Answer:
Part 1)
See Below.
Part 2)
[tex]\displaystyle (-0.179, -0.178) \cup (-0.010, 0.012)[/tex]
Step-by-step explanation:
Part 1)
The linear approximation L for a function f at the point x = a is given by:
[tex]\displaystyle L \approx f'(a)(x-a) + f(a)[/tex]
We want to verify that the expression:
[tex]1-36x[/tex]
Is the linear approximation for the function:
[tex]\displaystyle f(x) = \frac{1}{(1+9x)^4}[/tex]
At x = 0.
So, find f'(x). We can use the chain rule:
[tex]\displaystyle f'(x) = -4(1+9x)^{-4-1}\cdot (9)[/tex]
Simplify. Hence:
[tex]\displaystyle f'(x) = -\frac{36}{(1+9x)^{5}}[/tex]
Then the slope of the linear approximation at x = 0 will be:
[tex]\displaystyle f'(1) = -\frac{36}{(1+9(0))^5} = -36[/tex]
And the value of the function at x = 0 is:
[tex]\displaystyle f(0) = \frac{1}{(1+9(0))^4} = 1[/tex]
Thus, the linear approximation will be:
[tex]\displaystyle L = (-36)(x-(0)) + 1 = 1 - 36x[/tex]
Hence verified.
Part B)
We want to determine the values of x for which the linear approximation L is accurate to within 0.1.
In other words:
[tex]\displaystyle \left| f(x) - L(x) \right | \leq 0.1[/tex]
By definition:
[tex]\displaystyle -0.1\leq f(x) - L(x) \leq 0.1[/tex]
Therefore:
[tex]\displaystyle -0.1 \leq \left(\frac{1}{(1+9x)^4} \right) - (1-36x) \leq 0.1[/tex]
We can solve this by using a graphing calculator. Please refer to the graph shown below.
We can see that the inequality is true (i.e. the graph is between y = 0.1 and y = -0.1) for x values between -0.179 and -0.178 as well as -0.010 and 0.012.
In interval notation:
[tex]\displaystyle (-0.179, -0.178) \cup (-0.010, 0.012)[/tex]
Two cars that are 150 miles apart start driving toward each other on parallel roads. The average speed of the first car is 60 miles per hour. The average speed of the second car is 55 miles per hour. Which equation can be used to determine t, the time it takes for the two cars to pass each other? A table showing Rate in mile per hour, Time in hours, and Distance in miles. The first row shows First Car and has 60, t, and 60 t. The second row shows Second Car and has, 55, t, and 55 t.
Answer:
60t + 55t = 150
Step-by-step explanation:
I took the test. I know it's correct!!!
Solve for m∠WUV if m∠TUV= 100 and m∠TUW = 60.
Answer:
20
Step-by-step explanation:
100 + 60 = 160
There are 180 degrees in a triangle so we do 180-160 = 20
here bro hope you answer,if you can't just blank it:)
Answer:
DIRECTION: On your activity notebook, answer each of the following:
A. MODIFIED TRUE OR FALSE. Determine whether each statement is true or false. If the statement is false, explain why.
1. The total area under the normal distribution is infinite.False [its 1]
2. The standard normal distribution is a continuous distribution .True.
3. All variables that are approximately normally distributed can be transformed to standard normal variables.True
4. The z value corresponding to a number below the mean is always negative true..
5. The area under the standard normal distribution to the left of z-0 is negative.
True
To the nearest 100th feet, find the volume of a hollow cylinder having inner radius =150 in, outer radius= 170 in and the height = 220 in
Answer:
R1 = 150 in = 12.5 ft
R2 = 170 in = 14.167 ft
H = 220 in = 18.333 ft
Volume of solid cylinder = Pi * R^2 * H
So the volume of a hollow cylinder must be V = Pi * H * (R2^2 - R1^2)
V = 3.142 * 18.33 * (14.17^2 - 12.5^2) = 2565 ft^3
.
Students in a school were surveyed about their study habits. Forty-two percent of students said they study on weeknights and weekends, 47% said they studied on weekends, and 65% said they study either on weeknights or weekends. If you were to pick one student at random, what is the probability that he or she studies on a weeknight?
Answer:
0.6 = 60% probability that he or she studies on a weeknight.
Step-by-step explanation:
We solve this question treating these events as Venn probabilities.
I am going to say that:
Probability A: Probability of a student studying on weeknights.
Probability B: Probability of a student studying on weekends.
Forty-two percent of students said they study on weeknights and weekends
This means that [tex]P(A \cap B) = 0.42[/tex]
47% said they studied on weekends
This means that [tex]P(B) = 0.47[/tex]
65% said they study either on weeknights or weekends.
This is [tex]P(A \cup B) = 0.65[/tex]
If you were to pick one student at random, what is the probability that he or she studies on a weeknight?
This is P(A), and the equation used is:
[tex]P(A \cup B) = P(A) + P(B) - P(A \cap B)[/tex]
Considering the values we have:
[tex]0.65 = P(A) + 0.47 - 0.42[/tex]
[tex]0.05 + P(A) = 0.65[/tex]
[tex]P(A) = 0.6[/tex]
0.6 = 60% probability that he or she studies on a weeknight.
Answer: 60% joaobezerra Is Right, and Confirmed by Buzz (Acceleration Education)
Step-by-step explanation:
We solve this question by treating these events as Venn probabilities. Forty-two percent of students said they study on weeknights and weekends. This means that 47% said they studied on weekends. This means that 65% said they study either on weeknights or weekends. This is If you were to pick one student at random, what is the probability that he or she studies on a weeknight?
0.6 = 60% that he or she studies on a weeknight.
(02.02)At the Fast-Pack It shipping, the employees can unload 25 trucks in 5 hours. Which of the following is a correct unit rate for this situation?
O 5 hours per truck
1 truck per hour
of a truck per hour
of of an hour per truck
Answer:
1 truck per hour
Step-by-step explanation:
Responde las preguntas 10 y 11 con base al siguiente gráfico. A 10. ¿Cuáles son los nombres de los ángulos de color azul y rojo respectivamente? A. Obtuso y llano. B. Llano y obtuso. C. Obtuso y agudo. D. Agudo y llano. 11. ¿Cuáles son los colores de un ángulo agudo y uno recto respectivamente? A. Naranja y verde. B. Morado y rojo. C. Morado y naranja. D. Verde y naranja. firmaciones ac
Answer:
10) Los ángulos en azul y rojo son llano y obtuso, respectivamente. (Respuesta: B)
11) Los ángulos agudo y recto están diferenciados por los colores morado y naranja, respectivamente. (Respuesta: C)
Step-by-step explanation:
Basándonos estrictamente en lo descrito en la figura, tenemos la siguiente clasificación por colores:
Agudo - Morado.
Plano o Recto - Naranja.
Obtuso - Rojo.
Llano - Azul.
Completo - Negro.
A continuación, se consigna las respuestas en forma de oración:
10) Los ángulos en azul y rojo son llano y obtuso, respectivamente. (Respuesta: B)
11) Los ángulos agudo y recto están diferenciados por los colores morado y naranja, respectivamente. (Respuesta: C)
Please please help me
i dont really know.....
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Ау
What is the pre-image of vertex A' if the image shown
on the graph was created by a reflection across the y-
axis?
(-8. -6)
4-6. 8)
(8.6)
06. -
4
BY
-
Answer:
(- 6, 8 )
Step-by-step explanation:
Under a reflection in the y- axis
a point (x, y ) → (- x, y ) , then
A' (6, 8 ) → A (- 6, 8 )
Then the pre-image of A' is A (- 6, 8 )
The pre-image of vertex A' would be (-8, 6) on the graph was created by a reflection across the y- axis
The pre-image of vertex A' after a reflection across the y-axis can be found by taking the corresponding point on the other side of the y-axis.
If the image is shown on the graph, and vertex A' is located at (8, 6), then the pre-image of vertex A' would be the point on the opposite side of the y-axis, which has the same x-coordinate but the opposite sign for the y-coordinate.
So, the pre-image of vertex A' would be (-8, 6).
To know more about vertex , here
https://brainly.com/question/21191648
#SPJ2
Robin will choose a movie from the Red Box when all movies are in stock. If she
randomly chooses a Romance, Comedy, or Action, what is the probability she will
choose a Romance?
One number is 2 less than a second number.
Twice the second number is 16 more than 4 times
the first. Find the two numbers.
Answer:
x = one number
y = second number
Where,
x = y - 3
2y = 4x - 16
Multiply the first equation by 2 and substitute the second equation into it.
