Explanation:
In general, for arbitrary (x, y) pairs, the problem is called an "interpolation" problem. There are a variety of methods of creating interpolation polynomials, or using other functions (not polynomials) to fit a function to a set of points. Much has been written on this subject. We suspect this general case is not what you're interested in.
__
For the usual sorts of tables we see in algebra problems, the relationships are usually polynomial of low degree (linear, quadratic, cubic), or exponential. There may be scale factors and/or translation involved relative to some parent function. Often, the values of x are evenly spaced, which makes the problem simpler.
Polynomial relations
If the x-values are evenly-spaced. then you can determine the nature of the relationship (of those listed in the previous paragraph) by looking at the differences of y-values.
"First differences" are the differences of y-values corresponding to adjacent sequential x-values. For x = 1, 2, 3, 4 and corresponding y = 3, 6, 11, 18 the "first differences" would be 6-3=3, 11-6=5, and 18-11=7. These first differences are not constant. If they were, they would indicate the relation is linear and could be described by a polynomial of first degree.
"Second differences" are the differences of the first differences. In our example, they are 5-3=2 and 7-5=2. These second differences are constant, indicating the relation can be described by a second-degree polynomial, a quadratic.
In general, if the the N-th differences are constant, the relation can be described by a polynomial of N-th degree.
You can always find the polynomial by using the given values to find its coefficients. In our example, we know the polynomial is a quadratic, so we can write it as ...
y = ax^2 +bx +c
and we can fill in values of x and y to get three equations in a, b, c:
3 = a(1^2) +b(1) +c
6 = a(2^2) +b(2) +c
11 = a(3^2) +b(3) +c
These can be solved by any of the usual methods to find (a, b, c) = (1, 0, 2), so the relation is ...
y = x^2 +2
__
Exponential relations
If the first differences have a common ratio, that is an indication the relation is exponential. Again, you can write a general form equation for the relation, then fill in x- and y-values to find the specific coefficients. A form that may work for this is ...
y = a·b^x +c
"c" will represent the horizontal asymptote of the function. Then the initial value (for x=0) will be a+c. If the y-values have a common ratio, then c=0.
__
Finding missing table values
Once you have found the relation, you use it to find missing table values (or any other values of interest). You do this by filling in the information that you know, then solve for the values you don't know.
Using the above example, if we want to find the y-value that corresponds to x=6, we can put 6 where x is:
y = x^2 +2
y = 6^2 +2 = 36 +2 = 38 . . . . (6, 38) is the (x, y) pair
If we want to find the x-value that corresponds to y=27, we can put 27 where y is:
27 = x^2 +2
25 = x^2 . . . . subtract 2
5 = x . . . . . . . take the square root*
_____
* In this example, x = -5 also corresponds to y = 27. In this example, our table uses positive values for x. In other cases, the domain of the relation may include negative values of x. You need to evaluate how the table is constructed to see if that suggests one solution or the other. In this example problem, we have the table ...
(x, y) = (1, 3), (2, 6), (3, 11), (4, 18), (__, 27), (6, __)
so it seems likely that the first blank (x) will be between 4 and 6, and the second blank (y) will be more than 27.
Here is your answer | To determine the relationship between quantities, you must determine what to do to the x-values to make them into y-values. The correct operation must turn every x-value into the corresponding y- value in the table. Once you know the relationship, you can use the same operation on all of the x-values that have unknown y-values.
The best player on a basketball team makes 70% of all free throws. The second-best player makes 65% of all free throws. The third-best player makes 55% of all free throws. Based on their experimental probabilities, estimate the number of free throws each player will make in his or her next 60 attempts. Explain.
For the best player, one equation that gives the estimated number of free throws is
▼
The best player will make about
nothing free throws.
Answer:
Best: 42/60 free throws
Second Best: 39/60 free throws
Third Best: 33/60 free throws
Step-by-step explanation:
Assume the readings on thermometers are normally distributed with a mean of 0degreesC and a standard deviation of 1.00degreesC. Find the probability that a randomly selected thermometer reads between negative 2.05 and negative 1.49 and draw a sketch of the region.
Answer:
[tex]P(-2.05<X<-1.49)=P(\frac{-2.05-\mu}{\sigma}<\frac{X-\mu}{\sigma}<\frac{-1.49-\mu}{\sigma})=P(\frac{-2.05-0}{1}<Z<\frac{-1.49-0}{1})=P(-2.05<z<-1.49)[/tex]
And we can find this probability with this difference
[tex]P(-2.05<z<-1.49)=P(z<-1.49)-P(z<-2.05)=0.068- 0.0202= 0.0478[/tex]
And we can see the figure in the plot attached.
Step-by-step explanation:
Let X the random variable that represent the redings on thermometers of a population, and for this case we know the distribution for X is given by:
[tex]X \sim N(0,1)[/tex]
Where [tex]\mu=0[/tex] and [tex]\sigma=1[/tex]
We are interested on this probability
[tex]P(-2.05<X<-1.49)[/tex]
We can use the z score formula given by:
[tex]z=\frac{x-\mu}{\sigma}[/tex]
Using this formula we got:
[tex]P(-2.05<X<-1.49)=P(\frac{-2.05-\mu}{\sigma}<\frac{X-\mu}{\sigma}<\frac{-1.49-\mu}{\sigma})=P(\frac{-2.05-0}{1}<Z<\frac{-1.49-0}{1})=P(-2.05<z<-1.49)[/tex]
And we can find this probability with this difference
[tex]P(-2.05<z<-1.49)=P(z<-1.49)-P(z<-2.05)=0.068- 0.0202= 0.0478[/tex]
And we can see the figure in the plot attached.
What’s the value of x?
Answer:
Step-by-step explanation:
here ,
6x +238 = 3x+178 ( vertically opposite angles are equal)
so 6x - 3x = 178 -238
3x =-60
x =-60/3
x=-20
hope it helps / please mark me as the brainliest..
Answer:
x= -20
Step-by-step explanation:
The 2 angles are opposite each other. Therefore, they are vertical angles and congruent. We can set them equal to each other and solve.
6x+238=3x+178
To solve the equation, we want to find out what x is. In order to do this, we have to get x by itself. Perform the opposite of what is being done to the equation. Keep in mind, everything done to one side, has to be done to the other.
First, subtract 3x from both sides
6x-3x+238=3x-3x+178
6x-3x+238=178
3x+238=178
Next, subtract 238 from both sides
3x+238-238=178-238
3x=178-238
3x=-60
Finally, divide both sides by 3.
3x/3= -60/3
x=-60/3
x= -20
Recently, the average amount of time to foreclose on a house in the U.S. was reported to be 359 days. Assume that the standard deviation for this population is 90.4 days. A random sample of 42 homes that have completed the foreclosure process was selected. What is the probability that the sample average was less than 375 days?
Answer:
87.49% probability that the sample average was less than 375 days
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal probability distribution
Problems of normally distributed samples are solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem estabilishes 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 can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
In this question, we have that:
[tex]\mu = 359, \sigma = 90.4, n = 42, s = \frac{90.4}{\sqrt{42}} = 13.95[/tex]
What is the probability that the sample average was less than 375 days?
This is the pvalue of Z when X = 375. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{375 - 359}{13.95}[/tex]
[tex]Z = 1.15[/tex]
[tex]Z = 1.15[/tex] has a pvalue of 0.8749.
87.49% probability that the sample average was less than 375 days
In a large population, 57 % of the people have been vaccinated. If 3 people are randomly selected, what is the probability that AT LEAST ONE of them has been vaccinated?
