The pool's water is changing height at a pace of 0.283 feet per minute.
Given,
Right circular cylinder shaped pool.
The radius of the pool = 3 feet
The height of the pool = 8 feet
Imagine that 6 cubic feet of water per minute is continuously being poured into a swimming pool in the shape of a right circular cylinder.
We have to find the rate of change of the height of the water in the pool when the depth of the water in the pool is 6 feet;
Here,
Due to the swimming pool's right circular cylinder shape, its volume equals;
V(c) = π × r² ×h
Where r is the radius of the base and h the height
We take differentiation on both sides of the equation to get:
dV/dt = π × r² × dh/dt
Since the pool is a right circular cylinder and dV/dt is constant at 6 ft3/min, the rate of change in water height in the pool is independent of water height.
Then:
6 = π × r² × dh/dt
dh/dt = 6 / π × 3²
dh/dt = 8/113,04
dh/dt = 0.283 ft/min
Therefore,
The rate of change of the height of the water in the pool is 0.283 feet/min
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In ACDE, M/C = (x-4)°, m/D = (9x + 4)°, and m/E = (2x + 12)°.
Find m/D.
Thus, in ΔCDE the m/∠D = 130⁰, which can be calculated using angle sum property of triangle.
What is triangle?Triangle is derived from the Latin word triangulus, which means "three-cornered" or "having three angles," and is composed of the roots tri-, "three," and angulus, "angle or corner." Triangles are three-sided polygons with three vertices. The angles of the triangle are formed by connecting the three sides end to end at a point. The total of the triangle's three angles equals 180 degrees.
Given that: In ΔCDE
m/∠C = (x-4)°
m/∠D = (9x + 4)°
m/∠E = (2x + 12)°
Now, to find m/∠D
So, We know that sum of internal angles of a triangle is equal to 180⁰ .Here, we are given a ΔCDE and all its three internal angles.
Putting the sum of all three equal to 180⁰:
∠C + ∠D + ∠E = 180⁰(x-4)°+ (9x + 4)°+ (2x + 12)°
= 180⁰12x +12
= 180⁰x +1 = 15⁰
x = 14⁰
Thus, Putting value of x in m/∠D = (9x + 4)°.
m/∠D = (9 × 14 +4)⁰
m/∠D = 130⁰
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The complete question is as follows:
In ΔCDE, m ∠ C = ( x − 4 ) ∘ m∠C=(x−4) ∘ , m ∠ D = ( 9 x + 4 ) ∘ m∠D=(9x+4) ∘ , and m ∠ E = ( 2 x + 12 ) ∘ m∠E=(2x+12) ∘ . Find m ∠ D.
the typing speeds for the students in a typing class is normally distributed with mean 44 (μ) words per minute and standard deviation 6 (σ) words per minute. what is the probability that a randomly selected student has a typing speed of less than 38 words per minute? use the empirical rule provide the final answer as a percent. if necessary round the percent to the nearest whole number.
The probability that a randomly selected student has a typing speed of less than 38 words per minute is 15.87%.
What is normal distribution?
A probability distribution that is symmetric about the mean is the normal distribution, sometimes referred to as the Gaussian distribution. It demonstrates that data that are close to the mean occur more frequently than data that are far from the mean. The normal distribution appears as a "bell curve" on a graph.
The formula for z-score is z = (x -μ)/σ
Where,
Z is standard score.
x is observed value.
μ is mean of the sample.
σ is standard deviation of the sample.
According to the given question.
The mean of the distribution is μ = 44
The standard deviation of the distribution is σ = 6
The observed value is x = 38
Therefore, z-score = (38 -44)/6 = -1
So, the are P(z > -1) = 15.87%
Hence, the probability that a randomly selected student has a typing speed of less than 38 words per minute is 15.87%.
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Select the equation of the line that passes through (3, 4) and (-1, -4).
y= -1/2x+2
y=2x+2
y=2x-2
y=-1/2x+4
none of the above
The equation of the line that passes through (3, 4) and (-1, -4) will be y = 2x - 2. Then the correct option is C.
What is the equation of a line passing through two points?Let the equation of the line pass through (x₁, y₁) and (x₂, y₂).
Then the equation of the line is given as,
[tex]\rm (y - y_2) = \left (\dfrac{y_2 - y_1}{x_2 - x_1} \right ) (x - x_2)[/tex]
The points are (3, 4) and (-1, -4). Then the equation of the line is given as,
(y + 4) = [(4 + 4) / (3 + 1)](x + 1)
y + 4 = 2(x + 1)
y = 2x + 2 - 2
y = 2x - 2
The equation of the line that passes through (3, 4) and (-1, -4) will be y = 2x - 2. Then the correct option is C.
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a conducting sphere of radius r is connected to ground through a battery with a voltage vo as shown. a. assuming ground is at infinity, find the net charge on the sphere. the sphere is disconnected from the battery, and a thick shell of a neutral, polarizable material is placed around the sphere. b. on the diagram, sketch vectors to indicate the direction of the polarization density in the shell. where do positive and negative bound charges appear? explain. c. consider a point inside the polarizable shell. at this point, is the magnitude of the net electric field greater than, less than, or equal to the magnitude of the electric field before the shell was added? explain. consider a point outside the shell. at this point, how does the magnitude of the electric field with the shell compare to before the shell was added? explain. d. is the electric potential difference between the sphere and ground in this case greater than, less than, or equal to the electric potential difference before the shell was added? explain. the sphere is re-connected to the battery with the shell still attached. e. will the total amount of charge on the sphere change? explain why or why not. f. does adding this polarizable shell change the capacity of the sphere to hold charge? explain.
when the charged rod is brought closer to the sphere negative charges get induced on the sphere by gathering some electrons from the ground and the negative remain on the sphere even after disconnecting it.
here the ground acts as a reservoir of electrons.a conducting sphere of radius r is connected to ground through a battery with a voltage vo as shown. a. assuming ground is at infinity, find the net charge on the sphere. the sphere is disconnected from the battery, and a thick shell of a neutral, polarizable material is placed around the sphere.
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Which of the following lines have the greatest slope? EXAM DUE IN 20 MINUTES!!
express 8 3/5 in simplest radical form
5 radical 8 to the power of 3
Step-by-step explanation:
WILL GIVE BRAINLEST! AND 20 POINTS!
The relationship is not proportional because the number of used bottles increases more. Option B
What is a proportional relationship?A relationship is said to be proportional when the two variables that are in question are either increasing or decreasing at the same rate. It could also be that one one quantity is increasing and the other is decreasing.
If we look at the proportionality in the proper sense of it, there appears to be no relationship between the two variables as the number of used bottles is increasing at a much higher rate than the number of bottles that is recycled.
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a tree is 37.95 feet tall. what is its height in meter? use the following conversion: 1 meter is 3.3 feet
The height of tree in meter is 11.5 meter after the conversion from 37.95 feet to meter.
What is conversion factor?A conversion factor is measurement value in numbers that is used in converting one unit to another unit by arithmetic operations.
Given that a tree is 37.95 feet tall and 1 meter is 3.3 feet.
So to find 37.95 feet tree in meter we have to divide 37.95 by 3.3
= 37.95 / 3.3
= 11.5 meter
1 meter is 3.3 feet, then 11.5 meter is 37.95 feet.
Therefore, the height of tree in meter is 11.5 meter.
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the unemployment rate does not reflect the true extent of the unemployment problem. which of the following groups is not counted as unemployed in the official unemployment statistics?
Groups not counted as unemployed in the official unemployment statistics are the underemployed and discouraged workers.
A discouraged worker is someone who can work and is qualified for employment but is not already working and has not looked for work in the past four weeks. Discouraged workers typically have given up looking for work because they have discovered no relevant employment possibilities or have not been successful in getting a job after applying.
Discouragement among employees has a wide range and complex root causes. Because they lack the skills to deal with technological change at work, workers occasionally leave the workforce. During the Great Recession, the manufacturing industry let go of senior workers who were unable to operate the modern computer numeric control (CNC) equipment, which was used to cut wood and other hard materials.
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One karaoke location, Singing Star, is charging $20 for 10 songs. Construct a graph to model the relationship between cost and number of songs.
A graph to model the proportional relationship between cost and number of songs is shown in the image attached below.
How to construct the required graph?Mathematically, a proportional relationship and the constant of proportionality can be represented or modeled with the following equation or mathematical expression:
y = kx
Where:
x represents the cost in dollars.y represents the number of songs.k represents the constant of proportionality.Next, we would determine the constant of proportionality (k) for a song as follows:
Constant of proportionality (k) = y/x
Constant of proportionality (k) = 10/20
Constant of proportionality (k) = 0.2
Therefore, an equation for any number of song for this karaoke is given by:
y = 0.2x.
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لیا
The prism below is made of cubes which measure 1/4 of a centimeter on one side. What is the volume?
Answer:
Below
Step-by-step explanation:
You didn't include the picture......
each cube has a volume of 1/4 * 1/4 * 1/4 = 1/64 cm^3
count the total number of cubes and multiply by 1/64
to get volume in cm^3
Laptop computers are measured according to the diagonals of their screens.
8 in.
19 in.
A(n) 19-inch laptop has a screen that is 8 inches tall. How wide is the screen?
Round your approximation to 2 decimal places.
Check the picture below.
Planet A has a mass of 6 x 10^28 kilograms. Planet B has a mass of 8 x 10^25 kilograms. Choose which planet has the lager mass. Then fill in the blank with a number written in scientific notation.
Answer:
Step-by-step explanation:
Planet A has a mass of 8× 10²5 kilograms. Planet B has a mass of 6×10 kilograms. Choose which planet has the larger mass. Then fill in th blank with a number written in standard notation. Planet A has the larger mass. The mass of Planet A is times as large as the mass of Planet B. O Planet B has the larger mass. $0 times as large as the mass of Planet A.
Answer:
10
Step-by-step explanation:
im him trust
a credit card company surveys its customers to determine the number of times they use the card each month. there are 5,500 customers and 2,756 indicate that they use the card at least twice each month. find the population proportion, as well as the mean and standard deviation of the sampling distribution for samples of size n
The standard deviation of the sampling w would be 0.06.
What is a standard deviation?
The standard deviation in statistics is a measure of the amount of variation or dispersion in a set of values. A low standard deviation indicates that the values are close to the set's mean, whereas a high standard deviation indicates that the values are spread out over a larger range.
Population proportion
[tex]p=\frac{2756}{5500} \\\\\\p=0.501091\\\\p=0.501[/tex]
The mean of the sampling distribution for samples of size n=70 customers = 0.501
The standard deviation of the sampling distribution for samples of size n=70 customers is
[tex]=\sqrt{\frac{p* (1-P)}{n}} \\\\=\sqrt{\frac{ 501091(1-0.501091) }{2}}\\\\ = 0.059761 \\\\=0.06[/tex]
Hence, the standard deviation of the sampling w would be 0.06.
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Samuel prob please answer
The system of equation that is used to determine the number of cans of soup purchased and the number of frozen dinners purchased is 300x+450(x+5)=6000mg.
What is meant by linear equation?A linear equation can be generated by equating a linear polynomial over some field with zero coefficients. The values that, when substituted for the unknowns, make the equality true are the solutions of such an equation. The phrase linear equation is frequently used to refer to this specific scenario, in which the variable is appropriately referred to as the unknown.
Each solution in the case of two variables can be regarded as the Cartesian coordinates of a point on the Euclidean plane. A linear equation's solutions form a line in the Euclidean plane, and every line can be seen as a set.
Sodium contains in a can of soup is 300mg
Sodium contains in a can of frozen dinners is 450mg
Let the number of cans of soup purchased be x
Then, the number of frozen dinners purchased=x+5
Total sodium purchased=6000mg
So, 300x+450(x+5)=6000mg
Therefore, the system is 300x+450(x+5)=6000mg
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three regular dice are rolled simultaneously. if the probability that the sum of the faces is 7 can be represented by m n in simplest form, what is m n?
The probability that the sum of the faces is 7 = 15/216
The value of m = 15 and the value of n = 216
In this question, we have been given three regular dice are rolled simultaneously.
We need to find the probability that the sum of the faces is 7.
When three dice are rolled simultaneously, the total number of outcomes
n(S) = 6 * 6 * 6
n(S) = 216
Let event A: sum of the faces is 7
A = {(1, 2, 4), (1, 4, 2), (4, 1, 2), (4, 2, 1), (2, 1, 4), (2, 4, 1), (1, 3, 3), (3, 3, 1), (3, 1, 3), (2, 2, 3), (2, 3, 2), (3, 2, 2), (1, 5, 1), (5, 1, 1), (1, 1, 5)}
n(A) = 15
So, the probability that the sum of the faces is 7 = 15/216
Hence, if the probability that the sum of the faces is 7 can be represented by m/n in simplest form then m = 15 and n = 216
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Help me please :) thank you
Answer:
a=90°
c=45°
b=45°
Step-by-step explanation:
this triangle is a right triangle. (shown by the box in angle a) this means a must equal 90°
and by extension means the other two angles have to equal 45° each because right angles always have two angles of the same degree and the angles of a triangle always Equal 180°
5. Find the measure of each angle in the figure below.
Lines are named with the capital letter; angles are named with the lower case letter.
B
A a
e d
C
The measure of each angle are mentioned below
What is angle ?
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.
An angle is a figure in plane geometry that is created by two rays or lines that have a shared endpoint. The Latin word "angulus," which meaning "corner," is the source of the English term "angle." The shared terminus of two rays is known as the vertex, and the two rays are referred to as sides of an angle.
The measure of each angle is
∠a = 90°
∠b = 45°
∠c = 45°
∠d = 90°
∠e = 45°
∠f = 45° {coordinate judgment angle }
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4.) 2x + 3y = 12
x + y = 5
Answer:
x = 3
and
y = 2
Step-by-step explanation:
Find the distance between the two points.
(3,2)
(3,0)
✓ [?]
Enter the number
that goes beneath the
radical symbol.
Enter
4
[tex] \Large{\boxed{\sf d = \sqrt{40} }} [/tex]
[tex] \\ [/tex]
Explanation:The distance between two points is given by the following formula:
[tex] \Large{\sf d = \sqrt{(x_B - x_A)^2 + (y_B - y_A)^2}} [/tex]
Where:
d is the distance between the points.[tex] \sf (x_A \: , \: y_A) [/tex] and [tex] \sf (x_B \: , \: y_B) [/tex] are the coordinates of the points.[tex] \\ [/tex]
First, let's identify our values:
[tex] \sf (\underbrace{\sf -3}_{\sf x_A} \: , \: \overbrace{\sf 2}^{\sf y_A}) \: \: and \: \: (\underbrace{\sf 3}_{\sf x_B} \: , \: \overbrace{\sf 0}^{\sf y_B}) [/tex]
[tex] \\ [/tex]
Now, substitute these values into our formula:
[tex] \sf d = \sqrt{\sf (3 - (-3))^2 + (0 - 2)^2} \\ \\ \sf d = \sqrt{\sf 6^2 + (-2)^2} \\ \\ \sf d = \sqrt{\sf 36 + 4 } \\ \\ \boxed{\boxed{\sf d = \sqrt{40} }} [/tex]
[tex] \\ [/tex]
[tex] \hrulefill [/tex]
[tex] \\ [/tex]
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you need to buy some chicken for dinner tonight. you found an ad showing that the store across town has it on sale for $3.19 a pound, which is cheaper than your usual neighborhood store, which sells it for $3.59 a pound. is it worth the extra drive? first, determine what information you need to answer this question, then click here to display that info (along with other info). how much chicken will you be buying? 3 pounds how much far are the two stores? my neighborhood store is 2.1 miles away, and takes about 7 minutes. the store across town is 8.5 miles away, and takes about 23 minutes. how kind of mileage does your car get? it averages about 19 miles per gallon in the city. how many gallons does your car hold? about 17 gallons how much is gas? about $3.83/gallon right now. going to the close store is cheaper going to the further store is cheaper the cheaper option saves you $
Yes, it is worth the extra drive, going to the further store is cheaper.
The cheaper option saves you $0.09.
Given:
Price or sale = $3.19 a pound
1.) Neighborhood store
Distance = 2.1 miles away
As, the car averages about 19 miles per gallon,
=2.1 miles / (19 miles/gallon)
= 0.1105 gallons of gas < 17 gallons
The gas is about $3.83/gallon, then the cost be
=0.1105 gallons x ($3.83/gallon)
= $0.42
The chicken is sold for $3.59 a pound, and you need 3 pounds, then you would pay:
= 3 pounds x ($3.59/pound)
= $10.77
So, the total is
= $0.42 (gas) + $10.77 (chiken)
= $11.19
2.) Store across town
Distance = 8.5 miles away
The car averages about 19 miles per gallon, then you would need:
=8.5 miles / (19 miles/gallon)
= 0.447 gallons of gas < 17 gallons
The gas is about $3.83/gallon, then the gas would cost:
=0.447 gallons x ($3.83/gallon)
= $1.71
The chicken is sold for $3.19 a pound, and you need 3 pounds, then you would pay:
= 3 pounds x ($3.19/pound)
= $9.57
The total cost
= $1.71 (gas) + $9.57
= $11.28
Thus, $11.19 < $11.28, then it is worth the extra drive.
Hence, cheaper option saves you= $11.28 - $11.19 = $0.09
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plsss don't pickk E
...................................
Answer:
answer is c!
because it's domain is -7!!
Question
The points in the table lie on a line. Find the slope of the line.
to get the slope of any straight line, we simply need two points off of it, let's use those in the picture below.
[tex](\stackrel{x_1}{-3}~,~\stackrel{y_1}{0})\qquad (\stackrel{x_2}{7}~,~\stackrel{y_2}{4}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{4}-\stackrel{y1}{0}}}{\underset{run} {\underset{x_2}{7}-\underset{x_1}{(-3)}}} \implies \cfrac{4 }{7 +3} \implies \cfrac{ 4 }{ 10 } \implies \cfrac{2 }{ 5 }[/tex]
The graph below shows the number of hours Dario
worked and the amount he earned.
DARIO'S EARNINGS
Earnings (in dollars)
100
90
80
70
60
30
20
10
(2, 24).
Review / End Test
(5, 60)
0 1 2 3 4 5 6 7 8 9 10
Time (in hours)
Flag
(8, 96)
Options
V
What was Dario's hourly wage?
A $10
B
$12
(C) $24
D $54
Answer:
Step-by-step explanation:
B.
Consider the figure shown below. Find the value of each variable mentioned in the figure below
-------------------
The measure of an inscribed angle is half the measure of the intercepted arc:
a = 52/2 = 26,c = 84/2 = 42.Angles a and b sum to a right angle since inscribed between the tangent and diameter.
Then we have:
a + b = 9026 + b = 90b = 90 - 26b = 64480 people went to the Yellowstone National Park yesterday.
180 of them were children, and the remaining were adults.
What percent of the visitors at the park were adults?
%
Answer:
11
Step-by-step explanation:
Phone-Phriends charges $35 for a text-message plan with 250 text messages included. If the customer goes over the 250 messages, the cost is $0.14 per extra text message.
A customer sent and received 329 text messages last month. What are the total charges?
Answer:
Step-by-step explanation:
11.
A person weighing 150 pounds burns about 320 calories per hour walking at a moderate rate. Suppose the same person burns about 1500 calories per day through basic activities. The total calories y burned by that person can be represented by the equation y=320x+1500, where x represents the number of hours spent walking. What is the slope and y- intercept
The slope of the equation and y- intercept is 320 and 1500 respectively.
What is the slope?The slope is the ratio of the vertical changes to the horizontal changes between two points of the line.
Given that the total calories y burned by that person can be represented by the equation y=320x+1500, where x represents the number of hours spent walking.
To find the slope and y- intercept.
y=320x+1500
Therefore, the slope of the line is;
m =320
Then the y- intercept is 1500
Hence, The slope of the equation and y- intercept is 320 and 1500 respectively.
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How would I prove that RTP is congruent to JKO by SAS?
When two pairs of corresponding sides and the corresponding angles between them are congruent, the triangles are congruent.
How do you prove that something is congruent in SAS?Side-Angle-Side (SAS) Rule
Side-Angle-Side is a rule used to prove whether a given set of triangles are congruent. The SAS rule states that: If two sides and the included angle of one triangle are equal to two sides and included angle of another triangle, then the triangles are congruent.SAS theorem of congruence: The SAS (side-angle-side) theorem of congruence states that if two sides and their included angle in one triangle are exactly equal to the corresponding two sides and their included angle in another triangle, then the two triangles are congruent.Using words: If two sides in one triangle are congruent to two sides of a second triangle, and also if the included angles are congruent, then the triangles are congruent. Using labels: If in triangles ABC and DEF, AB = DE, AC = DF, and angle A = angle D, then triangle ABC is congruent to triangle DEF.The proof by S A S congruence rule is given below.
Given from fig, JK || LM.
And JK = LM
Since JK is parallel to LM and JN is a transversal so the angle made on the same side of JN are corresponding angles which are equal to each other.
So, angle KJL = angle MLN........equation 1
Also given L is the midpoint of JN so, JL = NL.....equation 2
Now, in triangle JLK and triangle LNM
JK = LM (given)
angle KJL = angle MLN (from 1)
JL = NL (from 2)
So by S A S congruence rule, triangle JLK conguent triangle LNM proved.
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Someone answer this please
Answer:
Step-by-step explanation:
B because that is the letter of my first name!