Answer:
1705/64
Step-by-step explanation:
A geometric series contains terms that are in the form [tex]a_1\cdot(r)^{n-1}[/tex] where [tex]a_1[/tex] is the first term and [tex]r[/tex] is common ratio.
A common ratio is the number that is used to find the next term by multiplying previous term by [tex]r[/tex].
Now we can use a formula and we would be using [tex]S_n=\frac{a_1(1-r^n)}{1-r}[/tex] where n is the number of terms you are adding and [tex]a_1[/tex] is the first term and r is the common ratio.
Before we do that, I'm going to do this without that formula. Sum means we are just going to add these terms after finding them.
The first term is 20.
The second term is (1/4)(20)=5.
Third term is (1/4)(5)=5/4.
Fourth term is (1/4)(5/4)=5/16.
The fifth term is (1/4)(5/16)=5/64.
Now we add them (20)+(5)+(5/4)+(5/16)+(5/64)
Putting this into the calculator gives me: 1705/64.
Now let's do the formula way as well.
Again we have:
r=1/4
[tex]a_1=20[/tex]
n=5 since we adding the first 5 terms:
[tex]S_5=\frac{20(1-(\frac{1}{4})^5}{1-\frac{1}{4}}[/tex]
[tex]S_5=\frac{20(1-\frac{1}{1024}){\frac{3}{4}}[/tex]
[tex]S_5=\frac{20-\frac{20}{1024}}{\frac{3}{4}}[/tex]
Dividing by 3/4 is the same as multiply by 4/3.
[tex]S_5=(20-\frac{20}{1024})\frac{4}{3}[/tex]
[tex]S_5=20 \cdot \frac{4}{3}-\frac{20}{1024}\cdot\frac{4}{3}[/tex]
[tex]S_5=\frac{80}{3}-\frac{5}{256} \cdot \frac{4}{3}[/tex]
[tex]S_5=\frac{80}{3}-\frac{20}{256 \cdot 3}[/tex]
[tex]S_5=\frac{80}{3}-\frac{5}{64 \cdot 3}[/tex]
[tex]S_5=\frac{80}{3}-\frac{5}{192}[/tex]
Multiplying first fraction by 64/64:
[tex]S_5=\frac{80(64)}{3(64)}-\frac{5}{192}[/tex]
[tex]S_5=\frac{5120}{192}-\frac{5}{192}[/tex]
{tex]S_5=\frac{5115}{192}[/tex]
Dividing to and bottom by 3:
[tex]S_5=\frac{1705}{64}[/tex].
Help lolll!!!!!!!!!!!!!!!!! Will mark as brainliest
Answer:
Last one.
Step-by-step explanation:
Let's look at the fist one
x+1<-1 and x+1<1
Subtract one on both sides for both inequalities:
x<-2 and x<0
Graph it!
*********************************o x<0
*************o x<-2
________(-2)_________(0)____________
So the inequalities do have some common sets of numbers shared so there is a solution and it is any number less than -2.
Let's look at the second one
x+1<=1 and x+1>=1
Subtract one on both sides for both inequalities:
x<=0 and x>=0
Graph it!
@***************** x>=0
*********************@ x<=0
-----------------------(0)-------------------
The only number included by both graphs is 0 so it still has a solution. The solution is 0.
Let's look at the third one:
x+1<1 and x+1>1
Subtract one on both sides for both inequalities:
x<0 and x>0
Graph it!
************************O x<0
O************************* x>0
---------------------------(0)------------------------------
These inequalities have no overlap. They don't even both include zero because of the open circle (the lack of equal sign). This is the compound inequality that has no solution.
Emily had $56 in her account. She deposited a $265 check, and bought three equally priced backpacks for her children. The next day, when she checked her balance, it was $243. What was the price of each backpack?
Answer:
$26
Step-by-step explanation:
Start with $56.
Add $265, obtaining a + balance of $321.
Let x represent the unit price of the backpacks. Then:
$321 - 3x = $243.
Combining like terms:
3x = $78
Then x, the price of the individual backpack, was $78/3, or $26.
Given the equation 3x + 1 = 16, solve for x
Answer:
x = 5
Step-by-step explanation:
3x + 1 = 16
Subtracting 1 on both sides of the equation,
3x + 1 – 1 = 16 – 1
Summing algebraically (in this case subtracting by having different signs) on both sides,
3x = 15
Isolating x by dividing both sides by 3
3x / 3 = 15 / 3
Dividing,
x = 5
Answer:
[tex]x=5[/tex]
Step-by-step explanation:
We have the following expression:
[tex]3x+1=16[/tex]
and we need to solve for [tex]x[/tex], so the first thing we have to do (in order to leave the x alone on one side of the equation) is move the +1 to the left sife with the opposite sign (-1):
[tex]3x=16-1\\3x=15[/tex]
now we divide each side by 3, and we get:
[tex]\frac{3x}{3}=\frac{15}{3} \\x=5[/tex]
the answer is [tex]x=5[/tex]
assume the probability of having a boy or a girl is the same. what is the probability of have a boy then a girl then another girl
Answer:
[tex]\dfrac{1}{8}[/tex]
Step-by-step explanation:
If the probability of having a boy or a girl is the same, then
the probability of having a boy = a probability of having a girl = 1/2.
Let B denote boy and G denote the girl.
The sample space of having three children is:
BBB, BBG, BGB, GBB, BGG, GBG, GGB, GGG.
The probabilities of each of those events is
[tex]Pr(BBB)=Pr(BBG)=Pr(BGB)=Pr(GBB)=\\ \\=Pr(BGG)=Pr(GBG)=Pr(GGB)=Pr(GGG)=\\ \\=\dfrac{1}{2}\cdot \dfrac{1}{2}\cdot \dfrac{1}{2}=\dfrac{1}{8}.[/tex]
Which statements are true about parallelogram LMNO? Check all that apply.
x = 11
please insert the entire of the question
Answer:
1, 4, 5
Step-by-step explanation:
???? I’m very confused
What is the measure of
Answer:
I think (c) 120 is right answer.
Answer:
C. 120°
Step-by-step explanation:
Since this is an isosceles triangle [two congruent sides], m<B is also 30°. Now, we have to the m<A by using the Interior Angles Theorem [m<1 + m<2 + m<3 = 180°]. So we do this:
60 + m<A = 180; 120 = m<A
I am joyous to assist you anytime.
Which of the following expressions is equal to
-3x^2 - 27 ?
Answer: D. -3x+9i)(x+3i) i hope this helped :)
Answer: D is the correct answer
Step-by-step explanation:
A P E X
Only a triangle can be the base of a pyramid. True or False
Answer:
True
Step-by-step explanation:
I did it on ap3x and got it right!
What is the area of △ABC ? Enter your answer, as a decimal, in the box. Round only your final answer to the nearest tenth. units² Triangle A B C has leg A C labeled 10 and leg B C labeled 17. Angle A C B is labeled 25.1 degrees.
Answer: [tex]36.1\ units^2[/tex]
Step-by-step explanation:
You need to use the SAS area formula. This is:
[tex]A=\frac{a*b*sin(\alpha)}{2}[/tex]
Given the triangle ABC, you know that:
[tex]a=AC=10\ units\\b=BC=17\ units\\\alpha=\angle ABC=25.1\°[/tex]
Therefore, substituting these values into the formula, you get that the area of the triangle ABC is:
[tex]A=\frac{(10\ units)(17\ units)*sin(25.1\°)}{2}\\\\A=36.1\ units^2[/tex]
solve the equation V/7=3
Answer:
21
Step-by-step explanation:
[tex] \frac{v}{7} = 3[/tex]
Multiplying both sides by 7, we get
[tex] \frac{v}{7} \times 7 = 3 \times 7 [/tex]
The two 7s on the left cancel out to give 1, so
[tex]v = 21[/tex]
Please mark Brainliest if this helps!
Over the last 3 evenings, Keisha received a total of 81 phone calls at the call center. The first evening, she received 6 fewer calls than the second evening. The third evening, she received 3 times as many calls as the first evening. How many phone calls did she receive each evening
Answer:
First: 15
Second: 21
Third: 45
Step-by-step explanation:
In order to create the equation we need to represent the evenings with an alebraic term, in thsi case we are going to represent the second evening with an X
Second evening:x
The first night she got 6 fewer calls than the second: Second-6=x-6
The third night she received 3 times the first: 3(first night)=3(x-6)
The equation is First Night plus second night plus third night equals 81.
