The answer of the question about the points a, b, and c are the sample size is large enough to use the central limit theorem, the mean is $62,000, the standard error $2,700. and the probability of the sample mean is approximately 0.0002.
How the calculation draw the answer?A) The sample size is large enough to use the central limit theorem for means. This is because the central limit theorem states that the sampling distribution of the mean will approach a normal distribution as the sample size increases, and a sample size of 100 is generally considered to be large enough for the central limit theorem to apply.
B) The mean of the sampling distribution is equal to the population mean, which is $62,000. The standard error of the sampling distribution is equal to the standard deviation of the population divided by the square root of the sample size, or $27,000 / √100 = $2,700.
C) The probability that the sample mean will be more than $2,700 away from the population mean can be found using the standard normal distribution. We can find the z-score for $2,700 using the formula z = (x - μ) / σ, where x is the sample mean, μ is the population mean, and σ is the standard error. Plugging in the values gives us z = ($2,700 - $62,000) / $2,700 = -22.04. Using a standard normal table, we find that the probability of the sample mean being more than $2,700 away from the population mean is approximately 0.0002.
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Help Help Help Help Help Help (Just yes or no, I don’t need explanation)
Answer:
No
Step-by-step explanation:
The y intercept is 7. For it to be proportional it has to go through (0,0).
Answer:
Yes
Step-by-step explanation:
2.38 Baggage fees: An airline charges the following baggage fees: $20 for the first bag and $40 for the second (note $40 is just the price for the 2nd bag, they still need to pay for the first bag on top of that). Suppose 55% of passengers have no checked luggage, 31% have only one piece of checked luggage and 14% have two pieces. We suppose a negligible portion of people check more than two bags.
a) The average baggage-related revenue per passenger is: $ to the nearest cent)
b) The standard deviation of baggage-related revenue is: $ the nearest cent)
c) About how much revenue should the airline expect for a flight of 130 passengers? $ (please round to the nearest dollar)
The average baggage-related revenue per passenger is $29.80, using the variance the standard deviation of the baggage-related revenue is $27.35 and the airline should expect about $3874 in revenue from baggage fees for a flight of 130 passengers (rounded to the nearest dollar).
What is the average baggage-related revenue per passengera) To find the average baggage-related revenue per passenger, we need to calculate the expected value of the baggage fees. Let X be the random variable that represents the number of checked bags per passenger. Then the expected value of the baggage fees per passenger is:
E[Baggage Fees] = E[20X + 40(max(0, X-1))]
= 20E[X] + 40E[max(0, X-1)]
= 20(0.31 + 0.14(2)) + 40(0.14 + 0.31)
= 29.80
Therefore, the average baggage-related revenue per passenger is $29.80
b) To find the standard deviation of the baggage-related revenue, we can use the formula for the variance:
Var[Baggage Fees] = E[(Baggage Fees - E[Baggage Fees])^2]
= E[(20X + 40(max(0, X-1)) - 29.80)^2]
= E[(20X - 40(max(0, X-1)))^2]
= E[400X^2 - 1600X(max(0, X-1)) + 1600(max(0, X-1))^2]
= 400E[X^2] - 1600E[X(max(0, X-1))] + 1600E[(max(0, X-1))^2]
To calculate these expected values, we can use the fact that:
E[X^2] = Var[X] + (E[X])^2
E[X(max(0, X-1))] = E[X^2] - E[X]
E[(max(0, X-1))^2] = Var[X] + (E[X])^2 - 2E[X] + 1/4
Plugging in the values, we get:
Var[Baggage Fees] = 400(0.31 + 0.14(4)) - 1600(0.31 + 0.14) + 1600(0.31 + 0.14 + 1/4)
= 748
Therefore, the standard deviation of the baggage-related revenue is $27.35 (rounded to the nearest cent).
c) For a flight of 130 passengers, the total revenue from baggage fees can be found by multiplying the average baggage-related revenue per passenger by the number of passengers:
Total revenue = 130($29.80)
= $3874
Therefore, the airline should expect about $3874 in revenue from baggage fees for a flight of 130 passengers (rounded to the nearest dollar).
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Please help me solve this
All of the solutions of the given system of linear inequalities above include the following:
A. (0, 3).
C. (6, 2)
E. (0, -1)
What is an ordered pair?In Mathematics, an ordered pair is sometimes referred to as a coordinate and it can be defined as a pair of two (2) elements that are commonly written in a fixed order within parentheses as (x, y), which represents the x-coordinate (abscissa) and the y-coordinate (ordinate) on the coordinate plane of any graph of a system of linear inequalities.
