A)The probability that the yield strength is greater than 60 is approximately 0.0003.
B)The yield strength value that separates the strongest 75% from the others is approximately 45.3725 ksi.
What is probability?
Probability is a fundamental concept in mathematics and statistics that quantifies the likelihood or chance of an event occurring. It provides a numerical measure of uncertainty or the relative frequency with which an event is expected to happen. In simpler terms, probability is a way of expressing how likely it is for a particular outcome or event to take place.
(a) The probability that yield strength is at most 39:
Using the standard normal distribution, we can calculate the z-score as follows:
[tex]\[ z = \frac{{39 - 42}}{{5.0}} = -0.6 \][/tex]
The cumulative probability associated with a z-score of -0.6 represents the probability of obtaining a value less than or equal to 39. Using a standard normal distribution table or a calculator, we find that this cumulative probability is approximately 0.2743.
Therefore, the probability that the yield strength is at most 39 is approximately 0.2743.
The probability that yield strength is greater than 60:
Converting 60 to a z-score:
[tex]\[ z = \frac{{60 - 42}}{{5.0}} = 3.6 \][/tex]
The cumulative probability associated with a z-score of 3.6 represents the probability of obtaining a value greater than 60. Using a standard normal distribution table or a calculator, we find that this cumulative probability is approximately 0.9997.
Since we want the probability of a value greater than 60, we subtract this cumulative probability from 1:
[tex]\[ P(\text{{yield strength}} > 60) = 1 - 0.9997 = 0.0003 \][/tex]
Therefore, the probability that the yield strength is greater than 60 is approximately 0.0003.
(b) The yield strength value that separates the strongest 75% from the others:
To find the yield strength value that separates the strongest 75% from the others, we need to find the z-score corresponding to the cumulative probability of 0.75. Using a standard normal distribution table or a calculator, we find that the z-score associated with a cumulative probability of 0.75 is approximately 0.6745.
Next, we can use the z-score formula to find the yield strength value:
[tex]\[ z = \frac{{x - \mu}}{{\sigma}} \][/tex]
Rearranging the formula to solve for x:
[tex]\[ x = \mu + (z \times \sigma) \][/tex]
Substituting the values into the formula:
[tex]\[ x = 42 + (0.6745 \times 5.0) = 45.3725 \][/tex]
Therefore, the yield strength value that separates the strongest 75% from the others is approximately 45.3725 ksi.
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At a certain school, 8/9 of the students are boys. Today, 2/5 of the boys brought their lunch. What fraction of the students are
boys who brought their lunch today?
Answer:
the answer is I think 2/3
Fraction of boys brought lunch today is 16/25.
Here,
Given that:
The ratio of boys at certain school = 8/9
And 2/5 of boys brought lunch today
We have to find fraction of boys brought lunch today.
What is fraction?
Fractions denote the parts of a whole or collection of objects.
Now,
The ratio of boys at certain school = 8/9
And 2/5 of boys brought lunch today
Since, the ratio of boys 8/9 denotes 8 boys out of 9 students
Therefore, number of boys = 8
Thus, Fraction of boys brought lunch today = 8 x 2/5
= 16/25
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Carly loves to run while Riley prefers walking. Carly can run 3 miles per hour faster
than her sister Riley can walk the same distance. If Carly ran 15 miles in the same time
it took Riley to walk 9 miles, which equation can be used to find the speed of each
sister?
Answer:
Step-by-step explanation:
build a binary search tree for the words banana, peach, apple, pear, coconut, mango, and papaya using alphabetical order.
To build a binary search tree using alphabetical order for the given words, we start with an empty tree and insert each word in the appropriate position based on its alphabetical order.
Here's the step-by-step process:
Start with an empty tree.
Insert the first word, "banana," as the root of the tree.
Insert the second word, "peach," comparing it to the root. Since it comes after "banana," it becomes the right child of the root.
