the probability that the sample contains two white balls and one green ball is 21/40.
In probability and statistics, an urn problem is an idealized mental exercise in which some objects of real interest (such as atoms, people, cars, etc.) are represented as colored balls in an urn or other container. One pretends to remove one or more balls from the urn; the goal is to determine the probability of drawing one color or another, or some other properties.
Total number of balls: 7 White and 3 Green = 10 balls
Cases for three balls are drawn at random:
Selection of 3 balls from 10 balls = [tex]^1^0C_3[/tex]
Case A: 1 White and 2 Green = [tex]\frac{^7C_1 * ^3C_2}{^1^0C_3} = \frac{7*3}{120} = \frac{21}{120} \\[/tex]
Case B: 2 White and 1 Green = [tex]\frac{^7C_2 * ^3C_1}{^1^0C_3} = \frac{21*3}{120} = \frac{63}{120}[/tex]
Case C: 3 White and 0 Green = [tex]\frac{^7C_3 * ^3C_0}{^1^0C_3} = \frac{28*1}{120} = \frac{28}{120}[/tex]
Case D : 0 White and 3 Green = [tex]\frac{^7C_0 * ^3C_3}{^1^0C_3} = \frac{1*1}{120} = \frac{1}{120}[/tex]
The probability that the sample contains two white balls and one green ball = Case B
So, the probability that the sample contains two white balls and one green ball = 63/120 = 21/40
Therefore, the probability that the sample contains two white balls and one green ball is 21/40.
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the probability that the sample contains two white balls and one green ball is 21/40.
In probability and statistics, an urn problem is an idealized mental exercise in which some objects of real interest (such as atoms, people, cars, etc.) are represented as colored balls in an urn or other container. One pretends to remove one or more balls from the urn; the goal is to determine the probability of drawing one color or another, or some other properties.
Total number of balls: 7 White and 3 Green = 10 balls
Cases for three balls are drawn at random:
Selection of 3 balls from 10 balls = [tex]^1^0C_3[/tex]
Case A: 1 White and 2 Green = [tex]\frac{^7C_1*^3C_2}{^1^0C_3} =\frac{7*3}{120}= \frac{21}{120}[/tex]
Case B: 2 White and 1 Green = [tex]\frac{^7C_2*^3C_1}{^1^0C_3} =\frac{21*3}{120}= \frac{63}{120}[/tex]
Case C: 3 White and 0 Green = [tex]\frac{^7C_3*^3C_0}{^1^0C_3} =\frac{35*1}{120}= \frac{35}{120}[/tex]
Case D : 0 White and 3 Green = [tex]\frac{^7C_0*^3C_3}{^1^0C_3} =\frac{1*1}{120}= \frac{1}{120}[/tex]
The probability that the sample contains two white balls and one green ball = Case B
So, the probability that the sample contains two white balls and one green ball = 63/120 = 21/40
Therefore, the probability that the sample contains two white balls and one green ball is 21/40.
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I give up I’m so confuse rn pls help answer these
A
Which of the following does
not have a horizontal line of
symmetry?
E
B
A
C
O
Answer:
A
Step-by-step explanation:
In math, symmetry is when an object, thing, etc is identical on both ends. Split a horizontal(left to right) line through the middle of each letter. Every letter has identical top and bottom sides except for A.
Therefore, the answer is A.
If 0.6 J of work is needed to stretch a spring from 7 cm to 9 cm and another 1 J is needed to stretch it from 9 cm to 11 cm, what is the natural length (in cm) of the spring?
We need to know about concept of work done on spring to solve the question.The natural length of the spring is 5cm.
We will need to make assumptions to solve this problem, we will assume that the natural length of the srping is [tex]x_{0}[/tex] and the work done to stretch the spring from it's natural length to a specific length is given by
W=[tex]\frac{1}{2} k(x-x_{0} )^{2}[/tex] , where W is the work done, x is the final length of the spring
We have to find out the work done to get to 7cma nd 9cm separately and then subtract one from the other to get the work done to stretch from 7cm to 9cm. We repeat the process for 9cm and 11cm and we will find the final result which is the natural length.
W=[tex]\frac{1}{2} k(7-x_{0} )^{2}[/tex]
W=[tex]\frac{1}{2} k(9-x_{0} )^{2}[/tex]
[tex]\frac{1}{2} k(9-x_{0} )^{2} -\frac{1}{2} k(7-x_{0} )^{2} =0.6\\(9-x_{0} )^{2} - (7-x_{0} )^{2} =\frac{1.2}{k}[/tex]...(i)
W=[tex]\frac{1}{2} k(9-x_{0} )^{2}[/tex]
W=[tex]\frac{1}{2} k(11-x_{0} )^{2}[/tex]
[tex]\frac{1}{2} k(11-x_{0} )^{2} -\frac{1}{2} k(9-x_{0} )^{2} =1\\(11-x_{0} )^{2} -(9-x_{0} )^{2} =\frac{2}{k}[/tex]...(ii)
Dividing equation (ii) by (i)
[tex]\frac{(11-x_{0} )^{2} -(9-x_{0} )^{2} }{(9-x_{0} )^{2} -(7-x_{0} )^{2} } =\frac{2}{1.2} \\\frac{(20-2x_{0} )2}{(16-2x_{0})2 } =\frac{1}{0.6} \\12-1.2x_{0} =16-2x_{0} \\0.8x_{0} =4\\x_{0} =5[/tex]
Thus using the concept of work done to stretch a spring we get the natural length of the spring which is 5cm.
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Professor Halen has 184 students in his college mathematics lecture class. The scores on the midterm exam are normally distributed with a mean of 72 and standard deviation of 9.
a. How many students in the class can be expected to receive a score over 60?
b. What percent of the class is expected to receive a score between 82 and 90?
Using the normal distribution, it is found that:
a) 167 students in the class can be expected to receive a score over 60.
b) 11.07% of the class is expected to receive a score between 82 and 90.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean represented by [tex]\mu[/tex] and standard deviation represented by [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
It measures how many standard deviations the measure is above(in case the score is positive) or below(in case the score is negative) the mean. Looking at the z-score table, the p-value associated with the z-score is found, which represents the percentile of the measure X.The mean and the standard deviation for the scores are given, respectively, by:
[tex]\mu = 72, \sigma = 9[/tex]
The proportion of students who scored over 60 is given by one subtracted by the p-value of Z when X = 60, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Z = (60 - 72)/9
Z = -1.33.
Z = -1.33 has a p-value of 0.0918.
1 - 0.0918 = 0.9082.
Out of 184 students:
0.9082 x 184 = 167.
167 students in the class can be expected to receive a score over 60.
For item b, the proportion is the p-value of Z when X = 90 subtracted by the p-value of Z when X = 82, hence:
X = 90:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Z = (90 - 72)/9
Z = 2.
Z = 2 has a p-value of 0.9772.
X = 82:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Z = (82 - 72)/9
Z = 1.11
Z = 1.11 has a p-value of 0.8665.
0.9772 - 0.8665 = 0.1107.
Hence:
11.07% of the class is expected to receive a score between 82 and 90.
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7 Write down two square roots for each of these numbers. b 36 d 196 e 225 f 400
The square roots of 36,196,225 and 400 are ±6,±14,±15 and±20
There exits two square roots of any number one with positive sign and one with negative sign
The first number we have is 36
The square roots of 36 = ±√36 = ±6 or it can be written as 6 and -6
The second number we have is 196
The square roots of 196 = ±√196 = ±14 or it can be written as 14 and -14
The third number we have is 225
The square roots of 225 = ±√225 = ±15 or it can be written as 15 and -15
The fourth number we have is 400
The square roots of 400 = ±√400 = ±20 or it can be written as 20 and -20
Hence, the square roots of 36,196,225 and 400 are ±6,±14,±15 and±20
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The table shows the linear relationship between the playing time in minutes of high-definition videos and the file size of these videos in megabytes (MB) What is the rate of change of this function?
180
60
120
30
the slope of the linear equation is 120, then the correct option is the third counting from the top.
What is the rate of change of this function?For any linear equation with two points (a, b) and (c, d), the slope (or rate of change) of that line is given by:
s = (d - b)/(c - a)
So here we can use the first two points so we get:
(0.5, 60)
(1.5, 180)
With these two points we will get the slope:
s = (180 - 60)/(1.5 - 0.5) = 129
We conclude that the slope is 120, then the correct option is the third counting from the top.
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Therefore, if Yolanda deposits $1,900 at the end of each six months for 2 years in a savings account earning 8% interest compounded semiannually, to the nearest cent, she can expect to have
$
.
The amount that Yolanda can expect to have in her account at the end of 2 years is $8,068.28.
What is the future value of the amount deposited?The amount of money that Yolanda deposits twice in a year represents an annuity. An annuity is a series of payment that is made over a specified period of time. An ordinary annuity is when payment is made at the end of each period and not at the beginning of the period. Yolanda's deposit is an ordinary annuity.
When the amount deposited in an account earns interest that is compounded semi-annually, it means that both the amount that is invested and the interest that is already accrued increases in value two time in a year, every six month.
The formula that can be used to determine the future value of the amount that was deposited in the account is:
Future value = amount deposited x annuity factor
Annuity factor = {[(1+r)^n] - 1} / r
Where:
r = interest rate : 8 / 2= 4%n = number of periods : 2 x 2 = 41,900 x[ {(1.04^4) - 1} / 0.04] = $8,068.28
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The cost for a salad depends on its weight, x, in ounces, and is described
by c(x) = 4.5+ 0.32x. Describe how c(x) is related to its parent function and
interpret the function in the context of the situation.
The relationship c(x) = 4.5+ 0.32x it is a linear relationship.
The factor 0.32 is used to reduce the cost of the weight before adding to the fixed cost of 4.5
Given data
c(x) = 4.5+ 0.32x
How c(x) is related to its parent functionThe relationship c(x) = 4.5+ 0.32x it is a linear relationship. It can be compared to the equation of a straight line which is
y = mx + c
m is the slope and c is the y intercept
The comparison shows that
y = c(x)
c = 4.5
m = 0.32
Interpreting the function in the context of the situationIf the cost is related with the relationship c(x) = 4.5+ 0.32x.
it can be seen that even when there is no weight or no salad that is at x = 0 the cost is c = 4.5.
This means that there is a fixed cost of 4.5 for any salad weight, in ounces bought.
The factor 0.32 is used to reduce the cost of the weight before adding to the fixed cost of 4.5.
The 0.32 is a reduction factor because the value is less than 1 and will reduce any number it multiplies.
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The width of a rectangle measures (9v-3)(9v−3) centimeters, and its length measures (10v+10)(10v+10) centimeters. Which expression represents the perimeter, in centimeters, of the rectangle?
The expression which represents the perimeter, in centimetres of the rectangle as described in the task content is;
What is the expression which represents the perimeter, in centimeters, of the rectangle?According to the task content, the expression which represents the perimeter, in centimetres of the rectangle as described in the task content is to be determined.
Since the perimeter of a rectangle is given by the formula;
Perimeter = 2(l +w).
where; l = (10v +10) and w = (9v -3)
Therefore, the expression which represents the perimeter is;
P = 2(10v +10 + 9v -3)
P = 2 (19v +7)
P = 38v +14.
Ultimately, the expression which represents the perimeter, in centimetres of the rectangle as described in the task content is; 38v +14.
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given line m graphed on the grid shown which of the following would be the slope of a line perpendicular to m
The correct option is (3) 5/2
The slope of a line perpendicular to m is 5/2.
What is slope of a line ?The slope of a line can be find by dividing its vertical change, or the rise of line by its horizontal change or the run . No matter which two locations on the line you choose, the slope of a line is always constant (it never varies). The word "slope" is represented by the letter "m," and it describes how steep a line is.
In the given question,
from the graph take any two points on the line say point A (2,1) and point B (-3,3)
now using the slope formula,
slope = m1 = [tex]\frac{delta \ Y}{delta \ X} = \frac{y2-y1}{x2-x1}[/tex]
=> m1 = [tex]\frac{3-1}{-3-2} = - \frac{2}{5}[/tex]
Now, for perpendicular lines:
m1.m2 = -1
=> m2 = 5/2
Thus, slope of a line perpendicular to m is 5/2.
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The complete question is:
Given line m graphed on the grid shown, which of the following would be the slope of a line perpendicular to m ?
(1) -3 /2
(2) 7/3
(3) 5/2
(4) -3/4
Trashia's bedroom is 11 feet by 11 feet. She has chosen a carpet which costs $33.05 per square yard. This includes installation. Determine the cost to carpet her room. Use the dimensional analysis method (use units in your calculations).
The cost to carpet the bedroom of size 11 feet × 11 feet will be equal to $1332.90.
What is area of rectangle ?
Area of rectangle is the region occupied by a rectangle within its four sides or boundaries.
It is given that size of bedroom is 11 feet by 11 feet.
Carpet costs $33.05 per square yard.
Firstly, we need to find out the the area of bedroom in feet. The room has the shape of a rectangle.
We know that , the area of rectangle is given by :
A = Length x Width.
So ,
Area of room will be :
= 11 x 11
= 121 square feet
Convert this area of the room in square feet to square yards.
We know that , 1 feet = 1/3 yards
So , 121 square feet will be :
= 121 /3
= 40.33 square yards
So , the cost to carpet the bedroom will be :
= 40.33 x $33.05
= $1332.90
Therefore , the cost to carpet the bedroom of size 11 feet × 11 feet will be equal to $1332.90.
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Please show work ThankYou very much 25 points to whoever does it
Answer: 3 answer
Step-by-step explanation:
Suppose you make $5 an hour as a dog walker. Let h represent the number of hours you work in a week. Write an expression that represents the amount of money you earn in a week and evaluate it for h = 20.
Answer:
e = 5h
$100
Step-by-step explanation:
Let e = earnings
e = 5h
For h = 20,
e = 5h = 5(20) = 100
Answer:
$ 100
Step-by-step explanation:
1 hour = $ 5
h (hours worked in a week) = 20 hrs
EXPRESSION: amount of money earned in a week = h × 5
EVALUATION: amount of money earned in a week = 20 × 5
amount of money earned in a week = $ 100 ... answer
hope that helps...
wh...
>
<
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Equivalent ratios with equal groups
Use the following image to complete the sentences describing the ratio of windows with
penguins to total windows.
There are
windows with a penguin for every 18 total windows.
There is 1 window with a penguin for every
total windows.
Second blank is 6 windows for every 1 penguin
given,
there are _18_ windows for every 3 penguins.
There are _6_ windows for every 1 penguin.
its is already given that 3 penguins = 18 windows,
the first blank is 18
To get number of windows for 1 penguin, we divide 18 by 3,
18/3=6
therefore second blank is 6 windows for every 1 penguin.
Window functions—otherwise known as weighting functions, tapering functions, functions—are mathematical functions that are zero-valued outside the chosen interval. They are well established as a vital part of digital signal processing.
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A water bird is flying 11 feet above the surface of a pond.
It dives 15 feet down and then rises 3 feet to catch a fish.
What is the new position of the bird relative to the
surface of the water?
The bird is 1 feet below the pond relative to the surface of the water.
It is given that the bird is flying 11 feet above the pond.
So, the distance between flying bird and surface of pond = 11 Feet
Dive :
Plunge steeply downward through the air or plunge head first into water.
After diving 15 feet down, it means that the bird is 4 feet under the pond as bird was flying 11 feet above the surface of pond.
So, the distance between surface of pond and the bird after diving down = 4 Feet
After that, it says that bird rises 3 feet to catch the fish,
So, after rising 3 feet above in the pond the distance between surface of pond and the bird is 1 feet.
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Evaluate the expression. Check all possible sets that
the solution may belong in.*
√0+7
*More than one answer may be correct; mark all that apply.
-rational
-integers
-real
-whole
-natural
-irrational
-none of these
The possible sets of the solution of the expression given as √0 + 7 are integer, whole number, natural number, rational number and real numbers
How to determine the possible set of the solution?The expression is given as
√0 + 7
Start by evaluating the radical expression
So, we have
√0 + 7 = 0 + 7
Continue by evaluating the sum of the terms
So, we have
√0 + 7 = 7
The above implies that the result of the expression √0 + 7 is 7
The sets the number 7 belong to are:
The number 7 is an integer because it does not have any decimal pointThe number 7 is a whole number because it does not have any decimal point and it is not negativeThe number 7 is a natural number because it does not have any decimal point and it is greater than 0The number 7 is a rational number because it can be expressed as a fraction of integersThe number 7 is a real number because it does not have any imaginary partHence, the possible sets of the solution of the expression given as √0 + 7 are integer, whole number, natural number, rational number and real numbers
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F(x) = 2x-6 and f(7) -9
Answer:
-1
Step-by-step explanation:
Plug 7 in for wherever there's an "x."
f(x) = 2(7) - 6
f(x) = 14 - 6
f(x) = 8
Now subtract 9 from 8.
8 - 9 = -1
15. Find the following bases.
a. 8% of ? = 20
b. 75% of ? = 30
c. 20% of ? = 45
d. 150% of ? = 36
Solve: 5,449 ÷ 220 Show the remainder as a fraction.
the remainder as a fraction= 49
Solution :
Divide two numbers, a dividend and a divisor, and find the answer as a quotient with a remainder. Learn how to solve long division with remainders or practice your own long division problems and use this calculator to check your answers.
Long division with remainders is one of two methods of doing long division by hand. It is somewhat easier than solving a division problem by finding a quotient answer with a decimal. If you need to do long division with decimals use our Long Division with Decimals Calculator.
Long Division:
Long Division is a method for dividing large numbers, which breaks the division problem into multiple steps following a sequence. Just like the regular division problems, the dividend is divided by the divisor which gives a result known as the quotient, and sometimes it gives a remainder too. Let us learn more about the long division method along with its steps and examples in this article.
5549 divided by 220 =
[tex]\frac{5549}{220} = 25*220+49\\\\\\so , quotient = 25\\divisor = 220\\reminder = 49\\\\divided = 5549[/tex]
the remainder as a fraction= 49
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Answer:
C 24 169|220
Step-by-step explanation:
I'm on the quiz
Simplify 1,999,9990.
The value of 1,999,999 with an exponent of 0 is 1,999,999 × 10⁰
What is an exponent?Exponentiation is a mathematical process that involves the base b and the exponent or power n. It is represented as bn and is pronounced as "b to the n."
Knowing that every number raised to the power of zero equals one is necessary before we can simplify using a zero exponent. Hence:
1,999,999 = 1,999,999 × 1
Since 1 can be expressed as 10⁰, the value becomes:
1,999,999 = 1,999,999 × 10⁰
Therefore, the value of 1,999,999 with an exponent of 0 is 1,999,999 × 10⁰.
The complete question is given below:-
Simplify 1,999,999 with an exponent of 0
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(100 POINTS!!! NEED HELP, PLEASE HURRY!!) Valerie estimates that a used vehicle will require regular maintenance every 3 months. The average costs for this is $45. The insurance premiums are estimated at $100 per month. She saves $100 per month for tires and unexpected repairs since there is no warranty on the used vehicle. The interest rate is 11% to finance the vehicle. (Interest rates are traditionally higher on used vehicles.) Valerie can afford $400 per month for four years to buy a vehicle. Excluding tax, tag, and title, approximately what is the most Valerie can pay for a vehicle?
Answer Valerie can afford 21,312 car
Step-by-step explanation:
8d+14 awnser needed
Answer:
22d
Step-by-step explanation:
Write the domain and range of the function using interval notation.
The domain of the function is -5 ≤ x < 3 and the range is 0 ≤ y ≤ 2
How to determine th domain and range of the function using interval notation?We have the following endpoints on the graph of the function;
(x, y) = Closed (-5, 2)
(x, y) = Open (3, 2)
Minimum y = 0
Remove the y values to determine the domain
x = Closed -5
x = Open 3
The closed statement represents the inequality ≤, while the closed statement represents the inequality < or >
So, we have
Domain = -5 ≤ x < 3
Also, we have:
(x, y) = Closed (-5, 2)
(x, y) = Open (3, 2)
Minimum y = 0
Remove the x values to determine the range
x = Closed 2
x = Open 2
Minimum y = 0
The above means that the y value does not include a negative value
So, we have
Range = 0 ≤ y ≤ 2
Hence, the domain of the function is -5 ≤ x < 3 and the range is 0 ≤ y ≤ 2
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How are the values in the
ordered pairs affected by the translation?
In arithmetic, a shape is translated when it is moved up, down, left or right. The translated shapes are congruent to the original shapes because they appear to be the same size. Just one or more of their routes have been changed. No changes to the shape are made because it is simply being moved from one location to another.
By utilizing the aforementioned guidelines, we can move the provided graph to the left, right, up, or down and graph the translated graphs. The coordinates of some points on a graph can be used to translate a graph as an alternative to this. Translation f(x + k) + C for a function graph To get the new x and y coordinates of each point when the graph of the function f(x) is supplied, simply select a few key spots on the graph (where the shape is changing or turning) and proceed as follows.
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a. Write an inequality that represents the numbers that are not solutions of x+3.8>11.3 .
Inequality:
Question 2
b. Graph the inequality from part (a).
Inequality that represents the coordinates that are not the solutions of this inequality is x < 7.5. The graph of the inequality is attached at the end.
What are the various operators used in inequalities for comparison?The various operators used in inequalities for expression are -
greater than - ' > 'less than - ' < 'greater than or equal to - ' ≥ 'less than or equal to - ' ≤ 'Given is a inequality in one variable which is → x + 3.8 > 11.3.
PART - A
The inequality that represents the coordinates that are not the solutions of this inequality is -
x + 3.8 < 11.3
or
we can simplify it to get -
Subtract 3.8 from both sides -
x + 3.8 - 3.8 < 11.3 - 3.8
x < 7.5
PART - B
In order to plot the graph of this inequality, firstly we will plot the line of equation -
x = 7.5.
Since, the inequality is strict, make a dashed line to represent the equation.
Take the coordinates of origin O(0,0), and substitute it in the inequality -
0 < 7.5
which is true. Therefore, we will shade the complete side where origin lies.
The graph of the inequality is plotted an attached with the answer.
Therefore, inequality that represents the coordinates that are not the solutions of this inequality is x < 7.5. The graph of the inequality is attached at the end.
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A woman is 43 years old, and her daughter is 15 years old. How many years will
it be before the woman's age is just twice her daughter's?
Answer:
13.
Step-by-step explanation:
1) if the required number of years is 'x', then it is possbile to make up the equation:
43+x=2(15+x);
2) finally, x=13 [years].
solve the following simultaneous equation graphically 2x-y=1 and 3x+y=9
The solution to the system of linear equations is (x, y) = (2, 3).
How to solve graphically a system of linear equation
Graphic methods are useful to solve systems of two linear equations with two variables, as it is seen in the statement of the problem. In accordance with geometry, a line can be constructed by knowing the coordinates of two distinct points on Cartesian plane. First, rewrite each linear equation into its explicit form:
y = 2 · x - 1 (1)
y = - 3 · x + 9 (2)
Second, look for two points lying on each line:
y = 2 · x - 1
(0, - 1) and (1, 1)
y = - 3 · x + 9
(0, 9) and (- 3, 6)
Third, plot the points on a Cartesian plane and pass each line through corresponding pair of points. The result is presented by the image attached below.
The solution to this system is the point of intersection of the two lines. The point of intersection is (2, 3).
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Problem Solving
6. Sandi's school has 1,030 students. If
Karla's school had 43 more students, it
would have 3 times as many students as
Sandi's school. How many students are in
Karla's school?
Help Please I will mark Brainliest
Answer:
the first question is multipleling or division
the second one js given
the third one commutative property
the forth one is disturve property
last one is addition or sub
Answer:
Given, Distributive Property, Addition or Subtraction Property of Equality, Multiplication or Division Property of Equality, Commutative Property
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how to simplify 5(2x-8) using distributive property
Answer:
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Step-by-step explanation:
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The formula for the distributive property is expressed as, a × (b + c) = (a × b) + (a × c); where, a, b, and c are the operands. Here, the number outside the brackets is multiplied with each term inside the brackets and then the products are added.