Answers
Option A is the correct answer.
Answer:
SAS
Step-by-step explanation:
According to the given information both the triangles are congruent by SAS postulate.
The given triangles are congruent by SAS rule.
What is congruency in triangles?Two triangles are said to be congruent if all three corresponding sides are equal and all the three corresponding angles are equal in measure.
Given are two triangles, ABC and DEF,
They have congruent parts, given;
AB ≅ DE
BC ≅ EF
∠ B ≅ ∠ E
The triangles have two congruent sides and one congruent angle between them.
The Side-Angle-Side theorem of congruency states that, if two sides and the angle formed by these two sides are equal to two sides and the included angle of another triangle, then these triangles are said to be congruent.
Hence, The given triangles are congruent by SAS rule.
For more reference on congruent triangles, click;
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Related Questions
If the average American sleeps 8 hours a night, with a standard deviation of 1 hour, and I plan on gathering a sample of 12 college students to compare to this population, find the following:
mu =
sigma =
mu_x bar =
sigma_x bar =
Answers
Answer:
8 hours
1 hour
8 hours
0.288675
Step-by-step explanation:
We complete the answer as follows;
mu = mean = 8 hours
sigma = standard deviation= 1 hour
Mu_x bar = mu = 8 hours
sigma_x bar = sigma/√(n) = 1/√(12) = 0.288675
please what's the solution for 2a²×4a³
Answers
Answer:
8a^5
Step-by-step explanation:
Well to start off 2*4=8
So the coefficent will be 8
and when multipling ezponents we add the exponents and 2+3=5 so the exponent will be 5.
So 8a^5 is the answer
Heights of women (in inches) are approximately N(64.5,2.5) distributed. Compute the probability that the average height of 25 randomly selected women will be bigger than 66 inches.
Answers
Answer:
the probability that the average height of 25 randomly selected women will be bigger than 66 inches is 0.0013
Step-by-step explanation:
From the summary of the given statistical dataset
The mean and standard deviation for the sampling distribution of sample mean of 25 randomly selected women can be calculated as follows:
[tex]\mu_{\overline x} = \mu _x[/tex] = 64.5
[tex]\sigma_{\overline x }= \dfrac{\sigma}{\sqrt n}[/tex]
[tex]\sigma_{\overline x }= \dfrac{2.5}{\sqrt {25}}[/tex]
[tex]\sigma_{\overline x }= \dfrac{2.5}{5}[/tex]
[tex]\sigma_{\overline x }[/tex] = 0.5
Thus X [tex]\sim[/tex] N (64.5,0.5)
Therefore, the probability that the average height of 25 randomly selected women will be bigger than 66 inches is:
[tex]P(\overline X > 66) = P ( \dfrac{\overline X - \mu_\overline x}{\sigma \overline x }>\dfrac{66 - 64.5}{0.5} })[/tex]
[tex]P(\overline X > 66) = P ( Z>\dfrac{66 - 64.5}{0.5} })[/tex]
[tex]P(\overline X > 66) = P ( Z>\dfrac{1.5}{0.5} })[/tex]
[tex]P(\overline X > 66) = P ( Z>3 })[/tex]
[tex]P(\overline X > 66) = 1- P ( Z<3 })[/tex]
[tex]P(\overline X > 66) = 1- 0.9987[/tex]
[tex]P(\overline X > 66) =0.0013[/tex]
the probability that the average height of 25 randomly selected women will be bigger than 66 inches is 0.0013
Find the number of unique permutations of the letters in each word. SIGNATURE RESTAURANT
Answers
Answer:
Ok, we have two words:
"Signature"
The letters are: "S I G N A T U R E"
9 different letters.
Now, we can make only words with 9 letters, so we can think on 9 slots, and in each of those slots, we can input a letter of those 9.
For the first slot, we have 9 options.
For the second slot, we have 8 options (because on is already taken)
For the second slot, we have 7 options and so on.
Now, the total number of combinations is equal to the product of the number of options in each selection:
C = 9*8*7*6*5*4*3*2*1 = 362,880.
Now, our second word is Restaurant.
The letters here are " R E S T A U N" such that R, T and A appear two times each, so we have a total of 10 letters and 7 unique letters.
So first we do the same as beffore, 10 slots and we start with 10 options.
