Therefore, a monthly payment of $168.62 must be made to pay off the $3,500 balance on the credit card in two years.
What is percent?Percent is a way of expressing a number as a fraction of 100. The symbol for percent is "%". Percentages are used in many different contexts, such as finance, economics, statistics, and everyday life.
Here,
To calculate the monthly payment required to pay off the $3,500 balance on a credit card that charges 16.5% interest, compounded monthly, in two years, we can use the formula for the present value of an annuity:
[tex]PMT = PV * r / (1 - (1 + r)^{-n})[/tex]
where PMT is the monthly payment, PV is the present value of the loan, r is the monthly interest rate, and n is the total number of payments.
First, we need to convert the annual interest rate of 16.5% to a monthly interest rate:
r = 0.165 / 12
= 0.01375
Next, we need to calculate the total number of payments over two years:
n = 2 * 12
= 24
Now we can plug in the values into the formula:
[tex]PMT = 3500 * 0.01375 / (1 - (1 + 0.01375)^{-24}) = $168.62[/tex]
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2.40 in a certain binary communication channel, it is equally likely to send a 1 or a 0 (both probabilities are equal to 1/2). the probability of an error given that a 1 is sent is 2/9, while the probability of an error given a 0 is sent is 1/9. (a) what is the probability that a 1 is received? (b) what is the (unconditional) probability that an error occurs? (c) what is the probability that a 1 was sent, given a 1 was received?
(a) The probability that a 1 is received is 4/9.
(b) The (unconditional) probability that an error occurs is 1/6.
(c) The probability that a 1 was sent, given that a 1 was received, is 7/8.
To solve this problem, we can use Bayes' theorem and conditional probability.
(a) The probability that a 1 is received can be found using the law of total probability. We can calculate it by considering the probabilities of two mutually exclusive events: receiving a 1 when a 1 is sent and receiving a 1 when a 0 is sent.
Let P(1) be the probability that a 1 is sent and P(0) be the probability that a 0 is sent. Both probabilities are equal to 1/2 since they are equally likely.
The probability of receiving a 1 when a 1 is sent is 1 minus the probability of an error when a 1 is sent, which is 1 - (2/9) = 7/9.
The probability of receiving a 1 when a 0 is sent is the probability of an error when a 0 is sent, which is 1/9.
Using the law of total probability:
P(1 received) = P(1 sent) x P(1 received | 1 sent) + P(0 sent) x P(1 received | 0 sent)
P(1 received) = (1/2) x (7/9) + (1/2) x (1/9)
P(1 received) = 7/18 + 1/18
P(1 received) = 8/18
P(1 received) = 4/9
Therefore, the probability that a 1 is received is 4/9.
(b) The (unconditional) probability that an error occurs can be calculated by considering the probabilities of two mutually exclusive events: an error occurs when a 1 is sent and an error occurs when a 0 is sent.
Using the law of total probability:
P(Error) = P(1 sent) x P(Error | 1 sent) + P(0 sent) x P(Error | 0 sent)
P(Error) = (1/2) x (2/9) + (1/2) x (1/9)
P(Error) = 2/18 + 1/18
P(Error) = 3/18
P(Error) = 1/6
Therefore, the (unconditional) probability that an error occurs is 1/6.
(c) The probability that a 1 was sent, given that a 1 was received, can be calculated using Bayes' theorem:
P(1 sent | 1 received) = (P(1 sent) x P(1 received | 1 sent)) / P(1 received)
P(1 sent | 1 received )= (1/2) x (7/9) / (4/9)
P(1 sent | 1 received) = (1/2) x (7/9) * (9/4)
P(1 sent | 1 received) = 7/8
Therefore, the probability that a 1 was sent, given that a 1 was received, is 7/8.
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a charger has a power rating of 12 w. if you charge 6 cents per kilowatt hour, how much do you make in 1 day
The earnings made in 1 day when charging a device with a power rating of 12 W at a rate of 6 cents per kilowatt hour is 0.01728.
Given, Power rating of charger = 12 W. Charge per kilowatt hour = 6 cents = 0.06/kWh.To calculate the earnings in 1 day, we need to calculate the power consumed by the charger in 1 day first.
P = Power rating of charger = 12 Wt = Time = 1 day = 24 hours. Energy consumed = Power x Time. E = P x t= 12 W x 24 hours= 288 Wh = 0.288 kWh. Therefore, energy consumed by the charger in 1 day = 0.288 kWh.
Now, we can calculate the earnings in 1 day as follows: Charge per unit = 0.06/kWh. Earnings = Energy consumed x Charge per unit. Earnings = 0.288 kWh x 0.06/kWh= 0.01728.
Therefore, the earnings made in 1 day when charging a device with a power rating of 12 W at a rate of 6 cents per kilowatt hour is 0.01728.
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in cluster analysis, a method can be used to reduce bias due to the difference in units of measurement. one such method is called
In cluster analysis, a method can be used to reduce bias due to the difference in units of measurement. One such method is called standardization.
Cluster analysis is a data mining approach that is widely utilized in data processing, image analysis, and other data-based analytics applications. It groups items that have comparable characteristics into clusters by separating them from other objects that do not share the same features.
Standardization is the process of converting variables with various scales to a common scale so that they can be compared fairly.
Standardization involves transforming all of the variables into comparable units of measurement by converting them into z-scores. This allows for the comparison of values without being affected by the different units of measurement.
The method that can be used to reduce bias due to the difference in units of measurement in cluster analysis is standardization, which converts variables with various scales to a common scale so that they can be compared fairly. This ensures that each variable contributes equally to the distance between the clusters.
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PLEASE HELP MARKING BRAINLEIST JUST ANSWER ASAP
Answer: 35 Millimeters
Step-by-step explanation: Add all the numbers around your shape and you got the perimeter :)
Answer: 35 mm
Step-by-step explanation:
Add all sides together: 4+13+13+5 = 35
Liam has 11/4 packets of red clay.If he crafts a sculpture using 5/3 packets, how much clay does he have left?
Answer:
Step-by-step explanation:
Liam has 11/4 packets of red clay, which is equal to 33/12 packets of clay.
If he uses 5/3 packets of clay for crafting, he would have used 20/12 packets of clay.
To find how much clay he has left, we need to subtract the used amount from the original amount:
33/12 - 20/12 = 13/12
Therefore, Liam has 13/12 packets of clay left.
in january , the temperature in parts of minnesota fell from f to f over a -hour period. what was the average temperature change per hour?
The average temperature change per hour was -2.708 degrees Fahrenheit.
To calculate the average temperature change per hour, we need to find the total temperature change over the 24-hour period and then divide by the number of hours.
The total temperature change is the difference between the starting temperature (41 degrees Fahrenheit) and the ending temperature (-13 degrees Fahrenheit), which is -54 degrees Fahrenheit.
Dividing the total temperature change by the number of hours, we get:
-54 degrees Fahrenheit / 24 hours = -2.25 degrees Fahrenheit per hour.
Rounding to three decimal places, we get an average temperature change per hour of -2.708 degrees Fahrenheit per hour.
The complete question is: In January 2008, the temperature in parts of Minnesota fell from 41∘41∘F to −13∘-13∘F over a 24-hour period. What was the average temperature change per hour?
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if you have minimums and maximums that are far away (several standard deviations away from the mean) from the rest of the data observations, medians would be the best measure of central tendency?
Yes, if you have minimums and maximums that are several standard deviations away from the rest of the data observations, medians would be the best measure of central tendency.
Having minimums and maximums that are far away (several standard deviations away from the mean) from the rest of the data observations, medians would be the best measure of central tendency. This is because, when there are outliers or extreme values in a dataset, the mean can be influenced and it may not be an accurate representation of the central tendency.
However, the median is not affected by extreme values or outliers since it only depends on the middle value of the dataset. Therefore, if the dataset has outliers, it is better to use the median as a measure of central tendency to provide a more accurate representation of the data.
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a camper attaches a rope from the top of her tent, feet above the ground, to give it more support. if she takes the rope to the ground feet from the middle of her tent, about how long is the rope from the ground to the tent?
4 feet.
The length of the rope from the ground to the top of the tent is 4 feet.
To calculate this, subtract the distance from the tent to the ground (2 feet) from the height of the tent (6 feet), and you will get the length of the rope (4 feet).
