Kaitlin will have $4657 as the total amount in her account after 3 years which was found using the compound interest formula.
What exactly is Compound Interest?
The interest earned on savings that is computed using both the original principle and the interest accrued over time is known as compound interest. The compound interest formula is calculated as: A = P (1+r)^tGiven: Kaitlin put $4000 into an account earning 5.2% annual compound interest.
We need to find how much will she have in the account after 3 years.
Let,
P = initial sum of money
r = interest rate,
t = number of years in decimal form
A = total amount in her account
Using the compound interest formula we obtain,
A = P (1+r)^t
A = 4000(1 + 0.052)³
A = 4000(1.052)³
A = 4000(1.164)
A = $4657
Therefore, Kaitlin will have $4657 as the total amount in her account after 3 years.
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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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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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< 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.
your R&D department is testing the falling pattern for a new shell to be used for artillery. To perform this test your team tosses a test shell off the edge of a cliff towards a river. Molly, a mathematician team member, was observing and obtained a digital picture of this fall. Using her mathematical knowledge molly modeled the shells fall with the following quadratic functions.
h(t)=-16t^2+32t+48
h(t)=-16(t+1)(t-3)
h(t)=-16(t-1)^2+64
a) why does molly have three equations?
b)could you convince the others that all three of these rules are mathematically equivalent? Justify your answer.
c) which of the forms would be most helpful in answering questions d-f? explain.
d)what is the maximum height the shell reaches and when will it occur? show your work.
E)when should the shell splash into the river? show your work
F)at what height was the shell when it was tossed off the cliff? show your work
a) She has three quadratic equations as one is the standard form, the other gives the roots, and the other gives the vertex.
b) If the distributive property is applied and the like terms combined, all the equations will have the same result.
c) The most helpful equations will be given for each point.
d) Maximum height of 64 feet after 1 second from h(t)=-16(t-1)^2+64.
e) The shell splashes into the river after a time of three seconds, from h(t)=-16(t+1)(t-3).
f) The shell was at a height of 48 feet when tossed into the river, from h(t)=-16t^2+32t+48.
What is the meaning of each quadratic function?In standard format, the quadratic function is given as follows:
h(t) = -16t² + 32t + 48.
From this, the relevant information is the initial height from which the shell was tossed off the cliff, which is the c-coefficient of 48 feet.
The roots of the equation are given from the rule presented as follows:
h(t)=-16(t+1)(t-3).
Hence the shell splashes into the river at the positive root of h(t), that is:
t - 3 = 0 -> t = 3.
Expanding the equation, we have that it is equivalent to the first one, as:
-16(t + 1)(t - 3) = -16(t² - 2t - 3) = -16t² + 32t + 48.
The vertex-form quadratic equation is given as follows:
h(t) = -16(t - 1)² + 64.
Meaning that a maximum height of 64 feet was reached after one second.
Expanding the equation, we have that:
h(t) = -16(t - 1)² + 64 = -16(t² - 2t + 1) + 64 = -16t² + 32t - 16 + 64 = -16t² + 32t + 48.
Which is also equivalent to the first one.
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A right triangle has a hypotenuse of length 4 inches. If one angle is 41°, find the length of each leg.
The perpendicular of the right triangle is 2.62441 inches and the base of the triangle is 3.0164 inches.
According to the question,
We have the following information:
A right triangle has a hypotenuse of length 4 inches. And one angle is 41°.
Now, we will use trigonometric functions of Sin and Cos to find the length of each leg of this triangle.
Sin 41 = Perpendicular/hypotenuse
Perpendicular = 0.6561*4
Perpendicular = 2.62441 inches
Cos 41 = base/hypotenuse
Base = 0.7541*4
Base = 3.0164 inches
Hence, the perpendicular of the right triangle is 2.62441 inches and the base of the triangle is 3.0164 inches.
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50 POINTS TO WHOEVER ANSWERS!!
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
It was observed over the past year that it rained on 105 of 365 days. What was the probability of any day being rainy last year?
Express your answer as a simplified fraction.
The probability of any day being rainy last year is 21/73 .
In the question ,
it is given that ,
In past year ,
the number of days it rained in last past year = 105 days
total number of days in past year = 365 days .
So , the probability of any day being rainy last year is = (number of days it rained )/(total number of days ) .
Substituting the values , we get
probability of any day being rainy last year = 105/365
Simplifying further , we get
= 21/73
Therefore , The probability of any day being rainy last year is 21/73 .
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Solve the inequality 4x-14<6
Answer:
x<5
Step-by-step explanation:
1. add 14 to both sides
4x - 14 + 14 < 6 + 14
4x<20
2. divide both sides by 4
[tex]\frac{4x}{4} < \frac{20}{4}[/tex]
x<5
Answer = x<5
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
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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Find the critical values, and, for confidence level = 90% and n = 15.
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]
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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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
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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Write the point-slope (y - k = m(x - h)) form of the equation from
the information given.
1. Slope =ï½; (h, k) = (1, -2) I
2. Slope equals 2 and the line goes through the point (-1, 3)
3. The line goes through the points (8,5) and (9, 6)
4. The line goes through the points (-1, -7) and (-8, -2)
5. The line goes through the points (1/2, 3/2) and (-1/4, 5/4)
The point-slope forms of the equation from the information given is 1. y + 2 = ï½(x-1), 2.y - 3 = 2(x+1) , 3.y - 5 = 1(x-8), 4. y + 7 = -5/7(x+1) and 5.y - 3/2 = -1(x-1/2).
1.
slope m = ï½ and (h, k) = (1, -2)
The point slope is y + 2 = ï½(x-1)
2.
slope = 2 , point (-1, 3)
y - 3 = 2(x+1)
3.
The line goes through the points (8,5) and (9, 6).
slope m = 6-5 / 9-8
= 1/1
= 1
y - 5 = 1(x-8)
4.
The line goes through the points (-1, -7) and (-8, -2)
slope m = -2+7 / -8+1
= 5/-7
= -5/7
y + 7 = -5/7(x+1)
5.
The line goes through the points (1/2, 3/2) and (-1/4, 5/4)
slope m = 5/4 - 3/2 / -1/4 - 1/2
= 5 - 6 / 4 / -1 + 2 / 4
= -1/1
= -1
y - 3/2 = -1(x-1/2).
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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:
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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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 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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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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What is 2 2/3 of 52 in fractions
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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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]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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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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Someone help please???????
$841,500 is the maturity value.
Given in question,
MV = P(1+RT)
P = $750,000
R = 13.35%
= 13.35/100
= 0.1335
T= 11 months
= 11/12 years
= 0.917 years
Putting the value in equation,
MV = 750000(1+0.1335*0.917)
= 750000(1+0.122)
= 750000*1.122
= 814500
Hence, Maturity Value is $814,500.
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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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2 1/2 times [1 2/3] please help