trey is draining an aquarium. the graph shows the amount of water (in liters) in the aquarium versus time (in minutes)
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Given the graph represents the amount of water in the aquarium versus time.
A) As shown in the graph :
as the time increases the amount of water in the aquarium decreases
The rate of water decreasing =
[tex]\frac{480}{8}=60[/tex]so, the rate = 60 litres per minute
Related Questions
Hello! I'm feeling unsure on this answer. Can we please review?
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From the given graph, let's identify the solution.
The solution will be the point(s) where both lines meet.
In this given graph, the lines meet at one point.
So we have just one solution.
From the graph, the point of intersection(point where both line meet) is:
(x, y) ==> (-1, -2)
Therefore, the solution of the graphed system is:
(-1, -2)
ANSWER:
(-1, -2)
Vanessa cycled from her home to the beach at a speed of 18 meters per second The distance between her home and the beach is 1,350 m. How long did she ta to cycle from her home to the beach? speed + distance=time
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Vanessa took 75 sec time to cycle from her home to the beach
What is Speed?Speed is the time rate at which an object is moving along a path
Speed =Distance/time
Given,
Vanessa cycled from her home to the beach at a speed of 18 meters per second
Speed=18 m/s
The distance between her home and the beach is 1,350 m.
Distance=1,350 m
Now we need to find the time for Vanessa to cycle from her home to the beach
Time=?
We have formula of speed
speed=Distance/time
Time=Distance/speed
Time=1350/18
=75 sec
Hence Vanessa took 75 sec to cycle from her home to the beach
To learn more on Speed click:
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Find the volume of this object.Use 3 for π.Volume of a CylinderV= πr²h6 in8 in12 in V[?]in³310 in
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ANSWER
V = 366 in³
EXPLANATION
This object is composed of two cylinders. The total volume of the object is the sum of the volumes of the cylinders.
As stated in the problem, the volume of a cylinder is given by,
[tex]V=\pi r^2h[/tex]Where r is the radius of the base and h is the height of the cylinder.
For the tallest cylinder, the diameter is 6 in - so the radius is 3 in, and the height is 8 in. Using 3 for π, the volume is,
[tex]V_1=3\cdot3^2in^2\cdot8in=216in^3[/tex]For the shortest cylinder, the diameter is 10 in, so the radius is 5 in, and the height is 2 in. The volume of this cylinder is,
[tex]V_2=3\cdot5^2in^2\cdot2in=150in^3[/tex]And the total volume of the object is,
[tex]V=V_1+V_2=216in^3+150in^3=366in^3[/tex]Hence, the volume of the object is 366 cubic inches.
Solve the system of equations. If the system has no solution, say that it is inconsistent.
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Answer:
D. The system is inconsistent
Step-by-step Explanation:
Given the below system of equations;
[tex]\begin{gathered} 2x-2y+5z=11\ldots\ldots\ldots\text{Equation 1} \\ 6x-5y+13z=30\ldots\ldots\ldots\text{.}\mathrm{}\text{Equation 2} \\ -2x+3y-7z=-13\ldots\ldots\ldots\text{Equation 3} \end{gathered}[/tex]We'll follow the below steps to solve the above system of equations;
Step 1: Add Equation 1 and Equation 3;
[tex]\begin{gathered} (2x-2x)+(-2y+3y)+(5z-7z)=(11-13) \\ y-2z=-2 \\ y=2z-2\ldots\ldots\text{.}\mathrm{}\text{Equation 4} \end{gathered}[/tex]Step 2: Multiply Equation 3 by 3, we'll have;
[tex]-6x+9y-21z=-39\ldots\ldots\text{.Equation 5}[/tex]Step 3: Add Equation 2 and Equation 5, we'll have;
[tex]4y-8z=-9\ldots\ldots\ldots\text{Equation 6}[/tex]Step 4: Put Equation 4 into Equation 6 and solve for z;
[tex]\begin{gathered} 4(2z-2)-8z=-9 \\ 8z-8-8z=-9 \\ 8z-8z=-9+8 \\ 0=-1 \end{gathered}[/tex]From the above, we can see that we do not have a solution for z, therefore, we can say that the system of equations has no solution, hence, it is inconsistent.
