By the chain rule,
[tex]\dfrac{\mathrm dw}{\mathrm dt}=\dfrac{\partial w}{\partial x}\dfrac{\mathrm dx}{\mathrm dt}+\dfrac{\partial w}{\partial y}\dfrac{\mathrm dy}{\mathrm dt}+\dfrac{\partial w}{\partial z}\dfrac{\mathrm dz}{\mathrm dt}[/tex]
We have
[tex]w=7ye^x-\ln z\implies\begin{cases}\dfrac{\partial w}{\partial x}=7ye^x\\\\\dfrac{\partial w}{\partial y}=7e^x\\\\\dfrac{\partial w}{\partial z}=-\dfrac1z\end{cases}[/tex]
and
[tex]\begin{cases}x=\ln(t^2+1)\\y=\tan^{-1}t\\z=e^t\end{cases}\implies\begin{cases}\dfrac{\mathrm dx}{\mathrm dt}=\dfrac{2t}{t^2+1}\\\\\dfrac{\mathrm dy}{\mathrm dt}=\dfrac1{t^2+1}\\\\\dfrac{\mathrm dz}{\mathrm dt}=e^t\end{cases}[/tex]
Putting everything together, we get
[tex]\dfrac{\mathrm dw}{\mathrm dt}=\dfrac{14ye^xt}{t^2+1}+\dfrac{7e^x}{t^2+1}-\dfrac{e^t}z[/tex]
[tex]x=\ln(t^2+1)[/tex], so [tex]e^x=e^{\ln(t^2+1)}=t^2+1[/tex], and [tex]z=e^t[/tex], so [tex]\frac{e^t}z=1[/tex].
[tex]\dfrac{\mathrm dw}{\mathrm dt}=14yt+7-1[/tex]
[tex]\dfrac{\mathrm dw}{\mathrm dt}=14t\tan^{-1}t+6[/tex]
Then when [tex]t=1[/tex], the derivative has a value of [tex]\frac{7\pi}2+6[/tex].
Example 3
Question:
The perimeter of a rectangular swimming pool is 150 feet. The length is 15 feet more than the width. Find the length and width.
THE WIDTH=67.5 feet & LENGTH=67.5+15=82.5 feet
What is perimeter of a rectangle?Perimeter of a rectangle (A) is the 2× sum of of its length (l) and width (w).
A=2(l+ w)
Here, given that,
Perimeter=150 feet
Let, width be x
then, length be x +15
ATQ
x+x+15=150
2x+15=150
2x=150-15
2x=135
x=135/2
x=67.5 feet
Then:
WIDTH=67.5 feet
LENGTH=67.5+15
=82.5 feet
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Write the correct order of letter to the finish line. HELP ITS URGENT and btw it’s not L
Answer:
M
hope this helps
Answer:3rd row (abcg) skip a line h
Step-by-step explanation:
Determine the slope of the line that passes through the points: x−8,0,4,5,y,−33,−1,15,19
Answer:
The equation of a line y = ax + b passes point (-8, -33) and point (0, -1) can be formulated by:
(Note: we do not need all of 4 points, 2 points are enough)
-33 = a x (-8) + b
-1 = a x 0 + b
From 2nd equation, we have:
b = -1
From 1st equation, we have:
b - 8 x a = -33
=> -1 - 8 x a = -33
=> 8 x a = 32
=> a = 4
=> The equation of line: y = 4a - 1
Hope this helps!
:)
If y=sin2x+cos2x then dy/dx
2(cos2x - sin2x)
Step-by-step explanation:
Y = sin2x + cos2x
Differentiate wrt x
dy/dx = cos2x . 2 - sin2x . 2
= 2(cos2x - sin2x)
Question 5 (20 points)
A six-sided number cube is rolled twice.
What is the probability that the first roll is an even number and the second roll is a number greater than 4?
