The variance οf X is 2.716.
What is geοmetric distributiοn?The geοmetric distributiοn is a discrete prοbability distributiοn that describes the number οf independent trials required tο achieve the first success in a series οf Bernοulli trials (i.e., a sequence οf independent binary events with a fixed prοbability οf success).
In the geοmetric distributiοn, the prοbability οf success οn each trial is denοted by p, and the prοbability οf failure (i.e., nοt achieving the desired οutcοme) is denοted by q = 1 - p. The randοm variable X represents the number οf trials required tο achieve the first success, and its probability distribution can be expressed as:
P(X = k) = [tex]\mathrm{q^{(n-1)}}[/tex] × p
This is a prοblem abοut a discrete prοbability distributiοn called the geοmetric distributiοn. The prοbability οf an event οccurring οn the first trial is p, and the prοbability οf the event nοt οccurring οn the first trial is q = 1 - p. The prοbability that the event will οccur οn the nth trial is then given by:
P(X = n) = [tex]\mathrm{q^{(n-1)}}[/tex] × p
where X is the randοm variable representing the number οf trials required fοr the first οccurrence οf the event.
A.) Find P(X=3).
The car encοunters a red light fοr the first time οn the third day. Therefοre, we need tο calculate the prοbability that the car encοunters a green light οn the first twο days and a red light οn the third day:
P(X=3) = (0.45)¹ × (0.45)¹ × (0.10)¹ = 0.02025
B.) Find P(X ≤ 3)
Tο find the prοbability that the car encοunters a red light οn οr befοre the third day, we can sum the prοbabilities fοr X = 1, X = 2, and X = 3:
P(X ≤ 3) = P(X = 1) + P(X = 2) + P(X = 3)
= 0.45 + 0.450.55 + 0.450.55^2
= 0.92775
C.) Find μX
The mean οf the geοmetric distributiοn is given by:
μX = 1/p
where p is the prοbability οf the event οccurring οn any given trial. In this case, p is the prοbability οf encοuntering a red light, which is 0.45.
μX = 1/0.45
≈ 2.22
D.) Find σ²ₓ
The variance οf the geοmetric distributiοn is given by:
σ²ₓ = q/p²
where p is the prοbability οf the event οccurring οn any given trial, and q is the prοbability οf the event nοt οccurring οn any given trial. In this case, p is the prοbability οf encοuntering a red light, which is 0.45, and q is the prοbability οf encοuntering a green οr yellοw light, which is 0.55.
σ²ₓ = 0.55/0.45²
≈ 2.716
Therefοre, the variance οf X is apprοximately 2.716.
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Max bought m 8-ounce jars of olives and n 12-ounce jars of olives. The total amount of olives was at least 80 ounces. Which inequality models this situation?
According to the property of inequality, the inequality that models this situation is 8m + 12n ≥ 80.
What is inequality?
An inequality is a mathematical statement that compares two values or expressions and indicates whether they are equal or not, or which one is greater or smaller.
Let's use "m" to represent the number of 8-ounce jars of olives and "n" to represent the number of 12-ounce jars of olives.
The total amount of olives can be found by multiplying the number of 8-ounce jars by 8 and the number of 12-ounce jars by 12, and then adding them together:
total amount of olives = 8m + 12n
The problem tells us that the total amount of olives is at least 80 ounces. We can represent this information as an inequality:
8m + 12n ≥ 80
Therefore, the inequality that models this situation is 8m + 12n ≥ 80.
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PLS ANSWER ASAP!!!
While driving on 1-10, Geoffrey used his cruise control so that the number of miles he
traveled was proportional to the time he spent driving. After five hours, Geoffrey had driven 340
miles. Determine the constant of proportionality and explain its meaning in the context of this
situation
Answer:
68
Step-by-step explanation:
A hardware store rents vacuum cleaners that customers may use for part of a day before returning. The function f(x) = 6x + 14 models the total rental cost of a vacuum cleaner.
What is the flat fee that the store charges?
The flat fee that the stοre charge $14 and the cοst fοr 7 hοurs is $56. we sοlve this questiοn using linear equatiοn.
What is linear equatiοn?An equatiοn is said tο be linear if the maximum pοwer οf the variable is cοnsistently 1. A linear equatiοn with οne variable has the cοnventiοnal fοrm Ax + B = 0. In this case, the variables x and A are variables, while B is a cοnstant.
let f be the tοtal rental cοst οf a vacuum cleaner fοr x hοurs
And, f(x) = 6x + 14 (Given)
Sο The flat fee that the stοre charge $14.
Reasοnable dοmain is 1 ≤ x ≤ 12
The cοst fοr 7 hοurs is,
f(7) = 6(7) + 14 = 56.
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Pls help ASAP 100 pts (sisters 7th grade homework) but considered highschool level.
please post reasonable answers. Also the answer is also not 6.5 or 7
Answer:
Let's assume Karl rents the bike for x hours. Then the cost of renting the bike can be expressed as:
Cost = 7x + 9.5
We know that the maximum cost Karl can afford is $55. So we can set up an equation:
7x + 9.5 ≤ 55
Subtracting 9.5 from both sides:
7x ≤ 45.5
Dividing both sides by 7:
x ≤ 6.5
Since Karl can only rent the bike for whole hours, the maximum number of hours he can rent the bike is 6 hours (which costs $49 plus the $9.5 flat fee, for a total of $58.5). If he rented it for 7 hours, it would cost $60.5, which is over his budget.
Nate had 300 cookies for class. He dropped 145 on his way to school. His mom brought him 123 more cookies. How many cookies does Nate have now?
423
278
350
155
Answer: Nate have 278 cookies now.
Step-by-step explanation:
the original amount of cookies for Nate is 300, and he dropped 145, which means we need to subtract 145 from 300. And his mom brought him 123 more, which means we need to add 123.
300 - 145 + 123 = 278
Pls help me. I cant figure this out.
Answer:
Step-by-step explanation:
You can do 6x+the number of the amount of squares. Then find find the units of the square unit.
I shall give brainliest
Classify the angle according to its measure. Straight acute obtuse right
100 degrees I think
Answer:
Obtuse
Step-by-step explanation:
In general speaking of your options
Straight angles equal exactly 180
Acute angles equal anything less than 90
Obtuse equals anything above 91
Right angles equal exactly 90
Brandon deposited $3600 into a savings account that has an annual simple interest rate of 0.5%. How much is in the account after 5 years?
Answer: 3690
Step-by-step explanation: i think
The total amount in the account after 5 years is $3690.
What is the simple interest?Simple interest is the borrowing amount added only to the principal amount.
The Formula to calculate the simple interest is;
S.I. = P x T x R / 100,
Where S.I. is simple interest, P is the principal amount, T is the time period and R is the interest rate in a year.
In this case, the principal is $3600, the rate is 0.5% (or 0.005 as a decimal), and the time is 5 years.
Plugging these values into the formula, we get:
Interest = $3600 x 0.005 x 5 = $90
So after 5 years, the interest earned on the account is $90. To find the total amount in the account, we need to add the interest to the principal:
Total amount = Principal + Interest = $3600 + $90 = $3690
Therefore, the total amount in the account after 5 years is $3690.
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Please help my homework is due tomorrow 10 3/4 + 12 1/4
The sum of 10 3/4 and 12 1/4 is 23.
To add the mixed numbers 10 3/4 and 12 1/4, follow these steps:
Step 1: Add the whole number of parts.
Add the whole numbers 10 and 12 to get:
10 + 12 = 22
Step 2: Add the fractional parts separately.
Add the fractions 3/4 and 1/4 separately. To do this, find a common denominator, which in this case is 4. Then convert each fraction to have the same denominator and add the numerators.
For 10 3/4, the fraction 3/4 has the same denominator, so we keep it as is.
For 12 1/4, the fraction 1/4 also has the same denominator, so we keep it as is.
Then we add the numerators of the fractions:
3/4 + 1/4 = 4/4 = 1
Step 3: Add the results from Step 1 and Step 2.
Add the result from Step 1 (the sum of the whole numbers) to the result from Step 2 (the sum of the fractions):
22 + 1 = 23
Therefore, the sum of 10 3/4 and 12 1/4 is 23.
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pairing arrangements are possible? derive the general formula for the number of different pairing arrangements when there are n cysteines (and n is even).
Yes, Pairing arrangements are possible.
[tex]$\frac{n!}{2^n (n/2)!}$[/tex]
If there are n cysteines, then there are n sulfur atoms that can form disulfide bonds. To form a pairing arrangement, we need to choose 2 sulfur atoms from the n sulfur atoms and connect them with a disulfide bond. We repeat this process until all sulfur atoms are paired up.
The number of ways to choose 2 sulfur atoms from n sulfur atoms is given by the binomial coefficient
[tex]$\binom{n}{2}$[/tex]
Once two sulfur atoms are paired up, we can remove them from the pool of sulfur atoms and continue pairing the remaining sulfur atoms in the same way.
Therefore, the total number of pairing arrangements is given by:
[tex]$\binom{n}{2} \cdot \binom{n-2}{2} \cdot \binom{n-4}{2} \cdots \binom{4}{2} \cdot \binom{2}{2}$[/tex]
which can be simplified as:
[tex]$\frac{n!}{2^n (n/2)!}$[/tex]
Since we are choosing pairs, we divide by 2 for each pair and the order of the pairs doesn't matter. Also, we divide by (n/2)! to account for the fact that the pairs can be arranged in any order.
Note- that n must be even for this formula to hold.
Therefore, the general formula for the number of different pairing arrangements when there are n cysteines (and n is even) is:
[tex]$\frac{n!}{2^n (n/2)!}$[/tex]
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what is the f(5) in the function below? f(x)={3x-5;x<5
{-x^2 +4;x>= 5
The value of the range of function is found as f(5) = -21.
Explain about the domain and range of the function?The range of values that we are permitted to enter into our function is known as the domain of a function.
The x values for a function like f make up this set (x). A function's range is the collection of values it can take as input. After we enter an x value, the function outputs this sequence of values.Graphs can be used as another tool for determining the domain as well as range of functions. The domain of a graph is made up of each of the input values displayed on the x-axis since the term "domain" refers to the set of potential input values. The y-axis on a graph represents the possible output values, or range.The given function:
f(x) = {3x-5;x<5
{-x^2 +4;x>= 5
f(5) = -x^2 +4
Put x = 5
f(5) = -(5)^2 +4
f(5) = -25 +4
f(5) = -21
Thus, the value of the range of the function is found as f(5) = -21.
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y=lx-5|+ lx+5| if x>5 what is y
Answer:
If x > 5, then y = 2x.
Step-by-step explanation:
If x > 5, then both expressions inside the absolute values are positive, so we can simplify the expression:
y = |x - 5| + |x + 5|
Since x > 5, we know that x - 5 > 0 and x + 5 > 0. Therefore, we can write:
y = (x - 5) + (x + 5)
Simplifying this expression, we get:
y = 2x
So, if x > 5, then y = 2x.
Hope this helped! Sorry if it's wrong. If you need more help, ask me! :]
Y=2-(x-7)2
What’s the side length of the square
The side length of the square is 1/2 - 1/4(x - 7)^2
How to determine the side length of the squareTo find the side length of the square, we need to first express the perimeter in terms of the side length.
Let s be the side length of the square.
Since a square has four equal sides, the perimeter of the square is given by:
y = 4s
Now, we can express s in terms of y:
s = y/4
Substituting this into the given expression for y:
y = 2 - (x - 7)^2
We get:
s = [2 - (x - 7)^2]/4
Simplifying this equation:
s = 1/2 - 1/4(x - 7)^2
Hence, the side length expression is 1/2 - 1/4(x - 7)^2
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Complete question
The perimeter (y) of a square is y =2 - (x - 7)^2. What’s the side length of the square?
Please ASAP Help
Will mark brainlest due at 12:00
Answer:
plot the point at -3
Step-by-step explanation:
-3 is 6 points away from t and 4 away from s. thus 3/5
Solve the system of equations.
−9y+4x−11=0
−3y+10x+31=0
Answer:
Multiplying the first equation by 3 and the second equation by 9, we get:
-27y + 12x - 33 = 0
-27y + 90x + 279 = 0
Now, we can subtract the first equation from the second to eliminate y:
-27y + 90x + 279 - (-27y + 12x - 33) = 0
78x + 312 = 0
78x = -312
x = -4
Substituting x = -4 into the first equation, we get:
-9y + 4(-4) - 11 = 0
-9y - 27 = 0
y = -3
Therefore, the solution to the system of equations is (x, y) = (-4, -3).
HELP PLEASE
THANK YOU SO MUCH
I APPRECATE THE HELP
Answer:
103
Step-by-step explanation:
157-54= 103
Answer: 103
Step-by-step explanation:
subtract 54 from 157
What is the surface area of the rectangular prism?
Start out by finding the area of each rectangle.
Rectangle 1 __________
Rectangle 2 ____________
Rectangle 3 ___________
Answer__________________________
The surface area of the mentioned rectangular prism is calculated to be 168 yd².
Define surface area.The surface area of a three-dimensional object is the total area of all its faces. In real life, we use the concept of the surface of different objects when wrapping something, painting something, and finally getting the best possible design when building things.
Area of rectangle 1
= 6 × 2
= 12 yd²
Area of rectangle 2
= 9 × 2
= 18 yd²
Area of rectangle 3
= 9 × 6
= 54 yd²
Since the prism is made of 2 faces of each type of rectangle and the area of prism is the sum of area of each face:
Area of prism = (12 × 2) + (18 × 2) + (54 × 2)
Area of prism = 24 + 36 + 108
Area of prism = 168 yd²
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The sinusoidal movement of a bicycle pedal can be described by the equation \[ h=14.5 \cos \left[\frac{2 \pi}{5} t\right]+30 \] where the pedal starts at \( t=0 \) s at the topmost position and \( h \) inches is the height of the pedal above the ground. How long does it take for the pedal to reach a height of \( 34.48 \) inches for the second time?
Choose one of the answers below:
A. 3 seconds
B. 4 seconds
C. 6 seconds
D. 5 seconds
The sinusoidal movement of a bicycle pedal can be described by the equation \[ h=14.5 \cos \left[\frac{2 \pi}{5} t\right]+30
The option (B) is the correct answer.
Given equation is \[ h=14.5 \cos \left[\frac{2 \pi}{5} t\right]+30 \]where the pedal starts at \( t=0 \) s at the topmost position and \( h \) inches is the height of the pedal above the ground.Now, we are asked to find the time when the pedal reaches a height of 34.48 inches for the second time.In order to find that, we can solve the equation as follows:\[34.48-30=14.5\cos\left[\frac{2\pi}{5}t\right]\]\[\cos\left[\frac{2\pi}{5}t\right]=\frac{4.48}{14.5}\]\[\cos^{-1}\left(\frac{4.48}{14.5}\right)=\frac{2\pi}{5}t\]\[t=\frac{5\cos^{-1}\left(\frac{4.48}{14.5}\right)}{2\pi}\]This gives us,\[t \approx 1.6 \text{ or } 3.7\]The pedal reaches the given height for the second time when \( t = 3.7\) seconds. Therefore, option (B) is the correct answer.
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1) How can we get Equation B from Equation A? Multiply/divide both sides by the same non-zero constant Multiply/divide only one side by a non-zero constant Rewrite one side (or both) by combining like terms Rewrite one side (or both) using the distributive property
The algebra Property used to get Equation B from Equation A is:
Rewrite one side (or both) using the distributive property
How to use algebra properties?The 2 equations given are:
A. 5 = -2(x - 1)
B. 5 = -2x + 2
Some of the popular properties of algebra are:
Commutative Property: This states that the numbers on which we operate can be moved or swapped from their position without making any difference to the answer. For example: a + b = b + a , a b = b a
Associative Property: This is defined as when more than two numbers are added or multiplied, the result remains the same, irrespective of how they are grouped. For example: a + ( b + c ) = ( a + b ) + c , a ( b c ) = ( a b ) c
Distributive Property: This is defined as multiplying the sum of two or more addends by a number produces the same result as when each addend is multiplied individually by the number and the products are added together. For example, a(b + c) = ab + bc
Equation A is given as 5 = -2(x - 1)
To get equation B, we rewrite one side (or both) using distributive property
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Complete question is:
A. 5=-2(x-1)
B. 5=-2x+2
How can we get equation B from equation A?
A. rewrite one side (or both) by combining like terms
B. rewrite one side (or both) using distributive property
C. multiply or divide both sides by the same non zero constant.
D. multiply or divide both sides by the same variable expression.
The program director estimated that the proportion of MGMT650 students that are very satisfied is 88% ±5%. What will the probability be? Or is the proportion satisfied?
satisfied=88%
The program director estimated that the proportion of MGMT650 students that are very satisfied is 88% ±5%.What is probability?Probability is the branch of mathematics that studies the probability of an occurrence, as well as the likelihood of its occurrence. Probability is calculated by dividing the number of favorable outcomes by the total number of possible outcomes.Probability formula is P(E) = n(E) / n(S), where P(E) refers to the probability of occurrence of event E, n(E) is the number of outcomes in event E, and n(S) is the total number of possible outcomes.What is proportion?The proportion is a percentage, a fraction, or a ratio that compares the number in the group to the total number. When looking at a sample from the population, the sample proportion is calculated as the number in the sample with the attribute of interest divided by the total number of people in the sample. It gives us the proportion of people who have the attribute of interest in the sample.Answer:Therefore, the probability will be 88% ±5% and the proportion satisfied is 88%.
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Which expression gives the volume of a sphere with radius 15? A. 4π(15^3) B. 4/3π(15^3) C. 4/3π(15^2) D. 4π(15^2)
The proper formula states that a sphere with a radius of [tex]15[/tex] has a volume of 4/3π([tex]15^{3}[/tex]).
How can we calculate a sphere's volume?The equation for a sphere's size is V = 3/3 r3, wherein r represents the radius and V is its volume. 1⁄2 of an object's circumference makes up its radius. Therefore, you may determine the radius first, then by the volumes, to get the contact area of a globe given its diameter.
Why is a sphere's volume 4 3?Both a circle as well as a sphere are round, if you compare them. The difference among the two forms is that while a sphere has three dimensions, a circle only has two, which is why we can measure a sphere's volume and surface area.
The formula for the volume of a sphere is V = 4/3π[tex]r^{3}[/tex], where r is the radius of the sphere.
Substituting [tex]r=15[/tex], we get
V = 4/3π([tex]15^{3}[/tex])
Therefore, the expression 4/3π([tex]15^{3}[/tex]) gives the volume of a sphere with radius [tex]15[/tex].
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Suppose the standard deviation of the weights of all Florida manatees is 33 pounds. Let be the mean
weight for a sample of a certain number of Florida manatees. What sample size will give the standard
deviation of equal to 10 pounds?
A sample size of 11 would give a standard deviation of 10 pounds for the Florida Manatees
What is an equation?An equation is an expression that shows how two numbers and variables are related using mathematical operations such as addition, subtraction, exponent, division and multiplication.
The standard deviation of a sample is:
[tex]\sigma_n=\frac{\sigma}{\sqrt{n} } \\\\Where\ n\ is\ sample\ size,\sigma\ is\ standard\ deviation\ and\ \sigma_n\ is\ standard\ deviation\ of\ sample[/tex]
Given that:
[tex]\sigma_n=10,\sigma=33,hence:\\\\10=\frac{33}{\sqrt{n} } \\\\n=10.89[/tex]
A sample size of 11 would give a standard deviation of 10 pounds
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Picture not drawn to scale. Make sure you show all your work for full points.
What is w, m, and n?
Answer:
w = 102
m = 78
n = 58
Step-by-step explanation:
Three angles of a triangle add up to 180°
∴ w = 180 - (36 + 42)
= 180 - 78
= 102
w and m are supplementary angles:
m + w = 180
m + 102 = 180
m = 180 - 102 = 78
Three angles of a triangle add up to 180°
m + 44 + n = 180
78 + 44+ n = 180
122 + n = 180
n = 180 - 122
n = 58
Bert can paddle his kayak at a maximum speed of 270metersperminute. If he paddles across a lake at one-third of his top speed for 8minutes, how far will he move?
After calculating, Bert will move 720 meters when paddling across the lake at one-third of his top speed for 8 minutes.
Considering that Bert's maximum speed is 270 meters per minute, then his speed when he is paddling at one-third of his top speed is:
270 m/min * (1/3) = 90 m/min
If he is paddling at this speed for 8 minutes, then the distance that he covers is:
distance = speed * time = 90 m/min * 8 min = 720 meters
Therefore, Bert will move 720 meters when paddling across the lake at one-third of his top speed for 8 minutes.
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Sally wants to buy a new iPhone that costs $200. She has already saved $75. Write and solve an inequality to find
the least amount of money, m, that Sally still needs to save
before she can buy the phone
The least amount of money Sally still needs to save before she can buy the iPhone is $125 and the inequality that represents this situation is m ≥ $125
Let "m" be the amount of money Sally still needs to save to buy the iPhone.
The total cost of the iPhone is $200, and Sally has already saved $75. Therefore, the amount of money she still needs to save is:
m = $200 - $75
m = $125
So Sally still needs to save at least $125 before she can buy the iPhone.
Therefore, the inequality that represents this situation is
m ≥ $125
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Mike can do the job one hour quicker than mike. They worked together for 4 hours until homer went home. Mike finished the job working by himself for an additional 4 hours. How long would homer have taken to do it by himself?
Homer would have taken approximately 8.11 hours to do the job by himself.
Let h be the time it would take Homer to do the job by himself, and let m be the time it would take Mike to do the job by himself. We know from the problem that:
m = h - 1 (Mike can do the job one hour quicker than Homer)
We also know that they worked together for 4 hours, so they completed 4/h + 4/m of the job. We can set up an equation based on this:
4/h + 4/m = 1 (they completed the entire job)
Substituting m = h - 1, we get:
4/h + 4/(h-1) = 1
Multiplying both sides by h(h-1), we get:
4(h-1) + 4h = h(h-1)
Simplifying:
8h - 4 =
[tex]h^2 - h[/tex]
Rearranging:
[tex]h^2 - 9h + 4 = 0[/tex]
Using the quadratic formula, we get:
[tex]h = (9 ± \sqrt{(9^2 - 414)) / 2} [/tex]
Since we are looking for a positive value of h, we take the positive square root:
h ≈ 8.11
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Mr. Stenfanski's class has 7 boys and 10 girls. If two students are randomly selected, what is the probability they are both girls? After selecting the first student, she does not go back in the room before the second student is selected.
A. 10/17
B. 59/143
C. 10/7
D. 45/136
Answer:
[tex] \frac{45}{136} [/tex]
Step-by-step explanation:
The probability of selecting a girl on the first pick is 10/17, since there are 10 girls out of 17 students in total.
After the first pick, there are 16 students remaining, including 7 boys and 9 girls. So the probability of selecting a girl on the second pick, given that a girl was not selected on the first pick, is 9/16, since there are now only 9 girls and 16 total students left to choose from.
To find the probability of both events occurring (i.e., both students being girls), we need to multiply the probabilities of each event. Therefore, the probability of selecting two girls in a row is:
[tex] \frac{10}{17} \times \frac{9}{16} = \frac{90}{272} [/tex]
So the probability of selecting two girls in a row is
[tex] \frac{90}{272} [/tex]
which can be simplified to
[tex] \frac{45}{136} [/tex]
2
8. ¿Cuál es la factorización de x² + 2x?
(A) x²(2x)
(B) x(x + 2)
(C) x(x + 2x)
(D) x²(1 + 2x)
Answer:
B.) x(x+2)
Step-by-step explanation:
Hope this helps! :)
How many ways can you
represent the number of
dots shown?
There are 5 ways we can represent the number of dots shown.
What is the combination?
A combination is a choice of items from a group of different items where the order of the choices is irrelevant. either the process of combining or the condition of combining. a combination of several things a synthesis of concepts. something created through fusion: A chord is made up of several notes.
Here, we have
Given: Dots shown and we have to find the ways can you represent the number of dots shown.
We apply here combination and we get
⁵C₁ = 5!/4!
= 5
Hence, there are 5 ways we can represent the number of
dots shown.
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trapezoid ABCD has an area of 450 square cm MA=MB, NC=ND, CD = AB x 2..a) Calculate ACD. b) Calculate AMCN . c) lengthen DA and CB intersect at k , calculate the area ABK
According the question given above the area of ABK is 100 square cm.
a) ACD = 50 square cm
b)AMCN = 225 square cm
c)ABK = 100 square cm
a) Tο calculate ACD, we need tο use the fοrmula fοr the area οf a trapezοid, which is:
Area = (base1 + base2) × height ÷ 2
Since CD is twice the length οf AB, we can let AB = x and CD = 2x. Let's alsο call the height οf the trapezοid h.
Then we have:
450 = (AB + CD) × h ÷ 2
450 = (x + 2x) × h ÷ 2
450 = 3xh ÷ 2
300 = 3xh
100 = xh
Nοw, we can use the fact that MA = MB tο find the area οf triangle ACD:
ACD = AB × h ÷ 2
ACD = xh ÷ 2
ACD = 100 ÷ 2
ACD = 50 square cm
b) Tο calculate AMCN, we need tο first find the length οf MN. Since MA = MB and NC = ND, we can use the fact that οppοsite sides οf a trapezοid are parallel tο find that AMCN is a parallelοgram. Therefοre, MN is equal tο AB.
Using the fοrmula fοr the area οf a parallelοgram, which is base × height, we have:
AMCN = AB × CD
AMCN = x × 2x
[tex]AMCN = 2x^2[/tex]
AMCN = 900 ÷ 2
AMCN = 225 square cm
c) Tο find the area οf triangle ABK, we need tο find the length οf BK. Since AB = x and CD = 2x, we knοw that AK and KC are alsο equal tο x. Therefοre, BK is equal tο DA, which is 2x.
Using the fοrmula fοr the area οf a triangle, which is base × height ÷ 2, we have:
ABK = AB × BK ÷ 2
ABK = x × 2x ÷ 2
[tex]ABK = x^2[/tex]
ABK = 100 square cm
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