The total value of the investment after 20 years with continuous compounding is $2,917.76.
Given information:
P = principal = $1000.
R = 5.5%
t = 20 years.
First, convert R as a percent to 'r' as a decimal
r = R/100
r = 5.5/100
r = 0.055 rates per year,
Then solve the equation for A:
The total value of the investment can be calculated using the formula:
A = P(1 + r/n[tex])^{nt}[/tex]
A = 1,000.00(1 + 0.055/1[tex])^{(1)(20)}[/tex]
A = 1,000.00(1 + 0.055[tex])^{(20)}[/tex]
A = $2,917.76
The total amount accrued, principal plus interest, with compound interest on a principal of $1,000.00 at a rate of 5.5% per year compounded 1 time per year over 20 years is $2,917.76.
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Which place should we compare to determine the greater of the given numbers -7295 and 7259
The tens place is what we have to compare to determine the greater of the given numbers -7295 and 7259
How to compare the numbersTo determine which number, 7259 or -7295, is greater, we can compare their place values starting with their leftmost digit.
7295 and 7259 have sevens in the thousands place; 7259 also has one; however, when we compare the next digit -7295 has twos while 7259 only has one in its hundreds place.
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I have a question for y'all now LOL so a piano Grand weighs 0.5 ton what is the weight in pound I need an answer right now please and thank you
Answer:
This gives you 1000 pounds. So, a piano grand that weighs 0.5 ton has a weight of 1000 pounds.
Step-by-step explanation:
Answer:
a ton is 2,000 lbs so 0.5 tons would be 1,000 lbs
Step-by-step explanation:
and rn i need a comically large pianoto fall on top of my head :D
Graph the system of equations to determine the solution.
y=1/2 x+3
2y = x +6
The system of equations have infinite solution.
We have to given that;
The system of equations are,
⇒ y = 1/2 x +3
⇒ 2y = x +6
Here, Equation (i);
⇒ y = 1/2 x +3
⇒ 2y = x + 6
Which is same as (ii).
Now, We can draw system of equations we can see that both line are coincide.
Hence, The system of equations have infinite solution.
Thus, The system of equations have infinite solution.
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he tables represent the points earned in each game for a season by two football teams.
Eagles
3 24 14
27 10 13
10 21 24
17 27 7
40 37 55
Falcons
24 24 10
7 30 28
21 6 17
16 35 30
28 24 14
Which team had the best overall record for the season? Determine the best measure of center to compare, and explain your answer.
Eagles; they have a larger median value of 21 points
Falcons; they have a larger median value of 24 points
Eagles; they have a larger mean value of about 22 points
Falcons; they have a larger mean value of about 20.9 points
Eagles; they have a larger mean value of about 22 points. Therefore, option C is the correct answer.
The best measure of center to compare the team records for the season would be the mean value, as it takes into account all the points earned in each game and provides an average value.
In this case, the Eagles have a larger mean value of about 22 points compared to the Falcons, who have a mean value of about 20.9 points. Therefore, the Eagles had the best overall record for the season.
Therefore, option C is the correct answer.
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a study of the effects of exercise used rats bred to have high or low capacity for exercise. the 8 high-capacity rats had mean blood pressure 89 mm hg and standard deviation 9 mm hg; the 8 low-capacity rats had mean blood pressure 105 mm hg with standard deviation 13 mm hg. we suspect that rats with low capacity for exercise tend to have a higher blood pressure than rats with a high capacity for exercise. to see if this is true, test these with hypotheses for the mean blood pressure of all rats with high capacity (hc) and all rats with low capacity (lc) for exercise. given this scenario, how would you specify the null and alternative hypothesis? (keep in mind the preferred alternative hypothesis for this kind of test)
The null hypothesis is that there is no significant difference between the mean blood pressure of rats with high capacity for exercise and rats with low capacity for exercise. The alternative hypothesis is that rats with low capacity for exercise tend to have a higher blood pressure than rats with high capacity for exercise.
This is the preferred alternative hypothesis for this kind of test because it is a one-tailed test with a directional hypothesis, indicating that we are specifically interested in whether the mean blood pressure of low-capacity rats is higher than that of high-capacity rats.
Therefore, the null hypothesis can be written as H0: μhc = μlc, and the alternative hypothesis can be written as Ha: μlc > μhc.
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A random sample of 30 students at a high school was allowed to play a popular cell phone game for an hour in order to score as many points as possible. The sample yielded an average score of 375 and a standard deviation of 100. The resulting 90% confidence interval is 375 +31. Which of the following statements best summarizes the meaning of this confidence interval? If we repeated this procedure many times, about 10% of the confidence intervals constructed will fail to include the mean number of points scored by all students at a high school. If we repeated this procedure many times, the average number of points scored by our sample of 30 students will be between 344 and 406 points approximately 90% of the time. o Approximately 10% of all students at the high school will score more than 406 points. Approximately 90% of the students at a high school will have an average score between 344 and 406 points.
If we repeated this procedure many times, the average number of points scored by our sample of 30 students will be between 344 and 406 points approximately 90% of the time.
This means that we are 90% confident that the true population mean of points scored by all students at the high school falls within this range based on the sample of 30 students who played the game for an hour.
A random sample of 30 students at a high school was allowed to play a popular cell phone game for an hour, yielding an average score of 375 with a standard deviation of 100. The 90% confidence interval is 375 ± 31. The statement that best summarizes the meaning of this confidence interval is: If we repeated this procedure many times, the average number of points scored by our sample of 30 students will be between 344 and 406 points approximately 90% of the time.
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What is the value of x?
x = 1/2 × 68
= 34
That's the rule just its half also y is the same thing while x and y are looking at the same arc
:>
Which of the following choices describes the sequence 12, 17, 22, 27, 32,…? each term has two more than the previous term each term has five more than the previous term each term is twice the previous term None of these choices are correct.
Answer:
Each term has five more than the previous term
Step-by-step explanation:
The difference in each term is 5.
12 + 5 = 17
17 + 5 = 22
22 + 5 = 27
And so on. Thus, each term has five more than the one before it. 17 has 5 more than 12.
Solve for x trigonometry
Answer:
12.29 cm
Step-by-step explanation:
You want the side adjacent to the 35° angle in a right triangle with hypotenuse 15 cm.
CosineThe trig relation of interest is ...
Cos = Adjacent/Hypotenuse
cos(35°) = x/(15 cm)
Multiplying by 15 cm gives ...
x = (15 cm)·cos(35°)
x ≈ 12.29 cm
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your friend deposits $6500 in an investment account that earns 8.4% annual interest. Find the balance after 12 years when the interest is compounded monthly.
Answer:
We can use the formula for compound interest to solve this problem:
A = P(1 + r/n)^(nt)
where:
A = the balance after t years
P = the principal amount (initial deposit)
r = the annual interest rate (as a decimal)
n = the number of times the interest is compounded per year
t = the number of years
In this problem, P = $6,500, r = 0.084, n = 12 (monthly compounding), and t = 12. Plugging in these values, we get:
A = $6,500(1 + 0.084/12)^(12*12)
A = $6,500(1.007)^144
A = $6,500(2.008)
A = $13,052.20
Therefore, the balance after 12 years is $13,052.20 when the interest is compounded monthly.
I really need help please
The events are dependent "d". And the probability of selecting a number less than 6 both times is 5.3%
Probability of an event without replacementThe probability of an event without replacement implies that once an item is drawn, then we do not replace it back to the sample space before drawing another item.
The events are dependent since the probability of selecting a number on the second draw will depend on what number was selected on the first draw.
Total possible outcome = 20
numbers less than 6 = 5
probability of both selected are less than 6 = 5/20 × 4/19
probability of both selected are less than 6 = 1/19
1/19 in percentage = 1/19 × 100 = 5.3%.
Therefore, the events are dependent "d". And the probability of selecting a number less than 6 both times is 5.3%.
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Please answer quickly (for notes)
Use the image to determine the direction and angle of rotation.
Options:
A 90° counterclockwise rotation
B 180° counterclockwise rotation
C 90° clockwise rotation
D 270° clockwise rotation
Answer:
The answer should be B. :3
Step-by-step explanation:
How would you solve this!?
Answer:
Step-by-step explanation
since you have a volume cube, you have to multiply. So it'll be like length x width x height. And the multiplication will be 9x5x8 which is 360 cubic inches.
