Probability that an ace is pulled from the deck = A/T=4/52=1/13
52 cards are there in all.
Four aces are found in all of the card A's.
Thirteen spades in all.
Probability that an ace is pulled from the deck = A/T=4/52=1/13
likelihood that a spade will be the next card drawn =S/T=13/52=1/4
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charlyn walks completely around the boundary of a square whose sides are each 55 km long. from any point on her path she can see exactly 11 km horizontally in all directions. what is the area of the region consisting of all points charlyn can see during her walk, expressed in square kilometers and rounded to the nearest whole number?
The area of the region consisting of all the points Charlyn can see during her walk is equal to, A = 4840 km.
Charlyn is walking around the boundary of square A, which is 55 km long, and she has a horizontal vision of 11 km.
So as she walks around the square of 55 km, let there be another square B which lies outside square A, which is created due to her 11 km field of vision.
length of sides of square B = 55+(2×11) which is equal to 77 km.
And as she walks around the square of 55 km, let there be yet another square C which lies inside square A, which is created due to her 11 km field of vision.
length of sides of square C = 55-(2×11) which is equal to 33 km.
The area that Charlyn can see throughout her walk is equal to,
A = Area of square B - Area of square C.
The area of square B = Side² = 77² = 5929.
The area of square C = Side² = 33² = 1089.
A = 5929 - 1089.
A = 4840 km.
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A candy box is made from a piece of cardboard that measures by inches. Squares of equal size will be cut out of each corner. The sides will then be folded up to form a rectangular box. What size square should be cut from each corner to obtain maximum volume?.
Using the concept of Application of Derivatives(A.O.D),we got 4.79 inches will be the square size for making the volume of candy box maximum.
A candy box is made from a piece of a cardboard that measures 43 × 23 inches.
Let squares of equal size will be cut out of each corner with the measure of x inches.
Therefore, measures of each side of the candy box will become
Length = (43 - 2x)
Width = (23 - 2x)
Height = x
Now we have to calculate the value of x for which volume of the box should be maximum.
Volume (V) = Length×Width×Height
=>V = (43 -2x)×(23 - 2x)×(x)
=>V= [(43)×(23) - 46x - 86x + 4x²]×x
=>V= [989 - 132x + 4x²]×x
=>V= 4x³- 132x² + 989x
Now we find the derivative of V and equate it to 0
[tex]\frac{dV}{dx}[/tex]= [tex]12x^{2} -264x+989[/tex]=0
Now we get values of x by quadratic formula
x=(264±[tex]\sqrt{264^{2}-4.12.989 }[/tex] )/24
=>x=(264±[tex]\sqrt{69696-47472}[/tex])/24
=>x=(264+√22224)/24, and x=(264-√22224)/24
=>x=(264+149.07)/24 and x=(264-149.07)/24
=>x=17.212 and x=4.79
Now we test it by second derivative test for the maximum volume.
[tex]\frac{d^{n}V }{dx}[/tex]=24x-264
For x = 17.212
[tex]\frac{d^{n}V }{dx}[/tex]=(24×17.212)-264=413.088-264=149.088
This value is > 0 so volume will be minimum.
For x = 4.79
[tex]\frac{d^{n}V }{dx}[/tex]=(24×4.79)-264= -149.04
-149.04 < 0, so volume of the box will be maximum.
Therefore, for x = 4.79 inches volume of the box will be maximum.
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(Complete Question) is
A candy box is made from a piece of cardboard that measures 43 by 23 inches. Squares of equal size will be cut out from each corner. The sides will then be folded up so that to form a rectangular box. What size square should be cut from each corner so that to obtain maximum volume?
Which equation is true when x=10 but not when x= – 10? Select all that apply.
Applying power rules, the equations that is true when x = 10 but false when x = -10 is given as follows:
x³ = 10000.
Exponents of 10The behavior of the exponents of 10 is different for even and for odd exponents, as follows:
Even exponents generate even functions, that is, 10^n = (-10)^n if the exponent n is even.Odd exponents generate odd functions, that is 10^n = -(-10)^n if the exponent is odd.In this problem, we have two exponents, as follows:
Exponent 2 is even.Exponent 3 is odd.We want different results for the power when x = 10 and when x = -10, hence the correct option will involve the odd exponent 3.
The third power of 10 is calculated as follows:
10³ = 10 x 10 x 10 = 100 x 10 = 1000.
Hence the equation that is true for x = 10 and false for x = -10 is:
x³ = 10000.
As when x = -10, the result is:
(-10)³ = (-10) x (-10) x (-10) = 100 x (-10) = -1000.
Missing informationThe options are given by the image at the end of the answer.
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cheesebugers and pizza are on todays menu. if the cafeteria serves cheeseburgers every 4th day and pizza every 6th day, how many more days until cheeseburgers and pizza are both on the menu again?
Answer:
12 more days
Step-by-step explanation:
Every time cheeseburger will be served: 4th day, 8th day, 12th day, 16th day
Every time pizza wil be served: 6th day, 12th day, 18th day
Since 12 is a common number, every 12 days both cheeseburgers and pizzas will be served
Which of the following is TRUE for every polynomial P with degree = n ?a) The highest power of x in P(x) is n-1b) There are at most n-1 solutions to P(x) = 0c) The graph of P has at most n-1 turning pointsd) The graph of P has at most n-1 x-intercepts
We need to identify the true statement for every polynomial P with degree n.
The degree n of a polynomial is the exponent of the highest power of x in that polynomial. For example, the polynomial
[tex]x³+3x²+3[/tex]has degree 3, since the highest power of x has exponent 3.
Thus, if the degree is n, then the highest power is n (not n-1). Therefore, (a) is False.
About the number of solutions to P(x) = 0, it can equal the number of the polynomial degree. For some polynomials, the solutions can repeat, so the number of solutions will be less than n. For some of them, the solutions may not belong to the real numbers.
As an example, for P(x) = x²+4, we have:
[tex]\begin{gathered} x²+4=0 \\ \\ x²=-4 \\ \\ x=\pm\sqrt{-4} \\ \\ x=\pm2\sqrt{-1} \\ \\ x=\pm2i \\ \\ x_1=-2i \\ \\ x_2=2i \end{gathered}[/tex]The above polynomial has degree 2 and 2 solutions. Therefore, (b) is False.
Each turning point is where the graph of the polynomial P(x) changes from decreasing to increasing or vice versa. The graph of any polynomial of degree n has at most n-1 turning points.
Therefore, (c) is True.
We can see that (d) is False from the following example:
the line P(x) = x+1 has degree n = 1 and n = 1 x-intercept, which is its zero x = -1.
Answer:
c) The graph of P has at most n-1 turning points
if square one is the largest of the three squares in the model,which statement is true?
_______________
I'm reading your question
___________________
According to the Pythagorean theorem
Hypotenuse ^2 = Side 1 ^2 + Side 2 ^2
The hypotenuse is the case (Square 1 )
area of the sqaure= side of the square^2
________________________
That means the area of 1 is = area of square 2 + area fo square3 (J is false)
_______________________________
We are not sure about the relation between square 2 and 3 just the addition is the square 1 (F and H we have no certainty)
______________________________
G is true
______________________________
Answer
G
Anna is computing 266 - 39. To do so, she first says that 266 is close to 270 and 39 is
close to 40, so she starts out computing 270 - 40 = 230. She then computes 230 - 3 =
227, and declares that 227 is her final answer. Is Anna's strategy correct? If yes, explain
why. If no, explain why not. Be mathematically specific, and support your reasoning
with a number-line model.
Yes, her strategy was correct.
What is BODMAS?When compared to operations involving just two numbers, solving an arithmetic expression that includes multiple operations like addition, subtraction, multiplication, and division is more difficult. A two-number operation is simple, but how do you work out an expression with brackets as well as multiple operations, as well as how to make a bracket simpler? Let's review the BODMAS rule as well as discover how brackets can be made simpler. For Bracket, Order, Division, Multiplication, Addition, and Subtraction, the acronym BODMAS is used. The acronym PEMDAS, which stands for Parentheses, Exponents, Multiplication, Division, Addition, as well as Subtraction, is also known as BODMAS in some areas. Thus, the following figure illustrates the order in which BODMAS and PEMDAS operate.
Simplification is done following BODMAS rule.
266-39 gives 227.
Hence, her strategy was correct.
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What is the solution to the inequality?
17<9+x
OA. x<8
OB. x>8
OC. x > 26
OD. x< 26
SUBMIT
Answer:
B) x > 8
Step-by-step explanation:
1-Step: Combine like terms by subtracting 9 on both sides : 17-9 < X
8 < X
2- Step: flip the signs (Since 8 is less than X, Then X is greater than X)
X > 8
In Exercises 1 and 2, find m/1 and m<2
1.
Answer:
m/1 = 87
m/2 = 93
Step-by-step explanation:
m1 and m2 need to have an angle of 180
so 180-87 = 93
Given m||n, find the value of x.
(6x-20)°
(6x-4)°
Answer:
x = 7
Step-by-step explanation:
2/7×7/10 reduced to the smallest fraction
Answer:
1/5
Step-by-step explanation:
I multiplied 2 * 7, which is 14. Then, I multiplied 7 * 10 which equals 70. Then, I divided 14/70 by 14. The answer is 1/5.
Hey! Could anybody help me out with this? I would like a very brief explanation leading to the answer as I already kinda understand the topic. Thanks!
Domain and Range of a Function
The domain of a function f is the set of values of the input (or independent) variable, often called x. The range is the set of values of the output (or dependent) variable, often called y, or f(x).
The function shown in the image has a shape that opens up to infinity (marked with the two arrows). This means that x can have any real value from minus infinity to plus infinity, that is, all real numbers.
Now for the range, we can see not every value of y belongs to the function. The graph decreases down to the vertex of the parabola that is located at (3,-12). This means that from y=-12 and up, the function exists, but not below this value.
Summarizing:
Domain: All real numbers
Range: y ≥ -12
The boxplot displays the arm spans for 44 students.
Which of the following is not a true statement?
There are no outliers in this distribution.
The shape of the boxplot is fairly symmetric.
The range of the distribution is around 60 cm.
The center of the distribution is around 180 cm.
The statements The range of the distribution is around 60 cm and
the center of the distribution is around 180 cm are true.
What is statistics?Statistics is the study and manipulation of data, including ways to gather, review, analyze, and draw conclusions from data.
In the given statements
There are no outliers in this distribution.
The shape of the boxplot is fairly symmetric.
The range of the distribution is around 60 cm.
The center of the distribution is around 180 cm.
The statement "The range of the distribution is around 60 cm" is true.
The range is the spread of your data from the lowest to the highest value in the distribution.
In the given graph
Range=200-140
=60
So it is true.
The center of the distribution is around 180 cm is also true.
Hence the statements The range of the distribution is around 60 cm and
the center of the distribution is around 180 cm are true.
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HELP ME PLEOPLE THIS IS SO CONFUSING HELP ME I WILL GET SUSPENDED IF I DON"T ANSWER THIS HELP ME PLEASE HELP I WILL GET A 0 AND SUSPENDED HELP HELP
ashley’s house and the public Library are plotted on the coordinate plane as shown.What is the distance between Ashely’s house and the public library to the nearest tenth
The distance between Ashely’s house and the public library is of 7.8 miles.
What is the distance between two points?Suppose that we have two points with coordinates [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]. The shortest distance between these two points is given by the following rule:
[tex]D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
This formula is derived from the Pythagorean Theorem, as the points form a right triangle in the Cartesian plane, with the hypotenuse representing the distance between them.
In the context of this problem, the coordinates of her house and of the library are given as follows:
House: (4,2).Library: (10,7).Hence the distance is calculated as follows:
[tex]D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
[tex]D = \sqrt{(10 - 4)^2+(7 - 2)^2}[/tex]
D = sqrt(61)
D = 7.8 miles, as each unit on the plane represents one mile.
Missing informationThe problem states that each unit on the plane represents one mile and the image gives their position on the plane.
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if 1 cm is equivlent to 10km what is 50 cm equivlant to
Answer:
50cm is equivalent to 500km
Have a good one!
Answer the question below
A) 4/5 or 0.8
B)7
C)1/81
Jan uses 78 yard of fabric for one quilt square and 17 yard in another. how much fabric has jan used? responses 914 of a yard 9 over 14 of a yard 618 yards 6 and 1 eighth yards 756 of a yard 7 over 56 of a yard 1156 yards
Based on the yards of fabric used by Jan for the quilt squares, the total fabrics used by Jan was 1 ¹ / ₅₆ yards
How to find the number of yards used?The yards of fabric used by Jan were 7 / 8 of a yard and 1 / 7 of another yard.
The total yards used by Jan can be found by adding these fractions up. To add both fractions, you first need to find the common denominator of 8 and 7 which is 56.
Then the numerators can be found by dividing 56 by the denominator and then multiplying the numerator by the result.
Fraction 7 / 8 yards:
= 56 / 8 x 7
= 49 / 56
Fraction 1 / 7:
= 56 / 7 x 1
= 8 / 56
The total number of yards used is:
= 49 / 56 + 8 / 56
= 57 / 56
= 1 ¹ / ₅₆ yards
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Find the mean for the data set. 6, 14, 7, 4, 12, 8, 13, 4, 18, 14
Answer:
Concept:
Mean is just another name for average. To find the mean of a data set, add all the values together and divide by the number of values in the set. The result is your mean!
The values are given below as
[tex]6,14,7,4,12,8,13,4,18,14[/tex]The image below shows how to calculate the mean
By substituting values, we will have
[tex]\begin{gathered} \bar{x}=\frac{\sum ^{}_{n\mathop=0}x}{n} \\ n=10 \end{gathered}[/tex][tex]\begin{gathered} \bar{x}=\frac{6+14+7+4+12+8+13+4+18+14}{10} \\ \bar{x}=\frac{100}{10} \\ \bar{x}=10 \end{gathered}[/tex]Hence,
The mean = 10
To calculate the variance, we will use the formula below
[tex]^{}\sigma^2=\frac{\sum ^{\infty}_{n\mathop=0}(x-\bar{x})^2}{n}[/tex][tex]\begin{gathered} \sigma^2=\frac{\sum ^{\infty}_{n\mathop{=}0}(x-\bar{x})^2}{n} \\ (x-\bar{x})^2=(6-10)^2+(14-10)^2+(7-10)^2+(4-10)^2+(12-10)^2+(8-10)^2+(13-10)^2+(4-10)^2+(18-10)^2+(14-10)^2 \\ (x-\bar{x})^2=16+16+9+36+4+4+9+36+64+16 \\ (x-\bar{x})^2=210 \end{gathered}[/tex][tex]\begin{gathered} \sigma^2=\frac{\sum ^{\infty}_{n\mathop{=}0}(x-\bar{x})^2}{n} \\ \sigma^2=\frac{210}{10} \\ \sigma^2=\frac{210}{10} \\ \sigma^2=21 \end{gathered}[/tex]Hence
The variance = 21
To calculate the standard deviation,
[tex]\begin{gathered} \sigma=\sqrt[]{variance} \\ \sigma=\sqrt[]{21} \\ \sigma=4.58 \end{gathered}[/tex]Hence,
The standard deviation is = 4.58
1. The public primary/secondary school dropout rate in Washington State is 6%. Suppose 35
individuals of primary/secondary school age are interviewed at random on a city street. What is
the probability that:
a. (5 points) Exactly 7 of them are dropouts?
The probability that exactly 7 individuals are dropouts out of 35 is 0.0033288.
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 several outcomes.
Given,
Probability of dropouts=p= 6%= 0.06
Probability of not dropouts=q=1-p=1-0.06=0.94
n=35
We use the probability mass function of binomial distribution, as there are only two possible outcomes for the given situation. If the individual is dropout or not a dropout.
P(X=x)= nCr x p^r x q^(n-r)
P(X=7)= 35C7x(0.06)^7x(0.94)^28
P(X=7)=6724520x(0.06)^7x(0.94)^28
P(X=7)=0.00332889
Therefore, the probability of exactly 7 of them are dropouts is 0.00332889.
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Find the slope between these two points:
(3, 0), (-11, -15)
Answer:
Slope = (15/14)
Step-by-step explanation:
(3, 0), (-11, -15)
(x₁, y₁) (x₂, y₂)
y₂ - y₁ -15 - 0 -15 15
m = ------------ = ----------- = ----------- = ---------
x₂ - x₁ -11 - 3 -14 14
I hope this helps!
-1/5 = -1/2w - 1/7 solve for w and simplify your answer as much as possible
Answer:
w = (4/35)
Step-by-step explanation:
-1/5 = -1/2w - 1/7
+1/7 +1/7
-----------------------------
-2/35 = -1/2w
÷-1/2 ÷-1/2
-----------------------
4/35 = w
Extra:
-1(7) 1(5)
------- + -------
5(7) 7(5)
-7 5 -2
------- + ------- = -------
35 35 35
------------------------------------------------------------
-2 -1
------- ÷ -------
35 2
-2 -2 4
------- × ------- = -------
35 1 35
I hope this helps!
URGENT DUE TODAY!!!!!
49. Which of the following is the solution of
0.125x +1 -0.25x < -3?
a. x < -0.5
b. x < 0.5
C. x > 0.5
d. x < 32
e. x > 32
The solution of 0.125x +1 -0.25x < -3 is x > 32
Difference between equality and inequality equations
Both mathematical phrases, equations and inequalities, are created by connecting two expressions.The equal sign (=) indicates that two expressions in an equation are believed to be equivalent. The symbols show that the two expressions in an inequality are not always equal: >, <, ≤ or ≥. Or in simple words the equation which has '=' sign is an equality equation while the inequality equation has the signs are >, <, ≤ or ≥.
The given expression is,
0.125x +1 - 0.25x < -3
subract the x value,
0.125x - 0.25x + 1 < -3
-0.125x + 1 < -3
-0.125x < -3 - 1
-0.125x < -4
Now, if on both the sides the signs are -ve then change the inequality sign, like this
x > 4 / 0.125
x > 32
Hence, The solution of 0.125x +1 -0.25x < -3 is x > 32
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I m struggle with this problem can someone help me
Check below, please
1) The way to tackle this problem, is by dividing those numerators by the denominators so we can get the decimal form of each fraction, and count the marks to plot them.
2) Let's divide them:
[tex]\begin{gathered} -\frac{5}{6}=-0.83 \\ \frac{17}{6}=2.83 \end{gathered}[/tex]So now, we can plot them:
Thus, this the answer.
Last year, Milan had $10,000 to invest. He invested some of it in an account that paid 9% simple interest per year, and he invested the rest in an account that
paid 7% simple interest per year. After one year, he received a total of $780 in interest. How much did he invest in each account?
Answer:
$4000 at 9% and $6000 at 7%Step-by-step explanation:
Let the amount invested at 9% be x.
Then the amount invested at 7% is 10000 - x.
The amount of interest after one year is $780.
Set up equation to represent this:
0.09x + 0.07(10000 - x) = 7800.09x + 700 - 0.07x = 7800.02x = 780 - 7000.02x = 80x = 80/0.02x = 4000Amount invested at 7% is:
10000 - 4000 = 6000Answer:
Milan invested:
$4,000 into the account earning 9% interest.$6,000 into the account earning 7% interest.Step-by-step explanation:
Given information:
Total amount invested = $10,000.Account A = 9% simple interest per year.Account B = 7% simple interest per year. Total interest earned after one year = $780.Let x be the amount invested in Account A.
Therefore, the amount invested in Account B is (10000 - x).
Simple Interest Formula
I = Prt
where:
I = Interest earned.P = Principal invested.r = Interest rate (in decimal form).t = Time (in years).Create two equations using the given information:
[tex]\begin{aligned}\textsf{Interest: Account A} &= x \cdot 0.09 \cdot 1\\& = 0.09x\end{aligned}[/tex]
[tex]\begin{aligned}\textsf{Interest: Account B} &= (10000 - x) \cdot 0.07 \cdot 1 \\& = 0.07(10000 - x)\\& = 700-0.07x\end{aligned}[/tex]
As the total interest earned was $780, set the sum of the two found equations to 780 and solve for x:
[tex]\begin{aligned}\implies 0.09x+700-0.07x&=780\\0.02x+700&=780\\0.02x&=80\\x&=4000\end{aligned}[/tex]
Therefore, Milan invested:
$4,000 into the account earning 9% interest.$6,000 into the account earning 7% interest.A boy bought some pencils for N60.00. If he had paid N1 less for each pencil, he could have bought 5 more pencils. How many pencils did he pay for?
The number of pencils he paid for is 15.
How to find the number of pencil he paid for?He bought some pencils for N60.00.
If he had paid N1 less for each pencil, he could have bought 5 more pencils.
Let
x = cost of each pencil that amount to N60.00
y = number of pencil
Therefore,
xy = 60
y = 60 / x
(y + 5)(x - 1) = 60
(60 / x + 5)(x - 1) = 60
60 - 60 / x + 5x - 5 = 60
- 60 / x + 5x + 55 = 60
- 60 / x + 5x = 60 - 55
- 60 / x + 5x = 5
- 60 + 5x² / x = 5
5x = -60 + 5x²
5x² - 5x - 60 = 0
x² - x - 12 = 0
x² + 3x - 4x - 12 = 0
x(x + 3) - 4(x + 3) = 0
(x - 4)(x + 3)
Hence,
x = 4 and x = -3
We can only use positive value.
xy = 60
y = 60 / 4
y = 15
Therefore, he paid for 15 pencils.
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you spin two wheels with equal size wedges labeled with numbers 1 through 9. what is the probability that at least one wheel lands on a multiple of 4 or the first value is strictly greater than 8?
The probability that at least one wheel lands on a multiple of 4 or the first value is strictly greater than 8 is 53/99
The greatest number that can be formed by the two wheels is 99
Let event A be multiple of 4
Multiples of 4 between 1 to 9 is 4,8
Probability that at least one wheel land at a multiple of 4 is
[tex]\frac{2}{9} + \frac{2}{9}[/tex] = 4/9
Let event B be first value greater than 9
P(B) = 9/99 = 1/11
P(A∩B) = 0
Probability of at least one wheel lands on a multiple of 4 or the first value is strictly greater than 8
P(A∪B) = P(A) + P(B) - P(A∩B)
= 4/9 + 1/11 - 0
= [tex]\frac{4(11)}{9 (11)} + \frac{1 (9)}{11(9)}\\\\ \frac{44 + 9}{99}\\\\ \frac{53}{99}[/tex]
Therefore, the probability that at least one wheel lands on a multiple of 4 or the first value is strictly greater than 8 is 53/99
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A middle school took all of its 6th grade students on a field trip to see a play at a
theater that has 1080 seats. The students filled 35% of the seats in the theater. How
many 6th graders went on the trip?
Answer:
there are 378 students
Step-by-step explanation:
you can see this as a simple proportion.
You know that the 100% of the seats are 1080 and you need to know the 35% of the seats, so you do:
[tex] \frac{1080}{100} = \frac{x}{35} [/tex]
so you do
x = 35 * 1080 ÷ 100 which gives 378
Nick was thinking of a number. Nick adds 11 then divides by 11 to get an answer of 28. Form an equation with
x
from the information.
Answer:
??
Step-by-step explanation:
-12/7 = 6y solve for y and simplify your answer as much as possible
Answer:
[tex]\displaystyle y = \frac{-2}{7}[/tex]
Step-by-step explanation:
To solve, we will isolate the variable.
Given:
-12/7 = 6y
Divide:
[tex]\displaystyle \frac{\frac{-12}{7} }{6} =\frac{6y}{6}[/tex]
Simplify the right side:
[tex]\displaystyle \frac{\frac{-12}{7} }{6} =y[/tex]
"Keep, change, flip" on the left side:
[tex]\displaystyle \frac{-12}{7} *\frac{1}{6} = y[/tex]
Multiply:
[tex]\displaystyle \frac{-12*1}{7*6}= y[/tex]
[tex]\displaystyle \frac{-12}{42}= y[/tex]
Simplify and reflexive property:
[tex]\displaystyle y = \frac{-2}{7}[/tex]