S(x) of Alex's new probability distribution will be 0.599.
What is Probability distribution ?
A mathematical function called a probability distribution explains how likely it is that a variable will take on several possible values. Utilizing graphs or probability tables, probability distributions are frequently represented.
Given, The no. of cups of coffee he drank with the probability.
If he drinks 1.471 cups per day, So the S(X) will be calculated in the following manner:
Step 1 : calculate the deviation of X from N.( here N = 1.471 )
Step 2 : find the square of (X- N).
Step 3 : multiply it with the given P(X).
Step 4 : find the sum of the (X-N)^2* P(X).
Hence, By following the given steps, we get S(X) as 0.599.
(Refer to the table given in Excel file).
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Write an expression for "c fewer than 4."
Answer: c<4
Step-by-step explanation:
C fewer than 4 means that c is smaller than 4! So we use this mark <
So the answer is c<4
The function y=f(x)y=f(x) is graphed below. What is the average rate of change of the function f(x)f(x) on the interval -7\le x \le 2−7≤x≤2?
Consequently, the function's average rate of change is -11.
What is function?A mathematical expression, rule, or law that describes the relationship between two independent variables and one dependent variable In mathematics, functions exist everywhere, and they are crucial for creating physical links in the sciences.
The function is given by .
The ratio of the dependent variable's change to the independent variable's change is referred to as the rate of change.
f(x)=[tex]x^{2}[/tex]-6x+6
x ranges from -7 to 2, with 2 being the highest value.
=> f(-7) = 49 + 42 + 6 = 97.
=> f(2) =- 12 + 6+4 = -2.
The average rate of change is
f(-7)-f(2)/-7-2
=> 97-(-2)/-9
=> 99/-9
=> -11
Consequently, the function's average rate of change is -11.
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define the level of significance. multiple choice it is the probability of a type ii error. it is the probability of a type i error. it is a z-value of 1.96. it is the beta error.
By information provided in the question, we can say that It is the probability of a Type I error.
what is probability?The proportion of favorable outcomes to all possible outcomes for an event is known as the probability. The quantity of positive outcomes in an experiment with 'n' outcomes is represented by x. The following equation can be used to determine the likelihood of an event:
Probability (event) = positive outcome / overall outcome = x/n
It refers to the likelihood of a Type I mistake.
The likelihood that a Type I error will occur, or the likelihood that a null hypothesis will be rejected when it is true, determines the degree of significance.
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question content area top part 1 compare the slopes of the lines for y=f(x) and y=g(x) to determine if they are parallel.
A line's steepness can be determined by looking at its slope.Slope of the line is 15.
How do you find slope of a line?Determine the coordinates of two points along the line that you choose.Find the difference between these two points' y-coordinates (rise). Find the difference between these two points' x-coordinates (run).
Slope of a line passing through two points (x1 ,y1)and will be given by,
Slope 'm' =y2 - y2/ x2- x1
Function 'f' passes through two points (0, 20) and (1, 35).
Slope of the line = 35 -20/1-0= 15
In a similar manner, function 'g' passes through (0, 22) and (1, 37).
Slope of the line = 37 - 22/ 1-0 = 15
Therefore, m1 = m2
Since, slopes of both the lines are equal, lines will be parallel.
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The lid of a rectangular box of side
[tex]40cm \: by \: 10m[/tex]
is to be sealed all round with tape.
[tex]what \: is \: the \: length \: of \: the \: tape \: required[/tex]
Find the 14th term of the arithmetic sequence -x-5, 6x - 7, 13x - 9,...
Answer: a₁₄=90x-31
Step-by-step explanation:
-x-5, 6x-7, 13x-9 ...
Hence,
a₁=-x-5
a₂=6x-7
a₃=13x-9
d=a₂-a₁
d=6x-7-(-x-5)
d=6x-7+x+5
d=7x-2
aₙ=a₁+d(n-1)
a₁₄=-x-5+(7x-2)(14-1)
a₁₄=-x-5+13(7x-2)
a₁₄=-x-5+91x-26
a₁₄=90x-31
How do you write 0.0045 in scientific notation?
Answer:
[tex]4.5 x 10^{-3} \\[/tex]Step-by-step explanation:
Graph the functions to find the x values that satisfy the inequality.
f(x)=-2(x+3)^2+5
g(x)=x+7
For what values of x is f(x)≤g(x)?
Options:
(-∞,∞)
No values of x
[-5, -2]
(-∞, -5]∪[-2, ∞)
no value of x for f(x) ≤ g(x)
What do you mean by function?
Function, in mathematics, a formula, rule, or law that defines the relationship between one variable (the independent variable) and another (the dependent variable).
The types of functions can be roughly classified into four types. Based on item:
One-to-one functions, many-to-one functions, on functions, one-to-one, and within functions.
Given functions:
f(x)=-2(x+3)^2+5
g(x)=x+7
According to the graph given for the functions there is no value of x for which f(x) ≤ g(x) .
Therefore, no value of x for f(x) ≤ g(x)
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Tristan has $1.40 worth of nickels and dimes. He has twice as many nickels as dimes. Write a system of equations that could be used to determine the number of nickels and the number of dimes that Tristan has. Define the variables that you use to write the system.
The equation will be d(x+2y) = $1.40,where x = cost of dimes , y = cost of nickels, t = number of dimes.
What is an equation?
In mathematics, equation represent two expressions are equal.
e.g. x + 2y = 3,
Here , x + 2y is one expression and 3 is another, which are equated using equal to symbol.
Let's us consider ,
Number of dimes = t
Then number of nickels = 2t
Cost of one dime = x
Cost of one nickel = y
Then the total cost = xt +2yt
And total cost given = $1.40
So, the final equation = t(x+2y) = 1.40
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If a student had homework 65 days out of 100, what fraction and what
percentage of days did the student not have homework? Choose two
answers.
A. 0.65%
B.
C.
35
100
40
100
D. 65%
E. 35%
65
OF. 100
Answer:
B and E
Step-by-step explanation:
100-65=35 so the number of days they didn't have homework was 35. 35/100 and 35% represent this.
at a gas station, lora took 1/6 minute to fill 3/5 gallon of gas. at this rate, how many gallons of gas could lora fill in 1 minute?
The number of gallons of gas that Lora can fill in 1 minute will be 18/5 or 3.6 gallons.
What are ratio and proportion?A ratio is a group of sequentially ordered numbers a and b expressed as a/b, where b is never equal to zero. When two objects are equal, a statement is said to be proportional.
The rate is the ratio of the amount of something to the unit. For example - If the speed of the car is 20 km/h it means the car travels 20 km in one hour.
At a gas station, Lora took 1/6 minute to fill 3/5 gallons of gas. And we know that the ratio will remain constant.
Let 'x' be the number of gallons. Then the amount of gallons in each minute is calculated as,
(3/5) / (1/6) = x / 1
Simplify the equation, then we have
(3/5) / (1/6) = x / 1
(3/5) × 6 = x
x = 18 / 5
x = 3.6 gallons
The number of gallons of gas that Lora can fill in 1 minute will be 18/5 or 3.6 gallons.
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8x - 3 /AX 4x + 3 When angles form a linear pair, their sum is 180°. 8x - 3+ 4x + 3 = 180 [?]x + [] = 180
Answer:
12x + 0 = 180x = 15Step-by-step explanation:
You are given the equation 8x -3 +4x +3 = 180 and asked to simplify it and solve for x.
SimplifiedCollecting terms, we have ...
(8 +4)x +(-3 +3) = 180
12x + 0 = 180
Dividing by the coefficient of x gives ...
x = 180/12 = 15
The value of x is 15.
Jayden and his children went into a grocery store and he bought $8 worth of apples and bananas. Each apple costs $1 and each banana costs $0.50. He bought twice as many bananas as apples. By following the steps below, determine the number of apples, x,x, and the number of bananas, y,y, that Jayden bought.
Determine three ways to have twice as many bananas as apples:
The number of apples that Jayden bought is 4 and the number of bananas he wants to buy is 8.
The number of ways we can have twice as many bananas as apples is:
8 bananas 4 apples
10 bananas 5 apples
12 bananas 6 apples
How many apples and bananas did Jayden buy?The first step is to form of system of equations that represent the question:
x + 0.50y = 8 equation 1
y = 2x equation 2
The substitution method would be used to determine the required values.
x + (0.50 x 2x) = 8
x + x = 8
2x = 8
x = 8 / 2
x = 4
Substitute for x in equation 2:
y = (2 x 4)
y = 8
The total number of fruits bought is 12 (4 + 8):
The number of ways we can have twice as many bananas as apples :
8 bananas 4 apples
10 bananas 5 apples
12 bananas 6 apples
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Which of tha following describes the graph of a quadratic function? O a. It opens to the right O b. It opens to the left O c. Its axis of symmetry is a vertical line O d. Its axis of symmetry is a horizontal line
A parabola is a curved form that represents the graph of a quadratic function. The vertex of a parabola is one of its focal points. The highest or lowest point on the graph corresponds to it. Consider it similar to the parabola's endpoint.
