a) Heating cost for a month with 25°F is $67.10
b) Heating cost for a month with 0°F is $98.60
c) Decrease in the monthly heating cost is $1.26
Define the term graph?The visual representation of mathematical functions or data points on a Cartesian coordinate system is an x-y axis graphic. The vertical or dependent variable is represented by the y-axis, while the horizontal or independent variable is represented by the x-axis.
(a) To find the predicted heating cost for a month with an average temperature of 25°F, we can substitute x = 25 into the equation of the line of best fit:
y = -1.26x + 98.60
y = -1.26(25) + 98.60
y = 67.10
Hence, $67.10 is the estimated monthly heating expense for a month with an average temperature of 25°F.
(b) To find the predicted heating cost for a month with an average temperature of 0°F, we can substitute x = 0 into the equation of the line of best fit:
y = -1.26x + 98.60
y = -1.26(0) + 98.60
y = 98.60
Thus, $98.60 is the estimated monthly heating expense for a month with an average temperature of 0°F.
(c) The slope of the line of best fit is -1.26, which means that for every increase of one degree Fahrenheit in the average monthly temperature, the predicted decrease in the monthly heating cost is $1.26.
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ADEF-AABC. What is the sequence of transformations that maps AABC to ADEF?
A reflection across the y-axis and a translation 4 units down
A rotation of 180* about the origin and a dilation with center (0,0) and scale factor 2
A reflection across the y-axis and a translation 2 units down.
A rotation of 90° about the origin and a translation 2 units down
The series of transformations consists of a translation down two units and a reflection across the y-axis. Thus, option C is correct.
What is transformation?The points A and C will be replaced with D and F, respectively, by a reflection across the y-axis, leaving B in the same location. As a result, the image of AABC is given, A'D'BCF.
The final image, denoted by the letters ADEF, is produced by translating all the points of the image A'D'BCF' down by two units.
ADEF and AABC are not in the same location, even if they are the same height and shape.
The first thing we notice is that ADEF and AABC are oriented the same way, so we don't need to rotate them. Instead, by utilising a reflection over the y-axis, we may swap out the places where A and B were for D and E, respectively.
A'B'C' is still not in the appropriate place even though it is 2 units to the left of ADEF. Hence, we must translate 2 units down in order to position A'B'C' where ADEF is.
Therefore, A reflection across the y-axis and a translation 2 units down.
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-4
5 positive exponent form
A negative exponent indicates that the base should be inverted or flipped, and the exponent should become positive. Therefore, -45 in positive exponent form would be: 1/ (45²1) or 1/45
What is a negative component?
A negative exponent is a mathematical notation indicating that the number or variable should be inverted or flipped, and the exponent should be made positive. In other words, a negative exponent represents the reciprocal of the number or variable raised to the corresponding positive exponent.
For example, 2²-3 is read as "2 to the power of negative 3" and represents 1/(2²3), which is equal to 1/8. Similarly, x²-2 is read as "x to the power of negative 2" and represents 1/(x²2), which is the reciprocal of x squared.
Negative exponents are used in various mathematical and scientific applications, such as in calculations involving very small or large numbers, in scientific notation, and in the rules of exponents.
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Complete question:
Write -45 in positive exponent form.
could someone help out?
Answer:
adjacent = cos(angle) x hypotenuse
If the cost of 7m is Rs. 1470, find the cost of 5m cloth
By using unitary method, we found that the cost of 5m cloth is Rs. 1050.
According to the unitary method, the cost of 1 meter of cloth is equal to the total cost of 7 meters of cloth divided by 7. That is,
Cost of 1m cloth = Total cost of 7m cloth/7
We know that the total cost of 7m cloth is Rs. 1470. Therefore,
Cost of 1m cloth = 1470/7
Cost of 1m cloth = Rs. 210
This means that the cost of 1 meter of cloth is Rs. 210. Now, we need to find the cost of 5m cloth. To do that, we can use the unitary method again.
Cost of 5m cloth = Cost of 1m cloth x 5
Cost of 5m cloth = Rs. 210 x 5
Cost of 5m cloth = Rs. 1050
Therefore, the cost of 5m cloth is Rs. 1050.
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please help with geometry
Step-by-step explanation:
Since it is equilateral the angle at the top is 60 °
for right triangles sin (angle ) = opposite leg / hypotenuse
sin (60) = sqrt 6/ x
x = sqrt 6 / sin (60) = sqrt 6 / sqrt(3)/2 =
2 sqrt 2 = 2.83
PLEASE HELP MARKING BRAINLEIST JUST ANSWER ASAP AND BE CORRECT
PLEASE HELP MARKING BRAINLEIST JUST ANSWER ASAP AND BE CORRECT
Answer:
To find the perimeter, we need to add up the lengths of all the sides. In this case, we have four sides with lengths given by the expressions 2v-5, 4v+5, 2v-5, and 8v-7.
So the perimeter P is:
P = (2v-5) + (4v+5) + (2v-5) + (8v-7)
Simplifying and combining like terms, we get:
P = 16v - 12
Therefore, the perimeter is 16v - 12.
3x+4y=34. In the equation, what is the y-value when x=10? x= 10 , y= ?
When x=10, the value of y in the equation 3x+4y=34 is y=1.
To find the value of y when x=10 in the equation 3x+4y=34, we can substitute x=10 into the equation and solve for y:
3x+4y=34
3(10) + 4y = 34
30 + 4y = 34
4y = 34 - 30
4y = 4
y = 1
An equation is a mathematical statement that shows the relationship between two or more variables using symbols and numbers. It is a statement that asserts the equality of two expressions. An equation typically consists of two sides, separated by an equals sign (=). Each side of the equation may contain variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division.
Solving an equation involves manipulating the expressions on both sides of the equation to isolate the variable and find its value. Equations are used in various branches of mathematics, physics, engineering, economics, and other sciences to model and solve problems. For example, the equation "2x + 5 = 11" has two sides, left-hand side (2x + 5) and right-hand side (11), separated by an equals sign.
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Help me with this it's to hard for me
Answer:
Part B: Calculate the range and interquartile range (IQR) for each group and interpret what they tell us about the data.
For Group A:
Range = 5 - 1 = 4
Q1 = 2
Q3 = 4
IQR = Q3 - Q1 = 2
For Group B:
Range = 5 - 2 = 3
Q1 = 2
Q3 = 4
IQR = Q3 - Q1 = 2
The range for Group A is larger than the range for Group B, indicating that there is more variability in the growth of the plants in Group A. However, both groups have the same IQR, indicating that the middle 50% of the data in each group is similar. This suggests that while there may be some variability in the growth of the plants, the overall distribution of growth is similar between the two fertilizers.
PLEASE HELP ME! I NEED THE ANSWERS! ITS AN EMERGENCY
The dilated figure has the following coordinates: A' (-15, 0), B' (-5, 10), C' (10, 10), D' (15, -5), and E' (5, -10).
How do the coordinates translate?In this sense, coordinates are the points where a grid system intersects. Latitude and longitude are the traditional ways to express GPS coordinates. Degrees of separation north and south from the equator, which is 0 degrees, are measured by lines of latitude coordinates.
Just multiply the coordinates of each point by 5 to construct a figure about the origin using a scale factor of 5.
A (-3, 0)
B (-1, 2)
C (2, 2)
D (3, -1)
E (1, -2)
The coordinates of each point are multiplied by 5 to enlarge the image by a scale factor of 5:
A' = (-3 * 5, 0 * 5) = (-15, 0)
B' = (-1 * 5, 2 * 5) = (-5, 10)
C' = (2 * 5, 2 * 5) = (10, 10)
D' = (3 * 5, -1 * 5) = (15, -5)
E' = (1 * 5, -2 * 5) = (5, -10)
The coordinates of the dilated figure are:
A' (-15, 0)
B' (-5, 10)
C' (10, 10)
D' (15, -5)
E' (5, -10)
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a red cap fire hydrant provides 1700 liters per minute of water. how long (in minutes to the nearest minute) will it take to fill a water truck with a tank of the following dimensions: 68 inches diameter and 24 feet long? when the tank is full of water, how heavy will the water load be in pounds (lbm) to the nearest pound?
It will take approximately 8 minutes to fill the water truck, and the weight of the water load will be approximately 30,296 pounds.
