Answer: $250
Step-by-step explanation:
If Jake still owes $185 and only just paid back $65, you need to add 185 and 65 together to get the total amount that he borrowed.
how to simplify 6(1+10m)
Answer:
0.1
Step-by-step explanation:
1.distribute the 6 to 1 and 10
2.now its 6+60m
3. divide 60 on both sides
4. 60/60 cancels out.
5. 6/60 =0.1
11. The range of a cellular phone service area is a circular region bounded by the equation: x² +
y² = 400. A fire road represented by y-3x = 20 runs through the service area. Find the
point(s)) where the fire road intersects the outer boundary of the service area.
The point(s)) where the fire road intersects the outer boundary of the service area is found using the equation of circle which is (0,20) and (-12,-16).
What is the equation of circle?
A circle is a closed curve that extends outward from a set point known as the centre, with each point on the curve being equally spaced from the centre. A circle with a (h, k) centre and a radius of r has the equation:
(x-h)² + (y-k)² = r²
The equation of the circle is given as - x² + y² = 400 .... (1)
The equation of the fire road is given as - y - 3x = 20 .... (2)
Write the equation of fire road in slope-intercept form - y = mx + b
y = 3x + 20
Substitute the value of y in equation (1) -
x² + y² = 400
x² + (3x + 20)² = 400
Follow the (a + b)² rule, (a + b)² = a² + 2ab + b²
x² + (3x + 20)² = 400
x² + 9x² + 120x + 400 = 400
10x² + 120x + 0 = 0
x² + 12x = 0
x(x+12) = 0
x = 0, x = -12
Substituting the values of x in equation (2).
First calculate for x = 0.
y - 3x = 20
y - 3(0) = 20
y = 20
Now, calculate for x = -12.
y - 3x = 20
y - 3(-12) = 20
y + 36 = 20
y = 20 - 36
y = -16
Therefore, the points of intersection are (0,20) and (-12,-16).
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Two pools are being filled with water. To start, the first pool contains 1600 liters of water and the second pool contains 1186 liters of water. Water is being added to the first pool at a rate of 20.25 liters per minute. Water is being added to the second pool at a rate of 31.75 liters per minute. After how many minutes will the two pools have the same amount of water? How much water will be in each pool when they have the same amount?
At 36 minutes, the amount of water in both pools will be same. In amount, it will be 2329 liters.
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 two pools are being filled with water. To start, the first pool contains 1600 liters of water and the second pool contains 1186 liters of water. Water is being added to the first pool at a rate of 20.25 liters per minute. Water is being added to the second pool at a rate of 31.75 liters per minute.
We can write the equation for the first pool as -
y{A} = 1600 + 20.25x
Similarly, for the second pool is -
y{B} = 1186 + 31.75x
For the same amount of water -
y{A} = y{B}
1600 + 20.25x = 1186 + 31.75x
1600 - 1186 = 31.75x - 20.25x
x = 36
Amount of water in each pool will be -
y = 1600 + 20.25 x 36
y = 2329 liters
Therefore, at 36 minutes, the amount of water in both pools will be same. In amount, it will be 2329 liters.
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Which statements are true? Check all that apply.
On a coordinate plane, point A is (2, 3), point B is (3, 2), point C is (negative 2, 2), point D is (negative 3, negative 3), point E is (0, 3), point F is (2, 0), and point G is (0, 0).
A is in Quadrant I.
B is on the x-axis.
C is in Quadrant I.
D is in Quadrant III.
E is on the x-axis.
F is on the x-axis.
G is on the y-axis.
Answer is A, D, F, G
Answer: On a coordinate plane, the quadrants are defined as follows:
Quadrant I: x-coordinate is positive, y-coordinate is positive
Quadrant II: x-coordinate is negative, y-coordinate is positive
Quadrant III: x-coordinate is negative, y-coordinate is negative
Quadrant IV: x-coordinate is positive, y-coordinate is negative
Based on this information, the following statements are true:
A is in Quadrant I, because its coordinates are (2, 3) and both x and y are positive.
D is in Quadrant III, because its coordinates are (negative 3, negative 3) and both x and y are negative.
F is on the x-axis, because its y-coordinate is 0.
G is on the y-axis, because its x-coordinate is 0.
The other statements are not true:
B is not on the x-axis, because its y-coordinate is not 0.
C is not in Quadrant I, because its x-coordinate is negative.
E is not on the x-axis, because its y-coordinate is not 0.
Step-by-step explanation:
Meredith orders three items from an online retailer. the first item will arrive with equal likelihood in one of the first through third days of feburuary. the second will arrive with equal likelihood in one of the second through fourth days of february, and the third will arrive with equal likelihood in one of the third through fifth days of february. if at most one item can be delivered in a given day, what is the probability that the first time is not the first to be delivered?
how do i go about this?
The probability that the first item is not the first to be delivered will be 1/3.
What is probability?Its fundamental concept is that someone will nearly surely occur. The proportion of positive events in comparison to the total of occurrences.
Then the probability is given as,
P = (Favorable event) / (Total event)
The likelihood that the main thing shows up on the principal day of February is 1/3.The likelihood that the subsequent thing shows up on the principal day of February is 1/3,The likelihood that the third thing shows up on the principal day of February is 0.The probability that one of the other two items arrives first will be given as,
p = 1/3 + 1/3
p = 2/3
The probability that the first item is not the first to be delivered will be given as,
q = 1 - p
q = 1 - 2/3
q = 1/3
The probability that the first item is not the first to be delivered will be 1/3.
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a crane has a 200-foot arm whose lower end is 5 feet off the ground. the arm has to reach the top of the dome 80 feet high. at what angle x should the arm be set?
Using the trigonometry ratio, at angle 50.81° should the arm be set.
We have to determine the angle x should the arm be set.
A crane has a 200-foot arm whose lower end is 5 feet off the ground.
The arm has to reach the top of the dome 80 feet high.
The length of crane arm = 200ft
The height of building = 160ft
The initial height of the crane = 5ft
As a result, the height of the building in relation to the crane can be expressed as;
h = 160ft - 5ft
h = 155ft
The angle x the crane makes with the horizontal can be expressed mathematically as;
sin x = opposite/hypothesis
sin x = 155ft/200ft
sin x = 0.775
Taking [tex]\sin^{-1}[/tex] on both side, we get
x = [tex]\sin^{-1}[/tex](0.775)
Using the calculator
x = 50.81°
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Evaluate each expression using the Order of Operations. -4(-1)+4
Answer: 8
Step-by-step explanation:
First you multiply -4(-1) a negative times a negative is a positive so that is positive 4 then you simply add 4 which equals 8
Jackson is working two summer jobs, making $10 per hour washing cars and $12 per hour landscaping. Last week Jackson worked a total of 14 hours and earned a total of $152. Determine the number of hours Jackson worked washing cars last week and the number of hours he worked landscaping last week
The number of hours Jackson worked washing cars last week is 8 hours
The number of hours Jackson worked landscaping cars last week is 6 hours
How to write the required equationThe problem is a simultaneous equation of two unknowns with two equations.
The equations are formed as follows
Jackson worked a total of 14 hours
let the washing cars be x and landscaping be yx + y = 14
Jackson earned a total of $152
$10 per hour washing cars and $12 per hour landscaping
10x + 12y = 152
The simultaneous equation
x + y = 14
10x + 12y = 152
using calculator to solve the equation we have that
x = 8 and y = 6
hence hours of washing cars is 8 hours while hour s of landscaping is 6 hours
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in the following equation , what happens to the value of y when the value of x is divided by 6 y=3/x
The value of y is multiplied by 6 when x is divided by 6
How to determine what happens to yFrom the question, we have the following parameters that can be used in our computation:
y = 3/x
Also, from the question we understand that
x is divied by 6
This means that the new equation is
y = 3/(x/6)
Evaluate
y = 6 * 3/x
This means that the new value of y is multiplied by 6
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The table shows the relationship between r and s, where s is the independent variable 1 2 3 3 4 5 6 1 6 هما الا 1 2 2 3 5 6 1 Which equation represents the relationship between r and s? F. Os = GOr=8- 6 HOs=r- 1. Or = 1/2
The relationship between r and s represents by the equation r = 1/6 s. So the option D is correct.
We have to determine which equation represents the relationship between r and s.
When we analysis the table we see that
r(1) = 1 × 1/6 = 1/6
r(2) = 2 × 1/6 = 1/3
r(3) = 3 × 1/6 = 1/2
r(4) = 4 × 1/6 = 2/3
r(5) = 5 × 1/6 = 5/6
r(6) = 6 × 1/6 = 1
So we can say that
r = s × 1/6
So, r = 1/6 s
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The complete question is:
The table shows the relationship between r and s, where s is the independent variable.
s 1 2 3 4 5 6
r 1/6 1/3 1/2 2/3 5/6 1
Which equation represents the relationship between r and s?
A. 1/6 r
B. s - 5/6
C. r - 5/6
D. r = 1/6 s
How many solutions can be found for the system of linear equations represented on the graph?
Responses
A one solutionone solution
B no solutionno solution
C infinitely many solutionsinfinitely many solutions
D two solutions
The graph has (c) infinitely many solutions
How to determine the number of solutionsFrom the question, we have the following parameters that can be used in our computation:
The graph
On the graph, we have two equations represented by
y = x + 2
-3x + 3y = 6
On the graph, we can see that the equations have the same line
This means that there are lots of solutions in the system i.e. infinite many solutions
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A new club sent out 252 coupons to boost sales for next years memberships. They provided 5 times as many potential members than existing members. How many coupons did they sent to existing members?
Answer:
42
Step-by-step explanation:
Let's call the number of coupons sent to existing members as "x".
We know that:
They provided 5 times as many potential members than existing members, meaning that they sent 5*x coupons to potential members.
The total number of coupons sent is 252
So we can write an equation:
x + 5x = 252
6x = 252
x = 252/6
x = 42
Therefore, they sent 42 coupons to existing members.
Answer: 42
Step-by-step explanation:
5x + x = 252
6x = 252
x = 42
existing members = 1x
1 x 42
= 42
researching hairstyle ideas for herself, when Rohan, her
older brother, appeared at her door.
"Veena, can you trim my hair? The basketball team is
taking pictures tomorrow."
Veena rolled her eyes playfully. "If I have to!" she
replied, already reaching for the scissors and trimmer she
kept in her dresser.
"Like you'd give up the opportunity!" he teased back,
disappearing into the living room.
All anyone had to do was mention needing a cut or
style and Veena would materialize. Family, friends, and
everyone on their Staten Island block knew Veena wanted
to run her own hair empire one day. She had gotten her
start in elementary school by working on her dolls and
graduated to actual people in middle school when her
brother agreed to a haircut on a dare. Before long, Veena
had transformed everyone's hair around her except one
person's her own. Veena's mother loved her long black,
wavy hair and had requested that she keep it that way.
Complete the sentences to
summarize the events in this part of
the story.
Everyone knows that Veena has a
of running a large hair
ss someday. She got her
hair
dream
promise
fear
s a child. Now, the only
person's hair she hasn't cut is her own
because
prefers it
S
her
long.
Veena has a dream of running her own hair empire one day. She started cutting hair as a child and has since transformed everyone's hair. Her mother loves her long, black, wavy hair and has requested that she keep it that way. Veena is already well on her way to making her dream come true.
What is a summary?A summary is a shortened version of the key ideas in an article, book, speech, or other type of literature. It is a concise repetition of the key ideas, conclusions, and/or facts contained in the original text. Summaries are frequently used to provide a fast summary of the essential points in a larger book, making it simpler to absorb the main concepts in less time.
Summarize the events of the story.Veena has a dream of running her own hair empire one day. She first started cutting hair as a child, working on her dolls. In middle school, her brother agreed to a haircut on a dare and before long she was transforming everyone's hair around her. The only person's hair she hasn't cut is her own, because her mother loves her long, black, wavy hair and has requested that she keep it that way. Everyone knows that Veena wants to have her own hair salon someday and she is already well on her way to making that dream come true.
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Determine the approximate ordered pair for f(x) =g(x).
=
○ (26,4)
O (18,4)
O (4.26)
○ (4,18)
-50
40
-30
-20
8
10
10
f(x)
g(x)
20
농
50
The approximate solution of the system of equations is given as follows:
(4, 26).
How to obtain the solution to the system of equations?We want to obtain the graphic solution for the system of equations, hence we obtain the point of intersection of the two equations.
For the point of intersection in this problem, we obtain the coordinates as follows:
x-coordinate of approximately 4, as it is less than the half way between 0 and 10.y-coordinate of 26, as it is a value between 20 and 30.This means that the correct option is given by the third option.
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Can someone help me with this please? I need help ASAP
A: Classify the triangle above by its sides
B: Classify the triangle above by its angles
C: Explain your answer to part a and b
6 Total || Part Total 100 John has walked 15% of the way home from school. If he has walked 200 meters so far, how far does he walk home from school? Percent 100
John will walk 1,333.33 meters home from school.
What is percentage?Percentage is a mathematical concept used to express a number as a fraction of 100. It is generally used to compare one number to another, in terms of its relative size. For example, if 30 out of 100 people have voted for a certain candidate, then the percentage of those who voted for that candidate is 30%.
Percentage can also be used to express a change in a value over time.
For instance, if the price of a product has increased from $10 to $15, then the percentage increase in the price is 50%.
Percentage can also be used to compare different groups of data. For instance, if an organization has ten male employees and five female employees, then the percentage of male employees is 66.67%.
Percentage is an important concept in the field of mathematics and is used to calculate the percentage of a whole or part of a whole.
To find the total distance John will walk home from school, you need to multiply 200 meters, which is the distance he has already walked, by 100%, which is the total amount of the journey home from school, and then divide that answer by 15%, which is the percentage of the journey he has already walked.
200 x 100/15 = 1,333.33
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you started a project on 9/29/2019. the project ended on 08/01/2022. how many working days did you have for the entire project?
You started a project on 9/29/2019. The project ended on 08/01/2022. So 1037 working days you have for the entire project.
Project Start Date - 09/29/2019
Project End Date - 08/01/2022
Ignore the end date
No. of days spent for project in 2019 = 94
September - 2, October - 31, November - 30 & December - 31
No. of days spent for project in 2020 = 366
No. of days spent for project in 2021 = 365
No. of days spent for project in 2022 = 212
January - 31, February - 28, March - 31, April - 30, May - 31, June - 30 & July - 31
Total number of days spent for the project are 1037 days.
2019 - 94
2020 - 366
2021 - 365
2022 - 212
The Project took 1037 working days for its completion from 09/29/2019 to 08/01/2022.
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The histograms display the frequency of temperatures in two different locations in a 30-day period.
A graph with the x-axis labeled Temperature in Degrees, with intervals 60 to 69, 70 to 79, 80 to 89, 90 to 99, 100 to 109, 110 to 119. The y-axis is labeled Frequency and begins at 0 with tick marks every one unit up to 16. A shaded bar stops at 2 above 60 to 69, at 4 above 70 to 79, at 12 above 80 to 89, at 6 above 90 to 99, at 4 above 100 to 109, and at 2 above 110 to 119. The graph is titled Temps in Desert Landing.
A graph with the x-axis labeled Temperature in Degrees, with intervals 60 to 69, 70 to 79, 80 to 89, 90 to 99, 100 to 109, 110 to 119. The y-axis is labeled Frequency and begins at 0 with tick marks every one unit up to 16. A shaded bar stops at 2 above 60 to 69, at 4 above 70 to 79, at 9 above 80 to 89, at 9 above 90 to 99, at 4 above 100 to 109, and at 2 above 110 to 119. The graph is titled Temps in Flower Town.
When comparing the data, which measure of variability should be used for both sets of data to determine the location with the most consistent temperature?
IQR, because Desert Landing is skewed
IQR, because Desert Landing is symmetric
Range, because Flower Town is skewed
Range, because Flower Town is symmetric
Range provides a precise measurement of variability for both sets of data because it compares the greatest and lowest values in a dataset.
It is a helpful measure of variability for comparing the constancy of temperature between Desert Landing and Flower Town because it is unaffected by skewness or symmetry.
A Histogram: What Is It?The graphic representation of data points arranged into user-specified ranges is called a histogram.
The histogram, which resembles a bar graph in appearance, condenses a data series into an intuitive visual by collecting numerous data points and organizing them into logical ranges or bins.
A histogram is a visual depiction of data distribution in statistics. The histogram is shown as a collection of neighboring rectangles, where each bar represents a certain type of data. Numerous fields use statistics, which is a branch of mathematics.
In a bar graph, the frequency is represented by the length of each bar, which are ranked from longest to shortest. To illustrate the relationship between two sets of data, scatter plots plot observations as points.
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Transport truck carries stereo computer and television parts
. The mass of the truck and the parts is 28 t
. The mass of the empty truck is 6 t
. The mass of the computer parts is 2 t less than the mass of television parts
. The mass of stereo parts double the mass of television parts
What is the mass of each type of parts?
The mass of television is 6t, the mass of computer is 4t and the mass of stereo is 12t.
We have to determine the mass of each type of parts.
A transport truck transports television, computer, and stereo components
1. The mass of the truck and the parts is 28t.
2. The mass of the empty truck is 6t.
3. The mass of the computer parts is 2t less than the mass of television parts.
4. The mass of stereo parts double the mass of television parts.
truck = 6t
part = stereo + television + computer
computer = television - 2t
stereo = television × 2
truck + parts = 28t
part = 28t - 6t
part = 22t
part = computer + television + stereo
part = television - 2t + television + television × 2
part = 4 × television - 2t
22t = 4 × television - 2t
4 × television = 24t
television = 6t
computer = 6t -2t = 4t
stereo = 6t × 2 = 12t
television = 6t
computer =4t
stereo = 12t
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The table represents a linear relationship. x −1 0 1 2 y 2 0 −2 −4 Which of the following graphs shows this relationship? Group of answer choices graph of a line passing through the points negative 2 comma negative 4 and 0 comma 0 graph of a line passing through the points negative 2 comma negative 1 and 0 comma 0 graph of a line passing through the points negative 2 comma 4 and 0 comma 0 graph of a line passing through the points negative 2 comma 1 and 0 comma 0
The graph of the linear function y = -2x is given by the image presented at the end of the answer.
How to define the linear function?The slope-intercept definition of a linear function is given as follows:
y = mx + b.
In which:
m is the slope, representing the rate of change.b is the intercept, representing the value of y when x = 0.From the table, when x increases by 1, y decays by 2, hence the slope m is given as follows:
m = -2.
When x = 0, y = 0, hence the intercept b is given as follows:
b = 0.
Hence the function is:
y = -2x.
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Need help please I’m stuck on this
The average rate of rain displayed in the graph is 2.5 inches per day.
1. The C.R.O.C is 2.5.
2. The equation that can be used to find y, is y = 2.5x.
3. Yes, this is a proportional relationship.
4. Yes there is a C.O.P of 2.5.
5. The unit rate is 2.5 inch rain in 1 day.
6. The amount of rain that would fall in 15 days is 37.5 inches.
What is a graph?
In mathematics, a graph is a visual representation or diagram that shows facts or values in an ordered way.
The relationships between two or more items are frequently represented by the points on a graph.
In the graph the x-axis represents the number of days.
In the graph the y-axis represents the rain in inches.
The first point is (2,5) which tells that in 2 days the rain fell 5 inches.
So, the average rain will be 5/2 = 2.5 inches.
CROC stands for constant rate of change. The formula for constant rate of change is -
= (y2 - y1)/(x2 - x1)
= (10 - 5)/(4 - 2)
= 5/2
= 2.5
Therefore, the constant rate of change is 2.5
The first point in the graph is (2,5), the x-intercept being 2 and y-intercept being 5. The CROC is obtained as 2.5.
So the equation for y can be given as -
y = 2.5 x
A proportional relationship between two variables x and y is when one variable is always some constant value multiplied by the other.
So, yes the relationship between the x and y value in this graph is proportional.
The “constant of proportionality” is the name given to this constant. All proportional relationships can be represented by the equation y =kx , where k is the proportionality constant.
Since, the equation is y = 2.5x.
Therefore, the constant of proportionality is 2.5.
The unit rate is 2.5 inches of rain in one day.
The amount of rate that would fall in 15 days is -
y = 2.5 x
y = 2.5 (15)
y = 37.5
Therefore, the amount of rain will be 37.5 inches.
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What is the quotient of 7.584x 10^6 and 7.9x 10^2
Answer: the quotient is 957.07 x 10^4 which is equivalent to 957,070
Step-by-step explanation:
Solve the equation 3x - 4/5 = - 1/2 What is the value of x? Enter your answer as a fraction, formatted like this: 42/53
HELP ME!!! QUICK!!
Answer:1/10 hope im right :)
Step-by-step explanation:
Answer: 1/10
Answer step by step:
1) 3x - 4/5 = - 1/2
2) 3x = -1/2 + 4/5 (move -4/5 to the right side of the equation and inverse the negative sign)
3) 3x = 0.3 (add the values)
4) 3x / 3 = 0.3 / 3 (divide both side with 3 to get rid of the constant value)
5) x = 0.1
6) x = 1/10 (the 1 in 0.1 is in the tenth place so we convert it to 1/10)
eight rooks are placed in distinct squares of an 8 x 8 chessboard, with all possible placements being equally likely. in how many different ways can all the rooks be placed so that they are safe from each other i.e, that there is no row or column with more than one rook?
There are 5040 ways to place 8 rooks on an 8 x 8 chessboard.
A permutation is a systematic grouping of objects or numbers. Combinations allow you to select objects or numbers from a group of items without having to worry about the order in which they were collected. Contrary to permutations, when selecting components from a collection using the combination method, the order of selection is unimportant.
There are 8! ways to place 8 rooks on an 8 x 8 chessboard such that no two rooks are in the same row or column.
8! = 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1
= 5040
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could someone help me Q1
The complete statement is Δ MTS ≅ Δ RTS
What is Congruence?In geometry, two figures or objects are congruent if they have the same shape and size, or if one has the same shape and size as the mirror image of the other.
Given : Two triangles MTS and RTS
now in the triangles MTS and RTS
we have OM=RT , MN=SR , ON=ST
And therefore By SSS property of two triangles we can deduce that the two triangles are congruent.
Hence, The complete statement is Δ MTS ≅ Δ RTS
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PLEASE HELP 20 PTS!!!
True or false
The following graph represents a maximum:
f(x)=3x^2+2
Answer: I think true
Step-by-step explanation: guess
children aged 12years,9 years and 4 years shareR500 in the same ratio as their ages
If children aged 12years,9 years and 4 years shareR500 in the same ratio as their ages. They each got R240, R180,R80.
How to find the amount they each got?Total number of years = 12 years + 9 years + 4 years
Total number of years = 25 years
Now let find the amount they each got
12 years
Shares = 12/25×500
Shares = R240
9 years
Shares = 9/25×500
Shares = 180
4 years
Shares =4/25×500
Shares = 80
Therefore they each got R240, R180,R80.
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The complete question is:
Children aged 12 years,9 years and 4 years share R500 in the same ratio as their ages .How much do they each get?
An equation is shown below:
3 (2 x - 7) = 3
Part A: How many solutions does this equation have?
Part B: What are the solutions to this equation? Show your work
The solution of the equation 3(2x - 7) = 3 is x = 4. The equation has only one solution.
What is an equation?An equation is a mathematical expression that shows that two mathematical expressions are equal. Equation shows the relationships between variables, numbers and constant.
Therefore, let's solve the equation 3(2x - 7) = 3 as follows
3(2x - 7) = 3
Open the parenthesis
3(2x - 7) = 3
6x - 21 = 3
add 21 to both sides of the equation
6x - 21 = 3
6x - 21 + 21 = 3 + 21
6x = 24
divide both sides of the equation by 6
6x / 6 = 24 / 6
x = 4
Therefore, the equation has one solution which is x = 4.
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Help me write an Original oratory speech
Answer: I will help you, but not write because it depends on the topic
Introduction: Begin by grabbing your audience's attention with an interesting fact, story, or statistic. Then, introduce the main topic of your speech and provide some background information on it.
Body: Divide the body of your speech into several main points, each of which will address a different aspect of the topic. Use evidence, examples, and anecdotes to support your points and make them more persuasive.
Counterargument: Address any potential objections or counterarguments to your main points. This will demonstrate that you have considered multiple perspectives and will make your argument more convincing.
Conclusion: Sum up your main points and reiterate the importance of the topic. End with a strong call to action or a memorable quote.
Practice: Practice delivering your speech in front of a mirror or with friends/family to become more comfortable with the material and delivery.
Here's an example of an introduction for an Original Oratory speech on the topic of the benefits of solar energy:
"Imagine a world where our energy needs are met by a clean, renewable source that never runs out. That world is not just a dream – it's a reality that we can create by embracing solar energy. Today, I want to talk to you about the many benefits of solar energy and why it's time for us to take a closer look at this powerful technology. From reducing our dependence on fossil fuels to creating jobs and driving economic growth, solar energy has the power to change our world for the better. So, let's explore the reasons why solar energy is the energy of the future."
Please help. I'm not sure how to solve these.
In a large corporation, the times that it takes its employers to commute from home to office are normally distributed with a mean commute time of 29 minutes and a standard deviation of 7 minutes. Using this information, answer the following questions.
What is the probability that a randomly selected employee will take less than 20 minutes to commute to work?
If an employee can drive to work in 37 minutes, at what percentile would his commuting time rank?
What percentage of the employees take between 25 and 45 minutes to drive to work?
If an employee drives an hour to get from home to work, is that considered an unusually long commute?
The required probability and percentage for the employee to commute from home to office is :
a. probability for less than 20 minutes is 0.09852.
b. percentile for 37 minutes is 64%
c. percentage of the commute between 25 and 45 minutes is 70.49%.
Normally distributed data for the employers to commute from home to office :
Mean 'μ' = 29 minutes
Standard deviation 'σ' = 7 minutes
let 'X' represents the time taken by employee to commute.
a. Employee take less than 20 minutes to commute
Probability of taking time less than 20 minutes is:
P ( X < 20 )
= P [ ( X -μ )/ σ < ( 20 - 29)/7 ]
= P( Z < -9/7)
= P( Z < -1.29 )
= 0.09852
b. Employee take 37 minutes then percentile is :
P ( X =37 )
= P [ ( X -μ )/ σ = ( 37 - 29)/7 ]
= P( Z = 8/7)
= P( Z = 1.14)
= 0.64
= 64%
c. P ( 25 < X < 45 )
=P ( 25 -29 /7 < X -μ /σ < 45 -29 /7 )
=P ( -4/7 < Z < 16/7 )
= P( -0.571 < Z < 2.29 )
= P ( Z <2.29 ) - [1 - P( Z < 0.571 ) ]
= 0.9889 - ( 1 - 0.7160 )
= 0.7049
= 70.49%
Therefore, when the employee commute from home to office :
a. Probability of commuting less than 20 minutes is 0.09852.
b. Percentile of taking 37 minutes is 64%
c. Percentage between 25 and 45 minutes is 70.49%.
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