Answers
According to the figure of the right triangle
a = b = 10How to find angle a and b in the right triangleWhen a right triangle has one of the angles as 45 degrees the angle must be 45 degrees two. Also, the sides are equal, hence we have that
a = b
Using trigonometry we solve for b as follows
cos 45 = b / 10√2
multiplying both sides by 10√2
10√2 * cos 45 = 10√2 * b / 10√2
10√2 * cos 45 = b
rearranging
b = 10√2 * cos 45
where cos 45 = 1/√2 = √2/2
b = 10√2 * 1/√2
b = 10
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Related Questions
A metallurgist has one alloy containing 22% copper and another containing 53% copper. How many pounds of each alloy must he use to make 51 pounds of a third alloy containing 30% copper? (Round to two decimal places if necessary.)
Answers
Answer:
37.8387 pounds of the 22% alloy copper and 13.1612 pounds of the 53% alloy copper must be used.
Step-by-step explanation:
Let x represent the amount of 22% copper needed.
Therefore, 51-x represents the amount of 53% copper needed.
Therefore, we can write
(22% * x) + (53% * (51-x)) = 30% * (51)
⇒0.22x + 0.53(51-x) = 0.3(51)
⇒ x = 37.8387
Thus, x =37.8387 and 51-x = 13.1612
select the expression that is equivalent to (x + 6)^2 A. x^2 + 12x^2 + 36 B x^2 + 12x + 36 C 2x + 12x + 12 D x^2 + 6x + 36
Answers
3x
x equals ur mom so udhdhddhehehrhrhrhrrruur mom is ur mome
Which dotted line segment correctly represents the perpendicular bisector of line segment XY?
AB
CD
GF
TW
Answers
AB dotted line segment correctly represents the perpendicular bisector of line segment XY
What is Straight Line?A line is an infinitely long object with no width, depth, or curvature.
A perpendicular bisector can be defined as a line segment which bisects another line segment at 90 degrees.
In other words, a perpendicular bisector intersects another line segment at 90° and divides it into two equal parts.
In the given figure the XY is a straight line.
The perpendicular bisector to this line is AB.
Hence, AB dotted line segment correctly represents the perpendicular bisector of line segment XY
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-3x - 2y = 5
12x + 8y = -20
Answers
Answer:
y=-1
x=-1
Step-by-step explanation:
math problem help fast!!!!!!!!!!!!!!!!! write the answer on a paper please
Answers
Answer:
1. the lateral is 4.4 the total is 8.2
2. the lateral is 132 and the total is 41
Tyler gets his hair cut at the barber
shop once every 4 weeks. How many
trips will he make to the barber shop
in 2 years? You may use the table to
help, if needed. Note: There are
52 weeks in one year.
Answers
Answer:
he would go to the barber shop 21 times in 2 years
Step-by-step explanation:
divide 4 by 52 and then multiply by 2
Answer:
26
Step-by-step explanation:
52÷4 = 13 times a year
therefore, for two years
13 × 2 = 26
If 16 out of 20 vegetables are carrots, how many carrots vegetables will there be per 100 vegetables total?
Answers
Answer:
80
Step-by-step explanation:
16/20 —> 80/100
or
16/20 = 8/10 = 80%
Priyas's cat Wright y
5 and 1/2 pounds and her dog weights 8 and 1/4 pounds
Their combineta weight id pounds
Answers
Answer:
13 3/4
Step-by-step explanation:
5+8 = 13
1/2 = 2/4
2/4+1/4 = 3/4
Guess the value of the limit (if it exists) by evaluating the function at the given numbers. (It is suggested that you report answers accurate to at least six decimal places.) Let f(x) : (cos(12x) - cos(3x))/x^2 We want to find the limit lim x=0 from (cos(12x) - cos(3x))/x^2 Start by calculating the values of the function for the inputs listed in this table. x fx 0.2 24.987664 0.1 -98.998848 0.05 -19.923683 0.01 -99.853172 0.001 -998.62855 0.0001 -9989.29525 0.00001 -99862.9534' Based on the values in this table, it appears : lim x=0 from (cos(12x) - cos(3x))/x^2=
my answers don’t match when I put in calculator the cos of any x value
Answers
Answer: The value of the limit of the function may not be equal to the value of the function evaluated at a particular x-value. In other words, just because a function takes on a certain value at a particular x-value doesn't mean that the limit of the function at that x-value is equal to that value. To determine the limit of the function, you may need to use different methods such as L'Hopital's Rule or other limit laws. Additionally, it's important to keep in mind that the limit of the function may not exist, in which case it wouldn't be equal to any specific value.