In this scenario, we can reasonably infer and logically deduce that the solution to the given system of linear inequalities is the shaded region and it lies in both quadrant I and quadrant IV with the following ordered pairs:
Ordered pair = 0, 3).
Ordered pair = (6, 2)
Ordered pair = (0, -1)
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in an experiment to learn whether substance m can help restore memory, the brains of 20 rats were treated to damage their memories. first, the rats were trained to run a maze. after a day, 10 rats (determined at random) were given substance m and 7 of them succeeded in the maze. only 2 of the 10 control rats were successful. the two-sample z test for the difference in the true proportions. Gives z= 2.25, P< 0.02
The z-value obtained from the test was 2.25, and the p-value was less than 0.02.
What is probability ?
Probability can be defined as ratio of number of favourable outcomes and total number of outcomes.
Based on the experiment described, a two-sample z-test for the difference in proportions was conducted to determine if there is a significant difference between the proportion of rats that succeeded in the maze after being given substance m and the proportion of rats in the control group that succeeded in the maze.
This suggests that the difference in proportions between the two groups is statistically significant at the 0.05 level of significance (since the p-value is less than 0.05).
In other words, the results of the experiment suggest that substance m may be effective in helping to restore memory, as a greater proportion of rats in the substance m group succeeded in the maze compared to the control group. However, it's important to note that further experiments and analyses would be necessary to confirm these findings and determine the extent of the effect of substance m on memory restoration.
Therefore, The z-value obtained from the test was 2.25, and the p-value was less than 0.02.
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before the trunk of a large tree is felled, cables ab and bc are attached as shown. knowing that the tensions in cables ab and bc are 630 n and 735 n, respectively, determine the moment about o of the resultant force exerted on the tree by the cable at b
The moment about point O of the resultant force exerted on the tree by the cable at B is approximately 3830.06 N·m.
Since we know the tensions in cables AB and BC, we can find the horizontal and vertical components of the forces exerted by the cables at point B:
The horizontal component of the force exerted by the cable
AB = 630 cos(45) = 444.21 N
Similarly,
The vertical component of the force exerted by the cable = 444.21 N
The horizontal component of the force exerted by the cable = 637.55 N
The vertical component of the force exerted by cable = 367.50 N
Total horizontal force = 444.21 N + 637.55 N = 1081.76 N
Total vertical force = 444.21 N + 367.50 N = 811.71 N
The moment about point O of the resultant force exerted on the tree by the cable at B is given by:
Moment = F * d
Using the Pythagorean theorem, we can find the magnitude of the resultant force,
= 1351.44 N
Perpendicular distance = 4 m * sin(45) = 2.828 m
Therefore, the moment about point O of the resultant force exerted on the tree by the cable at B is,
Moment = F * d = 1351.44 N * 2.828 m = 3830.06 N·m
Therefore, the moment about point O of the resultant force exerted on the tree by the cable at B is approximately 3830.06 N·m.
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In this polygon, all angles are right angles. What is the area of this polygon? 18ft,12ft,21ft,8ft
In the given situation the required area of the polygon is 258ft².
What is a polygon?A polygon is a closed polygonal chain made up of a finite number of straight-line segments and is a type of planar figure in geometry.
A polygon is a region that is bounded by a bounding circuit, a bounding plane, or both.
A polygonal circuit's segments are referred to as its edges or sides.
Like other concepts in geometry that they created, the word "polygon" is Greek in origin. It merely denotes a lot of (poly) angles (gon).
There cannot be any bends, gaps, or openings in the shape of a polygon.
So, an object's area is how much space it takes up in two dimensions.
A rectangle's area is calculated as follows:
Area = length * breadth
Now, calculate the area as follows using the formula:
Area = [18 * (21 - 12)] + (12 * 8) = 258 ft²
Therefore, in the given situation the required area of the polygon is 258ft².
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Correct question:
In this polygon, all angles are right angles. What is the area of this polygon? Enter your answer in the box. ft² Polygon in the shape of a letter L, which could be formed by a horizontal rectangle attached along the bottom part of a vertical rectangle. The left side of the figure is 18 ft, the bottom side of the figure is 21 ft, the right side of the figure is 8 ft, and the top part of the horizontal rectangle to the right of the vertical rectangle is 12 ft.
Assume that the amounts of weight that male college students gain during their freshman year are normally distributed with a mean of mu equals 1.1
kg and a standard deviation of sigma equals 4.5
kg. Complete parts (a) through (c) below
The amounts of weight that male college students gain during their freshman year are normally distributed with a mean of μ equals 1.1 then the probability is 0.9979.
What is probability?Probability is a branch of mathematics that deals with the likelihood of an event occurring. It is the measure of the likelihood of an event occurring divided by the number of possible outcomes. Probability is used to determine the chances of a particular outcome occurring and can range from 0 to 1.
a) What is the probability that a randomly selected male college freshman will gain more than 5.6 kg?
To answer this question, we can use the z-score formula to calculate the z-score for a gain of 5.6 kg. The z-score formula is:
z = (x - μ) / σ
where x is the gain of 5.6 kg, μ is the mean of 1.1 kg, and σ is the standard deviation of 4.5 kg.
Therefore, z = (5.6 - 1.1) / 4.5 = 2.8
The probability that a randomly selected male college freshman will gain more than 5.6 kg is 1 - the cumulative probability of a z-score of 2.8. This can be found using a z-table. The probability is 0.9979.
b) What is the probability that a randomly selected male college freshman will gain between 1.1 kg and 5.6 kg?
To answer this question, we can use the z-score formula to calculate the z-scores for a gain of 1.1 kg and a gain of 5.6 kg.
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Antoine is renting a car for a day to drive to his sister's college and back. He estimates that the college is about 60 miles away. Low Price Rentals charges a $49 rental fee plus $0.16 per mile driven. Easy Rental charges a $25 fee plus $0.50 per mile.
Compare the two rental options.
Which company offers a better deal? How do you know?
Select the option that correctly answers both questions.
1.) Easy Rental, because it will charge $55.00 for the trip, while Low Price Rentals will charge $58.60 (wrong answer)
2.) Easy Rental, because it will charge $34.60 for the trip, while Low Price Rentals will charge $79.00
3.) Low Price Rentals, because it will charge $68.20 for the trip, while Easy Rental will charge $85.00
4.) Low Price Rentals, because it will charge $44.20 for the trip, while Easy Rental will charge $109.00
Easy Rental, because it will charge $55.00 for the trip, while Low Price Rentals will charge $58.60
What is slope intercept form of line?The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.
The cost of renting from Low Price Rentals can be calculated as follows:
Rental fee + Cost per mile × Distance driven = $49 + $0.16 ×60 = $58.60
The cost of renting from Easy Rental can be calculated as follows:
Rental fee + Cost per mile × Distance driven = $25 + $0.50× 60 = $55.00
Therefore, the correct answer is: Easy Rental, because it will charge $55.00 for the trip, while Low Price Rentals will charge $58.60. So, option 1 is the correct answer.
Hence, Easy Rental, because it will charge $55.00 for the trip, while Low Price Rentals will charge $58.60
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PLEASE HELPPPP
A soccer coach determines that there is a 50% chance that a star player, Ralph,
will play in a tournament.
• The probability that another star player, Dan, will play is 0.48.
• The probability that both Ralph and Dan will play in the tournament is 0.25.
Answer50.5
ffffffffffffffff
B
Alex sorted 20 toy cars into 4 groups with the same number of cars in each
group. Which expression represents the number of toy cars in each group
20 × 4
20+4
20 ÷ 4
20 - 4
1. Artisan Large-Cap Mutual Fund has a net asset value of $20.00. Mike Morgan invests $14,000. The loading rate is 5.5% back-loaded. Mike sold at $21.85 NAV. How much profit did Mike make in dollars? Round to the nearest hundredth.
2. Artisan Large-Cap Mutual Fund has a net asset value of $20.00. Mike Morgan invests $14,000. The loading rate is 5.5% back-loaded. Mike sold at $21.85 NAV. How much profit did Mike make in dollars? Round to the nearest hundredth.
3. Clara Teague buys a house for rental purposes for $115,800 with a $25,000 down payment. Her annual expenses total $12,430. What monthly rent should she charge in dollars, if she desires an annual yield of 8.00%? Round to the nearest hundredth.
4. Barry Severes purchased a $25,000 Baltic Ridge School District bond at a quoted price of 105.7. The bond pays annual interest at a rate of 3.7%. Find the annual yield.
The annual yield of the bond is 3.50%.
