The formula to determine the density of a liquid with cubes, a meterstick and stopwatch is density of the liquid = mass / volume = 2.7 g / (volume of liquid displaced by the cube)
Density is a measure of how much mass is contained in a given volume of a material. In order to determine the density of a liquid, you will need three things: cubes, a meterstick, and a stopwatch.
First, gather your materials and select a cube of known dimensions. Place the cube on the surface of the liquid and start the stopwatch. Observe how long it takes for the cube to sink to the bottom of the container. Let's call this time t.
Next, use the meterstick to measure the height of the liquid in the container
With these two pieces of information, you can calculate the density of the liquid using the formula:
=> density = mass / volume
The mass of the cube can be calculated as:
=> mass = volume * density of the cube
where the volume of the cube is given by
=> volume = s³, where s is the length of one side.
Since we know the length of one side (s = 1 cm), the volume of the cube is 1 cm³.
The density of the cube can be assumed to be a constant value (for example, if the cube is made of aluminum, the density is approximately 2.7 g/cm³).
So,
=> mass = volume * density of the cube = 1 cm³ * 2.7 g/cm³ = 2.7 g.
The volume of the liquid displaced by the cube can be calculated as:
volume = mass / density of the liquid = mass / (h/t²)
where h/t² is the acceleration due to gravity.
Finally,
density of the liquid = mass / volume = 2.7 g / (volume of liquid displaced by the cube)
Complete Question:
Determine the density of an unknown liquid with only a meterstick, stopwatch, and cubes that sink.
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“Exchange rate is the value of a country's _______ in terms of another _______ currency.”
The exchange rate is the value of a country's currency in terms of another country's currency.
What is the exchange rate?The exchange rate is the cost of a country's currency in respect to another currency. If the exchange rate between the U.S. dollar (USD) and the Japanese yen (JPY) is 120 yen for every dollar, then one dollar may be exchanged for 120 yen in the foreign exchange market.
From the above definition, it is clear that the complete definition of the exchange rate is given as the exchange rate is the value of a country's currency in terms of another country's currency.
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help me please !! i’ll give the brainliest answers
Answer:1.25/
Step-by-step explanation:
Marjorie's school is 2 miles away from her house. If she rides her bicycle to school, and it takes her 20 minutes to get to school, what is her average rate of speed in miles per hour? Select one: a. 10 mi/h b. 1 mi/h c. 60 mi/h d. 0.1 mi/h e. None of the above
The average speed can be calculated by dividing the distance traveled by the time it takes to travel that distance. In this case, Marjorie's average speed can be calculated by dividing the distance from her house to school (2 miles) by the time it takes her to get there (20 minutes).
To convert minutes to hours, we need to divide the minutes by 60. So, 20 minutes is equal to 20/60 = 0.33 hours.
Next, we divide the distance (2 miles) by the time in hours (0.33 hours) to find Marjorie's average speed:
2 miles / 0.33 hours = 6 miles/hour
Therefore, Marjorie's average speed is 6 miles per hour, making the correct answer (c) 60 mi/h.
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the average temperatures recorded over a five-day period last winter in salt lake city is: 12 , 18 , 19, 22 , 25 formulas: the standard deviation of these temperatures is . a) the median m is [ select ] b) the variance is [ select ]
The standard deviation of the given data is 4.35.
The standard deviation of data is the calculation of the dispersion/ spreading of the data value about its mean. It can be mathematically defined as the square root of the variance of the data.Here we have, X = 12, 18, 19, 22, 25 N=5The variance of data can be expressed as the expectation of as
σ²[tex]= E(X^{2} ) - (E(X))^{2}[/tex]
[tex]E(X) = \frac{12 +18+ 19 + 22 + 25}{5}[/tex] [tex]= \frac{96}{5} = 19.2[/tex] ⇒ [tex](E(X))^{2} = 368.64[/tex]
Now we have,
[tex]E(X)^{2} = \frac{12^{2} +18^{2} +19^{2} + 22^{2} +25^{2} }{5}[/tex] = 387.6
From the above values we get the variance,
σ² = 387.6 - 368.64 = 18.96
σ = 4.35
Hence, the standard deviation of the given data is 4.35.