The total number of combinations will be:
C = 10*9*8*7*6*5*4*3*2*1 = 3,628,800
A lot of combinations, but we are counting only unique words.
For example, as we have two R, we are counting two times the word:
Restaurant (because we could permutate only the two letters R and get the same word)
So we must divide by two for each letter repeated.
we have 3 letters repeated, we divide 3 times by 2.
C = ( 3,628,800)/(2*2*2) = 453,600
Which expression is a cube root of -2
Answers
Answer:
∛-2
Step-by-step explanation:
The aritmetic expressión is:
∛-2
4 to the 4th power equals 256. Explain how to use that fact to more quickly evaluate 4 to the 5th power.
Answers
Answer: Because 4 is the base of what is being exponentially multiplied, you can multiply 256 by 4 to get 4^5
Hi there! Hopefully this helps!
--------------------------------------------------------------------------------------------------------
So, we know that 4 to the 4th power equals 256.
4 to the 4th power = 4 x 4 x 4 x 4.
So we can add another 4 to the equation to quickly get out answer for 4 to the 5th power.
4 to the 5th power = 4 x 4 x 4 x 4 x 4 = 1024.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Or you could break the equation into parts.
For example, there are FOUR 4s in the equation.
4 x 4 = 16.
4 x 4 = 16.
16 x 16 = 256.
Now since we've added ANOTHER 4, it should look like this:
16 x 16 = 256.
256 x 4 = 1024.
Find ZABD if ZABC = 121° in the given figure.
Answers
4x+21+3x-5=121
7x+16=121
x=15
angle ABD =4(15)+21=81
A 25-foot ladder is placed against a building and the top of the ladder makes a 32° angle with the building. How many feet away from the building is the base of the ladder?
Answers
Answer:
since the top of the ladder is making the angle, the of the ladder's base from the building is our opposite and the ladder is the hypotnuse,
sin (32)=opp/hyp, 0.52=opp/25, opp=13 ft
Which of the following can be used to find the area of a circle?
A.
B.
C.
D.
Answers
Answer:
option B
hope it was useful for you
stay at home stay safe
pls mark me as brain.....
Answer:
[tex]\boxed{Option \ B}[/tex]
Step-by-step explanation:
Area of a circle = [tex]\pi r^2[/tex]
Finding the area of the circle, we need to know what the radius of the circle is. So, We would get the area of the circle.
A newspaper reported that 4040% of people say that some coffee shops are overpriced. The source of this information was a telephone survey of 5050 adults. a. Identify the population of interest in this study. b. Identify the sample for the study. c. Identify the parameter of interest in the study. d. Find and interpret a 9595% confidence interval for the parameter of interest.
Answers
Answer:
a. Identify the population of interest in this study.
all the population of the countryb. Identify the sample for the study.
50 adults (the ones that were surveyed)c. Identify the parameter of interest in the study.
the parameter of interest is the people that believe that coffee shops are overpricedd. Find and interpret a 95% confidence interval for the parameter of interest.
z score for a 95% confidence level = 1.96
margin of error (E) = z score x √{[0.4(1 - 0.4)] / 50} = 1.96 x 0.069282 = 0.13579
95% confidence level interval:
0.4 - 0.13579 = 0.26421
0.4 + 0.13579 = 0.53579
95% confidence interval (0.26421 , 0.53579)
What is the solution to the system that is created by the equation y = 2 x + 10 and the graph shown below? On a coordinate plane, a line goes through (negative 2, 0) and (0, 2). (–8, –6) (–4, –2) (0, 2) (2, 4)
Answers
Answer:
(–8, –6)
Step-by-step explanation:
The given points represent the x- and y- intercepts of the line, so we can write the equation in intercept form as ...
x/(x-intercept) +y/(y-intercept) = 1
x/(-2) +y/2 = 1 . . . use the given intercepts
x - y = -2 . . . . . multiply by -2
Then the system is ...
y = 2x +10x - y = -2Using the first to substitute into the second, we get ...
x - (2x +10) = -2
-8 = x . . . . . . . . . . . add x+2, simplify
y = 2(-8) +10 = -6
The solution is (x, y) = (-8, -6).
Answer:
(-8,-6)
Step-by-step explanation:
Got it right on edge soooo <3
find the exact value of sin 0
Answers
Answer:
12/13
Step-by-step explanation:
First we must calculate the hypotenus using the pythagoran theorem
5²+12² = (MO)² MO = [tex]\sqrt{5^{2}+12^{2} }[/tex] MO = 13Now let's calculate sin0
sin O = 12/13So the exact value is 12/13
Answer:
C.) 12/13
Step-by-step explanation:
In a right angle triangle MN = 12, ON = 5 and; angle N = 90°
Now,
For hypotenuse we will use Pythagorean Theorem
(MO)² = (MN)² + (ON)²
(MO)² = (12)² + (5)²
(MO)² = 144 + 25
(MO)² = 169
MO = √169
MO = 13
now,
Sin O = opp÷hyp = 12÷13
Find the surface area of this shape (here is the grid too)
Answers
Answer:
12
Step-by-step explanation:
The second diagram is most helpful for finding the surface area.
Find the area of the middle square: 2 * 2 = 4Find the area of the triangle using A = 1/2*B*H, so A = 1/2 * 2 * 2 = 2Since there are 4 triangles, the surface area of all the triangles is 2 * 4 = 8Add the surface area of the triangles with the surface area of the square to get the total surface area: 8 + 4 = 12If you want further tutoring help in geometry or other subjects for FREE, check out growthinyouth.org.
Identify the value of the CRITICAL VALUE(S) used in a hypothesis test of the following claim and sample data:
Claim: "The average battery life (between charges) of this model of tablet is at least 12 hours."
A random sample of 80 of these tablets is selected, and it is found that their average battery life is 11.58 hours with a standard deviation of 1.93 hours. Test the claim at the 0.05 significance level.
a. -0.218
b. -1.645
c. -1.946
d. -1.667
Answers
Answer:
C
Step-by-step explanation:
The critical value we are asked to state in this question is the value of the z statistic
Mathematically;
z-score = (x- mean)/SD/√n
From the question
x = 11.58
mean = 12
SD = 1.93
n = 80
Substituting this value, we have
z= (11.58-12)/1.93/√80 = -1.946
stephano walks 2/5 mile in 1/4 hour. What is stephano's speed in miles?
Answers
Explanation:
V = d/t
V = 2/5 divide by 1/4
V = 2/5 x 4/1
V = 8/5 mi/hr
Find the length of the following tangent segments to the circles centered at O and O's whose radii are 5 and 3 respectively and the distance between O and O's is 12. Find segment AB
Answers
Answer:
AB = 2 sqrt(35) (or 11.83 to two decimal places)
Step-by-step explanation:
Refer to diagram.
ABO'P is a rectangle (all angles 90)
=>
PO' = AB
AB = PO' = sqrt(12^2-2^2) = sqrt(144-4) = sqrt(140) = 2sqrt(35)
using Pythagoras theorem.
PLEASE HELP QUICK!!! In how many ways can you put seven marbles in different colors into two jars? Note that the jars may be empty.
Answers
Answer: 14384 ways
Step-by-step explanation:
With 0 identical marbles permitted to be included in any of the jars, An expression can be developed to determine the total of marbles in jar arrangements, which is:
E = [(n+j -1)!]*{1/[(j-1)!]*[(n)!]}, where n = number of identical balls and j =number of distinct jars, the contents of all of which must sum to n for each marbles in j jars arrangement. With n = 7 and j = 4. E = 10!/(3!)(7!) = 120= number of ways 7 identical marbles can be distributed to 4 distinct jars such that up to 3 boxes may be empty and the maximum to any box is 7 balls.
The marble arrangements are: (7,0,0,0) in 4!/3! = 4 ways, (6,1,0,0) in 4!/2! = 12 ways, (5,2,0,0) in 4!/2! = 12 ways, (5,1,1,0) in 4!/2! = 12 ways, (4,3,0,0) in 4!/2! = 12 ways, (4,2,1,0) in 4! = 24 ways, (4,1,1,1) in 4!/3! = 4 ways, (3,3,1,0) in 4!/2! = 12 ways, (3,2,2,0) in 4!/2! = 12 ways, (3,2,1,1) in 4!/2! = 12 ways, (2,2,2,1) in 4!/3! = 4 ways.
Total of ways = 4+12+12+12+12+24+4+12+12+12+4 = 120 as previously determined above for identical marbles and distinct jars.
Taking into account distinct colored marbles, the number of ways of marble distribution into 4 jars becomes as follows:
For (7,0,0,0) = 4*(7!/7!) =4. For (6,1,0,0) = 12*[7!/(6!)(1!)] = 84. For (5,2,0,0) =
12*[7!/(5!)(2!)] = 252. For (5,1,1,0) = 12*[7!/(5!)(1!)(1!)] = 504. For (4,3,0,0) =
12*[7!/(4!)(3!)] = 420. for (4,2,1,0) = 24*[7!/(4!)(2!)(1!)] = 2,520. For (4,1,1,1) =
4*7!/(4!)(1!)(1!)(1!)] = 840. For (3,3,1,0) = 12*]7!/(3!)(3!)(1!) = 1,680. For (3,2,20) = 12*]7!/(3!)(2!)(2!) = 2,520. For (3,2,1,1) = 12*]7!/(3!)(2!)(1!)(1!) = 5,040. For (2,2,2,1) = 4*]7!/(2!)(2!)(2!)(1!) = 2,520.
Total of ways as requested for distinct colored marbles and distinct jars = 4+84+252+504+420+2,520+840+1,680+2,520+5,040+2,520 = 14,384.
A scrub nurse recorded the temperature in the operating theatre every two hours over a 12 hour period from noon to midnight. The results are shown in the following line graph
Answers
NoAnswer:
Step-by-step explanation:
Cause I’m good
−30=5(x+1) solve for x pls help
Answers
Answer:
[tex] \boxed{\sf x = -7} [/tex]
Step-by-step explanation:
[tex] \sf Solve \: for \: x: \\ \sf \implies - 30 = 5(x + 1) \\ \\ \sf - 30 =5(x+ 1) \: is \: equivalent \: to \: 5 (x + 1) = - 30: \\ \sf \implies 5(x + 1) = - 30 \\ \\ \sf Divide \: both \: sides \: of \: 5(x+ 1) = - 30 \: by \: 5: \\ \sf \implies \frac{5(x + 1)}{5} = - \frac{30}{5} \\ \\ \sf \frac{5}{5} = 1 : \\ \sf \implies x + 1 = - \frac{30}{5} \\ \\ \sf - \frac{30}{5} = - \frac{6 \times \cancel{5}}{ \cancel{5}} = - 6 : \\ \sf \implies x + 1 = - 6 \\ \\ \sf Subtract \: 1 \: from \: both \: sides: \\ \sf \implies x + (1 - 1) = - 6 - 1 \\ \\ \sf 1 - 1 = 0 : \\ \sf \implies x = - 6 - 1 \\ \\ \sf - 6 - 1 = - 7 : \\ \sf \implies x = - 7[/tex]
Answer:
[tex] \boxed{x = - 7}[/tex]
Step-by-step explanation:
[tex] \mathrm{ - 30 = 5(x + 1)}[/tex]
Distribute 5 through the parentheses
[tex] \mathrm{ - 30 = 5x + 5} [/tex]
Move constant to L.H.S and change its sign
[tex] \mathrm{ - 30 - 5 = 5x}[/tex]
Calculate
[tex] \mathrm{ - 35 = 5x}[/tex]
Swipe the sides of the equation
[tex] \mathrm{5x = - 35}[/tex]
Divide both sides of the equation by 5
[tex] \mathrm{ \frac{5x}{5} = \frac{ - 35}{5} }[/tex]
Calculate
[tex] \mathrm{x = - 7}[/tex]
Hope I helped!
Best regards!!
A nut-raisin mix costs $5.26 a pound. Rashid buys 15.5 pounds of the mix for a party. Rashid’s estimated cost of the nut-raisin mix is A.$16 B.$22 C.$61 D.$80
Answers
Answer:
D.$80
Step-by-step explanation:
$5.26 x 15.5= $81.53
The closest amount to $81.53 is D.$80
A swimming pool is circular with a 30-ft diameter. The depth is constant along east-west lines and increases linearly from 2 ft at the south end to 7 ft at the north end. Find the volume of water in the pool. (Round your answer to the nearest whole number.) ft3
Answers
Answer:
Volume of water in the pool is 3,182 ft^3
Step-by-step explanation:
In this question, what we want to calculate is the volume of water in the pool.
We proceed as follows;
diameter of pool = 30ft
depth: 2 to 7ft linearly
average depth = (2 + 7)/2 = 9/2 = 4.5 ft
Volume = area * average depth
V = pi * radius^2 * 4.5
where radius = diameter/2 = 30/2 = 15 ft
V = pi * 15^2 * 4.5
V = 22/7 * 225 * 4.5
V = 3,182.14 ft^3
which is 3,182 ft^3 to nearest whole number
The volume of water in the pool is; Volume = 3181 ft³
We are given;
Diameter of swimming Pool; d = 30 ft
Thus; radius; r = d/2 = 30/2 = 15 ft
We are told that the depth is constant along east-west lines and increases linearly from 2 ft at the south end to 7 ft at the north end.
Thus, average depth is;
h_avg = (2 + 7)/2
h_avg = 4.5 ft
Formula for area is; A = πr²
Thus;
A = π × 15²
A = 225π
Formula for volume here is;
Volume = Area × depth
Volume = 225π × 4.5
Volume = 3180.86 ft³
Approximating to a whole number gives;
Volume = 3181 ft³
Read more at; https://brainly.com/question/15276135
800x87979 cuanto es?
Answers
800x87979 es 70, 383, 200
Espero que esto te ayude
Answer:
Step-by-step explanation:
800*87979 = 70,383,200
8. Which statement is always true?
A. 9 times a number is always odd.
B. 9 times a number is always even
C. 10 times a number is always odd.
D. 10 times a number is always even.
Answers
Answer:
D
Step-by-step explanation:
Any number multiplied by an even number will always be even. 10 is an even number.
Answer:
d. 10 times a number is always even
Step-by-step explanation:
multiples of 9 contain 81 and 36 which one is even and the other is odd
multiples of 10 ONLY contain even numbers because the unit digit for a multiple of 10 is 0.
So whenever you multiply a number by 10 it will be even
Five thousand dollars is deposited into a savings account at 2.5% interest compounded continuously.
a. What is the formula for A(t), the balance after t years?
b. What differential equation is satisfied by A(t), the balance after t years?
c. How much money will be in the account after 5 years? (Do not round until your final answer. Round your final
answer to the nearest cent as needed.
d. When will the balance reach $7,000? (Do not round until your final answer. Round your final answer to the
nearest tenth as needed.)
Answers
Answer:
A). A(t) = P(1+r/n)^(nt)
B). DA/Dt = np(1+r/n)^(t)
C). A(5) =$ 5664.0
D).t = approximately 13.5 years
Step-by-step explanation:
A(t) = P(1+r/n)^(nt)
P = $5000
n= t
r= 2.5%
After five years t = 5
A(t) = P(1+r/n)^(nt)
A(5) = 5000(1+0.025/5)^(5*5)
A(5) = 5000(1+0.005)^(25)
A(5)= 5000(1.005)^(25)
A(5) = 5000(1.132795575)
A(5) = 5663.977875
A(5) =$ 5664.0
When the balance A= $7000
A(t) = P(1+r/n)^(nt)
7000= 5000(1+0.025/n)^(nt)
But n= t
7000= 5000(1+0.025/t)^(t²)
7000/5000= (1+0.025/t)^(t²)
1.4= (1+0.025/t)^(t²)
Using trial and error
t = approximately 13.5 years
A living room is two times as long and one and one-half times as wide as a bedroom. The amount of
carpet needed for the living room is how many times greater than the amount of carpet needed for the
bedroom?
1 1/2
2
3
3 1/2
Answers
Answer:
3
Step-by-step explanation:
let's call X the length of the bedroom, Y the wide of the bedroom, A the length of the living room and B the wide of the living room
A living room is two times as long as the bedroom, so:
A = 2X
A living room is one and one-half times as wide as a bedroom, so:
B = 1.5Y
The amount of carpet needed for the living room is A*B and the amount of carpet needed by the bedroom is X*Y
So, AB in terms of XY is:
A*B = (2X)*(1.5Y) = 3(X*Y)
It means that the amount of c arpet needed for the living room is 3 times greater than the amount of carpet needed for the bedroom.
Determine whether the value given below is from a discrete or continuous data set. In a test of a method of gender selection, 725 couples used the XSORT method and 368 of them had baby girls. Choose the correct answer below. A. The data set is neither continuous nor discrete. B. A continuous data set because there are infinitely many possible values and those values can be counted C. A continuous data set because there are infinitely many possible values and those values cannot be counted D. A discrete data set because there are a finite number of possible values
Answers
Answer:
D. A discrete data set because there are a finite number of possible values.
Step-by-step explanation:
Assuming in a test of a method of gender selection, 725 couples used the XSORT method and 368 of them had baby girls. The value given is from a discrete data set because there are a finite number of possible values.
In Mathematics, a discrete data is a data set in which the number of possible values are either finite or countable.
On the other hand, a continuous data is a data set having infinitely many possible values and those values cannot be counted, meaning they are uncountable.
Hence, if 725 couples used the XSORT method and 368 of them had baby girls; this is a discrete data because the values (725 and 368) are finite and can be counted.
A pharmacist wants to mix a 30% saline solution with a 10% saline solution to get 200 mL of a 12% saline solution. How much of each solution should she use
Answers
Answer:
30% constituents=20 mL
10% constituents=180 mL
Step-by-step explanation:
x= 30% volume
y=10% volume
For our first equation, we know the total volume is 200 mL and is the sum
x+y=200
y=200-x (1)
For our second equation, we do a mass balance for 200 mL of final solution.
12% w/v = 0.12 g/mL
This means that in 1 mL of solution, we have 0.12 g of NaCl.
For any solution, concentration multiplied by volume will give the mass of NaCl:
Mass in x mL= C*V (g/mL) (mL)
So in 200 mL, we have
0.12*200 (g/mL) (mL)
=24g of NaCl
Cx*Vx + Cy*Vy=24
0.3x+0.1y=24 (2)
Substitute y=200-x into (2)
0.3x+0.1(200-x)=24
0.3x+20-0.1x=24
0.2x=24-20
0.2x=4
Divide both sides by 0.2
0.2x/0.2=4/0.2
x=20
Substitute x=20 into (1)
y=200-x
y=200-20
y=180
30% constituents=20 mL
10% constituents=180 mL
1. find x and y 2. find the measure of each side of LMN
Answers
Answer:
X= 3
Y= 18
Each side of the triangle= 10 units
Step-by-step explanation:
LMN is equilateral so
LM = MN
3x+1= 4x-2
3x-4x = -2-1
-x = -3
X= 3
MP is the perpendicular bisector of line LN
so definitely angle lpm =90.
And lpm = 5y = 90
5y = 90
Y= 90/5
Y = 18°
For the side of the triangle
3x+1
But x= 3
3(3)+1
9+1
10
Each side of the triangle= 10 units
Use the functions m(x) = 4x + 5 and n(x) = 8x − 5 to complete the function operations listed below. Part A: Find (m + n)(x). Show your work. (3 points) Part B: Find (m ⋅ n)(x). Show your work. (3 points) Part C: Find m[n(x)]. Show your work. (4 points)
Answers
Answer:
Step-by-step explanation:
Part A
(m + n)x = 4x + 5 + 8x - 5
(m + n)x = 12x The fives cancel
Part B
(m - n)x = 4x + 5 - 8x + 5
(m - n)x = -4x + 10
Part C
The trick here is to put n(x) into m(x) wherever m(x) has an x.
m[n(x)] = 5(n(x)) + 5
m[n(x)] = 5(8x - 5) + 5
m[n(x)] = 40x - 20 + 5
m[n(x)] = 40x - 15
Evaluate the series
Answers
Answer:
the value of the series;
[tex]\sum_{k=1}^{6}(25-k^2) = 59[/tex]
C) 59
Step-by-step explanation:
Recall that;
[tex]\sum_{1}^{n}a_n = a_1+a_2+...+a_n\\[/tex]
Therefore, we can evaluate the series;
[tex]\sum_{k=1}^{6}(25-k^2)[/tex]
by summing the values of the series within that interval.
the values of the series are evaluated by substituting the corresponding values of k into the equation.
[tex]\sum_{k=1}^{6}(25-k^2) =(25-1^2)+(25-2^2)+(25-3^2)+(25-4^2)+(25-5^2)+(25-6^2)\\\sum_{k=1}^{6}(25-k^2) =(25-1)+(25-4)+(25-9)+(25-16)+(25-25)+(25-36)\\\sum_{k=1}^{6}(25-k^2) =24+21+16+9+0+(-11)\\\sum_{k=1}^{6}(25-k^2) = 59\\[/tex]
So, the value of the series;
[tex]\sum_{k=1}^{6}(25-k^2) = 59[/tex]