He must sell the car at R80,625 to make an overall profit of 25%
To find the selling price of the car that gives a 25% profit, we need to use the following steps:
Calculate the total cost of buying and transporting the car to Durban:
Total cost = Cost of car + Cost of transportation
Total cost = R60,000 + R4,500
Total cost = R64,500
Calculate the desired profit:
Profit = 25% of total cost
Profit = 0.25 x R64,500
Profit = R16,125
Calculate the total amount that the car needs to be sold for:
Total amount = Total cost + Profit
Total amount = R64,500 + R16,125
Total amount = R80,625
Therefore, the man needs to sell the car for R80,625 to make an overall profit of 25%.
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Ian stacks 5 glasses of juice. Each glass contains 185 milliliters of juice. Find the total volume of juice in the 5 glasses
The total volume of juice in the 5 glasses is 925 milliliters. To find the total volume of juice in the 5 glasses, we simply need to multiply the volume of juice in one glass by the number of glasses.
In this case, each glass contains 185 milliliters of juice and Ian has stacked 5 glasses, so we can use the formula:
Total volume of juice = Volume of juice per glass x Number of glasses
Plugging in the numbers, we get:
Total volume of juice = 185 ml/glass x 5 glasses
Total volume of juice = 925 ml
Therefore, the total volume of juice in the 5 glasses is 925 milliliters. This is a simple example of using multiplication to find the total quantity of something when we know the amount in one unit and the number of units. In this case, we were able to find the total volume of juice by multiplying the volume in one glass by the number of glasses.
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Please upload a picture of a piece of paper with the problem worked out, and draw the graph for extra points, there will be 6 of these, so go to my profile and find the rest, and do the same, for extra points.
The solution of the system of equations is given by the ordered pair (-4, 5).
How to graphically solve this system of equations?In order to graph the solution to the given system of equations on a coordinate plane, we would use an online graphing calculator to plot the given system of equations and then take note of the point of intersection;
x - y = -9 ......equation 1.
3x + 4y = 8 ......equation 2.
Based on the graph shown in the image attached above, we can logically deduce that the solution to this system of equations is the point of intersection of the lines on the graph representing each of them, which lies in Quadrant II, and it is given by the ordered pairs (-4, 5).
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This table shows dogs’ weights at a competition.
Dogs' Weights (pounds)
35, 22, 31, 23, 35, 22, 30, 35, 40
One 42-pound dog could not make it to the competition. ++++Select all++++ the ways the measures of center of the data set change if she had entered the competition.
A. The median increases
B. The mode increases
C. The mean increases
D. The median decreases
E. The mode decreases
F. The mean decreases
The measures of central tendencies changed as mode remained the same, the median increased and the mean increased.
How will the data set change if she had entered the competition?To determine how the data set would've changed if she entered the competition, we simply need to work on the mean, median and mode of the data.
Given data;
35, 22, 31, 23, 35, 22, 30, 35, 40
Rearranging this data;
22, 22, 23, 30, 31, 35, 35, 35, 40
The mean of this data will be
mean = 30.3
The mode = 35
The median = 31
When her weight is added, the measures of central tendencies change to;
mean = 31.5
median = 33
mode = 35
The median decreases, the mode remains the same and the mean increases
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Find the inflection points and the intervals in which the function f(x) = x^4 - 4x^3 is concave up and concave down.
the inflection points are x = 0 and x = 2, and the intervals of concavity are (-∞, 0) and (2, ∞) for concave down, and (0, 2) for concave up.
To find the inflection points and intervals of concavity of the function f(x) = x^4 - 4x^3, we need to find its second derivative.
f'(x) = 4x^3 - 12x^2
f''(x) = 12x^2 - 24x
The inflection points occur where f''(x) = 0 or is undefined. Therefore, we set 12x^2 - 24x = 0 and solve for x.
12x(x - 2) = 0
x = 0 or x = 2
These are the two possible inflection points.
To determine the intervals of concavity, we need to look at the sign of the second derivative in each interval. We can use test points to determine the sign.
