The students that will like exactly one of the two sports out of football and baseball is 200.
What is set theory?These are the fundamental set of set theory formulas. When there are two sets P and Q, the number of elements in one of the sets P or Q is denoted by n(P U Q). The number of elements in both sets P and Q is represented by the expression n(P ⋂Q). n(P U Q) is equal to n(P) + n(Q) - n (P Q).
Here,
F=140
B=144
F∩B=42
F-B=n(F)-n(F∩B)
=140-42
F-B=98
B-F=n(B)-n(F∩B)
=144-42
=102
So, the students that will like exactly one of the two sports,
=102+98
=200
There are 200 students who will only enjoy one of the two sports—football or baseball.
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a fence 8 ft tall runs parallel to a tall building at a distance of 4 ft from the building. what is the length of the shortest lad-der that will reach from the ground over the fence to the wallof the building? g
The length of the shortest ladder is 16.64 ft.
In triangle ABC, using Pythagoras theorem
[tex]AC^{2} = AB^{2} + BC^{2}[/tex] OR
[tex]L^{2} = h^{2} + (x+4)^{2}[/tex] .....(1)
We also have similar triangles if we consider:
△ABC and △DEC
Which gives us the proportional relationship:
AB:DE = BC:EC
or h/8 = (4+x) / x
h = 8( 4+x) /x
Substituting this last expression for h into Eq [1] we get:
[tex]L^{2} = \frac{(8(x+4))^{2} }{x^{2} } + (x+4)^{2}[/tex]
Our aim is to now minimize L wrt x, and this involves looking for critical points of the derivative, so differentiation wrt x we get:
[tex]2L\frac{dL}{dx} = 2( 8 + \frac{32}{x} ) (-\frac{32}{x^{2} } ) + 2(x+4)[/tex]
At a critical point the derivative is zero and so we have the equation:
= [tex]2 (x + 4) ( 1 - \frac{256}{x^{3} } ) = 0[/tex]
From here we can find the value x :
x + 4 = 0 1 - [tex]\frac{256}{x^{3} }[/tex] = 0
x = -4 x = [tex]\sqrt[3]{256}[/tex]
We require x > 0 so we neglect the -ve solution and only take +ve solution
therefore the minimum height of the ladder can be given by putting the value of x in eqn 1.
[tex]L^{2} = ( 8 + \frac{32}{\sqrt[3]{256} } )^{2} + ( \sqrt[3]{256} +4) ^{2}[/tex]
L² = 277.14
L = 16.64 ft
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which proportion is equivalent to the original equation
Original equation (1/2) + (1/2x) = (x² -7x +10)/4x is equivalent to the proportion (x+1)/2x = (x² -7x +10)/4x.
As given in the question,
Given equation is :
Original equation (1/2) + (1/2x) = (x² -7x +10)/4x
Simplify the original equation to get the equivalent equation
Least common multiple is 2 and 2x is equal to 2x
Original equation (1/2) + (1/2x) = (x² -7x +10)/4x is Equivalent to the proportion is given by:
( x + 1) / 2x = (x² -7x +10)/4x
Therefore, original equation (1/2) + (1/2x) = (x² -7x +10)/4x is equivalent to the proportion (x+1)/2x = (x² -7x +10)/4x.
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A company is expanding its building area from 12,500 square feet to 16,875 square feet. What is the percentage increase of the area of the building space?
A. 35%
B. 65%
C. 43.75%
D. 3.5%
The percentage increase in the area of the building from its initial space is 35% of the increase. Hence, option A is correct.
What is the Percentage?The Latin term "per centum," which signifies "by the hundredth," was the source of the English word "percentage." Segments with a denominator of 100 are considered percentages. In other terms, it is a relationship where the worth of the entire is always considered to be 100.
As per the data provided in the question,
The initial area of the building = 12,500
Increase in area of building = 16875
The percentage increase in the area will be,
% increase = (16875 - 12500)/12500 ×100
⇒ 4375/12500 × 100
% increase = 35%
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based on the graph what is the rate of the change for an airplane approaching an airport for landing
Answer:
(8, 9 000)
Step-by-step explanation:
. Use the distance formula to find the distance between the points (5,6) and (10,12). You
can leave the answer as a square root if it is not a perfect square.
The distance between the two points (5,6) and (10,12) is [tex]\sqrt{61}[/tex]
What is the distance between two points formula?
The length of the line segment bridging two points on a plane is known as the distance between the points. d=((x2 - x1)2 + (y2 - y1)2) is a standard formula to calculate the distance between two points. This equation can calculate the separation between any two locations on an x-y plane.
Solution explained:
First, Write the distance formula:
[tex]\sqrt{(x2 - x1)^{2} + (y2 - y1)^{2}}[/tex]
Now,
Substitute (5,6) and (10,12) into [tex]\sqrt{(x2 - x1)^{2} + (y2 - y1)^{2}}[/tex] :
[tex]\sqrt{(10 - 5)^{2} + (12 - 6)^{2}}[/tex] Calculate
[tex]\sqrt{(5)^{2} + (6)^{2}}[/tex] Calculate
[tex]\sqrt{25 + 36}[/tex] Calculate
Hence. the distance between points (5,6) and (10,12) is [tex]\sqrt{61}[/tex].
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Which of the following graphs represents the equation y−4.5=2.5(x−5)?
The graph that represents the equation y - 4.5 = 2.5(x - 5) is the third graph
What is a graph?The set of ordered pairings (x, y) where f(x) = y makes up the graph of a function.
These pairs are Cartesian coordinates of points in two-dimensional space and so constitute a subset of this plane in the general case when f(x) are real values.
Given, y - 4.5 = 2.5(x - 5).
y - 4.5 = 2.5x - 12.5.
y = 2.5x - 8.
Now, to determine the graph we'll choose some random values of x for which we'll have different values of y.
When x = - 1 , y = - 10.5 ⇒ (-1, -10.5 ).
When x = 0 , y = - 8 ⇒ (0, - 8).
When x = 1 , y = -5.5 ⇒ (1, -5.5).
When x = 2 , y = -3 ⇒ (2, -3).
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Multiply.
4 1/3 x 2 3/4
7 1/12
8 1/4
11 11/12
i dont know
a sample of student opinion at a big ten university selects an srs of 200 of the 30,000 undergraduate students and a separate srs of 100 of the 5,000 graduate students. what is the term for this kind of sample?
The term for this kind of sample is cluster sampling
Given
that, At a major ten university, 200 of the 30,000 undergraduate students and 100 of the 5,000 graduate students are chosen to represent a sample of student opinion.
What is cluster sampling ?
Cluster sampling involves breaking up a population into smaller units called clusters. Then, they randomly select a sample from each of these clusters. Cluster sampling is a probability sampling technique that is frequently used to examine large populations, especially those that are widely geographically dispersed.
Researchers frequently refer to pre-existing groups like cities or schools when referring to clusters. With an SRS of 200 students and an SRS score of 100, clusters have been utilized in this instance. Cluster sampling is the name given to this type of sample as a result.
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Which of the following describes the transionnation of g(x)=3(2) ^-x+2 from the parent iuciction f(x) =2^x?
O reflect across the x-axis, stretch the graph vertically by & factor of 3,shift 2 units up. O reflect across the y-axis, stretch the graph vertically by & factor of 2,shift 3 units up. O reflect across the x-axis, stretch the graph vertically by & factor of 2, shift 3 units up. O reflect across the y-axis, stretch the graph vertically by & factor of 3,shift 2 units up
The transformation of g(x) = 3(2)⁻ˣ+2 from the parent function f(x) = 2ˣ will be carried out by reflecting f(x) across the y-axis, then stretching the graph of f(x) vertically by a factor of 3 and then shifting 2 units up,
What is a transformation function?
A function that transforms one function or graph into another, typically a related function or graph, is called a transformation function.
How to convert the parent function into the transformation function?
The transformation of the parent function is shown in blue. It is a shift down (or vertical translation down) of 1 unit. A reflection on the x-axis is made on a function by multiplying the parent function by a negative. Multiplying by a negative “flips” the graph of the function over the x-axis.
