If you are outdoors, the wind may make it feel a lot colder than the thermometer reads. You feel the windchill temperature, which, if the air temperature is 20 degree F, is given in degree F by W(v) = 48.17 - 27.2v^0.16, where v is the wind velocity in mph for 5 lessthanorequalto v lessthanorequalto 60. If the air temperature is 20 degree F, and the wind is blowing at 40 mph, what is the windchill temperature, to the nearest degree? Find W'(40), and explain what this means in terms of windchill.
Previous question
Answers
The value of W'(40) is -1.4°F/mph. This means that for every 1 mph increase in wind velocity at 40 mph, the windchill temperature will decrease by approximately 1.4°F.
It highlights the importance of being aware of the windchill temperature, as even a small increase in wind velocity can make it feel significantly colder. To find the windchill temperature for 20°F and wind velocity of 40 mph, we plug in the given values in the formula:
W(v) = 48.17 - 27.2\(v^0^.^1^6\)
W(40) = 48.17 - 27.2\((40)^0.^1^6\) ≈ 1°F
Therefore, the windchill temperature is approximately 1°F.
To find W'(40), we take the derivative of W(v) with respect to v:
W(v) = 48.17 - 27.2\(v^0^.^1^6\)
W'(v) = \(-4.355v^-^0^.^8^4\)
W'(40) = -\(4.355(40)^-^0^.^8^4\) ≈ -1.4°F/mph
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Related Questions
You purchase a large screen tv for $2,300 to finance a purchase with a fixed installment simple interest loan for 30 months and the rate of 3.5% interest
Answers
The total cost of financing the $2,300 large screen TV over 30 months with a fixed installment simple interest loan at a rate of 3.5% interest is $2,555.50.
Supporting Answer: To calculate the total cost of financing the $2,300 large screen TV over 30 months with a fixed installment simple interest loan at a rate of 3.5% interest, we need to consider the formula for calculating simple interest:
Simple Interest = Principal * Rate * Time
Given that the principal (P) is $2,300, the rate (R) is 3.5%, and the time (T) is 30 months, we can substitute these values into the formula:
Simple Interest = $2,300 * 0.035 * 30
= $2415
The simple interest for financing the TV is $2415. Adding this to the original purchase price gives us the total cost:
Total Cost = Principal + Simple Interest
= $2,300 + $2415
= $5550.50
Therefore, the total cost of financing the $2,300 large screen TV over 30 months with a fixed installment simple interest loan at a rate of 3.5% interest is $2,555.50.
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Jane buys 3 magnets and 9 bookmarks at a craft fair. The magnets cost $5 each, and the bookmarks cost $2 each. Which equations can be used to find how many dollars, d, Jane spends at the craft fair? Choose all the correct answers.
Answers
Answer:
Choice A and C
Step-by-step explanation:
If 1 magnet costs $5, then 3 magnets cost $15 because adding 3 magnets to your bag, would equal to 5+5+5, or 5x3. If 1 bookmark cost $2, then 9 bookmarks would cost $18 to your bag, which would equal 9+9, or 9x2.
So, C is correct because 5x3 is 15, and 2x9 is 18. A is also correct because it's just the other way around, 2x9=18 and 5x3=15.
John, Britteny, Chloe, Kenji, Warner, and Juliette are in a race and are all considered equally fast what is the probability that John and Britteny would be the first two finishers
Detailed explanations are most welcome
Answers
Answer:
1/3
Step-by-step explanation:
There are 6 people partaking in this race.If John and Brittney are to be the first two finishers, then 2 out of the 6 people are the said first two finishers.That gives 2/6.By reducing the fraction, we have:(2÷2)/(6÷2) = 1/3.Hope this helps!
x/2>-2 solve the inequality
Answers
Hope this helped
what is 6 9/32 as a decimal
Answers
Just divide 9 by 32 then add 6
circle all that apply 13860a. divisible by 4b. divisible by 7d. divisible by 9c. divisible by 11e. none of the above
Answers
A number is divisible by another number if it yields a whole number when divided by that number. For example, 8 is divisible by 2 because 8/2 = 4, and 4 is a whole number.
Then, let us verify the options.
• 13860 is divisible by 4?
\(\frac{13860}{4}=3465\)3465 is a whole number. Thus, 13860 is divisible by 4.
• 13860 is divisible by 7?
\(\frac{13860}{7}=1980\)1980 is a whole number. Thus, 13860 is divisible by 7.
• 13860 is divisible by 9?
\(\frac{13860}{9}=1540\)1540 is a whole number. Thus, 13860 is divisible by 9.
• 13860 is divisible by 11?
\(\frac{13860}{11}=1260\)1260 is a whole number. Thus, 13860 is divisible by 11.
There is a bag filled with 5 blue and 6 red marbles.
A marble is taken at random from the bag, the colour is noted and then it is replaced.
Another marble is taken at random.
What is the probability of getting 2 of the same colour?
Answers
Answer:
The probability of getting two of the same color is 61/121 or about 50.41%.
Step-by-step explanation:
The bag is filled with five blue marbles and six red marbles.
And we want to find the probability of getting two of the same color.
If we're getting two of the same color, this means that we are either getting Red - Red or Blue - Blue.
In other words, we can find the independent probability of each case and add the probabilities together*.
The probability of getting a red marble first is:
\(\displaystyle P\left(\text{Red}\right)=\frac{6}{11}\)
Since the marble is replaced, the probability of getting another red is: \(\displaystyle P\left(\text{Red, Red}\right)=\frac{6}{11}\cdot \frac{6}{11}=\frac{36}{121}\)
The probability of getting a blue marble first is:
\(\displaystyle P\left(\text{Blue}\right)=\frac{5}{11}\)
And the probability of getting another blue is:
\(\displaystyle P\left(\text{Blue, Blue}\right)=\frac{5}{11}\cdot \frac{5}{11}=\frac{25}{121}\)
So, the probability of getting two of the same color is:
\(\displaystyle P(\text{Same})=\frac{36}{121}+\frac{25}{121}=\frac{61}{121}\approx50.41\%\)
*Note:
We can only add the probabilities together because the event is mutually exclusive. That is, a red marble is a red marble and a blue marble is a blue marble: a marble cannot be both red and blue simultaneously.
which statement is correct
Answers
I have to make this unnecessary long because yeah but the correct answer I believe is going to be the second one
Solve for x.
------------------------------------------------------------
Answers
x= 20
Why?
Look the image, there is the explanation
What are the solutions of 3(x – 4)(2x - 3) = 0? Check all that apply.
O-4
O-3
-
win
O 3
2
1 2 3 4
03
4
WILL MARK BRAINLIEST
Answers
Answer:
The solution to the equation is:
\(x=4,\:x=\frac{3}{2}\)
Step-by-step explanation:
Given the equation
\(3\left(x-4\right)\left(2x-3\right)=0\)
Using the zero factor principle
if ab=0, then a=0 or b=0 (or both a=0 and b=0)
\(x-4=0\quad \mathrm{or}\quad \:2x-3=0\)
now solving
\(x - 4 = 0\)
adding 4 to both sides
\(x - 4 + 4 = 0 + 4\)
simplifying
\(x = 4\)
and also solving
\(2x - 3 = 0\)
adding 3 to both sides
\(2x - 3 + 3 = 0 + 3\)
simplifying
\(2x = 3\)
divide both sides by 2
\(\frac{2x}{2}=\frac{3}{2}\)
simplifying
\(x=\frac{3}{2}\)
Therefore, the solution to the equation is:
\(x=4,\:x=\frac{3}{2}\)
Answer:
4 or 3/2
Step-by-step explanation:
I had this question on a quiz, I got it correct.
write an equations in slope intercept form for a line that passes through (-2,-1) and is perpendicular to 5x-3y
Answers
The given line is 5x - 3y = 0. It is required to write the equation of a line that is perpendicular to this line and passes through the point (-2,-1).We know that if two lines are perpendicular, then the product of their slopes is equal to -1.Therefore, the slope of the line 5x - 3y = 0 is given by:5x - 3y = 0-3y = -5x + 03y = 5x y = (5/3) x
The slope of the required line is negative reciprocal of the slope of this line: m = -3/5The point (-2,-1) lies on the required line and the slope of the line is -3/5.Therefore, the equation of the line in the slope-intercept form is given by:
y - y1 = m(x - x1),
where (x1,y1) = (-2,-1)
Substituting the values, we get:
y - (-1) = -3/5(x - (-2))y + 1 = -3/5(x + 2)y + 1 = (-3/5)x - 6/5y = (-3/5)x - 6/5 - 1y = (-3/5)x - 11/5
Thus, the equation of the required line in slope-intercept form is y = (-3/5)x - 11/5. The slope-intercept form of a linear equation is y = mx + b where m represents the slope and b represents the y-intercept. To find the equation of a line that passes through a given point and is perpendicular to a given line, we need to use the properties of perpendicular lines.In order for two lines to be perpendicular, their slopes must have opposite signs and be reciprocals of each other. We can find the slope of the given line by rearranging it in slope-intercept form as follows:
5x - 3y = 0-3y = -5x + 0y = (5/3)x
So the slope of the given line is 5/3. Since the slope of the perpendicular line must be the negative reciprocal of 5/3, we have:m = -1/(5/3) = -3/5Now we can use the point-slope form of the equation of a line to find the equation of the line passing through the point (-2,-1) with slope -3/5:
y - y1 = m(x - x1)y - (-1) = (-3/5)(x - (-2))y + 1 = (-3/5)(x + 2)y + 1 = (-3/5)x - 6/5y = (-3/5)x - 6/5 - 1y = (-3/5)x - 11/5
So the equation of the line that passes through (-2,-1) and is perpendicular to 5x - 3y = 0 is y = (-3/5)x - 11/5.
Therefore, the equation of the required line in slope-intercept form is y = (-3/5)x - 11/5.
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use the binomial theorem to expand the following expression. (u − 3v)4
Answers
The binomial theorem, we can expand (u - 3v)⁴ as follows: (u - 3v)⁴ = 1u⁴ + 4u³(-3v) + 6u²(-3v)² + 4u(-3v)³ + 1(-3v)⁴= u⁴ - 12u³v + 54u²v² - 108uv³ + 81v⁴ and the coefficient of x⁷ is 2187.
(a) Using the binomial theorem, we can expand (u - 3v)⁴ as follows:
(u - 3v)⁴ = 1u⁴ + 4u³(-3v) + 6u²(-3v)² + 4u(-3v)³ + 1(-3v)⁴
= u⁴ - 12u³v + 54u²v² - 108uv³ + 81v⁴
(b) To find the coefficient of x⁷ in the expansion of (3x + 4)¹⁰, we need to look at the term that contains x⁷, which is the term where x has a power of 7 and the constant has a power of 3:
(3x)⁷(4)³ = 2187x⁷
So the coefficient of x⁷ is 2187.
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Complete question:
Use the binomial theorem to expand the following expression. (u - 3v)⁴
Find the coefficient ofx7
56.01 56.10 56.011 greatest to least
Answers
Answer:
shshjshshsbs
Step-by-step explanation:
shzjshsjjsisjs
Can someone please help me asap ill mark brainlist!!!
Answers
Answer:
c
Step-by-step explanation:
The correct answer is a.
Teresa makes home made empanada and sells theme
Answers
Answer:
Step-by-step explanation:
Answer:
yum
Step-by-step explanation:
which of the following differential equations have x^2-4y^2=8 as a solution?
a) dy/dx = 4xy
b) dy/dx = 4x/y
c) y dy/dx = x/4
d) dy/dx = -x/4y
Answers
Answer:
B
dy/dx = 4x/y
Sorry if it's wrong!
Point A of a triangle ABC is at (7,-2). If triangle ABC is reflected across the y-axis,
what are the new coordinates of A?
A (-7,2)
B (-2,-7)
C (-7,-2)
D (7,2)
Answers
Answer: C
Step-by-step explanation:
Answer:
Step-by-step explanation:
Factor( special patterns): 36x^2-84x+49
Answers
Answer:
(6x - 7) (6x - 7)
Step-by-step explanation:
A perfect square trinomial will be in the form of \(a^2\) ± \(2ab + b^2.\) A trick to factoring a perfect square trinomial would to write it as \((a^2\)±\(b^2)\). (When doing this, the sign in the middle is determined by the middle sign in the original trinomial).
\(36x^2 -84x + 49\) is known as a perfect square trinomial, too. Its first and last terms are both perfect squares (6x squared makes \(36x^2\), 7 squared makes 49) and the middle term is 2 times the square roots of both of the other terms ( \((2) (7) (6x)\) is \(84x\)).
So, we can use the trick described earlier, and the answer would be \((6x-7)^2\), also known as (6x-7) (6x-7).
a student takes a true-false test that has 14 questions and guesses randomly at each answer. let x be the number of questions answered correctly. find p(5) group of answer choices 0.0001 0.0611 0.1833 0.1222
Answers
The probability to answer 5 questions correctly from 14 true or false questions is 0.1222
The given situation represents a binomial experiment, where there are only two possible outcomes for each trial: success (answering correctly) and failure (answering incorrectly). To find the probability of a particular number of successes, we use the binomial probability formula:
P(x)= nCx × p^x × q^(n-x)
Where, n is the total number of trials, p is the probability of success on each trial, q is the probability of failure on each trial (1-p), and x is the number of successes desired.
n = 14 (total number of questions)
p = 1/2 (probability of answering correctly when guessing randomly), and q = 1/2 (probability of answering incorrectly when guessing randomly).
To find P(5), we substitute these values in the formula
P(5) = 14C5 * (1/2)^5 * (1/2)^9= 2002 * (1/32) * (1/512)= 2002 / 16384≈ 0.1222
Therefore, the answer is option D, 0.1222.
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Find DE, please help me
Answers
Step-by-step explanation:
ABC and CDE are similar triangles.
similar shapes means that both shapes have the same angles. and : that there is one scaling factor for all lines of one of the shapes to calculate the lengths of the lines of the other shape.
we see that all the other sides of ABC are scaled 2:1 to the corresponding sides of CDE. that means the sides of ABC are twice a long as the sides of CDE.
the same scaling factor has to apply to AB vs. DE.
therefore,
11x - 25 = 2(4x + 1) = 8x + 2
3x = 27
x = 9
DE = 4x + 1 = 4×9 + 1 = 36 + 1 = 37
beginning and intermediate algebra the language and symbolism of mathematics
Answers
Beginning and intermediate algebra encompass the foundational aspects of mathematics, introducing students to the language and symbolism used in mathematical expressions and equations.
Beginning and intermediate algebra courses serve as stepping stones in a student's mathematical education, providing them with essential skills and knowledge in algebraic concepts.
These courses emphasize the language and symbolism of mathematics, teaching students to translate real-world problems into mathematical expressions and equations.
In these courses, students learn to work with variables, which represent unknown quantities, and manipulate algebraic expressions using operations such as addition, subtraction, multiplication, and division. They learn how to solve equations and inequalities, simplifying expressions and finding solutions that satisfy given conditions.
Furthermore, beginning and intermediate algebra introduce students to important mathematical concepts like functions, graphing, exponents, and factoring.
These topics help develop critical thinking and problem-solving skills, laying the foundation for more advanced mathematical disciplines. By learning the language and symbolism of mathematics in beginning and intermediate algebra.
Students gain a solid understanding of mathematical concepts and acquire the necessary skills to tackle more complex mathematical problems in higher-level courses and real-world applications.
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Of the variables affecting your insurance, are any of them truly random variables?
Answers
Yes, some of them are the random variables affecting your insurance, such as personal injury protection (PIP).
What is the insurance about?The insurance industry is known to be one that handles the random variables as well as the expected values.
Note that a lot of people will buy several kinds of insurance, such as homeowner’s or renter’s insurance, life insurance, and others.
Therefore, Yes, some of them are the random variables affecting your insurance, such as personal injury protection (PIP).
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See question below
Investigating Vehicle Insurance
All states require car insurance, but not all states require the same coverage. Each state defines the minimum insurance coverage that is required. According to the Minnesota minimum coverage requirements, for example, all licensed vehicles are required to have coverage for:
personal injury protection (PIP)
liability
uninsured motorist
underinsured motorist
Please help quickly
-3 - x = -12
What is x?
r over 8 = negative 1 over 8
What is r?
n - (3) = 4
What is n?
Answers
worked them out, hope this helps!
Find the value of a. then find the angle measures of the polygon
Answers
2a+2a+a+a=360
6a=360
a=60
2a
2(60)=120
Which quadrant is the following point in?
Point A (1,3)
Answers
Answer:
Its first quadrant bro.
4. The average speed of an Express train between New Delhi and Kota is 97 km/hr. The train
takes 4 hr to travel from New Delhi to Kota. Find the distance between New Delhi and Kota.
Answers
Answer:
Distance between New Delhi and Kota = 388 kilometers
Step-by-step explanation:
Given that:
Average speed of express train = 97 kilometer per hour
Time taken to travel = 4 hours
Distance between New Delhi and Kota = Speed * Time
Distance = 97 * 4
Distance = 388 kilometers
Hence,
Distance between New Delhi and Kota = 388 kilometers
Find the volume of the prism.
6 cm
8 cm
5 cm
9 cm
The volume is cubic centimeters.
Answers
Answer:
351 ccm
Step-by-step explanation:
Let's split the prism in a rectangular prism and a triangular prism:
- the volume of the rectangular prism is 6 * 5 * 9 = 270 ccm
- the volume of the triangular prism is base of the surface x height:
(3 * 6)/2 * 9 = 81 ccm
Total volume is 270 + 81 = 351 ccm
Step-by-step explanation:
As we observe on the prism we have the
. slant height of 9cm
. height of base of 6cm
. long side of the base of 8cm
. short side of the base which is 5 cm
So as we know the volume of the prism is A=(BA(base area)* slant Height) /2
So the area of the trapezium is A=((B(long base side)+b (short base side ))*h)/2
it's A=((8+5)*6)/2=39 square centimeters
So the volume is=(39*9)/2=175.5 cubic centimeters
Can someone help me on this plz
Answers
Answer:
y=4/3x+2.5
Step-by-step explanation:
im not 100% sure if i get it wrong reply
What is the geometric average of the following five returns: -36.81%, 19.14%, 23.77%, -6.34%, 31.17%.
Answers
The geometric average of the five returns is 20.14.%
What is geometric average?Geometric average or geometric mean is the average of a set of values calculated using the products of the terms or values.
The geometric average of a data set containing n observations is the nth root of the product of the values.
Calculating the geometric average of the following five returns: -36.81%, 19.14%, 23.77%, -6.34%, 31.17%:
n = 5
Geometric average = \(\sqrt[5]{(-36.81) \times (19.14) \times (23.77) \times (-6.34) \times (31.17)}\)
Geometric average = 20.14%
In conclusion, the geometric average mean is obtained as the nth root of the product of the values.
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Show that d/dx(csc x) = -csc x cot x
Answers
Quotient rule of differentiation.
d/dx(csc x) = (-1)(sin \(x)^{-2}\) (cos x) = -cot x (sin \(x)^{-1}\) = -csc x cot x
d/dx(csc x) = -csc x cot x.
To show that d/dx(csc x) = -csc x cot x, we will use the quotient rule of differentiation.
Recall that csc x is defined as 1/sin x.
Therefore, we can rewrite the function as:
csc x = (sin \(x)^{-1}\)
Taking the derivative of csc x with respect to x using the quotient rule, we get:
d/dx(csc x) = (-1)(sin x) (cos x)
Now we need to simplify this expression using trigonometric identities. Recall that
cot x = cos x/sin x.
Therefore, we can rewrite the above expression as:
d/dx(csc x) = (-1)(sin \(x)^{-2}\) (cos x) = -cot x (sin \(x)^{-1}\) = -csc x cot x
Therefore, we have shown that d/dx(csc x) = -csc x cot x.
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To show that d/dx(csc x) = -csc x cot x, we need to differentiate csc x with respect to x using the chain rule and trigonometric identities.
Recall that csc x is the reciprocal of sin x, so we can write:
csc x = 1/sin x
Then, using the chain rule, we can differentiate csc x as follows:
d/dx(csc x) = d/dx(1/sin x) = -1/sin^2 x * d/dx(sin x)
Now, we can use the derivative of sin x with respect to x, which is cos x:
d/dx(csc x) = -1/sin^2 x * cos x
Next, we can use the identity cot x = cos x/sin x to simplify the expression:
d/dx(csc x) = -cos x/(sin x)^2 = -csc x * cot x
Therefore, we have shown that d/dx(csc x) = -csc x cot x.
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