An online survey asked a sample of high school students their favorite type of music, and the results were tabulated above. Find the probability that a person chosen at random did not choose pop music, given that the student is a sophomore or a junior.
Answer:
87/103
Step-by-step explanation:
Let f(x) = x^6( x − 8 )^7 / (x^2 +2)^2
Use logarithmic differentiation to determine the derivative.
f ' (x) =________
If
f(x) = x⁶ (x - 8)⁷ / (x² + 2)²
then taking the logarithm of both sides lets us expand the right side as
ln(f(x)) = ln(x⁶ (x - 8)⁷ / (x² + 2)²)
ln(f(x)) = ln(x⁶) + ln((x - 8)⁷) - ln((x² + 2)²)
using the property ln(ab) = ln(a) + ln(b).
We can also use the property ln(aⁿ) = n ln(a), so that
ln(f(x)) = 6 ln(x) + 7 ln(x - 8) - 2 ln(x² + 2)
Then differentiating both sides using the chain rule gives
f'(x)/f(x) = 6 x'/x + 7 (x - 8)'/(x - 8) - 2 (x² + 2)'/(x² + 2)
f'(x)/f(x) = 6 (1)/x + 7 (1)/(x - 8) - 2 (2x)/(x² + 2)
f'(x)/f(x) = 6/x + 7/(x - 8) - 4x/(x² + 2)
Solve for f'(x) :
f'(x) = (6/x + 7/(x - 8) - 4x/(x² + 2)) f(x)
and replace f(x) with the given function :
f'(x) = (6/x + 7/(x - 8) - 4x/(x² + 2)) • x⁶ (x - 8)⁷ / (x² + 2)²
We can expand the product :
f'(x) = 6 x⁵ (x - 8)⁷ / (x² + 2)²+ 7x⁶ (x - 8)⁶ / (x² + 2)² - 4x⁷ (x - 8)⁷ / (x² + 2)³
then simplify by factoring :
f'(x) = x⁵ (x - 8)⁶/(x² + 2)³ • (6 (x - 8) (x² + 2) + 7x (x² + 2) - 4x² (x - 8))
Simplify the rest :
f'(x) = x⁵ (x - 8)⁶ (9x³ - 16x² + 26x - 96)/(x² + 2)³
Pls help and show ur work ASAP I’ll add extra points
Answer:
Slope: 7/5 , Y-int: 1/5
Step-by-step explanation:
To find the slope, lets use the points (-3,-4) and (2,3)
The slope formula is (y2-y1)/(x2-x1) so we will plug in the numbers.
(3-(-4))/(2-(-3))=7/5. 7/5 is the slope (you can also do rise over run)
We find the y-int in many ways but i will show two.
We can make an equation in point-slope form. The formula is: y-y1=m(x-x1) and we use the point (-3,-4).
y-(-4)=7/5(x-(-3))
y+4=7/5x+21/5 (then move the 4 to the other side)
y=7/5x+1/5
The 1/5 is our y-int since we now have it in slope intercept form!
The other method we can use is putting it into slope intercept form first and using (-3,-4) to find the missing variable.
Slope intercept form is y=mx+b, let m be slope, b is y int, and (x,y) is our point
-4=(7/5)(-3)+b
-4=-21/5+b (move -15/7 to other side)
1/5=b !
we get the same answer I hope this helps sorry its long
Problem Situation: Ben buys a table for $240. He also buys 6 chairs that all cost the same amount. His total cost is $720. What is the price of one chair? Use the drop-down menus to complete parts A and B below.
The price of one chair Ben bought is $80 and he bought 6 chairs in total.
What is a numerical expression?A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.
Given, Ben buys a table for $240. He also buys 6 chairs that all cost the same amount.
Assuming each chair costs $x and his total cost is $720.
∴ 240 + 6x = 720.
6x = 720 - 240.
6x = 480.
x = 80
learn more about numerical expressions here :
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What are the prime numbers out of 4 5 6 7 8 9 ?
The sum of two numbers is 58.25. The second number is 14 less than 2 times the first number. What are the two numbers?
plz fast
Answer:
The first number is 24.08 and the second number is 34.17
A line segment has endpoints (-1, -1) and (-1, 2).
Which vertex would form a triangle that is connected to the endpoints of the line segment?
А.
(-1, 6)
B
(-1, -2)
С
(-1,0)
D
(2,-1)
Answer:
D. (2, - 1)Step-by-step explanation:
Both the given points have x- coordinate of -1.
The first three of the answer options have same -1 as the x-coordinate, this means all three points are on the same line.
It is therefore impossible to have those as vertices of a triangle.
Correct option is D
Differentiate y = sin^2x - cos^2x
Using the power and chain rules, the derivative of
y = sin²(x) - cos²(x)
is
dy/dx = 2 sin(x) cos(x) - 2 cos(x) (-sin(x))
dy/dx = 2 sin(x) cos(x) + 2 sin(x) cos(x)
dy/dx = 4 sin(x) cos(x)
and using the double angle identity for sine, this is equivalent to
dy/dx = 2 sin(2x)
Alternatively, we can first simplify y using the double angle identity for cosine:
cos(2x)= cos²(x) - sin²(x)
so that
y = -cos(2x)
and the derivative is
dy/dx = sin(2x) • 2
dy/dx = 2 sin(2x)
2/8 and 1/2 write < or >
Answer:
0.5 > 0.25
Step-by-step explanation:
2/8 = 1/4 = 0.25
1/2 = 0.5
Answer:
<
Step-by-step explanation:
1/2 equals more than 2/8.
Because if u simplify 2/8 it would equal 1/4 which is less than 1/2.
you have to solve for X
Answer:
x = 5/8Step-by-step explanation:
(1/2) / 4 = x / 51 / 8 = x / 5x = 5 / 8Done
Joshua wanted to know the distance between two cities. The scale on the map was 1/2 in = 10 km. The distance between the cities on the map was 2 1/4 in. What was the actual distance between the cities?
Step-by-step explanation:
remark : it is very unusual for a map to mix two measurement norms. they are normally either fully in the American or fully in the metric system.
but let's do the exercise.
the scale says 1/2 in = 10 km
but our measurement on the map brought us quarter inches.
so,
1/2 in = 2/4 in = 10 km
therefore
1/4 in = 10/2 = 5 km
now,
2 1/4 = 9/4 in
this is 9 times 1/4.
therefore, the distance between the 2 cities is
9 × 5 = 45 km.
Find the difference (6d+5) - (2-3d)
Answer:
(9d+3)
Step-by-step explanation:
(6d+5)-(2-3d)
>(6d+5)+(-2+3d)
>{(6d+3d)+(5-2)}
=(9d+3)
A traffic study determined that a larger city population indicates a
longer commute time for drivers. What can we say from this
information?
Answer:
There must he a circulation. May not be causation.
Which expression is a factor of the function's equation? O A. X - 4 OB. 0 O C. X OD. x + 4
Answer:
im pretty sure it's A thx
Using substitution, evaluate the expression b-a, if a = -14 and b = -7.
O 21
O -21
-7
7.
Please help
Over a lengh of 101 inches the hight changes 5" what is the angle?
Answer:
2.83°
Step-by-step explanation:
The tangent of an angle is the ratio of rise to run.
θ = arctan(5/101) ≈ 2.83°
_____
We assume the length is referring to the horizontal distance.
If it is the distance along the path, then the angle is ...
θ = arcsin(5/101) ≈ 2.84°
07
Question 4
What is the 11th term of the geometric sequence
-1.5, -3, -6, -12, ...? /(5 pts)
Your Answer:
Answer:
-1536
Step-by-step explanation:
By taking the general formula for the geometric sequence, we substitute the variables with the values of our sequence, finding -1536 as the 11th term
If the cubic function P(x) includes the points (−4, 0), (0, 0), and (2, 0), which of the following represents this function?
Answer:
See below
Step-by-step explanation:
(-4,0) is the solution to x+4=0
(0,0) is the solution to x=0
(2,0) is the solution to x-2=0
Therefore, (x+4)(x-2)(x) = (x²-2x+4x-8)(x) = (x²+2x-8)(x) = x³+2x²-8x is the function that has the given zeroes
-5(x + 6) = -(5x-9)
Please give me answer!
Answer:
There is no solution to this equation.
Hope this helps :)
Answer:
no solution.
Step-by-step explanation:
carry the -5 and - sign and multiply the numbers within the () signs. so - 5×x and -5×6. which is -5x + -30. the other side will be -5x + 9. so then if you take away the -5x your left with -30 = 9 which is impossible.
Solve for x: 2x + 12= 18 (5 points)
Answer:
X = 3
Step-by-step explanation:
2x = 12 = 18
x +6 = 9
x = 9-6
x = 3
Hope its right <3 Like if it helped
Select the graph of the function f(x) = 4+ 1/x+6
Answer:
F(x) = 4+ 1/x + 6 = 10x + 1
x
I need help asap! Pls :)
Answer:
Step-by-step explanation:
6x + 10 + 2x + 26 = 180
8x + 36 = 180
8x = 144
x = 18
how to solve 1/2(x-6) = 1/2
Answer:
x=7
Step-by-step explanation:
1/2(x-6)=1/2
(1/2)(x)+(1/2)(−6)=1/2
1/2x+−3=1/2
1/2x−3=1/2
1/2x−3+3=1/2+3
1/2x=7/2
2*(1/2x)=2*(7/2)
x=7
tada!
What are the length and width of a rectangular traffic sign if the length exceeds the width by 4 inches and the perimeter is 152 inches?
Answer:
L = 40
w = 36
Step-by-step explanation:
P = 2*L + 2*w
L = w + 4
w = w
P = 152
P = 2*(w + 4) + 2*w Remove the brackets
P = 2w + 8 + 2w Combine and switch sides Use P = 152
4w + 8 = P
4w + 8 = 152 Subtract 8 from both sides.
4w = 152 - 8
4w = 144 Divide by 4
4w/w = 144/4
w = 36
L = w + 4
L = 36 + 4
L = 40
33. Jeremy works at a bank and earns $800 for a 40-hour week. His sister, Beth works at a school and only earns $700 for a 30-hour week. Who makes more per hour?
A. Jeremy makes $10 more per hour
B. Beth makes $10 less per hour
C. Beth makes at least $3 more per hour
D. Jeremy makes at least $5 more per hour
Answer:
Step-by-step explanation:
Jeremy
Pay = 800
Time = 40 hours
Per hour pay= 800/40 = 20 dollars per hour.
Beth
Pay = 700
Time = 30 hours
Per hour Pay= 700 / 30 = 23.33
The answer is C. She gets 23.33 which is 3.33 more than her brother makes.
3+3=6! Easy for kids to learn!
Answer:
indeed
Step-by-step explanation:
3+3=6
The ratio of girls to boys is 5:3 in a class. If there are 15 girls in the class, what is the class size? What is the unit ratio?
Answer:
Try setting up a proportion: [tex]\frac{5}{15}=\frac{3}{x}[/tex] then cross multiply to solve for x which will try you how many boys are in the class. Then add the number of boys and girls together.
Step-by-step explanation:
HELP ME ASAP!!!
Question 3(Multiple Choice Worth 5 points)
(04.04 MC)
If a sprinkler waters 1 over 15 of a lawn in 1 over 3 hour, how much time will it take to water the entire lawn?
5 hours
15 hours
18 hours
45 hours
It would take 5 hours.
1/15 of the lawn in 1/3 hours means it takes 1 hour to water 3/15 of the lawn aka 1/5
1/5 of the lawn in 1 hour would mean it takes 5 hours to finish watering the entire lawn.
Ax+2y=10 through the point (4,3)
Answer:
can you give more context to the question and I will answer it in the comments? thanks!
Answer:
Slope-intercept form y=10x-37
Point slope form y-3=10(x-4)
Step-by-step explanation:
QD = 20000 -3P QS = 15000 +2P
The equilibrium price of the commodity at the given demand and supply is 1,000.
The given parameters:
Quantity demanded, QD = 20,000 - 3PQuantity supplied, QS = 15,000 + 2PThe equilibrium price of the commodity is calculated as follows;
At equilibrium price, the demand curve and supply curve cross each other.
[tex]QS= QD\\\\15,000 +2P = 20,000 - 3P\\\\2P+3P = 20,000 - 15,000\\\\5P = 5,000[/tex]
[tex]P = \frac{5,000}{5} \\\\P = 1,000[/tex]
Thus, the equilibrium price of the commodity is 1,000.
The complete question is below;
Determine the equilibrium price, if QD = 20000 -3P and QS = 15000 +2P.
Learn more about equilibrium price here: https://brainly.com/question/22569960