5
6
2
3
Ос
1
6
1
3
Saved at 1:47 pm
Review Answers
Answer:
2 the probability would be2/5 because of the two dice
Answer:
6
Step-by-step explanation:
6/12 simpify 1/2
order the values from least to greatest
Step-by-step explanation:
64 2/3 = 16
4 square root 256 = 64
16 3/2 =64
3 square root - 64 = - 24
16 - 24 64 64
What are the solutions to this equation?
Answer:
It would be (1) 5/4 and -5
4x^2+15x-25+0
Answer: (1) 5/4 and -5
I had this in school and i got this right
Hope i helped
have a nice day
A bottling plant fills one-gallon jugs with milk. The labels on the jugs state that the volume of milk they contain is 128 fluid ounces (fl. oz.). Federal law mandates that the jugs must contain no less than the stated volume. The actual volume of milk in the jugs is normally distributed with mean μ=129 fl. oz. and standard deviation σ=0.8 fl. oz. Plant workers take a simple random sample (SRS) of 8 jugs, measure the volume of milk in each jug, and calculate the sample mean.
Use this information to answer questions1. What is the shape of the distribution of sample means?A. Skewed rightB. NormalC. Skewed left2. Calculate the mean of the distribution of sample means. Round your answer to the nearest whole number. 3. Calculate the standard deviation of the distribution of sample means. Round to three decimal places4. If plant workers sampled 100 jugs instead of 8, which one of the following changes in the distribution of means would they see?A. The mean would decrease.B. The standard deviation would increase.C. The standard deviation would decrease.D. The sample means would be uniformly distributed.
Answer:
(1) The correct option is (B).
(2) The mean of the distribution of sample means is 19 fl. oz.
(3) The standard deviation of the distribution of sample means is 0.283 fl. oz.
(4) The correct option is (C).
Step-by-step explanation:
According to the Central Limit Theorem if we have a normal population with mean μ and standard deviation σ and a number of random samples are selected from the population with replacement, then the distribution of the sample mean will be approximately normally distributed.
The mean of the sampling distribution of sample mean will be:
[tex]\mu_{\bar x}=\mu[/tex]
And the standard deviation of the sampling distribution of sample mean will be:
[tex]\sigma_{\bar x}=\frac{\sigma}{\sqrt{n}}[/tex]
The information provided is:
μ = 129
σ = 0.80
n = 8
(1)
The shape of the sampling distribution of sample mean will be Normal.
This is because the population from which the sample is selected is normal.
The correct option is (B).
(2)
Compute the mean of the distribution of sample means as follows:
[tex]\mu_{\bar x}=\mu[/tex]
[tex]=129[/tex]
Thus, the mean of the distribution of sample means is 19 fl. oz.
(3)
Compute the standard deviation of the distribution of sample means as follows:
[tex]\sigma_{\bar x}=\frac{\sigma}{\sqrt{n}}[/tex]
[tex]=\frac{0.80}{\sqrt{8}}\\\\=0.282843\\\\\approx 0.283[/tex]
Thus, the standard deviation of the distribution of sample means is 0.283 fl. oz.
(4)
Any change in the sample size will have no effect on the mean of the distribution of sample means.
But, if the sample is increased or decreased than the standard deviation will be decreased or increased respectively.
This is because the standard deviation of the distribution of sample means is inversely proportional to the sample size.
So, for n = 100 the standard deviation is:
[tex]\sigma_{\bar x}=\frac{\sigma}{\sqrt{n}}[/tex]
[tex]=\frac{0.80}{\sqrt{10}}\\\\=0.282843\\\\\approx 0.08[/tex]
Thus, the standard deviation was decreased.
The correct option is (C).
Using the Central Limit Theorem, it is found that:
1. B. Normal.
2. The mean is of 129 fl. oz.
3. The standard deviation is of 0.283.
4. C. The standard deviation would decrease.
Central Limit TheoremThe Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n is approximately normal with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].For a skewed variable, the sampling distribution is also approximately normal, as long as n is at least 30.Item a:
The underlying distribution is normal, hence the distribution is normal and option B is correct.Item b:
The mean of the population is of 129 fl. oz, hence it is the same for the distribution of sample means.Item c:
The population standard deviation is of [tex]\sigma = 0.8[/tex].A sample of size 8 is taken, hence [tex]n = 8[/tex].Then:
[tex]s = \frac{0.8}{\sqrt{8}} = 0.283[/tex]
Item d:
The standard deviation is inversely proportional to the square root of the sample size, hence it would decrease, and option C is correct.
To learn more about the Central Limit Theorem, you can take a look at https://brainly.com/question/24663213
What is the spread of the data in the dot plot? Number of Apples in Each Bag A dot plot going from 10 to 15. 10 has 2 dots, 11 has 0 dots, 12 has 4 dots, 13 has 3 dots, 14 has 5 dots, and 15 has 6 dots. from 0 to 5 from 10 to 15 from 12 to 15 from 0 to 6
Answer:
10 to 15 (B)
Step-by-step explanation:
Find attached the diagram of the dot plot.
A measure of spread is used to describe the variation in a sample or data set. It is sometimes referred to as a measure of dispersion.
It is usually used together with the mean or median, to provide an overall description of a set of data.
There are two measures of spread: range and standard deviation. Range is the simplest in terms of calculation.
In this question, the range is used to determine the spread of the data set.
From the dot plot,
The range = the highest value - lowest value in a data set.
The highest value = 15
The lowest value = 10
Therefore the spread of the data in the dot plot is from 10 to 15 (B)
Answer:
B: from 10 to 15
Step-by-step explanation:
edg2020
Lynn has two jobs. She earns $7.50 per hour as the hostess for a restaurant and earns
$10 per hour babysitting for a neighbor.
Part 1
Which inequality represents the number of hours working as a hostess, h, and the
number of hours babysitting, b, that Lynn needs in order to earn at least $150 in one
week?
A. h + b > $150
B. h + b 2 $150
7.5h + 10b > $150
• D
7.5h + 10b $150
e here to search
Answer:
7.5h + 10b > $150
Step-by-step explanation:
h represents the amount of hours Lynn works as a hostess for a restaurant, and she gets $7.50 per hour. $7.50h is how much money she gets per hour. b represents the amount of hours Lynn spends working as a babysitter, and she gets $10 per hour. $10b is how much money she gets from babysitting per hour. The total amount of money she gets this week must be more than $150. So the answer is 7.5h + 10b > $150. Hope this helped!
1.What values could replace the "?" in these equations to make them true?
2. How would you explain to a friend who doesn't know about logarithms what the equation
LaTeX: \log_{10}x\:=\:y
log
10
x
=
y
says about x and y?
Answer:
Remember that logarithms are inverse of exponentials. That means the result of the logarithm is equal to the exponent of a power with the same base.
1. (a)[tex]log_{10} (10)=1[/tex]
Notice that the result is one beacuse [tex]10^{1}=10[/tex]
(b)[tex]log_{10}(10000)=4[/tex]
Because [tex]10^{4}=10000[/tex]
(c)[tex]log_{10}(?) =7 \implies 10^{7} =10000000[/tex]
So, [tex]log_{10}(10000000)=7[/tex]
2.I would say to thim that [tex]x[/tex] and [tex]y[/tex] are variables of the logarithm, which be solved by imagine the logarithm as an exponential like
[tex]log_{10} (x)=y \implies 10^{y}=x[/tex]
In other words, the [tex]y[/tex] is the exponent and the [tex]x[/tex] is the result of the exponential.
What will the horizontal axis represent?
