On the NASA space shuttles, a substance called kevlar epoxy is employed. This epoxy's strands underwent testing for 90% breaking strength.
The range is: 7.87The values of ∑X and ∑X² are respectively: 62.12 and 164.3516The values of the sample mean, variance and standard deviation are respectively: 1.24, 1.78 and 1.334The coefficient of variation is: 107.356Mean, Range, variance, standard deviation
A) Formula for range is;
Range = Highest term - Lowest term
Range = 7.89 - 0.02
Range = 7.87
B) Sum of all the given 50 epoxy samples is gotten to be;
∑X = 62.12
From online statistics calculator, we have; ∑X² = 164.3516
C) Formula for sample mean here is;
x' = ∑x/n
x' = 62.12/50
x' = 1.24
Formula for variance is;
σ² = [∑x² - [(∑x)²/n]]/(n - 1)
σ² = (164.3516 - (62.12²/50))/(50 - 1)
σ² = 1.78
Formula for the standard deviation is;
σ = √variance = √1.78
σ = 1.334
D) Formula for coefficient of variation is;
CV = (σ/x') * 100
CV = (1.33379/1.2424) * 100
CV = 107.356
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What is the formula of standard deviation method?
The formula of standard deviation method is
[tex]P=\sqrt{\frac{ \sum(X-\mu)^2}{N}}[/tex]
[tex]S=\sqrt{\frac{ \sum(X-\bar{x})^2}{n-1}}[/tex]
What is the standard deviation?
A standard deviation is a measurement of the data's dispersion from the mean. Data are grouped around the mean when the standard deviation is low, and are more dispersed when the standard deviation is high.
Standard deviation It is a measure of how spread out numbers are. It is the square root of the Variance, and the Variance is the average of the squared differences from the Mean.
population mean:
[tex]P=\sqrt{\frac{ \sum(X-\mu)^2}{N}}[/tex]
X- the value in the data distribution
[tex]\mu[/tex] - the population mean
N- total number of observations
[tex]S=\sqrt{\frac{ \sum(X-\bar{x})^2}{n-1}}[/tex]
[tex]\bar{x}[/tex] - the sample mean
n- total number of observations
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Write the standard form of the equation of the circle with the given characteristics. Center: (6, 1); Solution point: (5,9) Select one: a. (x + 6)^2 + (y + 1)^2 + 65 = 0 | b. (x+6)^2 + (y + 1)^2 = 65 | c. (x – 6)^2 + (y - 1)^2 = 65 | d. (x-1)^2+(3-6)^2 = 65 | e. (x - 6)^2 + (y + 1)^2 – 65 = 0
The standard form of the equation of the circle with the given characteristics is (x - 6)² + (y - 1)² = 65.
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.
Given, center: (6, 1) and solution Point: (5,9)
By solution point, it means that the circle passes through that point. Hence, the radius of the circle is the distance between (6, 1) and (5,9)
Distance formula is given by
D = √[(x2 - x1)² + (y2 - y1)²]
D= √[(5 - 6)² + (9 - 1)²] = 8.062
r= 8.062 or r²=65
We have, equation of the circle centered ant (h, k) and radius ‘r’ as
(x - h)² + (y - k)² = r².
=> (x - 6)² + (y - 1)² = 65.
The standard form of the equation of the circle with the given characteristics is (x - 6)² + (y - 1)² = 65.
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If sin theta equals0.6224, cos theta equals0.8820 and tan theta equals20.8651, then what is sec theta plus cot theta?
The value of the operation sec theta plus cot theta using trigonometric ratios is; 2.465
How to solve trigonometric ratios?The primary trigonometric ratios are;
sin x = opposite/hypotenuse
cos x = adjacent/hypotenuse
tan x = opposite/adjacent
sec x = 1/cos x
cosec x = 1/sin x
cot x = cos x/sin x
The parameters are;
sin θ = 0.6224
cos θ = 0.8820
Thus;
sec θ = 1/cos θ = 1/0.8820
cot θ = cos θ/sin θ = 0.8820/0.6624
Thus
sec θ + cot θ = (1/0.8820) + (0.8820/0.6624)
= 2.465
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center: (6, 1); solution point: (5, 9)
If the Circle has Center: (6, 1); and solution point: (5, 9) , then the standard form of Equation is (x - 6)² + (y - 1)² = 65 .
