A mechanical engineer is creating a new composite carbon fiber material made from two different materials. The strength of the carbon fiber material depends on how much pressure it can withstand, and it follows a standard normal distribution. The new carbon fiber material will be slated for research and development purposes if it can withstand more than 2.45 standard deviations above the mean of pressure compared to the individual materials. Fiber material that withstand less than 2.45 standard deviations above the mean of pressure when compared to the individual materials are not of research interest. What is the probability that the carbon fiber composite material can withstand pressure less than 2.45 standard deviations above the mean when compared to the individual materials
Answer:
0.9929 = 99.29% probability that the carbon fiber composite material can withstand pressure less than 2.45 standard deviations above the mean when compared to the individual materials
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
What is the probability that the carbon fiber composite material can withstand pressure less than 2.45 standard deviations above the mean when compared to the individual materials?
2.45 standard deviations above the mean is Z = 2.45, so this probability is the p-value of Z = 2.45.
Looking at the z-table, Z = 2.45 has a p-value of 0.9929.
0.9929 = 99.29% probability that the carbon fiber composite material can withstand pressure less than 2.45 standard deviations above the mean when compared to the individual materials
Given that sin ø 21/29, what is the value of cos ø, for 0° < ø < 90%
Answer:
[tex] \frac{20}{29} [/tex]
Step-by-step explanation:
Let x replace theta.
Apply pythagorean trig identity
[tex] \sin {}^{2} (x) + \cos {}^{2} (x) = 1[/tex]
[tex] (\frac{21}{29} ) {}^{2} + \cos {}^{2} (x) = 1[/tex]
[tex] \frac{441}{841} + \cos {}^{2} (x) = 1[/tex]
[tex] \cos {}^{2} (x) = 1 - \frac{441}{841} [/tex]
[tex] \cos {}^{2} (x) = \frac{400}{841} [/tex]
[tex] \cos(x) = \frac{20}{29} [/tex]
Cosine is positve in 1st quadrant so the answer is
[tex] \frac{20}{29} [/tex]
A container has a 6 litres of juice. If 3⅕ litres are poured from it, How many juice is left in the container?
Answer:
2.8 liters
Step-by-step explanation:
6 - 3.20 = 2.8
Answer:
2 4/5
Step-by-step explanation:
6-3 1/5 = 2 4/5
a. 0
b. 4
c. 64
d. 128
Answer:
d. 128
Step-by-step explanation:
a. 0
b. 4
c. 64
d. 128
Quadratic below
2^2−7−4
Vertex -
Y-Intercept -
X-Intercept -
Answer:
The y-intercept is y = -4.
The x-intercepts are [tex]x = 4[/tex] and [tex]x = -\frac{1}{2}[/tex]
The vertex is [tex](\frac{7}{4},-\frac{81}{8})[/tex]
Step-by-step explanation:
Quadratic equation:
Has the following format:
[tex]y = ax^2 + bx + c[/tex]
The y-intercept is c.
Finding the x-intercepts:
Given a second order polynomial expressed by the following equation:
[tex]ax^{2} + bx + c, a\neq0[/tex].
This polynomial has roots [tex]x_{1}, x_{2}[/tex] such that [tex]ax^{2} + bx + c = a(x - x_{1})*(x - x_{2})[/tex], given by the following formulas:
[tex]x_{1} = \frac{-b + \sqrt{\Delta}}{2*a}[/tex]
[tex]x_{2} = \frac{-b - \sqrt{\Delta}}{2*a}[/tex]
[tex]\Delta = b^{2} - 4ac[/tex]
Vertex:
Suppose we have a quadratic function in the following format:
[tex]f(x) = ax^{2} + bx + c[/tex]
It's vertex is the point [tex](x_{v}, y_{v})[/tex]
In which
[tex]x_{v} = -\frac{b}{2a}[/tex]
[tex]y_{v} = -\frac{\Delta}{4a}[/tex]
Where
[tex]\Delta = b^2-4ac[/tex]
In this question:
The quadratic equation is [tex]2x^2 - 7x - 4[/tex], which has [tex]a = 2, b = -7, c = -4[/tex]. This means that the y-intercept is y = -4.
x-intercepts:
[tex]\Delta = (-7)^2-4(2)(-4) = 81[/tex]
[tex]x_{1} = \frac{-(-7) + \sqrt{81}}{2*2} = 4[/tex]
[tex]x_{2} = \frac{-(-7) - \sqrt{81}}{2*2} = -\frac{1}{2}[/tex]
The x-intercepts are [tex]x = 4[/tex] and [tex]x = -\frac{1}{2}[/tex]
Vertex:
[tex]x_{v} = -\frac{(-7)}{2*2} = \frac{7}{4}[/tex]
[tex]y_{v} = -\frac{81}{4(2)} = -\frac{81}{8}[/tex]
The vertex is [tex](\frac{7}{4},-\frac{81}{8})[/tex]
if you answers this question correctly i'll give you brainliest
Answer:
D. Both of the dot A and B have the same mean
Find the missing angle.
Answer:
=180-50-70
=50
Step-by-step explanation:
=180-50-70
50
The between-treatments variance is based on a weighted sum of squared differences between the ____________________________________________________. population variances and the overall mean of the data set population means and the overall mean of the data set sample means and the overall mean of the data set sample variances and the overall mean of the data set
Answer:
Sample means and the grand mean
Step-by-step explanation:
The total sum of squares present in the sample can be partitioned into two parts.
1) Within sum of squares ( also called error sum of squares)
2) Between sum of squares
The first part is the sum of squares of deviations of the observations from the sample mean and is called the within sum of squares ( also called error sum of squares).
The second part is the weighted sum of the square of deviations of the sample means from the grand mean and is called between sum of squares.
Thus symbolically
Totastal SS = Within SS + Between SS
1. Divide
1 point
1. On a standardized examination, Laura received a
score of 85, which was exactly 2 standard
deviations above the mean. If the standard
deviation for the examination is 4, what is the mean
for this examination?
Answer:
656×756÷765+656+65=
Step-by-step explanation:
it was soo easy now i get what it is talking about no
which equation best represents the relationship between x and y in the graph
Answer:
A
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (- 1, 0) and (x₂, y₂ ) = (0, 3) ← 2 points on the line
m = [tex]\frac{3-0}{0+1}[/tex] = [tex]\frac{3}{1}[/tex] = 3
The line crosses the y- axis at (0, 3 ) ⇒ c = 3
y = 3x + 3 ← equation of line → A
Write each expression using a single exponent.
H^14 over h^5
A. h-9
B. one over h to the ninth
C. h19
D. h9
Answer:
h^9
Step-by-step explanation:
When divided you subtract exponents 14-5=9
The expression using a single exponent is (d) h^9
Writing the expression using a single exponent.From the question, we have the following parameters that can be used in our computation:
h^14 over h^5
This means that
h^14/h^5
Apply the law of indices
So, we have
h^14/h^5 = h^(14 - 5)
This gives
h^14/h^5 = h^9
Hence, the solution is (d) h^9
Read more about expressions at
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Please help asap urgent! 20 pts!
Answer:
the mean of those numbers is 17.1
Answer:
The M.A.D (mean absolute deviation) is 2.3
Bonus (Just in case you need it): The Mean is 17.1
Have a good day!
Danny is measuring two pyramids whose bases are squares. Given the height hhh and volume VVV of the first pyramid, Danny uses the formula a=\sqrt{\dfrac{3V}{h}}a= h 3V a, equals, square root of, start fraction, 3, V, divided by, h, end fraction, end square root to compute its base's side length aaa to be 555 meters. The second pyramid has the same volume, but has 444 times the height. What is the side length of its base?
Answer: THE ONE ABOVE IS WRONG
A= 3V/h
Step-by-step explanation:
Formulas may contain multiple variables, along with known numbers and letters that stand for known constants like \piπpi.
We can highlight a certain variable in the formula by treating the formula as an equation where we want to solve for that variable.
In this case, we need to solve the equation V =\dfrac{1}{3}AhV=
3
1
AhV, equals, start fraction, 1, divided by, 3, end fraction, A, h for AAA.
Hint #22 / 3
\begin{aligned} V&=\dfrac{1}{3}Ah \\\\ \dfrac{3V}{h}&=A \end{aligned}
V
h
3V
=
3
1
Ah
=A
Hint #33 / 3
This is the result of rearranging the formula to highlight the base area:
A=\dfrac{3V}{h}A=
h
3V
It works I did it in Khan
Consider the equation x2 – 12x + 49 = 22. Which equation has the same solution(s) as the given equation?
Answer:
The correct solution is "x=3 or x=9".
Step-by-step explanation:
The given equation is:
⇒ [tex]x^2 - 12x + 49 = 22[/tex]
On subtracting "22" from both sides, we get
⇒ [tex]x^2-12x+49-22=22-22[/tex]
⇒ [tex]x^2-12x+27=0[/tex]
On factorizing the above equation, we get
⇒ [tex]x^2-9x-3x-27=0[/tex]
By taking common, we get
⇒ [tex]x(x-9)-3(x-9)=0[/tex]
⇒ [tex](x-3)(x-9)=0[/tex]
⇒ [tex]x-3=0[/tex]
[tex]x=3[/tex]
Or,
⇒ [tex]x-9=0[/tex]
[tex]x=9[/tex]
It took gigi 1 hour and 20 minutes to complete a bicycle race It took Johnny twice as long because he got a flat tire. How many minutes did it take Johnny to finish the race?
Plz help me well mark brainliest if correct!!....
Answer:
22 in. or B
Step-by-step explanation:
add all the sides
Answer:
The Answer would be B)22 in.
Step-by-step explanation:
if you add the sides together then multiply by 2 you will get 22 in. I hope this helpped!
at lunch four friends drink 8 pints of milk. How many fluid ounces is this equal to? 1) 128 FL oz 2)64 FL oz 3)32oz 4) 16 FL oz
at lunch four friends drink 8 pints of milk. how many fluid ounces is this equal to?
128 FL
Answer:
The answer is choice #1 or 128 Fluid ounces
Step-by-step explanation:
8 pints = 128 oz
Whats the answer?This is trigonometry
Answer:
100
Step-by-step explanation:
Use Euler's formula to find the missing number.
Vertices: 13
Edges: 26
Faces: ?
A.14
B.15
C.16
D.17
Answer:
15
Step-by-step explanation:
trust me bro
Someone help me out my math grads are bad
Answer:
15m^2
Step-by-step explanation:
2m*3m = 6m^2
3m*3m = 9m^2
Answer: 6m^2 + 9m^2 = 15m^2
Feel free to mark as brainliest :D
Please help and thanks whoever helps me!!
Answer:
2/3 km per minute
Step-by-step explanation:
kilometers
1 1/3 - 2/3 = 2/3km
Minutes
2 - 1 = 1 minute
----------------------------
Spped
(2/3 km) / (1 minute)
2/3 km per minute
What's the Area for each shape?
Answer:
[tex](6 \times 5) + (2 \times 3) \\ 30 + 6 \\ = 36cm^{2} [/tex]
Which numbers are equal to 24
8 divided by 1/3
6 divided by 1/8
9 divided by 1/4
4 divided by 1/6
12 divided by 1/2
Answer:
The first one
Step-by-step explanation:
I did this and got it right and I solved it
8×3 equal 24/1 so make it to a whole number 24
Tiffany quiz grades on 1st 4 quizzes are 72,87,83,90
Answer:
90
Step-by-step explanation:
72 is the least and 90 is the greatest
87 is the second most greatest and 83 is the third most.
Therefore the answer is 90
Can someone help me?
Answer:
7. D) 61in
8. A) 57in
9. A) 47in
Step-by-step explanation:
The perimeter is the distance around the area of a 2-dimensional figure. it can be found by adding up all of the sides of the figure. One can use this to solve for the value of the parameter (x). Then substitute the value back in to find the value of the side.
7.
AB + BC + AC = 145
Substitute,
2x + 2x + 5 + x = 145
Simplify,
5x + 5 = 145
Inverse operations,
5x + 5 = 145
-5
5x = 140
/5
x = 28
Substitute,
AC = 2x + 5= 2(28) + 5 = 61
8.
AB + BC + AC = 135
Substitute,
2x + 2x + 5 + x = 135
Simplify,
5x + 5 = 135
Inverse operations,
5x + 5 = 135
-5
5x = 130
/5
x = 26
Substitute,
AC = 2x + 5 = 2(26) + 5 = 57
9.
AB + BC + AC = 122
Substitute,
x + 22 + 2x + x = 122
Simplify,
4x + 22 = 122
Inverse operations,
4x + 22 = 122
-22
4x = 100
/4
x = 25
Substitute,
AB = x + 22 = 25 + 22 = 47
What is the period of the parent cosine function, y=cos(x)? degrees
What is the period of the cosine function shown in the graph? degrees
Answer: first 360 second 1080 third horizontal stretch
Step-by-step explanation:
The period of this parent cosine function [y=cos(x)] is equal to 360 degrees.
What is the period of a cosine function?The period of a cosine function can be defined as the overall length of the interval of values on the x-axis over which a graph lies and it's repeated. Mathematically, the period of this parent cosine function [y=cos(x)] is given by:
T = 2π/A
Where:
A is the coefficient of the x.When A = 1, we have:
T = 2π/1 = 360 degrees.
For the graphed function, the period of this cosine function is given by:
T = 6π
T = 6 × 360
T = 1080 degrees.
Read more on cosine function here: https://brainly.com/question/4599903
When solving for y, in which step did Ramon make a mistake?
a) step one,Ramona re-wrote the system incorrectly
b) step two,Ramona should have multiplied the first equation by -4 instead of -2
c) in step three Ramona simplify -28+10 as -18 instead of simplifying to 18
d) in step four, Ramona should have divided by -6 instead of dividing by 6
show work
The ages of job applicants for a security guard position are uniformly distributed between 25 and 65. Could a 25-year-old job applicant be two standard deviations below the mean (or more than two standard deviations)?
Answer:
No, a 25-year-old job applicant cannot be two standard deviations below the mean
Step-by-step explanation:
There are two frequencies 25 and 65
Mean of the two frequencies = 25+65/2 = 45
Standard deviation =
[tex]\frac{65-25}{\sqrt{12} } \\= 11.55[/tex]
Mean - 2 x standard deviation [tex]= 45 - 2 * 11.55 = 21.9[/tex]
[tex]21.9 < 25[/tex]
Thus, a 25-year-old job applicant cannot be two standard deviations below the mean
In which choice do all three points lie on the
same straight line?
A А.
(0, 1), (-1, 3), (1, 3)
B.
(4, 2), (2, 1), (4, -2)
C (0, 0), (8, 0), (0, 8)
D
(1, 2), (2, 4), (4,8)
Answer:
D (1, 2), (2, 4), (4,8)
Step-by-step explanation:
Points lying on the same line:
If three points lie on the same line, the change in y has to be always the same when x changes by 1.
А. (0, 1), (-1, 3), (1, 3)
(-1,3) to (0,1): x changes by 1, y by -2
(0,1) to (1,3): x changes by 1, y by 2
So these points are not on the same line.
B. (4, 2), (2, 1), (4, -2)
Two values for y when x = 4, so not on the same straight line.
C (0, 0), (8, 0), (0, 8)
Two values for y when x = 0, so not on the same straight line.
D (1, 2), (2, 4), (4,8)
Here, when x changed by 1(from 1 to 2), y changed by 2.
When x changed by 2(from 2 to 4), y changed by 2*2 = 4.
So these points are on a straight line, and D is the correct answer.
Kayla was cutting right triangles from wood to use for an art project. Two of the right triangles she cut are shown below
Answer:
The answer is "[tex]28^{\circ}[/tex]"
Step-by-step explanation:
Please find the complete question in the file.
The angle F measure is identical to the angle C measure.
The adjacent BC and the hypotenuse AC have been developed. That would be used cosine.
[tex]\cos C = \frac{15}{17}\\\\C =\ cos^{-1}\frac{15}{17} = 28.07\approx 28^{\circ}[/tex]