Answer:
a) 0.2981 = 29.81% probability that for 37 jets on a given runway, total taxi and takeoff time will be less than 320 minutes.
b) 0.999 = 99.9% probability that for 37 jets on a given runway, total taxi and takeoff time will be more than 275 minutes
c) 0.2971 = 29.71% probability that for 37 jets on a given runway, total taxi and takeoff time will be between 275 and 320 minutes
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
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.
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
Mean of 8.9 minutes and a standard deviation of 2.9 minutes.
This means that [tex]\mu = 8.9, \sigma = 2.9[/tex]
Sample of 37:
This means that [tex]n = 37, s = \frac{2.9}{\sqrt{37}}[/tex]
(a) What is the probability that for 37 jets on a given runway, total taxi and takeoff time will be less than 320 minutes?
320/37 = 8.64865
Sample mean below 8.64865, which is the p-value of Z when X = 8.64865. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{8.64865 - 8.9}{\frac{2.9}{\sqrt{37}}}[/tex]
[tex]Z = -0.53[/tex]
[tex]Z = -0.53[/tex] has a p-value of 0.2981
0.2981 = 29.81% probability that for 37 jets on a given runway, total taxi and takeoff time will be less than 320 minutes.
(b) What is the probability that for 37 jets on a given runway, total taxi and takeoff time will be more than 275 minutes?
275/37 = 7.4324
Sample mean above 7.4324, which is 1 subtracted by the p-value of Z when X = 7.4324. So
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{7.4324 - 8.9}{\frac{2.9}{\sqrt{37}}}[/tex]
[tex]Z = -3.08[/tex]
[tex]Z = -3.08[/tex] has a p-value of 0.001
1 - 0.001 = 0.999
0.999 = 99.9% probability that for 37 jets on a given runway, total taxi and takeoff time will be more than 275 minutes.
(c) What is the probability that for 37 jets on a given runway, total taxi and takeoff time will be between 275 and 320 minutes?
Sample mean between 7.4324 minutes and 8.64865 minutes, which is the p-value of Z when X = 8.64865 subtracted by the p-value of Z when X = 7.4324. So
0.2981 - 0.0010 = 0.2971
0.2971 = 29.71% probability that for 37 jets on a given runway, total taxi and takeoff time will be between 275 and 320 minutes
If y is inversely proportional to (tan x) and y = 2
when x = 30°, find the value of y when this value
of x is doubled.
Answer:
When something is inversely proportional it can be solved by using the equation:
y = k/x
where k is the constant.
So using this we can plug in x and y to find the value of k.
3 = k/4.
Next we isolate k and find that k = 12. Now we use this to find the value of y when x = 8. Plug in x and you get y = 12/8 or y = 3/2 or 1.5.
Another way to solve this is to look at how the value of x changes. When the value of x goes up, the value of y goes down.
In other words, when x is multiplied by some number, y is divided by that number. In this equation we can see that x is multiplied by 2 to go from 4 to 8.
Thus, y must be divided by 2.
Thus, y = 3/2 or 1.5.
Answer:
Step-by-step explanation:
y is inversely proportional to tan x means
[tex]y \ \alpha \ \frac{1}{tan x}\\\\y = k \times \frac{1}{tanx}[/tex]
Given y = 2 when x =30° . So we will find k.
[tex]y =k \times \frac{1}{tanx } \\\\2 = k \times \frac{1}{tan 30}\\\\k = 2 \times tan 30 = 2 \times \frac{1}{\sqrt{3}} = \frac{2}{\sqrt{3} }[/tex]
Now x is doubled, x = 60°, find y
[tex]y = k \times \frac{1}{tanx}\\[/tex]
[tex]= \frac{2}{\sqrt{3}} \times \frac{1}{tan 60}\\\\= \frac{2}{\sqrt{3}} \times \sqrt{3}\\\\=2[/tex]
PLEASE PLEASE HELP I will give BRAINLIEST
Anthony deposits 1,250 in a savings account with an interest rate of 6% if the Interest rate is compounded monthly than the account balance after t years is given by the expression below 1250(1+0.06/12)^12t what does (1+0.06/12t) represent
(nevermind srry, that was wrong)
Answer: represents the growth factor which reveals the monthly interest rate.
Step-by-step explanation:
Anthony's account balance can be modeled by the general compound interest formula shown below, where P is the initial amount, r is the annual interest rate, n is the number of times that the interest in the account is compounded per year, and t is the time period.
Consider the given expression.
1250(1+0.06/12)^12t
In the given expression, "1" represents 100% of the money in the account at the start of the month and "" represents the percentage of the account balance that gets added into the account at the end of each month. This is the monthly interest rate and the entire expression,(1+0.06/12t) , is the factor of growth.
Therefore, (1+0.06/12t)represents the growth factor which reveals the monthly interest rate.
Here is the function for the number of zombies, N, after t years, with the negative exponent expressed using the fraction ½:
N(t) = 300 • 0.5t/8
What is the half-life for the zombie population?
Answer:
The half-life for the zombie population is of 8 years.
Step-by-step explanation:
Exponential equation:
An exponential equation has the following format:
[tex]N(t) = N(0)(1-r)^t[/tex]
In which N(0) is the initial value and the part [tex](1-r)^t[/tex] is related to the decay.
In this question:
[tex]N(t) = 300(0.5)^{\frac{t}{8}}[/tex]
Thus N(0) = 300, that is, initial population of 300.
What is the half-life for the zombie population?
This is t for which N(t) = 0.5*300 = 150. So
[tex]N(t) = 300(0.5)^{\frac{t}{8}}[/tex]
[tex]150 = 300(0.5)^{\frac{t}{8}}[/tex]
[tex](0.5)^{\frac{t}{8}} = \frac{150}{300}[/tex]
[tex](0.5)^{\frac{t}{8}} = 0.5[/tex]
[tex](0.5)^{\frac{t}{8}} = (0.5)^1[/tex]
Equal exponents, so:
[tex]\frac{t}{8} = 1[/tex]
[tex]t = 8[/tex]
The half-life for the zombie population is of 8 years.
How
many solutions exist for the mixed-degree system graphed below?
Answer:
There is one solution
(2, 2)
Step-by-step explanation:
The solutions are where the line and curve intersect.
The isone point of intersection and therefor one solution (2, 2)
Answer:
answer is b.) one
Step-by-step explanation:
edge 2021
please help what's the exact value for x?
cos(x+pi)-sin(x-pi)=0
SHOW WORK PLEASE
Step-by-step explanation:
Recall that
[tex] \cos(x + \pi) = \cos x \cos\pi - \sin x \sin\pi[/tex]
and
[tex] \sin(x - \pi) = \sin x \cos \pi - \cos x \sin \pi[/tex]
But we also know that
[tex] \cos \pi = - 1 \\ \sin \pi = 0 \: \: \: \: [/tex]
so the above relations reduce to
[tex] \cos(x + \pi) = - \cos x \\ \sin(x - \pi) = - \sin x [/tex]
Therefore,
[tex] \cos(x + \pi) - \sin(x - \pi) = - \cos x + \sin x [/tex]
I need help
1−(−3)−5
answer is -1 you can check it on the calculator
pleaseeee mark me as the BRAINLIEST pleaseeee
Step-by-step explanation:
(-)(-)=+
1−(−3)−5
1+3-5
4-5
-1
A line passes through (-3,-2) and is perpendicular to 3x - 2y = 7.
What is the equation of the line in slope-intercept form?
Answer:
y=-2/3x
Step-by-step explanation:
Perpendicular gradients(slopes) are negative reciprocals so first rearrange the given equation to find the gradient. y=3/2x-7/2
the gradient of the new line will be m=-2/3 then use the point (-3,-2) to find the equation of the line
y=mx+b
-2=(-2/3)(-3)+b
-2=2+b
b=0
y=-2/3x
Which equation is written in factor form?
he slope distance between two points BM1 and TP1 is 600.00 ft. These two points arelocated on an inclined plane. A level is used to measure the backsight on BM1 (2.50 ft) andthe foresight on TP1 (10.20 ft). What is the horizontal length of the line to nearest 0.01 f
Answer:
the height is 599.950
Step-by-step explanation:
The computation of the horizontal length of the line is shown below:
The vertical distance is
= 10.20ft - 2.50ft
= 7.70 ft
Now use the pythagoreans theorem to determine the length of the line horizontally i.e presented below;
√horizontal distance^2 + √vertical distance^2 = Slope
√horizontal distance^2 + √7.7^2 = 600
So the height is 599.950
Can someone help me with this pls
Answer:
252
Step-by-step explanation:
To answer the equation, you first need to note that it asks for surface area.
To find surface area, you use an input formula, known as SA=2lw+2lh+2hw. 'H' stands for height, 'L' stands for length, and 'W' stands for width.
Since the current height is 12, the current length is 6, and the width is 3, you need to plug them into the equation.
SA=2(6)(3)+2(6)(12)+2(12)(3)
SA=252
Quick tip! It's tempting to just multiply them all at once, but using the power of distribution is vital to solving these equations.
How to find the equation of OB?
Answer:
Step-by-step explanation:
Since we are given the coordinates of A, and we know that another coordinate on segment OA is the origin, (0, 0), we can use that information in the slope formula to find the slope of segment OA:
[tex]m_{OA}=\frac{-3-0}{6-0}=-\frac{1}{2}[/tex]
Since segment OB is perpendicular to segment OA, then its slope is the opposite reciprocal of that of segment OA. Therefore, the slope of segment OB is 2. We will use that along with the coordinate of the origin to write the equation of OB in the slope-intercept form of a line:
y = mx + b where y = 0, x = 0, m = 2
0 = 2(0) + b so
b = 0 and the equation for the line is
y = 2x
please help!! 15 points i’m stressed out :/
Answer:
Since this (looks) like a homework assignment/test, I'll give you a hint.
Step-by-step explanation:
A function is where you have a input, that usually involves an equation that you have to replace the unknown with, to get the output.
Don't get it? Well, I didn't either.
What's great about this problem that you don't neccessarily have to know what the definition is.
A function can only output. So if you inputted the number 6, and got the output -3, you can't have another number that also had the output -3, and vice versa. This is my hint for the number 1.
Number 4 is a bit harder, but here's my hint:
Look for a pattern.
PLEASE HELP ASAP
PICTURE PROVIDED
Answer:
(x+1)(x+3)(x+5)
Step-by-step explanation:
Find the area of a triangle with a base of 18 inches and a height of 2 inches.
Answer:
The area is 36 inches
Step-by-step explanation: 18 * 2 = 36
Answer:
[tex]\boxed {\boxed {\sf 18 \ inches^2}}[/tex]
Step-by-step explanation:
The area is the amount of space inside the shape. The area of a triangle is half the product of the base and height.
[tex]a= \frac{1}{2} bh[/tex]
The base of the triangle is 18 inches and the height is 2 inches.
b= 18 in h= 2 inSubstitute the values into the formula.
[tex]a= \frac{1}{2} (18 \ in)(2 \ in)[/tex]
Multiply the numbers in parentheses.
[tex]a= \frac{1}{2}(36 \ in^2)[/tex]
Multiply by 1/2 or divide by 2.
[tex]a= 18 \ in^2[/tex]
The area of the triangle is 18 square inches.
what should be added to -13/25+21/5+-21/18 to get 5?
ATQ,
= [tex] \dfrac{ - 13}{25} + \dfrac{21}{5} + \frac{ - 21}{18} + x = 5[/tex]
Take the lcm of 25,5,18 and then manipulate it accordingly.= [tex] \dfrac{ 377}{150} + x = 5[/tex]
= [tex] x = 5 - \dfrac{ 377}{150}[/tex]
= [tex] x = \dfrac{ 373}{150}[/tex]
Answer
=727/150
Step-by-step explanation:
-13/25 + 21/18 + 21/18
= -13 + 105/25 + 21/18
= 92/25 + 21/18
= 1656 + 525/450
= 2181/450 = 727/150
Have nice day
Round 2.873 to the nearest tenth
Answer:
2.9
hope this helps
have a good day :)
Step-by-step explanation:
Find the 8th term of the geometric sequence 7, 28, 112, ...
if u can answer this that would rlly help:)
Answer:
x = 12
Step-by-step explanation:
First, we need to find the last interior angle of the triangle. Since we know the exterior angle next to it is 140° and they are supplementary, meaning they form a 180° angle, we can make an equation to solve for the last angle.
∠SRT + 140° = 180°
∠SRT = 40°
Now we know that the last interior angle is 40°. All triangles have a sum of 180°, therefore we can once again set up an equation to solve for x.
3x + 4 + 8x + 4 + 40 = 180
11x + 48 = 180
11x = 132
x = 12
Therefore, x = 12.
Find the Surface Area of this Prism
Answer:
formula - 2 (wl + hl + hw)
559,872 is the answer from how I learned it.
If i'm right, please mark me brainliest ! (๑・ω-)～♥”
Kelly is using a rectangular container to fill up a bucket of water. The container is 3.8 inches long, 2.5 inches wide, and 7.2 inches tall. If the bucket holds 1,368 cubic inches of water, how many times will Kelly have to fill the cup in order to fill the bucket
Answer:
Kelly will have to fill the cup 20 times.
Step-by-step explanation:
Volume of the cube:
Rectangular cube, so the volume of the cube is the multiplication of its three dimensions(3.8 inches, 2.5 inches and 7.2 inches).
V = 3.8*2.5*7.2 = 68.4 cubic inches.
If the bucket holds 1,368 cubic inches of water, how many times will Kelly have to fill the cup in order to fill the bucket?
Solved by proportions, using a rule of three.
1 time - 68.4 cubic inches
x times - 1368 cubic inches
Applying cross multiplication:
[tex]68.4x = 1368[/tex]
[tex]x = \frac{1368}{68.4}[/tex]
[tex]x = 20[/tex]
Kelly will have to fill the cup 20 times.
Lil' HydroPhil owns five pieces of precious apparel and wants to choose two to wear to the awards show. He defines his precious apparel as: platinum nose ring, diamond shirt, titanium boots, suede pants, and beryllium hat. Assuming the selection is random and each has an equally likely outcome, determine the probability HydroPhil chooses a combination that includes the suede pants.
Answer:
The probability HydroPhil chooses a combination that includes the suede pants is 0.40
Step-by-step explanation:
Given
Let
[tex]P \to Platin um\ no se\ ri ng[/tex]
[tex]D \to Diamond\ shirt[/tex]
[tex]T \to Titanium\ boots[/tex]
[tex]S\to Suede\ pants[/tex]
[tex]B\to Beryllium\ hat[/tex]
Required
Probability of selecting a combination that has S
First, list out all possible combinations (A) of 2
[tex]A = \{PD, PT, PS, PB, DT, DS, DB, TS, TB, SB\}[/tex]
The sample size is:
[tex]n(A) = 10[/tex]
The combinations that has S are:
[tex]S \to \{PS, DS, TS, SB\}[/tex]
The size is:
[tex]n(S) = 4[/tex]
So, the probability that he choose the combination that has S is:
[tex]Pr = \frac{n(S)}{n(A)}[/tex]
[tex]Pr = \frac{4}{10}[/tex]
[tex]Pr = 0.40[/tex]
1. Points scored by a basketball player are 12, 15, 8, 12, 15, 10, 3, 14, and 15
Calculate the:
a) mean
b) median
c) mode
d) midrange
e) Use the relative location of the mean, median, and mode calculated describe the sets as
symmetric, skewed left, or skewed right.
Answer:
mean : add all of them and divide by how much they are
mode: is what repeats it self like 15 is the most repeated.
Bonus problem. Find the ratio a :b if it is given that 3a=8b
Answer:
[tex]a:b = 8:3[/tex]
Step-by-step explanation:
To find the ration, we want to get in equation in the form [tex]\frac{a}{b} =\frac{x}{y}[/tex].
We can start by dividing by b on both sides:
3a = 8b
÷b ÷b
[tex]\frac{3a}{b} = 8[/tex]
Now, we can divide by 3 on both sides to get:
[tex]\frac{a}{b} = \frac{8}{3}[/tex]
We can change the format into a ratio:
[tex]a:b = 8:3[/tex]
HELP PLSS I DONT UNDERSTAND A THING
Answer:
1 no
angle 1 =53 degree (being vertically opposite angle)
angle 2=127 degree(being linear piar)
angle 3 =127 degree(being vertically opposite angles)
2 no
angle 1=155.1(being linear pair)
angle 2=24.9(being vertically opposite angles)
angle 3=155.1(beinf linear pair)
3 no
angle 1=68 degree(being linear pair)
angle 2=112 degree(being vertically opposite angle)
angle 3=68 degree(being vertically opposite angle)
4 no
angle 1=54.5 degree(being linear pair)
angle 2=125.5 degree(being vertically opposite angle)
angle 3=54.5 degree(being vertically oppostie angle)
Step-by-step explanation:
Plz help me well mark brainliest if correct!!....
Answer:
I'm pretty sure it is line plot
20 POINTS AND I WILL MARK YOU BRAINLIEST !!!
the london ferris wheel has a maximum height of 443 ft and a diameter of 394 ft . the wheel takes 30 mins to rotate
#1. what is the minimum height of the ferris wheel ?
94 , 85 , 49 , or 40
#2. where would the midline of the graph be ?
y=246 , y=221.5 , or y=197
#3. what is the amplitude of the graph ?
246 ft , 221.5 ft , or 197 ft
#4. what is the period of the function ?
15 , 30 , or 60 minutes
Step-by-step explanation:
#1 . the minimum height =
443 - 394 = 49 ft
#2. y = (394/2) + 49 = 197+49
=> y =246
#3. the amplitude is ½× diameter
= ½×394 = 197 ft
#4. the period of function is
the time that the wheel takes
one rotation =>30 minutes
A watering can contained 5 1/2 quarts water. After all the plants were watered, only 4 cups remained.
How many cups of water were used to water the plants?
Answer:
4 1/2 quarts.
Step-by-step explanation:
So 5 1/2 quarts to start. 4 left over.
Theres 4 cups in a quart.
So theres be 4 1/2 quarts used.. as 4 cups left would be a quart and 1 quart taken away from 5 1/2 quarts in 4 1/2.
Easton won best in show in 60% of the shows he entered. In how many show was Easton entered if he won best in show 15 times last year?
Answer:
Easton entered in 25 shows last year.
Step-by-step explanation:
Given that Easton won best in show in 60% of the shows I have entered, to determine how many show was Easton entered if he won best in show 15 times last year, the following calculation must be performed:
60 = 15
100 = X
(100 x 15) / 60 = X
1,500 / 60 = X
25 = X
Therefore, Easton entered in 25 shows last year.
brainliest and many poitns FAST
Answer:
you're answer is, 22
Answer:
Solution given;
[tex]11 \div \frac{1 }{2} = \frac{11}{ \frac{1}{2} } = 11 \times 2 = 22[/tex]
22 is a required answer:.
the cone has a radius of 6m and a height of 9cm what's the volume ?
Answer:
339.4cm³
Step-by-step explanation:
V
=
π
r
2
h
3
22/7×6²×9/3= 339.42