Find the sum of the arithmetic sequence. 15, 17, 19, 21, ..., 33
Answers
sum = [tex] n *\frac{ a_{1} + a_{n} }{2} [/tex]
in our case n = 10, a1 = 15 and An = 33 so the answer will be:
sum = 10 * (33 + 15)/2 = 10 * 48 / 2 = 10 * 24 = 240
Answer:
240
Step-by-step explanation:
Hope this helps! :)
Related Questions
20 is what percent of 50?
Answers
Hey!
Hope this helps...
~~~~~~~~~~~~~~~~~~~~~~~
First, you need to do 20 divided by 50 (or in your calculator 20/50)...
Second, you would do long division (or in the calculator, press 'enter')...
And boom-bada-boom, your answer is: 20 is 40% of 50
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For future reference, please try to avoid asking/posting questions that can be answered using the calculator...
(100/x)*x=(50/20)*x
100=2.5*x
100/2.5=x
40=x
x=40
So 20 is 40% of 50
A car uses an average of 8 litres of fuel for every 100 km travelled. At this rate, how many litres would the car use to travel 250 km?
Answers
The car would use 20 litres to travel 250 km.
Explanation:To determine the number of litres the car would use to travel 250 km, we can set up a proportion using the average fuel consumption rate of 8 litres per 100 km:
8 litres / 100 km = x litres / 250 km
To solve for x, we can cross-multiply and then divide:
x litres = (8 litres * 250 km) / 100 km
x litres = 20 litres
Therefore, the car would use 20 litres to travel 250 km.
Final answer:
The car would use 20 liters of fuel to travel 250 km.
Explanation:
To determine how many liters of fuel the car would use to travel 250 km, we can set up a proportion using the given information:
8 liters ÷ 100 km = x liters ÷ 250 km
Cross multiplying, we get:
x = (8 liters × 250 km) ÷ 100 km
x = 2000 liters ÷ 100 km
x = 20 liters
Therefore, the car would use 20 liters of fuel to travel 250 km.
The blueprint for landscaping a yard has a scale of 1/2" to 1 foot. If the blueprint is a rectangle 18 inches by22 inches, what are the dimensions of the yard? If u find the answer please explain how you got it that would be very helpful
Answers
[tex] \frac{bp}{actual} : \frac{.5"}{1ft} = \frac{18"}{xft} [/tex]
Now cross multiply to get the first dimension: .5x = 18 and x = 36. Do the same with the other dimension of the yard:
[tex] \frac{bp}{actual}: \frac{.5"}{1ft} = \frac{22"}{xft} [/tex]
and cross multiply to solve for that dimension: .5x = 22 and x = 44. So the dimensions of the actual yard are 36x44 ft
How many solutions can be found for the equation −4x − 11 = 2(x − 3x) + 13?
Answers
-4x-11=2 (x-3x)+13
-4x-11=2 (-2x)+13
-4x-11=-4x+13
-11 is not equal to 13 so there is no solution
Answer:
it is no solutions
Step-by-step explanation:
A)7/25
B)24/25
C)25/7
D)25/24
PLEASE HELP ME !!
Answers
The graph below represents the amount of change Jaxon would receive, y, if he bought a item with a cost of x.
Which equation represents the graph?
y = 10 – x
y = x – 10
y = –x – 10
y = 10 + x
Answers
The line is going down when you go from left to right so there must be a - before the x
The answer is A
Answer: The correct option is (A) [tex]y=10-x.[/tex]
Step-by-step explanation: The given graph represents the amount of change Jaxon would receive 'y' if he bought a item with a cost of 'x'.
We are to select the correct equation that represents the graph.
We notice from the graph that it is a straight line and the points (0,10) and (10, 0) lies on the line.
The slope of a straight line passing through the points (a, b) and (c, d) is given by
[tex]m=\dfrac{d-b}{c-a}.[/tex]
So, the slope of the given line is
[tex]m=\dfrac{0-10}{10-0}\\\\\\\Rightarrow m=-1.[/tex]
Since the line passes through the point (10, 0), therefore the equation of the line representing the graph is
[tex]y-10=m(x-0)\\\\\Rightarrow y-10=-1(x-0)\\\\\Rightarrow y-10=-x\\\\\Rightarrow y=10-x.[/tex]
Thus, the required equation is [tex]y=10-x.[/tex]
Option (A) is CORRECT.
At a local community college, it costs $450 to enroll in a morning section of an algebra course. Suppose that the variable n stands for the number of students who enroll. Then 450n stands for the total amount of money collected for this course. How much is collected if 38 students enroll? 90 students? 280 students?
Answers
90= 40,500
280= 126,000
In a geometric sequence, a4=54 and a7=1458. What is the 12th term?
a. 5,616
b. 354,294
c. 14,350,365
d. 234,812,358
Answers
Answer-
[tex]\boxed{\boxed{a_{12}=354294}}[/tex]
Solution-
If there are 2 terms of a Geometric Sequence [tex]a_n[/tex] and [tex]a_k[/tex] where (n > k), then
[tex]a_n=a_k\cdot r^{n-k}[/tex]
where, r = common ration of the G.P.
Here,
[tex]a_4 = 54\\\\a_7=1458[/tex]
Putting in the equation,
[tex]\Rightarrow a_7=a_4\cdot r^{7-3}[/tex]
[tex]\Rightarrow a_7=a_4\cdot r^3[/tex]
[tex]\Rightarrow 1458=54\cdot r^3[/tex]
[tex]\Rightarrow r^3=\dfrac{1458}{54}[/tex]
[tex]\Rightarrow r^3=27[/tex]
[tex]\Rightarrow r=3[/tex]
Again putting the values in the equation,
[tex]\Rightarrow a_{12}=a_7\cdot r^{12-7}[/tex]
[tex]\Rightarrow a_{12}=a_7\cdot r^5[/tex]
[tex]\Rightarrow a_{12}=1458\cdot 3^5[/tex]
[tex]\Rightarrow a_{12}=354294[/tex]
The 12th term of the geometric sequence is 354,294
The nth term of a geometric sequenceThe nth term of a geometric progression is given by the formula:
[tex]a_n = ar^{n-1}[/tex]
For n = 4
[tex]a_4=ar^{4-1}\\\\a_4=ar^3\\\\ar^3=54..................(1)[/tex]
For n = 7
[tex]a_7=ar^{7-1}\\\\a_7=ar^6\\\\ar^6=1458................(2)[/tex]
Divide equation (2) by equation (1)
[tex]\frac{ar^6}{ar^3} =\frac{1458}{54} \\\\r^3=27\\\\r^3=3^3\\\\r = 3[/tex]
Substitute r = 3 into equation (1)
[tex]a(3)^3=54\\\\27a=54\\\\a=\frac{54}{27}\\\\a=2[/tex]
The 12th term of the sequence is therefore calculated below
[tex]a_{12}=ar^{11}\\\\a_{12}=2(3^{11})\\\\a_{12}=354294[/tex]
The 12th term of the geometric sequence is 354,294
Learn more on geometric sequences here: https://brainly.com/question/1662572
How to solve; you roll a pair of number cubes what is the probability of rolling a number less than 4 on both cubes?
Answers
6 numbers per cube
3 numbers are less than 4 ( 1, 2 & 3)
so you have a 3/6, reduce to 1/2 probability of rolling a number less than 4 on each cube
2 cubes
so 1/2 * 1/2 = 1/4 probability
Find the sum of the three expressions and choose the correct answer.
-8a 3 b + 3a2 b 2 - 5
2 + 5a 2 b 2
3a 3 b + 7 - 9a 2 b 2
Choices:
A.) -5a3b - a2b2 + 2
B.) -5a3b + 8a2b2 + 4
C.) -5a3b - a2b2 + 4
Answers
= -5a^3 b - a^2 b^2 + 4
answer is
C.) -5a3b - a2b2 + 4
Answer:
Sum of -8a³b+3a²b²-5,2+5a²b² and 3a³b+7-9a²b² is:
-5a³b-a²b²+4
Step-by-step explanation:
We have to find the sum of:
-8a³b+3a²b²-5,2+5a²b² and 3a³b+7-9a²b²
-8a³b+3a²b²-5+2+5a²b²+3a³b+7-9a²b²
= -5a³b-a²b²+4
Hence, sum of -8a³b+3a²b²-5,2+5a²b² and 3a³b+7-9a²b² is:
-5a³b-a²b²+4
A circle has what type of symmetry?
Answers
can reflect symmetrically along x, y axis and origin
Answer:
Point of symmetry
Step-by-step explanation:
The circle is moves at the same distance from the center of the circle. Therefore, the circle is symmetrical around a single point.
