The probability that a randomly selected firm will earn less than 96 million dollars is 0.8907
The given data is that the mean income of firms in the industry for a year is 80 million dollars with a standard deviation of 13 million dollars. Now, it is required to find the probability that a randomly selected firm will earn less than 96 million dollars if incomes for the industry are distributed normally.
The probability is calculated by the Z-score formula which is given as below:
z = (x - μ) / σ
Where,μ = 80 (Mean), x = 96 (Randomly selected firm income), σ = 13 (Standard deviation)
Putting the values in the formula we have,
z = (96 - 80) / 13z = 1.23
Now we will use the Z-table to find the probability value. From the Z-table, we can say that the probability of Z-score = 1.23 is 0.8907.
Therefore, the probability that a randomly selected firm will earn less than 96 million dollars is 0.8907 (approx) when rounded off to four decimal places.
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16. In Δ ABC and Δ PQR, , AB = PR, BC = RQ and AC = PQ. Δ ABC is congruent to a) Δ RPQ b) Δ QRP c) Δ PQR d) Δ PRQ
In Δ ABC and Δ PQR, if AB = PR, BC = RQ and AC = PQ, then Δ ABC is congruent to Δ PRQ, which means option D is the right answer.
The congruency theorem is used to determine the relation between two similar looking figures in two dimensional space. The word congruent itself means being in harmony. There are different rules which are used to determine the congruency between the triangles.
These rules are given as follows:
All three pairs of corresponding sides are equal = SSS CongruencyTwo pairs of corresponding sides and the corresponding angles between them are equal = SAS congruencyTwo pairs of corresponding angles and the corresponding sides between them are equal = ASA CongruencyIn the given question, it is given that sides AB = PR, BC = RQ and AC = PQ, this implies that the congruency can be setup using SSS rule, which if followed will suggest that Δ ABC will be congruent to Δ PRQ.
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4. Circle the reason for each of the following manipulations used to simplify the product (8x²)(3x²).
(8.3).(x²-x²)
8x²-3x²
commutative or associative
8.3.x²-x²
commutative or associative
24x²
commutative or exponent property
8.3.x².x² = (8.3).(x².x²) - commutative and associative properties of multiplication.
What is commutative law?Commutative laws deal with arithmetic operations addition and multiplication. This means that changing the order or position when adding or multiplying two numbers does not change the final result. For example, 4 + 5 is 9 and 5 + 4 is also 9. The order in which the two numbers are added does not affect the sum. The same concept applies to multiplication. Commutativity does not apply to subtraction and division, because changing the order of the numbers yields a completely different final result.
(8x²)(3x²) can be simplified as follows:
(8x²)(3x²) = 8.3.x².x² = (8.3).(x².x²)
= [tex]24x^4[/tex]
The reason for each of the manipulations is as follows:
8.3.x².x² = (8.3).(x².x²) - commutative and associative properties of multiplication.
(8.3).(x².x²) = [tex]24x^4[/tex] - exponent property of multiplication.
Therefore, the final answer is [tex]24x^4[/tex].
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A series of locks manages the water height along a water source used to produce energy. As the locks are opened and closed, the water height between two consecutive locks fluctuates.
The height of the water at point B located between two locks is observed. Water height measurements are made every 10 minutes beginning at 8:00 a.m.
It is determined that the height of the water at B can be modeled by the function f(x)=−11cos(πx/48 − 5π/12)+28 , where the height of water is measured in feet and x is measured in minutes.
What is the maximum and minimum water height at B, and when do these heights first occur?
The given function f(x) = -11cos(πx/48 - 5π/12) + 28 models the height of water at point B between two locks, where x is the time in minutes beginning at 8:00 a.m.
The amplitude of the cosine function is 11, and the vertical shift is 28. The argument of the cosine function has a period of 96 minutes, which means that the function repeats itself every 96 minutes.
Therefore, the maximum water height at B is 39 feet and occurs at x = 120 minutes (10:00 a.m.), while the minimum water height at B is 17 feet and occurs at x = 0 minutes (8:00 a.m.). These heights occur because the cosine function attains its maximum value at x = 120 minutes and its minimum value at x = 0 minutes.
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Can some one help me? It’s three parts but the questions states use the interval notation to write the intervals over which f is (a) increasing, (b) decreasing, and (c) constant. The last question also says topics related to if its constant or not.
The function is constant from approximately x = -4 to x = -3 and from approximately x = -1 to x = 1. So, the constant intervals are (-4, -3) and (-1, 1)
What exactly are function and example?A function, which produces one output from a single input, is an illustration of a rule. The picture was obtained from Alex Federspiel. The equation y=x2 serves as an example of this.
a) We can see that the function is increasing from approximately x = -3 to x = -1 and from approximately x = 1 to x = 2.5. So, the increasing intervals are (-3,-1) and (1, 2.5)
(b) We can see that the function is decreasing from approximately x = -2 to x = -0.5 and from approximately x = 3 to x = 4. So, the decreasing intervals are (-2, -0.5) and (3, 4)
(c) We can see that the function is constant from approximately x = -4 to x = -3 and from approximately x = -1 to x = 1. So, the constant intervals are (-4, -3) and (-1, 1)
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Write a quadratic function in standard form that passes through the points (-8,0), (-5,-3), and (-2,0)
A quadratic function in standard form that passes through the points (-8,0), (-5,-3), and (-2,0) is equals to the f(x) = (1/3)( x² + 10x + 16).
A quadratic function is a polynomial function with one or more variables, the highest degree of the variable is two. It is also called the polynomial of degree 2. The form of quadratic function is
f(x) = ax² + bx + c ----(1)
is determined by three points and must be a≠ 0. That is for determining the f(x) we have to determine value of three values a, b, and c. Now, we have three ordered pairs (-8,0), (-5,-3), and (-2,0) and we have to determine quadratic function passing through these points. So, firstly, plug the coordinates of point ( -8,0), x = -8, y = f(x) = 0 in equation (1),
=> 0 = a(-8)² + b(-8) + c
=> 64a - 8b + c = 0 --(2)
Similarly, for second point ( -5,-3) , f(x) = -3, x = -5
=> - 3 = a(-5)² + (-5)b + c
=> 25a - 5b + c = -3 --(3)
Continue for third point (-2,0)
=> 0 = a(-2)² + b(-2) + c
=> 4a -2b + c = 0 --(4)
So, we have three equations and three values to determine.
Subtract equation (4) from (2)
=> 64 a - 8b + c - 4a + 2b -c = 0
=> 60a - 6b = 0
=> 10a - b = 0 --(5)
subtract equation (4) from (3)
=> 21a - 3b = -3 --(6)
from equation (4) and (5),
=> 3( 10a - b) - 21a + 3b = -(- 3)
=> 30a - 3b - 21a + 3b = 3
=> 9a = 3
=> a = 1/3
from (5) , b = 10a = 10/3
from (4), c = 2b - 4a = 20/3 - 4/3 = 16/3
So, f(x)= (1/3)( x² + 10x + 16)
Hence, required values are 1/3, 10/3, and 16/3.
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what is the probability that the gambler has to play at least n rounds of the game before getting his first win?
The probability that the gambler has to play at least 3 rounds of the game before getting his first win is equal to 3/4.
The probability that the gambler has to play at least n rounds of the game before getting his first win is equal to 1 - (the probability of winning in the first n-1 rounds). To calculate the probability of winning in the first n-1 rounds, use the following formula:
P = (1/2)^(n-1)
Where P is the probability of winning in the first n-1 rounds.
For example, if the gambler has to play at least 3 rounds of the game, the probability of winning in the first 2 rounds is equal to (1/2)^(3-1) = (1/2)^2 = 1/4.
So, the probability that the gambler has to play at least 3 rounds of the game before getting his first win is equal to 1 - (1/4) = 3/4.
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Let $ABCD$ be a parallelogram. Extend $\overline{DA}$ through $A$ to a point $P,$ and let $\overline{PC}$ meet $\overline{AB}$ at $Q$ and $\overline{DB}$ at $R.$ Given that $PQ = 735$ and $QR = 112,$ find $RC.$
The x ≤ 32Putting x = 24 in the expression we get RC = 96Therefore, the value of RC is 96.
In order to find RC, we will make use of the given information in the following manner: Given that ABDC is a parallelogram. Hence, AB = DC. We have also been given that PQ = 735 and QR = 112.Now, extend PQ to meet DC at S.Let PS = x; then DS = DC - x = AB - x. (Since AB = DC)We have that PS/SP = QR/RB (Since PQR is similar to DBR)Therefore, we getx/SP = 112/(AB - x)We can cross multiply and simplify to getSP = (112* x)/(AB - x)......(1)Further, we have that AQ/QB = SP/BR (Since PQR is similar to AQB)Therefore, we getx/(AB - x) = SP/BROn substituting the value of SP from equation (1) above, we getx/(AB - x) = (112* x)/(BR*(AB - x))Therefore, we getBR = (x*(AB - x)*QR)/[PQ*(AB - 2*x)]BR = (x*(32 - x)*112)/(735*(32 - 2*x))BR = (56*x*(16 - x))/(245*(16 - x))BR = (56*x/245)Since the sum of all sides of a parallelogram is equal to the sum of its opposite sides, we have thatRC + QR = AB + AQ - QBRearranging the terms we getRC = AB + AQ - QB - QR......(2)Now, AQ = PQ - APSubstituting the values of PQ and AP we get AQ = 735 - (DC - x) = 735 - 32 + x = x + 703Also, QB = AB - AQ = (32 - x) - (x + 703) = -x - 671Substituting the values of AQ and QB in equation (2) above we getRC = 32 + (x + 703) + (x + 671) - 112RC = 48 + 2xRC = 2(x + 24)We know that AB = 32, hence, x ≤ 32Putting x = 24 in the expression we get RC = 96Therefore, the value of RC is 96.
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Tiana has a new beaded necklace. The necklace has 3 blue beads and 17 white beads. What percentage of the beads on Tiana's necklace are blue?
Therefore, 15% of the beads on Tiana's necklace are blue.
What is percentage?Percentage is a way of expressing a fraction or a proportion out of 100. It is denoted by the symbol "%". For example, if we say that 50% of the students in a class are girls, it means that 50 out of every 100 students are girls.
Percentage can be calculated by dividing the given quantity by the total and multiplying by 100. For example, if there are 20 girls out of a total of 40 students in a class, the percentage of girls in the class can be calculated as follows:
Percentage of girls = (number of girls / total number of students) x 100%
= (20 / 40) x 100%
= 50%
by the question.
Tiana's necklace has a total of 3 + 17 = 20 beads.
To find the percentage of blue beads, we need to divide the number of blue beads by the total number of beads and then multiply by 100 to get the percentage:
percentage of blue beads = (number of blue beads / total number of beads) x 100
percentage of blue beads = (3 / 20) x 100
percentage of blue beads = 15
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Find the circumference of a circle with diameter, d = 1.26m.
Give your answer rounded to 2 DP
Answer: b
Step-by-step explanation: just took it on edge.
Is this a compound?
First, Gabriel planted the geraniums in a clay pot, and then he placed the pot on a sunny windowsill in his kitchen
A. YES
B. NO
Answer:
yes it is right now you can write it
a market sells five kinds of cups, 4 kinds of saucers, and 2 kinds of spoons. How many ways are there to buy two objects of different types?
There are 84 ways to buy two objects of different types.
How to choose two objects of different types ?To choose two objects of different types, we can choose one type of object first and then choose one object from that type and one object from the other two types.
The number of ways to choose one type of object is 3 (cups, saucers, or spoons). For each type of object, there are different numbers of objects to choose from:
Cups: 5 objectsSaucers: 4 objectsSpoons: 2 objectsSo, the total number of ways to choose two objects of different types is:
3 x (5 x 4 + 5 x 2 + 4 x 2) = 3 x 28 = 84
Therefore, there are 84 ways to buy two objects of different types.
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The terminal ray of angle A, drawn in standard position, passes through the point (-4,
-6). What is the value of sec(A)?
Give your answer in simpliest radical form.
The value of sec A as required to be determined in the task content is; -√13 / 2.
What value represents sec A in the given scenario?As evident from the task content; it follows that the terminal ray of angle A, drawn in standard position, passes through the point (-4, -6).
Therefore, the length that the line from the origin to A has length;
L = √((-4)² + (-6)²)
L = √52.
On this note, it follows that the value of sec A which is represented by; hypothenuse/ adjacent is;
sec (A) = -√52 / 4
sec (A) = -√13 / 2.
Ultimately, the value of sec (A) as required is; -√13 / 2.
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The random variable x is known to be uniformly distributed between 10 and 20. Show the graph of the probability density function: Compute P(x 15). Compute P(12 =x= 18). St Compute E(x). Compute Var(x).
Compute P(x ≤ 15) = (15-10)/(20-10) = 5/10 = 0.5.
Compute P(12 ≤ x ≤ 18) = (18-12)/(20-10) = 6/10 = 0.6.
Compute E(x): The expected value of x is: E(x) = (a+b)/2 = (10+20)/2 = 15
Compute Var(x):The variance of x is: Var(x) = (b - a)^2/12 = (20 - 10)^2/12 = 100/12 = 8.33.
The probability density function is as follows: As the random variable x is uniformly distributed between 10 and 20. Thus, f(x) = 1/(20-10) = 1/10 for 10 ≤ x ≤ 20.Compute P(x ≤ 15):Thus, P(x ≤ 15) = (15-10)/(20-10) = 5/10 = 0.5.Compute P(12 ≤ x ≤ 18):Thus, P(12 ≤ x ≤ 18) = (18-12)/(20-10) = 6/10 = 0.6.Compute E(x):The expected value of x is: E(x) = (a+b)/2 = (10+20)/2 = 15.Compute Var(x):The variance of x is: Var(x) = (b - a)^2/12 = (20 - 10)^2/12 = 100/12 = 8.33.
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why does a square root have a plus or minus sign attached to it.
Answer:
To indicate that we want both the positive and the negative square root of a radicand
Answer:
Because a negative number times a negative number has a positive answer
Step-by-step explanation:
A wire first bent into the shape of a rectangle with width 5cm and lenth 11 cm.then the wire is unbent and reshaped into a square what is the length kf a side of the square
The length of a side of the square is 8 cm.
What do you mean by perimeter of a rectangle and square?
When a wire is bent into the shape of a rectangle, its length becomes the perimeter of the rectangle. Similarly, when the wire is reshaped into a square, its length becomes the perimeter of the square.
The perimeter of a rectangle is given by the formula [tex]P=2(l+w)[/tex] , where [tex]l[/tex] is the length and [tex]w[/tex] is the width.
The perimeter of a square is given by the formula [tex]P=4s[/tex] , where [tex]s[/tex] is the length of a side.
Calculating the length of a side of the square:
The length of the rectangle is 11 cm and the width is 5 cm.
Therefore, the perimeter of the rectangle is [tex]P=2(11+5)=32[/tex] cm.
Since the wire is reshaped into a square, the perimeter of the square is also 32 cm.
Using the formula [tex]P=4s[/tex], we can solve for the length of a side of the square:
[tex]32 = 4s[/tex]
[tex]s = 32/4[/tex]
[tex]s = 8[/tex]
Therefore, the length of a side of the square is 8 cm.
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What is the value of x in √1+ 25/144 =1+ /12 ?
The solution to the equation √(1 + 25/144) = 1 + x/12 is x = 5/6. This was achieved by simplifying the left side of the equation and isolating x on one side.
To solve the equation √(1 + 25/144) = 1 + x/12, we start by simplifying the left side of the equation. The expression inside the square root can be simplified to (144 + 25)/144 = 169/144. Taking the square root of this fraction gives us √(169/144) = (13/12).
Next, we subtract 1 from both sides of the equation to isolate x on one side: (13/12) - 1 = x/12. This simplifies to 1/12 = x/12.
Finally, we multiply both sides by 12 to solve for x: x = (1/12)*12 = 5/6.
So the solution to the equation √(1 + 25/144) = 1 + x/12 is x = 5/6.
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Mark wants to buy a new pair of sneakers that cost 215. His aunt gave him 100 for the sneakers. Market also lnow sthat he can esrn 16 for each hour that he works at his aunts store how many full hours must mark work to buy the sneakers
Mark needs a total amount of 215 to buy sneakers and we know that his aunt gave him 100 for the same, he also know that he can earn 16 for each hour that he works at his aunt's store, therefore he needs to work 8 hours.
Mark needs a total amount of 215 to buy sneakers and we know that his aunt gave him 100 for the same,
therefore, we can say that 215 - 100 = 115
therefore, Mark now needs only 115 for him to buy sneakers and now we need to find how many full hours do Mark need to work to buy sneakers:
therefore, we need to divide 115 by 16 to find out the hours he needs to work at his aunt's store:
115/16 = 7.2
we get 7.2 which also means 7 hours 20 mins but we need to find full hours Mark needs to work, that will be:
8 hours.
Therefore, we know that Mark needs to work 8 full hours for him to buy sneakers.
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11. How much time will it take for ₹5000
5618 at 6% per annum
annually?
to become
compounded
Answer:
2.31 Years
Step-by-step explanation:
To calculate the time it will take for ₹5000 to grow to ₹5618 with a 6% annual interest rate when compounded annually, we can use the following formula:
A = P(1 + r/n)^(nt)
Where:
A = the final amount (₹5618)
P = the principal amount (₹5000)
r = the annual interest rate (6% or 0.06)
n = the number of times the interest is compounded per year (1, since it's compounded annually)
t = the time period in years
Plugging in the values, we get:
5618 = 5000(1 + 0.06/1)^(1t)
Simplifying:
1.1236 = 1.06^t
Taking the natural logarithm of both sides:
ln(1.1236) = ln(1.06^t)
Using the power rule of logarithms:
ln(1.1236) = t ln(1.06)
Solving for t:
t = ln(1.1236) / ln(1.06)
t ≈ 2.31 years
Therefore, it will take approximately 2.31 years for ₹5000 to grow to ₹5618 at a 6% annual interest rate when compounded annually.
To celebrate Halloween, Florence's class is making candy necklaces. Florence is helping pass out string from a 50-yard-spool. She gives 30 inches of string to each student. If there are 24 students in her class, how many yards of string will be leftover?
There will be 30 yards of the string that will be leftover.
What are Arithmetic operations?
It is a field of mathematics that deals with the study of numbers and the operations on those numbers that are relevant to all other areas of mathematics. The basic operations included in it are addition, subtraction, multiplication, and division. The term "arithmetic operator" refers to the operator that does the calculation.
Given that,
Total Length of string = 50 yards.
The total number of students = 24.
Total used string = 24 × 30 = 720.
We know that 1 foot = 12 inches,
So, 150 feet = 1800 inches.
Therefore, yards of string leftover = (1800 - 720)/36
= 1080/36
= 30 yards.
Hence, there will be 30 yards of string that will be leftover.
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fifty-three percent of all persons in the u.s. population have at least some college education. choose 10 persons at random. what is the probability that exactly one-half have some college education?
The probability that exactly one-half have some college education is 0.0439 (rounded to four decimal places)
Step by step explanation: We can use the binomial probability distribution formula for this problem, where:p = probability of success (i.e., having some college education) = 0.53q = probability of failure (i.e., not having some college education) = 0.47n = number of trials (i.e., persons chosen at random) = 10x = number of successes (i.e., persons with some college education) = [tex]5P(x = 5) = C(10,5)p^5q^5[/tex] where [tex]C(n,r)[/tex] is the combination function that gives the number of ways to choose r items from a set of n items.
It is given by:[tex]C(n,r) = n! / (r!(n-r)!)[/tex] Thus, we can substitute the given values and compute:[tex]P(x = 5) = C(10,5)p^5q^5 = 252(0.53)^5(0.47)^5= 0.0439[/tex] (rounded to four decimal places)Therefore, the probability that exactly one-half have some college education is 0.0439.
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The average mass of six people is 58kg. The lightest person has a body mass of 43kg. What is the average mass of the other 5 people.
Answer: 61 kg
Step-by-step explanation:
To find the average mass of the other 5 people, we need to subtract the mass of the lightest person from the total mass of all six people and then divide by 5 (since we're looking for the average of the other 5 people). Here are the steps:
Find the total mass of all six people:
To find the total mass of all six people, we can multiply the average mass by 6:
Total mass of all six people = 58 kg/person x 6 people = 348 kg
Subtract the mass of the lightest person:
We need to subtract the mass of the lightest person (43 kg) from the total mass of all six people:
Total mass of the other 5 people = Total mass of all six people - Mass of the lightest person
Total mass of the other 5 people = 348 kg - 43 kg = 305 kg
Find the average mass of the other 5 people:
Finally, we divide the total mass of the other 5 people by 5 to find the average mass:
Average mass of the other 5 people = Total mass of the other 5 people / 5
Average mass of the other 5 people = 305 kg / 5 = 61 kg
Therefore, the average mass of the other 5 people is 61 kg.
A triangle has side lengths of 6, 8, and 10. Is it a right triangle.
A. No, the sum of the legs is not equal to the hypotenuse.
B. Yes, the sum of the legs is equal to the hypotenuse.
C. No, the sum of the square of the legs is not equal to the square of the hypotenuse.
D. Yes, the sum of the square of the legs is equal to the square of the hypotenuse.
I know its a right angle so it's B or D, but which one.
Answer: D. Yes, the sum of the square of the legs is equal to the square of the hypotenuse.
Step-by-step explanation:
Pythagorean theorem is a^2 + b^2 = c^2
given side length of 6 and 8 and hypotenuse of 10
6^2 + 8^2 = 10^2
36 + 64 = 100
100 = 100
so yes, the sum of the square of the legs = the square of the hypotenuse.
The graph below shows petrol prices at two petrol stations, Station X and Station
Y.
Ellie went to one of the petrol stations and bought 20 litres of petrol for £24.
a) Did Ellie go to Station X or Station Y?
b) How much would 15 litres of petrol cost at the same station?
Give your answer in pounds (£).
Cost (£)
Cost against amount of petrol
40
30
20
10-
5
10 15 20 25
Amount of petrol (litres)
Key
Station X
Station Y
At Station Y, 15 litres of gasoline would cost £18.
What is cost in?Cost is the amount of money spent by a business to produce or create goods or services. It excludes the profit margin markup. Cost is the sum of money spent on making a good or product, as seen from the seller's perspective.
Ellie must have visited Station Y because she paid $24 for 20 litres of gasoline, proving that she did.
b) We can observe from the graph that 20 litres of gasoline at Station Y costs £24. With the help of this data, we can calculate how much a litre of gasoline costs:
Cost of 1 litre of petrol = Cost of 20 litres of petrol / 20
Cost of 1 litre of petrol = £24 / 20
Cost of 1 litre of petrol = £1.20
Therefore, 15 litres of petrol at Station Y would cost:
Cost of 15 litres of petrol = Cost of 1 litre of petrol x 15
Cost of 15 litres of petrol = £1.20 x 15
Cost of 15 litres of petrol = £18
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Explain how to solve the given equation for "x".
X = 2 is the solution of the given equation for "x".
What does a math equation mean?
An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used. For instance, 3x + 5 = 14 is an equation where 3x + 5 and 14 are two expressions separated by the 'equal' sign.
A mathematical statement known as an equation is made up of two expressions joined together by the equal sign. A formula would be 3x - 5 = 16, for instance. By solving for x, we discover that x equals 7, which is the value for the variable.
8ˣ = (25)
8ˣ = (5)²
X = 2
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4)) FH and IK are parallel lines. J K F G E Which angles are alternate exterior angles?
Answer: I couldn't honestly help with that I would if I could
Step-by-step explanation:
URGENT!!!!! Examine the graph of the function What is the initial value of the function?
Enter your answer as a number, like this: 42
The answer of the given question based graph of function on finding the initial value of the function the answer is the initial value of the function is 2.
What is Graph?A graph is visual representation of data that displays relationship between variables. It consists of points or vertices connected by lines or arcs that represent relationships between variables. Graphs can be used to represent various types of data, like numerical, categorical, and ordinal data.
Graph are commonly used in mathematics, science, engineering, and social sciences to help people understand complex data and relationships. Different types of graphs like bar graphs, line graphs, scatter plots, pie charts, and histograms. Graphs are powerful tool for data analysis and visualization, and they can help people identify patterns, trends, and outliers in data.
If the function intersects both the x-axis and y-axis at the point (2,4), then the function can be written in the form:
y = a(x - 2)(x - 4)
where a is some constant.
To find the value of a, we can use the fact that the function passes through the point (0,2). Substituting x = 0 and y = 2 into the equation above, we get:
2 = a(0 - 2)(0 - 4)
2 = 8a
Solving for a, we get:
a = 2/8 = 1/4
Therefore, the function is:
y = (1/4)(x - 2)(x - 4)
To find the initial value of the function, we need to determine the value of the function when x is equal to zero. Substituting x = 0 into the equation above, we get:
y = (1/4)(0 - 2)(0 - 4)
y = (1/4)(8)
y = 2
Therefore, initial value of function is 2.
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find the area of a quadrilateral ABCD in each case.
The area of the quadrilateral ABCD for this case is of 4 square units.
How to obtain the area of the quadrilateral ABCD?The quadrilateral ABCD in the context of this problem represents a diamond, hence it's area is given by half the product of the diagonal lengths of the diamond.
The lengths for each diagonal of the diamond are given as follows:
Diagonal AC = 2 - 0 = 2.Diagonal BD = 4 - 0 = 4.The product of the diagonal lengths is given as follows:
AC x BD = 2 x 4 = 8 square units.
Hence half the product of these diagonal lengths, representing the area of the quadrilateral, is given as follows:
0.5 x 8 square units = 4 square units.
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change the denominator of the fraction a+3/6-2a to 2(a^2-9)
The answer of the given question based on the changing the denominator of fraction the answer is the fraction a+3/6-2a can be rewritten with a denominator of 2(a²-9) as (3 + a)/(2(a - 3)).
What is Formula?In mathematics, formula is mathematical expression or equation that describes relationship between two or more variables or quantities. A formula can be used to solve problems or make predictions about particular situation or set of data.
Formulas often involve mathematical symbols and operations, like addition, subtraction, multiplication, division, exponents, and square roots. They may also include variables, which are typically represented by letters, and constants, which are fixed values that do not change.
To change the denominator of the fraction a+3/6-2a to 2(a²-9), we need to factor the denominator of the original fraction and then use algebraic manipulation to rewrite it in the desired form.
First, we can factor the denominator of the original fraction as follows:
6 - 2a = 2(3 - a)
Next, we can rewrite the denominator using the difference of squares formula:
2(a² - 9) = 2(a + 3)(a - 3)
Now, we can use the factored form of the denominator to rewrite the original fraction:
(a + 3)/(6 - 2a) = (a + 3)/(2(3 - a)) = -(a + 3)/(-2(a - 3)) = (3 + a)/(2(a - 3))
Therefore, the fraction a+3/6-2a can be rewritten with a denominator of 2(a²-9) as (3 + a)/(2(a - 3)).
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3) A lottery ticket says that the chances of winning are 1 in 8. Suppose you buy 10 of these lottery tickets. Find the probability that at least one of them will be a winner
The probability of at least one of your 10 lottery tickets being a winner is approximately 0.638 or 63.8%.
The probability of winning on a single lottery ticket is 1/8, which means that the probability of not winning is 7/8. If you buy 10 of these lottery tickets, the probability of not winning on any of them is:
(7/8)^10 = 0.362
This means that there is a 36.2% chance that none of your tickets will be a winner. To find the probability that at least one of your tickets will be a winner, we can use the complementary probability:
P(at least one winner) = 1 - P(no winners)
P(at least one winner) = 1 - 0.362
P(at least one winner) = 0.638
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if a traingle with all sides of equal legnth has a perimeter of 15x 27 , what is an expression for the legnth of one of the sides
If a triangle with all sides of equal length has a perimeter of 15x + 27, the expression for the length of one of the sides is (5x + 9).
How to find the expression for the length of one of the sides of a triangle?The perimeter of a triangle is the sum of the lengths of all three sides. If all the sides of the triangle are equal, you can find the length of one side by dividing the perimeter by 3. Here, the perimeter is given as 15x + 27. Therefore, the length of one side will be (15x + 27) / 3 = 5x + 9. Hence, an expression for the length of one of the sides is (5x + 9).
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