Answer:
(a) D(t) = 250t -500 miles
(b) Controller has 2 hours, but including time for pilots to divert course or altitude.
Step-by-step explanation:
Given:
two planes at same altitude heading in a collision course.
Plane A at 400 miles from collision point at 200 mph
Plane B at 300 miles from collision point at 150 mph.
Theoretical collision happens in
t = 400/200 = 300/150 = 2 hours
Distance ya of plane A from collision point as a function of time in hours
ya(t) = 400 -200t
Distance yb of plane B from collision point as a function of time in hours
yb(t) = 300-150t
(a) Distance between two planes,
Since the two planes are on courses perpendicular to each other, will need using pythagorean theorem
D(t) = sqrt(ya(t)^2+yb(t)^2)
= sqrt((400-200t)^2+(300-150t)^2)
= 250(t-2)
D(t) = 250t -500 miles
b. time available
Time until D(t) = 0
solve D(t) = 0
D(t) = 0
250(t-2) = 0
t = 2 (two hours)
Answer:
a) -500 mph
b) 1/2 h
Step-by-step explanation:
a)[tex]\frac{ (150(-300))+(200(-400))}{\sqrt{150x^{2} +200^{2} } }[/tex]
b) [tex]\frac{\sqrt{150^{2}+200^{2} } }{500}[/tex]
SIMPLIFY. m2 x m5 x m3=???? PLEASE HELP!!!!
Answer:
[tex]m^{10}[/tex]
Step-by-step explanation:
[tex]m^2m^5m^3\\=m^{2+5+3}\\\\=m^{10}[/tex]
===============================================
Explanation:
I'm assuming you meant to write m^2 * m^5 * m^3
If so, you add the exponents to get 2+5+3 = 10 which is the exponent over the original base m. The base does not change.
The rule I used is a^b*a^c = a^(b+c). We see that the base stays the same at 'a' the whole time.
-----------
A longer way to do this is to expand out m^2 into m*m. We have two copies of m multiplied together.
Similarly, m^5 = m*m*m*m*m. We have five copies now.
Saying m^2*m^5 will have seven copies because
m^2*m^5 = (m*m) times (m*m*m*m*m) = m*m*m*m*m*m*m = m^7
Tacking on m^3 will add on three more copies of m to multiply out, giving 10 copies of m total to multiply. This alternative method is not advised since there is a possibility to lose track and make an error somewhere. The formula in the previous section is preferred. Though I recommend you try this second method out to see how/why the formula works.
A zookeeper weighed an African elephant to be 9 × 103 pounds and an African lion to be 4 × 102 pounds. How many times greater is the weight of the elephant than the weight of the lion? A. 2.25x 10 B. 5 C. 13x10 D. 3.6x10
Answer:
2.25 x 10
Step-by-step explanation:
In the above question, we were given :
The weight of the Elephant = 9 × 10³ pounds
The weight of the African Lion = 4 × 10² pounds
We would compare both weights to determine which size is bigger
Weight of Elephant : Weight of Lion
9× 10³ : 4 × 10²
= 9 × 10³/4 × 10²
= 2.25 × 10¹
= 2.25 × 10
The weight of the elephant is 2.25 × 10 times greater than the weight of the lion.
find the value of b here
Answer:
Step-by-step explanation:
We will start with the angle that measures 57 degrees. This angle is supplementary to the one next to it coming off the straight line. 180 - 57 = 123.
The rule for quadrilaterals is that same side angles are supplementary, so the angle next to the 123-degree angle (to the immediate left of that angle 123) is 57. THAT 57-degree angle is supplementary to angle b, so angle b = 180 - 57 which is 123. So C is your answer.
Answer:
do you think you can send me the work for the program
Step-by-step explanation:
i got 1 day left and im not close to finishing it please help me out please respond with any way to contact you thanks
Which equation correctly uses the trigonometric ratio for sine to solve for y?
Answer:
b y = 9sin(36)
Step-by-step explanation:
sin A = opp/hyp
for the 36-deg angle, opp = y, and hyp = 9.
sin 36 = opp/hyp
sin 36 = y/9
y = 9 * sin 36
Answer: b y = 9sin(36)
Given the function, f (x) = sq3x+3+3, choose the correct transformation.
Answer:
B.
Step-by-step explanation:
First, let's start from the parent function. The parent function is:
[tex]f(x)=\sqrt{x}[/tex]
The possible transformations are so:
[tex]f(x)=a\sqrt{bx-c} +d[/tex],
where a is the vertical stretch, b is the horizontal stretch, c is the horizontal shift and d is the vertical shift.
From the given equation, we can see that a=1 (so no change), b=3, c=-3 (negative 3), and d=3.
Thus, this is a horizontal stretch by a factor of 3, a shift of 3 to the left (because it's negative), and a vertical shift of 3 upwards (because it's positive).
Determine whether the data set is a population or a sample. Explain your reasoning. The salary of each teacher in a school. Choose the correct answer below. A. Sample, because it is a collection of salaries for all teachers in the school comma but there are other schools. B. Population, because it is a subset of all schools in the city. C. Sample, because it is a collection of salaries for some teachers in the school. nothing D. Population, because it is a collection of salaries for all teachers in the school.
Answer:
D. Population, because it is a collection of salaries for all teachers in the school.
Step-by-step explanation:
In research, population refers to a complete set of subjects that share a characteristic and that the researcher is interested in. On the other hand, a sample is a subset of a population and it's usually the one the researcher takes to make a study with.
In this example, we have "The salary of each teacher in a school" since we are taking ALL the teachers of this school, this would be a population. If we were working with the salary of only a portion of the teachers of said school, it would be a sample.
Thus, the right answer is D. Population, because it is a collection of salaries for all teachers in the school.
Use the graph to evaluate the function below for specific inputs and outputs.
Answer:
g(x)=6 when x=-4
g(x)=-2 when x=3
Answer:
g(x) = 6 when x=-4
g(x)= -2 x=3
Step-by-step explanation:
plz check the graph of g(x) ,
when x= -4, the value of y = 6
when x=3, the value of y =-2
find the equation of a circle which passes through the point (2,-2) and (3,4) and whose centre lies on the line x+y=2
Answer:
Equation of the circle
(x - 0.7)² + (y - 1.3)² = 12.58
Step-by-step explanation:
The formula for the equation of a circle is given as:
(x - a)² + (y - b)² = r²,
where(a, b) is the center of the circle and r = radius of the circle.
a) We are told in the question that the equation of the circle passes through point(2, -2)
Hence,
Substituting 2 for x and -2 for y in the equation of the circle.
(x - a)² + (y - b)² = r²
(2 - a)² +(-2 - b)² = r²
Expanding the bracket
(2 - a) (2 - a) + (-2 - b)(-2 - b) = r²
4 - 2a - 2a +a² +4 +2b +2b +b² = r²
4 - 4a + a² + 4 + 4b + b² = r²
a² + b² -4a + 4b + 4 + 4 = r²
a² + b² -4a + 4b + 8 = r²............Equation 1
We are also told that the equation of the circle also passes through point (3,4) also, where 3 = x and 4 = y
Hence,
Substituting 3 for x and 4 for y in the equation of the circle.
(x - a)² + (y - b)² = r²
(3 - a)² +(4 - b)² = r²
Expanding the bracket
(3 - a) (3 - a) + (4 - b)(4- b) = r²
9 - 3a - 3a +a² +16 -4b -4b +b² = r²
9 -6a + a² + 16 -8b + b² = r²
a² + b² -6a -8b + 9 + 16 = r²
a² + b² -6a -8b + 25 = r²..........Equation 2
The next step would be to subtract Equation 1 from Equation 2
a² + b² -4a + 4b + 8 - (a² + b² -6a -8b + 25) = r² - r²
a² + b² -4a + 4b + 8 - a² - b² +6a +8b - -25= r² - r²
Collecting like terms
a² - a² + b² - b² - 4a + 6a + 4b + 8b +8- 25 = 0
2a + 12b -17 = 0
2a + 12b = 17...........Equation 3
Step 2
We are going to have to find the values of a and b in other to get our equation of the circle.
Since the center of the circle(a, b) lies on x + y = 2
Therefore, we have
a + b = 2
a = 2 - b
2a + 12b = 17 ..........Equation 3
Substituting 2 - b for a in
2(2 - b) + 12b = 17
4 - 2b + 12b = 17
4 + 10b = 17
10b = 17 - 4
10b = 13
b = 13/10
b = 1.3
Substituting 1.3 for b in
a + b = 2
a + 1.3 = 2
a = 2 - 1.3
a = 0.7
hence, a = 0.7, b = 1.3
Step 3
We have to find the value of r using points (2, -2)
(x - a)² + (y - b)² = r²
Where x = 2 and y = -2
(-2 - 0.7)² + (-2 - 1.3)² = r²
(-2.7)² + (-3.3)² = r²
1.69 + 10.89 = r²
r² = 12.58
r = √12.58 = 3.55
Step 4
The formula for the equation of a circle is given as:
(x - a)² + (y - b)² = r²,
where(a, b) is the center of the circle and r = radius of the circle
a = 0.7
b = 1.3
r² = 12.58
Equation of the circle =
(x - 0.7)² + (y - 1.3)² = 12.58
A bridge is shown. A quadrilateral is outlined. It has one pair of opposite sides that is parallel. Which best describes the structure outlined in the bridge. It is a parallelogram because it has one pair of opposite sides that is parallel. It is a parallelogram because it has exactly one pair of opposite sides that is congruent. It is a trapezoid because it has exactly one pair of opposite sides that is congruent. It is a trapezoid because it has exactly one pair of opposite sides that is parallel.
Answer:
It is a trapezoid because it has exactly one pair of opposite sides that is parallel.
Step-by-step explanation:
D
dont worry its right
happy learning
5 (x+4)=35.please solve it for me
Answer:
3 = x
Step-by-step explanation:
5(x+4) = 35
distribute: 5x + 20 = 35
subtract 20 to both sides
15 = 5x
divide by 5 to make x independent
x=3
Which property justifies this statement?
If x=3, then x−3=0.
Answer:
Step-by-step explanation:
identitiy property
Grade 7 students were surveyed to determine how many hours a day they spent on various activities. The results are shown in the circle graph below. Find the measure of each central angle in the circle graph for the following: a.sleeping b.eating
Answer:
C) 118.8; 28.8
Step-by-step explanation:
for eating, it didn't make sense for it to be 288 degrees, so i eliminated the two off the list. For sleeping, it made more sense for it to be a 118.8 degree angle, so I narrowed it down to C.
The central angle for sleeping is 118.8 degrees and the central angle for eating is 28.8 degrees.
What is the central angle of a pie chart?
The angle formed by an arc of the circle at the center of the circle is called central angle of a pie chart.
How to find the central angle of a pie chart?central angle = [tex]\frac{sector}{100}[/tex] × 360
According to the given question
We have a pie chart
In which, time spend by students in different activities is given.
Now,
The measure of central angle for sleeping is given by
Central angle for sleeping = [tex]\frac{sector}{100}[/tex] × 360
⇒ Central angle for sleeping =[tex]\frac{33}{100}[/tex] × 360 = 118.8 degrees.
Similarly,
The measure of central angle for eating is given by
Central angle for eating = [tex]\frac{8}{100}[/tex] × 360 = 28.8 degrees
Hence, first option is correct.
Learn more about the central angle of pie chart here:
https://brainly.com/question/9473378
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The areas of the squares adjacent to two sides of a right triangle are shown below
Answer:
The area of the square is 85 units^2
Step-by-step explanation:
Okay, here in this question, we are interested in calculating the area of the unknown square.
Kindly note that, since each of the other shapes are squares too, it means that the length of their sides is simply the square root of their areas.
Thus, the length of the squares are ;
√35 units and √50 units respectively
Now to find the area of the larger square, we employ the use of Pythagoras’ theorem which states that the square of the hypotenuse is equal to the sum of the squares of the two other sides
Let’s call the unknown length X
x^2 = (√35)^2 + (√50)^2
x^2 = 35 + 50
x^2 = 85
x = √85 units
Now as we know that the area of a square is simply the length of the side squared,
The area of the biggest square is simply (√85)^2 = 85 units^2
On the coordinate plane below, Point P is located at (2,-3), and point Q is located at (-4,4).
Find the distance between points P and Q Round your answer to the nearest whole number.
Answer:
9
Step-by-step explanation:
We can use the distance formula
d = sqrt ( ( y2-y1)^2 + ( x2-x1) ^2)
d = sqrt ( ( 4- -3)^2 + ( -4 -2) ^2)
= sqrt ( ( 7^2 + ( -6)^2)
= sqrt( 49+ 36)
= sqrt(85)
9.219544457
Rounding to the nearest whole number
= 9
An exponential growth function has a base that is____one?
Please help
Answer:
greater than
Step-by-step explanation:
An exponential growth function has a base that is__greater than__one.
If the base is less than one, it will be a decay function.
Note: the above assumes an exponent greater than one as well.
What is 7/35 converted into a decimal??
Answer:
0.2
Step-by-step explanation:
it works out to be 0.2 as a decimal and 20% as a percentage.
Answer:
.2
Step-by-step explanation:
Find the slope of the line that contains (6, 2) and (6,-3).
Find the slope of the line through the points (-4,-7) and (4, 3).
Answer:
A. Undefined slope (no slope)
B. [tex]\frac{5}{4}[/tex]
Step-by-step explanation:
A slope is rise over run.
The points (6, 2) and (6, -3) are located on the same x coordinate, therefore they have an undefined slope.
However, the points (-4, -7) and (4, 3) do have a slope. The rise is 10 ( | -7+ 3 | ) and the run is 8 ( | -4 + 4 | ). 10/8 is equivalent to 5/4.
Hope this helped!
If a line is perpendicular to each of two intersecting lines at their point of intersection, then the line:
A. not enough information
B. is parallel to the plane determined by the two lines
C. coincides with the plane determined by the two lines
D. is perpendicular to the plane determined by the two lines
D. The line is perpendicular to the plane determined by the two lines.
Remember how you get to 3D space?
You take one axis called x and perpendicularly intersect it with y axis and you get a 2D plane. Now take a 2D plane and perpendicularly intersect it with an axis z and you get 3D euclidean space.
Hope this helps.
determine (a) the area and (b) the circumference of the circle.
a. the area of the circle is ___
b. the circumference of the circle is ____
Step-by-step explanation:
a).To find the area of the circle we must first find the radius using the formula
radius = diameter / 2
From the question
diameter = 21 ft
The radius is
21/2 = 10.5 ft
Area of a circle = πr²
where r is the radius
Area = π(10.5)²
= 110.25π
= 346.36 cm²b).Circumference of a circle = πd
where d is the diameter
Circumference = π(21)
= 65.97cmHope this helps you
Answer:
[tex]\huge\boxed{Answer\hookleftarrow}[/tex]
Given,
Diameter of the ⭕ (d) = 21 ft
So, radius of the ⭕ (r) = ?
[tex]r = \frac{d}{2} \\ r = \frac{21}{2} \\ r = 10.5 \: \: ft[/tex]
[tex]\boxed{Radius \ = \ 10.5 \ ft}[/tex]
____________________
a) Find the area of the ⭕.
[tex]\boxed{Area \ (a) \ = \ πr^{2}}[/tex]
[tex]a = \pi \: r ^{2} \\ a = \pi(10.5) {}^{2} \\ a = 110.25 \: \pi \\ a = 110.25 × 3.14 \\ a = 346.18 \ ft^{2}[/tex]
[tex]\boxed{Area \ = \ 346.18 \ ft^{2}}[/tex]
____________________
b) Find the circumference of the ⭕.
[tex]\boxed{Circumference \ (c) \ = \ \pi \:d}[/tex]
[tex]c = \pi \: d \\ c = \pi(21) \\ c = 21\pi \\ c = 21 × 3.14 \\ c = 65.94 \ ft[/tex]
[tex]\boxed{Circumference \ = \ 65.94 \ ft}[/tex]
____________________
Value of [tex]\pi [/tex]is taken as 3.14
____________________
ʰᵒᵖᵉ ⁱᵗ ʰᵉˡᵖˢ
╭═══════ღ❦ღ══╮
[tex] ღRainbowSalt2^{2}2^{2} [/tex]
╰══ღ❦ღ═══════╯
Will mark BRAINIEST. Solve this.
Answer:
3x+7=10x+17
Step-by-step explanation:
1.9
10x
27x
Answers:
Equation is 3x+7 + 10x+17 = 180 (there are infinitely many other ways to write the equation)
x = 12
Angles are 43 and 137
==========================================================
Explanation:
The horizontal lines are parallel, so the same side interior angles marked are supplementary. The angles add to 180
(3x+7) + (10x+17) = 180 is the equation, or one variation of such
13x+24 = 180
13x = 180-24
13x = 156
x = 156/13
x = 12 is the value of x
Use this x value to find the measure of each angle
3x+7 = 3*12+7 = 43
10x+17 = 10*12+17 = 137
The two angles are 43 and 137 degrees
Note how 43 and 137 add to 180.
A random sample is drawn from a normally distributed population with mean μ = 31 and standard deviation σ = 1.9. Calculate the probabilities that the sample mean is less than 31.6 for both sample sizes
Answer:
For sample size n = 39 ; P(X < 31.6) = 0.9756
For sample size n = 76 ; P(X < 31.6) = 0.9970
Step-by-step explanation:
Given that:
population mean μ = 31
standard deviation σ = 1.9
sample mean [tex]\overline X[/tex] = 31.6
Sample size n Probability
39
76
The probabilities that the sample mean is less than 31.6 for both sample size can be computed as follows:
For sample size n = 39
[tex]P(X < 31.6) = P(\dfrac{\overline X - \mu}{\dfrac{\sigma }{\sqrt{n}}}< \dfrac{\overline X - \mu}{\dfrac{\sigma }{\sqrt{n}}})[/tex]
[tex]P(X < 31.6) = P(\dfrac{31.6 - \mu}{\dfrac{\sigma }{\sqrt{n}}}< \dfrac{31.6 - 31}{\dfrac{1.9 }{\sqrt{39}}})[/tex]
[tex]P(X < 31.6) = P(Z< \dfrac{31.6 - 31}{\dfrac{1.9 }{\sqrt{39}}})[/tex]
[tex]P(X < 31.6) = P(Z< \dfrac{0.6}{\dfrac{1.9 }{6.245}})[/tex]
[tex]P(X < 31.6) = P(Z< 1.972)[/tex]
From standard normal tables
P(X < 31.6) = 0.9756
For sample size n = 76
[tex]P(X < 31.6) = P(\dfrac{\overline X - \mu}{\dfrac{\sigma }{\sqrt{n}}}< \dfrac{\overline X - \mu}{\dfrac{\sigma }{\sqrt{n}}})[/tex]
[tex]P(X < 31.6) = P(\dfrac{31.6 - \mu}{\dfrac{\sigma }{\sqrt{n}}}< \dfrac{31.6 - 31}{\dfrac{1.9 }{\sqrt{76}}})[/tex]
[tex]P(X < 31.6) = P(Z< \dfrac{31.6 - 31}{\dfrac{1.9 }{\sqrt{76}}})[/tex]
[tex]P(X < 31.6) = P(Z< \dfrac{0.6}{\dfrac{1.9 }{8.718}})[/tex]
[tex]P(X < 31.6) = P(Z< 2.75)[/tex]
From standard normal tables
P(X < 31.6) = 0.9970
Use the zero product property to find the solutions to the equation x2 – 15x – 100 = 0.
Answer:
x= 20 x =-5
Step-by-step explanation:
x^2 – 15x – 100 = 0.
What two numbers multiply to -100 and add to -15
-20 * 5 = -100
-20 +5 = -15
(x-20) (x+5) =0
Using the zero product property
x-20 =0 x+5 = 0
x= 20 x =-5
x = 20 and x = -5
Step-by-step explanation:
x² – 15x – 100 = 0
First, find factors that multiply to get -100 and add to -15.
These factors are -20 and 5.
So we have (x - 20)(x + 5) = 0.
Now use the zero product property to get x - 20 = 0 or x + 5 = 0.
Solving from here, we get x = 20 or x = -5.
What is the midpoint of the line segment with endpoints (3.5, 2.2) and (1.5, -4.8)
Answer:
2.5, -1.8
Step-by-step explanation:
½(x¹+x²) ,½(y¹+y²)
½(3.5+1.5) ,½(2.2+(-4.8)
½(5.0), ½(2.2-4.8)
2.5 ,½(-3.6)
2.5, -1.8
Answer: It’s 2.5, -1.3, the other person must’ve misclicked lol
A simple random sample of 49 8th graders at a large suburban middle school indicated that 82% of them are involved with some type of after school activity. Find the 99% confidence interval that estimates the proportion of them that are involved in an after school activity.
Answer:
0.142
Step-by-step explanation:
From the question, we identify the following parameters;
n = 49
p = 82% = 82/100 = 0.82
alpha, α = 1-0.99 = 0.01
Zα/2 = Z_0.005 = 2.575
margin of error = Zα/2 * √( p(1-p)/n)
Margin of error = 2.575 * √(0.82)(1-0.82)/49
Margin of error =0.1416005 which is approximately 0.142
Using the linear combination method, what is the solution to the system of linear equations 5 x + 3 y = negative 10 and Negative 20 x minus 7 y = 15? (–5, 1) (–1, 5) (1, –5) (5, –1)
Answer:
work is shown and pictured
Answer:
The answer is C
Step-by-step explanation:
You want to install a 1 yd. Wide walk around a circular swimming pool. The diameter of the pool is 23 yd. What is the area of the walk? Use 3.14 for pi π.
Answer:
75.36 yd²
Step-by-step explanation:
To solve, you need to consider the walkway and the pool as one circle and find the are. The diameter of this circle is 25 yd. This means that the radius is 12.5 yd.
A = πr²
A = π(12.5)²
A = 156.25π
A = 490.625 yd²
Then, you need to find the area of the pool alone. Since the diameter of the pool is 23 yd., the radius is 11.5 yd.
A = πr²
A = π(11.5)²
A = 132.25π
A = 415.265 yd²
Subtract the two areas to find the are of the walk.
490.625 - 415.265 = 75.36 yd²
The area is 75.36 yd²
Find the sum of all solutions to $(4x+3)(x-8)+(x-1)(4x+3)=0$
Answer:
3 3/4
Step-by-step explanation:
(4x+3)(x-8)+(x-1)(4x+3)=0
Factor out 4x+3
(4x+3)( x-8+x-1) =0
Combine terms
(4x+3) ( 2x-9) =0
Using the zero product property
4x+3 = 0 2x-9 =0
4x=-3 2x = 9
x = -3/4 x = 9/2
Sum the solutions
-3/4 + 9/2
-3/4 + 18/4
15/4
3 3/4
Which movie had a greater range of ages of the audience? (Hint: The range is the difference between the max and min values)
Movie A
Movie B
Both about the same
Range = max - min
Visually the min and max are the leftmost and right most points on the whiskers. This is assuming we don't have outliers in either direction. The range represents the total width of the box and whisker plot. For movie B, it is wider, so therefore it has a larger range of ages.
We could compute the ranges numerically and compare to see which is bigger, or we could align one endpoint (say the right endpoints) to see that movie B has a wider range.
7+2x/3=5 what is x?????
The value of x is 3
The above expression in the question is referred to as an Algebraic expression
Step 1: Multiply all through by 3
7+ 2x/3 = 5
7 x 3 + (2x/3) x 3 = 5 x 3
21 + 2x = 5 × 3
21 + 2x = 15
Step 2 : Subtract 21 from both sides21 - 21 + 2x = 15 - 21
2x = -6
Step 3 : Divide both sides by 22x/2 = -6/2
x = -3
Therefore, the value of x is -3
To learn more, visit the link below:
brainly.com/question/15791428
A professor divided the students in her business class into three groups: those who have never taken a statistics class, those who have taken only one semester of a statistics class, and those who have taken two or more semesters of statistics. The professor randomly assigns students to groups of three to work on a project for the course. Find the requested probability. If 55% of the students have never taken a statistics class, 25% have taken only one semester of a statistics class, and the rest have taken two or more semesters of statistics, what is the probability that the first groupmate you meet has studied some statistics
Answer:
the probability that the first groupmate you meet has studied some statistics is 0.45
Step-by-step explanation:
From the information given :
A professor divided the students in her business class into three groups
Let consider then to be :
Group Statistics Class
A Never taken a statistics class
B Taken one statistics class
C Taken two or more statistics class.
If 55% of the students have never taken a statistics class,
Then ;
P(A) = 0.55
25% have taken only one semester of a statistics class
Then P(B) = 0.25
and the rest have taken two or more semesters of statistics
Then P(C) = 1 - 0.55 -0.25
P(C) = 1 - 0.80
P(C) = 0.20
The objective is to determine the probability that the first groupmate you meet has studied some statistics
The probability of the first groupmate you meet has studied some statistics = 1 - P(never taken a statistics course)
Let the probability of the first groupmate you meet that has studied some statistics be P(D)
Then P(D) = 1 - P(A)
P(D) = 1 - 0.55
P(D) = 0.45
the probability that the first groupmate you meet has studied some statistics is 0.45