Which type of quadrilatera can have exactly 1 pair of parallel side
A rectangle
B rhombus
C square
D trapezoid
6)
What is the discount for a iPod that’s $75 dollars but labeled “ save 15% “
Discount = [tex]\frac{15}{100}[/tex] x 75
= [tex]\frac{1125}{100}[/tex]
= $11.25
A flat object with two sides, one colored red (R), the other green (G), is tossed 2 times. List all possible outcomes of the experiment.
Answer:
3 possible outcomes
Step-by-step explanation
1) R R
2) R G
3) G G
135 UB students were surveyed and asked how many hours a week they spent studying. The results are in the table below?
135 UB students were surveyed and asked how many hours a week they spent studying. The results are in the table below?
Less than 5hrs (5 to10hrs) (More than 10) Total
Male (M) 25 25 20 70
Fmale (F) 20 30 15 65
Total 45 55 35 135
a) Complete the joint and marginal probability.
b) Find the probability that a student studied 5 to 10 hours.
c) Find the probability that a student is a male and spends less than 5 hours studying.
d) Find the probability that a student is a female or spends more than 10 hours studying.
e) Find the probability that a student spends more than 10 hours studying given that the student is a female?
f) Find the probability that a student is a male given that he spends less than 5 hours studyin
Answer:
B) 11/27 ; c.) 5/27; D.) 17/27; E.) 3/13 ; F) 5/9
Step-by-step explanation:
- - - - - <5hrs - - (5 - 10hrs) - - (>10 hrs) - - Total
Male (M) 25 - - - - -- 25 - - - - - 20 - - - - 70
Female (F) 20 - - - - - - 30 - - - - - 15 - - - - 65
Total - - - 45 - - - - - - 55 - - - - - 35 - - - - 135
Probability = (required outcome / Total possible outcomes)
B) probability that a student studied(5 - 10 hours)
P(5 to 10 hours) = n(5 - 10 hours) / n(total) = 55/135 = 11/27
C) Find the probability that a student is a male and spends less than 5 hours studying
P(male and < 5 hours) = n(male ∩> 5 hours) / n(total) = 25/135 = 5/27
D) Find the probability that a student is a female or spends more than 10 hours studying.
P(female) + P(> 10hours) - P(Female ∩ > 10 hours) = 65/135 + 35/135 - 15/135 = 85/135 = 17/27
E.) Find the probability that a student spends more than 10 hours studying given that the student is a female?
n(Female ∩ > 10 hours) / n(Female)
15/65 = 3/13
F) Find the probability that a student is a male given that he spends less than 5 hours studying
n(male ∩ < 5hrs) / n(< 5 hours) = 25/ 45 = 5/9
work out the size of this angle x
Answer:
x = 60 deg (alternate interior angle)
Hope this helps!
:)
Answer:
60
Step-by-step explanation:
“The story began badly,” said the smaller of the small girls, “but it had a beautiful ending.”
“It is the most beautiful story that I ever heard,” said the bigger of the small girls, with immense decision.
“It is the only beautiful story I have ever heard,” said Cyril.
A dissentient opinion came from the aunt.
“A most improper story to tell to young children! You have undermined the effect of years of careful teaching.”
“At any rate,” said the bachelor, collecting his belongings preparatory to leaving the carriage, “I kept them quiet for ten minutes, which was more than you were able to do.”
“Unhappy woman!” he observed to himself as he walked down the platform of Templecombe station; “for the next six months or so those children will assail her in public with demands for an improper story!”
–“The Storyteller,”
Saki
How does the character of the bachelor add to the satire of "The Storyteller”?
His character provides humor in the story by revealing human weaknesses.
His character is greatly exaggerated to make fun of single men such as himself.
He exposes the aunt’s flaws by telling an improper story that occupies the children.
He exposes the aunt’s hypocrisy and ineffectiveness by being mean to the children.
Answer:
Its C, and if your looking for a different answer, try the one above this one.
Step-by-step explanation:
Answer:
C.
Step-by-step explanation:
I think of a number and I add one and then I double it
Answer:
I think of a number "4"
4+1 = 5
then 5+5 or (5X2) = 10
Step-by-step explanation:
Hope this helped :)
The length of a rectangle is increasing at a rate of 4 cm/s and its width is increasing at a rate of 8 cm/s. When the length is 8 cm and the width is 5 cm, how fast is the area of the rectangle increasing?
Answer:
Step-by-step explanation:
[tex]A = lw \nl\frac{\dA}{\dt}[/tex] =[tex]\frac{\dA}{\text{d}l}\frac{\text{d}l}{\dt} + \frac{\dA}{\text{d}w}\frac{\text{d}w}{\dt}[/tex] =[tex]w\frac{\text{d}l}{\dt} + l\frac{\text{d}w}{\dt}[/tex] [tex]\nll = 20 \text{ cm}[/tex] \;\; [tex]\frac{\text{d}l}{\dt} = 8 \text{ cm/s}[/tex] \;\;w = 10 \text{ cm}, \;\; [tex]]\frac{\text{d}w}{\dt} = 3 \text{ cm/s}[/tex] [tex]\nl\frac{\dA}{\dt} =( 10 \text{ cm} )( 8 \text{ cm/s} ) + ( 20 \text{ cm} )( 3 \text{ cm/s} ) =140 \text{ cm}^2\!\text{/s} [/tex]
Given :
The length of a rectangle is increasing at a rate of 4 cm/s and its width is increasing at a rate of 8 cm/s. When the length is 8 cm and the width is 5 cm .To find :-
how fast is the area of the rectangle increasing?Solution :-
As we know that :-
A = lbTo find the rate :-
d(A)/dt = d(lb)/dt .Differenciate :-
dA/dt = l (db/dt ) + b (dl/dt )Substitute :-
dA/dt = 8*8 + 5*4dA/dt = 64 + 20 cm²/s dA/dt = 84 cm²/sJenny runs a daycare center and charges $60 per day for each child. There are currently 50 children enrolled at the daycare. At a recent conference, Jenny was advised to lower her rates in order to stay competitive in her area. For each price decrease of $4 per day, the number of children enrolled at the center increases by two.
Answer:
(60 - 4x)(50 + 2x) = 2,800
Step-by-step explanation:
please help with this
Answer:
10x^2 -4x +6
Step-by-step explanation:
The area of the blue square is
2* 5x^2 = 10x^2
The area of the pink square is
2 * -2x = -4x
The area of the green square is
2 *3 = 6
Add it all together
10x^2 -4x +6
What’s the correct answer for this?
Same slopes, different constant, so parallel lines.
Answer: ... parallel because their slopes are equal. Last choice.
Answer:
D
Step-by-step explanation:
Yes, lines l and k are parallel since they are having equal slopes
The shape of the Gateway Arch in St. Louis,
Missouri resembles a parabola with the
equation h - 0.00635x^2 +4.0005x -0.07875,
where h is the height in feet and z is the
distance from one base in feet,
What is the distance from one base of the arc
to the other? This answer to the nearest foot is equal to u.
Answer:
630 ft
Step-by-step explanation:
The equation of the parabola shaped arc is given as:
[tex]h =-0.00635x^2 +4.0005x -0.07875[/tex]
In a parabola, the line of symmetry divides the parabola into two equal parts.
Therefore, to find the distance from one base of the parabola to the other, we simply multiply the x-value at the line of symmetry by 2.
For a quadratic equation of the form [tex]y=ax^2+bx+c[/tex]:
Equation of symmetry: [tex]x=-\dfrac{b}{2a}[/tex]Therefore, distance from one base of the arc to the other
[tex]=-\dfrac{b}{2a} X 2\\\\=-\dfrac{b}{a}[/tex]
In our given equation:
[tex]a=-0.00635, b=4.0005\\$Therefore:Distance = $ -\dfrac{4.0005}{-0.00635}\\=630$ ft[/tex]
The distance from one base of the arc to the other is 630 ft.
An engineer wants to determine how the weight of a​ gas-powered car,​ x, affects gas​ mileage, y. The accompanying data represent the weights of various domestic cars and their miles per gallon in the city for the most recent model year. Complete parts​ (a) through​ (d) below.Weight (pounds), x Miles per Gallon, y3648 163847 172709 253550 183286 202922 233654 172533 253427 183809 173372 19A) Find the​ least-squares regression line treating weight as the explanatory variable and miles per gallon as the response variable.y with caret = ___x + ___(Round the x coefficient to five decimal places as needed. Round the constant to two decimal places as​ needed.)B) Interpret the slope and​ y-intercept, if appropriate.C) A certain? gas-powered car weighs 3600 pounds and gets 20 miles per gallon. Is the miles per gallon of this car above average or below average for cars of this? weight?D) Would it be reasonable to use the​ least-squares regression line to predict the miles per gallon of a hybrid gas and electric​ car? Why or why​ not?
Answer:
Step-by-step explanation:
Given the following data :
(Weight, miles per gallon) (x, y) = 3648, 19), (1638, 47), (1727, 09), (2535, 50), (1832, 86), (2029, 22), (2336, 54), (1725, 33), (2534, 27), (1838, 09), (1733, 72)
Using the least square regression calculator :
y = -0.00941x + 59.07
B) slope = -0.00941
The slope 'm' of the graphical relationship is -0.009406
Intercept = 59.07 ( where the regression line crosses the x-axis)
C.) Using the regression equation:
y = -0.00941(3600) + 59.07
y = 25.194 gallons (above)
D.) No, because other factors also contribute to gas mileage such as cylinders, Displacement, mdoel e. T. C
Hints- A net is folded at shared edges. Visualize the folding of each shared edge to meet an opposite edge. PLEASEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEDEEEEEEEEEEE answer ASAP! I don’t have much time.
Answer:
The net folds into a cube
Step-by-step explanation:
* The net folds into a cube *
How can we guess? Well here all the surfaces of this 3-dimensional figure are squares, provided the dimensions of each surface are congruent, all being 2 inches. In addition, if we were to fold each of these squares on the net on the appropriate lines, we could imagine it to be a cube, perfectly fit to be as well!
I need more help (: sorry
Answer:
Converse: If I passed, then I studied.
Inverse: If I don't study, then I will not pass
Contrapositive: If I didn't pass, then I didn't study.
Step-by-step explanation:
I will ark the brinlest to the first person who answers.
A student submitted a drawing of their playroom with a scale of 2 inches = 5 feet. On the drawing, the playroom was 6.5 inches wide and 9.25 inches long. What is the ACTUAL AREA of the playroom? (round to the nearest tenth; show your work in numbers)
Answer:
area = 375.8 ft^2
Step-by-step explanation:
The scale is 2 inches = 5 feet.
The room is 6.5 inches wide in the drawing. We need the real width, x.
2 in./5 ft = 6.5 in./x
2x = 5 * 6.5
2x = 32.5
x = 16.25
The real width is 16.25 ft.
The room is 9.25 inches wide in the drawing. We need the real length, y.
2 in./5 ft = 9.25 in./y
2y = 5 * 9.25
2x = 46.25
x = 23.125
The real length is 23.125 ft.
Area of rectangle = length * width
area = 23.125 ft * 16.25 ft
area = 375.78125 ft^2
area = 375.8 ft^2
calculo la superficie de las figuras sabiendo que cada cuadrado mide 5m2
what does the pythagorean theorem and it’s Converse state? why is this theorem important? what are some real world examples in which this theorem is used?
Answer:
The converse of the Pythagorean Theorem states that: If the square of the longest side of the triangle is equal to the sum of the squares of the other two sides of the triangle, then the triangle is a right triangle.
Step-by-step explanation: