Answer:
50(1.15)^n-1
Step-by-step explanation:
1. Let's consider the first three terms of g(n) to get a sense of how the function values change as n increases.
2. The first term is Luiza's account balance at the first year of the saving, which is the initial amount she deposited. We know this to be $50.
The second term is Luiza's account balance at the second year. Since the account accumulated 15% each year, it was 1.15 times the balance in the first year, which is $50*1.15=$57.50.
The third term is Luiza's account balance at the third year. Again, this is 1.15 times the balance of the year before that, which is $57.50*1.15=$66.125.
To summarize:
g(1)=50 g(2)=50*1.15 g(3)=50*1.15*1.15
We can see that each term is 1.15 times its preceding term. There is a constant ratio between consecutive terms. Therefore, this is a geometric sequence.
3. We can write an explicit formula for this geometric sequence using the form A*B^n-1. In this form, A, is the first term and B is the common ratio. What are the appropriate values for our case?
The first term is Luiza's initial deposit, which is $50.
The common ratio corresponds to the percentage of accumulated interest. Since that percentage is 15%, the common ratio is 1.15.
4. In conclusion, g is a geometric sequence.
An explicit formula for the sequence is g(n)=50*1.15^n-1
Note that this solution strategy results in this formula; however, an equally correct solution can be written in other equivalent forms as well.
the fraction 14/5 lies between what to whole numbers
Answer:
2 and 3
Step-by-step explanation:
What is the probability of drawing two yellow marbles if the first one is NOT placed back into the bag before the second draw?
Answer:
2/10 on the first draw and 1/9 on the second draw
Step-by-step explanation:
In the first draw, 2 marbles are yellow out of 10, but on the second draw, you don't replace a yellow marble leaving 1 yellow marble out of 9 total marbles in the bag.
how many dose 35 get to 56?
Help plz this is my last question of my quiz anybody know the answer don't send file plz ? Question 24
Answer:
4 units count the boxes from a to b and that's 4
If the angle measure of the section for giraffes is 72∘, how many students said giraffes were their favorite zoo animal?
Answer:
12 students
Step-by-step explanation:
Here is the complete question
Alex surveyed 60 students about their favorite zoo animals and made the circle graph of the results shown below. A circle graph titled Favorite Zoo Animals is shown. There are five sections. One section is labeled Bears, one section is labled Lions, one section is labeled Monkeys, one section is labeled Elephants, and one section is labeled Giraffes.
If the angle measure of the section for giraffes is 72∘, how many students said giraffes were their favorite zoo animal?
Number of students that said the giraffe was their favorite zoo animal = (angle measuring the section for giraffes / sum of angles in a circle graph) x number of students surveyed
the sum of angles in a circle = 360 degrees
(72 / 360) x 60 = 12 students
1. If you toss a coin 30 times, you expect the coin lands on the tail _____ times.
Answer:
15 times
Step-by-step explanation:
50% of the time, 50% of 30=15
Answer: 15 times
Step-by-step explanation:
A coin has a 50/50 chance to get either heads or tails. 50% of the time it's heads, 50% is tails. So, if you tossed a coin 30 times, you would expect the coin to land on the tail 15 times because 30 / 2 = 15.
Ignore the top equation
But PLEASE
A study of a local high school tried to determine the mean number of text messages that each student sent per day. The study surveyed a random sample of 70 students in the high school and found a mean of 161 messages sent per day with a standard deviation of 68 messages. Determine a 95% confidence interval for the mean,
Answer:
k
Step-by-step explanation:
If the circle has a diameter of a team meters in a central angle of 210° what is the area of the sector
Answer:
[tex]Area = 45.82m^2[/tex]
Step-by-step explanation:
Given
[tex]d = 10m[/tex] --- diameter
[tex]\theta = 210^\circ[/tex]
Required
Determine the area of the sector
The ares of the sector is calculated as:
[tex]Area = \frac{\theta}{360} * \pi r^2[/tex]
Where
[tex]r = \frac{d}{2}[/tex]
This gives:
[tex]r = \frac{10m}{2} = 5m[/tex]
So, we have:
[tex]Area = \frac{210}{360} * 3.142 * 5^2[/tex]
[tex]Area = \frac{210}{360} * 78.55[/tex]
[tex]Area = \frac{210 * 78.55}{360}[/tex]
[tex]Area = \frac{16495.5}{360}[/tex]
[tex]Area = 45.82m^2[/tex]
If g(x) = 3x2 + 8 were shifted 5 units
to the right and 2 units down, what
would be the new equation, h(x)?
Give explanation
Answer:
g(x) = 3(x - 5)^2 + 6
Step-by-step explanation:
(x - k) moves it to the right
8 - 2 moves it 2 down
Please help me!!!! i cant see files so just tell me!
A flock of sheep has 182 white sheep and 98 spotted sheep. Which proportion can be used to determine p, the percent of the flock that has spots?
Answer:
D) 98/280 = p/100
Step-by-step explanation:
Since p is the missing percentage, it has to be OVER 100, so C is eliminated.
Total:
182 + 98 = 280
Spotted sheep probability:
98/280 = 0.35 or 35%
To check:
[tex]\frac{98}{280} =\frac{p}{100} \\\\280p=9800\\x=35[/tex]
PLEASE HELPPPPPPPPPPPPPPPPPPPP
Answer:
35 cm ^2
Step-by-step explanation:
5x5 = 25
5-3 = 2
5x2 = 10
25+10 = 35cm^2
Answer:
10 x 2 = 20
3 x 5 = 15
_________+
35
In Waxahachie the library is 8 miles due to east of the post office and the zoo is 6 miles due to south of the library.What is the distance from the post office to the zoo? Round to the nearest tenth one decimal place
Answer:
10 miles
Step-by-step explanation:
The Pythagoras theorem : a² + b² = c²
where a = length
b = base
c = hypotenuse
6^2 + 8^2
36 + 64 = 100
square root = 10
What is the exact value of cos 45°? Enter your answer, as a simplified fraction, by filling in the boxes
Answer:
The value of cos 45° is equal to 1/√2
Answer:
Its 1/2
Step-by-step explanation:
I just took the test
Brian and sonya each have a container. They mark their containers to show tenths. Brian and sonya both fill their containers with 0.7 units of juice. However, brian has more juice in him container. Explain how this is possible.
Answer:
Step-by-step explanation:
Brian could have more juice than Sonya in actual sense, This is because the representation used, that is the container has been calibrated to show tenth. This means that decimal values of juice in the container will not show explicit volume beyond tenth. Hence the volume will be rounded.
For instance, if the actual volume of juice Brian has Is 0.74 and that owned by Sonya is 0.69. In actual sense, 0.74 > 0.69 . However, if both pour their juice into the calibrated container, Brian's volume will be rounded to the nearest tenth as 0.7 and Sonya's (0.69) will also be rounded to 0.7.
But in actual sense, Brian has more Juice than Sonya.
Solve for b. b³ = 8 Enter your answer in the box. b =
Answer:
The answer is 2
plz mark me as brainliest.
Rewrite in simplest terms:
10(7g-9h)-4h-8(-h+8g)10(7g−9h)−4h−8(−h+8g)
ASAP
Karen saved Pho 200.00 this week from
her allowance. If this amount is Pho 50.00
more than twice the amount she caved last
Select the correct answer.
William buys two bags of peaches and three bags of apricots for $17. Sylvia buys four bags of peaches and two bags of apricots for $22 from the same store. What is the cost of one bag of peaches?
A.
$3
B.
$4
C.
$5
D.
$7
wer:
B 4
Step-by-step explanation:
Find the product 8/6n-4 • (9n^2-4).
An expression can be written in rational form by writing it as a fraction with a denominator of
Answer:
The correct answer is 1 for the first part, and 12n+8 for the second part.
Step-by-step explanation: I got them wrong for you guys. Edge 2021.
The product of the expression given is 12n + 8.
What are Expressions?Expressions are mathematical statements which consist of two or more terms and terms are connected to each other using mathematical operators like addition, multiplication, subtraction and so on.
The given expression is ([tex]\frac{8}{6n-4}[/tex]) . (9n² - 4)
Multiplying the numerators together,
([tex]\frac{8}{6n-4}[/tex]) . (9n² - 4) = [8 (9n² - 4)] / [6n - 4]
= {8 [ (3n)² - (2)² ] } / {6n - 4}
We have an algebraic identity, a² - b² = (a + b) (a - b)
Using this identity (3n)² - (2)² = (3n + 2) (3n - 2)
And the expression in the denominator, 6n - 4 = 2 (3n - 2)
([tex]\frac{8}{6n-4}[/tex]) . (9n² - 4) = [8 (3n + 2) (3n - 2)] / [2 (3n - 2)]
The expression 3n - 2 gets cancelled as it lies in both numerator and denominator.
([tex]\frac{8}{6n-4}[/tex]) . (9n² - 4) = [8(3n + 2)] / [2]
= 4 (3n + 2)
= 12n + 8
Hence the product is 12n + 8.
Learn more about Expressions here :
https://brainly.com/question/16804733
#SPJ2
2 The points (-15, -3) and (-7, -1) both
lie on the graph of the linear function
y = f(x). What is the rate of change of
f(x) with respect to x?
Answer:
The rate of change of f(x) with respect to x is 1/4
Step-by-step explanation:
What this question simply ask is to find the slope of the line that passes through the two points
to find this, we use the slope equation
we have this as;
m= (y2-y1)/(x2-x1)
(x1,y1) = ((-15,-3)
(x2,y2) = (-7,-1)
m = (-1 + 3)/(-7 + 15) = 2/8 = 1/4
The cost of a pen at the office supply store is $2.65. The school store sells the pen for $3.45. How much does the school store markup the pen?
Enter the correct answer in the box.
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Find the exact value of cos A in simplest radical form.
Answer:
Root7/4
Step-by-step explanation:
Root63=(7x9)^(1/2)=3root7
CosX =adjacent/hypotenuse
Cos A=3root7/12=root7/4
Find the volume of the cylinder below??
Answer:
V≈339.12
Step-by-step explanation:
songs is lorea - secret
https://www.you tube.com/watch?v=f2bsbMEucRI
(take out the space btwn you and tube)
Find an exponential equation that passes through the points (0, 4) and (2, 9).
Given:
An exponential equation passes through the points (0,4) and (2,9).
To find:
Exponential equation that passes through the given points.
Solution:
Let the required exponential function is:
[tex]y=ab^x[/tex] ...(i)
The function passes through the points (0,4) and (2,9). It means the above equation must be true for these points.
[tex]4=ab^0[/tex]
[tex]4=a(1)[/tex]
[tex]4=a[/tex]
And,
[tex]9=ab^2[/tex]
Substituting [tex]a=4[/tex], we get
[tex]9=(4)b^2[/tex]
[tex]\dfrac{9}{4}=b^2[/tex]
[tex]\pm \sqrt{\dfrac{9}{4}}=b[/tex]
[tex]\pm \dfrac{3}{2}=b[/tex]
In an exponential function b>0. So, [tex]b=\dfrac{3}{2}[/tex].
Putting [tex]a=4,b=\dfrac{3}{2}[/tex] in (i), we get
[tex]y=4\left(\dfrac{3}{2}\right)^x[/tex]
Therefore, the required exponential function is [tex]y=4\left(\dfrac{3}{2}\right)^x[/tex].
What is the difference of the two expressions shown below?
(3/4x + 2) - (1/4x + 5)
Answer:
-4. (e) (2-7)(5–3)+32. (-5)(2) +9. -10+9. -8710. 913 - 12 - 13. Ex: Evaluate 4x-7 when x=5. 4(5)-7 ... Ex: In the following exercise we show how two linear expressions are ... equivalency of the two expressions you determined to be equivalent above? ... Ex: Determine an expression that is equivalent to 10x+15? lox+1. 5(2X+3).
Step-by-step explanation:
Here is my notes hope it helped
Solve for x and complete the table
Answer:
x = 2
Table:
0,0
3,9
-2,-6
4,12
Step-by-step explanation:
distribute
3(2x+1)=15
6x+3 = 15
subtract 3 from both sides
6x + 3 = 15
6x + 3 - 3 = 15 - 3
simplify
6x= 12
divide both sides by 6
answer= x=2
figure out by using substitution
5x + 2 y = 7
4x + y = 8
Answer:
(3, - 4 )
Step-by-step explanation:
Given the 2 equations
5x + 2y = 7 → (1)
4x + y = 8 → (2)
Rearrange (2) expressing y in terms of x by subtracting 4x from both sides
y = 8 - 4x → (3)
Substitute y = 8 - 4x into (1)
5x + 2(8 - 4x) = 7 ← distribute and simplify left side
5x + 16 - 8x = 7
16 - 3x = 7 ( subtract 16 from both sides )
- 3x = - 9 ( divide both sides by - 3 )
x = 3
Substitute x = 3 into (3) for corresponding value of y
y = 8 - 4(3) = 8 - 12 = - 4
solution is (3, - 4 )
2(x-3)-5 equal to or less than 9
Answer:
x ≤ 10
Step-by-step explanation:
2x-6-5 ≤ 9
2x-11 ≤ 9
2x ≤ 20
x ≤ 10
Question 6 of 10
Which equation matches the graph of the greatest integer function given
below?
Answer:
B. y = [x] + 3
Step-by-step explanation:
The answer to this graph would be
B. y = [x] + 3
This is because the graph is translated up by 3 units. Such that a value of 0 passed into x would give us a y value of 3 on the graph, which is represented as a black dot. For a value of -4 passed as x, the largest integer that is less than -4 would be -4 itself and if we add 3 to it due to following this function, we get a y value of -1 which is what is represented in the graph.