thousand raffle tickets for $2 each. There is one grand prize worth $500, three secondary prizes worth $200 each, and eight third level prizes worth $20 each. What is the expected value of a $2 ticket? Answer is negative $1.358 but how do you calculate that?
The expected value of a $2 ticket is $0.63
How to determine the expected value of a $2 ticketTo calculate the expected value of a $2 ticket, we need to multiply the probability of winning by the value of the prize, then sum those products:
The Probability of winning the grand prize = 1/2000
Product: (1/2000) x $500 = $0.25
The Probability of winning a secondary prize: 3/2000
Product: (3/2000) x $200 = $0.30
The Probability of winning a third level prize: 8/2000
Product: (8/2000) x $20 = $0.08
The sum of the products:
$0.25 + $0.30 + $0.08 = $0.63
So the expected value of a $2 ticket is $0.63, meaning that on average, a person can expect to win $0.63 for every $2 they spend on a ticket.
The charity is expected to make a profit, which is why the answer is negative.
That is -$2 + $0.63 = -$1.37
So the expected profit for the charity per ticket sold is -$1.37, which is approximately the same as the given answer of negative $1.358(rounding off)
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Brian set his compass equal to the radius of circle C and drew two circles centered at points A and B on circle C. He labeled the points of intersection of the two circles as shown.
Two circles are drawn by having another circle in the center. The center circle has points A, M, N, B, P, Q, and C. At C the two circles intersect, and at P the center circle and the top circle intersect.
To complete his construction, Brian only needs to use his straightedge to draw some chords of circle C.
Which figures could Brian be constructing?
equilateral triangle MNQ inscribed in circle C
equilateral triangle ANP inscribed in circle C
regular hexagon AMNBPQ inscribed in circle C
square MNPQ inscribed in circle C
square ANBQ inscribed in circle C
The correct options that could be constructed by Brian using his straightedge to draw some chords of circle C are:
Equilateral triangle MNQ inscribed in circle C
Regular hexagon AMNBPQ inscribed in circle C
Brian is constructing figures inscribed in circle C.
Equilateral triangle MNQ inscribed in circle C:
This option is possible since the points M, N, and Q are labeled and they lie on circle C.
Equilateral triangle ANP inscribed in circle C:
This option is not possible. The points A and P are labeled, but the third vertex of the equilateral triangle is not specified.
Regular hexagon AMNBPQ inscribed in circle C:
This option is possible since the points A, M, N, B, P, and Q are labeled and they lie on circle C.
Square MNPQ inscribed in circle C:
This option is not possible based on the given information. The label points do not form a square.
Square ANBQ inscribed in circle C:
This option is not possible . The points A, N, B, and Q are labeled, but they do not form a square.
The correct options that could be constructed by Brian using his straightedge to draw some chords of circle C are:
Equilateral triangle MNQ inscribed in circle C
Regular hexagon AMNBPQ inscribed in circle C
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Solve y = ax² + c for x.
O x
x= ± √ay-c
O
O
x = ±₁
X=
X=
у-с
a
y
y + c
a
In the quadratic equation y = a\(x^{2}\) + c ,the value of x = ± \(\sqrt \frac{y-c}{a}\)
A quadratic equation is any equation containing one term wherein the unknown is squared and no term wherein it's far raised to a higher power.
A quadratic equation is an algebraic equation of the second degree in x. The quadratic equation in its standard form is ax2 + bx + c = 0, in which a and b are the coefficients, x is the variable, and c is the constant term.
To find the value of x
Assuming \(a\neq o\)
First, subtract c from both the sides to get:
\(y-c=ax^{2}\)
then, divide both sides by \(a\) and transpose to get:
\(x^{2} =\frac{y-c}{a}\)
So, \(x\) must be a square root of \(\frac{y-c}{a}\) and we can deduce:
\(x=\) ± \(\sqrt \frac{y-c}{a}\)
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What is the value of the variable x? a.20 b.14 c.12 d.16
What is the measurement of angle zxy? a.35 b.40 c.55 d.60
Answer:
12°
55°
Step-by-step explanation:
∠WXY=90°
∠ZXY=∠WXY- ∠WXZ= 90° - 35°= 55°
4x+7°= 55°4x= 48°x= 48°/4x= 12°Answer:
The first question: The answer is C.12
The second question: The answer is C. 55
Step-by-step explanation:
The first question : Explanation: since WXY is 90 degrees and WXZ is 35 degrees subtract those two to get ZXY: 90 - 35 is 55
So it would like this for ZXY: 4x + 7 = 55
x = 12
So your first answer would be C. 12
The second question: Explanation: Since we got the answer for X value we substitute it in the equation: 4x12 + 7 = 55
So the second answer would be C. 55
PLEASE HELPPPP
Find m∠BXY.
Answer:
I think 30°Step-by-step explanation:
Pls make me brainliest plssssssssssssssImsureeeeeeee123
Please help me solve this. I will give you brainliest.
Answer: 3
Step-by-step explanation:
Let’s write it out as an equation:
15s + 5 = 50
where s is the number of shirts she will buy.
Simplifying this equation, you get:
15s = 50 - 5 (since you move 5 to this right side)
15s = 45
\(\frac{15s}{15}\)= \(\frac{45}{15}\)
s = 3
Therefore, Sara can buy 3 shirts
GUYS, I GOTM 1MILLIO0N DOLARS IN THE STOCK MAARKAT HOW MUCH IS 1 MILLION DOLLARS IN NE GOTIABLE US CUERENCY CONVERTED TO RUSSIAN RUBELS????/// PLS ILL GIV BRANLEST!11
Hi! I believe your answer is 77,435,300.00 Russian Rubles, which is equivalent to 1,000,000 U.S. dollars. I hope this helps you! Good luck and have a great day. ❤️✨
Answer:
76,922,200.00 RUB
Step-by-step explanation:
wow how in the heck did you do that 0-o your rich dude pls explain how u did it T-T
DQ1: Consider the vertex matrix T in application 1 page 185. How can we extend this into 3 dimensional objects in space? Add a vector, or vectors to T and describe the object for which you have created vertices (i.e., a cube, a pyramid, etc.) What are the dimensions of your new matrix? What do the dimensions represent?
Thus, for any vector x = (x1, x2, x3) in R3, we have: L(x) = Ax where A is the matrix given above.
What is matrix?A matrix is a rectangular array of numbers, symbols, or expressions, arranged in rows and columns. Matrices are used extensively in mathematics, science, engineering, and computer science to represent and manipulate linear equations, systems of equations, vectors, and other mathematical objects. Matrices can be added, subtracted, multiplied, inverted, and transformed in various ways to solve problems in algebra, calculus, statistics, and other fields. Matrices are also used in computer graphics, machine learning, and other areas of artificial intelligence to represent data, images, and other information. The size of a matrix is given by its number of rows and columns, and matrices can be classified as square (when they have the same number of rows and columns) or rectangular (when they have different numbers of rows and columns).
Here,
To find the matrix A that corresponds to the linear transformation L, we need to write L(e1), L(e2), and L(e3) as linear combinations of the standard basis vectors in R2.
L(e1) = (1+0, 0+0) = (1, 0)
L(e2) = (0+1, 1+0) = (1, 1)
L(e3) = (0+0, 1+0) = (0, 1)
So we can write:
L(x) = L(x1 e1 + x2 e2 + x3 e3)
= x1 L(e1) + x2 L(e2) + x3 L(e3)
Now we can assemble the coefficients of this linear combination into a matrix A:
A= \(\left[\begin{array}{ccc}1&1&0\\0&1&1\end{array}\right]\)
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What were the rental rates?
answer/explanation:
d = daily rental chargem = the charge per mileJon rented a car from a company that charged a daily rental fee and a mileage charge. He rented the car for 6 days and drove 300 miles and was charged $285.6d + 300m = 285His friend Amanda later rented the same car for 7 days and drove 260 miles and was charged $310.7d + 260m = 310by solving the system of equations6d + 300m = 2857d + 260m = 310we findd = $35m = $0.25the daily rental charge is $35.the company charge per mile is $0.25.hope this helps
Which graph represents the compound inequality?
h ≥ –5 and h < 2
Both h ≥ –5 and h < 2 represent the area more than or equal to negative 5 and less than 2.
What is inequality?Inequality is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's relative size and can be used to compare these two claims.
The inequality equation is given below.
h ≥ –5 and h < 2
Then h ≥ –5 represents the area more than or equal to negative 5.
And h < 2 represents the area less than 2.
Then both h ≥ –5 and h < 2 represent the area more than or equal to negative 5 and less than 2.
The graph is given below.
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Answer:
THe Answer is A
Step-by-step explanation:
SAT scores have been found to predict 36% of the variance in college
GPA. What is the correlation coefficient between SAT score and college GPA?
A. 0.18
B. 0.6
C. 0.06
Evaluate 48 + 24 ÷ 8 − 22
Answer:
I solved it and my answer is 29
simplify 36ab divided by 40ab
The measure of one small angles of a right triangle is 45 less than twice the measure of the other small angle. Find the measure of both angles
Answer:
x + x - 45 = 90
2x - 45 = 90
2x = 135
x = 67.5, so x - 45 = 22.5
The other two angles measure 22.5° and 67.5°.
HELP MEH PLZ! THIS IS DUE TODAY! 1ST GETS BRAINILIEST!
Why is the study of the Hebrew Bible such an important part of the practice of Judaism?
EXPLAIN
Answer: Prophets
Step-by-step explanation: The Jewish profits where people who were thought to be chosen by god as messengers. They were preachers who reminded people to obey gods laws
Answer:
The Jewish profits where people who were thought to be chosen by god as messengers. They were preachers who reminded people to obey gods laws
Step-by-step explanation:
For the function G(x)=5x+5−3x−4, evaluate G(8).
G(8) = 40 + 5 - 24 - 4
45 - 28 = 17
G(8) = 17
how can i make 5 1/2 into a decimal?
Answer:
5.5
Step-by-step explanation:
1/2 of 1 is 0.5 so you just add that to the end of the number. Or where the fraction would be.
Answer:
5 is just 5, as a whole number, decimal, or fraction. the 1/2 can be multiplied by 50 on both sides(numerator and denominator) to get 50/100. 100 is a decimal number, so the ANSWER is 5.50 or 5.5.
Step-by-step explanation:
What is the value of n? Write your answer as a number only
Answer:
45
Step-by-step explanation:
What is the difference?
StartFraction x Over x squared minus 2 x minus 15 EndFraction minus StartFraction 4 Over x squared + 2 x minus 35 EndFraction
Answer:
(x^2 + 3x - 12)/(x^3 + 5x^2 - 29x - 105)
Step-by-step explanation:
(x/(x^2 - 2x - 15) ) - (4/(x^2 + 2x - 35)) =
(x/((x-5)(x+3))) - (4/((x-5)(x+7))) =
((x * (x+7)) - (4 * (x+3)))/((x-5)(x+3)(x+7)) =
(x^2 + 7x - 4x - 12)/(x^3 + 5x^2 - 29x - 105) =
(x^2 + 3x - 12)/(x^3 + 5x^2 - 29x - 105)
Answer:
the Answer is D: x^2+3x-12/(x+3)(x-5)(x+7)
Step-by-step explanation:
Edge2020 ;D
help me with this please
Answer:
i have no idea good luck i will try to get the answer for ya though
Step-by-step explanation:
.
This graph shows the solution to which inequality?
A market researcher would like to know how much time the average college student spends watching sports. Suppose he does a preliminary study based upon a sample of 25 college students. The mean amount of time spent watching sports, by those in the sample, is 90 minutes per day with a standard deviation of 15 minutes per day.
(a) Which of the following numbers gives the value of the point estimate?
a. 15.
b. 25.
c. 90.
d. 0.
e. 95.
(b) Using the information given above, calculate the margin of error (in minutes) of the point estimate. Assume we would like to estimate the population mean with 95% confidence.
(c) Suppose that the researcher is not content with the current margin of error. He would like the margin of error of the point estimate to be no more than 4 minutes with 95% confidence. The researcher is unwilling to trust that the sample standard deviation from his previous study accurately estimates the true population standard deviation. He does, however, know that college students tend to watch sports between 0 and 120 minutes per day. What is the minimum sample size needed to obtain this amount of precision?
Answer:
a) c. 90.
b) The margin of error of the point estimate is of 6.19 minutes.
c) The minimum sample size needed to obtain this amount of precision is 289.
Step-by-step explanation:
(a) Which of the following numbers gives the value of the point estimate?
The value of the point estimate is the sample mean, of 90 minutes. So the answer is given by option c.
(b) Using the information given above, calculate the margin of error (in minutes) of the point estimate. Assume we would like to estimate the population mean with 95% confidence.
We have the standard deviation for the sample, which means that the t-distribution is used 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 = 25 - 1 = 24
95% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 24 degrees of freedom(y-axis) and a confidence level of \(1 - \frac{1 - 0.95}{2} = 0.975\). So we have T = 2.0639.
The margin of error is:
\(M = T\frac{s}{\sqrt{n}}\)
In which s is the standard deviation of the sample and n is the size of the sample.
Here, we have \(s = 15, n = 25\). So
\(M = T\frac{s}{\sqrt{n}}\)
\(M = 2.0639\frac{15}{\sqrt{25}}\)
\(M = 6.19\)
The margin of error of the point estimate is of 6.19 minutes.
Question c:
College students tend to watch sports between 0 and 120 minutes per day, which means that the standard deviation for population can be estimated as the standard deviation of an uniform distribution with \(a = 0, b = 120\). This standard deviation is:
\(\sigma = \sqrt{\frac{(b-a)^2}{12}}\)
Then
\(\sigma = \sqrt{\frac{(120-0)^2}{12}}\)
\(\sigma = 34.64\)
Minimum sample size:
Now, since we have an estimate for the standard deviation of the population, we use the z-distribution.
We have that to find our \(\alpha\) level, that is the subtraction of 1 by the confidence interval divided by 2. So:
\(\alpha = \frac{1 - 0.95}{2} = 0.025\)
Now, we have to find z in the Ztable as such z has a pvalue of \(1 - \alpha\).
That is z with a pvalue of \(1 - 0.025 = 0.975\), so Z = 1.96.
Now, find the margin of error M as such
\(M = z\frac{\sigma}{\sqrt{n}}\)
In which \(\sigma\) is the standard deviation of the population and n is the size of the sample.
The minimum sample size is n for which M = 4. So
\(M = z\frac{\sigma}{\sqrt{n}}\)
\(4 = 1.96\frac{34.64}{\sqrt{n}}\)
\(4\sqrt{n} = 1.96*34.64\)
\(\sqrt{n} = \frac{1.96*34.64}{4}\)
\((\sqrt{n})^2 = (\frac{1.96*34.64}{4})^2\)
\(n = 288.1\)
Rounding up:
The minimum sample size needed to obtain this amount of precision is 289.
The sales tax for an item was $13.60 and it cost $340 before tax.
Find the sales tax rate. Write your answer as a percentage.
Answer:
4%
Step-by-step explanation:
13.60/340=.04 or 4%
I really need someone to explain to me on how to solve these!! :(
Answer:
3.7%
Step-by-step explanation:
(p)principal=$3400
(t)time=9months=9÷12year=3÷4year
(i)interest=$94.50
(r)rate=?
we have
r%=i/(pt)
r%=94.50÷(3400×3÷4)
r÷100=94.50÷2550
r=0.37×100
r=3.7
required rate is 3/7%
HELP PLEASE AS SOON AS POSSIBLE WILL GIVE U BRAINLIST
Answer:
The table represents a nonlinear function because the rate is not constant.
Step-by-step explanation:
As shown in the picture below, the x side of the table has the same rate of change of +1. However, due to the fact that the y side does not have the same rate of change, +6 and +3, the table represents a non linear function. If the rate on the y side of the table were all the same, then this would be a Linear function.
The height of cylinder B is twice the height of cylinder A the total surface area of cylinder A is 180 Calculate the total surface area of cylinder B
Main Answer: The total surface area of cylinder B is approximately 476.7 square units.
Supporting Question and Answer:
How is the surface area of a cylinder calculated?
The surface area of a cylinder is the sum of the areas of its curved surface and two circular bases. It can be calculated using the formula:
A = 2πrh + 2π\(r^{2}\)
where "r" is the radius of the circular base, "h" is the height of the cylinder, and π (pi) is a mathematical constant that represents the ratio of the circumference of a circle to its diameter, approximately equal to 3.14159.
The first term, 2πrh, represents the area of the curved surface of the cylinder, while the second term, 2π\(r^{2}\), represents the combined area of the top and bottom circular bases.
Body of the Solution: Let the height and radius of cylinder A be "h" and "r" respectively. Then, the height and radius of cylinder B are "2h" and "R" respectively, since cylinder B has twice the height of cylinder A but the same radius.
The total surface area of a cylinder is given by the formula:
Area = 2πrh + 2π\(r^{2}\)
For cylinder A, we know that the surface area is 180, so we can substitute the values and solve for "r" as follows:
180 = 2πrh + 2π\(r^{2}\)
90 = πrh + π\(r^{2}\)
We can rearrange this equation to solve for r:
r² + rh - 90/π=0
Using the quAdratic formula,we get:
r = (-h ± √((h)² + 4(90/π)))/2
r = -h/2 ± √(h² + 4(90/π))/2
Now we have an expression for r in terms of h . We can use this expression to find the radius of cylinder B, since we know that cylinder B has twice the height of cylinder A.
R = 2r= -h ± √(h² + 4(90/π))
We can use this expression to find the surface area of cylinder B:
Surface area of cylinder B = 2πR² + 2πR(2h)
Surface area of cylinder B= 2π( -h ± √(h² + 4(90/π)))² + 4πh( -h± √(h² + 4(90/π)))
We can use the value we found for 2h using the quadratic formula in the expression to get:
Surface area of cylinder B = 476.7 square units (rounded to one decimal place)
Therefore, the total surface area of cylinder B is approximately 476.7 square units.
Final Answer: Therefore, the total surface area of cylinder B is approximately 476.7 square units.
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D. Rom has just given an insurance company $35,000. In return, he will receive an annuity of $3,700 for 20 years. At what
rate of return must the insurance company invest this $35,000 in order to make the annual payments?
Answer:
0.53%
Step-by-step explanation:
hope it is well understood
Which of these shapes will tessellate without leaving gaps? A. Hexagon B. Octagon C. Pentagon D. Circle
The shape that can tessellate without leaving gaps is the hexagon (option A).
The shapes that can tessellate without leaving gaps are shapes that can be repeated to completely cover a flat surface without any overlaps or gaps. Among the options provided, the shape that will tessellate without leaving gaps is the hexagon (option A).
A hexagon is a six-sided polygon with equal sides and angles. It is a regular polygon, which means all of its sides and angles are equal. A regular hexagon can be arranged and repeated in a pattern to fill a plane without any gaps or overlaps. Bees' honeycombs are a real-world example of hexagonal tessellation.
On the other hand, octagons (option B) and pentagons (option C) do not tessellate by themselves without gaps. While they can be used in combination with other shapes to create tessellations, they cannot tessellate on their own.
A circle (option D) cannot tessellate without leaving gaps. A circle is a curved shape, and it cannot form a repeating pattern that completely covers a flat surface without overlaps or gaps.
In summary, the shape that can tessellate without leaving gaps is the hexagon (option A).
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Given that A={1,2,3,4,5} list the elements of the following sets. i.{x2:x€A} ii.{ :x€A} iii.{2x :x€A} iv.{4x+1:x€A}
Answer:no idea
Step-by-step explanation: