Answer:
(a) 0.94
(b) 0.20
(c) 90.53%
Step-by-step explanation:
From a population (Bernoulli population), 90% of the bearings meet a thickness specification, let [tex]p_1[/tex] be the probability that a bearing meets the specification.
So, [tex]p_1=0.9[/tex]
Sample size, [tex]n_1=500[/tex], is large.
Let X represent the number of acceptable bearing.
Convert this to a normal distribution,
Mean: [tex]\mu_1=n_1p_1=500\times0.9=450[/tex]
Variance: [tex]\sigma_1^2=n_1p_1(1-p_1)=500\times0.9\times0.1=45[/tex]
[tex]\Rightarrow \sigma_1 =\sqrt{45}=6.71[/tex]
(a) A shipment is acceptable if at least 440 of the 500 bearings meet the specification.
So, [tex]X\geq 440.[/tex]
Here, 440 is included, so, by using the continuity correction, take x=439.5 to compute z score for the normal distribution.
[tex]z=\frac{x-\mu}{\sigma}=\frac{339.5-450}{6.71}=-1.56[/tex].
So, the probability that a given shipment is acceptable is
[tex]P(z\geq-1.56)=\int_{-1.56}^{\infty}\frac{1}{\sqrt{2\pi}}e^{\frac{-z^2}{2}}=0.94062[/tex]
Hence, the probability that a given shipment is acceptable is 0.94.
(b) We have the probability of acceptability of one shipment 0.94, which is same for each shipment, so here the number of shipments is a Binomial population.
Denote the probability od acceptance of a shipment by [tex]p_2[/tex].
[tex]p_2=0.94[/tex]
The total number of shipment, i.e sample size, [tex]n_2= 300[/tex]
Here, the sample size is sufficiently large to approximate it as a normal distribution, for which mean, [tex]\mu_2[/tex], and variance, [tex]\sigma_2^2[/tex].
Mean: [tex]\mu_2=n_2p_2=300\times0.94=282[/tex]
Variance: [tex]\sigma_2^2=n_2p_2(1-p_2)=300\times0.94(1-0.94)=16.92[/tex]
[tex]\Rightarrow \sigma_2=\sqrt(16.92}=4.11[/tex].
In this case, X>285, so, by using the continuity correction, take x=285.5 to compute z score for the normal distribution.
[tex]z=\frac{x-\mu}{\sigma}=\frac{285.5-282}{4.11}=0.85[/tex].
So, the probability that a given shipment is acceptable is
[tex]P(z\geq0.85)=\int_{0.85}^{\infty}\frac{1}{\sqrt{2\pi}}e^{\frac{-z^2}{2}=0.1977[/tex]
Hence, the probability that a given shipment is acceptable is 0.20.
(c) For the acceptance of 99% shipment of in the total shipment of 300 (sample size).
The area right to the z-score=0.99
and the area left to the z-score is 1-0.99=0.001.
For this value, the value of z-score is -3.09 (from the z-score table)
Let, [tex]\alpha[/tex] be the required probability of acceptance of one shipment.
So,
[tex]-3.09=\frac{285.5-300\alpha}{\sqrt{300 \alpha(1-\alpha)}}[/tex]
On solving
[tex]\alpha= 0.977896[/tex]
Again, the probability of acceptance of one shipment, [tex]\alpha[/tex], depends on the probability of meeting the thickness specification of one bearing.
For this case,
The area right to the z-score=0.97790
and the area left to the z-score is 1-0.97790=0.0221.
The value of z-score is -2.01 (from the z-score table)
Let [tex]p[/tex] be the probability that one bearing meets the specification. So
[tex]-2.01=\frac{439.5-500 p}{\sqrt{500 p(1-p)}}[/tex]
On solving
[tex]p=0.9053[/tex]
Hence, 90.53% of the bearings meet a thickness specification so that 99% of the shipments are acceptable.
The manufactures bearings.
As per the question, the process that a manufacturer bears 90% of the bearings and meet the thickness specifications. The shipment consists of 500 bearings. The shipment if taken has a least 440 and 500 bearings.
the answer is 0.94, 0.20, and 90.53%.
The assumption is that each shipment is randomly taken in a sample of bearings. The chances or the probability that that given shipment are acceptable are 0.94% and the probability that they are more than 285 out of the 300 bearings is 0.205. The part of bearings that must meet the specifications in order to be 99% of shipments is 90.5%.Learn more about the manufactures bearings.
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Find the ordered pair $(x,y)$ that satisfies the system of equations
Answer:
(9,6)
Step-by-step explanation:
9+6=15
9-6=3
Answer:
(9,6)
that's the answer
need help answering
Answer:
I haven't done this in a while but wouldn't it just be--
17. X=40
18. X=40
19. X=55
Step-by-step explanation:
The hypotenuse of a right triangle is 5inches long. The shorter leg is 1 inch shorter than the longer leg. Find the side lengths of the triangle.
Length of the shorter leg:
Length of the longer leg:
Length of the hypotenuse:
Answer:
Hypotenuse = 5 in
Longer leg = 4 in
Shorter leg = 3 in
Step-by-step explanation
The longer leg = x
The shorter leg = x - 1
Now through Pythagoras theorem:
hyp^2 = leg1^2 + leg2^2
5^2 = x^2 + (x - 1)^2
25 = x^2 + x^2 - 2 x + 1^2
25 = 2 x^2 - 2 x + 1
2 x^2 - 2 x - 24 = 0
2 ( x^2 - x - 12) = 0
2 (x - 4) (x + 3) =0
then x = 4 or x = - 3
We use the positive answer since we are looking for a length
then longer leg is 4 inches long,
and therefore the shorter one is one inch shorter than 4 in . That is:
shorter leg = 3 inches
Raoul make shell necklaces to sell at a craft fair. the supplies for each necklace cost $3.75. Raoul sells the necklaces for $11.25. what is the percent markup for a shell necklace?
Answer: The percent markup for a shell necklace = 200%
Step-by-step explanation:
Given: Cost price per necklace = $3.75
Selling price per necklace = $11.25
Mark up = (Selling price - Cost price )
= $ (11.25 -3.75 )
=$ 7.5
The percent markup for a shell necklace = [tex]\dfrac{\text{Mark up}}{\text{cost price}}\times100\%[/tex]
[tex]=\dfrac{7.5}{3.75}\times100\%\\\\=2\times100\%=200\%[/tex]
Hence, The percent markup for a shell necklace = 200%
The percent markup for a shell necklace is 200%.
Definition of markupMarkup can be defined as the rate at which the cost of a product is increased. The higher the markup, the higher the profit earned by a seller all things being equal.
Calculation of percentage markupPercentage markup = (profit / cost price) x 100
Profit = $11.25 - $3.75 = $7.50
Percentage markup = ($7.50 / $3.75) x 100 = 200%
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In baseball, two statistics, the ERA (Earned Run Average) and the WHIP (Walks and Hits per Inning Pitched), are used to measure the quality of pitchers. For both measures, smaller values indicate higher quality. The following computer output gives the results from predicting ERA by using WHIP in a least-squares regression for the 2017 baseball season.
Answer:A
Step-by-step explanation:
The best interpretation of the value of 6.8 is shown in the output, ERA is predicted to increase by 6.8 units.
What are statistics?Statistics is the study of the discipline that concerns the organization, collection, analysis, and presentation of data.
In baseball, two statistics, the ERA (Earned Run Average) and the WHIP (Walks and Hits per Inning Pitched), are used to measure the quality of pitchers.
For both measures, smaller values indicate higher quality.
Variable DF Estimate SE T
Intercept 1 −5.0 0.26 −19.3
WHIP 1 6.8 0.14 47.4
ERA is predicted to increase by 6.8 units for each 1 unit increase of WHIP.
Thus, the best interpretation of the value of 6.8 is shown in the output, ERA is predicted to increase by 6.8 units.
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The dependent variable of Ally works in a shop for 18$ per hour
Answer:
$18 is the dependent variable
Step-by-step explanation:
$18 depends on the duration of time worked. Hope this helps and good luck on your assignment. (mark me brainliest please?)
Suppose we write down the smallest positive 2-digit, 3-digit, and 4-digit multiples of 9. what is the sum of these three numbers?
Answer: 1134
Step-by-step explanation:
Please find angles s and k
Answer:
s-64 and k-116
Step-by-step explanation:
3x - 15 = 7 - 8x how do you solve this
Answer:
X=2
Step-by-step explanation:
3x-15=7-8x
3x+8x=7+15
11x=22
x=[tex]\frac{22}{11}[/tex]
x=2
Answer:
324
Step-by-step explanation:
3x3 = 9
9-15 = -6
8x8=64
7-64=-54
-54 x -6 = 324
Based on the lesson, identify the first operation needed to solve the following equation. x/11 - 2 = 3 multiplication subtraction addition division
The number 2 should be added to both sides of the given linear
equation to enable the variable x be made the subject of the equation.
Response:
The first operation that needed to solve the equation is; AdditionWhich sequence of steps are needed to solve the given equation?The given equation is presented as follows;
[tex]\mathbf{\dfrac{x}{11} - 2} = 3[/tex]
The solution of the above equation van be found by making x the
subject of the equation.
Removing the 2 from the left hand side of the equation will isolate the [tex]\dfrac{x}{11}[/tex]
, from which the value of x can be found by multiplying by 11.
First operation;
To remove the 2, we have;
2 - 2 = -2 + 2 = 0, adding 2 to both sides of the equation gives;[tex]\dfrac{x}{11} - 2 \mathbf{+ 2 }= 3 + 2[/tex]
[tex]\dfrac{x}{11} + 0 = 3 + 2 = 5[/tex]
[tex]\dfrac{x}{11} = 5[/tex]
Second operation;
[tex]\dfrac{x}{11} \times 11 = 5 \times 11 = 55[/tex]
x = 55
The first operation that needs to be needed to solve the given equation
is therefore;
AdditionLearn more about solving equations here:
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Answer: It would be addition
Mark as brainliest <3
6.) The length of a rectangle is 19 feet longer than the width. If the perimeter is 46
feet, write an equation for this scenario where "x" represents the width.
Step-by-step explanation:
The perimeter can be expressed as
P=2L+2W
let the width be x
W=x
L=x+19
perimeter P=46ft
Therefore substituting and solving for x we have
46=2(x+19)+2x
46=2x+38+2x
46=2x+2x+38
46-38=4x
8=4x
x=8/4
x=2
the width is 2
the lenght = 2+19=21
Big chickens: The weights of broilers (commercially raised chickens) are approximately normally distributed with mean 1535 grams and standard deviation 169 grams. Use the TI-84 Plus calculator to answer the following. (a) What proportion of broilers weigh between 1136 and 1243 grams? (b) What is the probability that a randomly selected broiler weighs more than 1600 grams? (c) Is it unusual for a broiler to weigh more than 1710 grams? Round the answers to at least four decimal places. Part 1 of 3 The proportion of broilers that weigh between 1136 and 1243 grams is .
Answer:
(a) 0.0329
(b) 0.3502
(c) It is not unusual for a broiler to weigh more than 1710 grams.
Step-by-step explanation:
Using the TI-84 Plus calculator:
z-score is z = (x-μ)/σ,
where
x is the raw score
μ is the population mean
σ is the population standard deviation.
mean is 1535 grams and standard deviation is 169 grams.
(a) What proportion of broilers weigh between 1136 and 1243 grams?
For x = 1136 grams
z = (x-μ)/σ
= 1136 - 1535/169
= -2.36095
Determining the probability value from Z-Table:
= P(x = 1136)
= P(z =-2.36095)
= 0.0091142
For x = 1243 grams
z = (x-μ)/σ
= 1243 - 1535/169
= -1.72781
Determining the probability value from Z-Table:
P(x = 1243) = 0.042011
The proportion of broilers weigh between 1136 and 1243 grams is calculated as:
P(x = 1243) - P(x = 1136)
= 0.042011 - 0.0091142
= 0.0328968
≈ 0.0329
(b) What is the probability that a randomly selected broiler weighs more than 1600 grams?
For x = 1600 grams
z = (x-μ)/σ
= 1600 - 1535/169
= 0.38462
Determining the Probability value from Z-Table:
P(x<1600) = 0.64974
P(x>1600) = 1 - P(x<1600) = 0.35026
The probability that a randomly selected broiler weighs more than 1600 grams is 0.3502
(c) Is it unusual for a broiler to weigh more than 1710 grams?
For x = 1600 grams
z = (x - μ)/σ
= 1710 - 1535/169
= 1.0355
P-value from Z-Table:
P(x < 1710) = 0.84978
P(x > 1710) = 1 - P(x < 1710) = 0.15022
From the above calculation, it is not unusual for a broiler to weigh more than 1710 grams because 15.022% of the broilers weigh 1710 grams.
What is the perimeter of the shape below, given a = 8.16, b = 234, C = 461,0 =
2.56, e = 8.00, f = 2.51, g = 9.81
Answer: It’s unfinded
Step-by-step explanation:
HELP PLEASE ITLL MEAN A LOt ILL GOVE A GOOD RATING AND BRAIN
Answer:
24, -5, -5, -40, -5
Step-by-step explanation:
To add integers having the same sign, keep the same sign and add the absolute value of each number. To add integers with different signs, keep the sign of the number with the largest absolute value and subtract the smallest absolute value from the largest. Subtract an integer by adding its opposite.
Answer:
12) 24
13) -5
14) -5
15) -40
16) 5
Step-by-step explanation:
Things to remember when you multiply/divide with negatives.
*Two negatives that are multiplied/divided are positive.
*A positive multiplied/divided by a negative turns negative.
*A negative multiplied/divided by a positive remains a negative.
Simplified version of the equations:
12) 6×4= 24
13) 20÷(-4)= -5 *The negative sign of the 4 turns the outcome into a negative.
14) -15÷3= -5
15) 5×(-8)= -40 *Don't forget the negative sign from the 8.
16) 10÷2= 5
You can also input these equations into a calculator.
Hope this helps!
Simplify 12x7y3 divided by 6x3y
Answer:
12x7y3
----------- = 6x4y3
6x3y
Step-by-step explanation:
In dividing these numbers, you simply subtract 6x from 12x and subtract 3y from 7y because 6x and 3y are both in the denominator. 3 is left alone.
I’ll mark brainliest!!!! What is the length of BC in the right triangle below?
A. 63
В. 3
С. 21
D. -/63
E. 15
Е 225
Answer:
E. 15
Step-by-step explanation:
Use the Pythagorean theorem: a²+b²=c²
9²+ 12²= c² (This is the info we have so far.)81 + 144 = c² (Simplify. 9² = 81 ; 12² = 144)
225 = c² (Added 81 + 144 = 225)√225 = 15 (Square root of 225 is 15.)
Answer:
Step-by-step explanation:
15
Please help me with this problem and if you can show your work
Answer:
2.9
just answering wrong because i need points sorry
this is all my 30 points please help
Find the surface area of the composite solid.
Answer:
221 I am sorry if I am wrong. I tried
Step-by-step explanation:
HELP NEEDED MATHS PLEASE!!!
Answer:
f(3)= 3+1
=4
gf(3) is attached.
Luci cuts a board that is 5/9 yard long into pieces that are 5/18 yard long. How many pieces does she cut?
Luci cuts ___ pieces
Answer:
2
Step-by-step explanation:
9x2=18
5x2=10
10/18=5/9
10/18 divided by 2 5/18
so its 2
Some softball players hit a softball. Amalia hit the softball 36 inches. Nick hit the softball 6 feet. Lila hit the softball 108 inches. Pablo hit the softball 2 yards. Which two players hit the softball the same distance?
Answer: Nick and Pablo
Step-by-step explanation:
6 feet and 2 yards are the same distance because each yard is 3 feet
Answer:
6 feet 2 yards
Step-by-step explanation:
A bakery sells 3 muffins for every 5 pizza pies. The bakery sold a total of 24 muffins and pizza pies together. How many of each kind did the bakery sell?
6 muffins and 18 pizza pies
9 muffins and 15 pizza pies
15 muffins and 6 pizza pies
18 muffins and 6 pizza pies
Answer:
b
Step-by-step explanation:
9 muffins and 15 pizza pies. im pretty sure
Find j. 6 + 2(3j – 2) = 4(1 + j)
Answer:
j=1
Step-by-step explanation:
What transformation occurs to the graph f (x) =2x + 3 if the 3 in the equation is changed to a 5?
What is the square root of 16?
A.4
B.6
C.8
D.10
Answer:
4
Step-by-step explanation:
because i know how to do it
Answer:
A. 4
Step-by-step explanation:
Square root means " a number which produces a specified quantity when multiplied by itself."
When you multiply 4 and 4, you get 16.
Solve the equation because I really need help
Answer:
No Solution
Step-by-step explanation:
P.E.M.D.A.S
4(x+5) = 21 + 4x
4x+20 = 21+4x
we would subtract 4 on both sides to isolate 4 by it self.
subtract 4x on both sides but when we do we get 0 for x
4x-4x + 40 = 21 + 4x-4x
we get 40 = 21
So our answer is no Solution or unless your just tryning to find out that the total is with out x 40 = 21
high hopes ^^
Barry
A train travels at an average rate of 40 miles per hour. How many hours does it take the train to travel 2760 miles?
Answer:the correct answer is 69 hours
Step-by-step explanation:
Answer:
69 hours
Step-by-step explanation:
GIVEN:
Unit rate of 40 mphOverall miles of 2760Using this information, all we have to do is divide 2760 by 40! This will give us an estimate of how many miles this train should take to travel 2760 miles.
[tex]\frac{2760}{40} = 69[/tex]
Hope I was of assistance! #SpreadTheLove <3
What is the factored form of this expression? 4x^3 - 8x^2 - 9x + 18
A. (2x + 3)(2x - 3)(x - 2)
B. (2x + 3)(2x + 3)(x - 2)
C. (2x + 3)(2x - 3)(x + 2)
D. (2x - 3)(2x - 3)(x - 2)
Answer: D
Step-by-step explanation:
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.
(2x + 3)(2x - 3)(x - 2) is the factor form of the expression (2x + 3)(2x - 3)(x - 2).
Option A is the correct answer.
(2x + 3)(2x - 3)(x - 2).
What is an expression?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.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
4x³ - 8x² - 9x + 18
We will check the expression in factor form:
A.
(2x + 3)(2x - 3)(x - 2)
(2x + 3) (2x² - 4x - 3x + 6)
4x³ - 8x² - 6x² + 12x + 6x² - 12x - 9x + 18
4x³ - 8x² - 9x + 18 ____(1)
B.
(2x + 3)(2x + 3)(x - 2)
(2x + 3) (2x² - 4x + 3x - 6)
4x³ - 8x² + 6x² - 12x + 6x² - 12x + 9x - 18
4x³ + 4x² - 15x - 18 ____(2)
C.
(2x + 3)(2x - 3)(x + 2)
(2x + 3) (2x² + 4x - 3x - 6)
4x³ + 8x² - 6x² - 12x + 6x² + 12x - 9x - 18
4x³ + 14x² + 3x - 18 ____(3)
D.
(2x - 3)(2x - 3)(x - 2)
(2x - 3) ( 2x² - 4x - 3x + 6)
4x³ - 8x² - 6x² + 12x - 6x² + 12x + 9x - 18
4x³- 20x² + 33x - 18 ____(4)
From (1), (2), (3), and (4) we see that,
(2x + 3)(2x - 3)(x - 2) is the factor form of the expression (2x + 3)(2x - 3)(x - 2).
Option A is the correct answer.
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What is the slope of a line that contains the points (-6 , 1) and (4 , -4)?
Answer:
-1/2
Step-by-step explanation:
For this question we use the slope formula: [tex]m = (y_{1} - y_{2})/(x_{1}-x_{2})[/tex]
chug and plug: m = (1 - (-4))/(-6-4)
m = -0.5 or [tex]-\frac{1}{2}[/tex]
The slope of a straight line passing through the points (-6 , 1) and (4 , -4) is -1/2.
What is Slope of a straight line?The slope of a straight line measures the rate of change of variable 'y' with respect to independent variable 'x'. Mathematically -
m = (y₂ - y₁)/(x₂ - x₁)
Given is a line that passes through the points (-6 , 1) and (4 , -4).
The slope of a straight line passing through two points is given by -
m = (y₂ - y₁)/(x₂ - x₁)
The coordinates given are (-6 , 1) and (4 , -4).
Substituting them in the formula, we get -
m = (- 4 - 1)/(4 + 6)
m = (- 5)/(10)
m = -1/2
m = -1/2
Therefore, the slope of a straight line passing through the Points (-6 , 1) and (4 , -4) is -1/2.
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(5,9), (5-3)
what is the slope?
Answer:
Hello!!! Princess Sakura here ^^
Step-by-step explanation:
When you want to find out what the slope is, you have to remember what the formula is first....
[tex]m=\frac{y}{x} =\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
so in this case -3 would be the [tex]y_{2}[/tex] because it's the y in the ordered pair and it's the second one. Then one of the 5's would be [tex]x_{2}[/tex] and 9 would be [tex]y_{1}[/tex] and then the other 5 would be [tex]x_{1}[/tex].
now if we plug it in
[tex]\frac{-3-9}{5-5} =\frac{-12}{0}[/tex]
now we can tell that we can't divide by zero so the slope would be unidentified and that's it.