Answer:0.92
Step-by-step explanation:
Given
[tex]57\%[/tex] of Population is vaccinated
So, Probability of a person being vaccinated is [tex]P=0.57[/tex]
and simultaneously , probability of not vaccinated is [tex]1-P[/tex]
[tex]=1-0.57=0.43[/tex]
Now, Probability that atleast one of them has been vaccinated is given by
[tex]=1-P(\text{None of them is vaccinated})[/tex]
[tex]=1-0.43\times 0.43\times 0.43[/tex]
[tex]=1-0.0795[/tex]
[tex]=0.92[/tex]
Answer:
The probability that AT LEAST ONE of them has been vaccinated
P( X ≥1) = 0.920493
Step-by-step explanation:
Step(i):-
Given 57 % of the people have been vaccinated
p = 57% =0.57
q = 1-p =1-0.57 = 0.43
n = 3
[tex]P(X=r) = n_{C_{r} } p^{r} q^{n-r}[/tex]
Step(ii):-
The probability that AT LEAST ONE of them has been vaccinated
P( X ≥1) = P( x =1) + P(x =2)+P(x=3) [tex]P(X\geq 1) = 3_{C_{1} } (0.57)^{1} (0.43)^{3-1} + 3_{C_{2} } (0.57)^{2} (0.43)^{3-2} + 3_{C_{3} } (0.57)^{3} (0.43)^{3-3}[/tex]
[tex]P(X\geq 1) = 3 (0.57) (0.43)^{2} + 3 (0.57)^{2} (0.43) + 1 (0.57)^{3} (0.43)^{0}[/tex]
= 0.316179 + 0.419121 +0.185193
= 0.920493
Final answer:-
The probability that AT LEAST ONE of them has been vaccinated
P( X ≥1) = 0.920493
In a certain school district, it was observed that 24% of the students in the element schools were classified as only children (no siblings). However, in the special program for talented and gifted children, 119 out of 415 students are only children. The school district administrators want to know if the proportion of only children in the special program is significantly different from the proportion for the school district. Test at the α=0.05 level of significance.What is the hypothesized population proportion for this test?
Answer:
We conclude that the proportion of only children in the special program is significantly different from the proportion for the school district.
Step-by-step explanation:
We are given that in a certain school district, it was observed that 24% of the students in the element schools were classified as only children
However, in the special program for talented and gifted children, 119 out of 415 students are only children.
Let p = proportion of only children in the special program.
So, Null Hypothesis, [tex]H_0[/tex] : p = 24% {means that the proportion of only children in the special program is equal to the proportion for the school district}
Alternate Hypothesis, [tex]H_A[/tex] : p [tex]\neq[/tex] 24% {means that the proportion of only children in the special program is significantly different from the proportion for the school district}
The test statistics that would be used here One-sample z-test for proportions;
T.S. = [tex]\frac{\hat p-p}{\sqrt{\frac{p(1-p)}{n} } }[/tex] ~ N(0,1)
where, [tex]\hat p[/tex] = sample proportion of only children in the special program = [tex]\frac{119}{415}[/tex] = 0.29
n = sample of students = 415
The hypothesized population proportion for this test is 0.24.
So, the test statistics = [tex]\frac{0.29-0.24}{\sqrt{\frac{0.24(1-0.24)}{415} } }[/tex]
= 2.385
The value of z test statistic is 2.385.
Now, at 0.05 significance level the z table gives critical value of -1.96 and 1.96 for two-tailed test.
Since our test statistic doesn't lie within the range of critical values of z, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which we reject our null hypothesis.
Therefore, we conclude that the proportion of only children in the special program is significantly different from the proportion for the school district.
Match each term with its notation. Enter the number corresponding to the correct notation in the blank.
______:The number of treatment conditions
______:The number of scores in each treatment
______:The total number of scores in the entire study
______:The sum of the scores for each treatment condition
______:The sum of all of the scores in the research study
______:The F-ratio
1. G
2. k
3. n
4. T
5. n
6. F
Question:
Match each term with its notation. Enter the number corresponding to the correct notation in the blank.
______:The number of treatment conditions
______:The number of scores in each treatment
______:The total number of scores in the entire study
______:The sum of the scores for each treatment condition
______:The sum of all of the scores in the research study
______:The F-ratio
1. G
2. k
3. N
4. T
5. n
6. F
Answer:
i) K :The number of treatment conditions
ii) n :The number of scores in each treatment
iii) N :The total number of scores in the entire study
iv) T :The sum of the scores for each treatment condition
v) G :The sum of all of the scores in the research study
vi) F :The F-ratio
Step-by-step explanation:
Here we are dealing with ANOVA notations.
ANOVA which is the short form for Analysis of Variance is a test in staristics used to compare two population samples to check if they are equal.
Here, we have the following ANOVA notations:
G, K, n, T, N, F
Where, G is said to be the sum of scores in the research study.
K is the number of treatment.
n is the number of scores in each treatment
T is the sum of scores for each treatment condition.
N is the total number of scores in whole study
F is the F-ratio.
Matching them with the terms given, we have the following:
i) K :The number of treatment conditions
ii) n :The number of scores in each treatment
iii) N :The total number of scores in the entire study
iv) T :The sum of the scores for each treatment condition
v) G :The sum of all of the scores in the research study
vi) F :The F-ratio
Note the difference between "N" and "n"
Find the equation of the straight line passing through the point (0, 1)
which is perpendicular to the line
y = -2x + 2
:)
Answer:
[tex]y = \frac{1}{2} x+1[/tex]
Step-by-step explanation:
Perpendicular => So, it will have a slope of a negative reciprocal to this slope
Slope = m = 1/2
Now,
Point = (x,y) = (0,1)
So, x = 0 and y = 1
Putting this in slope-intercept equation to get b
=> [tex]y = mx+b[/tex]
=> 1 = (1/2)(0) + b
=> b = 1
Now putting m and b in the slope intercept equation to get the required equation
=> [tex]y = \frac{1}{2} x+1[/tex]
Answer:
y = \frac{1}{2} x+1
Step-by-step explanation:
Consider that recycling an aluminum can only requires 6% of the energy needed to make the can in the first place. Given that the energy saved by recycling the can will result in enough energy to run a 100W TV for 3 hours. How much energy does it take to make 19 Aluminum cans
Answer:
21829787.23 joules
Step-by-step explanation:
The recycling will require 6%energy if initial energy, let's say x.
94% of x will be used to power a 100W TV for 3 hours
X = (100*3*60*60)/0.94
X = 1148936.17 joules.
To make 19 aluminum cans ,
It will take 1148936.17*19
= 21829787.23 joules
What is the equation of the line perpendicular to y=2/3x + 1 that passes through the point (12,-6) ?
Answer:
y=-3/2x+12
Step-by-step explanation:
perpendicular lines their gradient multiply to form -1 thus gradient line 1=2/3
gradient line 2= -3/2
equation= y=mx+c where m represents gradient
y-(-6)/x-12=-3/2
y+6/x-12=-3/2
y+6=-3/2(x-12)
y+6=-3/2x+18
y= -3/2x+18-6
y=-3/2x+12
An amusement park has 15 roller coasters. In how many ways can you choose 10 of the roller coasters to ride during your visit to the park? *
Answer:
3003 ways
Step-by-step explanation:
We are in a combination or permutation exercise, the difference between them is if the order matters (permutations) or does not matter (combinations),
in this case the order does not matter, since they only ask us for the ways to choose 10 of 15 roller coasters, therefore it would be a combination:
nCr = n! / (r! * (n-r)!
we know that n = 15 and r = 10, we replace:
15C10 = 15! / (10! * (15-10)!
15C10 = 3003
In other words, there are 3003 ways to choose 10 of the 15.
What’s the correct answer for this question?
C. 1/5 chance that they boy did not see the movie.
Answer:
C.
Step-by-step explanation:
The answer is c. Probability has a formula it is, what we want/what we don't want. This means that we can use the table to calculate what the probability is that a randomly selected boy didn't see the movie.
