Answer:
Descriptive statistics
Explanation:
The population average is a descriptive statistic. It informs about how the population looks like, in this case, the population looks like having a average of 1000.
If, using her class's average where to infer the population average that is inferential statistic. But that is not the case
17. How would you find x and solve for it?
The formula for secant lines is the outside x the overall length is equal to the outside times the overall length of the second line.
A) 5*(x+5) = 6*10
SImplify:
5x +25 = 60
Subtract 25 from both sides:
5x = 35
Divide both sides by 5:
x = 35/5
x = 7
B) 3*8 = 4*(x+4)
Simplify:
24 = 4x +16
Subtract 16 from both sides:
4x = 8
Divide both sides by 4:
x = 8/4
X = 2
Statistics is defined as a body of techniques used to facilitate the collection, organization, presentation, analysis, and interpretation of information for the purpose of making better decisionsa) trueb) flase
Answer:
The given statement is true.
Step-by-step explanation:
Statistics is defined as a body of techniques used to facilitate the collection, organization, presentation, analysis, and interpretation of information for the purpose of making better decisions : TRUE statement.
Statistics helps the people to use limited sample to make accurate conclusions about a greater population. In stats we use tables, charts and graphs to present the data to draw some conclusions.
Owen went to the grocery store and purchased cans of soup and frozen dinners. Each can of soup has 500 mg of sodium and each frozen dinner has 650 mg of sodium. Owen purchased a total of 19 cans of soup and frozen dinners which collectively contain 11000 mg of sodium. Determine the number of cans of soup purchased and the number of frozen dinners purchased.
Answer: 2 with the remainder of 200
Step-by-step explanation:
first you are going to times 19 cans by 500 mg of sodium and get 9,500
then you are going to subtract 11,000 by 9,500 and get 1,500
lastly you are going to take 1,500 and divide it by 650.
in the end you will get 2 with the remainder of 200.
Answer:
Owen bought [tex]9[/tex] cans of soup and [tex]10[/tex] cans of frozen dinners.
Step-by-step explanation:
We can solve this problem by writing the linear equation system that represents the situation.
Let be ''x'' the number of cans of soup purchased and ''y'' the number of frozen dinners purchased.
By reading the question we can write the following linear equation system :
[tex]x+y=19[/tex] (I)
[tex]x.(500)+y.(650)=11000[/tex] (II)
Working with the equation (I) we find that [tex]x=19-y[/tex] (III)
If we replace (III) in (II) :
[tex](19-y).(500)+y.(650)=11000[/tex]
[tex]9500-500y+650y=11000[/tex]
[tex]150y=1500[/tex]
[tex]y=10[/tex]
We find that Owen bought [tex]10[/tex] cans of frozen dinners.
If we replace the value of ''y'' in (I) :
[tex]x+10=19[/tex]
[tex]x=9[/tex]
We find that Owen bought [tex]9[/tex] cans of soup.
Slope and y intercept
Answer:
can you elaborate
Step-by-step explanation:
I think you're talking about the slope formula so I'll tell you that y=x+b
y2-y1/x2-x1 (x1,y1) is the first coordinate and (x2,y2) is the second coordinate
Answer:
Step-by-step explanation:
1 ) the slope formula for the line passes by : A(XA,YA) B(XB,YB)
the slope is : (YB - YA)/(XB -XA)
2) y intercept for the line when : x = 0
Two vectors A and B are added together to form a vector C. The relationship between the magnitudes of the vectors is given by a2 + b2 > c2. Which one of the following statements concerning these vectors is true?
The angle between the two vectors must be an obtuse angle, i.e, greater than 90 The two vectors must point in opposite directions
The two vectors must point in opposite directions
The two vectors must be parallel.
The angle between the two vectors must be an acute angle, l-e, less than 900.
Answer:
D.The angle between the two vectors must be an acute angle which is less than 90 degrees.
Step-by-step explanation:
We are given that two vectors A and B are added together to form a vector C.
The relationship between the magnitudes of the vectors is given by [tex]a^2+b^2 >c^2[/tex]
We have to find which statement is true about given vectors.
We know that if a triangle is an obtuse triangle then
[tex]c^2 >a^2+b^2[/tex]
If a triangle is an acute triangle then
[tex]a^2+b^2 >c^2[/tex]
If a triangle is right angle triangle then
[tex]c^2=a^2+b^2[/tex]
Therefore,the angle between the two vectors must be an acute angle which is less than 90 degrees.
Option D is true.
A shrew, the mammal with the fastest metabolism, has a mass of only 0.004 kg. What is its mass in grams? A. 0.4 g B. 0.04 g C. 4 g D. 0.000004 g
Answer:
C
Step-by-step explanation:1 kilogram = 1000 grams so if you multiply 0.004 times 1000 you get 4 grams
Only have one question left. Help?
Answer:
50Step-by-step explanation:
[tex]i=\sqrt{-1}\to i^2=-1\\\\(3+\sqrt{-16})(6-\sqrt{-64})\\\\\sqrt{-16}=\sqrt{(16)(-1)}=\sqrt{16}\cdot\sqrt{-1}=4i\\\sqrt{-64}=\sqrt{(64)(-1)}=\sqrt{64}\cdot\sqrt{-1}=8i\\\\(3+4i)(6-8i)\\\\\text{use FOIL}\ (a+b)(c+d)=ab+ac+bc+bd\\\\=(3)(6)+(3)(-8i)+(4i)(6)+(4i)(-8i)\\\\=18-24i+24i-32i^2\qquad\text{cancel}\ 24i\\\\=18-32(-1)=18+32=50[/tex]
Alex has 360 yards of fencing to enclose a rectangular area. Find the dimensions of the rectangle that maximize the enclosed area. What is the maximum area?
Answer:
90 yd by 90 yd (square)8100 yd²Step-by-step explanation:
When the perimeter of the rectangle is 360 yd, the sum of the lengths of two adjacent sides is 180 yd. If x is the length of one side of the rectangle, then the adjacent side is (180-x). The area is the product of these lengths,
area = x(180 -x)
This describes a downward-opening parabola with zeros at x=0 and x=180. The vertex (maximum) of the parabola is halfway between, at x=90. The adjacent sides of the maximum-area rectangle are the same length: the rectangle is a square with sides 90 yards each.
The area is (90 yd)² = 8100 yd².
The maximum area is achieved when Alex uses the fencing to create a square. Dividing 360 yards by 4 gives each side a length of 90 yards. Thus, the maximum area that can be enclosed is 8100 square yards.
Explanation:Alex is attempting to maximize the area of a rectangular enclosure by manipulating the length and width dimensions. In this circumstance, the maximum area will be achieved when the rectangle is square. This is because for a fixed perimeter, in this case 360 yards, a square provides the largest possible area.
The rectangle will be square if all its sides are equal. Hence, to find the dimensions of the rectangle, divide the total length of the fencing by 4 (as a square has 4 equal sides), i.e., 360 yards/4 = 90 yards. Thus, the rectangle's dimensions will be 90 yards by 90 yards.
To find the maximum area, multiply the length by the width, i.e., 90 yards * 90 yards = 8100 square yards. Therefore, the maximum area that can be enclosed by the fencing is 8100 square yards.
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HELP ASAP! Algebra II Questions!!
Answer:
The answer to your question is: the last option 5a² + 3b + 6a
Step-by-step explanation:
7a² + 3b + 6a - 2a²
look for like terms
7a² - 2a² 3b 6a
Simplify like terms
5a² + 3b + 6a
To determine her power usage, Keri divides up her day into three parts: morning, afternoon, and evening. She then measures her power usage at 4 randomly selected times during each part of the day. What type of sampling did she use?
Answer:
Stratified Sampling
Step-by-step explanation:
Since Keri divides the day into different strata and each unit is selected from each strata randomly. So, it is Stratified Sampling.
Further, In Stratified Sampling population is divided into several groups such that within the group it is homogeneous and between the group it is heterogeneous. And now a selection of each stratum and unit has an equal chance of selection.
How many oranges are in a crate if the price of a crate of oranges is $1.60 and the price of oranges is $0.20 per pound and there are 3 oranges per pound?
The crate contains 24 oranges.
What is unitary method ?Unitary method is a mathematical technique for first finding the value of a single unit and then deriving the given units from it by multiplying with the single unit.
According to the given question a no. of oranges are in a crate which costs 1.60 dollars also given that per pound of orange costs 0.20 dollars.
∴ The crate contains (1.60/0.20) pounds of oranges which is
= 8 pounds of oranges.
Given 3 oranges are of 1 pound
∴ In 8 pounds of oranges pieces of oranges are (8×3) = 24 oranges.
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A health clinic uses a solution of bleach to sterilize petri dishes in which cultures are grown. The sterilization tank contains 120 gal of a solution of 4% ordinary household bleach mixed with pure distilled water. New research indicates that the concentration of bleach should be 6% for complete sterilization. How much of the solution should be drained and replaced with bleach to increase the bleach content to the recommended level?
Answer:
2.5 gal
Step-by-step explanation:
let be x = galons of solution to be drained and replace with bleach
so, we have to substract to the current solution of bleach 0.04*120, x gallons that have a concentration of 0.04 x
and also, we have to add the same gallons of bleach to the solution, that is x
and have to obtain a final concentration of 0.06*120
we can express the problem with the follow equation:
0.04*120 - 0.04*x + x = 0.06*120
solving the equation for x:
4.8+0.96*x=7.2
0.96*x=7.2-4.8
0.96*x=2.4
x =2.5 gallons
A real estate office manages an apartment complex with 50 units. When the rent is $780 per month, all 50 units are occupied. However, when the rent is $825, the average number of occupied units drops to 47. Assume that the relationship between the monthly rent p and the demand x is linear (Note:The term demand refers to thenumber of occupied units.)
(a) Write a linear equation giving the demand x in terms of the rent p. (b) Linear extrapolation - Use a graphing utility to graph the demand equation and use the trace feature to predict the
number of units occupied when the rent is raised to $855. (c) Linear interpolation - Predict the number of units occupied when the rent is lowered to $795.
Answer:
A) The linear equation is [tex]x=\frac{-1}{15}p+102[/tex]
B) When the rent is raised to $855 the number of units occupied is 45.
C) When the rent is lowered to $795 the number of units occupied is 49.
Step-by-step explanation:
A) A linear equation for the demand is written as [tex]x=mp+p_{0}[/tex], where [tex]m[/tex] is the slope, [tex]x[/tex] is the number of occupied units, [tex]p[/tex] is the rent.
[tex]m[/tex] is calculated using the problem information. When the rent is [tex]p=$780[/tex] then [tex]x=50[/tex] and when the rent is [tex]p=$825[/tex] then [tex]x=47[/tex].
Using the slope equation we have:
[tex]m=\frac{50-47}{780-825}=\frac{-3}{45}=\frac{-1}{15}[/tex]
Thus the linear equation is:
[tex]x=\frac{-1}{15}p+p_{0}[/tex]
In order to calculate [tex]p_{0}[/tex] we use the problem information, When the rent is [tex]p=$780[/tex] then number of occupied units is [tex]x=50[/tex], thus:
[tex]50=\frac{-1}{15}780+p_{0} \\\\50=-52+p_{0} \\\\p_{0}=102 \\[/tex]
Finally, the linear equation is:
[tex]x=\frac{-1}{15}p+102[/tex]
B) The demand equation is plot in the attached file, the number of units occupied when the rent is raised to $855 is 45.
C) In order to predict the number of occupied units lets use the equation:
[tex]x=\frac{-1}{15}p+102[/tex]
where [tex]p=$795[/tex], then:
[tex]x=\frac{-1}{15}795+102\\ \\x=-53+102\\\\x=49[/tex]
Thus, when the rent is lowered to $795 the number of units occupied is 49.
A checking account has the following balances:
1. Check register balance of $459.70
2. Bank statement balance of $562.43
3. Two outstanding checks of $76.40 and $29.83
4. Service charge of $3.50.
What is the true balance?
Answer:
The true balance is $562.43
Step-by-step explanation:
1. Check register balance of $459.70
2. Bank statement balance of $562.43
3. Two outstanding checks of $76.40 and $29.83
4. Service charge of $3.50.
The working is shown like -
Subtract the service charge from check register balance
[tex]459.70-3.50=456.20[/tex] dollars
Then add the outstanding checks to this
[tex]456.20+76.40+29.83=562.43[/tex] dollars
Hence, the true balance is $562.43.
Answer:
THIS ANSWER IS CORRECT!!
Step-by-step explanation:
What is the true balance?
$456.20
You have the Check registar balance which includes your outstanding checks. You minus the $3.50 fee to get the true balance.
On a coordinate plane, a circle has a center at (negative 2, 1). Which is the general form of the equation of the circle shown? x2 + y2 + 4x – 2y – 4 = 0 x2 + y2 + 4x – 2y + 2 = 0 x2 + y² – 4x + 2y – 4 = 0 x2 + y² – 4x + 2y + 2 = 0
Final answer:
The correct general form of the equation of a circle with a center at (-2, 1) is x² + y² - 4x + 2y - 4 = 0, as it aligns with the pattern of the standard circle equation upon completion of the square.
Explanation:
The general form of the equation of a circle on a coordinate plane with a center at (-2, 1) can be found using the standard equation of a circle (x - h)² + (y - k)² = r², where (h, k) is the center of the circle and r is the radius. Since we do not have the radius given, our primary goal is to expand and arrange the given options to match this standard form and check which one relocates the center to (-2, 1).
The equation that matches this pattern would be x² + y² - 4x + 2y - 4 = 0. Here's why: when you complete the square to revert it back to the standard equation, you'll add 4 to both sides to get (x - (-2))² + (y - 1)² = 4, which indicates a center at (-2, 1) when you compare with the standard equation.
Study the following distribution chart
Answer:
40 and 70
Step-by-step explanation:
The mode is the most occurring value in a data set. In this data set, the mode is 40 and 70 because
Anyone know how to solve this
Hey!
----------------------------
Solution:
5 1/5% = 0.052
325 x 0.052 = 16.9
----------------------------
Answer:
D. 16.899...
----------------------------
Hope This Helped! Good Luck!
Answer:
16,9
Step-by-step explanation:
To convert from a percentage to a decimal, move the decimal point twice to the left:
5,2% = 5⅕%
5,2% → 0,052
[tex](0,052)(325) = 16,9[/tex]
I am joyous to assist you anytime.
Bao was given $\$1,\!000$ for his birthday. He decided to invest the money in a bank account that earns $10\%$ interest, compounded annually. In dollars, how much total interest will Bao have earned 3 years later?
Bao's initial investment is $1,000, the annual interest rate is 10% or 0.10, and the interest is compounded annually. Plugging in these values into the formula, Bao will earn a total interest of $331 after 3 years.
Explanation:To calculate the total interest Bao will have earned after 3 years, we can use the formula for compound interest: [tex]A = P(1+r/n)^(nt)[/tex] where A is the final amount, P is the principal amount (initial investment), r is the annual interest rate (as a decimal), n is the number of times interest is compounded per year, and t is the number of years.
In this case, Bao's initial investment (P) is $1,000, the annual interest rate (r) is 10% or 0.10, and the interest is compounded annually (n = 1). We need to find the final amount (A) after 3 years (t = 3).
Plugging in these values into the formula:
[tex]A = 1000(1+0.10/1)^3[/tex]
= $1,331.
Therefore, Bao will earn a total interest of $331 after 3 years.
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Final answer:
Bao will have earned $331 in total interest after 3 years by investing his $1,000 at an annual compound interest rate of 10%.
Explanation:
The student's question involves calculating the amount of interest earned from a compound interest formula over a period of 3 years. To determine the total interest earned by Bao after 3 years, we need to apply the compound interest formula:
[tex]A = P (1 + r/n)^{nt}[/tex]
Where:
A is the amount of money accumulated after n years, including interest.
P is the principal amount (the original sum of money).
r is the annual interest rate (decimal).
n is the number of times that interest is compounded per year.
t is the time the money is invested for, in years.
For Bao's investment:
P = $1,000
r = 10% or 0.10
n = 1 (since interest is compounded annually)
t = 3 years
Using the formula:
[tex]A = 1000 (1 + 0.10/1)^{(1*3)} = 1000 (1.10)^3 = 1000 * 1.331 = $1,331[/tex]
The total interest earned after 3 years is:
Interest = A - P = $1,331 - $1,000 = $331
So, Bao will have earned $331 in total interest 3 years later.
Mrs. Drew wants to build a square sandbox with an area of 400 square feet. What is the total length of wood Mrs. Drew needs to make the sides of the sandbox?
Answer:
80 ft
Step-by-step explanation:
The area can be used to find the side length. The perimeter is the sum of side lengths.
A = s² . . . . . the area of a square is the square of its side length
s = √A . . . . the side length is the square root of the area
s = √(400 ft²) = 20 ft
The perimeter is the sum of the four equal-length sides of the square, so is ...
P = 4s
P = 4(20 ft) = 80 ft
Mrs. Drew needs 80 ft of wood to make the sides of the sandbox.
Final answer:
To build a square sandbox with an area of 400 square feet, each side of the sandbox is 20 feet long, and Mrs. Drew will need a total of 80 feet of wood to construct the sides.
Explanation:
Finding the Total Length of Wood for a Sandbox
The question asks us to determine the total length of wood necessary to build a square sandbox with an area of 400 square feet. To find the length of one side of the sandbox, we take the square root of the area. The square root of 400 square feet is 20 feet, which means each side of the sandbox is 20 feet long. Since the sandbox is square, it has four equal sides.
The total length of wood Mrs. Drew needs for the sandbox is the sum of the lengths of all four sides:
20 feet + 20 feet + 20 feet + 20 feet = 80 feet.
Therefore, Mrs. Drew will require 80 feet of wood to construct the sides of the sandbox.
It's helpful to remember when working with square areas that the perimeter (or total length around the square) is always four times a single side. This is a key concept in geometry and is useful in practical applications such as planning the construction of a sandbox.
True or false?
An even function is one in which f(x) = f(-x) for all x's and odd function is one where g(x) = -g(-x) for all x's.
Answer:
True
Step-by-step explanation:
f is odd if the graph of f is symmetric with respect to the origin.
f is even if and only if f(-x) = f(x) for all x in the domain of f.
I hope this helps you out alot, and as always, I am joyous to assist anyone at any time.
Write a complete two-column proof for the following information.
Given: AB = 3y - 1, BC = 7y, AC = 29
Prove: AB = 8
Answer:
The answer to your question is below
Step-by-step explanation:
Data
AB = 3y - 1
BC = 7y
AC = 29
Prove AB = 8
AB + BC = AC
3y - 1 + 7y = 29
10y -1 = 29
10y = 29 + 1
10y = 30
y = 30/10
y = 3
AB = 3y - 1
= 3(3) - 1
= 9 - 1
= 8
You are a bus driver and are scheduled to depart from Terminal A at 9:18 a.M. And arrive at Terminal B at 10:03 a.M. You arrive at a stop on your route at 9:58 a.M., and you have 5 more stops remaining, including your arrival at Terminal B. Average travel time between stops is 2 minutes, and loading and unloading takes an average of 1 minute. How many minutes past your scheduled arrival time should you expect to arrive at Terminal B?
You should expect to arrive at Terminal B approximately 17 minutes past the scheduled arrival time, factoring in remaining stops and travel times.
Let's calculate the expected delay in arrival at Terminal B.
Given:
- Scheduled departure from Terminal A: 9:18 a.m.
- Scheduled arrival at Terminal B: 10:03 a.m.
- Arrival at a stop on the route at 9:58 a.m.
- 5 more stops remaining, including the arrival at Terminal B.
- Average travel time between stops: 2 minutes
- Loading and unloading time: 1 minute
1. Total travel time from the current stop to Terminal B:
[tex]\[ 10:03 \text{ a.m.} - 9:58 \text{ a.m.} = 5 \text{ minutes} \][/tex]
2. Remaining stops:
[tex]\[ 5 \text{ stops} \times (2 \text{ minutes travel time} + 1 \text{ minute loading/unloading}) = 5 \text{ stops} \times 3 \text{ minutes per stop} = 15 \text{ minutes} \][/tex]
3. Total time from the current stop to Terminal B, including remaining stops:
[tex]\[ 5 \text{ minutes (travel time to Terminal B)} + 15 \text{ minutes (remaining stops)} = 20 \text{ minutes} \][/tex]
4. Determine how many minutes past the scheduled arrival time at Terminal B this would be:
[tex]\[ 20 \text{ minutes} - (10:03 \text{ a.m.} - 10:00 \text{ a.m.}) = 20 \text{ minutes} - 3 \text{ minutes} = 17 \text{ minutes} \][/tex]
Therefore, you should expect to arrive at Terminal B 17 minutes past the scheduled arrival time.
If the correct answer is indeed 10 minutes, then there might be a misunderstanding or a mistake in the problem statement.
You can expect to arrive at Terminal B approximately 10 minutes past your scheduled arrival time. This is calculated based on the average travel time and loading/unloading time for the remaining stops.
To determine how many minutes past your scheduled arrival time you should expect to arrive at Terminal B, let's break down the time required for the remaining stops.
You arrive at a stop on your route at 9:58 AM. You have 5 more stops remaining, including Terminal B.Average travel time between stops is 2 minutes, and loading and unloading takes 1 minute. Therefore, each stop takes 3 minutes on average (2 minutes travel + 1 minute loading/unloading).For 5 stops, the total time required will be 3 minutes per stop × 5 stops = 15 minutes.If you start this 15-minute period at 9:58 AM, the calculation is: 9:58 AM + 15 minutes = 10:13 AM.Your scheduled arrival at Terminal B is 10:03 AM.The delay is then 10:13 AM minus 10:03 AM, which results in a 10-minute delay.Therefore, you should expect to arrive at Terminal B approximately 10 minutes past your scheduled arrival time.
At a hotdog stand they serve regular and foot-long hotdogs are the ratio of 3 to 2 based on this ratio how many foot-long hotdogs will be served if there are a total of 80 hotdogs served
To calculate the number of foot-long hot dogs served, divide the total number of hot dogs by the total parts of the ratio (80/5 = 16) and then multiply by the number of parts for foot-long hot dogs (2 * 16 = 32 foot-long hot dogs served).
If the ratio of regular hot dogs to foot-long hot dogs at a hot dog stand is 3 to 2, and there are a total of 80 hot dogs served, we can calculate the number of foot-long hot dogs served using proportional reasoning.
To find out how many foot-long hot dogs are served, first add up the parts of the ratio: 3 parts regular hot dogs + 2 parts foot-long hot dogs = 5 parts total. Since there are 80 hot dogs served in total, we divide this number by the total number of parts to find the value of one part.
80 hot dogs \/ 5 parts = 16 hot dogs per part.
Now, multiply the value of one part by the number of parts for foot-long hot dogs to get the total number of foot-long hot dogs served:
2 parts foot-long hot dogs x 16 hot dogs per part = 32 foot-long hot dogs.
A survey was given to 259 people asking where the people like dogs and or cats 186 people said they like dogs 105 people say they like cats 58 said they don't like dogs or cats how many said they like both
Answer:
90
Step-by-step explanation:
There are several ways you can go at this, but the basic idea is that "likes dogs" includes "likes both", as does "likes cats."
That means ...
(likes dogs) + (likes cats) + (likes neither)
= (likes dogs only + likes both) + (likes cats only + likes both) + (likes neither)
= [likes dogs only +likes cats only +likes both +likes neither] + (likes both)
= [total] + (likes both)
In numbers, ...
186 + 105 + 58 = 259 + (likes both)
90 = likes both . . . . . . subtract 259
The distance from Los Angeles to Mumbai is 14,000 km. Flights take 22
hours, whilst the return flight from Mumbai to Los Angeles takes only 17
hours because of the direction of the prevailing wind. Assuming the
airplane would fly the same speed in both directions in still air, what is
the average wind velocity?
Answer:
about 93.6 km/h
Step-by-step explanation:
The speed westbound is ...
14000 km/(22 h) ≈ 636.364 km/h
The speed eastbound is ...
14000 km/(17 h) ≈ 823.529 km/h
The difference in speeds is twice the wind speed, so the wind speed is ...
(823.529 -636.364)/2 km/h ≈ 93.6 km/h
To find the wind velocity, first calculate the plane's average speed in still air by averaging its speeds in opposite directions. Then subtract the plane's speed against the wind from its speed in still air. The result is the wind velocity, which in this case is 93.59 km/h.
Explanation:To calculate the wind velocity, we will first need to find out the airplane's speed in still air. This can be calculated by getting the average of the two speeds in opposite directions. You see, when a plane flies from Los Angeles to Mumbai, it takes 22 hours, while the return flight from Mumbai to Los Angeles takes only 17 hours because of wind assistance. Here's how to work it out:
First, calculate the plane’s speed for both directions: For the LA to Mumbai direction it’s 14,000 km / 22 hours = 636.36 km/h, and for the Mumbai to LA direction it’s 14,000 km / 17 hours = 823.53 km/h.Now, get the average speed of the plane in still air. It would be the sum of these two speeds divided by two: (636.36 km/h + 823.53 km/h) / 2 = 729.95 km/h. This is the plane’s speed in an environment without wind.To find the wind velocity, subtract the plane's speed against the wind (LA to Mumbai direction) from the speed in still air. This gives us: 729.95 km/h - 636.36 km/h = 93.59 km/h. Therefore, the average wind velocity is 93.59 km/h.Learn more about Wind Velocity here:https://brainly.com/question/34068902
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Latanya leaves her house at 12:30 p.M. And bikes at 12 mi/h to Marta's house. She stays at Marta's house for 90 minute. Both girls walk back to latanya's house at 2.5 mi/h. They arrive at latanya's house at 3:30 p.M. How far is Marta's house from latanya's house?
Answer:
Marta's house is 3.10 miles from Latanya's house
Step-by-step explanation:
Marta's house is at 3.1 miles fron Latanya's house.
How far is Marta's house from latanya's house?From 12:30pM to 3:30pM there are a total of 3 hours, remember that.
Let's say that the distance between the two houses is D, then we can write the equations:
12mi/h*t₁ = D
2.5mi/h*t₂ = D
These are equations of the form:
speed*time = distance
Where t₁ is the time that Latanya takes to arrive to Marta's house, and t₂ is the time that they take to arrive to Latanya's house.
We know that the total time of this is 3 hours, and they spent 90 minutes = 1.5 hours in Marta's house, then:
t₁ + t₂ + 1.5 = 3
t₁ + t₂ = 3 - 1.5 = 1.5
Now we have a system of equations:
12*t₁ = D
2.5*t₂ = D
t₁ + t₂ = = 1.5
We can write:
D/12 = t₁
D/2.5 = t₂
And replace that in the last equation:
D/12 + D/2.5 = 1.5
2.5*D + 12D = 1.5*2.5*12
14.5D = 45
D = 45/14.5
D = 3.10 miles
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Ms. Bergen is a loan officer at Coast Bank and Trust. From her years of experience, she estimates that the probability is .025 that an applicant will not be able to repay his or her installment loan. Last month she made 40 loans. Use the poisson approximation to the binomial.
a. What is the probability that three loans will be defaulted?
b. What is the probability that at least 3 loans will be defaulted?
Answer:
a) 0.0613 b)0.0803
Step-by-step explanation:
Ms. Bergen estimates that the probability is 0.025 that an applicant will not be able to repay his or her installment loan.
p = 0.025
Let's consider that an applicant is not be able to repay his or her installment loan as a ''success''
p (success) = 0.025
Last month she made 40 loans ⇒ n = 40
For the poisson approximation to the binomial we need to calculate n.p that will be the λ parameter in our poisson approximation
[tex]n.p=40.(0.025)=1[/tex]
λ=n.p=1
Let's rename λ = j
In our poisson approximation :
[tex]f(k,j)=\frac{e^{-j} .j^{k} }{k!}[/tex]
f(k,j) is the probability function for our poisson variable where we calculated j,e is the euler number and k is the number of success :
[tex]f(k,1)=\frac{e^{-1} .1^{k} }{k!}[/tex]
For a) We are looking the probability of 3 success :
[tex]f(3,1)=\frac{e^{-1} .1^{3} }{3!}=0.0613[/tex]
For b) We are looking for the probability of at least 3 success
If ''L'' is the number of success
[tex]P(L\geq 3)=1-P(L\leq 2)[/tex]
[tex]P(L\leq 2)=P(L=0)+P(L=1)+P(L=2)[/tex]
[tex]P(L\leq 2)=f(0,1)+f(1,1)+f(2,1)[/tex]
[tex]P(L\leq 2)=e^{-1} +e^{-1}+\frac{e^{-1}}{2} =e^{-1}(1+1+\frac{1}{2} )[/tex]
[tex]P(L\geq 3)=1-P(L\leq 2)=1-e^{-1}(1+1+\frac{1}{2} )=0.0803[/tex]
The probability that three loans will default is 0.0613
The probability that at least 3 loans will default is 0.0803
Calculations and Parameters:Ms. Bergen estimates that the probability is 0.025 that an applicant will not be able to repay his or her installment loan.
p = 0.025
Hence, we consider that an applicant is not able to repay his or her installment loan as a ''success''
p (success) = 0.025
Last month she made 40 loans ⇒
n = 40
For the Poisson approximation to the binomial, we need to calculate n.p which will be the λ parameter in our Poisson approximation
n.p= 40.(0.025) =1
λ=n.p=1
Let's rename λ = j
In our Poisson approximation :
f(k,1) = e^-j.j^k/k!
Hence, the probability of 3 success is:
f(3,1)= e^-1.1^3/3!
=0.0613.
The probability of at least 3 successes is:
If ''L'' is the number of successes.
P(L≥ 3) = 1- P(L≤ 2)
P(L≥ 3)= 0.0803.
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To make a greeting card, Bryce used 1/8 sheet of red paper, 3/8 sheet of green paper, and 7/8 sheet of white paper. How many sheets of paper did Bryce use?
A researcher conducts a repeated-measures study to evaluate a treatment with a sample of n = 16 participants and obtains a t statistic of t = 1.94. The treatment is expected to increase scores and the sample mean shows an increase. What is the correct decision for a hypothesis test using α = .05?
Given : Sample size : n= 16
Degree of freedom = n-1=15
The obtained t-statistic value = 1.94
Since, The treatment is expected to increase scores and the sample mean shows an increase.
Let [tex]\mu_0[/tex] be the population mean before and [tex]\mu[/tex] denotes the population mean after the treatment.
then the related hypothesis will be :-
[tex]\text{Null hypothesis }H_0:\mu_0=\mu\\\\\text{Alternative hypothesis } H_1:\mu_0<\mu[/tex]
Since the alternative hypothesis is left-tailed, so the test is a left tailed test.
The critical value for [tex]\alpha=0.05[/tex]=1.753
Since, the obtained value (1.94) is greater than the critical value (1.753) so we reject the null hypothesis .
Therefore, we have enough evidence to support the alternative hypothesis.
Hence, we conclude that treatment may successful to increase scores and the sample mean shows an increase.
A gecko is in a room that is 12 feet long, 10 feet wide and 8 feet tall. The gecko is currently on a side wall ($10^{\prime}$ by $8^{\prime}$), one foot from the ceiling and one foot from the back wall ($12^{\prime}$ by $8^{\prime}$). The gecko spots a fly on the opposite side wall, one foot from the floor and one foot from the front wall. What is the length of the shortest path the gecko can take to reach the fly assuming that it does not jump and can only walk across the ceiling and the walls?
The shortest path the gecko can take is 20 feet long, consisting of 8 feet along the ceiling and 12 feet along the opposite side wall.
Explanation:Distances:
Gecko to ceiling edge: 1 foot
Ceiling edge to opposite wall edge: 10 feet (room width)
Opposite wall edge to fly: 1 foot
Path calculation:
Ceiling path: 1 foot (to edge) + 8 feet (along edge) = 9 feet
Side wall path: 1 foot (to edge) + 11 feet (remaining wall) = 12 feet
Shortest path:
Add ceiling and wall paths: 9 feet + 12 feet = 20 feet
Therefore, the shortest path for the gecko is 20 feet long.