f(x) = -3x + 8 for f(2h – 5)
Answer:
f(x+2h)=−(f(x)+2hf′(x)+4h22f′′(x)+o(h3)==−f(x)−2hf′(x)−4h22f′′(x)−o(h3)
f(x−2h)=f(x)−2hf′(x)+4h22f′′(x)−o(h3)
8f(x+h)=8(f(x)+hf′(x)+h22f′′(x)+o(h3)=8f(x)+8hf′(x)+8h22f′′(x)+8o(h3)
−8f(x−h)=−8(f(x)−hf′(x)+h22f′′(x)−o(h3)=−8f(x)+8hf′(x)−8h22f′′(x)+8o(h3)
So
|f′(x)−112h[−f(x+2h)+8f(x+h)−8f(x−h)+f(x−2h)]|==|f′(x)−112h[−4hf′(x)−2o(h3)+16hf′(x)+16o(h3)]|==|f′(x)−f′(x)−14o(h3)12|=o(h3)?
2.
We just plug x+2h,x+h,x−h,x−2h to the approximation and get:
f′′(x)≈[−f(x+4h)−16f(x+3h)+16f(x+h)−130f(x)+64f(x+2h)+64f(x−h)+64f(x−2h)−64f(x−3h)]144h2
Step-by-step explanation:
It the 1980 s, it was generally believed that congenital abnormalities affected about 7% of a large nation's children. Some people believe that the increase in the number of chemicals in the environment has led to an increase in the incidence of abnormalities. A recent study examined 393 randomly selected children and found that 32 of them showed signs of an abnormality. Is this strong evidence that the risk has increased? (We consider a P-value of around 5% to represent reasonable evidence.) Complete parts a through f. Assume the independence assumption is met. a) Write appropriate hypotheses. Let p be the proportion of children with genetic abnormalities. Choose the correct answer below. A. H 0
:p=0.07 vs. H A
:p<0.07 B. H 0
:p=0.07 vs. H A
:p>0.07 C. H 0
:p=0.0814 vs. H A
:p<0.0814 D. H 0
:p=0.0814 vs. H A
:p
=0.0814 E. H 0
:p=0.0814 vs. H A
:p>0.0814 F. H 0
:p=0.07 vs. H A
:p
=0.07
The appropriate hypotheses for assessing whether there is strong evidence of an increased risk of congenital abnormalities are: H₀: The proportion of children with genetic abnormalities is equal to or less than 0.07, and H₁: The proportion of children with genetic abnormalities is greater than 0.07.
The appropriate hypotheses in this case would be:
H₀: The proportion of children with genetic abnormalities is equal to or less than 0.07.
H₁: The proportion of children with genetic abnormalities is greater than 0.07.
The hypotheses can be written as:
A. H₀: p = 0.07 vs. H₁: p > 0.07
In this case, we are testing whether there is evidence of an increase in the risk of congenital abnormalities.
The alternative hypothesis (H₁) suggests that the proportion of children with abnormalities is greater than the previously believed 7%, while the null hypothesis (H₀) assumes that the proportion is equal to or less than 7%.
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f(x)= 2x+3/x-1, x ≠ 1, dan f^-1 adalah invers dari f
tentukan :
A. infers fungsi F
B. Nilai dari f^-1 (-3)
Answer:
The answer are
A.
\( {f}^{ - 1} (x) = \frac{x + 3}{x - 2} \)
B.
\( {f}^{ - 1} ( - 3) = 0\)
Step-by-step explanation:
To find the infers we do that
\(f(x) = \frac{2 x + 3}{x - 1 } \\ (x - 1)f(x) = 2x + 3 \\ xf(x) - f(x) = 2x + 3 \\ xf(x) - 2x = f(x) + 3 \\ x(f(x) - 2) = f(x) + 3 \\ x = \frac{f(x) + 3}{f(x) - 2} \\ then \: \\ {f}^{ - 1} (x) = \frac{x + 3}{x - 2} \\ then \\ {f }^{ - 1} ( - 3) = \frac{ - 3 + 3}{ - 3 + 2} = 0\)
∆DEF is similar to ∆ABC and the scale factor from ∆ABC to ∆DEF is 2. In ∆ABC, the largest angle measures 82º. Which measurements below could represent the largest angle in ∆DEF? Select all that apply.
Answer:
B
Step-by-step explanation:
the scale factor of 2 means the sides of Δ DEF are twice those of Δ ABC.
However, corresponding angles remain congruent , then
largest angle in Δ DEF is also 82°
Bill is ten years older than his sister. If Bill was twenty-five years of age in 1983, in what year could he have been born?
