Answer:
common ratio is 2/5
First term is 125/2
The sum of the first n terms is: [tex]S_n=\frac{125}{2} \, \frac{1-(2/5)^n}{3/5}[/tex]
The infinite sum is: [tex]S_\infty =\frac{625}{6}[/tex]
Step-by-step explanation:
The 4th term is 4, and the seventh term is 32/125 so we use the definition of nth term of a geometric sequence to create the following two equations:
[tex]a_4=a_1\,*\,r^{4-1} = a_1\,*\,r^3\\4=a_1\,*\,r^3\\and\\a_7=a_1\,*\,r^{7-1} = a_1\,*\,r^6\\\frac{32}{125} = a_1\,*\,r^6[/tex]
Now we divide a7 by a4 to get rid of a1 and work on determining the common ratio of the sequence:
[tex]\frac{a_7}{a_4} =\frac{8}{125} =\frac{a_1\,r^6}{a_1\,r^3} =r^3\\then\\r=\sqrt[3]{\frac{8}{125} } =\frac{2}{5}[/tex]
So, the common ratio is 2/5
we can now determine the first term:
[tex]a_4=4=a_1\,*\,(2/5)^3\\a_1=\frac{125*4}{8} =\frac{125}{2}[/tex]
The sum of the first n terms is given by the formula:
[tex]S_n=\frac{125}{2} \, \frac{1-(2/5)^n}{1-(2/5)} \\S_n=\frac{125}{2} \, \frac{1-(2/5)^n}{3/5}[/tex]
and therefore, the infinite sum is:
[tex]S_\infty = a_1\,\frac{1}{1-r} = \frac{125}{2} \,\frac{5}{3} =\frac{625}{6}[/tex]
Helpppppppp pleaseeeee
Answer:
108 cm^2
Step-by-step explanation:
A= 1/2 b×h
so
1/2 12×18
Please answer!! Will make brainliest (Photo is the question)
Rewrite the function f(x)=-4(x-3)^2+16 in the form f(x)=ax^2+bx+c
Identify and write the hypothesis and the conclusion of the following conditional statement. "If I am running, then I am not awake."
Answers:
Hypothesis = "I am running"
Conclusion = "I am not awake"
===================================
Explanation:
All conditional statements are in the form "If P, then Q" where P and Q are placeholders for the hypothesis and conclusion respectively.
So you can say the basic format of a conditional is "If hypothesis, then conclusion".
what is the value of |3.25| ?
Answer:
3.25
Step-by-step explanation:
The answer is 3.25 because the absolute value of a number is basically that same number but it ALWAYS comes out positive.
Hope this helps :)
The value of |3.25 according to the question is; 3.25|.
The absolute value of a number is always positive irrespective of its initial sign polarity.
As such, since the number 3.25 is nested in the | | sign.The absolute value is 3.25.
Read more:
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Solve the following
Answer:
Q1
|a-b| = b-a when a<b
Q2
104159/33000
Step-by-step explanation:
Q1
If a<b then a-b will always be negative. To get the absolute value, we can take -(a-b) = -a+b = b-a.
Q2
Let x = 3.12789789789...
We isolate the repeating decimal to start after the decimal, so we multiply by 100.
100x = 312.789789789...
We want to multiply by 10 for each digit that repeats (in this case 3), to get the repeating part to the left of the decimal.
100000x = 312789.789789
Subtracting the two...
x(100000-100) = 312789.789789 - 312.789789
99900x = 312477
x = 312477/99000 = 104159/33000
Which finction results in f(2)=13?
Answer:
6.5
Step-by-step explanation:
plz mark brainlyest
Suppose a population has a mean weight of 180 pounds and a standard deviation of 25 pounds. A sample of 100 items is drawn from this population. What is the standard error of the mean?
Answer:
We are given:
μ=180,σ=25,n=100
Therefore the standard error of the mean is
2.5
Step-by-step explanation:
Determine the unknown side of the similar triangle.
A)
2
B)
3
4
D)
5
Answer:
(C). 4
Step-by-step explanation:
Sides of the similar triangles are proportional.
if X ~ Y , then [tex]\frac{12}{6}[/tex] = [tex]\frac{8}{x}[/tex] ⇒ x = 4
What is the probability that a coin tossed in the air will land heads up? 25% 50% 75% 100%
Answer:
50%
Step-by-step explanation:
Answer: 50%
Step-by-step explanation: the normal probability is 1/2 sooo it translates to 50/100 which is 50%
If oranges cost 5 for 75cents how
many can you buy for $2.70?
Answer:
15 oranges
Step-by-step explanation:
Only if im correct in assuming you get 5 oranges per 75 cents if not then im not sure because im confused by the question
WHAT ARE THE X AND Y INTERCEPTS FOR THIS??
PLEASE ANSWERRRRR
Answer:
Y-intercept = 0.4
X-intercept = 0.3
Step-by-step explanation:
Which of the following fractions is closest to
5/8
2/3
13/20
11/16
Rectangle ABCD is congruent to rectangle HGJK.
Rectangles A B C D and H G J K are shown. The length of A B is 11 inches. The length of K H is 18 inches.
What is the area of rectangle ABCD?
square inches
Answer:
It is 198
Step-by-step explanation:
(Width)(Height)
mutliply (11) times (18)
The area of rectangle ABCD is 198 square inches
The given parameters are:
[tex]\mathbf{AB = 11}[/tex]
[tex]\mathbf{KH = 18}[/tex]
Because the rectangles are congruent, then:
[tex]\mathbf{HG = AB = 11}[/tex]
[tex]\mathbf{KH = DA= 18}[/tex]
So, the area of rectangle ABCD is the product of side lengths AB and DA
So, we have:
[tex]\mathbf{Area = AB \times DA}[/tex]
Substitute values for AB and DA
[tex]\mathbf{Area = 11 \times 18}[/tex]
[tex]\mathbf{Area = 198}[/tex]
Hence, the area of rectangle ABCD is 198 square inches
Read more about areas at:
https://brainly.com/question/9655204
write the slope-intercept form of the equation of each line. identify the slopes y-intercept.
Answer:
1. 3,0,y=3x
2. -3/5, 1, y=-3/5x+1
3. -2/3, -4,y=-2/3x-4
4. 0, 4, y=4
5. 1, 5, y=x+5
6. 2, 0, y=2x
7. 4, 5, y=4x+5
8. 3/2, 4, y=3/2x+4
hopefully this helps :)
A system of equations is graphed on the coordinate plane.
y=−2x−4y=2x+4
What is the solution to the system of equations?
Answer:
No solution
Step-by-step explanation:
How long will it take an investment to double in value if the interest rate is 6% compounded continuously
Answer:
11.55 years
Step-by-step explanation:
Formula to calculate the final value when the money is compounded continuously is,
Final value = [tex]\text{(Present value)}.e^{rt}[/tex]
Here 'r' = rate of interest
t = duration for the investment
Let the money invested = $x
We have to find the duration in which the present value gets doubled.
Final value = $2x
Rate of interest = 6% per year ≈ 0.06
By substituting these values in the formula,
[tex]2x=x.e^{0.06t}[/tex]
[tex]2=e^{0.06t}[/tex]
ln(2) = [tex]\text{ln}e^{0.06t}[/tex]
0.693147 = 0.06t
t = 11.55 years
Therefore, invested amount will be doubled in 11.55 years.
Find the midpoint of the line segment with the given endpoints. R(-12, 8), S(6, 12)
1 (-3, 10) 2 (9, 2) 3 (10. -3) 4 (-9.2)
Answer:
The answer is one.
Step-by-step explanation:
What is the GCF of x2 - 64?
Pls I really need help!
Answer:
The greatest common factor of x2-64 is 1
Step-by-step explanation:
Why are arithmetic sequences discrete data?
Answer:
If you take any number in the sequence then subtract it by the previous one, and the result is always the same or constant then it is an arithmetic sequence.
Step-by-step explanation:
Answer:
A sequence is a discrete structure used to represent an ordered list.
Step-by-step explanation:
Discrete values are values between the terms if the sequences are not included in the sequence. If you collect all the terms of the sequence into a set, that set will always be discrete, because there's only countably many of them, and every interval is uncountable. So in that sense, yes, sequences are discrete. A sequence is a discrete structure used to represent an ordered list. A sequence is a function from a subset of the set of integers (usually either the set {0,1,2,. . .} or {1,2, 3,. . .}to a set S. We use the notation an to denote the image of the integer n. We call an a term of the sequence.
choose the letter that corresponds to the correct answer
Answer:
A
Step-by-step explanation:
PLEASE HELP AND BE REAL I WILL GIVE BRAINLY. Simplify 8.7+ (1.5) ²+4(3.5+6.2)-3.1 - 3.5
Answer:
43.15
Step-by-step explanation:
See attachment below
Determine if the following argument always applies, sometimes applies, or never applies. Provide at least 2 examples in your explanation.
"The sum of a number and its opposite is always 1."
Answer:
Never applies
Step-by-step explanation:
Given
Argument: The sum of a number and its opposite is always 1
Assume a positive number x
The opposite of the number is negative x (i.e. -x)
The sum of both numbers is:
[tex]Sum = x + (-x)[/tex]
Open Bracket
[tex]Sum = x -x[/tex]
[tex]Sum = 0[/tex]
Now, take for instance.
[tex]Number = 5[/tex]
Opposite would be
[tex]Opposite = -5[/tex]
Their sum is:
[tex]Sum = 5 + (-5)[/tex]
[tex]Sum = 5 -5[/tex]
[tex]Sum = 0[/tex]
Another instance is:
[tex]Number = -8[/tex]
Opposite would be
[tex]Opposite = 8[/tex]
Their sum is;
[tex]Sum = -8 + 8[/tex]
[tex]Sum = -0[/tex]
Hence, the argument never applies because the sum is never 1
which graph represents the function h(x)=2sin(x+pi/2)-1 ?
This graph represents the function h(x)=2sin(x+π/2)-1.
What is graph?
A graph can be defined as a pictorial representation or a diagram that represents data or values.
This graph represents the function h(x)=2sin(x+π/2)-1.
The range is the set of values that correspond with the domain.
Domain of graph: (−∞,∞),{x|x∈R}
Range of graph: [−3,1],{y|−3≤y≤1}
Use the form asin (bx−c)+d to find the amplitude, period, phase shift, and vertical shift.
Amplitude: 2
Period: 2π
Phase Shift: −π/2 (π/2 to the left)
Vertical Shift: −1
Learn more about graph
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What is twenty six million four hundred five thousand twenty in standard form?
Answer:
26,405,020
Step-by-step explanation:
Answer:
26,405,020
Step-by-step explanation:
hope this helpssss
have a good nighttttt
here's the question
Find the Lowest Score bounding upper 5%. The mean is 35 and the SD is 7
Answer:
get the mean deviation
<3 and <4 are vertical. m<3=5x+22 and m<4=7x+2. Find the measure of each angl.
Answer:
72°
Step-by-step explanation:
Vertical angles are congruent.
m∠3 = m∠4
7x + 2 = 5x + 22
2x = 20
x = 10
m∠3 = m∠4 = 72°
7/3 to 2 1/3
HELP ASAP PLSPLS !! :)
Find the value of 4+ (27 - 12.2) - 2.
19
5.5
3.5
Answer:
5.5
Step-by-step explanation:
