A swimming pool is being filled at a constant rate measured in gallons per minute. The water increases by 10 gallons every 5 minutes. There was originally 100 gallons in the pool when filling started. Determine the water level W as a function of time in minutes, t.
Answers
The water level W as a function of time t, in minutes, is given by the equation W = 2t + 100.
The problem states that the water increases by 10 gallons every 5 minutes. This means that the rate of increase is 10 gallons per 5 minutes, which can be simplified to 2 gallons per minute.
Since the pool initially had 100 gallons of water, we can consider this as the starting water level at t = 0.
As time progresses, the water level increases by 2 gallons per minute. Therefore, we can express the water level W as a function of time t using the equation W = 2t + 100, where t represents the number of minutes that have passed.
This equation reflects a linear relationship between the water level and time, with a constant rate of increase of 2 gallons per minute. The initial water level of 100 gallons is represented by the y-intercept (100) in the equation. As time increases, the water level continues to rise at a steady rate of 2 gallons per minute.
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Related Questions
Having the mean delivery time (10:28am) and the standard deviation (0:55 mins), you now estimate the times within which 95% of the deliveries are made. the interval is: between 8:12 am and 12:43 pm between 8:38 am and 12:18 pm between 9:45 am and 10:15 am between 10:17 am and 12:32 pm
Answers
Based on the given mean delivery time of 10:28am and the standard deviation of 0:55 mins, the estimated times within which 95% of the deliveries are made is (a) between 8:38 am and 12:18 pm.
To calculate this interval, we need to use the z-score formula, where we find the z-score corresponding to the 95th percentile, which is 1.96. Then, we multiply this z-score by the standard deviation and add/subtract it from the mean to get the upper and lower bounds of the interval.
The upper bound is calculated as 10:28 + (1.96 x 0:55) = 12:18 pm, and the lower bound is calculated as 10:28 - (1.96 x 0:55) = 8:38 am.
Therefore, we can conclude that the interval between 8:38 am and 12:18 pm represents the estimated times within which 95% of the deliveries are made based on the given mean delivery time and standard deviation.
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You are responsible for buying a week's supply of food for the dogs and cats at a local shelter, Pawsitively Pets. The cost of food for each dog is twice as much as for a cat. You need to feed 16 cats and 10 dogs. Your budget is $720. How much can you spend on each dog for food? How much can you spend on each cat for food? how would you set up this problem in a system of equations
Answers
Answer: Dog=$40 per a dog and $20 per a cat
Step-by-step explanation:
Let the dog be x and cat be y
x=2y
10x=20y
20y+16y=32y
720/32=20
2x20=40
x=40
y=20
Unit 3: Functions& Linear Equations Homework 1: Relations & Functions Name: Date: Bell: This is a 2-page document! Find the domain and range, then represent as a table, mapping, and graph. Domain Range 2. {(-3,-4), (-1, 2), (0,0), (-3, 5), (2, 4» Domain Range - Determine the domain and range of the following continuous graphs 3. 4. Domain = Range = 5. Domain Range 6. Domain - Domain - Range - Range = Gina Wlson (AlI Things Aigebral 2
Answers
The domain and range are the set of x and values of the function are in the table.
the function as a table,
Input (x) | Output (y)
-3 | -4
-1 | 2
0 | 0
-3 | 5
2 | 4
What is the domain and range?
The domain and range are fundamental concepts in mathematics that are used to describe the input and output values of a function or relation.
The domain of a function refers to the set of all possible input values, or x-values, for which the function is defined.
The range of a function refers to the set of all possible output values, or y-values.
To find the domain and range of functions and represent them in different formats.
To find the domain and range of a function:
The domain refers to the set of all possible input values (x-values) for the function.
The range refers to the set of all possible output values (y-values) for the function.
To represent the function as a table, you would list the input-output pairs. For example:
Input (x) | Output (y)
-3 | -4
-1 | 2
0 | 0
-3 | 5
2 | 4
To represent the function as a mapping, you would indicate the correspondence between the input and output values.
For example:
-3 -> -4
-1 -> 2
0 -> 0
-3 -> 5
2 -> 4
To represent the function as a graph, The x-values would be on the horizontal axis, and the y-values would be on the vertical axis.