Here, we have
Transformation Function - g(x) = 3(2)⁻ˣ+2
Parent Function - f(x) = 2ˣ
To convert the parent function into the transformation function, we will follow some steps:
Multiply 3 by the function f(x). Due to this the graph of f(x) shift vertically by 3 units. f(x) = 3(2ˣ )Now, replace x with -x. Due to this the graph of f(x) reflects the y-axis. f(x) = 3(2)⁻ˣAdd 2 to the function f(x). Due to this the graph of f(x) shift by two units. f(x) = 3(2)⁻ˣ+2 = g(x)Hence, the transformation of g(x) = 3(2)⁻ˣ+2 from the parent function f(x) = 2ˣ will be carried out by reflecting f(x) across the y-axis, then stretching the graph of f(x) vertically by a factor of 3 and then shifting 2 units up.
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2
Previous
Rectangle A'B'C'D' is the image of rectangle ABCD after which of the following rotations?
C₁
B
D'
A'
y
B
00
>>
A
C
D
X
A 90° counter clockwise about the origin
B 180° rotation about the origin
c) 90° clockwise rotation about the origin
D) 45° counter clockwise rotation about origin
a) 90° counterclockwise about the origin
How can a rectangle be rotated?
A shape with rotational symmetry is a rectangle, for instance. When a rectangle is rotated around its center, the shape and placement remain unchanged. The placement of the specified points is the only distinction. Rectangles are of order 2 because they have half-turn symmetry.
When rectangle ABCD is rotated 90° counterclockwise about the origin , the vertex of 'A' in rectangle ABCD is (2,1) becomes (-1,2) in rectangle A'B'C'D'.
Therefore when rectangle ABCD is rotated we get rectangle A'B'C'D'.
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Theo mows a lawn. After working for 1 3/5 hours, he has mowed 7/9 of the lawn. Can Theo mow the lawn in 2 hours if he continue to mow at the same rate?
Yes, he can mow the lawn in 2 hours.
What is work done?We can define the work done as, a work done in a given period of time.
Given that, Theo mows a lawn. After working for 1 3/5 hours, he has mowed 7/9 of the lawn
In [tex]1\frac{3}{5}[/tex] hours he mows 7/9 part of lawn
Therefore, in 8/5 hours he is mowing 7/9 part of lawn
In 1 hour = 7/9*5/8 = 35/72
In 2 hours = 35/72*2 = 35/36 ≈ 1
Hence, Yes, he can mow the lawn in 2 hours.
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If the public debt of a country in 2009 was $11,982,000,000,000and the
budget for 2010 was in deficit by $101,347,000,000 , what was the public debt
in 2010? Do not include commas in your answer.
If a country's public debt in 2009 was $11,982,000,000,000 and its budget for 2010 was $101,347,000,000 in deficit, the public debt in 2010 is $12083347000000.
What is public debt?Government obligations, particularly those evidenced by securities, to pay certain sums to holders at some future time. Private debt, which includes the obligations of individuals, businesses, and nongovernmental organizations, is distinct from public debt. A debt-to-GDP ratio compares a country's total debt to its economic productivity. Divide a country's debt by its GDP to calculate the debt-to-GDP ratio. Governments can use public debt to raise funds to expand their economies or pay for services. Politicians would rather increase the national debt than raise taxes. The national debt includes public debt, and when the national debt reaches 77% or more of GDP, the debt begins to slow growth.As given
if the public debt of a country in 2009 was $11,982,000,000,000 and the budget for 2010 was in deficit by $101,347,000,000 .
Total public debt in 2010 = Public debt in 2009 + Amount by which 2010 budget deficit .
= $ 11982000000000 + 101347000000
= $ 12083347000000
Therefore the public debt in 2010 is $12083347000000.
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Two glasses of milk and 3 snack bars have a total of 67 carbohydrates (carbs), and 4 glasses of milk and 2 snack bars have a total of 74 carbs. Determine how many carbs are in one glass of milk and in one snack bar.
A plane is 80 miles south and 95 miles east of an airport. How far is the plane from the airport? What bearing should be plane take to fly directly to the airport?
Answer:
124.2 miles
∠310.1°
Step-by-step explanation:
You want to know the bearing and distance to the airport from a plane that is 95 miles east and 80 miles south of it.
DistanceThe Pythagorean theorem or the distance formula can be used to find the distance to the airport.
d = √((x2 -x1)² +(y2 -y1)²)
d = √((95 -0)² +(-80 -0)²) = √(9025 +6400) = √15425
d ≈ 124.197 . . . . miles
The plane is about 124.2 miles from the airport.
BearingThe reference angle with respect to the +y axis can be found using the tangent relation.
Tan = Opposite/Adjacent
tan(α) = 95/80 = 19/16
α = arctan(19/16) ≈ 49.9° . . . . . . CCW from +y axis
The bearing angle is measured clockwise from the +y axis (north), so is ...
bearing = 360° -49.9° = 310.1°
The bearing to the airport is 310.1°.
__
Additional comment
Some navigators would refer to the bearing as N 49.9° W.
Less commonly, it might be referred to as W 40.1° N. Usually, N and S are the reference directions, with the modification being E or W from there. The less common usage might be chosen if an angle less than 45° is wanted.
The bearing is often reported to the nearest degree, without any degree symbol, as N50W.
ana and bonita are born on the same date in different years, nn years apart. last year ana was 55 times as old as bonita. this year ana's age is the square of bonita's age. what is nn?
Ana and Bonita were born nn year apart and its value of nn is 12.
Here we have to find nn which difference in the year in which Ana and Bonita were born.
Let x be the age of Ana and y be the age of Bonita.
It is given that last year Ana was 5 times as old as Bonita so from this statement we get the first equation:
x - 1 = 5(y -1)
x -1 = 5y - 5
5y -x = 4--------(1)
The second statement is Ana is square of Bonita's age. From this we get another equation:
x = y²-----------(2)
Putting equation 2 in equation 1 we get:
5y - y² = 4
y² - 5y +4 = 0
y² - 4y - y + 4 = 0
y(y-4) -1(y -4) = 0
(y - 4)(y -1) = 0
y = 4,1
As x = y²
x = 4² = 16 or x = 1² =1
We cannot take 1 as there is a difference in their age
So we get x = 16 and y =4
So the difference in their age = 16-4= 12
Therefore we get the value of nn as 12.
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y=5/x. Make x the subject of the formula
Solve in terms of x.
[tex]y=\frac{5}{x}[/tex]
Multiply by x on both sides to remove it from the denominator.
xy =5
Divide by y to get x by itself
[tex]x=\frac{5}{y}[/tex]
Answer:
x=5/y
Step-by-step explanation:
y=5/x
cross multiplying
yx=5
x=5/y
9. If mBED=(15x-47) and mBD = (9x-1), find m/CBD.
125° is the angle of CBD
An angle pair that forms a straight line is referred to as a straight angle pair. This pair's sum of any two or more angles is always equal to 180°.
What is the straight-angle angle?A straight angle has a 180° angle.
The two angles are from a straight line, and they sum to 180 degrees.
A + B + C = 180
8x -41+ 9x+17 = 180
Conjoin similar terms
17x -24 = 180
24 more on each side
17x -24+24 = 180 +24
17x = 204
multiply by 17
17x/17 = 204/17
x =12
We desire CBD angled.
CBD = 9x+17
= 9*12+17=108+17
= 125
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every week roger pays for a movie ticket and a soda out of his allowance. last week, roger's allowance was aa dollars. the cost of his movie ticket was 20\ % of the difference between aa and the cost of his soda, while the cost of his soda was 5\%5% of the difference between aa and the cost of his movie ticket. to the nearest whole percent, what fraction of aa did roger pay for his movie ticket and soda?
Answer:
23%
Step-by-step explanation:
We can create two equations:
\[m = \frac{1}{5}(A - s)\]\[s = \frac{1}{20}(A - m)\]
Substituting we get:
\[m = \frac{1}{5}(A - \frac{1}{20}(A - m))\]which yields:
\[m = \frac{19}{99}A\]
Now we can find s and we get:
\[s = \frac{4}{99}A\]
Since we want to find what fraction of $A$ did Roger pay for his movie ticket and soda, we add $m$ and $s$ to get:
\[\frac{19}{99}A + \frac{4}{99}A \implies \boxed{\text{(D)}\ 23\%}\]
Can someone help me on this question? I’ll mark you brainliest if you answer.
The picture is a 45-45-90 triangle
Answer: D
Step-by-step explanation:
Select all of the following equation(s) that are quadratic in form. x4 – 6x2 – 27 = 0 3x4 = 2x 2(x + 5)4 + 2x2 + 5 = 0 6(2x + 4)2 = (2x + 4) + 2 6x4 = -x2 + 5 8x4 + 2x2 – 4x = 0
The equations that are quadratic in form are:
x4 – 6x2 – 27 = 0
6(2x + 4)2 = (2x + 4) + 2
6x4 = -x2 + 5
How can the quadratic functions be written?The concept that is been used here is quadratic functions which can be written in three ways :
Standard Form: [y = ax^2 + bx + c ]Factored Form: [y = a ( x − r 1 ) ( x − r 2 ) ](x−r2)Vertex Form: [y = a ( x − h ) 2 + k ]Where vertical line x = h and a not equal to zero, Hence we can see that the three selected options above followed the concept that is decribed as the quadratic function.
Therefore, the first, fourth and fifth options are correct.
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Answer:
A, D, E
Step-by-step explanation:
how many ways are there to distribute seven identical apples and six identical pears to three distinct people?
In 286 ways are there to distribute seven identical apples and six identical pears to three distinct people.
There are 7 identical apples and 6 identical pears.
So total number of fruits here = 7+6 = 13 identical fruits
The number of ways to distribute 13 fruits in three distinct people is given by [tex]=^{13}C_3=286[/tex] ways.
Hence the number of ways is 286.
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1. The slope of the line
y = x + 17 is ___.
2. The slope of the line
y = x - 7/9 is ___.
Answer:
1. 1
2. 1
Step-by-step explanation:
Step 1
recall the eqn of a line y = mx + c
where m is the slope
step 2
compare you eqn given with the eqn y = mx + c
y = mx + c
y = 1 x + 17
then m = 1 which is slope.
both qns follows the same procedure
given the equation y(t)= -14t + 500, what is y (25)
The value of the equation y(t) at y(25) is 150
What is an equation?An equation is a mathematical statement with an 'equal to' symbol between two expressions that have equal values.
Equations can be linear, quadratic or polynomials.
if y(t) = -14t + 500
The y(25) means substitute t = 25 into the equation
y(25) = -14(25) + 500
y(25) = -350 + 500
y(25) = 150
In conclusion, the value of y(25) is 150
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Solve these using the balance method show steps of working out pls I’ll brainlist/5star it’s urgent!!!!!!
1) 5x - 4 = 31
2) 7(x+5) = 49
3) 3x + 7 = -2x + 22
4) x+8 = 6
3
A linear function f has values f(-9)=-2 and f(-3)=-6 . The y-intercept of a linear function g is six greater than the y-intercept of f , and the x-intercept of g is the same as the x- intercept of f . Write equations that represent f and g.
The equations for the functions are f(x) = (-2/3)x - 8 and g(x) = (-2/3)x - 2
What is a function rule?The function rule is the relationship between the input or domain and the output or range. A relation is a function if and only if there exists one value in the range for every domain value.
A function is a relation from a set of inputs to a set of possible outputs where each input is related to exactly one output.
Given data ,
Let the function be represented as A
y - y1 = m(x - x1)
where m is the slope of the line, and (x1, y1) is a point on the line.
Using the two given points for f, we can find the slope:
m = (y2 - y1) / (x2 - x1)
m = (-6 - (-2)) / (-3 - (-9))
m = -4 / 6
m = -2/3
Let's use the point (-9, -2):
y - (-2) = (-2/3)(x - (-9))
y + 2 = (-2/3)(x + 9)
Multiplying both sides by 3 to get rid of the fraction:
3y + 6 = -2x - 18
3y = -2x - 24
y = (-2/3)x - 8
So the equation for f is:
f(x) = (-2/3)x - 8
To find the equation for g, we can use the fact that the y-intercept is 6 greater than the y-intercept of f. So if the y-intercept of f is b, then the y-intercept of g is b + 6.
f(x) = (-2/3)x - 8
0 = (-2/3)x - 8
2/3 x = -8
x = -12
The x-intercept of both f and g is -12.
Now we can use the y-intercept and x-intercept to write the equation for g. The slope of g is the same as the slope of f, which is -2/3.
y - (b + 6) = (-2/3)(x - (-12))
y - b - 6 = (-2/3)(x + 12)
Multiplying both sides by 3 to get rid of the fraction:
3y - 3b - 18 = -2x - 24
3y = -2x + 3b - 6
y = (-2/3)x + (3/3)b - 2
y = (-2/3)x + b - 2
So the equation for g is:
g(x) = (-2/3)x + b - 2
We know that the x-intercept of g is -12, so we can plug that in and solve for b:
0 = (-2/3)(-12) + b - 2
0 = 8 + b - 2
b = -6
So the y-intercept of g is -6 + 6 = 0.
Therefore, the equation for g is:
g(x) = (-2/3)x - 2
Hence , the equations for f and g are: f(x) = (-2/3)x - 8 and g(x) = (-2/3)x - 2
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HELP!!
Find three consecutive odd integers that twice the sum of the second and the third is 43 more than three times the first
Answer: 31, 33, 35
Step-by-step explanation:
The ratio of c and 10
The ratio of c and 10 is c:10.
According to the question,
We have the following information:
We have one variable and one number which are c and 10 respectively.
Now, we already know that ratio can be simply understood as division. So, to find the ratio of c and 10 we will divide c by 10. We also know that a variable can not be divided by a number.
(For example, x can not be divided by 20.)
So, we will replace the sign of division by that of the ratio.
c/10
c:10
Hence, the ratio of c and 10 is c:10.
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5. A road has a 6% downgrade (meaning for every 100 feet you could go horizontally, you go down 6
feet). What is the angle the road makes?
The angle the road makes is 3.43°
What is an angle?
An angle is a shape created by two rays that share a terminus and are referred to as the angle's sides and vertices, respectively. Angles created by two rays are in the plane where the rays are located. The meeting of two planes also creates angles. We refer to these as dihedral angles.
Here, we have
A 6% downgrade means that for every 100 units of horizontal run.
The vertical height decreases by 6 units.
The grade has a downward angle of
tan⁻1(6/100) = 3.43°
Hence, the angle the road makes is 3.43°
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1 Test (1.4, 2.1 - 2.8)
K
Solve the equation P=n+k+ m for n.
n=
(Simplify your answer.)
In the given equation, the value of n is (p - k - m).
What is an equation?An equation is a mathematical statement that shows that two mathematical expressions are equal.
Given an equation, p = n + k + m
Solving for n, we get
n = p - k - m
Hence, In the given equation, n = p - k - m
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a physics professor wants to know what percent of physics majors will spend the next several years doing post-graduate research. he has the following probability distribution. x p (x) 1 0.35 2 0.2 3 0.15 4 ? 5 0.10 6 0.05 (a) on average, how many years would you expect a physics major to spend doing post-graduate research?
It can take 3 years that a physics major to spend doing post-graduate research
Given that,
A physics professor is curious about the proportion of physics majors who will pursue post-graduate study during the coming years. He has the probability distribution shown below. x P(x) x*P (x) 1 0.35 2 0.20 3 0.15 4 5 0.10 6 0.05
To find P(X<=3)
P(X<=3)=P(X=0,1,2,3)=P(X=0)+P(X=1)+P(X=2)+P(X=3)
= 0.35+0.20+0.15
= 0.7
P(X<=3)=0.7
Hence, A physics major may need to spend three years conducting post-graduate research. and the probability that a physics major will spend no more than three years conducting post-graduate research is 70% or 0.7
Learn more about probability distribution :
brainly.com/question/14210034
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