The balance of the account after 20 years with continuous compounding interest is $733.86.
What is the balance of the account after 20 years?The formula accrued amount compounded continuously is expressed as;
A = P × e^(rt)
Where A is accrued amount, P is principal, r is interest rate and t is time.
Given that:
Principal P = $200Compounded contiouslyTime t = 20 yearsInterest rate r = 6.5%Accrued amount A = ?First, convert R as a percent to r as a decimal
r = R/100
r = 6.5/100
r = 0.065
Plugging in the given values, we get:
A = P × e^(rt)
A = $200 × e^( 0.065 × 20)
A = $733.86
Therefore, the accrued amount after 20 years is $733.86.
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what is the surface area of 2in 5.2in 4in
The surface area of a rectangular prism of dimensions 2 in, 5.2 in and 4 in is given as follows:
S = 78.4 in².
What is the surface area of a rectangular prism?The surface area of a rectangular prism of height h, width w and length l is given by:
S = 2(hw + lw + lh).
This means that the area of each rectangular face of the prism is calculated, and then the surface area is given by the sum of all these areas.
The dimensions for this problem are given as follows:
2 in, 5.2 in and 4 in.
Hence the surface area of the prism is given as follows:
S = 2 x (2 x 5.2 + 2 x 4 + 5.2 x 4)
S = 78.4 in².
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Please help i’m in 10th grade and i don’t understand this-
Answer:
negative linear association
5. What is the Boolean duality principle?
The Boolean duality principle is a fundamental concept in Boolean algebra which states that any statement or expression in the algebra can be transformed into an equivalent form by interchanging the roles of AND and OR operators, as well as 0's and 1's.
The Boolean duality principle, also known as De Morgan's laws, is a fundamental concept in Boolean algebra that states that every Boolean expression remains valid if you perform the following steps:
1. Swap AND (⋅) operators with OR (+) operators and vice versa.
2. Replace all 1's with 0's and all 0's with 1's.
3. Complement (invert) all variables.
In other words, the Boolean duality principle allows us to derive a dual expression from an original Boolean expression by applying these transformations. This principle is useful in simplifying Boolean expressions and designing digital circuits.
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A student mows lawns on the weekends. It takes him 140 minutes to mow 4 lawns. What prediction can you make about the time he will spend this weekend if he has 12 lawns to mow?
It will take him 12 hours to mow 12 lawns.
It will take him 10 hours to mow 12 lawns.
It will take him 7 hours to mow 12 lawns.
It will take him 3 hours to mow 12 lawns.
Answer:
C. It will take him 7 hours to mow 12 lawns
Step-by-step explanation:
140 mins = 4 lawns
12 lawns = 4 x 3
140 x 3 = 420 minutes (12 lawns)
420 ÷ 60 = 7 hours
Area = 55
Perimeter = 23
Area = 47.6
Perimeter = 23
Area = 55
Perimeter = 32
Area = 47.6
Perimeter = 32
Solve x^2-4x+4=0 by graphing. Select all solutions that apply.
Answer:
−
x
2
−
4
x
−
4
=
0
Graph each side of the equation. The solution is the x-value of the point of intersection.
x
=
−
2
image of graph
Step-by-step explanation:
−
x
2
−
4
x
−
4
=
0
Graph each side of the equation. The solution is the x-value of the point of intersection.
x
=
−
2
image of graph
Higher Order Thinking Suppose
you have the three cups shown at the
right. List two different ways you can
measure exactly 1 liter.
Plsss help
Two different ways we can measure exactly 1 Liter are:
Use of the 500 mL cup two times
Use the 300 mL cup 3 times in total and the 100 mL cup once
What is the volume of the cups?This question we want to know the different combination of the given cups that can lead to us getting a volume of 1 liter.
Now, we know that
1 L = 1000 mL
This means that we can make use of the 500 mL cup two times in total to get:
500 mL + 500 mL= 1000 mL = 1 L
Another way we can do the 1 liter is that we can use the 300 mL cup 3 times in total and the 100 mL cup once to get:
300 mL + 300 mL + 300 mL + 100 mL = 1000 mL = 1 L
Other ways are:
- use of the 500 mL cup two timese the 100 mL cup
- Take 10 times the 100-mL cup
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Complete question is:
Suppose you have a 100-mL cup,a 300-mL cup, and a 500-mL cup. list two different ways you can measure exactly 1 L
Luis is deciding between two truck rental companies. Company A charges an initial fee of $40 for the rental plus $0.50 per mile driven. Company B charges an initial fee of $10 for the rental plus $1 per mile driven. Let A A represent the amount Company A would charge if Luis drives x x miles, and let B B represent the amount Company B would charge if Luis drives x x miles. Graph each function and determine the interval of miles driven, x , x, for which Company A is cheaper than Company B.
match the list on the left with the possible number of times the binary search algorithm splits the list when searching for a term in the list.
The possible number of times the binary search algorithm splits the list when searching for a term in the list varies depending on the length of the list and the position of the term within the list.
However, in general, the number of times the list is split during the binary search algorithm is proportional to the logarithm of the length of the list. So, for example, if the list has 8 items, the binary search algorithm may split the list up to 3 times (log base 2 of 8 is 3), while if the list has 1024 items, the binary search algorithm may split the list up to 10 times (log base 2 of 1024 is 10).
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Unit 7 right triangles and trigonometry homework 2 special right triangles
The values of x, y and z from the triangle are z = 12√2, x = 6 and y = 12
What is trigonometrical ratio of angles?Trigonometrical ratio of angles is used to find the sine, cosine, and tangent of angles in right triangles
The ratios are denoted by SOHCAHTOA
Tan A = Oppo/Adj
Tan 60 = 6√3/x
√3/ 1 = 6√3/x
Cross and multiply to have
x√3/3 = 6√3/√3
x = 6
To find y
First from pyth. rule
6² + (6√3)² = m²
36 + 36*3 = m²
144 = m²
m =√144 = 12
Using tan 45 = 1/1
Tan 45 = y/12
1/1 = y /12
y = 12
To find x w use sine
Sin 45 = 1/√2
1/√2 = 12/x
x = 12√2
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Company's Complaints
Number
of Complaints
225
205
187
169
147
130
Week
1
23
3
45
6
Based on the line of best fit, how many complaints should the company expect at the end of week 8?
A 110
B 96
C 91
D 75
The company ought to anticipate 96 complaints at the conclusion of week 8 based on the line of best. (Option B).
How to Solve the Problem?To anticipate the number of complaints at the conclusion of week 8, we got to utilize the line of best fit condition, which speaks to the relationship between the weeks and the number of complaints.
Expecting that we have as of now calculated the line of best fit and determined that it may be a straight relationship, we are able utilize the slope-intercept frame of a line:
y = mx + b
where:
y = the anticipated number of complaints at the conclusion of week 8
m = the slant of the line of best fit
x = 8 (since we need to predict the number of complaints at the conclusion of week 8)
b = the y-intercept of the line of best fit
We will calculate the slant and y-intercept utilizing the given information:
Incline (m): To discover the slant of the line of best fit, we got to utilize the equation:
m = (n∑xy - ∑x∑y) / (n∑x^2 - (∑x)^2)
where:
n = the number of information focuses (in this case, 6 weeks)
∑xy = the entirety of the items of the x and y values
∑x = the whole of the x values
∑y = the whole of the y values
∑x^2 = the entirety of the squared x values
Utilizing the information given within the table, ready to calculate:
∑xy = (1225) + (2205) + (3187) + (4169) + (5147) + (6130) = 2859
∑x = 1 + 2 + 3 + 4 + 5 + 6 = 21
∑y = 225 + 205 + 187 + 169 + 147 + 130 = 1063
∑x^2 = 1^2 + 2^2 + 3^2 + 4^2 + 5^2 + 6^2 = 91
Utilizing these values, ready to calculate the incline:
m = ((62859) - (211063)) / ((6*91) - (21^2)) = -17.5
Y-intercept (b): To discover the y-intercept of the line of best fit, we will utilize the equation:
b = y - mx
where:
y = the cruel of the y values
m = the slant of the line of best fit
x = the cruel of the x values
Utilizing the information given within the table, able to calculate:
y = (225 + 205 + 187 + 169 + 147 + 130) / 6 = 177.17
x = (1 + 2 + 3 + 4 + 5 + 6) / 6 = 3.5
Utilizing these values, ready to calculate the y-intercept:
b = 177.17 - (-17.5 * 3.5) = 235.92
Presently that we have the incline and y-intercept, we are able to utilize the condition for a line to anticipate the number of complaints at the conclusion of week 8:
y = -17.5x + 235.92
where x = 8 (since we need to anticipate the number of complaints at the conclusion of week 8)
y = -17.5(8) + 235.92
y = 96.42
Adjusting to the closest entirety number, the answer is (B) 96 complaints. Therefore, the company ought to anticipate 96 complaints at the conclusion of week 8 based on the line of best
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a piece of metal 24 inches by 20 inches is made into a box by cutting out sqaures of side x from each corner let V(x) be the volume of the box
write a function in standard form to represent the volume V(x) of the open box
staye an approximate domain for V(x)
calculate V(x)
To determine the volume of the box, we need to find the length, width, and height of the box. We can do this by subtracting twice the length of the square cutouts from the original length, twice the width of the square cutouts from the original width, and the height will be the length of the square cutouts.
Let's assume that the side length of the square cutouts is x. Then the length of the box is (24 - 2x), the width of the box is (20 - 2x), and the height of the box is x. Thus, the volume of the box can be expressed as:
V(x) = (24 - 2x) * (20 - 2x) * x
To simplify this expression, we can expand it using the distributive property and then combine like terms:
V(x) = 4x^3 - 88x^2 + 480x
The approximate domain for V(x) would be [0, 10] since the side length of the square cutouts cannot be greater than half the length or width of the original piece of metal, which is 12 and 10 respectively.
To calculate V(x), we simply substitute x into the formula for V(x):
V(x) = 4x^3 - 88x^2 + 480x
Let's say we want to calculate V(2):
V(2) = 4(2)^3 - 88(2)^2 + 480(2)
= 16 - 352 + 960
= 624
Therefore, the volume of the box when the side length of the square cutouts is 2 inches is 624 cubic inches.
Suppose that the miles-per-gallon (mpg) rating of passenger cars is normally distributed with a mean and a standard deviation of 33.7 mpg and 4.4 mpg, respectively. What is the probability that a randomly selected passenger car gets more than 35 mpg?
P(X > 35) ≈ 0.384
To find the probability that a randomly selected passenger car gets more than 35 mpg given that the miles-per-gallon (mpg) ratings are normally distributed with a mean of 33.7 mpg and a standard deviation of 4.4 mpg, follow these steps:
1. First, calculate the z-score, which represents how many standard deviations away from the mean our target value (35 mpg) is:
z = (X - μ) / σ
z = (35 - 33.7) / 4.4
z ≈ 0.295
2. Next, use a standard normal distribution (z) table or an online calculator to find the probability that corresponds to the z-score of 0.295. This gives you the probability of a car having 35 mpg or less.
3. Since we want to find the probability of a car getting more than 35 mpg, subtract the probability obtained in step 2 from 1:
P(X > 35) = 1 - P(X ≤ 35)
Using a z-table or an online calculator, the probability for a z-score of 0.295 is approximately 0.616. Thus,
P(X > 35) = 1 - 0.616
P(X > 35) ≈ 0.384
So, the probability that a randomly selected passenger car gets more than 35 mpg is approximately 38.4%.
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Are these correct or not?
There are 19 ounces
There are 107 visitors per day
He needs 63 boxes
What is the meaning of division in mathematics?1) We have to convert the money to cents thus we have;
$10.45 = 1045 cents
Then Number of ounces = 1045/ 55
= 19 ounces
2) The total number of days the museum was open is 365 - 4 = 361 days
Thus we have that the number of visitors in a day is; 38627/361
= 107 visitors per day
3) If 1 box holds 45 books
x boxes will hold 2835 books
x = 2835/45
x = 63 boxes as shown
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Kenny is making creamy rice pudding his rice requires 4 cups of milk he has a quart of milk in his fridge does he have enough milk explain
Answer:
Yes
Step-by-step explanation:
Kenny will have enough milk to make his dessert because 1 quart contains 4 cups. Since he has 1 quart he has the equivalent to 4 cups.
What if the measure of angle B?
A. 39.8
B. 48.59
C. 33.56
D. .015
Applying the tangent ratio, the measure of angle B in the image given is calculated as: A. 39.8°
How to Find the Measure of the Angle Using the Tangent Ratio?In order to find the measure of angle B, we will need to apply the tangent ratio which is expressed as the formula below:
tan ∅ = length of opposite side / length of adjacent side
From the image given, we have:
∅ = angle B
Length of opposite side = 10 cm
Length of adjacent side = 12 cm
tan B = 10/12
B = tan^(-1)(10/12)
Measure of angle B = 39.8°
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on the next test one of the students in mr arthur's class scores 100 but the other 4 score 50 what is the average
Answer
The average for the next test would be 60
Step-by-step explanation:
50+50+50+50+100= 300
then divide by 5 students
300/5 = 60
What is the domain and range y=x^2+10x+26
The domain will be all real numbers and the range will be all real numbers greater than or equal to 1.
The domain of a function is the set of all possible input values that can be used as arguments for the function. In this case, there are no restrictions on the input values of x, so the domain is all real numbers.
Domain: All real numbers
Range:
To find the range of the function, we can complete the square to rewrite the function in vertex form:
f(x) = x^2 + 10x + 26
f(x) = (x + 5)^2 + 1
Since the square of a real number is always nonnegative, the minimum value of the function is 1, which occurs when x = -5. Therefore, the range of the function is all real numbers greater than or equal to 1.
Range: All real numbers greater than or equal to 1.
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a random sample of 85 supervisors revealed that they worked an average of 7.9 years before being promoted. the population standard deviation was 3.1 years. using the 0.95 level of confidence, what is the confidence interval for the population mean?
the confidence interval for the population mean is (7.245, 8.555) at a 0.95 level of confidence.
To find the confidence interval for the population mean, we can use the formula:
Confidence interval = sample mean +/- margin of error
where the margin of error is calculated as:
Margin of error = z* (population standard deviation / sqrt(sample size))
z* is the z-score corresponding to the confidence level of 0.95, which can be found using a standard normal distribution table or calculator. For a 0.95 confidence level, the z* value is 1.96.
Plugging in the given values, we have:
Sample mean = 7.9 years
Population standard deviation = 3.1 years
Sample size (n) = 85
z* = 1.96
Margin of error[tex]= 1.96 * (3.1 / \sqrt(85)) = 0.655[/tex]
Confidence interval = 7.9 +/- 0.655
Therefore, the confidence interval for the population mean is (7.245, 8.555) at a 0.95 level of confidence.
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the mayor of a town has proposed a plan for the construction of an adjoining bridge. a political study took a sample of 1100 voters in the town and found that 55% of the residents favored construction. using the data, a political strategist wants to test the claim that the percentage of residents who favor construction is more than 51% . determine the p-value of the test statistic. round your answer to four decimal places.
Therefore, at the 8% level of significance, there is strong evidence to suggest that the percentage of residents who favor construction is greater than 51%.
To determine the p-value of the test statistic, we need to follow these steps:
State the null hypothesis and the alternative hypothesis:
Null hypothesis: The percentage of residents who favor construction is equal to 51%.
Alternative hypothesis: The percentage of residents who favor construction is greater than 51%.
Calculate the test statistic:
The test statistic for a one-sample proportion test is given by:
z = (p - P) / √(P * (1 - P) / n)
where:
p is the sample proportion
P is the hypothesized proportion under the null hypothesis
n is the sample size
Plugging in the values we have:
z = (0.55 - 0.51) / √(0.51 * 0.49 / 1100)
= 3.286
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graph 4x-y=3 and 3x+y=4
Answer:
Step-by-step explanation:
You have 7 different video games. How many different ways can you arrange the games side by side on a shult? You can arrange the 7 different video games in different ways
There are 5,040 different ways to arrange the 7 video games side by side on a shult.
To calculate the number of different ways you can arrange the 7 different video games on a shult, you can use the formula for permutations, which is n!/(n-r)!. In this case, n is the total number of games (7) and r is the number of games being arranged at once (also 7, since you are arranging all of them).
So the calculation would be:
7! / (7-7)! = 7! / 0! = 7 x 6 x 5 x 4 x 3 x 2 x 1 = 5,040
Therefore, there are 5,040 different ways you can arrange the 7 different video games side by side on a shult.
To arrange the 7 different video games side by side on a shult, you can use the concept of permutations. In this case, there are 7 video games, and you want to arrange all of them. So, the number of ways to arrange the video games can be calculated using the formula:
Number of arrangements = 7! (7 factorial)
7! = 7 × 6 × 5 × 4 × 3 × 2 × 1 = 5,040
Therefore, there are 5,040 different ways to arrange the 7 video games side by side on a shult.
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I need help please I will give my 10 points I have left.
Answer:
divide and 16 per pound...
Answer:
divide, 16
Step-by-step explanation:
To find the weight, we have to divide the total number of ounces, 96, by the unit rate, which is the baseline for the conversion, 16 ounces.
Hope this helps! :)
karma earns $36 in 3 hours. at this rate, how many dollars will he earn in 20 hours
Answer:
$240
Step-by-step explanation:
We Know
Karma earns $36 in 3 hours.
$36 in 3 hours = $12 in 1 hour
At this rate, how many dollars will he earn in 20 hours?
We Take
12 x 20 = $240
So, he earns $240 in 20 hours.
Answer: 240 dollars
Step-by-step explanation:
divide 36 dollars by 3 (=12)to know how much he earns per hour
then multiply the quotient by 20 which is 240
In a population of N = 10 scores obtained for a discrete variable for which is not a possible score, the smallest score is X = 8 and the largest is X = 20. What is the range for this population? 8 10 12 20
The range for this population is 12, which is calculated by subtracting the smallest score from the largest score (20-8 = 12). Since the variable is discrete, only whole numbers are possible scores, and the score that is not possible is not relevant to the range calculation.
To find the range for this population, you'll need to use the largest and smallest scores.
Given:
- Population (N) = 10
- Discrete variable
- Smallest score (X) = 8
- Largest score (X) = 20
To find the range, simply subtract the smallest score from the largest score:
Range = Largest score - Smallest score
Range = 20 - 8
Range = 12
So, the range for this population is 12.
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WILL MARK BRAINLIEST!!!
Estimate an equation for the line of best fit for the following scatter plot.
The estimated equation for the line of best fit for the scatter plot is y = -5000/3x + 15000
Estimating the equation for the line of best fit for the scatter plot.From the question, we have the following parameters that can be used in our computation:
The scatter plot
When the line of best fit is drawn, we have the following points
(3, 10000) and (0, 15000)
The linear equation is represented as
y = mx + c
Where
c = y when x = 0
So, we have
y = mx + 15000
Using the other point, we have
10000 = 3m + 15000
So, we have
3m = -5000
Divide by 3
m = -5000/3
Hence, the equation is y = -5000/3x + 15000
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32% of drivers have driven drowsy in the past month. law enforcement officials are planning a survey or 1,000 drivers to determine what proportion are driving drowsy. what is the mean of the sampling distribution?
The mean of the sampling distribution can be estimated using the formula for the mean of a binomial distribution, which is μ = np, where n is the sample size and p is the probability of success (in this case, the proportion of drivers who have driven drowsy in the past month).
Given that 32% of drivers have driven drowsy in the past month, we can convert this proportion to a decimal by dividing 32 by 100, which gives us p = 0.32.
The sample size in this case is 1,000 drivers, which we can represent as n = 1,000.
Therefore, the mean of the sampling distribution would be:
μ = np
μ = 1,000 x 0.32
μ = 320
So the mean of the sampling distribution would be 320 drivers who have driven drowsy in the past month, assuming that the sample of 1,000 drivers is representative of the larger population of drivers.
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325 degrees to radians in terms of pi
[tex]\begin{array}{ccll} degrees&radians\\ \cline{1-2} 180 & \pi \\ 325& r \end{array} \implies \cfrac{180}{325}~~=~~\cfrac{\pi }{r} \\\\\\ \cfrac{ 36 }{ 65 } ~~=~~ \cfrac{ \pi }{ r }\implies 36r=65\pi \implies r=\cfrac{65\pi }{36}[/tex]
Answer:
[tex]\dfrac{65\pi}{36}[/tex]
Step-by-step explanation:
To convert 325° to radians in terms of π, we can use the conversion ratio:
[tex]\dfrac{2\pi}{360\°}[/tex]
Multiplying 325° by the conversion ratio:
[tex]325\° \cdot \dfrac{2\pi}{360\°}[/tex]
↓ multiplying the numerators
[tex]\dfrac{650\pi\°}{360\°}[/tex]
↓ canceling degree signs
[tex]\dfrac{650\pi}{360}[/tex]
↓ simplifying the fraction
[tex]\boxed{\dfrac{65\pi}{36}}[/tex]
use the differential to find a decimal approximation of the radical expression. round to four decimal places. (60)^1/2
The decimal approximation of √60, rounded to four decimal places, is 7.7450. Approximate the square root of 60 using the differential method. To do this, we will use linear approximation and the derivative of the square root function.
Let f(x) = x^(1/2), and we want to find f(60). Choose a nearby value of x that is easy to work with, such as x = 64, because f(64) = 8. Now, we will find the derivative of f(x) to determine the rate of change at x = 64.
f'(x) = (1/2)x^(-1/2)
Now, we'll find f'(64):
f'(64) = (1/2)(64)^(-1/2) = 1/16
Using the linear approximation formula, we have:
f(60) ≈ f(64) + f'(64)(60-64)
f(60) ≈ 8 + (1/16)(-4)
f(60) ≈ 8 - (1/4)
f(60) ≈ 7.75
So, the decimal approximation of √60, rounded to four decimal places, is 7.7450.
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A Supermarket Offers a discount OF 5 Cent per EuroE How much will a Custo- mer pay for an article which is priced at €8500?