Answer:
A university wants to estimate the average distance that commuter students travel to get to class with an error of ±3 miles and 90 percent confidence. What sample size would be needed, assuming that travel distances are normally distributed with a range of X = 0 to X = 50 miles, using the Empirical Rule μ ± 3σ to estimate σ.
The required sample size, n=(zσ/E)² = 21.0
Step-by-step explanation:
The estimated σ here = (range)/6 = (50/6) = 8.33
In the case of 90 % , CI value of z = 1.64
standard deviation, σ= 8.33
margin of error E = 3
The required sample size, n=(zσ/E)² = 21.0
Answer:
n = 21
Step-by-step explanation:
Solution:-
- Let denote a random variable "X" : average distance that commuter students travel to get to class.
- The population is given to be normally distributed, such that:
Range X: [ 0 , 50 ] miles
- We will use the given range coupled with the empirical rule for normal distribution to determine the mean (u) and standard deviation of population (σ):
P ( μ - 3σ < X < μ + 3σ) = 0.997 ..... (Empirical Rule)
- According to the standardized results for Z-table:
P ( -3 < Z < 3 ) = 0.997
So, P ( Z ≤ 3 ) = 1 - (1 - 0.997) / 2 = 0.9985
P ( Z ≥ -3 ) = 1 - (1 - 0.997) / 2 = 0.9985
- The standardized values for the given data can now be determined:
P ( X ≥ μ - 3σ ) = P ( Z ≥ -3 ) = 0.9985
X ≥ μ - 3σ = Upper limit - 0.9985*( Range )
X ≥ μ - 3σ = 50 - 0.9985*( 50 )
μ - 3σ = 0.075 ..... Eq1
P ( X ≤ μ + 3σ ) = P ( Z ≤ 3 ) = 0.9985
X ≤ μ + 3σ = Lower limit + 0.9985*( Range )
X ≤ μ + 3σ = 0 + 0.9985*( 50 )
μ + 3σ = 49.925 ..... Eq2
- Solve the Eq1 and Eq2 simultaneously:
2μ = 50 , μ = 25 miles
3σ = 24.925
σ = 8.30833
- Hence, the normal distribution parameters are:
X ~ N ( μ , σ^2 )
X ~ N ( 25 , 8.308^2 )
- The standard error in estimation of average distance that commuter students travel to get to class is E = ±3 miles for the confidence level of 90%.
- The Z-critical value for confidence level of 90%, Z-critical = 1.645
- The standard error estimation statistics is given by the following relation with "n" sample size.
E = Z-critical*σ /√n
n = [ Z-critical*σ /E ]^2
- Plug in the values:
n = [ 1.645*8.308/3]^2
n = 20.75306 ≈ 21
Answer: The sample size needed to estimate average distance that commuter students travel to get to class with error of ±3 miles and 90 percent confidence, is n = 21.
To save for a car when he turns 18, Pascale deposited $500 each year into a savings account with a 7.5% interest rate compounded annually. Year Beginning Balance Interest Earned Ending Balance 1 $500.00 $37.50 $537.50 2 $1,037.50 $77.81 $1,115.31 3 $1,615.31 $121.15 $1,736.46 4 $2,236.46 $167.73 $2,404.19 5 Using the formula A = P (1 + r) Superscript t, what is the value of the account at the end of the fifth year? $3,071.92 $3,122.00 $3,851.77 $4,140.65
The value of Pascale's savings account at the end of the fifth year, with a 7.5% interest rate compounded annually and an additional $500 deposited each year, is approximately $3,122.00.
Explanation:To calculate the value of Pascale's account at the end of the fifth year, we must use the compound interest formula which is A = P (1 + r)^t, where:
A is the amount of money accumulated after n years, including interest.P is the principal amount (the initial amount of money).r is the annual interest rate (decimal).t is the time the money is invested for in years.However, since Pascale deposits an additional $500 at the beginning of each year, the calculation is more complex than a single application of the formula. Our calculation should reflect the compound interest earned on each individual $500 deposit, not just the initial deposit.
Let's calculate the value at the end of year 5 step by step, adding $500 at the beginning of each year:
The balance at the beginning of year 5 is $2,404.19.Pascale deposits an additional $500 at the start of year 5, making the new starting balance $2,904.19.Now apply the compound interest formula for year 5: A = $2,904.19 * (1 + 0.075)^1 (since interest is compounded annually).This equals: A = $2,904.19 * 1.075 = $3,122.00 (approximately).Therefore, the value of the account at the end of the fifth year is approximately $3,122.00.
A rectangle has an area of 0.24 square meter what is one possibility for the length and width of the rectangle?
S=wl
0.24=wl
it can be w=0,6 and l=0,4 or w=0,4 and l=0,6
how many swimmers are holding exaclty 3 toy whales?
Answer:
3 swimmers
Step-by-step explanation:
The electronic sign that showed the speed of motorists was installed on a road.the line plots below show the speeds of some motorists before and after the sign was installed. based on these data which statement is true about the speeds of motorists after the sign was installed?
Answer:
The correct option is;
A. The mean speed and the range of the speeds of the motorists decreased
Step-by-step explanation:
Here we have the speeds given as
Before Sign Installation
Speed Frequency
20 1
24 1
25 4
30 2
35 2
38 1
40 1
∑ 212 12
Mean = 17.67
Median (25 + 30)/2 = 27.5
Range = 40 - 20 = 20
After Sign Installation
Speed Frequency
20 1
22 1
25 4
28 1
30 3
35 2
∑ 160 12
Mean = 160/12 = 13.33
Median = (25+28)/2 = 26.5
Range = 35 - 20 = 15.
Therefore, the mean speed and the range of the speeds of the motorists decreased
Write an equation to find the amount of money in Pertro’s account if the total of all their accounts is $148.
Answer:
P = 2(21 + 3)
= 2(24)
=$48
Step-by-step explanation:
Add them all up.
s + 2(s+3) + 4s-5 = 148
s + 2s + 6 + 4s - 5 = 148
Group all s together and all numbers together 7s + 1 = 148
7s = 147
Divide by 7
s = 21
Plug s=21 back in for Petro
To find the amount of money in Pertro's account, use the equation x = 148 - (y + z), where y and z represent the amounts in the other two accounts.
Explanation:The equation to find the amount of money in Pertro's account can be written as:
x + y + z = 148
where x, y, and z represent the amounts in different accounts. To find the amount in Pertro's account, we need to set up another equation using the information given. If we know that the total of all accounts is $148 and we want to find the amount in Pertro's account (x), we can write:
x = 148 - (y + z)
where y and z represent the amounts in the other two accounts.
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Find the measure of GHI
Answer:
119°
Step-by-step explanation:
In circle with center B, JH is diameter.
[tex]m\angle GHI = 360° - (90° + 151°)\\
m\angle GHI = 360° - 241°\\
m\angle GHI = 119°\\
\because\overset{\frown}{GHI} =m\angle GHI\\
\huge \red{ \boxed{\therefore \overset{\frown}{GHI} =119°}}\\ [/tex]
original price? percent of discount: 80% sales price: $90
Answer:
18.00 dollars
Step-by-step explanation:
message me if you need help. Or this was not the answer you were looking for.
what are the 5 perfect prime numbers between 50 and 140
Answer:
61 67 71 73 79
There you go:)
Answer:
53, 59, 61, 67, 71.
Step-by-step explanation:
It goes on....
53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109
, 113, 127, 131, 137, 139
I hope this helps :)
Marta bought a paperweight in the shape of a cone. The radius was 10 centimeters and the height 9 centimeters. Find the volume. Round to the nearest tenth.
Answer:
The volume of the paper weight is 942.8 cubic cm.
Step-by-step explanation:
We are given the following in the question:
Dimensions of paperweight :
Radius, r = 10 cm
Height,h = 9 cm
Volume of paper weight = Volume of cone
[tex]V= \dfrac{1}{3}\pi r^2 h[/tex]
where r is the radius and h is the height of the cone.
Putting values, we get,
[tex]V = \dfrac{1}{3}\times \dfrac{22}{7}\times (10)^2\times 9\\\\V = 942.8\text{ cubic cm}[/tex]
Thus, the volume of the paper weight is 942.8 cubic cm.