What does the term "quadratic function" mean?
A quadratic function has the formula f(x) = ax2 + bx + c, with a, b, and c being integers and a not equal to zero. A parabola is the shape of a quadratic function's graph.
The basic "U" shape of a parabola is the same whether it opens upward or downward, or with a different "width" or "steepness."
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how many weighings of a balance scale are needed to find a lighter counterfeit coin among four coins?
The weighing of the balance scale required to find a lighter counterfeit coin among four coins, is twice.
In just two balance scale weighs, it is feasible to identify which of four coins is the lighter fake coin. Here is one approach:
Then, weigh the two groups against one another after splitting the four coins into two groups of two coins each. The lighter counterfeit currency must belong to the group that is lighter than the other if there are two groups. If the two groups of coins weigh the same, then one of the two remaining coins must be the lighter counterfeit coin.
Weigh the two coins from the lighter group (or the two still present, if the first step was unsuccessful) against one another.
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The graph of a linear function passes through (-8,4) and (4,5).What is the equation of the function?
The linear function that passes through (-8,4) and (4,5) will be y = (1/12)x + 14/3.
What is a linear function?A straight line on the coordinate plane is represented by a linear function.
A linear function always has the same and constant slope.
The formula for a linear function is f(x) = ax + b, where a and b are real values.
A linear equation or function is given as ;
y = mx + b
The slope (m) associated with two points (x₁, y₁) and (x₂, y₂) is given by
Slope = (y₂ - y₁)/(x₂ - x₁)
The slope associated with (-8,4) and (4,5) will be as,
m = (5 - 4)/(4 + 8) = 1/12
Thus, y = (1/12)x + b
Put (4,5)
5 = (1/12)4 + b
b = 5 - 1/3
b = 14/3
Thus, y = (1/12)x + 14/3
Hence "The linear function that passes through (-8,4) and (4,5) will be y = (1/12)x + 14/3".
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a simple random sample of 64 concert tickets was drawn from a normal population. the mean and standard deviation of the sample were $120 and $25, respectively. we want to determine whether the mean of tickets is not equal to $125. find the p-value for this hypothesis testing.
By using the hypothesis test, to determine whether the mean of tickets is not equal to $125 is calculated as 58%.
We must compute the sample's z-score using the sample mean and standard deviation in order to determine the p-value for this hypothesis test. The z-score calculates how far the sample mean deviates from the population mean by standard deviations.
The difference between the two means is $5 if the population mean is $125 and the sample mean is $120. Given that the sample's standard deviation is $25,
z-score = [tex]\frac{5}{25}[/tex] = 0.2.
We must utilize the z-score to hunt for the equivalent value in a typical normal table in order to determine the p-value. The chance of selecting a sample with a mean of $120 from a population with a mean of $125 is known as the p-value.
The probability that a sample with a z-score of 0.2 would be taken from a population with a mean of $125 is the p-value in this instance. When we look for 0.2 in a typical normal table, we discover that the p-value is roughly 0.58. As a result, 0.58 is the p-value for this hypothesis test. The probability that a sample with a mean of $120 would be taken from a population with a mean of $125 is therefore 58%.
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Karen has a bag containing 423 rubber ducks.
If Karen gives 30 rubber ducks to every person she meets, then she will have enough for _____ people and she will have _____ extra ducks left over.
Answer:
karen will have enough for 14 people, and she will have 3 extra ducks left over
Step-by-step explanation:
divide 423 by 30
423/30 = 14
14 times 30 is 420, so subtract 420 from the total number of rubber ducks
423 - 420 = 3
so, karen will have enough for 14 people and 3 ducks will be left over !!
Answer:
Karen we'll have enough for 14 people and have 3 ducks left over.
Solve the following equation for x. 10 = 2 - 4 (ax - 3) a. -5/a b. 5/a c. 1/a d. -1/a
Answer: c. [tex]\frac{1}{a}[/tex].
Step-by-step explanation:
10 = 2 - 4(ax - 3)
10 = 2 - 4ax + 12
10 = 14 - 4ax
Minus 14 on both sides.
-4 = -4ax
Divided -4 on both sides.
1 = ax
Divided a by both sides to solve x.
[tex]\frac{1}{a}[/tex] = x
Therefore, the answer is c.
What is the first step made in copying the length of a line segment AB onto another line from the lesson? O Without changing the setting of the compass, place the compass point on one endpoint of the new line segment and swing it so that it intersects the second segment. O Using your straightedge, construct a segment that is longer than the given segment. O Use the compass to measure the length of the segment. O Find a line segment or create a line segment by using your straightedge.
The first step is to draw a line longer than the given AB line.
What is line segment?An area or portion of a line with two endpoints is referred to as a line segment. A line segment, in contrast to a line, has a known length. A line segment's length can be calculated using either metric measurements like millimeters or centimeters, or conventional measurements like feet or inches.
What is the difference between line and line segment?A line can be extended on both ends forever while a line segment has endpoints.
Step 1: You are instructed to copy line segment AB.
Step 2: A line segment that is longer than line segment AB is drawn in step two. Identify C as one of its endpoints.
Step 3: Position the anchor on one endpoint of line segment AB and the pencil point on the other endpoint of the segment by opening your compass.
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a card is drawn from a standard deck of 52 playing cards. what is the probability that the card will be a spade or a club? express your answer as a fraction or a decimal number rounded to four decimal places.
The probability that the card will be a spade or a club 50%
Probability in math is referred as how likely an event is to occur, or how likely it is that a proposition is true.
Here we have given that a card is drawn from a standard deck of 52 playing cards.
And we need to find the probability that the card will be a spade or a club and we have to express your answer as a fraction or a decimal number rounded to four decimal places.
While we looking into the given question, we have identified the the total number of cards is 52.
And the number of spade cards = 13 and the number of club cards = 13
Therefore, the total number of spade and club cards
=> 13 + 13
=> 26
Therefore, the probability of getting a spade or a club from a single draw is,
=> 26/52
When we simplified this one, then we get,
=> 0.5
When we convert this into percentage then we get
=> 50%.
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use the counting techniques from the last chapter. a bag contains two red marbles, three green ones, one fluorescent pink one, three yellow ones, and two orange ones. suzan grabs three at random. find the probability of the indicated event. she gets all the red ones, given that she gets the fluorescent pink one.
The probability of the indicated event is 1/110.
P(2red, pink) = P(2red, pink)/P (pink)
There are a total of 1 ways to get 2 red and pink, for a total of 1 possible triples. P(2red and pink) = 1/220 P(pink) = Number of ways to get 1 pink = 1*11*10 Number of potential triples = 220 P(1 pink in 3) = 110/220 = 1/2 ———-
P(2red | pink) = (1/220)/(1/2) = 2/220 = 1/110 ————————————————
Cheers,
Stan H.
How do you determine an event's probability?To determine the likelihood, apply the procedure below: Find an event with a single result in Step 1. 2. Determine the total number of possible results. Step 3: Subtract the number of fortunate occurrences from the total number of potential outcomes.
How can I determine the suggested probability?You can attempt to find the indicated probability using a variety of equations. The normal distribution model and the standard normal distribution are two techniques that you could choose to adopt since they are both frequently used to calculate suggested probability precisely.
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the following percentages of chloride were found: 42.62%, 43.10%, 42.90%, and 42.75%. what is the average deviation from the mean
The average deviation from the mean is 0.19 that can be calculated from the mean.
An average is calculated for a set of numbers that are of the same value range.
Mean = (32.52+32.14+32.61+32.75)/4 = %32.50
Standard deviation =
|32.50-32.52| = 0.02
|32.50-32.14| = 0.36
|32.50-32.61| = 0.11
|32.50-32.75| = 0.25
(.02+.36+.11+.25)/4= 0.19
So the standard deviation is 0.19
Relative deviation = .19/32.50=0.0058 or %0.58
Yes, %32.14, because it deviates too far from the average.
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The soccer team voted on what they wanted to eat. There are 20 members on the team. Six members voted for pizza, 10 voted for chicken, and the rest voted for hot dogs.
Which ratio represents the number of votes for hot dogs to chicken?
Responses
1/5
2/5
3/5
5/2
The ratio represents the number of votes for hot dogs to chicken is 2/5 ,
What is ratio?
Comparing two numbers by dividing them is how ratios work. Your formula would be A/B if you were contrasting one data point (A) with another data point (B). By doing so, you are multiplying information A by information B.Given,
Number of members voted for pizza = 6
Number of members voted for chicken = 10
Number of members voted for hot dogs = 20 - (10 +6) = 4
Now we have to determine the ratio represents the number of votes for hot dogs to chicken.
Number of members voted for hot dogs / Number of members voted for chicken = 4/10
= 2/5
Thus, the ratio represents the number of votes for hot dogs to chicken is 2/5.
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How do you simplify i^100?
The solution of i^100 = 1 is [tex]i^{100} = 1[/tex] .
Simplify
Simplify simply means to make it simple. In mathematics, simply or simplification is reducing the expression/fraction/problem in a simpler form. It makes the problem easy with calculations and solving.
Power
In mathematical relationships, power is referred to the number of times a number is multiplied by itself meaning the number you get raising a number to an exponent whereas an exponent can be defined as the number of times the number is used in a multiplication. Exponents are often known as powers or indices.
Exponents
Exponents and powers are ways used to represent very large numbers or very small numbers in a simplified manner. For example, if we have to show 3 x 3 x 3 x 3 in a simple way, then we can write it as 34, where 4 is the exponent and 3 is the base. The whole expression 34 is said to be power.
Rewrite [tex]i^{100}[/tex] as [tex](i^{4} )^{25}[/tex]
One to any power is one.
1
From the fact that [tex]i^{2}[/tex] = −1,
Then
([tex]-1^{50}[/tex]) = 1 as −1 raised to any even power is 1.
[tex]i^{100} = 1[/tex]
i^100 = 1
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examine the linear relationships. linear equation a: y=45xy=45x linear equation b is represented by this graph.
The correct option 1. the slope of Equation A is steeper because 4/5 is bigger than 2/5.
Explain the term slope of the line?A line's steepness can be determined by looking at its slope. Slope is calculated mathematically as "rise over run" (variation in y divided by change in x).The format of a linear function is as follows:
y = ax + b
That where:
The rate of change is represented by the slope, or a.The function is steeper the higher the slope:Given by: Linear equation A
y = 4/5 x.
Points (0, 2) and pass through linear equation B. (5, 4).
Given that changes in y divided by change in x determines the slope between two points, we have that:
m = (4 - 2)/(5 - 0)
m = 2/5
Equation A is steeper as it contains a higher slope, so the appropriate response is:
Due to the fact that 4/5 is greater than 2/5, Equation A has a steeper slope.
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The complete question is-
Linear equation A: y=45x
Linear equation B is represented by this graph.
A line that passes through points (0, 2) and (5, 4).
Which statement is entirely correct?
Equation A has a steeper slope, because 4/5 is greater than 2/5.Equation A has a steeper slope, because 4 fifths is greater thanEquation B has a steeper slope, because 4/5 is greater than 2/5.Equation B has a steeper slope, because 4 fifths is greater thanEquation A has a steeper slope, because 5/2 is greater than 4/5.Equation A has a steeper slope, because 5 halves is greater thanEquation B has a steeper slope, because 5/2 is greater than 4/5.Draw a line with the given slope through the given point. What other point
lies on that line?
Answer:
a. Point B
b. Point D
c. Point E
d. Point B
Step-by-step explanation:
See the attached image for a graphed solution with color-coded lines drawn.
Which of the following are quadratic equations?
(v) 2x^2 −3x +9=0
2x^2 −3x +9=0 is the given equation that is quadratic.
What is quadratic?The definition of a quadratic as a second-degree polynomial equation demands that at least one squared term must be included. It also goes by the name quadratic equations. The quadratic equation has the general form ax^2 + bx + c = 0. where a, b, and c are numerical coefficients and x is an unknown variable.
Is a quadratic 2 or 4?Quadratic expressions are those involving powers of x up to the second power, not the fourth power, hence the prefix quad signifies "four" rather than "two."
As highest power of variable is 2 so the expression 2x^2 −3x +9=0 is quadratic.
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Question 11
Erica recorded the number of sales she made during each of the first 4 months when she began her new career. Erica plotted the data on a coordinate grid, and she noted that the data correlate to an exponential equation, as shown What is the domain of the function shown in the graph?
The domain of the graph is {1, 2, 3, 4}
What is Domain?"All the values" that are input into a function are referred to as the domain of a function. The set of all potential inputs for a function is its domain.
Given:
As, we know domain of a function is the set of all possible inputs for the function.
from the Graph, we can find the coordinates ( 1, 10), (2, 20), (3, 40) and ( 4, 80)
So, the domain of the graph is {1, 2, 3, 4}
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Does the picture represent a function?
Yes or No
Answer: Yes
Step-by-step explanation: To determine if this graph represents a function, we use what is called the vertical line test.
In other words, if we can draw a vertical or straight up and down line that passes through more than one point on the graph, the relation is not classified as a function.
In this case, it's impossible to draw such a line that hits more than one point on the graph so the relation is a function.