If f(x) = 5x - 2 and g(x) = 1 - 2x, find (fg)(x).I am not sure if my answer is right please help me
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Given:
f(x) = 5x - 2
g(x) = 1 - 2x
Let's find (fg)(x).
To solve the function operation, we have:
(fg)(x) = f(x) * g(x)
Thus, we have:
[tex](fg)(x)=(5x-2)(1-2x)[/tex]Solving further:
Expand using FOIL method, then apply distributive property
[tex]\begin{gathered} (fg)(x)=5x(1-2x)-2(1-2x) \\ \\ (fg)(x)=5x(1)+5x(-2x)-2(1)-2(-2x)_{} \\ \\ (fg)(x)=5x-10x^2-2+4x \\ \\ (fg)(x)=+5x+4x-10x^2-2 \\ \\ (fg)(x)=9x-10x^2-2^{} \end{gathered}[/tex]ANSWER:
[tex]9x-10x^2-2^{}[/tex]Match definition to the terms below Circle Sector Ranger Radians Arc Chord Circumcenter Circumscribed polygon Circumscribed circle Inscribed angle
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Given
Circle, Sector, Tangent, Radians, Arc, Chord, Circumcenter, Circumscribed polygon, Circumscribed circle, Inscribed angle.
To match with the definition of the terms.
Explanation:
Circle: A set of points in a plane that are equidistant from a given point.
Sector: Region of a circle bounded by an arc and two radii.
Tangent: A line that intersects a circle in exactly 1 point.
Radians: Another way to measure the angles using the ratio of
arc length /radius.
Arc: The part of circle lying between two points on the circle.
Chord: A line segment whose endpoints are on the circle.
Circumcenter: The intersection of all three perpendicular bisectors of a triangle's sides and the center of the triangle.
Circumscribed Polygon: Circle about a polygon in which all vertices intersect the circle.
Circumscribed circle: Polygon in which all the sides are tangent to the inscribed circle.
Inscribed angle: An angle formed by two chords in a circle that share an end point.
How do you write 37.5% as a mixed number?
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FIrst, write the given percentage as a fraction:
37.5% = 37.5/100 = 375/1000 = 75/200 = 15/40 = 3/8
3/8 is the same as 0 3/8 as a mixed number
f(x)=4x^2-17x + 3What is the value the discriminant F?How many distinct real numbers zeros does F have?
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Answer:
• D=249
,• Two real numbers zeros
Explanation:
Given the quadratic function:
[tex]f\mleft(x\mright)=4x^2-17x+3[/tex]a=4, b=-17, c=3
The discriminant is obtained using the formula:
[tex]\begin{gathered} D=b^2-4ac \\ =(-17)^2-4(4)(3) \\ =289-48 \\ =249 \end{gathered}[/tex]Since the discriminant is greater than 0, the equation has 2 real solutions (or zeros).
Note:
• If D<0, the equation has 0 real solutions.
,• If D=0, the equation has 1 real solution.
Find the formula for the geometric sequence 1, 5, 25, 125,...OA4, = 5-1OB. 0,= 5.50-1OC. a, = (-2)"-1D. 0,= -2"-1Reset Selection
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Given: geometric series 1 , 5, 25 , 125,.................
Find: formula for the geometric series
Explanation: the general formula for the series is
[tex]\begin{gathered} ar^{n-1} \\ 1.5^{n-1} \\ 5^{n-1} \end{gathered}[/tex]Final answer:
[tex]a_n=5^{n-1}[/tex]What is the value of this matrix at az?Matrix A
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ANSWER:
27
STEP-BY-STEP EXPLANATION:
A matrix is represented by an uppercase letter (A,B, …) and its elements with the same lowercase letter (a,b, …), with a double subscript where the first indicates the row and the second the column a the one that belongs.
Just like that:
Therefore, if we look at the matrix of the statement, we can determine that a2,1 is equal to 27
a rectangular Park is 172 yards long and 92 yd wide. what is its perimeter?