The points (-3, -4), (-1, 2), (0, 0), (-3, 5), and (2, 4) would be plotted accordingly.
Hence, The domain and range are the set of x and values of the function are in the table.
the function as a table,
Input (x) | Output (y)
-3 | -4
-1 | 2
0 | 0
-3 | 5
2 | 4
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i need help quick for this math question
Answers
Answer:
i think option 3
Step-by-step explanation:
im not sure but i think
Answer:
Option 3
Step-by-step explanation:
Hoped I helped like plss
What is 91.35 divided by 36.75
Answers
Answer:
2.48571428571
Step-by-step explanation:
Answer: 2.48
Step-by-step explanation:
Please help will give brainliest number 8.
Answers
Answer:
x = 1
Step-by-step explanation:
Were trying to solve for x so we would say 3 1/2 - 2 1/2 and we would be left with 1. So x=1, which you then substitute into the problem to make sure it's correct so 2 1/2 + 1 = 3 1/2.
Hope this helped
find x3dx y2dy zdz c where c is the line from the origin to the point (4, 3, 4). x3dx y2dy zdz c
Answers
The value of the given integral ∫ x³dx +y²dy +z dz is 81.
What is line origin?
The point of departure. It is zero on a number line. Where the X and Y axes cross on a two-dimensional graph, like in the graph shown here: O is sometimes used as a symbol.
Here, we have
Given; x³dx +y²dy +zdz, where c is the line from the origin to the point (4, 3, 4).
Let x =4t , y =3t ,z =4t ,0≤t ≤1
dx =4dt , dy =3dt , dz =4dt
∫ x³dx +y²dy +zdz
=\(\int\limits^1_0 {x} \, dx\)[(4t)³4dt +(3t)²3dt +(4t)4dt]
=\(\int\limits^1_0 {x} \, dx\)[(256t³ +27t² +16t] dt
=\(\int\limits^1_0 {x} \, dx\)[([64t⁴ +(9)t³ +8t²]
= [64×1⁴ +(9)×1³ +8×1²] - [64×0⁴ +(9)×0³ +8×0²]
= 81
∫ x³dx +y²dy +z dz = 81
Hence, the value of the given integral ∫ x³dx +y²dy +z dz is 81.
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can anyone help meeee plssss
Answers
Answer:
A. 14 nickles
Step-by-step explanation:
1945 men and 2849 women regiter to audition for a inging competition. The number of participant who are not ucceful in their audition what’ five time the number of thoe who are ucceful. How many participant were ucceful
Answers
1945 men and 2849 women register to audition for a singing competition. The number of participants who are not successful in their auditions what’s five times the number of those who are successful. There are 799 participants were successful.
The successful participants can be calculate by solving a linear equation as follows
First, it's crucial to understand linear equations.
Equation connects the two algebraic expressions with an equal to sign to demonstrate the equality between the two algebraic expressions.
Linear equations are those with one degree.
In this case, a linear equation must be resolved.
1945 for the men's total
Women are present in 2849.
Participants in total: 1945 + 2849 = 4794
Let x be the proportion of participants that were successful.
Men who failed were 5 times as numerous.
Participants in total: 5x + x = 6x
Due to the issue,
The linear formula is
6x = 4794
x = 4794/6
x = 799
799 of the participants had success.
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Question 4 Multiple Choice Worth 1 points)
(01.02 MC)Which number line shows the solution to -6-(-2)?
+
-2
-10
8
6
4
2
4
6
8
10
O
5
4
-2
2
4
8
10
o
4
-2
O
2
6
8
O
Answers
Answer:
-4
Step-by-step explanation:
I calculated it straight forward. lol
Answer:
the first option
The graph below represents which of the following functions?
Will give brainliest
Answers
Answer:
Choice D
Step-by-step explanation:
Easiest way is to plot each graph and determine which of the functions the graph matches. The graph of the function in choice D is attached to show it matches that function
Which rule must be used to find out the number of ways that two representatives can be picked so that one is a mathematics major and the other is a computer science major? (You must provide an answer before moving to the next part.) es Multiple Choice the division rule the subtraction rule the sum rule the product rule
Answers
The rule that must be used to find out the number of ways that two representatives can be picked, where one is a mathematics major and the other is a computer science major, is the product rule.
