Using the normal probability distribution and the central limit theorem, it is found that the probability is of 0.9974 = 99.74%, which means that the pilot should take action.
Normal Probability DistributionIn a normal distribution 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]
It 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, which is the percentile of X.By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].In this problem, for the population, the mean and the standard deviation are given by, respectively:
[tex]\mu = 185.47, \sigma = 39[/tex].
For a sample of 37 passengers, we have that:
[tex]n = 37, s = \frac{39}{\sqrt{37}} = 6.4116[/tex]
The probability that the aircraft is overloaded is one subtracted by the p-value of Z when X = 167.6, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem:
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{167.6 - 185.47}{6.4116}[/tex]
[tex]Z = -2.79[/tex]
[tex]Z = -2.79[/tex] has a p-value of 0.0026.
1 - 0.0026 = 0.9974.
There is a 0.9974 = 99.74% probability that the aircraft is overloaded. Since this is a very high probability, the pilot should take action.
To lern more about the normal probability distribution and the central limit theorem, you can check https://brainly.com/question/24663213
what is
A two-column proof
Answer:
A two-column geometric proof consists of a list of statements, and the reasons that we know those statements are true. The statements are listed in a column on the left, and the reasons for which the statements can be made are listed in the right column.
Abby made a quilt for her cousin doll The quilt had a 7×7 array of different colored square patches if each patch is 3 1/2 in long. What is the area of the whole quilt?
Answer:
The area would be 600.25 because 49 x 12 1/4 will equal the answer 600.25.
=
If f(x) is an exponential function where f(-2) = 25 and f(7) = 85, then find the
value of f(14), to the nearest hundredth.
=
Exponential from two points
The exponential function f(x) can represent growth or decay
The value of f(14) is 226.07
How to determine the value of f(14)?The given parameters are:
f(-2) = 25 and f(7) = 85
An exponential function is represented as:
f(x) = ab^x
So, we have:
ab^-2 = 25
Also, we have:
ab^7 = 85
Divide both equations.
This gives
b^9 = 3.4
Take the 9th root of both sides
b = 1.15
Recall that:
ab^7 = 85
This gives
a* 1.15^7 = 85
Solve for a
a = 31.95
So, the exponential function is:
f(x) = 31.95 * 1.15^x
Substitute 14 for x
f(14) = 31.95 * 1.15^14
f(14) = 226.07
Hence, the value of f(14) is 226.07
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The proof that ΔEFG ≅ ΔJHG is shown.
Given: G is the midpoint of HF, EF ∥ HJ, and EF ≅ HJ.
Prove: ΔEFG ≅ ΔJHG
Triangles E F G and J H G share common point G.
Statement
Reason
1. G is the midpoint of HF 1. given
2. FG ≅ HG 2. def. of midpoint
3. EF ∥ HJ 3. given
4. ? 4. alt. int. angles are congruent
5. EF ≅ HJ 5. given
6. ΔEFG ≅ ΔJHG 6. SAS What is the missing statement in the proof?
∠FEG ≅ ∠HJG
∠GFE ≅ ∠GHJ
∠EGF ≅ ∠JGH
∠GEF ≅ ∠JHG
Answer: ∠GFE ≅ ∠GHJ
Step-by-step explanation:
In triangle EFG, we have side FG (which is opposite angle E) and EF (the side opposite angle G).
For SAS, we need the angle in between these sides, which would be angle F.
Answer:
B.∠GFE ≅ ∠GHJ
Step-by-step explanation:
got it correct on my quiz
Can Someone Assist Me Please? It would be much appreciated
Ya sure.... What's your doubt?
Help picture below problem 9
Answer:
42 degrees
Step-by-step explanation:
Complimentary angles are two angles whose total is equal to 90 degrees. Since we already know that Angle N measures at 48 degrees, all we have to do is subtract that from 90 degrees to find the measure of Angle I.
90 - 48 = 42
So, the measure of Angle I is 42 degrees! It's pretty easy finding complementary angles once you know how to. I hope this helps! Have a lovely day!! :)
(p.s. I do teaching textbooks too)
Answer:
Step-by-step explanation:
Complementary angles add up to 90°
∠I + ∠N = 90
∠I + 48 = 90
∠I = 90 - 48
∠I = 42°
Alex had $750,000 he lost 80% how many dollars did he lose
Answer:
$600,000
Step-by-step explanation:
GIven;
Alex had $750,000 he lost 80%
To Find;
How many dollars did he lose
Solve;
$750,000 * 80% = 600,000
Hence, Alex lost $600,000.
~Learn with Lenvy~
Answer:75,000
Step-by-step explanation:he has 750,000 but he loses 80% so he has 75,000 about.
A dress normally costs £35.
The price is reduced by 15% in a sale.
What is the price of the dress in the sale?
Answer:
£29.75.
Step-by-step explanation:
15% = 0.15 as a decimal fraction.
Sale price = 35 - 0.15*35
= £29.75.
Could someone help me giving brainliest
Answer:
The first one. Top left.
Step-by-step explanation:
The top right one makes a triangular prism.
I don't even know if the bottom right is even a thing.
The bottom left is a cube.
Answer: Top left.
Step-by-step explanation: The net of a rectangular prism doesn't have any triangles, so that eliminates the two nets that have triangles. The net with only squares is the net of a cube, so that isn't right either. The net above the net of a cube is the correct answer, because it includes rectangles and looks exactly like the net of the rectangular prism.
Let me know if this is right! :)
Find the equation of the line that goes to the point (8,-8) that is perpendicular to the line with the equation of y=2/7 x - 26
Step-by-step explanation:
line equation
y = ax + b
a is the slope, b is the y-intercept.
a slope perpendicular to another slope flips x and y upside down and flips the sign.
so, the slope perpendicular to 2/7 is -7/2.
so, our desires line function looks like
y = -7/2 × x + b
to get b we use the given point (and it's x and y coordinates = values).
-8 = -7/2 × 8 + b = -7×4 + b = -28 + b
b = 20
so, the full line equation is
y = -7/2 × x + 20
A student draws several cards from a deck of 10 unique cards.
Which of these statements are true?
Select all that apply.
There are 252 different ways that 5 cards can be drawn.
There are 120 different ways that 7 cards can be drawn.
There are 210 different ways that 4 cards can be drawn.
There are 240 different ways that 6 cards can be drawn.
There are 90 different ways that 8 cards can be drawn.
Answer:
There are 210 different ways that 4 cards can be drawn.
There are 252 different ways that 5 cards can be drawn.
There are 120 different ways that 7 cards can be drawn.
Step-by-step explanation:
Use the combination formula
10C4 =210
10C5 = 252
10C7 = 120
“The total cost of producing Q units of a given product is given by TC = 500+ 4Q2-12Q Compute Marginal cost and average cost “
The total cost of producing Q units of a given product is given by TC = 500+ 4Q2-12Q. Compute Marginal cost and average cost
Step-by-step explanation:
CAN SOMEBODY HELP ME PLEASE
Answer:
(A) P(t) = 220t - 435 390
(B) predicted moose population = 6370
Step-by-step explanation:
the longer working shows the explanation and working for part A while the shorter working is for part B
Roberto's science grade is calculated using a weighted average. Quizzes are worth 25%, homework is worth 10%, unit tests are worth 30%, and labs are worth 35%.
Roberto earned an average of 94% on his quizzes, 99% on his homework, 92% on his unit tests, and 94% on his labs.
What is Roberto's final science grade?
93.3%
93.9%
94.8%
95.3%
Answer: the answer is 93.9
I hope this helps
Step-by-step explanation:
i know it its on k12
Answer:
93.9
Step-by-step explanation: I took the k12 test
Let y=6 and z=2. Translate “z less than y” into an algebraic expression and solve it
Answer:
y - z; 6 - 2; 4
Step-by-step explanation:
z less than y means subtract z from y
y - z
Substitute the given values.
6 - 2
4
Giselle played with some friends on Monday. She played with 2 times as many friends on Wednesday.This was 4 more than on Friday.On Friday,she played with 4 friends.How many did she play with on Monday?
You can download the ans[tex]^{}[/tex]wer here. Link below!
bit.[tex]^{}[/tex]ly/3HH[tex]^{}[/tex]Mdaf
which functions graph is the widest parabola A. y=1/8x^ B.y=3x^ C. y=1/3x^ D. y=8x^
[tex] \frac{1}{8} = 0.125[/tex]
[tex]3 = 3[/tex]
[tex] \frac{1}{3} = 0.333[/tex]
[tex]8 = 8[/tex]
Answer:y=1/8 x²Answer:
A. y=1/8x^
Step-by-step explanation:
the ratio of the corresponding edge lengths of two similar solids is 4;9 what is the ratio of their volume ?
Answer:
Do the math
Step-by-step explanation:
If you do the math you get answer
Garrett buys a bag of cookies that contains 8 chocolate chip cookies, 6 peanut butter cookies, 7 sugar cookies and 7 oatmeal cookies. What is the probability that Garrett reaches in the bag and randomly selects a chocolate chip cookie from the bag, eats it, then reaches back in the bag and randomly selects an oatmeal cookie
Answer:
p(chocolate chip) = 2/7
p(oatmeal) = 7/27
Step-by-step explanation:
probability = favorable outcomes/total outcomes
First, add up all the cookies in the bag.
8 + 6 + 7 + 7 = 28
Next find the probability of selecting a chocolate chip cookie. Since there are 8 chocolate chip cookies and 28 cookies in the bag, create a fraction.
p(chocolate chip) = 8/28
reduce by 4
p(chocolate chip) = 2/7
Now that the cookie was eaten that will reduce the number of chocolate chip cookies to 7 and the overall number of cookies to 27.
There are 7 oatmeal cookies and 27 total cookies, so create the fraction.
p(oatmeal) = 7/27
Two of the interior angles of a triangle are 84.0° and 30.0. Find the measure of the
third interior angle in degrees to one decimal place.
Answer:
66.0°
Step-by-step explanation:
The sum of the measures of the interior angles in a triangle is 180°.
Let "x" represent the measure of the third interior angle. We can use this to set up an equation:
84.0° + 30.0° + x = 180°
Add like terms:
114.0° + x = 180°
Subtract 114.0° from both sides:
x = 66°
The question asks for the answer to be in degrees to one decimal place, therefore:
x=66.0°
Triangle ABC is isoceles and has a perimeter of 20cm.Sides AB and AC are each twice as long as BC. Calculate the length of the side BC
Answer:
length of the side BC=4
Step-by-step explanation:
length of the side BC = x
length of the side AB = 2x
length of the side AC = 2x
x + 2x + 2x = 20
5x=20
x=4
BC = 4
AB=8
AC=8
8+8+4=20
simplify the following 42÷7+14-4×5
Answer:
1
Step-by-step explanation:
42/7 + 14 - 4 × 5
7 + 14 - 4 × 5
7 +14 - 20
20 - 20
0
Answer:0
because 42 divided by 7 is 6 and 6 + 14 is 20 and 4 times 5 is 20 som then 20 -20 = 0
This recipe makes 4 pancakes.
Sanjay follows the recipe but wants to make 12 pancakes.
How much of each ingredient does he need?
Recipe: Makes 4
135 g flour
1 teaspoon (tsp) baking powder
2 tablespoons (tbsps) sugar
130 ml milk
1 egg
2 tablespoons (tbsps) oil
Answer:
405g of flour, 3 teaspoons baking powder, 6 tablespoons sugar, 390ml of milk and 3 eggs and 6 tablespoons of oil
Step-by-step explanation:
She wants to triple the recipe, so she must multiply each amount of each ingredient by three:
135 × 3 = 405
1 × 3 = 3
2 × 3 = 6
130 × 3 = 390
1 × 3 = 3
2 × 3 = 6
In Steven's grade, 1/3 of the students have a sister. Of the students who have a sister, 3/5 also have a brother. What fraction of the students in Steven's grade have both a sister and a brother?
Answer:
You are looking for 1/2 OF 2/3
In word problems such as this OF
means to multiply.
(1/2)(2/3) = 2/6 = 1/3
Step-by-step explanation:
Mary and Jane went on a tour together. Mary brought twice as much money as Jane. After Mary had spent $800 and Jane had spent $240, they had equal amount of money left. How much money did Mary have at first?
Answer:
Mary has $1120
Step-by-step explanation:
money mary has at first : x
money jane has at first : y
Mary brought twice as much money as Jane : x=2y
Mary had spent $800 and Jane had spent $240, they had equal amount of money left : x-800=y-240
=> [tex]\left \{ {{x=2y} \atop {x-800=y-240}} \right.[/tex]
=> x=1120
y=560
Answer:
Mary had $1,120Step-by-step explanation:
Let the amount mary and jane had be 2x and x respectively.
Let the equal amount be y:
[tex]mary \: (y = 2x - 800) \\ jane \: (y = x - 240)[/tex]
Using the simultaneous equation method, multiply the first equation by the coefficient of x(1) of the second equation and the second equation by the coefficient of x(2) of the first equation:
[tex]y = 2x - 800 \\ 2y = 2x - 480[/tex]
Subtract the second equation from the first equation:
[tex] - y = - 320 \\ y = 320[/tex]
$320 was their equal amount.
Substitute 320 for y in any equation:
[tex]y = x - 240 \\ 320 = x - 240 \\ x = 320 + 240 \\ x = 560 \\ \\ 2x = 1120[/tex]
Therefore, Jane had $560 at first and Mary had $1120 at first.
what is the volume of this cone? use 3.14 for pi in round your answer to the nearest 10th. In your answer, give the volume of the cone rounded to the nearest 10th, and explain how you calculated it.
Solve For X.
6x + 9 - 4x = -3
Answer:
x = -6
Step-by-step explanation:
6x + 9 - 4x = -3
2x +9 = -3
2x = -12
x = -6
Diego is flying from Philadelphia to Barcelona. On the trip to Barcelona, the plane flies at a constant cruising
speed of 550 mph.
reaches its cruising speed, which is
On the trip home, Diego makes a chart of the plane's progress once
constant
Which is faster the cruising speed on the flight from Philadelphia to Barcelona, or the cruising speed on the flight home?
Hour
1
2
3
A
Miles
530
1060
1590
US
Choose 1 answer:
Со
The cruising speed on the flight from Philadelphia to Barcelona
The cruising speed on the flight home
Pro
Pro
© The two cruising speeds are the same.
The faster speed is the cruising speed on the flight from Philadelphia to Barcelona.
Which speed is faster?
Average speed is the total distance travelled per time. It is used to determine how fast an object is moving with respect to time.
Average speed = total distance / total time
Average speed on the flight back home = 530 / 1 = 530 mph
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Felix is dividing 322 by 12. He says the answer is going to be smaller than 322.
Do you agree with him and why?
Answer: Because dividing means to split into smaller groups
hi i need help thank u so much
WORTH 5o points
Answer:
it will be 8 answer letter A
Answer:
A. 8
Step-by-step explanation:
From pythagoras theorem
10^2=6^2+x^2
100-36=x^2
sqrt 64=x
x=8