Exercice 1 On remplit le réservoir d’eau. Voici la
quantité d’eau notée en fonction du temps écoulé :
Durée (min) 5 15 20 30
Volume (L) 36 108 142 210
1. a. Représenter graphiquement les données de ce tableau en mettant :
• en abscisses les durées : 1 cm pour 5 min.
• en ordonnées les quantités d’eau : 1 cm pour 24 L.
Answer:
55 L
Step-by-step explanation:
how many real fourth roots does -1 have?
There are zero or null real fourth roots of -1.
What are real fourth roots?This means that the square root of the square root of a number is equal to the number's fourth root. Symbolically, the fourth root is also represented by multiplying the radical by 4, creating the number 4. The fourth root of 16, for instance, is 2, which means that 2 2 2 2 = 16. n, also known as the degree of the root, is a positive integer in this situation. The terms "square root" and "cube root" are used to describe roots of degree 2 and 3, respectively. The ordinal numbers fourth root, twentieth root, etc. are used to refer to roots of higher degree. It is a root extraction to calculate the nth root. A integer y such that y2 = x is referred to as the square root of an x in mathematics.
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algebra 2 help needed!
As per the given equation of the parabola, the directrix of the parabola is equal to y = -2.5.
What is directrix?
A directrix in mathematics is a curve which is associated with the process generating a geometric object, such as:
Directrix - conic section
Directrix - generatrix
Directrix - rational normal scroll
The equation of a quadratic function, with vertex (h,k), is:
y = (a)(x - h)² + k
In which, a is the leading coefficient.
The directrix is: y = k + 4a.
In this problem, the equation of parabola is given as:
y = (1/8)(x-2)² - 3
The coefficients in the given equation are a = 1/8 = 0.125,
h = 2, k = -3,
Hence the directrix is given by:
y = -3 + 4 x 0.125
y = -3 + 0.5
y = -2.5.
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Write the coordinates of the verticals after a rotation 90 degrees counterclockwise around the origin
After a counterclockwise 90° rotation, the coordinates of A'B'C' are:
A' = (3, 3)B' = (6, 5)C' = (3, 6)What are Coordinates?A coordinate system in geometry is a method for determining the precise location of points or other geometrical objects on a manifold, such as Euclidean space, using one or more numbers, or coordinates.The origin is the point at which all lines in a coordinate system intersect. When x and y are both equal to zero, the axes intersect. The origin's coordinates are (0, 0). The coordinates of one point in the coordinate system are included in an ordered pair.So, the coordinates after the counterclockwise rotation of 90°:
The coordinates of ABC are:A = (3, -3)B = (6, -3)C = (5, -6)After counterclockwise 90° rotation, coordinates of A'B'C' are:
A' = (3, 3)B' = (6, 5)C' = (3, 6)(Refer to the graph attached below)
Therefore, after a counterclockwise 90° rotation, the coordinates of A'B'C' are:
A' = (3, 3)B' = (6, 5)C' = (3, 6)Know more about Coordinates here:
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Absolutely value equations |m-2|-1=4
The value of 'm' in the absolute value equation is 3
What is a linear equation?A linear equation can be described as an equation having the highest power of the variable as 1.
It is also referred to as a one-degree equation.
Example;
x + 1 = 4
What is absolute value?Absolute value of a number can be defined as the value of that number irrespective of its direction to zero on the number line.
The value must take a positive sign.
The symbol used to represent the absolute value of a number is '| '
We have the equation;
|m-2|-1=4
Let's take the absolute value
m + 2 - 1 = 4
Now, collect like terms, we get;
m = 4 - 1
Add or subtract like terms
m = 3
Hence, the value is 3
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1. what would the effect have been on the calculated formula weight ([9] above) of your unknown as compared to the true formula weight if the solution had been blue green when you filtered your product? too high, too low, or unchanged? explain.
If the solution is blue-green, this indicates that some copper is still present in the solution and that not all of it has precipitated. Expect it to be too low because you will have less mass.
With very few exceptions, all copper(I) (cuprous) compounds are diamagnetic and colorless. Cu2O, Cu2Cl2, and cuprous sulfide are a few of the significant commercial compounds of copper(I) (Cu2S).
The molar mass of the element copper is determined by looking at its average atomic mass, which is 63.55 AMU on the periodic table. Since it is also our molar mass, we will now put it in a different unit: grams over moles (63.55 gmol). That is copper's molar mass.
If the solution is blue-green, there is still copper in the solution and not all of it has precipitated. Because you will have less bulk, anticipate it to be too low.
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Help please!!!!!!!!!!!!!!
Find the product of 3 1/4 and 1/2
The product of the improper fraction 3 1/4 and 1/2 is 1 5/8.
What is mixed fraction?
A fraction that has the numerator higher than or equal to the denominator is said to be inappropriate. a fraction when the denominator (bottom number) and the numerator (top number) are both more than or equal (the bottom number). When the numerator is equal to or more than the denominator, the fraction is said to be improper fraction. It always has a value of one or higher.
Here the given fraction 3 1/4 convert into 13/4.
Now the product of the fractions is
=> 13/4 × 1/2
=> 13/8
=> 1 5/8.
Therefore product of the given fraction is 1 5/8.
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24m/s into mph. If your answer is a decimal, give it to 1 d.p
24 meters per second = 53.6865 miles per hour
53.6865 to 1 d.p = 53.7
Answer: 53.7
. A cash register contains nickels and dimes. There are 12 nickels in the
cash register. The total amount of money in the cash register is $2.30.
How many dimes are in the cash register?
Answer: 17 Dimes.
Step-by-step explanation:
Expand using Pascal's triangle: (x + 1)4.
Answer:
[tex] {x}^{4} + 4 {x}^{3} + 6 {x}^{2} + 4x + 1[/tex]
Step-by-step explanation:
as shown in photo attached :")
elect the correct answer. A game involves rolling a fair six-sided die. If the number facing upward on the die is a whole number multiple of three, the player wins an amount equal to the number on the die times $20. If the number is not a multiple of three, the player gets nothing. What is the expected value of a player's winnings on each roll?
The expected value of a player's winnings on each roll is: $30.
How can we calculate the expected value of a player's winnings on each roll?We can calculate the expected value of a player's value on each winning by first understanding that there are only two multiples of three on the six-sided die. These multiples are 3 and 6.
So, if 3 is obtained facing upward, the player wins 3 × 20 = $60
Also, if the player obtained 6 facing upward, the player wins 6 × 20 = $120
So, the total amount is $180.
However, the question expects us to calculate the expected value of a player's winnings on each roll. Thus, we will have $180 ÷ 6 = $30.
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Find the slope of the line that contains the points:
(-6, 3) and (-4, 5).
1
-1
-5
-1/5
Carlos is a receptionist at a law firm. he spends 2 minutes routing each phone call as it comes in. write an equation that shows how the total number of minutes carlos spends routing calls, y, depends on the number of calls, x.
The equation to show the total no. of minutes Carlos spends routing calls is y = 2x
To find the required equation, use the following given data:
Time taken by Carols for routing each call = 2 minutes
Total number of calls = x
Total number of minutes Carol spends routing calls = y
The one-dimensional function takes up a single input value (x) and outputs a single evaluation of the given input (y).
So, by practical application of one-dimensional function,
Total number of minutes Carols spends routing calls (y) = Time taken by Carols for routing each call * Total number of calls (x)
∴ The equation will be y = 2*x
Thus, y = 2x shows the total number of minutes Carlos spends routing the calls.
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need help please I cant find the answer
Answer:
6
1/3
Step-by-step explanation:
Similar triangles
The corresponding side on triangle A is 18 units
18 * 1/3 = 6
The side length of the missing side on B is 6 units
Side B 5
------ = ----------- = 1/3
Side A 15
The ratio is 1/3
Answers:
question one: 6
question two: 1/3
==========================================
Explanation:
The side 12 from triangle A corresponds to the side 4 from triangle B.
The scale factor is A/B = 4/12 = 1/3 which tells us that sides in triangle B are 1/3 as long compared to sides in triangle A. This takes care of the second question.
We'll use this scale factor to determine the missing side of triangle B.
The side 18 in triangle A corresponds to this missing side in triangle B.
Take 1/3 of 18 to get (1/3)*18 = 6 which is that missing side.
--------------
Another way to look at it: Take any side of triangle B, triple it, and you'll get a corresponding side of triangle A.
Example: The jump from 5 to 15 is "times 3".
math problem - help i need the answer for this, im very desperate for an answer.
Answer:
(x+10,y+8)
Step-by-step explanation:
If you look at the point (0,2) and it image (10,10) To go from 0 to 10 you must move 10 spaces to the right. That would be x + 10.
If you look at the same two points. You would have to move up 8 spaces to go from 2 to 10. That would be y + 8.
The same thing is true with the second two points given.
1. The following data represents the amount of time Algebra II students at NVLA prepare for their math exams. Study Time (min) 7 14 17 23 27 33 38 43
Test Score 61 54 63 65 70 69 75 77 I Find the quadratic regression model of the data. Then, predict the test score of a student who studies for 60 minutes. Show your work.
The quadratic regression model of the data is 0.007x² + 0.168x + 56.63 and the the test score of a student who studies for 60 minutes is 94.114
Quadratic regression model:
Quadratic regression refers the process of determining the equation of a parabola that best fits a set of data.
The set of data is a given set of graph points that make up the shape of a parabola.
The general equation of the parabola is y = ax² + bx + c, where a can never equal zero.
Given,
Here we have the following data represents the amount of time Algebra II students at NVLA prepare for their math exams.
Now, we need to find the the quadratic regression model of the data and then, predict the test score of a student who studies for 60 minutes. Show your work.
When we plot these value of the graphing calculator, then we get the following graph.
Through the graph we have identified that the value of
a = 0.007
b = 0.168
c = 56.63.
Therefore, the quadratic regression model of the data is 0.007x² + 0.168x + 56.63
And through the graph we have identified that test score of a student who studies for 60 minutes is approximately 94.114.
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in how many ways can a math team of 6 students be chosen from a math club which consists of 6 seniors and 14 juniors if the team must consist of 2 seniors and 4 juniors? a) 24,024 b) 225 c) 1,002,001 d) 84 e) 15,015 f) none of the above.
There are 84 ways.
What is probability?The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true.An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.The likelihood that an event will occur increases with its probability.A straightforward illustration is tossing a fair (impartial) coin.The chance of both outcomes ("heads" and "tails") is equal because the coin is fair, "heads" is more likely than "tails," there are no other conceivable outcomes, and the likelihood of either outcome is half.
acc to our question-
Number of commities: If now any sinyour then N1 = C6,4 = 15. If one sinyour then number of commities is =N2 = C4,1C6,3 = 4·20 = 80.hence,There are 84 ways.
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estimate a 15% tip on a dinner bill of $61.53 by first rounding the bill amount to the nearest $10
well, 61.53 is really 10 + 10 + 10 + 10 + 10 + 10 + 1.53.
well, 1.53 doesn't really come nowhere near close to round up to 10, so it boils down to 0, so 61.53 will just be 10 + 10 + 10 + 10 + 10 + 10 + 0 or just 60 once rounded up, now, what's 15% of 60?
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{15\% of 60}}{\left( \cfrac{15}{100} \right)60}\implies 9[/tex]
well, we can get the 15% of 61.53 by just (15/100) * 61.53
however, the exercise is asking on rounding it up to "tens" first
61.53 has "10" six times plus 1.53, the rounding happens with the "surplus"
in this case the surplus is 1.53.
now, for rounding anything the tipover point is at the half, for $10 the half is $5, so if the amount is $5 or more, rounds up to $10, if less than that goes to 0.
1.53 is nowhere near 5, which is the halfpoint or tipover point, because of that, it rounds up to 0, so 61.53 rounded up to "tens" only will be "six tens" only, or 60.
Find the slope of the line passing through the following points: (-12, -56), (-57,39).
[tex](\stackrel{x_1}{-12}~,~\stackrel{y_1}{-56})\qquad (\stackrel{x_2}{-57}~,~\stackrel{y_2}{39}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{39}-\stackrel{y1}{(-56)}}}{\underset{run} {\underset{x_2}{-57}-\underset{x_1}{(-12)}}} \implies \cfrac{39 +56}{-57 +12} \implies \cfrac{ 95 }{ -45 } \implies {\Large \begin{array}{llll} - \cfrac{19 }{ 9 } \end{array}}[/tex]
Answer:
- 19/9
Step-by-step explanation:
The slope formula is y1 - y2 divided by x 1 - x2. What u do is u take the y coordinates from both points, and subtracted them. And you do he same for the x coordinates. Then you divide the y coordinates by the x coordinates. IN this case, this is how we would solve it.
-56 - 39 / -12 - (-57) = -95 / 45 = - 19/9
There are approximately 420 national parks in the United States. A survey
showed that 85% of the national parks allow overnight camping. Based on
this information, how many national parks allow overnight camping?
Answer:
357 national parks
Step-by-step explanation:
420x85/100
420x17/20
21x17=
357
Please help, I am timed and I have no clue what to do here!
Answer:
Step-by-step explanation:
Re-order terms so constants are on the left
Then divide both sides by the same factor its -2
then Simplify answer is 1
A line segment is shown on the coordinate grid.
What is the domain displayed on the line graph above?
Answer: x = -2 through 1
Step-by-step explanation:
The domain are the x values that exist on the line. The line goes between -2 and 1. Therefore, that's the domain!
Anna received a gift of $5,000 from her grandmother and decided to invest it. The expression 5000(1.0005)^12t represents the amount of money Anna is earning on her investment. Select all of the following that are equivalent expressions so that Anna can better understand how her money is invested.
a) 5000(1.0005^12)^t
b) 5025^12t
c) 5000(1+0.0005)^12t
d) 5000(1.0005^t)^12
e) (5000+2.5)^12t
f) 5000(1+0.06/12)^12t
The equivalent expression that represents the amount Anna can better understand how her money is invested is 5000(1+0.0005)^12t.
The correct answer option is option c.
What is the equivalent expression of Anna's investment?Based on the expression given, Anna's investment is compounded monthly.
The formula for calculating future value:
FV = P (1 + r)^(nm)
Where,
FV = Future valueP = Present valueR = interest ratem = number of compoundingn = number of years5000(1.0005)^12t
Given options:
a) 5000(1.0005^12)^t
False
b) 5025^12t
False
c) 5000(1+0.0005)^12t
= 5,000(1.0005)^12t
True
d) 5000(1.0005^t)^12
False
e) (5000+2.5)^12t
False
f) 5000(1+0.06/12)^12t
= 5000(1 + 0.005)^12t
= 5000(1.005)^12t
False
In conclusion, the expression equivalent to Anna's investment is 5000(1+0.0005)^12t
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suppose a population has a mean of 7 for some characteristic of interest and a standard deviation of 9.6. a sample is drawn from this population of size 64. expressing your answer to one decimal place, what is the standard error of the mean?
The standard error with "mean of 7 for some characteristic of interest and a standard deviation of 9.6 and a sample is drawn from this population of size 64" is 1.2.
What is standard error?Standard deviation of the theoretical distribution of a large population of such estimates is equal to the standard error, which is a measure of an estimate's statistical accuracy. The population mean's likelihood to differ from a sample mean is indicated by the standard error of the mean, or simply standard error. It reveals how much the sample mean would change if a study were to be repeated with fresh samples drawn from a single population.
Here,
Sample size=64
Standard deviation= 9.6
Error=Standard deviation/Sample size
=σ/√n
=9.6/√64
=9.6/8
=1.2
The sample is taken from this population of 64 people, with a mean of 7 for some relevant characteristics, a standard deviation of 9.6, and a standard error of 1.2.
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The number of computer security breaches is expected to increase at a yearly rate of 86%. Use the exponential growth model to determine the equivalent monthly rate. Enter the rate, to the nearest tenth of a percent, in the box. ___ %
The equivalent monthly growth rate is 7.2 %
How to find the equivalent monthly growth rate?Since the number of computer security breaches is expected to increase at a yearly rate of 86%. Using the exponential growth model we need to determine the equivalent monthly rate
.
What is exponential growth model?The exponential growth model is given by y = A(1 + r)ⁿ where
A = initial value,r = growth rate and n = timeWhat is growth rate?This is the rate at which the function increases.
Since the number of computer security breaches is expected to increase at a yearly rate of 86% we have that the growth rate, r = 86% per year.
To find the monthly growth rate, we covert this to per month by dividing by 12.
So, the monthly growth rate r' = r/12
= 86%/12
= 7.16 %
≅ 7.2 %
So, the monthly growth rate is 7.2 %
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Answer:
5.3%
Step-by-step explanation:
I took the test.
how many groups of participants would be needed to partially (e.g., using latin square arrangement) counterbalance a within-subjects experiment with three treatment conditions?
24 groups of participants would be needed to partially counterbalance a within-subjects experiment with three treatment conditions.
Given that;
How many groups of participants would be needed to partially counterbalance a within-subjects experiment with three treatment conditions.
Every participant in an experiment is exposed to every treatment or condition in a within-subject design, sometimes referred to as a repeated measures design.
The term "between-subjects design" is comparable to this within-subjects design. People are solely assigned to one treatment in a between-subjects design. As a result, one therapy would be given to one group of volunteers, while a different treatment would be given to another group. After that, the variations between the two groups would be contrasted.
24 groups would be required for a perfectly counterbalanced design for even four treatment conditions. This would obviously be impracticable because a large enough sample size would be required to conduct such an experiment.
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hello can someone help me pls
The size of the angle x = 54 degrees
The regular pentagon is given
Number of sides of the pentagon = 5
O is the center of the pentagon
The sum of all the angle around a point is 360 degrees
From the figure we can see that the it equally divided by 5 parts
The measure of each angle = 360/5
= 72 degrees
Consider the corresponding triangle
Sum of all the interior angles of the triangle is 180 degrees and the two sides of the triangle is equal, therefore it is an isosceles triangle
Then,
x + x+ 72 = 180
2x + 72 = 180
2x = 180- 72
2x = 108
x = 108/2
x = 54 degrees
Hence, the size of the angle x = 54 degrees
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Aurora is planning to participate in an event at her school's field day that requires her to complete tasks at various stations in the fastest time possible. To prepare for the event, she is practicing and keeping track of her time to complete each station.
The x-coordinate is the station number, and the y-coordinate is the time in minutes since the start of the race that she completed the task.
(1, 2), (2, 4), (3, 8), (4, 16)
Part A: Is this data modeling a linear function or an exponential function . (2 points)
Part B: Write a function to represent the data. Show your work. (4 points)
Part C : Determine the average rate of change between day 2 and day 4. Show your work (4 points )
Step-by-step explanation:
A
it is an exponential function.
for a linear function the charge rate would have to be constant between any pair of data points.
the change rate is
( f ( interval end ) - f ( interval begin ) ) /
( interval end - interval begin )
between (1, 2) and (2, 4) we have a charge rate of
(4 - 2) / (2 - 1) = 2
between e.g. (3, 8) and (4, 16) we have a charge rate of
(16 - 8) / (4 - 3) = 8
the change rate is therefore not constant, and it is not a linear function.
B
we see
x1 = 1, y1 = 2
x2 = x1 + 1, y2 = y1×2
x3 = x2 + 1, y3 = y2×2
we get the impression that
xn = xn-1 + 1 = x1 + (n - 1)
yn = yn-1 × 2 = y1 × 2^n
so, while going linearly along the x-axis, y increases by the powers of 2.
the function is then
f(x) = 2^x
C
the change rate between station 2 and 4 (NOT day 2 and 4) is
(16 - 4) / (4 - 2) = 12/2 = 6
if three sides of a trapezoid are 10 inches long, how long should the fourth side be if the area is a maximum?
The area of the trapezoid is maximum when the fourth side be 20 inches.
What is meant by trapezium?Trapezoids are quadrilaterals with two parallel and two oblique sides. It is also known as a trapezium. A trapezoid is a four-sided closed shape or figure with a perimeter that covers some area.
By applying Pythagorean theorem,
[tex]c^2=a^2+b^2[/tex]
[tex]10^2=h^2+x^2[/tex]
[tex]100=h^2+x^2[/tex]
[tex]h^2=100-x^2[/tex]
[tex]h=\sqrt{100-x^2}[/tex]
Area of the trapezoid is,
[tex]A=\frac12 \times h\times (b_1+b_2)[/tex]
By substituting the values of h, b1, and b2 in the above equation,
[tex]A=\frac12 \times \sqrt{100-x^2} \times (10+2\times x+10)[/tex]
[tex]A=\sqrt{100-x^2} \times (x+10)[/tex]
If we take the derivative of both sides of the equation in relation to x, we get
[tex]\frac{dA}{dx}=\frac{d}{dx}[\sqrt{100-x^2} \times (x+10)][/tex]
[tex]\frac{dA}{dx}=\sqrt{100-x^2} \ \frac{d}{dx} (x+10) + (x+10) \ \frac{d}{dx} \sqrt{100-x^2}[/tex]
[tex]\frac{dA}{dx}=\sqrt{100-x^2} - \frac{x^2+10 x}{\sqrt{100-x^2}}[/tex]
[tex]\frac {dA}{dx}=0[/tex]
[tex]0=\sqrt{100-x^2} - \frac{x^2+10 x}{\sqrt{100-x^2}}[/tex]
[tex]\sqrt{100-x^2} = \frac{x^2+10 x}{\sqrt{100-x^2}}[/tex]
100-x²=x²+10x
2x²+10x-100=0
x²+5x-50=0
(x-5)(x+10)=0
If, x+10=0
x=-10
The above value is not accepted because it is a negative value,
If, x-5=0
x= 5
The value is accepted because it is positive value
The length of the trapezium which should be fourth is,
b₂=2x+10
b₂= 2(5)+10
b₂=20
The area of the trapezoid is maximum when the fourth side be 20 inches
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