Check out this cube: The figure presents a cube. The length of one edge is labeled as 3 units The figure presents a cube. The length of one edge is labeled as 3 units Find the surface area of the cube (above) using its net (below). The figure presents a surface net of a cube. The net consists of 4 squares connected in a row. The second square from the left is also connected to a square above it, and a square below it. The length of one side of one square is labeled as 3 units. The figure presents a surface net of a cube. The net consists of 4 squares connected in a row. The second square from the left is also connected to a square above it, and a square below it. The length of one side of one square is labeled as 3 units. units 2 2
Answer: look it up-
Step-by-step explanation:
Consider the given equation and graph. x^2 \: - \: 5x \: + \: 6 \: = \: \sqrt{x \: + \: 3} What are the approximate solutions to the equation?
Answer:
.
Step-by-step explanation:
.
a fair die is rolled times. what is the probability that a is obtained on at least one of the rolls? round your answer to three decimal places.
The probability that a 6 is obtained on at least one of the rolls is 67%.
The probability of getting a 6 on one roll of a fair die is 1/6. The probability of not getting a 6 on one roll is 5/6.
Let's use the complementary probability approach to calculate the probability of getting no 6 on any of the 5 rolls. The probability of not getting a 6 on one roll is 5/6, so the probability of not getting a 6 on all 5 rolls is (5/6)^5 ≈ 0.327.
Therefore, the probability of getting at least one 6 on 5 rolls is 1 - 0.327 ≈ 0.673.
So the probability of getting at least one 6 on 5 rolls of a fair die is approximately 0.673, or 67.3% when rounded to three decimal places. This means that if you roll a fair die 5 times, you have about a 67% chance of getting at least one 6.
Correct Question :
A fair die is rolled 5 times. What is the probability that a 6 is obtained on at least one of the rolls? Round your answer to three decimal places.
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Determine how many TRIANGLES can be constructed with angles measuring 112°, 54°, and 16°.
a) State whether there are NO TRIANGLES, MORE THAN 1 TRIANGLE, OR 1 TRIANGLE.
b) Show your work to prove your answer from part a.
Using the information provided, no triangle will be formed.
This is shown by, summing the angles
How to find the number of triangles to be formedThe number of triangles to be formed considering the given angles is achieved knowing the basic properties of triangle which is:
sum of angles of a triangle is equal to 180 degreesWith this knowledge, we sum the angles of the triangle
= 112 + 54 + 16
= 182
No triangle is formed as the sum is not equal to 180 degrees
If the angles are summed to 180 degrees, this is a criterion of formation of unlimited number of triangle
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the u.s. senate of the 109th congress consisted of 55 republicans, 44 democrats, and 1 independent. how many committees can be formed if each committee must have 4 republicans and 3 democrats?
4,516,932,420 committees can be formed if each committee must have 4 republicans and 3 democrats
We have,
Republicans= 55
Democrats = 44
Independent= 1
Using Combination, the number of committees can be formed
= C(55, 4) / C(44, 3)
= 55! / 4! (55-4)! ÷ 44!/ 3! (44-3)!
= 55! / 4! 51! x 44! / 3! 41!
= 55 x 54 x 53 x 52 x 44 x 43 x 42/ 4 x 3 x 2 x 3 x 2
= 650,438,268,480 / 144
= 4,516,932,420
Thus, there are 4,516,932,420 committees can be formed.
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how many constant terms are in n²÷3+6n
Answer:
3
Step-by-step explanation:
Travis bought 14 tickets to the school play for 54$. Children tickets cost $3 and adult tickets cost $5. How many adult tickets did he buy?
Answer:
Step-by-step explanation:
Let x be the number of adult tickets Travis bought, and y be the number of children tickets he bought.
We know that Travis bought a total of 14 tickets, so x + y = 14.
We also know that the total cost of the tickets was $54, so 5x + 3y = 54.
We can use the first equation to solve for y in terms of x: y = 14 - x.
Substituting this into the second equation, we get:
5x + 3(14 - x) = 54
Simplifying and solving for x, we get:
5x + 42 - 3x = 54
2x + 42 = 54
2x = 12
x = 6
Therefore, Travis bought 6 adult tickets and 14 - 6 = 8 children tickets.
to find maximum wage of number equality of boy adult and child.
I mean: 48 = 6.8
12 person from here
2 person remain
6 $ remain as well
6 = 2 child ticket
so the answer is 6
a company screens job applicants for illegal drug at a certain stage in their hiring process. their test has a 2% false positive rate and 1% false negative rate. suppose 5% of all applicants are using illegal drugs. given the applicant tests positive, what is the probability that randomly selected applicant is on drugs? question 8 options:
The probability of randomly selecting an applicant who is on drugs is 71% under the given condition that test has a 2% false positive rate and 1% false negative rate and suppose 5% of all applicants are using illegal drugs.
Let us consider the probability of a person on drugs as P(D) = 0.05.
The probability of a person not on drugs is P(¬D) = 0.95.
The probability of a positive test result given that the person is on drugs is P(T|D) = 1 - False Negative Rate = 0.99.
The probability of a positive test result given that the person is not on drugs is P(T|¬D) = False Positive Rate = 0.02.
Applying Bayes' theorem, we can evaluate the probability that a randomly selected applicant is on drugs
P(D|T) = (P(T|D) × P(D)) / (P(T|D) × P(D) + P(T|¬D) × P(¬D))
= (0.99 × 0.05) / (0.99 × 0.05 + 0.02 × 0.95)
≈ 0.71
Converting into percentage
= 0.71 × 100
= 71%
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What shape is a prism?
Rectangular
triangular
spherical
Answer:
A prism is a three-dimensional shape with two congruent and parallel polygonal bases connected by parallelogram-shaped sides. The base shape can vary, so a prism can have rectangular, triangular, or other polygonal bases. When you search up a prism on the Internet, the first result that appears is a rectangular prism. We cannot provide much help without further elaboration, as all of the answers are types of prisms.
Answer:
Prisms can be both triangle and rectangle. if you can't circle or choose 2 answers then you should've been given a picture. hope it helps
5/16 with bar notation
Answer:
5/16 with bar notation is written as 0.3125, where the bar is placed over the digit "5" to indicate that it repeats infinitely. This notation is used to represent a repeating decimal, where the digit or group of digits after the bar repeats infinitely without terminating. In this case, the digit "5" repeats infinitely after the decimal point.
Answer:
The bar notation is used to indicate that a digit or a sequence of digits repeats indefinitely. To express 5/16 with a bar notation, we need to find the decimal equivalent of 5/16 and identify any repeating digits.
To convert 5/16 to a decimal, we can perform the division as follows:
0.3125
The decimal equivalent of 5/16 is 0.3125. Since there are no repeating digits, we cannot express it with a bar notation.
~'
can anyone help me with this
Answer:
A.
1. 16=(1+3)²
2. 25=(2+3)²
3. 36=(3+3)²
4. 49=(4+3)²
Un = (n +3)²
64=(5+3)²
B.
2^3,3^3,4^3,5^3,so the next one is 6^3, which is 216.
An empty shipping box has a mass of. 3 pounds. A clothing store
The maximum weight of clothes that can be shipped in the box without exceeding the weight limit for shipping is 47 pounds.
To determine the maximum weight of clothes that can be shipped in the box, we first need to know the weight limit for shipping. This will vary depending on the shipping method and destination. Let's assume that the weight limit for shipping is 50 pounds.
We subtract the weight of the empty box from the weight limit for shipping: 50 pounds - 3 pounds = 47 pounds.
It is always a good idea to check the specific weight limit for the shipping method and destination before packing and shipping any items to avoid any issues or additional fees.
The complete question is:
What is the maximum weight of clothes that can be shipped in the box without exceeding the weight limit for shipping?
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Suppose y varies directly with x. When x is 7, y is 28. What is y when x is 13?
Therefore, when x is 13, y is 52 if y varies directly with x.
What is equation?In mathematics, an equation is a statement that two expressions are equal. It is usually written using an equal sign (=). Equations can contain variables, which are usually represented by letters, and the goal is often to solve the equation for the value(s) of the variable(s) that make the equation true.
Here,
If y varies directly with x, then we can write the relationship between y and x using the equation:
y = kx
where k is the constant of proportionality. To solve for k, we can use the given information that when x is 7, y is 28:
28 = k(7)
Solving for k, we get:
k = 4
Now that we know k, we can use the equation to find y when x is 13:
y = 4(13)
y = 52
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Janice is searching for a cellular phone plan. The table shows information about monthly
prices for two different cellular phone plans.
Cellular Phone Plan
Digital Talk
Cell-to-Cell
Cost Description
Variable rate: $0.20 per minute
Fixed rate: $50 per month
Janice has a coupon for 25% off the fixed cost per month for the first year of service with
Cell-to-Cell. What will the discounted cost be for an entire year of service with Cell-to-Cell?
The discounted cost for an entire year of service with cell-to-cell would be = $450
How to calculate the discounted cost for cell-to-cell services?The fixed rate for cell-to-cell services for a month = $50
Therefore the cost for a year would be = 50×12 = $600
The percentage of discount on the coupon = 25%of cost Price.
That is 25% of 600
= 25/100 × 600/1
= 25×6
= $150
Therefore, the discounted cost for an entire year of service with cell-to-cell would be = 600-150=$450
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you can bet on single squares or combinations of squares. each square has a number and a color. eighteen of the squares are red, 18 are black, and 2 are green. one thing you can do is bet red (or black), and it pays even money. (you risk $1, but if the roulette lands on any red space, you get back your $1 plus $1 in winnings.) if you play 30 times, betting $1 on red each time, what is the probability you will come out ahead?
The probability that you will come out ahead is 16.9%.
The probability of winning a single bet on red is 18/38 because there are 18 red squares out of a total of 38 squares (18 red, 18 black, and 2 green).
The probability of losing a single bet on red is 20/38 because there are 20 non-red squares out of a total of 38 squares.
The expected value of a single bet on red is:
(18/38) x 1 + (20/38) x (-1) = -0.0526
This means that for every $1 bet on red, you can expect to lose about 5.3 cents on average.
Now, if you play 30 times, betting $1 on red each time, the total amount you bet will be $30. The expected value of your total winnings will be:
-0.0526 x 30 = -$1.58
This means that, on average, you can expect to lose about $1.58 if you play 30 times and bet $1 on red each time.
The probability of coming out ahead after 30 bets is the probability of winning more than $30 - $1.58 = $28.42.
To calculate this probability, we need to use the binomial distribution with n=30 and p=18/38. Let X be the number of times you win:
P(X > 30 - 1.58) = P(X > 28.42)
Using a binomial distribution calculator, we find that this probability is approximately 0.169 or 16.9%.
Therefore, the probability of coming out ahead after 30 bets of $1 on red is about 16.9%.
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A survey found that 8 of 15 people chose apples as their favorite fruit. If you ask people, how many can you predict will choose apples as their favorite fruit?
The predicted number of people from a size of n who choose apples as their favorite fruit is equal to (8n)/15.
Total number of people surveyed = 15
Total number of people chose apple as their favorite fruit = 8
Based on the survey results,
8 out of 15 people chose apples as their favorite fruit.
Let us consider x be the number of people who chose apples in the original survey
And n be the size of the new group we want to make a prediction for.
To predict how many people out of a different group would choose apples as their favorite fruit, use the proportion.
⇒ 8/15 = x/n
To solve for x, we can cross-multiply and simplify,
⇒ 8n = 15x
⇒ x = (8n)/15
Therefore, predicted number of people will choose apples as their favorite fruit is approximately equal to (8n)/15 .
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a 30 gram sample of a substance that's used to sterilize surgical instruments has a k value of 0.1253 find the substance's half life in days round your answer to the nearest tenth
When, a 30 gram sample of a substance that's used to sterilize surgical instruments has a k value of 0.1253. Then, the half-life of the substance is 8.0 days.
The half-life of a substance is the amount of time it takes for half of the initial amount of the substance to decay. The decay of the substance can be modeled using the formula;
N = N0 × [tex]2^{(-kt)}[/tex]
where N is the amount of substance at time t, N0 is the initial amount of substance, k is the decay constant, and t is the time.
In this case, we know that the initial amount of the substance is 30 grams, and the decay constant (k value) is 0.1253. We want to find the half-life, which we can denote as [tex]t_{1/2}[/tex]
When half of the initial amount of substance remains, the amount of substance is [tex]N_{0}[/tex]/2. So we can substitute N = [tex]N_{0}[/tex]/2 and solve for [tex]t_{1/2}[/tex];
N = [tex]N_{0}[/tex]/2
[tex]N_{0}[/tex]/2 = [tex]N_{0}[/tex] × [tex]2^{(-kt1/2)}[/tex]
1/2 = [tex]2^{(-kt1/2)}[/tex]
log2(1/2) = log2([tex]2^{(-kt1/2)}[/tex])
-1 = [tex]-kt_{1/2}[/tex]
[tex]t_{1/2}[/tex] = 1/k × log2(2)
[tex]t_{1/2}[/tex] = 1/k
Substituting the given value of k, we get:
[tex]t_{1/2}[/tex] = 1/0.1253
[tex]t_{1/2}[/tex] ≈ 7.9816
Therefore, the half-life of the substance is approximately 8.0 days.
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