The probability that exactly 2 people are left handed if 11% people are left handed and 5 are selected at random is 100.
Probability is a method with the help of which we chose a particular object on random from many given objects.
P(E) = no of favorable outcomes/total number of outcomes
Let there are 100 people
11% are left handed = 11% of 100 = 11
5 are selected randomly.
No of favorable outcomes = 5
Total no of outcomes = 11
Hence, the probability that people selected are left handed is 5/11
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From the given percent of people are left handed and probability of exactly 2 of them are left handed from 5 selected at random is equal to 0.0853.
As given in the question,
Number of people selected at random 'n' = 5
Percent of people are left handed = 11%
Probability of success 'p' = 0.11
Probability of failure 'q' = 1- p
= 1-0.11
= 0.89
Exact number of left handed people 'x' = 2
Probability of people that are exactly left handed
= ⁿCₓ (p)ˣ(q)ⁿ⁻ˣ
=⁵C₂(0.11)²(0.89)⁵⁻²
= (5!/ (5-2)!2!) × (0.0121) × (0.704969)
= 10 × (0.0121) × (0.704969)
= 0.0853
Therefore, from the given percent of people are left handed and probability of exactly 2 of them are left handed from 5 selected at random is equal to 0.0853.
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I need working out for the questions because I don’t understand it that much.
Find the sum of the interior angles for a pentagon. 180° 360° 540° 900°
The sum of the interior angles for a pentagon is 540°
Sum of Interior Angles of a Pentagon :
The interior angles of a pentagon sum up to 540 degrees.. Regardless of how regular or irregular the pentagon is, this is true. By dividing the whole amount by 5, we can calculate the size of each internal angle in the case of regular pentagons. To determine the measure of a missing angle in the situation of irregular pentagons, we must first know the measurements of other angles.
Any pentagon's internal angles add up to 540° in the same way. This holds true regardless of how regular or irregular the pentagon is. By using the polygon angle sum formula, the following sum is obtained:
(n-2)180(n−2)×180°
where n represents the polygon's number of sides. We have n = 5 in the case of a pentagon. Consequently, utilizing the formula:
=(n-2)180=(n−2) ×180°
= (5-2) 180= (5−2) ×180°
= (3) 180= (3) ×180°
= 540=540°
Consequently, a pentagon's interior angles add up to 540 degrees.
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on june 1, grey co. borrows $15,000 cash from national bank by signing a 120-day, 10% interest-bearing note. grey will record interest during the year totaling $ ____
Grey will record interest during the year totaling $500.
Define the term interest-bearing note?An interest-bearing note is a sum of money that a lender lends to a borrower, with interest accruing in line with the conditions of the contract.Notes with an interest component have a defined rate of interest that must be paid on top of the principal amount. There is no specified interest rate on zero-bearing and non-interest bearing notes.For the stated question-
Borrowed money from national bank = $15,000.
Time 120 days.
10% interest-bearing note
Thus, interest during the year;
interest = 15000 x 120 x 0.10 / 360 (days)
interest = 500
Thus, Grey will record interest during the year totaling $500.
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Your class is learning to tie knots. Each student needs a piece of rope that is 3/8 yards long. How many yards of rope are needed for the 16 students in your class
The length of the rope that is needed for the 16 students of the class is 6 yards .
In the question ,
it is given that
the class is learning to tie knots .
the length of rope required by 1 student to tie the knot = 3/8 yards ,
the length of rope for 16 students can be calculated using the formula
length of rope for 16 students = 16 × (length of rope required by 1 student)
Substituting the values
we get ,
length of rope for 16 students = 16 × 3/8
= 2 × 3
= 6
Therefore , 16 students will require 6 yards of rope .
The given question is incomplete , the complete question is
Your class is learning to tie knots. Each student needs a piece of rope that is 3/8 yards long. How many yards of rope are needed for the 16 students in your class ?
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3.4
Practice
In Exercises 1-4, write an equation of the parabola in vertex form.
The vertex form of the parabola is y = a[tex](x-h)^2[/tex]+ k.
What is vertex form ?
When a graph crosses its symmetry axis, the vertex formula in mathematics aids in determining the parabola's vertex coordinate. The typical representation of the vertex point is (h, k). We are aware that y=a[tex]x^2[/tex]+bx+c is the typical equation for a parabola. The vertex in this case, if the coefficient of [tex]x^2[/tex] is positive, should be at the base of the U-shaped curve. The vertex of a U-shaped curve should be at the top if the coefficient of [tex]x^2[/tex] is negative.
Here We know that the standard form of the parabola is y=a[tex]x^2[/tex]+bx+c.
Thus, the vertex form of a parabola is y = a[tex](x-h)^2[/tex]+ k.
The vertex formula is used to find the vertex of a parabola. There are two ways to find the vertex of a parabola.
Vertex, (h, k) = (-b/2a, -D/4a)
Where “D” is the discriminant where D = [tex]b^2[/tex] – 4ac.
“h” and “k” are the coordinates of the vertex.
Hence the vertex form of the parabola is y = a[tex](x-h)^2[/tex]+ k.
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in a manufacturing process a machine produces bolts that have an average length of 3 inches with a variance of .03. if we randomly select three bolts from this process: what is the standard deviation of the sampling distribution of the sample mean?
The standard deviation of the sampling distribution of the sample mean is 0.1 when a machine produces bolts that have an average length of 3 inches with a variance of .03.
What is standard deviation?The positive square root of the variance is the standard deviation. One of the fundamental techniques used in statistical analysis is standard deviation. Standard deviation, also known as SD or denoted by the symbol "σ" indicates how far a value deviates from the mean value.
Here,
σx = σ/√n
= √.03/√3
= .1732/1.732
= 0.1
When a machine creates bolts with an average length of 3 inches and a variance of.03, the standard deviation of the sampling distribution of the sample mean is 0.1.
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Explain how you would find the coordinates of the image
of (5, 2) if it was reflected over the x-axis and then that
image was reflected over the y-axis. What would be the
end result?
The coordinates of the image of (5, 2) if it was reflected over the x-axis and then that image was reflected over the y-axis. is (-5, -2)
We need to find the coordinates of the image of (5, 2) if it was reflected over the x-axis and then that image was reflected over the y-axis.
When an object is reflected over the x axis, the y coordinate changes
(x, y) reflected in x axis gives (x, -y)
So, the point (5, 2) is reflected over x axis, it becomes (5, -2)
Now this image is gain reflected over y axis
When an object is reflected over the y axis, the y coordinate changes
(x, y) reflected in y axis gives (-x, y)
So, the point (5, -2) is reflected over y axis, it becomes (-5, -2)
Therefore, the coordinates of the image of (5, 2) if it was reflected over the x-axis and then that image was reflected over the y-axis. is (-5, -2)
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3 of 4
A, B & C lie on a straight line.
BD = CD.
BCD = 70° and / BAD = 5°.
Work out x, explaining each stage of your
working in the comment box.
The value of x is 65°
From the question, we have
BD = CD.
As the sides are equal
∠BCD=∠CBD= 70°
70° = x + 5°
x = 70°-5°
x = 65°
Subtraction:
Subtraction symbolizes the activity of deleting elements from a collection. A negative symbol is used to denote subtraction. The stack will include nine oranges less four oranges, or five oranges, for example, if there are nine oranges stacked together (as seen in the above figure) and four of those oranges are later moved to a basket. As a result, the difference between 9 and 4 is equal to 5, or 9. In addition to being used with natural numbers, subtraction can also be incorporated into other sorts of numbers. The letter "-" stands in for subtraction. The difference, the minuend, and the subtrahend are the three numerical components that make up the subtraction operation.
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7/10 × 1/3 × 5/11 Write your answer in simplest form
Answer:
7/66
Step-by-step explanation:
Given problem,
→ (7/10) × (1/3) × (5/11)
Let's solve the given problem,
→ (7/10) × (1/3) × (5/11)
→ (7 × 1 × 5)/(10 × 3 × 11)
→ 35/330
→ 7/66
Hence, the answer is 7/66.
Factor completely: 49x² - 4
Answer:
Factor 49x^2-4 49x2 − 4 49 x 2 - 4 Rewrite 49x2 49 x 2 as (7x)2 (7 x) 2. (7x)2 − 4 (7 x) 2 - 4 Rewrite 4 4 as 22 2 2.
Step-by-step explanation:
Hoped it helped
Answer:
(7x-2)(7x+2)
Step-by-step explanation:
This was the easiest thing I had in Analytic Geometry!!
Is 1/3y = -1 linear or nonlinear?
The equation:
1/3y = -1
Is equivalent to a horizontal line, so the equation is linear.
Is the equation linear or non-linear?A general linear equation is written as:
y = m*x + b
Where m is the slope of the line and b is the y-intercept
In this case, we have the equation:
1/(3y) = -1
So "y" is on the denominator, if we multiply both sides by y, we get:
1/3 = -y
Now we can multiply both sides by -1:
-1/3 = y
So we have a linear equation with a slope equal to zero:
y = 0*x - 1/3 = -1/3
This is a horizontal line.
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The length of a rectangle is 3 yd longer than its width.
If the perimeter of the rectangle is 50 yd, find its length and width.
Answer:
Length is 14 yd width is 11 yd
Step-by-step explanation:
The equation to find the perimeter is ( 2 x Length ) + ( 2 x Width ), so first you divide the perimeter by 2 so we only have to add length + width, you get 25 yds. Since the length is 3 yds longer than width, you can mentally assume Length is going to be 14 yds and width is 11 yd, since Length is 3 yd longer, and finally if you add them together, 14 + 11 = 25. (Apologies if you don't understand I'm not good at explaining)
system of equations?
Answer:
Equation 1: 3x + 4y = 31
Equation 2: 3x - 4y = -1
Add Equation 1 to Equation 2 gets you:
6x = 30
6x/6 = 30/6
x = 5
The answer is x = 5.
help me with my math homework pleasw
Solve one fifth times quantity x plus 15 end quantity equals negative 5.
x = −10
x = −40
x = 8
x = 15
The value of x is -40.
What is an equation?
An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used. In the equation 3x + 5 = 14, for instance, the two expressions 3x + 5 and 14 are separated.
One fifth times quantity x plus 15=(1/5)(x+15)
So, one fifth times quantity x plus 15 end quantity equals negative 5 shows"
(1/5)(x+15)= -5
0.2(x+15)= -5
0.2x+3= -5
0.2x=-5-3
0.2x=-8
x=-8/0.2 = -40
So, the value of x is -40.
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Polly surveyed 850 teenagers to find out their favorite type of music. She found that 32% of the teenagers surveyed like hard rock.
Part A: How many teenagers surveyed like hard rock? Show your work. (4 points)
Part B: In another survey, Damian found that 75% of the total number of teenagers surveyed like pop music. If 150 teenagers like pop music, what is the total number of teenagers that Damian surveyed? Show your work. (4 points)
Part C: Give an example of a situation in which a percentage is greater than 100%. (
a. The number of teenagers that like hard rock is of: 272.
b. The number of teenagers surveyed is of: 200.
c. A percentage greater than 100% is when the percentage of an amount is calculated relative to an smaller amount.
How to obtain the measures?The measures are obtained applying the given proportions and percentages in the context of the problem.
For item a, the amount is of 32% of 850, hence:
0.32 x 850 = 272 teenagers like hard rock.
For item b, we have that 75% = 0.75 of the amount x is of 150, hence the total amount of teenagers surveyed is obtained as follows:
0.75x = 150
x = 150/0.75
x = 200 teenagers were surveyed.
A percentage is calculated as the division of an amount a by an amount b. Hence, if the amount a is greater than the amount b, the percentage will be greater than 100%.
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Julian wants to use a sheet of fiberboard 19 inches long to create a skateboard ramp
with a 16° angle of elevation from the ground. How high will the ramp rise from the
ground at its highest end? Round your answer to the nearest tenth of an inch if
necessary
The ramp would be 5.4 inches high
What is Angle of elevation?The angle of elevation is an angle that is formed between the horizontal line and the line of sight. If the line of sight is upward from the horizontal line, then the angle formed is an angle of elevation.
Length of fiber board = 19 inches
Angle of elevation of ramp = 16°
Height of ramp = h
The height of the ramp, length off fiber board and length of ramp form a right angle triangle with acute angle 16°
tan 16 = opposite/adjacent
tan 16 = h /19
By cross multiplying,
h = 19 tan 16
but tan 16 = 0.2867
h = 19 x 0.2867
h = 5.4 inches
In conclusion the height of the rise of the ramp would be 5.4 inches
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Answer:5.2
Step-by-step explanation:
hard way
A gym employee earn the ame amount each mouth. After working for three month, he earned $4,500. Complete the table to determine how much money he will make over a five-month period. I the relationhip proportional?
The money he will make in a five-month period is $7500.
According to the question,
We have the following information:
A gym employee earn the same amount each month. After working for three month, he earned $4,500.
Now, we will first find how much he has earned in one month by dividing the total salary with the number of months.
Note that the salary is directly proportional to the number of months with constant $1500.
So, we have the following expression:
3 months = 4500
1 month = 4500/3
1 month = $1500
Now, we can find the amount in five months period using multiplication.
5 months = 5*1500
5 months = $7500
Hence, the money he will make in a five-month period is $7500.
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4. After 4 hours of work, a worker has made 12 cars, and after 8 hours he has made 24 total cars. Is this an
example of a proportional relationship? What is the expression of the proportional relationship?
a. Yes
b. No
1 Pt
A
B
Expression:
Answer:
lmfa you answer my questions i recently posted ill answer yours...
Step-by-step explanation:
okay?
A mean ogre stole 9 of your muffins. That 3 was of all of them! With how many did 8 you start?
We started with 11 muffins in total.
What is Addition?
Addition is a method of merging items and counting them as a single large group. In mathematics, addition is the process of joining two or more integers. The numbers added are referred to as addends, while the result or final response obtained after the procedure is referred to as the total.
Solution:
Since the orge stole 9 muffins and still we have 3 muffins left.
This implies that we started with 9+3 = 11 muffins
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pls help me its due tomarow!!!!
Answer:
A: 1
Step-by-step explanation:
the lines only intersect once and will never intersect again so only 1 solutions
Hopes this helps please mark brainliest
What could the answer be? What is Y equal to? Please show your work!
For the given triangle the value of y would be 55°.
What are the angles in a linear pair?
When two lines intersect at a single point, a linear pair of angles is formed. If the angles are adjacent to each other after the two lines intersect, they are said to be linear. The sum of the angles of a linear pair is always 180°.
In the given triangle, x and 100° forms angles in a linear pair,
by using the property of angles in a linear pair,
x + 100 = 180
x = 180 - 100
x = 80°.
Now by using the property of angles of a triangle.
Sum of all angles of a triangle = 180
45 + y + 80 = 180
y + 125 = 180
y = 180 - 125
y = 55°.
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3) Hugh has a goal of exercising 12/4 hours a day. He plans to go on several runs
today. His runs take him 4/6 of an hour. How many runs will Hugh need to go on?
Answer:
Hugh will go on 3 runs !
Step-by-step explanation:
12/4=4/6
HELP ME PLS When solving a proportion to find the 12% tax, t, on a purchase price of $124.29, your cross multiplication led to the cross product equation:
100t = 1,491.48
Describe what step you can take from there in order to find the tax, t, and then state the amount of tax you calculated. Be sure to label your answer and round any decimal to the nearest hundredth.
Answer:
Below
Step-by-step explanation:
100t = 1491.48 divide both sides of the equation by 100 to get
t = 14.9148 round
t = 14. 91
Answer:
t = 14. 91
Step-by-step explanation:
When a certain rubber band is stretched a distance x, it exerts a restoring force of magnitude f = ax+bx2, where a and b are constants. The work done in stretching this rubber band from x = 0 to x = l is:.
This rubber band's work in stretching from x = 0 to x = l is:
[tex]W=(\frac{aL^2}{2}+\frac{bL^3}{3}})[/tex]
Work is a measure of energy transfer that occurs when an object is moved over a distance by an external force that is applied in the direction of Work is a measure of energy transfer that occurs when an object is moved over a distance by an external force that is applied in the direction of displacement .
We say that work has been done whenever a force moves an object. When a ball rolls down a hill due to gravity, when you pick up your backpack from the ground, or when your car's internal engine applies a force to move your wheels, all of these events involve a force moving an object over a distance and thus involve some work. No work is done when a force is applied to an object but it does not move.
Given,
force , [tex]f=ax+bx^2[/tex]
work done can be determined by formula,
[tex]W=\int\limits^a_b F\, dx \\\\W=\int\limits^L_0(ax+bx^2)dx\\\\W=(\frac{ax^2}{2}+\frac{bx^3}{3}})|\limits^L_0\\\\W=(\frac{aL^2}{2}+\frac{bL^3}{3}})-0\\\\W=(\frac{aL^2}{2}+\frac{bL^3}{3}})[/tex]
Thus, the work done is [tex]W=(\frac{aL^2}{2}+\frac{bL^3}{3}})[/tex].
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When 6x = 2y - 18 is graphed in the standard (x,y)
coordinate plane, what is the y-intercept?
A. 2
B. 3
C. 4
D. 6
E. 9
The co-ordinate of y intercept is 9 i.e. option (E)
What is Co-ordinate Geometry?
A coordinate system in geometry is a system that employs one or more integers, or coordinates, to define the position of points or other geometric components on a manifold such as Euclidean space.
Solution:
Given the equation 6x = 2y - 18
See the attached graph below
So we can observe that on x = 0
The y intercept is equal to 9
So, the co-ordinates of the point of intercept is (0,9)
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A local charity is running a fundraiser selling cookies. Each box contains 15 cookies. The ratio of chocolate : vanilla is 2:1.
If the charity sells 2210 boxes of
cookies, how many chocolate
cookies were sold?
The number of chocolate cookies that were sold is 22100.
What is a ratio?Ratio demonstrates how many times one number can fit into another number. Ratios contrast two numbers by ordinarily dividing them. A/B will be the formula if one is comparing one data point (A) to another data point (B).
Since the ratio of chocolate : vanilla is 2:1 and the charity sells 2210 boxes of cookies, the number of chocolate will be:
= 2/(2+1) × 2210 × 15
= 2/3 × 2210 × 15
= 22100
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suppose the height of children age 2 years has a probability of 0.54 to be 34 inches or taller. a random sample of 31 children age 2 years is collected.a) Calculate the mean of the sampling distribution of the sample proportion(b) Calculate the standard deviation of the sampling distribution of the sample proportion. (Round your answer to three decimal places.)
Rounded to three decimal places, the standard deviation of the sampling distribution of the sample proportion is 0.024.
What is the standard deviation?The degree of variance or dispersion of a collection of numbers from the mean is measured by standard deviation. It is calculated as the square root of variance, which is the average of the squared deviations from the mean. A low standard deviation suggests that the values are close to the mean, whereas a high standard deviation suggests that the values are dispersed over a wider range. In many other disciplines, including finance and economics, standard deviation is frequently used to assess the risk or volatility of a particular dataset. It is also frequently used in statistics and probability theory. Due to its ability to objectively compare and contrast various values, it is a crucial statistic for comprehending and analyzing data.
How to solve?
sqrt( (population proportion * (1 - population proportion)) / sample size)
sqrt( (0.54 * (1 - 0.54)) / 31) = 0.024
Rounded to three decimal places, the standard deviation of the sampling distribution of the sample proportion is 0.024.
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Which ordered pair can be plotted together with these four points, so that the resulting graph still represents a function?
(1,3)
(3, 1)
(-3,1)
(0,0)
Answer:
(0, 0)
Step-by-step explanation:
Step 1: Define a Function
Recall that a graphed relation can only be a function if every input (x-value) has exactly one output (y-value), and not the other way around. That is, a function can have the points (2, 3) and (3, 3), but not (2, 3) and (2, 4), for example. This information will be very useful in solving this problem.
Step 2: Take Inventory of the Current Points
Let's first take into account what points we already have plotted. Using the graph, we can see that our current 4 points are (-3, 0), (-1, 1), (1, 2), and (3, 3). Again, the y-values do not really matter here as they can be repeated, but the x-values are what we need to pay attention to, so let's disregard the y-values of the points and just list the x-values as x = -3, -1, 1, and 3.
Step 3: Use this Information to Choose the Correct Answer
We know that in order to still be a function, the point we add must have an x-value that is not among the above list (and if it is, it must be the same exact point - e.g. if one of the options was (-3, 0), then it would technically work, but that is not the case with any of these points so we can ignore this possibility).
We can see that the x-values of the options are x = 1, 3, -3, and 0. Of these options, 1, 3, and -3 are already in our list, so those are not correct. Therefore, the only point that will keep the graphed relation a function is (0, 0). (Don't worry that the graph doesn't look like a straight line, a function is defined as any set of points that has exactly one output for every input - this does not necessarily mean the function follows an equation as we may normally think!)
Answer:
(0,0)
Step-by-step explanation:
All of the other choices would result in there being two values of y for a given x (thus NOT a function)
A cla i made up of 6 boy and 14 girl. Half of the boy wear glae. A tudent i elected at random from the cla. What i the probability that the tudent i a boy with glae?
Write your anwer a a fraction in implet form
The probability that the student is a boy with glass is 3/20
Number of boys in the class = 6 boys
Number of girls in the class = 14 girls
Half of the boys wear glass
The number of boys that wear glass = 6 / 2
= 3 boys
Total number of students in the class = 6 + 14
= 20 students
Probability = Number of favorable outcomes / Total outcomes
= The number of students that wear glass / Total number of students
Substitute the values in the equation
= 3/20
Hence, the probability that the student is a boy with glass is 3/20
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