The next term of the given geometric series is the fifth term which is; a₅ = 4
What is the nth term of the geometric series?We are given the geometric series as;
1024, -256, 64, -16,.....
The formula to find the nth term of a geometric series is;
aₙ = ar^(n - 1)
where;
a is first term
r is common ratio
n is position of term
Thus, from the given series, we have that;
a = 1024
r = -256/1024
r = -1/4
Thus, the formula for the nth term of the series is;
aₙ = 1024(-¹/₄)^(n - 1)
Next term is the fifth term and so we have;
a₅ = 1024(-¹/₄)^(5 - 1)
a₅ = 1024(-¹/₄)^(4)
a₅ = 4
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Messages arrive at an electronic mail server at the average rate of 4 messages every 5 minutes. Their number is modeled by a binomial counting process. (a) What frame length makes the probability of a new message arrival during a given frame equal 0.05? (b) Suppose that 50 messages arrived during some 1-hour period. Does this indicates that the arrival rate is on the increase? Use frames computed in (a).
There is a modest rise in arrival rates as compared to the prior arrival because the value is bigger than 0.05. It is a minuscule rise.
Given that,
The Message is arrive at an electronic mall server at the average
rate is 4 messages for every 5 minutes. Then the average
number of message is said to be a and mean is 4 to 5 interval.
Therefore ,we can use poission's approximation to binomial distribution in this case,
λ=4/5 min
( a ) Then , The Number of messages arrived in 1 hour
4x 12 = 48 . , So 48 messages per hour.
Now , our New arrival rate of messages , λ =48
By using possion's distribution ,
θ = time/rate
= 60/48= 1.25
NOW
probability density function of X is given as
f (x ) = θ e^-θx
for X>0
Given , the probability of new message arrival during given frame
equal is 0.05
p (X > x ) = 0.05
Now , of θ ∫e^-θx dx = 0. 05 .
then, e^-θx =0.05
Apply logarithm on both sides , then
In( e^-θx) = In 0.05
By solving,
1- 25
X = 2. 39658
(b) Now , probability of arrival of 50 messages in 60 minutes
p (X>2.39658 ) = 0.05
Now arrival gap is θ = 60/50 = 1.2
P(x> 2.39658 ) =e^-θx
=e^- 1- 2 * 2.39658 = 0.0564
NOW ,
p(x>2- 39658) = 0.0564.
It is greater than 0.05 , so it is called there is slight increase in arrival rates as compared to the previous arrival. It is very small increase .
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Use the x-values: 1, 2, 3, and 4 to write solutions of the equation y = 17x + 8 as ordered pairs.
In the equation y= 17x + 8 ,
the value of x = (1,25) ,(2,42) ,(3,59) ,(4,76).
Given that,
y= 17x + 8
When x = 1
y = 17 × 1 + 8 = 25
when x=2,
y = 17 × 2 + 8 = 42
When X=3,
y = 17 × 3+ 8 = 59
when X=4
y = 17 × 4+ 8 ]= 76
Therefore, the required solution is :
x = (1,25) ,(2,42) ,(3,59) ,(4,76).
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Find an ordered pair (x, y) that is a solution to the equation.
-x+5y=3
The ordered pair that is the solution to the equation -x + 5y = 3 is (-3,0) and (0, 0.6)
Ordered pair:
Ordered pairs refers a set of 2 numbers that exist in a particular order. The first one represents the x value and the second one refer the y value.
Given,
Here we need to find the ordered pair (x, y) that is a solution to the equation -x + 5y = 3
In order to find the solution ordered pair we have to plot this equation on the graph.
To plot this equation, we have to use the graphing calculator, and then input the given equation as the function, then we get the graph like the following.
While we looking into the graph, we have identified that the solution ordered pairs are (-3,0) and (0, 0.6)
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in a group of 100 sports car buyers, 40 bought alarm systems, 30 purchased bucket seats, and 20 purchased an alarm system and bucket seats. if a car buyer is chosen at random, what is the probability they bought an alarm system or bucket seats?
