The equation that represents the formula for the sequence is f(n) = −4(−5)^n−1
What is geometric sequence?A geometric sequence is a sequence of numbers that follows a pattern were the next term is found by multiplying by a constant called the common ratio, r.
The ratio of any term to the one that precedes it should be the same for all terms. If they are all the same, then r, the common difference, is that value
The nth term of a geometric sequence is given as
a(n) = ar^n -1
where a is the first term which is -4
r is the common ratio = 20/-4 = -5
Therefore f(n) = -4(-5)^n -1
Therefore the expression that represents the formula of the sequence is f(n) = -4(-5)^n - 1
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A Fast Food Restaurant is offering 5 different toys in a kid's meal. A simulation was conducted to predict how many kid's meals must be bought in order to get all 5 toys. The results of 30 trials are shown in the stem and leaf plot below. (Each data point represents the number of kid's meals one person had to buy to receive all 5 toys.)
Based on the results of the simulation, what is the total number of people out of 200 who would need to buy less than 10 boxes of cereal to get all 5 toys? Show or Explain or work.
Answer:
Step-by-step explanation:
look for the stem and leafs that are less than 10 and add them all up
5+7+9
At a recent soccer game at Red Bulls stadium, 7500 fans were rooting for the New England Revolution while 17,500 fans were rooting for the New York Red Bulls. What percent of the soccer fans were rooting for the New England Revolution?
Answer:
30%
Step-by-step explanation:
add the number of fans together: 7500+17500 = 25000
write as fraction, fans of New England Revolution over total number: 7500/25000
simplify or use calculator: 3/10 or 0.3
convert fraction or decimal to percentage: 30%
A scientist wanted to measure the constant rate of the current in a particular section of the river. She released a tracker into the river. The tracker sent her back the following information:
After 3.5 seconds since the tracker was released into the river the tracker had traveled 5.5 meters.
After 10.9 seconds since the tracker was released into the river the tracker had traveled 16.5 meters.
What is the constant rate of the current?
Answer:
1.486m/s
Step-by-step explanation:
The rate of change is defined as the change in distance divided by the change in time
Rate = ∆distance/∆time
Distance = 16.5 and 5.5
Time = 10.9 and 3.5
When we put this into the formula above, we have:
Rate of change = 16.5 - 5.5 / 10.9 - 3.5
= 11/7.4
= 1.486m/s
The constant rate of change has been calculated to be equal to 1.486m/s
You can use the fact that the rate of the change of a value when some other independent value changes is the ratio of change in the dependent variable to the change in the independent variable.
The constant rate of the current is given by 1.4865 meters per second.
How to measure the rate of change of something as some other value changes?Suppose that we have to measure the rate of change of y as x changes, then we have:
[tex]Rate = \dfrac{y_2 - y_1}{x_2 - x_1}[/tex]
where we have
[tex]\rm when \: x=x_1, y = y_1\\when\: x = x_2, y= y_2[/tex]
Remember that, we divide by the change in independent variable so that we get some idea of how much the dependent quantity changes as we change the independent quantity by 1 unit.
(5 change per 3 unit can be rewritten as 5/3 change per 1 unit)
How to measure the constant rate of the current for the given situation?The distance traveled by the tracker depends on the time passed.
Let the variable "t" tracks the amount of time passed and let the variable "d" tracks the distance traveled by the tracker, then we have:
[tex]\rm At \: t = t_1 = 3.5, d=d_1 = 5.5 \: m\\At \: t = t_2 = 10.9, d = d_2 = 16.5 \: m[/tex]
Thus, the constant rate of current is obtained by
[tex]Rate = \dfrac{d_2 - d_1}{t_2 - t_1} = \dfrac{16.5 - 5.5}{10.9 - 3.5} = \dfrac{11}{7.4} \\\\Rate \approx 1.4865 \: \text{meters per second}[/tex]
Thus,
The constant rate of the current is given by 1.4865 meters per second.
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7/16+3/8
Simplify or answer in regular fractions or improper fractions
Answer:
hope it helps you
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Answer:
13/16
Step-by-step explanation:
Turn [tex]\frac{7}{16} +\frac{3}{8}[/tex] into [tex]\frac{7}{16} +\frac{6}{16}[/tex]
If both denominators are the same the number it makes it easier to add.
