The amount of money that Lena needs to put each quarter for the annuity to have a total value of $96,000 is $953.45.
What amount should Lena deposit each quarter?An annuity is when a series of payment is made either at the beginning of a period or at the end of a period over a period of time.
An ordinary annuity is when the payment is made at the end of the period. When the interest is compounded quarterly, it means that four times in a year, the amount that is invested and the interest that has already being earned increase in value.
The formula that can be used to determine the quarterly payments is:
Payment = future value / annuity factor
Annuity factor = {[(1+r)^n] - 1} / r
Where:
r = interest rate = yearly interest / number of compounding = 3.6 / 4 = 0.9%n = total number of periods the payment is made = number of years x number of compounding = 18 x 4 = 72Payment = $96,000 / [{(1.009^72) - 1} / 0.009] = $953.45
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Write the standard form equation for an
ellipse with vertices: (4, 10) and (-12, 10)
and foci: (2, 10) and (-10, 10)
Check the picture below, so the ellipse looks more or less like so
[tex]\textit{ellipse, horizontal major axis} \\\\ \cfrac{(x- h)^2}{ a^2}+\cfrac{(y- k)^2}{ b^2}=1 \qquad \begin{cases} center\ ( h, k)\\ vertices\ ( h\pm a, k)\\ c=\textit{distance from}\\ \qquad \textit{center to foci}\\ \qquad \sqrt{ a ^2- b ^2} \end{cases} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\begin{cases} h=-4\\ k=10\\ a=8 \end{cases}\implies \cfrac{(x- (-4))^2}{ 8^2}+\cfrac{(y- 10)^2}{ b^2}=1\implies \cfrac{(x+4)^2}{ 8^2}+\cfrac{(y- 10)^2}{ b^2}=1 \\\\\\ \stackrel{\textit{we know that c = 6}}{6=\sqrt{8^2 - b^2}}\implies 6^2=8^2-b^2\implies b^2=8^2-6^2\implies \underline{b^2=28} \\\\\\ \cfrac{(x+4)^2}{ 8^2}+\cfrac{(y- 10)^2}{ b^2}=1\implies {\Large \begin{array}{llll} \cfrac{(x+4)^2}{ 64}+\cfrac{(y- 10)^2}{ 28}=1 \end{array}}[/tex]
2. The graph of f'(x), the derivative of f(x), is graphed below. Use this graph to answer the following questions.
Answer:
Step-by-step explanation:
a) x2 to x4 and x6 to x7
b) x1 to x2 , x3 to x5 , x6 to x7
c) x2, x3, x5, x6, x7
d) x2.5 , x4 , x5.5 , x6.5
50 POINTS TO WHOEVER ANSWERS!!
You started this year with $458 saved and
you continue to save $14 per month.
Write an equation to model this situation
(use m for months and s for savings).
Answer:
s = 14m + 458
Step-by-step explanation:
current amount = 458
14 per month
s = 14m + 458
Suppose that the walking step lengths of adult males are normally distributed with a mean of 2.8 feet and a standard deviation of 0.5 feet. A sample
of 73 men's step lengths is taken.
Step 1 of 2: Find the probability that an individual man's step length is less than 2.2 feet. Round your answer to 4 decimal places, if necessary.
The probability that an individual man’s step length is less than 2.2 feet is 0.10 or 10%
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean and standard deviation , the z-score of a measure X is given by:
Z = (X - mean)/S.D
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Mean of 2.8 feet and a standard deviation of 0.5 feet.
Find the probability that an individual man’s step length is less than 2.2 feet.
This is the p-value of Z when X = 2.2. So
Z = (2.2 - 2.8)/0.5
Z = 0.6/0.5 = 1.2
Z = 1.2
has a p-value of 0.10
Therefore, the probability that an individual man’s step length is less than 2.2 feet is 0.10 or 10%
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Carolyn’s homeroom sold 207 magazine subscriptions. Of the magazine subscriptions sold, 28% were fashion magazines. About how many fashion magazine subscriptions were sold?
The number of fashion magazines subscription that were sold is approximately 58.
How to find the number of fashion magazine that was sold?In mathematics, a percentage is a number or ratio that can be expressed as a fraction of 100.
In other words, percentage is a fraction or a ratio in which the value of whole is always 100.
Therefore, Carolyn’s homeroom sold 207 magazine subscriptions. Of the magazine subscriptions sold, 28 percent were fashion magazines.
The number of fashion magazine subscriptions that were sold can be calculated as follows:
number of fashion magazine sold = 28% of 207
number of fashion magazine sold = 28 / 100 × 207
number of fashion magazine sold = 5796 / 100
number of fashion magazine sold = 57.96
Therefore, about 58 fashion magazines were sold.
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Maximize: z = 3x + y
subject to: x-y≤9 3x + 5y ≤45 x≥0, y≥0
Objective function is a maximum at (3,2), Z = 3x+y = 3(3) + 1(2) = 9 + 2 = 11
Given,
Maximize: z = 3x +y
Subject to:
x-y≤9
3x + 5y ≤45
x≥0, y≥0
For the purpose of representing and resolving the linear programming optimization issues, objective functions are frequently used. The choice variables x and y are used in the objective function, which has the form Z = axe + by. The best answer can be obtained by maximizing or minimizing the function Z = ax + by
Plot the constraints and the objective function Z, or z = 3x +y
Push the objective function to the limit permitted by the feasible region to find the maximum.
Objective function is a maximum at (3,2),
Z = 3x+y = 3(3) + 1(2) = 9 + 2 = 11
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Need Help filling in the table?
Answer: Down there,
Step-by-step explanation:
Row 1 = 29
Row 2 = 5
Row 3 = -1
Row 4 = -7
Calculator
What is the area of this rectangle?
O 40 units²2
O 45 units²
O 50 units²
O 55 units²
-10-9-8-7-6-5-4
10-
9
8
8
9.10
Answer:
(c) 50 units²
Step-by-step explanation:
You want to know the area of the rectangle with vertices (-5, 5), (-1, 7), (4, -3), and (0, -5).
Distance formulaThe distance formula can be used to find the lengths of the sides. That formula is ...
d = √((x2 -x1)² +(y2 -y1)²)
The distance between the first two points is ...
d = √((-1 -(-5))² +(7 -5)²) = √(4² +2²) = √20
The distance between the next two points is ...
d = √((4 -(-1))² +(-3 -7)²) = √(5² +(-10)²) = √125
AreaThe area is the product of two adjacent side lengths:
A = LW
A = (√125)·(√20) = √(125·20) = √2500 = 50 . . . . square units
The area of the rectangle is 50 units².
PLEASE SOMEONE HELP
ASAP!!!!!!!!!!!!!
The value of x in the given trigonometric function is 7.37
what is trigonometric ratios?Trigonometric ratios are the ratios of the length of sides of a triangle. These ratios in trigonometry relate the ratio of sides of a right triangle to the respective angle. The basic trigonometric ratios are sin, cos, and tan, namely sine, cosine, and tangent ratios. The other important trig ratios, cosec, sec, and cot, can be derived using the sin, cos, and tan respectively.
5cos(5x) = 4
divide both sides by 5, it becomes,
cos(5x) = 4/5
cos(5x) = 0.8
taking Arc cos on both sides
5x = Arc cos 0.8
5x = 36.87
x = 36.87/5
x = 7.37 to 2 decimal places
In conclusion the value of x is 7.37
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If u = 15, t = 8, s = 40 and s (u+v)t 2 evaluate v.
The value of v is -12.5 when u = 15, t = 8, and s = 40.
According to the question,
We have the following expression:
s = (u+v)[tex]t^{2}[/tex]
We have the following values:
u = 15, t = 8, s = 40
Now, we can easily find the value of v by putting all these values in the given expression.
So, we have the following expression:
40 = (15+v)8*8
40 = (15+v)16
Multiplying 16 into the bracket:
40 = 15*16+16v
40 = 240+16v
Subtracting 240 from both sides:
40-240 = 16v
-200 = 16v
Dividing by 16 on both sides:
-200/16 = v
v = -12.5
Hence, the value of v is -12.5 when u = 15, t = 8, and s = 40.
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When my dad was 31, I was just 8 years old now his age is twice as old as my age. What is my current age
Riddle
Answer: 23 years old
Step-by-step explanation: 31-8=23
Find an equation of the line containing the given pair of points (3,4) and (9,9)
Answer:
y = 5x/6 + 3/2
Step-by-step explanation:
First, find the slope (m):
m=(y2-y1)/(x2-x1)
m=(9-4)/(9-3)
m=5/6
y=mx+b ==> slope-intercept form equation
y = 5x/6 + b==> substitute the value of the slope for m
9 = 5(9)/6 + b ==> substitute a point (x, y) or (9, 9) into the equation
9 = 45/6 + b ==> simplify
(9 = 45/6 + b)*6 ==> multiply the equation by 6 to remove denominators
54 = 45 + 6b ==> simplify
54 - 45 = 45 - 45 + 6b ==> solve for b
9 = 6b
9/6 = 6b/6
b = 3/2
y = 5x/6 + 3/2 ==> plug in b for the slop-intercept equation
x + 2x
Helpp, no link :/
Answer:
3x
Step-by-step explanation:
When the equation is like this and they both are being multiplied by x you can just add the coefficients
x+2x
1x+2x
3x
Hopes this helps please mark brainliest
Hello..!
Similar Terms:[tex] \sf{x + 2x = 3x}[/tex]
It is known that in similar terms "x" is an unknown quantity and that in this problem "x" is 1 and that we only have to add it to 2:
[tex] \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf2 + 1 = 3[/tex]
So the result is 3x
2 1/2 times [1 2/3] please help
75 litres of water by 15%
Answer:
11.25 litres
Step-by-step explanation:
75 ×15/100
=11.25 so the answer should be 11.25 litres
Can you help with these vocabulary questions
find the number that is opsite of 1/15 and 1/16
The numbers that opposite 1/15 and 1/16 are -1/15 and -1/16
How to determine the opposite numbers?From the question, we have the following numbers that can be used in our computation:
Numbers = 1/15 and 1/16
The opposite of numbers is the negative equivalent of the number
Take for instance, we have a number x
The opposite of x is -x
Using the above as a guide, we have the following representation
Numbers = 1/15 and 1/16
This means that, the opposite numbers can be represented as
Opposite numbers = -1/15 and -1/16
Hence, the opposite numbers are -1/15 and -1/16
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Please answer. Thanks.
The missing statements/ reasons are:
Statement Reason
LN bisects ∠MLO Given
LM ≅ LO Given
∠MLN ≅ ∠NLO Def of angle bisector
LN ≅ LN Common side
ΔLMN ≅ ΔLON SAS postulate of triangle congruence
In this question, we have been given some information about triangles LMN and LON.
We need to prove ΔLMN ≅ ΔLON
LN bisects ∠MLO ....................(Given)
LM ≅ LO ...................(Given)
∠MLN ≅ ∠NLO ...................(Def of angle bisector)
LN ≅ LN ....................(Common side)
ΔLMN ≅ ΔLON ...................(SAS congruence postulate)
Therefore, the missing statements/ reasons are:
Statement Reason
LN bisects ∠MLO Given
LM ≅ LO Given
∠MLN ≅ ∠NLO Def of angle bisector
LN ≅ LN Common side
ΔLMN ≅ ΔLON SAS postulate of triangle congruence
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How many fifths equal 1/5
Answer: only 1
Step-by-step explanation:
Answer: One-fifth.
Step-by-step explanation:
2/5 is two-fifths, 3/5 is three-fifths, and so on.
1/10 is one-tenth, 2/10 is two-tenths, and so on.
PROBLEM SOLVING Volunteers work for six hours to clean up litter in a park. The graph represents
the time x (in hours) and the number y of garbage bags filled.
Garbage bags
(6, 69)
(5, 57.5) (4, 46)
(2, 23)
10 (1, 11.5)
(3, 34.5)
Write an equation that represents the garbage bags filled as a function of time
Interpret the slope and the y intercept
The domain is____ the range is____
How many garbage bags could the volunteers fill in 12 hours
____ garbage bags
Explain.
The equation of the function is: y = 11.5x.
The slope = 11.5 garbage bag per hour.
Y-intercept = 0 bag at 0 hour.
The domain: number of hours
Range of the function: number of garbage bags filled.
138 bags will be filled in 12 hours.
How to Write the Equation of a Function?The equation of a function can be written as y = mx + b in slope-intercept form. Here, we have:
m represents slopeb represents y-intercept.Given the graph with the points that represents the number of garbage bags filled as a function of time as:
(6, 69); (5, 57.5); (4, 46); (2, 23); (1, 11.5); (3, 34.5)
Use two points, (6, 69) and (4, 46) to find the slope of the function:
Slope (m) = change in y / change in x = (69 - 46)/(6 - 4)
Slope (m) = 23/2
Slope (m) = 11.5
To find the y-intercept (b), substitute m = 11.5 and (x, y) = (6, 69) into y = mx + b:
69 = 11.5(6) + b
69 = 69 + b
69 - 69 = b
b = 0
To write the equation of the function, substitute m = 11.5 and b = 0 into y = mx + b:
y = 11.5x + 0
y = 11.5x
The slope, 11.5, means 11.5 garbage bags were filled per hour.
Y-intercept is zero, which means no bag was filled at 0 hour.
The domain is the set of the number of hours, while the range of the function is the set of number of garbage bags filled.
To find the number of garbage bags that volunteers fill in 12 hours, substitute x = 12 into y = 11.5x:
y = 11.5(12)
y = 138 bags.
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A data set has a lower quartile of 3 and an interquartile range of 5. Which box plot could represent this data set?
5
10
10
10
10
15
15
15
15
20
20 25
20
25
20
25
25
The box plot that could represent a data set that has an interquartile range of 5 is the box plot first option shown in the image.
What is Interquartile Range?
The interquartile range of a data set is the distance between the lower quartile and the upper quartile on a box plot.
Thus, a box plot that has a lower quartile of 3 and an interquartile range of 5 will have a distance of 5 from the lower quartile to the upper quartile.
Therefore, the box plot that could represent a data set that has an interquartile range of 5 is the box plot shown in the image attached below (see attachment).
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Last year, wind turbines along a hilly ridge had an average output of 600 kilowatt hours per year. The turbines were upgraded, and now their average annual output is 87% more. What is the new average yearly output?
PLEASE HELP ASAP DUE TODAY
The new annual output from the turbine is 1122kw to give a percentage of 87
PercentagePercentage, a relative value indicating hundredth parts of any quantity. One percent (symbolized 1%) is a hundredth part; thus, 100 percent represents the entirety and 200 percent specifies twice the given quantity.
Data;
Percentage = 87%old output = 600kwnew output = yThis can be represented mathematically as
87 / 100 = y - 600/ 600
We can solve for y
0.87 = y - 600 / 600
x = 1122kw
The new annual output from the turbine is 1122kw
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NEED to know today PLSS.
Game Station 4: Spinner of 4 equal parts: Red, Purple, Green and Orange - Rules: If the arrow lands in the red quadrant, "Team Y" gets 7 points. If it lands in the other quadrants, both teams lose 1 point
A. "Team Y" spins 5 times. How many of the possible outcomes could have landed in Red exactly 3 times and on purple exactly 2 times?
B. "Team Z" spins 4 times. How many of the possible outcomes could have landed in Red
C. "Team Y" spins 5 times. How many of the possible outcomes could have landed in Red at least once?
use combinations, not probability.
The results of the combinations are given as follows:
A. Number of possible outcomes with red exactly 3 times and Purple exactly 2: 10.
B. Number of possible outcomes with red at least ounce in 4 spins: 175.
C. Number of possible outcomes with red at least ounce in 5 spins: 781.
How to obtain the number of outcomes?The outcomes are obtained in two ways, as follows:
Combination -> Item a, as it is an arrangement with repetition, which is equivalent to combination.Fundamental Counting Theorem -> Items b and c.CombinationThe combination formula calculates the number of different combinations of x objects from a set of n elements, according to the equation presented as follows:
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
From item a, there are 5 outcomes with 3 and 2 repetitions, hence the number of results is obtained as follows:
[tex]C_{5,3} = \frac{5!}{3!2!} = 10[/tex]
Fundamental Counting TheoremIt states that the number of outcomes of n independent trials is given by the multiplication of the number of outcomes for each trial.
For item b, we have that:
There are 4 spins.Each with 4 outcomes.Hence the total number of outcomes, without considering the restriction is:
Total = 4^4 = 256.
With no red results, the number of outcomes is:
Total no red = 3^4 = 81.
Hence the number of outcomes with at least one red result, considering complementary events, is:
256 - 81 = 175.
Item c follows the same logic, only with 5 trials instead of four, hence:
4^5 - 3^5 = 781.
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9 feet is the same as how many meters? Hint: 1 ft≈ 0.305 m Learn with an example Round your answer to the nearest tenth. Submit (
9 feet is the same as = 2.74 m
Given
1 ft≈ 0.305 m
To find out 9 feet is the same as how many meters:
To convert a foot measurement to a meter measurement, multiply the length by the conversion ratio.
Since one foot is equal to 0.3048 meters, you can use this simple formula to convert:
meters = feet × 0.3048
= 9 * 0.3048
= 2.7432 m
The length in meters is equal to the feet multiplied by 0.3048.
Hence the answer is the 9 feet is the same as meters = 2.74m.
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if cabbage coats 0.27 per pound then how many pounds of cabbage can you buy for $3.90.
Answer:.15
Step-by-step explanation:
390/27= 130/9
130/9=14.444...
divide by 100
.1444... is approxomatly .15 so there is your answer
Answer:
14 or 15
u can do 3.90 divied by 0.27
Step-by-step explanation:
Answer below if you can!! Would help me A LOT^^
Answer:
Think its B.
Step-by-step explanation:
Answer:
[tex]4cd(6-9c)[/tex]
Step-by-step explanation:
Factor out what all terms have in common
[tex]24cd-36c^{2} d[/tex][tex]cd(24-36c)[/tex][tex]4cd(6-9c)[/tex]Find the domain of the function using interval notation.
f(x)=−2x(x−3)(x−6)
The domain of the polynomic function f(x)=−2 · x · (x − 3) · (x − 6) is (- ∞, + ∞).
What is the domain of a polynomic function?
In this problem we find a polynomic function in factor form, whose definition is presented below:
f(x) = a · Π (x - rₙ), for n = {1, 2, 3, ..., n - 1, n}
Where:
a - Lead coefficientrₙ - n-th Root of the polynomial.The grade of the polynomial is equal to the number of roots. The statement shows a polynomial of grade 3 and, according to function theory, the domain of polynomic functions is the set of all real numbers, whose interval notation is (- ∞, + ∞).
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< ABC and , CBD ate complementary and adjacent. Can you show me how to draw it
Answer: Refer to the drawing below
Explanation:
Complementary angles always add to 90 degrees.
Draw a right angle, aka 90 degree angle. Plot points A, B and D on it as shown below. Then add point C somewhere inside the rectangular region formed by this right angle. Lastly, connect a segment from B to C. This helps form angles ABC and CBD. Note how these smaller angles combine to a 90 degree angle.
(angleABC) + (angleCBD) = angle ABD = 90 degrees
The angles are adjacent because they share a common wall, which in this case is segment BC.
How many terms are in this expression? n² + 2k³ + 3m²
The expression has 3 terms, that are
1st term n²
2nd term 2k³
3rd term 3m²
Given that,
The expression is n²+2k³+3m².
We have to find how many terms are in the expression.
A term may be a number, a variable, the product of two or more variables, a number and a variable, or any combination of these. A single term or a collection of phrases can be used to create an algebraic expression. For instance, 4x and y are the two terms in the formula 4x + y.
Take the expression,
n²+2k³+3m²
There are 3 terms
1st term n²
2nd term 2k³
3rd term 3m²
Therefore, The expression has 3 terms, that are
1st term n²
2nd term 2k³
3rd term 3m²
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