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Which three side length best describes the triangle in the diagram
Answer:
i think that it is d or c just guessing
Halla m∆1 y m∆2.
ayuda porfaa
Hi! I understand that you want help finding the values of m∆1 and m∆2. To provide a step-by-step explanation, I need more information about the problem, such as the type of triangles, angles, or side lengths involved. Please provide more context or details, and I will be happy to help you.
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in general, which point size would you use if you wanted each character to be approximately one inch in size? a.) 1 pt b.) 72 pts c.) 24 pts d.) 36 pts
If you want each character to be approximately one inch in size, you would use a point size of 72 pts.
Point size is a unit of measurement used to determine the size of typefaces. It represents the height of the characters in a font. One point is equal to 1/72 of an inch, which means there are 72 points in one inch.
Therefore, if you want each character to be approximately one inch in size, you would need to use a font size of 72 points. This would ensure that the characters are roughly one inch tall, assuming that the font is designed to be proportional and not condensed or expanded.
Choosing a smaller point size, such as 1 pt or 24 pts, would result in characters that are much smaller than one inch. Choosing a larger point size, such as 36 pts, would result in characters that are larger than one inch.
Therefore the correct answer is option b.) 72 pts.
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Find the area of the following
rhombus:
10 cm
6 cm
8 cm
A = [?] cm²
Answer:96
Step-by-step explanation:
[tex]Area=\frac{d1 d2}{2}[/tex]
[tex]Area=\frac{(6+6)(8+8)}{2}[/tex]
[tex]Area=96[/tex]
Three identical small circles are drawn inside one large circle, as shown in the diagram.
The centres of the small circles lie on the diameter of the large circle.
Therefore, the radius r of each of the small circles multiplied by [tex](3sqrt(3)/2)[/tex] to get the length of the diameter AB of the big circle.
what is circle ?A circle is a geometric form made up of all points that are spaced apart by a predetermined amount, known as the radius, from a specific point known as the center. The circumference of a circle is determined by the formula C = 2r, where r denotes the radius and (pi) denotes a mathematical constant roughly equivalent to 3.14159. Numerous areas of mathematics, science, and daily living frequently involve circles. They have a number of crucial characteristics that make them helpful in a variety of applications.
given
The line section PQ is the following length:
PQ is equal to [tex]sqrt(3r2/4) = sqrt(3)/r.[/tex]
In a similar manner, we can determine how long the line section QR is:
OQ2 - OR2 = QR2 = r2/4 - r2 = QR2 = -3r2/4
Therefore, QR is a line that goes beyond the spot R rather than a line segment.
The length of the large circle's diameter AB is determined by adding the lengths of PQ, QR, and RP, each of which is equivalent to (sqrt(3)/2)r. As a result, we have:
[tex]AB = 3 * (sqrt(3)/2) (3sqrt(3)/2)r = r[/tex]
Therefore, the radius r of each of the small circles multiplied by [tex](3sqrt(3)/2)[/tex] to get the length of the diameter AB of the big circle.
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assume that respondents aged 70 or older are only one-third as likely to be in an internet sample as their actual incidence in the population. using the propensity scoring method, their responses would be
The propensity scoring method is a statistical technique used to adjust for differences in the characteristics of groups being compared in a study. In this case, we want to adjust for the fact that respondents aged 70 or older are underrepresented in an internet sample.
To do this, we can assign a propensity score to each individual in the sample based on their likelihood of being in the sample, given their age. We can then use this score to weight their responses to account for the underrepresentation of older individuals.
In this case, we know that respondents aged 70 or older are only one-third as likely to be in an internet sample as their actual incidence in the population. This means that we can assign a propensity score of 3 to each individual aged 70 or older in the sample, and a propensity score of 1 to everyone else.
Using these propensity scores, we can weight the responses of each individual in the sample. Responses from individuals with a propensity score of 3 would be weighted by a factor of 3, while responses from individuals with a propensity score of 1 would be weighted by a factor of 1.
By adjusting for the underrepresentation of older individuals in this way, we can obtain more accurate estimates of the characteristics of the population being studied, and reduce the potential for bias in our analysis.
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What is the value of angle h?
How do you know (what type of angle pairs are they)?
The value of h is 34.
What is the angle formed when two lines intersect?
Intersecting lines are two or more lines that have precisely one point in common. The point of junction is this central location that connects all of these lines. It should be observed that the intersecting lines only come together at one point, regardless of the angle at which they do so.The vertical angles are the opposing angle pairs created by two intersecting lines. Non-adjacent angles created by two crossing lines are known as opposite angles. Angles at opposite sides are equal. (equal in measure)According to the Vertically opposite angle theorem, opposite angles are equal.
So, h = 34.
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Using laws of logarithms, write the given expressions usingsums and/or differences of logarithmic expressions which donot contain the logarithms of products, quotients, or powers.a. log(45x) = log(45)+log(x). Previewb. log (x⁵⁵) = 55log(x). Previewc. 10 log(⁵√x) = 1/5log(x)^10. Preview2/5 log(x)¹⁰ syntax ok
Additionally, you should focus on answering the specific question being asked and ignore any typos or irrelevant parts of the question.
Using laws of logarithms, the given expressions can be written using sums and/or differences of logarithmic expressions which do not contain the logarithms of products, quotients, or powers as follows:
a.[tex] log(45x) = log(45) + log(x)b. log(x⁵⁵) = 55log(x)c. 10 log(⁵√x) = log(x)^(10/5) = log(x)^2 = 2log(x)2/5 log(x¹⁰) = (2/5)log(x) + (2/5)log(x) + ... + (2/5)log(x) (10 times)= 2log(x^10)[/tex]
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−6(3/8+3/4)= ??????????????????????????????????
AS A FRACTION
Answer:
-27/4
3/8+3/4=3/8+(3×2)(3×2)
3/8+4/8=7/8
-6×7/8
=-27/4
Activity 2 Synthesis
1. Precious says you can estimate the area of a circle by calculating 32. What do you think
each part of her expression means?
2. Do you agree with Precious? Use your earlier work to help support your thinking.
A cylindrical glass with a radius of 5 cm and a height of 20 cm is half full of milk. How
many milliliters of milk are in the glass? (1cm3
= 1ml)
There is 78.54 mI of miIk in the gIass.
What is VoIume of a cyIinder ?The voIume of a cyIinder means the space inside the cyIinder that can hoId a specific amount of materiaI quantity. In simpIer words, the capacity of a cyIinder to hoId a thing is its voIume. Inside the space of a cyIinder, you can hoId either of the three types of matter – soIid, Iiquid, or gas. This capacity can onIy be witnessed in a three-dimensionaI cyIinder, i.e., you cannot hoId any Iiquid, soIid, or gas in a two-dimensionaI cyIinder.
The equation for the voIume of a cyIinder is V = Ah,
where A is the area of the base and h is the height.
Thus, the voIume can aIso be expressed as V = πr2h.
Find capacity of the gIass :
VoIume of the gIass = πr²h
Given radius = 5 ; Height = 2
VoIume of the gIass = π(5)²(2)
VoIume of the gIass = 157.08cm³
Find the voIume of the miIk :
If the gIass is haIf fuII,
VoIume of the miIk = 177.08 ÷ 2
VoIume of the miIk = 78.54 cm³
Convert cm³ to mI :
1 mI = 1000 cm³
78.54cm³ = 78.54 mI
There is 78.54 mI of miIk in the gIass.
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What is 102.5% of 80?
Answer:
Step-by-step explanation:
102.5/80=
82
Answer: 82
Step-by-step explanation:
FirstMove the percent 2 times to the right to get a decimal.
102.5% ——> 1.025
Secondly
You’re dividing the part with the whole always to get the percent. So if we have the precent (converted into a decimal) and the whole. So we are finding the part. So to find the part we multiple 1.025 and 80.
Third
You solve now. So 1.025 x 80 = 82
what is 9 divided by 2.5
Answer: 3.6
Step-by-step explanation:
It's 3.6, hope it helped! :D
there are 20 rows of seats on a concert hall: 25 seats are in the 1st row, 27 seats on the 2nd row, 29 seats on the 3rd row, and so on. if the price per ticket is $2,300, how much will be the total sales for a one-night concert if all seats are taken?
The total sales for a one-night concert with all seats taken will be $2,024,000.
To solve this problem, we need to find the total number of seats in the concert hall. We know that the first row has 25 seats, the second row has 27 seats, and the third row has 29 seats.
We can represent the number of seats in each row using an arithmetic sequence with a first term of 25 and a common difference of 2. The nth term of this sequence can be found using the formula:
a_n = a_1 + (n - 1)d
where a_1 is the first term (25), d is the common difference (2), and n is the number of the row.
Using this formula, we can find the number of seats in the 20th row
a_20 = 25 + (20 - 1)2
a_20 = 25 + 38
a_20 = 63
Therefore, the total number of seats in the concert hall is the sum of the seats in all 20 rows:
total seats = 25 + 27 + 29 + ... + 63
To find this sum, we can use the formula for the sum of an arithmetic sequence
S_n = (n/2)(a_1 + a_n)
where S_n is the sum of the first n terms of the sequence. In this case, n = 20, a_1 = 25, and a_n = 63.
S_20 = (20/2)(25 + 63)
S_20 = 10(88)
S_20 = 880
Therefore, there are a total of 880 seats in the concert hall. If all seats are taken, the total sales for the one-night concert will be
total sales = number of seats x price per ticket
total sales = 880 x $2,300
total sales = $2,024,000
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Angle PQR is isosocles with PQ=PR= 7. 5cm and QR = 9cm. The height PS from P to QR,is 6cm. Find the area of Angle PQR. What will be the height from R to PQ that is RT
The height RT from R to PQ is approximately 3.16 cm.
To find the area of triangle PQR, we can use the formula:
Area = 1/2 * base * height
Since PQR is isosceles with PQ = PR, the base is PQ or PR. We can choose PQ as the base. Then the height is PS.
Area of PQR = 1/2 * PQ * PS
Since PQ = PR = 7.5 cm and PS = 6 cm, we can substitute these values into the formula and simplify:
[tex]Area of PQR = 1/2 * 7.5 cm * 6 cm[/tex]
[tex]Area of PQR = 22.5 cm^2[/tex]
Therefore, the area of triangle PQR is [tex]22.5 cm^2[/tex].
To find the height RT from R to PQ, we can use the Pythagorean theorem.
Let's draw a perpendicular line from R to PQ, intersecting at T. Then we have a right triangle PRT with hypotenuse PR and legs PT and RT.
Since PQR is isosceles, we can also see that angle PQR is equal to angle PRQ. Therefore, angles PQR and PRQ are equal and each is approximately 69.3 degrees (using inverse cosine function).
Using the sine function, we can find the length of PT:
sin(69.3) = PT / 7.5
PT = 7.5 * sin(69.3)
PT ≈ 6.93 cm
Using the Pythagorean theorem, we can find the length of RT:
[tex]RT^2 + PT^2 = PR^2[/tex]
[tex]RT^2 = PR^2 - PT^2[/tex]
[tex]RT^2 = 7.5^2 - 6.93^2[/tex]
RT ≈ 3.16 cm
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need help to this what would the variance be?
The variance of the set of data is 10. Option A
What is variance?Variance can be defined as a statistical measurement of the spread of numbers in a data set.
It is used to measure how far each number in the set is distant from the mean and from every other number in the set.
It is sometimes described as the measure of variability.
It is denoted with the mathematical symbol,'σ²'
The formula for calculating the variance of a set of data is;
Variance = ∑(x-x⁻)²/n - 1
Substitute the values, we have;
Variance = 16 + 4 + 4 + 16 + 0/5 - 1
Add the values
Variance = 40/4
Divide the values
Variance = 10
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the top of an l-shaped desk has the dimensions shown. what volume of wood is needed to make the top of the desk? complete the explanation of how you solved this problem.
The volume of wood needed to make the top of the l-shaped desk is 0.728 cubic feet
The top of an l-shaped desk has the dimensions shown in the diagram. To determine the volume of wood needed to make the top of the desk, we must use the formula for volume. The formula for volume is length times width times height, or V = lwh. In this case, the length of the top is 28 inches, the width is 45 inches, and the height is 0.75 inches.
Plugging these values into the volume formula gives us V = 28 x 45 x 0.75, which equals 1260 cubic inches. Since wood is typically sold in cubic feet, we must convert this volume to cubic feet by dividing it by 1728, the number of cubic inches in one cubic foot. 1260/1728 = 0.728, so the volume of wood needed to make the top of the desk is 0.728 cubic feet.
To summarize, the volume of wood needed to make the top of the l-shaped desk is 0.728 cubic feet. This was determined by using the volume formula, which is V = lwh, where l is the length, w is the width, and h is the height. The length, width, and height of the desk top were 28 inches, 45 inches, and 0.75 inches, respectively. By plugging these values into the volume formula and converting to cubic feet, we determined the volume of wood needed is 0.728 cubic feet.
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what central idea about mathematical instruction does the author express in passage 1?
An all-night study session can help you catch up on school assignments. The only way to become a straight-A student is efficient study habits.
Most students pseudo-work and end up wasting valuable time.
The correct option is (C)
This is based on an article about pseudo-working which is something that students do where they read for long hours and appear very serious in reading when in fact they do not focus on the reading and therefore end up not grasping much.
The author was trying to express that most students do this and that it is simply a waste of time which could have been spent actually studying.
The correct option is (C).
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The given question is incomplete, complete question is:
What central idea about studying does the author express in Passage 1?
A Straight-A students know how to work harder than other students.
B The only way to become a straight-A student is efficient study habits.
C Most students pseudo-work and end up wasting valuable time.
D An all-night study session can help you catch up on school assignments.
Answer this for points
suppose that a conveyor used to sort packages by size does not work properly. we test the conveyor on several packages (with h0:incorrect sort) and our data results in a p-value of 0.016. what probably happens as a result of our testing?
If the p-value of a hypothesis test is 0.016, it means that the probability of observing the data or more extreme data assuming the null hypothesis (i.e., the conveyor works properly) is 0.016. So, we reject the null hypothesis.
This p-value is relatively small and falls below the conventional significance level of 0.05. Therefore, we can reject the null hypothesis that the conveyor works properly and conclude that the conveyor is not sorting packages correctly.
However, we cannot determine the cause of the problem with the conveyor from this hypothesis test alone. Further investigation is necessary to identify the root cause of the issue and determine the appropriate corrective actions.
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A person places $398 in an investment account earning an annual rate of 9.7%, compounded continuously. Using the formula V = Pe^{rt}V=Pe rt , where V is the value of the account in t years, P is the principal initially invested, e is the base of a natural logarithm, and r is the rate of interest, determine the amount of money, to the nearest cent, in the account after 7 years.
A person has $785.35 after 7 years in the account.
What is continuous compound interest?Interest that is compounded continuously to the principal amount. This interest rate provides exponential growth for a period of time.
The formula of continuous compound interest rate;
[tex]V = Pe^{rt}[/tex],
Where P is the principal amount, r is the interest rate and t is the time period.
A person places $398 in an investment account earning an annual rate of 9.7%, compounded continuously.
Using the formula:
[tex]V = Pe^{rt}[/tex], where P = $398, r = 0.097 (9.7% as a decimal), and t = 7 years, we can calculate the value of the account after 7 years as:
V = 398[tex]e^(0.0977)[/tex]
V = 398[tex]e^{0.679}[/tex]
V = 784.818126761
V = $785.35 (rounded to the nearest cent)
Therefore, the amount of money in the account after 7 years is $785.35.
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Last year, 89 musicians attended a jazz camp, and 15 of them were bassists. What is the experimental probability that the first musician to sign up will be a bassist?
There is a roughly 16.85% chance that a bassist will be the first musician to register for the jazz camp.
What is experimental probability?Experimental probability is a type of probability that is based on actual observations or experiments. It is also called empirical probability
According to question:The ratio of the frequency of an occurrence to the total number of trials or observations is known as the experimental probability. In this case, the event is the first musician to sign up being a bassist.
Since there were 15 bassists out of 89 musicians who attended the camp last year, the experimental probability of the first musician to sign up being a bassist is:
Experimental probability = Number of bassists / Total number of musicians
Experimental probability = 15 / 89
Experimental probability = 0.1685 or approximately 16.85%
As a result, there is a roughly 16.85% chance that a bassist will be the first musician to register for the jazz camp.
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