The relation accepts reflexive, symmetry, and transitive.
Recall that a relation R is reflexive if the element (x, x) belongs to R for all elements X in the domain of R.
If (x, y) belongs to R, then follows that (y, x) must likewise belong to R, making the situation symmetric.
And it is transitive if (x, y) and (y, z) belongs to R necessarily implies that (x, z) belongs to R.
Given r is a relation on the set of all nonnegative integers R(a,b)
Reflexive - YES. A given number a will always have the same remainder when divided by 5.
Symmetric - YES. If a and b have the same remainder when divided by 5, then b and a are the same pair, so again they will have the same remainder.
Transitive - YES. If a and b as well as b and c have the same remainder when divided by 5, this is possible if both a and c also have the same remainder when divided by 5.
Therefore the relation accepts reflexive, symmetry, and transitive.
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what are the number of possible outcomes on a 5 question test with each question having 4 possible answers
There would be 1024 possible outcomes on a 5 question test with each question having 4 possible answers.
Based on the given information, there are 4 possible ways for each of the 5 questions.
4 possible ways to answer Question # 1
4 possible ways to answer Question # 2
4 possible ways to answer Question # 3
4 possible ways to answer Question # 4
4 possible ways to answer Question # 5
Fundamental Principle of Counting, also called the counting rule, is the method to count how many ways multiple independent events can occur.
Thus, by Fundamental Principle of Counting, the number of possible outcomes is
4 x 4 x 4 x 4 x 4 = 1024
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. a trough has ends shaped like isosceles triangles, with width 3 m and height 4 m, and the trough is 10 m long. water is being pumped into the trough at a rate of 5m3/min. at what rate does the height of the water change when the water is 1 m deep?
The rate at which the height of the water changes when the water is 1m deep is; dh/dt = 1.5m/min
We are given;
width; w = 3m
Height; h = 4m
Length of trough; L = 10m
According to similar triangle property; w =3/4h
volume of water; V = 1/2×w×h×L = 1/2 × 3/4h × h × 10 = 15/4 h²
Differentiate using chain rule for both sides with respect to t gives;
dV/dt = (1/2)(15/2)h(dh/dt).
Now, we are given dV/dt = 5m³/min and we want to find the rate at which the height of water changes when the water is 1 m deep.
Thus;
5 = ×dh/dt
At h = 1m; 5 = 15(1)/2 × dh/dt
⇒ dh/dt = 2/3
dh/dt = 1.5 m / min
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Three friends go grocery shopping together and buy apples. Logan buys 4
pays $7.00. Lin buys 6 lb and pays $10.50. Chita buys 2 lb
pounds (lb) and
and pays
$3.50.
Identify the graph and unit price that represent the cost of the apples.
The relationship between the data, the line and the unit price of apples of $1.50 per pound is best represented by option C Graph.
What is the slope of a line?
The slope of a line is the tangent of the angle that the line makes with the positive direction of the x-axis. It signifies the rise in the y-variable for a unit change in the x-variable.
If the line passes through the points (x, y) and (x, y), then the slope of the line, m = (y - y)/(x - x).
(2, 3) representing the purchase by Logan,
(5, 7.5) representing the purchase by Lin,
(3, 4.5) representing the purchase by Chita.
The unit price can be calculated by the slope of the line;
m = (7.5 - 4.5)/(5 - 3) = 3/2 = 1.5.
Hence, The relationship between the data, the line and the unit price of apples of $1.50 per pound is best represented by option C Graph.
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4. Round the number 39,944 to the nearest hundred.
Answer:
39.94
Step-by-step explanation:
Ask? :)
Answer:40,000 porque dice que redondees a la centecima mas cercana
connie has a number of gold bars, all of different weights. she gives the 2424 lightest bars, which weigh 45\e% of the total weight, to brennan. she gives the 1313 heaviest bars, which weigh 26\&% of the total weight, to maya. she gives the rest of the bars to blair. how many bars did blair receive?
Blair received 15 bars as the average weight of the bars given to Brennan (light), Blair, and Maya, as well as the average weight of the bars given to the other recipients.
What is average weight?The weighted average is calculated by adding up all the variables, multiplying by their weight, and dividing by the sum of the weights. Instead of treating each item equally, a weighted average or mean multiplies each item being averaged by a number based on its relative importance. The weights or weightings correspond to including that many comparable items of the same value in the average.
Here,
The average weight of the bars given to Brennan (light), Blair, and Maya was higher than the average weight of the bars given to the other two recipients (heavy).
Let X represent the combined weight of all the bars.
The weight of the bars Brennan was given was equal to 45% of X, or 0.45X.
Maya was given bars that weighed 26% of X, or 0.26X.
The weight of the bars Claire was given was the rest, or 29% of X, or 0.29X.
Brennan received bars with an average weight of 0.45 x/ 24.
The weight of the Maya-received bars, on average, is 0.26X/13.
Similar to the previous example, if Blair receives B bars, then their average weight is 0.29X/B.
Similarly, the average weight of the bars given to Brennan (light), Blair, and Maya, as well as the average weight of the bars given to the other recipients. So blair received 15 bars.
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Explain why (5 + 4) (5 + 4) could be used to determine the total number of computers.
Answer:
The numbers that we use are expressed in base 10. Every 10 1s equals 1 ten For example, if you are adding 5 + 4, you get: 0101 + 0100.
A classroom has twenty-five students that are all 14-years old. If you list their ages and their heights as ordered pairs (age, height), which statement is true?
It is not a relation, but it is a function.
It is a relation but not a function.
It is neither a relation nor a function.
It is both a relation and a function.
When one lists their ages and their heights as ordered pairs (age, height), the statement that is true is D. It is both a relation and a function.
In mathematics, what is a relation?A relation between two sets is a collection of ordered pairs that each contain one object from the other set. If the ordered pair (x,y) is in the relation and the object x is from the first set and the object y is from the second set, the objects are said to be related. A relation is a type of function.
A function is a relation that states that there should be only one output for each input (or) we can say that a function is a special type of relation (a set of ordered pairs) that follows a rule, i.e., every X-value should be associated with only one y-value.
It should be noted that based on the information, only one value can be attributed to each person. Therefore, the correct option is D.
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By rounding each number to 1 significant figure estimate to 6235.1 x 21.5
By rounding each number to 1 significant figure estimate to 6235.1 x 21.5 is 120000.
How can the numbers be rounded up?The concept of significant fiqure is based on the looking for the first non zero number that is resnt in the numbers , and that will be one significant figure, and it goes like that.
Then let us round each of the given fiqures into 1 significant fiqure as instructed:
6235.1 to 1 significant figure will be 6000 , because 6 is the first significant fiqure and the value that follow 6 is less than 5, it can not been approximated
21.5 to 1 significant figure will be 20
Then (6000*20) =120000
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factorise x squared - 6x
The quadratic expression can be factorized to:
x*(x - 6)
How to factorize the expression?Here we have the expression:
x^2 - 6x
To factorize this, first, we need to find the roots, which are the solutions of:
x^2 - 6x = 0
Notice that one of the solutions is trivial, and it is x = 0.
If now we assume that x ≠ 0 and divide both sides by x, we get:
x - 6 = 0
x = 6
That is the other solution.
Now, for a square polynomial with the roots a and b, the factorized form is:
(x - a)*(x - b)
In this case, the roots are 0 and 6, then:
x^2 - 6x = (x - 0)*(x - 6) = x*(x - 6)
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in a two-factor anova, if there is a significant interaction effect, what should be your interpretation for the main effects of factor a and factor b?
In two - factor ANOVA , if there is significant interaction effect then Not necessary that main effects of both factors a and b is significant.
A two- way ANOVA (analysis of variance) is a statistical test used to analyze the difference in means of three or more groups.
Two-Way ANOVA is used to estimate how the mean of a quantitative variable varies according to the levels of two categorical variables. Use two-way ANOVA when you want to know how the combination of two independent variables affects the dependent variable.
Interaction effects occur when the effect of one variable depends on the value of another variable. Interaction effects are common in ANOVA and designed experiments.
We see that interaction effect in ANOVA test is significant . but interaction effect significant is not implies the significance of main effects of factors a and b. So, we conclude that main effects of factor a and b need not be significant.
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Order from least to greatest 5.5 7.428, 5.5081, 5.58
Answer:
5.5,5.5081, 5.58, 7.428
Step-by-step explanation:
to look from least to greatest just look at each place value and see which one is slower and any that you can’t see is zero
Hopes this helps please mark brainliest
Answer two questions about Equations A and B:
A. 3(x+2) = 18
B. x+2=6
1) How can we get Equation B from Equation A?
Choose 1 answer:
Add/subtract the same quantity to/from both sides
Add/subtract a quantity to/from only one side
Multiply/divide both sides by the same non-zero constant
Multiply/divide only one side by a non-zero constant
2) Based on the previous answer, are the equations equivalent? In other words, do they have
the same solution?
Part A
We can get equation B from A by Multiply/divide both sides by the same non-zero constant.
Part B
The two equations are equivalent, they have same solution
The equations are
3(x+2) = 18
x + 2 = 6
Part A
Consider the first equation
3(x + 2) = 18
Divide both side of the equation by 3
3(x+2) / 2 = 18/3
x + 2 = 6
We will get equation B from equation A, if we divide both side of the equation by 3
Part 2
The first equation
3(x+2) = 18
x + 2 = 6
x = 6-2
x = 4
The second equation
x+2 = 6
x = 6-2
x = 4
Both the equation has same solution
Hence,
Part A
We can get equation B from A by Multiply/divide both sides by the same non-zero constant.
Part B
The two equations are equivalent, they have same solution
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Write an equation for each line using slope intercept form
Answer:
y = -5/3 - 3
Step-by-step explanation:
Since it's given a graph, we can use rise over run to figure it out
We pick 2 points that are integers on the graph , which means two points on the graph that the line goes through
Example- I picked (-3, 2) and (0, -3), you can indicate them so you don't forget or anything
We now draw a triangle formed by those two points (a line that goes from (-3, 2) to (-3, -3) and a line from (0, -3) to (-3, -3)
Rise (Which is the height of the triangle you just drew) is 5 units, but it's going down, so -5
The base (Run) is 3 units. Using rise/run, the slope is -5/3
The y-intercept, which is at the point where the graph crosses the y-axis, is -3.
The slope intercept form is y=mx+b, where m = slope and b = y-intercept, so the equation of the graph is y = -5/3x -3
Two similar pots have heights of 16 cm and 10 cm. The smaller pot holds 0.75 litres. Find the capacity of the larger pot.
Answer: 1,2L
Step-by-step explanation:
10 cm ------------ 0.75 L
16 cm ------------ ?
?= (16 x 0.75) : 10
?= 12 : 10
?= 1,2 L
the patient recovery time from a particular surgical procedure is normally distributed with a mean of 5.2 days and a standard deviation of 2.3 days. what is the probability of spending more than 2 days in recovery? (round your answer to four decimal places.)
When the patient recovery time from a specific surgical procedure is normally distributed, with a mean of 5.2 days and a standard deviation of 2.3 days, the probability of spending more than 2 days in recovery will be 0.61.
What is probability?Simply put, probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of various outcomes. Statistics is the study of events that follow a probability distribution. Information about the likelihood that something will happen is provided by probability. For instance, meteorologists use weather patterns to forecast the likelihood of rain. Probability theory is used in epidemiology to comprehend the connection between exposures and the risk of health effects.
Here,
z=(X-μ)/σ
X=2
μ=5.2
σ=2.3
Z=(2-5.2)/2.3
Z=-1.39
-1.39+1
=0.39
1-0.39=0.61
The probability of spending more than 2 days in recovery will be 0.61 when the patient recovery time from a particular surgical procedure is normally distributed with a mean of 5.2 days and a standard deviation of 2.3 days.
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pls answer all the questions FOIL pre calc
Answer for Part I: x² - 3x - 10
Step-by-step explanation:
The FOIL method means to multiply the "First, Outside, Inside, and Last" in order of the terms. See attached for a visual and the work behind the answer.
Using this method, we end up with;
x² - 3x - 10
Determine which integer(s) from the set S:{−24, 2, 20, 35} will make the inequality five sixths m minus five is less than one half m plus 3 false.
S:{−24, 2}
S:{35}
S:{−24, 2, 20}
S:{20}
The inequality five-sixths m minus five is less than one-half m plus 3 false is false for 35 option (B) is correct.
What is inequality?It is defined as the expression in mathematics in which both sides are not equal they have mathematical signs either less than or greater than known as inequality.
It is given that:
The set of integers:
S:{−24, 2, 20, 35}
Plug the value 35 in the inequality:
= 5/6(35 - 5) < 1/2(35 + 3)
= 5/6(30) < 1/2(38)
= 25 < 19 (False)
Thus, the inequality five-sixths m minus five is less than one-half m plus 3 false is false for 35 option (B) is correct.
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Given the following exponential function, identify whether the change represents
growth or decay, and determine the percentage rate of increase or decrease.
y = 90(1.02)
The exponential equation represents an exponential growth because the rate of decay is 1.02 which is greater than 1.
y = 90(1.02)^x
The general form equation is:
y(x)= a(1+r)^x such that r is the decay percent.
on comparing,
1 + r = 1.02
r = 1.02 - 1
r = 0.02
converting into percent
r = 0.02 * 100
r = 2%.
Hence the exponential growth is 2%.
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you can answer any 17 questions from a total of 20 questions on an exam. in how many different ways can you select the questions?
With the help of probability we can say that there are 1140 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-
permutation= 20!/ (20-17)!ncr= 20!/ 17!(20-17)!=1140Hence,we can say that there are 1140 ways.
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a telemarketing company is conducting a study of new calling scripts. seventy-five employees will be randomly assigned to three new scripts using a table of random digits. the study leader will assign the subjects to the groups using a table of random digits. how many unique two-digit numbers within the range of 01 to 75 will the study designer need to select from the table? 3 25 50 75
Answer:
50
Step-by-step explanation:
Which monomial function has a minimum value?
Oy = 5x¹0
Oy=-4x¹1
Oy=-x¹2
y=6x7
A monomial function that has a minimum value is y = 5x^10
In this question, we have been given four monomial functions.
y = 5x^10
y = -4x^11
y = -x^12
y = 6x
we need to find a monomial function that has a minimum value.
For function y = 5x^10, as x > 0 increases, f(x) increases. And as x < 0 decreases, f(x) increases.
We know that for even, positive monomial function if coefficient > 0 and exponent is even then a monomial has a minimum value.
Therefore, a monomial function that has a minimum value is y = 5x^10
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Find the slope between the points
below. Simplify your answer.
(-10, 5) and (14,-3)
Slope between the points (-10, 5) and (14,-3) is -1/3.
What is Slope of Line?The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.
The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.
The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is
m=y₂-y₁/x₂-x₁
We need to find slope between points (-10, 5) and (14,-3)
m=-3-5/14+10
m=-8/24
m=-1/3
Hence, slope between the points (-10, 5) and (14,-3) is -1/3.
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The mass of a test sample is 10 g, and it has a volume of 2.5 cm³. What is its density?
A. 10 g/cm³
B. 2.5 cm³/g
C. 4 g/cm³
D. 4 cm³/g
E. 0.25 g/cm³
The density is the ratio of mass to volume of an object thus the density of the given test sample is 4 g/cm³ thus option (C) will be correct.
What is density?Density or mass density is the mass of any object per volume.
For example, if the metal has a 100 kg mass and an area of 10-meter square then 100/10 = 10 kg/meter square will be the density of the given object.
Density can be uniform or non-uniform.
Density is the division of mass and volume and the mass must be for the quantity of the volume only.
Given that,
Mass = 10 g
Volume = 2.5 cm³
Density = 10/2.5 = 4 g/cm³
Hence "The density is the ratio of mass to volume of an object thus the density of the given test sample is 4 g/cm³".
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What is the rate of change of the function y = 5x + 4?
Answer:
The slope of y = 5x - 4 is 5.
Notice that the equation, y = 5x - 4, of the line is written in the form y = mx + b. Thus, it is in slope-intercept form. When the equation of a line is in slope-intercept form, we know that the slope of the line is equal to m, the coefficient of x.
In y = 5x - 4, the coefficient of x is 5. Thus, the slope of the line, y = 5x - 4, is 5.
1) What is the slope of the following graph?