Step-by-step explanation:
Please select the best answer from the choice provided.
Answers
Answer:12
Step-by-step explanation:
n*11=4*33
n=4*33/11=3*4=12
1
A red die is tossed and then a green. die is tossed.
What is the probability that the red die shows a
number larger than 4 or the green die shows a
number less than 2?
The two events are not mutually exclusive. So to find the
probability of the union, use:
P(A or B) = P(A) + P(B) - P(A and B)
[?]
P(A or B)
=
8
P(B)
Green die
What is the probability of the red die rolling a
P(A)
Red die
+
-
8)
P(B)
P(A)
Red die Green die
number greater than 4?
Enter your answer in simplest form.
Enter
Answers
On solving the provided question, we can say that the probability of the red die rolling is 16.67% probability = 0.1667
What is probability?A branch of mathematics called probability theory determines the chance that an event will occur or that a statement is true. A probability is a number between 0 and 1, where 1 denotes certainty and about 0 denotes how probable an event is to occur. The possibility or likelihood that a specific event will occur is expressed numerically as a probability. Probabilities can also be expressed as percentages from 0% to 100% or as numbers between 0 and 1. the proportion of occurrences among all equally likely alternatives that lead to a certain event relative to all possible outcomes.
red die, there are 3 numbers greater than 3 out of 6 numbers
Probability (A) = 3/6 = 1/2.
green die, there are 2 numbers less than 3 out of 6 numbers
Probability (B) = 2/6 = 1/3.
events are independent
P(A and B) = [tex]P(A)P(B) = 1/2 X 1/3 = 1/6 = 0.1667[/tex][tex]P(A)P(B) = 1/2 X 1/3 = 1/6 = 0.1667.[/tex]
16.67% probability = 0.1667
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An airline has two flights traveling from CVG to ORD on a busy Friday evening. Flight A is scheduled to leave at 6:30 p.m. The airplane for flight A has a capacity of 96 passengers. The second flight, Flight B, leaves one hour later and has a capacity of only 68 passengers. Based on historical data, the airline knows that the probability that a passenger on Flight A will be a no-show is 0.03 and the probability that a passenger will be a no-show on Flight B is 0.02. For this exercise, we will assume that passenger no-shows are independent events. Round all answers to four decimal places. 6. If the airline chooses not to oversell flight A and sells exactly 96 tickets, what is the probability that it will have a full flight (i.e. all 96 passengers show up)? 7. If the airline oversells flight A with 99 tickets sold, what is the probability that all passengers that show up will have a seat on the flight (i.e. 3 or more no-shows)? 8. If the airline oversells flight B with 70 tickets sold, what is the probability that the flight will have exactly 68 customers show up? 9. If the airline oversells flight B with 72 tickets, what is the probability that all passengers that show up will have a seat on the flight?
Answers
6. The probability that Flight A will have a full flight is 0.4163.
7. The probability that all passengers who show up will have a seat on the flight is 0.5731.
8. The probability that Flight B will have exactly 68 customers show up is 0.0904.
9. The probability that all passengers that show up will have a seat on the flight is 0.9707.
6. If the airline chooses not to oversell flight A and sells exactly 96 tickets, the probability that it will have a full flight can be calculated using the binomial distribution. Let X be the number of passengers who show up for the flight.
Then, X follows a binomial distribution with n = 96 and p = 0.97 (since the probability that a passenger shows up is 1 - 0.03 = 0.97). Thus, the probability that all 96 passengers show up is:
P(X = 96) = (96 choose 96) × [tex]0.97^{96}[/tex] × [tex]0.03^0[/tex] = 0.4163
So, the probability that Flight A will have a full flight is 0.4163.
7. If the airline oversells Flight A with 99 tickets sold, the probability that all passengers who show up will have a seat on the flight (i.e. 3 or more no-shows) can be calculated using the binomial distribution again. Let Y be the number of no-shows for the flight. Then, Y follows a binomial distribution with n = 99 and p = 0.03. We want to find the probability that Y is greater than or equal to 3 (i.e. there are 3 or more no-shows), which can be calculated as:
P(Y >= 3) = 1 - P(Y <= 2) = 1 - ((99 choose 0) × [tex]0.03^0[/tex] × [tex]0.97^{99}[/tex] + (99 choose 1) × [tex]0.03^1[/tex] × [tex]0.97^{98}[/tex] + (99 choose 2) × [tex]0.03^2[/tex] × [tex]0.97^{97}[/tex]) = 0.5731
So, the probability that all passengers who show up will have a seat on the flight is 0.5731.
8. If the airline oversells Flight B with 70 tickets sold, the probability that the flight will have exactly 68 customers show up can be calculated using the binomial distribution with n = 70 and p = 0.98 (since the probability that a customer shows up is 1 - 0.02 = 0.98). Let Z be the number of customers who show up for the flight. Then, the probability that exactly 68 customers show up is:
P(Z = 68) = (70 choose 68) × [tex]0.98^{68}[/tex] × 0.02² = 0.0904
So, the probability that Flight B will have exactly 68 customers show up is 0.0904.
9. If the airline oversells Flight B with 72 tickets sold, the probability that all passengers who show up will have a seat on the flight can be calculated using the binomial distribution again. Let W be the number of no-shows for the flight. Then, W follows a binomial distribution with n = 72 and p = 0.02. We want to find the probability that W is less than or equal to 3, which can be calculated as:
P(W <= 3) = (72 choose 0) × [tex]0.02^0[/tex] × [tex]0.98^{72}[/tex] + (72 choose 1) × [tex]0.02^1[/tex] × [tex]0.98^{71}[/tex] + (72 choose 2) × [tex]0.02^2[/tex] × [tex]0.98^{70}[/tex] + (72 choose 3) × [tex]0.02^3[/tex] × [tex]0.98^{69}[/tex] = 0.9707.
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The square root of a number will always have two outcomes One is positive and the other is negative.
true or false
Answers
The square root of zero is a counterexample of the statement, so it is false.
Is the statement true or false?Here we have the following statement about square roots:
"the square root of a number will always have two outcomes One is positive and the other is negative."
This seems to be true because:
-2*-2 = 2*2 = 4
So √4 = 2 and -2
But, particularly the square root of zero is:
√0 = 0
So here we have only one outcome that is neither positive nor negative, then the statement is false.
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what is the product of these bionomials? (x - 6)(x + 2) =
Answers
Answer:
Step-by-step explanation:
Multiply x*x, then X*2, then -6*2, lastly -6*x. So in other words multiply all of the factors. pay close attention to the + and - negative signs.
Answer: [tex]x^{2}[/tex]+2x-6x+2x
Simplify: [tex]x^{2}[/tex]-4x+2x
What kind of problem is "What number multiplied by the expression of 5 x 10^3 is equivalent to the expression 5 x 10^6?"
Answers
The problem is the multiplication with exponent or scientific notation kind of problem.
What is meant by Scientific Notation?Scientific notation is a way of writing a large number or small number with many digits in a simpler form using the power of 10.
For example, 30,000 can be written as 3 × 10⁴.
Here, the problem is defined as multiplying the expression 5 × 10³ with some number to get the expression 5 × 10⁶.
Let x be the number that is multiplied.
(5 × 10³) x = 5 × 10⁶
x = (5 × 10⁶) / (5 × 10³)
x = 10⁶ / 10³
x = 10⁶⁻³ = 10³
So here we are using the scientific notation to solve the whole problem and the answer itself is in the scientific notation.
Hence the given problem is a Multiplication of numbers in scientific notation kind of problem.
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How can 1% of 800 be used to
determine 28% of 800?
1% of 800 is
SO 28% of 800 is
Answers
28*8=224
this was the attendance at 3 football matches one day, each round to the three nearest 1,000. what's the largest total number of people who attended 3 matches on the day
Answers
The largest total number of people who attended 3 matches on the day was 17, 000 people.
How to find the number of people ?The largest total number of people who attended 3 matches on the day would be the sum of the largest rounded attendance numbers for each match:
Match 1: 5,000
Match 2: 8,000
Match 3: 4,000
Rounding each attendance number to the nearest 1,000 gives us:
Match 1: 5,000
Match 2: 8,000
Match 3: 4,000
Adding these rounded numbers together gives us:
5,000 + 8,000 + 4,000 = 17,000
Therefore, the largest total number of people who attended the three matches on the day was 17,000.
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The full question is:
Match 1 - 5, 000 people
Match 2 - 8, 000 people
Match 3 - 4, 000 people
This was the attendance at 3 football matches one day, each round to the three nearest 1,000. what's the largest total number of people who attended 3 matches on the day
Using your calculus skills derive the equations for the critical saturation ratio and the critical radius. (Hint: the critical point on the Kohler curve represents a maximum value). The equations you should end up with are as follows: r* = V3b/a and S* = 1+V4a3/27b Where r is the critical radius and S is the critical saturation ratio
Answers
The derivation of the critical radius(r*) as and critical saturation(S*) as is explained below .
To derive the critical saturation ratio (S*) and critical radius (r*),
We use calculus to find the maximum value of the saturation ratio for a given radius on the Kohler curve.
First, let us consider the equation for the saturation ratio, S, as a function of radius, r:
that is : S = 1 + ar²/3b ;
where a and b are constants.
Next, we find the derivative of S with respect to r:
On differentiating Curve "S" with respect to "r" ;
⇒ dS/dr = 2ar/3b ;
Equating the derivative = 0 , we can find the critical points:
⇒ dS/dr = 0 = 2ar/3b ;
On Solving for r, we have ;
⇒ r* = √(3b/a)
Next , to find the critical saturation ratio(S*) , we substitute r* back into the original equation for S:
⇒ S* = 1 + ar²/3b = 1 + a×(3b/a)/3b = 1 + √(4a³/27b)
Therefore , the critical saturation ratio and critical radius are written as r* = √(3b/a) and S* = 1 + √(4a³/27b) .
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The given question is incomplete , the complete question is
Using your calculus skills derive the equations for the critical saturation ratio and the critical radius. (Hint: the critical point on the Kohler curve represents a maximum value).
The equations you should end up with are as follows:
r* = √(3b/a) and S* = 1 + √(4a³/27b) Where r* is the critical radius and S* is the critical saturation ratio .
Gregory runs a 100-meter race. 5 seconds after the race started Gregory is 30 meters from the starting line and reaches his max speed; he runs at this max speed for the rest of the race. Gregory notices that he is 62 meters from the starting line 9 seconds after the race started.
What is Gregory's max speed?
Suppose Gregory runs for an additional
z
seconds after reaching his max speed...
How far will Gregory travel during those additional
z
seconds?
What is Gregory's distance from the starting line
5
+
z
seconds after the race started?
What is Gregory's distance from the starting line
x
seconds after the race started (provided
x
≥
5
)?
Answers
(a) The max speed of Gregory is, [tex]v_{max} =\frac{32}{4} =8s[/tex]
(b) distance covered in additional z seconds is [tex]distance= 4zmeter[/tex]
(c)[tex]d(x)=30m+4(x-7s)[/tex]
What is velocity?Velocity is defined as the rate of change position of the object with respect to the time and frame of reference.
Gregory runs a 100-meter race. 5 seconds after the race started he is 30 meters from the starting line and reaches his max speed.
(a)The max speed covered by Gregory is ,
For constant speed, we know,
[tex]v=\frac{distance}{time taken}[/tex]
distance= 62m-30m=32m.
And the time take to reach 62m will be
time =9s-5s=4s
So, Gregory's max speed is,
[tex]v_{max} =\frac{32}{4} =8s[/tex]
(b) Suppose Gregory runs for an additional z seconds after reaching his max speed,
As the velocity of Gregory's is [tex]v_{max}[/tex], the distance covered by him is,
[tex]distance=v_{max}*zs[/tex]
[tex]distance= 4zmeter[/tex]
(c) At time 5+ z seconds the distance will be the30
meters he covers in the first part of the race plus the distance he traveled at constant speed. this is:
[tex]distance=v_{max}*z+30\\distance=4\frac{m}{s} *z s[/tex]
At time x ( x greater or equal to 5 seconds) the distance will be the 30 meters he covers in the first part of the race plus the distance he traveled at constant speed. this is:
[tex]d(x)=30m+v_{max}*(x-5s)\\ d(x)=30m+4(x-7s)[/tex]
Hence,(a)The max speed of Gregory is, [tex]v_{max} =\frac{32}{4} =8s[/tex]
(b) distance covered in additional z seconds is [tex]distance= 4zmeter[/tex]
(c)[tex]d(x)=30m+4(x-7s)[/tex]
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Solve the following equation
Answers
Answer:
x=
Step-by-step explanation:
⅔x= 7x-1
2/3x=6
multiply both sides by 3/2
(3/2)(2/3x)= 6×3/2
x=
You flip a coin, spin the spinner, and flip a coin again. Find the probability of flipping heads, spinning an odd number, and then flipping tails.
Answers
The probability of flipping heads, spinning an odd number, and then flipping tails is 1/8.
How to find the probabilityThe probability of flipping heads, spinning an odd number, and then flipping tails is given by the product of the individual probabilities of each event.
The probability of flipping heads is 1/2,
the probability of spinning an odd number is 2/4 or 1/2, and
the probability of flipping tails is 1/2.
So, the probability of flipping heads, spinning an odd number, and then flipping tails is:
1/2 * 1/2 * 1/2 = 1/8
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Find the quotient. 2/5÷ 3 2/3 ?
Answers
Answer:
6/55
Step-by-step explanation:
2/5 ÷ 3 2/3
3 2/3 = 11/3
2/5 ÷ 11/3
= 2/5 x 3/11
= 6/55
So, the answer is 6/55
The company president thought that type of music listened to (country vs. classical) could predict production line output. For one week the entire plant listened to country music, then for the next week the entire plant listened to classical music. He then compared the production line output between the country and classical music production line outputs.
(a) What type of research hypothesis is tested in this study?
associative RH
causal RH
(b) What type of design is being used in this study?
true experiment
non-experiment
(c) What type of design is being used in this study (mark all that apply)
cross-sectional design
within-group design
between subjects design
repeated measures design
longitudinal design
within-subjects design
between groups design
(d) Will the design used in this study provide an appropriate test of the research hypothesis?
Yes, this design can be used to test this research hypothesis
No, this design can not be used to test this research hypothesis
Answers
a) Type of research hypothesis is tested in this study is causal RH
b) Type of design is being used in this study is non-experiment
c) Type of design is being used in this study is within-subjects design
d) No, the design used in this study cannot provide an appropriate test of the research hypothesis.
(a) The research hypothesis being tested in this study is a causal hypothesis. The company president believes that the type of music listened to can predict production line output.
(b) The type of design being used in this study is a non-experiment. The researcher is not manipulating the type of music listened to; instead, the plant is naturally exposed to either country or classical music.
(c) The design being used in this study is within-subjects design, as the same group of individuals is exposed to both types of music. It is also a repeated measures design, as the same individuals are measured twice (once under country music and once under classical music).
(d) No, the design used in this study cannot provide an appropriate test of the research hypothesis. Since the researcher is not manipulating the type of music listened to, it is possible that other variables could be affecting the production line output, such as different environmental conditions on each week, or different levels of motivation.
Therefore, it is difficult to determine if any differences in production line output are actually due to the type of music listened to. A true experiment with random assignment of workers to the two music conditions would provide a better test of the research hypothesis.
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Write a extended metaphor poem about Tennis
Answers
Answer:
Tennis, a game of skill and grace,
A dance upon a court of green.
Racquets are partners in this space,
A symphony of motion seen.Each stroke a crescendo to the ear,
A harmony of speed and spin.
The ball, a fleeting, flashing sphere,
A fleeting moment to win.The court is life, a battlefield,
Of challenges and victories.
A test of strength, both heart and mind,
Of courage, skills, and agility.The net, a barrier, divides,
Two opponents in their quest.
A symbol of the tension that resides,
In every match, every test.But when the final point is served,
And winner takes the day.
The court transforms, a stage, preserved,
For celebration in its way.
Step-by-step explanation:
there are 20 oranges in the basket.if Ayo picks two oranges how many is left
Answers
Answer: 18
Step-by-step explanation: 20 - 2 = 18
find the value of x. SIMPLEST RADICAL FORM
Answers
Step-by-step explanation:
Pythagoras
c² = a² + b²
c being the Hypotenuse (the side opposite of the 90° angle). a and b are the legs.
so, in our case,
27² = 16² + x²
729 = 256 + x²
473 = x²
x = sqrt(473)
473 = 11×43 and has therefore no squared factors.
therefore, it cannot be further simplified.
At 6.pm the temperature in phoenix is the same at the temperature in Tucson.By 9.pm the temperature in phoenix has dropped 2 degrees in Tucson it has dropped 4 degrees by 11.pm the temperature in phoenix has dropped another 3 degress represent each city temperature at 11 pm with an algebraic expression and bar model
Answers
Answer: 58 degrees
Step-by-step explanation:
The graph on the right shows the remaining life expectancy, E, in years for females of age x.
Find the average rate of change between the ages of 50 and 60. Describe what the average rate of
change means in this situation.
The average rate of change of life expectancy between the ages of 50 and 60 is
(Type an integer or a decimal.)
Answers
The average rate of change of life expectancy between the ages of 50 and 60 will be 0.88.
What is the average rate change?It is the average amount by which the function varied per unit throughout that time period. It is calculated using the gradient of the line linking the interval's ends on the graph depicting the function.
Average rate = [f(x₂) - f(x₁)] / [x₂ - x₁]
The graph on the right shows the remaining life expectancy, E, in years for females of age x.
Then the average rate of change is given as,
Average rate = (32.8 - 24) / (60 - 50)
Average rate = 8.8 / 10
Average rate = 0.88
The average rate of change of life expectancy between the ages of 50 and 60 will be 0.88.
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The sides of a triangle are 44, 73, and 86. Use the Pythagorean Theorem to determine
if the triangle is right, acute, or obtuse.
The triangle is
of the squares of the other two sides.
because the square of the largest side
Submit Answer
the sum
at
Answers
The triangle with sides 44, 73, and 86 is an obtuse triangle.
The Pythagorean Theorem states that the square of the length of the hypotenuse (the side opposite the right angle) in a right triangle is equal to the sum of the squares of the lengths of the other two sides, can be used to determine whether the triangle is right, acute, or obtuse.
In an acute triangle, the square of the hypotenuse length is less than the sum of the squares of the other two sides; in an obtuse triangle, the square of the hypotenuse length is greater than the sum of the squares of the other two sides.
Begin by calculating the square of each side:
[tex]44^2 = 1936[/tex]
[tex]73^2 = 5329[/tex]
[tex]86^2 = 7396[/tex]
Let us now see if the triangle fulfils the Pythagorean Theorem:
1936 + 5329 = 7265
We know the triangle is not obtuse because 7265 is less than 7396.
1936 + 7396 = 9332
We know the triangle is not acute because 9332 is greater than 5329.
5329 + 7396 = 12725
We know the triangle is obtuse because 12725 is greater than 7265 but less than 9332.
As a result, the triangle with sides 44, 73, and 86 is obtuse.
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Question 4 pts (Lesson 2.11: Covariance and Correlation ) Suppose that the correlation between December snowfall and temperature in Siberacuse NY is -0.5. Further suppose that Var(S) =100 in2 and Var(T) = 25 (degrees F)2 . Find Cov(S,T) (in units of degree inches, whatever those are): a. -25 0 b. - 0 c 0 d. 25
Answers
The answer is (a) -25. The covariance is negative, indicating that the December snowfall and temperature in Syracuse NY have an inverse relationship. Snowfall, in particular, tends to decrease as temperatures rise. Covariance units are the product of the units of the two variables, which in this case are in2 and (degrees F)2, so covariance units are degree inches.
We are given the following details:
Correlation coefficient between December snowfall and temperature in Syracuse, New York: -0.5
December snowfall variation (S): 100 in2
Temperature variation in December (T): 25 (degrees F)2
We are asked to calculate the correlation between December snowfall and temperature in degrees inches.
Cov(S,T) can be calculated using the covariance formula:
Corr(S,T) = Cov(S,T) * sqrt(Var(S)) * sqrt(Var(T))
Plugging in the values from the problem yields:
Cov(S,T) = (-0.5) * sqrt(100 in2) * sqrt(25 (degrees F)2) = (-0.5) * 10 in * 5 degrees F = -25 degree inches
As a result, the answer is (a) -25. The covariance is negative, indicating that the December snowfall and temperature in Syracuse NY have an inverse relationship.
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