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A rectangular Park is 172 yards long and 92 yd wide :
The general expression for the perimeter of the rectangle = 2( Length + Breadth)
In the given rectangular park :
Length = 172 yd
Breadth = 92 yd
[tex]\begin{gathered} \text{ Perimeter of rectangle = 2(Length + Breadth)} \\ \text{ Perimeter of rectangle = 2(172+92)} \\ \text{ Perimeter of rectangle = }2(264) \\ \text{ Perimeter of rectangle = }528yards^2 \end{gathered}[/tex]The perimeter of rectangular park is 528 yards²
Answer : 528 yards²
Identify the equation without applying a rotation of axes.x squared +10xy+25y squared-2x-4y+10=0a. parabolab. ellipsec. hyperbolad. circle
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Solution
We are given the equation
[tex]x^2+10xy+25y^2-2x-4y+10=0[/tex]We will first simplify the equation
[tex]\begin{gathered} x^{2}+10xy+25y^{2}-2x-4y+10=0 \\ \left(x+5y\right)^2-2\left(x+y\right)+10=0 \\ (x+5y)^2=2(x+y)-10 \end{gathered}[/tex]We draw the graph
From the graph, one can see that this is a rotated parabola
Correct answer is a Parabola
Option A
11. A fair die is rolled 8 times. What is the probability of getting a. I on each of the 8 rolls? b. 6 exactly twice in the 8 rolls? c. 6 at least once in the 8 rolls?
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To asnwer this questions we can use the binomial distribution. The probability of having a number k of successes in a binomial experiment is given by:
[tex]P(X=k)=\frac{n!}{k!(n-k)!}p^k(1-p)^{n-k}[/tex]where n is the number of trials and p is the probability of succes.
a.
Since we like to have a one in each roll this means that in this case the probability of succes will be 1/6 (1 possibility out of 6). Also we have 8 rolls then n=8, and we like that the one is the result in each of them, then k=8. Plugging this values in the distribution we have:
[tex]\begin{gathered} P(X=8)=\frac{8!}{8!(8-8)!}(\frac{1}{6})^8(1-\frac{1}{6})^{8-8} \\ =\frac{1}{1679616} \\ =0.595\times10^{-6} \end{gathered}[/tex]Therefore the probability of getting a one in each roll is 0.00000595.
b.
Since we like a 6 exactly twice this means that k=2. The probability of succes is 1/6. Plugging the values in the distribution we have:
[tex]\begin{gathered} P(X=2)=\frac{8!}{2!(8-2)!}(\frac{1}{6})^2(1-\frac{1}{6})^{8-2} \\ =0.26 \end{gathered}[/tex]Therefore the probability of obtaining 6 exactly twice is 0.26.
c.
The probability of obtaining at least once a six is the sum of obtaining 1 and obtaining 2 and obtaining 3 and so on.
That means that the probability is:
[tex]\begin{gathered} P=P(X=1)+P(X=2)+P(X=3)+P(X=4) \\ +P(X=5)+P(X=6)+P(X=7)+P(X=8) \end{gathered}[/tex]but this is more easily obtain if we notice that this is the same as:
[tex]P=1-P(X=0)[/tex]This comes from the fact that the sum of all the successes possibilities (in this case obtaining a 6) have to be 1.
Then the probability of obtaniing at least once a six is:
[tex]\begin{gathered} P=1-P(X=0) \\ =1-\frac{8!}{0!(8-0)!}(\frac{1}{6})^0(1-\frac{1}{6})^{8-0} \\ =0.767 \end{gathered}[/tex]Therefore the probability of obtaining at least once a six is 0.767.
Corresponding Angles are congruent.Which angle corresponds with « 2?756 4.36.268 21152414.14 [?]A
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Corresponding angles are a pair of equal angles that are found in the same relative positions of the intersection of a transversal and a pair of parallel lines.
Based on this definition, <2 is corresponding/congruent with <6
In the same vein, <3 = <7, <8 = <4, <5 = <1.
solve quadratic by completing the squarex^2 + 12x + 23 = 0which form do i use and solve(x+___)^2(x - ___) ^2solutionx = ___
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Quadratics are in the general form:
[tex]ax^2+bx+c[/tex]For completing the square, we use:
[tex](x+\frac{b}{2})^2=c+(\frac{b}{2})^2[/tex]Now, we have:
[tex]\begin{gathered} (x+\frac{12}{2})^2=-23+(\frac{12}{2})^2 \\ (x+6)^2=-23+(6)^2 \\ (x+6)^2=13 \end{gathered}[/tex]From here, we can easily solve for x with a little algebra. Shown below:
[tex]\begin{gathered} \sqrt[]{(x+6)^2}=\pm\sqrt[]{13} \\ x+6=\pm\sqrt[]{13} \\ x=-6\pm\sqrt[]{13} \end{gathered}[/tex]The answer(s) are:
[tex]\begin{gathered} x=-6+\sqrt[]{13} \\ x=-6-\sqrt[]{13} \end{gathered}[/tex]For further clarification
Form:
[tex](x+\frac{12}{2})^2=13[/tex]please help me I truly dont understand this question also this is not college work this is for middle school
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To answer this question we need to remember the definition of the trigonometric functions:
[tex]\sin \theta=\frac{\text{opp}}{\text{hyp}}[/tex][tex]\cos \theta=\frac{\text{adj}}{\text{hyp}}[/tex][tex]\tan \theta=\frac{\text{opp}}{\text{adj}}[/tex]where opp denotes the opposite leg of the angle, adj the adjacent leg of the angle and hyp the hypotenuse.
Now, in this triangle we notice that for angle B the opposite leg is 15, the adjacent leg is 8 and the hypotenuse is 17. Plugging this values into the definitions above we have that:
[tex]\tan B=\frac{15}{8}[/tex][tex]\sin B=\frac{15}{17}[/tex][tex]\cos B=\frac{8}{17}[/tex]consider the following.find formula simplify answer .Find the domain for the formula and round answer to two decimal places if necessary.
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The sum of functions is given as:
[tex](f+g)(x)=f(x)+g(x)[/tex]In this case we have:
[tex](f+g)(x)=5x+\sqrt[]{x-1}[/tex]The domain of the functions is any number that makes the squared root a real number, then:
[tex]\begin{gathered} x-1\ge0 \\ x\ge1 \end{gathered}[/tex]Hence the domain of the functions is:
[tex]\lbrack1,\infty)[/tex]Adams house, the local park, and the nearest hospital are mapped on a coordinate plane. what's the distance between Adams house and the hospital?
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The distance between two points is given by:
[tex]d(A,B)=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]From the plane we notice that Adam's house is located in the point (-4,2) and the hospital in the point (5,7).
Plugging this values in the formula we get:
[tex]\begin{gathered} d(A,H)=\sqrt[]{(7-2)^2+(5-(-4))^2} \\ =\sqrt[]{(5)^2+(9)^2} \\ =\sqrt[]{25+81} \\ =\sqrt[]{106} \end{gathered}[/tex]Therefore the distance between Adam's house and the hospital is the square root of 106 and the answer is D.
I need help with this question... which one is the correct choice
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Given:
The image of the point (-2, 3) under translation T is (3, -1)
So, we will find the rule of the translation T
[tex]\begin{gathered} (-2+h,3+k)=(3,-1) \\ -2+h=3\rightarrow h=5 \\ 3+k=-1\rightarrow k=-4 \end{gathered}[/tex]so, the rule of translation is: shift 5 units right and 4 units down
[tex](x,y)\rightarrow(x+5,y-4)[/tex]Now, we will find the image of the point (4, 2)
So,
[tex](4,2)\rightarrow(4+5,2-4)=(9,-2)[/tex]So, the answer will be (9, -2)
How to find the value of x so that the function has a given value
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we have the function
f(x)=6x
f(x)=-24
substitute the given value of f(x)
-24=6x
solve for x
divide both sides by 6
-24/6=6x/6
simplify
-4=x
rewrite
x=-4(B) How many participants selected an image that is associated with being indeclsive
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Answer:
8
Explanation:
The images that are associated with the trait 'indecisive' are 3 and 5.
• The frequency of the image 3 = 5
,• The frequency of the image 5 = 3
Add the two:
[tex]5+3=8[/tex]Therefore, the number of participants that selected an image that is associated with being indecisive is 8.
Monica wants to know how many students take the bus home from Morton Middle School. She handed out 100 surveys and 86 said they take the bus home and rest were car-riders. If 1200 students attend Morton Middle School, what is Monica's estimate for the number of students who take the bushome? How many students take the bus home?
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Let the number of students who take the bus home be x.
Determine the value of x as ratio of number of students who take the bus home to total number of student is equal.
[tex]\begin{gathered} \frac{86}{100}=\frac{x}{1200} \\ x=\frac{86\cdot1200}{100} \\ =1032 \end{gathered}[/tex]Answer: 1032 students.
How many square feet are there in 288 square inches (1 foot=12 inches)
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Given:
1 foot = 12 inches
So, 288 square inches are:
[tex]288\text{ in}^2=288\text{ in}^2\times(\frac{1\text{ ft}}{12\text{ in}})^2[/tex]Solve:
[tex]288\text{ in}^2\times\frac{1^2\text{ ft}^2}{12^2\text{ in}^2}=288\text{ in}^2\times\frac{1\text{ ft}^2}{144\text{ in}^2}[/tex]Simplify:
[tex]2\text{ ft}^2[/tex]Answer: 2 square feet
What is the mode of the following numbers?8, 1, 2, 6, 1, 4
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it's easier if I show you the question I'm not good with math
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Find the value of f(-2);
[tex]\begin{gathered} f(x)=\frac{1}{2}x^2 \\ f(-2)=\frac{1}{2}(-2)^2 \\ f(-2)=\frac{1}{2}(4) \\ f(-2)=2 \end{gathered}[/tex]The answer is 2
f(-2) = 2
Select the correct answer.What is the area of STR?A. 30 square feetB. 34.5 square feetC. 57.5 square feetD. 60 square feet
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Hello!
To calculate the area of a triangle, we must use the formula below:
[tex]\mathrm{Area=\dfrac{base\times height}{2}}[/tex]In this triangle, we have:
• base,: 6 feet
,• height,: 10 feet
Knowing it, let's replace the formula with the values:
[tex]\mathrm{Area=\dfrac{6\times10}{2}}=\frac{60}{2}=30\text{ }\mathrm{feet^2}[/tex]Answer:A. 30 square feet
F(x) = (x + 3)^2 Graphing
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Explanation:
F(x) = (x + 3)^2
let y = F(x)
y = (x + 3)^2
Graphing the function:
we need to set values for x and get corresponding values of y
Assigned values:
x =
what is the greatest possible integer solution of the inequality 2.877x <27.174 ?
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We have to isolate the x in the inequality:
[tex]\begin{gathered} 2.877x<27.174 \\ x<\frac{27.174}{2.877} \\ x<9.45 \end{gathered}[/tex]So, the greatest possible integer is 9.
What is the type of dilation and what is the scale factor?
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We have that in the first one the dilation is a reduction and the scale factor is 1/2 with the scale factor we prove that the dilation is a reduction.
In the second one we have that the dilation is an enlargement and the sclae factor is 3 with the scale factor we prove that the dilation is an enlargement.
We can find the sacle factor with the next equation
[tex]scale\text{ factor = }\frac{image}{preimage}[/tex]you can take a side or the area of the figures and find the scale factor, for example in the first one we can do with one side od the triangle
[tex]\frac{image}{preimage}=\frac{4}{8}=\frac{1}{2}\text{.}[/tex]Question 3 of 10
Which of the following is equal to 7%?
O A. 17
OB. 17.3
O C. 73
OD. 17
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Since the exponent of 7 is 1/3, when this is converted to radical expression, the denominator of the exponent becomes the root of the radical. Hence,
[tex]7^{\frac{1}{3}}\Leftrightarrow\sqrt[3]{7}[/tex]Therefore, 7^1/3 is equivalent to the cube root of 7. (Option A)