The Hypergeometric distribution is 0.7717, and the binomial distribution is 0.7763. The probability from the binomial approximation is greater than the probability from hypergeometric distribution.
What is Hypergeometric distribution?In statistics, a hypergeometric distribution is a distribution function in which members of two groups are chosen from without being replaced. The absence of replacements in the hypergeometric distribution sets it apart from the binomial distribution. As a result, it is frequently used in random sampling to ensure statistical quality.
Given that,
The number of defective bolts are 5 out of 200.
Thus, the probability of 0 defective bolts is given as:
1. Hypergeometric distribution:
P (X= 0) = 5C 0 (195C 10) / (200C 10)
= 0.7717
2. Binomial approximation:
B(n, m/ N)
P (X= 0) = 10C 0 (0.025)^0 (1-0.025)^10
= 0.7763
Thus, probability from the binomial approximation is greater than the probability from hypergeometric distribution.
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If a Ferris wheel makes 1 full revolution every 12 minutes, what is its angular speed?
Answer:
0.5236 radians per minute
or
0.00872665 radians per second
Step-by-step explanation:
Let's first define angular speed
Angular speed is the rate at which an object changes it angles which we measure in radians in a given time. Angular speed has a magnitude (a value only whereas velocity is a vector with speed and direction)
The angular speed, ω of an object is given by the formula
ω = θ/t
where θ is the angle in radians
1 full revolution is 360° or 2π radians
t = time taken for completing θ radians of rotation
We are given that the Ferris wheel completes 1 full revolution in 12 minutes
1 full revolution = 2π radians
t = 12 minutes
Angular speed = ω = θ/t = 2π/12 radians/minute
ω = 0.5236 radians per minute
or in radians per second
ω = 0.5236/60 = 0.00872665 radians per second
1-
Use the price-demand function below, to answer parts (A) and (B).
p(x)=75-3x
1≤x≤20
(A) What is the revenue function?
R(x) =
What is the domain of the revenue function?
(B) complete table
X R(x)
1 72
4
8
12
16
20
The revenue function (Rx) when x is 1, 4, 8, 12,16, 20 are 72,252,468,432, and 300 respectively.
What is revenue function?Revenue function is a formula or equation representing the way in which particular items of income behave when plotted on a graph. For example, the most common revenue function is that for total revenue in the equation y = bx, where y is the total revenue, b is the selling price per unit of sales, and x is the number of units sold.
R(x) = x × P(x)
When x = 1
R(x) = 1(75-3)
R(x) = 72
when x = 4
R(x) = 4( 75-12)
= 252
when x = 12
R(x) = 12(75-36)
R(x) = 468
when x = 16
R(x) = 16( 75-48)
= 432
when x = 20
R(x) = 20( 75-60)
= 300
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✓ Completed Question Help A nursery owner buys 7 panes of glass to fix some damage to her greenhouse. The 7 panes cost $20.65. Unfortunately, she breaks 2 more panes while repairing the damage. What is the cost of another 2 panes of glass? 2.1.PS-10
Answer: $ 5.90 is the the cost of 2 panes of glass
In order to solve this we must divide the number of panes, by the cost spent on the panes. 20.65 divided by 7 is 2.95. This means that each pane is $ 2.95. If there are two panes that were also broken, we have to add 2.95 twice, which is $5.90. This means that the nursey owner must spend another $5.90 on two panes.
I hope this helps & Good Luck <3 !!!
Find n if (n + 1)! = 16n! + 16(n-1)!
Step-by-step explanation:
(n+1)! = (n+1)n(n-1)(n-2)...×3×2
16n! = 16n(n-1)(n-2)...×3×2
16(n-1)! = 16(n-1)(n-2)...×3×2
we can now divide both sides by (n-1)! and get
(n+1)n = 16n + 16
n² + n = 16n + 16
n² - 15n - 16 = 0
1×n² - 15n - 16 = 0
we try to bring this into a form
(n + a)(n - b)
one factor has to contain "-", because we have "-16".
and because -15 = 1 - 16, we see that
a = 1
b = 16
n² - 15n - 16 = (n + 1)(n - 16)
and that is 0, when at least one of the factors is 0, because 0×... = 0.
so, the solutions are
n = -1
n = 16
n = -1 does not make any sense for n!
so, n = 16 is the solution.
Each ounce of a substance A supplies 3% of the nutrition a patient needs. Substance B supplies 10% of the required nutrition per ounce, and substance C supplies 15% of the required nutrition per ounce. If digestive restrictions require that substances A and C be given in equal amounts, and the amount of substance B be1 1/5
of either of these other amounts, find the number of ounces of each substance that should be in the meal to provide 100% of the required nutrition.
Incorrect: Your answer is incorrect.
______oz of substance A
______oz of substance B
______oz of substance C
Answer:
x = 17.2 oz of substance A and C
x = 3.7 oz of substance B
Step-by-step explanation:
This is a word problem in mathematical optimization, which involves finding the values that maximize or minimize some objective function. To solve this problem, we need to find the optimal number of ounces of each substance to provide 100% of the required nutrition.
Let x be the number of ounces of substance A and C. Then the amount of substance B is 1 1/5 times either of these, or 1 1/5 x.
Since each ounce of substance A supplies 3% of the nutrition, the total contribution from A is 3x%. Similarly, the total contribution from B is 10 * 1 1/5 x = 11 x/5% and from C is 15x%.
The objective is to find x such that the total contribution from all three substances is 100%, or 3x + 11 x/5 + 15x = 100.
Solving for x, we have
29x/5 = 100
x = 100 * 5 / 29 = 17.24 oz
So, 17.24 oz of substance A and C, and 1 1/5 * 17.24 oz = 3.65 oz of substance B should be in the meal. Rounding to the nearest tenth, we have:
x = 17.2 oz of substance A and C
x = 3.7 oz of substance B
Tanya decided to lease a car.
the lease includes a money factor of 0.00324.
What interest rate is shawna being charged in her lease? ( round to the nearest hundredth).
A. 0.78%
B. 7.78%
C. 1.35%
D. 13.5%
A correct answer is option (B) 7.78%. so, the interest rate is 7.78% being charged in her lease.
What is the interest rate?
Interest rate is the amount charged over and above the principal amount by the lender from the borrower. In terms of the receiver, a person who deposits money to any bank or financial institution also earns additional income considering the time value of money, termed as interest received by the depositor.
The interest rate in a lease can be calculated using the money factor, which is essentially a type of interest rate used in auto leasing.
To calculate the interest rate from the money factor, multiply the money factor by 2400.
In this case, the money factor is 0.00324, so the interest rate would be:
0.00324 * 2400 = 7.776%
Therefore, the correct answer is option (B) 7.78%. so, the interest rate is 7.78% being charged in her lease.
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A correct answer is option (B) 7.78%. so, the interest rate is 7.78% being charged in her lease.
Which interest rate is it?The amount that the lender charges the borrower over and beyond the principal amount is referred to as the interest rate. A person who deposits money in a bank or other financial institution also earns additional income in terms of the recipient, known as interest, taking into account the time value of money.
The money factor, which is essentially a sort of interest rate utilized in auto leasing, can be used to compute the interest rate in a lease.
By multiplying it by 2400, you can determine the interest rate from the money element.
Given that the money component in this situation is 0.00324, the interest rate would be:
The result of three consecutive conversions from an interest rate to a money factor is 2400 (1/2 × 1/12 × 1/100). 6/2400 = 0.0025 money factor, which can be multiplied by the entire amount borrowed to see how much the monthly interest would be roughly.
(1/2 × 1/12 × 1/100). 6/2400 = 0.0025
0.00324 × 2400 = 7.776%
Therefore, the correct answer is option (B) 7.78%. so, the interest rate is 7.78% being charged in her lease.
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6. Which quadrant is the pre-image located in?
B
Quadrant III
Quadrant I
O Quadrant II
O Quadrant IV
9
A
Therefore , the solution of the given problem of data plotting comes out to be Pre image is located in II quadrant.
What is data plotting?Graphing the correlation between two additional variables is the most common way to use a chart to present data. It is also permitted to use hand-drawn or digitally generated diagrams. Go three pieces up and 2 types to the right starting at the origin. Displaying the numbers for rows 2, 3, and 4 on the standard system is crucial. Make sure to be very clear in what you say.
Here,
Given :
A figure having pre image and post image ,
We have to find in which quadrant the pre image is located,
So,
In order to find that,
We see the image are in quadrant II and quadrant III
Since ,
After II quadrant III quadrant comes,
Thus , Pre image is located in II quadrant.
Therefore , the solution of the given problem of data plotting comes out to be Pre image is located in II quadrant.
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PLEASE HELP!! .1.PS-8 A package of 6 pairs of insulated gloves costs $43.74. What is the unit price of the pairs of gloves?
Answer:
Step-by-step explanation:
divide $43.74 by 6 = 7.29 per pair
A tree planted today had a height of 5 feet and grows one foot each month is the height of the tree a function of the number of months?if so is it a linear or nonlinear function
linear function
x=5+n
given:
height of tree = 5ft
growth per month = 1ft
Find:
equation:
Computation:
asume:
New height of x
number of month = n
x=5+1(n)
x=5+n
hope this helped.
18) In the adjoining figure, ABCD is a parallelogram in which DE _|_ AB and DF _|_BC, If AB=6 cm, BC=4.5 cm, DE=3 cm, find the length of DF.
The solution is, EF = 4√3
What is area of a rectangle?Area of a rectangle (A) is the product of its length (l) and width (w).
A= l. w
here, we have,
In rectangle ABCD, AB = 6, BC = 8, and DE = DF.
ΔDEF is one-fourth the area of rectangle ABCD.
We want to determine the length of EF.
First, we can find the area of the rectangle. Since the length AB and width BC measures 6 by 8, the area of the rectangle is:
A = 48 cm^2
The area of the triangle is 1/4 of this. Therefore:
A = 12 cm^2
The area of a triangle is half of its base times its height. The base and height of the triangle is DE and DF. Therefore:
12 = 1/2 * DF *DE
Since DE = DF:
24 = DF^2
Thus:
DF = 2√6 = DE
Since ABCD is a rectangle, ∠D is a right angle. Then by the Pythagorean Theorem:
DF^2 + DE^2 = EF^2
Therefore:
now, Squaring & Adding , we get,
FE^2 = 48
And finally, we can take the square root of both sides:
EF = 4√3
Hence, The solution is, EF = 4√3
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A circular railroad-crossing sign has a diameter of 30 inches.Which measurement is closest to the area of the sign in square inches?
Answer:
706.86
Step-by-step explanation:
The area of the sign will be found with the formula πr^2
r = 15 since the radius is half of the diameter
π(15)^2 = 706.86
Answer:
707 square inches.
Step-by-step explanation:
The area of a circle can be found using the formula A = πr^2, where r is the radius of the circle. The diameter of a circle is equal to twice the radius, so we can find the radius by dividing the diameter by 2.
In this case, the diameter of the circular railroad-crossing sign is 30 inches, so the radius is 30/2 = 15 inches.
So, the area of the sign is A = π * 15^2 = π * 225 = 706.86 square inches.
Rounding to the nearest whole number, the area of the sign is 707 square inches.
Can somebody please help awnser these questions!
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 a charitable organization.
{ a } -
Assume that the annual salary of the baseball player is ${x}. The amount donated would be -
10% of {x} = ${x/10}
In $120, you can send 1 child to school.
In $1, you can send (1/120) childrens to school.
In ${x/10}, you can send {x/1200} childrens to school.
{ b } -
Same answer as in the case of part {a}.
Therefore, the answers to each part is given above.
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Determine by trigonometry the magnitude of the force P so that the resultant force exerted on the stake is vertical. (Round the final answer to a single decimal place.)The magnitude of the force is N.
by trigonometry the magnitude of the force P so that the resultant force exerted on the stake is vertical. The magnitude of the force is 196.6 N.
What is resultant force?When a force system acts on an item, the difference between the forces is referred to as the Resultant force. When an item is under the influence of two or more forces, the combined force may be calculated by adding up the separate forces. The forces in all directions will be the same for all the forces if they are all acting in the same direction. The SI unit for resultant force is the Newton.
Given that,
α = 30°
Using the triangle rule, and the law of sines:
120 N / Sin 30° = P / Sin 25°
or, P = (Sin 25° / Sin 30°) × 120
or, P = 101.428 N
or, P = 101.4 N
and also, θ = 180 - 25 - 30
θ = 125°
the value of resultant is:
120 N / Sin 30° = R / Sin 25°
or, R = 196.6 N
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use differentials to approximate the value of sqrt(99.4). what is the percent error oin this calculation
The percentage error by calculating by differentials to approximate value of sqrt(99.4) = 0.00045 percentage.
For percentage error Here first we have to find the value of sqrt(99.4) by normal calculation and second we will calculate it by differential method then we will find the percentage error .
To approximate sqrt(99.4) we will use formula for linear approximation as given below
f(x) = f(c) + f′(c)(x−c)
and we are dealing with square root so we have to find the f(x) ad here
f(x) = √x
and we will calculate f'(x) and here it is
f'(x) = 1/(2√x)
Here, x=99.4 and we choose c =100 because that’s the closest perfect square number to 99.4. so
f(c) = f(100) = √100 = 10
f'(c) = f'(100) =1/(2√100) = 1/20
f(x) =f(c) + f′(c)(x−c)
f(x) = f(99.4)=f(100)+f'(100)(99.4-100)
=10+1/20*(-0.6)
=9.97
Here we find the value by differential = 9.97
and by simple calculation the value is = 9.96995486
ans percentage error = (real value - differential value)/100
= (9.96995486-9.97)/100 = 0.00045 percentage
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Given quadrilateral DEFG with vertices
D(-9,-5), E(5,4), F(-6,-2), and G(4,2).
Determine the coordinates of the image of
DEFG after being reflected about the origin.
The coordinates of the image of quadrilateral DEFG after being reflected about the origin include the following:
D' = (9, 5).
E' = (-5, -4).
F' = (6, 2).
G' = (-4, -2).
What is a reflection?In Geometry, a reflection can be defined as a type of transformation which moves every point of the object by producing a flipped but mirror image of the geometric figure.
Generally speaking, reflecting a point about the origin is a a type of transformation which causes both the x-coordinate and the y-coordinate to become negated (the signs are changed);
(x, y) → (-x, -y)
Ordered pair D = (-9, -5) → Ordered pair D' = (9, 5).
Ordered pair E = (5, 4) → Ordered pair E' = (-5, -4).
Ordered pair F = (-6, -2) → Ordered pair F' = (6, 2).
Ordered pair G = (4, 2) → Ordered pair G' = (-4, -2).
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. . Write all the three-digit numbers between 100 and 160 which are divisible by 2 and not divisible by 4 and divisible by 5 14
Independent practice 5.how many 1 • 1/6
Find the measure of
Answer:
C = 5x+6
Step-by-step explanation:
one of the properties of triangle is the supplemental angle of B = sum of the other 2 angles
so 11x+1=6x-5+c
C = 5x+6
A proportional relationship between x and y exists whose slope is 2/3. Write the equation of this relationship in terms of x and y.
Answer:
The equation of the proportional relationship can be written as y = (2/3)x.
Step-by-step explanation:
This equation is derived by using the fact that the slope of the relationship between x and y is 2/3. The slope of a line can be expressed as the ratio of the change in y to the change in x, which is represented by (delta y) / (delta x).
Since the slope is 2/3, the change in y for a unit change in x can be expressed as 2/3 * x. This relationship can then be written in terms of x and y by solving for y:
y = (2/3) * x.
In this equation, y is directly proportional to x with a constant of proportionality equal to 2/3.
find the surface area
Answer: 1468.17
Step-by-step explanation:
3. Find the area of the following shape. Make sure to indicate what shapes were used, by sketching on the image, listing formulas, and show work listed for each shape. (5 total points – 2 for accurate shapes, 2 for accurate work, 1 for total area answer)
the total area of the figure will be 53.13 unit square.
What is Area?The area is the entire amount of space occupied by a flat (2-D) surface or an object's form. On a sheet of paper, draw a square using a pencil. It has two dimensions. The area of a form on paper is the area that it occupies.
Given a figure that we will transform into three parts A, B, and C as shown in the attached figure
Where A is a semicircle with a radius of 3 unit
b is a triangle with a height of 6 and a base of 3 units
and C is a rectangle with a length of 6 and a width of 5 units
From the general formulas of area,
area of semicircle = pi/2 radius * radius
Area of rectangle = length * width
Area of triangle = 1/2 height * base
in our case,
area of semicircle = pi/2 3* 3
Area of semicircle = 14. 13 unit square
Area of rectangle = 6* 5
Area of rectangle = 30 unit square
Area of triangle = 1/2 6* 3
Area of triangle = 9
Thus, the total area of the figure will be = 14. 13 + 30 +9
Therefore, the total area of the figure will be 53.13 unit square.
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what is the area model for 1778/7 -
It should be noted that the area model method is based on the simple equation that is used to find the area of a rectangle:
the length times the width equals the total area (LxW=A).
What is an area?The area of a shape simply means the total space that is taken by the shape. It simply expresses the extent of the region on a particular plane as well as a curved surface.
For example, the area of a rectangle with the length of 48 units and a width of 21 units can be measured by multiplying 48 by 21. This will be 1008 units².
A overview was given as your information is incomplete
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Sort the terms into groups of "like terms."
The terms, when sorted into groups of " like terms " gives:
Like terms :
- 7 y ² and y ²0. 5 kt and - 10 kt6 and 9Unlike terms :
- 4 p and p ²5 x and 5 3 ad and 2 bd Which terms are like and unlike terms ?To sort a set of algebraic terms into groups of like terms, you must look for terms that have identical variables and exponents. These terms can be combined and simplified using the rules of addition and subtraction. in this scenario, they include: - 7 y ² and y ², 0. 5 kt and - 10 kt, 6 and 9.
Terms that have different variables or exponents are considered unlike terms and cannot be combined in this way. They include : - 4 p and p ², 5 x and 5, 3 ad and 2 bd .
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Find the nth term of the sequence. When the first 4 terms are
1st term 2nd term 3rd term 4th term
4.75 10.5 16 21
Answer:
5564+746655754673346
Which of the following is not a reason for testing if the population correlation coefficient is zero?
-To see if r and rho (rho. are equal)
-All of the options are correct.
-To determine if a significant X-Y relationship exists.
-To make inference from sample to population.
-To bring sample size into the analysis.
The correct option on this statistics topic is (c) To determine if a significant X-Y relationship exists.
What is statistics as a subject?Statistics is a science and perhaps also the art of learning from data. As a discipline, it deals with the collection, analysis, and interpretation of data, and the effective communication and presentation of data-based results.
What is correlation coefficient?In statistics correlation coefficient is a single number that represents the strength and direction of the relationship between variables.
Different types of correlation coefficients may be appropriate for your data, depending on the measurement level and distribution. Pearson's product-moment correlation coefficient (Pearson's r) is commonly used to assess the linear relationship between two quantitative variables.
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Find the equation of the line with z-intercept (-1,0) and y-intercept (0, -3).
y =
The line's equation is y = 3x - 3 with the z-intercept (-1, 0) and the y-intercept (0, -3).
What does "intercept" signify in mathematics?What do intercepts mean? The x-intercept and y-intercept are the points at which a line crosses the x- and y-axes, respectively.
Put x = 0 and work out y to determine the y-intercept. The purpose will be (0, y). Set y = 0 and solve for x to determine the x-intercept. The purpose will be (x, 0).
What does intercept form mean exactly?It gives both a slope and an intercept, hence the name "slope intercept form." Thus, this is your slope. You can move by keeping in mind that slope is rise over run.
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Use Heron's Area Formula to find the area of the triangle. (Round your answer to two decimal places.) a = 57 , b = 43 , c = 58
The Area of the given triangle is 1146.27 sq. units.
Heron's Formula:An important plane geometry theorem also referred to as Hero's formula.
By dividing the quadrilateral into two triangles along its diagonal, this formula is also used to determine the quadrilateral's surface area.
Given the semiperimeter and the lengths of the sides a, b, and c
[tex]p=\frac{a+b+c}{2}[/tex]
of a triangle, Heron's formula gives the area of the triangle as
[tex]A=\sqrt{p(p-a)(p-b)(p-c)}[/tex].
Now in the given question,
a = 57
b = 43
c = 58
Hence, the semi-perimeter,
[tex]p=\frac{a+b+c}{2}[/tex]
[tex]p=\frac{57+43+58}{2} =79[/tex]
Now we calculate the area,
[tex]A=\sqrt{p(p-a)(p-b)(p-c)} \\A=\sqrt{79(79-47)(79-43)(79-58)} \\A=\sqrt{79(22*36*21)} \\A=\sqrt{79*16632} \\A=\sqrt{1313928} \\A=1146.266[/tex]
Hence, the area of triangle is 1146.27 sq. units.
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Answer the questions below
Two triangles having two pairs of congruent sides and a pair of congruent angles do not necessarily meet the SAS congruence criterion, therefore Angie is incorrect.
What is congruency?The Side-Angle-Side Congruence Theorem (SAS) defines two triangles to be congruent to each other if the included angle and two sides of one is congruent to the included angle and corresponding two sides of the other triangle.
An included angle is found between two sides that are under consideration.
In the image, the triangles are congruent to each other by the Side-Angle-Side Congruence Theorem (SAS).
Thus, two triangles having two pairs of corresponding sides and one pair of corresponding angles that are congruent to each other is not enough justification for proving that the two triangles are congruent based on the SAS Congruence Theorem.
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Diego measures the pulse rate of some of his friends. What is the
modal class of pulse rates? Please help
Answer:
modal class is 70 - 79
Step-by-step explanation:
the modal class is the interval which occurs most often
in this case 70 - 79 occurs 6 times
then modal class is 70 - 79
A company wants to have 5 digit phone extensions with the first digit not being zero. How many different phone extensions are possible?
90, 000 will be the total number of different phone extensions.
What are permutation and combination?A permutation is an orderly arrangement of things or numbers. Combinations are a means to choose items or numbers from a collection or set of items without worrying about the items' chronological order.
Given, A company wants to have 5-digit phone extensions with the first digit not being zero.
This problem is an application of the Basic Counting Rule which was discussed above. We want to compute the number of different 5-digit phone extensions.
there are 10 different digits, which are 0,1,2,3,4,5,6,7,8,9. The first digit can't be 0.
There are 9 choices for the first digit. For each choice of the first digit, there are 10 choices for the second digit. For each choice of the first and second digits, there are 10 choices for the third digit, and so on.
According to the Basic Counting Rule, we know that the total number of phone extensions is the product of the number of ways to choose each digit (the product of the 6 above numbers).
the total number of different phone extensions is = 9 *10 *10 *10 *10
therefore, the total number of different phone extensions is = 90,000.
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