Answer:
The answer is 20 L
Step-by-step explanation:
if 1/2 minutes = 1 L
10 minutes = 20 L
Answer:
20 liters
Step-by-step explanation:
when working with math problems about the rate that something is happening, it is typically helpful to find the unit rate.
In this case, the unit rate will be how many liters are lost in 1 minute (per unit essentially means per "1" )
we know that 1 liter is lost in 1/2 minute
1/2 minute = 1 liter
×2 ×2 {multiply both sides by 2 to find "1 minute"}
1 minute = 2 liters
So, for every 1 minute, we lose 2 liters
if we have 10 minutes, we can multiply both sides by 10:
1 minute = 2 liters
×10 ×10
10 minutes = 20 liters
So, after 10 minutes, 20 liters are lost
hope this helps!!
Choose the system of inequalities that best match the graph below.
The system of the linear inequality that fulfill the condition of the graph will be y ≥ 2x – 1 and y ≤ 1/3 x + 1. Then the correct option is A.
The complete question is attached below.
What is inequality?Inequality is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's relative size and can be used to compare these two claims.
The system of the linear inequality that fulfill the condition of the graph will be
y ≥ 2x – 1
y ≤ 1/3 x + 1
Then the correct option is A.
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please help me solve what is on that document
The most misleading graph is graph B because the blue rectangle and the red rectangle do not have the same width when plotted on the same scale
The ratio of the median weekly earningsFrom the graph, we have the median weekly earnings to be:
High school diploma = $750Bachelor's degree = $1250So, the ratio is:
Ratio = $750 : $1250
Simplify
Ratio = 3 : 5
Hence, the ratio of the median weekly earnings is 3 : 5
The ratio of the area of the red rectangle to the blue rectangle in graph A?
In (a), we have:
Ratio = 3 : 5
The scale on the horizontal axis is given as:
1 unit per grid mark
Both rectangles have a width of 1 unit.
So, we have:
Ratio = 3 * 1: 5 * 1
Simplify
Ratio = 3 : 5
Hence, the ratio of the area of the red rectangle to the blue rectangle in graph A is 3 : 5
The ratio of the area of the red rectangle to the blue rectangle in graph B?In (a), we have:
Ratio = 3 : 5
The scale on the horizontal axis is given as:
1 unit per grid mark
The red rectangle has a width of 3 units, while the blue has 5 units as its width
So, we have:
Ratio = 3 * 3 : 5 * 5
Simplify
Ratio = 9 : 25
Hence, the ratio of the area of the red rectangle to the blue rectangle in graph B is 9 : 25
The ratio of the volume of the red cube to the blue cube in graph C?
In (a), we have:
Ratio = 3 : 5
The scale on the horizontal axis is given as:
1 unit per grid mark
The red rectangle has a width of 3 units, while the blue has 5 units as its width.
Since the base are squares, we have:
Ratio = 3 * 3 * 3 : 5 * 5 * 5
Simplify
Ratio = 27 : 125
Hence, the ratio of the volume of the red cube to the blue cube in graph C is 27 : 125
The most misleading graph
The most misleading graph is graph B.
This is so because the blue rectangle and the red rectangle do not have the same width when plotted on the same scale
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Find the solutions to the equation below. check all that apply. x^2-2x-15=0
The student did not make any mistake, the solution is correct. Then the correct option is A.
What is a factorization?It is a method for dividing a polynomial into pieces that will be multiplied together. At this moment, the polynomial's value will be zero.
A student perform the following steps to find the solution of the equation x² – 2x – 15 = 0.
The factor of the equation will be
Step 1 : x² – 2x – 15 = (x – 5)(x + 3)
Step 2 : (x – 5) = 0 and (x + 3) = 0
Step 3 : x = 5 and – 3
The student did not make any mistake, the solution is correct.
Then the correct option is A.
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Find the average rate of change of f ( x ) = 9 x 2 − 7 on the interval [ 2 , a ] . Your answer will be an expression involving a
Answer:
9a + 18
Step-by-step explanation:
so the first step is to evaluate the value of f(2).
[tex]f(2) = 9(2)^2-7\\f(2)=9(4)-7\\f(2)=36-7\\f(2)=29[/tex]
Now that we have this value we can use the slope formula (y2 - y1) / (x2 - x1) where y2 is f(a), y1 is 29, x2 is a, and x1 is 2
[tex]\frac{f(a)-29}{a-2}\\\\\frac{(9a^2-7)-29}{a-2}\\\frac{9a^2-36}{a-2}[/tex]
Now from here we can use long division to simplify it further
[tex]9a^2/a = 9a\\9a(a-2)=9a^2-18a\\(9a^2-36)-(9a^2-18a)\\18a-36\\\\18a/a=18\\18(a-2)=18a-36\\(18a-36)-(18a-36)\\0\\\\9a+18[/tex]
Select the correct answer from each drop-down menu.