Test point x = 1:
f''(1) = 12 - 24 = -12, so the function is concave down on the interval (-∞, 0) and concave up on the interval (0, ∞).
Test point x = 3:
f''(3) = 108 - 72 = 36, so the function is concave up on the interval (2, ∞) and concave down on the interval (-∞, 2).
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Sampling at the mall you have probably seen the mall interviewer, approaching people passing by with clipboard in hand. explain why even a large sample of mall shoppers would not provide a trustworthy
estimate of the current unemployment rate.
While a sample of mall shoppers may be useful for certain types of research, it may not provide a trustworthy estimate of the current unemployment rate. Instead, a more appropriate method would be to conduct a survey that is designed to be representative of the population, using a random sampling technique, and ensuring that the sample size is large enough to provide reliable estimates.
Find out the estimate of the current unemployment rate?While sampling at the mall may be a convenient way to gather data, it may not be an appropriate method for estimating the current unemployment rate for several reasons:
Sampling Bias: The people who visit malls may not be representative of the general population. For instance, people who are unemployed may not have the time or money to go to the mall during the day, which could skew the results.
Sampling Size: The sample size may not be large enough to provide an accurate estimate of the unemployment rate. Even if the interviewer approaches a large number of shoppers, it may not be sufficient to represent the entire population of the city or country.
Self-Selection Bias: People who choose to participate in the survey may not be representative of the population as a whole. For instance, people who are more interested in the topic may be more likely to participate, which could bias the results.
Data Collection Bias: Even if the sample is representative, the data collection method may introduce biases. For instance, the interviewer may have a certain tone of voice or demeanor that could influence how people respond to the questions.
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Select the statement that best describes how pollination begins.
The statement that best describes how pollination begins is that it starts when pollen from the male reproductive organ of a flower is transferred to the female reproductive organ of the same or a different flower. Pollination is an essential step in the reproduction of plants, and it allows for the exchange of genetic material between different plants.
Pollination can occur through various methods, including wind, water, and animals such as bees, butterflies, and birds. Once the pollen is transferred, it begins to grow and develop, ultimately leading to the formation of a seed and the growth of a new plant.
Pollination is vital to the continuation of plant life, and without it, many plant species would not be able to survive. It is essential for plant breeders to understand the pollination process, as they can use it to cross different plant varieties and produce new and improved plants.
In conclusion, pollination begins when pollen from the male reproductive organ of a flower is transferred to the female reproductive organ of the same or a different flower, allowing for the exchange of genetic material and the growth and development of new plants.
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This wooden frame is made of three planks of wood attached with glue and nails. The wood will be painted with emulsion paint which takes 80ml of paint per metre of wood. Calculate the amount of paint needed to cover all the wood
amount of paint needed to cover all the wood in the frame, we need to first determine the total length of the wood in meters. Let's assume that each plank of wood is 1 meter long, so the total length of wood in the frame is 3 meters.
Next, we need to calculate the amount of paint required per meter of wood. The problem states that 80ml of emulsion paint is needed per meter of wood. So, we can multiply 80ml by 3 meters to get the total amount of paint needed for the entire frame.
80ml/meter x 3 meters = 240ml
Therefore, we need 240ml of emulsion paint to cover all the wood in the frame.
It is important to note that this calculation assumes that only one coat of paint will be applied to the wood. If multiple coats are desired, the amount of paint required will need to be adjusted accordingly.
In conclusion, to paint the wooden frame made of three planks of wood attached with glue and nails, we would need 240ml of emulsion paint.
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Do you pay less at Payless? Mary Ann and Abigail were shopping for prom shoes and wondered
how the prices at Payless compared to the prices
at Famous Footwear. At each store, they randomly
selected 30 pairs of shoes and recorded the price of
each pair. The table shows summary statistics for
the two samples of shoes. 28
Store
Mean
SD
Famous Footwear
$45. 66
$16. 54
Payless
$21. 39 $7. 47
Do these data provide convincing evidence at the
0. 05 significance level that shoes cost less
, on
average, at Payless than at Famous Footwear?
a =
To test whether shoes cost less on average at Payless than at Famous Footwear, we can conduct a two-sample t-test for the difference in means.
The null hypothesis is that there is no difference in the mean prices between the two stores, and the alternative hypothesis is that the mean price at Payless is less than the mean price at Famous Footwear.
We can calculate the t-statistic using the formula:
t = [tex](x1 - x2 - 0) / sqrt(s1^2/n1 + s2^2/n2)[/tex]
where x1 and x2 are the sample means, s1 and s2 are the sample standard deviations, and n1 and n2 are the sample sizes.
Substituting the values given in the table, we get:
t =[tex](21.39 - 45.66 - 0) / sqrt((7.47^2/30) + (16.54^2/30))[/tex] = -10.78
The degrees of freedom for this test is (30-1) + (30-1) = 58.
Using a t-table or calculator, we find the p-value to be very small, much less than 0.05.
Therefore, we reject the null hypothesis and conclude that there is convincing evidence at the 0.05 significance level that shoes cost less on average at Payless than at Famous Footwear.
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(co 4) market research indicates that a new product has the potential to make the company an additional $3.8 million, with a standard deviation of $1.7 million. if this estimate was based on a sample of 10 customers, what would be the 90% confidence interval?
The 90% confidence interval of the new product has the potential to make the company an additional $3.8 million is (2.81, 4.79), option B.
Confidence intervals quantify how confident or uncertain a sampling technique is. They can take any number of probability thresholds, with a 95% or 99% confidence level being the most popular. The calculation of confidence intervals is done using statistical techniques like the t-test.
[tex]\bar x = $3.8[/tex]
sample standard deviation = s =1.7
sample size = n =10
Degrees of freedom = df = n - 1 = 10 - 1 = 9
At 90% confidence level
[tex]\alpha[/tex] = 1 - 90%
[tex]\alpha[/tex] =1 - 0.90 =0.1
[tex]\alpha/2[/tex] = 0.05
[tex]t\alpha/2[/tex] ,df = t0.05,9 =1.833
At 90% confidence level, the critical value is t = 1.833
The 90% confidence interval is:
[tex]\bar x \pm t*\frac{s}{\sqrt{n} }[/tex]
[tex]=3.8\pm 1.833*\frac{1.7}{\sqrt{10}}\\\\=3.8\pm 0.99[/tex]
=(2.81,4.79).
Therefore, 90% confidence interval estimate of the population mean is, (2.81,4.79).
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Complete question:
Market research indicates that a new product has the potential to make the company an additional $3.8 million, with a standard deviation of $1.7 million. If this estimate was based on a sample of 10 customers, what would be the 90% confidence interval? (2.76, 4.84) O (2.81, 4.79) (2.11, 5.56) (3.06, 4.54)
The number of fish in a lake is growing exponentially. The table shows the values, in thousands, after different numbers of years since the population was first measured.
years population
0 10
1
2 40
3
4
5
6
By what factor does the population grow every two years? Use this information to fill out the table for 4 years and 6 years.
By what factor does the population grow every year? Explain how you know, and use this information to complete the table
The population grows by a factor of 2 every year.
The number of fish in a lake is growing exponentially, with given data for different numbers of years since the population was first measured as follows:
Years | Population (in thousands)
0 | 10
1 |
2 | 40
3 |
4 |
5 |
6 |
By what factor does the population grow every two years?
From year 0 to year 2, the population grows from 10,000 to 40,000. To find the growth factor, divide the population in year 2 by the population in year 0:
40,000 ÷ 10,000 = 4.
Thus, the population grows by a factor of 4 every two years.
Using this information, we can calculate the population for years 4 and 6:
Year 4: 40,000 × 4 = 160,000 (160 in thousands)
Year 6: 160,000 × 4 = 640,000 (640 in thousands)
By what factor does the population grow every year?
To find the yearly growth factor, take the square root of the growth factor every two years:
√4 = 2.
Thus, the population grows by a factor of 2 every year.
Using this information, we can complete the table:
Years | Population (in thousands)
0 | 10
1 | 20
2 | 40
3 | 80
4 | 160
5 | 320
6 | 640
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An author works on a new book and after writing a few chapters, begins a new plan to write 600
words per day. On the fifth day of working on this plan. 4,500 words have been written.
