Answers
The answers to the questions are:
a) P(A|B) = 1/3
b) P(B|A) = 1.15
c) A. A student given a $1 bill is more likely to have kept the money.
What is the probability?
Probability is simply how likely something is to happen. Whenever we're unsure about the outcome of an event, we can talk about the probabilities of certain outcomes—how likely they are. The analysis of events governed by probability is called statistics.
Because the probability of 0.659 is almost two times greater than 0.341
Assuming the following table:
Purchased Gum Kept the Money Total
Students Given 4 Quarters 25 19 44
Students Given $1 Bill 13 26 39
Total 38 45 83
a. find the probability of randomly selecting a student who spent the money, given that the student was given a $1 bill.
For this case let's define the following events
B= "student was given $1 Bill"
A="The student spent the money"
For this case we want this conditional probability:
P(A|B) = P(A And B) / P(B)
We have that
P(A) = 38/83, P(B) = 39/83
P(A And B) = 13/83
And if we replace we got:
P(A|B) = (13/83)/(45/83) = 13/39 = 1/3
b. find the probability of randomly selecting a student who kept the money, given that the student was given a $1 bill.
For this case let's define the following events
B= "student was given a $1 Bill"
A="The student kept the money"
P(A|B) = P(A And B) / P(B)
We have that
P(A) = 45/83, P(B) = 39/83
P(A And B) = 26/83
And if we replace we got:
P(B|A) = (45/83)/(39/83) = 45/39 = 1.15
c. what do the preceding results suggest?
For this case the best solution is:
A. A student given a $1 bill is more likely to have kept the money.
Because the probability of 0.659 is almost two times greater than 0.341
Hence, The answers to the questions are:
a) P(A|B) = 1/3
b) P(B|A) = 1.15
c) A. A student given a $1 bill is more likely to have kept the money.
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Related Questions
A sample of blood pressure measurements is taken for a group of adults, and those values (mm Hg) are listed below. The values are matched so that 10 subjects each have a systolic and diastolic measurement. Find the coefficient of variation for each of the two samples; then compare the variation.
Systolic
116
130
157
94
155
122
115
138
124
122
Diastolic
82
78
74
51
89
88
56
63
72
83
Answers
Answer:
To find the coefficient of variation (CV) of a sample, we divide the standard deviation by the mean and multiply by 100 to get the percentage.
1. For the systolic sample:
•Find the mean:
mean = (116 + 130 + 157 + 94 + 155 + 122 + 115 + 138 + 124 + 122) / 10 = 130
•Find the standard deviation:
sum = (116 - 130)^2 + (130 - 130)^2 + (157 - 130)^2 + (94 - 130)^2 + (155 - 130)^2 + (122 - 130)^2 + (115 - 130)^2 + (138 - 130)^2 + (124 - 130)^2 + (122 - 130)^2
sum = 165.4
std = sqrt(sum/9) = 7.3
•Calculate the coefficient of variation:
CV = (std / mean) × 100 = (7.3 / 130) × 100 = 5.62%
2. For the diastolic sample:
•Find the mean:
mean = (82 + 78 + 74 + 51 + 89 + 88 + 56 + 63 + 72 + 83) / 10 = 72.5
•Find the standard deviation:
sum = (82 - 72.5)^2 + (78 - 72.5)^2 + (74 - 72.5)^2 + (51 - 72.5)^2 + (89 - 72.5)^2 + (88 - 72.5)^2 + (56 - 72.5)^2 + (63 - 72.5)^2 + (72 - 72.5)^2 + (83 - 72.5)^2
sum = 624.75
std = sqrt(sum/9) = 12.24
•Calculate the coefficient of variation:
CV = (std / mean) × 100 = (12.24 / 72.5) × 100 = 16.82%
So the CV for systolic is 5.62% and the CV for diastolic is 16.82%. We can see that the diastolic measurement has higher variation than the systolic measurement.
I will give brainliest and ratings if you get this correct
Answers
The first order derivative of the given function is f'(x) = [tex](1+\frac{1}{2(x+x^{\frac{1}{2} })}(1+\frac{1}{2x^{\frac{1}{2} }} )) \frac{1}{2(x+(x+x^{\frac{1}{2} })^{\frac{1}{2} })^{\frac{1}{2} }}[/tex].
What is the differentiation?The process of finding derivatives of a function is called differentiation in calculus. A derivative is the rate of change of a function with respect to another quantity.
The given function is [tex]f(x)=\sqrt{x+\sqrt{x+\sqrt{x} } }[/tex].
The derivative using the chain and power rules is
f'(x) = [tex](1+\frac{1}{2(x+x^{\frac{1}{2} })}(1+\frac{1}{2x^{\frac{1}{2} }} )) \frac{1}{2(x+(x+x^{\frac{1}{2} })^{\frac{1}{2} })^{\frac{1}{2} }}[/tex]
Therefore, the first order derivative is f'(x) = [tex](1+\frac{1}{2(x+x^{\frac{1}{2} })}(1+\frac{1}{2x^{\frac{1}{2} }} )) \frac{1}{2(x+(x+x^{\frac{1}{2} })^{\frac{1}{2} })^{\frac{1}{2} }}[/tex].
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Find the value of each variable. Round to the nearest tenth, if necessary.
Answers
The values are a = 16.69, c=16.68 ad m∠C = 22.07°.
What are trigonometric ratios?
Trigonometric ratios are mathematical functions that describe the relationship between the angles and sides of a right triangle. The three main trigonometric ratios are the sine, cosine, and tangent.
In the given figure, by using trigonometric ratios, we can find
sin68° = a/18
18 sin 68° = a
Using a calculator, we can find that sin 68° is approximately 0.9272. Multiplying 18 by 0.9272 gives us:
a ≈ 16.69
Therefore, a is approximately 16.69.
cos68° = c/18
18 cos 68° = c
Using a calculator, we can find that cos 68° is approximately 0.3714. Multiplying 18 by 0.3714 gives us:
c ≈ 6.68
Now
sinC = c/18
[tex]C = sin^{-1}(\frac{6.68}{18})\\\\C = sin^{-1}(0.3714)\\\\C = 22.07\degree[/tex]
Hence, the values are a = 16.69, c=16.68 ad m∠C = 22.07°.
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Look at picture please
Answers
Answer:
EF this is the correct answer
The ratio of horizontal distance to height of the ramp is 15:1. A builder has a roll of nonslip rubber mat that is 15 feet long. Does he have enough forever to cover the Ramp completely?
Answers
Answer:
No. The length of the ramp is [tex]\sqrt{226[/tex] The rubber mat will be too short
Step-by-step explanation:
Talking on the telephone causes cancer.
6. There are marbles of four different colors in a bag. The
ratio of red to white to blue marbles is 3:4:5. There are half
as many green marbles as there are blue marbles. What is
the least possible number of marbles in the bag?
(A) 12
(B) 24
(C) 29
(D) 58
Answers
Answer:
(C) 29
Step-by-step explanation:
Answer:
the least possible number of marbles in the bag is 12.
Step-by-step explanation:
As for the question about the marbles, let's call the number of red marbles "x". Then the number of white marbles is 4x, the number of blue marbles is 5x, and the number of green marbles is (1/2) * 5x = 2.5x.
The total number of marbles in the bag is x + 4x + 5x + 2.5x = 12.5x.
To find the least possible number of marbles, we need to find the smallest possible value of x, which will give us the smallest total number of marbles. Since x represents the number of red marbles, it must be a positive integer. The smallest positive integer value of x is 1.
So, if there is one red marble, there are 4 white marbles, 5 blue marbles, and 2.5 green marbles. The total number of marbles in the bag is 1 + 4 + 5 + 2.5 = 12.5.
Therefore, the least possible number of marbles in the bag is 12.
5 redused to lowest terms make it easy kid friendly for my 10 year old equation please
Answers
Sure! To reduce the fraction 5 to its lowest terms, we need to find the greatest common factor of 5 and divide both the numerator and denominator by it.
The greatest common factor of 5 and 5 is 5, so we divide both the numerator and denominator by 5 to get:
5 / 5 = 1
So, 5 reduced to its lowest terms is 1.
To make it kid-friendly, you could explain it like this: "We can simplify the fraction 5 by dividing the top and bottom by the biggest number that they both share. In this case, 5 is the biggest number that 5 and 5 share, so we divide both 5 and 5 by 5 to get 1."
DIANA WORKED 5 1/3 HOURS AND GABE WORKED 1 1/4 HOURS. PAULA WORKED ON HERS 3/4 TIMES AS LONG AS DIANA.
