Consider the arithmetic sequence with a first term of 11 and sixth term of 21. What is the
sum of these first six terms?
A: 192
B: 52
C: 142
D: 96
Answer:
96Consider the arithmetic sequence with a first term of 11 and sixth term of 21. What is the
sum of these first six terms?
The required sum of the first 6th term of an arithmetic progression is 96. Option D is correct.
Given that,
Consider the arithmetic sequence with the first term of 11 and the sixth term of 21. To determine the sum of these first six terms.
Arithmetic progression is the series of numbers that have common differences between adjacent values
What is geometric progression?Geometric progression is a sequence of series whose ratio with adjacent values remains the same.
Here,
First term a = 11
6th term = a + 5d
21 = 11 + 5d
5d = 10
d = 2
Now,
sum of the six terms, = 6 / 2{11 + 21}
= 3 (32)
= 96
Thus, the required sum of the first 6th term of an arithmetic progression is 96. Option D is correct.
Learn more about arithmetic progression here: https://brainly.com/question/20334860
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Can someone help with number 4 please
Answer:
.(0,4,3,1,2,5)..............
please help meeeeeeeee
Answer:
3.32 dollars/gallon
Step-by-step explanation:
Simply divide the cost by its corresponding amount in gallons
15.77 ÷ 4.75 = 3.32
19.92 ÷ 6 = 3.32
etc etc
COORDINATE GEOMETRY Find the perimeter and area of each figure with the given vertices. 20. D(-2,-2), E(-2, 3), and F(2, -1)
Step-by-step explanation:
Find the sides and perimeter:
DE = 3 - (-2) = 5EF = [tex]\sqrt{(2+2)^2+(-1+2)^2} =\sqrt{17}[/tex] ≈ 4.1DF = [tex]\sqrt{(2+2)^2+(3+2)^2} =\sqrt{41}[/tex] ≈ 6.4Perimeter:
P = 5 + 4.1 + 6.4 = 15.5 unitsFind the area using shoelace formula:
A = 1/2|(x₁y₂ + x₂y₃ + x₃y₁) - (y₁x₂ + y₂x₃ + y₃x₁)|=1/2|(-2*3 + -2* -1 + 2* -2) - (-2* -2 + 3*2 - 1* -2)|=1/2|(-6 + 2 - 4) - (4 + 6 + 2)| =1/2|-8 - 12| =1/2(20) = 10 units²I am a quadrilateral with all four sides congruent. My all interior angles are congruent. The sum of my interior angles is 360°. My area is equal to the square of my length. I am?
(T^3 - T)/a = b make T the subject of the formula
(t^3-t)/a=b because a t the simple of questions
jamarius 5th grade class was working on a reading project during the school year he wants to read 22 pages for 125 days if jamarius wants to meet his goal how man books will he have to read
Answer:
2750 pages
Step-by-step explanation:
but i am not sure how many books exactly .
Find the quotient of 2 2 3 and 3 1 2 Give your answer as a fraction in its simplest form.
The correct answer is: " [tex]\frac{16}{21}[/tex] " .
_______
Step-by-step explanation:
" [tex]2\frac{2}{3}[/tex] ÷ [tex]3\frac{1}{2}[/tex] " =
" [tex]\frac{(2\frac{2}{3})}{(3\frac{1}{2})}[/tex] " ;
_______
" [tex]2\frac{2}{3} = \frac{[(3*2)+2]}{3} = \frac{(6+2)}{3} = \frac{8}{3}[/tex] " .
_______
" [tex]3\frac{1}{2} = \frac{[(2*3)+1]}{2} = \frac{(6+1)}{2} = \frac{7}{2}[/tex] " .
_______
→ " [tex]\frac{(2\frac{2}{3})}{(3\frac{1}{2})}[/tex] " ;
[tex]} = \frac{8}{3}[/tex] ÷ [tex]\frac{7}{2}[/tex] ;
Note that "dividing by a value" results in the same value as "multiplying by the reciprocal of that value" ;
The reciprocal of: " [tex]\frac{7}{2}[/tex] " ; is: " [tex]\frac{2}{7}[/tex] " ;
_______
[tex]= \frac{8}{3} *\frac{2}{7}= \frac{(8*2)}{(3*7)} = \frac{16}{21}[/tex] ; which cannot be further reduced as a fraction.
