The expected of your account to be worth when you retire at 67 years old is $1,118,473.61.
To calculate the future value of your savings account, we can use the formula for compound interest:
FV = PV * (1 + r/n)^(n*t)
Where:
FV = Future Value of the account
PV = Present Value of the account
r = Annual interest rate (as a decimal)
n = Number of times the interest is compounded per year
t = Number of years
In this case, the present value (PV) is zero because you haven't started saving yet. The interest rate (r) is 7% per year, or 0.07 as a decimal. You will be depositing $200 every 2 months, which means 6 times a year (n=6). You have 45 years until you retire (t=45), and want to find the future value (FV) of the account.
We can start by calculating the total number of deposits you will make:
45 years * 12 months/year / 2 months/deposit = 270 deposits
Each deposit will be for $200, so the total amount you will deposit is:
270 deposits * $200/deposit = $54,000
Now we can use the formula for compound interest to calculate the future value of the account:
FV = $0 * (1 + 0.07/6)^(645) + $54,000 * (1 + 0.07/6)^(645)
FV = $0 + $1,118,473.61
So, you can expect your savings account to be worth approximately $1,118,473.61 when you retire at 67 years old, assuming you make regular deposits of $200 every 2 months and earn an annual interest rate of 7%.
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Find the value of x.
Answer: x = 11
Step-by-step explanation:
We know that vertical angles are congruent to each other. We will create an equation to help us solve. Then, will isolate the x-variable with inverse operations.
128° = 8x + 40°
8x + 40° = 128°
8x = 88°
x = 11
Enter the number that belongs in the green box 11 12 20
The number that belongs in the green box, using the law of cosines, is given as follows:
15.97º.
What is the law of cosines?The Law of Cosines states that for any triangle with sides a, b, and c and angle C opposite to side c, the following equation is true to obtain the missing length:
c² = a² + b² - 2abcos(C)
For this problem, the parameters are given as follows:
c = 11, a = 12, b = 20.
Hence the missing angle measure is given as follows:
11² = 12² + 20² - 2 x 11 x 20cos(C)
440cos(C) = 423
cos(C) = 423/440
C = arccos(423/440)
C = 15.97º.
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In a data distribution that is skewed left.
The median will be greater than the mean in a left-skewed distribution
We have,
In statistics, skewness is a measure of the asymmetry of a probability distribution around its mean.
A distribution is said to be skewed left if it has a long tail on the left side and the bulk of the data is on the right side.
When the data is skewed left, it means that the distribution is being pulled towards the left side.
This is because there are a few extreme values on the left side that are pulling the mean in that direction.
In contrast, the median is the middle value of the dataset, and it is not influenced by outliers.
For a left-skewed distribution,
The median will be greater than the mean because the mean is being pulled towards the left by the few extreme values.
In a data distribution that is skewed left, the mean will be less than the median.
This is because the mean is sensitive to outliers and is pulled towards the direction of the skewness, while the median is not affected by extreme values and is a more robust measure of central tendency.
Therefore,
The median will be greater than the mean in a left-skewed distribution
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If the variance for a set of data equals 8.1, find the standard deviation.
The standard deviation for this set of data is approximately 2.85.
To find the standard deviation, we first need to take the square root of the variance. Therefore, the standard deviation for the given data set is the square root of 8.1, which is approximately 2.846.
To find the standard deviation of a set of data when the variance is given, you simply need to take the square root of the variance. In this case, the variance equals 8.1.
Step 1: Identify the variance, which is 8.1.
Step 2: Take the square root of the variance.
Standard Deviation = √(Variance) = √(8.1)
Step 3: Calculate the square root of 8.1.
Standard Deviation ≈ 2.85
So, the standard deviation for this set of data is approximately 2.85.
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Show that every subgroup [tex]H \neq G[/tex] of a finite group is contained in a maximal subgroup?
K is a maximal subgroup of G, and we have[tex]H ⊆ K[/tex] since H is a proper subgroup of G and thus H is in M.
Let G be a finite group and let H be a subgroup of G. We want to show that H is contained in a maximal subgroup of G.
First, we note that if H is already a maximal subgroup of G, then we are done. So assume that H is not maximal.
Let M be the set of all subgroups of G that contain H. Note that M is non-empty, since G is itself in M. Since G is finite, M has a maximal element, say K. Then K is a maximal subgroup of G, and we have [tex]H ⊆ K[/tex] since H is in M.
To show that every subgroup H of G, where H is not equal to G itself, is contained in a maximal subgroup of G, we can use the same argument as above.
Let M be the set of all proper subgroups of G (i.e., subgroups that are not equal to G itself). Note that M is non-empty, since {e}, the subgroup consisting only of the identity element, is in M. Since G is finite, M has a maximal element, say K. Then K is a maximal subgroup of G, and we have[tex]H ⊆ K[/tex] since H is a proper subgroup of G and thus H is in M.
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simplify the expression (x+6)^2
The simplified expression for (x+6)^2 is x^2 + 12x + 36.
The expression (x+6)^2 represents the square of the sum of x and 6. To simplify this expression, we need to use the formula for expanding a binomial squared, which is (a+b)^2 = a^2 + 2ab + b^2.
Applying this formula to our expression, we get:
(x+6)^2 = x^2 + 2(x)(6) + 6^2
Simplifying further:
(x+6)^2 = x^2 + 12x + 36
In summary, to simplify the expression (x+6)^2, we use the formula for expanding a binomial squared and simplify the resulting terms to get the simplified expression x^2 + 12x + 36.
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The figure on the right shows the cross-section of a pipe. The internal radius is 5cm and the thickness of the metal is 6mm. What is the external circumference of the pipe? (Take π = 22)
The external circumference of the metal pipe is approximately 31.4 centimeters.
We know that the circumference of the circle that has a radius of r is defined as the product of diameter to the pie value.
The circumference of the circle = 2πr
We are given that internal radius is 5cm and the thickness of the metal is 6mm.
The circumference of the external circle = 2πr
= 2 x 3.14 x 5
= 31.4
The circumference of the metal pipe is approximately 31.4 centimeters.
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A plant is given plant food that contains 54 milligrams of magnesium. The plant is given this food each week for 20 weeks. How many grams of magnesium does the plant receive in 20 weeks?
The plant receives a total of 1.08 grams of magnesium in 20 weeks.It's important to note that when performing unit conversions, it's crucial to keep track of the units and ensure that they cancel out correctly. In this case, we converted milligrams to grams and then multiplied by the number of weeks to find the total amount of magnesium in grams.
To calculate the total amount of magnesium the plant receives in 20 weeks, we need to convert the milligrams to grams and then multiply it by the number of weeks.
Given that the plant food contains 54 milligrams of magnesium, we need to convert it to grams. Since there are 1,000 milligrams in 1 gram, we divide 54 by 1,000 to convert milligrams to grams:
54 milligrams ÷ 1,000 = 0.054 grams
Now, we multiply the amount of magnesium received per week (0.054 grams) by the number of weeks (20) to find the total amount of magnesium received in 20 weeks:
0.054 grams/week × 20 weeks = 1.08 grams.
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Given f(x) = x − 2 and g(x) = 5x + 3, evaluate the function for f(g(4))?
Three brothers share some money. The oldest 5/11 of the money. The next boy gets gets 7/12 of the remainder. What fraction of the money does the youngest boy get?
The fraction of the money the youngest boy does get is 5x/22.
Given that, three brothers share some money. The oldest 5/11 of the money.
Let the total money be x.
Share of oldest boy = 5/11 ×x
= 5x/11
Remainder = x-5x/11
Remainder = 6x/11
The next boy gets 7/12 of the remainder.
Share of next boy = 7/12 × 6x/11
= 7x/22
Share of youngest boy = 6x/11 - 7x/22
= (12x-7x)/22
= 5x/22
Therefore, the fraction of the money the youngest boy does get is 5x/22.
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i need help graphing 2x-5y=10
A graph and table for the linear equation y = 2x/5 - 2 in slope-intercept form is shown in the image attached below.
What is a graph?In Mathematics, a graph is a type of chart that is typically used for the graphical representation of data points or ordered pairs on both the horizontal and vertical lines of a cartesian coordinate, which are the x-axis and y-axis respectively.
Next, we would rearrange and simplify the given given linear equation in slope-intercept form in order to enable us plot it on a graph;
2x - 5y = 10
5y = 2x - 10
y = 2x/5 - 2
In conclusion, we would use an online graphing calculator to plot the given linear equation in slope-intercept form as shown in the graph attached below.
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A company introduces a customer service app. They track the number of customers who use it over an 8-month period. The scatter plot shows the data and a good line of fit. Write an equation of the line. Then predict the number of customers that will use the app after 12 months. Show your work.
The Y-intercept (b), we can substitute one of the points into the equation y = mx + b and solve for b.
The equation for the line of fit on the scatter plot, we need to determine the slope and y-intercept. Then, using the equation, we can predict the number of customers that will use the app after 12 months.
Given that we have a good line of fit, let's assume the equation of the line is in the form y = mx + b, where y represents the number of customers and x represents the number of months.
the scatter plot, we can determine two points on the line of fit. Let's say the coordinates of the first point are (x1, y1) and the coordinates of the second point are (x2, y2).
Next, we can calculate the slope (m) using the formula:
m = (y2 - y1) / (x2 - x1)
the y-intercept (b), we can substitute one of the points into the equation y = mx + b and solve for b.
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Si la secuencia es 7,12,17,22 y la regla es agregar 5 cuales son los siguentes dos terminos ?
the next two terms in the sequence would be 12 and 17.
Drag the tiles to the correct boxes to complete the pairs.
Match each function with the graph of its inverse function. fx=5x-1 fx= 1/5 x fx=x-5 fx=7x+1
The inverse of the functions are solved
Given data ,
Let the inverse of the function be represented as f⁻¹ ( x )
a)
f(x) = 5x - 1
y = 5x - 1
x = 5y - 1
x + 1 = 5y
y = (x + 1)/5
Inverse: f⁻¹(x) = (x + 1)/5
b)
f(x) = (1/5)x
y = (1/5)x
x = (1/5)y
y = 5x
Inverse: f⁻¹(x) = 5x
c)
f(x) = x - 5
y = x - 5
x = y - 5
y = x + 5
Inverse: f⁻¹(x) = x + 5
d)
f(x) = 7x + 1
y = 7x + 1
x = 7y + 1
x - 1 = 7y
y = (x - 1)/7
Inverse: f⁻¹(x) = (x - 1)/7
Hence , the inverse of the functions are solved
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What is the measure of an interior angle of a regular 12-gon?
Answer:
150°
Step-by-step explanation:
Measure of and interior angle of 12-gon:
[tex]\sf \boxed{\text{\bf Sum of all angles of n-polygon = (n -2) * 180}}[/tex]
n is the number of sides.
Sum of all angles of 12-gon = (12 - 2) * 180
= 10 *180
= 1800°
In a regular 12-gon, all the interior angles will be equal.
[tex]\text{\bf Measure of each interior angle = $\bf \dfrac{Sum \ of \ all \ the \ angles}{number \ of \ sides}$}[/tex]
[tex]\sf = \dfrac{1800}{12}\\\\=150^\circ[/tex]
Encuentra el siguen termino de la sucesión 23,18,13
Answer: 8
Step-by-step explanation:
We see that each term is 5 less than the previous one. We will subtract 5 from 13 to find the next term in the sequence.
13 - 5 = 8
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Determine the measure of each arc.
The measure of each arc is calculated as: 16. m(MN) = 72°; 17. m(NQR) = 180°; 18. m(NQ) = 108°; 19. m(MRP) = 265°; 20. m(QR) = 72°; 21. m(MR) = 108°; 22. m(QMR) = 288°; 23. m(PQ) = 13°.
How to Determine the Measure of Arcs?To determine the measures of each of the arcs, note that the central angle will have the same measure as the arc.
16. m(MN) = m<QRN [vertical angles are equal}.
m(MN) = 72°.
17. m(NQR) = 180° [half of a circle is 180 degrees]
18. m(NQ) = 180 - 72 = 108°
19. m(MRP) = 180 + (180 - 95)
m(MRP) = 180 + 85 = 265°
20. m(QR) = 72°
21. m(MR) = 180 - 72 = 108°
22. m(QMR) = 360 - 72 = 288°
23. m(PQ) = 180 - 95 - 72 = 13°
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746x75755 tell me the answer please because its my only answer
Answer: number is the number so we can be a number
Step-by-step explanation:
Answer:
56,513,230
Step-by-step explanation:
Hope this helps! pls mark as brainiest!
A laptop has a listed price of $710.98 before tax. If the sales tax rate is 7.25%, find the total cost of the laptop with sales tax included.
Answer:
$762.53
Step-by-step explanation:
think of 710.98 as the whole.
then 7.25% = an increase of 0.0725.
710.98 X (1 + 0.0725)
= $762.53 (to nearest cent)
A car travels 200 kilometres in 5 hours. How far does it travel in 7 hours at the same speed?
Answer:
Speed =distance divide by time
=200 kilometres divide by 5
=40km/h
Distance =speed multiple by time
=40 multiple by 7 hours
=280km
pls help guys calculus 30pts
What is the side length of AB
Answer:
AB ≈ 8.1
Step-by-step explanation:
using the cosine ratio in the right triangle
cos40° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{AC}{AB}[/tex] = [tex]\frac{6.2}{AB}[/tex] ( multiply both sides by AB )
AB × cos40° = 6.2 ( divide both sides by cos40° )
AB = [tex]\frac{6.2}{cos49}[/tex] ≈ 8.1 ( to the nearest tenth )
Ofelia is typing an essay on her computer. She typed 3/5 of a page in 1/5 hour. At this rate, how many hours would it take her to type a 3 page paper?
It would take Ofelia 1 hour to type a 3-page paper at her current typing rate.
. Given that Ofelia typed 3/5 of a page in 1/5 hour, we can determine her typing rate. To do so, we can divide the amount of work completed (3/5 of a page) by the time it took (1/5 hour):
(3/5) / (1/5) = 3 pages/hour
This means Ofelia's typing rate is 3 pages per hour. Now, we need to find out how many hours it would take her to type a 3-page paper at this rate. We can use the formula:
Time = Work / Rate
Here, the work is the 3-page paper, and the rate is 3 pages/hour. Plugging in the values:
Time = 3 pages / 3 pages/hour = 1 hour
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Convert the following binary to decimal numbers 1112
[tex]1\cdot2^2+1\cdot2^1+1\cdot2^0=4+2+1=7\\\\111_2=7_{10}[/tex]
Joe has to take two quizzes tomorrow. He has only enough time to study for one of them.
• The science quiz has 7 true-or-false questions.
• The English quiz has 5 multiple-choice questions.
Joe calculates the probability that he will get each question correct by guessing.
Science
English
To get 100% correct:
Answer 7 of 7 correctiv
Answer 5 of 5 correctiv
P(guess is correct)
0.5
0.25
Joe will study for the quiz on which he is likely to do worse by guessing. Which quiz should he study for?
• A. Science, because the probability of getting all questions correct is
(0.008), which is lower than for English (0.125).
• B. English, because the probability of getting all questions correct is 0.001, which is lower than for science (0.008).
• c. English, because the probability of getting all questions correct is
(0.125), which is lower than for science (0.5).
• D. Science, because he must get more questions correct.
Answer: B
Step-by-step explanation:
English: 0.25^5=0.001
Science:0.5^7=0.008
English is harder to get 100% on, since the probability 0.001 is lower than 0.008.
Find the mean of 7,9,4,3,9,4 graphically
Answer:
6
Step-by-step explanation:
To find the mean you've got to add 7, 9,4,3,9 and 4 (which gives you 36) and divide that by the number of figures/numbers (which is 6 numbers in total) and it gives you 6
what is the inverse of the function? pls help thank you sm
Step-by-step explanation:
y= rad(x+3)
y²=x+3
x= y²-3
change the variables
y= x²-3
Jose wants to advertise how many chocolate chips are in each Big Chip cookie at his bakery. He randomly selects a sample of 57 cookies and finds that the number of chocolate chips per cookie in the sample has a mean of 18.2 and a standard deviation of 2.9. What is the 90% confidence interval for the number of chocolate chips per cookie for Big Chip cookies? Assume the data is from a normally distributed population. Round answers to 3 decimal places where possible.
The 90% confidence interval for the number of chocolate chips per cookie for Big Chip cookies is approximately (17.569, 18.831), rounded to three decimal places.To determine the 90% confidence interval for the number of chocolate chips per cookie in Big Chip cookies, we can use the sample mean and standard deviation along with the appropriate formula.
Given that Jose randomly selected a sample of 57 cookies and found a sample mean of 18.2 and a standard deviation of 2.9, we can calculate the confidence interval using the following formula:
Confidence Interval = Sample Mean ± (Z * (Standard Deviation / √Sample Size))
Since the data is assumed to be from a normally distributed population and we want a 90% confidence interval, we need to find the Z-value for a 90% confidence level. Using a standard normal distribution table or a calculator, the Z-value for a 90% confidence level is approximately 1.645.
Substituting the values into the formula:
Confidence Interval = 18.2 ± (1.645 * (2.9 / √57))
Calculating the values:
Confidence Interval = 18.2 ± (1.645 * 0.383)Confidence Interval ≈ 18.2 ± 0.631.
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4. Graph the exponential function y = 2* and its inverse y = log₂ x. Table of values: (3 marks) Graph: y (2 marks)
The graph of the exponential function y = 2ˣ and its inverse y = log₂ x are shown in figure.
Since, A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
Here, Functions are,
⇒ y = 2ˣ
And, Its inverse function is,
⇒ y = log₂ x
Thus, The graph of the exponential function y = 2ˣ and its inverse y = log₂ x are shown in figure.
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help me with the question below
The value of the x is 31.4 mm
Surface area = 282.6
According to the given figure,
Radius of circle = 5 mm
The length of x is the circumference of the circle,
⇒ x = 2πr
Here r is the radius of the circle,
Therefore, r = 5
Then put it into the circumference expression,
⇒ x = 2x3.14x5
= 31.4 mm
Total surface area,
= 2 x area of circle + area of rectangle
= 2(πr²) + (LxW)
= 2xπx5² + 10xπx4
= 50π + 40π
= 90 π
= 90x3.14
= 282.6
Hence,
Surface area = 282.6 mm³
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