The total amount of water that flows from the storage tank between the 7 minute mark and the 37 minute mark is 720 liters.
What is rate of flow?The amount of fluid that moves through a pipe or other container over a given amount of time.
The amount of water that flows from the storage tank between the 7 minute mark and the 37 minute mark can be calculated using the equation for the rate at which the water is flowing.
Given that the rate at which the water is flowing at time t is r(t)=200-4t liters per minute and that 0≤t<50, the total amount of water that flows from the storage tank between the 7 minute mark and the 37 minute mark can be calculated as follows:
Total amount of water = ∫r(t)dt
= ∫(200 - 4t)dt
= (200t - 4t²)
= (200(37) - 4(37²)) - (200(7) - 4(7²))
= 1924 - 1204
= 720 liters
The rate of flow decreases linearly with time, which means that the total amount of water flowing from the tank at any given time is equal to the area under the graph of the rate of flow.
This means that the total amount of water that flows from the tank between the 7 minute mark and the 37 minute mark can be calculated by integrating the rate of flow function over the given time interval.
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Suppose that the function f is defined as follows.
A graph of the piecewise function is shown on the coordinate plane in the image attached below.
What is a piecewise-defined function?In Mathematics, a piecewise-defined function can be defined as a type of function that is defined by two (2) or more mathematical expressions over a specific domain.
Generally speaking, the domain of any piecewise-defined function simply refers to the union of all of its sub-domains. By critically observing the graph of the given piecewise-defined function, we can reasonably infer and logically deduce that it is constant over several intervals such as -1 < x ≤ 0.
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13pi/6 terminal point
The terminal point of 13π/6 is (-√3/2, 1/2) by using unit circle.
What are the quadrants of a graph?The quadrants of a graph are the four sections that divide the coordinate plane. The quadrants are numbered in a counterclockwise direction starting from the positive x-axis.
1. Quadrant I is located in the upper-right section and contains points with positive x and y-coordinates.
2. Quadrant II is located in the upper-left section and contains points with negative x-coordinates and positive y-coordinates.
3. Quadrant III is located in the lower-left section and contains points with negative x and y-coordinates.
4. Quadrant IV is located in the lower-right section and contains points with positive x-coordinates and negative y-coordinates.
The quadrants are useful for determining the signs of coordinates, angles, and for plotting points on a graph.
To find the terminal point of 13π/6, we can start by recognizing that this angle is greater than 2π, which is one complete revolution around the unit circle.
To bring the angle back within one revolution, we can subtract 2π, which gives us 13π/6 - 2π/1 = 13π/6 - 12π/6 = 1π/6.
The angle 1π/6 is in the standard position between the positive x-axis and the first quadrant. The reference angle is π/6, which is the angle between the terminal side and the x-axis.
Since the angle is in the 2nd quadrant, the x-coordinate will be negative and the y-coordinate will be positive. Using the unit circle, we can find the values of sine and cosine at π/6 and then negate the value of cosine since the angle is in the second quadrant.
cos(π/6) = √3/2
sin(π/6) = 1/2
Therefore, the terminal point of 13π/6 is (-√3/2, 1/2).
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Which of the following sets of numbers could not represent the three sides of a right
triangle?
11, 60, 61}
{14, 48, 50
{46, 60, 75}
(39,80,89}
Answer: D
Step-by-step explanation: it equals 181
evaluate the expression
After substituting the values as x=3 and y=7, the value of the expression "2x²-y¹+3x⁰" is 14.
In mathematics, an expression is a combination of numbers, variables, and mathematical operations (such as addition, subtraction, multiplication, and division) that can be simplified or evaluated to a numerical value.
To evaluate the expression 2x²-y¹+3x⁰ for x=3 and y=7, we substitute the given values, which are x=3 and y=7 into the expression and simplify:
On substituting the values,
We get,
= 2x² - y¹ + 3x⁰
= 2(3)² - 7¹ + 3(1)
= 2(9) - 7 + 3
= 18 - 7 + 3
= 14
Therefore, when x=3 and y=7, the value of the expression 2x²-y¹+3x⁰ is 14.
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The Regular polygon has the following measures.
a=7√3cm
s=14 cm
Segment a is drawn from the center of the polygon perpendicular to one of its sides.
What is the vocabulary term for segment a?
what is the area of the polygon?
Round to the nearest tenth and include correct units
The vocabulary for a is called the apothem
The area of the regular polygon is [tex]2419.68 cm^2.[/tex]
How to solve for areaa = 7√3 cm
s = 14 cm
The perimeter of the polygon is:
P = ns
where n is the number of sides of the polygon. We can find n using the formula:
[tex]n = 360 / (180 - (360 / 2n))[/tex]
where n is the number of sides. Substituting the given value for s, we get:
[tex]n = 360 / (180 - (360 / 2*7)) = 14[/tex]
Therefore, the polygon has 14 sides.
a = [tex]\sqrt{31.820 cm)^2 - (14 cm/2)^2}[/tex])
= 24.615 cm
A = (1/2) * apothem * perimeter
[tex](\frac{1}{2} ) * 24.615 cm * 196 cm \\=\\ 2419.68 cm^2[/tex]
Therefore, the area of the regular polygon is [tex]2419.68 cm^2.[/tex][tex]2419.68 cm^2.[/tex]
In summary,
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Can yall help me with this pls
Answer:
x=6.4
Step-by-step explanation:
2/3.2 = 4/x
2x=4(3.2)
2x=12.8
x=6.4
Lin has 9 plates she puts 1/4 of a sandwich on each plate which expression represents the sandwiches in the situation
A. 9x4
B. 9x1/4
C. 4x9
D. 4x1/9
what is the area of a circle with the diameter of 22 in
Answer:380.1 square inches
Step-by-step explanation:Area of a circle in terms of diameter: Area = π· (d2) 2 = 3.14· (222) 2 = 3.14· (11) 2 = 380.1 square inches (*)
I would be thankful if you help
To get a 1 in matrix row 1, column 1 all we have to do is divide the row by 7 which gives us:
[tex]\left[\begin{array}{ccc} 1\frac {-4}{7}&\frac{8}{7} \\-12&7&-13\end{array}\right][/tex]
Understanding MatrixThe solution provided above uses a method of matrix called Echelon.
Echelon matrix is a matrix that has been transformed using row operations into a specific form that makes it easier to solve systems of linear equations.
By applying these row operations, a matrix can be transformed into row echelon form, which is a weaker form of echelon form where the leading non-zero entry of each row is to the right of the leading non-zero entry of the row above it, but not necessarily strictly to the right.
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WILL GIVE BRAINLIEST IF CORRECT
Will report is answer is a guess. Include reasoning behind answer
The image of point R by rotation is equal to R'(x, y) = (- 4, 7).
How to find the image of a point by rotation
The statement of the problem asks us to find the image of point by a kind of rigid transformation known as rotation, whose formula is:
(x, y) → (x · cos θ - y · sin θ, x · sin θ + y · cos θ)
Where:
x, y - Coordinates of the original point.θ - Angle of rotation, in degrees.If we know that x = 4, y = 7 and θ = - 180°, then the coordinates of the image of point R are:
R'(x, y) = (4 · cos 180° - 7 · sin 180°, 4 · sin 180° + 7 · cos 180°)
R'(x, y) = (- 4, 7)
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Based on the results, whaBased on the results,, what is the probability of needing fewer than 4 rolls to get doublest
The probability of needing fewer than 4 rolls to get doubles is 13/25.
What is Probability?Probability is a branch of mathematics that deals with the likelihood of something happening. It is used in many areas such as finance, engineering, and even gambling. Probability is the measure of how likely an event is to take place. This is usually expressed as a number between 0 and 1, where a 0 indicates an impossible event, and a 1 indicates an event that is certain to happen. Probability is an important component of decision making, as it allows us to calculate the chances of different outcomes.
This can be calculated by using the binomial probability formula. The binomial probability formula is used to calculate the probability of a certain number of successes in a certain number of trials. In this case, the number of successes is 2 (the number of doubles required to win the game) and the number of trials is 4 (the maximum number of rolls necessary to win the game).
Using the formula P(x) = nCx * pˣ* qⁿ⁻ˣ, where n is the number of trials, x is the number of successes, p is the probability of success and q is the probability of failure, we can calculate the probability of needing fewer than 4 rolls to get doubles as follows:
P(2) = 4C2 * (1/2)² * (1/2)⁴⁻² = 4 * ( 1/4 ) * (1/4) = 1/4
P(1) = 4C1 * (1/2)¹ * (1/2)⁴⁻¹= 4 * (1/2) * (1/2) = 1/4
The total probability of needing fewer than 4 rolls to get doubles is the sum of the probabilities of needing 1 or 2 rolls to get doubles, which is 1/4 + 1/4 = 1/2, or 13/25.
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Complete questions as follows-
Based on the results, what is the probability of needing fewer than 4 rolls to get doubles? 13/25.
sum of 213341 & 444233 base 5
Answer:
1213124
To add 213341 and 444233 in base 5, we need to line up the digits of the two numbers according to their place values, and then add them digit by digit, carrying over to the next place value if the sum of the digits is 5 or greater.
Here's how to do it:
2 1 3 3 4 1
+ 4 4 4 2 3 3
-----------------------
1 2 1 3 1 2 4
Therefore, the sum of 213341 and 444233 in base 5 is 1213124.
If the profit function for a product is
P(x) = 2400x + 105x^2 − x^3 − 167,000
dollars, selling how many items, x, will produce a maximum profit?
x = items
Selling 80 items will produce maximum profit if the profit function is [tex]P(x) = 2400x + 105x^2 - x^3 - 167,000[/tex].
What is the value of x that produces maximum profit?To find value of x that produces maximum profit, we must get critical points of the profit function and determine which one corresponds to a maximum.
The profit function is given as:
[tex]P(x) = 2400x + 105x^2 - x^3 - 167,000[/tex]
Taking the derivative of P(x) with respect to x, we get:
[tex]P'(x) = 2400 + 210x - 3x^2[/tex]
Setting P'(x) equal to zero and solving for x, we get:
[tex]0 = 2400 + 210x - 3x^2\\3x^2 - 210x - 2400 = 0\\x^2 - 70x - 800 = 0\\(x - 80)(x + 10) = 0[/tex]
Here, the critical points are x = 80 and x = -10.
To determine one that corresponds to a maximum, we can use the second derivative test. Taking the derivative of P'(x), we get:
[tex]P''(x) = 210 - 6x[/tex]
Evaluating P''(80), we get:
[tex]P''(80) = 210 - 6(80)\\P''(80) = 210 - 420\\P''(80) = -330[/tex]
Since P''(80) is negative, the critical point x = 80 corresponds to a maximum. So, selling 80 items will produce maximum profit.
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Help please
Expand the logarithm as much as possible
logy^10
Answer: 2.303
Explanation: In image
Please solve this for me!
Answer: 1; 520/9 number 2: 9/2 number 3: d number 4:d number 5: 151.7
Step-by-step explanation:
help me solve this please 2x+5y
Answer:
35
Step-by-step explanation:
Simply plug in the value of your 'x' and 'y':
x = 4.5
y = 5.2
[tex]2(4.5)+5(5.2)=9+26=35[/tex]
In the figure, TR−→− and TV−→− are secants to circle A.
mRV=99∘
mSU=45∘
What is the measure of ∠RTV?
The measure of <RTV = 1/2 * (99 - 45) = 27 degrees
What is a Secant of a Circle?Geometrically speaking, a secant is an intersecting line that marks two separate points on the circumference of a circle.
Primarily, it serves as a chord drawn across the diameter which transverses through each endpoint connecting them. The magnitude of the secant is determined by the distance between these intersectional points. This particular element of geometry has various applications in trigonometry, particularly in computing angles and lengths within circles.
According to the Exterior Angle of a Circle Theorem, the measure of an exterior angle of a circle formed by two secants is equal to half the difference of the measures of the intercepted arcs:
Using this theorem,
Thus, the measure of ∠RTV is given as 27
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Which of the following new vehicle borrowers is likely to be offered the lowest APR?
A.Stephanie who is buying a new vehicle and has a FICO score of 780
B. Tyler who is buying a used vehicle and has a FICO score of 780
C. Emily who is buying a new vehicle and has a FICO score of 600
D. Daniel who is buying a used vehicle and has a FICO score of 600
Tyler who is buying a used vehicle and has a FICO score of 780 is likely to be offered the lowest APR. The Option A is correct.
Since, When it comes to APR for a new or used vehicle loan, a borrower's credit score is one of the main factors considered by lenders.
The higher the credit score, the very more likely that a borrower is to be offered a lower APR.
Hence, In this case,
Tyler has a FICO score of 780 which is considered excellent, and is buying a used vehicle.
This combination of a high credit score and a used vehicle purchase makes Tyler the most likely candidate to be offered the lowest APR.
Thus, Tyler who is buying a used vehicle and has a FICO score of 780 is likely to be offered the lowest APR. The Option A is correct.
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5. Which box-and-whisker plot represents this set of data? (1 point)
90, 98, 75, 84, 89, 91, 70, 81, 93, 84, 100
Hawk thinks his heartrate will increase as he increases his skateboarding speed. To see if this relationship exists, he records six different speeds and models it with a scatterplot and regression output.
A scatterplot is shown with the x axis labeled Speed, miles per hour, and the y axis labeled Pulse, beats per minute. The points on the graph increase from 9.5 and 68 to 15.8 and 116.
Regression Statistics
Multiple R 97.28153%
R Square 94.63696%
Adjusted R Square 93.29620%
Standard Error 4.806846736
Observations 6
df SS MS F
Regression 1 1,630.910231 1,630.910231 70.58453
Residual 4 92.42310217 23.10577554
Total 5 1,723.333333
Coefficients Standard Error t Stat p-Value
Intercept 1.301246992 10.66036651 0.122064001 0.908735
Speed 7.315685846 0.870763656 8.401459797 0.001098
Part A: Write the equation of the regression line using the regression output. (2 points)
Part B: What do the slope and intercept parameters mean using the context of the problem? (4 points)
Part C: Compute the margin of error that Hawk should use if he wants to provide a 99% confidence interval for the slope. Assume that conditions for inference are satisfied. (4 points)
The equation of the regression line is Pulse = 1.301 + 7.316 * Speed. The slope parameter represents how pulse rate changes with skateboarding speed. The margin of error for a 99% confidence interval for the slope is 2.517.
Explanation:Part A: The equation of the regression line can be written as: Pulse = 1.301 + 7.316 * Speed
Part B: The slope parameter of 7.316 means that for every 1 unit increase in skateboarding speed, the pulse rate increases by an average of 7.316 beats per minute. The intercept parameter of 1.301 represents the pulse rate at a speed of 0 miles per hour (which doesn't have a specific meaning in this context).
Part C: To compute the margin of error for a 99% confidence interval for the slope, we use the formula: margin of error = critical value * standard error. The critical value for a 99% confidence interval is approximately 2.896. Plugging in the values, we get margin of error = 2.896 * 0.870 = 2.517 (rounded to three decimal places).
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what is pi * 12 * 2
Answer: 3.14 x 12 x 2
= 75.36
Step-by-step explanation:
I need help to get the residual plot from this data 13.8 1.42 16.7 3.21 0.7 1.11 18 4 16.7 3.21 20 4 18 3.8 19.5 3.78 21.9 3.69 0.7 1.11
Answer:
To create a residual plot, you need to first fit a model to the data. Without any information about the problem you are trying to solve or the model you are fitting, I will assume that you are trying to fit a linear regression model to these data points.
First, you would need to find the equation of the line that best fits the data using a regression analysis software or by hand. Let's assume that the equation of the line is:
y = 0.2x + 2.5
where y is the response variable (dependent variable) and x is the predictor variable (independent variable).
Next, you would calculate the predicted values of y (i.e., the values that the model predicts) for each value of x in your dataset, using the equation of the line. For example, for the first data point (13.8, 1.42), the predicted value of y would be:
y_predicted = 0.2 * 13.8 + 2.5 = 5.06
The residual for this data point would be the difference between the actual value of y and the predicted value of y:
residual = 1.42 - 5.06 = -3.64
You would repeat this process for each data point in your dataset, to get a list of residuals.
Suppose that the function is defined as follows.
Answer:
Step-by-step explanation:
Please help!!!!!!!!!!!!
The calculated values of the sum of interior angles of the shapes are 1080 degrees and 360 degrees
Calculating the sum of interior angles of the shapesThe formula of the sum of interior angles of a polygon is
Sum = (n − 2) * 180
For the octagon, we have
n = 8
This means that
Sum of angles = (8 − 2) * 180
Evaluate
Sum of angles = 1080
For the square, we have
n = 4
This means that
Sum of angles = (4 − 2) * 180
Evaluate
Sum of angles = 360
Hence, the sum of interior angles of the shapes are 1080 degrees and 360 degrees
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A metallurgist made two purchases. The first purchase, which cost $1224, included 48 kilograms of an iron alloy and 40 kilograms of a lead alloy. The second purchase, at the same price, cost $507 and included 24 kilograms of the iron alloy and 13 kilograms of the lead alloy. Find the cost per kilogram of the iron and lead alloys. What is the cost of the iron alloy and the lead alloy?
Suppose that the functions f and g are defined as follows.
Answer:
[tex]\dfrac{f}{g}(x) = \boxed{\dfrac{7}{x\left(x-3\right)}\\\\}[/tex]
Domain of [tex]\dfrac{f}{g}: \boxed{\:\left(-\infty \:,\:0\right)\cup \left(0,\:3\right)\cup \left(3,\:\infty \:\right)}[/tex]
Step-by-step explanation:
Given
[tex]f(x) = \dfrac{7}{x} , g(x) = x - 3[/tex]
[tex]\dfrac{f}{g} = \dfrac{f(x)}{g(x)} = \dfrac{7}{x} \div x - 3\\\\= \dfrac{7}{x} \times \dfrac{1}{x-3}\\\\ = \dfrac{7}{x\left(x-3\right)}[/tex]
To find the domain of
[tex]\dfrac{f}{g} = \dfrac{7}{x\left(x-3\right)}[/tex]
note that this function is defined everywhere in the range (- ∞, ∞) except for x = 0 and x = 3
At these two points, the function is undefined since the denominator becomes 0 and division by 0 is undefined
Therefore the domain consists of three parts expressed in inequality and interval forms
-∞ < x < 0 (-∞, 0)
0 < x < 3 (0, 3)
3 < x < ∞ (3, ∞)
Therefore the domain is obtained by combining these three intervals
- ∞ < x < 0 or 0 < x < 3 or x > 3
In interval notation with union:
[tex]\:\left(-\infty \:,\:0\right)\cup \left(0,\:3\right)\cup \left(3,\:\infty \:\right)[/tex] ANSWER
Gruden Company produces golf discs which it normally sells to retailers for $7 each. The cost of manufacturing 20,000 golf discs is:
Answer:
$140,000
Step-by-step explanation:
7*20,000 = 140,000
The whole page tysmmmm plsss step by step explanation
Answer:
Step 1:
a.) 16 pets in total (1 + 0 + 2 + 0 + 3 + 8 + 0 + 2)
b.) the mean is 2 (16 is the total number of pets, divide that by 8 which is the total number of students asked, 16/8 = 2)
Step 2:
a.) 0, 0, 0, 1, 2, 2, 3, 8 (zero, one, two, three, four, five, six, seven, eight.)
b.) 0 and 3 are the middle numbers (center.)
c.) 3/2 = 1.5 (0+3 = 3 divided by 2 = 1.5)
Step 3:
- most of the students did not have any pets, so the mode would be 0 (it is zero because zero appears in the set of numbers 3 times. More than any other number).
Step 4:
They should use the mean of the amount of pets the students have; this is because the mean is the average amount of pets counting everyone in class—regardless on if there were zeros in the list.
can someone please helppp
Answer:
6 presents / minute
Step-by-step explanation:
We can represent the given information in a ratio:
amount of present wrapped : minutes it took to wrap
2/3 : 1/9
Then, we can multiply both sides by 9 (the reciprocal of 1/9) so that the right side of the ratio is 1 minute.
presents : minutes
2/3 : 1/9
× 9 × 9
6 : 1
So, Patricia can wrap 6 presents in 1 minute.
Write 3.5 as a mixed number and as an improper fraction.
Write your answers in simplest form.
3.5= 35/10
35/10= 7/2
which is equal to 3 1/2
Therefore: 3 1/2 and 7/2