Answer:
83 There is an elixir
total quantity of elixir = 500 mL
quantity of elixir use in one dose = 6 mL
number of dose in 500 mL = 500/6
83.333
Suppose you and a friend are playing a game that involves flipping a fair coin 3 times. Let X = the number of times that the coin shows heads. The probability distribution of X is shown in the table.
The expected number of heads is ______.
The standard deviation of the number of heads is _____. Round to three decimal places.
Answer:
Step-by-step explanation:
i’m highly confused somebody help me please
In the diagram, the area of the square c is 2009
How to find the area of square cThe area of the square is solved using the formula
length x length
The lenght is caluclalted using Pythagoras theorem given by the the formula
hypotenuse² = opposite² + adjacent²
plugging the values as in the problem
let x be the required dimensions
x² = 35² + 28²
x² = 1225 + 784
x² = 2009
x = √2009
x = 44.82
Area of the square is x² = 2009
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g 28. explain whether a variable can be both a. nominal and ordinal b. interval and categorical c. discrete and interval
A variable can be both Nominal and ordinal as shown in the explanation below.
Nominal data is defined as data that's used for naming or labeling variables, without any quantitative value. It's occasionally called “ named ” data – a meaning chased from the word nominal.
Ordinal data is a type of categorical data with an order. The variables in ordinal data are listed in an ordered manner. The ordinal variables are generally numbered, so as to indicate the order of the list.
Age can be both nominal and ordinal data depending on the question types. I.e “ How old are you ” is used to collect nominal data while “ Are you the firstborn or What position are you in your family ” is used to collect ordinal data.
An interval variable is analogous to an ordinal variable, except that the intervals between the values of the numerical variable are inversely spaced.
A categorical variable( occasionally called a nominal variable) is one that has two or further orders, but there's no natural ordering to the orders.
separate variables are innumerable in a finite quantum of time. For illustration, you can count the change in your fund. You can count the plutocrat in your bank account. You could also count the quantum of plutocrat in everyone’s bank accounts. It might take you a long time to count that last item, but the point is it’s still innumerable.
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determine whether the lines and are parallel, skew, or intersecting. if they intersect, find the point of intersection. stewart, james. essential calculus (p. 579). cengage textbook. kindle edition.
The lines L1 and L2 are not parallel and intersect at a single point. We have also found the point of intersection.
If the direction vectors are parallel, then the lines are parallel. If the direction vectors are not parallel but do not intersect, then the lines are skew. If the direction vectors are not parallel and do intersect, then the lines intersect at a single point.
To determine whether the given lines are parallel, skew, or intersecting, we need to compare their direction vectors. The direction vectors of the lines are the coefficients of the parameters t and s in the respective equations. Thus, the direction vector of L1 is <2,-1,3> and the direction vector of L2 is <4,-2,5>.
To check whether the direction vectors are parallel, we can compute their cross product. If the cross product is the zero vector, then the direction vectors are parallel.
<2,-1,3> × <4,-2,5> = (7,2,-10)
Since the cross product is not zero, the direction vectors are not parallel. Thus, the lines are either skew or intersecting.
To determine whether the lines are intersecting, we can set the parametric equations of the lines equal to each other and solve for t and s. This will give us the point of intersection.
3 + 2t = 1 + 4s
4 - t = 3 - 2s
1 + 3t = 4 + 5s
Rearranging the equations, we get:
2t - 4s = -2
t + 2s = 1
3t - 5s = 3
Using Gaussian elimination or other methods, we can solve for t and s:
t = 11/13
s = 2/13
Substituting these values back into either equation gives us the point of intersection:
x = 3 + 2(11/13) = 37/13
y = 4 - (11/13) = 41/13
z = 1 + 3(11/13) = 40/13
Thus, the lines intersect at the point (37/13, 41/13, 40/13).
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Complete Question:
Determine whether the lines L1 and L2 are parallel, skew, or intersecting. If they intersect, find the point of intersection.
L1: x = 3 + 2t, y = 4 – t, z = 1 + 3t
L2: x = 1 + 4s, y = 3 – 2s, z = 4 + 5s
A species with an initial population of 350
is growing in an environment where the
carrying capacity is 7000. After 5 years
the population is up to 900. Find the
logistic function that models this
population as a function of time.
Answer:
the logistic function that models the population of this species as a function of time is P(t) = 7000 / (1 + 0.05 * e^(-0.1682 * t)).
Step-by-step explanation:
We can use the logistic growth equation to model the population of this species as a function of time:
P(t) = K / (1 + A * e^(-r * t))
Where:
P(t) is the population at time t
K is the carrying capacity of the environment
A is the initial population as a proportion of the carrying capacity (A = P(0)/K)
r is the growth rate of the population
We are given that the initial population A is 350/7000 = 0.05 (since the carrying capacity is 7000). We are also given that after 5 years the population has grown to 900. So we can use this information to find the growth rate r:
P(5) = 900 = K / (1 + A * e^(-r * 5))
We also know that the carrying capacity K is 7000. Substituting these values, we get:
900 = 7000 / (1 + 0.05 * e^(-r * 5))
Multiplying both sides by the denominator and simplifying, we get:
1 + 0.05 * e^(-r * 5) = 7.777...
Subtracting 1 from both sides, we get:
0.05 * e^(-r * 5) = 6.777...
Dividing both sides by 0.05, we get:
e^(-r * 5) = 135.555...
Taking the natural logarithm of both sides, we get:
-ln(135.555...) = -r * 5
Solving for r, we get:
r = 0.1682...
Now that we have the growth rate r, we can use the logistic growth equation to find the function that models the population as a function of time:
P(t) = 7000 / (1 + 0.05 * e^(-0.1682 * t))
Therefore, the logistic function that models the population of this species as a function of time is P(t) = 7000 / (1 + 0.05 * e^(-0.1682 * t)).
In a running competition, a bronze, silver and gold medal must be given to the top three girls and top three boys. If 7 boys and 14 girls are competing, how many different ways could the six medals possibly be given out?
Answer:
there are 458640 different ways to award the six medals.
Step-by-step explanation:
There are two distinct groups in the competition, boys and girls. The order in which the medals are awarded to the groups does not matter, so we can count the number of ways to award medals to the boys and the girls separately, and then multiply the results.
For the boys, there are 7 possible candidates for the gold medal. Once the gold medalist is chosen, there are 6 remaining candidates for the silver medal, and 5 candidates for the bronze medal. So, there are 7 x 6 x 5 = 210 ways to award medals to the boys.
Similarly, for the girls, there are 14 possible candidates for the gold medal. Once the gold medalist is chosen, there are 13 remaining candidates for the silver medal, and 12 candidates for the bronze medal. So, there are 14 x 13 x 12 = 2184 ways to award medals to the girls.
To get the total number of ways to award the six medals, we multiply the number of ways to award medals to the boys by the number of ways to award medals to the girls:
Total number of ways = 210 x 2184 = 458640
Therefore, there are 458640 different ways to award the six medals.
The cost of 2 game apps is $3.50; the cost of 5 game apps is $8.75. The graph below represents this linear relationship. Select all true statements about the graph.
The statement (i) and (iv) is true.
What is linear equation?An equation containing variables with its highest power as one is called linear equation.
The cost of 2 game apps is $3.50; the cost of 5 game apps is $8.75.
The graph below represents the linear relationship.
By the graph, the equation of the graph is y=1.75x
And the point (0,0) lies on the graph.
The points (7.3,6) and (31.75,51) is not on the line.
Hence, the statement (i) and (iv) is true.
Question:
The cost of 2 game apps is $3.50; the cost of 5 game apps is $8.75.The graph below represents this linear relationship. Select all true statements about the graph.
(i) The equation of the graph is y=1.75x.
(ii) The point (7.3,6) lies on the line.
(iii) The point (31.75,51) lies on the line.
(iv) The point (0,0) lies on the line.
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To determine if a sum is reasonable you can round each
number to the nearest whole and compare the
estimated sum to the actual sum.
What key phrases did you use?
Look at the tenths place to round to the nearest
whole number.
Compare the estimated sum to the actual sum.
The estimated answer is close to the actual answer.
Round each number to the nearest whole
Compare the estimated sum to the actual sum
Look at the tenths place to round to the nearest whole number
The estimated answer is close to the actual answer
What is Equation?Two or more expressions with an Equal sign is called as Equation.
The key phrases used are:
Round each number to the nearest whole
Compare the estimated sum to the actual sum
Look at the tenths place to round to the nearest whole number
The estimated answer is close to the actual answer
These phrases are all related to the process of approximating a sum by rounding the addends to the nearest whole number and comparing the resulting estimate to the exact sum.
Hence, Round each number to the nearest whole
Compare the estimated sum to the actual sum
Look at the tenths place to round to the nearest whole number
The estimated answer is close to the actual answer
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Chris needs 9 tiles to cover length of floor each tile is 7/8 of an inch what is the total length of tiles
The total length of the tiles that Chris needs to cover the floor is 63/8 inches.
What is Multiplication?Multiplication is a method of finding the product of two or more numbers
We need to find the total length of the tiles, we need to multiply the number of tiles by the length of each tile.
The number of tiles Chris needs is 9.
The length of each tile is 7/8 of an inch.
To find the total length of the tiles, we can multiply the number of tiles by the length of each tile as follows:
Total length of tiles = Number of tiles x Length of each tile
Total length of tiles = 9 x (7/8) inches
Total length of tiles = 63/8 inches
Therefore, the total length of the tiles that Chris needs to cover the floor is 63/8 inches.
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Complete question is given below.
Chris needs 9 tiles to cover length of floor, each tile is 7/8 of an inch what is the total length of tiles?
2 is added to five times a number and the result is 72 what is the number
Answer:
the number is 14.
Step-by-step explanation:
Let's start by using algebra to solve the problem.
We can translate the given information into an equation:
5x + 2 = 72
where x is the unknown number.
To solve for x, we need to isolate it on one side of the equation. We can do this by first subtracting 2 from both sides:
5x = 70
Then, we can divide both sides by 5:
x = 14
Therefore, the number is 14.
A system may or may not be:
1.) Memoryless
2.) Time Invariant
3.) Linear
4.) Casual
5.) Stable
Determine which of these properties hold and which do not hold for each of the following continuous-time systems. Justify your answers. In each example, y(t) denotes the system output and x(t) is the system input.
a.) y(t)=x(t-2)=x(2-t)
b.) y(t)=[cos(3t)]x(t)
c.) y(t)=\int2t-infinity(x(?t)dt
d.) y(t)=0 for t<0 & x(t)+x(t-2) for t>or=0
e.) y(t)=0 for x(t)<0 & x(t)+x(t-2) for x(t)>or=0
f.) y(t)=x(t/3)
g.) y(t)=dx(t)/dt
A system may or may not be:
a.) Memoryless: Yes, Time Invariant: Yes, Linear: Yes, Casual: No, Stable: Yes
b.) Memoryless: No, Time Invariant: No, Linear: No, Casual: No, Stable: Yes
c.) Memoryless: No, Time Invariant: No, Linear: No, Casual: Yes, Stable: Yes
d.) Memoryless: Yes, Time Invariant: No, Linear: No, Casual: No, Stable: Yes
e.) Memoryless: Yes, Time Invariant: No, Linear: No, Casual: No, Stable: Yes
f.) Memoryless: No, Time Invariant: Yes, Linear: Yes, Casual: No, Stable: Yes
g.) Memoryless: Yes, Time Invariant: Yes, Linear: No, Casual: Yes, Stable: Yes
A memoryless, time invariant, linear, casual, and stable system is an idealized system in which the output is directly proportional to the input and the output at any given time is independent of the outputs at any other time.
The system is stable in the sense that the output does not grow indefinitely as the input increases, and it is casual in the sense that the output at any given time is only affected by the inputs at previous times.
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The linear system above represents the sales of large and small popcorn servings at a movie theater for two consecutive days. 42L+ 61S=$393
59L+78S=$529
What is the size of the augmented matrix for this system?
answer choices
3 x 2
2 x 3
3 x 3
2 x 4
The size of the augmented matrix for this system will be 2x3. Option B is the correct answer.
Augmented matrix is a mathematical tool developed in matrix theory to solve linear equations that combine two matrices or vectors to make a new matrix type.
For solving linear equations, the coefficients of the linear equations are written in a matrix form with a column beside it containing its constant values, which makes it an augmented matrix.
one example of an augmented matrix is,
x+y=1
x-y=2
can be represented as
= [tex]\left[\begin{array}{ccc}42&61&|393\\59&78&|529\\\end{array}\right][/tex]
In the given question the linear equations contain two variables, hence the number of rows in the augmented matrix will be 2.
Since it is an augmented matrix it will contain 3 columns with 2 columns of the coefficient matrix and 1 column of the constant matrix.
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What are the zeros of the function y = 2x^2+7x+3
x=-1/2 and x=-3 are the zeros of the function y =2x²+7x+3
What is quadratic equation?A quadratic equation is a second-order polynomial equation in a single variable x , ax²+bx+c=0. with a ≠ 0 .
The given function is y= 2x²+7x+3
Factor out the equation
2x²+6x+x+3
2x(x+3)+(x+3)
(2x+1)(x+3)=0
So the roots we get
2x+1=0
x=-1/2 is one zero and x=-3 is another zero.
Hence, x=-1/2 and x=-3 are the zeros of the function y =2x²+7x+3
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if it is assumed that all 52 5 poker hands are equally likely, what is the probability of being dealt
The probability of being dealt a flush is 0.001980, probability of being dealt a one pair is 0.422569, probability of being dealt two pairs is 0.04753.
a) First select a suit: 4 choices
then, we can have to select 5 cards out of 13: C(13, 5)
required probability: 4*C(13, 5)/C(52, 5)
= 0.001980
b)- We have to select two cards to make a pair: C(4, 2) choices (we have to select 2 from 4 because a suit can't have 2 cards of same number, so we are selecting 2 suits from 4),
then select a number for the pair: 13 choices,
now for remaining three cards: each card can be of same suit but number must be different, i.e. 4³*C(12, 3)
required probability: 13*C(4, 2) * C(12, 3) *4³ / C(52, 5)
= 0.422569
c)- First, we have to select two numbers for two pairs: C(13, 2) ,
Select suits for both pairs: C(4, 2) * C(4, 2) ,
For the remaining one card: 11 choices for the number and 4 choices for the suit,
required probability: C(13, 2)*C(4, 2)*C(4, 2)*11*4/C(52, 5)
= 0.04753
Probability means possibility. It's a branch of mathematics that deals with the circumstance of a arbitrary event. The value is expressed from zero to one. Probability has been introduced in Maths to prognosticate how likely events are to be. The meaning of probability is principally the extent to which commodity is likely to be.
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Complete question:
If it is assumed that all (52 5) poker hands are equally likely, what is the probability of being dealt (a) a flush? (A hand is said to be a flush if all 5 cards are of the same suit.)
(b) one pair? (This occurs when the cards have denominations a, a, b, c, d, wherea, b, c, and d are all distinct.)
(c) two pairs? (This occurs when the cards have denominations a, a, b, b, c, wherea, b, andc are all distinct.)
target sells24 bottles for 3 dollars and 36 for 4 dollars
Buying 36 bottles for $4 is cheaper than buying 3 bottles for 24.
What is a unitary method?A unitary method is a mathematical way of obtaining the value of a single unit and then deriving any no. of given units by multiplying it with the single unit.
