Answer:
Let's start by finding the volume of water in the trough as a function of its depth.
At a depth of h cm, the cross-sectional area of the water is an isosceles trapezoid with bases of length b1 = 40 + (h/5) cm and b2 = 90 + (h/2) cm, and height 50 cm. The average width of the trapezoid is (b1 + b2)/2 = 65 + (3h/10) cm. Therefore, the volume of water in the trough at this depth is:
V(h) = 10 m x [(65 + (3h/10)) / 100 cm] x h cm
Simplifying this expression, we get:
V(h) = (13/2000) h^2 m^3
Now, we can use the chain rule to find the rate of change of V with respect to time t, given that dV/dt = 0.1 m^3/min:
dV/dt = (dV/dh) x (dh/dt) = (26/2000) h (dh/dt)
At the moment when the water is 10 cm deep, we have:
h = 10 cm
dV/dt = 0.1 m^3/min
Plugging in these values, we get:
0.1 m^3/min = (26/2000) x 10 cm x (dh/dt)
Solving for dh/dt, we get:
dh/dt = 0.1 m^3/min / (26/2000) / 10 cm
dh/dt ≈ 0.192 m/min
Therefore, the water level is rising at a rate of approximately 0.192 m/min when the water is 10 cm deep.
Point GG is located at (-3,6)(-3,6) on the coordinate plane. Point GG is reflected over the xx-axis to create point G'G ′ . Point G'G ′ is then reflected over the yy-axis to create point G''G ′′ . What ordered pair describes the location of G''?G ′′ ?
For given coordinates, the ordered pair describing the location of G'' is (3,-6).
What are coordinates?
Coordinates are a set of numbers that specify the position or location of a point or object in space, relative to a reference point or system. In two-dimensional space, coordinates are usually represented by a pair of numbers (x, y), where the first number represents the horizontal position of the point along the x-axis, and the second number represents the vertical position of the point along the y-axis. In three-dimensional space, coordinates are usually represented by a triple of numbers (x, y, z), where the first number represents the horizontal position of the point along the x-axis, the second number represents the vertical position of the point along the y-axis, and the third number represents the position of the point along the z-axis, which is perpendicular to the x-y plane.
Now,
When a point is reflected over the x-axis, the y-coordinate is negated. So the image of G(-3,6) over the x-axis is G'(-3,-6).
When a point is reflected over the y-axis, the x-coordinate is negated. So the image of G'(-3,-6) over the y-axis is G''(3,-6).
Therefore, the ordered pair describing the location of G'' is (3,-6).
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Susan placed an order for a drum set priced at $71.28, cluding the taxes. The drum set is 30% off. 30% of $71.28, which means .3 x 71.28, is $21.39 off. How much does Susan have to pay in total?
Answer:
Step-by-step explanation:
take 71.28-21.39
Answer:
If the drum set is 30% off, this means that Susan only needs to pay 70% of the original price. We can calculate this using the following formula:
Total price = Original price x (1 - Discount rate)
where the discount rate is the percentage discount expressed as a decimal. In this case, the discount rate is 30% or 0.3. Substituting in the given values, we get:
Total price = $71.28 x (1 - 0.3)
Total price = $71.28 x 0.7
Simplifying, we get:
Total price = $49.896
However, we also know that Susan got a discount of $21.39. This means that she only needs to pay:
Total price - Discount = $49.896 - $21.39
Total price - Discount = $28.506
Therefore, Susan has to pay $28.506 in total.
A photographer is arranging 3 puppies in a row for a photo. There is one black puppy (B), one tan puppy (T) and one white puppy (W). Which list shows all the possible arrangements of the puppies?
Thus, the list BTW, BWT, TBW, TWB, WBT, and WTB is the correct response.
What is a number arrangement?The number of possible arrangements or orders for a set of items is known as the arrangement number, sometimes known as the permutation number or simply as the permutation.
The following is the accurate list of all conceivable pup arrangements:
BTW, BWT, TBW, TWB, WBT, WTB
This is due to the fact that the puppies' order is important, thus we may utilize permutations to discover every potential configuration. There are 3 pups to place in a row, which results in a total of 3! = 6 combinations. We can categories them as follows:
1. BTW
2. BWT
3. TBW
4. TWB
5. WBT
6. WTB
Thus, the list BTW, BWT, TBW, TWB, WBT, and WTB is the correct response.
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A cabinet was ordered from a carpenter with a volume of 1.08 m³. He wrote down the following measurements: 1.2 m wide and 1.8 m high, but forgot to write down the depth. Therefore, the depth measurement is
The depth of this cabinet is equal to 0.5 m³.
VolumeVolume is a three-dimensional measure that indicates the space occupied by an object. It is a physical quantity that expresses the amount of space an object occupies in three dimensions - length, width and height.
Note that this cabinet has the shape of a parallelepiped, and its volume is found by multiplying its dimensions. Calculating the depth measurement, we have:
1,08 m³ = 1,2 m * 1,8 m * p
p = 1,08 m³/(1,2 m * 1,8 m)
p = 1,08 m³ / 2,16 m³
p = 0,5 m
How do you write the standard form for 2 hundreds 9 tens and 18 ones
The standard form as: 298
What is standard form?
Standard form is a way of writing numbers a little differently for instance
The number "2 hundreds 9 tens and 18 ones" can be written in standard form as:
298
In standard form, we write the digits in the place value of their corresponding powers of 10. In this case, the digit 2 is in the hundreds place (10)², the digit 9 is in the tens place (10), and the digit 8 is in the ones place (10^0).
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If 9x+10=20
, what is the value of 18x+1
?
Answer:
21
Step-by-step explanation:
9x + 10 = 20
9x = 10
x = 10/9
What is the value of 18x + 1?
18(10/9) + 1
= 20 + 1
= 21
So, the value of 18x + 1 is 21
the sum of
44+45+46+47+...+131
Answer:313:)
Step-by-step explanation:
-5 + x-2 = 3x + 10 - x Which of the following statements correctly describe the solution(s) of the equation above? Select all that apply. • The equation has only one solution. • The equation has no solutions. F The equation has infinitely many solutions. ) The equation's only solution is x = - 17. • The equation is solved by all numbers less than 17.
The equation's only solution is x = -17.
Simplifying the left-hand side of the equation:
-5 + x - 2 = -7 + x
Simplifying the right-hand side of the equation:
3x + 10 - x = 2x + 10
Substituting into the original equation, we get:
-7 + x = 2x + 10
Subtracting x from both sides, we get:
-7 = x + 10
Subtracting 10 from both sides, we get:
-17 = x
So the only solution to the equation is x = -17. Therefore, the correct statement about the solution(s) of the equation is:
• The equation's only solution is x = -17.
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there are 3 containers of chocolate ice cream for every 2 containers of vanilla ice cream. What is the constant of proportionality in terms of vanilla to chocolate.
Answer: 2:3
Step-by-step explanation:
PLEASE HELP! URGENT AND WORTH 50 POINTS!!!
Answer: 3.5
Step-by-step explanation: sry if im wrong ):
Write a quadratic function in standard form to represent the data in the table.
Therefore, the quadratic function in standard form that represents the data in the table is: y = 1/2 x² - 5/2 x + 5.
What is function?A function is a mathematical concept that describes the relationship between two sets of numbers. It is a rule that assigns to each input (or element in the domain) exactly one output (or element in the range). In simpler terms, a function is like a machine that takes in a number and produces another number as output, according to some specific rules. The input is usually denoted by x, and the output by f(x), which is read as "f of x". Functions can take many forms, such as linear, quadratic, trigonometric, exponential, logarithmic, and more. They are widely used in mathematics, science, engineering, and many other fields to model and analyze various phenomena.
Here,
To write a quadratic function in standard form, we need to use the general form of the quadratic equation:
y = ax²+ bx + c
where a, b, and c are constants. We can use the values in the table to find these constants.
When x = 2, y = 3
When x = 4, y = 1
When x = 6, y = 3
When x = 8, y = 9
When x = 10, y = 19
Substituting these values into the quadratic equation, we get:
3 = 4a + 2b + c
1 = 16a + 4b + c
3 = 36a + 6b + c
9 = 64a + 8b + c
19 = 100a + 10b + c
We can now use these equations to solve for a, b, and c. One way to do this is to use a matrix equation:
|16 4 1| |a| |1|
|36 6 1| |b| = |3|
|64 8 1| |c| |9|
Using a calculator or matrix software, we can solve for a, b, and c:
a = 1/2
b = -5/2
c = 5
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what is required for a current to flow?
A. Electrons, protons, and an energy source
B. An insulator, battery, and recipient
C. A recipient, a connection, and something made out of rubber
D. An Energy source, a recipient, and a connection
Answer:
D. An Energy source, a recipient, and a connection
You went out to dinner and your meal $22.00. If you want to leave a 20% tip, how much will you pay total?
You will pay a total of $26.40 including the 20% tip.
To calculate the total amount including the 20% tip, you need to add 20% of the meal cost to the original meal cost:
A gratuity or a small amount of money given to someone for their service, such as a waiter or a hairdresser.
A piece of advice or a suggestion given to someone to help them do something better or more efficiently.
A pointed or tapered end of an object, such as the tip of a pen or a needle.
Tip amount = 20% of $22.00 = 0.2 x $22.00 = $4.40
Total amount including tip = $22.00 + $4.40 = $26.40
Therefore, you will pay a total of $26.40 including the 20% tip.
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129. (1+x)y' = (x + 2)(y − 1)
Calculus vol 2 need help solving this!!!!
By answering the question using the information provided, we can conclude that in order to arrive at the general solution, we must take into account the scenario in which [tex]y-1\neq 0 , y \neq 1[/tex], by constructing equations.
What do you mean by equations?Two equations are said to be equivalent when their bases and solutions line up. To create an equivalent equation, the same quantity, symbol, or expression must be added to or removed from both of the equation's two sides.
We can also create an analogous equation by multiplying or dividing both sides of an equation by a nonzero integer.
Solving differntial calculus
[tex](1+x)y'=( x+2) (y-1)[/tex]
We will first employ varying separation. The variables y and x will be placed on the opposite sides of the equation, and both sides will be integrated.
[tex](1+x)y'/(y-1) = (x+2)dx[/tex]
We will integrate both sides using the substitution[tex]u= y-1,\frac{du}{dy} =y'[/tex]
∫[tex](x+2)dx[/tex] =∫[tex](1+x)\frac{du}{u}[/tex]
㏑l[tex]u[/tex]l +[tex]x[/tex]㏑l[tex]u[/tex]l= [tex]\frac{1}{2} x^{2}+2x+c[/tex]
Substituting [tex]u= y-1[/tex]
㏑l[tex]y-1[/tex]l+ [tex]x[/tex]㏑l[tex]y-1[/tex]l= [tex]\frac{1}{2x^{2} } +2x+c[/tex]
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The complete question is: Find the general solution to the differential equation (1+x)y' = (x + 2)(y − 1).
Find the value of X
The measure or value of x = 55°. This is solved using the Tangent, Secant and Arc theorems.
What is the explanation for the above response?Note that the Measure of and x (m∠x) = (Far Arc - Near Arc)/2
Where
Far Arc = 360 - 65 - 120 = 175°
Near Arc = 65°
thus, m∠x = (175-65)/2
m∠x = 55°
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Majesty Video Production Inc. wants the mean length of its advertisements to be 35 seconds. Assume the distribution of ad length follows the normal distribution with a population standard deviation of 2 seconds. Suppose we select a sample of 14 ads produced by Majesty.
a. What percent of the sample means will be greater than 36.50 seconds? (Round your z-value and final answer to 2 decimal places.)
b. What percent of the sample means will be greater than 34.45 seconds. (Round your z-value and final answer to 2 decimal places.)
c. What percent of the sample means will be greater than 34.45 but less than 36.50 seconds? (Round your z-value and final answer to 2 decimal places.)
d. What is the probability that the sampling error would be less than or more than 1.5 seconds? (Round your z-value and final answer to 2 decimal places.)
The shape of the distribution of the sample mean time is normal.
The standard error of the mean time is 0.5.
The percentage of the sample means that would be greater than 31.25 seconds is 0.621%.
The percentage of the sample means that would be greater than 28.25 seconds is 99.977%.
The percentage of the sample means that would be greater than 28.25 but less than 31.25 seconds is 99.357%.
Given the following data:
Mean = 30.
Standard deviation = 2.
Sample = 16 ads.
What is a normal distribution?
A normal distribution is also referred to as the Gaussian distribution and it can be defined as a probability distribution that is continuous and symmetrical on both sides of the mean, which shows that all data near the mean have a higher frequency than data far from the mean.
a. The shape of the distribution of the sample mean time is normal.
b. To calculate the standard error of the mean time, we would apply this formula:
Standard error = 0.5.
c. To calculate the percentage of the sample means that would be greater than 31.25 seconds:
P(Z>2.5) = 0.621%.
d. To calculate the percentage of the sample means that would be greater than 28.25 seconds:
P(Z>2.5) = 99.977%.
e. To calculate the percentage of the sample means that would be greater than 28.25 but less than 31.25 seconds:
P(-3.5<Z<2.5) = 99.357%.
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Nicole bought
6
CDs that were each the same price. Including sales tax, she paid a total of
$
69.60
. Of that total,
$
4.20
was tax. What was the price of each CD before tax?
Answer: $11.60
Step-by-step explanation: Since ur finding the cost of one cd and she bought 6 and since is before tax you do 36.90/(divided by) 6 and boom #!
Points D, B, and E are collinear. Find
the value of a so that points A, B, and
C are collinear.
A
(4x)
O
E
B
148°
D
C
Using the supplementary angle theorem, the value for x so that points A, B, and C are collinear is 8.
What is a supplementary angle?
The definition of "supplementary" in mathematics relates to angles that combine to form a straight angle. It indicates that when two angles sum up to 180 degrees, they are said to be supplementary angles.
A line segment AC is drawn.
Point B is in between A and C.
A transversal DE is drawn passing through point B.
Points D, B, and E are collinear.
The measure of angle CBE is 148° and the measure of angle EBA is 4x°.
The angles ∠CBE and ∠EBA forms a pair of supplementary angles.
Their sum result in value of 180°.
Mathematically, this can be represented as -
∠CBE + ∠EBA = 180°
Substituting the values into the equation -
148° + 4x° = 180°
Solving for x, we get -
4x° = 180° - 148°
4x° = 32°
x = 32 / 4
x = 8
Therefore, the value for x is obtained as 8.
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Weathering and erosion are two processes that shape Earth’s surface. Which of the
following sets of factors cause both weathering and erosion?
a) acid rain, tree roots, waves
b) glaciers, waves, wind
c) moving water, plants, wind
d) acid rain, plants, ice
Lee watches TV for 4 hours per day. During that time, the TV consumes 200 watts per hour. Electricity costs (12 cents)/(1 kilowatt-hour). How much does Lee’s TV cost to operate for a month of 30 days?
The cost to operate Lee's Tv is 2.88 dollars.
How to find the cost to operate for a month?Lee watches TV for 4 hours per day. During that time, the TV consumes 200 watts per hour. Electricity costs (12 cents)/(1 kilowatt-hour).
Therefore, the cost for Lee to operate in 30 days can be calculated as follows:
200 watt = 0.2 kilowatt
Therefore,
1 day = 4 hours
30 days = ?
cross multiply
number of hours = 120 hours.
Therefore, in 30 days he watches television for 120 hours.
Let's find the cost
0.12 dollars = 12 cent
1 hour = 0.2 kilowatt
120 hours =
kilowatt use in 30 days = 0.2 × 120 = 24 kilowatts
Therefore,
1 kilowatts = 0.12 dollars
24 kilowatts = ?
cost of Tv for a month of 30 days = 24 × 0.12
cost of Tv for a month of 30 days = 2.88 dollars
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Un camino recto que continua para siempre en ambas direcciones es un
Answer: una linea
Step-by-step explanation:
Please help quick!! Given m || n, find the value of x.
In the given angles the required value of x is 17° respectively.
What are angles?An angle is a figure in Euclidean geometry made up of two rays that share a common terminal and are referred to as the angle's sides and vertices, respectively.
Angles created by two rays are in the plane where the rays are located.
The meeting of two planes also creates angles. We refer to these as dihedral angles.
Based on the measurement, there are many kinds of angles in geometry.
The names of fundamental angles include acute, obtuse, right, straight, reflex, and full rotation.
So, we know that:
2x+5 + 8x+5 = Straight angle
2x+5 + 8x+5 = 180
Now, solve for x as follows:
2x+5 + 8x+5 = 180
10x+10 = 180
10x = 170
x = 17
Therefore, in the given angles the required value of x is 17° respectively.
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In a survey of women in a certain country (ages 20−29), the mean height was 63.7 inches with a standard deviation of 2.75 inches. Answer the following questions about the specified normal distribution.
(a) What height represents the 95th percentile?
(b) What height represents the first quartile?
a) The height that represents the 95th percentile is approximately 68.1 inches.
b) the height that represents the first quartile is approximately 65.5 inches.
Percentile and Quartile Heights(a) To find the height that represents the 95th percentile, we need to find the z-score that corresponds to this percentile and then use that to find the corresponding height.
The z-score for the 95th percentile can be found using a standard normal distribution table or calculator. The area to the left of the z-score is 0.95, so the area to the right is 0.05. From the standard normal distribution table, the z-score corresponding to an area of 0.05 is approximately 1.645.
Now we can use the formula for z-scores to find the corresponding height:
z = (x - mu) / sigma
where x is the height we want to find, mu is the mean height (63.7 inches), sigma is the standard deviation (2.75 inches), and z is the z-score we just calculated (1.645).
Rearranging the formula, we get:
x = mu + z * sigma
Plugging in the values, we get:
x = 63.7 + 1.645 * 2.75 ≈ 68.1
Therefore, the height that represents the 95th percentile is approximately 68.1 inches.
(b) To find the height that represents the first quartile, we need to find the z-score that corresponds to the 25th percentile and then use that to find the corresponding height.
The z-score for the 25th percentile can be found using a standard normal distribution table or calculator. The area to the left of the z-score is 0.25, so the area to the right is 0.75. From the standard normal distribution table, the z-score corresponding to an area of 0.75 is approximately 0.67.
Using the formula for z-scores and the same values for mu and sigma, we get:
x = mu + z * sigma = 63.7 + 0.67 * 2.75 ≈ 65.5
Therefore, the height that represents the first quartile is approximately 65.5 inches.
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A company makes 140 bags. 47 of the bags have buttons but no zips. 48 of the bags have zips but no buttons. 22 of the bags have neither zips nor buttons. How many bags have zips on them?
Required number of bags which have zips on them are 71.
Here given, A company makes 140 bags.
So, total number of bags = 140
It is also given, 47 of the bags have buttons but no zips 48 of the bags have zips but no buttons.
So, number bags which have buttons but no zips = 47 and number bags which have zips but no buttons = 48
and numbers of bags which have neither zips nor buttons = 22.
If we subtract number of bags which have no zips from total number of bags then we will get total number of bags which have zips
So, number of bags have zips on them
[tex] = 140 - 47 - 22 = 71[/tex]
Therefore, 71 bags have zips on them.
This is a problem of Subtraction.
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A diner has 645 napkins. 325 napkins are used at lunch. 113 napkins are used at dinner.Melanie says that 325−113=n325-113= napkins are used in all, and that 645−212=r645-212= napkins are left.Is her answer reasonable? Explain why or why not.
Melanie's answer that 212 napkins were used in all and 433 napkins were left is reasonable and can be verified by using simple algebraic equations.
Yes, Melanie's answer is reasonable. She correctly determined that the total number of napkins used in lunch and dinner was 325-113 = 212. From this, we can also confirm that the total number of napkins left was 645 - 212 = 433. We can verify these answers by using simple algebraic equations to solve the problem. Using the equation 645 = 325 + x, where x is the number of napkins used at dinner, we can solve for x by subtracting 325 from both sides to get x = 320. Similarly, using the equation 645 = 433 + y, where y is the number of napkins used in all, we can solve for y by subtracting 433 from both sides to get y = 212. This confirms Melanie's answer that 212 napkins were used in all and 433 napkins were left.
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What is an equation for the linear relationship in slope-intercept form?
y = ? x + ?
Answer:
y = -4x + 5
Step-by-step explanation:
y = mx + b
From the graph, we see the line intersects the y-axis at 5, so the y-intercept, b, is 5.
y = mx + 5
slope = m = rise/run
rise = up and down
run = left and right
We go up 4 units from the lower point to the upper point. That is a rise of 4 units. Then we go left 1 unit. That is a run of -1.
slope = m = 4/(-1) = -4
y = mx + 5
y = -4x + 5
Please Help ASAP (sequence question)
The sequence goes like this: 1, .5, .33, .25, ____, _____, ______
Please fill out the next three terms and write a function for the sequence
f(x)=_____
Answer: .2, .14, .125
Step-by-step explanation:f(x)=1/x or 1/n
Find the value of x and y. Not drawn to scale
Using the definitions for the types of triangles in the image, we can see that the interior angles are:
x = 37°
y = 14°
How to find the value of x and y?First, on the right side we can see an equilateral triangle, then all its interior angles are of 60°.
Amd the triangle in the left side is isoceles, then the angle in the right side has the same measure than x, and now with that we can write the equation:
x + 83° + 60° = 180°
Solving for x, we will get:
x = 180° - 83° - 60°
x = 37°
Now let's find the value of y, we cansee that the triangle in the middle is also isoceles, and remember that for any triangle the sum of the interior angles must be 180°, so here we can write:
83° + 83° + y = 180°
y = 180° - 2*83°
y = 14°
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Write a paragraph proof of the Quadrilateral Sum Theorem.
Given: Quadrilateral ABCD
Prove: m
Step-by-step explanation:
Quadrilateral Sum Theorem. The total sum of the interior angles of a quadrilateral is 360°. A quadrilateral is formed by joining four non-collinear points. A quadrilateral has four sides, four vertices and four angles. Therefore, that is the Quadrilateral Sum Theorem.
Simultaneous Equations
y=x-2
y=3x+5
Hello and regards kiann09.
So the solution of the equation is:
x = - 7/2y = - 11/2Step-by-step explanation:y = x - 2
y = 3x + 5
We substitute the given value of y into the equation y = 3x + 5.
x - 2 = 3x + 5
We solve the equation for x.
x - 2 - 3x = 5
We move the variable to the left side and change its sign.
The sign of the variable must be changed because, in the process of "moving the variable", we are adding its opposite to both sides.
x - 2 - 3x = 5
Now we move the constant to the right hand side and change its sign.
x - 3x = 5 + 2
We group like terms.
-2x = 5 + 2 ⇒ We add the numbers ⇒ -2x + 7
We must divide both sides by -2.
x = - 7/2
We substitute the given value of x into the equation y = x - 2.
y = (-7/2)-2
We solve the equation for y. We write all the numerators above the common denominator.
y = -(7 + 4)/2
y = - 11/2
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