DID DIANA WORK ON HER PROJECT LONGER THAN GABE?
DID PAULA WORK LESS ON HER PROJECT THAN DIANA?
DID GABE WORK LONGER ON HIS PROJECT THAN PAULA?
DID GABE WORK LONGER ON HIS PROJECT THAN DIANA?
Answers
Solve the equation in the complex number system. X^2+x+8=0
(Simplify your answer. Type an exact answer, using radicals and i as needed. Use integers or fractions for any numbers in the expression. Use a comma to separate answers as needed.)
Answers
Answer:
Step-by-step explanation:
here's a step-by-step explanation with more detail:
The equation X^2 + X + 8 = 0 can be solved using the Quadratic Formula:
X = (-b ± √(b^2 - 4ac)) / 2a,
where a = 1, b = 1, and c = 8.
Plugging in the values, we get:
X = (-1 ± √(1^2 - 4 * 1 * 8)) / 2 * 1
X = (-1 ± √(-31)) / 2
Since the square root of a negative number is not a real number, the solution to the equation must be expressed using complex numbers. In this case, the square root of -31 can be expressed as the imaginary unit i times the square root of 31.
X = (-1 ± i * √31) / 2
So, the two solutions to the equation are:
X = (-1 + i * √31) / 2 and X = (-1 - i * √31) / 2
And these are the two solutions expressed in terms of the imaginary unit i.
A group consisting of 23 aggressive zombies quadruples in size every hour. Which equation matches the number of zombies after 2 hours
Answers
Answer:
The equation that matches the number of zombies after 2 hours would be:
23 × 4^2 = 23 × 16 = 368
So after 2 hours, there would be 368 aggressive zombies.
The probability that a married man watches a certain television show is 0.4,
and the probability that a married woman watches the show is 0.5. The
probability that a man watches the show, given that his wife does, is 0.7.
Find the probability that
a. a married couple watches the show;
b. a wife watches the show, given that her husband does;
c. at least one member of a married couple will watch the show.
Answers
Answer:
a. The probability that a married couple watches the show can be calculated by multiplying the probabilities that each spouse watches the show:
P(Married couple watches the show) = P(Husband watches the show) * P(Wife watches the show) = 0.4 * 0.5 = 0.2
Step-by-step explanation:
b. The probability that a wife watches the show, given that her husband does, can be calculated using Bayes' theorem:
P(Wife watches the show | Husband watches the show) = P(Husband watches the show | Wife watches the show) * P(Wife watches the show) / P(Husband watches the show)
P(Wife watches the show | Husband watches the show) = 0.7 * 0.5 / 0.4 = 0.875
c. The probability that at least one member of a married couple will watch the show can be calculated as the sum of the probabilities that either the husband or the wife watches the show:
P(At least one member of a married couple watches the show) = P(Husband watches the show) + P(Wife watches the show) - P(Married couple watches the show) = 0.4 + 0.5 - 0.2 = 0.7
Aɳʂɯҽɾҽԃ Ⴆყ ɠσԃKEY ꦿ
For each value of y , determine whether it is a solution to 10 < y
Answers
If a value of "y" is greater than 10, then it is a solution to the inequality 10 < y. If it is less than or equal to 10, then it is not a solution.
What is inequality?
In mathematics, an inequality is a statement that describes a relationship between two values, expressing that one value is greater than, less than, or equal to the other value. Inequalities are denoted by symbols such as "<" (less than), ">" (greater than), "≤" (less than or equal to), "≥" (greater than or equal to), or "≠" (not equal to).
The inequality 10 < y means that "y" is greater than 10. To determine whether a given value of "y" is a solution to this inequality, we simply need to check whether that value is indeed greater than 10.
For example:
If y = 11, then 10 < y is true, because 11 is greater than 10.
If y = 10, then 10 < y is false, because 10 is not greater than 10 (they are equal).
If y = 9, then 10 < y is false, because 9 is not greater than 10.
Hence, if a value of "y" is greater than 10, then it is a solution to the inequality 10 < y. If it is less than or equal to 10, then it is not a solution.
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Find the average rate of change of the function on the intervals specified for a real number h F(x) =6x^2 + 5. On [ x,x+h]
Answers
Step-by-step explanation:
The average rate of change of a function on an interval [x, x + h] is given by the formula:
(F(x + h) - F(x)) / h
For the function F(x) = 6x^2 + 5, the average rate of change on the interval [x, x + h] is:
(F(x + h) - F(x)) / h = (6(x + h)^2 + 5 - (6x^2 + 5)) / h = (6(x^2 + 2xh + h^2) - 6x^2 + 5) / h = (6(2xh + h^2)) / h = (12xh + 6h^2) / h
So the average rate of change of the function on the interval [x, x + h] is (12xh + 6h^2) / h for a real number h.
In the spinner below, each sector is equal in size.
If you spin the spinner 7 times, what is the prediction for the number of times it will not land on blue?
B
4
5
6
7
Answers
The number of times it is not land on the blue color sector is 7-1 = 6
What is a probability?A probability is defined as the ratio to the number of required outcomes to the total number of outcomes of an event.
The spinner is divided into 7 sectors, in which each sector is equal in size.
Among 7 sectors two of of them are blue in color.
We have to calculate that how many times the spinner not landing on the blue color sector.
For that we have to calculate the possible outcome for the blue color sector for 1 spin.
For 1 spin , the number of possible outcomes = 7.
Number of required outcomes = 2.
Probability of number of spins on blue sector for 1 spin = 2/7.
Probability of number of spins on blue sector for 7 spin = 7*(2/7) = 2.
Standard deviation = [tex]\sqrt{\frac{2}{7} *\frac{5}{7} }[/tex]= 0.4518.≅0.452.
Standard error=root(7)*0.452= 1.19≅1.2
Expected value =2-1.2 = 0.8 ≅1
Therefore the expected value is 1.
Number of times it will land on the blue color sector is 1.
Hence, the number of times it is not land on the blue color sector is 7-1 = 6.
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Can someone Solve this?
- 2 ( m + 1 ) = 10
Answers
Answer:
m = -4
Step-by-step explanation:
-2 ( m + 1 ) = 10
( m + 1 ) = 10 / -2
m + 1 = -5
m = -4
Three vertices of a parallelogram are located at (-4, 3), (1, -2), and (-1, 4). What are
two possible locations of the fourth vertex? Explain your reasoning.
Answers
The two possible locations of the fourth vertex are (4, -1) and (-6, 9). The solution has been obtained by using the properties of parallelogram.
What is a parallelogram?
A parallelogram has two sets of parallel sides, making it a quadrilateral. A parallelogram's opposing sides and angles are both the same length.
Finding the vector that depicts the shift from one of the given vertices to another is necessary in order to determine the fourth vertex of a parallelogram.
The third given vertex must then be added to the vector.
We know that the opposite sides of a parallelogram are parallel and equal in length, we may determine the coordinates of the other two vertices by adding the same displacement vector to two of the given vertices.
The difference between the first and second provided vertices i.e.
(1 - (-4), -2 - 3), is one potential displacement vector which is (5, -5).
On adding this vector to the third vertex, we get the fourth vertex as (4,-1).
Similarly, the difference between the second and third vertices i.e.
(-1 - 1, 4 - (-2)) is another potential displacement vector which is (-2, 6).
On adding this vector to the third vertex, we get the fourth vertex as
(-6, 9).
Hence, the two possible locations of the fourth vertex are (4, -1) and
(-6, 9).
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help would be appreciated
Answers
The perimeter of the parallelogram is 10units
What is perimeter of a parallelogram?A parallelogram is a quadrilateral with two pairs of parallel sides. The opposite sides of a parallelogram are equal in length, and the opposite angles are equal in measure. Also, the interior angles on the same side of the transversal are supplementary. The Sum of all the interior angles equals 360 degrees.
To obtain the perimeter of the parallelogram , we add all the sides together.
P = 2(l+b)
P= 2( c-2+12-c)
P = 2( c-c -2 +12 )
P = 2( 10)
P = 20
therefore the perimeter of the parallelogram is 20
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Camden is working two summer jobs, making $10 per hour babysitting and making $18 per hour lifeguarding. In a given week, he can work no more than 14 total hours and must earn no less than $180. If Camden worked 9 hours lifeguarding, determine the minimum number of whole hours babysitting that he must work to meet his requirements.
If there are no possible solutions, submit an empty answer.
Answers
Answer: 2 hours babysitting
Step-by-step explanation:
18 x 9 = 162
180-162= 18
meaning he'd have to work 2 hours babysitting to get to meet his requirement.
hours used = 11
hours left= 3
Connor collected 80 stamps last year. This year he increased his collection by 20%. How many stamps are in his collection?
Answers
Answer:
96 stamps
Step-by-step explanation:
We know
Connor collected 80 stamps last year. This year he increased his collection by 20%.
80 stamps = 100%
100% + 20% = 120%
So, this year he collected 120% of the number of stamps from last year.
120% = 1.2
How many stamps are in his collection?
We take
80 times 1.2 = 96 stamps
So, there are 96 stamps in his collection.
As modeled, a movie is projected into a large outdoor screen. The bottom of the 60 foot-tall
Answers
Answer:
-
Step-by-step explanation:
the question isn't clear enough to answer it
If the parent function is f(x) = x³, which transformed function is show in the graph?
Answers
The function g(x) = (x - 3)³ is shown in the graph. The solution has been obtained by using the concept of transformation.
What is transformation?
Any action that moves a polygon or other two-dimensional object on a plane or coordinate system is referred to as a transformation.
Translation, rotation, reflection, and dilation are all methods of transformation.
We are given a graph, from which we can say that when x = 3, then y = 0
The function must satisfy these values.
The functions g(x) = (x + 3)³ , g(x) = x³ + 3 and g(x) = x³ − 3 does not satisfy the point (3,0).
Also, the translation is 3 units to the right.
So the function shown in the graph is g(x) = (x - 3)³.
Hence, the transformed function is g(x) = (x - 3)³.
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Question: If the parent function is f(x) = x³, which transformed function is show in the graph?
g(x) = (x − 3)³ , g(x) = (x + 3)³ , g(x) = x³ + 3 , g(x) = x³ − 3
I need help with number 9, please.
Answers
8. The center and radius of the circle given the following equation:
(x + 4)^2 + (y - 2) ^ 2 = 5 is
c. center (-4, 2) radius: 59. The equation for the circle is
a. (x + 5)^2 + (y + 2)^2 = 910. The length of arc AB is
b. 4πHow to determine the equation the circleInformation given in the question
a circle whose equation is (x + 4)^2 + (y - 2) ^ 2 = 5
Equation of a circle is given as:
(x - h)² + (y - k)² = r²
Where
r = radius
h and k are coordinates of the center
x and y is the coordinate of point on the circumference
The equation of the circle is compared with the given equation and this shows that
center (-4, 2) radius: 5Using the graph the centers are (-5, -2) and the radius is 3, this will give equation (x + 5)² + (y + 2)² = 3²
If angle ACB = 60 deg and the radius is 12 cm, length of arc
= 60 / 360 * 2 * π * 12
= 4π
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A student receives the following grades, with an A worth 4 points, a B worth 3 points, a C worth 2 points, and a D worth 1 point. What is the student's weighted mean grade point score?
A. B in 3 three-credit classes
B. D in 1 three-credit class
C. in 1 four-credit class
D. C in 1 two-credit class
Answers
Weighed averages show that the student has a grade point average of 2.33.
How is the grade point determined?The grade point average (GPA) is calculated by multiplying the unit value for each course in which a student receives one of the aforementioned grades by the grade point total for that grade. Divide the total of these products by the total number of units. By dividing the total grade points by the total number of units, the cumulative GPA is determined.
A. The student's weighted mean grade point score is (3 classes) × (3 credits per class) × (3 points for a B) ÷ (9 total credits) = 3.00.
B. The student's weighted mean grade point score is (1 class) × (3 credits) × (1 point for a D) ÷ (3 total credits) = 1.00.
C. The student's weighted mean grade point score is (1 class) × (4 credits) × (2 points for a C) ÷ (4 total credits) = 2.00.
D. The student's weighted mean grade point score is (1 class) × (2 credits) × (2 points for a C) ÷ (2 total credits) = 2.00.
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Mr. Lopez surveyed some of the students in the after-school program to figure out whether he should buy jumbo chocolate chip cookies or cinnamon twists for dessert. The circle graph shows the results. Cinnamon twists were chosen by 12 students. How students said he should buy jumbo chocolate chips cookies?
Answers
68 students said that Mr.Lopez should buy jumbo chocolate chip cookies.
What is a circle graph?
A pie chart, often known as a circle chart, is a visual representation of the various values of a specific variable or a means to summarise a set of nominal data (e.g. percentage distribution). This kind of chart consists of a circle with numerous segments.
Let's say the total number of students = X.
From the circle graph, we can say that 15% of students chose cinnamon twists and their count is 12.
Which means that
[tex]X*\frac{15}{100}=12\\ X=80[/tex]
Therefore the total number of students is 80.
Among the 80 students except for 12 students, the remaining students asked for jumbo chocolate chip cookies.
Which is equal to 80-12=68.
Therefore 68 students said that Mr.Lopez should buy jumbo chocolate chip cookies.
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Hey what is 10(4/24 - 9) - 7.45
Answers
Answer
[tex] - 95.783[/tex]
x^{2}-2x+ and completing the square ( Algebra 2 )
Answers
x^2 - 2x + 1 is the required quadratic equation using the completing the square
Perfect square trinomials using the completing the square
Given the quadratic expression below
x^2 - 2x
We need to determine the constant that will make the expression a perfect square.
The constant will be the half of the square of coefficient of 'x'
Coefficient of 'x' = -2
Half of the coefficient of 'x' = -2/2 = -1
Square of the coefficient = (-2/2)^2
Square of the coefficient = 1
Hence the complete quadratic expression using the completing the square is x^2 - 2x + 1
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If Emily throws the ball at an angle of 30 ∘ below the horizontal with a speed of 12 m/s , how far from the base of the dorm should Allison stand to catch the ball? Assume the vertical distance between where Emily releases the ball and Allison catches it is 8.0 m .
Express your answer with the appropriate units.
Answers
The distance at which Allison should stand to catch the ball will be 8.32 m.
What is speed?
Speed of an object is defined as the ratio of distance covered by the object to the time taken by the object to cover that distance. In other words its tell how much times an object takes to cover a particular distance.
Now for the given question:
Emily throw the ball at 30° below the horizontal towards Allison at a speed of 12m/s. So here we will calculate the Horizontal and Vertical components of the speed.
[tex]v_{x}[/tex]=12cos30°=10.4 m/s
[tex]v_{y}[/tex]=12sin30°=6 m/s
Vertical distance between Alice and Emily according the question is 8 m.
s= 8 m.
Now by applying Second equation of motion to calculate time take by ball to move from Emily to Allison.
s=[tex]v_{y}[/tex]×t+[tex]\frac{1}{2}[/tex]×a×[tex]t^{2}[/tex]
4= 6×t+[tex]\frac{1}{2}[/tex]×9.8×[tex]t^{2}[/tex] (a=9.8 m/[tex]s^{2}[/tex] acc. due to gravity a constant)
By solving above quadratic equation we get
t= 0.8 s
To find horizontal distance
d= [tex]v_{x}[/tex]×t
d=10.4×0.8
d= 8.32 m
Hence Allison should stand at a distance of 8.32 m to catch the ball.
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i cant figure out the second number
Answers
our jobs are to be done on four different machines. The cost in rupees of
producing ith on the jth machine is given below. Assign the jobs to different machines
so as to minimise the total cost.
Jobs
M1
M2
M3
M4
J1
15
11
13
15
J2
17
12
12
13
J3
14
15
10
14
J4
16
13
11
17
Answers
The total optimal solution based on the information will be 49 rupees.
How to calculate the valueHere, four jobs and four machines are given, with the assignment matrix.
Find out the each row minimum element and subtract it from that row
Find out the each column's minimum element and subtract it from that column.
This assignment problem is being solved using Hungerian Method as the optimal solution is:
J1 to M2, J2 to M4, J3 to M1 and J4 to M3. The total optimal cost is:
= 11 + 13 + 14 + 11
= 49 rupees
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I will give brainliest to whoever answers this correctly.
Answers
Answer:
1625
Step-by-step explanation:
You want the sum of the first 25 terms of the series 5 +10 +15 +....
General termThe first term is 5, the common difference is 5, so the general term is ...
an = a1 +d(n -1)
an = 5 +5(n -1)
Last termThe last term of the sum is ...
a25 = 5 +5(25 -1) = 125
SumThe sum of the series is the average of the first and last terms, multiplied by the number of terms:
S25 = (a1 +a25)/2 · 25 = (5 +125)/2 · 25 = 65·25 = 1625
The sum of 25 terms of the series is 1625.
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