1. 4/16
2. 1/4
Hope this helps! (Please consider giving brainliest)
In 1925, Zbigniew Morón published a rectangle that could be dissected into nine different sized squares as shown in the diagram.
The lengths of the sides of these squares are
1
,
4
,
7
,
8
,
9
,
10
,
14
,
15
and
18.
1
,
4
,
7
,
8
,
9
,
10
,
14
,
15
and
18.
What is the area of Morón’s rectangle?
Answer:
Area of the rectangle = 1056 square units
Step-by-step explanation:
Rectangle published could be dissected into nine different squares with different sizes.
Area of the squares with different measure of sides will be,
For side length = 1 unit
Area of the square = (Side)²
= 1²
= 1 square units
For side length = 4 units
Area of the square = 4² = 16 units²
For side length = 7 units
Area of the square = 7² = 49 units²
For side length = 8 units
Area of the square = 8² = 64 units²
For side length = 9 units
Area of the square = 9² = 81 square units
For side length = 10 units
Area of the square = 10² = 100 square units
For side length = 14 units
Area of the square = 14² = 196 square units
For side length = 15 units
Area of the square = 15² = 225 square units
For side length = 18 units
Area of the square = 18² = 324 square units
Total area of the rectangle by adding these 9 squares
= 1 + 16 + 49 + 64 + 81 + 100 + 196 + 225 + 324
= 1056 square units
write the equation of the line that passes through the points(7, —4) and (—1, 3) first point-slope form, and then im slope-intersept form.
Answer:
The slope of the line is -7/8
When the point (7, –4) is used, the point-slope form of the line is
y+4=(-7/8)(x-7)
The slope-intercept form of the line is y=(-7/8)x+(17/8)
Step-by-step explanation:
plss help bring up my grade please
The easiest way to solve this problem is by calculating the areas of all the sides and adding them together.
Step 1; Calculate the area of the rectangular front & back
A = 2 * (l * w)
= 2 * (25 * 10)
Step 2; Calculate the area of the rectangular sides
A = 2 * (1 * w)
= 2 * (55 * 10)
= 1100 ft^2
Eric's average income for the first 4 months of the year is $1450.25, what must be his average income for the remaining 8 months so that his average income for the year is $1780.75
Answer:
$ 1,946.00
Step-by-step explanation:
Average income per year=total income per month/12 months
total income=average income for first 4 months*4+ total income for 8 months
Let x represent total income total income for remaining 8 months
$1780.75=($1450.25*4+x)/12
$1780.75*12=$5,801+x
$21,369==$5,801+x
x=$21,369-$5,801
x=$15,568
The average income for the remaining eight months=x/8=$15568/8 =$1,946.00
The average income for the remaining 8 months is $ 1,946.00
Complete the table to investigate dilations of
exponential functions.
2
2*
3-2
23.x
-2
1
4
3
4
64
1
8
-1
2
2 3 4
0
a
c
d
e
1
2
4.
12
64
Answer: itz 780
Step-by-step explanation:
If the first term in an arithmetic sequence is -3 and the tenth term is 15, what is the common difference?
A. d = 2
B. d = 3
C. d = 6
D. d = 12
Answer:
2
Step-by-step explanation:
a10=a1+(n-1)d
15=-3+(10-1)d
15+3=9d
d=2
In a game of poker a player receives a subset of 5 cards from a standard deck of 52 cards. There are four suites (clubs, spades, hearts, diamonds) with 13 cards in each suite. What is the probability your hand contains exactly 3 hearts (out of 5 cards)?
Answer:
8.15% probability your hand contains exactly 3 hearts
Step-by-step explanation:
A probability is the number of desired outcomes divided by the number of total outcomes.
The order in which the cards are chosen is not important, so we use the combinations formula to solve this question.
Combinations formula:
[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
What is the probability your hand contains exactly 3 hearts (out of 5 cards)?
We have 52 cards in total.
13 are clubs, 13 are spades, 13 are hearts, 13 are diamonds.
Desired outcomes:
3 hearts, from a set of 13.
Other 2 cards, from a set of 52-13 = 39.
So
[tex]D = C_{13,3}*C_{39,2} = \frac{13!}{3!(13-3)!}*\frac{39!}{2!(39-2)!} = 211926[/tex]
Total outcomes:
5 cards, from a set of 52. So
[tex]T = C_{52,5} = \frac{52!}{5!47!} = 2598960[/tex]
Probabilities:
[tex]p = \frac{D}{T} = \frac{211926}{2598960} = 0.0815[/tex]
8.15% probability your hand contains exactly 3 hearts
List four monthly cost that a homeowner needs to pay?
Answer:
A homeowner has to pay phone bill, home insurance, cable bill, internet bill
Step-by-step explanation:
If the homeowner doesn't pay these then they won't get to continue using it until they pay for it again.
Answer:
The answer should contain any four of the following:
utility fees
association fees
private mortgage insurance (PMI)
title insurance
homeowners insurance
property taxes
Step-by-step explanation: This is the PLATO answer.
The graph of a line passes through the points (0,5) and (-10, 0). What is the
equation of the line?
Answer:
The equation is y=1/2x+5
Step-by-step explanation:
Answer:
y=1/2x+5
Step-by-step explanation:
I learned this last year. I know this is the answer
One of the great mysteries of the world is my hotdogs and hotdog buns come in packages of different sizes hotdogs come in packs of eight and burns came in packs of 12 at your local store what is the least number of each you can buy in order to have a equal number of hot dogs and buns
Answer:
3 pack of hot dogs and 2 pack of buns 24
Step-by-step explanation:
hot dogs come in packs of 8
burns came in packs of 12
what is the least number of each you can buy in order to have a equal number of hot dogs and buns
so to get equal number
we have to look for the LCM of 8 and 12 = 24
therefore the packs will be equal to product
hot dogs come in packs of 8 = 8*3 = 24
burns came in packs of 12 = 12 *2 = 24
therefore, 3 pack of hot dogs and 2 pack of buns 24
10. A rectangular tank has length 4 m, width
12 m and height 3.5 m.
i) If the tank is filled with water to 2/3
of its capacity, calculate the volume
of the water in the tank.
Answer:
112m³
Step-by-step explanation:
VOLUME=L × W × H
= 4m × 12m × 3.5m
= 168m³
THE TANK IS FILLED TO 2/3 OF IT'S CAPACITY
= 2/3 × 168
= 112m³.
Solving a Real-World Inequality
Samuel is running a 3-mile race. He would like to finish the race in under 33 minutes. He has already run for 10.5
minutes. The inequality 10.5 +X< 33 represents the situation.
Solve the inequality. How is the solution interpreted in the context of the problem?
O x< 22.5; Sam hasa maximum of 22.5 minutes left to finish running.
Ox<22.5; Sam has fewer than 22.5 minutes left to finish running.
O x>43.5; Sam has at least 43.5 minutes left to finish running.
O x<43.5; Sam has no more than 43.5 minutes left to finish running.
Answer:
B) x < 22.5; Sam has fewer than 22.5 minutes left to finish running.
Step-by-step explanation:
For this case we have the following inequality:
From here, we define the variable x.
x: number of minutes remaining to finish the race.
From here, we clear the value of x.
We have then:
Therefore, Samuel has less than 22.5 minutes to finish the race in the estimated time.
Answer:
x < 22.5; Sam has fewer than 22.5 minutes left to finish running.
x < 22.5; Sam has fewer than 22.5 minutes left to finish running.
How to solve the inequality?For this case we have the following inequality:
From here, we define the variable x.
x = number of minutes remaining to finish the race.
From here, we clear the value of x.
We have then:
Therefore, Samuel has less than 22.5 minutes to finish the race in the estimated time.
What are examples of inequality?The major examples of social inequality include income gap, gender inequality, health care, and social class. In health care, some individuals receive better and more professional care compared to others.
Learn more about inequality here: brainly.com/question/25275758
#SPJ2
Video Example EXAMPLE 5 Where is the function f(x) = |x| differentiable? SOLUTION If x > 0, then |x| = and we can choose h small enough that x + h > 0 and hence |x + h| = . Therefore, for x > 0 we have
Answer:
Step-by-step explanation:
We say that a function is differentiable if it's derivative exists and it is continous over the domain of the original function. Recall that the function |x| is given as |x| = x if [tex]x\geq 0[/tex] and |x|=-x if x<0. In both cases, we have either the function x or -x, which are one-degree polynomials. So, we can find easily their derivatives. So if f(x) = |x|. Then, we have that
[tex]f'(x) = (x)' = 1 \text{if } x\geq 0[/tex]
[tex]f'(x) = (-x)' = -1 \text{if } x<0[/tex]
We should check what happens x=0, since that is the point where the definition of f changes. We can check that
[tex]\lim_{x\to 0^+} f'(x) = 1[/tex] and
[tex]\lim_{x\to 0^-} f'(x) = -1[/tex]
since this limits are not equal, the derivative is not continous at x=0. Hence, the derivative doesn't exist at x=0.
In this case, we say that |x| is differentiable at any x different from 0.
The waiting times between a subway departure schedule and the arrival of a passenger are uniformly distributed between 0 and 7 minutes. Find the probability that a randomly selected passenger has a waiting time greater than 2.25 minutes.
Answer:
The probability that a randomly selected passenger has a waiting time greater than 2.25 minutes is P=0.68.
Step-by-step explanation:
For a uniform distribution, any value within the minimum and maximum value have the same probability. Outside that interval, the probability is 0.
Then, for a uniform distribution within a and b, the probability P(X>c), being z<c<b is:
[tex]P(X>c)=\dfrac{b-c}{b-a}[/tex]
For our case, with a uniform distribution within 0 and 7 minutes, the probability that a randomly selected passenger has a waiting time greater than 2.25 minutes is:
[tex]P(t>2.25)=\dfrac{7-2.25}{7-0}=\dfrac{4.75}{7}=0.68[/tex]
you have 4 reindeer, Bloopin, Balthazar, gloopin abd prance, and you want to have 3 fly your sleigh. you always have your reindeer fly in a single-file line. How many different ways can you arrange your reindeer?
Answer:
24
Step-by-step explanation:
There are 4 options for the first reindeer.
After the first reindeer is selected, there are 3 options left for the second reindeer.
After the second reindeer is selected, there are 2 options left for the final reindeer.
The number of possible permutations is:
₄P₃ = 4×3×2 = 24
Notice that the alternative hypothesis is a two-tailed test. Suppose ttest_ind method from scipy module is used to perform the test and the output is (-1.99, 0.0512). What is the P-value for this hypothesis test
Answer:
The p-value of the test is 0.0512.
Step-by-step explanation:
The p-value of a test is well-defined as per the probability, [under the null hypothesis (H₀)], of attaining a result equivalent to or more extreme than what was the truly observed value of the test statistic.
In this case the output of the t-test_ind method from scipy module is provided as follows:
Output = (-1.99, 0.0512)
The first value within the parentheses is the test statistic value.
So the test statistic value is, -1.99.
And the second value within the parentheses is the p-value of the test.
So the p-value of the test is 0.0512.
What’s the correct answer for this question?
Answer:
PO = 20
Step-by-step explanation:
They are equidistant from the centre
PG = GO
x-4=1/2x+3
Multiplying both sides by 2
2(x-4)=x+6
2x-8=x+6
2x-x = 6+8
x = 14
Now
PO = 14-4+7+3
PO = 10+10
PO = 20
Convert 78% to a decimal
78% means 78/100=0.78