Answer:
1968
Step-by-step explanation:
In a recent survey of 600 randomly selected voters in the town of Brookland, 482 are in favor of increasing funding for the town's mental health services. Based on the survey results, approximately how many of Brookland’s 19,310 voters are in favor of increasing funding for the town's mental health services?
Using the information provided above how many in the town are in favor of mental health services funding being increased? From the number of those in favor of increasing funding what is the percentage of voters? If there is a margin of error of 3% what would happen if they increased the number of those randomly selected to 1,200?
Create a document to capture your response. Make sure to show your work and explain how you arrived at your answer with at least 3 complete sentences. Upload to Dropbox when complete.
80.49% of Brookland voters support increasing funding for mental health services.
To estimate the number of voters in favor of increased funding for mental health services in Brookland, one can use the percentage of voters who participated in the survey and apply it to the total number of voters in the city.
The percentage of supporters of the financial increase is calculated by dividing the number of supporters by the total number of survey respondents:
Ratio = (482 / 600) = 0.8033
To estimate the number of voters, we multiply the proportion by the total number of voters in the city:
Estimated number of voters = 0.8033 * 19,310 = 15,541
An estimated 15,541 voters in Brookland support increasing funding for the city's mental health services.
To calculate the percentage of voters, we divide the estimated number of voters by the total number of voters in the city and multiply by 100:
Percentage of voters = (15,541 / 19,310) * 100 = 80.49%
Therefore, approximately 80.49% of Brookland voters support increased funding for mental health services.
If you increase the number of randomly selected voters to 1200, the margin of error decreases. A larger sample size usually provides a more accurate representation of the population.
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Given the following exponential function,
identify whether the change represents
growth or decay, and determine the
percentage rate of increase or decrease.
y = 25(1.071)^x
Answer:
Step-by-step explanation:
The given exponential function will grow at 6.1%
Given,
y =
To find,
identify whether the change represents growth or decay, and determine the percentage rate of increase or decrease.
Solution,
We have,
y =
The equation represents exponential growth because the growth factor is greater than 1.
The general form equation is:
y(x)= a(1-r)^x such that r is the growth percent.
==> 1+r = 1.061
==> r = 0.061 = 6.1%
Find the value of a that makes the ordered pair a solution of the equation
9x - 5y = -9;(a-1,9)
help
Answer:
a = 5
Step-by-step explanation:
assuming (a-1, 9) is in the form of (x,y):
9(a-1) - 5(9) = -9
9a - 9 - 45 = -9
9a = 45
a = 5
Alonso went to the store to buy some almonds. The price per pound of
the almonds is $7.25 per pound and he has a coupon for $3.50 off the
final amount. With the coupon, how much would Alonso have to pay to
buy 5 pounds of almonds? Also, write an expression for the cost to buy
p pounds of almonds, assuming at least one pound is purchased.
The required price of almond and expression are $32.75 and c= $7.25P - $3.5 respectively.
What is pound?Pound is unit used to measure weight of quantity. It is used by the English speaking peoples.It equal to the 16 ounces and 0.454 kilogram.
According to given information:Alonso has a coupon of $3.5, let us consider P pound of almond. And price per pound of almond is $7.25
So, equation for the cost,
Cost(c) = $7.25P - $3.5
Then, the price of 5 pound of almond = $7.25×5 - $3.5
⇒ $36.25 - $3.5 = $32.75
Thus, the price of 5 pounds of almond is $32.75.
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10. The average resting heart rate of a population is 87 beats per minute, with a standard deviation of 11 bpm. Find the z-scores that correspond to each of the following heart rates. Round your answers to the nearest hundredth, if necessary.(a) 110 bpmz = (b) 80 bpmz =
The formula for determining the z score is expressed as
z = (data value - mean)/standard deviation
a) data value = 110
mean = 87
standard deviation = 11
z = (110 - 87)/11
z = 2.09
b) data value = 110
mean = 80
standard deviation = 11
z = (80 - 87)/11
z = - 0.64
Dunni earns money babysitting.She charges $20 for traveling to the job, plus another $5 for each hour she babysits.Yesterday Dunni earned $60 for babysitting job
If a field researcher wanted to learn a political organization's pattern of recruitment over time, the researcher mightbegin by interviewing a fairly recent recruit and ask who introduced that person to the organization. Then theresearcher might interview the person named and ask who introduced that person to the political organization.This would be an example of: systematic sampling. accidental sampling. snowball sampling. quota sampling deviant cases sampling.
Answer:
C. snowball sampling
Step-by-step explanation:
Snowball sampling also known as referral sampling or chain sampling is a sampling method in research where the participants in the research are recruited to find new participants. This is a non-probability sampling method because participants choose other participants through their own insight. Just as a ball takes up more snow as it rolls by, so also this research method takes up more participants as it progresses.
So, when the field researcher who wanted to learn about a political organization's recruiting pattern begins by interviewing a participant who in turn suggests another participant, he has applied the snowball sampling method.
The resulting vector for b − a is < , >, and the resulting vector for 2a − b is < , >.
The vectors are:
The resulting vector b - a is <-5, 7>.The resulting vector 2a - b is <8, -9>.What is a vector?In mathematics, a vector is a quantity that has both magnitude and direction but no position. Examples include velocity and acceleration.To find the vectors:
Use the graph to solve the problem:
The vector a is <3, -2>The vector b is <-2, 5>We can add and subtract the vectors:
a = <3 , -2>b = <-2 , 5>-To find b - a subtract a from b:
b - a = <-2 , 5> - <3 , -2> = <(-2 - 3) , (5 - -2)> = <(-5) , (7)>The resulting vector b - a is <-5, 7>2a means multiply vector a by 2:
a = <3 , -2>2a = <(2 × 3) , (2 × -2) = <6 , -4>Now let's find the resulting vector 2a - b.
- Subtract b from 2a:
2a = <6 , -4>b = <-2 , 5>2a - b = <6 , -4> - <-2 , 5> = <(6 - -2) , (-4 - 5> = <(8) , (-9)> = <8 , -9>The resulting vector 2a - b is <8, -9>
Therefore, the vectors are:
The resulting vector b - a is <-5, 7>.The resulting vector 2a - b is <8, -9>.Know more about vectors here:
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The complete question is given below:
The graph shows vectors a and b the resulting vector for b - a is blank, blank >, and the resulting vector for 2a -b is < blank, blank >.
Calculate for the area of the shaded portion. Take π=22/7.
In a certain chemical, the ratio of zinc to copper is 4 to 15 . A jar of the chemical contains 480 grams of copper. How many grams of zinc does it contain?
The grams of zinc the jar of chemical contain is 128 grams
How to find the number grams of zinc ?In a certain chemical, the ratio of zinc to copper is 4 to 15 .
Therefore, a jar of the chemical contains 480 grams of copper.
The grams of zinc in the jar as follows:
Hence,
ratio of zinc to copper = 4 : 15
Therefore,
let
x = total grams in jar
Hence,
480 = 15 / 19 x
15x = 480 × 19
15x = 9120
x = 9120 / 15
x = 608
Therefore,
amount of zinc = 4 / 19 × 608
amount of zinc = 2432 / 19
amount of zinc = 128 grams
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Can y’all help me out please
Answer:
may or may not be
Explanation:
Because we only know two sides, A-center and C-center, we cannot verify that ABCD is a parallelogram. Corner D could be 40 units away from the center, and Corner B might be 12 units away. If you imagine pulling back the corners (away from the center), the length between two corners can be equal even if the shape is not parallel.
For example, BC could have a length of 10, and AD could have a length of 15. These sides could be at completely different angles/slants (so they might not be parallel), and still maintain a middle measurement of 4.0 on both sides.
However, all sides could be parallel, but we are not provided enough information to confirm this possibility.
Calculate the circumference and area of this circle. 4cm radius
Answer:
the circumference is 25.133 and the area is 50.265
Answer: Using the formula,
Area=π×r2.
Area=π×r2.
=π×(4 cm)2.
=16π cm2≈50.24 cm2.
Step-by-step explanation:
If a finite number of terms are added to a convergent series, then the new series is still convergent.True/False
Answer:
True
Step-by-step explanation:
The statement is true. If a finite number of terms are added to a convergent series, then the new series is still convergent.
A convergent series is a series whose sum approaches a finite limit as the number of terms increases. When you add a finite number of terms to a convergent series, the sum of the series is simply increased by the sum of those additional terms. Since the original series converges to a finite limit, adding a finite sum to that limit will result in another finite limit, meaning that the new series will also be convergent.
In summary, adding a finite number of terms to a convergent series does not change its convergence properties and will result in a new convergent series with an updated finite limit.
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A principal wants to find out if her school needs more bike racks. A survey is taken of 30 students who ride the bus. Why might the sample be biased? Describe in words how a sample could have been done that is more representative of the entire school.
Answer:
The students who ride the bus most likely won't use the bike racks so it doesn't impact them and they probably don't know if they need more bike racks.
Step-by-step explanation:
How can you summarize the ruler placement postulate? you can measure the between points a and b by using as zero.
The summary of the ruler placement postulate is: A direct relationship exists between the set of points on the line and the collection of real numbers, where each point is matched to a single real number and The magnitude of the gap between two points is equal to the absolute value of the subtraction of the two associated values.
The ruler placement postulate states that if two points are given, it is possible to measure the distance between them by taking the point of reference as zero. This means that any point can be chosen as an origin, and the distance between the two points can be calculated by measuring the number of units between them. This postulate also applies to curves, and the distance between two points on a curve can be measured by taking a point of reference as zero and measuring the number of units between them. This postulate is essential in the measurement of distances between points and curves in geometry.
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Which of the following is not determined in the case of multiple linear regression?
Question 4 options:
1)Potential confounding effects from "lurking" variables included in the analysis
2)Observed relationship between predictor and outcome variables adjusting for confounding relationships
3)Causal relationships between predictor and outcome variables adjusting for confounding relationships
4) Potential observed interaction effects between variables Save
It does not determine the observed interaction effects between variables.
In the case of multiple linear regression, the option that is not determined is:
Variable interactions that have been observed to have effects.
Option 1: Multiple linear regression can estimate the observed relationship between predictor and outcome variables after adjusting for confounding relationships and option 2: it can determine the potential confounding effects from lurking variables. Furthermore, numerous direct relapse can evaluate the causal connections among indicator and result factors adapting to jumbling connections (choice 3).
However, the potential observed interaction effects between variables cannot be determined by multiple linear regression on its own. Association impacts happen when the connection between two indicators and the result variable isn't added substance however relies upon the mix of the indicator values. In order to evaluate the effects of interactions, additional analysis methods like including interaction terms and carrying out specific interaction tests are required.
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Two firms producing identical products engage in price competition. Cost of firm 1 is $20 per unit produced and cost of firm 2 is $15 per unit produced. There are no fixed costs. Firms produce only after they learn the quantity demanded. Each firm can choose any real number in the interval [15,25] as its price.
For tie-breaking we will assume that if both firms set the same price, all consumers purchase from firm 2.
The payoff/profit function of firm 1 is:
(p1 - 20)(100 - p1) if p1 is less than or equal to p2,
0 if p1 is greater than p2
The payoff/profit function of firm 2 is:
(p2 - 15)(100 - p2) if p2 is less than p1,
0 if p2 is greater than or equal to p1
Given all of this information, solve the following parts of the problem:
a) is p1 = 20, p2 = 19.50 a Nash Equilibrium?
b) is there a Nash Equilibrium in which Firm 2 makes a positive profit?
c) How many strategies does player 1 have?
d) is p1 = 15, p2 = 15 a Nash Equilibrium?
e) is p1 = 21, p2 = 21 a Nash Equilibrium?
a) No, p1 = 20, p2 = 19.50 is not a Nash Equilibrium.
b) Yes, there is a Nash Equilibrium in which Firm 2 makes a positive profit.
c) Player 1 has infinitely many strategies.
d) Yes, p1 = 15, p2 = 15 is a Nash Equilibrium.
e) No, p1 = 21, p2 = 21 is not a Nash Equilibrium.
What is Nash Equilibrium?Nash Equilibrium is a state of a strategic game where no player has an incentive to deviate from his or her chosen strategy after considering the strategies of other players. A game has more than one Nash equilibrium if players are unable to agree on a cooperative strategy to play.
Finding Nash Equilibrium
a) Is p1 = 20, p2 = 19.50 a Nash Equilibrium?No. Firm 1 has an incentive to decrease the price to 19.49, thus breaking the tie in its favour. So p1=20, p2=19.5 is not a Nash equilibrium.b) Is there a Nash Equilibrium in which Firm 2 makes a positive profit?Yes. There are several equilibria in which Firm 2 makes a positive profit. One such equilibrium is when both firms charge the same price of 15, at which both firms earn a profit of 375.c) How many strategies does player 1 have?Player 1 has infinitely many strategies to choose from as they can choose any real number in the interval [15,25] as their price.d) Is p1 = 15, p2 = 15 a Nash Equilibrium?Yes. This is a Nash Equilibrium because neither firm has an incentive to change their strategy as they are earning non-zero profits. Both firms earn a profit of 375.e) Is p1 = 21, p2 = 21 Nash Equilibrium?No. If Firm 1 changes its price to 20.99, its profit increases from 405 to 407.99. Therefore, p1=21 and p2=21 is not a Nash Equilibrium.Learn more about Nash equilibrium at
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PLS HELP ASAP!!! ^look at picture^^
Answer: f(2) = -2
The 2 is in the x position so look at the x-axis and go down until you reach the line. The point is at (2, -2).
Hope this helps!
Caesar has $180 in his bank account. He needs a total of $2,000 to purchase his uncle's car. He earns $60 per day and says $50 of that amount each day. Which equation can be used to determine the number of days, D, he needs to work to reach his goal of $2,000?
Answer:
Im not 100% sure because I dont have paper, but the answer is..YELLOW and Dark blue
Step-by-step explanation:
If this isnt the answer pls forgive me, and if you can pls gimme brainliest
please help me with both questions I will give brainliest , thank youu!!
Answer:
1st. yes
2nd. no
i don't know
Step-by-step explanation:
Show working out and a diagram.
A boat leaves a buoy and travels at 12km/h on a bearing of 310T for 2 hours and then changes to travel on a bearing of 040T for 1 hour at 16km/h. What is the bearing of the buoy from the boat?
The bearing of an object is the angle of its position to a reference point. It can be determined by considering the clockwise sum of angles starting from the North pole. Thus, the bearing of the buoy to the boat is \(177^{o}\).
The speed of an object is defined as the rate of distance covered with respect to the time taken.
speed = \(\frac{distance covered}{time taken}\)
Thus, the first distance covered is given by:
Distance covered = speed x time taken
= 12 km/h x 2 h
= 24 km
The second distance covered is given as:
Distance covered = speed x time taken
= 16 km/h x 1 h
= 16 km
Applying the Cosine rule to determine distance from the boat to buoy, we have:
\(c^{2}\) = \(a^{2}\) + \(b^{2}\) - 2abCos C
But, C = \(50^{o}\) + \(60^{o}\)
= \(110^{o}\)
\(c^{2}\) = \((16)^{2}\) + \((24)^{2}\) - 2(16)(24) Cos \(110^{o}\)
= 256 + 576 - 768(-0.3420)
= 832 + 262.656
\(c^{2}\) = 1094.656
c = \(\sqrt{1094.656}\)
c = 33.0856
c = 33.0 km
Apply the Sine rule to determine the angle at the stopping point of the boat;
\(\frac{b}{Sin B}\) = \(\frac{c}{Sin C}\)
\(\frac{24}{Sin B}\) = \(\frac{33}{Sin 110}\)
Sin B = \(\frac{24*Sin 110}{33}\)
= 0.6834
B = 43.11
B = \(43^{o}\)
The angle made at the stopping point to the buoy is \(43^{o}\).
So that,
The bearing of the buoy from the boat = \(180^{o}\)- \(3^{o}\)
= \(177^{o}\)
Therefore, the required bearing of the buoy to the boat is \(177^{o}\).
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The bearing of an object is the angle of its position to a reference point. Thus, the bearing of the buoy to the boat is 117°.
What is speed?The speed of an object is defined as the rate of distance covered to the time taken.
speed = Distance / time
Thus, the first distance covered is given by:
Distance covered = speed x time taken
= 12 km/h x 2 h
= 24 km
The second distance covered is given as:
Distance covered = speed x time taken
= 16 km/h x 1 h
= 16 km
Applying the Cosine rule to determine the distance from the boat to buoy, we have:
c² = a² + b² - 2abCos C
= ( 16 )² + ( 24 )² -2(16)(24)Cos110
= 256 + 576 - 768(-0.3420)
= 832 + 262.656
= 1094.656
c² = 1094.656
c= √1094.656
c = 33.10 Km
Apply the Sine rule to determine the angle at the stopping point of the boat;
\(\dfrac{b}{SinB}=\dfrac{c}{SinC}\)
\(\dfrac{24}{SinB}=\dfrac{33}{Sin110}\)
Sin B = \(\dfrac{24\times Sin110}{33}\)
B = 43.11°
The angle made at the stopping point to the buoy is 43.11° .
So that,The bearing of the buoy from the boat = 180 - 3 = 117°
Therefore the bearing of an object is the angle of its position to a reference point. Thus, the bearing of the buoy to the boat is 117°.
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Please help !! 25 points
(No links or ill report you, just reply the answer) thanks
Use the general form of the equation for a circle to help write equations for the circles described below:
a) Center (2, -1) and radius 4
b) center (-2, 2) and radius 3
Step-by-step explanation:
a. (x-2)^2 + (y+1)^2 = 16
b. (x + 2)^2 + (y-2)^2 = 9
Write 3^4 in expanded form. (3^4 means 3 raised to the fourth power.)
A: 3x3
B :3x3x3
C: 3x3x3x3
D: 3x3x3x3x3
Answer:
c because 3.3.3.3 is 3 to the 4th power expanded
if 1/4 of a journey is 100 km what is the length of the journey
Use the picture below please!!
Answer:
AB and BC are Skew
AE and BF are Parallel
Step-by-step explanation: