New game You pay 10 and roll a 6 die. If you get a you win 50 If not, you get to roll again. If you get a 6 this time, you get your 10 back.
a) Create a probability model for this game.
b) Find the expected value and standard deviation of your prospective winnings.
c) You play this game five times. Find the expected value and standard deviation of your average winnings.
d) 100 people play this game. What's the probability the person running the game makes a profit?

The first two events are not independent, with a probability P = 0.00603

The second pair of events is independent, and the probability is P = 0.0625

First, all the cards on the deck have the same probability of being randomly drawn, which will be p = 1/52.

A) Now, if Lacy first draws a spade card, now the number of cards in the deck are less (now there are 51 cards on the deck). So the probability of drawing now a spade is larger than before. Then the first two events are not independent.

The probability of drawing a 10 card at first is:

P = 4/52 (because there are 4 10's and a total of 52 cards).

The probability of drawing a 4's after is:

Q = (4/51)

The joint probability is the product of the individual probabilities, this will give: p = P*Q = (4/52)*(4/51) = 0.00603

B) Now we replace the first card, then the events are now independent, as the probability of drawing a spade after the first draw is not changed (because the total number of cards will be 52).

The probability of drawing a spade is:

P = 13/52

Now we replace the spade card drawn.

The probability of drawing a club will be:

Q = 13/52

The joint probability is:

p = P×Q = (13/52)² = 0.0625

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Answer:

a. 120 represents the total number of cow legs and chicken legs

b. 48 represents the total number of cow heads and chicken heads

c. System:

        Let x = number of cows

        Let y = number of chickens      

        1. 2x + 4y = 120

        2. x + y = 48

d. I am going to use substitution for this problem

    Step 1: Solve for y in the equation x + y = 48

         1. x + y = 48 → y = -x + 48

    Step 2: Substitute -x + 48 for y in 2x + 4y = 120    

         2. 2x + 4(-x + 48) = 120

    Step 3: Solve for x

         3. 2x - 4x + 184 = 120 → -2x + 184 = 120 → -2x = -64 → x = 32

    Step 4: Sustitute 32 for x in x + y = 48

         4. (32) + y = 48

    Step 5: Solve for y

         5. y = 16

    Number of chickens on the farm (y) = 16

    Number of cows on the farm (x) = 32

Step-by-step explanation:

All of it is above :)

The probability that a randomly selected jury of 12 people is all male is 2.01 × 10⁻⁵   .

In the question ,

it is given that ,

total number of people in the jury pool is 30 people ,

the total number of men in the jury pool is = 16 ,

total number of women in the jury pool is = 14 ,

So , 12 members can be selected from 30 people in ³⁰C₁₂ ways ,

So , total number of ways = ³⁰C₁₂ = 86493225 ways

and 12 male can be selected from 16 men in ¹⁶C₁₂ ways

= ¹⁶C₁₂ = 1820.

So , the probability of selecting 12 men is = 1820/86493225

= 0.00002104211

≈ 2.01 × 10⁻⁵

Therefore , the required probability is 2.01 × 10⁻⁵  .

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Answer:

Step-by-step explanation:

Chose 2 points (-3,6) and (0,8)

Using slope formula;   m=( y2 - y1 ). / ( x2 -x1)

m=(8-6)/(0+3)  = 2/3

slope 2/3 and y intercept is 8 because the  line cuts the y axis at (0,8)

the equation of the line is: y=2/3(x) + 8

The time at which the pool was full is 4:00 when the water is in the 4 inches tank .

In mathematics, multiplication is one of the four basic arithmetic operations. It represents the basic idea of repeated addition of the same number.

The height of the tank is 4 feet water pouring is turned on at 11:00 at 11:25 the depth of the water in the tank is 4 inches.

which means,

To fill 4 inches it takes = 25 min

To fill 1 inch it takes = 25/4 min 4 feet = 4×2.54 = 48 inches

To fill 48 inches it takes = 48 × 25/4

                     = 300 min

                          = 5 hours

So, 5 hours after 11:00 will be 4:00

Hence, the time at which the pool was full is 4:00

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Answer: Alternate exterior angles --> 1,8 and 2,7

Vertical angles --> 2,3 and 5,8

Corresponding angles --> 1,5 and 2,6

Alternate interior angles --> 3,6 and 4,5

[tex] \Large{\boxed{\sf Option \ D) \ \ Infinite \ solutions }} [/tex]

[tex] \\ [/tex]

We will solve this equation by isolating x.

