Answer:
A
Step-by-step explanation:
a geometric sequence is where we multiply a factor from element to element.
a1 = $900
a2 = 981 = a1 × f = 900 ×
a3 = 1069.29 = a2 × f = a1 × f × f = s1 × f²
[tex]an = 900 \times {f}^{n - 1} [/tex]
so, now let's try and get f.
remember, 981 = 900 × f
f = 981/900 = 109/100 = 1.09
just to control, we check for s3 :
900 × (1.09)² = 900 × 1.1881 = 1069.29
correct.
so,
a13 = 900 × (1.09)¹² = 2,531.398304
s13 is then the sum of all a1, ..., a13
there is a nice formula for sums of finite sequences
s13 = 900 × (1-f¹³) / (1-f) = 900×(1-(1.09)¹³) / (1-1.09) =
= 900×(1-3.065804612) / (-0.09) =
= 900×(-2.065804612) / (-0.09) = 20,658.04612
.
A Ferris wheel is boarding platform is 2 meters above the ground, has a diameter of 48 meters, and rotates once every 5 minutes. How many minutes of the ride are spent higher than 38 meters above the ground
Answer:
Step-by-step explanation:
I discounted the 2-m ramp. If we are supposed to be looking for the length of time the ride is above 38 m from the ground, that translates to 36 m from the very bottom of the circle that is the Ferris wheel (where the wheel would meet the "ground"). I first found the circumference of the circle:
C = 48(3.1415) so
C = 150.792 m
I enclosed this circle (the Ferris wheel is a circle) in a square and then split the square in 4 parts. Each square has a quarter of the circle in it. If you divide the circumference by 4, that means that the arc length of each quarter circle is a length of 37.698 m. But that doesn't put us 36 m above the ground, that only puts us 24 m above the ground (remember the diameter of the circle is 48, so half of that is 24, the side length of each of the 4 squares). What that means to us (so far, and we are not at the answer yet) is that when the height off the ground is 24 m, a car that starts at the bottom of the ride has traveled 37.698 m around the circle. Traveling in an arc around the outside of the circle is NOT the same thing as a height off the ground. Going around a circle takes longer because of the curve. In other words, if the car has traveled 37.698 m around the outside of the circle, it is NOT 37.698 m above the ground...it's only 24 m above the ground. Hence, the reason I enclosed the circle in a square so we have both the circle's curve {arc length} and height above the ground {side of the square}). As the car travels farther along the outside of the circle it gets higher off the ground. If one quarter of the circle is 24 m above the ground, we need to figure out how much farther around the circle we need to go so we are 36 m above the ground. The height difference is 36 - 24 = 12m. we need now to find how long the arc length of the circle is that translates to another 12 m (the difference between the 24 we found and the 36 total). Using right triangle trig I found that arc length to be 12.566. The total arc length on the circle that translates to 36 m above the ground is 50.26437 m.
Going back to the beginning of the problem, the circumference of the circle is 150.792, and it makes one complete revolution in 5 minutes. That means that a car will travel 30.1584 m in 1 minute. Since this is the case, we can use proportions to solve for how long it takes to get 36 m above the ground:
[tex]\frac{m}{min}:\frac{30.1584m}{1min}=\frac{50.26437m}{xmin}[/tex] and cross multiply:
30.1584x = 50.26437 so
x = 1.6667 minutes, the time it takes to reach a height of 36 m. BUT this is not what the question is asking. The question is asking how long it's HIGHER than that 36 m. Let's think.
The car starts at the bottom of the ride, gets to a height of 36 m, keeps going around the circle to its max height of 48 m, then eventually comes back down and keeps going til it's back on the ground. That means that there is a portion at the top of the wheel that is above 36 m. If it goes 50.2647 m around the circle til it's at 36 m, then when it passes the max height and drops back to 36 m, it's 50.2647 m around the other side of the circle. We just found that to travel that 50.2647 m, it took the car 1.6667 minutes. We travel this distance twice (once meeting the height going up and then again coming down) so that takes up 3.3334 minutes.
5 minutes - 3.3334 minutes leaves us off 36 m above the ground for 1.6664213 minutes.
Please help its due in 30 minutes will mark braniliest
Answer:
I think it is segment...........
Write the equation of the line that passes through the points (4,5) and (4,-6).
Put your answer in fully reduced point-slope form, unless it is a vertical or horizontal line.
Answer:
x=4
Step-by-step explanation:
First find the slope
m = ( y2-y1)/(x2-x1)
= ( -6-5)/(4-4)
= -11/0
This means the slope is undefined
Then means it is a vertical line
Vertical lines are in the form
x = constant
The constant in this case is the x value of the points
x=4
The point (-3,-1) is the midpoint of (x,y) and (5,4). Find the point (x,y).
Answer:
(-11, -6)
Step-by-step explanation:
Find the distance between the midpoint, (-3, -1) and (5, 4). This can be calculated by finding the difference between the x coordinates and y coordinates.
-3 - 5 = -8 (distance between x coordinates)
-1 - 4 = -5 (distance between y coordinates)
Find the point (x, y) by subtracting 8 from the midpoint's x value, and then subtracting 5 from the midpoint's y value.
-3 - 8 = -11
-1 - 5 = -6
So, the point (x, y) is (-11, -6)
solve 6x + 3 < x < 3x + 9 for integers values of x
Answer:
-9/2 < x < -3/5
Step-by-step explanation:
So first, we take the left part of the inequality to solve and ignore the right part for now, which leaves us 6x + 3 < x.
1. Subtract 3 from both sides:
6x < x - 3
2. subtract x from both sides:
5x < -3
3. divide 5 from both sides:
x < -3/5
Then, we do the same thing as part 1, but this time with x < 3x + 9.
1. Subtract 9 from both sides:
x - 9 < 3x
2. subtract x from both sides:
-9 < 2x
3. divide both sides by 2:
-9/2 < x.
Notice how we have a value that x is less than and a value that x is greater than. So now, all we have to do is to put the two inequalities together, leaving only one x in the middle. Hence, -9/2 < x < -3/5.
I hope this helped! :D
[tex]\\ \sf\longmapsto 6x + 3 < x < 3x + 9 \\ \\ \sf\longmapsto 6x - 3x < x < 9 - 3 \\ \\ \sf\longmapsto 3x < x < 6 \\ \\ \sf\longmapsto x < \frac{x}{3} < 2[/tex]
Help anyone can help me do the question,I will mark brainlest.
Answer:
<ADC=90
therefore AC= 20 using Pytagoras
BAC is a right angle triangle because it belongs to the Pytagoras theorem:25,20,15 i.e 25²=15²+20²
3) I DON'T THINK PQR IS A RIGHT ANGLE TRIANGLE because it doesn't belong to the Pytagoras triple.
An average of 20 apples were sold from Monday to Friday. After the sales on Saturday and Sunday, the average apples sold per day increased to 33. How many apples were sold on Saturday and Sunday?
Theodore recently hired a contractor to do some necessary work. On the final bill, Theodore was charged a total of $715. $315 was listed for parts and the rest for labor. If the hourly rate for labor was $50, how many hours of labor was needed to complete the job?
Answer:
Hours of labor needed = 8 hour
Step-by-step explanation:
Given:
Amount total charged = $715
Listed amount = $315
Hourly rate for labor = $50
Find:
Hours of labor needed
Computation:
Total amount of labour = Amount total charged - Listed amount
Total amount of labour = 715 - 315
Total amount of labour = $400
Hours of labor needed = Total amount of labour / Hourly rate for labor
Hours of labor needed = 400 / 50
Hours of labor needed = 8 hour
A deposited 7500 Dollars in a bank and received interest of 900 Dollars after one year. B received interest of 1440 Dollars after one year at the same rate. How much did B deposit in the bank?
Answer:
If the rate of interest is 12% than the answer is 12000
Step-by-step explanation:
If you like my answer than please mark me brainliest thanks
Express the value of the following scientific notation of the normal in general number system
a). 2.7 X10 cube
Answer:
2.7*10³=2700
note if power positive you add '0s' to the back eg 10³=1000 if the power is negative e.g10^-3 add to the front and a decimal e.g 0.001
[tex]\\ \sf \longmapsto 2.7\times 10^3[/tex]
[tex]\\ \sf \longmapsto 27\times 10^{-1}\times 10^3[/tex]
[tex]\\ \sf \longmapsto 27\times 10^{-1+3}[/tex]
[tex]\\ \sf \longmapsto 27\times 10^2[/tex]
[tex]\\ \sf \longmapsto 27\time 100[/tex]
[tex]\\ \sf \longmapsto 2700[/tex]
Simplifying the equation below! Please help.
Answer:
that would be -11
Step-by-step explanation:
it is asking for the absolute value of -7-4 however absolute value is always positive once you solve that you have a negative symbol on the outside that turns ur answer negative
Answer:
- 3
Step-by-step explanation:
- | -7+4|
Determine inside the absolute value first
-7+4 = -3
Replace inside the absolute value
- |-3|
The absolute value means take the non negative value
|-3| =3
- 3
Help anyone can help me do this question,I will mark brainlest.
Answer:
10. x is 15; y is \sqrt104. 11. \sqrt5
Step-by-step explanation:
for 10:
first we find the face on the left side; which according to the pythagorean theorem x is 144 + 81 =225 = x = 15. and y is 11^2 + y^2 = 225 = 225 - 121 = y^2 = y = the square root of 104.
for 11:
144 + y^2 = 169 = y^2 = 25 = y = 5. because the two sides are equivalent, the base is also 5 for the left part of the triangle. therefore, 5^2 + 5^2 = x^2 which means x is the square root of 5.
A piece of fabric 20m long sew 4/5 of that cloth, the rest of the fabric is sewn for each bag 2/3m, how many bags can be sewn in all?
Answer: 16 bags
Step-by-step explanation:
(20) (4/5) = 16
(16) (3) / 2 = 24
Need help asap... thanks!
Answer:
90
Step-by-step explanation:
We know that area of ∆BCD = half of the area of rectangle BEFD, since any triangle drawn from taking a side and base and a point on the opposite side as the 3rd vertex has the half area of the rectangle
so, area of ∆BCD = 15×12/2 = 90 (since two legs of the right triangle are 15 and 12)
since area ∆BCD is half the area rectangle BEFD and sum of the area of ∆BEC and ∆CFD will be the rest of the area of rectangle BEFD, which is 90
PLEASE HELP WITH BOTH SEPRATE QUESTIONS
1 Your mom asks you to take the family car to the gas station and put no more than 8 gallons of gas in it. Write an inequality for this scenario.
2Translate this statement into an inequality.
A number less than 5 is greater than 7
Answer:
(1) question no.1
x<=8
(2) question no.2
5<x<7
Answer:
1. 8≥g
2. A-5≥7
Step-by-step explanation:
“Determine which of the following lines has the larger y-intercept, and by how much. “
The line that passes through (3, 8) and (-3, 4)
The line that passes through
(2, -5) and is perpendicular to
y=1/3x-2
Answer:
The first line:
y₁ = (2/3)*x + 6
Has the larger y-intercept, by 5 units.
Step-by-step explanation:
Here we need to find the equation for each line.
First, some theory.
A linear relationship can be written as:
y = a*x + b
where a is the slope and y is the y-intercept.
We know that if the line passes through the points (x₁, y₁) and (x₂, y₂), then we can write the slope as:
a = (y₂ - y₁)/(x₂ -x₁)
And, if a line is:
y = a*x + b
a perpendicular line to that one must have a slope equal to:
-(1/a).
Now we can answer this question.
We know that the first line, let's call it y₁, passes through the points (3, 8) and (-3, 4), then its slope will be:
a = (8 - 4)/(3 - (-3)) = 4/6 = 2/3
then the line is something like:
y₁ = (2/3)*x + b
to find the value of b, we can use the fact that we know that the line passes through the point (3, 8)
this means that when x = 3, we must have y₁ = 8
replacing these in the above equation, we get:
8 = (2/3)*3 + b
8 = 2 + b
8 - 2 = b = 6
then the equation for this line is:
y₁ = (2/3)*x + 6
Now let's find the equation for the other line, that we will call y₂.
We know that this line is perpendicular to:
y = (1/3)*x - 2
The slope of that line is:
a = (1/3)
then the slope of a line perpendicular to that one will be:
slope = -(1/a) = -(1/1/3) = -3
slope = -3
then we have:
y₂ = -3*x + b
to find the value of b, we can use the fact that our line passes through the point (2, -5)
This means that when x = 2, we must have y₂ = -5
then:
-5 = -3*2 + b
-5 = -6 + b
-5 + 6 = b = 1
b = 1
then this equation is:
y₂ = -3*x + 1
Now we know both equations:
y₁ = (2/3)*x + 6
y₂ = -3*x + 1
Which equation does have the larger y-intercept?
We can see that the first line has an y-intercept of 6, and the second line has an y-intercept of 1, then the first line has the larger y-intercept, and is larger by 5 units.
Determine if the sequence below is arithmetic or geometric and determine the common difference / ratio in simplest form. 11, 7, 3, ... This is_ sequence and the _ is equal to_
the sequence is arithmetic because it's incrementing by a constant ratio of -4
The sequence 11,7,3,... is arithmetic because there is a constant increase of (-4)
Must click thanks and mark brainliest
) If a 480 pupils in a school are boys representing 80% of the school's enrolment . Find the total number of pupils in the school
Answer:
Total student= 600
Step-by-step explanation:
Let x be the number of students
[tex]x \times \frac{80}{100} = 480 \\ = 480 \times \frac{10}{8} \\ x = 600[/tex]
Brainliest please~
Answer:600
Step-by-step explanation:
by taking total number of pupils x
80/100×x=480
48000/80=600
x=600
Will give Brainliest!!
Jocelyn eats 5 gummy worms today. Each day she eats one more than the day before. How many gummy worms in all will she have eaten by the end of Day 32?
Answer:
Jocelyn will have eaten 620 (which is way too much) by the end of day 32.
Step-by-step explanation:
First find out all the numbers that have to be added.
5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35
Then, Add.
5+6+7+8+9+10+11+12+13+14+15+16+17+18+19+20+21+22+23+24+25+26+27+28+29+30+31+32+33+34+35
= 620
Jocelyn ate 620 gummy worms by the end of the 32nd day.
Thank YOu! Please mark me brainliest!
Answer:
656
Step-by-step explanation:
i took the test
The price of an item increased by 25 percent. if the price of the item after the increase is 2.00. What was the original price? (Show your work)
A. 1.50
B. 1.60
C. 1.75
D. 2.50
E. 3.20
Let the original price = x
From X to get the new price you multiply by 1 + the percent of the increase which is 25%
1,25X = 2.00
Divide both sides by 1.25:
X = 1.60
The original price was B. 1.60
Answer:
x=1.60
Step-by-step explanation:
Let x be the original price
We increase by 25%
x+ .25x = new price
1.25x = 200
Divide each side by 1.25
x = 2.00/1.25
x=1.60
Timothy has 72 coins, consisting of quarters, dimes, nickels, and 8 pennies. Samantha comes and takes all of his quarters, takes 3 of his dimes, takes 2 of his nickels, and leaves him with one penny, leaving him with 45 coins. What is the value of quarters that Samantha took?
Can someone explain how to solve this problem?
Answer:
The total value of quarters that Samantha took is $3.75
Step-by-step explanation:
Timothy has 72 coins.
He has:
Q quarters
D dimes
N nickels
8 pennies.
Then:
Q + D + N + 8 = 72
Samantha takes:
3 dimes
2 nickels
Leaves him with one penny, then she takes 7 pennies.
all of the quarters, so she took Q quarters.
So now Timothy has 45 coins.
And for each particular type of coin, Thimothy now has:
D - 3 dimes
0 quarters
1 penny
N - 2 nickels
And we know that he has 45 coins, then:
(N - 2) + 1 + ( D - 3) = 45
Which we can rewrite as:
N + D + 1 - 2 - 3 = 45
N + D - 4 = 45
N + D = 45 + 4 = 49
So we have two equations:
Q + D + N + 8 = 72
N + D = 49
Now we can replace the second equation into the first one:
(N + D) = 49
then:
Q + D + N + 8 = 72
Q + (D + N) + 8 = 72
Q + 49 + 8 = 72
Now we can solve this for Q
Q = 72 - 49 - 8 = 15
So Samantha took 15 quarters.
Each quarter has a value of $0.25
Then Samantha took:
15*$0.25 = $3.75
The total value of quarters that Samantha took is $3.75
What is 12x12 inch Square and 3/4 inch pixels?
A hobby store prices model train track using a proportional relationship between the length of track (in inches) and the cost in dollars.
If 6.4
6
.
4
inches of track costs $16
$
16
, what is the constant of proportionality?
Answer:
If... 6.4 inches : 16 dollars
Then... 32 inches = 80 dollars.
And, 1 inch of track = 80/32 dollars.
80/32 = 2.5.
So, the answer is: 1 inch of track costs 2.5 dollars.
The constant of proportionality is $2,50.
The equation used to represent direct proportionality is: y = kx
Where:
y = dependent variable
x = independent variable
k = constant of proportionality
Here, the dependent variable is the cost of the track. The independent variable is the length of the tracks.
$16 = 6.4k
k = 16 / 6.4 = $2.5
A similar question was answered here: https://brainly.com/question/17033082
will give brainliest!!! pls help with all questions
who can help me with this question?
[tex]\large\mathcal{\red{ \implies \: 2 \: \pi \: {r}^{2} \: + \: 2 \: \pi \: r \: h}}[/tex]
Option ( C ) is the correct answer.
Match each figure with the number of edges it has.
6
12
8
9
5
10
rectangular prism
rectangular pyramid
triangular pyramid
triangular prism
Answer:
Rectangular prism- 12 edges
Rectangular pyramid- 8 edges
Triangular pyramid- 6 edges
Triangular prism- 9 edges
I hope this helps!
Need help with this, don't understand it. we weren't taught how to do this
9514 1404 393
Answer:
A, C, D, E
Step-by-step explanation:
Any relation that is different from a straight line with a defined constant slope will be a relation that is either or both of ...
not a functionnot linear__
a) degree 3, not linear
b) a linear function
c) a vertical line with undefined slope, not a function
d) a curve opening downward, not linear
e) a line with a bend in the middle, not linear
f) a linear function
A county fair sold 1,750 tickets, each of which was either an adult or children's ticket, and earned a total of \$27,000. The fair earned 25\% more from adult tickets than from children's tickets, but sold 25\% fewer adult tickets than children's tickets. How much did a children's ticket cost
Answer:
Step-by-step explanation:
Let the number children tickets = c
Number of adult tickets = 75% of c = 0.75c
c + 0.75c = 1750
1.75c = 1750
c = 1750/1.75 = 1000
Number of children = 1000
Number of adults = 75% of 1000 = 750
Cost of adult ticket = $ x
Cost of child ticket = 75% of x = 0.75x
Cost of 750 adult ticket = 750x
Cost of 1000 children ticket = 1000 * 0.75x = 750x
750x + 750x = 27000
1500x = 27000
x = 27000/1500
x = $ 18
Cost of adult ticket = $ 18
Cost of children ticket = 75% of 18 = 0.75 * 18 = $ 13.5
Cost of children's ticket = $ 13.50
help please area geometry !!
Answer:
37.5 cm^2
Step-by-step explanation:
The area of a parallelogram is
A = bh where b is the base and h is the height
A = 7.5 * 5
A = 37.5 cm^2
Answer:
A = 37.5 cm²
Step-by-step explanation:
The area of a parallelogram is calculated as
A = bh ( b is the base and h the perpendicular height )
Here b = 7.5 and h = 5 , then
A = 7.5 × 5 = 37.5 cm²
A fair spinner has 12 equal sections: 5 red 4 blue and 3 green. its Spun twice what is the probability of getting the same colour twice?
Answer:
25/72
Step-by-step explanation:
P( blue) = blue / total = 4/12 = 1/3
P ( blue, blue) = 1/3 * 1/3 = 1/9
P ( red) = red / total = 5/12
P ( red, red) = 5/12 * 5/12 = 25/144
P ( green) = green /total = 3/12 =1/4
P ( green , green) = 1/4 * 1/4 = 1/16
Add these together to get
P( same colour twice) = 1/9+ 25/144 + 1/16
=16/144 + 25/144 + 9/144
=50/144
=25/72