Answer:1200
Step-by-step explanation:
Answer:
[tex]\textsf{Function:} \quad y=120\left(1.016\right)^{4t}[/tex]
The balance of the account after 6 years is $175.64 (nearest cent).
Step-by-step explanation:
To write a function that represents the balance y (in dollars) of the investment account after t years, substitute the given values into the compound interest formula.
[tex]\boxed{\begin{minipage}{8.5 cm}\underline{Compound Interest Formula}\\\\$ A=P\left(1+\frac{r}{n}\right)^{nt}$\\\\where:\\\\ \phantom{ww}$\bullet$ $A =$ final amount \\ \phantom{ww}$\bullet$ $P =$ principal amount \\ \phantom{ww}$\bullet$ $r =$ interest rate (in decimal form) \\ \phantom{ww}$\bullet$ $n =$ number of times interest is applied per year \\ \phantom{ww}$\bullet$ $t =$ time (in years) \\ \end{minipage}}[/tex]
Given values:
A = yP = $120r = 6.4% = 0.064n = 4 (quarterly)t = t yearsSubstitute these values into the formula:
[tex]\implies y=120\left(1+\dfrac{0.064}{4}\right)^{4t}[/tex]
[tex]\implies y=120\left(1+0.016\right)^{4t}[/tex]
[tex]\implies y=120\left(1.016\right)^{4t}[/tex]
To calculate the balance of the account after 6 years, substitute t = 6 into the function:
[tex]\implies y=120\left(1.016\right)^{4 \cdot 6}[/tex]
[tex]\implies y=120\left(1.016\right)^{24}[/tex]
[tex]\implies y=120\left(1.46368961...\right)^{24}[/tex]
[tex]\implies y=175.642753...[/tex]
Therefore, the balance of the account after 6 years is $175.64 (nearest cent).
3
3
4
Possible inputs for the quadratic when the
output is 3 are
(Note: Fill in the least input first)
or
[tex]x {}^{(1)} = - 3 \: \: \: \: \: \: x {}^{(2)} = - 1[/tex]
Find the slope and y-intercept of the line whose equation is y=6x=5
Answer:
the slope is 5 and the y intercept is 5
Step-by-step explanation:
I think that you meant to write y = 6x + 5.
y = mx + b
The number in in the m spot is the slope and the number in the b spot is the y intercept.
Simplify the following fractions.
Please Slove this 2 question
Answer:
b)14/3 or 4 2/3 C) 256/15 or 14 1/15
Step-by-step explanation:
In the second fraction, the "of" means to multiply
Answer:
#b
[tex] \displaystyle{ \pmb{ \pink{3 \frac{1}{5} \times 3 \frac{1}{2} \div 2 \frac{2}{5} }}}[/tex]
[tex]\frak{SOLUTION:}[/tex]
[tex]\displaystyle \frak{Here,}[/tex]
[tex]\displaystyle{3 \frac{1}{5} \times 3 \frac{1}{2} \div 2 \frac{2}{5} }[/tex]
Convert mixed fractions into improper fractions:[tex] = \displaystyle{ \frac{16}{5} \times \frac{7}{2} \div \frac{12}{5} }[/tex]
[tex]=\displaystyle{ \frac{16}{5} \times \frac{7}{2} \times \frac{5}{12} \frak{(Performing division)} }[/tex]
[tex]\displaystyle{ = \frac{ \cancel{16} \: {}^{2} \times 7 \times \cancel5}{ \cancel5 \times \cancel 2 \times 12} }[/tex]
[tex]\displaystyle{ = \frac{8 \times 7}{12} }[/tex]
[tex] =\displaystyle{} \frac{56}{12} [/tex]
[tex]\displaystyle{ = \frac{ \cancel2 \times \cancel2 \times 2 \times 7}{ \cancel2 \times \cancel 2 \times 3} }[/tex]
[tex]\displaystyle{ = \frac{14}{3} \frak {\: or} \: 4 \frac{2}{3} } [/tex]
#c
[tex]\displaystyle{\pmb{ \pink{2 \frac{2}{3} \div \frac{1}{2} \: of \: 3 \frac{1}{5} }}}[/tex]
[tex]\displaystyle{ \frak{SOLUTION:}}[/tex]
[tex]\displaystyle \frak{Here,}[/tex]
[tex] \displaystyle{2 \frac{2}{3} \div \frac{1}{2} \: of \: 3 \frac{1}{5} }[/tex]
[tex]\displaystyle{ = \frac{8}{3} \div \left( \frac{1}{2} \times \frac{16}{5} \right)\frak{(Performing "of")}}[/tex]
[tex] = \displaystyle{ \frac{8}{3} \div \left( \frac{1 \times \cancel{16} \: {}^{8} }{ \cancel2 \times 5} \right) }[/tex]
[tex]\displaystyle{ = \frac{8}{3} \div \frac{8}{5} }[/tex]
[tex]\displaystyle{ = \frac{8}{3} \times \frac{5}{8} \frak{(Performing \: division)} }[/tex]
[tex]\displaystyle{ = \frac{ \cancel8}{3} \times \frac{5}{ \cancel8} }[/tex]
[tex] = \displaystyle{ \frac{5}{3} \frak{ \: or \: }1 \frac{2}{3} }[/tex]
Answered by :
[tex]\frak{\pink{seolleaphrodite}}[/tex]
Solve for x if AB = 5x and BC = 3x + 24.
The value of x according to the given task is; 12.
What is the value of x?It follows from the task content that the value of x is to be determined.
Since, lines AB and BC are both tangent to the circle and they both share a point of intersection; it follows that;
5x = 3x +24
collect like terms2x = 24
divide both sides by 2x = 24/2
x = 12.
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AB = 6cm, AC = 12cm
Calculate the length of CD.
Give your answer to 3 significant figures.
In the given diagram, the length of CD is 12.7 cm
TrigonometryFrom the question, we are to determine the length of CD
First, we will calculate the length of CB
From the Pythagorean theorem,
|CA|² = |CB|² + |BA|²
12² = |CB|² + 6²
144 = |CB|² + 36
|CB|² = 144 - 36
|CB|² = 108
|CB| = √108
|CB| = 6√3 cm
Now, to find CD
Using SOH CAH TOA
sin55° = |CB| / |CD|
sin55° = 6√3 / |CD|
|CD| = 6√3 / sin55°
|CD| = 12.7 cm
Hence, the length of CD is 12.7 cm
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Type 4 points found on the circumference of the following equation. Exact points only, no approximations.
(x-3)^2 +(y+2)^2+49
The points on the circumference are (3, 5), (3, -9), (8, -2 + √24) and (8, -2 - √24))
How to determine the points on the circumference of the circle?The circle equation is given as:
(x-3)^2 +(y+2)^2= 49
Rewrite as:
(y+2)^2= 49 -(x-3)^2
Take the square root of both sides
y+2= ±√[49 -(x-3)^2]
Subtract 2 from both sides
y = -2 ± √[49 -(x-3)^2]
Next, we determine the points
Set x = 3
y = -2 ± √[49 -(3-3)^2]
Evaluate
y = -2 ± 7
Solve
y = 5 and y = -9
So, we have
(x, y) = (3, 5) and (3, -9)
Set x = 8
y = -2 ± √[49 -(8-3)^2]
Evaluate
y = -2 ± √24
Solve
y = -2 - √24 and y = -2 + √24
So, we have
(x, y) = (8, -2 + √24) and (8, -2 - √24)
Hence, the points on the circumference are (3, 5), (3, -9), (8, -2 + √24) and (8, -2 - √24)
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Which point lies on the circle represented by the equation x² + (y-12)² = 25²?
A. (20.-3)
B. (-7,24)
c. (0.13)
D. (-25,-13)
Answer: B
Step-by-step explanation: Trust me bro
what is the measure of the reference angle for a 102 degree angle? A. 78 degrees B. 68 degrees C. 57 degrees D. 12 degrees
Answer:
A. The reference angle measures 78 degrees
Two friends board an airliner just before departure time. There are only 11 seats left, 4 of which are aisle seats. How many ways can the 2 people arrange themselves in available seats so that at least one of them sits on the aisle?
The 2 people can arrange themselves in blank ways?
Using the Fundamental Counting Theorem, it is found that:
The 2 people can arrange themselves in 40 ways.
What is the Fundamental Counting Theorem?It is a theorem that states that if there are n things, each with [tex]n_1, n_2, \cdots, n_n[/tex] ways to be done, each thing independent of the other, the number of ways they can be done is:
[tex]N = n_1 \times n_2 \times \cdots \times n_n[/tex]
With one people in the aisle and one in the normal seats, the parameters are:
n1 = 4, n2 = 7
With both in the aisle, the parameters is:
n1 = 4, n2 = 3
Hence the number of ways is:
N = 4 x 7 + 4 x 3 = 28 + 12 = 40.
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Select all the terms that are like terms
Answer:
-8 x^2
1.25 x^2
1/2 x^2
Step-by-step explanation:
They are like terms because they have the same variable x^2, yx^2 is not the same because it has the variable y
Answer:
the 2nd, 3rd and 4th options (all with x²)
Step-by-step explanation:
"like terms" means the exactly same variable(s) with exactly the same exponents of these variables.
constants in the terms can be different and even have different signs.
5yx² is not "like", because of the additional y variable.
Which of the following expressions would simplify to be the multiplicative identity?
023.32
023.23
021
0 20
NEXT QUESTION
ASK FOR HELP
The expression that would be simplified to be a multiplicative identity is 2^0
How to determine the expression that would be simplified to be a multiplicative identity?The complete question is added as an attachment
Multiplicative identities are represented as:
a * 1 = a
This means that the definition of multiplicative identities is the product of a number and 1
From the list of options, we have
2^0
When the exponent of a non-zero number is 0, the result is 1.
This means that
2^0 = 1
Hence, the expression that would be simplified to be a multiplicative identity is 2^0
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The tables show proportional relationships between x and y. Match each table with its constant of proportionality.
xy
1 10
2 20
3 30
xy
4 20
8 40
12 60
x y
2 15
4 30
6 45
4
12/04
10
xy
14
2 8
3 12
You deposit $4000 each year into an account earning 2% interest compounded annually. How much will you have in the account in 30 years?
The amount that will be in the account after 30 years is $162,272.32.
How much would be in the account after 30 years?When an amount is compounded annually, it means that once a year, the amount deposited and the interest already accrued increases in value. Compound interest leads to a higher value of deposit when compared with simple interest, where only the amount deposited increases in value once a year.
The formula that can be used to determine the future value of the yearly deposit of $4,000 in 30 years is : annuity factor x yearly deposit
Annuity factor = {[(1+r)^n] - 1} / r
Where:
r = interest raten = number of years$4000 x [{(1.02^30) - 1} / 0.02] = $162,272.32
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Which is the only state that uses to calculate its area
Answer:
The answer is circle.
Step-by-step explanation:
For all the rest of the shapes, we use certain base x height formulas. Square uses base x height along with parallelograms and trapezoids. For a triangle, we use [tex]\frac{base x height}{2}[/tex]. Though, for a circle, we use the formula [tex]\pi r^{2}[/tex] where r= radius.
Three brothers, Jarek, Jerzy and Justyn, share a block of chocolate in the ratio of their ages. Jarek gets half of the bar. Jerzy gets 3\5 of the rest. Work out the ratio, in the form Jarek: Jerzy: Justyn, of how the brothers share the bar of chocolate.
Answer:
5:3:2
Step-by-step explanation:
see image
Jarek gets half. Then from the other half, Jerzy gets 3 pieces of 5 and Justyn gets the leftover 2 pieces. But Jarek's piece is all 5 pieces of the first half.
Jarek 5 parts:
Jerzy 3 parts:
Justyn 2 parts
5:3:2
see image
which statement describes the function below
f(x)=x^3-x^2-9x+9
2x3 i think maybe yes
Please help me solve this
If the sample mean is 51,sample size is 21 , sample standard deviation is 15 and confidence level is 95% then the lower bound is 45.35 and upper bound is 56.65.
Given sample mean of 51, sample size of 21, sample standard deviation be 15 and confidence level be 95%.
We are required to find the upper bound and lower bound.
We have to use t test as the sample size is less than 30.
Margin of error is the difference between calculated figures and real figures.
Margin of error= standard deviation* critical value of t
Critical value of t at 0.05 significance level with degree of freedom 20 [21-1] is 1.7247.
Margin of error=1.7247*15/4.5826
(4.5826 is the square root of 21)
=5.6454
Upper bound=51+5.6454
=56.6454
Lower bound=51-5.6454
=45.3546
After rounding off they will be 56.65 and 45.35.
Hence if the sample mean is 51,sample size is 21 , sample standard deviation is 15 and confidence level is 95% then the lower bound is 45.35 and upper bound is 56.65.
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what is the lower quartile in the following distribution 82, 90, 66, 78, 88, 72, 60, 80 A)69 B)78 C)79 D) 85
Answer:
A) 69
Step-by-step explanation:
• First , we put the numbers of the distribution in order:
60 , 66 , 72 , 78 , 80 , 82 , 88 , 90
• Notice that the set has 8 numbers which is an even number.
Then
→ the lower quartile is the mean of the set :
60 , 66 , 72 , 78
Which is the average of the two middle numbers 66 and 72.
Then
[tex]\text{the lower quartile}=\frac{66+72}{2} = 69[/tex]
Calculate the price elasticity of supply for Bobbie's Bakery's banana bread. When the price changes by 29% the quantity supplied changes by 55%. Round your answer to two decimal places.
The price elasticity of demand is 1.90.
What is the price elasticity of demand?Price elasticity of supply measures the responsiveness of quantity supplied to changes in price of the good. It is expected that quantity supplied would be positively related to the price of the good.
Price elasticity of supply = percentage change in quantity supplied / percentage change in price
55% / 29% = 1.90
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Find the equation of a line with a slope of 13/2
that passes through the point (−2, — 10).
Answer: [tex]y=\frac{13}{2} x+3[/tex]
Step-by-step explanation:
Remember the point-slope equation which is [tex]y-y_{1} = m(x-x_{1} )[/tex] where[tex](x_{1} , y_{1} )[/tex] is your point and [tex]m[/tex] is your slope.
Given that we substitute what you have:
[tex]y-(-10) =\frac{13}{2} (x - (-2))[/tex]
Minus and minus give us positive:
[tex]y+10 =\frac{13}{2} (x +2)[/tex]
Multiply slope into the parenthesis:
[tex]y+10= \frac{13}{2}x + \frac{13}{2}*2\\[/tex]
Calculate it:
[tex]y+10= \frac{13}{2}x +13[/tex]
Isolate the [tex]y[/tex] by subtracting 10 from both sides:
[tex]y=\frac{13}{2} x + 13 -10[/tex]
Your final equation is:
[tex]y=\frac{13}{2} x +3[/tex]
Hope this makes sense!
And here's the graph to prove that the line actually goes through the point [tex](-2,-10)[/tex]:
Select the correct locations on the graph.
Select the lines that represent functions.
Answer:
(I've marked the lines considered functions with a check mark)
Step-by-step explanation:
A concert manager counted 525 ticket receipts the day after a concert. The price for a student ticket was $10.50, and the price for an adult ticket was $18.00. The register confirms that $8,325.00 was taken in. How many student tickets and adult tickets were sold?
Answer:
150 student tickets and 375 adult tickets
Step-by-step explanation:
Let x = # of student tickets sold, and y = # of adult tickets sold.
Total of 525 tickets were sold, so the first equation is x + y = 525. The register gained $8325, so 10.50x + 18y = 8235 is the second equation.
x + y = 525
10.50x + 18y = 8325
18x + 18y = 9450
10.50x + 18y = 8325
7.5x = 1125
x = 150
150 + y = 525
y = 375
In the geometric pattern below, n represents the number of blocks in the bottom row of each figure.
n = 1
n=2
Write a function that models the total number of blocks in terms of n.
OA f(1) = 2; f(n) = f(n-1) + 2n; for n ≥ 2
OB. f(1) = 1; f(n) = f(n-1) + 2n; for n ≥ 2
Oc f(1) = 1; f(n) = f(n-1) + n; for n ≥ 2
OD. f(1) = 2; f(n) = f(n-1) + 4n; for n ≥ 2
n=3
∫[tex]\frac{xdx}{(x^{2}+4)^{3} }[/tex]
Substitute [tex]u=x^2+4[/tex] and [tex]du=2x\,dx[/tex]. Then the integral transforms to
[tex]\displaystyle \int \frac{x\,dx}{(x^2+4)^3} = \frac12 \int \frac{du}{u^3}[/tex]
Apply the power rule.
[tex]\displaystyle \int \frac{du}{u^3} = -\dfrac1{2u^2} + C[/tex]
Now put the result back in terms of [tex]x[/tex].