If the equation y=600. 0 + b represents the total number of words the author has written, y, based
on the number of days, x, since the new plan was started, what is the value of b?
The value of b is 1,500, which means that the author had already written 1,500 words before starting the new plan.
In the equation y = 600x + b, x represents the number of days since the author started the new plan to write 600 words per day, and y represents the total number of words written.
After the fifth day, the author has written 4,500 words. Thus, we can substitute x = 5 and y = 4,500 into the equation and solve for b:
4,500 = 600(5) + b
4,500 = 3,000 + b
b = 4,500 - 3,000
b = 1,500
Therefore, the value of b is 1,500, which means that the author had already written 1,500 words before starting the new plan.
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Which of the following are areas of sectors formed by Angle ABC?
B = 86.4º
AB=4.1cm
Answer:
about 12.67 cm²
Step-by-step explanation:
The area of a sector of a circle is given by:
A = (θ/360) x πr²
where A is the area of the sector, θ is the central angle of the sector (in degrees), and r is the radius of the circle.
In this case, we are given the central angle of the sector, which is 86.4 degrees, and the radius of the circle, which is 4.1 cm. Therefore, we can calculate the area of the sector formed by angle CBA as follows:
A = (86.4/360) x π(4.1)²
A ≈ 12.67 cm²
So, the area "about 12.67 cm²" is a possible area of the sector formed by angle CBA.
To determine if any of the other given areas are possible, we can calculate the central angle of each sector using the same formula as above, and then check if it matches the given angle of 86.4 degrees.
For the area "about 23.35 cm²":
23.35 = (θ/360) x π(4.1)²
θ ≈ 149.6 degrees
The central angle of this sector is approximately 149.6 degrees, which is not equal to the given angle of 86.4 degrees. Therefore, the area "about 23.35 cm²" is not a possible area of the sector formed by angle CBA.
For the area "about 3.09 cm²":
3.09 = (θ/360) x π(4.1)²
θ ≈ 19.16 degrees
The central angle of this sector is approximately 19.16 degrees, which is not equal to the given angle of 86.4 degrees. Therefore, the area "about 3.09 cm²" is not a possible area of the sector formed by angle CBA.
For the area "about 40.14 cm²":
40.14 = (θ/360) x π(4.1)²
θ ≈ 256.4 degrees
The central angle of this sector is approximately 256.4 degrees, which is not equal to the given angle of 86.4 degrees. Therefore, the area "about 40.14 cm²" is not a possible area of the sector formed by angle CBA.
Therefore, the only possible area of the sector formed by angle CBA is "about 12.67 cm²".
Solve each system by substitution
-5x-6y=2
Y=3
Answer:
x = -4, y = 3.
Step-by-step explanation:
Substitute y = 3 into the first equation:
-5x - 6(3) = 2
-5x = 2 + 18
-5x = 20
x = -4
Andi moved a game piece down 4 pieces
choose all of the expressions that could be used to indicate how many spaces the game piece was moved.
The expression 4 that could be used to find spaces in the game piece was moved.
Since Integers are the collection of negative, and positive numbers including zero. Then the positive integers lie on the right side of the zero on the number line and the negative lie on the left side of zero on the number line.
We are given that Andi moved a game piece down 4 pieces
The expression in option 1: |-4| which is equal to 4
The expression in option 2: |4| which is equal to 4
The expression in option 3: -|4| which is equal to -4
The expression in option 4: 4 which is equal to -4
∴The correct expression is option 4
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Differentiate between absolute and relative measure of dispersion
Absolute measures of dispersion give the actual spread or variability in the original units of measurement, while relative measures of dispersion express the dispersion relative to the mean or some other characteristic of the data.
Measures of dispersion are used to describe the spread or variability of a set of data. There are two common types of measures of dispersion: absolute measures and relative measures.
Absolute measures of dispersion, such as the range, interquartile range (IQR), and standard deviation, give an actual value or measurement of the spread in the original units of measurement.
