Answer:
31
Step-by-step explanation:
The series are given as geometric series because these terms have common ratio and not common difference.
Our common ratio is 2 because:
1*2 = 2
2*2 = 4
The summation formula for geometric series (r ≠ 1) is:
[tex]\displaystyle \large{S_n=\frac{a_1(r^n-1)}{r-1}}[/tex] or [tex]\displaystyle \large{S_n=\frac{a_1(1-r^n)}{1-r}}[/tex]
You may use either one of these formulas but I’ll use the first formula.
We are also given that n = 5, meaning we are adding up 5 terms in the series, substitute n = 5 in along with r = 2 and first term = 1.
[tex]\displaystyle \large{S_5=\frac{1(2^5-1)}{2-1}}\\\displaystyle \large{S_5=\frac{2^5-1}{1}}\\\displaystyle \large{S_5=2^5-1}\\\displaystyle \large{S_5=32-1}\\\displaystyle \large{S_5=31}[/tex]
Therefore, the solution is 31.
__________________________________________________________
Summary
If the sequence has common ratio then the sequence or series is classified as geometric sequence/series.
Common Ratio can be found by either multiplying terms with common ratio to get the exact next sequence which can be expressed as [tex]\displaystyle \large{a_{n-1} \cdot r = a_n}[/tex] meaning “previous term times ratio = next term” or you can also get the next term to divide with previous term which can be expressed as:
[tex]\displaystyle \large{r=\frac{a_{n+1}}{a_n}}[/tex]
Once knowing which sequence or series is it, apply an appropriate formula for the series. For geometric series, apply the following three formulas:
[tex]\displaystyle \large{S_n=\frac{a_1(r^n-1)}{r-1}}\\\displaystyle \large{S_n=\frac{a_1(1-r^n)}{1-r}}[/tex]
Above should be applied for series that have common ratio not equal to 1.
[tex]\displaystyle \large{S_n=a_1 \cdot n}[/tex]
Above should be applied for series that have common ratio exactly equal to 1.
__________________________________________________________
Topics
Sequence & Series — Geometric Series
__________________________________________________________
Others
Let me know if you have any doubts about my answer, explanation or this question through comment!
__________________________________________________________
A card is drawn from a well-shuffled deck of 52 cards. What is the probability of drawing an ace or a 6?
A. 13/2
B. 7/26
C. 2/13
D. 6/52
Answer:
C
Step-by-step explanation:
There are 4 aces and 4 sixes. 4 + 4 is 8 (since it says or) so the chance is 8 / 52. 8 / 52 simplified, divide both sides by 4 and you get 2 / 13.
Answer:
C
Step-by-step explanation:
there are 4 aces and 4 sixes in a deck of 52 cards.
"And" means a probability * another probability
"Or" means a probability + another probability.
In this case, it is (probability of picking an ace) + (probability of picking an six).
[tex]\frac{4}{54} + \frac{4}{54} = \frac{8}{54} = \frac{2}{13}[/tex]
Please pick as brainliest!
The Marshall Track Team is running a relay race. There are 7 students on the team. The race is ½ of a mile long and each student runs the same distance. How far does each student run? Show your thinking with a drawing, a number line or tape diagram, and an equation. Enter your answer, work and/or explanation in the space provided.
The distance run by each of the seven students is 1/14 miles.
What does division mean?
Division is the process of grouping a number into equal parts using another number. The sign used to denote division is ÷.
What is the distance run by each student?In order to determine the distance run by each student, we would divided the total miles by the number of students.
Miles run by each student = 1/2÷ 7
1/2 x 1/7 = 1/14 miles
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4) What is the slope of the line joining (7, 8) and (17, 13)
slope is = (13 - 8) / (17 - 7) = 5/10 = 1/2 or 0,5
slope for A (xa ; ya) and B (xb ; yb) = (yb - ya) / (xb - xa)
what the geometric mean of 18 and 30 as a square root?
The geometric mean of 18 and 30 is the product of 18 and 30 square rooted, so:
[tex]\sqrt{18*30} =\sqrt{540} =\sqrt{9*4*15} =\sqrt{36*15} =6\sqrt{15}[/tex]
Hope that helps!
If 2 fair dice are tossed what is the probability that the sum of the number of dots on the top faces will be 7
Answer:
⅙
Step-by-step explanation:
it could be 6 and 1, 5 and 2, 4 and 3, 3 and 4, 2 and 5 or 1 and 6.
It is 2 fair dice, so all together, the probability is 36.
6/36 can be simplified to ⅙
The measure of central tendency most influenced by outliers is the ______. A. Mode b. Median c. Mean d. Variance
Combine like terms
4x+3(2x+5b)-4b-2x+6
Answer:
[tex]\boxed{\sf{8x+11b+6}}[/tex]Step-by-step explanation:
To solve this problem, you have to combine like terms of x and b from one side of the equation.
4x+3(2x+5b)-4b-2x+6Combine like terms.
3(2x+5b)+4x-2x-4b+6
Solve.
4x-2x=2x
Rewrite the problem down.
3(2x+5b)+2x-4b+6
Expand the form.
Use a distributive property.
Distributive property:
A(B+C)=AB+AC
3(2x+5b)
Multiply.
3*2x=6x
3*5b=15b
Rewrite the problem.
6x+15b
6x+15b+2x-4b+6
Combine like terms.
6x+2x+15b-4b+6
Add the numbers from left to right.
6x+2x=8x
8x+15b-4b+6
Then, you add again.
15b-4b=11b
= 8x+11b+6
Therefore, the final answer is 8x+11b+6.I hope this helps you! Let me know if my answer is wrong or not.
Answer:
8x+11b+6
Step-by-step explanation:
Find area of the circle. Use 3.14 as (pie symbol) the diameter is 104. Please help will mark brainliest!!
Answer:
8490.56 yd^2
Step-by-step explanation:
find radius by dividing 104 by 2
we get 52 yd
now the area of circle is [tex]\pi r^{2}[/tex]
we use 3.14 for pi
so 3.14 times 52*52
3.14 times 2704
8490.56
Pleas help me (and pls don't ban my question this time Brainly)
Answer:
d = 7.2
Step-by-step explanation:
12 + d = -4.8
subtract 12 from both sides and you get
d = 7.2
Answer:
-16.8
Step-by-step explanation:
The equation can be solved by performing the inverse of the operation that is done to the variable. Here, 12 is added to the variable. The inverse of that operation is addition of the "additive inverse", or "opposite" of 12:
12 + d = -4.8 . . . . . . given equation
12 -12 +d = -4.8 -12 . . . . . the same operation is done to both sides
d = -16.8
The value of d that makes the equation true is -16.8.
_____
The addition (subtraction) property of equality tells you that adding (subtracting) the same number from both sides of an equation will not change the value of the variable.
Question 9 of 14 V
Question 9
Levi was designing a kite. He needs to determine the measure of A before cutting the fabric.
(1100
(6x + 4)º
A А
(4x + 26)
What is the measure of angle A?
The measure of angle A in the kite before cutting the fabric is 42 degrees.
What is a kite?A kite is a quadrilateral with four sides and four angles. Adjacent sides are equal, and the diagonals bisect each other at 90 degrees.
Also, there is a pair of equal opposite angles.
From the diagram:
110 + (6x + 4) + (4x + 26) = 180 (sum of angles in a straight line)
10x + 30 = 70
x = 4
∠A = 4(4) + 26 = 42°
The measure of angle A in the kite before cutting the fabric is 42 degrees.
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fill in the table using this function rule. y= 3x + 4
x- 3,6,7,8
y- blank
Answer:
y: 13, 22, 25, 28
ordered pairs: (3, 13) (6, 22) (7, 25) (8, 28)
Step-by-step explanation:
Given:
function: y = 3x + 4values of x: -3, 6, 7, 8To find the y-values, substitute the x-values into the function and solve.
when x = 3
y = 3(3) + 4
= 9 + 4
= 13
when x = 6
y = 3(6) + 4
= 18 + 4
= 22
when x = 7
y = 3(7) + 4
= 21 + 4
= 25
when x = 8
y = 3(8) + 4
= 24 + 4
= 28
Therefore, the ordered pairs are; (3, 13) (6, 22) (7, 25) (8, 28)
A factory makes light fixtures with right regular hexagonal prisms where the edge of a hexagonal base measures 4 cm and the lengths of the prisms vary. It cost $0.04 per square centimeter to fabricate the prisms and the factory owner has set a limit of $11 per prism. What is the maximum length of each prism?
The maximum length of the prism is highest length of the hexagonal prism
The maximum length of each prism is 8.0 cm
How to determine the maximum length of each prism?The surface area of the hexagonal prism is calculated using:
A = 6al + 3[tex]\sqrt[/tex]3 a^2
Where:
a represents the edge length; a = 4 cm
l represents the length (or height) of the prism
The surface area costs $0.04 per square centimeter.
So, we have:
C = 0.04 * [6al + 3[tex]\sqrt[/tex]3 a^2]
The maximum cost is $11.
So, the equation becomes
11 = 0.04 * [6al + 3[tex]\sqrt[/tex]3 a^2]
Substitute 4 for a
11 = 0.04 * [6 * 4l + 3[tex]\sqrt[/tex]3 * 4^2]
Evaluate the products and exponents
11 = 0.04 * [24l + 48[tex]\sqrt[/tex]3]
Divide both sides by 0.04
275 = 24l + 48[tex]\sqrt[/tex]3
Subtract 48[tex]\sqrt[/tex]3 from both sides
24l = 275 - 48[tex]\sqrt[/tex]3
Evaluate the difference
24l = 191.9
Divide both sides by 24
l = 8.0
Hence, the maximum length of each prism is 8.0 cm
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Answer:
275, 7.99
Step-by-step explanation:
i got it right
and please get me too branliest
Part B.
Directions: Solve for the area of the triangle in each of the following problems.
10) 22 cm 21 cm
11) 16 m 15 m
Answer:
#10=462
#11=240
Step-by-step explanation:
22x21=462
16x15=240
Which expressions are aquivalent to j + j + 2k ?
Choose all answers that apply:
A 2jk
B 2(j+j+k0
C None of the above
[tex]\qquad\qquad\huge\underline{{\sf Answer}}♨[/tex]
Let's see ~
[tex]\qquad \sf \dashrightarrow \:j + j + 2k[/tex]
[tex]\qquad \sf \dashrightarrow \:2j + 2k[/tex]
[tex]\qquad \sf \dashrightarrow \:2(j + k)[/tex]
・．━━━━━━━━━━†━━━━━━━━━━━━．・
Given m \| nm∥n, find the value of x.
Answer:
x=140(corresponding angle)
Corresponding angles that are in the same position on two parallel lines intersected by a transversal line on the parallel lines.
Corresponding angles are equal
The 140° angle on line m and the x° angle on line n are corresponding angles.
The value of x is 140°
What are corresponding angles?The angles that are in the same position on two parallel lines intersected by a transversal line on the parallel lines.
Corresponding angles are equal.
We have,
The figure is given,
Line m and Line n are parallel.
t line is the transversal line on the two parallel lines, line m and line n.
We see that,
140° angle on line m is corresponding to the x° angle on line n.
Corresponding angles are equal.
So,
140° = x°
x° = 140°
Thus,
The 140° angle on line m and the x° angle on line n are corresponding angles.
The value of x is 140°
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melanie and patrick have different phone services. the relationship of the monthly cost, y dollars, to send or receive x text messages, is a linear function. the cost of patricks texting is described by y = 0.03x + 5. the cost of melanies texting is shown in the table
Answer:
Melanie: y = 0.25x
Patrick: y = 0.03x + 5
Patrick's service is cheaper when 50 texts are sent or received in one month.
Step-by-step explanation:
Let's find out Melanie's monthly texting cost function using the table. We are given multiple points that the line describing her monthly text costs passes through, so we can use the slope formula to calculate the slope of this line first.
m = (y2 - y1) / (x2 - x1)Substitute (5, 1.25) and (10, 2.50) into this formula.
m = (2.5 - 1.25) / (10 - 5)m = 1.25 / 5 m = 0.25Now we can use the point-slope equation to determine the line that describes Melanie's monthly texting cost.
I'm going to use the point (5, 1.25) and the slope m = 0.25.
y - y1 = m(x - x1)y - 1.25 = 0.25(x - 5)y - 1.25 = 0.25x - 1.25 y = 0.25xWe have Melanie's function:
y = 0.25xWe have Patrick's function:
y = 0.03x + 5
We want to determine which service is cheaper when 50 texts are sent/received in one month.
The number of texts sent and received is represented with the variable "x", and the cost of this service is represented with the variable "y".
All we need to do is substitute 50 for x in both equations to see if Melanie or Patrick's service is cheaper.
Starting with Melanie:
y = 0.25x y = 0.25(50)y = 12.50Now with Patrick:
y = 0.03x + 5 y = 0.03(50) + 5y = 1.5 + 5 y = 6.5Patrick's service is substantially cheaper than Melanie's service when 50 texts are sent or received in one month.
Workers in an office of 60 staff were asked their favourite type of take-away.
The results are summarised in the table.
Pizza=8
Curry=8
Fish & chips=5
Kebab=9
Other=30
Work out the size of each angle to draw a pie chart.
The area of a room is 26.025 m sqaure. If its length is 12.5m . find the breadth of the room
Answer:
2.082.
Step-by-step explanation:
Solution,
Given,
Area ( A ) = 26.025 m².
Length ( L ) = 12.5 m.
Now,
Breadth ( B ) = Area ÷ Length.
= 26.025 ÷ 12.5
= 2.082.
Thus, The breadth of the room is 2.082 m.
Eman skateboarded 24 miles in 2 hours on Monday and 6 miles in half an hour on Wednesday . Hiro has been tracking his speed while riding his bike also. He noticed that he can bike 15 miles per hour. What is Eman's unit rate?
Eman's unit rate given the miles he skateboarded and the hours is 12 miles per hour.
What is his unit rate?The unit rate is the same as average speed. Average speed is the total distance travelled per time. The unit rate can be determined by dividing the distance by the time.
Average speed = total distance / total time
24/2 = 12 miles per hour
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y=- 8x - 20
How do I graph this
Answer: Here, this should help ya out :
With graphing lines and slopes use desmos graphing calulator dont worry, its safe ;)
Answer:
See below ↓
Step-by-step explanation:
Step 1 : Mark the y-intercept.
b = -20Therefore, the y-intercept's coordinates are : (0, b)⇒ (0, -20)Step 2 : Draw the slope.
m = -8Therefore after marking the y-intercept you can either mark a point 8 spaces up, 1 to the left or mark a point 8 spaces down, 1 to the rightAfter doing this, join the two points using a ruler and draw a line Your graph is ready!It should look like this :For what values of x will the function f(x) = 5x^2 + x - 6 equal zero?
A)x = -3 or 2
B)x=6/5 or -1
C)x = 3 or -2
D)x = -6/5 or 1
5x² + x - 6 = 0
Δ = 1² - 4*5*(-6) = 121 = 11²
x' = (-1 - 11) / (2x5) = -12/10 = - 6/5
x" = (-1 + 11) / (2x5) = 10/10 = 1
=> D
The values of x will the function [tex]f (x) = 5x^2 + x - 6[/tex] equal zero are x = - 6/5 and x = 1. Hence option D is true.
Used the concept of a quadratic equation that states,
An algebraic equation with the second degree of the variable is called a Quadratic equation.
Example; ax² + bx + c = 0
Given that the quadratic equation,
[tex]f (x) = 5x^2 + x - 6[/tex]
Now for the values of x at which the function equals zero, we have to find the zeroes of the function by using the factorization method.
[tex]f (x) = 5x^2 + x - 6[/tex]
[tex]f (x) = 5x^2 + (6 - 5)x - 6[/tex]
[tex]f (x) = 5x^2 + 6x - 5x - 6[/tex]
[tex]f (x) = x (5x + 6) - 1 (5x + 6)[/tex]
[tex]f (x) = (5x + 6) (x - 1)[/tex]
Hence, the value of zeroes,
[tex]5x + 6 = 0[/tex]
[tex]5x = - 6[/tex]
[tex]x = \dfrac{- 6}{5}[/tex]
And, [tex]x - 1 = 0[/tex]
[tex]x = 1[/tex]
So, the value of x is x = - 6/5 and x = 1. Hence option D is true.
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PLS HELP ME 50 POINTS AND I WILL MARK THE BRAINLIEST
Answer:
1. 392 in², 2. 94.99 cm², 3. 145.2 ft², 4. 161.5 m², 5. 17 ft and 81 cm
Step-by-step explanation:
1. A = 16 x 19
A = 304
A = 1/2(11x16)
A = 1/2(176)
A = 88
304 + 88 = 392 in²
2. A = πr²
A = 3.14*5.5²
A = 3.14*30.25
A = 94.985
A = 94.99 cm²
3. A = 1/2(bh)
A = 1/2(11x26.4)
A = 1/2(290.4)
A = 145.2 ft²
4. A = bh
A = 9.5*17
A = 161.5 m²
5. part 1
A = (1/2) · (p + q) · h
112 = (1/2)(11+q)(8)
112 = 4(11+q)
112 = 44 + 4q
68 = 4q
17 = q
17 ft
5. part 2
A = lw
364.5 = 27w
13.5 = w
P = 2l + 2w
P = 2(27) + 2(13.5)
P = 54 + 27
P = 81
81 cm
Hope this helps :)
Rhonda has 12 marbles more than douglas . Doughlas has 6 marbles more than bertha . Rhonda has twice as many marbles as bertha has . How many marbles does douglas have
24
Explanation:
R = D + 12 (1)
D = B + 6 (2)
R = 2*B (3)
Put (3) into (1): 2*B = D + 12 (4)
Rewrite (2) as B = D - 6 and put this into (4): 2*(D - 6) = D + 12
So: 2D - 12 = D + 12
Subtract D from both sides and add 12 to both sides to get: D = 24
(not suree)
I need help but I need the correct answer everyone is giving me the wrong answer !!
Answer:
y - 2 = 6 (x - 1)
Step-by-step explanation:
Slope intercept form equations look like this:
y - y1 = m (x - x1)
***m = [tex]\frac{y2-y1}{x2-x1}[/tex]
Using the point (1,2), we know that x1 = 1 and y1 = 2. Let's sub these values into the slope intercept equation:
y - 2 = m (x - 1)
To complete this equation, we need to find slope. Pick out another point on the graph and plug into the slope equation. We can use point (2,8), where (1,2) = Point 1 and (2,8) = Point 2.
[tex]\frac{y2-y1}{x2-x1}=\frac{8-2}{2-1} =\frac{6}{1} =6[/tex]
Now that we know m = 6, let's plug that back into the original equation to get our final answer:
y - 2 = 6 (x - 1)
I hope this helps!
Please help! WILL GIVE BRAINLIEST! George and Sarah were building a cone-shaped sand castle. After some time, the diameter of the sand shaped cone was 12 in. and the height was 14 in. What is the approximate volume of the sand cone rounded to the nearest hundreth? (Show your work. Remember you can draw a picture to help you solve the problem). Label your answers with the correct units.
Use 3.14 to approximate pi
Answer:
They kept adding sand, and ten minutes later the volume of the sand cone had increased by 30%. What is the approximate volume of the sand cone now? Label your answers with the correct units. (Show your work) Use 3.14 to approximate pi
Answer:
volume = 527.52 in³
volume increased by 30% = 685.776 in³
Step-by-step explanation:
Volume of a cone
[tex]V=\dfrac13\pi r^2h[/tex]
(where r is the radius and h is the height)
Given:
diameter = 12 in ⇒ radius = 6 inheight = 14 in[tex]\pi =3.14[/tex][tex]\implies V=\dfrac13 \cdot 3.14 \cdot 6^2 \cdot 14[/tex]
[tex]\implies V=527.52 \ \sf in^3[/tex]
---------------------------------------------------------------------------
If the volume increases by 30% then it will now be 130% of the original volume.