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What is the purpose of converting a random variable to a z-value? Select all that apply.
O To compare a normal distribution to a standard normal distribution.
O To convert a normal distribution to a uniform distribution
O To standardize the random variable so that the sum of the probabilities is one.
O To express the distance from the mean in terms of the standard deviation.
The purpose of converting a random variable to a z-value is to Compare a normal distribution to a standard normal distribution and Express the distance from the mean in terms of the standard deviation.
The purpose of converting a random variable to a z-value is to:
Compare a normal distribution to a standard normal distribution: By converting a random variable to a z-value, it can be compared to the standard normal distribution, which has a mean of 0 and a standard deviation of 1. This allows for the calculation of probabilities and the interpretation of the results in a standard way.
Express the distance from the mean in terms of the standard deviation: The z-value expresses the distance of the random variable from the mean in terms of the standard deviation. This standardization makes it easier to compare values and to perform statistical analysis.
Converting a normal distribution to a z-value does not convert it to a uniform distribution or ensure that the sum of the probabilities is one. The sum of the probabilities in a normal distribution does not equal one, but rather approaches one as the values approach infinity.
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Greg works at a floral company making flower arrangements. The table below represents the relationship between the number of hours, h, Greg works and a, the number of arrangements he can create. Which equation represents the relationship in the table?
Answer:
a
Step-by-step explanation:
because as time increases by 1 hr, the number of arrangements increases simultaneously by 3. so I can conclude that a=3hrs
4. The maximum value of the expression ax² + 10x + c
OPEN is 7. Find a pair of possible values of a and c.
The maximum value of the expression ax² + 10x + c is 7, which means that the parabola represented by this equation opens upwards and its vertex is at the highest point.
The vertex of a parabola represented by the equation ax² + 10x + c is given by (-b/2a, f(-b/2a)), where b is the coefficient of x, a is the coefficient of x² and f(x) is the function.
Therefore the vertex of this parabola is (-10/2a, 7 - c)
Since the vertex is the highest point, the y-coordinate of the vertex is the maximum value of the expression.
7 - c = 7
therefore c = 0
We also know that the x-coordinate of the vertex is -10/2a, this means that the x-coordinate of the vertex is -5/a
There are many possible combinations of a and c that work for this question, some possible combinations are:
a=1, c=0
a=2, c=0
a=-2, c=0
Another way to find a and c is by expanding the equation:
ax² + 10x + c = a(x²+ 10/a x) + c = a(x²+ 10/a x + (100-100a)/(4a²)) + c = a(x+5/a)² + c -25/a + 7
So, when a=1, c=0 and a=2, c=0 will give you the maximum value of 7, where it's a parabola that opens upwards and it's vertex is at the highest point.
please help!!
each small square represents 1 square centimeter.
The solid formed by rotating the above rectangle around the horizontal axis shown is best described as a_________.
-cylinder with radius 6cm and height 3cm.
-cone with radius 3cm and height 6cm.
-rectangular prism with 3cm x 6cm base and height of 3cm.
-cylinder with radius 3cm and height 6cm.
The volume of this solid is_______.
108 cubic centimeters
54 cubic centimeters
18 cubic centimeters
Answer:
The solid formed by rotating the above rectangle around the horizontal axis shown is best described as a cylinder with radius 3cm and height 6cm. The volume of this solid is 108 cubic centimeters, which can be calculated as follows: V = πr2h, where r is the radius and h is the height. In this case, r = 3cm and h = 6cm, so the volume is π x (3 cm)2 x 6 cm = 108 cubic centimeters.
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Of the total number of books in a library, 50% are non fiction,. 30% are historical fiction, and the rest are science fiction. There are 102 science fiction books in the library. How many books in the library are historical fiction?
Total number of historical fiction books are 153.
What are algebraic expressions?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.Given is that of the total number of books in a library, 50% are non fiction, 30% are historical fiction, and the rest are science fiction. There are 102 science fiction books in the library.
Assume that the total number of books in the library are {x}. Then, we can write -
(50 + 30)% of {x} = {x} - 102
80% of {x} = {x} - 102
(80/100){x} = {x} - 102
8x/10 = x - 102
x - 4x/5 = 102
(5x - 4x)/5 = 102
x = 102 x 5
x = 510
Number of historical fiction books will be -
30% of 510
(30/100) x 510
3/10 x 510
3 x 51
153
Therefore, total number of historical fiction books are 153.
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as a project for a psychology course, a student correlated weight and intelligence scores for 250 students. the computed correlation coefficient was .00. what did the scatter plot look like?
The scatter plot for the correlation of weight and intelligence scores for 250 students would likely be very close to the origin, meaning that the majority of the points would be clustered around the point (0,0), with a very small range of points scattered further away.
This would indicate that there is no correlation between the two variables, which is reflected in the computed correlation coefficient of .00.
A scatter plot is a type of plot that displays data points on a two-dimensional graph. The data points are represented as dots or circles on the graph and show the relationship between two variables. The location of each data point is determined by the value of the two variables for that point. Scatter plots can be used to identify patterns in data, such as clusters, linear relationships, or nonlinear relationships. They can also be used to identify outliers or unusual data points.
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A book has a front and back and 400pages the front and back are 0.9mm thick to 1 decimal place and each page is 0.13mm thick to two decimal places calculate the minimum thickness of book
Answer:
To calculate the minimum thickness of the book, we need to add the thickness of the front and back covers to the thickness of all the pages.
Step 1: Calculate the thickness of the front and back covers:
2 * 0.9 mm = 1.8 mm
Step 2: Calculate the thickness of all the pages:
400 pages * 0.13 mm/page = 52.0 mm
Step 3: Add the thickness of the front and back covers to the thickness of all the pages:
1.8 mm + 52.0 mm = 53.8 mm
Answer:
The minimum thickness of the book is 53.8 mm.
How many solutions does this equation have? 5y + 4 = 10 + 5y
0, no solutions
that is the answer
becca repeatedly tosses a fair coin until she gets a heads, while daniel repeatedly rolls a fair six-sided die until he gets a 3 or higher. calculate the probability that the number of die rolls needed is greater than the number of coin tosses needed.
We need to roll a die at least 3 times and a coin should be tossed at least 2 times.
What is probability?Probability is the chance of occurrence of a certain event out of the total no. of events that can occur in a given context.
Given this, Becca repeatedly tosses a fair coin until she gets a head.
The probability of getting a head P(H) is = 1/2.
The probability of getting a number 3 or higher is,
P(3) + P(4) + P(5) + P(6).
= 1/6 + 1/6 + 1/6 + 1/6.
= 4/6.
= 2/3.
So, to get a number 3 or higher we need at least 3 rolls, and to get a head we need at least 2 tosses.
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What part of the equation "g(x) = (x − 3)^2" says it's shifting to the right?
The part of the quadratic equation that says it's shifting to the right is -3.
What is a quadratic equation?
Any equation that can be written in the standard form where x is an unknown value, a, b, and c are known quantities, and a ≠ 0 is a quadratic equation.
f(x) = ax² bx + c = 0
The given equation g(x) = (x − 3)² is the equation of a parabola.
The general equation of a parabola is given by y = a(x – h)²+ k.
The graph of y=x² is shifted to h units to the right and k units up to produce the graph of y=a(x-h)²+k.
The above equation is similar to the equation given in the question.
Comparing,
a = 1
h = 3
So the given quadratic equation states that a parabola of the form g(x) = x² is shifted to the right by 3 units to give the resulting equation
g(x) = (x − 3)²
Therefore the part of the quadratic equation that says it's shifting to the right is -3.
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Write and exponential function in the form y=ab^x that goes through points (0,15) and (2,240)
Answer:
One possible exponential function that goes through points (0, 15) and (2, 240) is y = 15 * (2^x)
Another possible exponential function that goes through the points (0,15) and (2,240) is y= 15*(5^x)
Step-by-step explanation:
Triangle def contains right angle e. if angle d measures 40° and its adjacent side measures 7.6 units, what is the measure of side ef? round your answer to the nearest hundredth. 4.89 units 5.34 units 6.38 units 9.06 units
The measure of side EF in triangle DEF is 5.34 units when angle D measures 40° and its adjacent side measures 7.6 units.
To get this answer, use the Pythagorean Theorem:
a2 + b2 = c2,
where a and b are the lengths of the sides adjacent to the right angle, and c is the length of the hypotenuse.
In this case, a = 7.6 and b = 5.34, so c = 8.93. Round this to the nearest hundredth and you get 5.34.
The Pythagorean Theorem states that in a right triangle, the sum of the squares of the two sides adjacent to the right angle is equal to the square of the hypotenuse.
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2. Find the distance between (-4, -8) and (-4, 0). Round to the nearest tenth if needed.
A.-2
B. 2
C.-8
D. 8
-8
it is -8 because it is 8 blocks away, but since it os - it will be -8 your welcome
Kevin orders 3 pairs of socks and his friend Jerry orders 5 pairs of socks.
What is the total cost, including shipping, for both orders?
Answer: 100
Step-by-step explanation:
(3*12)+2 = 38
(5*12)+2 = 62
38+62 = $100
Which scale factors result in a expansion? -3, 0.25,9/7,-3/4
The scale factors of 9/7 and 0.25 would result in an expansion.
What is scale factor?Scale factor is a numerical value used to represent the proportional change between two similar objects. This value is often used to compare the size of objects in different measurements, such as inches to millimeters or feet to meters. Furthermore, the scale factor can be used to find the area, volume, or surface area of an object, as the measurements are proportional to the scale factor. This is especially useful when objects are enlarged or reduced, as it allows for the accurate calculation of the changed measurements.
Expansion occurs when the scale factor is greater than zero. In this case, the scale factors of 9/7 and 0.25 would result in an expansion. The scale factors of -3 and -3/4 would result in a contraction.
When an object is scaled, the size of the object changes in one or more directions. If the scale factor is greater than one, the object will expand. Conversely, if the scale factor is less than one, the object will contract. The scale factor can either be multiplied by the length of the object or by the area of the object to determine the change in size. For example, if the scale factor is two, the length of the object would double and the area of the object would quadruple.
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aa 6 m high 4m wide rectangular gate holds back liquid at a depth of
The rectangle volume is = 36000[tex]l[/tex] , where height = 6m, width = 4m , depth = 3m
The volume, V , of any rectangular volume solid is the product of the length, width, and height. We could also write the formula for volume of a rectangular solid in terms of the area of the base. The area of the base, B , is equal to length × width.
Given that,
Rectangle height (h) = 6m
Rectangle width(w) = 4m
Rectangle depth(l) = 3m
Volume = [tex]l*w*h[/tex]
Volume = 6m * 4m * 3m
Volume = 72[tex]m^{3}[/tex]
In this example the depth will be 10 inches. Insert the measurements into the formula. Multiply the length (L) times the width (W) times the height (H). The formula looks like this: [tex]l*w*h[/tex] For this example, to calculate the volume of the object the formula would be 10 x 10 x 10 = 1,000 cubic inches.
Then the,
Volume = 72/2
Volume = 36[tex]m^{3}[/tex]
1[tex]m^{3}[/tex] = 1000[tex]l[/tex]
36[tex]m^{3}[/tex] = (36*1000)[tex]l[/tex]
= 36000[tex]l[/tex]
Therefore,
The rectangle volume is = 36000[tex]l[/tex] , where height = 6m, width = 4m , depth = 3m
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A rectangles's lenght is twice its width and the perimeter of the rectangle is [tex]24\sqrt{3} - 6\sqrt{2}[/tex] units. What is the area of the rectangle?
A. [tex]100-16\sqrt{6}[/tex]
B.[tex]400-64\sqrt{6}[/tex]
C. [tex]92-16\sqrt{6}[/tex]
D. [tex]368-64\sqrt{6}[/tex]
The area of the rectangle whose length is twice its width, having a perimeter of 24√3 - 6√2 is 100 - 16√6.
What is the area of the rectangle?The perimeter and area of a rectangle are expressed as;
Perimeter = 2( length + Width )
Area = Length × Width
Let the width be represented by 'x'.
Width = xLength = 2xPerimeter = 24√3 - 6√2Area = ?Plug the given values in the formula above and solve for x.
Perimeter = 2( length + Width )
24√3 - 6√2 = 2( 2x + x)
24√3 - 6√2 = 2( 3x )
24√3 - 6√2 = 6x
6x = 24√3 - 6√2
x = ( 24√3 - 6√2 ) / 6
x = 4√3 - √2
Hence;
Width = x = 4√3 - √2
Length = 2x = 2(4√3 - √2) = 8√3 - 2√2
Now, we determine the area;
Area = Length × Width
Area = (8√3 - 2√2) × (4√3 - √2)
Expand using FOIL Method
Area = 8√3(4√3) + 8√3(-√2) - 2√2(4√3) - 2√2(-√2)
Area = 100 - 16√6
Therefore, the area is 100 - 16√6.
Option A) 100 - 16√6 is the correct answer.
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Given f(x) = x/(x-6), and f(g(x)) = 2x, find g(x).
Please help.
The composite function g(x) is g(x) = 12x/(2x - 1)
How to determine the function g(x)From the question, we have the following parameters that can be used in our computation:
f(x) = x/(x - 6)
f(g(x)) = 2x
This means that
f(g(x)) = g(x)/(g(x) - 6)
So, we have
g(x)/(g(x) - 6) = 2x
Rewrite as
y/(y - 6) = 2x
This gives
y = 2x(y - 6)
Open brackets
y - 2xy = -12x
This gives
y = -12x/(1 - 2x)
So, we have
y = 12x/(2x - 1)
Hence, the function g(x) = 12x/(2x - 1)
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Here is a list of numbers: -45,-21,-16,12,33,40
C) work out the sum off all numbers in the list
Answer:
To find the sum of all the numbers in the list, we can add each number together:
-45 + -21 + -16 + 12 + 33 + 40 = 59
So the sum of all the numbers in the list is 59.
how many nonempty collections of letters can be formed from four as and eight bs? justify your answer in terms of the addition and multiplication rules.
The number of nonempty sets of letters that can be formed from four a's and eight b's is 4096.
A set is a collection of distinct objects, called elements or members, that have some property or characteristics in common. Sets are used in mathematics to model and study the properties of objects and the relations between objects.
In set theory, sets are defined as unordered collections of elements that are well-defined and have certain properties.
We have,
The number of letters.
4 a's and 8 b's
This means,
a, a, a, a, b, b, b, b, b, b, b, b
Now,
The number of non-empty sets we can form is given by the formula.
= [tex]2^{n}[/tex]
Where n is the number of letters.
For example,
S = {1, 2, 3}
The number of nonempty sets.
[tex]2^{3}\\ =8[/tex]
= { {1}, {2}, {3}, {1, 2}, {1, 3}, {2, 3}, {1, 2, 3}, Ф }
Similarly,
The number of nonempty sets from 4 a's and 8 b's.
= [tex]2^{12}[/tex]
= 4096
Therefore, The number of nonempty sets that can be formed from 4 a's and 8 b's is 4096.
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in how many ways can a teacher distribute eight chocolate donuts and seven jelly donuts among three student helpers if each helper wants at least one donut of each kind?
Since probability each student helper must receive at least one of each type of doughnut, there are 120 ways to divide the 8 chocolate donuts and 7 jelly donuts among the three students.
If each student helper desires at least one doughnut of each flavor, there are 120 ways to divide 8 chocolate donuts and 7 jelly donuts among the three students who are helping. This is so because there are exactly as many ways to distribute donuts as there are different methods to distribute each type of doughnut. For instance, there are eight ways to divide the eight chocolate donuts among the three helpers—eight options for the first assistant, seven for the second, and six for the third—and seven ways to divide the eight jelly donuts (7 choices for the first helper, 6 for the second, and 5 for the third). The sum of these two figures (8 x 7 = 56) results in the number of combinations (56). (56). The total number of options must be multiplied by 2 to accommodate for the requirement that each helper receive at least one donut of each flavor: 56 x 2 = 120. If each student helper desires at least one doughnut of each flavor, there are 120 ways to divide 8 chocolate donuts and 7 jelly donuts among the three student volunteers.
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A company operates two plants which manufacture the same item and whose total cost functions are
C_1 = 9 + 0.02q1^2 and C_2 = 4.2 + 0.04q2^2,
where q_1 and q_2 are the quantities produced by each plant. The total quantity demanded, q = q1 + q2 , is related to the price, p , by
p = 50 - 0.04 q.
How much should each plant produce in order to maximize the company's profit?
q1=?
q2=?
The total quantity demanded, q = q1 + q2, should be set such that the total cost is minimized and the price is maximized. The optimal solution is q1 = 20 and q2 = 30, so that the total cost is minimized and the price is maximized.
To maximize the company's profit, we must find the optimal quantity of q1 and q2 that minimizes the total cost and maximizes the price. We start by finding the total quantity demanded, q: q = q1 + q2. We can then use this equation to relate the price, p, and the total quantity, q, by substituting the equation for q into the equation for price: p = 50 - 0.04q. Next, we use the cost functions for each plant to find the total cost: C = C1 + C2. We can then use calculus to find the minimum total cost by taking the partial derivatives of C with respect to q1 and q2 and setting them equal to zero.Finally, we can use the equations for price and total cost together to find the optimal values for q1 and q2 that maximize the company's profit. The optimal solution is q1 = 20 and q2 = 30, so that the total cost is minimized and the price is maximized.
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explain why the function defined by M(t) = 2t + 1 has no maximum value on the interval [0,4)
The function defined by M(t) = 2t + 1 has no maximum value on the interval [0,4) as the derivative of m(t) is not equal to zero.
The maxima of the function can be calculated by the derivative of the function. The derivative is equated to 0 to calculate the critical points. If the second derivative is negative at this critical point then a maximum exists at this point.
The function is M(t) = 2t + 1 . Differentiate the function with respect to t. Now equate the derivative to 0. This will give the critical point. Since 2 is not equal to 0, the critical point does not exist on the curve of the function. Therefore, the function M(t) = 2t + 1does not have a maxima. M(t) = 2t + 1
d/dt M(t) = d/dt 2t + 1
= 2
d/dt m'(t) = 0
2 not equal to 0
The function does not have a critical point. Therefore, the maxima do not exist for the function.
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a survey of 800 volunteers yielded the following information: 539 were tour guides, 430 were retirees, and 310 of the tour guides were retirees. how many of the 800 surveyed volunteers were tour guides or were retirees?
869 of the 800 surveyed volunteers were either tour guides or retirees. 539 were tour guides, and 430 were retirees, with 310 of the tour guides also being retirees.
Surveys are a type of data collection method in which individuals or organizations are asked to provide information about a particular topic or issue. Surveys can be used to collect information about people's opinions, behaviors, and preferences.
They can also be used to gather data on a particular population or group, such as demographics, employment, health, or other topics. Surveys are often used in research studies and can help to provide valuable insights into a variety of topics.
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{x is greater than or equal to 3, y is less than or equal to 2. Graph the solution of the system of linear inequalities. (and fill in)
The solution to the system of linear inequalities x ≥ 3 and y≤ 2.
What is a solution set to an inequality or an equation?If the equation or inequality contains variable terms, then there might be some values of those variables for which that equation or inequality might be true. Such values are called solution to that equation or inequality. Set of such values is called solution set to the considered equation or inequality.
This is represented on a coordinate plane, is a region that satisfies both inequalities. It is the half-plane formed by the line x= 2 and above the line y= 3 .
x ≥ 3
y ≤ 2.
It can be represented on a coordinate plane as a region that satisfies both inequalities.
To graph the solution, we first plot the line x = 2 on the coordinate plane. Since x <= 2, this line represents the boundary of the solution. Everything to the left of the line x = 2 is included in the solution.
Next, we plot the line y = 3. Since y less than 3, everything above the line y = 3 is included in the solution.
The solution set is x ≥ 3 and y≤ 2
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Hua 13. A car travelling at an average speed of 100 km/h covers a certain distance in 3 hours 20 minutes. At what constant speed must the car travel to cover the same distance in 2 hours and 40 minutes? (2)
Salut/Hello!
Answer: 133 km/h
Step-by-step explanation:
We need to first find out the distance travelled in 3 hours and 20 minutes.
We can say that 3 and 20 minutes is 3.20 by knowing that 100 km/h results that the distance travelled is 320 km
The same distance in 2 hours and 40 minutes:
We can say 2 hours and 40 minutes is 2,40 and we know our distance is 320 km results that the speed will be approximately 133 km/h
I hope it was useful! :]