To calculate Mike's profit, we first need to determine the total cost of his investment, including the back-end load. The back-end load is calculated by multiplying the initial investment by the loading rate:
Back-end load = $14,000 * 5.5% = $770
So the total cost of Mike's investment is:
Total cost = $14,000 + $770 = $14,770
To determine the profit, we need to subtract the total cost from the total amount Mike received when he sold his shares:
Profit = ($21.85 - $20.00) * 14,000 - $770 = $2,730
Therefore, Mike made a profit of $2,730.
Note that the problem statement is exactly the same as the previous question. The answer is $2,730.
The annual rental income that Clara Teague needs to receive to achieve an annual yield of 8% can be calculated as follows:
Annual rental income = Total investment * Yield
where Total investment = $115,800 - $25,000 = $90,800
So the annual rental income that Clara Teague needs to receive is:
Annual rental income = $90,800 * 8% = $7,264
To determine the monthly rent, we divide the annual rental income by 12:
Monthly rent = $7,264 / 12 = $605.33
Therefore, Clara should charge a monthly rent of $605.33 to achieve an annual yield of 8%.
The annual yield of the bond can be calculated as follows:
Annual yield = (Annual interest payment / Bond price) * 100%
The annual interest payment is:
Annual interest payment = Bond face value * Annual interest rate = $25,000 * 3.7% = $925
The bond price is quoted at 105.7% of its face value, so the bond price is:
Bond price = Bond face value * 105.7% = $25,000 * 1.057 = $26,425
So the annual yield is:
Annual yield = ($925 / $26,425) * 100% = 3.50%
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please please please help me my teacher has no idea how to reach and i desperately need to know this :D
The completed blanks in Nyala's solution that is used to prove that the measure of angle x is 40° is as follows;
If we perform a 180° rotation about the point O the following happens
Ray [tex]\overleftrightarrow{EF}[/tex] maps unto ray [tex]\overleftrightarrow{GH}[/tex]
Ray [tex]\overleftrightarrow{GH}[/tex] maps unto ray [tex]\overleftrightarrow{FE}[/tex]x
[tex]\overleftrightarrow{FG}[/tex] maps unto itself
Therefore, the image of angle x will be exactly where the pre-image of 40° was. Since rotation preserve angle measure, the measure of angle x must be 40°.
What is the measure of an angle?The measure of an angle is the degree of rotation between the initial side and the terminal side of the angle.
The details of the method Nyala used to prove that the measure of the angle x is 40° can be found as follows;
The rotation of a line 180° about the center of the line maps onto itself, and the rotation of a line about a non colinear point, is parallel to the original line.
Whereby the center of rotation of the line [tex]\overleftrightarrow{EF}[/tex] is equidistant from both the line [tex]\overleftrightarrow{GH}[/tex] which is parallel to the line [tex]\overleftrightarrow{EF}[/tex], the image of the line [tex]\overleftrightarrow{EF}[/tex] maps to the line [tex]\overleftrightarrow{GH}[/tex] following a 180° rotation about the point O, and the rotation of the line [tex]\overleftrightarrow{FG}[/tex] about the point O maps unto itself, such that the angle x maps to the angle 40°, therefore;
∠x ≅ 40° (A rotation transformation is a rigid transformation)
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one bowl of sambar is made using 3/4 cup dal . how many bowls of sambar can be made from 6 cups of ?
6 cups of dal may be used to make eight bowls of sambar.
What is ratio?The ratio can be defined as the number that can represent one quantity as a percentage of another. They can be compared only when the two numbers in a ratio have the same unit. Ratios are used to compare two objects.
Given, One bowl of sambar is made the use of 3/four cup dal.
If 1 bowl of sambar is made using 3/4 cup of dal, then the number of bowls of sambar that can be made from 6 cups of dal can be found by dividing 6 cups by 3/4 cup per bowl:
6 cups / (3/4 cup per bowl)
We can simplify by multiplying the numerator and denominator by the reciprocal of 3/4:
6 cups / (3/4 cup per bowl) * (4/3)
Simplifying, we get:
8 bowls
Therefore, 6 cups of dal can be used to make 8 bowls of sambar.
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In studying his campaign plans, Mr. Singleton wishes to estimate the difference between men's and women's views regarding his appeal as a candidate. He asks his campaign manager to take two random independent samples and find the 99% confidence interval for the difference. A random sample of 659 male voters and 629 female voters was taken. 282 men and 182 women favored Mr. Singleton as a candidate. Find this confidence interval. Step 1 of 4: Find the values of the two sample proportions, pˆ1p^1 and pˆ2p^2. Round your answers to three decimal places. confidence interval. Step 2 of 4: Find the critical value that should be used in constructing the confidence interval. Step 3 of 4: Find the value of the standard error. Round your answer to three decimal places Step 4 of 4: Construct the 99% confidence interval. Round your answers to three decimal places.
We can be 99% confident that the true difference between the proportion of men and women who favor Mr. Singleton as a candidate is between 0.059 and 0.219.
How to calculate [tex]\mathrm{\hat p_1}[/tex] and [tex]\mathrm{\hat p_2}[/tex] sample proportions?Step 1: Determine the values of the [tex]\mathrm{\hat p_1}[/tex] and [tex]\mathrm{\hat p_2}[/tex] sample proportions.
The percentage of men who, on average, support Mr. Singleton is:
[tex]\mathrm{\hat p_1}[/tex] = [tex]\dfrac{282}{659}[/tex], or around 0.428
The percentage of women who favour Mr. Singleton, as a sample, is:
[tex]\mathrm{\hat p_2}[/tex] = [tex]\dfrac{182}{629}[/tex], or around 0.289
Locate the critical value that must be utilised to build the confidence interval in step 2.
The level of significance is [tex]\alpha[/tex] = 0.01/2 = 0.005 (divided by 2 because it's a two-tailed test) because we want to determine a 99% confidence interval. The critical value for a z-score with [tex]\alpha[/tex] = 0.005 is roughly 2.576 when using a table or calculator.
Step 3: Determine the standard error's value.
The standard error of the difference between two sample proportions is calculated as follows:
[tex]\mathrm{(\Hat p 2-\Hat p 2) + n_1 + \frac {\hat p_2}{1}}[/tex]
When we enter the values from the issue, we obtain:
[tex]\mathrm{SE = \sqrt{\dfrac{\hatp_1}{SE}} = (\hat p_1 - \hat p_2) (\hat p_1 - \hat p_1) }[/tex]
Create the 99% confidence interval in step four.
We may create the confidence interval using the sample proportions, critical value, and standard error:
[tex]\mathrm{SE(\hat p_1 - \hat p_2) 1:00 \ p.m. \ to \ 2:00 \ p.m. \ z \ \alpha \ 2}[/tex]
When we change the values, we obtain:
2.576, × 0.031, = (0.428 - 0.289).
If we simplify, we get:
[tex]$$0.139 \pm \ 0.08$$[/tex].
3. Find the value of the standard error.
The following formula is used to compute the standard error of the difference between two sample proportions:
[tex]\mathrm{SE = \sqrt{\dfrac{\hatp_1}{SE}} = (\hat p_1 - \hat p_2) (\hat p_1 - \hat p_1) }[/tex]
[tex]\mathrm{(\Hat p 2-\Hat p 2) + n_1 + \frac {\hat p_2}{1}}[/tex]
When we type in the issue's values, we get:
[tex]$ \mathrm{\sqrt{(\frac{1-0.428}{0.659}) + \frac{1-0.288}{0.629}) }= about \ 0.031 \ for \ SE (\hat p_1 - \hat p_2)}[/tex]
In step four, calculate the 99% confidence interval.
With the sample proportions, critical value, and standard error, we can calculate the confidence interval:
[tex]\mathrm{SE(\hat p_1 - \hat p_2) 1:00 \ p.m. \ to \ 2:00 \ p.m. \ z \ \alpha \ 2}[/tex]
When the values are changed, we get the following result: [tex]$2.576 \times 0.031 = (0.428 - 0.289)$$[/tex]
Simplifying, we obtain: [tex]$$0.139 \pm \ 0.08$$[/tex].
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(10)² × (0.01)³
__________
10‐³
calculate the value of : :
Answer:
0.1
Step-by-step explanation:
10^2=100
0.01^3=0.000001
10^-3=0.001
Plug them in100 x 0.000001
---------------------- = 0.1
0.001
Sandra bought a triangular shelf to hang in the
corner of her room. Will this shelf fit in the 90°
corner? Explain.
Answer:
It depends. Depends on what? Depends on the type of triangle that this shelf forms. If Sandra wants the shelf to fit perfectly, she needs a shelf with the shape of a right triangle, the only type of triangles that have a 90° angle in one of their corners. Any other type of triangle will fit in some ways, but they won't fot perfectly.
Check the attached images to better understand this explanation.
As you can see on the images, the only type of shelf that fits the room's corner perfectly is a right triangle shaped shelf. Any other triangular shelf will fit in a specific orientation, but it won't fit perfectly.
A study was conducted showing the relationship between the average maintenance cost and the age of a car in years.
Number of observations: 13
Least Squares | Standard | T
Parameter | Estimate | Error | Statistic| P-Value
Intercept | 54.7757 | 54.87 | 0.998282 | 0.3396
Slope | 120.689 | 11.8442 | 10.1898 | 0.0000
a) What is the formula for the regression function based on the output above (Write your equation in the context of question)?
b) Interpret the slope of the regression equation (In the context of question)?
c) Construct an 95% interval to predict the maintenance cost for a car that is 7 years old?
d) Based on this analysis, can we conclude that a relationship exists between the maintenance cost and the age of the car in years? What is the null and alternative hypothesis? Justify your answer using three steps process.
Step-by-step explanation:
classic Christian from x x + 4 + 8 is equal to 21 what is the answer
The capital value (present sale value) CV of property that can be rented on a perpetual basis for R dollars annually is given by CV = integral_0^infinity Re^-it dt where i is the prevailing continuous interest rate. Show that CV = R/i. CV ~ integral_0^infinity Re^-it dt = lim_b rightarrow infinity integral_0^d Re0-it dt = lim_b rightarrow infinity Find the capital value of property that can be rented at $10#000 annually when the prevailing continuous interest rate is 6%/year. (Round your answer to the nearest whole number.)
Answer:
the capital value of the property that can be rented at $10,000 annually when the prevailing continuous interest rate is 6%/year is approximately $166,667.
Step-by-step explanation:
The capital value (present sale value) CV of property that can be rented on a perpetual basis for R dollars annually is given by the formula:
CV = ∫₀^∞ R e^(-it) dt
where i is the prevailing continuous interest rate.
To show that CV = R/i, we can evaluate the integral:
CV = ∫₀^∞ R e^(-it) dt
We can use the formula for the exponential integral, which is:
∫ e^(ax) dx = (1/a) e^(ax) + C
Using this formula, we can integrate the exponential function in the integral and obtain:
CV = [ (-R/i) e^(-it) ] from t = 0 to t = infinity
Since e^(-infinity) = 0, we have:
CV = [ (-R/i) e^(0) ] - [ (-R/i) e^(-i*0) ]
Simplifying this, we get:
CV = [ (-R/i) ] - [ (-R/i) ] = R/i
So we have shown that CV = R/i, as required.
Now, to find the capital value of property that can be rented at $10,000 annually when the prevailing continuous interest rate is 6%/year, we can use the formula CV = R/i with R = $10,000 and i = 0.06:
CV = $10,000 / 0.06 ≈ $166,667 (rounded to the nearest whole number)
Therefore, the capital value of the property that can be rented at $10,000 annually when the prevailing continuous interest rate is 6%/year is approximately $166,667.
Find the value of the expression. 8x^3 for x = –2, –1, 0, 3
Answer:
8(-2)^3= -64
8(-1)^3= -8
8(0)^3= 0
8(3)^3= 216
Hope this helps! Remember PEMDAS (Please forgive My Dear Aunt Sally)
Find the geometric mean of 4 and 8
Answer:
[tex]4\sqrt2[/tex]
Step-by-step explanation:
1) a=4 and b=8
2) Let geometric mean is g. [tex]g=\sqrt ab[/tex] or you can do [tex]g=\sqrt 4 times8[/tex]
3) g=[tex]4\sqrt2[/tex]
GROUP 'D' (4×5=20) A person purchases a piece of land in Rs.80, 00,000 in 2075 B.S. At the same time of 2075 B.S. a house is constructed on a piece of land in Rs. 2,70,00,000. If the price of land increases at the rate of 20% per annum and the price of house depreciates at the rate 20% per annum. After how many years the price of land and the price of house will be equal? Find it. combined solid is formed with the combination of hemisphere and cone having radius
After 2.5 years the price of land and the price of house will be equal.
What is Simple interest?A quick and easy method of calculating the interest charge on a loan is called a Simple interest.
Given that;
A person purchases a piece of land in Rs.80, 00,000 in 2075 B.S.
And, At the same time of 2075 B.S. a house is constructed on a piece of land in Rs. 2,70,00,000.
Since, The price of land increases at the rate of 20% per annum.
Hence, We get;
A = 80,00,000 (1 + 20/100)ⁿ
And, The price of house depreciates at the rate 20% per annum.
Hence, We get;
A = 2,70,00,000 (1 - 20/100)ⁿ
Let after n years the price of land and the price of house will be equal.
Thus, We get;
80,00,000 (1 + 20/100)ⁿ = 2,70,00,000 (1 - 20/100)ⁿ
8 (120/100)ⁿ = 27 (80/100)ⁿ
8 (6/5)ⁿ = 27 (4/5)ⁿ
Take log both side,
log 8 + n (log 6 - log 5) = log 27 + n (log 4 - log 5)
0.9 + n × 0.8 = 1.4 + n × 0.6
0.9 + 0.8n = 1.4 + 0.6n
0.2n = 0.5
n = 2.5 years
Therefore, After 2.5 years the price of land and the price of house will be equal.
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Can you please solve and see which one is a function and which one is not a function
For each relation, we would determine whether or not it is a function as follows;
Relation 1 is: B. not a function
Relation 2 is: B. not a function.
Relation 3 is: B. not a function
Relation 4 is: A. a function.
How to determine the relations that represent functions?In Mathematics, a function is generally used for uniquely mapping an independent value (domain or input variable) to a dependent value (range or output variable).
This ultimately implies that, an independent value (domain) represents the value on the x-coordinate of a cartesian coordinate while a dependent value (range) represents the value on the y-coordinate of a cartesian coordinate.
Based on relations 1, 2, and 3, we can logically deduce that they do not represent a function because their independent value (domain) has more than one dependent value (range).
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find derivative of f(x) = 4x³ using first Principre and F(x) = 2x²-3x
Answer:
12x^2.
Step-by-step explanation:
let y = 4x^3
If y is increased by a small amount Δy then x is increased by a small amount Δx, so we write:
y + Δy = 4(x + Δx)^3
y + Δy = 4(x^3 + 3x^2 Δx + 3x(Δx)^2 + (Δx)^3)
y + Δy = 4x^3 + 12x^2 Δx + 12x(Δx)^2 + 4(Δx)^3
Δy = 4x^3 + 12x^2 Δx + 12x(Δx)^2 + 4(Δx)^3 - y
= 4x^3 + 12x^2 Δx + 12x(Δx)^3 + 4(Δx)^2 - 4x^3
Δy/Δx = (4x^3 + 12x^2 Δx + 12x(Δx)^3 + 4(Δx)^2- 4x^3 ) / Δx
= (12x^2 Δx + 12x(Δx)^3 + 4(Δx)^2) / Δx
= 12x^2 + 12x(Δx)^2 + 4Δx
Now as Δx approaches zero, the limit ( that is the derivative) of f(x)
= 12x^2
- as we can neglect the last 2 terms.
The second part can be solved by the same process.
The measures of the angles of △ABC are given by the expressions in the table.
The angles of the triangle are 125 degrees, 20 degrees, and 35 degrees.
Define triangles.A triangle is a closed geometric shape with three sides, three angles, and three line segments. Three non-collinear points are joined by line segments to create the simplest polygon, which has three non-collinear points.
Triangles can be categorized according to the size of their sides and angles. Triangles can be categorized as equilateral (all sides are equal in length), isosceles (both sides are equal in length), or scalene based on their sides (all sides are different in length). Triangles can be categorized as acute (all angles are less than 90 degrees), obtuse (one angle is greater than 90 degrees), or right (one angle is greater than 90 degrees) (one angle is exactly 90 degrees).
In any triangle, the sum of the three interior angles is always 180 degrees. Therefore, we can write:
a + b + c = 180
Substituting the given values, we get:
(6x-1) + 20 + (x+14) = 180
Simplifying and solving for x, we get:
7x + 33 = 180
7x = 147
x = 21
Now that we have the value of x, we can substitute it back into the expressions for the angles to find their values:
angle a = (6x-1) = (6*21-1) = 125 degrees
angle b = 20 degrees
angle c = (x+14) = (21+14) = 35 degrees
Therefore, the angles of the triangle are 125 degrees, 20 degrees, and 35 degrees.
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I need help with this question very fast !!
Answer:
angle a: 70°
angle d: 70°
angle dce: 35°
x: 15m
y: 14m
Step-by-step explanation:
all triangles add to 180° so 35 + 75 = 110 and 180-110 = 70
where the two triangles connect and cross, the angles will be the same so it will have the same angle measures as the first triangle which makes the triangles similar
knowing that they are similar triangles will help with figuring out the lengths of the sides.
since they are similar, their sides will be proportional, we just need to figure out the ratio
if we lay the triangles on top of each other, the two 75° angles match up and therefore the sides do too so we can make a fraction 12/18 = 10/x
now we can solve for x
multiply both sides by x
12x/18 = 10
now multiply both sides by 18
12x = 180
divide both sides by 12
x = 15
now we do the same for y
12/18 = y/21
12*21/18 = y
y = 14
hope this helps!
