Determine if the following equation is linear if the equation is linear converted to standard form AX+by=c
Answers
Given the equation:
[tex](-10+y^2)-y^2=-7x+10[/tex]To determine if the equation is a linear equation, the first step is to simplify it. To do so, erase the parentheses and simplify the like terms:
[tex]\begin{gathered} (-10+y^2)-y^2=7x+10 \\ -10+y^2-y^2=7x+10 \\ -10+0y^2=7x+10 \\ -10+0y=7x+10 \end{gathered}[/tex]The terms "+y²" and "-y²" canceled each other, this is why the variable y is multiplied by zero. Then the only variable left is "x", which suggests that the equation represents a vertical line.
To write this equation in standard form, you have to pass the x-term to the left side of the equation and the constant to the right side of it:
[tex]\begin{gathered} -10+0y=-7x+10\text{ \rightarrow add 10 to both sides of the equation} \\ -10+10+0y=-7x+10+10 \\ 0y=-7x+20\text{ \rightarrow add 7x to both sides of the equation} \\ 0y+7x=-7x+7x+20 \\ 0y+7x=20 \\ 7x+0y=20 \end{gathered}[/tex]The line written in standard form is 7x+0y=20.
Vertical lines are considered to be linear equations.
Related Questions
find the total and the interestprincipal $3200rate 5 1/2 yearscompounded semiannually for 6 years
Answers
Remember that
The compound interest formula is equal to
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]
where
A is the Final Investment Value
P is the Principal amount of money to be invested
r is the rate of interest in decimal
t is Number of Time Periods
n is the number of times interest is compounded per year
in this problem we have
P=$3,200
r=5 1/2 %=5.5%=0.055
t=6 years
n=2
substitute the given values
[tex]A=3,200(1+\frac{0.055}{2})^{2\cdot6}[/tex]A=$4,431.31 ------> the totalFind out the interest
I=A-P
I=4,431.31-3,200
I=$1,231.31 -----> interestConsider the following polynomial function.f(x) = (x+4)²(x - 2)5(x - 1)Step 2 of 3: Find the x-intercept(s) at which f crosses the axis. Express the intercept(s) as ordered pair(s).AnswerCorrectSelect the number of x-intercept(s) at which f crosses the axis.
Answers
Given the function:
[tex]f\mleft(x\mright)=(x+4)^2\left(x-2\right)^5(x-1\rparen[/tex]The x-intercept iswhen y =0, so:
[tex]\begin{gathered} x+4=0 \\ x+4-4=0-4 \\ x=-4 \\ \end{gathered}[/tex]And
[tex]\begin{gathered} x-2=0 \\ x-2+2=0+2 \\ x=2 \end{gathered}[/tex]And
[tex]\begin{gathered} x-1=0 \\ x-1+1=0+1 \\ x=1 \end{gathered}[/tex]Therefore, the x-intercepts are:
(-4, 0), (2, 0) and (1, 0)
Answer:
(-4, 0), (2, 0) and (1, 0)
Solve the system by substitution. 9y = x - 4x + y = -35 Submit Answer
Answers
Let:
[tex]\begin{gathered} 9y=x\text{ (1)} \\ -4x+y=-35\text{ (2)} \end{gathered}[/tex]Replace (1) into (2):
[tex]\begin{gathered} -4(9y)+y=-35 \\ -36y+y=-35 \\ -35y=-35 \\ y=1 \\ \text{ Replace y into (1)} \\ x=9(1) \\ x=9 \end{gathered}[/tex]what is the value of x and y ?2x+3=Y
Answers
There can be infinite solutions for x and y, this is because if we look at the equation like a slope intercept equation
[tex]\begin{gathered} 2x+3=y \\ y=2x+3 \end{gathered}[/tex]we can see that this is the equation for a straight line.
if we graph it
All values of x and y that are obtain by the line can be a solution to the equation given.
The key concepts used to convert units between different systems of measurement are shown without the final twosteps.1. Identify the units of measure to be converted,2. Write conversion factors,3. Cancel units.4.5.Which two steps will complete the list correctly?4. Divide the original measurement by the conversion factors.5. Check for reasonableness,4. Multiply the original measure by the conversion factors.5. Simplify the answer.4. Multiply the original measure by the conversion factors.5. Check for reasonableness,4. Divide the original measure by the conversion factors.
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Here, we want to select from the options, the two best statements that completes the steps
The two steps are;
Multiply the origi
answer choices:454ft square inches, 252ft square inches, 156ft square inches
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Tp fint the total area of the figure start by calculating the area of the square and the triangle separately.
Area of the square is calulated by mutiplying the side by the side
[tex]\begin{gathered} A=(14ft)\cdot(14ft) \\ A=196ft^2 \end{gathered}[/tex]Area of the triangle follows the formula:
[tex]A=b\cdot\frac{h}{2}[/tex]The base of the triangle is the same as the length of the square's side.
[tex]\begin{gathered} A=\frac{(14ft)\cdot(8ft)}{2} \\ A=56ft^2 \end{gathered}[/tex]Add both sides to find the total area
[tex]\begin{gathered} A_t=56ft^2+196ft^2 \\ A_t=252ft^2 \end{gathered}[/tex]Interpret Linear Function Coefficients (From Graph)
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Remember that the equation of the line in slope-intercept form is equal to
y=mx+b
where
m is the slope
b is the y-coordinate of the y-intercept
In this context
we have
C=mt+b
step 1
Find out the slope
we need two points
looking at the graph
we take (0,100) and (1,150)
so
m=(150-100)/(1-0)
m=50 --------> that means $50 per month (monthly fee to remain a member)
the y-intercept is the value of y when the value of x is zero
in this context, the y-intercept is the cost C when the value of t is zero
b=100 ------> that means a one-time fee to join
substitute
C=50t+100and the slope is $50 per month (monthly fee to remain a member)f(x) = 2x + 4 and g(x) = -8f(x). = What equation shows the correct rule for the function g? O g(x) = -4x O g(x) = -4x + 4 = g(x) = -8x - 32 O g(x) = -4x - 32 – -
Answers
The given functions are
[tex]\begin{gathered} f(x)=\frac{1}{2}x+4 \\ g(x)=-8f(x) \end{gathered}[/tex]Multiply f by -8 to get g
[tex]\begin{gathered} g(x)=-8(\frac{1}{2}x+4) \\ g(x)=-8(\frac{1}{2}x)+(-8)(4) \\ g(x)=-4x+(-32) \\ g(x)=-4x-32 \end{gathered}[/tex]The correct answer is D
If 8 people share 21 muffins, how many does each person get?
Answers
ANSWER
[tex]\frac{21}{8}or\text{ 2}\frac{\frac{5}{}}{8}[/tex]EXPLANATION
The total number of muffins is 21.
To find out how many muffins each person will receive, you have to divide the total number of muffins by the number of people it is to be shared with;
[tex]\begin{gathered} x=\frac{21}{8} \\ =2.625 \end{gathered}[/tex]Each person will receive 2.625 muffins
Two angles are complementary to each other. One angle measures 23°, and the other angle measures (6x − 20)°. Determine the value of x.
Answers
Answer:
15.5
Step-by-step explanation:
23-20=3
6x-3=90
3-90=93
93÷6=15.5
Answer:
14.5
Step-by-step explanation:
i got it right on the test
use the diagrams to answer the following questions Number 8
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In a cyclic quadrilateral opposite sides add up to 180:
Therefore:
[tex]\begin{gathered} x+82=180 \\ solve_{\text{ }}for_{\text{ }}x: \\ x=180-82 \\ x=98^{\circ} \end{gathered}[/tex]Answer:
∠x = 98
2. Here is a riddle: “I am thinking of two numbers that add up to 5.678. The difference between them is 9.876. What are the two numbers?”•Name any pair of numbers whose sum is 5.678. •Name any pair of numbers whose difference is 9.876.•The riddle can be represented with two equations. Write the equations.•Solve the riddle. Explain your reasoning.( You do not need to name a variable for each number in the first part)
Answers
• You know that the sum of the two numbers must be:
[tex]5.678[/tex]In order to find any pair of numbers whose sum is that number shown above, you can subtract 1 from it:
[tex]5.678-1=4.678[/tex]Now you can set up that:
[tex]1+4.678=5.678[/tex]• To find any pair of numbers whose difference is:
[tex]9.876[/tex]You can add 2 to it:
[tex]9.876+2=11.876[/tex]Then, you can set up that:
[tex]11.876-2=9.876[/tex]• Let be "x" and "y" the numbers that add up to 5.678. and whose difference is 9.876.
Then, you can set up these equations:
[tex]\begin{gathered} x+y=5.678\text{ (Equation 1)} \\ \\ x-y=9.876\text{ (Equation 2)} \end{gathered}[/tex]• To solve the riddle, you can follow these steps:
- Set up a System of equations using the equations found in the previous part:
[tex]\begin{gathered} \begin{cases}x+y=5.678 \\ \\ x-y=9.876\text{ }\end{cases} \\ \end{gathered}[/tex]- Apply the Elimination Method by adding both equations and solving for "x":
[tex]\begin{gathered} \begin{cases}x+y=5.678 \\ \\ x-y=9.876\text{ }\end{cases} \\ ------------ \\ 2x=15.554 \end{gathered}[/tex][tex]\begin{gathered} x=\frac{15.554}{2} \\ \\ x=7.777 \end{gathered}[/tex]- Substitute the value of "x" into one of the original equations and solve for "y":
[tex]\begin{gathered} (7.777)+y=5.678 \\ \\ y=5.678-7.777 \\ \\ y=-2.099 \end{gathered}[/tex]Therefore, the answers are:
• Any pair of numbers whose sum is 5.678:
[tex]1\text{ and }4.678[/tex]• Any pair of numbers whose difference is 9.876:
[tex]11.876\text{ and }2[/tex]• Equations that represents the riddle:
[tex]\begin{gathered} x+y=5.678\text{ (Equation 1)} \\ \\ x-y=9.876\text{ (Equation 2)} \end{gathered}[/tex]• Solution of the riddle:
[tex]\begin{gathered} x=7.777 \\ y=-2.099 \end{gathered}[/tex]
Find the sales tax in total cost of espresso machine that cost $46.95 the tax rate is 4% rounding your answer to the nearest cent
Answers
Given:
The total cost of espresso machine costs $46.95. and the tax rate is 4%.
To find:
Find the sales tax?
Explanation:
[tex]Sale\text{s tax=Sales tax percenatge}\times pre-tax\text{ cost}[/tex][tex]Total\text{ cost=Pre-tax value +Sales tax}[/tex]Solution:
We will start by converting sales tax percentage into a decimal by moving
the point two spaces to the left.
6%=0.06
Now, we need to multiply the pre-max cost of this item by this value
in order to calculate the sales tax cost
[tex]\begin{gathered} Sales\text{ tax=}0.04\times46.95 \\ Sales\text{ tax=1.878} \end{gathered}[/tex]Round to two decimal places
[tex]Sales\text{ tax=\$1.88}[/tex]Last, add this value of the pre-tax value of the item to find the total cost.
[tex]\begin{gathered} Total\text{ cost=Pre tax value + Sales tax} \\ Total\text{ Cost=46.95+1.88} \\ Total\text{ cost=}48.83 \end{gathered}[/tex]Hence, these are the required values.
Can you please help me out with a question
Answers
Step 1: Write out the formula
By the intersecting secant theorem (interior),
[tex]z=\frac{x+y}{2}[/tex]Step 2: Write out the given values and substitute them into the formula
[tex]x=40^0,y=52^0,z=m<1[/tex]Therefore,
[tex]m<1=\frac{40^0+52^0}{2}=\frac{92^0}{2}=46^0[/tex]Hence, m<1 = 46 degrees
Factor. x2 − x − 72 (x − 8)(x + 9) (x − 6)(x + 12) (x + 8)(x − 9) (x + 6)(x − 12)
Answers
The solution of the given equation are; (x + 8)(x − 9)
What is a quadratic equation?A quadratic equation is the second-order degree algebraic expression in a variable. the standard form of this expression is ax² + bx + c = 0 where a. b are coefficients and x is the variable and c is a constant.
We have been given the quadratic equation as;
x² − x − 72
Solving;
x² − (9-8)x − 72
x² − 9x +8x− 72
The factors are;
(x + 8)(x − 9)
Therefore, the solution of the given equation are; (x + 8)(x − 9)
Learn more about quadratic equations;
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2) Coefficient of u^2v^2 in expansion of (2u - 3v)^4
Answers
Answer
Step-by-step Explanation
In the expansion of variables in a bracket raised to a particular power, we either use the Binomial theorem or the Pascal's triangle.
The Binomial theorem teaches how to use permutaion and combination to obtain the coefficients of each term while the Pascal's triangle presents the coefficient of each term for different integer powers of the variables in a triangular form where the next line of the triangle can be obtained from the previous line just by starting with a 1 and adding two consecutive terms of that previous line and ending with 1.
the sum of 1/3 and 3/8
Answers
Answer:
17/24
Explanation:
To add the fractions
[tex]\frac{1}{3}+\frac{3}{8}[/tex]we first find their common denominators.
The common multiple of 3 and 8 is 24 because 3 * 8 = 24; therefore,
[tex]\frac{1}{3}+\frac{3}{8}=\frac{1\cdot8}{3\cdot8}+\frac{3\cdot3}{8\cdot3}[/tex][tex]=\frac{8}{24}+\frac{9}{24}[/tex]Adding the numerators gives
[tex]\frac{8}{24}+\frac{9}{24}=\frac{17}{24}[/tex]Hence,
[tex]\frac{1}{3}+\frac{3}{8}=\frac{17}{24}[/tex]Select the correct answer.Solve the equation using the method of completing the square.A. B. C. D.
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Answer:
C. -4 ± 2√6
Explanation:
The given equation is
3x² + 24x - 24 = 0
First, add 24 to both sides
3x² + 24x - 24 + 24 = 0 + 24
3x² + 24x = 24
And factorize 3 on the left side
3(x² + 8x) = 24
Then, to complete the square, we need to add and substract (b/2)² to the expression in parenthesis. In this case, b = 8, so
(b/2)² = (8/2)² = 4² = 16
Then, add and subtract 16 as follows
3(x² + 8x + 16 - 16) = 24
3(x² + 8x + 16) - 3(16) = 24
3(x² + 8x + 16) - 48 = 24
Finally, we can factorize and solve for x
3(x + 4)² - 48 = 24
3(x + 4)² - 48 + 48 = 24 + 48
3(x + 4)² = 72
3(x + 4)²/3 = 72/3
(x + 4)² = 24
Solving for x, we get
[tex]\begin{gathered} x+4=\pm\sqrt{24} \\ x+4-4=-4\pm\sqrt{24} \\ x=-4\pm\sqrt{24} \\ x=-4\pm\sqrt{4\cdot6} \\ x=-4\pm2\sqrt{6} \end{gathered}[/tex]Therefore, the answer is
C. -4 ± 2√6
I need help I am a teacher and have to explain this to my students
Answers
Solve the given inequality as shown below
[tex]\begin{gathered} r+6\ge11 \\ \Rightarrow r+6-6\ge11-6 \\ \Rightarrow r\ge5 \end{gathered}[/tex]Therefore, any number equal to or greater than 5 is a solution to the given inequality.
The correct answers are 5, 6, and, 7.
need help converting point slope form equation to slope intercept form(y+10)=1/3(x+9)
Answers
The slope-intercept form is
→ y = m x + b
→ m is the slope
→ b is the y-intercept
∵ The given equation is
[tex]y+10=\frac{1}{3}(x+9)[/tex]First, multiply the bracket (x + 9) by 1/3
[tex]\begin{gathered} \because y+10=\frac{1}{3}(x)+\frac{1}{3}(9) \\ \therefore y+10=\frac{1}{3}x+3 \end{gathered}[/tex]Subtract 10 from both sides
[tex]\begin{gathered} \because y+10-10=\frac{1}{3}x+3-10 \\ \therefore y+0=\frac{1}{3}x-7 \\ \therefore y=\frac{1}{3}x-7 \end{gathered}[/tex]The equation in the slope-intercept form is y = 1/3 x - 7
When a positive number x is divided by 7, the remainder is 4. What is
the remainder when x is divided by 4?
Answers
When a positive number x is divided by 7, the remainder is 4. The remainder when x is divided by 4 is 7.
What is a remainder?
The quantity "leftover" after executing a computation in mathematics is referred to as the remainder. The remainder is the integer that remains after dividing two integers to get an integer quotient in mathematics.
The remainder operator (%) returns the amount of one argument that is left over after dividing it by another operand. For instance, when 41 is divided by 7, the remaining is 6 and the quotient is 5.
Solution Explained:
A/Q
x / 7 = 4
Solving this equation
x = 4 X 7 = 28
Now putting the value of x in the equation
x / 4
= 28 / 4 = 7
Therefore, the remainder when x is divided by 4 is 7.
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5.) Figure 10.85 shows a method for constructing isosceles triangles. A. use the method of figure 10.85 to drawl two different isosceles triangles B. use the definition of circles to explain why this method will always produce an isosceles triangle.
Answers
You first draw two circles when different radii.
When you select two point over the circumference, and you connect a line in between these points and the center of the circle, you will always obtain two sides with the same length. It is because the length of these sides coincides witht the ratio of the circle.
Then, when you connect the points over the circumference between them, you have a side that can have a different length compared with the lengths of the lines connected to the center. Thus, you obtain an isosceles triangle; you have two sides with the same length (remember, it's the same as the radius) and one side with another length.
Find the slope vx and the distance Ay for this pair of coordinates. (-2,-4) (3,-1) Change in y Change in x
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The slope and the distance of two points (a,b), (c,d) is given by
[tex]\begin{gathered} m\text{ = }\frac{d-b}{c-a} \\ d=\sqrt[]{\mleft(c-a\mright)^2+(d-b)^2} \end{gathered}[/tex]Replacing our original points, we have
[tex]\begin{gathered} m=\frac{-1-(-4)}{3-(-2)}=\frac{-1+4}{3+2} \\ m=\frac{3}{5} \\ d=\sqrt[]{(3-\mleft(-2)\mright)^2+(-1}-(-4))^2 \\ d=\sqrt[]{5^2+3^2} \\ d=5.83 \end{gathered}[/tex]hi how do i solvle this word problem?An office building worth $1 million when completed in 2010 is being depreciated linearly over 40 years. What was the book value of the building in 2012? What will it be in 2025? (Assume the scrap value is $0.)2012 $ 2025 $
Answers
Answer:
2012: $950,000
2025: $625,000
Explanation:
Since the scrap value is $0, the amount depreciated each year is equal to the initial worth of the building divided by the number of years, so
[tex]\frac{1,000,000}{40}=25,000[/tex]It means that each year the worth of the building decreases by $25,000
Then, 2012 is 2 years after 2010, so the book value of the building in 2012 is:
$1,000,000 - 2($25,000) = $950,000
In the same way, 2025 is 15 years after 2010, so the book value is
$1,000,000 - 15($25,000) = $625,000
Therefore, the answers are
2012: $950,000
2025: $625,000
I need answers fast
What else would need to be congruent to show that ASTU = AJKL by SAS?
7
R
Glven:
STK
ZSE
S
A. TU. KL
B. TU = JL
C. SU - KL
D. SU JL
Answers
Given:
[tex]STU\cong JKL[/tex]Therefore by the SAS theorem::
[tex]\begin{gathered} ST\cong JK \\ \angle S\cong\angle J \\ SU\cong JL \end{gathered}[/tex]Answer: D.
Which expression is equivalent to (3x^5+ 8x^3) – (7x^2 - 6x^3)?3x^5 +14x^3 – 7x^23x^5+ 2x^3 – 7x^2- 4x^5+ 14x^3- 4x^3 + 14
Answers
so the answer is option #1
Find the equation of a line with given slope and containing the given point. Write the equation in slope-intercept form. M= -2, point ( 2,1 )Y=
Answers
The equation of a line in slope-intercept form is;
[tex]y=mx+b[/tex]For the given information, that is the slope and a point on the line, we now have;
[tex]\begin{gathered} (x,y)=(2,1) \\ m=-2 \\ y=mx+b\text{ now becomes;} \\ 1=-2(2)+b \\ 1=-4+b \\ \text{Add 4 to both sides} \\ 1+4=-4+4+b \\ 5=b \\ \text{Now that we have }\det er\min ed\text{ the value of b,} \\ We\text{ can substitute for m and b as follows; } \\ y=mx+b\text{ becomes;} \\ y=-2x+5 \end{gathered}[/tex]ANSWER:
The equation of the line therefore is;
[tex]y=-2x+5[/tex]Answer:
y = -2x + 5
Step-by-step explanation:
Pre-SolvingWe are given that a line contains the point (2,1) and a slope (m) of -2.
We want to write the equation of this line in slope-intercept form, which is y=mx+b, where m is the slope and b is the value of y at the y-intercept.
Since we are already given the slope of the line, we can plug that value into the equation.
Replace m with -2.
y = -2x + b
Now, we need to solve for b.
As the line passes through (2,1), we can use those values to help solve for b.
Substitute 2 as x and 1 as y.
1 = -2(2) + b
Multiply.
1 = -4 + b
Add 4 to both sides.
5 = b
Substitute 5 as b.
y = -2x + 5
Which inequality represents all values of x for which the product below is defined?A.x 0B.x 6C.x -3D.x 6
Answers
Solution
Step 1:
Write the expression:
[tex]\sqrt{x\text{ - 6}}\text{ . }\sqrt{x\text{ + 3}}[/tex]Step 2:
[tex]\begin{gathered} Apply\text{ the rule below:} \\ \sqrt{a}\text{ . }\sqrt{b}\text{ = }\sqrt{ab} \end{gathered}[/tex]Step 3:
[tex]\begin{gathered} \sqrt{x\text{ - 6}}\text{ . }\sqrt{x\text{ + 3}} \\ \\ \sqrt{(x-6)(x+3)} \\ \\ For\text{ the function to be defined} \\ (x\text{ - 6\rparen\lparen x + 3\rparen }\ge\text{ 0} \end{gathered}[/tex]Step 4:
[tex]x\le \:-3\quad \mathrm{or}\quad \:x\ge \:6\:[/tex]Final answer
[tex]\begin{gathered} Option\text{ D } \\ x\text{ }\ge\text{ 6} \end{gathered}[/tex]5EColumn AColumn B1. eTriangle GAFa. Right, Scalene2.Triangle BECb. Obtuse, Isoscelesa3.bTriangle BFGObtuse, Scalene4.d. Equiangular, Equilateralc сTriangle CFEe. Right, Isoscelesf. Acute, Isosceles
Answers
Triangle GAF is an
[tex]\begin{gathered} Isosceles\text{ triangle as 2 sides are equal and acute angles as all } \\ \text{the angles is less than 90 degre}e \end{gathered}[/tex]Triangle BEC is a
[tex]\begin{gathered} Isosceles\text{ triangle as 2 sides are the same.} \\ it^{}\text{ is an obtuse triangle } \end{gathered}[/tex]Triangle BFG is an
[tex]\begin{gathered} \text{Equilateral triangle as all sides are equal. } \\ Equilateral\text{ triangle are equiangular as all the angles are equal} \end{gathered}[/tex]Triangle CFE is
[tex]\begin{gathered} \text{Right angle triangle .} \\ A\text{ right angle triangle has one angle equal to 90 degre}e. \\ \text{The triangle is also scalene as all the sides are different} \end{gathered}[/tex]mean is 95.3standard deviation is 15.4 finf the probability that a randomly selected adult IQ is greater than 119.8
Answers
we are asked to determine the probability that a variable x is greater than 119.8. To do that we will assume a normal distribution of probability and use the following relationship:
[tex]P(x>119.8)=1-P(x\le119.8)[/tex]To determine the probability that x is smaller than 119.8 we need first to find the z-score of the data set using the following formula:
[tex]z=\frac{x-\bar{x}}{\sigma}[/tex]Where
[tex]\begin{gathered} \bar{x}\colon\operatorname{mean} \\ \sigma\colon\text{ standard deviation} \end{gathered}[/tex]replacing we get:
[tex]z=\frac{119.8-95.3}{15.4}=1.59[/tex]Now we use this value to look into the chart for probabilities, we get 0.94408. This is the probability that x is smaller than 119.8. Replacing in the initial relationship we get:
[tex]P(x>119.8)=1-0.94408=0.056[/tex]Therefore, the probability is 5.6%.