Using the normal distribution, it is found that:
a) The probability of a defect is of 0.4532, and out of 1000 parts, 453 will be classified as defective.
b) The probability of a defect is of 0.0324, and out of 1000 parts, 32 will be classified as defective.
c) The reduction in the variability also reduces the number of defective parts.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable that has mean given by [tex]\mu[/tex] and standard deviation represented by [tex]\sigma[/tex] is given as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure X is above(in case the score is positive) or below(in case the score is negative) the mean. From the z-score table, the p-value associated with the z-score is found, which represents the percentile of the measure X.For item a, the mean and the standard deviation are given as follows:
[tex]\mu = 15, \sigma = 0.2[/tex]
The proportion of defectives is two times the p-value of Z when X = 14.85, as 14.85 and 15.15 are the same distance from the mean and the normal distribution is symmetric, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Z = (14.85 - 15)/0.2
Z = -0.75
Z = -0.75 has a p-value of 0.2266.
2 x 0.2266 = 0.4532 = 45.32%
Out of 1000, the number of defectives is:
0.453 x 1000 = 453.
For item b, we have that [tex]\sigma = 0.07[/tex], hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Z = (14.85 - 15)/0.07
Z = -2.14
Z = -2.14 has a p-value of 0.0162.
2 x 0.0162 = 0.0324.
Out of 1000, the number of defectives is:
0.032 x 1000 = 32.
For item c, we can see that the reduction of variability will make the parts having measures closer to the desired, hence reducing the number of defectives.
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The sum of two numbers is 402. The difference between the two numbers is 148. Find the two numbers
After solving the equations we can conclude that the two numbers are 265 and 137.
What exactly are equations?An equation is a mathematical statement that contains the symbol "equal to" between two expressions with identical values.such as 3x + 5 = 15 as an example.There are many different types of equations, including linear, quadratic, cubic, and others.So, let the first number be 'x' and the second is 'y'.
Now, the two equations can be formed as:
x + y = 402x - y = 128Merge equations as follows:
x + y - 402 = x - y - 128x - x + y + y = -128 + 4022y = 274y = 137So x will be:
x + y = 402x + 137 = 402x = 402 - 137x = 265Therefore, after solving the equations the two numbers are 265 and 137.
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Adam is baking 4 pizzas. Each pizza is a rectangle. It takes Adam 35 minutes to bake the pizzas. He divides each pizza into the equal-size square slices shown.
Adam multiplies to find the total number of square Slices for each pizza.
For each pizza tell the factors Adam multiplies .
For Pizza 1, Adam multiplies 6 by 6 slices
For Pizza 2, he multiplies 6 by 7 slices
For Pizza 3, he multiplies 4 by 7 slices, while
for Pizza 4, he multiplies 4 by 8 slices.
What is multiplication?A product is the outcome of multiplication or an expression that indicates factors to be multiplied in mathematics.
To put it another way, we may deduce that in math, multiplying implies adding equal groups.
The number of items in the group grows as we multiply. A multiplication issue includes the two elements and the product. The factors in the multiplication problem, 4 7 = 28, are the numbers 4 and 7, while the result (product) is the number 28.
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The sum of three consecutive odd integers is 237. What are the integers?
I need help with this question please. The graph below is just option A. Also, I have options to choose from.
From geogebra
Answer Letter A
What is the measure of angle LJK? Round to the tenths.
Answer:
90 degrees
Step-by-step explanation:
We can take a look at that each these triangles are in truth right triangles, seeing that the two angles of and both have measures of 90 degrees.
2.
Give an example of two fractions whose product is an integer due to common factors.
An example of two fraction whose product is an integer due to common factors is [tex]\frac{6}{3}[/tex].
What is fraction?Any number of equal parts is represented by a fraction, which also represents a portion of a whole. A fraction, such as one-half, eight-fifths, or three-quarters, indicates how many components of a particular size there are when stated in ordinary English.
What is a common factor?
The largest positive integer that divides each of the integers is known as the greatest common divisor of two or more non-zero integers. The greatest common divisor of two integers x and y is indicated by the display style "gcd"
Given that,
Two fraction whose product is an integer due to common factor.
The fraction is
[tex]\frac{6}{3}[/tex].
Since,
2 x 3 = 6
1 x 3 = 3
Here, 3 is the common factor.
[tex]\frac{6}{3}[/tex] = 2
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Solve for x.
4 + x/3 =9
x =
Answer:
x = 15
Step-by-step explanation:
[tex]4 + \frac{x}{3} = 9[/tex]
[tex] \frac{x}{3} = 5[/tex]
[tex]x = 15[/tex]
Answer:
x = 15
Step-by-step explanation:
Subtract 3 from each side: 12 + x = 27
Subtract 12 from both sides: x =27 − 12
Subtract 12 from 27 to get 15: x = 15
I need help with my practice starr
Is valid proportion here
(10 + 5 )/ 18 = 10/d
then find d
d= 18• 10/ (10+5)
d= 180/15 =
d= 12
Then answer is
d = 12 mm
An artist is designing a mural that will be 3 feet wider than it is tall. If the area of the mural is 108 square feet, what will be height of the mural?
Part 1. Create two radical equations: one that has an extraneous solution, and one that does not have an extraneous solution. Use the equation below as a model:a√x+b+c=dUse a constant in place of each variable a, b, c, and d. You can use positive and negative constants in your equation.Part 2. Show your work in solving the equation. Include the work to check your solution and show that your solution is extraneous.Part 3. Explain why the first equation has an extraneous solution and the second does not.
we have the equation
[tex]a\sqrt[\square]{x+b}+c=d[/tex]i will assume
a=2
b=5
c=3
d=5
solve for x
substitute the given values
[tex]2\sqrt[\square]{x+5}+3=5[/tex]subtract 3 both sides
[tex]2\sqrt[\square]{x+5}=5-3[/tex][tex]2\sqrt[\square]{x+5}=2[/tex]Divide by 2 both sides
[tex]\sqrt[\square]{x+5}=\frac{2}{2}[/tex][tex]\sqrt[\square]{x+5}=1[/tex]squared both sides
[tex]\begin{gathered} x+5=\pm1 \\ x=-5\pm1 \end{gathered}[/tex]the values of x are
x=-4 and x=-6
Verify each solution
For x=-4
[tex]\begin{gathered} \sqrt[\square]{-4+5}=1 \\ 1=1 \end{gathered}[/tex]x=-4 ------> is a solution
Verify x=-6
[tex]\begin{gathered} \sqrt[\square]{-6+5}=1 \\ \sqrt[\square]{-1}=1 \end{gathered}[/tex]Is not true
therefore
x=-6 --------> is an extraneous solution
....................
1220 km apart
rates
320 km/ hr
290 km/hr
___________________________________
x= t* rate
t = time in hours
x = distance in km
__________________
total distance = t1 * 320 Km/h + t2* 290 km/h
because they started at the same time
Total distance = 1220 km = t * 320 Km/h + t* 290 km/h
1220 = (320 + 290 ) t
1220 = 610 t
t = 1200/ 610
t = 2 hours
_______________________--
Answer
2 hours
Calculate the missing value. (Not drawn to scale.)
Answer:5in
Step-by-step explanation:
1. Identify the triangle
you are given a right triangle with the hypotonus missing and are given the side lengths 3 and 4 you know the hypotonus is 5 by the 3,4,5 Pythagorean tripe, if you do not notice this it can be solved with the Pythagorean theorem a^2+b^2=c^2
2. solve (if not done with 3,4,5 triple)
3^2+4^2=c^2
9+16=c^2
25=c^2
5=c | square root both sides to cancel the square
Calculate the property tax on a condominium located in a city in British Columbia and assessed at $496,300 if the current tax rate is 1.825%
In this case, we'll have to carry out several steps to find the solution.
Step 01:
data:
property value = $496300
tax rate = 1.825%
Step 02:
percentage:
property tax:
= 1.825 / 100 = 0.01825
property tax = property value * tax rate
$496300 * 0.01825 = 9057.475$
The answer is:
property tax =
Please help me, it's due today!
Answer:
I believe it is -123
Step-by-step explanation:
you have to replace all the x's with -4 so you would do the equation -6(-4)^2+8(-4)+5
-6(-4)^2 is -96
-96+8(-4) is -128
-128+5 is -123
Rachel sketches the graph of quadratic function that never crosses the X axis. which statement is true concering the roots of the function?
SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Define a quadratic equation that does not passes through the x-axis
When a quadratic function never crosses the x-axis, then it has no real roots or solutions. Hence, the discriminant must be negative. meaning the solutions are imaginary/complex.
Hence, the answer will be:
The function has two imaginary roots
Write an absolute value equation from the solutions -5 and 7.
An electrician has a 16 foot spool of wire and he needs to cut an 11 foot, 4 inch piece from the spool to make a repair. How many inches of wire will he have left on a spoop after he makes the repair
The inches of wire that he will have left on a spoop after he makes the repair is 4 2/3 feet.
How to calculate the fraction?From the information, the electrician has a 16 foot spool of wire and he needs to cut an 11 foot, 4 inch piece from the spool to make a repair.
Therefore, the inches of wire that he will have left will be:
Note that 1 feet = 12 inches
11 foot 4 inches = 11 4/12 = 11 1/3
The amount left will be:
= 16 - 11 1/3
= 4 2/3 feet.
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Consider the equation 3x3 + 14x2 – 14x + 60 = 0. The real solution is –6. What are the nonreal solutions?
HURRY Negative 2 i StartRoot 26 EndRoot, 2 i StartRoot 26 EndRoot.
4 minus 2 i StartRoot 26 EndRoot, 4 + 2 i StartRoot 26 EndRoot.
StartFraction negative 2 + i StartRoot 26 EndRoot Over 3 EndFraction, StartFraction negative 2 minus i StartRoot 26 EndRoot Over 3 EndFraction.
StartFraction 2 + i StartRoot 26 EndRoot Over 3 EndFraction, StartFraction 2 minus i StartRoot 26 EndRoot Over 3 EndFraction.
The non-real solutions of the polynomial expression are x = (2 + i√26)/3 and x = (2 - i√26)/3
How to determine the non-real solutions?The equation of the polynomial expression is given as:
3x^3 + 14x^2 - 14x + 60 = 0
From the question, we have
Real solution = -6
Rewrite the above equation as
x = -6
Add 6 to both sides of the equation
So, we have
x + 6 = 0
The next step is to divide the polynomial equation 3x^3 + 14x^2 - 14x + 60 = 0 by x + 6 = 0
This is represented as
3x^3 + 14x^2 - 14x + 60/x + 6
Using a graphing calculator, we have
3x^3 + 14x^2 - 14x + 60/x + 6 = 3x^2 - 4x + 10
Next, we determine the solution of the quadratic expression 3x^2 - 4x + 10 using a quadratic formula
So, we have
x = (-b ± √(b² - 4ac))/2a
This gives
x = (4 ± √((-4)² - 4 * 3 * 10))/2 * 3
So, we have
x = (4 ± √-104)/6
This gives
x = (4 ± 2√-26)/6
Divide
x = (2 ± √-26)/3
Rewrite as
x = (2 ± i√26)/3
Split
x = (2 + i√26)/3 and x = (2 - i√26)/3
So, the conclusion is that
Using the polynomial expression, the non-real solutions are x = (2 + i√26)/3 and x = (2 - i√26)/3
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Check off the methods of differentiation required, and complete the derivative.
Given:
[tex]f(x)=\sqrt[]{5x^2-2}[/tex]f(X) will be differentiated by chain rule.
[tex]\begin{gathered} f^{\prime}(x)=\frac{1}{2\sqrt[]{5x^2-2}}\lbrack5(2x)\rbrack \\ f^{\prime}(x)=\frac{5x}{\sqrt[]{5x^2-2}} \end{gathered}[/tex]3430
3. A price increased by 18.2%. How could you write the new amount
as a percentage of the price before the increase?
The new amount as a percentage of the price before the increase is =[tex]\frac{118.2x}{100}[/tex]
What is percentage?The Latin word "per centum," which means "by the hundred," is where the word "percentage" originally came from. With 100 as the denominator, percentages are fractions. To put it another way, it's the relationship between a component and a whole in which the value of the whole is always assumed to be 100.
Let, the odd price be x then
we can write the new amount as a percentage of the price before increasing as
x ×[tex]\frac{(100+18.2)}{100}[/tex]
=[tex]\frac{118.2x}{100}[/tex]
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1. Let U = {q, r, s, t, u, v, w, x, y, z} A = {q, s, u, w, y} B = {q, s, y, z} C = {v, w, x, y, z}. List the elements in the set: (Ac ∩ B).
The elements in the set A'∩B is { z } .
Set theory is a branch of mathematical logic that studies sets, which are essentially collections of objects.
Despite the fact that any type of object can be assembled into a set, set theory is a branch of mathematics that primarily deals with issues that are relevant to mathematics as a whole.A straightforward binary link between an object o and a set A serves as the basis of set theory. If o is a component (or member) of A, it is expressed as o A. When describing a set, members are listed with commas to indicate separation, or a property of those components is contained in braces. Since sets are objects, they can be related by the membership relation.Given universal set U = {q, r, s, t, u, v, w, x, y, z}
set A = {q, s, u, w, y}
∴A' = {r, t, v, x, z}
set B = {q, s, y, z}
Now A'∩B = { z }
Hence the elements in the set A'∩B is { z } .
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A monkey can eat 24 pieces of fruit in 12 hours.
The equation y = 2x can be used to represent
this situation. What is the constant of
proportionality? What does the constant of
proportionality represent in the context of the
problem?
The constant of proportionality for the equation y = 2x is k = 2.
The number of pieces of fruit the monkey can eat is two times the amount of time the monkey takes.
The equation y = 2x can be used to represent a monkey eating 24 pieces of fruit in 12 hours.
The constant of proportionality, which is a fixed value that represents the rate at which two or more ratios rise or decrease, is used to compare them. The result of dividing the denominator by the numerator when a ratio is expressed as a fraction is the constant of proportionality.
When a ratio is expressed as a fraction, the constant of proportionality is found by dividing the denominator by the numerator. The constant of proportionality, k, can be calculated from the equation if x is the ratio's numerator and y is its denominator.
k = y/x
Therefore, the constant of proportionality in this case is:
y = 2x
k = y/x = 2
The constant of proportionality in this case represents that the number of pieces of fruit a monkey eats is two times the amount of time the monkey takes.
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How do you graph: y=75x + 2
Explanation
[tex]y=75x+2[/tex]we have a linear function, to graph a linear function you need 2 points
Step 1
find 2 coordinates of the line
a) when x= 0
then
[tex]\begin{gathered} y=75x+2 \\ y=75(0)+2 \\ y=0+2 \\ y=2 \\ \text{coordinate 1(0,2)} \end{gathered}[/tex]b)when x=2
[tex]\begin{gathered} y=75x+2 \\ y=75(2)+2 \\ y=150+2 \\ y=152 \\ \text{coordinate 2(2,152)} \end{gathered}[/tex]Step 2
now, draw a line that passes through the points
I hope this helps you
Complete the square to solve the equation below.
X²+10x-13 17
O A. x= 4+ √√30; x = 4 - √30
OB. x= -10 + √55; x = -10 - √55
C. x = 5 + √√29; x = 5-√√√29
OD. x= -5+ √55; x = -5- √55
Answer:
D
Step-by-step explanation:
...................
The solutions to the quadratic equation x² + 10x - 13 = 17 are x = -5 + √55 and x = -5 - √55. The correct answer is option D.
The quadratic equation is given as:
x²+10x-13 =17
Move the constant term to the right side of the equation:
x² + 10x - 13 - 17 = 0
x² + 10x - 30 = 0
Take half of the coefficient of the x-term (10) and square it: (10/2)² = 25.
Add the squared value to both sides of the equation:
x² + 10x + 25 - 30 = 25
(x + 5)² - 30 = 25
Simplify the equation:
(x + 5)² = 25 + 30
(x + 5)² = 55
Take the square root of both sides of the equation:
√((x + 5)²) = ±√55
x + 5 = ±√55
Solve for x by subtracting 5 from both sides:
x = -5 ± √55
Therefore, the solutions to the equation x² + 10x - 13 = 17 are:
x = -5 + √55 and x = -5 - √55.
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How many terms does the expression 2x + 7 have
The total number of terms in the given expression 2x + 7 is equal to two.
As given in the question,
Expression is given by:
2x + 7
Number of terms in the given expression 2x + 7 are as follow:
7 is the constant term of the given expression 2x + 7
x is the variable which is multiply by two written as 2x in the given expression 2x + 7.
Both the terms 7 and 2x in the given expression are related with the operation addition'+'
Therefore, the total number of terms in the given expression 2x + 7 is equal to two.
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Can someone please help me with this geometry question
Answer:
Step-by-step explanation:
나무
7 1
al
117)
10) The level of water in a pail has changed by -7 in. from the original water level.
If the original level was 23 3/8 in., what is the current water level?
URGENT!! ILL GIVE
BRAINLIEST! AND 100 POINTS
Jimmy ran 20 meters west from home and then turned north to jog 25 meters. Jimmy ran 45 meters, but could have arrived at the same point by in a straight line. How many meters could he have using a line distance?
A. 3.5 meters
B. 7 meters
C. 32 meters
D. 45 meters
Jimmy would've jogged 32.02m if he ran through a straight line by Pythagorean theorem.
What is Pythagorean theorem?
The Pythagorean Theorem states that the squares on the hypotenuse of a right triangle, which is the side that faces the right angle, are equal when added together. This is written as a2 + b2 = c2 in the usual algebraic notation.We can proceed to use this to find the distance from point a to point b assuming he ran through a straight line.
Mathematically, the theorem can be expressed as
x² = y² + z²
Let's substitute the values into the equation and solve
x² = 20² + 25²
x = 32.02m
Jimmy would've jogged 32.02m if he ran through a straight line.
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5 plus twice a number
Where “a number” is the letter x
Answer:
5 + 2x
Since 2 times a number is multiplication we make it 2x
Please help fast I need help
The mapping diagram above does not represent a function since
for each number in Set A (the input) where there are multiple mappings
from Set B (the output).
What is a function?In Mathematics, a function simply refers to a mathematical expression which is typically used for defining and representing the relationship that exists between two or more variables such as an ordered pair.
This ultimately implies that, a function is typically used in mathematics for uniquely mapping an input variable (Set A) to an output variable (Set B).
Based on the mapping diagram shown above, we can reasonably infer and logically deduce that Set A with inputs (-4, 8), (1, 8) and (1, -3) are ordered pairs which does not represent a function because they indicate multiple mappings in Set B (the output).
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