Insert the third word, "apple." Comparing it to the root, it comes before "banana," so we traverse to the left child of the root. Since the left child is empty, "apple" becomes the left child of "banana."
Insert the fourth word, "pear." Comparing it to the root, it comes after "banana," so we traverse to the right child. Comparing it to "peach," it comes before "peach," so we traverse to the left child of "peach." Since the left child is empty, "pear" becomes the left child of "peach."
Insert the fifth word, "coconut." Comparing it to the root, it comes before "banana," so we traverse to the left child. Comparing it to "apple," it comes after "apple," so we traverse to the right child. Comparing it to "pear," it comes before "pear," so we traverse to the left child of "pear." Since the left child is empty, "coconut" becomes the left child of "pear."
Insert the sixth word, "mango." Comparing it to the root, it comes after "banana," so we traverse to the right child. Comparing it to "peach," it comes before "peach," so we traverse to the left child. Comparing it to "pear," it comes after "pear," so we traverse to the right child. Comparing it to "coconut," it comes after "coconut," so we traverse to the right child. Since the right child is empty, "mango" becomes the right child of "coconut."
Insert the seventh word, "papaya." Comparing it to the root, it comes after "banana," so we traverse to the right child. Comparing it to "peach," it comes after "peach," so we traverse to the right child. Comparing it to "pear," it comes after "pear," so we traverse to the right child. Comparing it to "coconut," it comes after "coconut," so we traverse to the right child. Comparing it to "mango," it comes after "mango," so we traverse to the right child. Since the right child is empty, "papaya" becomes the right child of "mango."
The resulting binary search tree will look like this:
banana
/ \
apple peach
\ \
pear papaya
/
coconut
\
mango
Note: The tree might have different structures depending on the order of insertion, as long as it maintains the binary search tree property.
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Who is Pythagorean? when was he born? when did he die?
Answer:
" Pythagoras established the first Pythagorean community in Crotone, Italy. Early Pythagorean communities spread throughout Magna Graecia. "
"was an ancient Ionian Greek philosopher and the eponymous founder of Pythagoreanism . " <---------- Credits to: Yahoo
He was born in about 570 BC on the Greek island of Samos
He died in 495 BC
se desea constrir una barda utilizando block . las dimensiones de la barda son 25 m de largo y 2 m de altura . si se requieren 12 blocks para cada metro cuadrado de barda ¿ cuantos blocks se usaran en su construcción?
respuesta urgente !!!
Answer:
I don't understand the language
Step-by-step explanation:
am not form Paris
What is the value of y when x=-1?
P
Answer:
is there an equation to find y? Because all you gave was x=-1
6) The cost of a computer system increases with increased processor speeds. The cost C
of a system as a function of processor speed is estimated as C = 1234 - 35 + 1900,
where S is the processor speed in MHz. Find the processor speed for which cost is at a
minimum. [4 marks]
Answer:
The speed is: 0.0142MHz
Step-by-step explanation:
Given
[tex]C(s) = 1234s^2 - 35s + 1900[/tex]
Required
The processor speed when the cost is at minimum
First, differentiate C(s) with respect to s
[tex]C(s) = 1234s^2 - 35s + 1900[/tex]
[tex]C'(s) = 2468s - 35[/tex]
The cost is at minimum when [tex]C'(s) = 0[/tex]
So, we have:
[tex]C' = 2468s - 35 = 0[/tex]
[tex]2468s - 35 = 0[/tex]
Solve for s
[tex]2468s = 35[/tex]
[tex]s=\frac{35}{2468}[/tex]
[tex]s\approx0.0142[/tex]
5/7+1/2+3/4
i need help please
Answer:
1.96428571429
Step-by-step explanation:
Answer:
55/28
Step-by-step explanation:
5×2+7/14+3/4
17/14+3/4
68+42/56
110/56
55/28
Can someone help me with this. Will Mark brainliest.
Answer:
pt B: (-1, -8)
Step-by-step explanation:
(x - 7)/2 = -4
x - 7 = -8
x = -1
(y-6)/2 = -7
y - 6 = -14
y = -8
Find the area of the painted part of the image below. (Units in m)
Answer:
11 meters square.
Step-by-step explanation:
if the painted area is the gray it would be 10m
if its the white area its 9m
El elemento neutro de la suma es el 1.
If angle A=320∘, what is the radian measure of A? Give your answer as an exact fraction in terms of π.
The radian measure of angle A is (16/9)π.
To convert degrees to radians, we use the conversion factor:
[tex]1\ degree = \pi /180\ radians[/tex]
Given that angle A is 320 degrees, we can calculate its radian measure as follows:
Angle A in radians = (320 degrees) * (π/180 radians/degree)
= (320π)/180 radians
= (16/9)π radians
Therefore, the radian measure of angle A is (16/9)π.
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Bryan is a waiter. He waits on a table of 4 whose bill comes to $110.31. If Bryan receives a 15% tip, approximately how much will he receive?
If Bryan receives a 15% tip, then he will receive an amount of approximately $16.55 as a tip.
In order to calculate the tip-amount, we need to multiply the total-bill by the tip percentage. In this case, the "bill-amount" is $110.31, and the tip percentage is 15%.
To find the tip amount, we can use the formula:
Tip amount = (Total bill) × (Tip percentage),
Simplifying further,
We get,
Tip amount = $110.31 × 0.15,
= $16.5465 (rounded to the nearest cent)
Therefore, Bryan will receive approximately $16.55 as a tip.
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help pls first awnser get brainest
Answer:
124
Step-by-step explanation:
the top square is 16 by 6 which will give you an area of 124 the bottom square has dimensions of 2 by 14 which is 28 add those numbers together to get your answer.
Use the Laplace transform to solve the following initial value problems. 2 a) ' +5/- y = 0, (O) = -1/(0) = 3 b) +4+ 30) = -1. V(0) - 2
To solve the initial value problems using the Laplace transform, we can apply the Laplace transform to the given differential equations and initial conditions.
For the first problem, the Laplace transform of the differential equation is s^2Y(s) + 5sY(s) + 2Y(s) = 0. Solving for Y(s), we find Y(s) = -3/(s+1).
Taking the inverse Laplace transform, we obtain the solution y(t) = -3e^(-t). For the second problem, the Laplace transform of the differential equation is sY(s) + 4Y(s) + 3/(s+1) = -2. Solving for Y(s), we find Y(s) = (-2s - 1)/(s^2 + 4s + 3). Taking the inverse Laplace transform, we obtain the solution y(t) = (-2t - 1)e^(-t).
a) The Laplace transform of the given differential equation is:
s^2Y(s) + 5sY(s) + 2Y(s) = 0
Using the initial condition Y(0) = -1 and Y'(0) = 3, we can apply the initial value theorem to obtain:
Y(s) = -1/s + 3
Taking the inverse Laplace transform of Y(s), we find:
y(t) = -3e^(-t)
b) The Laplace transform of the given differential equation is:
sY(s) + 4Y(s) + 3/(s+1) = -2
Using the initial condition Y(0) = -1, we can apply the initial value theorem to obtain:
Y(s) = (-2s - 1)/(s^2 + 4s + 3)
Taking the inverse Laplace transform of Y(s), we find:
y(t) = (-2t - 1)e^(-t)
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Some unsound arguments are valid. True or False?
The statement "Some unsound arguments are valid" is false.
The statement "Some unsound arguments are valid" is false.
A valid argument is a statement that follows the rules of logic.
An argument is known to be sound when it is valid and has true premises. When the premises of an argument are correct, the argument is considered sound. When an argument is valid, it follows logically from its premises, which are the statements that provide evidence or support for the argument's conclusion.
The unsound argument is the one that contains at least one false premise.
The sound argument is the one that contains only true premises and is valid (that is, follows logically from the premises).
If an argument is unsound, it can never be valid because it contains at least one false premise.
Therefore, the statement "Some unsound arguments are valid" is false.
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Which of the following is equivalent to the expression below?
Answer:
A. 7✓6 - 6x✓6
Explanation:
7✓6 - 5x✓6 - x✓6
= 7✓6 - (5x + x)✓6
= 7✓6 - 6x✓6
Find the distance between the points (7,–9) and (–2,–4).
5. How far can you get away from your little brother with a squirt gun filled point
with paint if you can travel at 3 m/s and you have 15 s before he sees you?"
45 m
5 m
2 m
20 m
Answer:
45 meters
Step-by-step explanation:
I hope this helps.
Please answer correctly! I will mark you as Brainliest
Answer:
Choice D
Step-by-step explanation:
Choice D, 3072ft^2 is the correct answer.
Here's how! The length AND width are both 24, so we know that 24 * 24 is our start. Then the height of the pyramid is 16, which now makes our equation 24 * 24 * 16. When finding the volume of a pyramid, you must divide by 3, so now the answer is (24 * 24 * 16) / 3. Making the answer 3072ft^2.
Hope this helped!
Answer:
3072
Step-by-step explanation:
volume =(1/3) hight ×width×length
v=(1/3) × 16 × 24 × 24
v=3072
Select all the expressions that have a value 10
[tex](2 \div 2 \sqrt{2) ^{2} } [/tex]
what is the answer
PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!! PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!! PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!! PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!!PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!! PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!! PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!!
Answer:
Infinitely many solutions
Step-by-step explanation:
7x - 11 = 5(x - 2) + 2x - 1
7x - 11 = 10x - 10 + 2x - 1
7x - 11 = 7x - 11
No matter what number you plugin, it will always be equal.
1) 7x-11 = 5(x-2)+2x-1
2) 7x-11=5x-10+2x-1
3)7x-11=7x-11
4)0=0
5)Would cancel each other out.
6) So I guess no solutions?
please please please help
Answer:
I wanna say 16 but im not sure
Step-by-step explanation:
Freddie is reading a book that has
440 pages. He has already read
140 pages. What decimal
describes the part of the book that
Freddie has already read?
PLEASE HELP ME
Answer:
140÷440(you can write it as a fraction)
=0.318181882
=0.32
what weight is shown
Answer:
325 grams is the weight.
what is m (angle) 2 if m (angle) 4 = 120°?
Answer:
if 4 is 120° then 2 is also 180° since they are opposite angles.
Which expression is equivalent
Answer:
the first one
Step-by-step explanation:
Aubrey has a new art box in the shape of a rectangular prism. The box is 12\text{ cm}12 cm12, start text, space, c, m, end text by 20\text{ cm}20 cm20, start text, space, c, m, end text by 5\text{ cm}5 cm5, start text, space, c, m, end text. The only thing in the art box is a new pink eraser with the dimensions shown below.
Answer:
1196 cm3
Step-by-step explanation:
Answer:
1196
Step-by-step explanation:
Right triangle EFG it is known that the side opposite of acute angle F has a length of 18 inches and the leg adjacent to F has a length of 14 inches. Which of the following is closest to angle F
1. 38° 2. 65° 3. 52° 4. 72°
Answer:
3
Step-by-step explanation:
The closest angle to F in the triangle is 52 degrees.
What is Trigonometry?Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.
Given that Right triangle EFG it is known that the side opposite of acute angle F has a length of 18 inches and the leg adjacent to F has a length of 14 inches.
We can use the tangent function to find the measure of angle F:
tan(F) = opposite/adjacent = 18/14
we can find the inverse tangent of this value:
F = tan⁻¹(18/14)
= tan⁻¹(1.28)
F= 52.15°
Hence, the closest angle to F in the triangle is 52 degrees.
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