When A plug is removed from a trough to drain the water, The appropriate form of the expression is 10(x - 1)² - 3. Option D
How to determine the appropriate form of expressionThe appropriate form of the expression that would reveal the time, in minutes, when the trough is empty is: 10(x - 1)² - 3.
This expression represents the volume of the trough after the plug is removed, with x representing the time in minutes. When the volume of the trough is equal to zero, it means the trough is empty.
Therefore, setting the expression equal to zero and solving for x will give us the time when the trough is empty.
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A rocket is launched upward with an initial velocity of 1960 m/s. After how many minutes does it fall to the ground? (in meter the formula h=rt-4.9t^2 is used
Answer:
3.33 minutes
Step-by-step explanation:
h = rt - 4.9t^2
In this case, the rocket is launched upward, so the initial velocity (r) is positive 1960 m/s. The rocket will fall to the ground when the height (h) becomes zero.
0 = 1960t - 4.9t^2
To solve this quadratic equation, we can set it equal to zero and use the quadratic formula:
4.9t^2 - 1960t = 0
Using the quadratic formula:
t = (-b ± √(b^2 - 4ac)) / (2a)
Here, a = 4.9, b = -1960, and c = 0. Plugging in these values:
t = (-(-1960) ± √((-1960)^2 - 4 * 4.9 * 0)) / (2 * 4.9)
Simplifying further:
t = (1960 ± √(3841600)) / 9.8
t = (1960 ± 1960) / 9.8
t = 1960 / 9.8 = 200
So, the rocket will fall to the ground after 200 seconds. To convert this to minutes, divide by 60:
200 seconds / 60 = 3.33 minutes (approximately)
Therefore, the rocket will fall to the ground after approximately 3.33 minutes.
Joe is working out by riding his bike. He starts by biking at a constant rate. Then he gradually picks up speed until he reaches his peak. He maintains this peak speed for the rest of the workout
The graph that represents the motion of Joe on his bike is: Graph D
How to Interpret Speed Time Graph?A speed time graph is defined as a graph that shows the motion of an object against time. They can also be referred to as even a velocity-time graph.
In a speed-time graph, we note that the speed is always plotted on the vertical axis and time is always plotted on the horizontal
Now, since Joe started at a constant rate, then it means that the line will be horizontal.
When he picks up the pace, the graph line will ascend upwards and when he maintains the peak speed, it means that the graph line remains horizontal.
Thus, option D is the correct option.
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What is x-3(9+7)x-(-3x)
x - 3(9+7)x-(-3x) equals -43x, which is the answer we get after applying the order of operations.
To simplify this expression, we need to use the order of operations, which is PEMDAS (parentheses, exponents, multiplication and division, and addition and subtraction). We can simplify the expression step-by-step, following the rules of PEMDAS.
First, we need to simplify the parentheses, which contain an addition operation. We have:
x - 3(9 + 7)x - (-3x)
= x - 3(16)x + 3x (remember that -(-3x) is the same as +3x)
= x - 48x + 3x (multiplying 3 by 16 gives us 48)
= -44x + x
= -43x
Therefore, the expression x - 3(9+7)x-(-3x) simplifies to -43x.
In summary, x - 3(9+7)x-(-3x) equals -43x, which is the answer we get after applying the order of operations. Remember to follow the rules of PEMDAS carefully, and take your time simplifying each part of the expression.
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Isabel went to the grocery store. She spent $15.91 on vegetables and $11.22 on fruit. She also bought some bread. If she paid with 3 ten dollar bills and got 45 cents back in change, how much did she spend on bread?
Someone help me please. The net signed area in the above graph can be written as……
The net signed area in the above graph can be written as
(x² + 10x - 2√2)dx.
How do we know?The net signed area can be found by summing the areas of the three parts:
The three being
A line with slope 2 A Vertical line The area under the Parabolic curveHence the area
: 48 + 0 + 8 = 56
We now calculate values:
of c, d, a, and b:
c = 8 - (-2) = 10
d = 3 - 2 = 1
a = 2 + 8 = 10
b = -2√2
It is important to note that since the area under the x-axis is negative hence the reason value of b is negative.
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If you roll a die, what is the probability of not
rolling a 4? Write your answer as a fraction.
Step-by-step explanation:
NOT rolling a four means out of six posssible rols you can roll a 1.2.3.5 or 6
or 5 / 6
In a college, some courses contribute more towards an overall GPA than other courses. For example, a science class is worth 4 points; mathematics is worth 3 points; history is worth 2 points; and English is worth 3 points. The values of the grade letters are as follows, A= 4, B=3, C=2, D=1, F=0. What is the GPA of a student who made a “C” in Trigonometry, a “B” in American History, an “A” in Botany, and a “B” in Microbiology?
The GPA of the student who earned a "C" in Trigonometry, a "B" in American History, an "A" in Botany, and a "B" in Microbiology is 3.
How to find the valuesTo calculate the GPA, we need to assign point values to each grade and then calculate the weighted average.
Given:
Trigonometry (C) = 2 points
American History (B) = 3 points
Botany (A) = 4 points
Microbiology (B) = 3 points
To calculate the GPA, we'll sum the total points earned and divide by the total number of courses:
Total Points = 2 + 3 + 4 + 3 = 12
Total Courses = 4
GPA = Total Points / Total Courses = 12 / 4 = 3
Therefore, the GPA of the student who earned a "C" in Trigonometry, a "B" in American History, an "A" in Botany, and a "B" in Microbiology is 3.
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Rewrite the following in the form log(c). 2log(5)
The expression 2log(5) can be rewritten as log(25) in the form log(c), representing the Logarithm to the base 10 that yields the value 25.
The expression 2log(5) in the form log(c), we can use the logarithmic property that states:
nlog(b) = log(b^n)
Applying this property, we can rewrite 2log(5) as:
2log(5) = log(5^2)
Simplifying further, we have:
2log(5) = log(25)
Therefore, the expression 2log(5) can be written in the form log(c) as log(25).
The logarithmic function log(c) represents the exponent to which a given base must be raised to obtain the value c. In this case, log(25) represents the exponent to which the base 10 must be raised to obtain the value 25.
In summary, the expression 2log(5) can be rewritten as log(25) in the form log(c), representing the logarithm to the base 10 that yields the value 25.
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Jack leaves home for school on his bike every day at 6 a.m., travelling at 32 km/h.
One day he forgot his homework, which his mother discovered in the car 15 minutes after he had left.
She immediately left home and chased after Jack, travelling at 52 km/h.
At what time did she catch up to him?
Find the average value of f(x)=……..
The average value of the function over the interval is 0
Finding the average value of the functionFrom the question, we have the following parameters that can be used in our computation:
f(x) = √(49 - x²)
The interval is given as
From x = 0 to x = 7
The function is a square root function
Calculating f(0) and f(7), we have
f(0) = √(49 - 0²) = 7
f(7) = √(49 - 7²) = 0
Next, we have
Average value = (7 * 0 + 0 * 7)/(0 + 7)
Evaluate
Average value = 0
Hence, the average value is 0
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75% of what number is 18?
Answer: So the number is 24.
Step-by-step explanation:
what is 37 and 1/4 x 24
¿Cual es la longitud del lado de un cuadrado de ´área 441 cm2 ?
Answer:21 cm.
Step-by-step explanation:
Para encontrar la longitud del lado de un cuadrado con un área de 441 cm², podemos usar la fórmula del área de un cuadrado.
El área de un cuadrado se calcula elevando al cuadrado la longitud de uno de sus lados, es decir, A = L², donde A es el área y L es la longitud del lado.
Dado que el área del cuadrado es 441 cm², podemos escribir la ecuación:
441 = L²
Para encontrar L, podemos tomar la raíz cuadrada de ambos lados de la ecuación:
√441 = √L²
21 = L
Por lo tanto, la longitud del lado de un cuadrado con un área de 441 cm² es de 21 cm.
If triangle has a side 16.5 side 29 and side x What is value of x
The third side of the triangle 12.5
A triangle is a polygon with three edges and three vertices. The important property of a triangle is that the sum of the internal angles of a triangle is equal to 180 degrees. This property is called angle sum property of triangle.
we the measurements of given two sides of the triangle 16.5 and 29
In a triangle, the sum of any two sides should be greater than the third side and the difference between any two sides should be lesser than that of the third side.
The sum of two sides rule
[tex]x + 16.5 > 29\\ x > 29 - 16.5\\ x > 12.5\\[/tex]
The difference between the two sides rule
[tex]29 - 16.5 < x \\ 12.5 < x[/tex]
Therefore, the value of x is 12.5
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You jump 3 1/2 feet. How far do
you jump in inches?
Answer: 42 inches
Step-by-step explanation: Simple Math.
Answer: 42 inches
Step-by-step explanation:
There is 12 inches per foot and 6 inches for every 1/2 a foot so 12 x 3 = 36 + 6 = 42 inches
Find the cross product of v = (1, 0, 1) and u = (2, 6, 4).
Answer:
The cross product of v x u is (-6, 2, 6).
Step-by-step explanation:
The two vectors are v = ( 1, 0, 1) and u = (2, 6, 4).The formula for vector cross product v x u.v x u = ( v₂u₃ - v₃u₂, v₃u₁ - v₁u₃, v₁u₂ - v₂u₁).so,
v x u = ( 0 x 4 - 1 x 6 , 1 x 2 - 1 x 4, 1 x 6 - 0 x 2)
v x u = ( 0 - 6, 2 -4, 6 - 0)
v x u = ( -6, 2, 6)
Therefore the cross product of u, v is ( -6, 2, 6).
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figure A is a dilated from point E the center of dilation which figure is a dilation of figure A
A figure that is a dilation of figure A include the following: B. figure C.
What is a dilation?In Geometry, a dilation is a type of transformation which typically transforms the dimension (size) or side lengths of a geometric object, without affecting its shape.
This ultimately implies that, the dimension (size) or side lengths of the dilated geometric object would be stretched or shrunk depending on the scale factor that is applied.
In this context, we can reasonably infer and logically deduce that both figure A and figure C are congruent to figure E because they all share a common center of dilation.
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Missing information:
The question is incomplete and the complete question is shown in the attached picture.
Find the surface area of a cylinder with a height of 9 ft and diameter of 4
Answer:50.2654812288
Step-by-step explanation:
The two circles :
Sa = πr²
= π x 2²
= 12.5663706144
= 12.5663706144 x 2
= 25.1327412288
The rectangle :
C x h = 2πr
= 25.13274
= 25.13274 + 25.1327412288
= 50.2654812288
Step-by-step explanation:
50.2654858683848
because it is equivalent to this. Also I can tutor you
6. Suppose this preference schedule gives the results of an election among three candidates: Abe
(A), Benny (B), and Chloe (C). Which candidate, if any, wins using the plurality method?
number of votes 20 19 5
A|B|C
B CB
1st
2nd
3rd
CAA
O Abe (A)
OBenny (B)
O Chloe (C)
ONo candidate wins using the plurality method.
(1
Benny (B) would win the election using the plurality method.
To determine the winner using the plurality method, we need to calculate the total number of first-place votes for each candidate and see which candidate receives the most votes.
According to the given preference schedule, the number of first-place votes for each candidate is as follows:
Abe (A): 1st - 20 votes, 3rd - 2 votes (from the 2nd preference of voter 1)
Benny (B): 1st - 19 votes, 2nd - 5 votes
Chloe (C): 1st - 5 votes, 2nd - 19 votes, 3rd - 3 votes (from the 1st and 2nd preferences of voter 1)
Now, let's calculate the total number of first-place votes for each candidate:
Abe (A): 20 + 2 = 22 votes
Benny (B): 19 + 5 = 24 votes
Chloe (C): 5 + 0 + 3 = 8 votes
Based on the plurality method, the candidate with the highest number of first-place votes wins.
In this case, Benny (B) received the most first-place votes with a total of 24 votes.
Therefore, Benny (B) would win the election using the plurality method.
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A square has the perimeter of 88cm, find the area of the square
Answer: 484cm
Step-by-step explanation:
Every side of a square has equal lengths.
88/4 = 22
A = LW
= 22 x 22
= 484cm
100 Points! Algebra question. Sketch the angle. Then find its reference angle. Show your calculations. Photo attached. Thank you!
Answer:reference angle shoudl be 156 degrees srry if im wrong :)
Step-by-step explanation:
csc² 0 - cot²0 - sin² 0 = cos² 0
Answer:
see below
Step-by-step explanation:
You want to show that csc²(θ) -cot²(θ) -sin²(θ) = cos²(θ).
ProofIt often works well to express the trig functions in terms of sine and cosine. The identity sin²(θ) +cos²(θ) = 1 is also useful.
[tex]\csc^2\theta-\cot^2\theta-\sin^2\theta=\cos^2\theta\\\\\dfrac{1}{\sin^2\theta}-\dfrac{\cos^2\theta}{\sin^2\theta}-\sin^2\theta=\cos^2\theta\\\\\\\dfrac{1-\cos^2\theta}{\sin^2\theta}-\sin^2\theta=\cos^2\theta\\\\\\\dfrac{\sin^2\theta}{\sin^2\theta}-\sin^2\theta=\cos^2\theta\\\\\\1-\sin^2\theta=\cos^2\theta\\\\\cos^2\theta=\cos^2\theta\qquad\text{Q.E.D.}[/tex]
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please help! thank uu ~ :)
Answer:
The word or phrase that describes the probability that Ariana will win the raffle if she buys 50 tickets is "likely." Therefore, option (d) is the correct choice.
Since there are 100 tickets in total and Ariana buys 50 of them, her chance of winning the raffle is 50/100 or 1/2, which is equal to 0.5 or 50%. This means that it is more likely than not that she will win the raffle, but it is not guaranteed, as there is still a 50% chance that someone else will win the prize.
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7
Post Test: Ratios and Proportional Relationships
Select the correct answer.