_______
The correct answer is: " [tex]\frac{16}{21}[/tex] " .
_______
Hope this is helpful!
Best wishes to you!
_______
Place the numbers in order from greatest to least.
Answer:
C
Step-by-step explanation:
0.528 is the smallest number and C is the only one that starts with it
If l || m, find the value of each missing variable(s).
Answer:
12
Step-by-step explanation:
13x-21=5x+75
8x=96
x=96/8=12
Answer:
x=12
Step-by-step explanation:
Since the 2 lines are parallel we can use the rules of transversals. These 2 angels are alternate side interior. This means that they are congruent and have the same measurement. Because they have the same measurement, we can set them equal to each other and solve for x.
First, set the expressions equal to each other13x-21 = 5x+75
Next, add 21 to both sides13x = 5x+96
Then, subtract 5x from both sides8x = 96
Finally, divide both sides by 8x=12
Ok please help me and no links or I will report you
Answer:
B 33
Step-by-step explanation:
What is 6% of 90? Helpp
Answer:
54
Step-by-step explanation:
6/100 = x/90
6×90=540
540/100=54
The total weight limit for a truck is 100,000 lb. The truck weighs 36,000 lb empty. What is the most that the truck's load can weigh?
Answer: 64,000} lbs
Step-by-step explanation: hope it helps ! <3!
A fish store can place 5 fish in each fish bowl. If there are 263 fish to place, how many fish bowls are needed for all 263 fish?
Answer:
Step-by-step explanation:
1 bowl holds 5 fish
x bowls hold 263 fish
1/x = 5/263 Cross multiply
5x = 263 Divide by 5
5x/5 = 263/5
x = 52.6
So you actually need 53 fishbowls. One of them holds only 3 fish
Please help! What values of x make the matrix M have an inverse?
Answer:
I'm not sure I'm only in middle school, but I'll put what I know.
Step-by-step explanation:
Step 1: Calculate the minor for the given matrix.
Step 2: Turn the obtained matrix into the matrix of cofactors.
Step 3: Then, the adjugate, and.
Step 4: Multiply that by reciprocal of determinant.
Suppose that an individual has a body fat percentage of 17.6% and weighs 139 pounds. how many pounds of her weight is made up of fat? round your answer to the nearest tenth.
Answer:
24.5 pounds
Step-by-step explanation:
0.176*139= 24.5
Translate the sentence into an inequality.
The sum of a number times 9 and 16 is at least 22.
Use the variable c for the unknown number.
Frida owed
$75
on
her credit card. Then she charged
$21
more. What was her new
balance?
Suppose that $3000 is placed in a savings account at an annual rate of 3.6%, compounded monthly. Assuming that no withdrawals are made, how long will it take for the account to grow to $4500? Do not round any intermediate computations, and round your answer to the nearest hundredth.
Using compound interest, it is found that it will take 11.28 years for the the account to grow to $4500.
The compound interest formula is given by:
[tex]A(t) = P(1 + \frac{r}{n})^{nt}[/tex]
A(t) is the amount of money after t years.
P is the principal(the initial sum of money).
r is the interest rate(as a decimal value).
n is the number of times that interest is compounded per year.
t is the time in years for which the money is invested or borrowed.
In this problem:
$3000 is placed in the account, thus [tex]P = 3000[/tex].Interest rate of 3.6%, thus [tex]r = 0.036[/tex].Monthly compounding, thus [tex]n = 12[/tex].We have to solve for t when [tex]A(t) = 4500[/tex], thus:
[tex]A(t) = P(1 + \frac{r}{n})^{nt}[/tex]
[tex]4500 = 3000(1 + \frac{0.036}{12})^{12t}[/tex]
[tex](1.003)^{12t} = 1.5[/tex]
[tex]\log{(1.003)^{12t}} = \log{1.5}[/tex]
[tex]12t\log{1.003} = \log{1.5}[/tex]
[tex]t = \frac{\log{1.5}}{12\log{1.003}}[/tex]
[tex]t = 11.28[/tex]
It will take 11.28 years for the the account to grow to $4500.
A similar problem is given at https://brainly.com/question/24507395
Hey , can you help please and thanks
Answer:
13/4 gallons per bucket or (as a mixed number) 3 and 1/4
Step-by-step explanation:
a gallon is made up of 4 quarts
so 13 qt/bucket* 1 gal/4 qts = 13/4 gal/bucket This label is because, since the quart labels are on opposite sides of the slash or division line this means we can cancel them which is why I multiplied it by 1 gal/4 gts instead of 4 qts/1 gal because even though both are true, one would cancel and one wouldn't.
Marie is reading a 271-page book. She has already read 119 pages. She uses the equation 119+8h=271 to find out how long it will take her to finish the book if she reads at about 8 pages per hour.
Solve for h.
Answer: the answer is 19
Step-by-step explanation:okay so she already have read 119 pages and the total pages is 271 so we substract 271-119=152 so she has 152 pages left so we divide 152 pages divided by 8 because she read 8 pages per hour so 152/8=19
I NEED HELP ON THIS 10 POINTS
Answer:
-x-x-0.7
is equivalent to 1-2x-1.7
medical tests. Task Compute the requested probabilities using the contingency table. A group of 7500 individuals take part in a survey about a rare disease and medical test. The data for the group is given in the table below. A person listed as "Sick" has the disease, while someone listed as "Not Sick does not "Tested Positive means the test indicated the person was sick, and "Tested Negative" means the test indicated they were not sick. The test is believed to be around 99% accurate. Sick Not Sick Tested Positive 59 75 Tested Negative 1 7365 h One person at random is chosen from the group (3 pts) Find the probability the person is sick. b. (3 pts) Find the probability the test is positive given that the person is sick (3 pts) Find the probability the test is negative given that the person is not sick. d. (pts) Find the probability the person is sick given that the test is positive (3 pts) Find the probability the person is not sick given that the test is negative. f. (5 pts) When we say a test is 99% accurate, to what is that referring? Given vour calculations, should information other than a single test be considered when diagnosing a rare condition? If so, what other information might be considered? Criteria for Success
Probabilities are used to determine the chances of an event
The probability that a person is sick is: 0.008The probability that a test is positive, given that the person is sick is 0.9833The probability that a test is negative, given that the person is not sick is: 0.9899The probability that a person is sick, given that the test is positive is: 0.4403The probability that a person is not sick, given that the test is negative is: 0.9998A 99% accurate test is a correct test(a) Probability that a person is sick
From the table, we have:
[tex]\mathbf{Sick = 59+1 = 60}[/tex]
So, the probability that a person is sick is:
[tex]\mathbf{Pr = \frac{Sick}{Total}}[/tex]
This gives
[tex]\mathbf{Pr = \frac{60}{7500}}[/tex]
[tex]\mathbf{Pr = 0.008}[/tex]
The probability that a person is sick is: 0.008
(b) Probability that a test is positive, given that the person is sick
From the table, we have:
[tex]\mathbf{Positive\ and\ Sick=59}[/tex]
So, the probability that a test is positive, given that the person is sick is:
[tex]\mathbf{Pr = \frac{Positive\ and\ Sick}{Sick}}[/tex]
This gives
[tex]\mathbf{Pr = \frac{59}{60}}[/tex]
[tex]\mathbf{Pr = 0.9833}[/tex]
The probability that a test is positive, given that the person is sick is 0.9833
(c) Probability that a test is negative, given that the person is not sick
From the table, we have:
[tex]\mathbf{Negative\ and\ Not\ Sick=7365}[/tex]
[tex]\mathbf{Not\ Sick = 75 + 7365 = 7440}[/tex]
So, the probability that a test is negative, given that the person is not sick is:
[tex]\mathbf{Pr = \frac{Negative\ and\ Not\ Sick}{Not\ Sick}}[/tex]
This gives
[tex]\mathbf{Pr = \frac{7365}{7440}}[/tex]
[tex]\mathbf{Pr = 0.9899}[/tex]
The probability that a test is negative, given that the person is not sick is: 0.9899
(d) Probability that a person is sick, given that the test is positive
From the table, we have:
[tex]\mathbf{Positive\ and\ Sick=59}[/tex]
[tex]\mathbf{Positive=59 + 75 = 134}[/tex]
So, the probability that a person is sick, given that the test is positive is:
[tex]\mathbf{Pr = \frac{Positive\ and\ Sick}{Positive}}[/tex]
This gives
[tex]\mathbf{Pr = \frac{59}{134}}[/tex]
[tex]\mathbf{Pr = 0.4403}[/tex]
The probability that a person is sick, given that the test is positive is: 0.4403
(e) Probability that a person is not sick, given that the test is negative
From the table, we have:
[tex]\mathbf{Negative\ and\ Not\ Sick=7365}[/tex]
[tex]\mathbf{Negative = 1+ 7365 = 7366}[/tex]
So, the probability that a person is not sick, given that the test is negative is:
[tex]\mathbf{Pr = \frac{Negative\ and\ Not\ Sick}{Negative}}[/tex]
This gives
[tex]\mathbf{Pr = \frac{7365}{7366}}[/tex]
[tex]\mathbf{Pr = 0.9998}[/tex]
The probability that a person is not sick, given that the test is negative is: 0.9998
(f) When a test is 99% accurate
The accuracy of test is the measure of its sensitivity, prevalence and specificity.
So, when a test is said to be 99% accurate, it means that the test is correct, and the result is usable; irrespective of whether the result is positive or negative.
Read more about probabilities at:
https://brainly.com/question/11234923
13, 69, 89, 25, 55, 20, 99, 75, 42, 18, 66, 88, 89, 79, 75, 65, 25, 99, 66, 78. Order from least to greatest
At a hockey game, a vender sold a combined total of 127 sodas and hot dogs. The number of sodas sold was 43 more than the number of hot dogs sold. Find the number of sodas sold and the number of hot dogs sold. Number of sodas sold:
Answer:
85 sodas
Step-by-step explanation:
Total sold was 127
The number of sodas was 43 + the number of hotdogs
Let x represent hotdogs:
x + (43 + x) = 127 (The 43 + x is the number of sodas sold.)
2x + 43 = 127
2x = 84
x = 42
42 hotdogs were sold., Since sodas are 42 + 43, 85 sodas were sold
-Chetan K
NO LINKS OR ASSESSMENT!!!
Part 2: Graph a function when give the following Domain and Range:
Answer:
Step-by-step explanation:
The domain is the x value between - 5 and 7
The range is the y value between -2 and 6
You can find all sorts of definitions for the domain and range, but in this example it is really straight forward. If you put - 5 into the function, you get -2. If you put 7 into the function, you get 6. Now just draw a line between the two end points.
9514 1404 393
Answer:
see attached
Step-by-step explanation:
The point at the left end of the domain is not included in the function, but the function includes the limits of its range. One such function is shown in the attachment.
4. (4)5 =
a. 12
b. 13
c. 14
d. 15
[tex]▪▪▪▪▪▪▪▪▪▪▪▪▪ {\huge\mathfrak{Answer}}▪▪▪▪▪▪▪▪▪▪▪▪▪▪[/tex]
[tex](4 {}^{3} ) {}^{5} [/tex][tex](4{}^{3 \times 5} )[/tex][tex]4 {}^{15} [/tex]therefore, the Correct choice is d) 15
A cable 84 meters long is cut into two pieces so
that one piece is 20 meters longer than the other.
Find the length of each piece of cable.
Answer: 33
Step-by-step explanation: Let x equal the shorter piece.
x + (x + 18) = 84
2x + 18 = 84
2x = 66
x = 33
Which of the following is an infinite set?
A)The Set of numbers between 4 and 5
B){1,2,3,…………..1000}
C)The Set of positive integers less than 100
D)None of these
Answer:
The number of elements in a finite set A is denoted by n(A). Examples: If A is the set of positive integers less than 12 then. A = {1, 2, 3, 4, 5, 6, 7, 8, ...
help I'm going to die here I have a 23% in this class
Answer:
0.0026
I don't know how to add the work here