[tex]\displaystyle \int \frac{x\,dx}{(x^2+4)^3} = \frac12 \left(-\dfrac1{2u^2} + C\right) = -\dfrac1{4u^2} + C = \boxed{-\dfrac1{4(x^2+4)^2} + C}[/tex]
Question 2(Multiple Choice Worth 2 points)
(03.01 LC)
Assume you are working with a standard deck of 52 cards. There are 13 cards (2, 3, 4, 5, 6, 7, 8, 9, 10, jack, queen, king, and ace) in each of four suits
and spades).
What is P(Jack Heart) if you draw one card?
O
-
52
13
52
Question 3(Multiple Choice Worth 2 points)
(03.02 MC)
Answer:
Assume you are working with a standard deck of 52 cards. There are 13 cards (2, 3, 4, 5, 6, 7, 8, 9, 10, jack, queen, king, and ace) in each of four suits
and spades).
What is P(Jack Heart) if you draw one card? 13
The equations of four lines are given. Identify which lines are parallel.
Line 1: y=−5x−5
Line 2: x+12y=−4
Line 3: y=−2x+4
Line 4: y+8=−15(x−9)
None of the equation of the line is parallel because there slope are not equal.
How to find lines that are parallel?Parallel line have the same slope.
Therefore, using slope intercept equation,
y = mx + b
where
m = slopeb = y-interceptHence,
y = −5x − 5 , slope = -5
x + 12y = −4; y = -1 / 3 - 1 / 12 x, slope = 1 / 12
y = −2x + 4: slope = -2
y + 8 = -15x + 135; y = -15x + 127, slope = -15
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There are two bags containing only orange and red marbles. Bag A has 2 orange marbles and 6 red marbles. Bag B has 4 orange marbles and 16 red marbles. A marble is randomly chosen from each bag. List these events from least likely to most likely. Event 1: choosing an orange or red marble from Bag B. Event 2: choosing an orange marble from Bag B. Event 3: choosing an orange marble from Bag A. Event 4: choosing a purple marble from Bag A. Least likely Event Event, Event, X Most likely Event Ś ?
Answer:
From least to most likely:
Event 4, Event 2, Event 3, Event 1
Step-by-step explanation:
Event 1 has a 100% chance because there are only red and orange marbles in the bag.
In event 2, there are 4 orange marbles in the bag, giving us a (4/20) chance. This is 20%
In event 3, there are 2 orange marbles of 8 total, giving us an (2/8) chance. This is 25%
Lastly, there are no purple marbles in either bag, giving us a 0% chance of this occurring.
cual es el valor de 10=z-6
Answer:
z=16
Step-by-step explanation:
10=z-6
10+6=z-6+6
16=z
Answer:
10=z-6
or, z= 10+6
or, z = 16
the vale of y is 16
A scientist wants an 81milliliter of saline solution with a concentration of 5% she has concentrations of 3% and 9%. How much of each solution must she use to get the desired concentration
The quantity of each concentrations of 3% and 9% needed to get the desired concentration is 54 milliliters and 27 milliliters respectively
Simultaneous equationLet
Quantity of 3% needed = xQuantity of 9% needed = yx + y = 81
0.03x + 0.09y = 81 × 5%
0.03x + 0.09y = 4.05
x + y = 81
0.03x + 0.09y = 4.05
From (1)
x = 81 - y
Substitute into0.03x + 0.09y = 4.05
0.03(81 - y) + 0.09y = 4.05
2.43 - 0.03y + 0.09y = 4.05
- 0.03y + 0.09y = 4.05 - 2.43
0.06y = 1.62
y = 1.62/0.06
y = 27
substitute y = 27 intox = 81 - y
x = 81 - 27
x = 54
Simultaneous equation:
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Select the story problem that this division problem represent 1/2 2/5 (Repost)
The story problem that aligns with the division problem is A. A whiteboard is 2/5 meter long and has an area of 1/2 square meter. How wide is the whiteboard?
How to illustrate the division problem?From the information given, it can be seen that 1/2 is divided by 2/5.
In this case, the story that aligns with it is that a whiteboard is 2/5 meter long and has an area of 1/2 square meter. How wide is the whiteboard?
In this case, the length is multiplied by width to get the area.
Therefore, the correct option is A.
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