[tex] \\ [/tex]

Given equation:

[tex] \sf 2.5(5x + 2) = 12.5x + 5 [/tex]

[tex] \\ [/tex]

Expand the left side of the equation using the following distributive property:

[tex] \blue{\begin{gathered}\begin{gathered} \\ \boxed { \begin{array}{c c} \\ \green { \boxed{ \sf Distributive \: property \text{:}}} \\ \\ \sf A(B + C) = AB + BC \\ \end{array}}\\\end{gathered} \end{gathered}} [/tex]

[tex] \\ [/tex]

[tex] \sf \overbrace{\sf 2.5}^{A} (\underbrace{\sf 5x}_{B} + \overbrace{\sf 2}^{C}) = 12.5x + 5 \\ \\ \sf 2.5 \times 5x + 2.5 \times 2 = 12.5x + 5 \\ \\ \sf 12.5x + 5 = 12.5x + 5 [/tex]

[tex] \\ [/tex]

Now, subtract 5 from both sides of the equation:

[tex] \sf 12.5x +5 - 5 = 12.5x + 5 - 5 \\ \\ \sf 12.5x = 12.5x [/tex]

[tex] \\ [/tex]

Finally, divide both sides of the equation by 12.5:

[tex] \sf \dfrac{12.5x}{12.5} = \dfrac{12.5x}{12.5} \\ \\ \\ \boxed{\boxed{\sf x = x}} [/tex]

[tex] \\ [/tex]

Since any value is equal to itself, the equation has infinite solutions.

[tex] \\ [/tex]

[tex] \hrulefill [/tex]

[tex] \\ [/tex]

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The triangles when enlarged by a scale factor of 3 the final image is at the coordinates: (7, 3), (5, 3), and (7, 7)

The coordinates of the preimage are

(5, 3), (4, 3), and (5, 5)

translate to the origin

= (5 - 3, 3 - 3), (4 - 3, 3 - 3), and (5 - 3, 5 - 3)

= (2, 0), (1, 0), and (2, 2)

dilate about the origin

2 * { (2, 0), (1, 0), and (2, 2) }

(4, 0), (2, 0), and (4, 4)

translate back to usual position

(4 + 3, 0 + 3), (2 + 3, 0 + 3), and (4 + 3, 4 + 3)

(7, 3), (5, 3), and (7, 7)

Therefore the image is at (7, 3), (5, 3), and (7, 7)

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The Expected Value to the player for one play of the game is - 7.784.

In probability theory, the weighted average is expanded upon by the expected value. The arithmetic mean of a sizable number of outcomes of a random variable that were independently selected is, informally, the anticipated value.

Price of raffle ticket= $10

First price= $5460

Second prize= $496

Remaining 18 prize= $100

$0 for the remaining tickets= 3500-20=3480 tickets

When winning the 1st prize, the winnings = $5460−$10=$5450.

When winning the 2nd prize, the profit= $496−$10=$486.

When winning the other 18 prizes, the profit= $100−$10=$90.

When there is no winning, the loss= $0

The probability is calculated by dividing the number of likely outcomes by the total number of outcomes:

P(X=5450)= 1/3500

P(X= 486)= 1/3500

P(X= 90)= 18/3500

P(X= -10)= 3480/3500

The product of each alternative and its probability equals the expected value, which is added up:

E(X)= ∑ xP(x)

      = 5450 * [tex]\frac{1}{3500}[/tex] + 486 * [tex]\frac{1}{3500}[/tex] + 90 * [tex]\frac{18}{3500}[/tex] + (-10) * [tex]\frac{3480}{3500}[/tex]

      = [tex]\frac{-27224}{3500}[/tex]

      = - 7.784

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Answer:

A. 20,000 is 10% of 200,000, so the percentage of the purchase price is 10%.

B. 90,000 is 45% of 200,000, so the percentage of the 90,000 down payment is 45%.

Answer:

5(v-1)/9

Step-by-step explanation:

(2/9v) - (-1/3v + 5/9)

To find the opposite of -1/3v + 5/9, find the opposite of each term.

2/9v  - (-1/3v) - 5/9

The opposite of -1/3v is 1/3v.

2/9v + 1/3v - 5/9

Combine 2/9v and 1/3v to get 5/9v

5/9v - 5/9

We must first transform matrix A into a triangular or diagonal matrix in order to determine its determinant.

Using the row operations to change the matrix, having three rows and five columns, in a triangular matrix, having three rows and three columns.

combining the first and second rows, then the first and third rows:

(1 0 2 0 3 0 1 2 3 4 1 0 3 0 5         (1 0 0 2 4            (1 0 3 0 8        (3 0 5 2 11

  0 0 0 2 4                                +   0 0 0 2 4)    +     1 0 3 0 8)   =   0 0 0 2 4

   1 0 3 0 8)                                                                                      2 0 6 0 16)

subtracting the second and third rows from the first row

We get a triangular matrix

(3 0 5 2 11           (0 0 0 2 4        (2 0 6 0 16             (1 0 5 0 3

0 0 0 2 4      -     0 0 0 2 4)    -    2 0 6 0 16)     =     0 0 0 2 4

2 0 6 0 16)                                                                 0 0 0 0 0)

Now that the matrix is triangular, we can use the determinant formula for triangular matrices, which states that the determinant of a triangular matrix is equal to the product of the diagonal elements. The diagonal elements of matrix A are 1, 0, and 0, so the determinant of matrix A is 0.

Therefore, the determinant of matrix A is 0, and we can find it by only using the three basic properties in Treil section the determinant formula for triangular and diagonal matrices, and row or column operations.

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The probability that the cost will be between $250 and $470 is 0.7354.

What is probability?

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a proposition is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.

Given:

Automobile repair costs continue to rise with the average cost now at $367 per repair.†

Assume that the cost for an automobile repair is normally distributed with a standard deviation of $88.

We have to find the probability that the cost will be between $250 and $470.

P( 250 < x < 470 ) = P( x <470 ) - P( x < 250 )

P( x < 470 ) = NORMDIST( 470 , 367, 88, 1 ) = 0.8272

P( x < 250 ) = NORMDIST( 250 , 367, 88, 1 ) = 0.09183

P( 250 < x < 470 ) = 0.8272 - 0.09183 = 0.7354

P( 250 < x < 470 ) = 0.7354

Hence, the probability that the cost will be between $250 and $470 is 0.7354.

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At that point, the area of the rhombus is changing at a rate of -1 cm²/min (measured in square centimeters per minute).

A quadrilateral with all equal sides is a rhombus. Rhombuses are a particular kind of parallelogram in which all of the sides are equal since the opposing sides of a parallelogram are equal. A quadrilateral with four equal sides that has the form of a diamond is called a rhombus. In everyday life, rhombus-shaped objects can be seen. The graphic below illustrates some examples of rhombuses in everyday objects, like a diamond, a kite, an earring, etc.

Here,

The area of a rhombus is given in terms of its diagonal lengths x and y,

A = (1/2)xy

A' = (1/2)(x'y +xy')

A' = (1/2)((-7 cm/min)(6 cm) +(4 cm)(10 cm/min))

A' = (1/2)(-42 cm²/min +40 cm²/min)

A' = -1 cm²/min

The rate of change of the area of the rhombus at that instant (in square centimeters per minute) is -1 cm²/min.

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Mean and standard deviation for the sample distribution is in the main body.

What is standard deviation?

Standard Deviation is a measure that shows what quantity variation (such as unfold, dispersion, spread,) from the mean exists. the quality deviation indicates a “typical” deviation from the mean. it's a well-liked live of variability as a result of it returns to the first units of live of the info set.

Main body:

sample Mean

Population mean =mu = ∑ xi /N

Mu represents pop mean

∑xi = the sum of all scores in the dataset

sample mean is the average score of a sample on a given variable and is represented by

x bar = ∑ xi /N

SE.M(Sample error of the Mean) is

=σ/√n

standard deviation is

σ = √∑(xi - υ)²/N

hence the formula for each of terms is as follows.

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The expected value of the product of the numbers on the marbles is

6.

Given:

There are 5 marbles numbered 1 through 5 in a bag.

Suppose if two different marbles are taken out at random.

what is the expected value of the product of the numbers on the marbles = ?

5C 2  =  10

So we have ten possible sums

1 + 2  = 3       2 + 3  = 5      3  + 4  =  7      4 + 5  =  9

1+ 3  =  4       2 + 4  = 6      3 +  5  =  8

1 + 4 =  5       2 + 5 =  7

1 + 5  = 6

Expected value  =

3 *  Prob of occurence  + 4 * Prob of occurence + 5*Prob of occurence + 6 * Prob of occuence +7 * Prob of occurence   + 8 * Prob of occurence  + 8 * Prob of occurence

3 (1/10)  + 4(1/10) + 5(2/10) + 6(2/10)  + 7 (2/10) + 8 (1/10) + 9(1/10)  =

3/10  + 4/10  + 10/10  + 12/10 + 14/10  + 8/10 + 9/10 =  

60/10

= 6

Hence we get the required answer.

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the probability that all 36 problems in the homework will be completed in less than 180 minutes

P(∑[tex]\left \{ {{i=36} \atop {i=1}} \right.[/tex] [tex]X_{i}[/tex] < 180) = P(X<5) = P(Z<-1) = ∅(-1)

given that

there are 36 independent problems

mean(μ) = 6minutes

standard deviation(σ) = 3 minutes

sample standard deviation = σ/[tex]\sqrt{n}[/tex]

 = 3/[tex]\sqrt{36}[/tex]

 =3/6

 =0.5

the sample mean x of 36 questions answering time approximately follows a normal distribution with mean 6 minutes and sample standard deviation is 0.5 minutes

now we need to find the probability that all 36 problems in the homework will be completed in less than 180 minutes

P(∑[tex]\left \{ {{i=36} \atop {i=1}} \right.[/tex] [tex]X_{i}[/tex] < 180) = P(X<5) = P(Z<-1) = ∅(-1)

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The values of a, b and c in the mixed fractions are 1, 5 and 9 respectively.

The fractions are mixed fractions . let's convert it to improper fraction be we simplify its.

A mixed fraction is a whole number and a proper fraction combined. Improper fractions are defined as fractions for which the numerator is greater than the denominator.

Therefore, let's solve the fractions as follows:

[tex]3\frac{1}{2}[/tex] ÷ [tex]2\frac{1}{4}[/tex]

[tex]3\frac{1}{2} = \frac{7}{2}[/tex]

[tex]2\frac{1}{4} = \frac{9}{4}[/tex]

Therefore,

[tex]\frac{7}{2} (\frac{4}{9} ) = \frac{28}{18} = 1\frac{10}{18} = 1\frac{5}{9}[/tex]

Hence,

a = 1

b = 5

c = 9

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There are 358,800 different ways that a 4-letter password might be used.

For the stated question-

For the fourth letter, we might select any letter between A and Z besides the first, second, and third letters.

SO;

Number of possible combinations for 4-letter passwords

= 26 × 25 × 24 × 23

= 358,800

Thus, there are 358,800 different ways that a 4-letter password might be used.

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The complete question is-

To log on to a certain computer account, the user must type in a 4-letter password. In such a password, no letter may be repeated, and only the lower case of a letter may be used. How many such 4-letter passwords are possible.

A large sample size of 15 is necessary if the width of the 95% interval is to be 0.40

Sample size determination is the act of choosing the number of observations or replicates to include in a statistical sample. The sample size is an important feature of any empirical study in which the goal is to make inferences about a population from a sample. In practice, the sample size used in a study is usually determined based on the cost, time, or convenience of collecting the data, and the need for it to offer sufficient statistical power. In complicated studies there may be several different sample sizes.

Sample sizes may be chosen in several ways:

Given in the question:

A sample size of n is needed.

n is found when M = 0.4.

95% Central interval

Z = 1.96

  M = z × σ /√n

⇒ 0.40 = 1.96 × 0.75 /√n

⇒ 0.40√n = 1.96 ×0.75

⇒ √n = 1.96 ×0.75/0.40

⇒ (√n)² = (1.96 ×0.75 / 0.40 )²

⇒ n = 14.6

Rounding up 14.6

n = 15

The sample size of 15 is needed.

Thus, A large sample size of 15 is necessary if the width of the 95% interval is to be 0.40

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Answer:

8%

Step-by-step explanation:

pls mark brainliest

Answer : The interest rate have been 8 %

Step-by-step explanation :

First we have to calculate the simple interest.

As we know that:

Simple interest = Total amount - Principle

Simple interest = $130,000 - $50,000

Simple interest = $80,000

Now we have to calculate the interest rate.

Using simple interest formula:

where,

S.I = simple interest = $80,000

P = principle = $50,000

R = interest rate = ?

T = time = 20 years

Now put all the given values in the above formula, we get:

Therefore, the interest rate have been 8 %

Found answer from Alleei!

The probability of obtaining at least 1 false positive if the number of employees is 500 is 0.5

Probability

In the statistics concept, the probability refers the possible number of way of happening the particular event.

Given,

A test for a certain drug has a 0.1% probability of producing a false positive.

Here we need to find  the probability of obtaining at least 1 false positive if  a company hired 500 drug-free employees.

In the given question, we have the following values,

=> number of employees = 500

=> Probability of false positive = 0.1%

So, the probability of obtaining at least 1 false positive is calculated as,

=> 500 x 0.1/100

=> 5 x 0.1

=> 0.5

Therefore, the probability of obtaining at least 1 false positive is 0.5.

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Using the definition of covariance, Cov(Y(1)Y(2))= 0. From the given information the two variables Y(1), and Y(2), are dependent and, p(y(1)y(2)) ≠ P(y(1))p(y(2)). So, it can be concluded that Uncorrelated variables need not be independent.

Given joint probability function of Y(1) and Y(2), is

p(Y(1)*Y(2)) = 1/3, for (y(1)*y(2)) = (- 1, 0), (0, 1), (1, 0)

So Y(1), takes random variable -1,0,1.

And Y(2) takes random variable 0,1.

Y(2)|Y(1)      -1               0             1

0                  1/3            0             1/3

1                   0               1/3           0

From the table:

The marginal probability function of Y(1) is;

P(Y(1)=y(1)) = ∑P(Y(1)=y(1)), y(1)= -1,0,1. That is;

Y(1)=y(1)                      -1                   0               1

P(Y(1)=y(1))                  1/3                 1/3             1/3

From the definition of expectation,

E[y(1)]= [tex]\Sigma_{y_{1}}[/tex] y(1)P(Y(1)=y(1))

E[y(1)]= -1(1/3)+0(1/3)+1(1/3)

E[y(1)]= -1/3+0+1/3

E[y(1)]= 0

The marginal probability mass function of y(2) is

P(Y(2)=y(2)) = ∑P(y(1)y(2)), y(2)= 0,1. That is;

Y(2)=y(2)                    0               1

[tex]P_{Y(2)}[/tex](y(2))                  2/3             1/3

Now E[y(2)]= [tex]\Sigma_{y_{2}}[/tex] y(2)P(Y(2)=y(2))

E[y(2)]= 0(2/3)+1(1/3)

E[y(2)]= 1/3

And

E[y(1)y(2)]= [tex]\Sigma_{y_{1}}\Sigma_{y_{2}}[/tex] y(1)y(2)P(y(1)y(2))

E[y(1)y(2)]= -1(0)(1/3)+0(1)(1/3)+1(0)(1/3)

E[y(1)y(2)]= 0

From the definition of covariance.

The Cov(Y(1)Y(2))= E[Y(1)Y(2)]-E[Y(1)E[Y(2)]

Cov(Y(1)Y(2))= 0-1/3 (0)

Cov(Y(1)Y(2))= 0

The Cov(Y(1)Y(2))=0, implies that the two variables are uncorrelated. But from the given information the two variables Y(1), and Y(2), are dependent and, p(y(1)y(2)) ≠ P(y(1))p(y(2))

Hence, it can be concluded that Uncorrelated variables need not be independent.

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In the given triangle MNO, the length of MN is 10

From the question, we are to determine the length of the unknown side in the triangle

The side is MN

From the given information, we have that  

In ΔMNO,

∠M ≅ ∠O

Thus,

ΔMNO is an isosceles triangle

Since angle M is congruent to angle O, the sides facing the two angles will also be congruent.

That is,

NO ≅ MN

From the given information,

NO = 10

Therefore,

MN = 10

Hence, the length of MN is 10

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The lowered value will thus be £16265.28.

What is the percentage?

A percentage that represents a tenth of a quantity. One percent, denoted by the symbol 1%, is equal to one-hundredth of something; hence, 100 percent denotes the full thing, and 200 percent designates twice the amount specified. A portion per hundred is what the percentage denotes. The percentage refers to one in a hundred. The % sign is used to denote it.

Therefore, the decreased sum is: 16265.2777 = 16855.21 - (16855.21 3.5/100) = (16855.21 - 589.93235).

Next, we'll round the number to two decimal places: 16265.2777, 16265.278, and 16265.28

Hence, The lowered value will thus be £16265.28.

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The total cost for a team of 10 player in a baseball league is $978.5.

For the stated question,

The cost of each equipment for each player is-

Thus,

Total cost for each player =  $50. 95  + $20. 95  +  $25. 95

Total cost for each player = $97.85

Total number of player in a baseball league = 12

Total cost for team = 10 x $97.85

Total cost for team = $978.5

Thus, the total cost for a team of 10 player in a baseball league is $978.5.

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Step-by-step explanation:

"with replacement". that means any pulled ball is returned into the bag, and we have the full 7+3 = 10 balls to pull from every time.

remember, a probability is always

desired cases / totally possible cases

(a) 2 back will be red. I understand this, that exactly 2 balls will be red (not fewer, not more).

to get exactly 2 red balls we get 2 red balls and 4 black balls.

the probability for such a single event is

7/10 × 7/10 × 3/10 × 3/10 × 3/10 × 3/10 = 49×81/1000000 =

= 0.003969

because the probably to get a red ball (one from 7 out of 10) is 7/10.

the probability to get a black ball is 3/10.

how many different such single events are possible ?

as many as there are combinations to pick 2 out of 6 :

C(6, 2) = 6! / (2! × (6-2)!) = 6! / (2 × 4!) =

= 6×5 / 2 = 3×5 = 15

so, the probability to get exactly 2 red balls is

15 × 0.003969 = 0.059535 ≈ 0.05954

(b)

the probability of all 6 balls being black is

3/10 × 3/10 × 3/10 × 3/10 × 3/10 × 3/10 =

= 3⁶/1000000 = 0.000729 ≈ 0.00073

(c)

"at least 4 black balls" means exactly 4, or exactly 5, or exactly 6 balls are black.

that means we need to calculate all 3 probabilities and add them (non-overlapping "or"-cases means addition of probabilities, "and" cases mean multiplication as above).

to get exactly 4 black balls (= 4 black balls and 2 red balls) is the same as (a) : 0.059535

to get exactly 5 black balls (= 5 black balls and 1 red ball) in one specific constellation is

3⁵/10⁵ × 7/10 = 243×7/1000000 = 0.001701

and we have C(6, 5) possible constellations

C(6, 5) = 6! / (5! × (6-5)! = 6! / 5! = 6

the total probability to get exactly 5 black balls is

6 × 0.001701 = 0.010206

to get exactly 6 black balls is (b) : 0.000729

the probability to get at least 4 black balls is

0.059535 + 0.010206 + 0.000729 =

= 0.07047

Using the area formula, we know that the width of the pan is 18 inches.

An area is a unit of measurement used to describe a region's size on a flat or curved surface.

While a plane region or area refers to the area of a shape or planar lamina, a surface region or plane area refers to the area of an open surface or the boundary of a three-dimensional object.

So, the width of the pan will be:

We know that:

The length of a rectangular pan is exactly 4/3 the width.

The pan's total surface area is 432in².

Formula: Area = 432 = length*width = w*4w/3

Now, calculate the width as follows:

Formula: Area = 432 = length*width = w*4w/3

4w^2/3 = 432

w^2 = 432*3/4 = 324

w = 18

Therefore, using the area formula, we know that the width of the pan is 18 inches.

Know more about the area here:

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Complete question:
A rectangular pan has a length that is 4/3 the width. The total area of the pan is 432 in.2. What is the width of the cake pan

Answer: B. 18 in

Step-by-step explanation:

You will get this answer using the Area formula, which is A-lw

By using the concept of arithmetic series, it can be calculated that

y - x = 1250

What is arithmetic series?

Arithmetic series are those series whose difference between two consecutive terms are same.

The odd integers forms an arithmetic series

For the sum of first 25 odd integer

First odd integer = 1

25th odd integer = 49

Sum of first 25 odd integers = [tex]\frac{25}{2}(1 + 49)[/tex] = 625

x = 625

For the sum of first 50 odd integers

First odd integer = 1

50th odd integer = 99

Sum of first 50 odd integers = [tex]\frac{50}{2}(1 + 99)[/tex] = 2500

Sum of next 25 odd integers = 2500 - 625 = 1875

y = 1875

y - x = 1875 - 625 = 1250

To learn more about arithmetic series, refer to the link-

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