The product rule is a fundamental principle in combinatorics that states that if there are m ways to perform one task and n ways to perform another task, then there are m * n ways to perform both tasks together. In this case, we can consider the selection of a mathematics major representative as one task and the selection of a computer science major representative as another task.
To apply the product rule, we need to determine the number of ways each task can be performed. Let's say there are k mathematics majors and j computer science majors available. To select one mathematics major representative, we have k choices, and for the computer science major representative, we have j choices. Therefore, according to the product rule, the total number of ways to pick one mathematics major and one computer science major representative is k * j.
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To get to her parents' house, Karen would have to drive due north 9 miles. To get to her grandparents' house, she would have to drive due east 12 miles. What is the straight-line distance between the parents' and grandparents' houses
Answers
Answer:
in total 21 miles
Step-by-step explanation:
The length of the diagonal of a wooden cube is 24 cm. The cube is cut into the cylinder of the
biggest volume possible. The volume of the cylinder is:
Answers
The volume of the cylinder is \(384\pi \sqrt{3cm }^{2}\).
What is the diagonal of the cube?The diagonal that runs through the middle of a cube is it's main diagonal; the diagonal that runs along one of its faces is not. Any cube's major diagonal can be calculated by multiplying one side's length by the square root of three.Cos-1(2/3) is the angle formed between a cube's diagonal and the diagonal of one of its faces.Body of the diagonal=24cm.
Assume the length of the side= a.
\(a^{2} +(a^{2} +a^{2} )=24^{2}\)
\(a=\sqrt[8]{3} cm\)
The area of the cylinder base=\(\pi R^{2}\)
=\(\pi (\frac{1}{2} \sqrt[8]{3} )^{2}\)
=\(48cm^{2}\)
The high of the cylinder is\(\sqrt[8]{3}cm\)
The volume of the cylinder:
=s*h
=\(48\pi *\sqrt[8]{3}\)
=\(384\pi \sqrt{3} cm^{3}\)
The volume of the cylinder is \(384\pi \sqrt{3cm }^{2}\).
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The biggest possible volume of the cylinder will be \(2089.497\hspace{1mm}\text{cm}^3\).
What will be the diameter and height of the cylinder obtained from a cube and what are the formulas for the diagonal of a cube and the volume of a cylinder?If a cylinder with the biggest possible volume is cut inside the cube, the height of the cylinder and the diameter of the cylinder will be equal to the side length of the cube.For example, consider the following figure in which the cylinder is cut inside of the cube and since the side length of the cube is \(x\), the diameter and the height of the cylinder are also \(x\)If the side length of a cube is \(x\) unit, then its diagonal will be \(x\sqrt{3}\) unit.The formula for the volume of a cylinder is \(V=\pi r^2h\), where \(r\) is the radius and \(h\) is the height of the cylinder. If \(d\) is the diameter, then \(r=\frac{d}{2}\).Now, given that the diagonal of the cube is \(24\) cm. So, if the side length of the cube is \(x\) cm, then we must have
\(x\sqrt{3}=24\\\Longrightarrow x=\frac{24}{\sqrt{3}}\\\Longrightarrow x=8\sqrt{3}\)
Thus, the side length of the cube is \(8\sqrt{3}\) cm.
So, the height of the cylinder with maximum volume will be \(h=8\sqrt{3}\) cm and the diameter will be \(d=8\sqrt{3}\)cm i.e. the radius will be \(r=\frac{d}{2}=\frac{8\sqrt{3}}{2}=4\sqrt{3}\) cm.
So, using the above formula for the volume of a cylinder, we get
\(V=\pi r^{2}h=\pi\times (4\sqrt{3})^2\times 8\sqrt{3}=2089.497\hspace{1mm}\text{cm}^3\).
Therefore, the biggest possible volume of the cylinder will be \(2089.497\hspace{1mm}\text{cm}^3\).
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if there was a girl staring at the wall then 2 apples hit her in the head then a man slapped her in the head how many things hit her in the head?
Answers
2 things because a hand is not a thing
Answer:
3
Step-by-step explanation:
se the divergence theorem to evaluate s (11x 2y z2) ds where s is the sphere x2 y2 z2 = 1.
Answers
The divergence theorem states that the surface integral of the divergence of a vector field over a closed surface is equal to the triple integral of the divergence of the vector field over the volume enclosed by the surface
we are given the vector field F = (11x, 2y, \(z^{2}\)) and the surface S defined by the equation \(x^2 + y^2 + z^2\)= 1, which represents a unit sphere.
To evaluate the surface integral ∬S F · ds using the divergence theorem, we first need to calculate the divergence of the vector field F. The divergence of F, denoted as ∇ · F, is given by the sum of the partial derivatives of the components of F with respect to their corresponding variables. Therefore, ∇ · F = ∂(11x)/∂x + ∂(2y)/∂y + ∂(z^2)/∂z = 11 + 2 + 2z.
Applying the divergence theorem, the surface integral ∬S F · ds is equal to the triple integral ∭V (∇ · F) dV, where V represents the volume enclosed by the surface S.
Since the surface S is a unit sphere centered at the origin, the triple integral ∭V (∇ · F) dV can be evaluated by integrating over the volume of the sphere.
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: a) Moving to another question will save this response. Question 16 A hank rell of 40 coins weighs approximalely 0.313 kg. What a tre mass in grams of a single coin?
Answers
A hank rell of 40 coins weighs approximalely 0.313 kg, then the mass of a single coin is 7.825 g.
From the question above, the weight of 40 coins is approximately 0.313 kg. We need to find the mass of a single coin.
Let's say that the mass of a single coin is x. We know that weight = mass x gravitational acceleration (g).
We know that weight of 40 coins is 0.313 kg, Therefore, weight of one coin will be: `0.313 kg/40 = 0.007825 kg`.
We need to find the mass of one coin in grams, we will convert kg to g: `1 kg = 1000 g`.
Thus, the mass of one coin in grams will be `0.007825 kg × 1000 g/kg = 7.825 g`.
Therefore, the mass of a single coin is 7.825 g.
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In a 19-sided polygon, what is the sum of the exterior angles?
Answers
Answer:
360
Step-by-step explanation:
the sum of the measures of the exterior angles of a polygon is equal to 360 degrees
Answer: 360
Step-by-step explanation: the sum of the exterior angles are 360
help please this i will mark brainliest please
Answers
Step-by-step explanation:
please complete your question
x-y=4 et xy=21 calculer x^3-y^3
Answers
Answer:
316 or -316.
Step-by-step explanation:
x^3 - y^3 = (x - y)(x^2 + xy + y^2)
= 4(x^2 + y^2 + 21)
x - y = 4
xy = 21
Substitute x = 4 + y in the last equation
(4 + y) y = 21
y^2 + 4y - 21 = 0
(y + 7)(y - 3) = 0
y = 3, -7.
So, x = 7, - 3.
So, x and y are 7 and 3 or -7 and -3.
But x^2 + y^2 = 9 + 49 = 58 whichever is true,
So, x^3 - y^3
= 4(x^2 + y^2 + 21)
= 4 (58 + 21)
= 316,
If x = -3 and y = -7 , then the answer is
-316.
Step 3 solving equations Solve -9v 2-108.
Answers
Answer:
-18v-108
Step-by-step explanation:
negative 18v minus 108
Please help I will give brainliest
Answers
Answer:
B. 2.2 kilometers
Step-by-step explanation:
⭐What is the change in the cyclist's elevation?
The change in the cyclist's elevation is the value of the height (x) - the value of their starting point (0)Thus, we need to solve for the value of the height (x) of the hill.
Notice that the hill is in the shape of a right triangle. In order to find an unknown side length for right triangles, we need to use a trigonometric function.
⭐What is a trigonometric function?
There are 3 trigonometric functions:sin(θ) = opposite/hypotenusecos(θ) = adjacent/hypotenusetan(θ) = opposite/adjacentθ = an angle measureFirst, let's see what kind of side lengths we are given (opposite, hypotenuse, or adjacent).
We are given a side length of 10km, which is the hypotenuse of the triangle, and we are given a side length of x, which is the opposite of θ (13°).
Therefore, we will use the trigonometric function sin(θ) to solve for x.
Substitute the side lengths and angle measures we are given:
\(sin(13) = \frac{x}{10}\)
Set the equation equal to x:
\(10sin(13) = x\)
Solve for x. I recommend using a scientific calculator (e.g. Desmos Scientific Calculator):
\(2.2 = x\)
∴ The cyclist's change in elevation is 2.2 kilometers.
What is the standard deviation and its meaning given this population of customer ages? 45, 76, 30, 22, 51, 40, 63, 66, 41
Answers
The standard deviation is 16.54 if the population of customers ages is 45, 76, 30, 22, 51, 40, 63, 66, and 41.
What is the standard deviation?It is defined as the measure of data disbursement, It gives an idea about how much is the data spread out.
\(\rm SD = \sqrt{\dfrac{ \sum (x_i-X)^2}{N}\)
SD is the standard deviation
xi is each value from the data set
X is the mean of the data set
N is the number of observations in the data set.
It is given that:
The data set:
45, 76, 30, 22, 51, 40, 63, 66, 41
From the formula:
∑(x(i) - X)² = 2463.55
N = 9
SD = √(2463.55/9)
SD = 16.54
Thus, the standard deviation is 16.54 if the population of customers ages is 45, 76, 30, 22, 51, 40, 63, 66, and 41.
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4. A pizza shop has 12" pizzas with 6 slices and 16" pizzas with slices. Which pizza has bigger slices?
Answers
Estimate and then solve 8,712 ÷ 44 Pls help I will mark u BRAINLEIST
Answers
Answer:
I think 198 the correct
Answer:
198
Step-by-step explanation:
If you made 3 lawns and made 25.50 how much per lawn
Answers
Answer:
76.5
Step-by-step explanation:
25.50 x 3 = 76.5
Answer:
$8.50
Step-by-step explanation:
put 25.50/3 and you get 8.50
There are 354 mangoes. They have to be made into trays of 9 mangoes each. How many trays can be made? How many mangoes are left behind?
Answers
There are 3 mangoes left behind after making 39 trays of 9 mangoes each
To find out how many trays can be made from 354 mangoes, we divide the total number of mangoes by the number of mangoes per tray.
Number of mangoes per tray = 9
Number of trays = 354 mangoes / 9 mangoes per tray
Number of trays = 39 trays
So, 39 trays can be made from 354 mangoes.
To determine how many mangoes are left behind, we subtract the number of mangoes used for the trays from the total number of mangoes.
Number of mangoes left behind = Total number of mangoes - Number of mangoes used for trays
Number of mangoes left behind = 354 mangoes - (39 trays * 9 mangoes per tray)
Number of mangoes left behind = 354 mangoes - 351 mangoes
Number of mangoes left behind = 3 mangoes
Therefore, there are 3 mangoes left behind after making 39 trays of 9 mangoes each
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if one score is randomly selected from a normal distribution with µ = 100 and σ = 20, the probability of obtaining a score less than x = 70 is p = 0.0013.
Answers
If the probability of obtaining a score less than x = 70 is p = 0.0013, the score that corresponds to a probability of 0.0013 is x = 38.2.
We are referring to a normal distribution with a mean (µ) of 100 and a standard deviation (σ) of 20. You want to find the probability of obtaining a score less than x = 70, and you provided that the probability (p) is 0.0013. In a normal distribution with µ = 100 and σ = 20, the probability of obtaining a score less than x = 70 is p = 0.0013. Based on the information given, we know that the probability of obtaining a score less than x = 70 is p = 0.0013. This means that the z-score for x = 70 is -3.09 (found using a standard normal distribution table or calculator).
To find the z-score, we use the formula:
z = (x - µ) / σ
Plugging in the values we know:
-3.09 = (70 - 100) / 20
Solving for x:
-3.09 = (x - 100) / 20
-3.09 * 20 = x - 100
-61.8 + 100 = x
x = 38.2
Therefore, the score that corresponds to a probability of 0.0013 is x = 38.2.
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A cylinder has a height of 17 feet and a radius of 6 feet. What is its volume? Use ≈ 3.14
and round your answer to the nearest hundredth.
Answers
Answer:
1921.68 \(ft^{3}\)
Step-by-step explanation:
V = pi*r*r*h
= 3.14*6*6*17
= 1921.68
Answer in fraction form. Simplify if needed. 89 + (-23)