The answer is d. 27 is not a correct answer as it is much smaller than the required sample size of 271.
To create a 90% confidence interval estimate for a population mean with a width of no more than 1 unit, we need to find the sample size required to achieve this level of precision.
Using the formula for the margin of error of a confidence interval, we have
Margin of Error = z* (σ / sqrt(n))
where z* is the critical value from the standard normal distribution corresponding to a 90% confidence level, σ is the population standard deviation (given as 10), and n is the sample size.
We want the margin of error to be no more than 1 unit, so we can write
1 = z* (σ / sqrt(n))
Solving for n, we get
n = (z* σ / 1)^2
Using a standard normal distribution table or calculator, we can find that the critical value z* corresponding to a 90% confidence level is approximately 1.645. Substituting this value and the given population standard deviation into the formula for n, we get
n = (1.645 * 10 / 1)^2 = 270.25
Rounding up to the nearest integer, we get n = 271. Therefore, the answer is d. 27 is not a correct answer as it is much smaller than the required sample size of 271.
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Agriculturists in a certain state claim that 43% of the residents in the northern portion of the state prefer flour tortillas over corn tortillas, while 59% of the residents in the southern portion of the state prefer flour tortillas over corn tortillas. Suppose random samples of 33 northerners and 41 southerners are selected. Let p hat Subscript Upper N and P hat Subscript s be the sample proportions of northern and southern residents of this state, respectively, who would prefer flour tortillas over corn tortillas
The sample proportions of northern and southern residents of this state will depend on the actual preferences of the individuals in the samples.
We have a sample of 33 Northerners and 41 Southerners from a certain state. The sample proportions of northern residents (pN) and southern residents (ps) who prefer flour tortillas over corn tortillas can be calculated based on the provided information.
According to the claim by agriculturists, 43% of northern residents and 59% of southern residents prefer flour tortillas. To estimate the proportions in the population, we use the sample proportions.
For the northern residents:
pN = Number of northerners preferring flour tortillas / Total number of northerners in the sample
Assuming that the sample is representative, we can multiply the sample size by the claimed proportion to estimate the number of northerners preferring flour tortillas:
pN = 33 * 0.43 = 14.19 (approximately)
For the southern residents:
ps = Number of southerners preferring flour tortillas / Total number of southerners in the sample
Again, assuming the sample is representative, we can estimate the number of Southerners preferring flour tortillas:
ps = 41 * 0.59 = 24.19 (approximately)
The sample proportions pN and ps are estimates of the proportions in the respective populations. They provide an indication of the preferences of the residents in the northern and southern portions of the state based on the selected samples.
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sidra buys a large circular pizza that is divided into eight equal slices. she measures along the outer edge of the crust from one piece and finds it to be 5.5 inches. what is the diameter of the pizza to the nearest inch?
diameter of the pizza is twice the radius, so the diameter is approximately 11 inches to the nearest inch.
Since the pizza is divided into eight equal slices, the central angle of each slice is 45 degrees (360 degrees divided by 8).
The length of the outer edge of one slice is equal to the circumference of the circle divided by 8. Let's call this length "x".
We can set up the equation x = (2πr)/8, where r is the radius of the pizza.
Simplifying the equation, we get x = (πr)/4.
We know that x = 5.5 inches, so we can plug this in to get 5.5 = (πr)/4.
Solving for r, we get r = (4 x 5.5) / π ≈ 5.54 inches.
diameter of the pizza is twice the radius, so the diameter is approximately 11 inches to the nearest inch.
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true of false: the normal distribution follows a bell shaped curve, where probabilities are found by calculating the area under the curve
True.
The normal distribution is a probability distribution that follows a bell-shaped curve. The curve is symmetric around the mean, with the majority of the data falling within one standard deviation from the mean. Probabilities for a given range of values can be calculated by finding the area under the curve for that range. This is because the area under the curve represents the probability of a random variable falling within that range. The properties of the normal distribution make it a useful tool for statistical analysis, as it can be used to model many natural phenomena and is often assumed in hypothesis testing and confidence interval calculations.
True, the normal distribution follows a bell-shaped curve, where probabilities are found by calculating the area under the curve. This distribution is symmetrical around its mean, with probabilities decreasing as values move away from the mean. To find the probabilities, we calculate the area under the curve using integration, which gives us the likelihood of a value occurring within a specific range. The total area under the curve is equal to 1, representing 100% probability. The normal distribution is useful for understanding real-world phenomena and predicting outcomes based on patterns of data.
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in the eai sampling problem, the population mean is 51800 and the population standard deviation is 4000 . when the sample size is 64 , what is the probability of obtaining a sample mean within 500 of the population mean.
the probability of obtaining a sample mean within 500 of the population mean is approximately 0.6827.
To solve this problem, we need to use the central limit theorem which states that the distribution of the sample means will be approximately normal with mean equal to the population mean and standard deviation equal to the population standard deviation divided by the square root of the sample size.
Given that the population mean is 51800 and the population standard deviation is 4000, we can calculate the standard error of the mean as follows:
Standard error of the mean = 4000 / sqrt(64) = 500
We want to find the probability of obtaining a sample mean within 500 of the population mean. This can be written as:
P(51800 - 500 < X < 51800 + 500)
where X is the sample mean.
We can standardize this interval using the standard error of the mean:
P(-1 < Z < 1)
where Z is a standard normal variable.
Using a standard normal table, we find that the probability of Z being between -1 and 1 is approximately 0.6827.
Therefore, the probability of obtaining a sample mean within 500 of the population mean is approximately 0.6827.
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assume the callers to a cable company is normally distributed with a mean of 3.4 minutes and a standard deviation of 0.8 minutes. determine the percent of callers who are on hold between 2.9 and 4.4 minutes.
Approximately 68% of callers are on hold between 2.6 and 3.4 minutes. To find the per cent of callers on hold between 2.9 and 4.4 minutes, we need to find the area under the normal distribution curve between these two values.
Using a standard normal distribution table or calculator, we can find the z-scores for 2.9 and 4.4, which are -0.63 and 1.5, respectively. Then, we can use the cumulative distribution function (CDF) to find the area under the curve between these z-scores. The result is approximately 65.6%. Therefore, we can conclude that about 65.6% of callers are on hold between 2.9 and 4.4 minutes.
To explain the calculation in more detail, we can use the formula for the standard normal distribution, which is:
z = (x - μ) / σ
where z is the z-score, x is the value we are interested in, μ is the mean, and σ is the standard deviation. Using the given values, we can find the z-scores for 2.9 and 4.4 as follows:
z1 = (2.9 - 3.4) / 0.8 = -0.63
z2 = (4.4 - 3.4) / 0.8 = 1.25
We need to use the CDF to find the area under the curve between these two z-scores. The CDF gives the probability that a random variable is less than or equal to a certain value. We can use a standard normal distribution table or calculator to find the CDF for each z-score.
The CDF for z1 is approximately 0.2643, and the CDF for z2 is approximately 0.8944. To find the area between these two values, we subtract the smaller CDF from the larger CDF:
0.8944 - 0.2643 = 0.6301
This means that about 63.01% of the area under the normal distribution curve is between z1 and z2. However, we are interested in the per cent of callers who are on hold between 2.9 and 4.4 minutes, not the per cent of the area under the curve. To convert this percentage to the per cent of callers, we can multiply by 100:
0.6301 * 100 = 63.01%
Therefore, approximately 65.6% of callers are on hold for between 2.9 and 4.4 minutes.
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Help I don't understand.
The profit P(x) = -0.5x² + 23x - 13.
We have,
Q(x) = 45x - 0.5x² and L(x) = 12x + 13
To calculate the profit the formula used
P(x) = Q(x) - L(x)
P(x) = 45x - 0.5x² - (12x+ 13)
P(x) = 45x - 0.5x² -12x - 13
P(x) = -0.5x² + 23x - 13
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the angle between the chord line of an airfoil and the relative wind is known as the angle of
The Angle of Attack is the term used to describe the angle between an airfoil's chord line and the relative wind.
The angle between the chord line of an airfoil and the relative wind is known as the angle of attack. This angle is a crucial factor in determining the lift and drag of the airfoil, and is affected by factors such as the speed of the airfoil and the shape of its surface.
In aviation, maintaining the proper angle of attack is essential for achieving optimal performance and safety during flight.
The angle between the chord line of an airfoil and the relative wind is known as the Angle of Attack (AOA).
Chord Line: This is the imaginary straight line connecting the leading edge to the trailing edge of an airfoil.
Relative Wind: This is the flow of air as it interacts with the airfoil. It's the direction of airflow relative to the airfoil's motion.
Angle of Attack (AOA): This is the angle formed between the chord line of an airfoil and the direction of the relative wind.
In summary, the Angle of Attack is the term used to describe the angle between an airfoil's chord line and the relative wind.
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Robert recorded the monthly rent of various apartment homes. What is the median rent of the apartments he is looking into?
450, 1695, 1250, 650, 575, 880
The median rent of the apartments Robert is looking into is $765.
When dealing with a set of numbers, it is important to know the different measures of central tendency. One of them is the median, which is the middle value in a dataset when arranged in order.
In this case, Robert recorded the monthly rent of various apartment homes: 450, 1695, 1250, 650, 575, and 880.
To find the median rent of these apartments, we need to arrange them in order first: 450, 575, 650, 880, 1250, and 1695.
Since there are six numbers in total,
The median would be the average of the third and fourth values, which is (650 + 880) / 2 = 765.
Therefore, the median rent of the apartments Robert is looking into is $765.
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Consider a triangle ABC like the one below. Suppose that a=19, b=45, and c=41. (The figure is not drawn to scale.) solve the triangle. Carry your intermediate computations to at least four decimal places, and round your answers to the nearest tenth. If there is more than one solution, use the button labeled “or”.
Answer:
A ≈ 25.6°, B ≈ 52.3°, C ≈ 68.8° or A
Step-by-step explanation:
To solve the triangle ABC, we can use the Law of Cosines, which relates the lengths of the sides of a triangle to the cosine of the angles opposite those sides. The law states that:
c^2 = a^2 + b^2 - 2ab cos(C)
where c is the length of the side opposite angle C, a is the length of the side opposite angle A, and b is the length of the side opposite angle B.
Using the given values of a, b, and c, we can substitute into the formula and solve for cos(C):
41^2 = 19^2 + 45^2 - 2(19)(45) cos(C)
1681 = 361 + 2025 - 1710 cos(C)
cos(C) = (361 + 2025 - 1681) / (21945)
cos(C) = 0.37103
Now we can use the inverse cosine function to find the measure of angle C:
C = cos^-1(0.37103)
C ≈ 68.8°
Next, we can use the Law of Sines to find the measures of angles A and B:
sin(A)/a = sin(C)/c
sin(A)/19 = sin(68.8°)/41
sin(A) ≈ 0.4250
A ≈ 25.6°
Similarly, we can find the measure of angle B:
sin(B)/b = sin(C)/c
sin(B)/45 = sin(68.8°)/41
sin(B) ≈ 0.7873
B ≈ 52.3°
Therefore, the solution for the triangle ABC is:
A ≈ 25.6°, B ≈ 52.3°, C ≈ 68.8° or A
Mike walked a distance of 12 laps. Juan walked 2/3 of the distance Mike walked. How many laps did Juan walk?
Answer:
8 laps.
Step-by-step explanation:
12 x (2/3) = 8. Juan walked 8 laps.
Answer:
8 laps
Step-by-step explanation:
We know that Mike walked 12 laps.
We also know that Juan walked 2/3 of 12 laps, meaning Juan walked less laps than Mike, as 2/3 is less than 1.
To solve, we can multiply 2/3 by 12 to find out how many laps Juan walked:
[tex]12(\frac{2}{3})[/tex]
=8
So, Juan walked 8 laps.
Hope this helps! :)
A swimming pool is shaped like a cylinder. It has a height of 4 feet and a base radius of 5 feet. The pool is being filled with water at a rate of 10 gallons per minute. About how long will it take to fill the pool if 1 cubic foot is about 7.5 gallons? Round to the nearest whole minute.
Answer:
236 minutes
Step-by-step explanation:
You want to know the time to fill a cylindrical pool with radius 5 feet and depth 4 feet if 1 cubic foot is 7.5 gallons and the fill rate is 10 gallons per minute.
VolumeThe volume of the pool is ...
V = πr²h
V = π(5 ft)²(4 ft) = 100π ft³ ≈ 314.159 ft³
TimeThe time to fill the pool will be found by dividing the number of gallons by the fill rate in gallons per minute.
t = V/rate
t = (314.159 ft³)(7.5 gal/ft³)/(10 gal/min) ≈ 236 min
It will take about 236 minutes to fill the pool.
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help need this asap!
Answer:
9,100
Step-by-step explanation:
We have a rectangle with a length of 130 and a width of 70.
We are asked to find how much turf will cover the entire field.
We can multiply:
130·70
=9100
This means that 9,100 yds² is needed.
Hope this helps! :)
[tex]y=-2x-3\\4y+x=16[/tex]
x = -4 and y = 5 is the solution to the given system of equations.
The given equations are:
y = -2x - 3
4y + x = 16
To solve this system of equations, we can use either the substitution method or the elimination method. Let's use the substitution method here:
Solve one equation for one variable in terms of the other variable. Let's solve the first equation for y:
y = -2x - 3
Substitute the expression for that variable from Step 1 into the other equation. Substitute y = -2x - 3 into the second equation:
4y + x = 16
4(-2x - 3) + x = 16
Simplify and solve for the remaining variable. Distribute the 4:
-8x - 12 + x = 16
-7x = 28
x = -4
Substitute the value found in Step 3 into one of the original equations and solve for the other variable. Let's use the first equation:
y = -2x - 3
y = -2(-4) - 3
y = 5
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Complete Question:
Solve the system of equations:
y = -2x - 3
4y + x = 16
Halp me this question
The fact family of the numbers are given by
a) 4 , 7 , 11
b) 2 , 6 , 8
c) 5 , 4 , 9
d) 9 , 7 , 16
Given data ,
Numbers that do not form a fact family are any set of numbers that do not follow this pattern.
And , fact family of the numbers are given by
a) 4 , 7 , 11
b) 2 , 6 , 8
c) 5 , 4 , 9
d) 9 , 7 , 16
Hence , the fact family of numbers are solved
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Work out the length of DG in this cuboid.
Give your answer in centimetres (cm) to 1 d.p.
Answer:
[tex] \sqrt{ {20}^{2} + {44}^{2} } = \sqrt{400 + 1936} = \sqrt{2336} = 4 \sqrt{146} = 48.3[/tex]
The length of DG is about 48.3 cm.
Nazdar wants to buy a perfume that is on sale for 10% off the marked price. If
the marked price is 75 000 Dinars, about how much will the perfume cost after
the discount?
Answer: 67,500
Step-by-step explanation:
75,000 divided by 10% = 7,500
75,000 - 7,500 = 67,500
The piecewise defined function f(x) is graphed below. What is the value of f(2)?
rectangle ABCD is translated 5 units to the right. What is the length of the line segment B'C'?
The length of the line segment B'C' is 3 units.
We can see that from the given graph that,
The coordinates of the points are:
B = (-2, 6)
C = (-2, 3)
If we translate the points 5 units to the right then the changed coordinates will be -
B' = (-2 + 5, 6) = (3, 6)
C' = (-2 + 5, 3) = (3, 3)
So the length of the B'C' is given by,
B'C' = √((3 - 3)² + (6 - 3)²) = √(0² + 3²) = √(0 + 9) = √9 = 3 units.
Hence the length of the line segment B'C' is 3 units.
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a ___ is one of two pieces of a double cone divided at the vertex.
A frustum is one of two pieces of a double cone divided at the vertex. A double cone is a three-dimensional shape that is created by connecting two cones with their vertices touching.
