Suppose that a certain college class contains 42 students. Of these,17 are sophomores, 27 are biology majors, and 11 are neither. A student is selected at random from the class.
(a) What is the probability that the student is both a sophomore and a biology major?
(b) Given that the student selected is a sophomore, what is the probability that he is also a biology major? Write your responses as fractions.

Answers

Answer 1

The probability that the student is both a sophomore and a biology major is 2/55 and the probability that he is also a biology major given that he is a sophomore is 2/17.

The number of sophomores is 17, the number of biology majors is 27 and the number of neither is 11.

Therefore, 17+27+11=55 people in the class.

The probability that the student is both a sophomore and a biology major is 2/55 and the probability that he is also a biology major given that he is a sophomore is 2/17.

(a) For this we need to find the number of students who are both sophomores and biology majors.

This is  the intersection of these two groups of students.

The number of students who are both sophomores and biology majors is the sum of their numbers minus the total number of students which is 42.

So, P (student is both sophomore and biology major) = (17+27-42) / 55=2/55.

(b) We need to find the probability that the student is a biology major given that he is a sophomore.

In other words, we want to find the conditional probability.

Now, P (student is a sophomore and a biology major)

= 2/55 (from part (a)) and P (student is a sophomore)

= 17/55 (since there are 17 sophomores out of 55).

Therefore, P (student is a biology major given that he is a sophomore)

= P (student is both sophomore and biology major) / P (student is a sophomore)

= (2/55) / (17/55) = 2/17.

So, the probability that the student is both a sophomore and a biology major is 2/55 and the probability that he is also a biology major given that he is a sophomore is 2/17.

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Related Questions

interference is a property of a. light waves. b. sound waves. c. water waves. d. all of these e. none of these

Answers

Interference is a property of (d. All of these)

Interference is a property of ALL the given wave options, which are light waves, sound waves, and water waves.

Interference is the phenomenon of two or more waves combining to form a resultant wave of greater, lower, or the same amplitude.

When two waves meet at the same point at the same time, they either combine constructively (resulting in the formation of a wave of greater amplitude) or destructively (resulting in the formation of a wave of lower amplitude).

For instance, when two sound waves or light waves meet, they create a resultant wave whose amplitude is equal to the sum of the two original waves.

This is known as constructive interference.

On the other hand, when two waves meet and their amplitudes are in opposite directions, they produce a resultant wave whose amplitude is equal to the difference between the two waves.

This is known as destructive interference.

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help!
solve for:
sin (pi/4 -x) - sin (x + pi/4) for 0 < x < 2pi

help!solve for: sin (pi/4 -x) - sin (x + pi/4) for 0 &lt; x &lt; 2pi

Answers

Answer:

sin(pi/4 - x) - sin(x + pi/4) = 1

\( \frac{ \sqrt{2} }{2} ( \cos(x) - \sin(x) ) - \frac{ \sqrt{2} }{2} ( \sin(x) + \cos(x) ) = 1 \\ \\ < = > - 2 \times \frac{ \sqrt{2} }{2} \sin(x) = 1 \\ \\ < = > \sin(x) = \frac{ - 1}{ \sqrt{2} } \\ \\ < = > x = - \frac{\pi}{4} + k2\pi \: or \: x = \frac{5\pi}{4} + k2\pi\)

but 0 < x< 2pi => x = { 5pi/4; 7pi/4 }

Your Turn! Triangle ABC is located at A (1,3), B(4,1) and (3, 4). Perform the following sequence of transformations Reflection across the line y=x, translation right S units and down 3 units, 90° rotation about the origin, A (1,3) A'=A"=A"'= B( 4,1)B'=B"=B"'=C(3,4)C'=C"=C"'=

Answers

A', A'', A''' means the coordinate where the point A is ending at after the transformation.

A',B' and C' will be after the first transformation (reflection accros the line y=x)

First reflection inverts the points.

A'=(3,1) B'=(1,4) C'=(4,3)

Second transformation, you start from the last points and begin by in every x poisition for every point you should add 5 on every point, and on the y position goes down

A''=(3+5,1-3)

A''=(8,-2) , B''=(6,1) C''=(9,0)

Third transformation, rotation 90° around the origin.

we know that degrees are measured counter-clockwise and 90° will turn the figure sideways.

