A z-score of z = −2.00 indicates a position in a distribution __________.
A- above the mean by a distance equal to 2 standard deviations
B- below the mean by 2 points
C- below the mean by a distance equal to 2 standard deviations
D- above the mean by 2 points
Answer:
C- below the mean by a distance equal to 2 standard deviations
Step-by-step explanation:
The Z-score, or standard score, is the number of standard deviations a given data point lies above or below the mean.The z-score is positive if the value lies above the mean, and negative if it lies below the mean.So, a z-score of z = −2.00 indicates a position in a distribution below the mean by a distance equal to 2 standard deviations.overbooking flights is a common practice of most airlines. a particular airline, believing that 4% of passengers fail to show for flights, overbooks (sells more tickets than there are seats). suppose that for a particular flight involving a jumbo-jet with 267 seats, the airline sells 278 tickets. question 1. what is the expected number of ticket holders that will fail to show for the flight? (use 2 decimal place in your answer.) question 2. what is the probability that the airline will not have enough seats for all the ticket holders who show for the flight? (use 3 decimal places.)
1. 3.2673 is the expected number of ticket holders that will fail to show for the flight.
2. 0.425 is the probability that the airline will not have enough seats for all the ticket holders who show for the flight.
P(airline will not have enough seats for all the ticket holders who show for the flight) = P(more than 267 people show up for the flight)
p = P(will show for flight) = 1 - 0.04 = 0.96
n = 278
µ = n * p = 278 * 0.96 = 266.88
σ = [tex]\sqrt{ n*p* (1 - p)} = \sqrt{278 * 0.96 * 0.04} = 3.2673[/tex]
P(X > 267) = P(X > 267.5)
p(x- µ) / σ > 267.5- µ /σ
= P(Z> 267.5 – 266.88/ 3.2673 )
= P(Z > 0.19)
= 0.425.
What is probability?Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events. The degree to which something is likely to happen is basically what probability means. To understand the potential outcomes for a random experiment using this fundamental theory of probability, which is also applied to the probability distribution. Knowing the total number of outcomes is necessary before we can calculate the likelihood that a specific event will occur.
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solve the following proportionx 2— = —32 8x=
We have to solve for x:
Multiply both sides of the proportion by 32:
[tex]\frac{x}{32}(32)=\frac{2}{8}(32)[/tex][tex]x=\frac{64}{8}[/tex]Simplify:
[tex]x=8[/tex]Write an equation in slope-intercept form of the line that passes through the given points.
The equation of the line is y = -2.5x - 1
How to determine the line equation?The table represents the given parameter
On the table, we have the following points
Point, (x, y) = (0, -1) and (2, -6)
So, we start by calculating the slope of the line using the following slope equation
Slope = (y₂ - y₁)/(x₂ - x₁)
Where x and y are defined above
So, we have
Slope = (-6 + 1)/(2 - 0)
Evaluate
Slope = -2.5
The equation of the line is then calculated as
y = m(x - x₁) +y₁
Where
Slope, m = -2.5
(x₁, y₁) = (0, -1)
So, we have
y = -2.5(x + 0) - 1
Open the brackets and evaluate
y = -2.5x - 1
Hence, the line has an equation of y = -2.5x - 1
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A kite is gliding 74 feet above sea level. There is a stingray coasting 7 feet below sea level. What is the vertical distance between the kite and stingray.
The vertical distance between the kite and stingray is 81 feet.
Given that, a kite is gliding 74 feet above sea level. There is a stingray coasting 7 feet below sea level.
What is the vertical distance?Vertical distance or vertical separation is the distance between two vertical positions. Many vertical coordinates exist for expressing vertical position: depth, height, altitude, elevation, etc.
The vertical distance between the kite and stingray is
74-(-7)
= 74+7
= 81 feet
Therefore, the vertical distance between the kite and stingray is 81 feet.
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8. Find the area of the kite.
Answer:
A=16, the formula to find the area of a kite is A=pq/2
Step-by-step explanation:
A=pq/2 = 4×8/2=16
sat scores have a mean of 500 and standard deviation of 200. act scores have a mean of 20 and a standard deviation of 5. suppose that student a has an sat score of 600, and student b has an act score of 25. using z-scores, which student had a better college entrance exam score?
‘B’ had a better college entrance exam score due to the higher value of Z-Score.
The Z-score of an observation is the number of standard deviations it falls above or below the mean. Standard deviation is a statistic that is used to measure the dispersion of a dataset relative to its mean and is calculated by doing the square root of the variance.
[tex]Z=\frac{(observation-mean)}{standard deviation}[/tex]
By putting the values as given in the question,We get,
A's score is (600 - 500) / 200 = 0.5 standard deviation i.e. above the mean.
B's score is (25 - 20) / 5 = 1 standard deviations i.e. above the mean.
Thus ‘B’ had a better score.
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what are the appropriate measures of central location for interval data? mean and median median and mode mean, median, and mode what are the appropriate measures of variability for interval data? range, interquartile range, variance, standard deviation, and coefficient of variation variance coefficient of variation what are the appropriate measures of relative standing for interval data? interquartile range percentiles and quartiles none
The appropriate measures of central location for interval data are Mode, median, and average
The measure of a data set's most valuable position is its core location. Basically, they are mean, median, and mode.
Mean: The mean is the data set's average value. It is the total number of data divided by the sum of the data set.
The data point in the middle of the data collection is known as the median.
It can be obtained by halving the data set, which will show where the median is located.
Simply put, mode refers to the data that occurs most frequently.
Each of these provides positional information on the data, as can be seen from the definition.
The one value that other values in the data center around is given by the mean.
Therefore, the correct options are Mode, median, and average
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Help please i need it for a grade
Answer:
(3,13 ) & (-1,5)
Step-by-step explanation:
a. 2x + 7 = x^2 + 4
b. move all terms to the left side and set equal to zero. then set each factor equal to zero. which gives you the x values 3, -1
c. substitute x with the x values to get y. 2(3) + 7 = -1^2 + 4
d. the solution is (3,13 ) & (-1,5)
Christina is doing an obstacle course in gym class. First, she runs 100 feet and jumps over a hurdle. Then, she crawls through a 20-foot tunnel. Finally, she dribbles a soccer ball 60 feet to the finish line. How many yards long is the obstacle course?
Answer:
60 yards
Step-by-step explanation:
100 feet + 20 feet + 60 feet = 180 feet
180 feet = 60 yards (there are 3 feet in 1 yard)
27. A table and five chairs cost $3500. The cost of three chairs is $1050. What is the cost of a table if all the chairs cost the same price?
a television program director has 14 shows available for monday night but can choose only 5 shows. how many different possible combinations are there?
There are 240240 possible permutations of choosing 5 shows from 14 available shows. It can be obtained by applying the formula of permutation.
What is permutation?
In mathematics, it is the number of ways in which given number of items can be arranged in different orders.
Here, we need to select 5 iteams from the given 14 iteams.
[tex]P(14,5)=\frac{14!}{(14-5)!}\\=\frac{14!}{(9!)}\\=\frac{(14)(13)(12)(11)(10)(9!)}{(9!)}\\=(14)(13)(12)(11)(10)\\=240240[/tex]
Hence, there are 240240 possible permutations of choosing 5 shows from 14 available shows.
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Dwayne puts $200.00 into an account to use for school expenses. The account earns 9% interest, compounded quarterly. How much will be in the account after 4 years? nt 1 Use the formula A = P 1 + where A is the balance (final amount), P is the principal (starting n amount), r is the interest rate expressed as a decimal, n is the number of times per year that the interest is compounded, and t is the time in years. Round your answer to the nearest cent.
Solution
For this case we can use the following formula:
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]where:
P= 200
r= 0.09
n = 4
t= 4
And solving we got:
[tex]A=200(1+\frac{0.09}{4})^{4\cdot4}=285.52[/tex]Find the area of the figure. Use 3.14 for pi.
Ryan Pick 6 1/2 cups of berries from his garden he use 3 3/8 cups of to make fruit salad if he needs 3 cups of berries to make a pie does Ryan have enough very stuff to also make a pie?
We will simply subtract 3 3/8 from 6 1/2
That is;
6 1/2 - 3 3/8
= 3 4-3/8
=3 1/8
The amount of berry left is more than 3 cups, hence Ryan have enough very stuff to also make a pie
Lexi and Raymond are hosting events that are catered by the same company. Lexi plans to have 63 adults and 59 children attend, so the total projected cost of her meals is $2,582. Raymond has 63 adults and 93 children on her guest list, so he will pay the caterer $3,126. How much does the caterer charge for each meal?
Every adult's meal costs $
, and every child's meal costs $
.
The cost for children meal is $16 and the.cost for adult meal is $26.
How to calculate the value?Let cost of adult meal = a
Let cost of child meal = c
Lexi plans to have 63 adults and 59 children attend, so the total projected cost of her meals is $2,582.This will be:
63a + 59c = 2582 ...... i
Raymond has 63 adults and 93 children on her guest list, so he will pay the caterer $3,126. This will be;
63a + 93c = 3126 ...... ii
Collect both equations
63a + 59c = 2582 ...... i
63a + 93c = 3126 ...... ii
Subtract i from ii
34c = 544
Divide
c = 544 / 34
c = 16
The cost of children meal is $16.
From equation i, 63a + 59c = 2582
63a + 59(16) = 2582
63a + 944 = 2582
Collect like terms
63a = 2582 - 944
63a = 1638
a = 1638/63
a = 26
Adult meals is $26.
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A car, initially traveling east with a speed of 15 meters per second , is accelerated uniformly at 4 meters per second 2 east for 10 seconds along a straight line. what is the total distance the car travels during this 10 second interval?
Answer:
350m
Step-by-step explanation:
Vi = 15 m/s
A = 4 m/s^2
delta t = 10s
delta x = ?
delta x = (Vi)(delta t) + 1/2(A)(delta t)^2
delta x = (15m/s)(10s) + 1/2(4m/s^2)(10s)^2
delta x = 350 m
any given season, a soccer team plays 65 % of their games at home.
When the team plays at home, they win 83 % of their games.
When they play away from home, they win 26 % of their games.
find the probability the team wins with explanation
Based on the percentage of games played at home by the team, and the percentage win rate, the probability that the team wins is 63.05%
How to find the probability the team wins?First, find the probability that the team wins playing at home:
= Percentage win rate at home x Percentage played at home
= 83% x 65%
= 53.95%
Then find the probability of winning away:
= Percentage win rate away x Percentage played away
= 26% x (1 - 65%)
= 9.1%
The probability the team wins is:
= 53.95 + 9.1
= 63.05%
In conclusion, the probability of the team winning at home and the probability of them winning away, can be summed up to find the probability of the team winning which is 63.05%.
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Do the interior angles of a quadrilteral always add up to the same thing? Explain why you think so.
Write the sum of 7√28x6 + 4√7x6 in simplest form, if x # 0
The sum equivalent to 7√28x⁶+4√7x⁶ is :
18√7x⁶ .
Solution:Remove parentheses and combine like terms to simplify each side of the equation.To isolate the variable term on one side of the equation, use addition or subtraction.To find the variable, use multiplication or division.Given ,7√28x⁶+4√7x⁶,
To find sum in simplest form ;
7√28x⁶+4√7x⁶
By splitting to factors,
= 7√(7*4)x⁶+4√7x⁶
= 7*2√7x⁶+4√7x⁶
= 14√7x⁶+4√7x⁶
By factoring out like terms,
= 2√7x⁶(7+2)
= 2√7x⁶(9)
= 18√7x⁶
Therefore sum is = 18√7x⁶.
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2 varieties of gift wrap paper are to be mixed. The assortment will cost $7. One sells for 50 cents a sheet the other for 25 cents a sheet. the number of 50 cents sheets is 3 times the number of 25 cent sheets. how many of each type of sheet should be included in the package
Given:
One variety of gift wrappers sells for 50 cents a sheet the other for 25 cents a sheet.
In dollars,
One variety of gift wrappers sells for 0.5 dollars a sheet the other for 0.25 dollars a sheet.
The assortment will cost $7.
Let x be the number of 50 cents sheets.
Let y be the number of 25 cents sheets.
It is also given that,
The number of 50 cents sheets is 3 times the number of 25 cent sheets.
x=3y ........ (1)
0.5x+0.25y=7 ....... (2)
Substitute (1) in (2) we get,
[tex]\begin{gathered} 0.5(3y)+0.25y=7 \\ 1.5y+0.25y=7 \\ 1.75y=7 \\ y=\frac{7}{1.75} \\ y=4 \end{gathered}[/tex]Hence, x=3(4)
x=12
So, the number 50 cents sheets are 12 and the number of 25 cents sheet is 4.
8. Find the polynomial function of degree 3 for the given conditions I.f(1) = 32 and x-2, x-3,x+1 are factors of the polynomial II.f(3) = -24 and 5,2,4 are zeros of the polynomial
Part I
In factored form, [tex]f(x)=a(x-2)(x-3)(x+1)[/tex]. Substituting x=1,
[tex]f(1)=32=a(1-2)(1-3)(1+1)\\\\\implies 32=4a\\\\a=8\\\\\therefore f(x)=8(x-2)(x-3)(x+1)[/tex]
Part II
In factored form, [tex]f(x)=a(x-5)(x-2)(x-4)[/tex]. Substituting x=3,
[tex]f(3)=-24=a(3-5)(3-2)(3-4)\\\\\implies 24=2a\\\\a=12\\\\\therefore f(x)=12(x-5)(x-2)(x-4)[/tex]
The shaded portion in each glass represents an amount of grape drink Martin's glass of grape drink has a weaker tasting grape flavor than Tia's glass of grape drink.
The stronger flavor of grape is in Tia's glass.
Given,
Martin's glass of grape drink has weaker tasting grape flavor
Tia's glass of grape drink has stronger tasting grape flavor
3 ounces of water is added to Martin's glass
One table spoon of grape mix is added to Tia's glass
We have to find the glass which contain the stronger grape flavor
Already in Martin's glass flavor is low. When we add water again to his glass, the flavor will again dissolves with water.
In Tia's glass grape flavor is stronger. By adding one tablespoon of grape mix the flavor will become more stronger.
That is,
The stronger flavor of grape is in Tia's glass.
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brainly 100!!! Which of the following functions is graphed below?
The function that is represented on the graph is (a) y = x^2 + 4, x < 2 and y = x + 4, x ≥ 2
How to determine the graphed function?The graph represents the given parameter
From the graph, we have the following function types
Whole graph: Piecewise functionQuadratic function to the leftLinear function to the rightUsing the options as a guide, we have the equations to be
Quadratic function: y = x^2 + 4Linear function: y = x + 4Next, we calculate the domain
The quadratic function stops at x = 2 with an open circle
So, the domain is x < 2
The linear function starts at x = 2 with a closed circle
So, the domain is x ≥ 2
Hence, the graphed function is (a)
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Help, I don’t get this
The total earnings for the week for the same wage per hour is $501.6.
In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication and division,
Here,
For 5 of working earnings is $76
Hourly rate = 76 / 5 = $15.2 per hour
Now for 33 hours of working in a week,
Earning = 15.2 * 33 = $501.6
Thus, the total earnings for the week for the same wage per hour is $501.6.
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What is the absolute value of the number plotted on the number line?.
A. -1.75
B. -1.25
C. 1.25
D. 1.75
Answer:
D. 1.75
Step-by-step explanation:
Absolute value cannot be negative, so that gets rid of A & B. The point is at -1.75 so it has to be D.
For the equation, complete the given ordered pairs.Need help solving the last order pair.
Hello!
First, let's remember:
In an ordered pair, we will have two variables represented as (x, y).
In the first two ordered pairs, the exercise informed the value of x. In the third ordered pair, it informs the value of y. We will solve it in a similar way, look:
[tex]\begin{gathered} 4x-y=7 \\ 4x-7=7 \\ 4x=7+7 \\ 4x=14 \\ x=\frac{14}{4}=\frac{7}{2} \end{gathered}[/tex]Answer:x = 7/2 or also x = 3.5.
If M is between G and T, MG = 2x + 1, MT = 3x + 3, and GT = 19, Then X = ___.MG = ___.MT = __.
We are given the following information
M is between G and T
MG = 2x + 1
MT = 3x + 3
GT = 19
Let us draw a sketch to better understand the problem
As you can see, the sum of MG and MT must be equal to the GT
Mathematically,
[tex]\begin{gathered} GT=MG+MT \\ 19=(2x+1)+(3x+3) \end{gathered}[/tex]Let us solve the above equation or x
[tex]\begin{gathered} 19=2x+1+3x+3 \\ 19=2x+3x+1+3 \\ 19=5x+4 \\ 19-4=5x \\ 15=5x \\ \frac{15}{5}=x \\ 3=x \\ x=3 \end{gathered}[/tex]So, the value of x is 3
[tex]\begin{gathered} MG=2x+1 \\ MG=2(3)+1 \\ MG=6+1 \\ MG=7 \end{gathered}[/tex][tex]\begin{gathered} MT=3x+3 \\ MT=3(3)+3 \\ MT=9+3 \\ MT=12 \end{gathered}[/tex]Therefore, the required values are
x = 3
MG = 7
MT = 12
Claire scheduled a taxi to pick her up at her house. The taxi service says it will take 15 minutes to get to her house based on normal traffic routines. However, due to either no traffic or more traffic than normal, the time could vary by as much as 4 minutes. Which inequality and solution show the range of possible minutes, t, it will take for the taxi to get to Claire's house?
The inequality would be 15 ≤ t ≤ 19 showing the range of possible minutes it will take for the taxi to get to Claire's house.
What is inequality?Inequality is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are not equal.
The time could vary by as much as 4 minutes.
Let t be the range of possible minutes
The taxi service says it will take 15 minutes to get to her house based on normal traffic routines.
So the inequality as 15 ≤ t
The time could vary by as much as 4 minutes.
So the inequality as 15 ≤ t ≤ 15 + 4
⇒ 15 ≤ t ≤ 19
Therefore, the inequality would be 15 ≤ t ≤ 19 showing the range of possible minutes.
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-6 = -2/9w solve for w and simplify your answer as much as possible
Answer:
w = 27
Step-by-step explanation:
Solve for w: -6 = -2/9w
-6 = -2/9w
divide both sides by -2/9:
-6/(-2/9) = -2/9w/(-2/9)
27 = w