For example, the range is simply the difference between the maximum and minimum values in a data set, while the standard deviation is a measure of how far each value is from the mean.
Relative measures of dispersion, such as the coefficient of variation (CV), express the dispersion relative to the mean or some other characteristic of the data. These measures are useful when comparing the variability of different sets of data that have different units of measurement or different means
For example, the CV is the ratio of the standard deviation to the mean, expressed as a percentage, and it can be used to compare the variability of different data sets that have different means.
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For each of the 7 weeks babysitting Kelly earned the following dollars amounts: 16,28,28,21,32,21,18, and 35. Kelly made at least ____ in 75% of the weeks she worked
Kelly made at least $28 in 75% of the weeks
To determine the amount Kelly made in at least 75% of the weeks she worked, we will follow these steps:
1. Arrange the weekly earnings in ascending order:
16, 18, 21, 21, 28, 28, 32, 35.
2. Calculate 75% of the total number of weeks:
0.75 x 8 = 6 weeks.
3. Identify the earning corresponding to the 6th week: 28 dollars.
So, Kelly made at least $28 in 75% of the weeks she worked.
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Find all solutions of the equation algebraically.
|x2 + 9x| = 6x + 54
The solutions to the equation are x= -9 and x = 6
How to determine the valueFrom the information given, we have that;
|x2 + 9x| = 6x + 54
To solve the quadratic equation, collect the like terms, we have;
x² + 9x - 6x = 54
subtract the terms
x² + 3x = 54
Put in standard form
x² + 3x - 54 = 0
Find the pair factors of -54 that add up to give 3 and substitute the values
x² + 9x - 6x - 54 = 0
group in pairs
(x² + 9x) - (6x - 54) = 0
factorize the expressions
x(x + 9) - 6(x + 9) = 0
Then, we have;
x- 6 = 0
x = 6
x + 9 = 0
x = -9
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someone help pls!! giving brainlist to anyone who answers
Answer: csc M = [tex]\frac{\sqrt{86} }{8}[/tex]
Step-by-step explanation:
The csc is related to sin
csc x = 1/sin x
find sin M first then flip it to find csc M
sin M= opposite/hypotenuse
sin M= [tex]\frac{8}{\sqrt{86} }[/tex] >flip that
csc M = 1/sin M
csc M = [tex]\frac{\sqrt{86} }{8}[/tex] >root cannot be simplified it breaks down into 2 and 43
which are 2 prime numbers
Sarah is saving for a vacation. she kept track of how much she saved each month over the last six months in the following table. what did sarah save per month on average? sep oct nov dec jan feb $135.00 $144.00 $104.00 $80.00 $90.00 $160.00 a. $118.80 b. $119.50 c. $713.00 d. $118.83
To find the average amount that Sarah saved per month over the last six months, we need to add up the total amount saved and divide by the number of months.
Total amount saved = $135.00 + $144.00 + $104.00 + $80.00 + $90.00 + $160.00 = $713.00
Number of months = 6
Average amount saved per month = Total amount saved / Number of months = $713.00 / 6 = $118.83
Therefore, the correct answer is d. $118.83.
It is important to note that when working with numbers and calculations, accuracy is crucial. In this case, rounding off the answer to the nearest cent would result in a different answer.
Additionally, checking the calculations multiple times to ensure accuracy is always recommended.
Overall, tracking and analyzing expenses and savings is important for financial planning and achieving financial goals. By keeping track of how much she saved each month,
Sarah can make informed decisions about her spending and saving habits and adjust accordingly to reach her vacation savings goal.
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In a restaurant 1/5 of the customers are vegetarian and 3/4 eat meat. The remainder of the customers are dairy intolerant. What fraction of the customers are dairy intolerant? Give your answer as a fraction in its lowest terms
1/20 of the customers are dairy intolerant.
We know that 1/5 of the customers are vegetarian, and 3/4 eat meat. Let's first find the total fraction of vegetarian and meat-eating customers:
1/5 (vegetarian) + 3/4 (meat)
To add these fractions, we need a common denominator. The least common denominator (LCD) for 5 and 4 is 20. So, we'll convert both fractions to have the same denominator:
(1/5)*(4/4) = 4/20 (vegetarian)
(3/4)*(5/5) = 15/20 (meat)
Now, let's add the fractions:
4/20 (vegetarian) + 15/20 (meat) = 19/20 (vegetarian and meat)
Now we know that 19/20 of the customers are either vegetarian or meat-eaters. The remainder must be dairy intolerant. To find this fraction, subtract the combined fraction from 1:
1 - 19/20 = 1/20
So, 1/20 of the customers are dairy intolerant.
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Kirill is doing a puzzle in 10 hours and max can do the same but in 12 hours if kirill and max work together what part of the puzzle will take an hour
When Kirill and Max work together, they can complete 11/60 of the puzzle in one hour.
To find out what part of the puzzle Kirill and Max can complete together in one hour, we need to calculate their combined work rate.
Step 1: Find the work rate of Kirill.
Kirill can complete the puzzle in 10 hours, so his work rate is 1/10 of the puzzle per hour.
Step 2: Find the work rate of Max.
Max can complete the puzzle in 12 hours, so his work rate is 1/12 of the puzzle per hour.
Step 3: Add Kirill's and Max's work rates together.
(1/10) + (1/12) = (12 + 10) / (10 * 12) = 22 / 120
Step 4: Simplify the fraction.
The simplified fraction is 11/60.
So, when Kirill and Max work together, they can complete 11/60 of the puzzle in one hour.
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Which statement explains how to determine whether triangle ABC is similar to triangle XYZ?
option D is correct ,the triangle are not similar because only angle c and z are congruent .
what is congruent ?
In mathematics, congruent means having the same size and shape. Two objects are said to be congruent if they have the same dimensions and angles, and can be transformed into each other by a combination of translations, rotations, and reflections.
In the given question,
congruent means having the same size and shape. Two objects are said to be congruent if they have the same dimensions and angles, and can be transformed into each other by a combination of translations, rotations, and reflections.
so we can conclude that option D is correct answer as other 2 angle are not equal
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Roy made a pizza that is 12 inches in diameter. He knows he can eat about 84. 8 in, at what angle should Roy cut the pizza in radians? Round your answer to the tenths place
Roy should cut the pizza at an angle of 4.7 radians if the total diameter of the pizza is 12 inches.
Diameter of the pizza = 12 inches
The area he can eat = 84. 8 inches
The area of the pizza for 12 inches diameter can be calculated by using the formula:
Area = π*[tex]r^2[/tex]
Area = π* ([tex]6^2[/tex])
Area = 36π
The angle of the slice of pizza he can eat about 84.8 square inches can be calculated as:
Area of sector = (θ/2) ×[tex]r^2[/tex]
84.8 = (θ/2) × [tex]6^2[/tex]
84.8 = 18*θ
θ = 84.8 / 18
θ = 4.71 radians
Therefore, we can conclude that Roy should cut the pizza at an angle of 4.7 radians.
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25. A small cone of height 8 cm is cut off from a bigger cone to leave a frustum of height 16 cm. If the volume of the smaller cone is 160 cm, find the volume of the frustum.
The volume of the frustum is approximately 634.3 cubic centimeters.
How to find the volume?Let the radius of the smaller cone be 'r' and the radius of the bigger cone be 'R'.
Since the height of the smaller cone is 8 cm and its volume is 160 cm³, we have:
1/3 * π * r² * 8 = 160
r² = 60/π
r ≈ 4.03 cm
Now, using similar triangles, we can find the radius 'R' of the bigger cone:
(R - r)/16 = R/24
24R - 24r = 16R
R = 2r/3
R ≈ 2.69 cm
Therefore, the volume of the frustum is:
1/3 * π * (2.69² + 2.69*4.03 + 4.03²) * 16 - 1/3 * π * 4.03² * 8
≈ 634.3 cm³
So, the volume of the frustum is approximately 634.3 cubic centimeters.
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10. When travelling along King Street or
Queen Street, the distance between any two
parallel streets is always about 1. 42 km.
Queen St.
King St.
Water St.
1. 42 km
,1. 42 km
1 km
Albert St.
1 km
Park St.
How much greater is the distance along
Park Street from King Street to Queen
Street than the distance along Albert Street
from King Street to Queen Street?
Answer:
The distance along Park Street from King Street to Queen Street is 0.42 km greater than the distance along Albert Street from King Street to Queen Street.
Step-by-step explanation:
Since the distance between any two parallel streets along King Street or Queen Street is always about 1.42 km, the distance along Park Street from King Street to Queen Street is:
1.42 km + 1 km + 1.42 km = 3.84 km
Similarly, the distance along Albert Street from King Street to Queen Street is:
1 km + 1.42 km + 1 km = 3.42 km
Therefore, the difference in distance is:
3.84 km - 3.42 km = 0.42 km
So, the distance along Park Street from King Street to Queen Street is 0.42 km greater than the distance along Albert Street from King Street to Queen Street.
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If f(x) is an exponential function where f(4. 5) = 22 and f(14) = 40,
then find the value of f(26. 5), to the nearest hundredth.
So, to the nearest hundredth, the value of f(26.5) is approximately 59.81.
To find the value of f(26.5) for the given exponential function f(x), we will first determine the base and initial value of the function using the given points f(4.5) = 22 and f(14) = 40.
An exponential function has the form f(x) = ab^x, where a is the initial value and b is the base.
1. Write the two equations using the given points:
22 = ab^(4.5)
40 = ab^(14)
2. Divide the second equation by the first to eliminate the initial value, a:
(40/22) = (ab^(14))/(ab^(4.5))
3. Simplify and solve for the base, b:
1.81818 = b^(9.5)
b ≈ 1.05459
4. Now, plug b back into one of the original equations to solve for the initial value, a:
22 = a(1.05459)^4.5
a ≈ 16.08364
5. With a and b found, we can now find the value of f(26.5):
f(26.5) = 16.08364 * (1.05459)^26.5
f(26.5) ≈ 59.81
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The value of exponential function f(26. 5), to the nearest hundredth is 144.42.
To find the value of f(26.5) for the exponential function, we can use the given data points and apply the exponential function formula.
Let's assume the exponential function is of the form: f(x) = a * b^x, where a and b are constants.
Using the given data points:
f(4.5) = 22
f(14) = 40
Substituting these values into the exponential function equation:
22 = a * b^4.5 ---(1)
40 = a * b^14 ---(2)
Dividing equation (2) by equation (1), we can eliminate the constant 'a':
40/22 = (a * b^14) / (a * b^4.5)
1.8182 = b^(14 - 4.5)
1.8182 = b^9.5
To find the value of b, we take the 9.5th root of 1.8182:
b ≈ 1.109
Now we can substitute the value of b into equation (1) to solve for 'a':
22 = a * (1.109)^4.5
a ≈ 4.95
Therefore, the exponential function can be approximated as: f(x) ≈ 4.95 * (1.109)^x
Now we can find the value of f(26.5):
f(26.5) ≈ 4.95 * (1.109)^26.5 ≈ 144.42
Hence, the value of f(26.5), to the nearest hundredth, is approximately 144.42.
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find the extremes of 4x−4y subject to condition x2 + 2y2 = 1
To find the extremes of 4x−4y subject to the condition x2 + 2y2 = 1, we can use the method of Lagrange multipliers.
First, we set up the Lagrange equation:
∇f(x,y) = λ∇g(x,y)
where f(x,y) = 4x-4y and g(x,y) = x2 + 2y2 - 1.
Taking partial derivatives, we have:
∂f/∂x = 4
∂f/∂y = -4
∂g/∂x = 2x
∂g/∂y = 4y
Setting these equal to their respective Lagrange multipliers, we have:
4 = 2λx
-4 = 4λy
x2 + 2y2 = 1
Solving for x and y in terms of λ, we get:
x = 2λ/4 = λ/2
y = -λ/4
Substituting these back into the constraint equation, we have:
(λ/2)2 + 2(-λ/4)2 = 1
λ2/4 + λ2/8 = 1
3λ2/8 = 1
λ2 = 8/3
Taking the positive and negative square roots of λ2, we have:
λ = ±2√2/3
Substituting these values back into x and y, we get:
For λ = 2√2/3:
x = (2√2/3)/2 = √2/3
y = -(2√2/3)/4 = -√2/6
For λ = -2√2/3:
x = (-2√2/3)/2 = -√2/3
y = -(-2√2/3)/4 = √2/6
Now we can find the extreme values of f(x,y) by plugging in these values of x and y:
f(√2/3, -√2/6) = 4(√2/3) - 4(-√2/6) = 4√2
f(-√2/3, √2/6) = 4(-√2/3) - 4(√2/6) = -4√2
Therefore, the maximum value of 4x-4y subject to the condition x2 + 2y2 = 1 is 4√2 and the minimum value is -4√2.
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A health insurance company wants to know the proportion of admitted hospital patients who have a type 2 diabetes at orlando health hospitals. how large of a sample should be taken to estimate the proportion within 6% at 93% confidence?
To estimate the proportion of admitted hospital patients who have type 2 diabetes at Orlando Health Hospitals within a certain margin of error and confidence level,
we can use the following formula to determine the necessary sample size:
[tex]n = [(Z^2 * p * q) / E^2] / [1 + ((Z^2 * p * q) / E^2N)][/tex]
where:
n = sample size
Z = z-score for the desired confidence level (in this case, 1.81 for a 93% confidence level)
p = estimated proportion of patients with type 2 diabetes (unknown)
q = 1 - p
E = margin of error (0.06)
N = population size (unknown)
Since we do not know the estimated proportion of patients with type 2 diabetes or the population size,
we can assume a conservative estimate of p = q = 0.5, which maximizes the sample size required.
Plugging in the values, we get:
[tex]n = [(1.81^2 * 0.5 * 0.5) / 0.06^2] / [1 + ((1.81^2 * 0.5 * 0.5) / 0.06^2N)][/tex]
Simplifying, we get:
[tex]n = 1242.95 / [1 + (2.4 / N)][/tex]
To satisfy the requirements of the problem, we need to round up to the nearest whole number, so we need a sample size of at least 1243 patients.
Note that if we had a better estimate for p or N, we could use those values in the formula to get a more precise sample size.
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Let y=tan(5x+3)
.
Find the differential dy when x= 5 and dx= 0.1.
Find the differential dy when x= 5 and dx= 0.2.
When x = 5 and dx = 0.1, the differential dy is approximately 96.375.
When x = 5 and dx = 0.2, the differential dy is approximately 192.75.
We can use the chain rule to find the differential of y with respect to x. Let u = 5x + 3, then y = tan(u).
Using the chain rule, we have:
dy/dx = dy/du * du/dx
Taking the derivative of y with respect to u, we have:
dy/du = sec^2(u)
Substituting u = 5x + 3, we have:
dy/du = sec^2(5x + 3)
Taking the derivative of u with respect to x, we have:
du/dx = 5
Substituting x = 5 and dx = 0.1, we have:
dy = dy/du * du/dx * dx
= sec^2(5(5) + 3) * 5 * 0.1
= 192.75 * 0.5
= 96.375
Therefore, when x = 5 and dx = 0.1, the differential dy is approximately 96.375.
Substituting x = 5 and dx = 0.2, we have:
dy = dy/du * du/dx * dx
= sec^2(5(5) + 3) * 5 * 0.2
= 192.75 * 1
= 192.75
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The base of a triangular prisms has an area of 18 square inches if the height of the prism is 9. 5 inches then what what is the volume of the prism
The volume of the triangular prism is 171 cubic inches.
To find the volume of a triangular prism, you need to multiply the area of the base by the height of the prism. In this case, the base of the prism has an area of 18 square inches and the height is 9.5 inches. So, the volume of the prism can be calculated as follows:
Volume = Base Area x Height
Volume = 18 sq. in. x 9.5 in.
Volume = 171 cubic inches
Therefore, the volume of the triangular prism is 171 cubic inches.
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