Given, Target sells 24 bottles for 3$,
Therefore, The unit price of a bottle is $(3/24) = $0.125.
Target also sells 36 bottles for $4,
Therefore, The unit price of a bottle is,
= $(4/36) = $0.11.
So, Buying 36 bottles for $4 is cheaper.
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What is the answer??? I need help ASAP
Answer: x = 41
Step-by-step explanation:
When you add supplementary angles together, you should have a total of 180 degrees. You can set up and equation like this...
(2x - 25) + 3x = 180
Combine like terms. 5x - 25 = 180
Add 25 to both sides to help isolate x 5x = 205
Divide by 5 to both sides to get x by itself. x = 41
Identify the circumstances in which the median rather than the mean is the preferred measure of central tendency. (Select all that apply.)
undetermined scores
nominal scale
large mean
skewed distribution
open-ended distribution
normal distribution
large variance
ordinal scale
The circumstances in which the median is the preferred measure of central tendency is given as follows:
Skewed distribution.Ordinal scale.What is the mode?There are three measures of central tendency of a data-set, which are defined as follows:
Mean.Median.Mode.The median represents the middle value of the distribution, hence it should be used in these following cases:
Skewed distribution.Ordinal scale.They should be used in this case as the median is less affected by outliers compared to the mean.
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If the daughter's quilt has a length of 2 yards and a width of 1 yard, and the doll's quilt has a length of what is the width of the doll's quilt?
The similar doll's quilt has a width of (1/4) yards.
What is similarity of shapes?Two or more than two shapes are said to be similar if they have equal corresponding measures of angles and the ratio of corresponding sides should be the same.
Given, The daughter's quilt has a length of 2 yards and a width of 1 yard
and the other similar quilt ahs a length of (1/2) yards.
Now, (1/2)/(2) = 1/4.
Therefore, The width of a similar quilt is (1/4)×1 = 1/4 yards.
Q. A woman sews similar quilts for her daughter's doll. If the daughter's quilt has a length of 2 yards and a width of 1 yard, and the doll's quilt has a length of 1/2 yard, what is the width of the doll's quilt?
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"A shipment of 1500 washers contains 400 defective and 1100 non-defective washers. two hundred washers are chosen at random (without replacement) and classified as defective or non-defective. A. what is the probability that exactly 90 defective washers are found? (do not compute out.) B. what is the probability that at least 2 defective items are found? (do not compute out.)"
The probability of exactly 90 defective washers is approximately 0.021, and the probability of at least 2 defective items is approximately 0.985.
A shipment of 1500 washers contains 400 defective and 1100 non-defective washers. The probability of exactly 90 defective washers being chosen and the probability of at least 2 defective items being found can be calculated using the hypergeometric distribution formula.
A. The probability of exactly 90 defective washers being chosen can be calculated using the hypergeometric distribution. The probability mass function of the hypergeometric distribution is given by:
P(X = 90) = (400 choose 90) * (1100 choose 110) / (1500 choose 200)
Substituting the given values, we get:
P(X = 90) ≈ 0.021
B. The probability of at least 2 defective items can be calculated as 1 minus the probability of 0 or 1 defective item. The probability of 0 defective items is given by:
P(X = 0) = (1100 choose 200) / (1500 choose 200)
The probability of 1 defective item is given by:
P(X = 1) = (400 choose 1) * (1100 choose 199) / (1500 choose 200)
Substituting these values, we get:
P(X >= 2) = 1 - P(X = 0) - P(X = 1) ≈ 0.985.
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The complete question is:
A shipment of 1500 washers contains 400 defective and 1100 non-defective washers. Two hundred washers are chosen at random (without replacement) and classified as defective or non-defective_ a) What is the probability that exactly 90 defective washers are found? (Do NOT compute out:) b) What is the probability that at least 2 defective items are found?
For each of the following three populations, indicate what the sampling distribution for samples of 25 would consist of: a. Customer receipts for a supermarket for a year. b. Insurance payouts in a particular geographical area in a year. c. Call center logs of inbound calls tracking handling time for a credit card company during the year
The sampling distribution of the mean will be approximately normal, regardless of the underlying population distribution.
What is population sampling?Population sampling is the process of selecting a representative sample from a larger population for the purpose of making statistical inferences about the population.
a. The sampling distribution for samples of 25 customer receipts for a supermarket for a year would likely be approximately normally distributed. This assumes that the receipts are randomly selected from the entire population of receipts and that the population distribution of receipts is roughly normal.
The central limit theorem suggests that for a sufficiently large sample size (usually at least 30), the sampling distribution of the mean will be approximately normal, regardless of the underlying population distribution.
b. The sampling distribution for samples of 25 insurance payouts in a particular geographical area in a year would likely be positively skewed, assuming that most payouts are relatively small and a few are very large. The central limit theorem may still apply, but the distribution of the sample means would not be exactly normal.
c. The sampling distribution for samples of 25 call centre logs of inbound calls tracking handling time for a credit card company during the year would likely be approximately normally distributed. This assumes that the call centre logs are randomly selected from the entire population of logs and that the population distribution of handling times is roughly normal.
The central limit theorem suggests that for a sufficiently large sample size (usually at least 30), the sampling distribution of the mean will be approximately normal, regardless of the underlying population distribution.
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City Donuts
recently sold 14 donuts, of which 4 were cream-filled donuts. Considering this
data, how many of the next 7 donuts sold would you expect to be cream-filled donuts?
cream-filled donuts
The expected value of cream-filled donuts the store City Donuts is selling should be 2.
What is the expected value?We are aware of In the realm of probability theory, the expected value, commonly referred to as the expected average, is a generalization of the weighted average.
Given, City Donuts recently sold 14 donuts, of which 4 were cream-filled donuts.
So, The probability of cream-filled donuts is = 4/14 = 2/7.
Therefore, The expected number of cream-filled donuts is,
= (2/7)×7.
= 2.
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4 A set of data has a normal distribution with a mean of 50 and a standard deviation of 8. What percent of the data should be greater than 34?
The Standard Normal Curve
O
2.5%
97.5%
99%
95%
13.5%
13.5%
34% 34%
13.5% 2.5
Answer: 97.5% ( look at the image for the solution )
Step-by-step explanation:
A certain affects virus 0.2% of the population. A test used to detect the virus in a person is positive 88% of the time if the person has the virus (true positive) and 10% of the time if the person does not have the virus (false postive). Fill out the remainder of the following table and use it to answer the two questions below.
Infected Not Infected Total
Positive Test
Negative Test
Total 200 99,800 100,000
a) Find the probability that a person has the virus given that they have tested positive. Round your answer to the nearest tenth of a percent and do not include a percent sign.
P(Infected | Positive Test)=
%
b) Find the probability that a person does not have the virus given that they test negative. Round your answer to the nearest tenth of a percent and do not include a percent sign.
P(Not Infected | Negative Test) =
%
If a certain affects virus 0.2% of the population:
a. The probability that a person has the virus given that they have tested positive is 1.7%.
b. The probability that a person does not have the virus given that they test negative is 99.8%.
How to find the probability?a) Using Bayes' theorem, we can find the probability that a person has the virus given that they have tested positive:
P(Infected | Positive Test) = P(Positive Test | Infected) * P(Infected) / P(Positive Test)
where P(Positive Test) is the probability of a positive test result, regardless of whether the person is infected or not. This can be calculated as:
P(Positive Test) = P(Positive Test | Infected) * P(Infected) + P(Positive Test | Not Infected) * P(Not Infected)
= 0.88 * 0.002 + 0.1 * 0.998
= 0.10064
Now we can plug in the given values:
P(Infected | Positive Test) = 0.88 * 0.002 / 0.10064 ≈ 0.0174
So the probability that a person has the virus given that they have tested positive is approximately 1.7%.
b) Similarly, we can use Bayes' theorem to find the probability that a person does not have the virus given that they test negative:
P(Not Infected | Negative Test) = P(Negative Test | Not Infected) * P(Not Infected) / P(Negative Test)
where P(Negative Test) is the probability of a negative test result, regardless of whether the person is infected or not. This can be calculated as:
P(Negative Test) = P(Negative Test | Infected) * P(Infected) + P(Negative Test | Not Infected) * P(Not Infected)
= 0.12 * 0.002 + 0.998 * 0.998
= 0.99796
Now we can plug in the given values:
P(Not Infected | Negative Test) = 0.998 * 0.99796 / 0.998 = 0.99796
So the probability that a person does not have the virus given that they test negative is approximately 99.8%.
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Linda wants to buy a charm bracelet. Greenville Fine Jewelry charges $12 per charm, plus
$14 for the bracelet. Hanson Jewelers, in contrast, charges $11 per charm and $21 for the
bracelet. If Linda wants to add a certain number of charms to her bracelet, the cost will be
the same at either jewelry shop. What would the total cost of the bracelet be? How many
charms would that be?
The answers to each part is given below.
What are algebraic expressions?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.Given is that Greenville Fine Jewelry charges $12 per charm, plus $14 for the bracelet. Hanson Jewelers, in contrast, charges $11 per charm and $21 for the bracelet.
For the Greenville Fine Jewelry, we can write -
A{x} = 14 + 12x
For the Hanson Jewelers, we can write -
B(x) = 21 + 11x
To add a certain number of charms to her bracelet, the cost will not be same.
Therefore, the answers to each part is given above.
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Please help me with this math!
The transformed function is g ( x ) = ( -1/2 ) | x - 1 | + 2
How does the transformation of a function happen?The transformation of a function may involve any change.
Usually, these can be shifted horizontally (by transforming inputs) or vertically (by transforming output), stretched (multiplying outputs or inputs), etc.
If the original function is y = f(x), assuming the horizontal axis is the input axis and the vertical is for outputs, then:
Horizontal shift (also called phase shift):
Left shift by c units: y=f(x+c) (same output, but c units earlier)
Right shift by c units: y=f(x-c)(same output, but c units late)
Vertical shift:
Up by d units: y = f(x) + d
Down by d units: y = f(x) - d
Stretching:
Vertical stretch by a factor k: y = k × f(x)
Horizontal stretch by a factor k: y = f(x/k)
Given data ,
Let the parent function be represented a f ( x )
Now , the value of f ( x ) = | x |
Let the function be plotted on the graph and
when the function is transformed by a reflection on y axis , we get
h ( x ) = - | x |
Let the function be shifted left by 1 unit , we get
h' ( x ) = - | x - 1 |
Now , when the function is transformed by a vertical stretch of ( 1/2 ) units , we get
j ( x ) = - ( 1/2 ) | x - 1 |
Now , when the function is shifted vertically up by 2 units , we get
g ( x ) = ( -1/2 ) | x - 1 | + 2
Hence , the transformed function is g ( x ) = ( -1/2 ) | x - 1 | + 2 and it is plotted
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camilla walks at a steady pace for 5 minutes, stops in the same location for 2 minutes, then continues on at a faster pace for 3 more minutes until she reaches her destination. camilla claims that the relationship between the time spent walking and the distance traveled is not a function because of the time she stood still. which of the following correctly explains why this is still a function?
The given relationship is a function, as of the given condition it consists of 3 sub-functions,
Functions are the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.
here,
Let's assume that, 3-time intervals
1 . 0 to 5
2. 5 to 7
3. 7 to 10
So for intervals, we have 3 different equation of functions which represents the distance traveled by Camilla in time t.
Thus, the given relationship is a function, as of the given condition it consists of 3 sub-functions.
When she increased her pace, she principally made up for lost time standing at the position. assuming that she made it in the same quantum of time if she did not stop, you can assume that she didn't waste presently time because she picked up the pace.
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You want to estimate the mean SAT score for a population of students with a 90% confidence interval. Assume that the population standard deviation is\sigma=100 If you want the margin of error to be approximately 10, which of the following would be the required minimal sample size?
A) 13
B) 271
C) 26
D) 165
The required minimal sample size would be 26. This is because in order to estimate the mean score with a margin of error of 10 and a confidence level of 90%, the sample size must be large enough for the Central Limit Theorem to apply. Therefore, in this case, the sample size would be (1.96*100)/10 = 19.6, which is approximately 26.
1. Calculate the sample size, n: n = (1.96*σ)/m
2. Plug in the values: n = (1.96*100)/10
3. Calculate: n = 19.6
4. Round up: n = 26
The required minimal sample size of 26 is necessary in order to estimate the mean SAT score for a population of students with a 90% confidence interval and a margin of error of 10. This is because, in order for the Central Limit Theorem to apply, the sample size must be large enough. The formula for the sample size is (1.96*σ)/m, where σ is the population standard deviation and m is the margin of error. Plugging in the values, we get (1.96*100)/10, which is approximately 19.6. Therefore, the required minimal sample size is 26. This sample size is necessary in order to make sure that the estimates have a high degree of accuracy and reliability.
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Add or subtract.
7z^2 − 2z^4 − 2z^2 − 5z^4
a.−2z^6
b.9z^2 + 3z^4
c.5z^2 − 7z^4
d.5z^4 − 7z^8
what is the answer to the blanks
The distance between point D and E is 17.89 units
What is distance between two points?Distance between two points is the length of the line segment that connects the two points in a plane. The formula to find the distance between the two points is usually given by d=√((x2 – x1)² + (y2 – y1)²). This formula is used to find the distance between any two points on a coordinate plane or x-y plane.
d=√((x2 – x1)² + (y2 – y1)²).
d = √ (11-3)² + 13-(-3)²
d = √ 8²+ 16²
d = √ 64 + 256
d = √320
d = 17.89 units
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3 Answer:
Solve the proportion: 4/(x+1) = 3/(x+2)
4 Answer:
Solve the proportion: x/(x+3) = (x-2)/x
The solution to the proportion 4/(x+1) = 3/(x+2) is x = -5 and
The solution to the proportion x/(x+3) = (x-2)/x is x = 2.
What do you mean by quadratic polynomials?A quadratic polynomial is a polynomial of degree 2, which means that the highest power of the variable in the polynomial is 2. A quadratic polynomial can be expressed in the general form:
a[tex]x^2[/tex] + bx + c
where a, b, and c are constants, and x is the variable.
In this form, coefficient a is the leading coefficient, and it determines the concavity of the quadratic function. If a is positive, the function is concave up, meaning that it opens upward and has a minimum value. If a is negative, the function is concave down, meaning that it opens downward and has a maximum value.
The quadratic polynomial is named as such because it is a polynomial of degree 2, and the term "quad" means "square." The quadratic function is commonly seen in geometry, algebra, and physics, and it has many applications in real-life problems, such as finding the maximum or minimum values of a function, determining the trajectory of a projectile, and modeling certain natural phenomena.
Quadratic polynomials can be solved by various methods, including factoring, completing the square, and using the quadratic formula.
To solve the proportion 4/(x+1) = 3/(x+2), we can cross-multiply to get:
4(x+2) = 3(x+1)
Expanding the brackets gives:
4x + 8 = 3x + 3
Subtracting 3x from both sides gives:
x + 8 = 3
Subtracting 8 from both sides gives:
x = -5
To solve the proportion x/(x+3) = (x-2)/x, we can cross-multiply to get:
[tex]x^2[/tex] - 2x = (x+3)(x-2)
Expanding the brackets gives:
[tex]x^2[/tex]- 2x = [tex]x^2[/tex] + x - 6
Subtracting[tex]x^2[/tex] from both sides gives:
-2x = x - 6
Subtracting x from both sides gives:
-3x = -6
Dividing both sides by -3 gives:
x = 2
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