Answer: I don’t know lol maybe 1460
Step-by-step explanation:
Let Z be the standard normal random variable. Use a probability calculator to answer the following questions: What is the probability Z will be within one standard deviation of average?
Answer:
0.6826 = 68.26% probability Z will be within one standard deviation of average.
Step-by-step explanation:
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
What is the probability Z will be within one standard deviation of average?
This is the p-value of Z = 1 subtracted by the p-value of Z = -1.
Z = 1 has a p-value of 0.8413.
Z = -1 has a p-value of 0.1587.
0.8413 - 0.1587 = 0.6826
0.6826 = 68.26% probability Z will be within one standard deviation of average.
In a certain town, 22% of voters favor the construction of a new hospital. For groups of 21 voters, find the variance for the number who did not favor the new hospital.
a. 1.9 voters
b. 4.6 voters
c. none of the given answers is correct
d. 3.6 voters
e. 13 voters
Answer:
Variance = 3.6 voteres
Step-by-step explanation:
Probability of favour voters, P = 0.22
Total number of voters, n = 21
The probability of voters who are in not favour of new hospital construction = 1 - P
The probability of voters who are in not favour of new hospital construction = 1 - 0.22
The probability of voters who are in not favour of new hospital construction, P* = 0.78
Variance = n x p* x (1 - p*)
Variance = 21 x 0.78 x 0.22
Variance = 3.6 voters
Flying with a tailwind, a flight crew flew 500 km in 4 hours. Flying against the tailwind, the crew flew 468 km in 4 hours. Find the speed of the plane in calm air and the speed of the wind, both in km per hour.
Answer:
spped of the plane in calm air=121 km/h
speed of the wind= 4km/h
Step-by-step explanation:
Let say V the speed of the plane in calm air
and v the speed of the wind
Flying with a tailwind, a flight crew flew 500 km in 4 hours ==> 500= (V+v)*4
Flying against the tailwind, the crew flew 468 km in 4 hours ==> 468 = (V-v)*4
We divide the 2 equations by 4 and then add the 2 results equations:
(500+468)/4=2V ==> V=121 (km/h)
We replace that value in the first equation:
V+v=500/4=125
v=125-121=4 (km/h)
I need help thank you so much !
Answer:
mana saya tau iwnisbagcayabaonsoanuwvsybwiwnusvwuagwyvwkwnwibsyafa
The mean monthly rent for a one-bedroom apartment without a doorman in Manhattan is 2630. Assume the standard deviation is$500 . A real estate firm samples 100 apartments. Use the TI-84 Plus calculator.a) What is the probability that the sample mean rent is greater than $27007?b) What is the probability that the sample mean rent is between $2450 and $2550? c) Find the 25th percentile of the sample mean. d) Would it be unusual if the sample mean were greater than $26457?e) Do you think it would be unusual for an individual to have a rent greater than $2645? Explain. Assume the variable is normally distributed.
Answer:
a) 0.0808 = 8.08% probability that the sample mean rent is greater than $2700.
b) 0.0546 = 5.46% probability that the sample mean rent is between $2450 and $2550.
c) The 25th percentile of the sample mean is of $2596.
d) |Z| = 0.3 < 2, which means it would not be unusual if the sample mean was greater than $2645.
e) |Z| = 0.3 < 2, which means it would not be unusual if the sample mean was greater than $2645.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
If |Z|>2, the measure X is considered unusual.
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
The mean monthly rent for a one-bedroom apartment without a doorman in Manhattan is $2630. Assume the standard deviation is $500.
This means that [tex]\mu = 2630, \sigma = 500[/tex]
Sample of 100:
This means that [tex]n = 100, s = \frac{500}{\sqrt{100}} = 50[/tex]
a) What is the probability that the sample mean rent is greater than $2700?
This is the 1 subtracted by the p-value of Z when X = 2700. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{2700 - 2630}{50}[/tex]
[tex]Z = 1.4[/tex]
[tex]Z = 1.4[/tex] has a p-value 0.9192
1 - 0.9192 = 0.0808
0.0808 = 8.08% probability that the sample mean rent is greater than $2700.
b) What is the probability that the sample mean rent is between $2450 and $2550?
This is the p-value of Z when X = 2550 subtracted by the p-value of Z when X = 2450.
X = 2550
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{2550 - 2630}{50}[/tex]
[tex]Z = -1.6[/tex]
[tex]Z = -1.6[/tex] has a p-value 0.0548
X = 2450
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{2450 - 2630}{50}[/tex]
[tex]Z = -3.6[/tex]
[tex]Z = -3.6[/tex] has a p-value 0.0002
0.0548 - 0.0002 = 0.0546.
0.0546 = 5.46% probability that the sample mean rent is between $2450 and $2550.
c) Find the 25th percentile of the sample mean.
This is X when Z has a p-value of 0.25, so X when Z = -0.675.
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]-0.675 = \frac{X - 2630}{50}[/tex]
[tex]X - 2630 = -0.675*50[/tex]
[tex]X = 2596[/tex]
The 25th percentile of the sample mean is of $2596.
Question d and e)
We have to find the z-score when X = 2645.
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{2645 - 2630}{50}[/tex]
[tex]Z = 0.3[/tex]
|Z| = 0.3 < 2, which means it would not be unusual if the sample mean was greater than $2645.
If it's possible to tell, decide if a and b are positive or negative: a-3>b-3 and b>4
PLEASE HELP NEED ASAPPPPPPP
Answer:
a and b are positive
Step-by-step explanation:
We are given that
[tex]a-3>b-3[/tex]
[tex]b>4[/tex]
We have to find that a and b are positive or negative.
We have
[tex]b>4[/tex]
It means b is positive and greater than 4.
[tex]a-3>b-3[/tex]
Adding 3 on both sides
[tex]a-3+3>b-3+3[/tex]
[tex]a>b>4[/tex]
[tex]\implies a>4[/tex]
Hence, a is positive and greater than 4.
Therefore, a and b are positive
Charles spent 1/4 of his allowance on a shirt, and 2/5 of the remainder on a book. A.What fraction of his allowance did he have left? B.If he spent $18 on the book, how much did he have at first?
Answer:
18.65
Step-by-step explanation:
1/4+2/5+18=18.65
18.65
hope it helps you good luck
How do i solve this quesiton 6(x − 2) > 15
Answer:
Step-by-step explanation:
[tex]\displaystyle\ \!\!6(x-2)>15 \\\\6x-12>15 \\\\6x>27\\\\ \boldsymbol{x>4,5 \ \ or \ \ x\in(4,5\ ; \infty)}[/tex]
Which quadratic function has minimum value at x = -b/2a?
O y=-3x2 + 5 X + 6
O y=x2 + 5 x + 6
O y=-x2 + 5x + 6
O y = -4 x2 + 5x + 6
Answer:
The choose (2)
y=x²+5x+6
Step-by-step explanation:
y=x²+5x+6 —> (–5/2 , –1/4)
y=-3x² + 5 X + 6 —> (5/6, 97/12)
y=-x² + 5x + 6 —> (5/2,49/4)
y = -4 x² + 5x + 6 —> (5/8 , 121/16)
Write an equation of the line through each pair of points in slope-intercept form.
a(– 3,–2) and (–3,4)
b(3,2)and (–4,–5)
Answer and I will give you brainiliest
Answer:
see below
Step-by-step explanation:
a) (– 3, –2) and (–3, 4)
First you want to find the slope of the line that passes through these points. To find the slope of the line, we use the slope formula: (y₂ - y₁) / (x₂ - x₁)
Plug in these values:
(4 - (-2) / (-3 - (-3))
Simplify the parentheses.
= (4 + 2) / (-3 + 3)
Simplify the fraction.
(6) / (0)
= undefined
If your slope is undefined, it is a vertical line. The equation of a vertical line is x = #.
In this case, the x-coordinate for both points is -3.
Therefore, your equation is x = -3.
b) (3, 2) and (–4, –5)
First you want to find the slope of the line that passes through these points. To find the slope of the line, we use the slope formula: (y₂ - y₁) / (x₂ - x₁)
Plug in these values:
(-5 - 2) / (-4 - 3)
Simplify the parentheses.
= (-7) / (-7)
Simplify the fraction.
-7/-7
= 1
This is your slope. Plug this value into the standard slope-intercept equation of y = mx + b.
y = 1x + b or y = x + b
To find b, we want to plug in a value that we know is on this line: in this case, I will use the first point (3, 2). Plug in the x and y values into the x and y of the standard equation.
2 = 1(3) + b
To find b, multiply the slope and the input of x(3)
2 = 3 + b
Now, subtract 3 from both sides to isolate b.
-1 = b
Plug this into your standard equation.
y = x - 1
This is your equation.
Check this by plugging in the other point you have not checked yet (-4, -5).
y = 1x - 1
-5 = 1(-4) - 1
-5 = -4 - 1
-5 = -5
Your equation is correct.
Hope this helps!
Which graph shows data that would allow the most accurate prediction for the number of water bottles a vendor sells based on the daily high temperature?
Graph A
Daily High Temperatures and Bottled Water Sales
On a graph, points are scattered all over the graph.
Graph B
Daily High Temperatures and Bottled Water Sales
On a graph, points are scattered all over the graph.
Graph C
Daily High Temperatures and Bottled Water Sales
On a graph, points are grouped together and form a line with positive slope.
Graph D
Daily High Temperatures and Bottled Water Sales
On a graph, points are grouped together and increase.
PLS HELP ILL GIVE BRAINLIEST FAST
9514 1404 393
Answer:
Graph C: Daily High Temperatures and Bottled Water Sales
On a graph, points are grouped together and form a line with positive slope.
Step-by-step explanation:
Apparently, Graph C shows data with the greatest degree of correlation. This suggests that any model of the data is likely to have less error than if the data were less well correlated.
Answer:
Graph C: Daily High Temperatures and Bottled Water Sales
On a graph, points are grouped together and form a line with positive slope.
Step-by-step explanation:
What is the simplified form of the following expression?
Answer:
-( cube root of 2x)-6(cube root of x)
what is 32⋅(12)x+1=2x−14?
Answer:
[tex]x=-\frac{15}{382}[/tex]
Step-by-step explanation:
32 × 12x + 1 = 2x - 14
384x + 1 = 2x - 14
384x + 1 - 1 = 2x - 14 - 1
384x = 2x - 15
384x - 2x = 2x - 2x - 15
382x = - 15
382x ÷ 382 = - 15 ÷ 382
[tex]x=-\frac{15}{382}[/tex]
Suppose 5 men and 7 women are on a crowded elevator. At the next floor, four people get off the elevator. Find the probability that three are women.
0.010
0.354
0.424
0.25
Total People=5+7+4=16
Women=7We know
[tex]\boxed{\sf P(W)=\dfrac{No.\:of\:women}{Total\:People}}[/tex]
[tex] \\ \sf \longmapsto \: p(w) = \frac{7}{16} [/tex]
What is an equation of the line that passes through the points (4,-2) and (8,-7)?
Answer:
the slope-intercept form for any line is y = mx + b, where m is the slope and b is the y-intercept.
now, let's calculate the slope:
=
here is the equation we currently have solved: y = x + b
now we have to solve for the y-intercept. to do this, we substitute one of the given points into the equation, and solve for b.
let's use (8, 2). in this ordered pair, the 8 is the x, and the 2 is the y.
2 = 8 + b
2 - 8 = b
b = -6
and now we have our final equation!
y = x - 6
hope this helped! please let me know if you are confused about anything i did smiley
Step-by-step explanation:
Answer:
y = -5/4x + 3Step-by-step explanation:
Find the slope first:
m = (y2 - y1)/ (2 - x1)m = (-7 + 2)/(8 - 4) = -5/4Use point-slope form and the coordinates of one of the points:
y - y1 = m(x - x1)y - (-2) = -5/4(x - 4)y + 2 = - 5/4x + 5y = -5/4x + 3Random samples of size 100 are taken from an infinite population whose population proportion is 0.2. The mean and standard deviation of the sample proportion are:__________
a) 0.2 and .04
b) 0.2 and 0.2
c) 20 and .04
d) 20 and 0.2
Answer:
c I think
Step-by-step explanation:
just cuz I did the math but I don't wanna type rn
Please help , write your answer I will be giving 10 points
Answer:
yes it represents the graph accurately
A nut company is determining how to package their new type of party mix. The marketing department is experimenting with different-sized cans for the party mix packaging. The designers use the equation r=Vhπ⎯⎯⎯⎯⎯⎯√r=Vhπ to determine the radius of the can for a certain height hh and volume VV. The company decides they want the can to have a volume of 1280πcm31280πcm3. Find the radius of the can if the height is 16cm16cm. Keep your answers in simplified radical form.
Answer:
The radius of the can, in centimeters, is of [tex]4\sqrt{5}[/tex]
Step-by-step explanation:
Radius of the can:
The radius of the can is given by:
[tex]r^2 = \frac{V}{h\pi}[/tex]
In which V is the volume and h is the height.
In this question:
[tex]V = 1280\pi, h = 16[/tex]
Thus
[tex]r^2 = \frac{V}{h\pi}[/tex]
[tex]r^2 = \frac{1280\pi}{16\pi}[/tex]
[tex]r^2 = 80[/tex]
[tex]r = \sqrt{80}[/tex]
[tex]r = \sqrt{5*16}[/tex]
[tex]r = \sqrt{5}\sqrt{16}[/tex]
[tex]r = 4\sqrt{5}[/tex]
The radius of the can, in centimeters, is of [tex]4\sqrt{5}[/tex]
6/5 times 17/18 in lowest terms
Answer:
17/15
Step-by-step explanation:
6/5 * 17/18
1/5 * 17/3
17/15
Select the correct answer
The equation of a line is y= 15x-2 What are its slope and y-intercept?
A.slope = 15 and y-intercept=-2
B.slope = 15 and y-intercept = 2
C.slope = 2 and y-intercept=15
D.siope =-2 and y-intercept=15
RES
Answer:
A
Step-by-step explanation:
Slope = term that multiply x
y intercept = the number without a variable
Please help, I’m not sure about this question.
How many 10-letter words real or imaginary can. Be formed from the following letters R,S,P,Q,H,J,S,M,B,A
Answer: 3628800
Step-by-step explanation: there are 10 letters so we multiply each with the other 1x2x3x4x5x6x7x8x9x10 or 10! to know all possible combinations so the answer will be 3628800.
Hope it helped!
Answer:
[tex]1,814,400[/tex]
Step-by-step explanation:
The number of ways to arrange a word with [tex]d[/tex] distinct digits is each to [tex]d![/tex]. Since there are 10 letters, there are [tex]10![/tex] permutations initially formed.
However, there is one letter that is repeated, S. We need to account for that fact that switching the placement of the S's does not change the word, as they still appear the same. Therefore, divide [tex]10![/tex] by the number of ways you can arrange the 2 S's, which is simply [tex]2![/tex]. Therefore, our answer is:
[tex]\frac{10!}{2!}=10 \cdot 9\cdot 8\cdot 7\cdot 6\cdot 5\cdot 4\cdot 3=\boxed{1,814,000}[/tex]
Write an equation for a line containing (–2,8) that is perpendicular to the line containing the points (3,–4)and (–7,1).
Answer and I will give you brainiliest
Answer:
y = 2x + 12
Step-by-step explanation:
the formula for a line is typically
y = ax + b
a is the slope of the line (expressed as y/x ratio describing how many units y changes, when x changes a certain amount of units).
b is the offset of the line in y direction (for x=0).
we have the points (3, -4) and (-7, 1).
to get the slope of the line let's wander from left to right (x direction).
to go from -7 to 3 x changes by 10 units.
at the same time y changes from 1 to -4, so it decreases by 5 units.
so, the slope is -5/10 = -1/2
and the line equation looks like
y = -1/2 x + b
to get b we simply use a point like (3, -4)
-4 = -1/2 × 3 + b
-4 = -3/2 + b
-5/2 = b
so, the full line equation is
y = -1/2 x - 5/2
now, for a perpendicular line the slope exchanges x and y and flips the sign.
in our case this means +2/1 or simply 2.
so, the line equation for the perpendicular line looks like
y = 2x + b
and to get b we use the point we know (-2, 8)
8 = 2×-2 + b
8 = -4 +b
12 = b
so, the full equation for the line is
y = 2x + 12
Answer:
2x-y+12= 0 or y = 2x+12 is the answer
Step-by-step explanation:
slope of the line joining (3,-4) and (-7,1) is 1-(-4)/-7-3
= -5/10
= - 1/2
slope of the line containing (-2,8) and that is perpendicular to the line containing (3,-4) and (-7,1) = 2
Equation of the line line containing (-2,8) and that is perpendicular to the line containing (3,-4) and (-7,1) is y-8 = 2(x-(-2))
y-8 = 2(x+2)
y- 8 = 2x+4
y=2x+12 (slope- intercept form) or 2x-y+12= 0 (point slope form)
1/2-5(2/3x + 6)+4/5x?
Answer:
[tex]-29.5-\frac{38}{15}x[/tex]
Step-by-step explanation:
First, we must expand out the -5.
-5 times 2/3x is equal to -10/3x, and -5 times 6 is equal to -30. 1/2 minus 30 is equal to -29.5, and 4/5x minus 10/3x is equal to -38/15x.
x=cos(2t), y=sin(2t) find a rectangular coordinate equation for the curve by eliminating the parameter
Answer:
x^2+y^2=1
Step-by-step explanation:
Since cos^2(x)+sin^2(x)=1, x^2+y^2=1
The number of calls received by an office on Monday morning between 8:00 AM and 9:00 AM has a mean of 5. Calculate the probability of getting at least 4 calls between eight and nine in the morning.
Answer:
0.735 = 73.5% probability of getting at least 4 calls between eight and nine in the morning.
Step-by-step explanation:
We have the mean during a time interval, which means that the Poisson distribution is used to solve this question.
In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:
[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]
In which
x is the number of sucesses
e = 2.71828 is the Euler number
[tex]\mu[/tex] is the mean in the given interval.
The number of calls received by an office on Monday morning between 8:00 AM and 9:00 AM has a mean of 5.
This means that [tex]\mu = 5[/tex]
Calculate the probability of getting at least 4 calls between eight and nine in the morning.
This is:
[tex]P(X \geq 4) = 1 - P(X < 4)[/tex]
In which
[tex]P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)[/tex]
So
[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]
[tex]P(X = 0) = \frac{e^{-5}*5^{0}}{(0)!} = 0.0067[/tex]
[tex]P(X = 1) = \frac{e^{-5}*5^{1}}{(1)!} = 0.0337[/tex]
[tex]P(X = 2) = \frac{e^{-5}*5^{2}}{(2)!} = 0.0842[/tex]
[tex]P(X = 3) = \frac{e^{-5}*5^{3}}{(3)!} = 0.1404[/tex]
Then
[tex]P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) = 0.0067 + 0.0337 + 0.0842 + 0.1404 = 0.265[/tex]
[tex]P(X \geq 4) = 1 - P(X < 4) = 1 - 0.265 = 0.735[/tex]
0.735 = 73.5% probability of getting at least 4 calls between eight and nine in the morning.
Suppose we take a poll (random sample) of 3923 students classified as Juniors and find that 3196 of them believe that they will find a job immediately after graduation. What is the 99 % confidence interval for the proportion of GSU Juniors who believe that they will, immediately, be employed after graduation.
Answer:
The 99% confidence interval for the proportion of GSU Juniors who believe that they will, immediately, be employed after graduation is (0.7987, 0.8307).
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].
Suppose we take a poll (random sample) of 3923 students classified as Juniors and find that 3196 of them believe that they will find a job immediately after graduation.
This means that [tex]n = 3923, \pi = \frac{3196}{3923} = 0.8147[/tex]
99% confidence level
So [tex]\alpha = 0.01[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.01}{2} = 0.995[/tex], so [tex]Z = 2.575[/tex].
The lower limit of this interval is:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.8147 - 2.575\sqrt{\frac{0.8147*0.1853}{3923}} = 0.7987[/tex]
The upper limit of this interval is:
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.8147 + 2.575\sqrt{\frac{0.8147*0.1853}{3923}} = 0.8307[/tex]
The 99% confidence interval for the proportion of GSU Juniors who believe that they will, immediately, be employed after graduation is (0.7987, 0.8307).
Need Help! ASAP!!! I gave a screen shot. Please someone give me the correct answer.
9514 1404 393
Answer:
x ∈ {-35, 0, 35}
Step-by-step explanation:
We can solve for x and equate those values to find corresponding y-values. Substituting into the original expressions for x gives the possible x-values.
[tex]x+xy^2=250y\ \Rightarrow\ x=\dfrac{250y}{1+y^2}\\\\x-xy^2=-240y\ \Rightarrow\ x=\dfrac{-240y}{1-y^2}\\\\\dfrac{250y}{1+y^2}+\dfrac{240y}{1-y^2}=0\\\\\dfrac{25y(1-y^2)+24y(1+y^2)}{(1+y^2)(1-y^2)}=0\\\\y(-y^2+49)=0=y(7-y)(7+y)\ \Rightarrow\ y\in\{-7,0,7\}\\\\x=\dfrac{250(\pm 7)}{1+(\pm7)^2}=\pm35,\quad=\dfrac{250(0)}{1+0^2}=0\\\\\boxed{x\in\{-35,0,35\}}[/tex]
Clear parentheses by applying the distributive property.
-(-4s + 9t + 7)
Answer:
4s-9t-7
Step-by-step explanation:
multiply the negative one with all terms inside the bracket, since they are all unlike terms the answer remains the same
Please Help me and don't report this
8 < x < 8.5 is your answer
other sides has to always be less than the hypotenuse
9514 1404 393
Answer:
0.5 < x < 16.5
Step-by-step explanation:
The sum of the two shortest sides of a triangle must always exceed the length of the longest side.
If x and 8.0 are the short sides, then ...
x + 8.0 > 8.5
x > 0.5
If 8.0 and 8.5 are the short sides, then ...
8.0 +8.5 > x
16.5 > x
So, for the given triangle to exist, we must have ...
0.5 < x < 16.5
_____
Additional comment
You will notice that the value 0.5 is the difference of the given sides, and 16.5 is their sum. This will always be the case for a problem like this. The third side length always lies between the difference and the sum of the other two sides.