The standard form of a circle is given by ⇒ (x - h)² + (y - k)² = r²,
where (h, k) is the center of the circle and r is the radius.
To find the standard form of the circle that has center (6, 1) and a solution point (5, 9), we need to find the radius "r" first.
The distance(r) between the center and the solution point is given by the Pythagorean theorem:
⇒ r = √((5 - 6)² + (9 - 1)²)
⇒ r = √((-1)² + (8)²)
⇒ r = √65
Now substituting radius(r = √65) in the standard form of the circle:
we get ;
⇒ (x - 6)² + (y - 1)² = √65²
⇒ (x - 6)² + (y - 1)² = 65
Therefore , the standard form of circle is (x - 6)² + (y - 1)² = 65 .
The given question is incomplete , the complete question is
Write the standard form of the circle that has Center: (6, 1); and solution point: (5, 9) .
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2,500 centimeters equals how many meters?
a2 b2 c2 is equal to ?
Hence the formula of [tex]a ^2 + b^ 2 + c^ 2[/tex] is [tex]( a + b + c )^ 2 - 2 ( ab + bc + ca ) .[/tex]
What is meant by formula?Formulas are equations that compute values from your spreadsheet. A formula always starts with the equal sign (=).
Using a calculating operator and a constant, you can make a straightforward formula.
For instance, the equation =5+2*3 multiplies two numbers before adding one more to the outcome.
A formula is a rule or relationship in mathematics that utilizes letters to indicate amounts that might change; these amounts are known as variables. For instance, the triangular area calculation formula.
The word "formula" is pluralized to "formulas." A list of elements that are employed in various concoctions and potions is referred to as a formula, which can also refer to a specific mathematical calculation.
Because English might be erratic at times, newborns can also be fed formula.
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On a cold winter day in
Poston, MA the
temperature
fell 27 degrees over the
course of 9 hours. Pased on
this change in temperature,
how many degrees did the
temperature fall each hour?
Answer:
3 Degrees each hour
Step-by-step explanation:
27 divided by 9 = 3
d. q • q + r² and 2q + (r + r)
Answer:
q² + r² and2q + 2r
Step-by-step explanation:
q x q + r² and 2q + (r + r)
q × q + r² = q² + r²
----------
2q + (r + r) = 2q + 2r
Question 1 of 10
Ponyboy shivered as he recalled the Socs jumping him and asking if he ---
Ponyboy shivered as he recalled the Socs jumping him and asking if he was a greaser.
Ponyboy Shivers Recall Socs JumpThe statement is referencing a scene from the novel "The Outsiders" by S.E. Hinton. In the novel, Ponyboy is a member of a poor, lower-class gang called the "greasers." The Socs are the wealthier, more privileged gang in town. The scene described in the statement is likely one in which Ponyboy is confronted and beaten up by members of the Socs gang, who are asking him if he is a member of the greaser gang.
The scene highlights the tensions and conflicts between the two gangs and their different experiences growing up in different social classes.
"The Outsiders" is considered a young adult novel, so it can be read by kids who are at or near the target age range for that genre, typically around 12 to 18 years old. However, the themes and content of the novel may be mature for some younger readers, so it is always a good idea for parents or guardians to read the book first and determine if it is appropriate for their child.
Additionally, individual reading levels can vary greatly, so it is always best to assess a child's individual abilities and interests when determining if a particular book is suitable for them to read.
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Z varies jointly with x and y. If x = 7, y = 3, and z = −14, write the variation equation and find y when z = −8 and x = 3
The equation is z = (-2/3)*xy with of x , y and z are jointly varied.
