Answer:
False. See explanation below.
Step-by-step explanation:
False
A simple random sample "is a subset of a statistical population in which each member of the subset has an equal probability of being chosen"
In other words that means in order to apply a random sampling we need to ensure that we have the same probability of inclusion for every possible element of the population of interest.
And for this case a collection of any numerical information is not referred as random sampling since we don't know if these scores are representative of the population of interest.
And we don't know if this information is obtained using any sampling frame or sampling methodology.
Sergio thinks he will need 90 cups of fruit juice to make 210 cups of punch. Explain his method. How many cups of fruit juice would Sergio need to make 154 cups of punch? Explain your calculations.
Answer:
66 cups of fruit juice will be required .
Step-by-step explanation:
According to the question ,
90 Cups of fruit juice is required for making of 210 cups of punch .
So,
For making of one cup of punch ,
[tex]\frac{90}{210}[/tex] = [tex]\frac{3}{7}[/tex] cups of fruit juice will be required ,
Thus,
For making of 154 cups of punch ,
Total number of cups of fruit juice required will be [tex]\frac{3}{7}[/tex]×154.
= 66 cups.
Thus a total of 66 cups of fruit juice will be required.
If one number is a multiple of 3 and the other is not, then the sum of these numbers is not a multiple of 3
A. true
B. false
Answer:
A.True
Step-by-step explanation:
Multiple of 3 is given by
3,6,9,12,15,18,,,,
Let one number a=6
6 is a multiple of 3.
Another number =5
5 is not a multiple of 3.
Sum of 6 and 5=6+5=11
We know that
11 is not a multiple of 3.
Therefore, if one number is a multiple of 3 and the other is not , then the sum of these number is not a multiple of 3 is true.
Option A is true
Line segment AB is dilated to create line segment A'B' using point Q as the center of dilation. Point Q is the center of dilation. Line segment A B is dilated to create line segment A prime B prime. The length of Q A is 1.25 and the length of A A prime is 1.25. What is the scale factor?
Answer:
2
Step-by-step explanation:
A is on the line QA', which is 1.25+1.25 = 2.50 units long*. Thus the scale factor is ...
QA'/QA = 2.50/1.25 = 2
The scale factor is 2.
_____
* There are two points on the line QA that are 1.25 units from A. One of them is point Q. If A' is coincident with Q, then the scale factor is 0, and line segment A'B' is the single point Q. We don't believe that is intended to be the case, so we assume that point A' is farther along AQ, hence 2.5 units from Q.
What is the effect on the graph of the parent function f(x) = x when f(x) is replaced with f(x) - 4? A) shifts the line 4 units up B) shifts the line 4 units down C) increases the slope of the line by a factor of 4 D) decreases the slope of the line by a factor of 4
Answer:
B) shifts the line 4 units down
Step-by-step explanation:
The point (x, f(x)) is moved to the point (x, f(x)-4), one with a y-coordinate 4 units lower. The line is shifted down 4 units.
Answer:
B) shifts the line 4 units down.
Step-by-step explanation:
The constant negative number makes a vertical translation of the parent function in the -y direction. Slope keeps intact. So, the right answer is B.
6. Sue goes to the bakery and purchases cupcakes and cookies for a picnic. She needs to serve 36 people. Cupcakes cost $2.50 each, cookies cost $1.00 each. She spends $54.00. How many cupcakes did she purchase?
Answer:the number of cupcakes that Sue purchased is 12
Step-by-step explanation:
Let x represent the number of cupcakes that Sue purchased at the bakery.
Let y represent the number of cookies that Sue purchased at the bakery.
She needs to serve 36 people. This means she would purchase a total of 36 people. Therefore,
x + y = 36
Cupcakes cost $2.50 each, cookies cost $1.00 each. She spends $54.00. This means that
2.5x + y = 54 - - - - - - - - - 1
Substituting x = 36 - y into equation 1, it becomes
2.5(36 - y) + y = 54
90 - 2.5y + y = 54
- 2.5y + y = 54 - 90
- 1.5y = - 36
y = - 36/ - 1.5
y = =24
x = 36 - y = 36 - 24 = 12
She purchased 24 cupcakes
Let the number of cupcakes be xLet the number of cookies be yIf she needs to serve 36 people, then;
x + y = 36 .................... 1
if cupcakes cost $2.50 each, cookies cost $1.00 each while she spends $54.00, then;
2.5x + y = 54 ...................... 2
From equation 1, x = 36 - y
Substitute into equation 2;
2.5(36-y) + y = 54
90 - 2.5y + y = 54
-1.5y = - 36
y = 36/1.5
y = 24
Hence she purchased 24 cupcakes
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Explain the rules for multiplication and division to convert units. How do you know when to multiply and when to divide to convert units of measurement?
Write three to four sentences.
Answer:
To convert larger units to smaller units, multiply. When the units are smaller, you need more of them to express the same measure. To convert smaller units to larger units, divide. When the units are larger, you need fewer of them to express the same measure.
Multiply to convert larger units to smaller units.
Divide to convert smaller units to larger units.
When the units are smaller, you need more of them to express the same measure.
When the units are larger, you need fewer of them to express the same measure.
Answer:
To convert between units, you're usually given one measure and asked to convert to another measure.
Step-by-step explanation:
Going to smaller units means going to bigger numbers so you multiply and going to bigger units means going to small. or in other words if you need to convert from a larger unit to a smaller unit Multiply. and if you need to convert from a smaller unit into a larger unit Divide. When converting customary units of measure from a larger unit to a smaller unit, multiply the the larger unit by its smaller equivalent unit.
Two runners are saving money to attend a marathon. The first runner has $112 in savings, received a $45 gift from a friend, and will save $25 each month. The second runner has $50 in savings and will save $60 each month. Which equation can be used to find m, the number of months it will take for both accounts to have the same amount of money?
Answer: it would take 3.1 months
Step-by-step explanation:
Let m represent the number of months that that it will take either of the runners to have the same amount of money in their accounts.
Let y represent the total amount that runner 1 saves for m months
Let z represent the total amount that runner 2 saves for m months
The first runner has $112 in savings, received a $45 gift from a friend, and will save $25 each month. This means that the total amount that he will save for m months would be
y = 112 + 45 + 25m
y = 157 + 25m
The second runner has $50 in savings and will save $60 each month. This means that the total amount that he will save for m months would be
z = 50 + 60m
To determine the number of months before the amount in the account of both runners becomes the same, we would equate y to z. It becomes
157 + 25m = 50 + 60m
157 - 50 = 60m - 25m
35m = 107
m = 107/35
m = 3.06
When using your portable radio, you must push the "press to talk" button and wait one second before speaking. This is essential to effective communication because your EMS system must use:
Answer:
Repeaters.
Step-by-step explanation:
This is essential to effective communication because your EMS system must use Repeaters.
These are machines used to carry signals across a great distance. We may be in ambulances or put around an EMS network in different areas. The repeater receives and re transmits signals from lower power systems, such as mobile and handheld phones, to a higher power.
Final answer:
When using portable radios in an EMS system, waiting before speaking is necessary to prevent frequency interference with medical equipment like AEDs. This ensures effective communication and prevents disruptions with critical equipment operations.
Explanation:
When using a portable radio and instructed to push the "press to talk" button and wait one second before speaking, it is essential for effective communication because it ensures that the EMS system has time to establish a clear connection. This waiting period is crucial because communications or medical equipment may use similar radio frequencies. Interruptions and interference on these frequencies can arise from external devices, such as mobile phones operating at 1.9 GHz. Moreover, important medical devices, like automated external defibrillators (AEDs), which provide verbal instructions during cardiac emergencies, rely on these frequencies to function correctly without disruption. Therefore, allowing a small delay ensures that all emergency communication and equipment can operate without interference.
Additionally, speaking slowly and clearly is also vital to ensure that the message is conveyed accurately, especially in situations where there might be wi-fi delays or microphone malfunctions.
Eight women of different heights are at a party. Each woman decides to only participate in a handshake with women shorter than herself. How many handshakes take place?
Answer:
0 handshakes
Step-by-step explanation:
There are 8 women of different heights.
Let the eight women be A, B, C, D, E, F, G and H
Assume A is taller than B and A decides to shake hands with B, B will refuse because A is taller. If this happens across the eight women then there will be 0 hand shakes.
If this assumption is taken out, we have 7+6+5+4+3+2+1 = 28
Answer:
0
Step-by-step explanation:
There are 0 handshakes because if A is taller than B, then A will want to shake hands with B, but B will not participate because she is shorter.
1. Use the graph of the rational function
to complete the following statement.
As x → -3*, f(x) →
N
Answer:
As [tex]x \to -3^{+}, f(x) \to -\infty[/tex]
Step-by-step explanation:
Given:
From the graph, we can conclude that:
The function has vertical asymptotes at [tex]x=-3\ and\ x=2[/tex]
The function has horizontal asymptote at [tex]f(x)=0[/tex]
Vertical asymptotes are those values of 'x' for which the functions tends towards infinity. Horizontal asymptote is the value of the function as the 'x' value tends to infinity.