Area Buckeye Butterflies Monarch Butterflies
A
B
C
D
E
Rachel traveled to five different areas (A, B, C, D, and E) to study the number of buckeye butterflies and the number of monarch butterflies living
there. The table shows her findings.
OA
OB.
n. All rights reserved
15
27
12
24
44
areas A and B
areas C and E
Submit Test
16
36
25
32
33
The relationship between the number of buckeye butterflies and the number of monarch butterflies is not proportional across all areas. Which two
areas have buckeyes and monarchs in the same proportion?
Reader Tools
The two areas where buckeyes and monarchs have the same proportion are areas A and B.
How to determine the two areas have buckeyes and monarchs in the same proportionBased on the information given, we can determine the two areas where the number of buckeye butterflies and the number of monarch butterflies are in the same proportion.
Comparing the data in the table, we can see that the ratio of buckeye butterflies to monarch butterflies is consistent in areas A and B.
In area A, there are 15 buckeye butterflies and 27 monarch butterflies, which simplifies to a ratio of 5:9.
In area B, there are 27 buckeye butterflies and 48 monarch butterflies, which also simplifies to a ratio of 5:9.
Therefore, the two areas where buckeyes and monarchs have the same proportion are areas A and B.
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if the measure of boa=44 and the radius of circle o is 4 what is the length plesa HURRY
Answer:
To determine the length you're referring to, we need more information about the specific configuration or diagram you're referring to. Please provide additional details or clarify your question so that I can assist you more accurately.
Step-by-step explanation:
Solve |x-5| > -2. Write your solution in interval notation.
Answer:
(−∞,∞)
Step-by-step explanation:
Since |x−5| is always positive and −2 is negative, |x−5| is always greater than −2, so the inequality is always true.
All real numbers
So, the answer is (−∞,∞)
Area and perimeter of a circle with a 13 ft radius
Answer:
Step-by-step explanation:
area of a circle = πr²
perimeter of a circle = 2πr
all we have to do is substitute the value into the formula:
area of this circle = 22/7 × 13² = 531.14 ..
perimeter of this circle = 2 × 22/7 × 13 = 81.71 ..
hope this helps!
You are washing cars over the summer. It costs you $3 to wash each car and a one-time cost of $35 for some supplies to market your car wash. You plan to charge $10 per wash. Write an equation and solve to determine the amount of cars you need to break even.
The amount of cars you need to break even is 5.
To determine the number of cars you need to break even, we can set up an equation where the revenue equals the total cost.
Let's denote the number of cars as x.
Revenue = Number of cars × Price per wash
= x × $10
Total cost = Cost per car × Number of cars + One-time cost
= $3x + $35
To break even, the revenue should be equal to the total cost:
x × $10 = $3x + $35
Now, let's solve this equation to find the value of x:
10x = 3x + 35
Subtract 3x from both sides:
10x - 3x = 3x + 35 - 3x
7x = 35
Divide both sides by 7:
x = 35 / 7
x = 5
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Directions: Use the given rules to complete the table for each sequence and
create the ordered pairs. Plot the ordered pairs on the coordinate plane and
connect them in order. Then, write a short description of how the corresponding
terms are related.
1. Rule 1: 2y, where y is equal to 5, 6, 7, 8, 9.
Rule 2: Add 10, then subtract 9, starting from 5.
Sequence 1
Sequence 2
Ordered Pair
What is the relationship between the
corresponding terms in the two sequences?
Here are the completed tables for each sequence:
Sequence 1 Sequence 2 Ordered Pair
5 15 (5, 15)
6 14 (6, 14)
7 13 (7, 13)
8 12 (8, 12)
9 11 (9, 11)
How to explain the sequenceThe corresponding terms in the two sequences are related by a linear function. The slope of the line is 1, which means that for every 1 increase in y, there is a 1 increase in x.
The corresponding terms in the two sequences are related by a linear function. The slope of the line is 1, which means that for every 1 increase in y, there is a 1 increase in x. This means that the two sequences are increasing at the same rate.
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I need help with this as well please same thing
The length of the variable are as follows;
x = 27.4 units
y = 12.7 units
How to find the variables in the tangent, secant and chord?When two secants intersect outside a circle, the circle divides the secants into segments that are proportional with each other.
Therefore,
5(x + 5) = 6(21 + 6)
5x + 25 = 126 + 36
5x + 25 = 162
5x = 162 - 25
5x = 137
x = 137 / 5
x = 27.4 units
Let's find variable y as follows;
If a secant and a tangent are drawn to a circle from the same external point, the product of the length of the secant and its external segment equals the square of the tangent segment.
Therefore,
y² = (21 + 6)6
y² = 27 × 6
y² = 162
y = √162
y = 12.7279220614
y = 12.7 units
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