There is a formula to determine the new position in which

A=(X,Y) A'=(Y,-X)

Apply this to the last points you have.

A'''=(-2,-8) B'''=(1,-6) C'''=(0,-9)

Your Turn! Triangle ABC is located at A (1,3), B(4,1) and (3, 4). Perform the following sequence of transformations

m∠A and angles m∠B are vertical angles. If m< A =(6x-16) degrees and angle and
m

Answers

The value of x in the vertical angles A and B is 13 degrees

How to determine the value of x?

The angles are gvien as

A = 6x - 16

B  = 5x - 3

The angles are vertical angles

Because vertical angles are congruent angles, we have

6x - 16 = 5x - 3

Collect the like terms oin the  above equation

So, we have

6x - 5x = 16 - 3

Evaluate the like terms oin the  above equation

So, we have

x = 13

Hence, the value of x in the vertical angles A and B is 13 degrees

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Complete question

m∠A and angles m∠B are vertical angles. If m< A =(6x-16) degrees and angle and ∠B =(5x − 3)∘,  find the measure of x

13 m
12 m
wall
ladder
The ladder, the ground, and the wall form a right triangle.
ground
How far away from the wall does the ladder need to be placed so that it reaches 12 meters up the wall? If needed, ROUND TO THE NEAREST TENTH.
A
17.7 meters
B.
25 meters
С
5 meters
D
313 meters

13 m12 mwallladderThe ladder, the ground, and the wall form a right triangle.groundHow far away from

Answers

Answer:

The ladder needs to be placed at 5 m from the wall.

Step-by-step explanation:

Pythagoras's Theorem

Being a and b the legs of a right triangle and c its hypotenuse, then

\(c^2=a^2+b^2\)

The image shows a ladder of length c=13 m as the hypotenuse of the right triangle formed by the height, the ladder, and the ground.

We are given the height up the wall as a=12 m.

We calculate the distance b solving it from the equation above:

\(b^2=c^2-a^2\)

Substituting:

\(b^2=13^2-12^2\)

Operating:

\(b^2=169-144\)

\(b^2=25\)

Taking the square root:

\(b=\sqrt{25}\)

b = 5 m

The ladder needs to be placed at 5 m from the wall.

5y+25= -13 help me out please i need help and can you show me how you got the answer

Answers

Answer:

=−38/5

Step-by-step explanation:

Subtract 25 from both sides of the equation

5+25−25=−13−25

5=−13−25

5=−38

Divide both sides of the equation by the same term

5/5 =−38/5

which equal to =−38/5

Answer:

y = -38/5

Step-by-step explanation:

5y + 25 = -13

5y = -13 - 25 (Minus both sides by 25)

5y = -38 (Divide both sides by 5 to solve for y)

y = -38/5

Y=2x+6
3y-x+3=0

Substitute to solve

Brainliest for correct answer

Answers

Answer:

-21/5 or -4.2

Step-by-step explanation:

y = 2x + 6

3y - x + 3 = 0

Substitute the value for y from the first equation into the second equation.  Solve for x.

3y - x + 3 = 0

3(2x + 6) - x  + 3= 0

6x + 18 - x + 3 = 0

5x + 18 + 3 = 0

5x + 21 = 0

5x + 21 - 21 = 0 - 21

5x = -21

x = -21/5 or -4.2

Jacob R. Scored a 25 on his quiz Last week. This week he scored a 70 on his quiz. By what percent did jacobs improve his grade?

Answers

Based on his score last week and his score this week, we can say that Jacob increased his score by 180%

Jacob scored 25 in his test last week and then this week scored 70.

The increase can be found as:

= (New score - Old score) / Old score x 100%

Solving gives:

= (70 - 25) / 25 x 100%

= 180%

In conclusion, Jacob increased by 180%

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Solve the equation in standard form

Solve the equation in standard form

Answers

The solutions to the equation -30x² + 9x + 60 = 0 are x = 5/2 and x = -4/5.

To solve the equation, we can start by bringing all the terms to one side to have a quadratic equation equal to zero. Let's go step by step:

-5/3 x² + 3x + 11 = -9 + 25/3 x²

First, let's simplify the equation by multiplying each term by 3 to eliminate the fractions:

-5x² + 9x + 33 = -27 + 25x²

Next, let's combine like terms:

-5x² - 25x² + 9x + 33 = -27

-30x² + 9x + 33 = -27

Now, let's bring all the terms to one side to have a quadratic equation equal to zero:

-30x² + 9x + 33 + 27 = 0

-30x² + 9x + 60 = 0

Finally, we have the quadratic equation in standard form:

-30x² + 9x + 60 = 0

Dividing each term by 3, we get:

-10x² + 3x + 20 = 0

(-2x + 5)(5x + 4) = -10x² + 3x + 20

So, the factored form of the equation -30x² + 9x + 60 = 0 is:

(-2x + 5)(5x + 4) = 0

Now we can set each factor equal to zero and solve for x:

-2x + 5 = 0 --> x = 5/2

5x + 4 = 0 --> x = -4/5

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Suppose the population of a town is 27,000 in 2021. The population increases at a rate of 3.7 percent per year. What will the population of the town be in 2026? Round your answer to the nearest whole number.

Answers

Answer:

36,993 by 2026

Step-by-step explanation:

Suppose the population of a town is 27,000 in 2021. The population increases at a rate of 3.7 percent

sat scores have a mean of 500 and standard deviation of 200. act scores have a mean of 20 and a standard deviation of 5. suppose that student a has an sat score of 600, and student b has an act score of 25. using z-scores, which student had a better college entrance exam score?

Answers

‘B’ had a better college entrance exam score due to the higher value of Z-Score.

The Z-score of an observation is the number of standard deviations it falls above or below the mean. Standard deviation is a statistic that is used to measure the dispersion of a dataset relative to its mean and is calculated by doing the square root of the variance.

\(Z=\frac{(observation-mean)}{standard deviation}\)

By putting the values as given in the question,We get,

A's score is (600 - 500) / 200 = 0.5 standard deviation i.e. above the mean.

B's score is (25 - 20) / 5 = 1 standard deviations i.e. above the mean.

Thus ‘B’ had a better score.

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The average score of students in the first group is 39, the second group is 32, and the third group is 43. If the numbers of students in the three groups are 24, 26, and 27, respectively, find the average score of all students.

Answers

The average score of all students, calculated by taking a weighted average based on the number of students in each group, is 38. The overall performance is slightly below the group averages.

The average score of students in the first, second, and third groups are 39, 32, and 43, respectively. There are 24 students in the first group, 26 students in the second group, and 27 students in the third group.

To find the average score of all students, we need to take a weighted average of the scores in each group, with the number of students in each group as the weights.

Here's how to do it: First, we calculate the total number of students:24 + 26 + 27 = 77. Then, we calculate the total score across all students: 39*24 + 32*26 + 43*27 = 936 + 832 + 1161 = 2929

Finally, we divide the total score by the total number of students to get the average score:2929/77 = 38. The average score of all students is 38.

This means that the overall performance of all the students is slightly below the average of the scores in each group.

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the probability is 0.6826 that x is in the symmetric interval about the mean between which two numbers?

Answers

the probability is 0.6826 that x is in the symmetric interval about the mean between  two numbers then the two numbers are 70.002 and 89.998

What is the mean ?

it is the weighted average of numbers.

the probability is 0.6826 that x is in the symmetric interval about the mean between  two numbers then the two numbers are 70.002 and 89.998

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Round to the nearest tenth: 17.643

Answers

Answer:

17.6 or 17.600

Step-by-step explanation:

4 in 17.643 makes the six stay the same and the other numbers become 0 so that would be 17.6 or 17.600

The graph below shows the price of different numbers of beach balls at a store: Which equation can be used to determine p, the cost of b beach balls? b = 5.50p p = 5.50b p = 11b b = 11p

The graph below shows the price of different numbers of beach balls at a store: Which equation can be

Answers

Answer:

p = 5.50b

Step-by-step explanation:

2 beach balls cost 11

4 beach balls cost 22

6 beach balls cost 33

So each (1) ball b costs 5.50 ($) p

is this a positive linear, negative linear no association or non-linear.

