Answer:
a) the probability that the strength of a sample is less than 38 lb/in² is approximately 0.9332
b) approximately 0.62% of the sample are scrapped
Step-by-step explanation:
a)
What is the probability that the strength of a sample is less than 38 lb/in²?
lets X rep the paper tensile strength in pounds per square inch.
the probability that the strength of the sample is less than 38 lb/in²
i.e P( X < 38 )
so assuming that X is normally distributed with u = 35 lb/in² and α = 2 lb/in²,
so the probability expression P( X < 38 ) can be standardized as
P( X < 38 ) = P( (X-35)/2 < (38-35)/2)
= P( X < 1.5 )
from the cumulative standard normal distribution table,
we find P( X < 1.5 ) = 0.9332
so
P( X < 38 ) = P( X < 1.5 )
= 0.9332
therefore the probability that the strength of a sample is less than 38 lb/in² is approximately 0.9332
b)
If the specifications require the tensile strength to exceed 30 lb/in², what proportion of the samples is scrapped?
this can be represented as P( X < 30 )
By standardization the probability expression P( X < 30 ) can be transformed as;
P( X < 30 ) = P( (X-35)/2 < (30-35)/2)
= P( z < -2.5 )
from the cumulative standard normal distribution table,
we find P( X < -2.5 ) = 0.0062
so
P( X < 30 ) = P( X < -2.5 )
= 0.0062
therefore, approximately 0.62% of the sample are scrapped
At noon, the minute and the hour hands of a clock overlap. In how long will they again overlap?
Answer:
1 hour 5 9/20 minutes
Step-by-step explanation:
Use Newton's method to approximate the given number correct to eight decimal places. 4√73
Answer:34.17601498.
Step-by-step explanation:
Newton's method of approximation is used to approximate values.
The value of [tex]\mathbf{4\sqrt{73}}[/tex] is 34.17601498
Let the number be x.
So, we have:
[tex]\mathbf{x = 4\sqrt{73}}[/tex]
Square both sides
[tex]\mathbf{x^2 = 1168}[/tex]
Subtract 1168 from both sides
[tex]\mathbf{x^2 - 1168 = 0}[/tex]
Express as a function
[tex]\mathbf{f(x) = x^2 - 1168 }[/tex]
Set x1 to 73/2.
So, we have:
[tex]\mathbf{x_1 = \frac{73}{2} = 36.5}[/tex]
Where:
[tex]\mathbf{x_{n+1} = x_n- \frac{x_n^2-1168}{2x_n}}[/tex]
So, we have:
[tex]\mathbf{x_{1+1} = x_1- \frac{x_1^2-1168}{2x_1}}[/tex]
[tex]\mathbf{x_{2} = x_1- \frac{x_1^2-1168}{2x_1}}[/tex]
This gives
[tex]\mathbf{x_{2} = 36.5- \frac{36.5^2-1168}{2 \times 36.5}}[/tex]
[tex]\mathbf{x_{2} = 34.25}[/tex]
[tex]\mathbf{x_{3} = x_2- \frac{x_2^2-1168}{2x_2}}[/tex]
[tex]\mathbf{x_{3} = 34.25- \frac{34.25^2-1168}{2 \times 34.25}}[/tex]
[tex]\mathbf{x_{3} = 34.1760948905}[/tex]
[tex]\mathbf{x_{4} = x_3- \frac{x_3^2-1168}{2x_3}}[/tex]
[tex]\mathbf{x_{4} = 34.1760948905- \frac{34.1760948905^2-1168}{2\times 34.1760948905}}[/tex]
[tex]\mathbf{x_{4} = 34.1760149814}[/tex]
[tex]\mathbf{x_{5} = x_4- \frac{x_4^2-1168}{2x_4}}[/tex]
[tex]\mathbf{x_{5} = 34.1760149814- \frac{34.1760149814^2-1168}{2\times 34.1760149814}}[/tex]
[tex]\mathbf{x_{5} = 34.1760149813}[/tex]
The values of x4 and x5 are the same up till the 8th decimal place.
Hence, the value of [tex]\mathbf{4\sqrt{73}}[/tex] is 34.17601498
Read more about Newton's method of approximation at:
https://brainly.com/question/14279052
Mittens, a baby kitten, gained 120 grams of weight in 1/3 of a month. If Mittens kept growing at this rate, how much weight would he gain in 1 month?
Answer:
Step-by-step explanation:
Given
A baby kitten, gained 120 grams of weight in 1/3 of a month.
he gain in 1 month
Solution
1/3 month =120gram weight
1 month =120×3
=360 gram is the answer
Step 1:Choose the lowest common denominator
Find the sum of 1/5 and 7/10
The expression written in equation from with common denominator is______
The sum is___
Answer:
-6/8 +5/8 and -1/8
Step-by-step explanation:
just got done doing it.
The manufacturer of a certain brand of lightbulbs claims that the variance of the lives of these bulbs is 4100 square hours. A consumer agency took a random sample of 26 such bulbs and tested them. The variance of the lives of these bulbs was found to be 5900 square hours. Assume that the lives of all such bulbs are (approximately) normally distributed. Test at the 20% significance level whether the variance of such bulbs is different from 4100 square hours. a)The value of the test statistic x is 15.743; we fail to reject the null hypothesis. b)The value of the test statistic x is 32.859; we fail to reject the null hypothesis. c)The value of the test statistic y is 32.859; we reject the null hypothesis. d)The value of the test statistic is 35.976; we fail to reject the null hypothesis. e)The value of the test statistic is 15.743; we reject the null hypothesis. f)The value of the test statistic x is 35.976; we reject the null hypothesis.
Answer:
124345
Step-by-step explanation:
Every triangle must have an acute angle. True or false?
Answer:
This is true every triangle has to have 1 acute angle.
Step-by-step explanation:
Please help its important!!
Triangle ABC in the figure above represents the area serviced by a shipping company that plans to build a distribution center at the incenter of the triangle located at point E. A circle is constructed to represent the location of the center. The diameter of the circle is 28 miles. The existing road is perpendicular to the incenter and the company is looking to build 2 more perpendicular roads but connecting the other 2 sides of the triangle. How many more miles of road will be needed?
Select one:
A. 28
B. 34
C. 43
D. 56
Answer:
A. 28
Step-by-step explanation:
A. 28
step 1.
We know that the diameter of the circle inscribed within the triangle is 28 miles, and we know that E is the incenter of triangle ABC.
step 2.
Next, we learned that the perpendicular legs from the incenter to the sides of the triangle are congruent, and we know that the radius of a circle is 1/2 of the diameter of the circle.
step 3.
Since the diameter of the circle is 28, we know the distance of segment DE is 14. Next, we know the perpendicular legs are equal to segment DE. Thus, we can solve for the amount of additional miles of road by writing 14 + 14 = 28.
△ABC is a right triangle with right angle C. Side AC¯¯¯¯¯¯¯¯ is 6 units longer than side BC¯¯¯¯¯¯¯¯. If the hypotenuse has length 217−−√ units, find the length of AC¯¯¯¯¯¯¯¯.
Given:
In △ABC is a right angle triangle.
AC is 6 units longer than side BC.
[tex]Hypotenuse=2\sqrt{17}[/tex]
To find:
The length of AC.
Solution:
Let the length of BC be x.
So, Length of AC = x+6
According to the Pythagoras theorem, in a right angle triangle
[tex]Hypotenuse^2=Base^2+Perpendicualar^2[/tex]
△ABC is a right angle triangle and AC is hypotenuse, so
[tex](2\sqrt{17})^2=(x)^2+(x+6)^2[/tex]
[tex]68=x^2+x^2+12x+36[/tex] [tex][\because (a+b)^2=a^2+2ab+b^2][/tex]
Subtract 68 from both sides.
[tex]0=2x^2+12x+36-68[/tex]
[tex]0=2x^2+12x-32[/tex]
[tex]0=2(x^2+6x-16)[/tex]
Divide both sides by 2.
[tex]x^2+6x-16=0[/tex]
Splitting the middle term, we get
[tex]x^2+8x-2x-16=0[/tex]
[tex]x(x+8)-2(x+8)=0[/tex]
[tex](x+8)(x-2)=0[/tex]
[tex]x=-8,2[/tex]
Side cannot be negative, so x=2 only.
Now,
[tex]AC=x+6[/tex]
[tex]AC=2+6[/tex]
[tex]AC=8[/tex]
Therefore, the length of AC is 8 units.
A sign says that the price marked in all music instruments equipment is 30% off the original price. You buy a guitar of $315. What is the original price?
Answer:
$450
Step-by-step explanation:
Lets make a proportion: 315/x = 70/100
Now lets cross multiply: (315) * (100) = 70* x
Multiply: 31500 = 70x
Solve for x: x = 31500/70, x = 450
I hope this helped, please mark Brainliest, thank you!
Father to his first biological son true or false?
Answer:
True
Step-by-step explanation:
have a great day!
Helpppppp pleaseeeee
Save me from this questionnnnn
help please I’m struggling badly because Im sooo bad at math
Answer:
40˚ degrees
Step-by-step explanation:
HOPE THIS HELPS
PLZZ MARK BRAINLIEST
Is the following relation a function?
Yes
or
No
Answer:
no
Step-by-step explanation:
Answer:
I think that it is yes but not sure
A football team loses 2 yards every 5 minutes. How many yards did the team lose after 15 minutes?
y = 3x. How do you graph it???
Answer:
If you go to desmos.com, select the graphing calculator, and enter in y = 3x you should be able to see how it's graphed! Hope this helps!
Answer:
(0, 0) and (1, 3)
happy to help!
18 divided by 4
Please help
Answer:
Step-by-step explanation: 4.5
Answer:
4.5
Step-by-step explanation:
18/4=4.5
hope this helps :3
if it did pls mark brainliest
4 hours worked for $12; 7 hrs worked for $28 are the pair of ratios equal?