Evaluate the expression. (2 + 4)(8 + 3)^0 Responses
Answer: The answer is 6.
Step-by-step explanation:
interpolating polynomial. f(x) = ln x
Data points at x = 1, x2 = 4, x3 = 6 and x, = 5 were used to estimate in 2 with a third-order Newton's
Using third-order Newton's interpolating a polynomial the value of f(2) is (25ln(2))/9.
What is the value of f(2)To estimate the value of f(2) using a third-order Newton's interpolating polynomial with the given data points, we first need to calculate the divided differences. The divided differences are defined as:
f[xi] = f(xi) for i = 1, 2, 3
f[x1,x2] = (f[x2] - f[x1]) / (x2 - x1) = (ln(4) - ln(1)) / (4 - 1) = ln(4) / 3
f[x2,x3] = (f[x3] - f[x2]) / (x3 - x2) = (ln(6) - ln(4)) / (6 - 4) = ln(3) / 2
f[x1,x2,x3] = (f[x2,x3] - f[x1,x2]) / (x3 - x1) = ((ln(3) / 2) - (ln(4) / 3)) / (6 - 1) = -0.018
Using these divided differences, we can write the third-order Newton's interpolating polynomial as:
f(x) = f[x1] + f[x1,x2](x - x1) + f[x1,x2,x3](x - x1)(x - x2) + f[x1,x2,x3,x4](x - x1)(x - x2)(x - x3)
Substituting the values of the data points and the divided differences we calculated, we get:
f(x) = ln(1) + ln(4)/3 (x - 1) - 0.018 (x - 1)(x - 4)
Simplifying this expression, we get:
f(x) = ln(1) + (ln(4)/3)x - (11ln(2)/9) + (ln(2)/9)x^2
To estimate f(2), we plug in x = 2:
f(2) = ln(1) + (ln(4)/3)(2) - (11ln(2)/9) + (ln(2)/9)(2)^2
f(2) = 2ln(2) - (11ln(2)/9) + (ln(2)/9)(4)
f(2) = (25ln(2))/9
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Sunny earns
$
12
$12dollar sign, 12 per hour delivering cakes. She worked for
�
xx hours this week. Unfortunately, she was charged
$
15
$15dollar sign, 15 for a late delivery on Tuesday.
How much money did Sunny earn this week?
Therefore , the solution of the given problem of expression comes out to be Sunny earned $12x - 15 this week.
Expression : What is it?Mathematical operations like addition, multiply, and division are necessary. They result in the following when combined: An equation, some information, and a mathematical operator Values, parameters, and arithmetic calculations like additions, subtractions, multiplication and division, and divisions are all found in a statement of fact. Different sentences and words can be contrasted and compared.
Here,
If Sunny worked for x hours and earns $12 per hour, her earnings before the late delivery charge would be:
$12x$
However, since she was charged $15 for the late delivery on Tuesday, her earnings for the week would be:
$12x - 15$
Therefore, Sunny earned $12x - 15 this week.
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The complete question is "Sunny earns $12 per hour delivering cakes. She worked for x hours this week. Unfortunately, she was charged $15 for a late delivery on Tuesday. How much money did Sunny earn this week?"
The question is in image form. It's about geometry pls help me to solve this question
The area of the shaded region is 104 m².
What is a Triangle ?
The intersection of the two sides of a triangle's three sides, which are known as the vertex, is a sort of polygon. Between two sides, an angle forms. This is among geometry's crucial components.
We know that Area of a triangle = 1/2 × base × height
The area of Big triangle = 1/2 × 30 × 13
= 15 × 13
= 195 m²
Area of Small triangle = 1/2 × 14 × 13
= 91 m²
So, Area of the shaded region
= Area of big triangle - Area of small triangle
= 195 - 91
= 104 m²
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Simply expression
Please show steps
The simplified expression for this problem is given as follows:
-3(x + y) = -3x - 3y.
What is the distributive property?With the application of the distributive property, the outer term multiplies each of the inner terms of the expression. If possible, these inner terms than can be added or subtracted combining the like terms.
For this problem, the outer term -3 multiplies both of the inner terms, x and y, hence:
-3x.-3y.Hence the simplified expression is defined as follows:
-3(x + y) = -3x - 3y.
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