How to find out how long it will take to fill the tank.First, we need to convert the dimensions of the tank from inches to feet:
68 inches diameter = 68/12 feet = 5.67 feet diameter
24 feet long = 24 feet long
Next, we can calculate the volume of the tank in cubic feet:
Volume = [tex]pi x (diameter/2)^2 x length[/tex]Volume = [tex]3.14 x (5.67/2)^2 x 24[/tex]Volume = [tex]485.15 cubic feet[/tex]Since 1 cubic foot of water weighs 62.4 pounds, we can calculate the weight of the water in the tank in pounds:
Weight = Volume x DensityWeight = 485.15 x 62.4Weight = 30,296.16 poundsTo find out how long it will take to fill the tank, we can use the flow rate of the fire hydrant:
Flow rate = 1700 liters per minute1 liter = 0.264172 gallonsFlow rate = 1700 x 0.264172 = 449.10 gallons per minute1 gallon = 0.133681 cubic feetFlow rate = 449.10 x 0.133681 = 60.05 cubic feet per minuteFinally, we can divide the volume of the tank by the flow rate to find out how long it will take to fill the tank:
Time = Volume / Flow rateTime = 485.15 / 60.05Time = 8.08 minutesTherefore, it will take approximately 8 minutes to fill the water truck, and the weight of the water load will be approximately 30,296 pounds.
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The bottom of a cylindrical container has an area of 10 cm2. The container is filled to a height whose mean is 4 cm, and whose standard deviation is 0.2 cm. LetVdenote the volume of fluid in the container. Find μV.
The value of μV is 40 cm³.
Given,The area of bottom of cylindrical container = 10 cm²The height of container = h = Mean height = 4 cm Standard deviation of height = σ = 0.2 cm We are supposed to find the mean volume of fluid in the container.In order to calculate the mean volume, first we need to calculate the volume of fluid in the container.Volume of a cylindrical container = πr²h Where, r is the radius of the base of the container.So, we need to calculate the value of r.The area of the bottom of the container is given as 10 cm².
We know that the area of the base of a cylinder is given as:Area of base of cylinder = πr² We are given that area of the base is 10 cm². So,10 = πr²r² = 10/πr = √(10/π) We can find the volume of fluid using the values we have.Volume of fluid = πr²h = π(√(10/π))² x 4 = 40 cm³We know that mean volume, μV is given as:μV = πr²μh So, we need to calculate the value of μh. We know that standard deviation σh is given as:σh = 0.2 cm So,μh = h = 4 cm So,μV = πr²μh = π(√(10/π))² x 4 = 40 cm³
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could someone help out?
Answer:
r ≈ 44.25 cm
Step-by-step explanation:
You want the hypotenuse of a right triangle in which the side adjacent to the angle of 57° is 24.1 cm.
CosineThe cosine relation is ...
Cos = Adjacent/Hypotenuse
cos(57°) = (24.1 cm)/r
SolutionSolving for r gives ...
r = (24.1 cm)/cos(57°) ≈ 44.25 cm
The length r is about 44.25 cm.
__
Additional comment
The calculator shown in the attachment has its angle mode set to degrees.
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hi i want help with maths and the question i need help is
there are 32 students in a class and 20 of them owns at least one pet. what if the fraction of the class own pets? give answer in simplest form.
Get back to me quickly
Answer: 3/5
hope this helped you. Please brainliest! :D
Step-by-step explanation: If I am wrong tell me :D
Solve for X. Enter the solutions from least to greatest.
x^2+3x-4=0
Lesser x=
Greater x=
TEN POINTS!!!!
The sοlutiοns in οrder frοm least tο greatest are:
Lesser x = -4
Greater x = 1
Hοw dο yοu οrder frοm least tο greatest?Ascending οrder refers tο the arrangement οf numbers in which the smallest number cοmes befοre the largest.
Tο sοlve fοr x in the equatiοn [tex]x^2 + 3x - 4 = 0[/tex], we can use the quadratic fοrmula:
[tex]x= \frac{(-b+\sqrt{b^{2} -4ac} )}{2a} \\[/tex]
where a, b, and c are the cοefficients οf the quadratic equatiοn[tex]ax^2 + bx + c = 0.[/tex]
In this case, a = 1, b = 3, and c = -4. Substituting these values intο the quadratic fοrmula, we get:
[tex]x = (-3\± \sqrt{(3^2 - 4(1)(-4)))} / 2(1)\\\\x = (-3 \± \sqrt{(25))} / 2\\\\x = (-3 \± 5) / 2[/tex]
This gives twο pοssible sοlutiοns:
x1 = (-3 - 5) / 2 = -4
x2 = (-3 + 5) / 2 = 1
Therefοre, the sοlutiοns in οrder frοm least tο greatest are:
Lesser x = -4
Greater x = 1
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every year educational services (ets) selects readers for the advanced placement exams. recently the ap* statistics exam has been graded in lincoln, nebraska. one objective of ets is to achieve equity in grading by inviting teachers to be readers from all parts of the nation. however budgets are a consideration also. the accountants at ets wonder if the flights from cities west of lincoln are the same as flight costs from cities east of lincoln. a random sample of the expense vouchers from last year was reviewed for the cost of airline tickets. costs (in dollars) are shown in the table. indicate what inference procedure you would use to see if there is a significant difference in the costs of airline flights between the west and east coasts to lincoln, nebraska, then decide if it is okay to actually perform that inference procedure. (check the appropriate assumptions and conditions and indicate whether you could or could not proceed. you do not have to do the actual test.)
To see if there is a significant difference in the costs of airline flights between the west and east coasts to Lincoln, Nebraska, one can use a two-sample t-test. It is okay to perform the inference procedure, but the following assumptions and conditions must be checked.
Assumptions: Independence: The airfares for each coast should be independent of each other. Normality: The populations of airfares for both coasts should be approximately normally distributed .Equal variances: The population variances for both coasts should be equal.
Conditions: Sample sizes: Both samples should be large enough so that the Central Limit Theorem applies. Rule of thumb for t-tests is that the sample size should be at least 30.Random sampling: Both samples should be random .To test if the conditions are met, one can create a boxplot for each coast, check the normal probability plots, perform the F-test to check for equal variances, and check the sample sizes. If the assumptions and conditions are met, a two-sample t-test can be used to determine if there is a significant difference in the costs of airline flights between the west and east coasts to Lincoln, Nebraska.
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Part A: Graph the system of equations {−2x+y=6x−y=1
Part B: Determine the solution from Part A.
Answer:
Step-by-step explanation:
An important math tool is graphing. It can be a straightforward method for introducing more general concepts like most and least, greater than, or less than. It can also be a great way to get your child interested in math and get them excited about it. Using graphs and charts, you can break down a lot of information into easy-to-understand formats that quickly and clearly convey key points.
Given equation 2x + y = 6 we can drive from this equation that at x = 0 y will be 6 and y =0 x will be 3 hence we have two points of the line (0,6) and (3,0)
From the Given equation (2) 6X + 3Y = 12 we can drive from this equation that at x = 0 y will be 4 and y =0 x will be 2 hence we have two points of the line (0,4) and (2,0).
What is the exact value of the trigonometric expression? State your answer in simplified radical form and include all work.
*Please reference included picture for problem. Thank you!
Answer:
The exact value of the given trigonometric expression is undefined.
Step-by-step explanation:
Given trigonometric expression:
[tex]\dfrac{\cos\left(\dfrac{2 \pi}{3}\right)}{\tan\left(-\dfrac{7 \pi}{4}\right)}+\csc(\pi)[/tex]
To find the exact value of the given trigonometric expression, begin by finding the exact values of each of the trigonometric functions in the expression
The exact value of cos(2π/3) is:
[tex]\implies \cos\left(\dfrac{2 \pi}{3}\right)=-\dfrac{1}{2}[/tex]
The exact value of tan(-7π/4) is:
[tex]\implies \tan\left(-\dfrac{7 \pi}{4}\right)=1[/tex]
Since the cosecant function is the reciprocal of the sine function, the exact value of csc(π) is:
[tex]\implies \csc (\pi)=\dfrac{1}{\sin(\pi)}=\dfrac{1}{0}=\textsf{unde\:\!fined}[/tex]
Therefore:
[tex]\begin{aligned}\implies \dfrac{\cos\left(\dfrac{2 \pi}{3}\right)}{\tan\left(-\dfrac{7 \pi}{4}\right)}+\csc(\pi)&=\dfrac{-\dfrac{1}{2}}{1}+\dfrac{1}{0}\\&=-\dfrac{1}{2}+\dfrac{1}{0}\\\\&=\textsf{unde\:\!fined}\end{aligned}[/tex]
A random variable is normally distributed. It has a mean of 228 and a standard deviation of 16. If you take a sample of size 12, can you say what the shape of the sampling distribution for the sample mean is? Why?