Answer:
no they're not equal
Step-by-step explanation:
you can find the ratio by dividing 12/4 and 28/7. 12/4 = 3 and 28/7 = 4. 3 and 4 are not equal, so no.
Why is it important for mathematicians to graph functions? Select all that apply.
A. For them to determine if a function can be inverted.
B. For them to visualize the function.
C. For them to extrapolate beyond the known data.
D. For them to determine if the function can be graphed.
E. For them to determine characteristics of the function.
Answer:
e
Step-by-step explanation:
s
PLEASE ITS EASY I FOGOT HOW TO DO IT
Answer:
x> -1
Step-by-step explanation:
Open circle means > or <
1. Determine whether line KM and line ST are Parallel, Pers
Line KM has a slope of 5/8
Line ST has a slope of -8/5
Answer:
Since the slope of KM and ST are different, they are not parallel
Step-by-step explanation:
Slope of line KM = [tex]\frac{5}{8}[/tex]
Slope of ST = [tex]-\frac{8}{5}[/tex]
Determine whether the lines are perpendicular;
Solution:
We can use the slope of a line to determine whether they are perpendicular or parallel to one another.
Parallel lines do not meet one another
Perpendicular lines cross one another at an angle of 90°
Two lines are parallel if their slopes are the same;
Since the slope of KM and ST are different, they are not parallel
Chloe is remodeling her living room and wants to put down new wood floors. The wood floors cost $8.50 per square foot to buy and install. If her living room has an area of 156.5 square feet, how much will the new floors cost?
Answer:
1 330,25
Step-by-step explanation:
8.50x156,6=1330,25
What expressions are equivalent to 6G -18H
Answer:
(2·3g)-(6·3g)
Step-by-step explanation:
Here is a list of numbers 5 -17 -3 17 -6 -17 19 -14 -20 state the median.
Answer:
the answer is -6
Step-by-step explanation:
the median is the number that is directly in the middle of a sequence of numbers
Suppose that the amount of snowfall per storm in Lincoln is normally distributed with µ = 4.2 inches and standard deviation µ = 2.3 inches (totally made up data). If the mayor decides that only the top 5% of storms should have school cancelled, what is the cutoff snowfall for school to be cancelled?
Answer:
7.9835
Step-by-step explanation:
Given that :
Mean snowfall per storm (µ) = 4.2 inches standard deviation (s) = 2.3 inches
Only the top 5% of storm should result in school being canceled :
Cut off snowfall for school to be canceled '
P(Z ≥ 5%) ; p(Z ≥ 0.05) = 1.645
Using the z relation :
Z = (x - m) / s
1.645 = (x - 4.2) /2.3
x - 4.2 = 2.3 * 1.645
x - 4.2 = 3.7835
x = 3.7835 + 4.2
x = 7.9835
Cut off snowfall for school to be canceled 7.9835
Answer:
hopes this photo helps
I'll brainlist!!
Plant A is 18 inches tall after one week, 36 inches tall after two weeks, 56 inches tall after three weeks. Plant B is 18 inches tall after one week, 36 inches tall after two weeks, 54 inches tall after three weeks. Which situation represents a proportional relationship between the plants?
Height and number of weeks?
Answer:
There are 2 given situations:
Plant A and Plant B growing in 3 weeks. Find which plant grows proportional
Plant A
=> 1st week = 18 inches
=> 2nd week = 36 inches
=> 3rd week = 56 inches
=> 18 + 18 = 36 + 20 = 56
Thus, this is not proportional
Plant B
=> 1st week = 18 inches
=> 2nd week = 36 inches
=> 3rd week = 54 inches
=> 18 + 18 = 36 + 18 = 54 inches
thus, the growth of this plant is proportional
A nontoxic furniture polish can be made by combining vinegar and olive oil. The amount of oil should be five times the amount of vinegar. How much of each ingredient is needed in order to make 15 oz of furniture polish?
Answer:
Missing Information.
A cube has a volume of 216 cubic inches. What is the length of each edge of the cube?
Answer:
Each side is 6 units.
Step-by-step explanation:
The problem is not how to do the question. The problem is how to get your calculator to do the question.
V = s^3
s = ?
V = 216
So what you need is the cube root of 216
s^3 = 216
cube root(s^3) = cube root(216)
s = cube root 216
Your calculator should have a y^x or x ^y key.
Put in 216
Press the y^x key or the x^y key
Put in 0.33333333333
You should get something like 5.999999 which you should round to 6.
5z + 3n -z2 ; n = 4.5 , z = 6 PLZ answer this
Answer:
5(6)+3(4.5)- 6(2)= 31.5
Step-by-step explanation:
Answer:
hmmmmm
Step-by-step explanation:
The income earned at $6.51 per hour for w hours
what is 900+100 I'm stuck 100 points for the people who can answer i know its 1000 still 100 points go listen to (joey trap) bars
Answer:
1000
Step-by-step explanation:
x = 1, y = -1, and z = 2
Answer:
1000
Step-by-step explanation:
yw :)