Hope this will helpful.
Thank you.
If H(x)=4x^2-16 were shifted 9 units to the right and 1 down, what wold be the new equation?
A. H(x)= 4(x+9)^2-17
B. H(x)= 4(x-7)^2+16
C. H(x)= 4(x-17)^2-9
D. H(x)= 4(x-9)^2-17
Answers
to move a function c units up, add c to the whole function
so
we want 9 to the right and 1 down
basically we need to find f(x-9)-1 (-1 is up -1 units)
f(x-9)-1=4(x-9)²-16-1
f(x-9)=4(x-9)²-17
answer is D
Answer: H(x)=4(x-9)^2-17
Step-by-step explanation:
If you buy something at a 20% discount off the listed price of $ 97, but pay a sales tax of 10% after the discount is applied, how much do you end up paying? $
Answers
Event A is rolling a five on a six sided die and event B is rolling an odd number on the same die. Are the events dependent or independent, why?
Answers
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A = event of rolling a five
B = event of rolling an odd number
P(A) = (number of ways to roll a five)/(number of outcomes total)
P(A) = 1/6
P(B) = (number of ways to roll an odd number)/(number of outcomes total)
P(B) = 3/6
P(B) = 1/2
P(A and B) = (number of ways to roll an odd number AND five at the same time)/(number of outcomes total)
P(A and B) = 1/6
If A and B were independent, then P(A and B) = P(A)*P(B) would be true. Let's see if it is or not
P(A and B) = P(A)*P(B)
1/6 = (1/6)*(1/2)
1/6 = 1/12
The result is false, so P(A and B) = P(A)*P(B) isn't true
This means that A and B are dependent events
If we know B has happened, then that changes the probability of A
If we know A has happened, then B is automatically true (since 5 is odd). I.e, P(B|A) = 1
P(A and B) = 3/36 = 1/6*3/6 = P(A) * P(B)
Tossing coins either,... For not being independent there must be some 'memory'. Like extracting marbles *without* replacement, ... The first action changed the second one.
A certain forest covers an area of 2500 km2. Suppose that each year this area decreases by 5.25%. What will the area be after 15 years?
Use the calculator provided and round your answer to the nearest square kilometer.
Answers
2500(1-5.25/100)^15
=1113km2 (nearest square kilometer)
Complete the square to solve the equation below.
x²+x =7/4
A.)x=3, x= -1
B.)x= -2+ √2, x= -2- √2
C.) x= -1/2+√2, x= -1/2- √2
D.) x=1+ √-2, x= 1- √2
Answers
x² + x = 7/4
x² + - 7/4 = 0
Now we gonna use the quadratic formula to find x
a= 1
b=1
c = -1.75
x = -b+/-√b² -4ac all of them divide by 2a
x = -(1)+/-√(1)² - (4)(1)(-1.75) all of them divide by 2(1)
x= -1+/-√8 all of them divide by 2
x = -1/2 + √2 or x = -1/2 - √2
The correct option is option C
I hope that helps!
Answer: The correct answer is C
Step-by-step explanation: APPEX learning quiz
A horse owner has 50 lbs of hay that is 6% protein by weight. He adds x lbs of oats that is 12% protein by weight.
The function y=.06(50)+.12x/50+x
models the percent of protein, y, in the final mixture of feed. What is the y-intercept of the function that models the percent of protein in the final mixture?
y-intercept=
Answers
Answer:
y-intercept = 0.06 = 6%
Step-by-step explanation:
As per the statement:
A horse owner has 50 lbs of hay that is 6% protein by weight. He adds x lbs of oats that is 12% protein by weight.
Given the function:
[tex]y = \frac{0.06(50)+0.12x}{50+x}[/tex]
where, y represents the percent of protein in the final mixture of feed.
We have to find y-intercept of the function that models the percent of protein in the final mixture.
Y-intercept:
Substitute x = 0 and solve for y:
then;
[tex]y = \frac{0.06(50)+0.12(0)}{50+0}=\frac{0.60 \cdot 50}{50}[/tex]
⇒[tex]y = 0.06 =6\%[/tex]
Therefore, the y-intercept of the function that models the percent of protein in the final mixture is, 6%
Answer:
.06
Step-by-step explanation:
Question 12 the length of a rectangle is three times its width. if the perimeter of the rectangle is 40 m , find its area.
Answers
Length = 3x
Perimeter = 40
2*(L + W) = 40
L + W = 20
3x + x = 20
4x = 20
x = 5
Hence,
Length = 15 m
Width = 5 m
Area = L*W = 15 * 5 = 75 sq. m
Answer:
The area of the rectangle is 75 squared meters.
Step-by-step explanation:
Width of the rectangle = w
Length of the rectangle = l = 3w
Perimeter of the rectangle = P = 40 m
Perimeter of the rectangle = 2(l+w)
[tex]2(l+w)=40 m[/tex]
[tex]2(3w+w)=40 m[/tex]
[tex]8w=40 m[/tex]
[tex]w=\frac{40 m}{8}=5 m[/tex]
[tex]l=3w=3\times 5 m=15 m[/tex]
The area of the rectangle ,A= l × w
[tex]A = 5 m\times 15 m = 75 m^2[/tex]
The area of the rectangle is 75 squared meters.
Given that x = 7, write an equation that contains two different equivalent expressions each including at least one variable (x) and the operations: addition, subtraction, multiplication, and division.
Answers
Well here are two equivalent different expressions of my making that you could use for this question.
f(x) = 2x - 7
g(x) = 3x - 28 / 2
When x = 7, these two different expressions will equate to the same value of 7. If you meant something else let me know, otherwise this is what you should put for your essay-question.
The base of a cone can be
A. a triangle.
B. a pentagon.
C. a square.
D. an ellipse.
Answers
Find the 3rd term of (a-3b)^6
Answers
Solve for x. 12x = 2x^2 + 18
A. x = –3
B. x = 3
C. x = –3 or x = 0
D. x = 0 or x = 3
Answers
Factor out GCF
2(x^2-6x+9)
Factor trinomial
(x-3)(x-3)
Proof
-3-3=-6
-3^2=9
Zeros
x-3=0
x=3
Final answer: B
In triangle $abc$, the measure of $\angle a$ is $86$ degrees. the measure of $\angle b$ is $22$ degrees more than three times the measure of $\angle c$. what is the measure, in degrees, of $\angle c$?
Answers
m∠A = 86°
Because the measure of angle B is 22 degrees more than three times the measure of angle C, therefore
m∠B = 3*m∠C + 22 (1)
The sum of the angles should be 180°, therefore
m∠A + m∠B + m∠C = 180 (2)
Note that m∠A = 86°
Substitute equation (1) for m∠B in equation (2) to obtain.
86 + (3*m∠C + 22) + m∠C = 180
86 + 3*m∠C + 22 + m∠C = 180
4*m∠C = 180 - 86 - 22 = 72
m∠C = 72/4 = 18°
Answer: m∠C = 18°
How to find the distance between two points using pythagorean theorem?
Answers
c is the hypotenuse and is always the longest side of a triangle
a and b can be any side that isn't the hypotenuse
5. Reflection: Marissa wants to describe the relationship between the scale factor and perimeter of an image and its pre-image and between the scale factor and area of an image and its pre-image. What should she say about the relationship between the scale factor and perimeter of an image and its pre-image? What should she say about the relationship between the scale factor and area of an image and its pre-image? Support her statements using scale factors of 5 and 6.
Answers
Scale factor = k
Pre-image lengths: a, b => perimeter = 2a + 2b
Image lenghts: ka, kb => perimeter = 2ka + 2 kb = k (2a + 2b) = 2 * preimage permeter.
=> She has to say that the perimeter of the image is the perimeter of the preimage times the same scale factor.
What should she say about the relationship between the scale factor and area of an image and its pre-image?
area of the pre-image = ab
are of the image = (ka)(kb) = k^2 (ab)
=> The area of the image is the area of the preimage times the square of the scale factor.
Support her statements using scale factors of 5 and 6.
Scale factor 5
length of the pre-image = 3 x 4 => perimeter = 2 (3 + 4) = 2(7) = 14
length of the image = 3*5 x 4*5 = 15 x 20 => perimeter = 2 (15 + 20) = 2 (35) = 70
=> 14 * 5 = 70 which shows the prediction
area of the pre-image = 3 * 4 = 12
area of the image = 15 * 20 = 300
12 * (5^2) = 12*25 = 300 which is the value predicted.
Now you can do the same using scale factor 6.
If a stimulus plus a response results in a satisfying outcome, the probability of that response occurring again ________.
Answers
In terms of operant conditioning, if a response to a stimulus results in a satisfying or rewarding outcome, the probability of the response recurring to that stimulus in the future increases. Conditioning behavior is controlled by their consequences.
Explanation:If a stimulus plus a response results in a satisfying outcome, the probability of that response occurring again increases. This concept is central to the idea of operant conditioning in behavioral psychology. Operant conditioning is a type of learning where behavior is controlled by consequences. If the response to a stimulus results in a rewarding or satisfying outcome, this acts as positive reinforcement.
In operant conditioning, when a response yields a rewarding outcome (reinforcement), the likelihood of the behavior recurring in the future is increased. Take, for instance, the case of a dog that has learned if it sits when commanded, it receives a treat. The command ('Sit') is the stimulus, sitting is the response, and receiving a treat is the reinforcement. This scenario typically increases the likelihood of the dog sitting when given the command in the future.
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In terms of operant conditioning, if a response to a stimulus results in a satisfying or rewarding outcome, the probability of the response recurring to that stimulus in the future increases. Conditioning behavior is controlled by their consequences.
Explanation:If a stimulus plus a response results in a satisfying outcome, the probability of that response occurring again increases. This concept is central to the idea of operant conditioning in behavioral psychology. Operant conditioning is a type of learning where behavior is controlled by consequences. If the response to a stimulus results in a rewarding or satisfying outcome, this acts as positive reinforcement.
In operant conditioning, when a response yields a rewarding outcome (reinforcement), the likelihood of the behavior recurring in the future is increased. Take, for instance, the case of a dog that has learned if it sits when commanded, it receives a treat. The command ('Sit') is the stimulus, sitting is the response, and receiving a treat is the reinforcement. This scenario typically increases the likelihood of the dog sitting when given the command in the future.
Learn more about Operant Conditioning here:https://brainly.com/question/13044823
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Sam studied guinea pigs for his science fair project. He found that the amount of weight the guinea pigs gained varied directly with the number of calories they consumed. The guinea pigs gained 1 ounce for every additional 218 calories in their diet. How many additional ounces would they gain if their diet was increased by 1,090 calories? Let W represent the weight in ounces, and let C represent the number of calories.
Answers
From the given above, we can formulate the equation:
W = C / 218
By substituting the given values:
W = 1090 calories / (218 calories / 1 ounce)
W = 5 ounce
Therefore the guinea pigs will gain additional 5 ounce if the diet was increased by 1090 calories.
How much carpet is needed to cover 2 rooms, one of which is 12 ft by 6 ft and the other 10 ft by 8 ft?
Answers
Answer:
152 square feet
Step-by-step explanation:
The area of a rectangle is the product of its length and width. The total area of carpet required is the sum of the areas of the two rooms:
carpet area = (12 ft)(6 ft) +(10 ft)(80 ft) = 72 ft^2 +80 ft^2
carpet area = 152 ft^2
What is the result of isolating y2 in the equation below? 9x2 + 7y2 = 42
Answers
7y^2 = 42 - 9x^2
Then, divide 7 on both sides:
y^2 = 6 - 9/7 * x^2
Isolating a variable involves changing the subject of the equation.
The result of isolating y^2 is: [tex]\mathbf{y^2 = \frac{42 - 9x^2}7}[/tex]
The equation is given as:
[tex]\mathbf{9x^2 + 7y^2 = 42}[/tex]
Subtract 9x^2 from both sides
[tex]\mathbf{7y^2 = 42 - 9x^2}[/tex]
Divide through by 7
[tex]\mathbf{y^2 = \frac{42 - 9x^2}7}[/tex]
Hence, the result of isolating y^2 is: [tex]\mathbf{y^2 = \frac{42 - 9x^2}7}[/tex]
Read more about subject of formulas at:
https://brainly.com/question/21866313
37. A juice pitcher holds 1.5 gallons of liquid. How many 8-ounce glasses of juice can be poured from a full pitcher? (1 gallon 128 ounces) Explain your answer by writing or describing the steps you used to solve the problem.
Answers
1 gallon = 128 ounces
multiply 128 by 1.5 gallons:
1.5 x 128 = 192 ounces total
divide total ounces by 8 to get number of glasses:
192/8 = 24
you can pour 24 eight ounce glasses