When the double cone is cut through the vertex, it creates two pieces known as frustums. A frustum has a circular base and a smaller circular top, which are parallel to each other. The height of the frustum is the distance between the two circular bases.
The volume of a frustum can be calculated using the formula V = (1/3)h(a^2 + ab + b^2), where h is the height, a is the radius of the larger base, and b is the radius of the smaller top. Frustums are commonly found in architecture and engineering, such as in the design of buildings and bridges.
A "napped cone" is one of two pieces of a double cone divided at the vertex. When a double cone is bisected through its vertex, it results in two identical, mirror-image napped cones. These geometric shapes have various applications in mathematics, engineering, and design due to their unique properties.
Napped cones share some characteristics with regular cones, such as having a circular base, but their pointed vertex is replaced by a flat plane where the double cone was divided. This creates a shape that is both symmetrical and easy to manipulate for various purposes.
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Maddy bought 6 pairs of socks for $2.15 a pair. She had a coupon for $1.75 off her total purchase. Which calculation shows the total amount Maddy paid for the socks, not including sales tax?
The total amount paid by Maddy is $14.65.
It is given in the question that Maddy paid $2.15 for each pair of socks. She also had a coupon for $1.75 off the total purchase amount.
So, the total amount paid by Maddy will be the sum of the amount paid for 6 pairs of socks and the coupon amount i.e.
Total amount = $2.15*6 + $1.75
Total amount = $14.65
Hence, the total amount Maddy paid for the socks is $14.65.
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The center of a circle is at (-5,2) and the radius is 7. what is the equation of the circle
The equation of the circle with center (-5, 2) and radius 7 is ( x + 5 )² + ( y - 2 )² = 49.
What is the equation of the circle?The standard form equation of a circle with center (h, k) and radius r is:
( x - h )² + ( y - k )² = r²
Given that the center of the circle is (-5, 2) and the radius is 7.
Hence, we can substitute these values into the formula to get the equation of the circle:
Plug in h = -5, k = 2 and r = 7
( x - h )² + ( y - k )² = r²
(x - (-5) )² + ( y - 2 )² = 7²
Simplifying and expanding the equation, we get:
( x + 5 )² + ( y - 2 )² = 49
Therefore, the equation of the circle is ( x + 5 )² + ( y - 2 )² = 49.
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the community hospital is studying its distribution of patients. a random sample of 317 patients presently in the hospital gave the following information: type of patient old rate of occurrences of these types of patients present number of
From the chi-square test, the p-value is greater than significance level so, we can't reject the null hypothesis. The distribution of patients in this data set of wards in community hospital has not changed.
We have a community hospital is studying its distribution of patients. Random sample with
number of patients = 317
There is a table present in above figure contains the type of patients, old rate and present rate of occurrence of type of patients.
Level of significance = 0.05
We have to test the claim that the distribution of patients in these ward is same or not.
Now, For testing the claim we will use the chi-square test, null and alternative hypothesis are defined as [tex]H_0[/tex]: the distribution of patients has not Changed
[tex]H_a[/tex]: the distribution of patients has Changed
Patients observed Expected
Maternity ward 65 20% of 317 = 63.4
Cardiac ward 100 32% of 317 = 101.44
burn ward 29 10% of 317 = 31.7
children ward 48 15% of 317 = 47.55
All wards 75 23% of 317 = 72.91
Now, calculate the χ² statistic : [tex]χ² = \frac{ \sum( O_i - E_i)²} {E_i}[/tex]
where, Oᵢ --> observed value for iᵗʰ
Eᵢ --> excepted value for iᵗʰ
[tex]χ² = \frac{ \sum( 65 - 63.4)²} {63.4} + \frac{ \sum( 100 - 101.44)²} {101.4} + \frac{ \sum( 29 - 31.7)²} {31.7} + \frac{ \sum( 48 - 47.55)²} {47.55} + \frac{ \sum( 75 - 72.91)²} {72.91} \\ [/tex]
= 0.355
Now, we calculate p-value for χ² > 0.355, from the calculater the critical value for
[tex]χ² = 0.355[/tex] and degree of freedom = n - 1 = 5 - 1 = 4 , where 5 is number of categorical variables. So, [tex] P( χ² > 0.355)[/tex] = 0.99
Since, the p-value = 0.99 > 0.05, so we fail to reject the null hypothesis. Hence, from the above test we can accept the claim that the distribution of patients has not changed.
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Complete question:
the community hospital is studying its distribution of patients. a random sample of 317 patients presently in the hospital gave the following information: type of patient, old rate of occurrences of these types of patients and present number of occurrence of type of patients. Using a 5% level of significance, test the claim that the distribution of patients in these wards has not changed.
Find the quotient and express it in rectangular form
2(cos150° + isin150°) ÷ 8(cos210° + isin210°)
The quotient, expressed in rectangular form, is 1/2 - 1/2 - i(√(3)/2).
We can simplify this complex division by multiplying the numerator and denominator by the complex conjugate of the denominator.
The complex conjugate of 8(cos210° + isin210°) is 8(cos(-210°) + isin(-210°)), so we have:
2(cos150° + isin150°) ÷ 8(cos210° + isin210°)
= 2(cos150° + isin150°) x (8(cos(-210°) + isin(-210°))) / (8(cos210° + isin210°)) x (8(cos(-210°) + isin(-210°)))
= 28 x (cos150°cos(-210°) - sin150°sin(-210°) + i(cos150°sin(-210°) + sin150°cos(-210°))) / 88
= (1/4)(4cos(-60°) + 4isin(-60°))
= (1/4)(4cos60° - 4isin60°)
= cos60° - isin60°
= 1/2 - i(√(3)/2)
Therefore, the quotient, expressed in rectangular form, is 1/2 - 1/2 - i(√(3)/2).
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This box plot shows information about the marks scored in a test.
Nobody gained exactly 40, 68 or 82 marks. 80 students gained more then 68 marks.
How many student gained less than 40 marks?
Mathswatch
80 students gained more than 48 mark from box plot.
Since 120 students gained less than 70, and
70 is the upper quartile from box plot
120 people are in the 75% of all the students
we need to find the total number of students.
we need to multiply 0.75 (75%) by something to get 120. which is 160 (the total number of all students).
and since 48 is the median score, find 50% of 160 which is 80
Hence, 80 students gained more than 48 mark
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A cook whole preparing noodles adds the right ingredients for nine times and makes an error is adding the ingredients for three times what is the probability that the cook adds the right ingredients and cooks well
The probability that the cook adds the right ingredients and cooks the noodles well is 3/4 or 75%.
I understand that you need help calculating the probability of a cook adding the right ingredients while preparing noodles.
To determine the probability, we need to consider the number of successful attempts and the total number of attempts. In this scenario, the cook adds the right ingredients nine times and makes an error three times.
Therefore, there have been 12 attempts in total (9 successful attempts + 3 erroneous attempts).
The probability of adding the right ingredients is calculated by dividing the number of successful attempts (9) by the total number of attempts (12).
So, the probability is:
P(success) = 9 successful attempts / 12 total attempts
By simplifying this fraction, we get:
P(success) = 3/4
Therefore, the probability that the cook adds the right ingredients and cooks the noodles well is 3/4 or 75%. This means that out of every 12 attempts, the cook is likely to add the right ingredients and cook the noodles well nine times.
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In 2010 you purchased your home for $264,000. Today, you sold your home for $389,000. You have purchased a new home for $428,000 and have put down a deposit of 20%. How much money do you have left over from the selling of your home?
-$217,400 is the amount of money needed to cover the purchase of your new home by selling the old house at $389,000.
Cost of home = $264,000
Selling price = $389,000
Purchase price of new home = $428,000
Deposit percentage = 20%
The total amount received from selling the house is:
The amount received from the sale = selling price - purchase price
The amount received from sale = $389,000 - $264,000
Amount received from sale = $125,000
The amount spent on the new home is:
Amount spent on new home = purchase price - deposit
Amount spent on new home = $428,000 - 20% of $428,000
Amount spent on new home = $428,000 - $85,600
Amount spent on new home = $342,400
Finally, the leftover money is calculated as:
The amount left over = amount received from sale - the amount spent on a new home
The amount left over = $125,000 - $342,400
Amount left over = -$217,400
The negative amount indicates that you did not have enough money from the sale of your old home to cover the purchase of your new home.
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Select the correct answer. Which equation represents circle N?
A. (x+7)²+(y-6)² = 25
B. (x-7)² + (y + 6)² = 25
C. (x+7)² + (- 6)² = 50
D. (x-7)² + (y + 6)² = 50 L(-2,11)
The equation that represents circle N include the following: C. (x + 7)² + (y - 6)² = 50.
What is the equation of a circle?In Geometry, the standard or general form of the equation of a circle is modeled by this mathematical equation;
(x - h)² + (y - k)² = r²
Where:
h and k represent the coordinates at the center of a circle.r represent the radius of a circle.Radius, r = √[(x₂ - x₁)² + (y₂ - y₁)²]
Radius, r = √[(-2 + 7)² + (11 - 6)²]
Radius, r = √[(5)² + (5)²]
Radius, r = √50 units.
By substituting the given radius and center into the equation of a circle, we have;
(x - h)² + (y - k)² = r²
(x - (-7))² + (y - 6)² = (√50)²
(x + 7)² + (y - 6)² = 50.
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if the units for x are feet and the units for a(x) are pounds per foot, what are the units for da dx ?
The units for da/dx are pounds per foot squared.
The units for da/dx would be pounds per foot squared. This is because da/dx represents the rate of change of the function a(x), which has units of pounds per foot, with respect to x, which has units of feet. When we take the derivative of a(x), we essential do division of the change in a(x) by the change in x.
The change in a(x) has units of pounds, and the change in x has units of feet. Therefore, the units for da/dx are pounds per foot squared.
To further explain this, imagine that a(x) represents the weight of a beam that is x feet long. The units for a(x) would be pounds per foot, as it gives us the weight of the beam per unit of length. The derivative of a(x), or da/dx, would give us the rate at which the weight of the beam changes as we increase its length by one foot.
This rate of change would be in units of pounds per foot squared, as we are dividing the change in weight (pounds) by the change in length (feet squared).
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26.if a single singer is singing at 74db, how many singers have joined him if the level increases to 83 db and each singer is equally loud?
To find the number of singers that joined the single singer, we need to first determine the total increase in decibels (dB) and then divide it by the increase in decibels per singer.
1. Calculate the total increase in decibels: 83 dB - 74 dB = 9 dB
2. Since decibels use a logarithmic scale, we need to determine the number of times the sound intensity is multiplied. In general, an increase of 10 dB corresponds to a 10 times increase in intensity. Therefore, a 3 dB increase corresponds to doubling the intensity (approximately).
3. Now, we need to find how many times the intensity doubles to reach a 9 dB increase. Since each 3 dB increase doubles the intensity, 9 dB increase means tripling the doubling (9 dB / 3 dB = 3).
4. The intensity doubles 3 times: 2^3 = 8. This means the total sound intensity is 8 times greater than the original intensity.
5. Since the single singer's intensity is already included, the number of singers who joined him is 8 - 1 = 7 singers.
Seven singers have joined the single singer when the sound level increases from 74 dB to 83 dB, and each singer is equally loud.
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A tangent line drawn to the graph of y=4x/1+x^3 at the point (1,2) forms a right triangle with the coordinate axes. The area of the triangle is: either 3.0, 3.5, 4.0, 4.5, 5.0. Show your work.
The area of the triangle is 4.5 square unit.
We have, y= 4x/ (1 + x³)
Now, differentiating the above equation wrt to x we get
y' = 4(1 + x³)- 4x . 3x² / (1+ x³)²
y'= -8x³ + 4/ (1+x³)²
When x = 1 then y' = -4/4 = -1
so, y -2 = -1 (x-1)
y= -x+ 3
Here the x intercept is (3, 0) and y intercept is (0, 3).
so, Area of Triangle is
= 1/2 x 3 x 3
= 9/2
= 4.5 square unit
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