What is Joint Variation ?Joint variation describes a situation in which, while the other variables are held constant, the value of one variable relies on the values of two or more additional variables.
Joint variation is used to describe when more than two variables are directly correlated or when one variable changes as a result of the change product of more than two variables. X can be symbolically expressed as X YZ if it is in joint variation with Y and Z. If Y is also constant, then X and Z directly depend on one another.
Joint variation is a type of variation where a quantity changes when two or more other numbers are multiplied together. For instance, when a rectangle's length or breadth changes, so does its area. Where A is the area, l is the length, and w is the width, we say that A = lw.
Joint Variation of x,y and z
z = kxy
k is the cofficient
for x = 7, y = 3 and z = -14
-14 = k*3*7
⇒k = -2/3
for x= 3 and z = -8
-8 = (-2/3)*3*y
y = 4
The equation is z = (-2/3)*xy with of x , y and z are jointly varied.
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a store gathers some demographic information from their customers. the following chart summarizes the age-related information they collected:agenumber of customers7220-305230-4010040-507150-606960one customer is chosen at random for a prize giveaway.what is the probability that the customer is at least 20 but no older than 60? what is the probability that the customer is either older than 40 or younger than 20?
Given the following information, we can calculate the requested probabilities:
Probability that the customer is at least 20 but no older than 60:
Number of customers in the specified age range: 72 + 52 + 100 + 71 + 69 = 364
Total number of customers: 364 + 1 = 365
So, the probability is 364/365 = 0.997
Probability that the customer is either older than 40 or younger than 20:
Number of customers in the specified age range: 72 + 52 = 124
Total number of customers: 365
So, the probability is 124/365 = 0.338
Note: The chart doesn't provide information about customers who are older than 60 or younger than 20, so we can't calculate the probability for those ranges.
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find the equation of the plane with the given description. passes through (1, 3, 6) and is parallel to x = 11.
The equation of the plane that passes through (1, 3, 6) and is parallel to x = 11 is x = 1.
What do you mean by Algebraic Expression?An algebraic expression is a mathematical phrase that can contain numbers, variables, and operations (such as addition, subtraction, multiplication, and division). It represents a value that can be determined if the values of the variables are known. An algebraic expression does not contain an equal sign and cannot be solved like an equation, but it can be simplified or manipulated using algebraic rules. For example, the expression 2x + 3y is an algebraic expression, where x and y are variables.
A plane can be represented by a normal vector (a,b,c) and a point (x⁰,y⁰,z⁰) that lies on the plane. If a plane is parallel to the plane x = 11, the normal vector must be in the direction of the x-axis, meaning (a,b,c) = (1,0,0).
The equation of the plane can then be found using the point-normal form, which is given by:
ax + by + cz = d, where d = ax⁰ + by⁰ + cz⁰
Plugging in the values for (1,3,6) and (a,b,c) = (1,0,0), we get:
a(1) + b(3) + c(6) = d
1 + 0 + 0 = d
d = 1
So the equation of the plane that passes through (1,3,6) and is parallel to x = 11 is: x = 1
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PLEASE HELP!!! A right cone has a base with diameter 6 units. The volume of the cone is 72π cubic units.
What is the length of a segment drawn from the apex to the edge of the circular base
(slant height)?
Round to the nearest tenth. This is a multi-step problem so do not round until the final answer.
The segment drawn from the apex to the edge of the circular base is __ units.
The segment drawn from the apex to the edge of the circular base is 24.2 units.
The Pythagorean Theorem: What is it?A right triangle's hypotenuse, or side opposite the right angle, has a square length that, according to the Pythagorean theorem, is equal to the sum of the squares of the lengths of the other two sides.
The Pythagorean Theorem can be used to determine the slant height of a right cone. The circular base's radius is equal to its diameter times half, or 6/2 = 3 units.
The volume of the cone can be found using the formula:
V = (π/3)r²h
Where r is the radius, and h is the height of the cone. Plugging in the given values, we have:
72π = (π/3)r²h
72π = (π/3)3²h
72π = (π/3)9h
72π = 3πh
24 = h
Using the Pythagorean Theorem, we can find the slant height as follows:
c² = a² + b²
Where a and b are the height and radius of the cone, and c is the slant height. Plugging in the values we have:
c² = 24² + 3²
c² = 576 + 9
c² = 585
c = 24.2
Hence, the segment drawn from the apex to the edge of the circular base is 24.2 units.
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use the general slicing method to find the volume of the following solid. the solid whose base is the triangle with vertices , , and and whose cross sections perpendicular to the base and parallel to the y-axis are semicircles
The equation for the volume of a cylindrical shell is:
V = πr² * h * w, where r is the radius of the semicircle base, h is the height of the shell, and w is the width of the shell.
Volume Of Semicircular Cross-Section SolidThe volume of the solid can be found using the method of cylindrical shells. The volume of each cylindrical shell is equal to the product of the area of the base (a semicircle), the height of the shell, and the width of the shell (which is equal to the difference in the x-coordinates of the two vertices that define the height).
To find the total volume, we would sum up the volumes of all the cylindrical shells, from the top to the bottom of the solid.
The equation for the volume of a cylindrical shell is:
V = πr² * h * w, where r is the radius of the semicircle base, h is the height of the shell, and w is the width of the shell.
The height of the shell is given by the difference in the y-coordinates of the two points that define the height, and the width of the shell is given by the difference in the x-coordinates of these two points.
To find the total volume, we would integrate the volume of the cylindrical shell over the height of the solid. The limits of integration would be the y-coordinates of the bottom and top of the solid.
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Put the following percentages and fractions in order starting with the largest.
Largest
3%
11/100
77%
92/100
36/100
58%
Smallest
Answer:
[tex]\frac{92}{100\\}[/tex], 77%, 58%, [tex]\frac{36}{100}[/tex], [tex]\frac{11}{100}[/tex], 3%
Step-by-step explanation:
I changed them all to percents
3 %
[tex]\frac{11}{100}[/tex] Percent means what out of 100? 11%
77%
92/100 = 92%
36/100 = 36%
58%
Juana Moreno computed the unit price on a 32-ounce container of yogurt and
found it to be $0.002 more per ounce than the unit price on 6 8-ounce containers of the
same yogurt. If the 32-ounce container costs $1.33 less than the cost of 6 8-ounce con-
tainers, find the cost of a 32-ounce container and the cost of 6 8-ounce containers.
The cost of a 32-ounce container is 2.92 and the cost of 6 8-ounce containers is $4.18.
How to find the cost of a 32-ounce container and the cost of 6 8-ounce containers?Word problems are sentences describing a 'real-life' situation where a problem needs to be solved by way of a mathematical calculation.
Let's call the unit price of 8-ounce yogurt x.
32-ounce unit price = x + 0.002
32-ounce container cost = 32 * (x + 0.002) =0.064 + 32x
6 * 8-ounce container cost = 6 * 8 * x = 48x
Given, 32-ounce container cost = 6 * 8-ounce container cost - $1.33
Substituting the costs,
0.064 + 32x = 48x - 1.33
Solving for x,
48x - 32x = 0.064 + 1.33
16x = 1.394
x = $0.087125
So, the unit price of 8-ounce container is $0.087125
Cost of 32-ounce container = $0.064 + 32 * (0.087125 + 0.002) = $2.92
Cost of 6 8-ounce containers = 6 * 8 * 0.087125 = $4.18.
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Which equation can be used to find the value of x?
Please help me I really need it
The value of x for the expression is 168 = 18x + 12.2x.
What is an expression?Example: 2 + 3x + 4y = 7 is an expression.
We have,
168 = 18x + 12.2x
Add like terms.
168 = 30.2x
Divide both sides by 30.2
168/30.2 = x
x = 5.56
Thus,
The value of x is 5.56.
An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.This equation can be used to find the value of x, which is the length of the side of a triangle (abcd). The equation is 16818-3x+12.2x. The equation is derived from the known lengths of the sides of the triangle. The sides are ab, bc, cd, ef, and fa. We know the length of side ab, which is 18 cm, and the length of side cd, which is 12 cm. We also know the length of side ef, which is 6 cm. The length of side bc is 2x cm, and the length of side fa is x cm. Using these known lengths of the sides of the triangle, we can create an equation to find the length of side fa. We can do this by adding the lengths of the sides and subtracting 3x from the result. This equation, which is 16818-3x+12.2x, can then be used to find the value of x.To learn more about expression referto:
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What is the mean for the following set of data?
12, 10, 11, 13, 14
Answer: 12
Step-by-step explanation:
you would first add up all of the numbers togeather, and it would give you 60. You then need to divide 60 by the amount of numbers which is 5. So you would do 60 divided by 5 to get 12.
It’s not really that hard but I am just busy so please do this for me.
The Surface area are shown below.
What is Surface Area?The total area of an object's external facing surfaces is its surface area. The base, top, and lateral surfaces (sides) of the object's surface are added together to get the object's overall surface area.
1. The measure of sides are
A = 3
B = 15
C= 17
D= 8
So, the Lateral Surface Area
= ( 15+17+8) x 3
= 117 mm²
and, the total surface Area
= Area of two triangles + Area of rectangle
= 2 x 1/2 x 8 x 15 + 117
= 120 + 117
= 237 mm²
2. The measure of sides are
A = 5
B = 2
C= 9
D= 2
So, the Lateral Surface Area
= 2 x (5 x 9) + 2 (2 x 5)
= 110 m²
and, the total surface Area
= 110 + 2 (2 x 9)
= 146 m²
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Jack measured a line to be 17.2 inches long. If the actual length of the line is 16.6 inches, then what was the percent error of the measurement, to the nearest tenth of a percent?
Answer:
The percent error of Jack's measurement was 3.6%, to the nearest tenth of a percent. This is calculated by subtracting the actual length (16.6 inches) from the measured length (17.2 inches) and dividing by the actual length, then multiplying by 100.
Step-by-step explanation:
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Which postulate or theorem would you use to prove MXQ= PXN?
A. AAS
B. SAS
C. ASA
D. SSS
E. HL
The postulate theorem used to prove the congruence of triangles MNQ and PXN is given as follows:
B. SAS.
What is the Side-Angle-Side congruence theorem?The Side-Angle-Side congruence theorem states that if any of the two sides on a triangle are the same, along with the angle between them, then the two triangles are congruent.
The congruent sides are given as follows:
MX and XP.QX and XN.The angle between these two sides is a vertical angle, having the same measure in each of the triangles, hence the SAS theorem can be applied and the correct option is given by option B.
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In the diagram below AL || BK || CH || DG. If DG = 3, GE = 5,HG = 5, KH = 5, LK = 5 determine the length of AL, BK, and CH.
The length of AL, BK and CH are 12, 9 and 6 respectively.
What are Similar Triangles?Similar triangles are those triangles which has the same shape but different size.
The length of sides are proportional in similar triangles.
Given a figure of a big triangle.
We can clearly see that angles made by each of the triangles ALE, BKE, CHE and DGE are equal and thus they are similar triangles.
The sides of similar triangles are proportional.
DG / GE = CH / HE = BK / KE = AL / LE
We have DG = 3, GE = 5,HG = 5, KH = 5, LK = 5
HE = 5 + 5 = 10
KE = 5 + 5 + 5 = 15
LE = 5 + 5 + 5 + 5 = 20
Substituting,
Consider DG / GE = CH / HE
3 / 5 = CH / 10
CH = (3/5) × 10 = 6
Consider DG / GE = BK / KE
3 / 5 = BK / 15
BK = (3/5) × 15 = 9
Consider DG / GE = AL / LE
3 / 5 = AL / 20
AL = (3/5) × 20 = 12
Hence the length of AL is 12, length of BK is 9 and length of CH is 6.
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Consider the scatter plot.
What type of association does the scatter plot show?
Drag a word or phrase into the box to correctly complete the sentence.
The scatter plot shows [ BLANK ] association.
The scatter plot shows [negative linear] association.
How to determine the association of the scatterplotFrom the question, we have the following parameters that can be used in our computation:
The image of the scatter plot
On the scatter plot, we can see that
The points appear to be on a straight line
Also, we can see that
As the x values increases the y values decreases
This represents a negative linear] association.
Hence, the association is a negative linear] association.
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En el parque de una comunidad esta colocado un reloj de manecillas,el suplemento del angulo que forman las manecillas a las 2:30 horas es de.
Answer:
135°
Step-by-step explanation:
Please please please help
. Due in 30 minutes
Answer:
12. m = 1/3
14. m = 5/6
16. m = -5/2
Step-by-step explanation:
m = y2-y1/x2-x1
f(x) = 3x³ + 6x² + 4x +3; x+4 use synthetic division and the remainder theorem to find the remainder when f(x) is divided by x-c
The polynomials is divided using synthetic division and the remainder theorem to 3x³ -6x² - 20x - 77/x + 4
What is synthetic division?Synthetic division is described as one of the methods that is used to manually perform the Euclidean division of polynomials.
The steps taken in a synthetic division include;
Set up the polynomial, then bring the first number or the leading coefficient straight down.Put the result in the next column by multiplying the number in the division box with the number brought downWrite the result at the bottom of the row by the addition of the two numbers Repeat steps 3 and 4 till the last figureGiven the polynomial;
f(x) = 3x³ + 6x² + 4x +3 by x + 4
We have;
3 6 4 3
-4 _____-12__24___80__
3 -6 -20 -77
Then, we have;
3x³ -6x² - 20x - 77/x + 4
Hence, the expression is 3x³ -6x² - 20x - 77/x + 4
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Which angle measures 40
Check the picture below.
Costa is planning a lunch banquet. The equation c=450+28g models the relation between the cost in dollars, c, of the banquet and the number of guests, g. Interpret the slope of the equation.
The slope of the equation c=450+28g represents the increase in cost per additional guest.
Typically, a line's slope provides information about the steepness and direction of the line. Finding the difference between the coordinates of the locations will allow you to quickly compute the slope of a straight line connecting two points, (x1,y1) and (x2,y2). The letter "m" is frequently used to signify slope.
We can see that the preceding equation is in the slope-intercept format, where m denotes the line's slope and b is its y-intercept or starting point.
In this case, the slope is 28 dollars per additional guest. This means that for every additional guest, the cost of the banquet increases by $28.
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what is the cube density the volume was 9.01?
0.947 g/ml is the cube density the volume was 9.01.
What is density?The term "density" refers to the ratio between the volume (the amount of space taken up by an item or substance) and the amount of matter contained inside (its mass). The quantity of mass per unit of volume is another method to define density.
We are know that items float in liquids when their density is less than that of the liquid.
Objects floating in a liquid are those whose density is equal to that of the liquid.
So, in this case, the cube is solely suspended in the first liquid combination. Therefore, the first liquid mixture's density is the same as a cube. The other mixes have densities that are higher than that of the cube.
Density of methanol = 0.7913 g/ml
Density of water = 1 g/ml
Density of the 6th liquid mixture:
= {(2 × 0.7913 ) + (1 × 6)}/8 g/ml
= 0.947 g/ml
Therefore density of cube = 0.947 g/ml
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The complete question is as follows:
What Is The Cube Density The Volume Was 9.01? The Cube Floated Up To 8.1 Ml
What is the value of x in the following figure?
A: 128 degrees
B: 142 degrees
C: 52 degrees
D: 38 degrees
Show work.
Answer:
D: 38 degreesStep-by-step explanation:
this is a case of linear pair...
52° + 90° (of the right angled triangle) + x° = 180°
52° + x° = 180° - 90°
x° = 90° - 52°
x° = 38°