What point must a proportional equation pass through?

Answers

Answer 1

Answer:

A graph of a proportional relationship must pass through (0, 0).

Step-by-step explanation:

Each point (or pair) in a proportional relationship must share the same difference. 2


Related Questions

Order the following expressions by their values from least to greatest.

-2 a+c b

Answers

The expressions ordered from least to greatest are: -2 < b < (a + c)

What is expression?

In maths, an expressiοn is a cοmbinatiοn οf numbers, variables, functiοns (such as additiοn, subtractiοn, multiplicatiοn οr divisiοn etc.)

Expressiοns can be thοught οf as similar tο phrases. In language, a phrase οn its οwn may include an actiοn, but it dοesn't make a cοmplete sentence.

According to the question:

-1 < a < 0

2 < b < 3

4 < c < 5

Now, we have the expression a + c

= (-1 < a < 0) + (4 < c < 5)

= (-1 + 4) < (a + c) < (0 + 5)

= 3 < (a + c) <  5

Thus, we have the expressions ordered from least to greatest are:

-2 < 2 < b < 3 < (a + c) <  5

-2 < b < (a + c)

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Complete question:

Order the following expressions by their values from least to greatest.-2 a+c b

The sum of the first 15 terms of an arithmetic sequence is 480. Find the 8th term of the
sequence.

Answers

Given:

The sum of the first 15 terms of an arithmetic sequence is 480.

To find:

The 8th term of the sequence.

Solution:

We have,

\(S_{15}=480\)

We know that, the nth term of an AP is

\(a_n=a+(n-1)d\)

Where, a is the first term and d is the common difference.

Putting n=8, we get the 8th term of the sequence.

\(a_8=a+(8-1)d\)

\(a_8=a+7d\)

The sum of first n terms is

\(S_{n}=\dfrac{n}{2}[2a+(n-1)d]\)

Where, a is the first term and d is the common difference.

\(S_{15}=\dfrac{15}{2}[2a+(15-1)d]\)

\(480=\dfrac{15}{2}[2a+14d]\)

\(480=\dfrac{15}{2}[2(a+7d)]\)

\(480=15(a+7d)\)

Divide both sides by 15.

\(\dfrac{480}{15}=a+7d\)

\(32=a+7d\)

\(32=a_8\)

Therefore, the 8th term of the arithmetic sequence is 32.

Answer:

32

Step-by-step explanation:

32

Given triangle EFG, select the graph of image E 'F'G'and confirm that it preserves length and anglemeasures.(x,y) -(x-3, y + 1)

Given triangle EFG, select the graph of image E 'F'G'and confirm that it preserves length and anglemeasures.(x,y)

Answers

We have a transformation for the triangle EFG. In this case is a translation.

We can verify with one of the points which one of the graphs correspond to this transformation.

The transformation is:

(x,y) --> (x-3, y + 1)

We look at point E = (-0.5, 0).

We apply the transformation and get:

(-0.5, 0) --> (-0.5-3, 0+1) = (-3.5, 1)

Then, the graph that has E located in the point (-3.5, 1) is the right one.

HELPPPPPPPPPP PLEASEEEEEEEEE ASAPPPPPPPPP

HELPPPPPPPPPP PLEASEEEEEEEEE ASAPPPPPPPPP

Answers

Answer: i'm pretty sure the first option is correct. she wrote it down correctly

Jeremy wants to verify that the transformation shown is a dilation. He finds the lengths of segments QA and AD to be 4 units.

Point Q is the center of dilation. Triangle A B C is dilated to create triangle D E F. The length of Q A is 4 and the length of A D is 4.

To verify that the transformation is a dilation, Jeremy should also check which of the following? Select three options.

QB = One-halfQE
QC = CF
DE = 2AB
AC = One-halfEF
if BC = 2.25, then EF = 2.25

Answers

Answer:

1,2,3

Step-by-step explanation:

Based on the information given regarding the triangle, to verify that the transformation is a dilation, the things that should be checked include:

QB = One-halfQEQC = CFDE = 2AB

Solving the traingle.

From the information given, it was stated that Jeremy wants to verify that the transformation shown is a dilation and that he finds the lengths of segments QA and AD to be 4 units.

Therefore, to verify that the transformation is a dilation, Jeremy should also check QB = One-halfQE; QC = CF; and DE = 2AB.

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Bear Creek begins in themountains. What lake does itflow down to?

Answers

SOLUTION

Given the question, the following are the solution steps to answer the question.

The course of Bear Creek is entirely contained within San Bernardino County, and primarily within the San Bernardino National Forest. It rises near the community of Woodlands, and flows north into Baldwin Lake in the eastern Big Bear Valley.

Hence, the answer is Baldwin Lake.

1.1 Arithmetic and Geometric Sequences
1. Anthony worked all summer to save $1950 for spending money during the
account at the end of each week. Anthony can create an arithmetic
school year. He plans to withdraw the same amount from his savings
sequence that shows the balance of his savings account at the beginning
of each week of the school year.
Name:
2201
Class PD:
$1950, $1885, $1820
of the fourth week of the school year? How much money will be in
How much money will be in Anthony's savings account at the beginning
Anthony's savings account at the beginning of the fifth week of the school
year?

Answers

$1690 will be in Anthony's savings account at the beginning of the fifth week of the school.

What are Arithmetic Sequence and Series?

Arithmetic sequence is that sequence in which the difference between the one term and next term is constant.

the difference between term is called "common difference".

For example: 5, 10, 15, 20, 25, ..........

here difference between 10 and 5 is 5

difference between 15 and 10 is also 5 and so on.

The general Arithmetic Sequence is a, a + d, a + 2d, a + 3d, a + 4d.......

here first term = a

second term = a + d

third term = a + 2d

'nth' term = a + (n-1)d

and so on.

We have given that initially Anthony has $1950 in his savings bank account and after 1 week he withdraw some amount of money from his bank. So, after 1 week he has $1885 in his bank account. after 2 week he has $1820 in his bank account.

Here, we can notice the common difference 'd' i.e.

$1885 - $1950 = $1820 - $1885 = - $65.

common difference 'd' is negative because the Amount in Anthony's bank is decreasing per week.

so, we can say that he is withdrawing the money in Arithmetic Sequence.

using the Arithmetic Sequence Formula:

After 5th week,

A₅ = a + ( 5 - 1 ) d

here, a = $1950 and d = - $65

A₅ = $1950 - 4 x 65

A₅ = $1690

Hence,

$1690 will be in Anthony's savings account at the beginning of the fifth week of the school.

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you are a seamstress at a boutique that specializes in making prom dresses

Answers

To make a custom number of prom dress for a customer, I would begin by consulting with the customer to determine their vision for the dress.

I would take into consideration factors such as the customer's body type, style preferences, and desired color and fabric. I would then measure the customer to ensure that the dress fits correctly. Once I have all the number of necessary measurements and information, I would draft a pattern to create the dress. After the pattern is drafted, I would cut the fabric and sew the pieces together to create the dress. Once the dress is assembled, I would add any desired embellishments such as beading or embroidery. Finally, I would fit the dress on the customer and make any necessary adjustments until the dress fits perfectly.

The complete question is :

You are a seamstress at a boutique that specializes in making prom dresses. You have been asked to make a custom prom dress for a customer. How would you go about making the dress?

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suppose you were to collect data for the pair of given variables in order to make a scatterplot. for the variables time spent on homework before an exam and the exam grade, which is more naturally the response variable and which is the explanatory variable?

Answers

The time spent on homework will be naturally more an explanatory variable and exam grade a response variable.

The Linear equation for a scatter plot y = mx+b has two variables i.e., a Dependent Variable [Y] and an Independent variable [X] .

A student who spends more time on his work and do it nicely will automatically get good exam grade . On the other side, a student who did'nt dedicate much time to the homework and carelessly does it , will obviously score a low exam grade.We can see that the exam grade is dependent on the time spent on the homework which naturally makes exam grade a response variable and time spent on home a independent thus an explanatory variable.

Hence, the time spent on homework will be naturally more an explanatory variable and exam grade a response variable.

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Decide whether or not it is possible for a triangle to have three angle measurements or three side lengths given. If it is possible, then decide whether all such triangles are congruent.

Decide whether or not it is possible for a triangle to have three angle measurements or three side lengths

Answers

Answer:

First one is not possible

Second one is possible, and would be an isocèles triangle

Third one is possible, would be scalene

Last one is not possible

Comment any further questions :)

Step-by-step explanation:

Which scenario represents an exponential function?


A landlord collects monthly rent payments in the amount of $450 per month.

A landlord collects monthly rent payments in the amount of 450 dollars per month.


A restaurant serves an average of 35 patrons per hour.

A restaurant serves an average of 35 patrons per hour.


An athlete training for a race cuts the time it takes to complete a 10K by 5% each week.

An athlete training for a race cuts the time it takes to complete a 10K by 5 percent each week.


The volume of a cube is the length of the side of the cube raised to the third power.

Answers

The scenario in which an athlete cuts the time it takes to complete a 10K race by 5% each week represents an exponential function.

An exponential function is a mathematical function in which the independent variable is an exponent. It is characterized by a constant ratio between successive values.

In the given scenarios, the first two options involve a fixed amount or average (monthly rent payments or number of patrons per hour) and do not demonstrate exponential growth or decay. These scenarios can be represented by linear functions.

The third option, where an athlete cuts the time it takes to complete a 10K race by 5% each week, represents exponential decay. The time reduction each week can be expressed as a percentage of the previous week's time, resulting in a constant ratio between successive time values. This is a characteristic of exponential functions.

The fourth option describes the volume of a cube, which is calculated by raising the length of the side to the third power. This is an example of a polynomial function, specifically a cubic function, rather than an exponential function.

Therefore, the scenario in which an athlete cuts the time it takes to complete a 10K race by 5% each week represents an exponential function.

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A package of 5 pairs of insulated gloves costs ​$25.95. What is the unit price of the pairs of ​gloves

Answers

The unit price of the pair of gloves is $5.19.

Here, a package of 5 pairs of insulated gloves costs $25.95.

We have to find the unit price of the pairs of gloves.

5 pairs of insulted gloves = $25.95

So we have to find the value of 1 pair of gloves, so by dividing the value by 5 we will get the value of 1 pair of gloves.

Unitary method:

The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit.

So by using the unitary method we have:

1 pair of insulated gloves = 25.95/ 5

                                          = 5.19

Therefore the unit price of the pair of gloves = is $5.19.

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Mara is building a set of shelves supported by a diagonal brace, as shown in the diagram. Answer the questions to decide whether all three shelves are parallel. 1. If ∠2 measures 120°, what is the measure of ∠1? Explain how you found the measure of ∠1. (The image) 2. Think of the top and middle shelves as two lines cut by a transversal. What type of angles are ∠1 and ∠5? 3. Use the relationship between ∠1 and ∠5 to decide whether the top and middle shelves are parallel. 4. Is the bottom shelf parallel to the top shelf? Explain. Write your answer in the space below. 5. Is the bottom shelf parallel to the middle shelf? Explain.

Mara is building a set of shelves supported by a diagonal brace, as shown in the diagram. Answer the

Answers

Parallel Lines

1. Angles ∠1 and ∠2 are linear because they form a line. The sum of their measures is 180°: ∠1 + ∠2 = 180°.

Given m∠2 = 120°, then

m∠1 = 180° - m∠2 = 180° - 120° = 60°

Thus:

m∠1 = 60°

2. Angles ∠1 and ∠5 are called corresponding pair of angles.

3. We have found that m∠1 = 60° and we are given that m∠5 = 60°.

If corresponding angles are congruent, then the lines must be parallel.

4. Given that m∠5 = 60° and ∠7 and ∠5 are linear, thus m∠7 = 120°.

Being ∠7 and ∠11 corresponding angles and having the same measure, the middle and the bottom shelf are parallel.

What multiplication equattion can be used to explain the solution to 15 / 1/3

Answers

Step-by-step explanation:

15 / (1/3)  is equal to  15 x 3/1  = 15 x 3 = 45

To explain the solution to 15 divided by 1/3, we can use a multiplication equation. The division of 15 by 1/3 is equivalent to multiplying 15 by the reciprocal of 1/3.

Reciprocal of 1/3 = 3/1

So, the multiplication equation that explains the solution is:

15 * (3/1) = 45

Therefore, 15 divided by 1/3 is equal to 45.

a) Dan can eat three bananas in 90 seconds (bananas/min).​

Answers

The rate of dan that can eat three bananas in 90 seconds would be equal to 1banana/30sec.

What is the average rate of change?

The average Rate of Change of the function f(x) can be calculated as;

\(f(x) = \dfrac{f(b) - f(a)}{b-a}\)

Most of the times, you will get some other facts or information by which the unknown values of those items can be known. For simple daily life cases, we can use variables, which are nothing but just placeholders for those unknown values. We can then operate on those variables assuming them to be actual values, thus, getting near to their original values.

Given that Dan can eat three bananas in 90 seconds

Now

3banana= 90sec

1banana = 90/3

=30sec

Therefore, the rate of dan will be 1banana/30sec.

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Solve the system by substitution 5x+2y=17 -4x+7=y

HELP PLEASEEE

Solve the system by substitution 5x+2y=17 -4x+7=yHELP PLEASEEE

Answers

Answer:

y=−9/2 x+12

HEART IF IT HELPED!!

What is the domain? I need help on this problem

What is the domain? I need help on this problem

Answers

The domain of the function \(f(x) = \sqrt{\frac{1}{3}x + 2\) is (d) x  ≥ -6

How to determine the domain of the function

From the question, we have the following parameters that can be used in our computation:

\(f(x) = \sqrt{\frac{1}{3}x + 2\)

Set the radicand greater than or equal to 0

So, we have

1/3x + 2 ≥ 0

Next, we have

1/3x  ≥ -2

So, we have

x  ≥ -6

Hence, the domain of the function is (d) x  ≥ -6

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Insert < >, or= to make the following sentence true.

Insert &lt; &gt;, or= to make the following sentence true.

Answers

Answer:

it would be >, 100% guaranteed.

Answer:

answer is >

Step-by-step explanation:

hope this is helpful

Question 2 ab5 a7b2 is equivalent to: a a1017 10 a21 a4 a 63

Question 2 ab5 a7b2 is equivalent to: a a1017 10 a21 a4 a 63

Answers

ANSWER:

\(\frac{b^3}{a^4}\)

STEP-BY-STEP EXPLANATION:

We have the following expression:

\(\frac{a^3b^5}{a^7b^2}\)

When it is a quotient, and it is the same base, the exponents are subtracted, therefore

\(\frac{a^3b^5}{a^7b^2}=a^{3-7}b^{5-2}=a^{-4}b^3=\frac{b^3}{a^4}\)

What is the missing reason in the proof? vertical angles theorem alternate exterior angles theorem converse corresponding angles theorem converse alternate interior angles theorem

Answers

The missing reason in the list you provided is the "Converse Corresponding Angles Theorem."

The Converse Corresponding Angles Theorem states that if two lines are cut by a transversal and the corresponding angles are congruent, then the lines are parallel.

In other words, if a pair of corresponding angles formed by a transversal cutting two lines are congruent, then the two lines are parallel.

This theorem is commonly used in geometry to prove the parallelism of lines based on the congruence of corresponding angles.

In summary the missing reason in the list you provided is the "Converse Corresponding Angles Theorem," which states that if two lines are intersected by a transversal and the corresponding angles are congruent, then the lines are parallel.

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state the domain and range for the following relation. then determine whether the relation represents a function.

Answers

The domain and range need to be determined for a given relation, and it will be determined whether the relation represents a function.

To determine the domain and range of a relation, we need to examine the set of inputs (domain) and the set of corresponding outputs (range). The domain is the set of all possible input values for which the relation is defined, while the range is the set of all possible output values that result from the given inputs.

In the context of determining whether the relation represents a function, we need to ensure that each input value from the domain corresponds to a unique output value. If there is any input value that produces multiple output values, the relation is not a function.

To determine the domain, we examine the set of all valid input values. This can be based on restrictions or limitations stated in the problem or the nature of the relation itself. The range, on the other hand, is determined by observing the set of all output values that result from the given inputs.

Once the domain and range are determined, we can check if each input in the domain corresponds to a unique output in the range. If every input has a unique output, the relation represents a function. If there is any input that maps to multiple outputs, the relation does not represent a function.

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A bag contains an equal number of blue, green, pink, and red balls. If a ball is chosen at random 80 times, with replacement, predict the number of times the ball would be the color red. A. The color red would be chosen exactly 20 times. B. The color red would be of chosen roughly 20 times, but probably not exactly 20 times. C. The color red would be chosen roughly 10 times. D. The color red would be chosen roughly 8 times, but probably not exactly 8 times.

Answers

The probability of choosing a red ball out of the total number of balls (blue, green, pink, and red) is 1/4 or 0.25. Since the 80 selections are made with replacement, the probability of choosing a red ball on each selection remains constant at 0.25. To predict the number of times the ball would be the color red, we can multiply the probability of selecting a red ball by the total number of selections: 0.25 x 80 = 20. Therefore, the answer is A. The color red would be chosen exactly 20 times.
B. The color red would be chosen roughly 20 times, but probably not exactly 20 times.

Explanation: Since there are an equal number of blue, green, pink, and red balls, the probability of choosing a red ball is 1/4. With 80 random selections and replacement, we can predict the number of times a red ball would be chosen using the following calculation:

(Number of selections) x (Probability of choosing red) = 80 x (1/4) = 20

However, since the selections are random, it's likely that the actual number of red balls chosen may vary slightly from the predicted 20 times.

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Learning task 1 be referring them to each pair in letter i do the following a find the sum of each pair of radical be subtract the first radical from the second radical c find the product of each pair of radicals be divided the second radical by the radical​

Answers

For task 1, you need to find the sum of each pair of radicals, subtract the first radical from the second radical, and then find the product of each pair of radicals by dividing the second radical by the first. For example:

let a = 5, b = 10

let sumRadicals = a + b // 15

let differenceRadicals = b - a // 5

let productRadicals = differenceRadicals / a // 1

To further develop this topic, you can explore how to use radicals to simplify expressions, such as removing perfect squares from inside radical expressions and rationalizing denominators. You can also look into how to multiply and divide radical expressions, as well as examples of more complex equations involving radicals.

Additionally, you can look into how to use the properties of radicals, such as the first and second properties, to simplify radical equations.

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Four cars are for sale. The red car costs $15,000, the blue car costs $18,000, the green car costs $22,000, and the white car costs $20,000. Use the table to identify all possible samples of size n = 2 from this population and the proportion of each sample that is red. The first sample is done for you.


Sample
n = 2 R, B R, G R, W B, G B, W G, W
Red? yes, no yes, no yes,no no, no no, no no, no

Proportion
of red 0.5 0.5 0.5 0 0 0

What is the mean of all six sample proportions?
A. 0
B. 0.25
C. 0.5
D. 0.75
What is the population proportion of red cars?
A. 0
B. 0.25
C. 0.5
D. 0.75
Is the sample proportion an unbiased estimator of the population proportion?

Answers

The mean of all six sample means is equal to the population mean (18,750), the sample mean is an unbiased estimator of the population mean.

First, let's calculate the mean for each of the given samples:

1. R, B: (15,000 + 18,000) / 2 = 16,500 (already given)

2. R, G: (15,000 + 22,000) / 2 = 18,500 (already given)

3. R, W: (15,000 + 20,000) / 2 = 17,500 (already given)

4. B, G: (18,000 + 22,000) / 2 = 20,000 (already given)

5. B, W: (18,000 + 20,000) / 2 = 19,000 (already given)

6. G, W: (22,000 + 20,000) / 2 = 21,000 (already given)

Now, let's calculate the mean of all six sample means:

(16,500 + 18,500 + 17,500 + 20,000 + 19,000 + 21,000) / 6 = 112,500 / 6 = 18,750

The mean of all six sample means is 18,750.

Next, let's calculate the population mean:

(15,000 + 18,000 + 22,000 + 20,000) / 4 = 75,000 / 4 = 18,750

The population mean is 18,750.

Since the mean of all six sample means is equal to the population mean (18,750), the sample mean is an unbiased estimator of the population mean.

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wo large tanks A and B are each partially filled with 100 gallons of salt water. Initially,80 pounds of salt is dissolved in the solution in tank A, and 30pounds of salt is dissolvedin the solution in tank B. The system is closed so that the wellstirred saline solution ispumped only between tanks A and B. The saline solution in tankA travels to tank Balong a pipe at the rate of 3 gallons per minute, and the salinesolution in B travels totank A at the rate of 2 gallons per minute. Write a system of IVPs that will describe theamount of salt,x1, in tank A at timetand the amount of salt,x2in tank B at timet.

Answers

At the start, it's given that x₁ (0) = 80 lb and x₂ (0) = 30 lb.

The amounts of salt in either tank change according to

dx₁/dt = (2 gal/min) (x₂/(100 - t ) lb/gal) - (3 gal/min) (x₁/(100 + t ) lb/gal)

dx₂/dt = (3 gal/min) (x₁/(100 + t ) lb/gal) - (2 gal/min) (x₂/(100 - t ) lb/gal)

To break this down a bit, consider tank A, for instance:

• solution flows in from B at a rate of 2 gal/min

• the volume of liquid in tank B after t minutes is

100 gal + (2 gal/min - 3 gal/min) (t min) = (100 - t ) gal

because the tank starts with 100 gallons of liquid, and 2 gallons are pumped in while 3 gal are pumped out each minute

• at any time t, the solution in B contains x₂ pounds of salt

• the concentration of the solution in A is then x₂/(100 - t ) lb/gal

• multiplying this by the inflow rate tells you how much salt is moving around each minute

5. Quadrilateral LMNO has coordinates L(5,6),
M(9,8), N(11, 12), and 0(7,10). How can
quadrilateral LMNO be classified?
A. Square
B. rhombus but not a square
C. rectangle but not a square
D. parallelogram but neither a rhombus nor a
rectangle

5. Quadrilateral LMNO has coordinates L(5,6),M(9,8), N(11, 12), and 0(7,10). How canquadrilateral LMNO

Answers

Answer:

B- Rhombus but not square

Step-by-step explanation:

School sucks balls

please help with this

please help with this

Answers

a. Rate of change for linear function A would be 1/2

b. Rate of change for linear function B would be 1/3.

c. linear function A has a greater rate of change than linear function B.

What is the linear function?

A linear function is a function that can be written in the form f(x) = mx + b, where m is the slope of the line and b is the y-intercept. The slope of a line represents the rate of change of y with respect to x.

a. Rate of change for linear function A:

The rate of change for a linear function is the same as its slope, which is the amount by which the output changes for a one-unit increase in the input. For function A, the output is equal to the input divided by two, which means the slope is 1/2. Therefore, the rate of change for function A is 1/2.

b. Rate of change for linear function B:

To find the rate of change for function B, we can use the formula for slope, which is:

slope = (change in y) / (change in x)

Using the points (-6, -2) and (6, 2), we get:

slope = (2 - (-2)) / (6 - (-6))

= 4 / 12

= 1/3

Therefore, the rate of change for function B is 1/3.

c. Which linear function has a greater rate of change?

The rate of change for function A is 1/2, while the rate of change for function B is 1/3. Therefore, function A has a greater rate of change than function B.

Hence,

a. Rate of change for linear function A would be 1/2

b. Rate of change for linear function B would be 1/3.

c. linear function A has a greater rate of change than linear function B.

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Okay, so I need the one step equation for this question: Lee drove 420 miles and used 15 gallons of gasoline. How many miles did Lee's car travel per gallon of gasoline. I really need the one step equation version, as I know the number is 28. Please help me!​

Answers

Answer: *g is gallons of gasoline
15g=420miles so g=28miles. Lee's car traveled 28 miles per gallon of gasoline.

Hope this helped! :)

What is the product of the fractions below?
1/8 * 4/5

Answers

Answer: 1/10

Step-by-step explanation:

(1 x 4)/(8x5)

4/40

1/10

The U.S. Senate consists of 100 senators, with 2 from each of the 50 states. There are 50 Democrats in the Senate. A committee of size 10 is formed, by picking a random set of senators such that all sets of size 10 are equally likely. a) Find the expected number of Democrats on the committee. b) Find the expected number of states represented on the committee (by at least one senator) c) Find the expected number of states such that both of the state's senators are on the committee.

Answers

Note that based on probabilities,

The expected number of Democrats on the committee is 5.

The expected number of states represented on the committee is 26.

The expected number of states such that both of the state's senators are on the committee is 9.09.

 How is this so ?

a)  The probability that a randomly chosen senator is a Democrat is 50/100 = 1/2.

So, the expected number of Democrats on a committee of size 10 is

1/2 * 10 = 5.

b) The minimum number of   states that can be represented on a committee of size 10 is 2, and the maximum numberis 50.

The expected number of states representedon the committee is the average of these two values, which is (2 + 50)/  2 = 26.

c)  There are 50 states, and each state has 2 senators. So, there are a total of 100 pairs of senators.

The probability that a randomly chosen pair of senators both belong to the same state is 50/100 * 49/99

= 1/11.

The expected number of states such that both of the state's senators are on the committee is 100 * 1/11 = 9.09.

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