identify the reflection of the figure with vertices P (2, -12), Q (-3, 13), and R (-5, - 15) across the x-axis.
Answers
EXPLANATION:
We are given the following coordinates for a figure on the coordinate plane;
[tex]\begin{gathered} P(2,-12) \\ Q(-3,13) \\ R(-5,-15) \end{gathered}[/tex]To reflect any figure or any set of coordinates across the x-axis, we shall apply the rule;
[tex](x,y)\rightarrow(x,-y)[/tex]Note that the x-coordinate remains the same whereas, the y-coordinate changes its sign.
Imagine folding a graph page in two equal halves along the horizontal axis. You'll observe the y-coordinates will switch sides from top to bottom (positive to negative) or bottom to top (negative to positive). The x-coordinate remains the same since moving the folded page does not affect values along the horizontal line.
Therefore, for the vertices given, the reflection across the x-axis would be;
[tex]P(2,-12)\rightarrow P^{\prime}(2,12)[/tex][tex]Q(-3,13)\rightarrow Q^{\prime}(-3,-13)[/tex][tex]R(-5,-15)\rightarrow R^{\prime}(-5,15)[/tex]ANSWER:
The coordinates of the reflection across the x-axis therefore will be;
[tex]\begin{gathered} P^{\prime}(2,12) \\ Q^{\prime}(-3,-13) \\ R^{\prime}(-5,15) \end{gathered}[/tex]Related Questions
raw the hyperbola for each equation in problem l. the partial
Answers
B. given the equation of the hyperbola :
[tex]\begin{gathered} 9x^2-y^2=9 \\ \\ \frac{x^2}{1}-\frac{y^2}{9}=1 \end{gathered}[/tex]The graph of the hyperbola will be as following :
As shown in the figure :
vertices are : (-1,0) and (1,0)
Foci are ( -3.2 , 0) and (3.2 , 0)
End points are (0,-3) and (0,3)
Asymptotes are : y = 3x and y = -3x
LEVEL B 1.b) Solve for x angle relationship X+34" 2x-120
Answers
Answer
x = 46 degrees
Step-by-step explanation:
Alternate interior angles are equal
x + 34 = 2x - 12
Collect the like terms
x - 2x = -12 - 34
-x = -46
Divide both sides by -1
-x/-1 = -46/-1
x = 46 degrees
Hence, the value of x is 46 degrees
The population of a culture of bacteria, P(t), where t is time in days, is growing at a rate that is proportional to the population itself and the growth rate is 0.2. The initial population is 10.
Answers
Answer
Explanation
Using the formula for the population growth:
[tex]P(t)=P_0\cdot(1+r)^t[/tex]where P₀ is the initial population, r is the rate of growth, and t is the time.
From the given information, we know that:
• P₀ = 10
,• r = 0.2
1.
And we are asked to find P(50) (when t = 50), thus, by replacing the values we get:
[tex]P(50)=10\cdot(1+0.20)^{50}[/tex][tex]P(50)\approx91004.3815[/tex]2.
For the population to double, this would mean that P(t) = 2P₀. By replacing this we get:
[tex]2P_0=10e^{0.20t}[/tex][tex]2(10)=10e^{0.20t}[/tex][tex]20=10e^{0.20t}[/tex][tex]\frac{20}{10}=e^{0.20t}[/tex][tex]\ln\frac{2}{1}=\ln e^{0.20t}[/tex][tex]\ln2=0.20t[/tex][tex]t=\frac{\ln2}{0.20}\approx3.5days[/tex]v+8 over v = 1 over 2
Answers
The given expression is
[tex]\frac{v+8}{v}=\frac{1}{2}[/tex]First, we multiply 2v on each side.
[tex]\begin{gathered} 2v\cdot\frac{v+8}{v}=2v\cdot\frac{1}{2} \\ 2v+16=v \end{gathered}[/tex]Then, we subtract v on each side.
[tex]\begin{gathered} 2v-v+16=v-v \\ v+16=0 \end{gathered}[/tex]At last, we subtract 16 on each side.
[tex]\begin{gathered} v+16-16=-16 \\ v=-16 \end{gathered}[/tex]Therefore, the solution is -16.15. Deanna started a savings
account for her
when she was bom. She put
$1,500 in an account with a
simple 3.25% interest rate. What
will be the total amount in the
account after 18 years?
granddaughter
Answers
$23,775.00 will be the total amount in the account after 18 years, Formula of simple interest = A = P(1 + rt).
What is simple interest?
The straightforward interest formula makes figuring out how much interest will be applied to a loan quick and simple. Multiply the principle, this same number of days between payments, as well as the daily interest rate to determine simple interest.
Although this method of calculation is used in some mortgages, this type of interest is typically associated with auto loans as well as short-term loans.
Simple interest is calculated by multiplying the principle by the daily interest rate and number of days among payments.Simple interest rewards borrowers for making on-time or early monthly payments on their loans.Auto loans as well as short-term personal loans are two common uses for simple interest loans.A represents the total amount of accrued interest and principal.
P is the principal amount.
The interest rate is I.
The annual percentage real interest rate, abbreviated as r, is 1/10.
R is the interest rate in annual percentage terms; R = r * 100 t is the time period in months or years.
In light of the query
P=$1500
r=3.25%
=0.0325
t=18 years
simple interest = 1500(1+ 0.0325 x 18)
=$(1500+877.5)
=$ 23,775
Thus the simple interest is $23,775
Learn more about Simple interest from the link below
https://brainly.com/question/21020925
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Question 4 5 points)Part 1: Find the median of the Science Midterm Exam Scores (2 points)Part 2: Explain how you found the median of the Science Midterm Exam Scores. Be sure to explain the process you used to identity at themedian is. (3 points)
Answers
median = 75
See explanation below
Explanation:Part 1:
To find the emadian, we can state the data on the dot plot of the science midterm scores:
60, 65, 65, 70, 70, 75, 75, 75, 80, 80, 85, 85, 90, 95, 100
Total number of data set = 15
median = (N+1)/2
N = 15
Median = (15+1)/2 =16/2 = 8
Median = 8th position in the data
The 8th number = 75
Hence, the median of the science midterm scores = 75
Part 2:
The process is to write out all the data on the plot.
Count the number of data.
Then apply the median formula
Or because it is an odd number, the middle number after listing it out is the median.
The middle number here is 75
I am very confused can you help me please thanks!
Answers
Solution
For this case we know that :
1/8 of teaspoon for every 3 cups of frosting
Now the amount of cups increase to 4 cups then we can find the number teaspoon
We can use a proportional rule and we got:
[tex]\frac{\frac{1}{8}}{3}=\frac{x}{4}[/tex]The answer is:
C
Can you help me with this math question? it says "A cell phone plan costs $200 to start. Then there is a $50 charge each month, Write an expression that shows the total cost for x months on this plan" Is there a proportional relationship between time and cost of the cell phone plan?
Answers
Cost = 200 + 50x
The relationship between time and cost of the plan is not proportional. By definition, proportional ;relationships between two variables have equivalent ratio; one variable is always a constant value times the other which in this case is not .
To illustrate,
Month 1 Cost = 200 + 50(1) = 250 Ratio ( time:cost) = 1:250
Month2 Cost = 200 + 50(2) = 300 Ratio ( time:cost) = 2:300 = 1:150
Month 3 Cost = 200 + 50(3) = 350 Ratio ( time:cost) = 3:350
Month 4 Cost = 200 + 50(4)= 400 Ratio ( time:cost) = 4 :400 = 1:100
The ratios are not equivalent,thus the relationship is not proportional.
The triangular faces of the prism shown are equilateral triangles with perimeter 30 cm. Use a net to find the surface area of the prism.
Answers
Explanation:
[tex]\begin{gathered} The\text{ surface area is made up of the two equilateral triangles shown above as well as the three rectangles.} \\ Area\text{ of Triangles = 2\lparen}\frac{1}{2}b*h) \\ If\text{ the perimeter of the triangle is 30cm, the length of one side = 30/3 = 10 = base} \\ Area\text{ = 2\lparen}\frac{1}{2}*10*8.7) \\ \text{ =87} \\ Area\text{ of the three rectangles = 3\lparen length*width\rparen } \\ \text{ =3\lparen10*12\rparen} \\ \text{ =360} \\ Total\text{ Surface Area = 360 + 87 = 447} \end{gathered}[/tex]Surface Area of the two triangles in the net = 2*(0.5*b*h)
= 2*(0.5*10*8.7)
=87
Surface Area of three rectangles in the net = 3(l*b)
= 3*12*10
=360
Answer: Total Surface area = 360 + 87 = 447
Please helpIf the 100th term of an arithmetic sequence is 595, and its common difference is 6, thenits first term a1= ,its second term a2= ,its third term a3=
Answers
Given
100th term of an arithmetic sequence is 595 and common difference , d = 6
Find
First three terms of arithmetic sequences.
Explanation
As we know the general nth term of an arithmetic sequence is given by
[tex]a_n=a+(n-1)d[/tex]we have given 100th term = 595 , so
[tex]\begin{gathered} a_{100}=a+(100-1)6 \\ 595=a+99\times6 \\ 595-594=a \\ a=1 \end{gathered}[/tex]so , first term = 1
second term = a + 6 = 7
third term = a + 2d = 1 +2*6 = 13
Final Answer
Therefore , the first terms of an arithmetic sequences are
[tex]a_1=1,a_2=7,a_3=13[/tex]State if the give binomial is a factor of the given polynomial [tex](9x ^{3} + 57x^{2} + 21x + 24) \div (x + 6)[/tex]
Answers
We want to find out if (x+6) is a factor of the polynomial
[tex]9x^3+57x^2+21x+24[/tex]In order to find this, we can use the factor theorem.
If we have a polynomial f(x) and want to find if (x-a) is a factor of this polynomial, we plug in x = a into the function and if we get 0, (x-a) is a factor(!)
Now, let's plug in:
x = -6 into the polynomial and see if we get a 0 or not.
Steps shown below:
[tex]\begin{gathered} 9x^3+57x^2+21x+24 \\ 9(-6)^3+57(-6)^2+21(-6)+24 \\ =-1944+2052-126+24 \\ =6 \end{gathered}[/tex]AnswerSince it doesn't produce a 0, (x + 6 ) is not a factor of the polynomial given.
place the letter of the angle relationship that beat represents the given angle pair in the box.
Answers
Angle relationship that best represents the given angle
Considering the angles in the attached diagram above
<6 and <13 has no relationship because they are not parallel
Hence NO relationship between <6 and <13
Solve for x. Enter the solutions from least to greatest.6x^2 – 18x – 240 = 0lesser x =greater x =
Answers
Answer:
x = -5
x = 8
Explanation:
If we have an equation with the form:
ax² + bx + c = 0
The solutions of the equation can be calculated using the following equation:
[tex]\begin{gathered} x=\frac{-b+\sqrt[]{b^2-4ac}}{2a} \\ x=\frac{-b-\sqrt[]{b^2-4ac}}{2a} \end{gathered}[/tex]So, if we replace a by 6, b by -18, and c by -240, we get that the solutions of the equation 6x² - 18x - 240 = 0 are:
[tex]\begin{gathered} x=\frac{-(-18)+\sqrt[]{(-18)^2-4(6)(-240)}}{2(6)}=\frac{18+\sqrt[]{6084}}{12}=8 \\ x=\frac{-(-18)-\sqrt[]{(-18)^2-4(6)(-240)}}{2(6)}=\frac{18-\sqrt[]{6084}}{12}=-5 \end{gathered}[/tex]Therefore, the solutions from least to greatest are:
x = -5
x = 8
I need help with this please, I know that the opposite of 4.6 is -4.6 but I don’t know how to explain it.
Answers
Answer:
As a rational number is a fraction we had to convert our number to a fraction, and as the opposite number is the number with the same magnitude but a different sign, we had to change the sign.
[tex]-4\cdot\frac{3}{5}[/tex]
Explanation
• Rational numbers are the numbers that can be written as the fraction of two integers.
,• Additionally, opposite numbers are numbers with the same magnitude but different signs.
Thus, based on these definitions, we have to change the sign and search for a fraction.
Steps:
0. From 4.6 we go to -4.6.
,1. We convert -4.6 to a fraction: -4 is the whole number and we are left with -0.6, which is 6/10 (as it is in the tenth's place).
,2. Simplifying 6/10 to 3/5 dividing both numbers by 2.
Determine the measures of the unknown angle.
Answers
To find the measure of the unknown angle we can use the triangle sum theorem that states that the sum of the measures of the interior angle of a triangle is 180°. We know the measure of two of the interior angles of the triangle that are 50° and 88°, and we can use this information to find the unknown one:
[tex]\begin{gathered} 50+88+\measuredangle3=180 \\ 138+\measuredangle3=180 \\ \measuredangle3=180-138 \\ \measuredangle3=42 \end{gathered}[/tex]The correct answer is C. 42°.
Solve each inequality 15 > 2x-7 > 9
Answers
Given the inequality expression
15 > 2x-7 > 9
Splitting the inequality expression into 2:
15 > 2x-7 and 2x - 7 > 9
For the inequality 15 > 2x-7
15 > 2x-7
Add 7 to both sides
15 + 7 > 2x - 7 + 7
22 > 2x
Swap
2x < 22 (note the change in signg
2x/2 < 22/2
x < 11
For the inequality 2x - 7 > 9
Add 7 to both sides
2x-7+7 > 9 + 7
2x > 16
Divide both sides by 2
2x/2 > 16/2
x > 8
Combine the solution to both inequalities
x>8 and x < 11
8 < x < 11
Hence the solution to the inequality expression is n)8 < x < 11
2x/2 < 22/2
x < 11
For the inequality 2x - 7 > 9
Add 7 to both sides
5 + 7 > 2x - 7 + 7
22 > 2x
Swap
2x < 22 (note the change in si)5 + 7 > 2x - 7 + 7
22 > 2x
Swap
2x < 22 (note the change in si)1
Express: 12x-9x-4x+3 in factored form
Answers
SOLUTION:
Step 1:
In this question, we are given the following:
Expressing:
[tex]12\text{ x - 9x - 4x + 3}[/tex]Step 2:
The details of the solution are as follows:
[tex]\begin{gathered} 12\text{ x -9x - 4 x + 3} \\ \text{= -x + 3} \\ =\text{ -\lparen x -3\rparen } \end{gathered}[/tex]CONCLUSION:
The final answer in factored form =
[tex]-(x-3)[/tex]The graph shows the number of gallons of white paint that were mixed with gallons of blue paint in various diffrent ratios:
Answers
From the graph, we can note that the points are in a line.
Hence, we must find the line equation for these points.
The general form of the straigh line equation is
[tex]y=mx+b[/tex]where m is the slope and b the y-intercept. The slope can be computed as
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]where,
[tex]\begin{gathered} (x_1,y_1)=(2,4) \\ (x_2,y_2)=(6,12) \end{gathered}[/tex]By substituying these values into m, we have
[tex]m=\frac{12-4}{6-2}[/tex]hence,
[tex]\begin{gathered} m=\frac{8}{4} \\ m=2 \end{gathered}[/tex]the form of the line equation is
[tex]y=2x+b[/tex]where x is the blue paint and y the white paint.
In order to find b, we can substitute one point into the above equation. For instance, the point
(2,4):
[tex]\begin{gathered} 4=2(2)+b \\ 4=4+b \\ b=0 \end{gathered}[/tex]Thefore, the line equation is
[tex]y=2x[/tex]Hence, the number of galons when we mix 1 gallon of blue pain is
[tex]\begin{gathered} y=2(1) \\ y=2 \end{gathered}[/tex]in other words, for 1 gallon of blue paint we must have 2 gallons of white paint
Solve the following inequality. Write the solution set in interval notation
Answers
Given:
Inequality is
[tex]5(x-3)<2(3x-1)[/tex]To find:
The solution set of the given inequality:
Explanation:
[tex]\begin{gathered} 5(x-3)<2(3x-1) \\ 5x-15<6x-2 \\ 5x-6x<15-2 \\ -x<13 \\ x>-13 \end{gathered}[/tex]Therefore the solution set is
[tex](-13,\hat{\infty)}[/tex]Final answer:
The solution set is
[tex](-13,\infty)[/tex]Solve the following equation3(x+1)=5-2(3x+4)
Answers
The given equation is expressed as
3(x+1)=5-2(3x+4)
The first step is to open the brackets on each side of the equation by multiplying the terms inside the bracket by the terms outside the bracket. It becomes
3 * x + 3 * 1 = 5 - 2 * 3x + - 2 * 4
3x + 3 = 5 - 6x - 8
3x + 6x = 5 - 8 - 3
9x = - 6
x = - 6/9
x = - 2/3
A faraway planet is populated by creatures called Jolos. All Jolos are either green or purple and either one-headed or two-headed. Balan, who lives on this planet, does a survey and finds that her colony of 852 contains 170 green, one-headed Jolos; 284 purple, two-headed Jolos; and 430 one-headed JolosHow many green Jolos are there in Balans colony?A.260B.422C.308D. 138
Answers
A. 260
Explanation
Step 1
Let
[tex]\begin{gathered} green\text{ jolos,one-headed jolo=170} \\ \text{Purple ,two-headed jolos=284} \\ one\text{ headed jolos=430} \end{gathered}[/tex]as we can see
the total of green-one headed jolo is 170
and the total for one headed jolo is =430
so, the one-headed in counted twice
[tex]\begin{gathered} total\text{ of gr}en\text{ jolos= }430-170 \\ total\text{ of gr}en\text{ jolos= }260 \end{gathered}[/tex]so, the answer is
A.260
I hope this helps you
Jim invested $4,000 in a bond at a yearly rate of 4.5%. He earned $540 in interest. Howlong was the money invested? (just type the number don't write years)
Answers
Answer:
3 years
Explanation:
The interest simple interest rate formula is
[tex]undefined[/tex]Imagine you are working for Hasbro making Gummy Bear containers. On a day to day basis you fill up two different size containers with gummy bears. One of the containers is4.4x5.7 x 6.0 in dimensions and contains 385 gummy bears. The other is 8.1 x 8.1 x 8.3 in dimensions. About how many gummy bears would fit in the box? Round to the nearestwhole number
Answers
It is given that,
One of the containers is 4.4 x 5.7 x 6.0 in dimensions and contains 385 gummy bears.
So, 1 gummy bear occupies,
[tex]\frac{4.4\times5.7\times6.0}{385}=0.39086[/tex]The other is 8.1 x 8.1 x 8.3 in dimensions.
So, the number of gummy bears would fit in the box is,
[tex]\frac{8.1\times8.1\times8.3}{0.39086}=1393.24[/tex]Hence, the number of gummy bears is 1,393 (Rounded to the nearest whole number).
Use your compass to help with the direction. Also, the question is in the question box
Answers
1. Extending the dashed lines
2. Translating the triangle ABC in the direction EF
copy the vector in each vertice
then with the final points draw the new triangle a distance of EF
The blue triangle is the translated triangle (in your case you can your compass to help with the direction and protractor to verify the distance).
NO LINKS!! Use the method of to solve the system. (if there's no solution, enter no solution). Part 2z
Answers
Answer:
smaller x-value: (-4, 18)
larger x-value: (3, 11)
Step-by-step explanation:
Solving for x:
y = x^2 + 2
x + y = 14 ---> y = 14 - x
14 - x = x^2 + 2
0 = x^2 + x - 12
0 = (x + 4)(x - 3)
x = -4 or 3
Solving for y:
If x = -4
y = 14 + 4
y = 18
if x = 3
y = 14 - 3
y = 11
Answer:
[tex](x,y)=\left(\; \boxed{-4,18} \; \right)\quad \textsf{(smaller $x$-value)}[/tex]
[tex](x,y)=\left(\; \boxed{3,11} \; \right)\quad \textsf{(larger $x$-value)}[/tex]
Step-by-step explanation:
Given system of equations:
[tex]\begin{cases}\phantom{bbbb}y=x^2+2\\x+y=14\end{cases}[/tex]
To solve by the method of substitution, rearrange the second equation to make y the subject:
[tex]\implies y=14-x[/tex]
Substitute the found expression for y into the first equation and rearrange so that the equation equals zero:
[tex]\begin{aligned}y=14-x \implies 14-x&=x^2+2\\x^2+2&=14-x\\x^2+2+x&=14\\x^2+x-12&=0\end{aligned}[/tex]
Factor the quadratic:
[tex]\begin{aligned}x^2+x-12&=0\\x^2+4x-3x-12&=0\\x(x+4)-3(x+4)&=0\\(x-3)(x+4)&=0\end{aligned}[/tex]
Apply the zero-product property and solve for x:
[tex]\implies x-3=0 \implies x=3[/tex]
[tex]\implies x+4=0 \implies x=-4[/tex]
Substitute the found values of x into the second equation and solve for y:
[tex]\begin{aligned}x=3 \implies 3+y&=14\\y&=14-3\\y&=11\end{aligned}[/tex]
[tex]\begin{aligned}x=-4 \implies -4+y&=14\\y&=14+4\\y&=18\end{aligned}[/tex]
Therefore, the solutions are:
[tex](x,y)=\left(\; \boxed{-4,18} \; \right)\quad \textsf{(smaller $x$-value)}[/tex]
[tex](x,y)=\left(\; \boxed{3,11} \; \right)\quad \textsf{(larger $x$-value)}[/tex]
Mason calculated the sales tax on his clothing purchase to be $5.57375. Round to the nearest hundredth. ANS $ __________
Answers
As per given by the question,
There are given that the sales tax is $5.57375.
Now,
For find the value nearest hundredth,
Nearest hundredth is the second digit after the decimal point.
That means,
If there is given that the value , x.yzw
Then, the nearest hundredth number is x.yz.
So,
From the given value.
The nearest hundredth value is, secon digit after the decima.
Here, second digit after the decimal is 57.
Then,
The nearest value of hundredth is 5.57.
Hence, the value is $5.57
Lizzy is tiling a kitchen floor for the first time. She had a tough time at first and placed only 6 tiles the firstday. She started to go faster and by the end of day 4, she had placed 36 tiles. She worked at a steady rateafter the first day. Use an equation in point-slope form to determine how many days Lizzy took to placeall of the 100 tiles needed to finish the floor. Solve the problem using an equation in point-slope form.
Answers
We know that
• She placed 6 tiles on the first day.
,• By the end of day 4, she had placed 36 tiles.
Based on the given information, we can express the following equation.
[tex]y=3x+6[/tex]If she had placed 36 tiles in 3 days, it means she had placed 12 tiles per day, that's why the coefficient of x is 3. And the number 6 is the initial condition of the problem, that is, on day 0 she placed 6 tiles.
Now, for 100 tiles, we have to solve the equation when y = 100.
[tex]\begin{gathered} 100=3x+6 \\ 100-6=3x \\ 3x=94 \\ x=\frac{94}{3} \\ x=31.33333\ldots \end{gathered}[/tex]Therefore, she needs 32 days to place all the tiles.Notice that we cannot say 31 days, because it would be incomplete.
If you bought 12 gallons of gas for $26.00, how much did you pay per gallon?
Answers
To get pay per gallon, we divide the total payment by the total amount of gallons.
So,
Total Cost = 26
Total Gallons = 24
Pay Per Gallon = 26/24 = $1.08 per gallon
if triangle ABC has sides of length 9, 15, and 3x, between which two numbers must the value of x lie?
Answers
Let's employ the triangle inequality here.
If the sides were to form a triangle.
Then if 3x was the longest side, it must be less than the sum of 15 and 9, being the other 2 sides.
So;
[tex]\begin{gathered} 3x<15+9 \\ 3x<24 \\ x<8 \end{gathered}[/tex]If 3x was the shortest side, then 15 would be the longest side, and thus
3x plus 9 must be greater than 15,
So;
[tex]\begin{gathered} 3x+9>15 \\ 3x>15-9 \\ 3x>6 \\ x>2 \end{gathered}[/tex]So, the range of values for which x must lie is;
[tex]2i.e any values greater than 2 but less than 8.Heart Rates For a certain group of individuals, the average heart rate is 74 beats per minute. Assume the variable is normally distributed and the standarddeviation is 2 beats per minute. If a subject is selected at random, find the probability that the person has the following heart rate. Use a graphing calculator.Round the answers to four decimal places.Higher than 73 beats per minute,P (x> 73) =
Answers
we need to determine P (x> 73)
when
mean: μ = 74 beats/min
standard deviation: σ = 2 beats/min
First we need to use the following formula:
[tex]z=\frac{x-\mu}{\sigma}[/tex]where
x = 73
μ = 74
σ = 2
and
Z is the z-score
... therefore
[tex]z=\frac{73-74}{2}=-\frac{1}{2}=-0.5[/tex]If we check a table of z scores, we will find that when z = -0.5, then P = 0.3085
Now, since we need P(x>73)
therefore
[tex]P=1-0.3085=0.6915[/tex]P(x>73) = 0.6915