Answer:
Step-by-step explanation:
Given two series A and B;
Series A: 10 + 4 +8/5 + 16/25 + 13/125 + ...
Series B: 1/5 + 3/5 + 9/5 + 27/5 + 81/5 +...
Both series are geometric series since they have the same common ratio. Given the geometric series T₁, T₂, T₃, T₄..., the common ratio r is expressed as [tex]\frac{T_2}{T_1} =\frac{T_3}{T_2} =\frac{T_4}{T_3} = r[/tex].
a) For series A, Given T₁ = 10, T₂ = 4, T₃ = 8/5 and T₄ = 13/125
Its common ratio is expressed as [tex]\frac{4}{10} =\frac{8/5}{4} =\frac{13/125}{8/5} = 2/5[/tex]
Hence the common ratio of series A is 2/5
The sum to infinity of the geometric series will be expressed as [tex]s_\infty = \dfrac{a}{1-r}[/tex]
Note that the sum to infifnity is used since the series is tending to infinity.
a is the first term if the series = 10
r - 2/5
On substituting this values into the formula;
[tex]s_\infty = \dfrac{10}{1-2/5} \\\\s_\infty = \dfrac{10}{3/5} \\\\s_\infty = 10* 5/3\\s_\infty = 50/3[/tex]
Hence the sum of the series is 50/3
b) For the series B;
Series B: 1/5 + 3/5 + 9/5 + 27/5 + 81/5 +...
The common ratio of the series is expressed as shown;
[tex]\frac{3/5}{1/5} =\frac{9/5}{3/5}= \frac{27/5}{9/5 } = r\\ r = (3/5 * 5/1) = 9/5*5/3 = 27/5*5/9 = 3[/tex]
Hence its common ratio is 3.
Sun of the series is expressed similarly as:
[tex]s_\infty = \frac{a}{1-r}\\ s_\infty = \frac{1/5}{1-3}\\\\s_\infty = \frac{1/5}{-2}\\\\[/tex]
[tex]s_\infty = 1/5 * -1/2\\s_\infty = -1/10[/tex]
Hence the sum of series B is -1/10
The equation y=6x represents a proportional relationship. What is the constant of proportionality?
A. 0
B. 1/6
C. 6
D. x
find the surface area of the composite figure - image attached,, need answer now!!
Answer:
Surface Area = 392 cm²
Step-by-step explanation:
Green (front):
SA = 1/2bh
= 1/2 (12) (8)
= 48 cm²
Green (left side):
SA = bh
= 5 (10)
= 50 cm²
Green (right side):
SA = bh
= 5 (10)
= 50 cm²
Green (back):
SA = 1/2bh
= 1/2 (12) (8)
= 48 cm²
Blue (front):
SA = bh
= 12 (4)
= 48 cm²
Blue (left side):
SA = cm²
= 5 (4)
= 20 cm²
Blue (right side):
SA = bh
= 5 (4)
= 20 cm²
Blue (back):
SA = bh
= 12 (4)
= 48 cm²
Blue (bottom):
SA = bh
= 12 (5)
= 60 cm²
Total:
48 + 50 + 50 + 48 + 48 + 20 + 20 + 48 + 60 = 392 cm²
3. If a function maps Set A to Set B, do all elements of Set A
have to be used?
Answer:
So we have a function such that:
Takes elements of Set A, and maps them into Set B.
So Set A is the domain, and Set B is the range.
Where the domain is defined as the set of all the possible inputs of a function, and the range is the set of the possible outputs.
In principle, yes, if f(x) maps Set A into Set B, all the elements of Set A should be used, why?
Because we need to check if there is a problem with Set A, for example the function f(x) = 1/x has a problem when x = 0, so we remove x = 0 from the domain of that function.
So, a function is only a function if it maps ALL the elements of its domain into only one element in the range.
can somewon plz help me
Answer:
1253 in^3
Step-by-step explanation:
The volume of the smaller container is (7 in)(5 in)(5 in) = 175 in^3.