The volume is 942.5 [tex]cm^{3}[/tex].
To calculate the volume of a cone, you can use the formula:
V = (1/3)πr²h
where:
V is the volumer is the radius of the baseh is the height of the cone1. For Marta's paperweight with a radius of 10 centimeters and a height of 9 centimeters, you substitute the values into the formula as follows:
V = (1/3)π(10 cm)²(9 cm)
2. First, calculate the base area:
(10 cm)² = 100 cm²
3. Then, multiply by the height:
100 cm² × 9 cm = 900 cm³
4. Finally, multiply by (1/3)π:
V = (1/3)π × 900 cm³ ≈ 942.5 cm³
Therefore, the volume of the cone is approximately 942.5 [tex]cm^{3}[/tex], rounded to the nearest tenth.
Find the center, vertices, and foci for the ellipse 25x^2 + 64y^2 = 1600
Answer:
The answer to your question is below
Step-by-step explanation:
Data
Equation 25x² + 64y² = 1600
Process
1.- Divide all the equation by 1600
25x²/1600 + 64y²/ 1600 = 1600/1600
-Simplify
x²/64 + y²/ 25 = 1
2.- Equation of a horizontal ellipse
[tex]\frac{x^{2} }{a^{2}} + \frac{y^{2}}{b^{2}} = 1[/tex]
3.- Find a, b and c
a² = 64 a = 8
b² = 25 b = 5
-Calculate c with the Pythagorean theorem
a² = b² + c²
-Solve for c
c² = a² - b²
-Substitution
c² = 8² - 5²
-Simplification
c² = 64 - 25
c² = 39
-Result
c = √13
4.- Find the center
C = (0, 0)
5.- Find the vertices
V1 = (-8, 0) V2 = (8, 0)
6.- Find the foci
F1 = (-√13, 0) F2 = (√13, 0)
The center of the ellipse is (0,0), the vertices are (5.657, 0) and (-5.657, 0), and the foci are (3.317, 0) and (-3.317, 0).
Explanation:The given equation of the ellipse is 25x^2 + 64y^2 = 1600.
To find the center of the ellipse, we can rewrite the equation in standard form: x^2/32 + y^2/25 = 1. The center is (0,0) since the x and y terms are squared and have the same coefficients.
To find the vertices of the ellipse, we can calculate the distance from the center to the major axis. The length of the major axis is 2*a, where a is the square root of the denominator of the x term. In this case, a = sqrt(32) ≈ 5.657. So the vertices are (5.657, 0) and (-5.657, 0).
To find the foci of the ellipse, we can calculate the distance from the center to the foci. The length of the foci is 2*c, where c is the square root of the difference between the squares of a and b (sqrt(32-25) ≈ 3.317). So the foci are (3.317, 0) and (-3.317, 0).
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As part of an activity during math class, Kiera has to select a secret number containing 3 different digits from 1 to 4. How many different secret numbers can Kiera create?
Answer:
24.
Step-by-step explanation:
The is the number of permutations of 3 digits from 4
= 4P3
= 4! / (4- 3)!
= 4 *3 *2 *1 / 1!
= 24/1
= 24.
In a deck of cards what's the probability of drawing a Face Card (king, queen, jack)
Answer:
3/13
Step-by-step explanation:
There are 52 card in a deck of cards
12 of them are face cards 3 cards *4 suits =12
P (face card) = 12/52 = 3/13
Answer:1/3 decimal form: 0.333 repeating percent: 3.33%
An ice cream cone has a height of 6 inches and a radius of 2 inches. A scoop of ice cream sits on the top of the cone. The scoop is a sphere with a diameter of 4 inches. If the entire scoop of frozen yogurt melts into the cone, will the cone overflow? Show all your work and explain your reasoning.
Answer:
Yes, it will overflow, because the volume of the scoop of ice cream is higher than the volume of the cone.
Step-by-step explanation:
To know if the cone will overflow when the entire scoop of frozen yogurt melts, we need to compare the volume of the scoop and the volume of the cone: if the volume of the scoop is higher, it will overflow.
The volume of the cone is:
V_cone = (1/3)*pi*r^2*h
Where V_cone is the volume, r is the radius and h is the height. So:
V_cone = (1/3)*pi*2^2*6 = 25.1327 in3
The volume of a sphere is:
V_sphere = (4/3)*pi*r^3
Where V_sphere is the volume and r is the radius. If the diameter is 4, the radius is 4/2 = 2. So:
V_sphere = (4/3)*pi*2^3 = 33.5103 in3
The volume of the sphere is higher, so the cone will overflow.
The volume of the melted ice cream scoop[tex](\( 33.51032 \, \text{cubic inches} \))[/tex] is greater than the volume of the cone [tex](\( 25.13272 \, \text{cubic inches} \))[/tex] the cone will overflow if the entire scoop of ice cream melts into it.
Step 1: Volume of the Cone
The formula for the volume of a cone is:
[tex]\[V_{\text{cone}} = \frac{1}{3} \pi r^2 h\][/tex]
where [tex]\( r \)[/tex] is the radius and [tex]\( h \)[/tex] is the height.
Given:
[tex]\[r = 2 \, \text{inches}, \quad h = 6 \, \text{inches}\][/tex]
Substitute these values into the formula:
[tex]\[V_{\text{cone}} = \frac{1}{3} \pi (2)^2 (6)\][/tex]
[tex]\[V_{\text{cone}} = \frac{1}{3} \pi (4) (6)\][/tex]
[tex]\[V_{\text{cone}} = \frac{1}{3} \pi (24)\][/tex]
[tex]\[V_{\text{cone}} = 8 \pi \, \text{cubic inches}\][/tex]
Step 2: Volume of the Ice Cream Scoop
The formula for the volume of a sphere is:
[tex]\[V_{\text{sphere}} = \frac{4}{3} \pi r^3\][/tex]
where [tex]\( r \)[/tex] is the radius of the sphere.
Given that the diameter of the sphere is [tex]4\ inches[/tex], the radius [tex]\( r \)[/tex] is:
[tex]\[r = \frac{4}{2} = 2 \, \text{inches}\][/tex]
Substitute this value into the formula:
[tex]\[V_{\text{sphere}} = \frac{4}{3} \pi (2)^3\][/tex]
[tex]\[V_{\text{sphere}} = \frac{4}{3} \pi (8)\][/tex]
[tex]\[V_{\text{sphere}} = \frac{32}{3} \pi \, \text{cubic inches}\][/tex]
Step 3: Compare the Volumes
The volume of the cone:
[tex]\[V_{\text{cone}} = 8 \pi \, \text{cubic inches}\][/tex]
The volume of the ice cream scoop:
[tex]\[V_{\text{sphere}} = \frac{32}{3} \pi \, \text{cubic inches}\][/tex]
Let's convert them to decimal form for easier comparison:
[tex]\[V_{\text{cone}} = 8 \pi = 8 \times 3.14159 = 25.13272 \, \text{cubic inches}\][/tex]
[tex]\[V_{\text{sphere}} = \frac{32}{3} \pi = \frac{32}{3} \times 3.14159 = 33.51032 \, \text{cubic inches}\][/tex]
Write the equation in slope-intercept form of a line that has a slope of One-third and passes through the point (-6, 0).
y = one-third x
y = one-third x minus 6
y = one-third x minus 2
y = one-third x + 2
Slope-intercept form: y = mx + b
(m is the slope, b is the y-intercept or the y value when x = 0 --> (0, y) or the point where the line crosses through the y-axis)
You know:
m = [tex]\frac{1}{3}[/tex] So substitute/plug it into the equation
y = mx + b
[tex]y=\frac{1}{3} x+b[/tex] To find b, plug in the point (-6, 0) into the equation, the isolate/get the variable "b" by itself
[tex]0=\frac{1}{3} (-6)+b[/tex]
0 = -2 + b Add 2 on both sides to get "b" by itself
0 + 2 = -2 + 2 + b
2 = b
[tex]y=\frac{1}{3} x+2[/tex] Your answer is the 4th option
The equation in slope-intercept form is y = 1/3x + 2
Equation of a lineThe equation of the line in point slope form is expressed as:
y-y1 = m(x-x1)where:
m is the slope = 1/3(x1, y1) is the point on the line = (-6, 0)Substitute:
y - 0 = 1/3(x+6)
Write in slope-intercept form
y = 1/3(x+6)
3y = x + 6
y = 1/3x + 6/3
y = 1/3x + 2
Hence the equation in slope-intercept form is y = 1/3x + 2
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7n=30 what is the n
Answer:
n=4.28571429
Step-by-step explanation:
Solve for n by isolating it
7n=30
Divide both sides by 7 to "reverse" the multiplication being done to n
n=4.28571429
Answer "n" is 4 and 2 sevenths
Step-by-step explanation:
7n = 30 get "n" alone
7n / 7 = 30 / 7
n = 4 and 2/7
use the protractor to measure this angle
To measure an angle using a protractor, follow these steps: Place the center point of the protractor at the vertex, align the base line with one side, and read the measure where the other side intersects the scale.
Explanation:To measure an angle using a protractor, follow these steps:
Place the center point of the protractor at the vertex of the angle.Align the base line of the protractor with one of the sides of the angle.Read the measure on the protractor where the other side of the angle intersects the measure scale.For example, if the measure reads 45 degrees, then the angle is 45 degrees.
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The length of a rectangle is 14 centimeters and the width is 5 centimeters.
A similar rectangle has a width of 2.5 centimeters.
What is the length of the second rectangle in centimeters?
Answer:
7
Step-by-step explanation:
One side is half of the other (5/2.5=2)
So 14/2=7
Hi guys!
Im having trouble on the working out for this question could you please explain how to work it out?
Two-thirds of the jelly beans in a jar are black. There are 96 jelly beans in the jar. How many of them are black?
Thanks! Have an awesome day!
Answer:
64
Step-by-step explanation:
The first thing I would do is break down the question and put it into number form. 2/3 of the jelly beans are black. You want to find out the number of jelly beans out of 96 are black. I can try my best to explain how to do this.
Divide the number of jelly beans (96) by the denominator (3) to find out how many jelly beans would be 1/3. This is 32. To find out how many are 2/3 you would multiply the 1/3 (32) by 2 to find that it is 64.
To check your work simplify this. 64/96 and it should equal 1/3. Or put it in your calculator to find that it equals .667 which is the decimal form of 2/3.
Which graph is defined by the function given below?
y = (x+3)(x+3)
Answer:
Since you provided no graphs, I just graphed y=(x+3)(x+3). I hope this helps.
Final answer:
The graph defined by the function y = (x+3)(x+3) is a parabola opening upwards with its vertex at (-3, 0), represented by a U-shaped curve on the coordinate plane.
Explanation:
The function given by y = (x+3)(x+3) represents a quadratic equation, which can be expanded to y = x^2 + 6x + 9. This is a parabola that opens upwards because the coefficient of the x^2 term is positive. The graph of this function will have its vertex at the point (-3, 0), which is obtained by setting the inside of the parentheses to zero. To visualize this function, you would plot a series of points by choosing different values for x, calculate the corresponding y values, and then plot these points on a coordinate plane. Connecting these points will reveal the U-shaped curve typical for a quadratic function.
50 pts if correct and will mark brainliest
Answer:
see below
Step-by-step explanation:
Tally question
There are 6 marks for A out of 30 total
6/30 = 1/5
Sample space question
{run 50 run 100 run 150, swim 50 swim 100 swim 150}
We have to list all the possible choices that the spinners can land
run 50
swim 100
150
There are 2*3 = 6 choices
Tomas Game
1/36
The normal die has 1,2,3,4,5,6
P(5) = Number of 5's / total number of numbers = 1/6
Then roll another 5
P(5) = Number of 5's / total number of numbers = 1/6
P(5,5) = 1/6*1/6 = 1/36
Joe game
1/4
1,2,3,4,5,6 triangle, square
P(0dd) = {1,3,5}/ 6 numbers = 3/6 = 1/2
P (square) = square/ total = 1/2
Coin
1/2
HT HH TH TT
We want one heads and one tails
2 of the four
2/4 = 1/2
P (odd,square) = P(odd) * P(square) = 1/2*1/2 = 1/4
Answer:
1) ⅕
2) sample space: D
3) 1/36
4) P(odd & square) = ¼
5) ½
Step-by-step explanation:
1) P(A) = 6/30 = 1/5
2) sample space is the collection of all possible outcomes
{activity & distance}
3) P(5 & 5) = 1/6 × 1/6
1/36
4) odd: 1,3,5
P(odd) = 3/6 = 1/2
P(square) = 1/2
1/2 × 1/2 = 1/4
5) P(H & T) = 1/2 × 1/2 = 1/4
2 × 1/4 = 1/2
What is the area of the following figure?
Answer:
16.56
Step-by-step explanation:
The area of the square is 2 × 2
The area of the circle is-
A=πr²
A=3.14 × 2²
A=3.14 × 4
A=12.56
You don't need to divide it by half because there are two half circles so it would be a whole circle
12.56 + 4 = 16.56
Sorry if it is wrong
Answer:
Area of square =side( square)
(2) square
4
diameter= 2
radius=2/2
= 1
Area of circle=πrsquare
22/7×1×1
3.14
Area of figure= Area of square+area of circle
4+3.14
7.14
The archway to the entrance of an art gallery can be model by y= -1/3(x-5)(x+5) where x and y are measured in feet. The x-axis represents the floor. Find the width of the arch at floor level.
Answer:
x=5 feet
Step-by-step explanation:
At floor level y=0
If the expression is:
[tex]0=1/3(x-5)(x+5)\\0=1/3(x^2-25)\\0=1/3x^2-25/3\\25/3=1/3x^2\\25=x^2\\x=5[/tex]
But, with the negative sign, the answer is x= 5i (where i is imaginary)
Final answer:
The width of the arch at floor level is found by determining the points where the parabola intersects the x-axis, which are at x = 5 and x = -5. The width is the distance between these points, which is 10 feet.
Explanation:
To find the width of the arch at floor level, we need to determine the distance between the two points where the parabola represented by the equation y = -1/3(x-5)(x+5) intersects the x-axis. The x-axis represents the floor, and the points of intersection occur where y is equal to 0.
Setting the equation to 0 gives:
0 = -1/3(x-5)(x+5)
By solving for x, we get x = 5 and x = -5, which are the points where the parabola intersects the x-axis. The distance between -5 and 5 on the x-axis is 10 feet, so the width of the arch at floor level is 10 feet.
Melissa has a student dictionary on her desk. Her dictionary contains 90 pages. In this dictionary, more words start with the letter "S" than any other letter, occupying 14 full pages. If she opens up the dictionary at random, what is the probability that the page contains words starting with "S"?
Answer:
probability that the page opened will start with S
Step-by-step explanation:
14/90
0.15556
Landons car used 10 gallons of gas to drive 220miles. At what rate does his car use gas in gallons per mile
Answer:
1/22 gallons per mile
Step-by-step explanation:
We want to find gallons per mile, so we take the gallons and divide by the mile
10gallon/ 220 mile
1/22 gallons per mile
Answer:
1/22 gallons per mile
Step-by-step explanation:
(5 x 5) + (6 × 7) - 50 =?
Answer:
17
Step-by-step explanation:
5 x 5 is 25
6 x 7 42
25 + 42 is 67
67 - 50 = 17
17 is your answer :)
Carrie is finding the set of even numbers within the set of prime numbers.
Of the sets described, which is the universal set?
Group of answer choices
all real numbers
even numbers
prime numbers
all integers
Answer:
Universal set ( U ) = Set of prime numbers
Step-by-step explanation:
Solution:-
- All even numbers are numbers that are divisible by 2 or have at-least an LCM of 2 associated with that number.
- All prime numbers are divisible by 1 and the number itself. Which 2 which is divisible by 1 and itself is a prime number and an even number.
- Considering only positive integers.
- Carrie is looking for a set of even numbers within the set of prime number.
- As stated above, the only integer, 2, is common to both prime number set and even number set.
- Hence, universal set ( U ) should be prime numbers.
- Universal set ( U ) = Set of prime numbers.
Answer:
c. prime numbers
Step-by-step explanation:
edg 2020
PLEASE HELP IT IS VERY URGENT!!
Please help to find (b) (c) (d)
(b) is in the picture
(c) Given that the ratio of PL to LF is 2 : 3, find the ratio of the area of triangle PLM to the area of triangle PFG.
(d) A circle is drawn by using FG as the diameter. Explain if the point M lies on the circumference of this circle.
Step-by-step explanation:
(c)
[tex] In\: \triangle PLM \: \&\: \triangle PLM\\
\angle PLM \cong\triangle PFG.. (corresponding \:\angle s) \\
\angle LPM \cong \angle FPG.. (common \: \angle s) \\
\therefore \triangle PLM\sim\triangle PFG.. (by\: AA\:Postulate) \\
PF = PL + LF = 2 + 3 = 5[/tex]
By area of similar triangle theorem:
[tex] \frac {A(\triangle PLM)}{A(\triangle PFG)}= \frac{PL^2}{PF^2}\\
\therefore \frac {A(\triangle PLM)}{A(\triangle PFG)}= \frac{2^2}{5^2}\\
\therefore \frac {A(\triangle PLM)}{A(\triangle PFG)}= \frac{4}{25}\\
A(\triangle PLM)\: :\: A(\triangle PFG) = 4 \: :\: 25
[/tex]
Is 7, 20, 25 a right triangle?
Answer:
The answer to your question is below
Step-by-step explanation:
Process
To answer if they are right triangles or not use the Pythagorean theorem which states that the square of the hypotenuse equals the sum of the square of the legs.
a) 25² = 20² + 7²
625 = 400 + 49
625 ≠ 449 It is not a right triangle
b) 26² = 24² + 10²
676 = 576 + 100
676 = 676 it is a right triangle
c) 13² = 8² + (√10)²
169 = 64 + 10
169 ≠ 74 it is not a right triangle
d) 52² = 48² + 20²
2704 = 2304 + 400
2704 = 2704 it is a right triangle
s) An e-mail lter is planned to separate valid e-mails from spam. The word free occurs in 50% of the spam messages and only 3% of the valid messages. Also, 20% of the messages are spam. Determine the following probabilities: (a) The message contains the word free. (b) The message is spam given that it contains free. (c) The message is valid given that it does not contain free.
Answer:
A) P(F) = 0.124
B) P(S|F) = 0.8065
C) P(V|F^(c)) = 0.886
Step-by-step explanation:
Let us denote as follows;
F = Message contains word free
S = message is spam
V = message is valid
From the question, we are given that;
The probability that word free occurs in spam messages;P(F|S) = 50% = 0.5
The probability of the valid messages that contain free; P(F|V) = 3% = 0.03
Spam messages; P(S) = 20% = 0.2
Valid messages; P(V) = 1 - 0.2 = 0.8
A) From rule of total probability ;
probability that the message contains the word free is given as;
P(F) = P(F|S)•P(S) + P(F|V)•P(V)
P(F) = (0.5 x 0.2) + (0.03 x 0.8)
P(F) = 0.124
B) From Baye's theorem;
probability that the message is spam given that it contains free is given as;
P(S|F) = P(F|S)•P(S)/P(F)
P(S|F) = (0.5 x 0.2)/0.124
P(S|F) = 0.8065
C) From combination of complement rule and Baye's theorem;
probability that the message is valid given that it does not contain free is given as;
P(V|F^(c)) = P(F^(c)|V)•P(V)/P(F^(c))
Thus,
P(V|F^(c)) = [(1 - P(F|V))•P(V)]/(1 - P(F))
P(V|F^(c)) = ((1 - 0.03)•0.8)/(1 - 0.124)
P(V|F^(c)) = 0.776/0.876
P(V|F^(c)) = 0.886
Simplify:
7a² + ab - 4a² + 2a + 8ba + 4a
Group terms
= (7a² - ?a²) + (ab + 8ba) + ( ? + 4a)
Answer:
simplify question is 3a^2 +6a+9ab
Step-by-step explanation: