Answer:
The nth term Tn = -8(-1/4)^(n-1) or Tn = 6(1/3)^(n-1) can be used to find all geometric sequencesStep-by-step explanation:
Let the first three terms be a/r, a, ar... where a is the first term and r is the common ratio of the geometric sequence.
If the sum of the first two term is 24, then a/r + a = 24...(1)
and the sum of the first three terms is 26.. then a/r+a+ar = 26...(2)
Substtituting equation 1 into 2 we have;
24+ar = 26
ar = 2
a = 2/r ...(3)
Substituting a = 2/r into equation 1 will give;
(2/r))/r+2/r = 24
2/r²+2/r = 24
(2+2r)/r² = 24
2+2r = 24r²
1+r = 12r²
12r²-r-1 = 0
12r²-4r+3r -1 = 0
4r(3r-1)+1(3r-1) = 0
(4r+1)(3r-1) = 0
r = -1/4 0r 1/3
Since a= 2/r then a = 2/(-1/4)or a = 2/(1/3)
a = -8 or 6
All the geometric sequence can be found by simply knowing the formula for heir nth term. nth term of a geometric sequence is expressed as
if r = -1/4 and a = -8
Tn = -8(-1/4)^(n-1)
if r = 1/3 and a = 6
Tn = 6(1/3)^(n-1)
The nth term of the sequence above can be used to find all the geometric sequence where n is the number of terms
A player tosses a die 6 times.If gets a number 6 Atleast two times he wins 2 dollars ,otherwise he looses 1 dollar.. Find the expectation of the amount if he wins
Answer:
[tex]E(x)=-0.2101[/tex]
Step-by-step explanation:
The expected value for a discrete variable is calculated as:
[tex]E(x)=x_1*p(x_1)+x_2*p(x_2)[/tex]
Where [tex]x_1[/tex] and [tex]x_2[/tex] are the values that the variable can take and [tex]p(x_1)[/tex] and [tex]p(x_2)[/tex] are their respective probabilities.
So, a player can win 2 dollars or looses 1 dollar, it means that [tex]x_1[/tex] is equal to 2 and [tex]x_2[/tex] is equal to -1.
Then, we need to calculated the probability that the player win 2 dollars and the probability that the player loses 1 dollar.
If there are n identical and independent events with a probability p of success and a probability (1-p) of fail, the probability that a events from the n are success are equal to:
[tex]P(a)=nCa*p^a*(1-p)^{n-a}[/tex]
Where [tex]nCa=\frac{n!}{a!(n-a)!}[/tex]
So, in this case, n is number of times that the player tosses a die and p is the probability to get a 6. n is equal to 6 and p is equal to 1/6.
Therefore, the probability [tex]p(x_1)[/tex] that a player get at least two times number 6, is calculated as:
[tex]p(x_1)=P(x\geq2)=1-P(0)-P(1) \\\\P(0) =6C0*(1/6)^{0}*(5/6)^{6}=0.3349\\P(1)=6C1*(1/6)^{1}*(5/6)^{5}=0.4018\\\\p(x_1)=1-0.3349-0.4018\\p(x_1)=0.2633[/tex]
On the other hand, the probability [tex]p(x_2)[/tex] that a player don't get at least two times number 6, is calculated as:
[tex]p(x_2)=1-p(x_1)=1-0.2633=0.7367[/tex]
Finally, the expected value of the amount that the player wins is:
[tex]E(x)=x_1*p(x_1)+x_2*p(x_2)\\E(x)=2*(0.2633)+ (-1)*0.7367\\E(x)=-0.2101[/tex]
It means that he can expect to loses 0.2101 dollars.
Answer:
Expected value = -0.2101
Step-by-step explanation :
Givena discrete variable the expected value is given as:
E(x) = xp(x) + yp(y)
Where x and y are the values the variables can assume, and p(x) and p(y) are their respective probabilities.
Probability that a player gets 6 at least twice = p(x ≥ 2) = 1 - p(x≤ 2)
= 1 - p(0) - p(1)
But p(0) = 0.3349
p(1) = 0.4018
p(x ≥ 2) = 1 - 0.3349 - 0.4018
= 0.2633
p(y) = 1 - p(x)
= 1 - 0.2633
= 0.7367
Expected value = 2(0.2633) + (-1)(0.7367)
= -0.2101
A loss of $0.2101 is expected.
Any line perpendicular to the line y = 2x +4 has a slope of -2.
True
False
Thank you sm if you can help me :)
Answer: FALSE
You get y = 2x +4 so the slope is 2. Perpendicular lines have opposite-reciprocal slopes, so the slope of the line we want to find is -1/2.
please help i don’t understand what so ever
Answer:
x=6
Step-by-step explanation:
Because of the Pythagorean theorem, you know that the square of the two legs of a right triangle will be equal to the square of the hypotenuse. Conversely, the square of one of the legs will be equal to the square of the other leg subtracted from the square of the hypotenuse. Therefore:
[tex]x^2=10^2-8^2 \\\\x^2=100-64\\\\x^2=36\\\\x=6[/tex]
Hope this helps!
Answer:
6
Step-by-step explanation:
By Pythagoras theorem
10^2 = 8^2 + x^2
100= 64 + x^2
X^2 =100-64
X^2= 36
[tex]x = \sqrt{36} \\ x = 6[/tex]
Hope this helps..
Help someone cuhh please like omg
Answer:
5^1
Step-by-step explanation:
5^6/5^5
5^(6-5)
5^1
Answer:
5
Step-by-step explanation:
5^6=15625
5^5=3125
15,625/3,125=5
Hope this helps!
What is the simplified expression for the expression below? 4(x + 8) + 5(x – 3)Which expression is equivalent to 6(x – 4)
Answer:4x+32+5x-15
Step-by-step explanation: that’s the simplified equation, you would just have to distribute the 4 to its own equation and the 5 into its own equation.. but i think the second part of ur question is missing..
Answer:
C. 9x+17
Step-by-step explanation:
_____ of the basic trigonometric functions have inverse functions. None, 3, 6, 4
Answer:
6
Step-by-step explanation:
There are inverses for sine, cosine, tangent, secant, cosecant, and cotangent.
I will mark you brainliest!!
Answer:
C: .94
Step-by-step explanation:
7e^x=18
x=ln(18/7)
x=ln(2.5714)
x=.94
The 102nd floor of the sears tower in Chicago is the highest occupied floor. It is 1,431 feet above the ground . How many yards above the ground is the 102nd floor
Answer:
477 yards
Step-by-step explanation:
1 foot to a yard is 0.333333.
1431 times 0.333333=477yards
In a group of students , 12 read maths, 15 read statistics , 11 read physics, 4 read maths only , 7 read statistics only, 3 read statistics and physics only and 1 read maths and statistics only . What is the number of the students who were there altogether ( universal set)
Answer:
23 students
Step-by-step explanation:
In a group of students , 12 read maths, 15 read statistics , 11 read physics, 4 read maths only , 7 read statistics only, 3 read statistics and physics only and 1 read maths and statistics only.
Those that read maths only = 4, Those that read statistic only =7, Those that read statistics and physics only = 3, those that read maths and statistics only = 1.
Therefore those that read all three subjects = 15 - 7 - 3 - 1 = 4
Those that read maths and physics only = 12 - 4 - 4 - 1 = 3
Those that read physics only = 11 - 3 - 4 - 3 = 1
The number students = 4 + 7 + 3 + 1 + 4 + 3 + 1 = 23 students
Find the slope of the line that passes through (3, 2) and (10, 3).
Simplify your answer and write it as a proper fraction, improper fraction, or integer.
Answer:
m=1/7x
Step-by-step explanation:
Answer:
[tex] slope= \frac{1}{7} [/tex]
Step-by-step explanation:
[tex](3 \: \: \: \: \: \: \: 2) = > (x1 \: \: \: \: \: \: \: x2)\\ (10 \: \: \: \: 3) = > (y1 \: \: \: \: \: \: \: y2)[/tex]
[tex]slope \\ = \frac{y1 - y2}{x1 - x2} \\ = \frac{2 - 3}{3 - 10} \\ = \frac{ - 1}{ - 7} \\ = \frac{1}{7} [/tex]
hope this helps
brainliest appreciated
good luck! have a nice day!
Tanya has ten bills in her wallet. If she has one more $5 bill than $10 bills, and two more $1 bills than $5 bills, how many of each does she have?
Please tell me the steps will choose brainliest
Answer:
5 Ones dollar bills
3 five dollar bills
2 ten dollar bills
Step-by-step explanation:
What is the volume of a rectangular prism with a length of 5 ft, width of 6 ft and a height of 4.5 ft ?
Answer:
135ft^3
Step-by-step explanation:
Multiply all of the numbers to get your answer.
1. 2x + 5 = 3x + 1
2. 3x + 2 = 4x - 3
3. 4x - 3 = 3x + 3
Pls help equations. Find x, show workings. You are the best but answer only if u know it. If I report ur answer know that that's not the right answer. Love you all.Don't just work rubbish for points.
Answer:
1)4
2)5
3)6
Step-by-step explanation:
1)2x+5=3x+1
2x-3x=1-5
-1x=-4
x=4
2)3x+2=4x-3
3x-4x=-3-2
-1x=-5
x=5
3)4x-3=3x+3
4x-3x=3+3
1x=6
x=6
Hope it helps
Use the fishbowl to answer the following question.
a. How many fish are there in the bowl? fish.
b. Which color fish has the highest probability of being fished?
c. What is the probability of choosing this color?
Fraction
Decimal (provide the first 5 decimal numbers & yes round the number)
Percent % (round to the nearest tenth)
Answer:
a) 14
b) green
c) fraction 6/14
percentage: 42.8% rounded: 40%
not sure about the decimal tho
Answer:
a) 14
b) green
c) 6/14
d)percent 42.8 %
round up 40 %
An airplane lands at an airport 60 miles east and 25 miles north of where it took off, how far apart are the two airports?
Answer:
20 miles
Step-by-step explanation:
Use the circle to answer the questions.
A circle with radius 5.4 centimeters.
The diameter is
cm.
The circumference in terms of Pi is
Using 3.14 for Pi, the approximate circumference of the circle is
cm.
Answer:
C = 10 π cm
Step-by-step explanation:
Diameter is 2 x radius = 2*5.4 = 10.8 cm
radius r = 5 cm
diameter d = 10 cm
circumference C = 31.4 cm
area A = 78.5 cm2
In Terms of Pi π
circumference C = 10 π cm
area A = 25 π cm²
Formulas: Circle Formulas in terms of Pi π, radius r, and diameter d
Radius and Diameter:
r = d/2
d = 2r
Area of a circle:
A = πr2 = πd2/4
Circumference of a circle:
C = 2πr = πd
Answer:
c
Step-by-step explanation:
got it right on my test
Find Four Solutions For the following Linear equations in two variables: y = 5x
Answer:
see explanation
Step-by-step explanation:
To find solutions to the equation, choose any value for x, substitute into the equation and evaluate for y, that is
x = - 1 → y = 5(- 1) = - 5 ⇒ (- 1, - 5 )
x = 0 → y = 5(0) = 0 ⇒ (0, 0 )
x = 1 → y = 5(1) = 5 ⇒ (1, 5 )
x = 5 → y = 5(5) = 25 ⇒ (5, 25 )
Thus 4 solutions are
(- 1, - 5), (0, 0), (1, 5), (5, 25)
This month the local power company charges $9.12 per kilowatt-hour for electricity. Write an equation that represents the total amount a customer will pay for their usage.
Answer:
9.12 x time x kilowatt
Step-by-step explanation:
Las personas que venden computadoras en una tienda local ganan $100 en comisión por computadora por las primeras 5 computadoras que venden cada mes. Por cada computadora adicional que venden durante ese mes, la comisión por computadora es 1.5 veces la tarifa por las primeras cinco. ¿Cuál de las siguientes es la comisión total que gana una persona que venda 8 computadoras en un mes?
A. $190
B. $800
C. $950
D. $1,050 E. $1,200
3/16 Write as a decimal and as a percent
Answer:
0.1875 as a decimal and 18.75% as a percent
Step-by-step explanation:
0.1875 is the decimal. Move point over 2 spots right to get percent.
I’m a struggling please help :(
Answer:
It's constant
Step-by-step explanation:
at those points, the graph is going ---------------- so, it is constant.
// have a great day //
Michael is an engineer and is drawing a scale model of a centrifuge for an oil company. If the centrifuge is 24 meters tall and he's using a scale of 1 centimeter=6 meters, then how many centimeters tall should the centrifuge be in the drawing?
Students in a school are asked to pick either football, rugby or tennis to play in their lessons. the number of students who picked football and rugby are in the ratio of 4:3 the number of students who picked rugby and tennis in the ratio of 9:19 57 students picked tennis work out how many student picked football
Answer: 36 Students picked football
Step-by-step explanation: When calculating values by the use of given ratios, it is important to note that the ratio of one value as compared to the other is the same as the actual value compared to the other.
The ratio of students who picked rugby and tennis is given as ratio 9 : 19, which means for every 28 students (that was derived by 9 + 19), 9 would choose rugby and 19 would choose tennis. However, we have been given the total number of students who chose tennis as 57, hence the value 57 would now replace the ratio of 19. However the total number of those who chose rugby is not yet known, so we can write out an equation as shown below;
19/28 = t/x
Where t is the number of tennis players as represented by ratio 19 and x is the total number of both tennis and rugby players as represented by 28.
By cross multiplication we now have
19 * x = 28 * 57
x = (28 * 57)/19
x = 1596/19
x = 84
If a total of 84 students play both rugby and tennis, and 57 of them play only tennis, then the number of rugby players is derived as
r = x - t
r = 84 - 57
r = 27
Having determined that 27 students played rugby, and the ratio of football to rugby players is given as 4 : 3, the relationship can be mathematically represented as follows;
3/7 = r/y
Where r is the total number of rugby players and y is the total number of both football and rugby players
3/7 = 27/y
By cross multiplication you now have
3 * y = 7 * 27
y = (7 * 27)/3
y = 189/3
y = 63
If the total number of football and rugby players is 63 and out of these 27 play rugby only, then the number of football players is derived as;
f = y - r
f = 63 - 27
f = 36
Therefore the number of students who chose football is 36
Jacob can run 9 miles in 1 hour and
15 minutes. What is his average running speed per minute?
Answer:
0.12 miles per minute
Step-by-step explanation:
9/75 is 0.12. 9 miles in 75 minutes
Average speed of Jacob is 0.12 miles per minute.
What is unitary method ?Unitary method is a method of finding value of a single unit.After finding value of a single unit we can determine values of any given unit.
According to the given question Jacob can run 9 miles in 1 hour and
15 minutes.
We know 1 hour is 60 minutes.
∴ 1 hour and 15 minutes is
= (60 + 15) minutes.
= 75 minutes.
So, Jacob can run 9 miles in 75 minutes.
∴ In one minute Jacob can run 9/75 miles shich is
= 0.12 miles per minute.
learn more about unitary method here :
https://brainly.com/question/14793162
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When simplifying square root expressions, look for any ___________ that can be pulled out of the radical.
Answer:
perfect square number
Step-by-step explanation:
When simplifying square root expressions, look for any perfect square
that can be pulled out of the radical.
Given that,
When simplifying square root expressions, look for any ___________ that can be pulled out of the radical. blank space to be filled.
In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication, and division,
Here,
When simplifying the square root we see the number that is perfect squares, because only a perfect square can be pulled out from the square root.
Thus, When simplifying square root expressions, look for any perfect square that can be pulled out of the radical.
Learn more about arithmetic here:
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If f(x)=x^2+1 and g(x) = x-4 which value is equivalent to (f•g)(10)
What percentage of 220 is 130?
Answer:
59.09%
Step-by-step explanation:
You find it through the following formula:
Part divided by whole times 100.
Substitute it and you get the answer:
130 / 220 times 100 = 59.09
Need help people please help me
Answer:
The first option
Step-by-step explanation:
To get your answer you have to divide 5 and 4 and another way to write the answer is 5/4.
Answer: it is 1/4
Step-by-step explanation:
anybody know this :( please help
Answer:
the set of all the real values which are strictly greater than zero which is all positive real numbers
Step-by-step explanation:
In interval notation: (0, ∞)
Any exponential function with a positive base and positive multiplier will have a horizontal asymptote at y=0 and will extend to +∞. That's what this one does.
Range of a function--
The range of a function is the set of all the values that are attained by a function.
We are asked to find the range of the function f(x)
the set of all the real values which are strictly greater than zero
x > 0
please mark me brainliest :)
what is a slope of the line?
Answer
0
Step-by-step explanation:
A horizontal line has a slope of 0 always