The function f is given by the table of values as shown below.
x 1 2 3 4 5
f(x) 13 19 37 91 253
Use the given table to complete the statements.
If function f was translated down 4 units, the _
values would be _
A point in the table for the transformed function would be _
Using translation concepts, the correct statement is given by:
If function f was translated down 4 units, the f(x) values would be subtracted by 4. A point in the table for the transformed function would be (1,9).
What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.
A translation down 4 units means that the output values are subtracted by 4, hence the table would be given by:
x 1 2 3 4 5
f(x) 9 15 33 87 249
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Answer:
The CORRECT answer is:
1. f(x)
2. decreased by 4
3. (4, 87)
Step-by-step explanation:
Took the test
)The width of a rectangle is shown below:
A coordinate plane with a point A at negative 3, 3 and C at negative 3, negative 2.
If the area of the rectangle to be drawn is 20 square units, where should points B and D be located if they lie to the right of points A and C?
B(1, 3) and D(1, −2)
B(3, 3) and D(3, −2)
B(2, 3) and D(2, −2)
B(1, 2) and D(1, −3)
Answer: B(1, 3) and D(1, −2)
Step-by-step explanation:
The distance from A to C is 5, meaning we need the length to be 4.
If they lie to the right, we need to add 4 to the x coordinates, so the x coordinates should be 1, and the y coordinates should be 3 and -2.
The locations of B and D are given by (A) B(1,3) and D(1,-2).
The area of rectangle is given by the product of the length and width of that rectangle.
Area = Length*Width
Distance between two points (a,b) and (c,d) is given by,
[tex]d=\sqrt{(c-a)^2+(d-b)^2}[/tex]
Here in the given question it is mentioned that AC forms width of a rectangle and A is at (-3,3) and C is at (-3,-2)
Now the width is [tex]=\sqrt{(-3-(-3))^2+(-2-3)^2}=\sqrt{0^2+(-5)^2}=\sqrt{25}=5[/tex] unit.
Also it is given that, the area of the rectangle is 20 square units.
So the length is = 20/5 = 4 units
B and D lie to the right of points A and C respectively.
We have to go 4 units right to the A to find B and 4 units right to C to find D.
A is at (-3,3)
then B is at (-3+4,3) = (1,3)
C is at (-3,-2)
So D is at (-3+4,-2) = (1,-2)
Hence correct option is (A) B(1,3) and D(1,-2)
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Question 3 of 10
Mark all the statements that are true.
Evaluate the expression 3.14(a2 + ab) when a = 4 and b = 3
Answer:
87.92
Step-by-step explanation:
We are given this expression:
3.14(a² + ab)
And we want to evaluate it if a is 4 and b is 3.
To solve this, we need to follow the order of operations, usually known as PEMDAS (parentheses, exponents, multiplication, division, addition, subtraction) in the United States, although other countries have their own variations on the acronym.
Despite this, let's start with P, which would be parentheses.
Because we have the a² + ab in parentheses, we should evaluate this first.
We should substitute the values of a and b with 4 and 3 respectively, to get this (we can ignore the 3.14 for now):
(4)² + 4 * 3
First, let's go on to exponents.
We do have one exponent, which is the 4 being raised to the second power.
So let's evaluate that.
Raise 4 to the second power (multiply it by itself).
4 * 4 = 16
We can replace (4)² with 16.
16 + 4 * 3
Now, let's move on to multiplication.
We do have one multiplication operation, which is the 4 * 3, so let's evaluate that.
4 * 3 = 12
Replace 4 * 3 with 12.
16 + 12
We don't have any division in this, so we can skip that.
Moving on to addition:
We can add these two numbers together.
16 + 12 = 28
28 is the value of a² + ab.
We now multiply this by 3.14 to get the answer.
3.14 * 28 = 87.92
Topic: substituting values into an expression
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The value of expression 3.14([tex]a^{2}[/tex]+ab) when a =4 and b=3 is 87.92.
Given Expression :3.14([tex]a^{2}[/tex]+ab) and we have to find the value at a=4 and b=3
we know expressions are the combinations of numbers, symbols and coefficients and in the expression given the variable are a and b .Expression shows the relationship between the variables which are present in the expression. When we have to find the value of expression at a=4 and b=3 we have to just put the values of a and b in the expression .
[tex]a^{2}[/tex]=16 and ab=4*3=12
=3.14[tex]((4)^{2}+4*3)[/tex]
=3.14(16+12)
=3.14*28
=87.92
Hence the value of the expression 3.14(a2 + ab) at a=4 and b=3 is 87.92.
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which matrix equation has the soul ut ion X
Step-by-step explanation:
option 2 is correct
here the question ask for value of X
to find it we multiple the matrix X with the given matrix in question and equate the answer.
A line / passes through point (-2, 5) and has the same y-intercept as
the line y-3x-4. What is the equation for the line /?
I'm assuming you meant to write y = 3x-4
We know that the y-intercept of the given line is (0,-4), so we need to find the equation of the line passing through (-2,5) and (0,-4).
The slope is
[tex]\frac{-4-5}{0-(-2)}=-\frac{9}{2}[/tex]
So, this means the equation is [tex]\boxed{y=-\frac{9}{2}x-4}[/tex]
How do I get this answer?
Answer:
Step-by-step explanation:
Several trig identities are involved in the proof of this. This is the order in which they are used.
cos(2x) = cos²(x) -sin²(x)cos²(x) +sin²(x) = 1cos(x) = 1/sec(x)ProofStarting with the left side, we can transform it into the right side.
[tex]2\cos(2x)=2(\cos^2(x)-\sin^2(x)) = 2(\cos^2(x)-(1-\cos^2(x)))\\\\=2(2\cos^2(x)-1)=2\left(\dfrac{2}{\sec^2(x)}-\dfrac{\sec^2(x)}{\sec^2(x)}\right)\\\\=\boxed{\dfrac{4-2\sec^2(x)}{\sec^2(x)}}[/tex]
Given:
PLEASE HELP ASAP!
Part I: Use the given information to determine . Show all of your work.
Part II: Use complete sentences to explain the steps necessary in solving for . Justify your explanation by including all theorems, postulates, or definitions used.
The value of angle ∠DEC = 60 degree.
The complete question is
In the given the figure above, m∠BAC = 64° and m∠CBA = 56°.
Part I: Find the m∠DEC.
Part II: Explain the steps you took to arrive at your answer. Make sure to justify your answer by identifying any theorems, postulates, or definitions used.
What is a Triangle ?A triangle is a polygon with three sides and three vertices and three angles.
As it is given that
AB || CD
Let BC be the transversal , then
∠CBA = ∠DCB (alternate opposite angles)
∠DCB = 56 degree
As the sum of opposite interior angle sis equal to exterior angle therefore ∠ ECB = 120 degree
∠DCE = 120-56 = 64 degree
BC || DE
∠EDC = ∠DCB = 56 degree (alternate opposite angles)
Sum of all the interior angles of a triangle is equal to 180 degree
56 +64+∠DEC = 180
∠DEC = 60 degree.
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The pH can be calculated using the equation pH = –log(H+), where H+ is the hydronium ion concentration. Find the hydronium ion concentration of a particular soda if the pH level is 2.3.
Answer:
Step-by-step explanationp :
ph =lo 4
What 2 numbers add up to 37 and multiply to 210?
Answer: 30 and 7
Step-by-step explanation: 30 plus 7 is 37, 30 times 7 is 210
Which expression is equivalent to the given expression? 2√/20-4√6
A. 32/30
OB. 16√30
OC. 3/20
D. √120
Answer:
D.
because 2 times 120 reduced.
factorize of 2a³-a²+a-2
=========================================================
Explanation:
Use the rational root theorem to determine this list of possible rational roots: 1, -1, 1/2, -1/2
Plug each possible root one at a time into the original expression given. If the simplified result is 0, then that possible root is an actual root.
If we tried say a = -1, then,
2a³-a²+a-2 = 2(-1)³-(-1)²+(-1)-2 = -6
The result is not zero, so a = -1 is not an actual root.
But if we tried say a = 1, then,
2a³-a²+a-2 = 2(1)³-1²+1-2 = 0
We get 0 so a = 1 is an actual root. I'll let you try the other values, but you should find that a = 1 is the only rational root.
Since a = 1 is a root, this makes (a-1) to be a factor.
From here, use either synthetic or polynomial long division to determine the other factor. Refer to the diagram below for each method.
Regardless of which method you pick, the quotient is 2a² + a + 2 which is the other factor needed. The remainder of 0 tells us we have (a-1) as a factor. For more information, check out the remainder theorem.