The volume of the larger one is (11 in)(14 in)(7 in) = 1078 in^3
The total volume is the sum of these two volumes: 1253 in^3
Answer:
1253 in^3
Step-by-step explanation:
Volume of small one is 7*5*5 = 175
Volume of the large one is 11*14*7 = 1078
To find the total volume we add them up. We get 1253 and since we are talking about volume it is 1253 inches cubed
A is plotted on a coordinate grid at start bracket 3 and 1 over 2, negative 1 end bracket.. Choose the correct grid that best shows the location of the point. A coordinate grid that shows a point located 4 units to the left and 1 unit down from the origin. A coordinate grid that shows a point located halfway between 3 and 4 units to the right and 1 unit down from the origin. A coordinate grid that shows a point located halfway between 3 and 4 units to the left and 1 unit up from the origin. A coordinate grid that shows a point located halfway between 3 and 4 units to the right and 1 unit up from the origin.
Answer:
im so sorry for the other answer i reported it and im gonna help with this question because i have the same question on my test.
ok so i got C it makes the most sense to me but if im wrong then ill delete this.
If im correct please mark me as brainliest
Step-by-step explanation:
yes this is wrong but i cant delete it so just ignore it
Answer:
B 3 1/2 to the right and one unit down
Step-by-step explanation:
What is the solution of the inequality shown
below?
y+7<-1
Answer:
y<-8
Step-by-step explanation:
y<-1 - 7
y<-8
Answer:
y < -8
Step-by-step explanation:
To solve an inequality, we must get the variable, y, isolated on one side of the inequality.
[tex]y+7 < -1[/tex]
7 is being added to the variable, y. The inverse of addition is subtraction. Subtract 7 from both sides of the inequality.
[tex]y+7-7< -1-7[/tex]
[tex]y < -1-7[/tex]
[tex]y < -8[/tex]
The solution to the inequality is: y< -8
In two or more complete sentences, explain the theorem used in solving for the range of possible lengths of the third
side, AB of ^ABC
Answer:
pythagorean theorem - The length of the hypotenuse squared will always equal the sum of A squared and B sqaured. The equation is A^2 + B^2 = C^2.
Step-by-step explanation:
For Example
A = 4 A^2 = 16
B = 2 B^2 = 4
C = ? C^2 = ?
16 + 4 = 20
[tex]\sqrt{20}[/tex] ≈ 4.5
C/Hypotenuse = 4.5
Pls answer ASAP TY. TY. TY.
Answer:
x^ -10
Step-by-step explanation:
x^2 * x ^ -12
We know that a^b * a^c = a^ (b+c)
x^2 * x^-12
x^(2+-12)
x^ -10
Answer:
[tex]\frac{1}{x^{10}}[/tex]
Step-by-step explanation:
The two "x" terms are being multiplied, so combine the terms
Subtract the power signs:
[tex]x^2 * x^-12[/tex] = [tex]x^2/x^{12}[/tex]
[tex]x^(2 - 12)[/tex] = [tex]x^-10[/tex]
[tex]x^-10[/tex] = [tex]\frac{1}{x^{10}}[/tex]
[tex]\frac{1}{x^{10}}[/tex] is your answer.
~
Jill has two dimes she is going to use to perform a probability experiment. What will the sample space look like if she flips the two dimes simultaneously?
Help and show work please.
Any rectangle is also a parallelogram (but not the other way around). So AB is parallel to CD. The angles BAC and ACD are alternate interior angles that are congruent due to the parallel sides mentioned.
(angle BAC) = (angle ACD)
3x+4 = x+28
3x-x = 28-4
2x = 24
x = 24/2
x = 12
So,
angle BAC = 3x+4 = 3*12+4 = 40 degrees
and
angle CAD = 90 - (angle BAC) = 90 - 40 = 50 degrees
With any rectangle, the four interior angles are always 90 degrees. So that's why angles BAC and CAD add to 90.
what is (7*7*7*7*7*7) * (7*7) in exponential form?
Answer:
7^8
Step-by-step explanation:
Answer:7^8
Step-by-step explanation:
Plz help me and explain
**Solve the equation:
x(x+3)(x+3)=0
Answer:
three solutions: {-3, -3, 0}
Step-by-step explanation:
This polynomial has already been factored, and the factors are x, x + 3 and x = +3. To solve this equation, set each of the factors equal to zero separately and solve each of the resulting equations:
x = 0 is a solution; the given equation equals zero when x = 0.