Now, as [tex]x \to -3^{+}[/tex] means the right hand limit of the function at [tex] x=-3[/tex]
From the graph, the right hand limit is the right side of the asymptote of the function at [tex] x = -3[/tex]. The right side shows that the function is tending towards negative infinity.
Therefore, As [tex]x \to -3^{+}, f(x) \to -\infty[/tex]
The Morrison’s car uses one gallon of gasoline for every 28 miles. If gasoline costs $1.50 per gallon, how many miles can they drive if they spend $24 on gasoline?
Given:
$ 1.50 / gallon
1 gallon = 28 miles;
Solution:
$ 24.00 / $ 1.50 = 16 gallons
16 gallons x 28 miles = 448 miles
have a nice day:)
Answer:they would drive 448 miles if they spend $24 on gasoline
Step-by-step explanation:
The Morrison’s car uses one gallon of gasoline for every 28 miles. If gasoline costs $1.50 per gallon, then the cost of driving 28 miles would be $1.5.
Therefore, the number of miles can they drive if they spend $24 on gasoline would be
(28 × 24)/1.5 = 448 miles
A bag of rare spice that weighs pounds will be split equally among people. How much spice will each person get?
Completed question: A bag of rare spice that weighs 3/5 pounds will be split equally among 15 people. How much spice will each person get?
Answer:
0.04 pounds
Step-by-step explanation:
The number of spice received by each person will be equal to the total number of spice divided by the number of people sharing it.
Amount of spice received per person = (3/5) /15
= 0.04 pounds
For the following frequency distribution, how many individual scores are in the entire set?
X: 5 - 4 - 3 - 2
f: 2 - 4 - 1 - 3
a. N = 54
b. N = 14
c. N = 10
d. impossible to determine
Answer:
10
Step-by-step explanation:
The individual scores in the data are represented by frequency denoted by f column. f column depicts that how many times the individual scores are occurring in the data set. Hence to calculate the amount of individual score in the data set we simply add all frequencies. n=sum of f=2+4+1+3=10. Hence there are 10 individual scores present in the entire data set.
The number of individual scores in the given frequency distribution set is 10, obtained by adding the frequencies together.
Explanation:In the given question, it's the frequency distribution that is given with scores X: 5, 4, 3, and 2 with their respective frequencies f: 2, 4, 1, and 3. To find the total number of individual scores in the entire set, you simply sum up all the frequencies. So, 2+4+1+3 equals 10. So, the number of individual scores in the entire set is 10. Hence, the correct answer is c. N = 10.
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Kobe attends barber school so far he has completed 612 hours if Kobe attended School the same number of hours each day for a total of 68 days how many hours did he attend school each day?
Answer:
Kobe attended barber school for 9 hours each day.
Step-by-step explanation:
Total number of hours completed by Kobe in barber school = 612 hours
Total number of days Kobe attended the school for = 68 days
We are given that Kobe attended school for same number of hours each day.
So, in order to find the number of hours Kobe attended each day we will use unitary method.
In 68 days Kobe completed = 612 hours of school
So, in 1 day he will complete = [tex]\frac{612}{68}=9[/tex] hours
Thus, Kobe attended barber school for 9 hours each day.
The goals against average (A) for a professional hockey goalie is determined using the formula A = 60 a equals 60 left-parenthesis StartFraction g Over t EndFraction right-parenthesis.. In the formula, g represents the number of goals scored against the goalie and t represents the time played, in minutes. Which is an equivalent equation solved for g? StartFraction A t Over 60 EndFraction equals g.= g StartFraction A Over 60 t EndFraction equals g. = g StartFraction 60 A Over t EndFraction equals g. = g 60At = g
Answer:
Option 1 - [tex]\frac{At}{60}=g[/tex]
Step-by-step explanation:
Given : The goals against average (A) for a professional hockey goalie is determined using the formula [tex]A=60(\frac{g}{t} )[/tex]. In the formula, g represents the number of goals scored against the goalie and t represents the time played, in minutes.
To find : Which is an equivalent equation solved for g?
Solution :
Solve the formula in terms of g,
[tex]A=60(\frac{g}{t})[/tex]
Multiply both side by t,
[tex]At=60g[/tex]
Divide both side by 60,
[tex]\frac{At}{60}=\frac{60g}{60}[/tex]
[tex]\frac{At}{60}=g[/tex]
Therefore, option 1 is correct.
Answer:
a
Step-by-step explanation:
The number of math problems solved in a class, ????, varies directly with the length of time x and inversely with the number of student questions in that time y. If in 6 minutes of class there were 14 student questions and a total of 5 problems that were solved, then write ???? as a function of x and y. ???? = x/y function equation editor
The function that represents the number of math problems solved in a class is given by ????(x, y) = (15/7)* x / y, where x represents time and y represents the number of student questions. The constant of variation 'k' is 15/7.
Explanation:Given that the number of math problems solved (????) in class is influenced by time duration (x) and the number of student questions (y), we can infer a relationship. We can define a constant of variation (k), which stands for the number of problems solved per time unit and per question. Based on the provided situation where 5 problems were solved in 6 minutes with 14 questions, we calculate k as k = ????(x/y) = 5(6/14) = 30/14 = 15/7.
Therefore, the function that represents this scenario is ????(x, y) = (15/7)* x / y, where x is the length of time and y is the number of student questions.
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After sales tax your brand new car is $17,300. What is the total price of the car with DMV fees of 1.25% of the purchase price of the car?
A. $261.25
B. $17,516.25
C. $216.25
D. $17,561.25
The right answer is Option B.
Step-by-step explanation:
Given,
Purchase price of car with sales tax = $17300
DMV fees = 1.25%
Amount of DMV fees = 1.25% of purchase price
Amount of DMV fees = [tex]\frac{1.25}{100}*17300=\frac{21625}{100}[/tex]
Amount of DMV fees = $216.25
Total price = Purchase price + DMV fees
Total price = 17300 + 216.25
Total price = $17516.25
The total price of car with DMV fees is $17,516.25
The right answer is Option B.
Keywords: percentage, addition
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Final answer:
The total price of the car including DMV fees of 1.25% is (B) $17,516.25, which is found by adding the DMV fees of $216.25 to the purchase price of $17,300.
Explanation:
The question asks for the total price of a car including DMV fees, which are 1.25% of the purchase price of the car after sales tax.
To find the DMV fees, first convert the percentage to a decimal by dividing 1.25 by 100, which gives us 0.0125. Then multiply the purchase price after sales tax, $17,300, by 0.0125 to get the DMV fees.
The calculation is: $17,300 x 0.0125 = $216.25.
Finally, add the DMV fees to the purchase price to get the total price: $17,300 + $216.25 = $17,516.25. Therefore, the correct answer is B. $17,516.25.
Tim's Tacos sell 57 chicken tacos a night and 89 beef tacos a night for 3 weeks. How many of each kind of taco do they sell when the three weeks are up?
Answer:
see the explanation
Step-by-step explanation:
Remember that
[tex]1\ week=7\ days[/tex]
To convert weeks to days , multiply by 7
so
[tex]3\ weeks=3(7)=21\ days[/tex]
we know that
Each night Tim's Tacos sell 57 chicken tacos and 89 beef tacos
To find out how many of each type of taco sold after three weeks, multiply the number of taco sold daily by 21 (3 weeks)
Chicken tacos
[tex]57(21)= 1,197\ chicken\ tacos[/tex]
Beef tacos
[tex]89(21)= 1,869\ beef\ tacos[/tex]
1. Point A(-5,8) is reflected across the line y = x. What are the coordinates of A'? Show your work and explain.
Need help with this
Answer:
The coordinates of A'(8,-5)
Step-by-step explanation:
we know that
When you reflect a point across the line y = x, the x-coordinate and y-coordinate change places
so
The rule of the reflection across the line y=x is
(x,y) -----> (y,x)
we have the point A(-5,8)
Applying the rule of the reflection across the line y=x
A(-5,8) ----> A'(8,-5)
see the attached figure to better understand the problem
Last year, about 2,400 people participated in a local Fourth of July parade. This year, about 3,200 people participated. What was the approximate percent increase in participation?
Answer:
800 people a year
Step-by-step explanation:
When there is an increment in an observed value, the increment implies that there is a growth or percentage increase in the observed value. The percentage increase in participation is 33%:
Given that:
[tex]Initial = 2400[/tex] --- last year
[tex]New= 3200[/tex] --- this year
The percentage increase is calculated as:
[tex]\%Increase = \frac{New - Initial}{Initial} \times 100\%[/tex]
So, we have:
[tex]\%Increase = \frac{3200 - 2400}{2400} \times 100\%[/tex]
[tex]\%Increase = \frac{800}{2400} \times 100\%[/tex]
[tex]\%Increase = 0.3333 \times 100\%[/tex]
[tex]\%Increase = 33.33 \%[/tex]
Approximate
[tex]\%Increase = 33 \%[/tex]
Hence, the percentage increase in participation from last year to this year is 33%
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The sum of the first 100 positive integers is 5,050. What is the sum of the first 200 positive integers?
A. 10,000B. 10,200C. 15,050D. 20,050E. 20,100
The sum of the k for k=1 to k="n"=(n*(n+1))/2 , where "n" is the total integer.
In this problem n = 200
Sum = (200*201)/2 = 20,100
Select the correct answer from each drop-down menu.
Maggie is monitoring the number of fish in a fish breeding center. The table below shows the number of fish with respect to the number of months elapsed.
Number of Months 0 1 2 3 4
Number of Fish 1,024 1,280 1,600 2,000 2,500
The independent variable in the relationship is the_____________ and should be placed on the______________ .
The dependent variable in the relationship is the_____________ and should be placed on the__________________ .
Answer:
The independent variable in the relationship is the Number of Months and should be placed on the x-axis .
The dependent variable in the relationship is the Number of Fish and should be placed on the y-axis .
Step-by-step explanation:
Independent variable is the variable that is being changed or controlled. It's the value that you would graph on the x-axis. Intuitively you would graph the months on the x-axis. I don't really know how to explain it other than that.
Dependent variable is the variable that is being measured. It's the value that is being graphed on the y-axis. You're measuring the amount of fish so that's your dependent variable.
The cost c in £ of a monthly phone contract is made up of the fixed line rental l in £ and the price p in £ of the calls made. Enter a formula for the cost and enter the cost if the line rental is £35 and the price of calls made is £12
The cost of the phone contract will be C = 35 + 12m.
From the information given, the fixed line rental is £35 and the price of calls made is £12, therefore the monthly cost will be represented by:
C = 35 + (12 × m)
C = 35 + 12m
Therefore, the cost of the phone contract will be C = 35 + 12m where m represents the number of months.
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The cost of a monthly phone contract is made up of the fixed line rental and the price of the calls made. This can be represented with the formula: c = l + p, where c is the cost, l is line rental, and p is the price of calls. With a line rental of £35 and call price of £12, the total cost of the phone contract is £47.
Explanation:In the scenario presented, the cost, c, of a monthly phone contract is constituted by the fixed line rental or l and the price or p of the calls made. This can be represented with the formula: c = l + p. We can substitute in the provided costs - a line rental of £35 and call price of £12 - into the equation to find the total cost of the phone contract. Thus, c = £35 + £12 = £47.
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Identify the graphed linear equation.
A) y = 4x + 1
B) y = 4x - 1
C) y = -4x + 1
D) y = -4x - 1
Answer:
The answer to your question is letter C
Step-by-step explanation:
Process
1.- Find two points of the line
A ( 0, 1)
B ( 1, -3)
2.- Find the slope of the line
[tex]m = \frac{y2 - y1}{x2 - x1}[/tex]
[tex]m = \frac{-3 - 1}{1 - 0}[/tex]
[tex]m = \frac{-4}{1}[/tex]
m = -4
3.- Find the equation of the line
y - y1 = m (x - x1)
y - 1 = -4( x - 0)
y -1 = -4x
y = -4x + 1
Find the Values of k for which the following simultaneous equations have no solutions:
2x - 3ky = 1
4x + (k + 2)y = 5
Answer:
[tex]k=-\frac{2}{7}[/tex]
Step-by-step explanation:
The two equations given represent two straight lines in 2-D graph.
The two lines will not intersect if they are parallel.
Hence the two equations will not have solution if the lines are parallel and not coincident.
The condition for 2 lines given by the equations :
ax+by+c=0
dx+ey+f=0 to be parallel but not coincident is:
[tex]\frac{a}{d}=\frac{b}{e}\neq\frac{c}{f}[/tex]
here a=2 b=-3k c=-1 d=4 e=k+2 f=-5
[tex]\frac{2}{4}=\frac{-3k}{k+2}\\k+2=-6k\\k=-\frac{2}{7}[/tex]
But also:
[tex]\frac{-3k}{k+2}\neq\frac{1}{5}[/tex]
Hence the value of k is -2/7.
The local amusement park was interested in the average wait time at their most popular roller coaster at the peak park time (2 p.m.). They selected 13 patrons and had them get in line between 2 and 3 p.m. Each was given a stopwatch to record the time they spent in line. The times recorded were as follows (in minutes): 118, 124, 108, 116, 99, 120, 148, 118, 119, 121, 45, 130, 118.
What is the first quartile?
a. 100.8
b. 119.8
c. 128.8
d. 112
e. 122.5
Answer: d. 112
Step-by-step explanation:
First Quartile is the median of the first half of ordered data (from smallest to largest).
The given data : 118, 124, 108, 116, 99, 120, 148, 118, 119, 121, 45, 130, 118.
Arrange in Ascending order , we get
45,99, 108,116,118, 118, 118, 119,120, 121,124,130, 148
First half = 45,99, 108,116,118, 118
No. of elements = 6
First Quartile = Median of first half = Mean of middlemost terms
=[tex]\dfrac{108+116}{2}=\dfrac{224}{2}=112[/tex]
Hence, the First quartile = 112
Correct answer = d. 112
State the horizontal asymptote of the rational function. F(x)=9x^2-3x-8/4x^2-5x+3
Y=3/5
Y=9/4
Y=0
None
Answer:
y=0
Step-by-step explanation:
Answer:
y = [tex]\frac{9}{4}[/tex]
Step-by-step explanation:
The horizontal asymptote is the ratio of the coefficient of the highest degree term on the numerator and denominator, that is
9x² - 3x - 8 ← coefficient 9
4x² - 5x + 3 ← coefficient 4, thus
y = [tex]\frac{9}{4}[/tex] ← equation of horizontal asymptote
Need some help with this
Answer:
Step-by-step explanation:
The total number of outcomes the two fair number cubes are thrown is 36. This can be seen by counting the outcomes shown on the table.
a) for a sum of 4, there are only 3 possible outcomes. They are 3,2 2,2 and 1,3
Therefore, the probability of getting a sum of 4 will be
3/36 = 1/12
b) for a sum of 5, there are only 4 possible outcomes. They are 4,1 3,2 2,3 and 1,4
Therefore, the probability of getting a sum of 4 will be
4/36 = 1/9
c)for a sum of 6, there are only 5 possible outcomes. They are 5,1 4,2 3,3 2,4 and 1,5
Therefore, the probability of getting a sum of 6 will be
5/36 = 5/36
The probability that the sum of the results of the throw is 4,5 or 6 would be
1/12 + 1/9 + 5/36 = (3 + 4 + 5)/36 = 12/36 = 1/3
Charles is saving $5 each week.He earns an extra $15 by mowing his neighbor's lawn.Write the inequality to show how to find how many weeks,W,will he need to save in order to save at least $75.
Answer:
Minimum number of weeks = 4
Step-by-step explanation:
Charles earns $5 each week .Also he makes $15 each week by mowing his neighbours lawn.
Thus , in total , he earns a total of $20 each week.
We have to find the minimum number of weeks needed to make $75 .
Number of weeks required = [tex]\frac{money required}{money made per week}[/tex]
= [tex]\frac{75}{20}[/tex]
=3.75
Since the number of weeks, W, is an integer, choose the next highest integer.
Hence the minimum number of weeks required = 4
A system of inequalities is shown. Which symbol could be written in both circles in order to represent this system algebraically? y 3x x –2 ≤ ≥ < >
Answer:
"≥"
Step-by-step explanation:
1) Well, for the sake of clarity we'll use a circle on a number line to represent the point solution of each inequality.
2) Writing the system:
[tex]\left\{\begin{matrix}y\geqslant 3x&\\x\geqslant-2&\end{matrix}\right.[/tex]
3) We'll shade the circles and use "≥"
Final answer:
The correct inequality symbols that could be written in both circles for the system 'y 3x x –2' are '<=' and '>=', representing the relationships 'y <= 3x' and 'x >= -2' respectively.
Explanation:
To represent the given system of inequalities algebraically, one needs to identify the correct inequality symbols that could be used between the variables x and y. These symbols articulate the ordering and relationship between these variables.
Given the statement of the system 'y 3x x –2', the inequality symbols that could fit in the circles to complete the system algebraically could be '<=' for 'y <= 3x' and '>=' for 'x >= -2'. This means '<=' and '>=' are both inequality symbols that could be written in the circles to represent the relationship between the variables according to the rules of inequalities which define x is less than or equal to y (x <= y), and x is greater than or equal to y (x >= y).
Inequalities allow us to compare relative sizes or orders of numbers and to solve various algebraic problems dealing with quantity and relationships.