Answer:[tex]\frac{3}{-2}[/tex]
Step-by-step explanation:
slope= [tex]\frac{rise}{run}[/tex]
start at (0,1)
go up 3 units
then go left 2 units
slope= [tex]\frac{3}{-2}[/tex]
Can someone please help me with the following problems
The day which has the least change in temperature is Wednesday.
The two consecutive days which showed a drop in temperature is Wednesday and Thursday.The graph which was easier to read is table graph.Table graph illustrate the data because it clearly shows the data representation.How to read and explain graph?The day which has the least change in temperature can be calculated by finding the change in temperature:
Monday = High temperature - low temperature
= 82° - 58°
= 24°
Tuesday = High temperature - low temperature
= 85° - 60°
= 25°
Wednesday = High temperature - low temperature
= 77° - 62°
= 15°
Thursday = High temperature - low temperature
= 68° - 50°
= 18°
Friday = High temperature - low temperature
= 75° - 48°
= 27°
Saturday = High temperature - low temperature
= 70° - 52°
= 22°
Sunday = High temperature - low temperature
= 84° - 56°
= 28°
The day which has the least change in temperature is Wednesday
Which two consecutive days which showed a drop in temperature: Wednesday and Thursday with 77° and 68° respectively.
Unlike line graph, table graph is the graph that is easier to read.
Therefore, the graph which best illustrate the graph is table graph because it represent the data in a clearer way.
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The exponential model describes the population, A, of a country in millions, t years after 2003. Use the model A=384. 7e^0. 018t to determine when the population of the country will be 513 million.
The population of the country will be 513 million in __. (Round to the nearest year as needed. )
The population of the country will be 513 million in 2016 with The exponential model A=384. 7e^0. 018t describes the population, A, of a country in millions, t years after 2003.
What is exponential model?The exponential model represents the degrading failure process using an equation like: where Y = degradation, T = time, and A and B = parameters to be predicted using the regression approach using historical data. Exponentials are frequently utilized when the rate of change of a quantity is proportional to its beginning amount. Y represents exponential decay if the coefficient associated with b and/or d is negative. Y represents exponential growth if the coefficient is positive.
Here,
A = 384. 7e^0. 018t
513=384. 7e^0. 018t
513/384.7= e^0.018t
ln(513/384.7) = 0.018t
ln(513/384.7)/0.018 =t
t=15.9895575229 years
t=16 years
2003+16= 2019
In 2016, the country's population will be 513 million people. The exponential model A=384. 7e^0. 018t explains a country's population, A, in millions, t years after 2003.
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Due today help please!!
The equation of line: y = 2x - 9
slope = 2
y-intercept = (0, -9)
The graph of the line y = 2x - 9 is as shown below.
In this question we have been given a point (6, 3) and slope m = 2
We need to find an equation of line passing through (6, 3) with slope m = 2
Using formula of the point-slope form:
(y - y1) = m(x - x1)
(y - 3) = 2(x - 6)
y - 3 = 2x - 12
y = 2x - 12 + 3
y = 2x - 9
This is slope-intercept form of equation of line.
slope = 2
y-intercept = -9
Therefore, the equation of line: y = 2x - 9
slope = 2
y-intercept = (0, -9)
The graph of the line y = 2x - 9 is as shown below.
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Can you explain how you got your answer please
A software company bought 73 laptops and paid a total of $61,274 to buy them. How much money did each laptop cost the company?
Answer:
839.369863
(Might need to round it depending on what the question requests)
Step-by-step explanation:
Step 1: I divided $61,274 by 73.
Step 2: I multiplied 839.369863 by 73, and I got 61,274.
---------------------------------------------------------------
If it asks to explain say this:
"I divided the amount of money spent by the total amount of laptops bought, and i got 839.369863, To make sure it can be multiplied by 73 to get $61,274, I multiplied 839.369863 by 73 to get $61,274."
Hope this helps :)
Help Please!
Solve the inequality and graph it’s solution.
Answer:
A) m > -13
Step-by-step explanation:
[tex]-112-14m < 70\\-14m < 70+112\\-14m < 182[/tex]
[tex]\frac{-14m}{-14} < \frac{182}{-14}[/tex]
[tex]m > -13[/tex]
Hope this helps