A. If the sample size is 12, then you can say the sampling distribution of the sample mean is not normally distributed since the sample size is less than 30.
B. If the sample size is 12, then you can say the sampling distribution of the sample mean is normally distributed since the variable is normally distributed.
C. If the sample size is 12, then you can't say anything about the sampling distribution of the sample mean, since the population of the random variable is not normally distributed and the sample size is less than 30.
If a random variable is normally distributed, and has a mean of 228 and
a standard deviation of 16. If a sample of size 12 is taken, then the shape
of the sampling distribution for the sample mean is normally distributed
since the variable is normally distributed. Hence, option B is correct.
A normal distribution is a type of probability distribution in which the
value of the mean, standard deviation, and random variables are well
known. Sampling distribution refers to the probability distribution of the
statistics that have been derived from a sample taken from a population.
As per the Central Limit Theorem, if the sample size is large enough,
then the sampling distribution of the sample means will be normally
distributed, no matter how the population looks. If the random variable is
normally distributed, then the sampling distribution of the sample mean
will also be normally distributed, no matter what the size of the sample is.
Hence, option B is the correct answer as the sampling distribution of the
sample mean is normally distributed since the variable is normally distributed.
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the radius of a circle is increasing at a rate of 4 cm/s. how fast is the area of the circle increasing after 10 seconds? g
Answer:
A = 1600π cm²
Step-by-step explanation:
Pre-SolvingWe are given that a circle's radius increases 4 cm every second.
We want to know how large the area of the circle is after 10 seconds.
SolvingWe first need to find how large the radius will be.
We know the proportion of the rate increase / time; for every 1 second, the rate increases by 4 cm.
We can write this as a proportion:
[tex]\frac{4 cm}{1 s} = \frac{x}{10s}[/tex]
We can cross multiply to get:
4 cm * 10 s = x * 1 s
Divide both sides by 1 s
(4 cm * 10 s) / (1 s) = 40cm = x
So, after 10 seconds, the radius will be 40cm.
We aren't done yet though, remember that the question wants us to find the area of the circle.
The area can be calculated using the equation A = πr², where r is the radius.
We can substitute 40 as r in the equation to get:
A = πr² = π * (40)² = 1600π cm²
In a large population of adults, the mean IQ is 112 with a standard deviation of 20. Suppose 200 adults are randomly selected for a market research campaign. What is the sampling distribution of their sample mean IQ? Must show work (explain) to justify choice.
- exactly normal, mean 112, standard deviation 20
- approximately normal, mean 112, standard deviation 0.1
- approximately normal, mean 112, standard deviation 1.414
- approximately normal, mean 112, standard deviation 20
The sampling distribution is approximately normal.
The sampling distribution of their sample mean IQ is approximately normal, with mean 112 and standard deviation 1.414.What is the sampling distribution of their sample mean IQ?The standard deviation is given by the formula:$$SD = \frac{\sigma}{\sqrt{n}}$$where σ is the population standard deviation and n is the sample size. So, we have:$${SD} = \frac{20}{\sqrt{200}} = \sqrt{\frac{20^2}{200}} = \sqrt{2} = 1.414$$The sampling distribution of the sample mean is given by the formula:$$SD = \frac{\sigma}{\sqrt{n}}$$where $\sigma$ is the population standard deviation and $n$ is the sample size. Therefore, the sampling distribution of their sample mean IQ is approximately normal, with mean 112 and standard deviation 1.414. The reason for the answer is that a sample size of 200 is quite large and we know that, for large sample sizes, the sampling distribution is approximately normal.
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What is the solution to the trigonometric inequality sin(x) > cos(x) over the interval 0 ≤ x ≤ 2pi radians?
From the given information provided, the solution to the given trigonometric inequality is (π/4, 5π/4).
To solve the inequality sin(x) > cos(x) over the interval 0 ≤ x ≤ 2π radians, we can use the following steps:
Rewrite the inequality in terms of tangent:
Divide both sides by cos(x) to get:
tan(x) > 1
Find the solutions of the equation tan(x) = 1:
tan(x) = 1 when x = π/4 or x = 5π/4.
Check the sign of tangent in the intervals between the solutions:
We need to check the sign of tan(x) for x values in the following intervals:
(0, π/4), (π/4, 5π/4), and (5π/4, 2π).
In the interval (0, π/4), tan(x) is positive and less than 1.
In the interval (π/4, 5π/4), tan(x) is positive and greater than 1.
In the interval (5π/4, 2π), tan(x) is negative and less than -1.
Determine the solution set:
Since we are looking for x values that satisfy tan(x) > 1, the only interval that contains such values is (π/4, 5π/4). Therefore, the solution to the inequality sin(x) > cos(x) over the interval 0 ≤ x ≤ 2π radians is:
π/4 < x < 5π/4
In interval notation, we can write:
(π/4, 5π/4)
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5x - 16xy +16y to the power of 2* +7x + 17y to the power of 2*
(16y and 17y are both to the power of 2)
The value of variable x for the given equation, 5x - 16xy +16y² +7x + 17y² is −33 y²/ 4(3 − 4y).
Give a brief account on algebraic expression.An algebraic expression is the idea of using letters or alphabets to represent numbers without specifying the actual values. Algebra Basics taught us how to use letters like x, y, and z to represent unknown values. These characters are called variables here. An algebraic expression said to be a combination of variables and constants. Any multiplied value that is prefixed to a variable is a factor. An algebraic expression in mathematics is an expression that consists of variables and constants and algebraic operations (addition, subtraction, etc.).
5x - 16xy +16y² +7x + 17y²
= 12x - 16xy + 33y²
Using the Quadratic Formula, we have:
x = −33 y²/ 4(3 − 4y)
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Sally did a survey amongst her friends to
see how many hours homework they
each did per month.
Tim
Mary
Keith
Sidra
KEY:
Equals 4 hours
00
a) How many hours homework
does Sidra do?
b) How many hours, in total, do
Sally's friends spend on
homework per month?
1. The number of hours which Sidra did on homework is 12 hours
2. The total number of hours which Sally's friends spend on homework per month is 64 hours.
How many hours homework does Sidra do?Sidra does 3 keys worth of homework, and since a key equals 4 hours, she does:
= 3 keys x 4 hours/key
= 12 hours of homework.
How many hours, in total, do Sally's friends spend on homework per month?To find the total number of hours that Sally's friends spend on homework per month, we need to add up the hours of homework done by each of her friends:
Tim: 5 keys x 4 hours/key = 20 hours
Mary: 2 1/2 keys x 4 hours/key = 10 hours
Keith: 5 1/2 keys x 4 hours/key = 22 hours
Sidra: 3 keys x 4 hours/key = 12 hours
Total hours of homework per month:
= 20 + 10 + 22 + 12
= 64 hours.
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make a simple linear regression model using education level as independent variable. if the education level is 14 years, the estimated annual income is
The estimated annual income can be calculated using the equation above. If the data point is used to calculate the slope and y-intercept of the regression line, then the annual income can be estimated using the equation y = m(14) + b.
If the education level is 14 years,
To create a simple linear regression model using education level as the independent variable, you will need to input data for education level and annual income.
This data can be used to estimate the annual income for any given education level. The equation for this linear regression model is y = mx + b, where y represents the annual income, m is the slope of the line, x is the education level, and b is the y-intercept.
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An article reports that in a sample of 123 hip surgeries of a certain type, the average surgery time was 136.9 minutes with a standard deviation of 24.1 minutes.
find
A. The 95% confidence interval is (,)
B.The 99.5% confidence interval is(,)
C. A surgeon claims that the mean surgery time is between 133.71 and 140.09 minutes. With what level of confidence can this statement be made? Express the answer as a percent and round to two decimal places.
D. Approximately how many surgeries must be sampled so that a 95% confidence interval will specify the mean to within ±3 minutes? Round up the answer to the nearest integer.
F.Approximately how many surgeries must be sampled so that a 99% confidence interval will specify the mean to within ±3 minutes? Round up the answer to the nearest integer.
The minimum sample size required to get a 99% confidence interval that will specify the mean to within ±3 minutes is 597 (Rounded up to the nearest integer).
A) The 95% confidence interval for a sample of 123 hip surgeries of a certain type with an average surgery time of 136.9 minutes and a standard deviation of 24.1 minutes is (130.82, 142.98).Explanation:Given,Sample size, n = 123Average surgery time, μ = 136.9 minutesStandard deviation, σ = 24.1 minutesWe know that for a sample of size n, the 95% confidence interval is given by, (Formula1)Where, z is the z-score, α/2 = 0.05/2 = 0.025 is the level of significance and n - 1 = 122 degrees of freedom.Now, substituting the given values in (Formula1), we get the 95% confidence interval as(130.82, 142.98)Thus, the 95% confidence interval for a sample of 123 hip surgeries of a certain type with an average surgery time of 136.9 minutes and a standard deviation of 24.1 minutes is (130.82, 142.98).B) The 99.5% confidence interval for a sample of 123 hip surgeries of a certain type with an average surgery time of 136.9 minutes and a standard deviation of 24.1 minutes is (127.93, 145.87).Explanation:We know that for a sample of size n, the 99.5% confidence interval is given by, (Formula2)Where, z is the z-score, α/2 = 0.005/2 = 0.0025 is the level of significance and n - 1 = 122 degrees of freedom.Now, substituting the given values in (Formula2), we get the 99.5% confidence interval as (127.93, 145.87).Thus, the 99.5% confidence interval for a sample of 123 hip surgeries of a certain type with an average surgery time of 136.9 minutes and a standard deviation of 24.1 minutes is (127.93, 145.87).C) The surgeon's claim that the mean surgery time is between 133.71 and 140.09 minutes is equivalent to the confidence interval (133.71, 140.09). The surgeon's claim falls inside the 95% confidence interval, (130.82, 142.98), therefore we can say that the surgeon's claim can be made with 95% confidence.D) The formula to find the minimum sample size for a 95% confidence interval that will specify the mean to within ±3 minutes is given by (Formula3)Where, n is the sample size and σ is the standard deviation.Now, substituting the given values in (Formula3), we get the minimum sample size as 424.15.The minimum sample size required to get a 95% confidence interval that will specify the mean to within ±3 minutes is 425 (Rounded up to the nearest integer).F) The formula to find the minimum sample size for a 99% confidence interval that will specify the mean to within ±3 minutes is given by (Formula4)Where, n is the sample size and σ is the standard deviation.Now, substituting the given values in (Formula4), we get the minimum sample size as 596.73.The minimum sample size required to get a 99% confidence interval that will specify the mean to within ±3 minutes is 597 (Rounded up to the nearest integer).
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an arm wrestler is the champion for a period of 75 hours. (here, by an hour, we mean a period starting from an ex- act hour, such as 1 p. m ., until the next hour.) the arm wrestler had at least one match an hour, but no more than 125 total matches. show that there is a period of consec- utive hours during which the arm wrestler had exactly 24 matches.
In the following question, among the conditions given, There must have been at least one 24-hour period in the 75-hour period in which the arm wrestler had exactly 24 matches.
The arm wrestler had at least 75 matches and no more than 125 total matches. This means that the arm wrestler had a maximum of 50 matches in any consecutive period of 75 hours. Therefore, there must be a period of consecutive hours during which the arm wrestler had exactly 24 matches.
To show this, let us consider the following: in the 75-hour period, there must have been at least 3 periods of consecutive 24-hour periods (24 matches per period). If we subtract 3 x 24 matches from the total of 75 matches, we are left with 3 matches. Therefore, there must have been at least one 24-hour period in the 75-hour period in which the arm wrestler had exactly 24 matches.
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Need help to solve this please!!
Answer:
0.999
Step-by-step explanation:
If the driver wore a seat belt, that is the only column we have to look at.
The chance the driver survived is number survived / number total.
Plugging in, we get 412,042/412,493, or about 0.999.
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Using the other endpoint of the diameter, and the center of the circle write an equation of the circle
Answer:
Step-by-step explanation:
C(1,2), radius=6
Equation using [tex](x-h)^2+(y-k)^2=r^2[/tex]:
[tex](x-1)^2+(y-2)^2=36[/tex]
2 Rema has two jobs. In one year, she worked 276 hours at her first job. In the same year, she worked 3 times the number of hours at her second job. How many hours did Rema work that year at her second job?
Answer:
Step-by-step explanation:
Kind of like rema from the song calm down calm down!!
you an find it on youtub
A triangle is shown on the coordinate plane below.
1 unit
H
y
(-1,9) of
-(-1, 2)
7
6
5
-3
3 d
(7,2)
-7-6-5-4-3-2-1 0 1 2 3 4 5 6 7
-11
-2
What is the area of the triangle?
Il unit
X
You answer would be mate it would be x=66