Which of the following is the balance for a single $2.520 deposit in an account with an APR of 1.16% that compounds interest monthly and is invested for 37 years? Which of the following is the balance for a single $ 2.520 deposit in an account with an APR of 1.16 % that compounds interest monthly and is invested for 37 years ?
Answer:
The balance after 37 years is $3869.99
Step-by-step explanation:
Given:
Principal (P) = $2,520Rate of Interest (R) = 1.16%Time (t) = 37 yearsCompounds Interest Monthly (n) = 12The Amount (A),
A = P (1 + [tex]\frac{R}{100n}[/tex][tex])^{nt}[/tex] if compound n times per year
Amount (A) at 37 years,
A = ($2,520) (1 + [tex]\frac{1.16}{100(12)}[/tex][tex])^{12 x 37}[/tex]
A = ($2,520) (1 + [tex]\frac{1.16}{1,200}[/tex][tex])^{444}[/tex]
A = ($2,520) (1.00096667 [tex])^{444}[/tex]
A = ($2,520) (1.5357)
A = $3869.9944
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which equation has the solution x=6
Answer:
need more info
Step-by-step explanation:
what I can tell you is that when you change all the x's in the equation to 6s, both sides of the equation will equal eachother.
Select the solution(s) of the original equation.
0 x = √√√2
x = 1
X=1
x = -1
0 *=-√√2
X = -1
DONE ✔
0000
Answer:
the first,second,forth and fifth.
Step-by-step explanation:
I got it off of edg.
I WILL GIVE BRAINLIEST
PLEASE LOOK AT PICTURE
What are the foci of this ellipse?
ANSWER CHOICES: are in picture
The sum of a number and 3 is less than 10 if x denotes the number what would be the possible values of x
x>13
x<13
x>7
x<7
Answer:
x<7
Step-by-step explanation:
Consider the number x (as mentioned in the question). Now carefully pay attention to the given condition
⇒"The sum of a number and 3 is less than 10"
Remember the notation of the term "less than" in mathematical context is indicated by "<" sign. Hence our inequality is
⇒ x+3<10
adding or subtracting any number from the both sides of an inequality DOESN'T change its direction. Thus, if we cancel out 3 from both sides it won't swap the inequality. Therefore
⇒ x+3-3<10-3
⇒ [tex]x<7[/tex]
In terms of interval notation
[tex]\implies x\in( -\infty,7)[/tex]
In conclusion
The answer is D) [tex]x < 7[/tex]
Let the number be x
The sum of number and 3
x+3Is less than 10
x+3<10Lets solve it
x<10-3x<7Hence
Option D is correct
What percent of 48 listings is 36 listings
Answer:
75%
Step-by-step explanation:
48x=36
x=36/48
x=3/4
x=0.75=75%
Use the calculator to graph the function y = 2x2 25x + 3. What are the coordinates of the turning point of the graph to the nearest hundredth?
Vertex = (
,
)
The coordinates of the turning point of the graph of the quadratic equation is given by: (-6.25, -75.13).
What is the vertex of a quadratic equation?A quadratic equation is modeled by:
[tex]y = ax^2 + bx + c[/tex]
The vertex is given by:
[tex](x_v, y_v)[/tex]
In which:
[tex]x_v = -\frac{b}{2a}[/tex][tex]y_v = -\frac{b^2 - 4ac}{4a}[/tex]In this problem, the function is given by:
y = 2x² + 25x + 3.
Hence the coefficients are a = 2, b = 25, c = 3, then the coordinates of the vertex are given as follows:
[tex]x_v = -\frac{25}{2(2)} = -6.25[/tex][tex]y_v = -\frac{25^2 - 4(2)(3)}{4(2)} = -75.13[/tex]The coordinates of the turning point of the graph of the quadratic equation is given by: (-6.25, -75.13).
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Answer:
6.25, -75.13
Step-by-step explanation:
it just is
What’s the slope of this graph? Can y’all guys help please ! Thank y’all
Answer:
3
Step-by-step explanation:
we can think of the slope of a graph as [tex]\frac{rise}{run}[/tex]
the "rise" is the difference in y-values between two points (the change in y)
the "run" is the difference in x-values between two points (the change in x)
when we divide these (rise/run), we find the slope
you can choose any two well-defined points (with clear x and y values), here are the two we will be using:
(remember, points are written as (x, y) )
(0 , 2)
(-1 , -1)
for the "rise", we have risen 3 (difference between 2 and -1 = 3 [2- -1 = 3] )
for the "run" we have ran 1 (difference between 0 and -1 = 1) (0 - - 1 = 1)
so, the slope for this graph is: 3/1 ; which simplifies to 3
So, the slope of our graph is 3
--------------------------------------------------------------
technical layout:
[tex]m=\frac{y_{2} -y_{1}}{x_{2}-x_{1}}[/tex] (note: slope is called "m" in the format of y=mx + b)
[tex]y_{1}[/tex] means one y-value, [tex]y_{2}[/tex] means other y-value
[tex]x_{1}[/tex] means one y-value, [tex]x_{2}[/tex] means other x-value
{note: it is important to keep the y1 and x1 from the same point, and the y2 and x2 from a shared point}
our equation in this layout:
[tex]m=\frac{2 -(-1)}{0-(-1)}[/tex] = [tex]m=\frac{3}{1}[/tex]
m = 3
Two trains leave station 416 miles apart. One train is traveling 90 miles per hour while the other is traveling 70 miles per hour. How long will it take the two trains to meet
Answer:
2.6 hours
Step-by-step explanation:
Let t be the time that the trains meet.
[tex]90t = 416 - 70t[/tex]
[tex]160t = 416[/tex]
[tex]t = 2.6[/tex]
Can someone answer this
The order of the graphs from largest to lowest correlation coefficients is:
Graph D, Graph A, graph C, graph B.
Which graph has the largest correlation coefficient?The correlation coefficient between two variables is a coefficient that tells us "how much" these variables relate.
So, in the case for linear correlation, as "more linear" the data appears to be, a large correlation is between the two variables.
With that in mind, we conclude that the order of the graphs (going for larger correlation coefficient to smaller correlation coefficient) is:
Graph D, Graph A, graph C, graph B.
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the graph shows the value of a certain model of car compared with it's age. which statement is true?
A. The data show a negative linear relationship.
B. The correlation coefficient is close to 0.
C. The Car's age is the response variable.
D. The Car's age is not correlated to it value.
The only true statement is A:
"The data show a negative linear relationship."
Which statement is true?On the graph, we can see how the car's vale decreases almost linearly with the age of the car.
Where the response variable would be the one on the y-axis, which is the car's value.
For that linear behavior, we know that there is a correlation coefficient different than zero. So options B, C, and D are false.
Finally, we already saw the linear behavior (decreasing, so the slope is negative). Then we conclude that the only true statement is A.
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A linear function contains the following points: 0,-3 and 6,15.
WHat is the slope and y-intercept
The slope of the linear function is 3 and the y-intercept is -3 if the linear function contains the following points: (0,-3) and (6,15)
What is the slope?The ratio that y increase as x increases is the slope of a line. The slope of a line reflects how steep it is, but how much y increases as x increases. Anywhere on the line, the slope stays unchanged (the same).
[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}[/tex]
We have:
A linear function contains the following points: (0,-3) and (6,15)
The slope:
[tex]\rm m =\dfrac{15-(-3)}{6-0}[/tex]
m = 18/6
m = 3
The equation of a line:
y = mx + c
Plug x = 0, y = -3
-3 = c
Thus, the slope of the linear function is 3 and the y-intercept is -3 if the linear function contains the following points: (0,-3) and (6,15)
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Which equation describes the same line as y-5=-2(x+4)
. It costs C(x) = [tex]\sqrt{x}[/tex] dollars to produce x golf balls. What is the marginal production cost to make a golf ball? What is the marginal production cost when x = 25? when x= 100? (Include
units.)
The marginal cost when x = 25 and when x = 100 are $0.1 and $0.05 respectively.
What is a Marginal Production Cost?A marginal production cost is a derivative of a cost function. From the information given, the total cost is:
C(x) = [tex]\mathbf{\sqrt{x}}[/tex]The marginal production cost can be expressed as:
[tex]\mathbf{C'(x) = \dfrac{d}{dx}(\sqrt{x})}[/tex]
[tex]\mathbf{C'(x) = \dfrac{1}{2\sqrt{x}}}[/tex]
However, when the cost is 25, the marginal production is:
[tex]\mathbf{C'(25) = \dfrac{1}{2\sqrt{25} }}[/tex]
[tex]\mathbf{C'(25) = \dfrac{1}{2\times5}}[/tex]
[tex]\mathbf{C'(25) = \dfrac{1}{10}}[/tex]
C' (25) = $0.1
Also, when the cost is 100, the marginal production is:
[tex]\mathbf{C'(100) = \dfrac{1}{2\sqrt{100} }}[/tex]
[tex]\mathbf{C'(100) = \dfrac{1}{2\times10}}[/tex]
[tex]\mathbf{C'(100) = \dfrac{1}{20}}[/tex]
C' (100) = $0.05
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