a) the tangent plane at (1,4,ln5) is z =?
b) the tangent plane at (-1,-4,ln5) is z =?
Find an equation of the plane tangent to the following surface at the given points. z = In (1 + xy); (1,4, In 5) and (-1,-4, In 5)
Answers
To find the equation of the tangent plane to the surface z = ln(1 + xy) at the given points (1, 4, ln(5)) and (-1, -4, ln(5)) and therefore solutions are a) 4x + y + 5z = 5ln(5) + 4, b) -4x - y + 3z = 3ln(5) - 8/3
We need to find the partial derivatives of z with respect to x and y and use them to form the equation of the tangent plane.
First, let's find the partial derivative of z with respect to x, denoted as ∂z/∂x:
∂z/∂x = ∂/∂x[ln(1 + xy)]
To find this derivative, we can use the chain rule:
∂/∂x[ln(1 + xy)] = 1 / (1 + xy) * ∂/∂x[1 + xy]
Differentiating 1 + xy with respect to x gives us y:
∂/∂x[ln(1 + xy)] = 1 / (1 + xy) * y = y / (1 + xy)
Similarly, let's find the partial derivative of z with respect to y, denoted as ∂z/∂y:
∂z/∂y = ∂/∂y[ln(1 + xy)]
Using the chain rule again:
∂/∂y[ln(1 + xy)] = 1 / (1 + xy) * ∂/∂y[1 + xy]
Differentiating 1 + xy with respect to y gives us x:
∂/∂y[ln(1 + xy)] = 1 / (1 + xy) * x = x / (1 + xy)
Now, we can find the equation of the tangent plane at the point (1, 4, ln(5)) and (-1, -4, ln(5)) using the point-normal form of the equation of a plane.
For the point (1, 4, ln(5)):
The normal vector of the tangent plane is (∂z/∂x, ∂z/∂y) evaluated at (1, 4):
(∂z/∂x, ∂z/∂y) = (4 / (1 + 1*4), 1 / (1 + 1*4)) = (4/5, 1/5)
The equation of the tangent plane at (1, 4, ln(5)) is:
4/5 * (x - 1) + 1/5 * (y - 4) + (z - ln(5)) = 0
Simplifying, we have:
4x/5 + y/5 + (z - ln(5)) - 4/5 = 0
4x + y + 5z - 5ln(5) - 4 = 0
4x + y + 5z = 5ln(5) + 4
For the point (-1, -4, ln(5)):
The normal vector of the tangent plane is (∂z/∂x, ∂z/∂y) evaluated at (-1, -4):
(∂z/∂x, ∂z/∂y) = (-4 / (1 - 1*4), -1 / (1 - 1*4)) = (-4/3, -1/3)
The equation of the tangent plane at (-1, -4, ln(5)) is:
-4/3 * (x + 1) - 1/3 * (y + 4) + (z - ln(5)) = 0
Simplifying
, we have:
-4x/3 - y/3 + (z - ln(5)) + 4/3 + 4/3 = 0
-4x - y + 3z - 3ln(5) + 8/3 = 0
-4x - y + 3z = 3ln(5) - 8/3
Therefore, the equation of the tangent plane at the points (1, 4, ln(5)) and (-1, -4, ln(5)) on the surface z = ln(1 + xy) are:
a) 4x + y + 5z = 5ln(5) + 4
b) -4x - y + 3z = 3ln(5) - 8/3
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Related Questions
How do you graph linear inequalities 2x 3y 12?
Answers
Given linear inequalities is solved using graph paper line will pass through (6,0) and (-0,4) Area where required linear inequalities is satisfied is towards origin.
let's first try to understand what is linear inequalities?
A linear inequality in mathematics is an inequality involving a linear function. One of the symbols for inequality is found in a linear inequality. It displays non-equal data in graph style.
the linear inequality's graph Since the inequality is severe and the shaded region points in the direction of the origin, 2 x-3 y < 12 is a straight line passing through the points (6, 0) and (0, -4), with the line being dot-dotted.
x - coordinate of the given line 2x - 3y =12
y =0 2x = 12 x = 6 (6,0)
y - coordinate of the given line -3y = 12 y = -4 (0,-4)
line passes through (6,0) and (0,-4).
Given Question is incomplete complete Question here:
How do you graph linear inequalities 2x - 3y< 12?
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sorry for the bad picture but help needed asap! points!!!
Answers
Please answer I need help no rush.
Answers
Answer:
12 divided by -6
Step-by-step explanation:
12÷(-6) (3) + (-2)
PEMDAS
P There are no operations inside the parentheses
E There are no exponents
MD Multiply and divide from left to right
12 divided by -6 is the first from left to right
Pla answer asap I really need help on this
Answers
Answer:
measure of 1 = 117 degrees
measure of 2 = 63 degrees
*x = 39
Step-by-step explanation:
m1 = 3 x 39 = 117
m2 = 39 + 24 = 63
117 + 63 = 180 degrees
m∠1 = 3x and m∠2 = x + 24
now,
m∠1 + m∠2 = 180° (angle made in straight line)
3x + x + 24 = 180°
4x = 180-24
4x = 156
x = 156/4
x = 39°
also, 3x = 3×39 = 117
x + 24 = 39 + 24 = 63
Review this code snippet: var time = 15; var greeting; if ( time < 12 ) { greeting = “good morning”; } else if ( time < 18 ) { greeting = “good afternoon”; } else { greeting = “good evening”; } console.log(greeting); What is the message that gets printed to the console?
Answers
Explanation:
We're given that time = 15
From this, we see that time < 12 evaluates to false, because 15 is not smaller than 12. Put another way, 15 < 12 is false.
But time < 18 is true since 15 < 18 is true. So we execute the second block of code and have the greeting variable be set to the string "good afternoon". This is what's displayed to the console without any quotes of course.
You online store only sells one item, in either regular or deluxe version.
Because of high demand and restricted supply, you restrict each customer to buying 1 item - either buying the regular version of that item, or the deluxe version of that item, but not both.
On a typical day, you have 177 customers visit your online store. Each customer has a 0.29 chance of purchasing an item. If a customer purchases an item, there is a 9% chance they buy the regular item for $5.08 and if they do not buy the regular item, then they buy the deluxe item for $23.34.
Assume each customer makes their purchase decision independently of all other customers, and each customer has the same chance of purchasing the item.
What is your expected daily sales?
Answers
The expected daily sales for your online store are approximately $1196.28.
To calculate the expected daily sales, we need to multiply the number of customers by the probability of each customer purchasing an item and then sum up the expected sales for each type of item.
Given:
- Number of customers: 177
- Probability of a customer purchasing an item: 0.29
- Probability of buying the regular item: 0.09
- Probability of buying the deluxe item: 1 - 0.09 = 0.91
- Price of the regular item: $5.08
- Price of the deluxe item: $23.34
Let's calculate the expected daily sales:
Expected sales of regular items = Number of customers * Probability of purchasing * Probability of buying the regular item * Price of the regular item
Expected sales of deluxe items = Number of customers * Probability of purchasing * Probability of buying the deluxe item * Price of the deluxe item
Expected daily sales = Expected sales of regular items + Expected sales of deluxe items
Expected sales of regular items = 177 * 0.29 * 0.09 * $5.08 ≈ $85.74
Expected sales of deluxe items = 177 * 0.29 * 0.91 * $23.34 ≈ $1110.54
Expected daily sales = $85.74 + $1110.54 ≈ $1196.28
Therefore, the expected daily sales for your online store are approximately $1196.28.
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Find the surface area of the prism.
Answers
Answer: 26
Step-by-step explanation:
I would say 26 because you multiplying 3 and 4 and then add whatever number you get for 8 and 5.
write an equation of a line passing through the point (-6,-3) and perpendicular to jk with j-2.-7) and k(6, 5). a) y=-2/3x -- 4 b) y = -2/3x- 7 c) y = 2/3x + 1 d) y = 2/3x + 9 e) y = -3/2x - 4
Answers
The equation of a line passing through the point (-6,-3) is y=2/3x+9. The general equation of a straight line is y = mx + c, where m is the gradient, and y = c is the value where the line cuts the y-axis.
The equation of line is an algebraic representation of a set of points in a coordinate system that form a line. The numerous points in the coordinate axis that form a line are represented as a set of variables x, y to form an algebraic equation known as an equation of a line.
The equation of line is a one-degree linear equation. Let us learn more about the different types of line equations and how to find line equations.
A line's equation can be formed using the slope of the line and a point on the line. To better understand the formation of a line equation, let us learn more about the slope of the line and the required point on the line.
The slope of a line is its inclination with respect to the positive x-axis, and it is expressed as a numeric integer, fraction, or the tangent of the angle it makes with respect to the positive x-axis. The term "point" refers to a coordinate system point with the x and y coordinates.
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A submarine is 42 feet below the surface of the water. A shark directly above the submarine is 19 feet below the surface of the water. How many feet above the submarine is the shark?
Ava’s credit card balance is $64. If she makes a $25 payment, then charges $79, find the balance on the card.
HURRY UP IN A TEST PLS HELP
Answers
Answer:
Step-by-step explanation:
3 feet above the shark
Five years ago, someone used her $40,000 saving to make a down payment for a townhouse in RTP. The house is a three-bedroom townhouse and sold for $200,000 when she bought it. After paying down payment, she financed the house by borrowing a 30-year mortgage. Mortgage interest rate is 4.25%. Right after closing, she rent out the house for $1,800 per month. In addition to mortgage payment and rent revenue, she listed the following information so as to figure out investment return: 1. HOA fee is $75 per month and due at end of each year 2. Property tax and insurance together are 3% of house value 3. She has to pay 10% of rent revenue for an agent who manages her renting regularly 4. Her personal income tax rate is 20%. While rent revenue is taxable, the mortgage interest is tax deductible. She has to make the mortgage amortization table to figure out how much interest she paid each year 5. In last five years, the market value of the house has increased by 4.8% per year 6. If she wants to sell the house today, the total transaction cost will be 5% of selling price Given the above information, please calculate the internal rate of return (IRR) of this investment in house
Can you show the math as far as formulas go?
Answers
Given the following information: Five years ago, someone used her $40,000 saving to make a down payment for a townhouse in RTP. The house is a three-bedroom townhouse and sold for $200,000 when she bought it. After paying down payment, she financed the house by borrowing a 30-year mortgage.
Mortgage interest rate is 4.25%. Right after closing, she rent out the house for $1,800 per month. In addition to mortgage payment and rent revenue, she listed the following information so as to figure out investment return: 1. HOA fee is $75 per month and due at end of each year 2. Property tax and insurance together are 3% of house value 3. She has to pay 10% of rent revenue for an agent who manages her renting regularly 4. Her personal income tax rate is 20%. While rent revenue is taxable, the mortgage interest is tax deductible. She has to make the mortgage amortization table to figure out how much interest she paid each year 5. In the last five years, the market value of the house has increased by 4.8% per year 6.
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Water Glasses on a shelf are broken and must be replaced.
The replacement cost can be cut in half if you can figure out how many glasses were broken.
Here are your clues:
There were more than 24 glasses, but less than 100 glasses.
If the glasses were in rows of 6, there would be 3 left over.
If the glasses were in rows of 8, there would be 7 left over.
Answers
The total number of water glasses on the shelf may be 39, 63 or 87.
Given, that there were more than 24 glasses, but less than 100 glasses.
If the glasses were in rows of 6, there would be 3 left over.
If the glasses were in rows of 8, there would be 7 left over.
Let the number of glasses be x,
So, x = 6k1 + 3
=> (x - 3) is a multiple of 6
x = 8k2 + 7
=> (x - 7) is a multiple of 8
Now, the numbers that can satisfy the given conditions are,
39 , 63 & 87.
So, the total number of glasses may be 39, 63 or 87.
Hence, the total number of water glasses on the shelf may be 39, 63 or 87.
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Caleb was building a birdhouse. He needed 2 boards that were each 6 inches long and one board that was 18 inches long. He was then able to cut the boards into pieces to use.
Answers
Answer: 30 inches
Step-by-step explanation:
Here is the complete question:
Caleb was building a birdhouse. He needed 2 boards that were each 6 inches long and one board that was 18 inches long. He was then able to cut the boards into pieces to use. What was the total length of the boards that he needed?
From the question, we are informed that Caleb needed 2 boards that were each 6 inches long and one board that was 18 inches long.
The total length of the boards that he needed goes thus:
For the first part, we are told that Caleb needed 2 boards that were each 6 inches long. This means that he needs a total of (2 × 6 inches) = 12 inches.
We are also told that he needed one board that was 18 inches long. This mean the total length of the birds needed will be the addition of the length of all the three boards. This will be:
= 12 inches + 18 inches
= 30 inches
Given that m-tan 30° and n= tan 45° simply without using a calculator m-n\mn leaving the answer in the form p+√q
Answers
The value of [ m - n ] / mn in the form of p+√q is 1 + ( - √3) when m = tan 30° and n = tan 45°.
The given values of m and n are:
m = tan 30° and n = tan 45°
Now,
[ m - n ] / mn = [ tan 30° - tan 45° ] / (tan 30°)(tan 45°)
Now, we know :
tan 30° = 1/√3 and tan 45° = 1
Therefore,
[ m - n ] / mn = [ 1/√3 - 1 ] / (1/√3)(1)
Taking LCM of √3 and 1 is √3.
[ m - n ] / mn = [ (1 - √3 ) /√3 ] / (1/√3)(1)
[ m - n ] / mn = [ (1 - √3 ) /√3 ] × √3
[ m - n ] / mn = 1 - √3
[ m - n ] / mn = 1 + ( - √3)
Now, the value of [ m - n ] / mn in the form of p+√q is 1 + ( - √3) where p = 1 and √q = - √3.
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The ratio of C:D is 5:3, the ratio of F:D is 6:1.
Find the ratio of C:D:F.
Answers
The ratio of C:D:F is 5:3:18.
What is ratio?The ratio is defined as the comparison of two quantities of the same units that indicates how much of one quantity is present in the other quantity.
here, we have,
given that,
The ratio of C:D is 5:3,
the ratio of F:D is 6:1.
i.e. F:D= 18:3
now,
C:D:F= 5:3:18.
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need help asap!!!!!! Marcel is performing the first test on his company’s new electric car. During the test, the electric car reaches a maximum speed of 81 mph.
The performance test results of the electric car can be modeled by the following table, where x represents time, in seconds at the start of the test, and y represents the speed, in miles per hour.
Answers
For this case we have the following variables:
x: represents time, in seconds at the start of the test.
y: represents the speed, in miles per hour.
We have then that:
x = 0 ---> y = 0
x = 12 ---> y = 0
Answer:
the electric car is not moving at 0 seconds and 12 seconds
I hope this helps!
the electric car is not moving at 0 seconds and 12 seconds
I hope this helps!
y is inversely proportional to the square of x find an equation for y in terms of x
Answers
hmmm from the table, let's just pick one point since we know "y" is inversely proportional, so hmmm let's say hmm the point when x = 4 and y = 9/16
a)
\(\qquad \qquad \textit{inverse proportional variation} \\\\ \textit{\underline{y} varies inversely with \underline{x}} ~\hspace{6em} \stackrel{\textit{constant of variation}}{y=\cfrac{\stackrel{\downarrow }{k}}{x}~\hfill } \\\\ \textit{\underline{x} varies inversely with }\underline{z^5} ~\hspace{5.5em} \stackrel{\textit{constant of variation}}{x=\cfrac{\stackrel{\downarrow }{k}}{z^5}~\hfill } \\\\[-0.35em] ~\dotfill\)
\(\stackrel{\textit{"y" inversely proportional to }x^2}{ {\LARGE \begin{array}{llll} y = \cfrac{k}{x^2} \end{array}}}\qquad \textit{we also know that} \begin{cases} x=4\\ y=\frac{9}{16} \end{cases} \\\\\\ \cfrac{9}{16}=\cfrac{k}{(4)^2}\implies \cfrac{9}{16}=\cfrac{k}{(16)}\implies \cfrac{9(16)}{16}=k\implies 9=k~\hfill \boxed{y=\cfrac{9}{x^2}}\)
b)
when y = 16, what's "x"?
\(16=\cfrac{9}{x^2}\implies x^2=\cfrac{9}{16}\implies x=\pm\sqrt{\cfrac{9}{16}}\implies x=\pm \cfrac{\sqrt{9}}{\sqrt{16}}\implies \stackrel{positive~value}{x=+\cfrac{3}{4}}\)
Given f of x is equal to the quantity 8x plus 1 end quantity divided by the quantity 2x minus 9 end quantity, what is the end behavior of the function? As x → -∞, f(x) → 9 ; as x → ∞, f(x) → 9. As x → -∞, f(x) → -9; as x → ∞, f(x) → -9. As x → -∞, f(x) → -4; as x → ∞, f(x) → -4. As x → -∞, f(x) → 4; as x → ∞, f(x) → 4.
Answers
Using limits, it is found that the end behavior of the function is given as follows:
As x → -∞, f(x) → 4; as x → ∞, f(x) → 4.
How to find the end behavior of a function f(x)?The end behavior of a function f(x) is given by the limit of f(x) as x goes to infinity.
In this problem, the function is:
\(f(x) = \frac{8x - 1}{2x - 9}\)
Considering that x goes to infinity, for the limits, we consider only the terms with the highest exponents in the numerator and denominator, hence:
\(\lim_{x \rightarrow -\infty} f(x) = \lim_{x \rightarrow -\infty} \frac{8x}{2x} = \lim_{x \rightarrow -\infty} 4 = 4\).\(\lim_{x \rightarrow \infty} f(x) = \lim_{x \rightarrow \infty} \frac{8x}{2x} = \lim_{x \rightarrow \infty} 4 = 4\).Hence the correct statement is:
As x → -∞, f(x) → 4; as x → ∞, f(x) → 4.
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Answer:
D
Step-by-step explanation:
What is the slope in the equation y = 2/5x - 6?
Answers
Answer:
2/5
Step-by-step explanation:
y=2/5x-6
m=2/5
y=mx+b
Slope: 2/5
y-intercept: 6
Step-by-step explanation:
Just Did Now, Am not Really good at asking questions
What is the kinetic energy of a 500kg elevator that is moving at 16 m/s
Answers
Answer:
KE=4000J
Step-by-step explanation:
KE=1/2*mv²
KE=1/2×500×16²
KE=250×16²
KE=4000J
PLZ HELP MEEEE!!!!!! IN TEST .....Use slope-intercept form to write the equation of a line that has a slope of −2
and passes through the point (-4, 1)
Answers
Answer:
you would end up at (-4,-1)
Step-by-step explanation:
75/100 reduced by 10
Answers
Answer: 3/4. fraction to decimal calculator to find what's an equivalent decimal for the fractional number 3/4.
0.75 is a decimal and 75/100 or 75% is the percentage for 3/4.
Step-by-step explanation:fraction simplification calculator to find what's a reduced or simplest form for 75/100 at its lowest terms. 3/4 is a simplified fraction for 75/100
Describe fully the single
transformation which maps
triangle T to triangle U.
-2-
-1
U
-5
-4
-3
-2
-1
0
1
2
3
4
-1
Answers
Answer:
Rotation 90⁰ clockwise about point (-1,-1)
Help look at the photo
Will mark the brainlest
Answers
Answer:
1. 6
2. 8
3. 10
4. 12
5. 14
Step-by-step explanation:
just solve
consider the functions f(x) = and g(x) = 6. what are the ranges of the two functions? f(x): {y| y > } g(x): {y| y > }
Answers
The ranges of the two functions is
f(x): {y| y > 0 }
g(x): {y| y > 6}
we have that
f(x) = (4/5)^x
g(x) = (4/5)^x + 6
using a graph tool
see the attached figure
we know that
f(x) has the horizontal asymptote y = 0
g(x) has the horizontal asymptote y = 6
therefore
the range of f(x) is the interval (0,∞)
the range of g(x) is the interval (6,∞)
the answer is
the range of f(x) is the interval (0,∞)
the range of g(x) is the interval (6,∞)
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The correct question is the attached image
3. Tom, Sam and Matt are counting drum beats.
Tom hits a snare drum every 4 beats.
Sam hits a kettle drum every 10 beats.
Matt hits a bass drum every 12 beats.
Tom, Sam and Matt start by hitting their drums at the same time.
How many times are each of their beats heard before Tom, Sam and Matt next hit
their drums at the same time?
Answers
Answer:
When 60 beats are heard, Tom hits 15 snare drums, Sam hits 6 kettle drums, and Matt hits 5 bass drums.
Step-by-step explanation:
The Least Common Multiple ( LCM )
The LCM of two integers a,b is the smallest positive integer that is evenly divisible by both a and b.
For example:
LCM(20,8)=40
LCM(35,18)=630
Since Tom, Sam, and Matt are counting drum beats at their own frequency, we must find the least common multiple of all their beats frequency.
Find the LCM of 4,10,12. Follow this procedure:
List prime factorization of all the numbers:
4 = 2*2
10 = 2*5
12 = 2*2*3
Multiply all the factors the greatest times they occur:
LCM=2*2*3*5=60
Thus, when 60 beats are heard, Tom hits 15 snare drums, Sam hits 6 kettle drums, and Matt hits 5 bass drums.
a grocery store has an average sales of $8000 per day. the store introduced several advertising campaigns in order to increase sales. to determine whether or not the advertising campaigns have been effective in increasing sales, a sample of 100 days of sales was selected. it was found that the average was $8200 per day. from past information, it is known that the standard deviation of the population is $1500. the value of the test statistic is\
Answers
The value of test statistics as calculated from the given data is 0.092.
p = 1 - P(Z < Z')
Z' = (8200-8000)/ (1500/√100)
Z'= 1.3
p = 1 - P(Z < Z')
= 1 - P(Z < 1.3)
= 1 - 0.908
= 0.092
The Z-score, also known as the standard score, indicates how far a data point deviates from the mean. It represents the number of standard deviations an element has from the mean. As a result, the Z-Score is expressed in terms of standard deviation from the mean.
A z score is a statistical measurement that indicates how far a raw score deviates from the mean of a distribution. A z score is used in a z test to test hypotheses. It is also used in prediction intervals to calculate the likelihood of a random variable falling between two values.
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Line $m$ is parallel to line $n$ and the measure of $\angle 1$ is $\frac 18$ the measure of $\angle 2$. What is the degree measure of $\angle 5$?
Answers
The angle of m∠5 is 116 degrees.
How to find angles when parallel lines are cut by a transversal?When parallel lines are cut by a transversal, angle relationships are formed. This include corresponding angles, alternate angles , vertical angles etc.
Therefore, line m and n are parallel lines cut by the a transversal.
Hence,
m∠2 = 64 degrees
Therefore,
m∠5 = m∠4 (alternate angles)
Therefore,
m∠5 + m∠2 = 180
m∠5 = 180 - 64
m∠5 = 116 degrees.
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The degree measure of the angle labelled 5; m<5 = 116°.
What is the measure of the angle labelled 5 in the task content?The angle measure of the angle labelled 5 as in the complete task content in the attached image can be determined as follows;
It follows from the complete task content that; that the measure of angle 2 is; 64°.
On this note, it follows from the sum of angle measures on a straight line theorem that; m<4 = 180° - 64° = 116°.
Additionally, it follows from the congruence of alternate angles theorem that <4 and <5 are congruent and hence, their measures are equal.
Therefore, m<5 = 116°.
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A manufacturer claims that its televisions have an average lifetimeof at least five years (60 months) with a population standarddeviation of seven months. Eighty-one televisions wereselected at random, and the average lifetime was found to be 59months.
a. Should z test or t test be used?
b. With α = 0.025, isthe manufacturer's claim supported?
Answers
a. In this scenario, a t-test should be used as it t is appropriate when the population standard deviation is unknown and needs to be estimated from the sample data.
But, since the population standard deviation is known, we can use the z-test.
However, it is generally more conservative to use the t-test when the sample size is small, as it provides more accurate results.
b. To determine whether the manufacturer's claim is supported, we need to perform a hypothesis test.
The null hypothesis (H0) would state that the average lifetime of the televisions is equal to or greater than 5 years. The alternative hypothesis (H1) would state that the average lifetime is less than 5 years.
By conducting the t-test, we can calculate the test statistic and compare it to the critical value. If the test statistic falls within the rejection region, we can reject the null hypothesis and conclude that the manufacturer's claim is not supported.
If the test statistic falls outside the rejection region, we fail to reject the null hypothesis, indicating that the claim is supported.
Using the given sample data and assuming a significance level (α) of 0.025, we calculate the t-test statistic based on the sample mean, sample size, and sample standard deviation.
We then compare it to the critical value from the t-distribution table. If the t-test statistic is greater than the critical value, we reject the null hypothesis and conclude that the claim is not supported.
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what the distance between (-10, -5) and (-2, 10) on a coordinate plane
Answers
Answer:
23 units
hope this helps
The shutter speed setting on a camera controls the length of time the shutter is open when taking a picture. Sidney set the shutter speed on his camera to open the shutter for 8 x 10-4 second to take a picture of a bee and for 2 x 10-2 second to take a picture of the sky. Was the shutter open for a longer amount of time for the picture of the bee or the sky, and how many times more seconds was it open?
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Therefore, the shutter was open 25 times longer for the picture of the sky than for the picture of the bee.
What is time?Time is a concept that humans use to measure and describe the sequence and duration of events and experiences. It is a fundamental aspect of the way we perceive and understand the world around us.
From a scientific perspective, time is often defined as a dimension in which events occur and can be ordered from the past through the present to the future. It is often measured in units such as seconds, minutes, hours, and years, and is usually represented on a timeline or clock.
by the question.
The shutter was open for a longer amount of time when Sidney took the picture of the sky. The difference between the two shutter speeds is:
2 x 10-2 seconds - 8 x 10-4 seconds = 1.92 x 10-2 seconds
So, the shutter was open 1.92 x 10-2 seconds longer for the picture of the sky than for the picture of the bee. To determine how many times longer the shutter was open for the picture of the sky, we can divide the longer time by the shorter time:
(2 x 10-2 seconds) / (8 x 10-4 seconds) = 25
To learn more about divide:
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