2(x=y-3) : 2x = 2y - 6
2x = (4x - 16) - 6
Combine like terms
2x = 4x - 22
2x - 2x + 22 = 4x - 2x -22 + 22
22 = 2x
22/2 = 2x/2
11 = x
Step-by-step explanation:
Simplify the expression3x 3√648x4y8
Answer:
= 1296x √ xy
Step-by-step explanation:
Apply exponent rule: a^b . a^c = a^b + c 3 . 3 = 3^ 1 + 1
= x . 3^1+1 √648x . 4y . 8
Add the numbers: 1 + 1 = 2
= x . 3^2 √648x . 4y . 8
= 3^2 . 144x √ xy
Refine
= 1296x √ xy
Find the height of a cone with a diameter of 12 m whose volume is 226m Use 3.14 for pi and round your answer to the nearest meter
Answer:
6m
Step-by-step explanation:
h=3(/V πr^2)=3(226/ π·6^2)≈5.99484
round to 6
ALEKS questions driving me insane
Answer:
3000
growth
3.4
Step-by-step explanation:
Answer:
k bestie here we go again...
Initial price: $3200
Function represents growth
Price increases by 4.1% every year
yo so ill give you a trick
the very first number in the equation is ALWAYS the initial price for exponential functions
if the decimal in the parantheses has a 1 in front of it (e.g. 1.041) it's ALWAYS going to be growth
To find how much it increases move the decimal forward by 2 places
I have 1/3 of my garden is parsely, I want to take 4/5 for lettuce. How much of my garden will be lettuce
PLEASE HELP ME ASAP (72 POINTS)
Answer:
d=10.45t
Step-by-step explanation:
The last one is the answer.
Hope this helps!
--Applepi101
Answer:
D) d=10.45t
Step-by-step explanation:
His distance(d) was 100. And his time(t) was 9.58 seconds.
So 100=9.58x
x≈10.44
The answer is D, because 10.45 is greater than 10.44.
I hope this helps!
Determine whether the variation between the indicated quantities is direct or inverse. The number of calories in a cheese pizza and the size of the cheese pizza
Answer:
The variance is direct.
Step-by-step explanation:
Since size of the pizza determines the amount of calories.
Let us say that a 2" x4" strip of pizza has 250 calories.
Then a pizza of twice the size (or 4" x 4") will have twice as many calories (500 calories) .
Home sizes in Anytown, USA have a mean of 2400 square feet and a standard deviation of 450 square feet. What is the probability that a random sample of 50 homes in Anytown, USA has mean square footage less than 2200 square feet
Answer:
0.00084
Step-by-step explanation:
We are given that
Mean,[tex]\mu=2400[/tex] square feet
Standard deviation, [tex]\sigma=450[/tex]square feet
n=50
We have to find the probability that a random sample of 50 homes in Anytown, USA has mean square footage less than 2200 square feet.
[tex]P(x<2200)=P(\frac{x-\mu}{\frac{\sigma}{\sqrt{n}}}<P(\frac{2200-2400}{\frac{450}{\sqrt{50}}})[/tex]
[tex]P(x<2200)=P(Z<\frac{-200}{\frac{450}{\sqrt{50}}})[/tex]
Using the formula
[tex]z=\frac{x-\mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex]P(x<2200)=P(Z<-3.14)[/tex]
[tex]P(X<2200)=0.00084[/tex]
Hence, the probability that a random sample of 50 homes in Anytown, USA has mean square footage less than 2200 square feet=0.00084
Find "n" if the Standard Error of M is 4 and the population standard deviation is 16.
Answer:
n = 16
Step-by-step explanation:
Givem that :
Population Standard deviation , σ = 16
Sample size, n =
Standard Error, S. E = 4
To obtain the standard Error, S. E, we use the relation :
S.E = σ / √n
4 = 16 / √n
√n * 4 = 16
Divide both sides by 4
(√n * 4) / 4 = 16 / 4
√n = 4
Square both sides
n = 4²
n = 16
Hence, Sample size = 16
Use the fact that 1 square mile=640 acres to find the area of a property that measures 7 hectares is for sale.
a. How large is the property in acres?
b. If the property is selling for $150,000, what is the price per acre?
Answer:
a) The property has 17.3 acres.
b) The price per acre is of $8,670.5.
Step-by-step explanation:
The questions are solved by proportions, using a rule of three.
a. How large is the property in acres?
Each hectare has 2.47105 acres.
So 7 hectares will have:
7*2.47105 = 17.3.
The property has 17.3 acres.
b. If the property is selling for $150,000, what is the price per acre?
17.3 acres for $150,000. So
150000/17.3 = $8,670.5.
The price per acre is of $8,670.5.
The cost function in a computer manufacturing plant is C(x) = 0.28x^2-0.7x+1, where C(x) is the cost per hour in millions of dollars and x is the number of items produced per hour in thousands. Determine the minimum production cost.
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Answer:
$562,500 per hour
Step-by-step explanation:
The cost will be a minimum where C'(x) = 0.
C'(x) = 0.56x -0.7 = 0
x = 0.7/0.56 = 1.25
The cost at that production point is ...
C(1.25) = (0.28×1.25 -0.7)1.25 +1 = -0.35×1.25 +1 = 0.5625
The minimum production cost is $562,500 per hour for production of 1250 items per hour.
_____
Additional comment
This is different than the minimum cost per item. This level of production gives a per-item cost of $450. The minimum cost per item is $358.30 at a production level of 1890 per hour.
When a < 0 in the quadratic function y = ax2 + bx + C, the graph of the quadratic function opens _____?
Answer:
downwards
Step-by-step explanation:
Given the quadratic function in standard form
y = ax² + bx + c ( a ≠ 0 )
• If a > 0 then the graph opens upwards
• If a < 0 then the graph opens downwards
Find f(5) for f(x) = 6 (3)
Answer:
5f=18
5f/5f=18/5f
f=3 2/5
p and q are two numbers.whrite down an expression of. a.) the sum of p and q. b) the product of p and q
The value of a car will “depreciate” over time. For example, a car that was worth $24 000 when it was new, is being sold for $13 500 three years later. Determine the annual depreciation rate on this car. Express your final answer as a percent, rounded to one decimal place.
Answer:
The car will depreciate at a rate of 21.14% per year.
Step-by-step explanation:
Given that the value of a car will “depreciate” over time, and, for example, a car that was worth $ 24,000 when it was new, is being sold for $ 13,500 three years later, to determine the annual depreciation rate on this car the following calculation must be performed:
13,500 x (1 + X) ^ 1x3 = 24,000
13,500 x (1 + 0.2114) ^ 3 = 24,000
X = 21.14%
Therefore, the car will depreciate at a rate of 21.14% per year.
Does anyone know which is bigger for a poster Size: 22.375" x 34" or Size: 14.725" x 22.375"
Answer:
22.375" × 34" is the bigger size for a poster
please show steps in solving: B/3 + B/4 + B/6 =
Answer:
= 3b/4
Step-by-step explanation:
= b . 4/12 + b . 3/12 + b . 2/12
Apply the fraction rule: a/c + b/c = a + b/c
= b . 4 + b . 3 + b . 2/12
= 4b + 3b + 2b/12
Add similar elements: 4b + 3b + 2b = 9b
= 9b/12
Cancel 9b/12: 3b/4
= 3b/4
Complete this
sentence: The shortest side
of a triangle is always opposite the
A. longest side
B. angle with the smallest measure
• C. second-longest side
•
D. angle with the greatest measure
Answer:
B
Step-by-step explanation:
The shortest side of a triangle is opposite the smallest angle
The longest side of a triangle is opposite the largest angle
*REVERSE PROPORTION*
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Answer:
33.3%
Step-by-step explanation:
The selling price of £42 is (1 +40%) times the total purchase price.
1.40 × purchase price = £42
purchase price = £42/1.40 = £30
The total profit is 40% of this, so is ...
£30 × 40% = £12
The purchase price of the skirt is ...
total cost - glove cost = skirt cost = £30 -3 = £27
The profit on the skirt is ...
total profit - glove profit = skirt profit = £12 -100% × £3 = £9
Then the percentage profit on the skirt is ...
skirt profit % = skirt profit / skirt cost × 100% = £9/£27 × 100% = 33.3%
The percentage profit on the cost of the skirt was 33.3%.
in a group of boys the number of arrangments of boys 4 boys is 12 times the number of arrangment of 2 boys the number of boys in the group is
Answer:
4*12*2
Step-by-step explanation:
it will be the right answer
Answer:
There are 6 boys in group.
Step-by-step explanation:
Since we have given that
Number of arrangement of 4 boys = 12 times the number of arrangement of 2 boys.
So, Let the number of boys in the group be 'x'.
So, Number of boys in the group will be
\begin{gathered}x=\frac{12\times 2}{4}\\\\x=\frac{24}{4}\\\\x=6\end{gathered}
x=
4
12×2
x=
4
24
x=6
Hence, there are 6 boys in the group.
hope it helps you a follow would be appreciated