[tex]First+second+third=81\\x+(x-7)+3(x-6)=81\\x+x-7+3x-18=81\\5x=81+21+6\\5x=105\\x=\frac{105}{5} \\x=21[/tex]
So the first evening he received 15 calls, the second he received 21 and the third one he received 45.
Which is the better deal? 12 pack of markers for $8.04, 8 pack of markers for $5.60, 24 pack of markers for $14.40, or 16 pack of markers for $10.40
Answer:
$14.40 for 24 markers
Step-by-step explanation:
Lets find the price per marker
$8.04 /12 = .67
$5.60/8 =.70
$14.40 /24 =.60
$10.40/16 =.65
The lowest amount is .60, which is the best deal
$14.40 for 24 markers
If y= x-6 were changed to y= x+8, how would the graph of the new fun
compare with the first one?
Answer:
Step-by-step explanation:
The graph of the new function would be the graph of the old one, translated 14 units to the left.
Help me fill the boxes in !! !! Will mark brainliest
Answer:
Three points that are member of the solution set could be (-2,10), (5,5) and (10,13)
The graph in the attached figure
Step-by-step explanation:
we have
[tex]-3x-y < 12[/tex] ----> inequality A
The solution of the inequality A is the shaded area above the dashed line [tex]-3x-y=12[/tex]
[tex]2x+3y\geq 9[/tex] -----> inequality B
The solution of the inequality B is the shaded area above the solid line [tex]2x+3y=9[/tex]
The solution of the system of inequalities is the shaded area between the dashed line and the solid line
see the attached figure
A solution to the system of inequalities is any point in the shaded area.
therefore
Three points that are member of the solution set could be (-2,10), (5,5) and (10,13)
Write the Explicit Rule for the arithmetic sequence:
Qp = Q1 +(n-1)d
8, 5, 2, -1, ...
Answer:
Last choice.
Step-by-step explanation:
8, 5, 2, -1, ...
Make a table
n | 1 2 3 4 5
an | 8 5 2 -1 -4
You really should just think of this as finding the equation of a line.
The slope can be used by using any two points.
How about
(1 , 8) and
(2 , 5)?
------------I really like to find the slope by lining up my points and subtracting vertically and then putting second number on top of first.
That is the same as using the formula directly which is (y2-y1)/(x2-x1)
or (y1-y2)/(x1-x2) which gives you the same thing too.
Subtracting the pairs now:
(1 , 8)
-(2 , 5)
-----------
-1 3
So the slope is 3/-1 or -3/1 or -3.
So you can already rule out choice B.
So we have the equation is y=-3x+b
where y really represents an and x really represents n here.
You can use any point that you know is on the line to find b.
How about (1,8)?
Plug it into y=-3x+b.
y=-3x+b
8=-3(1)+b
8=-3+b
11=b
So the line is y=-3x+11
Want to confirm?
No problem:
At x=1 you have y=-3(1)+11=-3+11=8 which is first number in the list.
At x=2 you have y=-3(2)+11=-6+11=5 which is second number in the list.
At x=3 you have y=-3(3)+11=-9+11=2 which is the third number in the list.
At x=4 you have y=-3(4)+11=-12+11=-1 which is the fourth number in the list.
So we have confirmed our solution of y=-3x+11.
So the answer is an=-3n+11
6. The digital sum for the year 1989 is 1 + 9 + 8 + 9 or 27. How many years from 1990 to
2800 have a digital sum of 27?
A.
O
B. 1
C. 2
D. 3
Answer:
c. 2
Step-by-step explanation:
if you mix up the numbers you can find that 1998 is 27. then you have to start adding and subtracting numbers. Your digital sum includes a basic three 9's so, you also have 2799.
TUL
The graph of y= -5x + 1 is:
Answer:
negative, with slope of -5 and the y-intercept is at 1.
Step-by-step explanation:
What is the scale factor of AABC to AXYZ?
Answer: A. 1/5 because it's the actual right answer.
Scale factor of ΔABC to ΔXYZ is [tex]\frac{1}{5}[/tex].
What is scale factor?The ratio of corresponding sides are equal, and this ratio is called the scale factor.
We know that
ΔABC and ΔXYZ are similar from the figure
[tex]\frac{XY}{AB}=\frac{YZ}{BC} =\frac{XZ}{AC}[/tex]
Substitute the values
[tex]\frac{9}{45} =\frac{12}{60}=\frac{7}{35} =\frac{1}{5}[/tex]
Therefore, Scale factor of ΔABC to ΔXYZ is [tex]\frac{1}{5}[/tex].
Find out more information about scale factor here
brainly.com/question/22312172
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In the election for class president, there were two candidates, Joel and Sean. Joel got 60% of the votes, which was 38 votes more than Sean. Find the total number of votes cast.
Answer:
190
Step-by-step explanation:
40/100 x 198= 76
40/100 x 198= 114
114-76= 38
Answer:
190.
Step-by-step explanation:
Let x represent total number of votes.
We have been given that Joel got 60% of the votes, which was 38 votes more than Sean.
60% of total votes: [tex]\frac{60}{100}x=0.60x[/tex]
Since Joel got 60% of total votes, so Sean got 40% of total votes that is [tex]\frac{40}{100}x=0.40x[/tex]
Since Joel got 38 votes more than Sean, so we can represent this information in an equation as:
[tex]0.60x=0.40x+38[/tex]
[tex]0.60x-0.40x=0.40x-0.40x+38[/tex]
[tex]0.20x=38[/tex]
[tex]\frac{0.20x}{.20}=\frac{38}{.20}[/tex]
[tex]x=190[/tex]
Therefore, the total number of votes cast is 190.
which is a graph of f(x)=5x-2/x+2with any vertical or horizontal asympototes indicated by the dash lines?
Answer:
See attachment
Step-by-step explanation:
The given function is [tex]f(x)=\frac{5x-2}{x+2}[/tex].
This rational function has a vertical asymptote at where the denominator is zero.
The denominator [tex]x+2=0[/tex] when [tex]x=-2[/tex]
There is vertical asymptote at [tex]x=-2[/tex]
The horizontal asymptote for this rational function is given by the ratio of the leading coefficient of the numerator to the leading coefficient of the denominator.
[tex]y=\frac{5}{1}[/tex]
The horizontal asymptote is [tex]y=5[/tex]
The graph of this rational function is shown in the attachment
An arithmetic sequence has this recursive formula:
A1=6
An=an-1-3
What is the explicit formula for this sequence?
Answer:
A
Step-by-step explanation:
Sn=a(n-1) d
this formula for Calculating arithmetic sequence
Answer: D. [tex]a_n=6+(n-1)(-3)[/tex]
Step-by-step explanation:
Given : An arithmetic sequence has this recursive formula:
[tex]a_1=6 \ \ \; \ a_n=a_{n-1}-3[/tex]
Using the given information, Second term of arithmetic sequence will be :-
[tex]a_2=a_{1}-3=6-3=3[/tex]
That means common difference = [tex]a_2-a_1=3-6=-3[/tex]
The explicit formula for arithmetic sequence is given by :-
[tex]a_n=a+(n-1)d[/tex], where a is the first term and d is the common difference.
Put a= 6 and d= -3, we get
The explicit formula for this sequence :-
[tex]a_n=6+(n-1)(-3)[/tex]
Which of the following describes a similarity between the British colonies in
India and Palestine during the Cold War?
O
A. After gaining independence, leaders in both former colonies
embraced Soviet-style communism.
O
B. After gaining independence, British authorities in both former
colonies still controlled the government.
O
C. After gaining independence, territory in both former colonies was
divided due to religious conflicts.
O
D. After gaining independence, both former colonies became close
allies of the United States.
Answer:
C. After gaining independence, territory in both former colonies was divided due to religious conflicts
Step-by-step explanation:
The British had India as their colony, and Palestine as their mandate. Once the World War II ended though, the British saw that they are not in a financial position to be able to keep their colonies and mandates, so they decided to grant them independence. The independence didn't went as desired by the locals though, as both India and Palestine got partitioned because of religious reasons. India was partitioned into Hindu and Muslim part, while Palestine and Muslim and Jewish part. The situation in the Indian subcontinent quickly escalated, as well as in Palestine where the Arabs saw the formation of Israel as stealing of their land.
Answer: C. After gaining independence, territory in both former colonies was divided due to religious conflicts.
5x^2 - 9 - 7x^2 - x + 1
Answer:
−2x^2−x−8
Step-by-step explanation:
5x^2 - 9 - 7x^2 - x + 1 = −2x^2−x−8
5*x^2-9-7*x^2-x+1 = (-2*x^2)-x-8
Use complete sentence to describe the net of a rectangular pyramid
Answer:
The net of a rectangular pyramid is consisting of a rectangle, for the base, and there are 4 more triangles that make up the lateral faces, and the triangles make the pyramid.
Solve the right triangle, ΔABC, for the missing sides and angle to the nearest tenth given angle B = 27° and side c = 15.
Answer:
Part 1) [tex]C=90\°[/tex]
Part 2) [tex]A=63\°[/tex]
Part 3) [tex]b=6.8\ units[/tex]
Part 4) [tex]a=13.4\ units[/tex]
Step-by-step explanation:
step 1
Find the measure of angle C
we know that
The triangle ABC is a right triangle
so
Angle C is a right angle
therefore
[tex]C=90\°[/tex]
step 2
Fin the measure of angle A
we know that
In the right triangle ABC
∠B+∠A=90° -----> by complementary angles
we have
[tex]B=27\°[/tex]
substitute
[tex]27\°+A=90\°[/tex]
[tex]A=63\°[/tex]
step 3
Find the length side b
we know that
In the right triangle ABC
[tex]sin(B)=b/c[/tex]
[tex]b=(c)sin(B)[/tex]
substitute the given values
[tex]b=(15)sin(27\°)=6.8\ units[/tex]
step 4
Find the length side a
we know that
In the right triangle ABC
[tex]sin(A)=a/c[/tex]
[tex]a=(c)sin(A)[/tex]
substitute the given values
[tex]a=(15)sin(63\°)=13.4\ units[/tex]
Answer:
A = 63 , a = 13.4, b = 6.8
Step-by-step explanation:
Refer to the coordinate system shown below. Write the ordered pair that names point M.
(9,2)
(1,8)
(1,9)
(9.1)
Answer:
(1,9)
Step-by-step explanation:
For this case we must locate the point M in the coordinate system, once we visualize it we count the number of grid that are between the axis "x" and the point M, we have that there are 9 grids, then the coordinate "y" from the point M is 9. Now we count the number of grids between the "y" axis and the point M, we see that there is a grid, so the coordinate "x" of the point M is 1.
Point M: (1,9)
Answer:
Option C
Form the union for the following sets.
X = {0, 10, 100, 1000)
Y = (100, 1000)
XU Y =
00)
{0, 10)
(100, 1000)
(0, 10, 100, 1000)
[tex]X\cup Y=\{0,10,100,1000\}[/tex]
27a⁰c³ for a =⅔, c = -⅓
need answer and if you could explain how to solve problem that would be much appreciated.
Answer:
- 1
Step-by-step explanation:
Using the rules of exponents
[tex]a^{0}[/tex] = 1
[tex](a^n)^{m}[/tex] = [tex]a^{nm}[/tex]
Given
27[tex]a^{0}[/tex][tex](-\frac{1}{3}) ^{3}[/tex]
Note [tex]a^{0}[/tex] = 1 for any value of a, thus
= 27 × 1 × - [tex]\frac{1}{3^{3} }[/tex]
= 27 × 1 × - [tex]\frac{1}{27}[/tex] ← cancel the 27 on numerator/ denominator
= 1 × - 1
= - 1
A watch company is developing packaging for its new watch. The designer uses hexagons with a base area of 25 in squared and rectangles with a length of 10 in to create a prototype for the new package. What is the volume of the prototype?
How do I set this up?
Answer:
The volume of the prototype is [tex]V=250\ in^{3}[/tex]
Step-by-step explanation:
we know that
The volume of a hexagonal prism is equal to
[tex]V=BH[/tex]
where
B is the area of the hexagonal base
H is the length of the rectangular face
we have
[tex]B=25\ in^{2}[/tex]
[tex]H=10\ in[/tex]
substitute
[tex]V=(25)(10)[/tex]
[tex]V=250\ in^{3}[/tex]
Answer:
Volume of the prototype is 250 in.³
Step-by-step explanation:
Given:
Base area of the watch packaging case = 25 in.²
Length of the rectangle on the side = 10 in.
To find: Volume of the packaging prototype.
Prototype of the packaging of the watch is in shape of prism whose base is a hexagon and sides are in shape of rectangle.
So, Volume of the prism = Base Area × Height
Thus, Volume of the Prototype = 25 × 10
= 250 in.³
Therefore, Volume of the prototype is 250 in.³