​i will give brainlest if answered correctly ​

 is this a positive linear, negative linear no association or non-linear. i will give brainlest if answered

Answers

Answer:

no association

Step-by-step explanation:

it's obviously not a positive or negative linear, and i'm sure non-linear graphs don't look like that

Can someone please help me with this one? Tysm!!

Can someone please help me with this one? Tysm!!

Answers

Answer:

-26

Step-by-step explanation:

well add the negative numbers first so you get

-17-18=(-35)

then you add 9 so its (-35)+9=26

Answer:

Step-by-step explanation:

-17 + 9 +(-18) = -8 -18 = -26 final answer

A shopkeeper sold an article for Birr 280. If its cost price is Birr 350 then what is his loss percentage? ​

Answers

Answer:

percentage loss = 20%

Step-by-step explanation:

percentage loss is calculated as

\(\frac{loss}{CP}\) × 100% ( CP is the cost price )

loss = SP - CP ( SP is selling price )

loss = CP - SP = 350 - 280 = 70 , then

percentage loss = \(\frac{70}{350}\) × 100% = 0.2 × 100% = 20%

find the perimeter of the given circle​

find the perimeter of the given circle

Answers

The circumference of the circle with a diameter of 28 cm will be 87.92 cm.

What is the circumference of a circle?

It is the close curve of an equidistant point drawn from the hub. The radius of a rotation is the distance between the center and the rim.

Let r be the radius of the circle. The circumference of the circle will be given as,

C = 2πr units

The diameter of the circle is 28 cm. Then the radius is calculated as,

r = d / 2

r = 28 / 2

r = 14 cm

Then the circumference of the circle is given as,

C = 2 · π · 14

C = 28 × 3.14

C = 87.92 cm

The circumference of the circle with a diameter of 28 cm will be 87.92 cm.

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Vanessa uses the expressions (3x² + 5x + 10) and (x² – 3x - 1) to represent the length and width of her patio.
Which expression represents the area (w) of Vanessa's patio?


a) 3x4-4x³-8x²-35x-10

b) 3x4+14x³+22x²+25x-10

c) 3x4-4x³+22x²+35x+10

d) 3x1+14x³+28x²+35x+10


I’m not really the best at math, my apologies. Thank you.

Answers

Answer:

a) 3x⁴-4x³-8x²-35x-10

Step-by-step explanation:

3x2(x²-3x-1)+5x(x²-3x-1)+10(x²-3x-1)

3x⁴-9x³-3x²+5x³-15x²-5x+10x²-30x-10

3x⁴-9x³+5x³-3x²-15x²+10x²-5x-30x-10

3x⁴-4x³-8x²-35x-10

The expression  3x⁴ + 11x³ - 15x² - 40x - 10 represents the area (w) of Vanessa's patio

What is Expression?

An expression is combination of variables, numbers and operators.

The area (w) of Vanessa's patio can be found by multiplying the length and width expressions:

w = (3x² + 5x + 10)(x² – 3x - 1)

Expanding this expression using the distributive property, we get:

w = 3x⁴ - 4x³ - 8x² + 15x³ - 25x² - 10x + 10x² - 30x - 10

Simplifying this expression, we get:

w = 3x⁴ + 11x³ - 15x² - 40x - 10

Hence, the expression  3x⁴ + 11x³ - 15x² - 40x - 10 represents the area (w) of Vanessa's patio

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An ice machine makes 1 pounds of ice every hour. Which graph shows this
proportional relationship?
Pounds of Ice
s of Ice
6
54321
Total Ice Made
0 1 2 3 4 5 6
Number of Hours
6
Total Ice Made
Pounds of Ice
of Ice
65432
Total Ice Made
0 1 2 3 4 5 6
Number of Hours
65
Total Ice Made

Answers

The graph that represents the situation is required.

What is graph?

A graph is a structure that resembles a set of items in discrete mathematics, more especially in graph theory, in which certain pairs of the objects are conceptually "connected." The items are represented by mathematical abstractions known as vertices, and each pair of connected vertices is referred to as an edge.

Graphs are a popular tool for graphically illuminating data connections. A graph serves the objective of presenting facts that are either too many or complex to be fully expressed in the text while taking up less room.

Here the  X- axis denotes the number of hours and

Y- axis denotes the pounds of ice.

The given ordered pair is

\(\left(\frac{1}{2}, 1 \frac{1}{2}\right)=(0.5,1.5)\)

At zero hours the ice produced will be zero so, the third and fourth options are incorrect.

The only graph where the line passes through (0.5,1.5).

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what is 60/2000
helphelphelphelphelp

Answers

Answer:

0.03

Step-by-step explanation:

please give me brainliest! :) :) :)

Answer:

The answer is 0.03

Step-by-step explanation:

parallel to y = 1/2x+3 and through the point (4,5)

Answers

Y-y1 = slope (x-x1)
Y-5=1/2(x-4)
Y-5= 1/2x-2

Final answer
Y=1/2x + 3

Helppp pls pls I’ll mark brainlest for the first comment

Helppp pls pls Ill mark brainlest for the first comment

Answers

Answer:

D. \(\frac{10}{12}\)

Step-by-step explanation:

Answer: D

Step-by-step explanation:

The fraction shown on the number line is 3/5. This fraction isn't equal to 10/12.

Write in expanded form the 3-digit number that has 5 tens, m units, and 2 more hundreds than units.

Answers

Step-by-step explanation:

We know that the number written as sum of the place-values of its digits is called the expanded form of a number.

We know that the number written as sum of the place-values of its digits is called the expanded form of a number.Standard Form

We know that the number written as sum of the place-values of its digits is called the expanded form of a number.Standard FormExpanded Form

We know that the number written as sum of the place-values of its digits is called the expanded form of a number.Standard FormExpanded Form20,37,81,405

We know that the number written as sum of the place-values of its digits is called the expanded form of a number.Standard FormExpanded Form20,37,81,405=

We know that the number written as sum of the place-values of its digits is called the expanded form of a number.Standard FormExpanded Form20,37,81,405=20,00,00,000 + 0 + 30,00,000 + 7,00,000 + 80,000 + 1,000 + 400 + 0 + 5

Answer:

2x100+mx100+5x10+mx1

Step-by-step explanation:

This is correct. TRUST ME!! pls if wrong.

Simplify the expression.
11.3 +9 - 7 = 1
Basic
Comm:

Answers

Here I hope this helps I have the handwritten work as well :)
Simplify the expression.11.3 +9 - 7 = 1BasicComm:

Melanie has saved 2200 cents from selling lemonade. How many dollars does Melanie have?

Answers

Answer:

$22

Step-by-step explanation:

Factor out the greatest common factor from the following polynomial.
5x^5−25x^4 ​+ 25x^3

Answers

Answer:

5x^5−25x^4 ​+ 25x^3

5x³(x² - 5x + 5)

Find the derivative of the following function. f(t)=t 7
( t

+1) The derivative is f ′
(t)=

Answers

The derivative of the function f(t) = t^7(t + 1) is f'(t) = 8t^6 + 7t^7. To find the derivative of the given function, we will apply the product rule and the power rule of differentiation.

The product rule states that if we have two functions u(t) and v(t), the derivative of their product is given by (u(t)v'(t) + v(t)u'(t)).

Let's apply the product rule to the function f(t) = t^7(t + 1):

f'(t) = (t^7)'(t + 1) + t^7(t + 1)'

Now, let's find the derivative of each term using the power rule:

The derivative of t^7 is given by (t^7)' = 7t^(7-1) = 7t^6.

The derivative of (t + 1) is simply 1.

Substituting these derivatives back into the product rule formula, we have:

f'(t) = 7t^6(t + 1) + t^7(1)

Simplifying further:

f'(t) = 7t^7 + 7t^6 + t^7

Combining like terms:

f'(t) = 8t^6 + 7t^7

Therefore, the derivative of the function f(t) = t^7(t + 1) is f'(t) = 8t^6 + 7t^7.

In summary, the derivative of the function f(t) = t^7(t + 1) is given by f'(t) = 8t^6 + 7t^7.

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Name a career in which one would have to use the Pythagorean Theorem. Give an example of when, where, and how it would be used.
FULL EXPLANATION NEEDED

Answers

Answer:

Engineers use the Pythagorean Theorem to figure out measurements of objects.

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