Since 8*2 is 16 you have to do 3*2 in order for 3/8 and 6/16 to be equivalent.
then add the top numbers, not the bottom bc the bottom stays the same.
7+6=13 so the answer is 13/16
hope that helps:)
Out of 4/10, 3/4, 2/5, and 1/3 which fraction is the biggest?
Answer:
3/4
Step-by-step explanation:
3/4 = .75
4/10 = .40
2/5 = .40
1/3 = .33
Answer:
3/4 is greater then 4/10 and 2/5 is greater then 1/3 and that's all I know
Step-by-step explanation:
Are there any vertical, complimentary, or any supplementary angles here ? And label for ex. 1 supplementary
Supplementary: 1 and 2 & 3 and 4
Supplementary angles: A pair of angles whose sum is equal to 180°.
Vertical: 1 and 3 & 2 and 4
Vertical angles: A pair of opposite angles that are made by two intersecting lines.
Complimentary: None
Complimentary angles: A pair of angles whose sum is equal to 90°.
Hope this helps! :D
Daniel has a total collection of 200 marbles. 10% of them are red. How many are red marbles in his collection? What is missing in the problem?
Answer:
40(i think)
Step-by-step explanation:
The store bought a table for $150, and sold it for $240. What percentage was the markup?
Answer:50%
Step-by-step explanation:
Answer:
the bought 65% porcentege
NEED HELP ASAPPP please
Answer:
it might be d I am not shore but I think that one sounds the best branley is making me do this to sigh. up sorry donjot use this
Find the value of x.
a) 21
b) 27
c) 31
d) 34
Answer:
21 is the answer
a question arises how?? right
so, 3x+1
3×21+1
63+1
64
Answer:
a) 21
Step-by-step explanation:
Since, in the figure
64° = (3x+1)° [Vertically Opposite Angles]
=> (3x+1)° = 64°
=> 3x = 64° - 1° = 63°
[tex] => x = \frac{63}{3} [/tex]
=> x = 21 (Ans)
please help me solve this geometry problem:)
Given:
The endpoints of a line segment are (-5,12) and (-5,0).
To find:
The coordinates of a points which divides the line segment in 2:1.
Solution:
Section formula: If a point divides a line segment in m:n.
[tex]Point=\left(\dfrac{mx_2+nx_1}{m+n},\dfrac{my_2+ny_1}{m+n}\right)[/tex]
Let point P divides the given line segment in 2:1. They, by using section formula, we get
[tex]P=\left(\dfrac{2(-5)+1(-5)}{2+1},\dfrac{2(0)+1(12)}{2+1}\right)[/tex]
[tex]P=\left(\dfrac{-10-5}{3},\dfrac{0+12}{3}\right)[/tex]
[tex]P=\left(\dfrac{-15}{3},\dfrac{12}{3}\right)[/tex]
[tex]P=\left(-5,4\right)[/tex]
Therefore, the coordinate of the point that partitions the given segment in the ratio 2:1 are (-5,4).
Sam has saved 1400 cents from selling lemonade how many dollars does Sam have
Answer: $14.
Step-by-step explanation: 100 cents is equal to 1 dollar. 1400 cents divided by 100 cents = 14. Therefore, you have 14 dollars.
[tex] \frac{ \sqrt{40} }{ \sqrt{3} } [/tex]
Answer:
[tex]\frac{ \sqrt{40} }{ \sqrt{3} } =\frac{2\sqrt{30} }{ 3 }[/tex]
Step-by-step explanation:
Given
[tex]\frac{ \sqrt{40} }{ \sqrt{3} }[/tex]
Required
Simplify
[tex]\frac{ \sqrt{40} }{ \sqrt{3} }[/tex]
Rationalize:
[tex]\frac{ \sqrt{40} }{ \sqrt{3} } =\frac{ \sqrt{40} }{ \sqrt{3} }*\frac{ \sqrt{3} }{ \sqrt{3} }[/tex]
[tex]\frac{ \sqrt{40} }{ \sqrt{3} } =\frac{ \sqrt{40*3} }{ \sqrt{3*3} }[/tex]
[tex]\frac{ \sqrt{40} }{ \sqrt{3} } =\frac{ \sqrt{120} }{ \sqrt{9} }[/tex]
[tex]\frac{ \sqrt{40} }{ \sqrt{3} } =\frac{ \sqrt{120} }{ 3 }[/tex]
Expand the numerator
[tex]\frac{ \sqrt{40} }{ \sqrt{3} } =\frac{ \sqrt{4*30} }{ 3 }[/tex]
[tex]\frac{ \sqrt{40} }{ \sqrt{3} } =\frac{ \sqrt{4}*\sqrt{30} }{ 3 }[/tex]
[tex]\frac{ \sqrt{40} }{ \sqrt{3} } =\frac{ 2*\sqrt{30} }{ 3 }[/tex]
[tex]\frac{ \sqrt{40} }{ \sqrt{3} } =\frac{2\sqrt{30} }{ 3 }[/tex]
When 2 times a number is increased by 9, the answer is the same as
when 30 is decreased by the number. Find the number. HELP ME
Answer:
its 7
Step-by-step explanation:
why did u delete my answer if its right?
Your friend says that the solutions to the inequality 7x-20x<52 are x<-4 Solve the inequality correctly. What error did your friend make?
What are the solutions of the inequality?
Answer:
instead of x < -4 it should be x > -4
Step-by-step explanation:
7x - 20x < 52
subtract 20x from 7x which is -13x
now the equation is -13x < 52
divide both sides by -13 but when you divide by a negative you switch the sign so it would x > -4 not x < -4
hope this helps :)
The population of a city decreases by 4.6% per year. If this year's population is
329,000, what will next year's population be, to the nearest individual?
Answer:
Your answer
313866
Mark it as Brainlist answer. Follow me to get more answer
Step-by-step explanation:
Solving
This figure is made up of two rectangular prisms.
12 in.
What is the volume of the figure?
in.
Enter your answer in the box.
2 in.
7 in.
in
21 in.
1
2.
3
4
Answer:
The question is invalid. Please provide a diagram.
what is the meaning of XII in roman numeral
Answer:
its 12 in mathematics....
what fraction of 9 is 3
Answer:
1/3
Step-by-step explanation:
Take the part over the whole
3/9
We can simplify
Divide the top and bottom by 3
1/3
1/3
Step-by-step explanation:
3/9 is 1/3 because dividing both sides by 3 is 1/3
Carlene is selling T-shirts for a fundraiser. The T-shirts cost $20.50 each. To date, she has raised $900. Her goal is to raise more than $10,740. How many more T-shirts, x, does Carlene need to sell to reach her goal?
Select the number line that includes the fewest number of T-shirts Carlene can sell and still meet her goal.
Find the midpoint between each pair of points.
13. (7,-2) (-4,2)
BONUS POINTS IF RIGHT
Enter the correct value in the space provided
Mariah is shopping at the mall for a sweatshirt. She finds a sweatshirt that is marked down 55% off the original price. The original price of the sweatshirt is $78.25. what is the sale price of the sweatshirt
Answer:
$35.21
Step-by-step explanation:
100%:$78.25
45% :$?
100?=78.25×45
?= 78.25×45/100
=$35.21
Answer: $35.21
Step-by-step explanation: 100%:$78.25
45% :$?
100?=78.25×45
?= 78.25×45/100
=$35.21
Given that a linear function goes through the points (3,2) and (5, 6) determine the slope
of the line.
Answer:
2
Step-by-step explanation:
The formula of slope from 2 points is change in y divided by change in x, so you can apply that to this problem.
First, find the change in y between the two points. To do this, do y2 - y1.
y2 = 6 and y1 = 2, so you have 6 - 2 = 4.
Next, find the change in x between the two points. To do this, do x2 - x1.
x2 = 5 and x1 = 3, so you have 5 - 3 = 2.
All you're really doing here is finding the distance between the x values and the y values of the points, if that makes sense.
The last step is to do change in y divided by change in x, so 4 / 2 = 2.
This means that the slope of the line is 2.
Melanie and Mark borrowed $2500 at a simple interest rate of 7% for a period of 3 years. What was the interest?
Answer:
525 $
Step-by-step explanation:
Amount borrowed = $2500
Rate = 7%
Time = 3 years
therefor interest = $2500 X 7/100 X 3
Hope it help You
Which of the following points have a distance of five units between them? Select all that apply 
A.)(-2,5) and (3,7)
B.)(10,5) and (7,9)
C.)(1,10) and (6,5)
D.)(-4,-8) and (-4,-5)
E.)(2,-5) and (6,-8)
Answer:
C. (1, 10) and (6, 5)
Step-by-step explanation:
To find the point with a distance of 5 units.
Let the points be x and y.
x = x1 and x2
y = y1 and y2
x2 - x1 = 5 units
y2 - y1 = 5 units.
A quick look at the options, we can tell that the correct option is C.
From points (1, 10) and (6, 5)
x1 = 1, x2 = 6, y1 = 10 and y2 = 5
Substituting into the equation above, we have;
x2 - x1 = 6 - 1 = 5 units
y2 - y1 = 5 - 10 = -5 units.
Therefore, option C with points (1,10) and (6,5) have a distance of five units between them.
WHAT IS THE PRUDTUCT OF 7\9 AND 6 A. 1 4/9 B. 3 7\9 C. 4 2\3 D. 7 5\7
Answer:
C.
Step-by-step explanation:
Write the ratio as a fraction in lowest terms. Be sure to make necessary conversions:
12 feet to 15 inches
------/---------
Answer:12533
Step-by-step explanation:
BRAILIEST for correct answer!! Pls help
What's the slope of a line that passes through (−12,15) and (0,4)?
Answer:
-11/12
Step-by-step explanation:
slope for points (x1,y1) and (x2,y2)
slope=(y2-y1)/(x2-x1)
(x,y)
(-12,15)
(0,4)
x1=-12
y1=15
x2=0
y2=4
slope=(4-15)/(0-(-12))=-11/(0+12)=-11/12
Answer:
Slope: -11/12x
Step-by-step explanation:
Slope-intercept equation:
y = mx + b
(m = slope)
The formula for slope is below.
m = [tex]\frac{y_{2} - y_{1} }{x_{2} - x_{1} }[/tex]
With your two points, you can accurately determine your slope.
(-12, 15) (0,4)
x1 = -12
y1 = 15
x2 = 0
y2 = 4
Apply this information in the slope formula to get:
[tex]\frac{4 - 15}{0 - -12}[/tex]
Change the 0 - -12 to 0 + 12
[tex]\frac{4 - 15}{0 + 12}[/tex]
4 - 15 = -11
0 + 12 = 12
Place -11 and 12 into a fraction.
[tex]\frac{-11}{12}[/tex] OR -11/12
Add "x" to the end from "mx" within the slope-intercept equation
-11/12x
vending machine dispenses hot chocolate or coffee. Service time is 30 seconds per cup and is constant. Customers arrive at a mean rate of 80 per hour, and this rate is Poisson-distributed. Determine the following: a. The percentage of time the machine is busy b. The average number of customers waiting in line c. The average time customers spend in the system d. The average number in the system
Answer:
0.667 ;
0.667 customers ;
0.0166708 hour ;
1.334 customers
Step-by-step explanation:
Given that:
Service time (μ) = 30 seconds ; 2 customers per minute ; 2 * 60 = 120 customers per hour
Arrival time, λ = 80 customers per hour
a.) percentage of time machine is busy (p) ; Utilization factor :
P = λ/ μ = 80 / 120 = 0.667
b.) average number of customers waiting in line Li = p² / 2(1-p)
= 0.667² / 2(1-0.667) = 0.667 customers
c) Average time customer spend in the system = Li/λ + 1/μ
= (0.667 / 80) + (1 / 120)
0.0083375 + 0.0083333
= 0.0166708 hour
= 0.0166708 * 60 = 1.00025 minutes
D) average number in the system ;
Li + p
= 0.667 + 0.667 = 1.334 customers
-1 subtracted by 2.5
Answer:
-3.5
Step-by-step explanation: