Answer:
f(x) = 15
Step-by-step explanation:
"If f(x)= 5x + 40, what is f(x) when x = -5?"
Substitute x for -5:
f(x) = 5x + 40
f(x) = 5(-5) + 40
f(x) = -25 + 40
f(x) = 15
Find the directional derivative of f at the given point in the direction indicated by the angle θ.
f(x, y) = y cos(xy), (0, 1), θ = π/4
Answer:
Directional derivative = 1/√2
Step-by-step explanation:
We are given f(x, y) = y cos(xy)
Now, we know that;
∇f(x, y) = ycos xy
Thus, applying that to the question, we have;
∇f(x, y) = [-y² sin xy, cos (xy) - xy sin xy]
At coordinates (0,1),we now have;
∇f(0, 1) = [-1²•sin0, (cos 0) - 0]
∇f(0, 1) = [0, 1]
Now, unit vector indicated by the angle θ is given as; u = [cos θ, sin θ]
From the question, since θ = π/4, thus
u = [cos π/4, sin π/4]
Cos π/4 in surd form is; 1/√2
Also, sin π/4 in surd form is; 1/√2
So, u = [1/√2, 1/√2]
Directional derivative = [∇f(0, 1)] • u
= [0, 1] × [1/√2, 1/√2] = 0 + 1/√2 = 1/√2
The article "Expectation Analysis of the Probability of Failure for Water Supply Pipes"† proposed using the Poisson distribution to model the number of failures in pipelines of various types. Suppose that for cast-iron pipe of a particular length, the expected number of failures is 1 (very close to one of the cases considered in the article). Then X, the number of failures, has a Poisson distribution with μ = 1. (Round your answers to three decimal places.) Obtain P(X ≤ 5) by using the Cumulative Poisson Probabilities What is the probability that X exceeds its mean value by more than one standard deviation?
Answer:
a. P(X ≤ 5) = 0.999
b. P(X > λ+λ) = P(X > 2) = 0.080
Step-by-step explanation:
We model this randome variable with a Poisson distribution, with parameter λ=1.
We have to calculate, using this distribution, P(X ≤ 5).
The probability of k pipeline failures can be calculated with the following equation:
[tex]P(k)=\lambda^{k} \cdot e^{-\lambda}/k!=1^{k} \cdot e^{-1}/k!=e^{-1}/k![/tex]
Then, we can calculate P(X ≤ 5) as:
[tex]P(X\leq5)=P(0)+P(1)+P(2)+P(4)+P(5)\\\\\\P(0)=1^{0} \cdot e^{-1}/0!=1*0.3679/1=0.368\\\\P(1)=1^{1} \cdot e^{-1}/1!=1*0.3679/1=0.368\\\\P(2)=1^{2} \cdot e^{-1}/2!=1*0.3679/2=0.184\\\\P(3)=1^{3} \cdot e^{-1}/3!=1*0.3679/6=0.061\\\\P(4)=1^{4} \cdot e^{-1}/4!=1*0.3679/24=0.015\\\\P(5)=1^{5} \cdot e^{-1}/5!=1*0.3679/120=0.003\\\\\\P(X\leq5)=0.368+0.368+0.184+0.061+0.015+0.003=0.999[/tex]
The standard deviation of the Poisson deistribution is equal to its parameter λ=1, so the probability that X exceeds its mean value by more than one standard deviation (X>1+1=2) can be calculated as:
[tex]P(X>2)=1-(P(0)+P(1)+P(2))\\\\\\P(0)=1^{0} \cdot e^{-1}/0!=1*0.3679/1=0.368\\\\P(1)=1^{1} \cdot e^{-1}/1!=1*0.3679/1=0.368\\\\P(2)=1^{2} \cdot e^{-1}/2!=1*0.3679/2=0.184\\\\\\P(X>2)=1-(0.368+0.368+0.184)=1-0.920=0.080[/tex]
Cora has some ice cream that she is serving for her friends. If Cora gives 1/6 of a quart of ice cream to each of her 8 friends, how much ice cream does she serve in total?
Answer:
8/6 of a quart (4/3)
Step-by-step explanation:
thats more than she has, unless she has 2 quarts
The answer is 4/3
Please see the attached picture for full solution
Hope it helps
Good luck on your assignment
a parabola intersects the x axis at x=2 and x=8. What is the x corrdinate
Answer:
The x coordinate of the parabola's vertex is: 5
Step-by-step explanation:
Although you didn't finish the phrases of the question, if they were asking the x-value for the x-coordinate of the parabola's vertex, which is a typical question for this type of problem, recall that the vertex is position equidistant from the parabola's branches because the parabola is a symmetric figure.
Therefore we need to find the point half way between x = 2 and x = 8.
Notice that the distance between these two points is "6" units, and half of such distance is "3" units, so the vertex must be located 3 units to the right of 2 (or equivalently 3 units to the left of 8).
Therefore, the x-coordinate of this parabola's vertex is "5"
What is the measure of
Answer: C. 84
Step-by-step explanation:
In triangles ABD y BCD:
- AD=CD
- Angle BAD = angle BCD
- BD common side
THEN the triangles are equal because they have two sides and the angle opposite the longest side respectively equal.
CBD = ABD = 42 because the triangles ABD y BCD are equal
ABC = CBD+ABD = 42+42= 84
Answer:
C. 84 degrees
Step-by-step explanation:
What is the amplitude ? How do I find it? do I add 7.7 to (-6.7) then divide? Thank you in advance
Answer:
7.2
Step-by-step explanation:
The amplitude is half the difference between the maximum and the minimum.
A = (7.7 − (-6.7)) / 2
A = 7.2
Please answer this question !! Will give brainliest !
Answer & Step-by-step explanation:
In order to find the y-intercept of this equation, we must turn this equation into a slope-intercept equation. The equation for slope-intercept form is y=mx+b. We can do this by using these steps. Our goal is to get y by itself on one side.
6x - 2y - 9 = 0
Step 1: Add 9 on both sides of the equation.
6x - 2y = 9
Step 2: Subtract 6x on both sides of the equation. Once you subtract, make sure you put the -6x in front of 9 so we are following the rules of variables and exponents.
-2y = -6x + 9
Step 3: Divide -2 on both sides of the equation.
y = 3x - [tex]\frac{9}{2}[/tex]
So, the y-intercept is -[tex]\frac{9}{2}[/tex]
g(x)=\dfrac{x+6}{2}g(x)=
2
x+6
g, left parenthesis, x, right parenthesis, equals, start fraction, x, plus, 6, divided by, 2, end fraction
What is the domain of g?g
Answer:
all real numbers
Step-by-step explanation:
The fraction simplifies to the polynomial ...
g(x) = (1/2)x +3
Every polynomial has a domain of "all real numbers."
Answer: All Real Values of X
Step-by-step explanation:
Khan said so
The zeros of a function P(x)=x2-2x-24
Answer:
x = -4 and x = 6
Step-by-step explanation:
Factor using AC method.
1 × -24 = -24
Factors of -24 that add up to -2 are +4 and -6.
P(x) = (x + 4) (x − 6)
Therefore, zeroes of P(x) are x = -4 and 6.
Please answer this correctly
Answer:
98.5
Step-by-step explanation:
64.4 x 2= 128.8
325.8-128.8=197.0
197 /2 = 98.5
brainliest plzz
Answer:
Hey mate,
here is your answer. Hope it helps you.
Step-by-step explanation:
x+x+64.4+64.4=325.8
2x+ 128.8 =325.8
2x = 325.8 - 128.8
2x = 197
x= 197/2
=98.5 inches
A new American graduate is contemplating buying a Japanese, German, or an American car. No matter the type of car, he plans to buy a new one at the end of 8 years. Japanese car will cost $30,000 and have a fuel usage of 23 Miles Per gallon (mpg) for the first 2 years, and will decrease by 3% per year thereafter. Repair cost will start at $700 per year, and increase by 3% per year. At the end of year 8, the car can be sold for $5000. Insurance cost will be $700 for the first year, increasing by 2% per year thereafter. A German car will cost $45,000 and have fuel usage of 21mpg for the first 5 years, and decrease by 1% thereafter to year 8. Repair cost will start at $1000 in year 1 and increase by 4% per year. It will have a salvage value of $7000 at the end of year 8. Insurance cost will be $850 the first year, increasing by 2% per year thereafter. The American car will cost $35,000 and have fuel usage of 20mpg for the first 3 years, and will decrease by 3% per year thereafter. Repair cost will be $800 in year 1, increasing by 4% per year thereafter. Being an American, the graduate will price the pride of owning an American car at $0.4 for every 20 miles driven, increasing by 2% per year. Insurance cost will be $800 per year increasing by 2.2% per year. The car can be sold for $5500 at the end of year 8. If the graduate anticipates driving 150000 miles by the end of year 8 and the average interest rate is expected to remain at 5% per year, which car is economically affordable based on present worth analysis? Assume fuel cost will be $3 per gallon in year 1 and increase by an average of 2% per year. Show all your workings.
Answer:
The best option is to buy Japanese Car.
Step-by-step explanation:
Fuel usage per year is 150000/ 8 = 18750 miles per year
Fuel cost (year 1 -8) = $3.0, $3.06, $3.12, $3.18, $3.25, $3.312, $3.38, $3.5
Japanese Car:
Fuel usage 18750 / 23 = 815 * $3 = $2446
Fuel charges (year 1 -8) = $2445, $2494, $2623, $2758. $2900, $3050, $3207, $3372
Repair Cost (year 1 - 8) = $700, $721, $742, $764, $787, $811, $835, $860
Insurance cost (Year 1 - 8) = $700, $714, $728, $742, $757, $772, $788, $804
Present value of cost at 5% = 24674.07
Cost of car is $30,000
Total cost = $54674.07
Amercian Car:
Cost $35,000
Fuel usage 18750/20 = 937.5 * $3 per gallon = $2812.5.
Fuel charges (year 1 -8) = $2812, $2913, $2986, $3011. $3098, $3124, $3176, $3208
Repair Cost (year 1 - 8) = $800, $894, $921, $978, $1109, $1176, $1207, $1301
Insurance cost (Year 1 - 8) = $800, $827, $876, $898, $908, $932, $954, $934
Present value of cost at 5% = 25302.18
Cost of car is $35,000
Total cost = $60302.
German Car:
Cost = $45,000
Fuel usage 18750 / 21 = 892 * $3 = $2678
Fuel charges (year 1 -8) = $2679, $2732, $2786, $2842. $2899, $2987, $3077, $3171
Repair Cost (year 1 - 8) = $1000, $1040, $1081, $1124, $1169, $1216, $1265, $1316
Insurance cost (Year 1 - 8) = $850, $867, $884, $902, $920, $938, $957, $976
Present value of cost at 5% = 27105.73
Cost of car is $45,000
Total cost = $72105.
Find the slope of the line on the graph.
Write your answer as a fraction or a whole
number, not a mixed number or decimal.
Answer:
-3
Step-by-step explanation:
We can see that the line passes through (0,3) and (1,0)
So using rise over run we have
-3/1
or
-3
If 3^x=10, what is the value of 3^x-3? A. 10/3 B. 10/9 C. 10/27 D. 27/10
Answer:
B.
Step-by-step explanation:
Recall the properties of logs and once you find the value of x, substitute it into the equation.
Option C ([tex]\frac{10}{27}[/tex]) is the correct alternative.
Given expression is:
→ [tex]3^x = 10[/tex]
By taking log both sides, we get
→ [tex]ln \ 3^x = ln \ 10[/tex]
[tex]x \ ln \ 3= ln \ 10[/tex]
[tex]x = \frac{ln \ 10}{ln \ 3}[/tex]
By substituting the value of "x" in "[tex]3^{x-3}[/tex]", we get
→ [tex]3^{x-3}[/tex] = [tex]3^{\frac{ln \ 10}{ln \ 3} -3}[/tex]
= [tex]\frac{10}{27}[/tex]
So the above is the right solution.
Learn more:
https://brainly.com/question/47626
A population of bacteria is growing at a rate of 20% per hour. If the population starts at 320, what is it an hour later?
Answer:
384.
Step-by-step explanation:
The population is given by the expression;
[tex]Y(t) = Pr^{t}[/tex]
Where;
Y(t) is the number of bacteria at time, t.
P is the starting amount.
r is the growth rate.
Given that, P = 320, r = 20% = 0.2, t = 1
Substituting the parameters into the equation;
[tex]Y(t) = Pr^{t}[/tex]
Y(1) = 320 * 0.2¹
Y(1) = 320 * 0.2
Y(1) = 64.
Therefore, the population of bacteria increases hourly by 64.
An hour later; 320 + 64 = 384.
What else would need to be congruent to show that ABC PQR by SSS?
Answer:
A
Step-by-step explanation:
The SSS is the side-side-side way to prove the triangles are congruent, so each side needs to have a match between triangle 1 and triangle 2. Since AC and BC are congruent to sides, that leaves AC. Hope this helps :)
To prove that both triangles are congruent, the additional information needed is: A. AB ≅ PQ.
What is the SSS Congruence Theorem?Two triangles with three pairs of corresponding congruent sides can be proven to be congruent to each other based on the SSS congruence theorem.
We are already given that two pairs of corresponding sides of the two triangles are congruent. To prove that triangles ABC and PQR are congruent by SSS, the additional information needed is: A. AB ≅ PQ.
Learn more about SSS congruence theorem on:
https://brainly.com/question/2102943
#SPJ5
For the results of a certain survey, the estimated probability of being a car owner was 0.77 for males and 0.62 for females. Express each of these as a conditional probability. The probability of being a car owner (CO ) was 0.77 for males (M). Express this as a conditional probability.
Answer:
P(CO|M)=0.77 for male
and P(CO|M^c)=0.62 for female
Step-by-step explanation:
When we talk of conditional probability, we refer to the measure of the probability of an event given that another event has occurred
Here, we are to express the results of the survey as a conditional probability.
For the male part of the question, the conditional probability means that, given that the person is a male, the probability that he is a car owner would be;
P(CO|M)=0.77
For the female part of the question, what we have as a conditional probability is that if a person is a female that she is a car owner is;
P(CO|M^c)=0.62
Please kindly understand that the term M^c refers to M complement in words
in a survey of employee satisfaction , 60% of the employees are male and 45% of the employees are satisfied. what is the probability of randomly selecting an employee who is male and satisfied
Answer:
27%
Step-by-step explanation:
6/10*45/100=270/1000 which is 27/100 which is 27%
What is the measure of arc BC
Answer:
Option B
Step-by-step explanation:
As property of angle inside circle, arc BC = 2 x angle BDC.
Let's consider triangle ABD.
BAD = 98 deg
ABD = (1/2) x arc AD = (1/2) x 80 = 40 deg
As the property of sum of 3 angles in a triangle,
=> ADB + ABD + BAD = 180
=> ADB = 180 - ABD - BAD = 180 - 40 - 98 = 42 deg
=> BDC = 70 - 42 = 28
=> arc BC = 2 x 28 = 56 deg
=> Option B is correct
Eric’s average income for the first 4 months of the year is $1,450.25, what must be his
average income for the remaining 8 months so that his average income for the year is
$1,780.75?
Answer:[tex]\$1946[/tex]
Step-by-step explanation:
Given
Eric average income for four months is [tex]S_1=\$1450.25[/tex]
average Annual income [tex]S=\$1780.75[/tex]
Average income [tex]=\dfrac{\text{Total salary}}{\text{Time }}[/tex]
Sum of 4 month salary [tex]=4\times S_1[/tex]
Sum of 4 month salary [tex]=\$5801[/tex]
Average salary of remaining 8 months[tex]=S_2[/tex]
Sum of last 8 months salary[tex]=8\times S_2[/tex]
So average Salary [tex]S=\dfrac{4\times S_1+8\times S_2}{12}[/tex]
[tex]\Rightarrow 1780.75=\dfrac{4\times 1450.25+8\times S_2}{12}[/tex]
[tex]\Rightarrow 21,369=5801+8\times S_2[/tex]
[tex]\Rightarrow 15,568=8\times S_2[/tex]
[tex]\Rightarrow S_2=\dfrac{15,568}{8}=\$1946[/tex]
So, average salary of remaining 8 months is [tex]\$1946[/tex]
A geologist is making repeated measurements (in grams) on the mass of a rock. It is not known whether the measurements are a random sample from an approximately normal population. Below are three sets of replicate measurements, listed in the order they were made. For each set of readings, state whether the assumptions necessary for the validdity of the t-test appear to be met. If the assumptions are not met, explain why?
a. 213.03 212.95 213.04 213.00 212.99 213.01 221.03 213.05
b. 213.05 213.00 212.94 213.09 212.98 213.02 213.06 212.99
c. 212.92 212.95 212.97 213.00 213.01 213.04 213.05 213.06
Answer:
Step-by-step explanation:
The objective of this question is to known whether the assumptions of the known data set follows normal distribution or not and if it is appropriate to use t-test or not.
TO solve this question ; we construct a box plot for the known data set by using a MINITAB software
The process is as follows to guide you:
Enter your data in the worksheet
Then select Graph→ Boxplot→ EDA→ Boxplot
Under One Y , select simple, Then click OK
In Variables , enter measurements. Then click OK
So; for the first data set (a) 213.03 212.95 213.04 213.00 212.99 213.01 221.03 213.05 as shown in the attached file in word document for the boxplot below;
We will observe that there is a outliner present in the data set and the measurement do not meet the normal assumption ; as a result to that ; the t-distribution is not appropriate for this data.
(b) From the document attached below; we will realize and observe that the boxplot doesn't contains an outliner. Also; it is clear and obvious that the shape of the distribution is right skewed. The measurement thus did not meet the assumptions and as a result t- distribution is not appropriate for this data.
(c)
From the document attached below; we will realize and observe that the boxplot doesn't contains an outliner. Also; it is clear and obvious that the shape of the distribution is left skewed. The measurement thus did not meet the assumptions and as a result t- distribution is not appropriate for this data.
(a): The [tex]t-[/tex]distribution is not appropriate for this data.
(b): The [tex]t[/tex]-distribution is not appropriate for this data.
(c): The [tex]t[/tex]- distribution is not appropriate for this data.
[tex]t-[/tex]test:
A t-test is a statistical test that is used to compare the means of two groups.
Part(a):
Check whether the unknown data set follows the normal distribution or not and is it appropriate to use the [tex]t[/tex]-test or not.
Use the following MS excel instructions to draw a box plot.
Step-1: Enter the data into an excel sheet.
Step-2: Click add-ins-Mega stat-Descriptive statistics.
Step-3: Input the data into the input range box.
Step-4: Click Box-Plot -Click OK
It is observed that there is an outlier in the data set.
The obtained output is as follows:
So, the measurements do not satisfy the normality assumption.
Part(b):
Check whether the known data set follows normal distribution or not and is it appropriate to use the [tex]t[/tex]-test or not.
Use the above MS excel instruction to draw a Box plot.
The obtained output is as follows.
It is observed that there is no outlier in the data set and the shape of the distribution is appears to be right-skewed.
So, the measurement do not satisfy the normality assumption.
Part(c):
Check whether the known data set follows normal distribution or not and is it appropriate to use the [tex]t[/tex]- test or not.
Use the above MS Excel instruction to draw a Box-plot.
The obtained output is as follows.
It is observed that there is no outlier in the data set and the shape of the distribution is appears skewed to the left.
So, the measurement do not satisfy the normality assumption.
Learn more about the topic [tex]t-[/tex]test:
https://brainly.com/question/25999758
what is the equation of a quadratic function p with rational coefficients that has a zero of 3-i
Answer:
p = x² − 6x + 10
Step-by-step explanation:
Complex roots come in conjugate pairs. So if 3−i is a root, then 3+i is also a root.
p = (x − (3−i)) (x − (3+i))
p = x² − (3+i)x − (3−i)x + (3−i)(3+i)
p = x² − 3x − ix − 3x + ix + (9 − i²)
p = x² − 6x + 10
You can check your answer using the quadratic formula.
x = [ -b ± √(b² − 4ac) ] / 2a
x = [ 6 ± √(36 − 40) ] / 2
x = (6 ± 2i) / 2
x = 3 ± i
Find the number of real number solutions for the equation.
x2- 6=0
Answer:
x=3
Step-by-step explanation:
2x-6=0
2x=0+6
2x=6
2x/2=6/2
x=3
The 4th time of me posting this question
suppose that y and z are points on a number line if y z equals 16 + y lies at -4 where could z be located
Corrected Question
Suppose that y and z are points on a number line if yz equals 16 and y lies at -4. Where could z be located?
Answer:
z would be located at -4.
Step-by-step explanation:
If the product of y and z, yz=16
Point y lies at -4.
Substituting y=-4 into yz=16, we obtain:
[tex]-4z=16[/tex]
Divide both sides by -4
[tex]z=-4[/tex]
Therefore, z would be located at -4, which is the same point at which y is located.
y and z are the same points on the number line.
We know our result is correct because the product of two negative numbers is positive.
Determine whether the quadrilateral is a parallelogram using the specified method.
D(-8, 1), E(-3, 6), F(7, 4), G(2, -1)
Answer:
It is a parallelogram, I don't know what specified method you want us to use
Each situation described bellow requires inference about a mean or means. Identify each as involving (1) a single sample, (2) matched pairs, or (3) two independent samples.
1- Looking back on love. Choose 40 romantically attached couples in their midtwenties. Interview the man and woman separately about a romantic attachment they had at age 15 or 16. Compare the attitudes of men and women.
2- Chemical analysis. To check a new analytical method, a chemist obtains a reference specimen of known concentration from the National Institute of Standards and Technology. She then makes 20 measurements of the concentration of this specimen with the new method and checks for bias by comparing the mean result with the known concentration.
3- Chemical analysis, continued. Another chemist is checking the same new method. He has no reference specimen, but a familiar analytic method is available. He wants to know if the new and old methods agree. He takes a specimen of unknown concentration and measures the concentration 10 times with the new method and 10 times with the old method.
Answer:
1) matched samples
2) single sample
3) independent samples
Step-by-step explanation:
1) couples were taken and their behaviors matched
2) only one sample was used
3) two different samples were used and their average compared.
Jackie's broker charges her a commission of $8 per ten share of stock she buys or sells. If jackie buys 77 shares of Alesia insurance at 10.34 per share and 120 shares of Ergar Appliances at 8.11 per share, how much will Jackie spend on commission?
Answer:
$157.60
Step-by-step explanation:
77 shares + 120 shares = 197 total shares
197/10 = 19.7
19.7 x 8 = 157.60
Answer:
b on edge hope this helps :)
Step-by-step explanation:
Determine whether the underlined value is a parameter or a statistic. In a national survey of high school studentsIn a national survey of high school students (grades 9 to 12 )comma(grades 9 to 12), Modifying 25 % with underline25% of respondentsof respondents reported that someone had offered comma sold comma or given them an illegal drug onreported that someone had offered, sold, or given them an illegal drug on schoolschool property. nbspproperty. Is the value a parameter or a statistic?
Answer:
Parameter
Step-by-step explanation:
Parameter is a value that summarizes the data/information about a population in its entirety while a statistics summarizes the data/information about a small part/sample of the population.
In this context the underlined 25% represents the parameter because the value is a numerical measurement describing a characteristic of a population which are the national high school students.
Kathleen already owns 1 hair band, and additional hair bands are priced at 3 for a dollar.
Write an equation that shows the relationship between the money spent on additional hair
bands d and the total number of hair bands h.
Write your answer as an equation with h first, followed by an equals sign.
Submit
Not feeling ready yet? These can help:
Answer:
h= 1+3d
Step-by-step explanation:
total amount of hairbands equals the 1 hairband she has + 3 times how ever many more she decides to buy
A football team consists of 18 freshmen and 18 sophomores, 15 juniors, and 12 seniors. Four players are selected at random to serve as captains. Find the probability that at least 1 of the students is a senior.
Answer:
58.05% probability that at least 1 of the students is a senior.
Step-by-step explanation:
A probability is the number of desired outcomes divided by the number of total outcomes.
The order in which the captains are chosen is not important. So we use the combinations formula to solve this question.
Combinations formula:
A probability is the number of desired outcomes divided by the number of total outcomes.
In this question:
Either no seniors are captain, or at least one is. The sum of these probabilities is 100%. The easier way to solve this question is finding the probability of no seniors being captain, and subtratcing 100 from this. So
Probability of no seniors being captain:
Desired outcomes:
Four captains, from a set of 18 + 18 + 15 = 51. So
[tex]D = C_{51,4} = \frac{51!}{4!(51-4)!} = 249900[/tex]
Total outcomes:
Four captains from a set of 18 + 18 + 15 + 12 = 63. So
[tex]T = C_{63,4} = \frac{63!}{4!(63-4)!} = 595665[/tex]
Probability:
[tex]p = \frac{D}{T} = \frac{249900}{595665} = 0.4195[/tex]
41.95% probability of no seniors being captains.
Find the probability that at least 1 of the students is a senior.
p + 41.95 = 100
p = 58.05
58.05% probability that at least 1 of the students is a senior.