130% as a decimal = 130/100 = 1.3
Therefore, to find the new volume, multiply the original volume by 1.3.
[tex]\implies V=527.52 \cdot 1.3[/tex]
[tex]\implies V=685.776 \ \sf in^3[/tex]
O f 2 0 0 0 0 small businesses surveyed, about 82%
said they employed women in some capacity.
Of the businesses that employed women, 19. 5%
employed no female supervisors, 50% employed
only one female supervisor, and the remainder
employed more than one female supervisor,
a How many of the businesses surveyed
employed no women?
b W hat proportion of businesses surveyed
employed exactly one female supervisor?
c W hat proportion of businesses surveyed
employed no female supervisors?
d Given that a particular firm employed women,
what is the probability that it employed at
least one female supervisor
Using proportions, it is found that the desired amounts are given as follows:
a) 360 businesses employeed no women.
b) 41% of the businesses surveyed employed exactly one female supervisor.
c) 15.58% of the businesses surveyed employed no female supervisors.
d) 80.5% probability that it employed at least one female supervisor.
What is a proportion?A proportion is a fraction of a total amount.
Item a:
18% out of the 2000 businesses surveyed, hence:
n = 0.18 x 2000 = 360.
Item b:
50% out of 82%, hence:
p = 0.5(0.82) = 0.41.
41% of the businesses surveyed employed exactly one female supervisor.
Item c:
19% out of 82%, hence:
p = 0.19(0.82) = 0.1558.
15.58% of the businesses surveyed employed no female supervisors.
Item d:
100 - 19.5 = 80.5% probability that it employed at least one female supervisor.
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Pine Bluff, Ark has been continuously declining in population at a rate of 12.5 percent due to unemployment. If
the city's current population is 100,258 then in how long before the population drops to 87,751 at this current rate?
(Round your answer to the nearest year)
a. l
b. 3
C. 4
d. 2
Please help with this question thanks! :`D Also please give me simple explanations thank you.
Answer:
Step-by-step explanation:
The last one.
A would be a quadratic if the leading coefficient was anything but 0. 0 eleminates the x^2. Not A
B has no x^2 term to begin with. B is not the answer.
C is in exponential form. C is not the answer
D has an x^2 term. There is nothing using x that is higher. D is the answer.
If the probability that a person lives in an industrialized country of the world is 1/5 find
the probability that a person does not live in an industrialized country
Answer:
4/5
Step-by-step explanation:
5/5 - 1/5 = 4/5 is the probability that a person does not live in an industrialized country
The P( person does not lives in an industrialized country ) = 4/5
What is Probability?Probability refers to potential. A random event's occurrence is the subject of this area of mathematics.
The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events.
The degree to which something is likely to happen is basically what probability means.
Given:
P( person lives in an industrialized country ) = 1/5
Now, using the Completement probability
P ( person lives in an industrialized country ) + P( person does not lives in an industrialized country ) = 1
P( person does not lives in an industrialized country )
= 1- P ( person lives in an industrialized country )
P( person does not lives in an industrialized country )
= 1- 1/5
= 4/5
Hence, P( person does not lives in an industrialized country ) = 4/5.
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If you have
[tex]3^{n-1} *\frac{n(n+1)}{2} = 20412[/tex]
whats the process for solving n?
Answer:
Step-by-step explanation:
3^(n-1) * (n(n+1)/2 = 20412
The n(n +1)/2 is a factorial which is defined for integers so we are looking for a whole number solution.
We could draw a graph manually or using software and get the solution where the graph cuts the x axis.
Also we could find the prime factors of 20412:
20412 = 2^2 * 3^6 * 7
and try substituting 2, 3 and 7 into the equation
Using this method we see that one solution is n = 7.
I could have tried n = 7 first because 3^n-1 = 3^6!!