The probability that a car buyer bought an alarm system or bucket seats is 0.50.
Probability of ,
Alarm system p(A) = 40/100 = 0.40
Bucket seat p(B) = 30/100 = 0.30
Alarm system and bucket seat p(A and B) = 20/100 = 0.20
Probability of alarm system or bucket seat is :
= p(A)+p(B)-p(A and B)
= 0.40+0.30-0.20
= 0.50
In mathematics, probability is the likelihood of an event occurring. It is quantified as a number between 0 and 1, where 0 indicates impossibility and 1 indicates certainty. The higher the probability of an event, the more likely it is to occur. A simple example is the tossing of a coin, where the probability of either head or tail is 1/2.
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Camilla walk at a teady pace for 5 minute, top in the ame location for 2 minute, then continue on at a fater pace for 3 more minute until he reache her detination. Camilla claim that the relationhip between the time pent walking and the ditance traveled i not a function becaue of the time he tood till. Explain why the relationhip i a function
the relationship is a function because she "made up time".
A relation that states that there should only be one output for each input are called a function. alternatively, a function is a particular kind of relation—a set of ordered pairs—that adheres to a specific rule—each X-value should be associated with only one y-value.
if a relation is one-to-one or many-to-one it is a function.
Function Not a Function
one-to-one many-to-many
many-to-one one-to-many
In the above-mentioned scenario, She basically made up for the time she had spent standing at the location by increasing her pace. Since she picked up the pace, you can assume that she completed the task in the same amount of time as if she had not stopped.
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4(-3b-5s) use s=2 and b=3
I have a trouble with this question and I have a maths exam on Sunday on the same lesson. Could anyone please answer this with explanation please asap
The value of p in the given triangle is equal to 99.3°.
What is Law of Cosines?
The Law of Cosines, also known as the cosine formula or cosine rule, is a relation in trigonometry that links the lengths of a triangle's sides to the cosine of one of its angles.When the lengths of two sides and the measurement of the included angle are known (SAS) or the lengths of all three sides (SSS), the remaining pieces of an oblique (non-right) triangle can be found using the Law of Cosines.The formula of the Law of Cosines is given as, [tex]c^{2} =a^{2} +b^{2} -2abcosC[/tex], where, [tex]a,b,[/tex] and [tex]c[/tex] are the side lengths of the triangle and [tex]C[/tex] is the angle between [tex]a[/tex] and [tex]b[/tex].In the given question, the side lengths of the triangle are as follows,
[tex]a=3.6 cm,[/tex] [tex]b=2.8cm,[/tex] and [tex]c=5.3cm[/tex]
Here, the angle between a and b, [tex]\angle C=p[/tex]
We know that the angle p between the two sides of lengths a and b can be found using the Law of Cosines Formula, given as,
[tex]c^{2} =a^{2} +b^{2} -2abcosC[/tex]
Substituting the above values, we get
[tex]5.3^{2} =3.6^{2} +2.8^{2} -2 \times 3.6 \times 2.8 \times cos p[/tex]
Simplifying, we get
[tex]28.09=12.96+7.84-20.16cosp\\\implies 28.09=20.8-20.16cosp\\\implies 7.29=-20.16 cosp[/tex]
Rearranging in terms of p, we get
[tex]cosp=-\frac{7.29}{20.16} \\\implies p=cos^{-1} (-0.3616)\\\implies p=99.3\textdegree[/tex]
Therefore, the value of p is equal to 99.3°.
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help please ][][[][][][[][][][][][][[][][[]
Answer:
3.730 = b
Step-by-step explanation:
Givens
<B = 25 degrees
b = ?
a: = 8 meters
Formula
Tan(B) = opposite / Adjacent
Solution
Solve for b (opposite)
Put in values for the letters.
Tan(25) = b /8
0.4663 = b / 8 multiply both sides by 8
0.4663*8 = 8*b/8 Combine
3.730 = b
PLS HELP EITHER WILL RATE BRAINLY OR GIVE A THANKS AND RATE 5 STARS!!
1) 5 hours A. 96 hours
_____ 2) 72 hours B. 12 minutes
_____ 3) 360 seconds C. 1 hour
_____ 4) 540 minutes D. 3 days
_____ 5) 4 days E. 144 hours
_____ 6) 60 minutes F. 210 minutes
_____ 7) 720 seconds G. 6 minutes
_____ 8) 6 days H. 300 minutes
_____ 9) 3 ½ hours I. 180 seconds
_____ 10) 3 minutes J. 9 hours
Directions: Find the equivalent times.
11) 7 hours = _______ minutes
12) 480 seconds = _______ minutes
13) 120 hours = _______ days
14) 180 minutes = _______ hours
15) 11 minutes = _______ seconds
Student Name:
Converting Measures of Time
Directions: Match the times in the right column with the times in the right column that are equivalent.
Place the letter of the matching time on the line.
_____ 1) 5 h
Answer:
Match
1) 5 hours = H. 300 minutes
2) 72 hours = D. 3 days
3) 360 seconds = G. 6 minutes
4) 540 minutes = J. 9 hours
5) 4 days = A. 96 hours
6) 60 minutes = C. 1 hour
7) 720 seconds = 12 minutes
8) 6 days = E. 144 hours
9) 3 1/2 hours = F. 210 minutes
10) 3 minutes = I. 180 seconds
Equivalent times:
11) 7 hours = 420 minutes
12) 480 = 6 minutes
13) 120 hours = 5 days
14) 180 minutes = 3 hours
15) 11 minutes = 660 seconds
select the correct answer. rounded to the nearest whole number, approximately how many inches is 8.39 kilometers? a. 21,311 inches b. 33,018 inches c. 213,106 inches d. 330,180 inches
As we know 1 kilometer = 39370.079 inches
and, 8.39 kilometer = 330,315 inches.
Kilometers: - It is a unit of length in the international system of units (SI) equal to one thousand meters. It is now the measurement unit used for expressing distances between geographical places on land in most of the world.
Inches: - It is a unit of length in the British imperial and united states customary system of measurement. It is equal 1/36 yard or 1/12 of a foot.
To convert a kilometer measurement to an inch measurement, multiply the length by the conversion ratio.
Since 01 kilometer = 39,370.07874 inches,
We can use this simple formula to convert:
inches = kilometers × 39,370.079
Now, according to the question:
inches = 8.39 × 39370.079
inches = 33.315
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Joseph is going to invest $890 and leave it in an account for 15 years. Assuming the interest is compounded annually, what interest rate, to the nearest tenth of a percent, would be required in order for Joseph to end up with $1,710?
The interest rate in tenth of percentage that would be required in order for Joseph to end up with $1.710 is 4.4%.
What is interest rate?The interest rate is the amount a lender charges a borrower and is a percentage of the principal
To calculate the interest rate that would be required, we use the formula below.
Formula:
A = P(1+R)ⁿ.......... Equation 1Where:
A = AmountR = Interest raten = Total number of yearsP = Principle.From the question,
Given:
P = $890A = $1710n = 15 yearsSubstitute these values into equation 1 and solve for R
1710 = 890(1+R)¹⁵(1+R)¹⁵ = 1710/890(1+R) = [tex]\sqrt[15]{1.921}[/tex]1+R = 1.044R = 1.044-1R = 0.044R = 4.4%Hence, the interest rate is 4.4%.
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Write the shaded region
of the model as a percent.
The perimeter of a triangle is 72 cm and its sides are in the ratio
of 5:6:7 find the area of the triangle (please send how u got it in a picture thank u)
Answer:
235.15 sq.cm
Step-by-step explanation:
Perimeter:Perimeter of a triangle is sum of all three sides.
Ratio of sides = 5 : 6 : 7
Sides are 5x , 6x , 7x
Perimeter = 72 cm
5x + 6x + 7x = 72
Combine like terms.
18x = 72
Divide both sides by 18,
x = 72÷ 18
x = 4
5x = 5*4 = 20 cm
6x = 6*4 = 24 cm
7x = 7*4 = 28 cm
Sides: 20cm , 24 cm , 28 cm
So, it is a scalene triangle.
To find the area of scalene triangle use Heron's formula.
a = 20 cm ; b = 24 cm and c = 28 cm
[tex]\sf s = \dfrac{a + b+ c}{2} \ where \ s \ is \ the \ semi \ perimeter.[/tex]
[tex]\sf =\dfrac{72}{2}\\\\\\ = 36 \ cm[/tex]
s - a = 36 - 20 = 16 cm
s -b = 36 - 24 = 12 cm
s - c = 36 - 28 = 8 cm
[tex]\sf \boxed{Area = \sqrt{s(s-a)(s-b)(s-c)}}[/tex]
[tex]\sf =\sqrt{36*16*12*8}\\\\ = 6*4*4\sqrt{6}\\\\= 96 *2.45\\\\=235.15 \ cm^2[/tex]
number two
what is the length of PR?
The length of side PR will be 40.
What is mean by Triangle?
A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.
Given that;
In the isosceles triangle,
Two sides are,
⇒ PR = 5n and QR = (32 + n)
Now,
Since, The triangle is an isosceles triangle.
So, Two sides are equal.
We formulate;
5n = 32 + n
5n - n = 32
4n = 32
n = 8
Thus, The length of side PR = 5n
= 5 x 8
= 40
Therefore, The length of side PR will be 40.
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What is the equation of this line in slope-intercept form?
y = -3x +2
The general equation for a linear line is y = mx + b
Where:
m = the slope of the lineb = the y-interceptTo find the slope of a line we can use the formula [tex]\frac{rise}{run}[/tex]
Rise over run can be found suing two different points on the line.
in this case: (-1,5) and (1,-1)
The rise is the difference in y values: [tex]y_2 -y_1[/tex]
rise = (-1) - 5
rise = -6
run = [tex]x_2 - x_1[/tex]
run = 1 - (-1)
run = 2
rise/run = [tex]\frac{-6}{2}[/tex]
rise/ run = -3
We now have y = -3x + b
To find b we just look at the graph and locate a what point x = 0
this occurs at (0,2)b = 2A box of chocolates contain 10 milk chocates and 12 plain chocolates. Two chocolates are taken at random without replacement.
Work out the probability that :
a) both chocolates will be milk chocolates
b) at least one chocolate will be a milk chocolate
Answer:
B
explanation:
there's a high chance you might as well get at least one milk chocolate because there's plenty..
what two numbers multiply to -36 and add up to -6
The two numbers that we requires are; y=−3+3√5 or y=−3−3√5
What are the two numbers?We know that in this question, we are required to obtain the two numbers that multiply to -36 and add up to -6. Now we have to write the problem into a system of simultaneous equations.
Thus;
Let the numbers by x and y
x + y = -6 ---- (1)
xy = -36 ------ (2)
x = -36/y ------ (3)
If we substitute (3) into (1)
-36/y + y = -6
-36 + y^2/y = -6
Multiply through by y
-36 + y^2 = -6y
Forming a proper quadratic;
y^2 + 6y - 36 = 0
Solving the quadratic for y
y=−3+3√5 or y=−3−3√5
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Show 531x47 please thank you
Answer: 24.957
Step-by-step explanation: Calculator
you are going to the movie theater with your grandparents and your 5 year old brother. if you spent an additional $20 on soda and popcorn, what is the total cost of your trip to the movie theater? responses $23.50 $23.50 $7.25 $7.25 $20.00 $20.00 $43.50
The total cost of your trip to the movie theater is $43.50.
The total cost will be the sum of money spent on ticket and soda and popcorn.
Ticket cost for or cost price of Ticket for:
5 years old brother = $4.25
Grandparents = $6.00 × 2 = $ 12.00
For self= $7.25
Total cost of tickets = $4.25 + $ 12.00 + $ 7.25
= $ 23.50
Total Money spent = Cost of ticket + cost of soda and popcorn
= $ 23.50 + $20
= $ 43.50
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Translate this sentence into an equation.
The product of 6 and Victor's score is 102.
Use the variable v to represent Victor's score.
Answer:
6*v=102
Step-by-step explanation:
at wet pets, a starter aquarium kit costs $15 plus 60 cents per fish. at gills and frills, the same kit costs $13 plus 80 cents per fish
a. state the two equations for this system.
b. solve the system.
c. for what number of fish is the cost the same?
d. what is this cost?
The two equations for this system are C = 0.60f + 15 and C = 0.80f + 13.
The number of fish for which the cost is the same is 10 fishes.
The cost of this fish is equal to $21.
How to write the two equations for this system?In order to write a system of linear equations to model and describe this situation, we would assign variables to the number of fish and the cost of fish respectively, and then translate the word problem into algebraic equation as follows:
Let the variable f represent the number of fish.Let the variable C represent the cost of fish.Note: 1 dollar is equal to 100 cents.
Since the starter aquarium kit costs $15 plus 60 cents per fish at wet pets, we have:
C = 0.60f + 15 ........equation 1.
Since the starter aquarium kit costs $13 plus 80 cents per fish at gills and frills, we have:
C = 0.80f + 13 ........equation 2.
Next, we would solve the system of equations as follows:
0.80f + 13 = 0.60f + 15
0.80f -0.60f = 15 - 13
0.20f = 2
Number of fish, f = 2/0.20
Number of fish, f = 10 fishes.
What is this cost?From equation 1, we have:
Cost of fish, C = 0.60f + 15
Cost of fish, C = 0.60(10) + 15
Cost of fish, C = 6 + 15
Cost of fish, C = 21 dollars.
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A. yes because their ratios are the same B. yes because their ratios are the same C. no because their ratios are the same D. no because their ratios are the same
Answer:
No because their ratios are not the same
Step-by-step explanation:
The scalar from 5 to 10 is 2 but from 3 to 4, its 4/3.
Solve the system of linear equations by graphing.
X = -3
y = -8
Answer:
X = -3, y = -8
Please see the link to view the Graph:
Convert the inequality to interval notation: a > 10
Convert the inequality to interval notation: a > 10:
(10, ∞)
answer this attachment pls its upside down btw
The strategies that would eliminate a variable to help solve the system of equations are
B. Multiply the first equation by -2 and add it to the second equation
C. Multiply the first equation by 1/3 and add it to the second equation
D. Multiply the second equation by 3 and add it to the first equation
Determining strategies that would help solve system of equations by eliminationFrom the question we are to determine the strategies that would eliminate a variable to help solve the system of equations.
The given system of equations is
12x + 5y = 7
-4x + 10y = -7
To eliminate y,
Multiply the first equation by -2 and add it to the second equation
-2 × [12x + 5y = 7]
-24x - 10y = -14
Now add to the second equation
-24x - 10y = -14
+ (-4x + 10y = -7
-----------------------------
-28x = -21
To eliminate x
Multiply the first equation by 1/3 and add it to the second equation
1/3 × [12x + 5y = 7
4x + 5/3y = 7/3
Now, add it to the second equation
4x + 5/3y = 7/3
+ (-4x + 10y = -7
------------------------------
5/3y + 10y = 7/3 + (-7)
Also, to eliminate x
Multiply the second equation by 3 and add it to the first equation
3 × [-4x + 10y = -7
-12x + 30y = -21
Now, add to the first equation
-12x + 30y = -21
+ (12x + 5y = 7
----------------------------
35y = -14
Hence, the required strategies are the ones explained above.
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What is value of x?
A. 10
B. 12
C. 3
D. 9
Answer: 10
Step-by-step explanation:
Set the equal angles as x, as shown below.
Then, [tex]sin(x)=\frac{x+4}{8}[/tex] and [tex]sin(x)=\frac{2x+1}{12}[/tex]. Set them equal to each other and solve for x:
[tex]\frac{x+4}{8} =\frac{2x+1}{12} \\ \\12(x+4)=8(2x+1)\\12x+48=16x+8\\48-8=16x-12x\\4x=40\\x=10[/tex]
This is assuming those two triangles are right triangles. I'm actually not sure if they're right triangles.
The set of data in the table below represents a linear function.
X
-4
-2
0
2
4
y
2
2.5
3
3.5
4
Which is an equation for this function?
Answer:
It's D.
Step-by-step explanation:
I know I can't see that option, but it's D. If you use A for the first one, you get 4(-4) which is -16 and you add 3 to that, it's -12, so that's not 2 so it can't be A. If you use B for the first one, you get 2(-4) which is -8, and if you add 3, you get -5, not 2, so it can't be that either. If you use C, you get 0.5(-4) which is -2, and if you add 3 to that, you just get 1, so it can't be C either. I assume there is fourth option, so it's D.
given a vector/array with values 5, 10, 15, 20, 25, what are the fewest number of swaps needed to reverse the list? group of answer choices 2 3 4 5
The minimum number of swaps required to flip the list is 2.
Array : Generally, in the field of applied sciences, knowledge structures called arrays and typically regarded as just arrays, each containing at least one array-index award or key. Arrays are stored so that formulas can use each component's index tuple to determine the placement of that component within the array.
Given an array with values 5, 10, 15, 20,25
swap reverses the array:
25, 10, 15, 20, 5
25, 20, 15, 10, 5
So, for reversing the number of swaps required list is 2 ..
This may be the smallest variation possible.
Hence, the minimum exchange required to achieve list reversal is two.
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A biased dice is rolled and the results are recorded in a table. The dice is rolled once more. a) Use the table to estimate the probability that a 3 will be rolled. b) If the dice is rolled another 500 times, how many sixes would you expect to roll? Score 1 2 3 4 5 6 Frequency 12 35 11 23 7 12
The probability that a 3 will be rolled would be 0.125 and the expected number of 6's roll would be 68.
What is probability?
Probability is defined as the possibility of an event being equal to the ratio of the number of favorable outcomes and the total number of outcomes.
The events' estimated probabilities are as follows, according to the exponential probability theory:
P(3) = 0. 125
P(6 in 500 rolls) = 68 rolls
Number of times event occurs / number of trials
A number of attempts = sum of frequency:
(12+35+11+23+7+12) = 88
So the probability that a 3 will be rolled as
⇒ number of 3's / number of attempts
⇒ 11/88 = 0.125
The number of 6's probable in 500 rolls
⇒ (12 /88) × 500
⇒ 68.18 = 68
Therefore, the expected number of 6's roll would be 68.
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The area a person can paint varies directly with the amount of time he works. One morning, he painted 200 ft2 between 8:00 a.m. and 1:00 p.m. Write a function that represents this relationship.
The function that represents the relationship is y = 40x
The total area that he painted = 200 square feet
Time is between 8 am and 1 pm
Then the time taken = 5 hours
The relationship is given by the area a person can paint varies directly with the amount of time he works
Here we have to apply the unitary method
The area that he painted in one hour = 200 / 5
= 40 square feet
Consider the y is the total area that he painted and x is the number of hours
Then the function will be
y = 40x
Hence, the function that represents the relationship is y = 40x
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