The next factor is x + 3; setting this equal to 0 yields the solution x = -3.
The last factor is x + 3; x = -3 is the third solution.
In summary, (x + 3)(x = 3) = 0 has two solutions; we call them "repeated roots." x(x + 3)(x = 3) = 0 has three solutions: {-3, -3, 0} of which two are "repeated."
Help, show work please.
Answer:
A
Step-by-step explanation:
A: 0^2+8=8
B: 1^2+8=9
C: 2^2+8=12
D: 3^2+8=17
as 8 is the smallest, A is the answer
Write the equation for the following table:
x. y.
____
0 7
1 16
2 19
3 16
Answer:
B
Step-by-step explanation:
What's the recursive formula of the geometric sequence below?
2, 6, 18, 54, 162, 486,...
O ay = 3; an = an-1 · (2)n-1 for n 2 2
a1 = 2; an = an-1 . (3) for n 2 2
O a1 = 2; an = an-1 • (3)n-1 for n 2 1
ay = 2; an = an-1. (2) for n 2 1
Answer:
Hey there!
We have an=a1(r^n-1), which is the formula for a geometric sequence.
The common ratio is 3, and 2 is the 1st term.
Thus, we have a1=2(3)^(n-1)
Hope this helps :)
Answer:
Hey there!
We have an=a1(r^n-1), which is the formula
for a geometric sequence.
The common ratio is 3, and 2 is the 1st
term.
Thus, we have a1=2(3)^(n-1)
Help please will give brainliest
Answer:
18.
a) 6k + 2y
b) 2x^2 + 2x
c) 16h
19. 4.5 cm
20.
a) x > 4.5
b) x >= 32
Step-by-step explanation:
Use a number line to approximate the value of :
Answer:
9 < [tex]\sqrt{88}[/tex] < 10
Step-by-step explanation:
[tex]\sqrt{88}[/tex] = 9.38083152
Answer:
Third option
Step-by-step explanation:
Notice that √88 is close to √81 wich is 9.
● √88 is greater than √81 so it is greater than 9.
● √88 is less than √100 wich is 10
● so √88 is between 9 and 10
în 2017, the Pew Research Center published the results of a survey on gun ownership. A random sample of 3930 American
adults aged 18 years and older participated in this survey. Of these 3930 individuals, 1269 individuals reported that they
owned at least one gun. Of these self-reported gun owners, 850 said the reason they owned a gun was for protection. Based on
this information, determine the sample proportion, p, of gun owners from this survey who own a gun for protection.
(Use decimal notation. Give your answer to three decimal places.)
Answer:
The sample proportion, p, of gun owners who own gun for protection is 0.67
Step-by-step explanation:
The information given are;
The sample size = 3930
The number of individuals who reported that they owned guns at least on gun = 1269
The number of the self reported gun owners that said the reason they owned gun for protection = 850
The sample proportion, p, of gun owners who own gun for protection is given as follows;
p = (The number of the self reported gun owners that said the reason they owned gun for protection )/(The number of individuals who reported that they owned guns at least on gun)
p = 850/1269 = 0.6698 ≈ 0.670 (to three decimal places)
Therefore, the sample proportion, p, of gun owners who own gun for protection = 0.67.
Find the median of the data in the dot plot below.
Answer:
it's 40
Step-by-step explanation:
because, there's five numbers on each side of 40
Answer:
Step-by-step explanation:40
Please help! Solve for p: -p + 8 - 9 = 9
Answer:
-10
Step-by-step explanation:
-p+8-9=9
-p-1=9
-p=10
p=-10
12
121 °
9
can it make a triangle if so what the area ?
Answer:
no it can not
Step-by-step explanation:
Triangle is always 180° in total.
WILL GIVE BRAINLY!!!! describe the types of correlation between two variables on a graph
Negative Correlation - These variables point towards the left making them negative.
Positive Correlation - These variables point towards the right making them positive.
No Correlation - These variables have the same x coordinates or same y coordinates.
Hope that helped!!! k
HELP ME
solve for x
2x+9<2(x+5)
A parallelogram has a base of 9 centimeters and a height of 21 centimeters. What is the area of the parallelogram? Please include all work!!
Answer:
A =189 cm^2
Step-by-step explanation:
The area of a parallelogram is found by
A = bh where b is the base and h is the height
A = 9 * 21
A =189 cm^2
Question 5
Kate is finding the factors of a large number. Using
a calculator, she has just worked out that 66 is a
factor of this number.
Suddenly, she realises that 22 must be a factor of
the large number as well. Explain why Kate is
correct.
Explanation : If 66 is a factor of this unknown value, then 22 must be as well considering that 22 is a factor off 66. Let's say that this large value is 330. It is a multiple of 66, as 66 [tex]*[/tex] 5 = 330. At the same time 22 [tex]*[/tex] 15 = 330, so 330 is a multiple of 22 as well - or vice versa, 12 is a factor of 330.
We can also tell that 15, 22 fit into 330 through another approach. 22 [tex]*[/tex] 3 = 66, and 66 [tex]*[/tex] 5 = 330, so 5 [tex]*[/tex] 3 = 15 - the same value. This proves that 22 will always be a factor of a value that is the factor of 66.
If you're good at bearings please help meeeeee with full working out tyyyyyy
Solve the simultaneous equations. You must show all your working to find x and y. 1/2x -3y = 9 5x y + y = 28
Answer:
[tex]\huge\boxed{x = 6 , y = -2}[/tex]
Step-by-step explanation:
[tex]\sf \frac{1}{2} x - 3y = 9-----------(1)\\5x + y = 28 ----------(2)[/tex]
Taking equation (1)
[tex]\sf \frac{1}{2} x -3 y=9[/tex]
Multiplying both sides by 2
[tex]\sf x-6y = 18[/tex]
Adding 6y to both sides
[tex]\sf x = 18+6y[/tex]
Putting this in (2)
5(18+6y) + y = 28
5(18+6y) + y = 28
90 + 30y+y = 28
31y+90-28 = 0
31 y + 62 = 0
31y = -62
Dividing both sides by 31
y = -2
Now,
x = 18 + 6y
x = 18+6(-2)
x = 18-12
x = 6
Determine whether each sequence is an arithmetic sequence. If yes, then state the common difference
15, 13, 11, 9,...
Answer:
yes
Step-by-step explanation:
its 2
Find the probability of rolling a die and
getting a 6. Write your answer as a
fraction.
Answer:
1/6
Step-by-step explanation:
there are 6 sides/numbers on a die. 1 roll with a possibility of 6 outcomes.
Answer:
[tex]\frac{1}{6}[/tex]
Step-by-step explanation:
Because there are six possibilities and only one of those possibilities will yield a six, we can find the probability to be [tex]\frac{1}{6}[/tex]
f(x) = [tex]\sqrt{x+7} -\sqrt{x^2+2x-15}[/tex] find the domain
Answer:
x >= -7 ................(1a)
x >= 3 ...............(2a1)
Step-by-step explanation:
f(x) = [tex]\sqrt{x+7}-\sqrt{x^2+2x-15}[/tex] .............(0)
find the domain.
To find the (real) domain, we need to ensure that each term remains a real number.
which means the following conditions must be met
x+7 >= 0 .....................(1)
AND
x^2+2x-15 >= 0 ..........(2)
To satisfy (1), x >= -7 .....................(1a) by transposition of (1)
To satisfy (2), we need first to find the roots of (2)
factor (2)
(x+5)(x-3) >= 0
This implis
(x+5) >= 0 AND (x-3) >= 0.....................(2a)
OR
(x+5) <= 0 AND (x-3) <= 0 ...................(2b)
(2a) is satisfied with x >= 3 ...............(2a1)
(2b) is satisfied with x <= -5 ................(2b1)
Combine the conditions (1a), (2a1), and (2b1),
x >= -7 ................(1a)
AND
(
x >= 3 ...............(2a1)
OR
x <= -5 ................(2b1)
)
which expands to
(1a) and (2a1) OR (1a) and (2b1)
( x >= -7 and x >= 3 ) OR ( x >= -7 and x <= -5 )
Simplifying, we have
x >= 3 OR ( -7 <= x <= -5 )
Referring to attached figure, the domain is indicated in dark (purple), the red-brown and white regions satisfiy only one of the two conditions.