Answer:
Explained below.
Step-by-step explanation:
Let X represents the tree heights.
It is provided that X follows a normal distribution with mean μ = 112 inches and standard deviation σ = 10 inches.
(a)
Compute the 22nd percentile of the tree heights as follows:
[tex]P(X<x)=0.22\\\\P(Z<z)=0.22[/tex]
The z-score for the corresponding probability is, z = -0.77.
Compute the value of x as follows:
[tex]z=\frac{x-\mu}{\sigma}\\\\-0.77=\frac{x-112}{10}\\\\x=112-(0.77\times 10)\\\\x=104.3[/tex]
Thus, the 22nd percentile of the tree heights is 104.3 inches.
(b)
Compute the 80th percentile of the tree heights as follows:
[tex]P(X<x)=0.80\\\\P(Z<z)=0.80[/tex]
The z-score for the corresponding probability is, z = 0.84.
Compute the value of x as follows:
[tex]z=\frac{x-\mu}{\sigma}\\\\0.84=\frac{x-112}{10}\\\\x=112+(0.84\times 10)\\\\x=120.4[/tex]
Thus, the 80th percentile of the tree heights is 120.4 inches.
(c)
Compute the first quartile of the tree heights as follows:
[tex]P(X<x)=0.25\\\\P(Z<z)=0.25[/tex]
The z-score for the corresponding probability is, z = -0.67.
Compute the value of x as follows:
[tex]z=\frac{x-\mu}{\sigma}\\\\-0.67=\frac{x-112}{10}\\\\x=112-(0.67\times 10)\\\\x=113.3[/tex]
Thus, the first quartile of the tree heights is 113.3 inches.
(d)
The tallest 1% of the trees, i.e. P (X > x) = 0.01.
That is, P (X < x) = 0.99.
⇒ P (Z < z) = 0.99
The corresponding z-value is, z = 2.33.
Compute the value of x as follows:
[tex]z=\frac{x-\mu}{\sigma}\\\\0.99=\frac{x-112}{10}\\\\x=112+(0.99\times 10)\\\\x=121.9[/tex]
Thus, the tallest 1% of the trees are more than 121.9 inches tall.
4. Tell whether the equation is a linear equation.
4x-3y = 2
Answer:
What Is X and Y
Step-by-step explanation:
Answer:
It is a linear equation.
Step-by-step explanation:
It has no squares in the equation, meaning the line is straight, therefore meaning the equation is linear.
Pls helpppppp this stuff makes no sense
Answer:
x = 5
Step-by-step explanation:
a || b and a line intersecting them is their transversal.
[tex] \therefore m\angle 1=m\angle 5\\(corresponding \:\angle 's) \\\\
\therefore 60 - 2x = 70 - 4x\\\\
\therefore 4x - 2x = 70 - 60\\\\
\therefore 2x = 10\\\\
\therefore x =\frac{10}{2} \\\\
\huge \orange {\boxed {\therefore x = 5}}[/tex]
Given m|n, find the value of x.
t
xo
>m
53°
Answer:
32 degrees goto the x vaule
a baseball field is being constructed. the builders noticed that the batters would have the sun in their eyes when batting from point a. the builders decided to rotate the model 90 counterclockwise about the origin where is the new location of the batter?
A) E
B)F
C)G
D)H
Answer:
b
Step-by-step explanation:
Answer:
G
Step-by-step explanation:
The auxiliary equation for the given differential equation has complex roots. Find a general solution. y''-10y' 29y=0
Answer:
[tex]y = Acos5x - Bsin5x[/tex]
Step-by-step explanation:
Given the differential equation y''-10y'+29y=0
First, we need to rewrite it as an auxiliary equation as shown:
Let y'' = m²y and y' = my
Substitute the values into the general equation
m²y-10my+29y = 0
Factor out y:
(m²-10m+29)y = 0 [The auxiliary equation]
Solve the auxiliary equation and find the roots of the equation
m²-10m+29 = 0
m = -b±√(b²-4ac)/2a
a = 1, b = -10, c = 29
m = -10±√(10²-4(1)(29))/2(1)
m = -10±√(100-116)/2
m = -10±√-16/2
m = (-10±4i)/2
m = -10/2 + 4i/2
m = -5+2i
Comparing the complex number with a+bi, a = -5 and b = 2
The general solution for complex solution is expressed as:
[tex]y = Acosax + Bsinax[/tex]
Substitute the value of a in the equation
[tex]y = Acos(-5)x + Bsin(-5)x\\y = Acos5x-Bsin5x[/tex]
Hence the general solution to the differential equation is [tex]y = Acos5x - Bsin5x[/tex]
Pendiente 6 y puntos (5, -2)
Step-by-step explanation:
The state of Tennessee is shaped like a parallelogram. Its approximate dimensions are a base of 440 miles and a height of 120 miles. The state of Colorado is shaped like a rectangle, with approximate dimensions of 385 miles long and 275 miles wide. Ted works for a geographical company that is working on finding the areas of each state in the Union. Ted asked an assistant to double‐check his answers. Approximate area of Tennessee: 63,000 mi2 Approximate area of Colorado: 106, 000 mi2 11. If you were Ted’s assistant, would you agree with his answers? Explain why you answered yes or no by showing your work and explaining how it helped you come to your answer.
Answer:
Tennessee area we don´t know there is something wrong
Colorado area is ok close to 106000 mi²
Step-by-step explanation:
Tennessee is shaped like a parallelogram base is equal to 440 miles and the height is 120 miles. Therefore
Ap = b*h = 440 * 120 = 52800 mi²
But the area of Tennessee is 63000 mi²
Then there is something wrong because difference in mi² is
10400 mi²
10400/ 63000 = 0,165 % faraway of the real number
In the case of Colorado
Ac = 385 * 275
Ac = 105875 mi² pretty close to 106000 mi²
Then from double check in the areas, we conclude in a high difference in the figures for the state of Tennessee ( one or both of the figures are incorrect ). The state of Colorado area is oK
In the diagram, the origin is at the center of a cube that has edges 6 units long. The x-, y-, and z-axes are perpendicular to the faces of the cube. Give the coordinates of the corner at point E.
(3, 3, –3)
(3, –3, –3)
(–3, 3, 3)
(–3, –3, 3)
Answer:
I really think that (3 , -3 , -3) is the answer but I could be wrong.
Step-by-step explanation:
I'm taking the quiz right now and from the graph it looks like point E is in the position (3 , -3 , -3).
Once again, sorry if I'm wrong.
3^2 *3^x =81. Find the value of x.
Answer:
The answer is 16
Mark me as brainliest if it was helpful
What is
f(x) = x3 – 4x2 – 7x + 10 in factored form given that 5 is a zero of the function?
Answer:
(x-2)(x+1)(x-5)
Step-by-step explanation:
Una partícula se mueve sobre el eje x de acuerdo con la ecuación del movimiento
s=f(t) donde s es la distancia dirigida al origen en pies a los t segundos.
a) La velocidad v(t) y la aceleración a(t) en el instante t.
b) El instante t en el que la velocidad es cero.
s= 6t-t²
s=t²-6t
s= t²-9t+24
Answer:
a)
s= 6t-t² --> v = 6 -2t --> a = -2
s=t²-6t --> v = 2t-6 --> a = 2
s= t²-9t+24 --> v = 2t -9 --> a = 2
b)
v = 6 -2t = 0 --> t = 3
v = 2t-6 = 0 --> t = 3
v = 2t -9 = 0 --> t = 9/2
Step-by-step explanation:
si s(t) es la distancia, la velocidad es la primera derivada v(t) = s'(t)
y la acceleracion es la segunda derivada : a(t)= v'(t) = s''(t)
s= 6t-t² --> v = 6 -2t --> a = -2
s=t²-6t --> v = 2t-6 --> a = 2
s= t²-9t+24 --> v = 2t -9 --> a = 2
Suppose the horses in a large stable have a mean weight of 975lbs, and a standard deviation of 52lbs.What is the probability that the mean weight of the sample of horses would differ from the population mean by less than 15lbsif 31horses are sampled at random from the stable
Answer: The required probability = 0.8926
Step-by-step explanation:
Given: [tex]\mu=975\text{ lbs}[/tex], [tex]\sigma= 52\text{ lbs}[/tex]
Let x = weight of horse stable.
Sample size : n= 31
Then, the probability that the mean weight of the sample of horses would differ from the population mean by less than 15 will be:
[tex]P(-15<P(\overline{x}-\mu)<15)=P(\dfrac{-15}{\dfrac{52}{\sqrt{31}}}<\dfrac{\overline{x}-\mu}{\dfrac{\sigma}{\sqrt{n}}}<\dfrac{15}{\dfrac{52}{\sqrt{31}}})\\\\=P(-1.61<z<1.61)\ \ \ [z=\dfrac{\overline{x}-\mu}{\dfrac{\sigma}{\sqrt{n}}}]\\\\=2(z<1.61)-1\ \ \ [P(-z<Z<z)=2(Z<z)-1]\\\\=2( 0.9463)-1\\\\=0.8926[/tex]
Hence, the required probability = 0.8926
-2/3 - (-1 1/3)
A. -1 2/3
B. -2/3
C. -1/3
D. 2/3
Answer is 2/3
Hope this helps
juan feeds his dog 2 scoops of dry dog food every day. each scoop weighs 1/3 pound. he bought a new 12 pound of dog food. how many days will it last
how can you plot,compare,and order rational numbers using a number line?
Which of the following is equal to −|−43|
-43
0
43
-(-43)
Answer:
i think ur answer is -43.i hope u get it
Answer:
the answer is i guess -43
Step-by-step explanation:
|-43| = 43
so -|-43| = -43
Multiply. Express your answer in simplest form. 9 1/6 × 1 1/11. A. 10 B. 9 1/66 C. 10 1/17 D. 10 5/6
Answer:
9 1/66
Step-by-step explanation:
9 x 1 is 9 so its that but to add more proof the problem is 9 1/6, 1 1/11 multiply 6 and 11 it is 66 so the answer is 9 1/66
light travels 3 x 10^5 kilometers in one second. how far does it travel in 7.6 seconds?
Answer:
1800000 kilometers
Step-by-step explanation:
i think im not 100% sure
Andy was at Level –1 and took the elevator to Level 21. How many levels did the elevator move upward?
Answer: 22 Levels
Step-by-step explanation: He would need to go one level higher just to get to level one, and another 21 to get to the level that he wants to, so the total would be 22 levels.
Answer:
The elevator moved up 21 levels
Consider versus A random sample of 16 observations taken from this population produced a sample mean of 75.8. The population is normally distributed with a. Calculate the p-value. Round your answer to four decimal places.
Answer:
The p-value is 0.0012.
Step-by-step explanation:
The hypothesis is:
H₀: µ = 72 vs. Hₐ: µ > 72
The information provided is:
[tex]n =16\\\bar x=75.8\\\sigma=5[/tex]
Compute the test statistic value as follows:
[tex]z=\frac{\bar x-\mu}{\sigma/\sqrt{n}}[/tex]
[tex]=\frac{75.8-72}{5/\sqrt{16}}\\\\=3.04[/tex]
Compute the p-value as follows:
[tex]p-value=P(Z>3.04)\\\\=1-P(Z<3.04)\\\\=1-0.99882\\\\=0.00118\\\\\approx 0.0012[/tex]
*Use a z-table.
Thus, the p-value is 0.0012.
Please help me solve What is m
Answer:
a=60
b=85
c=35
Step-by-step explanation:
a is shown to be 60 in the text along with c being 85 with its angle so just add 60 and 85 to get 145 and fill in the remaining to get 180 which gives you c as 35
Please help!!
Square ABCD has vertices A(-2,-3), B(4, -1), C(2,5), and D(-4,3). Find the length of a side
of the square. Round your answer to the nearest tenth if necessary.
Answer:
The length of a side of the square is 6.3 units.
Step-by-step explanation:
When given vertices for a given shape, the length of the side is calculated using the formula:
√(x2 - x1)² + (y2 - y1)²
When given vertices (x1 , y1) and (x2 , y2)
Square ABCD has vertices A(-2,-3), B(4, -1), C(2,5), and D(-4,3). Find the length of a side
Side AB : A(-2,-3), B(4, -1)
√(x2 - x1)² + (y2 - y1)²
= √(4 -(-2))² + (-1 -(-3))²
= √ 6² + 2²
= √36 + 4
= √40
= 6.3245553203
≈ 6.3 units
B(4, -1), C(2,5),
√(x2 - x1)² + (y2 - y1)²
= √ (2- 4)² + (5- (-1))²
= √-2² + 6²
= √4 + 36
= √40
= 6.3245553203
≈ 6.3 units
C(2,5), D(-4,3).
√(x2 - x1)² + (y2 - y1)²
= √(-4 - 2)² + (3 - 5)²
= √-6² + -2²
= √36 + 4
= √40
= 6.3245553203
≈ 6.3 units
A(-2,-3), D(-4,3).
√(x2 - x1)² + (y2 - y1)²
= √(-4 -(-2))² + (3 - (-3))²
= √-2² + 6²
= √4 + 36
= √40
= 6.3245553203
≈ 6.3 units
On day 3 of a canned food drive, the students had collected 80 cans and were 40% of the way to their goal. What was their goal for the total number of cans they hoped to collect?
Answer:
200 cans
Step-by-step explanation:
use rate method
80 40
x 100
40x=8000
x=8000/40
x=200
A projectile is launched straight up from the ground with an initial velocity of 120 ft/s. If acceleration due to gravity is –16 ft/s2, after about how many seconds will the object reach a height of 200 ft?
Answer:
The projectile will reach a height of 200 ft after 1.910 seconds and 13.090 seconds of being launched.
Step-by-step explanation:
This projectile is experimenting a free fall, that is, an uniform accelerated motion of the projectile due to gravity and in which effects of air friction and Earth's rotation are neglected. Given that initial and final heights, initial velocity and gravitational acceleration are known, we need to calculate time by solving the appropriate equation of motion described below:
[tex]y = y_{o} +v_{o}\cdot t +\frac{1}{2}\cdot g \cdot t^{2}[/tex] (Eq. 1)
Where:
[tex]y_{o}[/tex] - Initial height of projectile, measured in feet.
[tex]y[/tex] - Final height of projectile, measured in feet.
[tex]v_{o}[/tex] - Initial velocity of projectile, measured in feet per second.
[tex]g[/tex] - Gravitational acceleration, measured in feet per square second.
As we must remember, quadratic functions have two roots and if we get that [tex]y_{o} = 0\,ft[/tex], [tex]y = 200\,ft[/tex], [tex]v_{o} = 120\,\frac{ft}{s}[/tex] and [tex]g = -16\,\frac{ft}{s^{2}}[/tex], then, the quadratic function is:
[tex]-8\cdot t^{2}+120\cdot t -200 = 0[/tex]
Roots are found by the Quadratic Formula:
[tex]t_{1,2} = \frac{-120\pm \sqrt{120^{2}-4\cdot (-8)\cdot (-200)}}{2\cdot (-8)}[/tex]
Whose solutions are:
[tex]t_{1} \approx 13.090\,s[/tex] and [tex]t_{2} \approx 1.910\,s[/tex].
Both roots are physically reasonable, first root represents the instant when the projectile reaches 200 feet when it is moving downwards, whereas second root represents the projectile moving upwards. Therefore, the projectile will reach a height of 200 ft after 1.910 seconds and 13.090 seconds of being launched.
Answer:
It will take 2.5 s to reach a height of 200ft.
Step-by-step explanation:
which expression is equivalent to the expression shown f(5^4)^2
What is the slope of the line passing through the points (0,-5) and (4,2)?
Enter your answer in the box
Answer:
[tex] \huge{ \boxed{ \tt{ \frac{ 7}{4} }}}[/tex]
Step-by-step explanation:
[tex] \text{Let \: the \: points \: be \: A \: and \: B}[/tex]
[tex] \sf{A \:( \: 0 \:, - 5 \: ) \longrightarrow{ \: (x1 \:, y1)}}[/tex]
[tex] \sf{B(4 \:, 2) \: \longrightarrow{ \:( x2 \:, y2)}}[/tex]
[tex] \underline{ \text{Finding \: the \: slope} }: [/tex]
[tex] \boxed{ \sf{Slope = \frac{y2 - y1}{x2 - x1}}} [/tex]
[tex] \sf{➳ \: Slope = \frac{2 - ( - 5)}{4 - 0}} [/tex]
[tex] \sf{➳ \: Slope = \frac{ 2 + 5}{4} }[/tex]
[tex] \sf{➳ \: Slope = \frac{7}{4} }[/tex]
[tex] \text{Hope \: I \: helped!}[/tex]
[tex] \text{Best \: regards!}[/tex]
~[tex] \text{TheAnimeGirl}[/tex]
your job requires that you work at least 40 hours a week you have already worked 15 and there are 4 more days left in the week how many hours do you have to work each day to get at least 40 hours: inequality and solution
Answer:
6.25 hours
Step-by-step explanation:
this is rather simple really,
first, you have to work 40 hours a week
you have already worked 15 so now you can subtract that
40-15= 25hrs
if you have 4 more days of the week you divide the remaining hours by the days left
25/4= 6.25hrs
that would be the bare minimum of hours for you to work a 40 hour week.
A line passes through the point (-9,8) and has a slope of
-4/3
Write an equation in slope-intercept form for this line.
Answer:
y = -4/3x - 4
Step-by-step explanation:
Given
(x1,y1) = (-9,8)
slope, m = -4/3
Required
Determine the line equation
The equation is of the form
y - y1 = m(x - x1)
Substitute values for y1, x1 and m
y - 8 = -4/3(x - (-9))
y - 8 = -4/3(x + 9)
y - 8 = -4/3x - 12
y = -4/3x - 12 + 8
y = -4/3x - 4
Problem 7.43 A chemical plant superintendent orders a process readjustment (namely shutdown and setting change) whenever the pH of the final product falls below 6.92 or above 7.08. The sample pH is normally distributed with unknown mu and standard deviation 0.08. Determine the probability: (a) of readjusting (that is, the probability that the measurement is not in the acceptable region) when the process is operating as intended and mu
Complete Question
Problem 7.43
A chemical plant superintendent orders a process readjustment (namely shutdown and setting change) whenever the pH of the final product falls below 6.92 or above 7.08. The sample pH is normally distributed with unknown mu and standard deviation 0.08. Determine the probability:
(a)
of readjusting (that is, the probability that the measurement is not in the acceptable region) when the process is operating as intended and [tex]\mu[/tex] = 7.0 probability
(b)
of readjusting (that is, the probability that the measurement is not in the acceptable region) when the process is slightly off target, namely the mean pH is [tex]\mu[/tex] = 7.02
Answer:
a
The value is [tex]P(X < 6.92 or X > 7.08 ) = 0.26431 [/tex]
b
The value is [tex]P(X < 6.92 or X > 7.08 ) = 0.29344 [/tex]
Step-by-step explanation:
From the question we are told that
The mean is [tex]\mu = 7.0[/tex]
The standard deviation is [tex]\sigma = 0.08[/tex]
Considering question a
Generally the probability of readjusting when the process is operating as intended and mu 7.0 is mathematically represented as
[tex]P(X < 6.92 or X > 7.08 ) = P(X < 6.92 ) + P(X > 7.08)[/tex]
=> [tex]P(X < 6.92 or X > 7.08 ) = P(\frac{X - \mu }{\sigma} < \frac{6.9 - 7}{0.08} ) + P(\frac{X - \mu}{\sigma} > \frac{7.08 - 7}{0.08} )[/tex]
Generally
[tex]\frac{X - \mu }{\sigma} = Z(The \ standardized \ value \ of \ X)[/tex]
So
=> [tex]P(X < 6.92 or X > 7.08 ) = P(Z < \frac{6.9 - 7}{0.08} ) + P(Z > \frac{7.08 - 7}{0.08} )[/tex]
=> [tex]P(X < 6.92 or X > 7.08 ) = P(Z < -1.25) + P(Z > 1 )[/tex]
From the z table the probability of (Z < -1.25) and (Z > 1 ) is
[tex]P(Z < -1.25) = 0.10565[/tex]
and
[tex]P(Z > 1 ) = 0.15866[/tex]
So
=> [tex]P(X < 6.92 or X > 7.08 ) = 0.10565 + 0.15866 [/tex]
=> [tex]P(X < 6.92 or X > 7.08 ) = 0.26431 [/tex]
Considering question b
Generally the probability of readjusting when the process is operating as intended and mu 7.02 is mathematically represented as
[tex]P(X < 6.92 or X > 7.08 ) = P(X < 6.92 ) + P(X > 7.08)[/tex]
=> [tex]P(X < 6.92 or X > 7.08 ) = P(\frac{X - \mu }{\sigma} < \frac{6.9 - 7.02}{0.08} ) + P(\frac{X - \mu}{\sigma} > \frac{7.08 - 7.02}{0.08} )[/tex]
Generally
[tex]\frac{X - \mu }{\sigma} = Z(The \ standardized \ value \ of \ X)[/tex]
So
=> [tex]P(X < 6.92 or X > 7.08 ) = P(Z < \frac{6.9 - 7.02}{0.08} ) + P(Z > \frac{7.08 - 7.02}{0.08} )[/tex]
=> [tex]P(X < 6.92 or X > 7.08 ) = P(Z < -1.5) + P(Z > 0.75 )[/tex]
From the z table the probability of (Z < -1.5) and (Z > 0.75 ) is
[tex]P(Z < -1.5) = 0.066807[/tex]
and
[tex]P(Z > 0.75 ) = 0.22663[/tex]
So
=> [tex]P(X < 6.92 or X > 7.08 ) = 0.066807 + 0.22663 [/tex]
=> [tex]P(X < 6.92 or X > 7.08 ) = 0.29344 [/tex]
5 of 10
Which of the following are one-dimensional figures?
Check all that apply.
O A. Segment
B. Ray
O C. Angle
O D. Line
D E. Plane
F. Cube
Its (Ray , Segment, line, )
Segment, ray and line are one-dimensional figures.
We need to check from the given options which are one-dimensional figures.
What are one-dimensional figures?One-dimensional: Only a single measurement is possible for a one-dimensional figure. A line segment drawn on a surface is a one-dimensional object, as it has only length and no width.
Here, the segment is a one-dimensional figure.
Ray is a one-dimensional figure.
Angle is a two-dimensional figure.
A line is a one-dimensional figure.
The plane is a two-dimensional figure.
A cube is a three-dimensional figure.
Therefore, segment, ray and line are one-dimensional figures.
To learn more about one-dimensional figures visit:
https://brainly.com/question/17967616.
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