Answers
Part A. We are asked to determine the derivative of each of the functions. To do that we will use the chain rule:
\(\frac{d}{dx}f(g(x))=f^{\prime}(g(x))g^{\prime}(x)\)This means that we take the derivative of the function as a whole and then we multiply it by the derivative of the function inside the parenthesis.
Let's take Alice's function.
\(f(x)=15(4+3x)^4\)We have the following:
\(\begin{gathered} f(x)=15(g(x))^4 \\ g(x)=4+3x \end{gathered}\)Taking the derivative of f(x) we get:
\(f^{\prime}(x)=60(g(x))^3g^{\prime}(x)\)Now, we take the derivative of g(x):
\(g^{\prime}(x)=3\)Now, we substitute the values:
\(\begin{gathered} f^{\prime}(x)=60(4+3x)^3(3) \\ \\ f^{\prime}(x)=180(4+3x)^3 \end{gathered}\)And thus we get the derivative of the function.
The same procedure is done for the other functions.
Part B.
Let's take the function for Dani's guess:
\(f(x)=\frac{1}{18}(4+3x)^6\)Applying the chain rule we get:
\(f^{\prime}(x)=\frac{6}{18}(4+3x)^5(3)\)Simplifying we get:
\(\begin{gathered} f^{\prime}(x)=\frac{18}{18}(4+3x)^5 \\ \\ f^{\prime}(x)=(4+3x)^5 \end{gathered}\)Therefore, Dani was the student that was correct.
Related Questions
Write in standard form: six hundred seven and twenty-three hundredths *
Answers
Answer:
607.23
Step-by-step explanation:
Answer:
6723
Step-by-step explanation:
What is the reference angle for 292°?
O A. 12°
O B. 22°
O C. 68°
O D. 78°
Answers
C. 68°
292° lies on 4th quadrant.
Reference angle:1st quadrant: angle
2nd quadrant: 180° - angle
3rd quadrant: angle - 180°
4th quadrant: 360° - angle
So, reference angle: 360° - 292° = 68°
PLEASE HELP ME.Match the shape with its area formula Column A Column B 1: Triangle a. A= LW2: Parallegram. b: A=(TTr^2)/23: Semi- circle. c:(bh)/2 or 1/2(bh)4:Trapizoid. D. A= (b1+b2)(h)2
Answers
1. Triangle: the area of the triangle is C. (bh)/2
2:Parallegram: the area is a. LW
3. Semi-circle: the area is b. (pi r^2)/2
4. Trapezoid: the area will be D. (b1+b2)(h)2
A company has two large computers. The slower computer can send all the company’s email in 50 minutes. The faster computer can complete the same job in 30 minutes. If both computers are working together, how long will it take them to do the job?
Answers
Answer:
18 minutes and 45 seconds
Step-by-step explanation:
\(\frac{1}{50}\) + \(\frac{1}{30}\) = \(\frac{3+5}{150}\) = \(\frac{4}{75}\)
1 ÷ \(\frac{4}{75}\) = \(\frac{75}{4}\) = 18' 45''
Answer:
18.75 minutes If A and B work together
Triangle HIJ is similar to triangle KLM find the measure of side KL around your answer to the nearest tenth if necessary
Answers
The measure of side KL from triangle KLM is 22 units.
What are similar triangles?Two triangles are similar if the angles are the same size or the corresponding sides are in the same ratio. Either of these conditions will prove two triangles are similar.
Given that, triangle HIJ is similar to triangle KLM.
From the similar triangles,
JH/MK =HI/KL
31/13.9 =49/KL
31KL=49×13.9
31KL=681.1
KL=681.1/31
KL=21.97
KL≈22
Therefore, the measure of side KL is 22 units.
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Shamin Jewelers sells diamond necklaces for $442 less 10%. Jewelers offers the same necklace for $527 less 34%, 14% What additional rate of discount must offer to meet the competitor's price
Answers
Answer:
The selling price of the diamond necklace at Shamin Jewelers after 10% discount is:
$442 * 0.9 = $397.80
The selling price of the same necklace at the competitor's store after 34% and 14% discount is:
$527 * 0.66 * 0.86 = $247.08
So, Shamin Jewelers needs to offer an additional discount to meet the competitor's price:
$397.80 - $247.08 = $150.72
To calculate the additional rate of discount, we divide the difference by the original selling price at Shamin Jewelers and multiply by 100:
($150.72 / $442) * 100 = 34.11%
Therefore, Shamin Jewelers must offer an additional 34.11% discount to meet the competitor's price.
Step-by-step explanation:
Find the center and radius of the circle with a diameter that has endpoints (-6,10)
and (2,3)Enter the center as an ordered pair, : Enter the radius as a decimal correct to three decimal places :
Answers
Step-by-step explanation:
the center of the circle is the midpoint of the diameter.
and the radius is the distance of the midpoint to either endpoint (or simply half of the distance between the diameter endpoints).
the midpoint between points A and B
(xm, ym) = ((xa + xb)/2, (ya + yb)/2)
in our case the midpoint (center of the circle) is
((-6 + 2)/2, (10 + 3)/2) = (-4/2, 13/2) = (-2, 6.5)
about the radius
diameter² = (-6 - 2)² + (10 - 3)² = (-8)² + 7² = 64 + 49 =
= 113
diameter = sqrt(113) = 10.63014581...
radius = diameter / 2 = 5.315072906... ≈ 5.315
15 POINTS TO ANYBODY THAT SOLVE THIS EQUATION
Answers
Answer:
This is how i had my answer
Hope it helped
Answer:
r=6
Step-by-step explanation:
divide 2.4 in the ratio 1:2
Answers
Answer:
0.8:1.6
Step-by-step explanation:
2.4÷3=0.8
0.8×2=1.6
0.8:1.6
Find The Sum or Difference
(-6x – 3) + (3x – 9)
Answers
Answer:
-3x -12
Step-by-step explanation:
-6x +3x = -3x
-3-9 = -12
The measures of the angles of a triangle are shown in the figure below. Solve for x.
Answers
Answer: 23
Step-by-step explanation:
x = 90 - 67
x = 23
was the expression a^2-b^2 = (a+b)(a-b) invented or discovered?
Answers
Answer:
the expression is invented
Expanding (a + b)(a - b)
= a(a - b) + b(a - b)
= a^2 - ab + ba - b^2
= a^2 - b^2
So factorising the difference between two squares simply reverses the equation
Can someone help me find the standard deviation of this data set plssss
35
27
24
42
25
31
41
34
32
46
29
44
29
35
39
27
41
63
52
31
38
46
39
27
58
32
33
47
36
28
65
53
40
32
39
44
48
59
46
62
22
39
35
29
36
66
33
45
50
62
27
27
41
33
54
44
26
31
45
33
42
63
51
70
42
53
38
28
35
49
47
54
44
40
39
62
30
35
38
26
34
61
19
30
34
26
41
35
26
54
28
32
50
27
31
35
38
26
47
30
28
62
57
56
30
32
31
36
32
42
33
51
35
30
28
20
23
27
33
36
35
42
43
28
36
44
58
41
36
37
49
34
23
39
34
37
62
23
28
26
29
30
37
46
43
56
53
31
36
44
39
51
21
51
34
30
25
31
38
52
49
43
50
31
36
32
28
44
61
57
24
63
28
31
32
26
28
Answers
since it was too long, I just made this python code in order to solve for it:
from math import *
data = [35, 27, 24, 42, 25, 31, 41, 34, 32, 46, 29, 44, 29, 35, 39, 27, 41, 63, 52, 31, 38, 46, 39, 27, 58, 32, 33, 47, 36, 28, 65, 53, 40, 32, 39, 44, 48, 59, 46, 62, 22, 39, 35, 29, 36, 66, 33, 45, 50, 62, 27, 27, 41, 33, 54, 44, 26, 31, 45, 33, 42, 63, 51, 70, 42, 53, 38, 28, 35, 49, 47, 54, 44, 40, 39, 62, 30, 35, 38, 26, 34, 61, 19, 30, 34, 26, 41, 35, 26, 54, 28, 32, 50, 27, 31, 35, 38, 26, 47, 30, 28, 62, 57, 56, 30, 32, 31, 36, 32, 42, 33, 51, 35, 30, 28, 20, 23, 27, 33, 36, 35, 42, 43, 28, 36, 44, 58, 41, 36, 37, 49, 34, 23, 39, 34, 37, 62, 23, 28, 26, 29, 30, 37, 46, 43, 56, 53, 31, 36, 44, 39, 51, 21, 51, 34, 30, 25, 31, 38, 52, 49, 43, 50, 31, 36, 32, 28, 44, 61, 57, 24, 63, 28, 31, 32, 26, 28]
def stand_dev(list_n):
x = 0
sum_num = 0
for x in list_n:
sum_num += list_n[x]
sum_of_n = sum_num
mean = float(sum_of_n / len(list_n))
float(mean)
i = 0
e = 0.0
for i in list_n:
subtract_then_square = (list_n[i] - mean)**2
e += subtract_then_square
result1 = e
new_mean = result1 / len(list_n)
final_result = float(sqrt(new_mean))
return final_result
print(stand_dev(data))
basically, the first chunk of the code calculated the mean of the data. The second chunk would take all of the values from the data, subtract it from the mean, and then square it. I then took the sum of all the new values and average it to get the new mean, then square rooted the new mean to get the answer.
it should be ~= 11.713, but you can always check it by searching up a python compiler online and then insert in the data.
Answer:
I used MS excel and got the attached results.
Note the data is sorted and the data size is 177.
The answer I got is 11.31045226
Consider two functions: f(x)=x2 and the function g(x) shown in the graph.Which statements are true?Select each correct answer.
Answers
Step 1
The graph of f(x) and g(x) are shown below:
1. Both graphs have the same y-intercepts 0.
2.
\(Both\text{ graphs increase on an interval \lparen0 , }\infty)\)3.
\(f(x)\text{ incrases at a faster rate than g\lparen x\rparen does on an interval \lparen0, }\infty)\)Final answer
\(\begin{gathered} f(x)\text{ and g\lparen x\rparen are both increases on an interval \lparen0, }\infty) \\ f(x)\text{ incrases at a faster rate than g\lparen x\rparen does on an interval \lparen0, }\infty) \end{gathered}\)
On thurday, lisa had 5$ in her bank account. she went to target to purchase stickers for her class. each pack of stickers cost 2$
write an inequality that represents s, the number of stickers purchased that resulted in her account ending in -10.
Answers
s = number of sticker packs purchased
x = ending balance in Lisa's bank account
We know that Lisa started with $5 and each pack of stickers costs $2. Therefore, her bank account balance after purchasing s packs of stickers is:
x = 5 - 2s
We also know that her account ended with a balance of -$10. Therefore, we can set up the following inequality:
x = 5 - 2s ≤ -10
Simplifying this inequality:
5 - 2s ≤ -10
-2s ≤ -15
s ≥ 7.5
However, since s represents the number of sticker packs, it must be a whole number. Therefore, the final inequality is:
s ≥ 8
This means that Lisa must have purchased at least 8 packs of stickers in order for her account to end with a balance of -$10.
The diagram shows three forces being applied to a crate on a floor. If the crate is to remain stationary, what amount of force must be applied for z?
Answers
Answer:
800 N
Step-by-step explanation:
I don’t know I just submitted it and that was the answer
In each case, indicate whether the distribution of the random variable X is best described as binomial, geometric, negative binomial, Poisson, uniform, exponential, or normal. (a) X is the sum of the numbers obtained by rolling a die 500 times. (b) X is the number, out of the next 15 customers at a clothing store, who are women. (c) X is the number of murders committed in a city during a week. (d) X is the time of day (measured in hours after midnight) that a meteor strikes Earth. (e) X is the amount of time that it will take until a call center receives a phone call. (f) X is the number of times we drive through an intersection before getting one red light. (g) X is the average GPA of 60 randomly chosen UC San Diego students.
Answers
for the given scenario the distribution is applicable, (a) negative binomial (b) binomial (c) normal (d) exponential (e) Poisson (f) uniform, (g) geometric.
The waiting process is frequently a part of geometric, negative binomial, and exponential random variables; in these cases, the waiting process is continuous until something occurs, rather than a count of trials. (Exponential). Large numbers of independent quantities that are averaged and summed typically have distributions that are close to normal. For observed counts, there are two models: Poisson and binomial. For binomial, there is a predetermined number of trials, leading to a clearly defined maximum count; for Poisson, there is no clearly defined maximum potential count. When there is no evident preference for one interval of distance or time over another such equal-length interval, the distribution is continuous.
We have to identify the best described as binomial, geometric, negative binomial, Poisson, uniform distribution and so on.
(a) X is the sum of the numbers obtained by rolling a die 500 times.
in that case negative binomial distribution suitable choice.
(b) X is the number, out of the next 15 customers at a clothing store, who are women. the binomial is the best distribution for this condition.
(c) X is the number of murders committed in a city during a week.
normal distribution.
(d) X is the time of day (measured in hours after midnight) that a meteor strikes Earth.
exponential distribution.
(e) X is the amount of time that it will take until a call center receives a phone call
Poission distribution.
(f) X is the number of times we drive through an intersection before getting one red light. uniform distribution.
(g)X is the average GPA of 60 randomly chosen UC San Diego students.
geometric distribution.
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TIME REMAINING
44:54
The table below shows the number of cars sold each month for 5 months at two dealerships.
Cars Sold
Month
Admiral Autos
Countywide Cars
Jan
4
9
Feb
19
17
Mar
15
14
Apr
10
10
May
17
15
Which statements are supported by the data in the table? Check all that apply.
The mean number of cars sold in a month is the same at both dealerships.
The median number of cars sold in a month is the same at both dealerships.
The total number of cars sold is the same at both dealerships.
The range of the number of cars sold is the same for both dealerships.
The data for Admiral Autos shows greater variability.
Answers
The statements supported by the data in the table are:
The mean number of cars sold in a month is the same at both dealerships.
The total number of cars sold is the same at both dealerships.
The data for Admiral Autos shows greater variability.
To determine which statements are supported by the data in the table, let's analyze the given information:
The mean number of cars sold in a month is the same at both dealerships.
To calculate the mean, we need to find the average number of cars sold each month at each dealership.
For Admiral Autos:
(4 + 19 + 15 + 10 + 17) / 5 = 65 / 5 = 13
For Countywide Cars:
(9 + 17 + 14 + 10 + 15) / 5 = 65 / 5 = 13
Since both dealerships have an average of 13 cars sold per month, the statement is supported.
The median number of cars sold in a month is the same at both dealerships.
To find the median, we arrange the numbers in ascending order and select the middle value.
For Admiral Autos: 4, 10, 15, 17, 19
Median = 15
For Countywide Cars: 9, 10, 14, 15, 17
Median = 14
Since the medians are different (15 for Admiral Autos and 14 for Countywide Cars), the statement is not supported.
The total number of cars sold is the same at both dealerships.
To find the total number of cars sold, we sum up the values for each dealership.
For Admiral Autos: 4 + 19 + 15 + 10 + 17 = 65
For Countywide Cars: 9 + 17 + 14 + 10 + 15 = 65
Since both dealerships sold a total of 65 cars, the statement is supported.
The range of the number of cars sold is the same for both dealerships.
The range is determined by subtracting the lowest value from the highest value.
For Admiral Autos: 19 - 4 = 15
For Countywide Cars: 17 - 9 = 8
Since the ranges are different (15 for Admiral Autos and 8 for Countywide Cars), the statement is not supported.
The data for Admiral Autos shows greater variability.
To determine the variability, we can look at the range or consider the differences between each data point and the mean.
As we saw earlier, the range for Admiral Autos is 15, while for Countywide Cars, it is 8. Additionally, the data points for Admiral Autos are more spread out, with larger differences from the mean compared to Countywide Cars. Therefore, the statement is supported.
Based on the analysis, the statements supported by the data are:
The mean number of cars sold in a month is the same at both dealerships.
The total number of cars sold is the same at both dealerships.
The data for Admiral Autos shows greater variability.
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The line plot shows the amount of grass seed that a landscaper needs for each of her jobs. What is the total amount of grass seed that the landscape needs?
Answers
Answer:
\(Total = 18\frac{1}{4}\)
Step-by-step explanation:
Given
The attached line plot
Required
The total
To do this, we simply multiply each grass seed by the frequency (i.e. number of dots), then add up the results.
So, we have:
\(Total = \frac{1}{4} * 2 + \frac{1}{2} * 3 + \frac{3}{4} * 1 + 1 * 2 + 1\frac{1}{4} * 1 + 1\frac{1}{2} * 3 + 1\frac{3}{4} * 1 + 2 * 3\)
\(Total = \frac{1}{2} + \frac{3}{2}+ \frac{3}{4} + 2 + 1\frac{1}{4} * 1 + 1\frac{1}{2} * 3 + 1\frac{3}{4} * 1 + 2 * 3\)
Convert fractions to improper fraction
\(Total = \frac{1}{2} + \frac{3}{2}+ \frac{3}{4} + 2 + \frac{5}{4} * 1 + \frac{3}{2} * 3 + \frac{7}{4} * 1 + 6\)
\(Total = \frac{1}{2} + \frac{3}{2}+ \frac{3}{4} + 2 + \frac{5}{4} + \frac{9}{2} + \frac{7}{4} + 6\)
Add fractions
\(Total = 18\frac{1}{4}\)
Hence, the total amount is: \(18\frac{1}{4}\b\) pounds
Need Help With This
Answers
Answer:
Area: 28 square ft
Perimeter: 22 ft
Step-by-step explanation:
To find the area:
A=Lw
A is area, L is length, w is width
A=4*7
A=28
The area is 28 square feet
To find the perimeter:
P=2L+2w
P=2(7)+2(4)
P=14+8
P=22
The perimeter is 22 feet.
Hope this helps!
What rigid motion maps the solid-line figure onto the dotted-line figure?
A. reflection
Brotation
Ctranslation
Answers
The rigid motion of the solid line figure is translated to the dotted line figure.
How to find the rigid motion maps a solid line?Translation describe a function that moves an object a certain distance.
In a translation, every point of the object must be moved in the same direction and for the same distance.
In translation, the object is not resized, rotated or reflected. The object usually remains the same but it moves a certain distance.
Therefore, the rigid motion maps the solid-line figure onto the dotted-line figure by translation
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Can someone help me find the solution for X? Please leave an explanation for me so I can do questions like this by myself!
Also, can you leave an equation that solves for x..?
Answers
The value of angle x in the straight line is 41 degrees.
How to find the angle x?The sum of angles on a straight line is 180 degrees. In other words, angles on a straight line add up to 180°. Angles on a straight line relate to the sum of angles that can be arranged together so that they form a straight line.
Therefore, let's find the angles x.
Using sum of angles on a straight line,
x + 139 = 180
subtract 139 from both sides of the equation
x + 139 - 139 = 180 - 139
Hence,
x = 41 degrees
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The diagram shows EFG. Which term describes point H?
A. Circumcenter
B. Incenter
C. Orthocenter
D. Centroid
Answers
Point H is the ortho-center of our given triangle and option c is the correct choice.
We have been given an image of a triangle. We are asked to find the term that describes point H.
We can see that point H is the point, where, all the altitudes of our given triangle EFF are intersecting.
We know that ortho-center of a triangle is the point, where all altitudes of triangle intersect. Therefore, point H is the ortho-center of our given triangle and option c is the correct choice.
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Write an expression to represent: 9 more than the quotient of 2 and x
Answers
Expression for given numerical is: 9+ (2/x)
Given that we have an word equation that is 9 more than the quotient of 2 and x
A quotient is a quantity produced by the division of two numbers.
Quotient of 2 and x is \(\frac{2}{x}\).
Nine(9) more than 2/x is = 9+ (2/x)
So we have an expression that is:
9+ (2/x)
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an apparel shop is running a special on t-shirts the first shirt cost $15 each additional shirt is cheaper the cost, c, for n t-shirts is given by the equation c=15+9(n+1)
how much will it cost for 2 t shirts
how much for 5 t shirts h
how much does additional cost after the first one? how do you know?
Answers
The equation for the cost of n t-shirts is c = 15 + 9(n + 1), the term 9(n + 1) represents the cost of additional shirts beyond the first shirt, and the coefficient 9 represents the amount by the cost decreases for each additional shirt.
The cost of n t-shirts is given by the equation:
c = 15 + 9(n + 1)
c is the cost in dollars and n is the number of t-shirts.
The cost for 2 t-shirts, we substitute n = 1 into the equation:
c = 15 + 9(1 + 1) = 33
So it will cost \($33\) for 2 t-shirts.
The cost for 5 t-shirts, we substitute n = 4 into the equation:
c = 15 + 9(4 + 1) = 51
So it will cost \($51\) for 5 t-shirts.
The cost of additional shirts after the first one is \($9\) per shirt.
The equation for the cost of n t-shirts is c = 15 + 9(n + 1), the term 9(n + 1) represents the cost of additional shirts beyond the first shirt, and the coefficient 9 represents the amount by which the cost decreases for each additional shirt.
The following formula calculates the price of n t-shirts: c = 15 + 9(n + 1).
n is the quantity of t-shirts, and c represents the price in dollars.
We change n = 1 to represent the price of 2 t-shirts:
c = 15 + 9(1 + 1) = 33
the price will be.
t-shirts for two.
We enter n = 4 to get the price for 5 t-shirts: c = 15 + 9(4 + 1) = 51
the price will be.
Five t-shirts worth.
After the first shirt, additional shirts cost each shirt.
The cost of n t-shirts is given by the equation c = 15 + 9(n + 1), where the phrase 9(n + 1) denotes the price of subsequent shirts after the first shirt and the coefficient 9 denotes the amount by which the cost increases.
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What will be the perimeter and the area of the rectangle below if it is enlarged using a scale factor of 6.5?
Answers
The perimeter and the area of the rectangle is as follows:
perimeter=182 cm
area=2028cm².
What is a rectangle?A rectangle is a closed, four-sided figure in two dimensions. The opposite sides of a rectangle are equal and parallel to one another, and all of its angles are 90 degrees.
The area of a rectangle is equal to the product of the rectangle's length and breadth, or "l" and "w," and is written as follows:
Rectangular Area = (l x w)
The formula for the perimeter, 'P' of a rectangle whose length and width are 'l' and 'w' respectively is 2(l + w).
Formula for the Perimeter of a Rectangle: 2 (Length + Width)
Now in the question given,
Length of the rectangle = 8cm.
Width of the rectangle = 6cm.
So, original perimeter=2 × (8+6) +28 cm and
original area=8 × 6= 48 cm²
Now the scale factor = 6.5
New length = 8 × 6.5 = 52cm
width = 6 × 6.5 = 39cm.
New perimeter = 2(52+39) =182 cm.
New area = 52 × 39 = 2028cm².
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The complete question is:
What will be the perimeter and the area of the rectangle below if it is enlarged using a scale factor of 6.5?
Question 5
60% of 50
Question 6
25% of 16
Answers
Question 6 answer: 4
6=2u + 42 + 2u
solve for u
Answers
Answer:
u = -9
Step-by-step explanation:
Answer:
u=-9
Step-by-step explanation:
2u+2u=4u
6-42=-36
-36/4
-9
What is the smallest positive integer n such that n! ends in at least 2019 zeros?
Answers
Answer:
I think there's 502
Step-by-step explanation:
if this is a olunomical question that should be it I believe, because you have to write in standered form then when it equals zero, then factor it
rewrite 25/99 into a decimal
Answers
Answer:it’s 25:99
Step-by-step explanation: